NEW INSTRUMENTS AND METHODS OF MEASUREMENT

EQUIPMENT AND TECHNIQUES OF INFRARED SPECTROMETRY*)

V. Ts. Williams

CONTENTS

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

II. History of the question . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

III. Techniques and applications in the near infrared region: 4000 cm\(^{-1}\)
(2.5 μ) — 400 cm\(^{-1}\) (25 μ) . . . . . . . . . . . . . . . . . . . . . . . . . . 188

    a) Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

    b) Experimental applications . . . . . . . . . . . . . . . . . . . . . . . . 192

        1. Spectral identification and qualitative determination of purity . . . . . . 193

        2. Qualitative group analysis . . . . . . . . . . . . . . . . . . . . . . . . . 194

        3. Quantitative analysis of mixtures . . . . . . . . . . . . . . . . . . . . . 195

IV. Experimental procedure in the near infrared region:
4000 cm\(^{-1}\) — 400 cm\(^{-1}\) . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

    a) Sources; emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

    b) Refracting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

    c) Optical systems; automatic spectrophotometers . . . . . . . . . . . . . . 206

    d) Receivers, amplifiers, recording . . . . . . . . . . . . . . . . . . . . . 212

    e) Cuvettes and specimens . . . . . . . . . . . . . . . . . . . . . . . . . . 225

    f) Instruments and apparatus . . . . . . . . . . . . . . . . . . . . . . . . 230

V. The nearest infrared region, or the overtone region: 13,300 cm\(^{-1}\)
(0.75 μ) — 4000 cm\(^{-1}\) (2.5 μ); infrared photosensitive receivers . . . . . . 234

VI. The far infrared region: 400 cm\(^{-1}\) (25 μ) — 30 cm\(^{-1}\) (350 μ) . . . . 238

VII. Microwave region: ~ 1 cm\(^{-1}\) (1 cm, 10,000 μ) . . . . . . . . . . . . . 240

VIII. Infrared filters; infrared gas analyzer . . . . . . . . . . . . . . . . . . 244

IX. Various applications of infrared radiation . . . . . . . . . . . . . . . . . 247

*) V. Z. Williams, Infra-Red Instrumentation and Techniques, Rev. Sci. Instr. 19, 135 (1948). Translated by A. A. Ilyina.

V. C. WILLIAMS

I. INTRODUCTION

The study of infrared radiation and its interaction with matter is a broad field of optics, since these studies cover a large part of the electromagnetic spectrum and use the most varied measurement techniques. The lower limit of the infrared region lies at 7500 Å, i.e., at the long-wavelength end of the sensitivity curve of the human eye; the upper end cannot be specified exactly. Often the upper boundary is taken to be \(\lambda = 350 \mu\), because up to these wavelengths measurements can be carried out by ordinary thermal radiometric methods. However, the advances of microwave radio engineering and the newly opened possibility of studying the rotational structure of bands in the region of centimeter waves make it possible to broaden the concept of the infrared region.

To characterize infrared radiation one usually uses the wavelength, measured in microns \(\mu = 10\,000\ \text{Å} = 10^{-4}\ \text{cm}\), or the frequency, i.e., the wave number \(\nu\), measured in reciprocal centimeters \((\text{cm}^{-1})\). Wavelength is the older unit, since its use was natural in earlier work with prisms, gratings, or in interferometric investigations.

With the introduction of energy quantization and molecular vibrational analysis, frequency units proved more useful and came into wide use. Here we shall use precisely these units, converting them, however, into wavelengths when this is needed.

It is customary to divide the infrared part of the spectrum into the following regions: a) the nearest part of the infrared spectrum, or the region of overtones—from \(13\,300\ \text{cm}^{-1}\) \((0.75\mu)\) to \(4000\ \text{cm}^{-1}\) \((2.5\mu)\); b) the near infrared region, or the region of the fundamental vibrational-rotational frequencies—from \(4000\ \text{cm}^{-1}\) \((2.5\mu)\) to \(400\ \text{cm}^{-1}\) \((25\mu)\); c) the far infrared region—from \(400\ \text{cm}^{-1}\) to \(30\ \text{cm}^{-1}\) \((300\mu)\); and, since recently, d) the region of microradio waves, \(\nu \sim 1\ \text{cm}^{-1}\) \((10\,000\mu)\).

II. HISTORY OF THE QUESTION

Infrared radiation was discovered by William Herschel \(^{1}\) in 1800 while observing a rise in the temperature of a thermometer placed beyond the red end of the solar spectrum (obtained by means of a glass prism). Fig. 1 shows Herschel’s apparatus, which was in essence the first infrared spectrometer. Herschel observed two maxima in the solar spectrum: a visual maximum of intensity in the yellow-green region and a maximum of thermal radiation lying outside the limits of the visible spectrum. On this basis Herschel supposed that there exist two types of radiation—light and heat.

Around 1835–1845 Ampère \(^{2}\), Melloni, and Herschel’s son suggested that visible and infrared radiation

are optical phenomena, differing only in the degree of refraction in the prism. The younger Herschel introduced a method of recording the infrared spectrum by means of the evaporation of alcohol from a blackened surface and photographing the resulting pattern. In his first photographs, infrared absorption bands of water vapor and carbon dioxide contained in the atmosphere are visible. Soon after this, insensitive thermopiles were introduced as receivers of thermal radiation, but in 1880 Langley placed the study of infrared radiation on a firm foundation by introducing the bolometer in combination with a sensitive galvanometer and by using a grating for spectral decomposition. The value of earlier work carried out with prisms was greatly reduced by the uncertainty in estimating wavelengths, and the use of gratings for the absolute determination of wavelengths greatly broadened the field of investigation. Improved bolometers, thermopiles, galvanometers, Crookes’s radiometer, and the Boys and d’Arsonval radiomicrometer appeared. The dispersion of glass, quartz, fluorite, NaCl, and KCl was accurately measured. In 1902, blackbody radiation was carefully investigated with the aim of verifying Wien’s displacement law and Planck’s radiation law.

Fig. 1. The first infrared spectrometer (from Herschel’s communication¹).

As a result of the work of Abney, Angström, Julius, and Aschkinass, together with the fruitful work of Coblentz³ on absorption molecular spectrometry, the first experimental data were obtained on the relation between molecular structure and the characteristic frequencies of absorption and emission. Work on infrared radiation provided confirmation of Ritz’s combination principle and established the principal atomic series for many elements. In 1897 residual rays were discovered. Their use for isolating narrow regions of the spectrum (Rubens) extended the range of investigations to \(300\,\mu\). In 1910 Wood⁵ introduced echelons for investigations requiring high resolving power.

In 1913 Eva von Bahr⁶ resolved the rotational structure of the HCl band at \(2890\ \text{cm}^{-1}\) (\(3.46\,\mu\)), which proved the quantization of rotational

levels of energy, which had already been proposed on the basis of work on specific heats. In 1916 Bjerrum\(^7\) introduced the representation of an oscillating polyatomic molecule as a mechanical system of point masses connected by Hooke’s law of forces, with the aim of calculating the fundamental vibrational frequencies. This latter point of view, supported by the methods of group theory\(^{8–11}\) for simplifying the computational operations, made it possible to obtain the fundamental frequencies and force constants for most of the simplest molecules. The results of the calculations were compared with experimental data from infrared and Raman spectroscopy. By combining data on frequencies and moments of inertia, specific heats and other thermodynamic constants\(^{12}\) of molecules were calculated. These two directions—the measurement of rotational structure in order to determine the geometrical structure of a molecule and to check theoretical calculations, on the one hand, and the calculation of vibrational spectra for the identification of frequencies and thermodynamic calculations, on the other—constitute the main content of purely scientific research in this field at the present time. Reviews may be found in Dennison\(^{13}\), Wu\(^{14}\), and Herzberg\(^{15}\).

During the period 1920–1930, infrared spectroscopy began to be applied more and more to the solution of chemical problems. Around 1935 the infrared region was “opened up” by industry, and since then these methods have widely entered the practice of industrial laboratories.

In addition to work on absorption and emission spectrometry, reflection and polarization in the infrared spectrum, infrared phosphors and photosensitive surfaces were also studied; astrophysical and radiometric applications and the determination of particle sizes were likewise developed. One may also mention certain medical and technical applications of infrared rays, such as, for example, diathermy, industrial heating, rapid drying of painted surfaces, etc.

Parallel with the growth of research and industrial applications, instrument making in this field also developed. Formerly infrared spectrometers were built to individual orders and designs*), but now, as a result of the numerous demands of industry, various firms have begun to manufacture precise standardized instruments. Modern bolometers and thermocouples, which have become standard infrared receivers, possess good sensitivity and sufficient speed of response and can receive intermittent infrared signals. Galvanometers with photographic recording are now being replaced by electronic amplification with direct recording of such stability that

) A recording spectrograph for the far-infrared part of the spectrum was first built by P. N. Lebedev in 1911 and used by K. P. Yakovlev (P. N. Lebedev, Collected Works, p. 202, Moscow, 1913). (Translator’s note.*)

only Johnson noise in the detector is the limiting factor in these measurements. The infrared spectrometer is now no longer a capricious instrument which must be placed in a basement in order to maintain mechanical and thermal stability. It has also changed in external appearance, and from a rough box, glued together with sealing wax, with all sorts of auxiliary devices that required a spacious room, it has turned into a compact instrument (Figs. 2–4), occupying no more space than a table. Modern prism instruments can truly be called “tools” in the sense that they can provide continuous, precise work in production1 or in the laboratory and can be operated by relatively unskilled personnel. Unfortunately, there are as yet no modern manuals in the field of infrared spectrometry. Schäfer and Matossi2 wrote an excellent book in 1930, and at the same time several less complete reviews appeared3–4. A considerable bibliography on the infrared—

Fig. 2. Beckman IR-2 infrared spectrophotometer.

Fig. 3. Perkin-Elmer infrared spectrometer, Model 12-C.

—region of the spectrum has been compiled by Barnes5 (1944) and in the symposium “The Application of Infrared Spectra to Chemical” prob-

lema” ^22 (1945). In view of the rapid growth of infrared spectrometry and of the personnel of infrared spectrometrists, the creation of an exhaustive handbook in this field is extremely necessary.

III. TECHNIQUE AND APPLICATIONS IN THE NEAR INFRARED REGION: 4000 cm\(^{-1}\) (2.5 μ) — 400 cm\(^{-1}\) (25 μ)

Since the study of the molecular absorption of radiation in the near infrared spectrum is at present the chief part of all investigations in the infrared region, this section of the article will also be the main one. Although we shall devote the greatest attention to instruments, below there is also given a brief survey of the techniques of investigation and of applications, in order to illustrate the significance of these studies and to provide a basis for a critical consideration of experimental technique.

Fig. 4. Byrd infrared spectrophotometer.

a) Theory

A molecule of a vapor or gas may be regarded as a certain system of point masses (atoms) held in equilibrium positions by Hookean forces, i.e. valence bonds, forces of angular deformation, etc. A molecule of \(N\) atoms must possess \(3N-6\) (\(3N-5\), if it is linear) fundamental internal natural vibrations, the frequencies of which can be exactly determined by the following methods of classical mechanics. Suppose that the expression for the potential energy of the bonding forces can be represented by quadratic terms of a Taylor series as a function of the Cartesian coordinates of the system \(q_i\). The kinetic energy \(T\) and the potential energy \(V\) will then be expressed as follows:

\[ 2T=\sum_i m_i \dot q_i^{\,2}\quad \text{and}\quad 2V=\sum_{ij} a_{ij}q_i q_j, \tag{1} \]

where \(q_i\) are Cartesian coordinates, \(m_i\) are the masses of the atoms, and \(\alpha_{ij}\) are functions of the Hookean forces, interaction constants, and the geometry of the molecule. The characteristic frequencies may be obtained from the solution of the secular equation:

\[ \left|\alpha_{ij}-\delta_{ij}m_i\lambda\right|=0;\qquad \delta_{ij} \begin{cases} =1 & \text{for } i=j,\\ =0 & \text{for } i\ne j, \end{cases} \tag{2} \]

where \(\lambda\) is related to the frequency \(\nu\) \((\text{cm}^{-1})\) by the expression \(\lambda = 4\pi^{2}c^{2}\nu^{2}\), where \(c\) is the velocity of light. The calculation is greatly simplified by using coordinates corresponding to the symmetry (or normal coordinates, if possible) in the case of a symmetric molecule. According to quantum theory, the energies corresponding to these frequencies are quantized; in the molecule there are characteristic energy values, expressed in the first approximation as

\[ E_{vib}=\sum_i \left(v_i+\frac{1}{2}\right)hc\nu_i,\qquad v_i=0,1,2,3,\ldots, \tag{3} \]

where \(v_i\) is the vibrational quantum number of the \(i\)-th fundamental vibration and \(h\) is Planck’s constant. Rotational energy is likewise quantized and may be represented by expressions containing rotational quantum numbers and the principal moments of inertia of the molecule. For a diatomic molecule this energy is expressed, in the first approximation, as follows:

\[ E_{rot}=J(J+1)\frac{h^{2}}{8\pi^{2}I},\qquad J=0,1,2,3,\ldots, \tag{4} \]

where \(J\) is the rotational quantum number and \(I\) is the moment of inertia.

The diagram of the energy levels of a molecule (without electronic energy) is the sum of two types of energy levels, with the rotational levels superposed on each vibrational level. If a fundamental vibration, or a combination of vibrations, leads to a change in the dipole moment of the molecule, it will be active, i.e. it can absorb infrared radiation with frequencies corresponding to the characteristic vibrational frequencies, and pass from lower to higher energy levels or states according to definite selection rules (if the vibrations change the polarizability, then they are active in the combination spectrum). A molecule in a higher energy state can emit characteristic radiation and pass to a lower energy level. The intensity of such transitions is a function of the number of molecules in the initial state and of the change in the dipole moment of the vibration.

Knowing the fundamental frequencies and the principal moments of inertia, it is possible to find the distribution function of the molecule and, by applying the corresponding differential operators, to obtain thermodynamic constants for the gaseous state—heat capacity, specific heats, etc. The share of the vibrational and rotational energy in this distribution function for a molecule in the general case is given by the expression

\[ Q_{int}= \frac{ \dfrac{1}{\sigma} \left[ \dfrac{\pi}{ABC} \left(\dfrac{kT}{hc}\right)^{3} \right]^{\frac{1}{2}} }{ \displaystyle \prod_i \left[ 1-\exp\left(-\frac{hc\nu_i}{kT}\right) \right]^{d_i} }, \tag{5} \]

where \(\sigma\) is the symmetry factor, \(A, B, C\) are rotational constants connected with the moments of inertia, \(T\) is the absolute temperature, \(\nu_i\) is the \(i\)-th fundamental frequency of vibration, and \(d_i\) is the degree of degeneracy of the \(i\)-th vibration. The experimental value of the specific heat is often used in the analysis of vibrations, in order to predict the values of the frequencies of inactive vibrations or of vibrations lying beyond the limits of experimental possibilities.

The preceding exposition is very compressed, but the material is standard and is fully set forth in Herzberg’s monograph\(^{15}\). This exposition is of interest as a basis for considering the present state of work of this type and the extent to which improved apparatus can be of importance. Considerable work has been carried out and is being carried out on vibrational analysis, on the calculation of the fundamental frequencies of a molecule, on comparison of these data with experimental data in the infrared region and in Raman spectroscopy, and on establishing suitable force constants and characteristic normal types of vibrations. An example is given in Fig. 5 and in Table I, where the infrared absorption spectrum of ketene\(^{23}\) is given with the fundamental frequencies of vibration, and the calculated and experimentally found values of the frequencies are compared. Since only the values of the vibrational frequencies are considered, and an accuracy of 1% is quite sufficient for calculations, one can often work with a nominal spectral resolution of \(3\)—\(10\ \mathrm{cm}^{-1}\) and an accuracy of frequency determination from 1 to \(3\ \mathrm{cm}^{-1}\), which can be obtained with a good prism spectrometer; nevertheless, sometimes in order to identify the fundamental frequencies it is necessary to determine the rotational structure with the aid of a diffraction grating.

Table I

Comparison of calculated and measured frequencies for the ketene molecule\(^{23}\)

No.	Frequency	Observed	Calculated
1	\(\nu_1\)	3162	— *)
2	\(\nu_2\)	3066	— *)
3	\(\nu_3\)	2153	2171
4	\(\nu_4\)	1386	1400
5	\(\nu_5\)	1120	1104
6	\(\nu_6\)	1011	1011
7	\(\nu_7\)	909	904
8	\(\nu_8\)	588	587
9	\(\nu_9\)	529	529

*) The frequencies were not calculated because of the approximate multiplier in the equations.

This type of investigation, however, is approaching the state of atomic spectrometry of the twenties of our century.

Although the solution of the secular equation of degree \(3N - 6\) is simplified in the case of a symmetric molecule (the highest equation encountered in the case of the 12-atom benzene molecule is of the fourth degree), the number of symmetric molecules that can be studied in the gaseous state is small and they have already been excellently studied. The principles of this method are now well substantiated, but the calculations, requi-

required for the consideration of more complex molecules or for obtaining better agreement between calculated and experimental data by selecting force constants, and also by studying isotopic molecules or introducing a larger number of interaction constants—

Fig. 5. Infrared absorption spectra of gaseous ketene. The principal frequencies are marked by arrows, and the types of vibrations are represented graphically.

actions, have become too complex for progress in this field. This situation cannot be changed by improving the design of the spectrometer. Good data can be obtained more quickly, but even so the time required for the experiment proves small in comparison with the time required for the calculations.

In this situation, some hope is offered by recently introduced^24–26 electrical methods for obtaining the roots of the secular equation. One of them is a circuit by means of which the diagonal and off-diagonal terms of a symmetric matrix can be obtained as quantities proportional to such constant circuit elements as inductive and capacitive reactances, or their combinations^24–26.

In the second method the matrix equation is solved as a system of linear homogeneous equations, and the roots are found by successive approximations. The first method has the advantage that it gives the solution directly; but the electrical parameters of the circuit are not simple functions of the parameters of the kinetic and potential energy. If one takes into account that at present most applications of vibrational analysis consist in calculating the values of these parameters in order to obtain known roots (experimental infrared and combination frequencies), then the first method may prove more laborious than the second. Wilson^27 has recently introduced a variational form of the secular equation (2), which is suitable for use with a linear-equation calculator. It may be hoped that the use of this instrument will make it possible to extend the calculations to less symmetric molecules and to molecules of liquids and solids, where intermolecular effects introduce additional forces and weaken or remove the selection rules^28. Further improvement of spectrometers would be very useful for the study and interpretation of rotational spectra, which make it possible to calculate moments of inertia, to compare observed and calculated rotational frequencies and band intensities, and also to study broadening due to pressure, perturbations in the band shape caused by the interaction of vibration and rotation, and Coriolis acceleration. The resolving limit of grating spectrometers, usually used in such work, is about \(0.5\ \mathrm{cm}^{-1}\)^20–30, whereas the typical width of rotational lines in rotational-vibrational bands is about \(0.08\text{--}0.12\ \mathrm{cm}^{-1}\)^31*. A larger number of new molecules could be successfully studied if the resolving power were increased fivefold. Therefore there is a real need here for improved spectrometers.

b) Experimental applications

The development of applied infrared spectrometry in the chemical industry has led to numerous studies in directions,

* The width of a line is the half-maximum width, and it gives the limiting distance between bands that can still be resolved; it is determined both by the Doppler effect, linear with respect to frequency, and by broadening under the influence of pressure (linear with respect to pressure up to \(\sim 10\ \mathrm{cm}\ \mathrm{Hg}\)). Both of these effects are of approximately the same order of magnitude (see Section VII).

completely independent of the theoretical investigations discussed above. Although these empirical applications are not yet presented in standard courses and there are no monographs on these questions, it may be that much more time and resources are being spent precisely on these studies. For this reason we shall examine in detail the technique and applications of industrial investigations.

What is especially valuable for the chemical industry is that the infrared absorption spectrum of a given compound is a unique physical characteristic of that compound. Moreover, this physical characteristic, unlike such nominally single-valued characteristics as refractive index, melting point, boiling point, specific gravity, etc., consists of a set of determining values—the eigenvalues of the frequencies and intensities of the absorption bands in the spectrum. Therefore a complete spectral correspondence between a known and an unknown compound is a reliable test of their identity. Since the spectrum of a mixture of compounds is in general a superposition of the individual spectra of the separate pure components, with allowance for concentrations, measurement of the intensities of specific bands makes it possible to carry out quantitative analysis of mixtures quickly and accurately. Absorption bands characterize not only the molecule as a whole, but many of them are also characteristic of individual atomic groupings within the molecule. Thus, in deciphering the spectrum of a certain unknown compound, we immediately obtain information about the presence or absence of particular atomic groups.

In applied infrared spectroscopy one may indicate three main directions of work: 1) identification of unknown substances and qualitative determination of the degree of purity, 2) qualitative analysis of unknown compounds—determination of characteristic groups, and 3) quantitative analysis of mixtures. In addition to these useful applications one may point to such technical advantages as rapidity of recording and the obtaining of the spectral record in a form suitable for storage and subsequent checking. Further: the possibility of using small quantities (of the order of a milligram) and the complete preservation of the substance in the course of analysis, the possibility of studying samples in solid, liquid, dissolved, gaseous states, etc. Perhaps the most important fact is that all organic compounds and the majority of inorganic substances have characteristic spectra, so that the method a priori has universal applicability.

Let us dwell in greater detail on the principal applications of infrared spectrometry.

1. Spectral identification and qualitative determination of purity. The usefulness of spectral identification of known and unknown compounds is entirely clear. Coincidence of the frequencies and intensity values of 20–30 bands is a reliable

a criterion for the identity of two substances. The basic requirement is good systematization of the material, so that the known spectra of pure substances can be found quickly. An empirical determination of purity is often required in the case when a new substance has been obtained and it is necessary to obtain a pure sample as an analytical standard or for determining the molecular structure. In such a case absorption spectra are taken after each purification, and the absorption bands of impurities will decrease in intensity. Although the nature of the admixtures or impurities may remain unknown, the success of the chemical operations will quickly be established. The ease and speed of this method make it useful; however, it cannot be used for quantitative measurements of the degree of contamination until all components are known.

It is clear that the procedure for such investigations must make possible rapid measurements of the spectrum; the instruments must have sufficient resolving power in order to reveal the entire structure of the spectrum and, above all, to give reproducible data. Spectral comparison is often performed by simply superposing spectrograms and viewing them by transmitted light.

Reproducibility of the frequency calibration of the instrument, of the spectral slit width, and of the sensitivity is required especially in those cases when a band of a small impurity is observed in the form of an inflection on a strong band of the principal component.

2. Qualitative group analysis. From empirical correlations\(^3, 21, 22, 32\), based on the study of the spectra of many compounds containing the same atomic groupings, and also from the complete vibrational analysis of the simplest molecules, it is known that certain atomic configurations, such as, for example, O—H, N—H, C—H, C≡N, C=O, C=C, etc., give characteristic absorption bands in certain narrow regions of the spectrum. Thus, from the presence or absence of absorption in a definite interval of frequencies one can judge the presence in the compound under investigation of definite atomic groups. Moreover, a small displacement of these characteristic bands gives additional information about the relation of such a grouping to the rest of the molecule.*)

For example, the carbonyl group

\[ >C=O \]

absorbs strongly in the region \(2150—1650\ \mathrm{cm}^{-1}\), but the exact position of the band in this region indicates its presence in a quinonoid, anhydride, lactone, ester, ketone, etc. In Figs. 6A and 6B a summary is given of the correlations between the principal atomic groupings and characteristic

*) In the USSR, the application of i.r. spectroscopy to qualitative group analysis has been developed by the laboratories of A. N. Terenin (Yu. A. Korsunovskii, N. G. Yaroslavskii; see, for example, Izvestiya AN SSSR, physical series, 5, 182, 1941) and V. M. Chulanovskii (see, for example, Proceedings of the All-Union Conference on Analytical Chemistry, Moscow, 1943). (Translator’s note.)

for them frequencies. Many of these indications are still preliminary; the question of the application of such tables has as yet been little developed and requires further verification and study. However, the value of this method, in which only an infrared

Fig. 6A. Possible correlation of atomic groups and characteristic infrared absorption frequencies.

absorption spectrum is needed instead of many special chemical tests, is obvious to the chemist.

The methodological requirements for such work are not very strict with respect to resolving power and accuracy of wavelength calibration. The success of the method depends rather on the experience and chemical knowledge of the investigator and on the richness of the set of standard spectra.

3. Quantitative analysis of mixtures. This application of infrared spectrometry may be considered the most widespread and the most valuable for industry. Among other things, it was used during the war, especially in the petroleum industry and the synthetic-rubber industry, and the resulting need for spectrometers attracted the attention of firms manufacturing instruments.

While this method is usually applied to the analysis of various mixtures in the gaseous \(^{33}\), liquid \(^{34}\), and solid \(^{35}\) states,

its most striking application is its combination with distillation analysis, since distillation leads to separation according to molecular weights, and infrared spectrometry is especially applicable to distinguishing isomers. The combination of distillation and infrared analysis has therefore now entered into the usual practice of analyzing complex mixtures of hydrocarbons, especially in petroleum chemistry.

Fig. 6B. Possible relationship of atomic groups and characteristic infrared absorption frequencies.

The general spectrometric analytical operation is based on the fact that infrared absorption obeys Beer’s law

\[ \frac{I_{\nu}}{I_{0\nu}} = e^{-\alpha_{\nu}cl}, \tag{6} \]

where \(I_{0\nu}\) and \(I_{\nu}\) are the intensities of the radiation entering and transmitted by the sample, \(\alpha_{\nu}\) are the absorption coefficients for frequency \(\nu\), \(c\) is the concentration, and \(l\) is the thickness of the layer. The law is usually applied in the form \(D_{\nu}=\)

\[ = \lg \frac{I_{0\nu}}{I_{\nu}}, \]

with the assumption being made that the optical densities of the components are additive, i.e., that the optical density of a mixture at frequency \(\nu\) is the arithmetic sum of the optical densities of the individual components. In setting up the analysis, the spectra of the pure components are first studied and frequencies are selected at each of which some component absorbs strongly, while the others absorb weakly. The thickness of the cuvettes is chosen so that the optical

density was the most convenient for spectrophotometry \(\left(\dfrac{dc}{c}\right.\) minimal at optical density \(=1\)). Throughout the entire analysis the same cuvette is used, and the layer thickness is not changed exactly*). The absorption coefficients \(a_\nu\) of each pure component are determined for each selected analytical frequency in the given cuvette. Then \(D_\nu\) is measured for the unknown mixture.

According to the assumption of additivity of optical densities, the optical density of the mixture for frequency \(\nu\) can be expressed as:

\[ D_\nu=\sum_i D_{i\nu}=\sum_i a_{i\nu}c_i l, \tag{7} \]

where the index \(i\) denotes the \(i\)-th component.

For \(i\) components, \(i\) equations of type (7) are set up, and since \(D_\nu\) and \(a_{i\nu}\) are known, the values of all \(c_i\) can be found from this system of equations. From equations (7), expressions for the concentrations can be calculated by the inverse-matrix method:

\[ c_i=\sum_\nu \alpha_{i\nu}D_\nu . \tag{8} \]

These expressions, however, are rather cumbersome. Electric calculators\(^{36,37}\), which have recently become available, simplify the computational operations.

The analysis is further complicated by the fact that Beer's law is not always obeyed exactly for molecules in the gaseous state because of broadening under the influence of pressure\(^{38,39}\), and for liquids and solids because of intramolecular effects. These deviations require second-order corrections in the solution of the linear equations. These corrections are usually introduced by means of a special method\(^{40}\), in which the values \(\Delta\), i.e., the difference between the experimental optical density of the pure component and the theoretical value of the same quantity (assuming the validity of Beer's law), are measured as functions of concentration for a weakly absorbing component of the mixture.

Equations (7) or (8) are first solved assuming the theoretical values \(a_\nu\), in order to obtain the first approximate values of \(c\). When these \(c\) and \(\Delta\)—the values of the optical densities of the mixture—are corrected, the equations are solved again. This process is repeated until constant correct optical densities are obtained. A second method\(^{41}\) is somewhat simpler; equations (7) are written in the form

\[ c_i=\frac{D_\nu}{a_{i\nu}}-\sum_j \frac{a_{j\nu}c_j}{a_{i\nu}} . \tag{9} \]

*) The error in the determination of \(l\) will thus enter implicitly into the obtained coefficients \(a_\nu\).

Optical density for a certain frequency is assigned to the principal absorbing component in the given region, and its concentration is calculated. This value is then used as a correction factor in the second equation, and the second concentration is obtained. This process is repeated until satisfactory agreement is obtained between the measured and calculated values of the optical density. A simpler, but less accurate, method consists in assigning optical densities to the principal absorbers and calculating approximate concentration values. The concentrations obtained in this way are used once more to calculate the small terms, and the principal components are obtained from the final solutions. For two-component mixtures, or when measuring small terms, a graphical method is often sufficient.^42

To determine \(\dfrac{I_\nu}{I_{0\nu}}\), there are two methods. In the first, all \(I_{0\nu}\) are measured through an empty cuvette or without it, and then all \(I_\nu\) are measured through a cuvette containing the substance under investigation. For convenience^43 in this analytical work, in some instruments a compensating potential from a constant source (battery) is applied. This full potential is applied when measuring \(I_{0\nu}\), and the instrument signal (its sensitivity) is adjusted so as to reduce the potential to zero. When the signal \(I_\nu\) is applied, the compensating potential is reduced by means of a precision potentiometer so as again to obtain zero. The potentiometer is graduated in percent transmission or optical density, which are read directly. In the other method^41 the spectral record marks all the bands, and a straight line is drawn through the base of the band between two precisely specified frequencies. \(I_{0\nu}\) is measured from the zero-signal point to the baseline drawn in the indicated manner, and \(I_\nu\) from the zero signal to the absorption band itself. The first method is simpler, but requires more careful calibration; the second method is better for detecting unknown impurities and ensures control of the calibration. Both methods, when properly applied, give the same accuracy, as shown in several works^34,41 on petroleum analysis. Table II shows the accuracy that can be obtained with the first method. A complete standard analysis, including preparation of the samples, measurements, and calculations, takes about 1 hour. In analytical work of this type, the accuracy of intensity measurements and the reproducibility of the frequency calibration are more important requirements than resolving power. A decrease in resolving power leads on average to a reduction in the values of \(a_\nu\) of the principal bands, but the increase in the accuracy of intensity measurements with increasing slit width is nevertheless more advantageous. One of the most important factors that must be carefully taken into account is scattered or stray light, which distorts intensity measurements—

sensitivity. It is desirable that the intensity of the scattered light be reduced to a minimum (\(<0.5\%\) of the true intensity), especially in those cases when high optical densities are being measured. An instrument satisfying all requirements for industrial applications must have the appropriate resolving power, stability of calibration, accuracy of intensity measurements, ease and speed of operations, convenience of devices for changing samples, prisms, etc. The spectral resolution attainable with the best modern instruments is of approximately the same order of magnitude as the width of the absorption band of substances usually studied in industrial applications;

Table II

Infrared analysis of synthetic mixtures*)

Hydrocarbon	Synth. %	Analys. %	Analys. %	Analys. %	Analys. %	Mean error in %
2,2,4-trimethylpentane	20.0	20.0	19.6	19.7	20.1	0.2
2,3-dimethylpentane	18.0	19.4	19.2	19.5	19.4	0.6
2,2,3-trimethylbutane	20.0	21.0	20.2	20.8	20.4	0.3
2,2-dimethylpentane	0.0	−0.7	−0.4	−0.2	−0.0	0.3
3-ethylpentane	1.0	1.0	1.0	1.1	1.0	0.0
2,4-dimethylpentane	20.0	19.6	20.0	19.9	19.7	0.2
3,3-dimethylpentane	0.0	0.4	0.1	0.0	−0.3	0.2
3-methylhexane	0.0	0.1	−0.1	−0.3	−0.4	0.2
2-methylhexane	0.0	0.0	0.0	0.0	−0.3	0.2
n-heptane	20.0	20.0	20.1	19.5	20.2	0.2
Mean error						0.25

*) See reference 34.

in view of this, further improvements in optical quality or resolving power are not especially significant. The use of modulated illumination eliminates errors associated with zero shifts under the action of direct currents. The accuracy of measurements of intensity \(\frac{I_\nu}{I_{0\nu}}\) at optimal resolving power is usually \(0.5—1.0\%\). It would be desirable to reduce the noise-to-signal ratio to \(0.1\%\), although the technique associated with the samples themselves (cuvettes, accuracy of measurement of layer thickness, etc.) must be improved in order to make full use of this progress. At present, instruments have appeared with automatic recording of transmittance or optical density and, in addition, achieved

sufficient inertia-free behavior of the detectors, so that oscillographic recording of parts of the spectrum on the screen with afterglow of the image over the course of one minute became possible. It would be desirable to extend the experimental possibilities below 400 cm\(^{-1}\), but this could lead to an expansion of the presently accessible region 4000—400 cm\(^{-1}\) by only 300—400 cm\(^{-1}\), and the experimental difficulties connected with this are very great. The present state of the design of spectrometers for industrial applications is in general quite satisfactory, although some improvements would nevertheless be desirable. The chief shortcoming of modern equipment is its high cost, unfortunately unavoidable because of the special nature of the dispersing media, thermal detectors, and electronic equipment required for amplifying weak signals. For this reason it is impossible to obtain simple and cheap spectrometers similar to those available for the visible part of the spectrum.

Infrared spectrometry is being applied more and more widely for quantitative analysis and for the identification of unknown compounds. The methods of its application to the determination of molecular structure are still insufficiently developed. The principal aim, of course, is to compute from an exact experimental study of the spectrum the molecular configuration that can lead to this spectrum. The modern empirical approach, which requires the study of a large number of compounds in order to identify definite absorption bands with vibrations of definite atomic groups, is already becoming less effective, as is the theoretical approach consisting in carrying out a complete vibrational analysis and extending the method to ever more complex molecules. It may be thought that a combination of both methods will be of substantial importance, namely, vibrational analysis of definite parts or active groups within the molecule and comparison with the experimental results obtained. Although the ultimate goal may not be achieved, it nevertheless seems that methods can be developed which will make it possible to obtain much more information than modern methods do. A beginning has recently been made on such a combined approach\(^{44,45}\), and the appearance of electrical calculators may help its wider dissemination.

IV. EXPERIMENTAL PROCEDURE IN THE NEAR INFRARED REGION 4000 cm\(^{-1}\)—400 cm\(^{-1}\)

For theoretical and practical applications of absorption spectrometry, or for special investigations of emission in the near infrared region—reflection or polarization—the principal instrument is the infrared spectrometer. In its most general form it consists of a) a source of continuous radiation in the given

regions of the spectrum, b) the dispersing system, c) the optical device and the system of slits for collimating the beam of rays and isolating narrow portions of the spectrum, d) the receiving-amplifying-recording device, e) the corresponding accessory for mounting and changing the samples under investigation. Owing to the experimental difficulties in the development of infrared spectrophotometry, many variants of all these components have been tried. Although there are several types of well-standardized instruments, it is nevertheless more convenient to consider all the components of an infrared spectrometric installation separately from the point of view of their desirable design and applications, and then to summarize the design criteria for modern spectrometers.

a) Sources; emission

Since all sources of infrared radiation now in use are thermal radiators, the ideal should be regarded as a black-body cavity at high temperature. In view of the fact that this is impractical and uneconomical, various incandescent filaments with characteristics close to black-body radiation are used instead. In early work, sources in the form of an incandescent metallic strip of tungsten or nichrome were widely used, but since their reflectivity increases at longer wavelengths and their emissivity decreases, they are now used only in the nearest region of the infrared spectrum or in the simplest instruments, for example in gas analyzers.

The modern, widely used emitters are the “Globar” and the Nernst filament. The Globar is made of a rod of pressed silicon carbide (2 inches long and \(^{3}/_{16}\) inch in diameter), which is clamped between two spring contacts. At a voltage of \(\sim 50\) V and a current of 4–5 A it is heated to a temperature of \(1200^\circ\)C and can operate for up to 250 hours. The use of an increased regime, giving a higher incandescence temperature, leads to a shortening of its lifetime, since the binding material burns out and the rod is partially destroyed. The Nernst filament is a hollow rod (small cylinder) \((l = 2.5\ \text{cm}\) and \(d = 1\ \text{mm})\), made from a mixture of rare-earth oxides (zirconia, yttria, and also thoria). At 76 V and 1.2 A (alternating current) it gives a temperature of \(\sim 1900^\circ\)C in air and lasts for a sufficiently long time. It is used less often than the Globar, since it is more fragile and sensitive to temperature changes (associated with air currents), requires a more cautious connection of the platinum contacts\(^{46}\), and is often placed under hydrogen pressure. Since the Nernst filament has a negative temperature coefficient, a ballast resistance or stabilizing device is required for it and, in addition, supplementary heating for incandescence. Its diameter is sometimes too smallע

for broad-slit spectrometers. The only advantages are the higher operating temperature and greater suitability for operation in an enclosed space, since it does not emit as much substance into the surrounding space as, for example, a globar. Another advantage is the possibility of modulation at audio frequencies, which is sometimes required for special purposes. Its higher energy in the region of high frequencies causes a larger amount of scattered light at low frequencies.

The emitter described by Smith^48 consists of a carbon arc rod 6 mm in diameter, in which a V-shaped cavity has been machined. It is mounted in a vacuum casing with water cooling. At 1.5 V and 40 A of alternating current this source gives a temperature of 1800° C and has a lifetime of about 100 hours. Sometimes a gas-mantle gauze is used, consisting of thorium oxide with a small amount of cerium oxide. It has a low emissive power in the region 10,000 cm\(^{-1}\) (1 μ)—1600 cm\(^{-1}\) (6 μ) and approaches black-body radiation at longer wavelengths. Pfund^49 proposed a method in which gas and electric heating are combined, which leads to emission of the gauze comparable with the emission of a Nernst pin at short wavelengths (2—9 μ), and to better properties in the long-wave region. The use of this source is advantageous at

Table III

Relative emission of a black body at 2000° K*)

Frequency \( \nu \) in cm\(^{-1}\)	Wavelength in μ	Relative energy
6950	1.44	1
5000	2	\(8\cdot 10^{-1}\)
2000	5	\(9\cdot 10^{-2}\)
1000	10	\(9\cdot 10^{-3}\)
200	50	\(2\cdot 10^{-5}\)
100	100	\(1\cdot 10^{-6}\)
50	200	\(8\cdot 10^{-8}\)

*) See reference ^20.

low frequencies, since the energy in the region of high frequencies in its radiation is relatively low, as a result of which the error due to scattered light is reduced.

In considering infrared-spectrum sources, one cannot fail to mention black-body radiation. Table III gives the relative intensities of black-body radiation at 2000° K. Although raising the temperature to 3000° K gives an almost fivefold increase in the emitted energy, the largest amount of this energy falls in the near infrared region: 100% in the region 2000 cm\(^{-1}\) (5 μ), 70% at 1000 cm\(^{-1}\) (10 μ), and 60% at 400 cm\(^{-1}\) (25 μ). In view of the fact that a large increase in high-frequency energy is a definite drawback for many applications because of the admixture of scattered light at low frequencies, raising the temperature

emitters proves harmful. For this reason, too, there is no tendency to work with high-temperature sources.

This situation may also be responsible for the lack in the literature of critical data relating to the comparison of various sources with a black body, or with one another. MacAlister et al.^50 compared the energy distribution given by a Globar with calculated data for a black body at \(1400^\circ\) K, and found good agreement when the absorption in the NaCl prism used in their spectrometer was taken into account. Smith^48 compared his carbon source with a Globar (at \(1000^\circ\) K in both cases) and found good agreement up to the region where the Globar begins to radiate as a gray body (80% relative emission at \(1100\ \mathrm{cm}^{-1}\) and 67% at \(750\ \mathrm{cm}^{-1}\)). Friedel and Sharkey^51 compared the output of a Globar at 200 W power with the output of a Nernst filament at 0.5, 0.8, 1.2, and 1.3 A, in the frequency interval from \(10\,000\ \mathrm{cm}^{-1}\) (\(1\ \mu\)) to \(650\ \mathrm{cm}^{-1}\) (\(15\ \mu\)). At a current of 1.2 A the emission of the latter was considerably higher than the emission of the Globar in the high-frequency region and fell rapidly toward low frequencies, reaching only two units at \(650\ \mathrm{cm}^{-1}\). Sometimes the material under study itself can be used as a radiation source, provided only that it can be excited electrically or thermally so that it will radiate with sufficient intensity. This method has been used for studying the emission lines of elements or the emission bands of many inorganic compounds that are unsuitable for transmission measurements. In addition, cold sources, such as the Moon^52 or the upper layers of the atmosphere, can be studied by measuring the loss of radiation from a thermal detector to the colder object.

The number of studies on the emission of organic compounds is at present small. The emission given by a substance follows the laws of black-body radiation, i.e., the radiation of a nonreflecting sample at frequency \(\nu\) and temperature \(T\) is equal to the radiation of a black body at the same temperature, multiplied by the absorption coefficient of the sample. Since organic compounds usually cannot be heated above \(1000^\circ\) C because of their decomposition, the conditions for studying them are difficult. It is also difficult to separate the emission of the material under investigation from the radiation of the holder or cuvette. The specimen studied must be of the same thickness as the absorbing specimen, in order to eliminate the full black-body radiation, and must be placed on a backing made of an ideally transparent or ideally reflecting substance. These requirements are difficult to satisfy, and most of the measured radiation is a combination of the radiation of the sample plus the radiation of the holder (cuvette), diminished by the absorption of the sample.

In some cases transmission measurements are altogether impossible. Kapf^53 studied the characteristics of certain substances in the form of thin films obtained by molecular distillation. It is also possible to use them for studying the streams arising during combustion, in which a sufficiently high temperature is attained.

b) Refracting materials

For the spectral decomposition of infrared radiation, prisms and echelette diffraction gratings are usually used. The near-infrared spectrum covers so many octaves that it is impossible to get by with a single prism or grating. We give a list of various transparent media with the lower limits of their applicability: quartz—\(3300\ \mathrm{cm}^{-1}\) (\(3.0\ \mu\)); LiF—\(1660\ \mathrm{cm}^{-1}\) (\(6\ \mu\)); CaF\(_2\)—\(1100\ \mathrm{cm}^{-1}\) (\(9\ \mu\)); NaCl—\(650\ \mathrm{cm}^{-1}\) (\(15\ \mu\)); KCl—\(500\ \mathrm{cm}^{-1}\) (\(20\ \mu\)); KBr—\(400\ \mathrm{cm}^{-1}\) (\(25\ \mu\)) and KJ—\(330\ \mathrm{cm}^{-1}\) (\(30\ \mu\)). These limits, apparently, will be considerably extended by the use of a prism made of Tl(Br + J). Most often prisms of rock salt are used, since NaCl gives the best combination of good dispersion and sufficient transparency. For work over the entire region of the near-infrared spectrum, the best combination of prisms is the following: LiF or CaF\(_2\) for the high-frequency region, NaCl for the middle frequencies, and KBr for the low frequencies*); NaCl and KBr are strongly hygroscopic, LiF slightly so, and CaF\(_2\) is not hygroscopic.

Fig. 7. Dependence of spectral resolution on frequency for various prisms under standard conditions.

Figure 7 shows curves of spectral resolution as a function of frequency for different prisms under standard experimental conditions. The obtainable resolution increases toward lower frequencies as a result of the increasing dispersion of the prism; the sharp decrease in resolution in the low-frequency region is due to absorption by the prism, since the slit has to be widened in order to keep the signal-to-noise ratio constant. Usually \(60^\circ\) prisms are used, since they provide a compromise between high angular dispersion and reflection losses. Owing to the use of long-wavelength light, the requirements on the optics are not very stringent, and polishing the prism surface to an accuracy of up to 5 wavelengths of sodium light is quite sufficient.

*) For the dispersion of these crystals see, for example, the Landolt–Börnstein tables.

Echelette-type gratings, first made by Wood,^5 have grooves of a definite shape, produced by stamping or cut with a diamond cutter^56 on a soft surface (for example, chromium-plated aluminum). The grooves (i.e., depressions) must have a V-shaped form with a shorter and a longer side, as shown in Fig. 8. The angle \(\alpha\) between the normal to the long side of the groove and the normal to the surface of the grating is called the blaze angle. It can be shown that light is diffracted by this grating in such a way that it is specularly reflected from the long side of the ridge (dashed lines in Fig. 8) and gives high intensity in a definite order, while the other orders will therefore have a much lower intensity. Consequently, the shape of the grooves must be such as to concentrate a large percentage of the diffracted light of a given wavelength in the desired order; for this reason, echelette-type gratings differ in grating constants and blaze angles.

Fig. 8. Cross section of an echelette grating.
\(\alpha\)—blaze angle.

It is somewhat more difficult to specify the characteristics of a grating for the near infrared spectrum than for a prism, because the choice of grating constant and blaze angle is broad. Stamm and Valen,^57 using Rowland’s equation, carried out general calculations of the intensities that can theoretically be obtained from a grating in a Littrow mounting with a definite ratio of blaze angle to grating constant. The calculations show that gratings of this type can be used over a range of more than one octave and give a theoretical intensity interval of \(\pm 15\%\). If the required octave is from \(\lambda\) to \(2\lambda\) for the first order, then the blaze wavelength should be about \(\lambda\)—\(1.2\lambda\), i.e., the intensities given by the grating are maintained better on the long-wavelength side than on the short-wavelength side. Similar considerations must be applied for higher orders, since the theoretical characteristic for the \(n\)-th order at \(\lambda\) is the same as for the first order at \(n\lambda\). The calculated values of the intensities under optimal conditions can reach 95–100% concentration, but in practice it is not possible to achieve more than 80%. Gratings used for work in the near

in the infrared region of the spectrum have 7200, 3600, 2400, 1800, 1440, and 1200 lines/inch. R. Wood made a plane replica grating by pouring a thin layer of Formvar onto the surface of a grating placed on a glass surface, and aluminizing it in vacuum. Recently R. Wood[^58] described the manufacture of plane or concave replica gratings which, in their qualities, were not inferior to the original.

Gratings give a much greater dispersion than prisms and permit the use of wider slits. The disadvantages of gratings are the need to introduce an additional prism for preliminary dispersion, or filters that do not transmit spectra of higher orders; the large amount of scattered light; and the smaller range of applicability. For the study of vibrational bands prisms are sufficient, while for work with rotational structure and for some vibrational analyses a grating is usually necessary.

c) Optical systems; automatic spectrophotometers

The optical part of installations for infrared spectrometry differs from ordinary ones only in the requirement of a high aperture in order to obtain sufficient energy, and in the use of mirrors instead of lenses because of the impossibility of achromatizing lenses* over a sufficiently wide frequency interval. To obtain maximum dispersion without loss

Fig. 9. Schematic diagram of a small prism spectrometer. \(C\) — cuvette, \(G\) — globar, \(M_I, M_{IV}, M_V, M_{VI}\) — plane mirrors, \(M_{II}, M_{VII}\) — spherical mirrors, \(M_{III}\) — off-axis paraboloid, \(M_S\) — slit micrometer, \(M_W\) — wavelength drum, \(P\) — prism, \(S\) — shutter, \(S_I\) — entrance slit, \(S_{II}\) — exit slit, \(T C\) — thermocouple, \(D\) — temperature compensator.

energy and possible reduction of the diffraction limits, the Littrow or Littrow–Wadsworth arrangement is usually used. Since large artificially prepared prisms appeared (in the period 1940–1947), large spectrometers have been constructed\(^{50,59-63}\) with \(f=100\ \mathrm{cm}\) and \(60^\circ\) prisms with a base of \(15\ \mathrm{cm}\) and a height of \(10\)–\(12\ \mathrm{cm}\). Instruments of this type are often supplied with several prisms or a combination of gratings for different spectral regions. The slits are often automatically linked with the wavelength drum, so that the outgoing energy or the spectral width of the slits remains constant for all frequencies. Standard instruments have smaller dimensions, for example \(f\) from \(75\ \mathrm{cm}\) to \(27\ \mathrm{cm}\) and prisms from \(8\times 10\ \mathrm{cm}\) to \(6\times 7.5\ \mathrm{cm}\). The entrance slit is often made curved\(^{64}\) so that the image of the lines is correct. The optical scheme of a typical prism spectrometer\(^{65}\) is given in Fig. 9.

The spectral slit width of the prism of a Littrow spectrometer is determined as half the frequency interval emerging from the exit slit of the instrument, or as the theoretical resolving power of the spectrometer, which is given by the approximate formula\(^*\)

\[ \Delta \nu\ (\mathrm{cm}^{-1}) = \nu^2 \frac{ \left[1-n^2 \sin^2\left(\frac{\alpha}{2}\right)\right]^{1/2}(s_1+s_2) }{ 8\sin\left(\frac{\alpha}{2}\right)\left(\frac{dn}{d\lambda}\right)\cdot f } + F(s)\, \frac{\nu}{2b\left(\frac{dn}{d\lambda}\right)}, \tag{10} \]

where \(\nu\) is the frequency in \(\mathrm{cm}^{-1}\), \(n\) is the refractive index for the frequency \(\nu\), \(\alpha\) is the angle of the prism, \(\frac{dn}{d\lambda}\) is the dispersion of the prism material, \(s_1, s_2\) are the slit widths, \(f\) is the focal length in the corresponding units, \(b\) is the base of the prism in centimeters, \(F(s)\) is a function varying from \(\sim 0.9\) for \(s=0\) to \(\sim 0.5\) for

\[ s=\frac{\nu}{\left[2b\left(\frac{dn}{d\lambda}\right)\right]}\ \mathrm{cm}^{-1}. \]

The first term is due to the finite width of the slit, whereas the second represents the diffraction limit of the prism itself. In good instruments the first term should be at least three times larger than the second.

For a given spectral slit width and \(s_1=s_2\), the radiation power \(E_\nu\) delivered by the spectrometer is proportional to the energy in \(1\ \mathrm{sec}\cdot\mathrm{cm}^2\) at the frequency \(\nu\) entering the instrument, \(h\times s\) is the slit area, and \(\frac{A}{f^2}\) is the solid angle of the radiation going from the entrance slit to the entrance pupil, usually determined by the projection of the prism surface perpendicular to the optical axis. If \(s\) is expressed in the form of the angular dispersion of the prism \(D\), then the expression for the energy has the form:

\[ E_\nu \sim I_\nu \frac{hDA}{f}. \tag{11} \]

\[ \text{---} \]

\(^*\) This formula is given for minimum deviation and is valid only in the case of an arrangement of the Wadsworth–Littrow type; for the Littrow arrangement it is only approximately valid.

From this it is clear that the most advantageous are a long slit, a large prism aperture, high dispersion, and a small focal distance. However, these factors are limited by the aberrations that occur at large off-axis apertures, and by the desire to reduce the image of the slit in order to increase sensitivity.

Fig. 10. Diagram of a prism-grating spectrometer. From \(N\) to \(S_1\)—collimation of the source and the region where the sample is placed; \(S_1\) and \(S_2\)—the entrance and exit slits of the first prism monochromator; \(M_4\)—off-axis paraboloid; \(P\)—front prism; \(S_2\) and \(S_3\)—the entrance and exit slits of the grating spectrometer; \(M_5\)—off-axis paraboloid; \(G\)—grating; \(T\)—thermocouple.

Instruments with gratings are in reality double monochromators, since in addition to the grating a prism for preliminary dispersion is always necessary. The arrangement of an instrument of this type is given in Fig. 10. Instead of parabolic mirrors, because of their high cost, the Pfund optical arrangement is often used\(^ {66}\).

The widths of the slits \(s_1\) and \(s_2\) determine the frequency interval [equation (10)] reaching the grating, while \(s_2\) and \(s_3\) determine the spectral width of the slit; the resolving power will be expressed by the following formula:

\[ \Delta \nu=\frac{\nu^2}{2n}\,d\cos\theta\,\frac{s_2+s_3}{f}+F\left(\frac{\nu}{Mn}\right), \tag{15} \]

where \(n\) is the order of the spectrum, \(d\) is the grating constant, \(\theta\) is the angle of incidence and diffraction (in the Littrow arrangement), and \(M\) is the total number of rulings; the two terms of expression (12) have the same meaning as in (10). Here too the first term is due to the finite width of the slit, and the second to the diffraction limit. For most gratings, which usually have a width of about 6 inches or more, the second term is considerably smaller than the first. It may be seen that the dispersion of the monochromator’s fore-prism must be chosen very carefully, since if it is too large, then \(s_2\) must also be large in order to pass a sufficiently large spectral interval; if the dispersion of the fore-prism is very small, then \(s_2\) must be very narrow in order to isolate a sufficiently narrow interval. Formula (12) shows that the spectral width of the slit is proportional to \(s_2 + s_3\), so that the limiting values of \(s_2\) must correspond to the limiting reciprocal values of \(s_3\). This situation is undesirable, since the energy reaching the detector in the case of a continuous spectrum is proportional to the product \(s_1 s_2\), which is maximal when \(s_1 = s_2\). Owing to the large dispersion of the grating, in a diffraction spectrometer, unlike a prismatic one, the limiting factor is to a greater degree the energy conditions rather than diffraction effects. In practice, the fore-prism is usually set to the middle of the spectral interval under study \((\Delta \nu = 200—300\ \text{cm}^{-1})\); after it has been fixed, the grating is rotated to select the required wavelength. When working with a grating it is more necessary than in the case of a prismatic instrument to remove \(\mathrm{CO}_2\) and water vapor by means of absorbents such as \(\mathrm{P}_2\mathrm{O}_5\), or by flushing with nitrogen, or, finally—and preferably—by evacuation.

Behind the exit slit of each type of spectrometer there is placed a spherical or elliptical mirror, which gives a strongly reduced image on the receiver slit.

The radiation source is focused on the entrance slit by one spherical mirror or by two such mirrors, giving an intermediate image of the source on the sample. Special optical devices are necessary for the study of reflection or polarization of infrared light. At present only a small number of works are devoted to reflection, although Pfund \(^{67}\) recently published an interesting method for identifying precious stones from infrared spectra. The study of polarization opens many interesting possibilities, but their application is hindered by the fact that the polarized beam is usually weakened, and the individual crystals for which such investigations might be of interest are usually small in size. At present, with the use of more perfect optics and more sensitive receivers, and also in connection with the growth of work on determining the structure of complex molecules, work on polarization must undoubtedly also expand.

Pfund \(^{68}\) and Elliot and Ambrose \(^{69}\) developed a method for obtaining purely polarized light upon reflection and transmission. Since the change of dipole moment in the vibrations of such groups as O—H, N—H, C=O must be very close to the direction of the bond, it becomes possible to find the direction of these bonds by varying the orientation of the crystalline specimen in the beam and finding the maximum or minimum of reflection (or transmission) \(^{70,71}\). Information of this kind must be of enormous importance in determining the structure of a crystal (as, for example, in the most recent work on the study of penicillin).

Another important point on which it is necessary to dwell is the question of scattered (spurious) light and of methods for eliminating it. When incandescent bodies are used as sources, the maximum of the energy falls at frequencies higher than those of the region under study, and the disturbing action of scattered light becomes especially noticeable below \(1900\ \text{cm}^{-1}\) (\(7\mu\)). The problem becomes very serious for quantitative work, where the intensity of the true flux must be measured accurately. Therefore we shall consider this in more detail for the prism spectrometer, although the methods will also be applicable to the case of a grating.

A possible source of spurious light in a Littrow instrument is “back-entering radiation,” i.e., dispersed radiation traveling in the direction of the focal plane and entering the prism at such an angle that it emerges together with the true beam. This can easily be avoided by mounting the prism in such a way that the energy of the higher frequencies moves away from it while the spectrum is being traversed. The chief source of spurious radiation is scattering at optical surfaces or multiple reflections from objects in the spectrometer. This latter factor can be greatly weakened by careful diaphragming of the optical beam. Direct scattered light can be reduced to a minimum by using a double monochromator \(^{59}\), filters (after Pfund \(^{72—74}\)) made of powders in which the particle sizes are chosen so as to reflect or scatter the higher frequencies; the residual-ray method or the use of echelette-type gratings instead of plane mirrors \(^{75}\); in these cases the light of low frequencies is specularly reflected, while the shorter-wavelength energy is absorbed or diffracted; and the use of partially absorbing materials (see Table V, Sect. 46) for determining the zero makes it possible to estimate the magnitude of the spurious radiation. Of all these methods, of course, the double-monochromator method is the best, although also more expensive. A combination of suitable gratings and partially absorbing filters is the best of the simple methods. In Fig. 11 a comparison is given of the filtering action of a grating and a MgO filter.

Operations for adjusting the optics of the spectrometer may be found in Martin et al. \(^{63}\), although in order to obtain the best image

At the exit slit the “knife-edge” method is used more often than microscopic examination of the image.

One of the most interesting achievements in the field of infrared technique is the spectrometer that automatically records the percentage transmission.

Descriptions of such devices may be found in several authors^22,76—80. In these instruments the beam from the source is divided in two, and then these two beams enter the entrance slit. This method is applicable both to prism and to diffraction instruments, but so far it has been developed only for the former. The specimen is placed in one beam and an empty cuvette in the other, so that the two beams can be compared simultaneously. In some cases the two beams fall on two separate thermal detectors, and the ratio of the two resulting signals is obtained by applying the signal, amplified in direct current, due to the beam bypassing the specimen, to the ends of a potentiometer with a sliding contact, and the signal due to the beam that has passed through the specimen to a definite point of the potentiometer.

Fig. 11. Comparison of an MgO filter and a grating for excluding high-frequency energy.

In other cases (Fig. 12) the two beams are fed alternately to the entrance slit in one and the same direction, which is achieved by means of a semicircular mirror rotating at a speed of 5—10 revolutions per second. The two signals act on one and the same receiver and, if the energies of the two beams are not balanced, an alternating current is excited in the receiver. This signal, with allowance for the phase shift, is amplified, rectified, and causes a comb diaphragm in the beam bypassing the specimen to operate until equilibrium is established. The position of the diaphragm is recorded and calibrated as percentage transmission. The latter method should be preferred, since it is an automatic zero method with alternating current and does not depend on shifts of the detector zero; in the former case it is difficult to obtain identity of the two detectors and an equal magnitude of response.

In the method described by Becker and Robb^81, discontinuous recording is obtained by means of a step-by-step device and an automatic slit, giving signals of constant energy. An entirely different method for obtaining the percentage transmission was described by Avery^82. First

radiation from the source, without the absorber being investigated, is directed into the spectrometer; the deflection of the galvanometer spot is directly observed and the position of the slide of the potentiometric device, operated by hand, is noted. Then the same thing is repeated with the sample inserted, and the potentiometer is adjusted so as to obtain the initial values of the galvanometer readings. This method requires much time and attention. Here, however, automatic recording of transparency can be introduced if the intensity of the radiation in the absence of the absorber is recorded, say, on magnetic tape, and then used for automatic and continuous change of the sensitivity of the receiver when the sample under investigation is introduced into the beam, until equal signals are obtained at all frequencies. The resulting absorption spectrum should be obtained directly in percentages of transmission and, as in the double-beam method, requires only one receiver. This method has an advantage in the case of very precise analytical work, since one and the same cuvette is tested with the sample and without it, and no adjustment of two identical cuvettes is required, as in the double-beam method. However, the method of sequential recording requires exceptional constancy of the energy sources, calibration, etc., during both measuring cycles, and is more laborious. We shall return to a discussion of this in Section IVe.

Fig. 12. Schematic of a split beam in automatic spectrophotometers. \(G\)—globar, \(Q\)—cuvette, \(M\)—rotating sector mirror, \(S\)—entrance slit, \(W\)—neutral wedge, \(SM\)—servomotor, \(R\)—recording.

d) Receivers, amplifiers, recording

Receivers. In this paragraph we encounter one of the most substantial difficulties in infrared spectroscopy, and there is no region of the electromagnetic spectrum in which there have been so many experimental difficulties. As for sources, the materials that can readily be used at high temperatures are usually poor black bodies and, even at not very high temperatures, give undesirable scattered light. Refracting media are usually expensive, not very durable, and are often spoiled by moisture. Good gratings are also expensive

and have limited dimensions. If one speaks of cuvettes and solvents, then here too the choice of transparent media is extremely difficult. However, the greatest difficulties are connected with the low sensitivity of the receivers used in the infrared region, which is clearly seen from the visual comparison of the sensitivity thresholds of radiation receivers in Fig. 13. As a consequence of this situation, the most varied thermal detectors and amplifiers have been tested, and the development of infrared detectors is at present one of the most important instrumental problems.

Adhering to the historical point of view, it is difficult to give a relative evaluation of the various types of receivers (as we shall see below,

Fig. 13. Sensitivity thresholds of modern receivers of electromagnetic radiation as a function of wavelength. Black-body radiation at 300° K is also shown.

this situation is only slightly better even at the present time). Formerly the minimum perceptible energy was not yet used as a quantitative criterion, and the noise of the amplifying system, which is the limiting factor, was often not measured. Moreover, thermal detectors were used in new spectrometers with improved amplifying systems. Success was often judged on the basis of spectral results, without attempting to differentiate the role of the individual parts.

As was indicated in Section II, Langley’s use of the bolometer gave, for the first time, a sensitive infrared receiver, although crude thermopiles were already in use. The first bolometers consisted of a Wheatstone bridge, into one arm of which was inserted a very thin

a blackened platinum strip upon which the radiation fell. The signal of the unbalanced bridge was observed with the aid of a galvanometer. Another type of instrument, already in use at that time, was the microradiometer^84, consisting of a gas thermometer, one of whose bulbs was exposed. The bulbs were connected with a capillary containing two electrodes and a drop of conducting liquid. Expansion of the gas in one bulb moved the drop and changed the resistance between the electrodes. This device was connected to a Wheatstone bridge in the same way as in the case of the bolometer. This instrument was never especially popular, since the detecting gases absorb selectively.

In order to get rid of complications associated with the sensitivity of galvanometers to extraneous electric and magnetic disturbances, the radiomicrometer^85,86 and the radiometer^87,88 were introduced. The radiomicrometer consists of a very small thermocouple (Ag-Pd or Bi-Sb), connected in series with a conducting wire in such a way that a loop is formed; it is suspended in a vacuum between the poles of a powerful permanent magnet. Heating of the thermocouple by radiant energy excites a current in the loop, and its rotation in the magnetic field is measured by the deflection of a light beam reflected from a mirror connected with the suspension system.

In the radiometer, two vanes (of very thin mica or of platinum), blackened on one side, are attached to a glass rod with a small mirror; the system is suspended on a quartz fiber in rarefied air at 0.1 mm Hg. Radiation falling on one of the vanes heats it, and the greater amount of motion of the reflected molecules causes rotation of the system. Coblentz, who studied instruments for measuring radiant energy thoroughly, considers the radiometer a very sensitive and stable instrument, although it has the disadvantage that its period under these conditions is about 1 minute.

Czerny^90,91 developed a quasiphotographic method for recording infrared radiation, which is the only method for the simultaneous recording of a wide spectral interval. For this he used a thin celluloid strip (0.1 μ thick), coated on one side with Bi or Al black and on the other side with a thin layer of paraffin oil. The spectrum is projected onto the blackened side, and the places corresponding to the transmission bands of the sample under study are heated, as a result of which the oil evaporates. A photograph of the oil film in reflected light should give a picture corresponding to the absorption spectrum of the sample.

From 1910 to 1935 these types of thermal detectors gradually led to a combination of thermopiles or thermocouples with galvanometers, which became the usual receiving-amplifying system. Johansson^92 gave a brilliant theoretical treatment of the sensitivity of thermopiles. In 1930–1934^93–97 the theory of these instruments was developed

further, and detailed descriptions of thermopile designs were given.

In all these theoretical works it is assumed that the measuring instrument used is a galvanometer, and usually the limiting factors are the period of the galvanometer and Brownian motion. Cartwright^97 described a thermocouple of Bi—Sb, soldered to (Bi—Sn), having the following characteristics: receiver area \(0.5\ \mathrm{mm}^2\), resistance \(20\ \Omega\), period \(< 1\) sec., sensitivity greater than \(1\ \mu\mathrm{V}\) for \(10^{-8}\ \mathrm{gcal/sec}\) \((20\ \mu\mathrm{V}/\mu\mathrm{W})\) of incident radiation. These figures are comparable with, or even exceed, the sensitivity of modern thermocouples. As a result of these investigations the following basic type of thermocouple design became standard. The thermocouple consists of two thin, short wires (\(0.01\ \mathrm{mm}\) in diameter), whose composition is: \(97\%\ \mathrm{Bi} + 3\%\ \mathrm{Sb}\) and \(95\%\ \mathrm{Bi} + 5\%\ \mathrm{Sn}\) (Hutchins alloys); the thermoelectric coefficient of the pair is \(120\ \mu\mathrm{V}/^\circ\mathrm{C}\). They are welded together at one end so as to form a junction, and the other ends are soldered to thick copper leads. The receiver is a gold leaf (thickness \(0.1\text{—}1\ \mu\)), blackened with lampblack bound with some varnish, or coated with it by evaporation^98 under low pressure and cut down to the size of the image obtained from the exit slit. This receiver is placed on the junction, supported by two quartz threads, and soldered to the junction by heating with radiation. Instead, one may first, by means of spot welding, connect the receiver and the wires and then, placing all this on quartz threads, solder it to the leads. Two such junctions are connected in series in opposite positions; one junction is acted on by the radiation, the other compensates temperature changes. Let us give the average characteristics of such a thermocouple: receiver area \(6 \times 0.4\ \mathrm{mm}\), resistance \(10\ \Omega\), period \(1\text{—}5\) sec., sensitivity \(3\text{—}6\ \mu\mathrm{V}/\mu\mathrm{W}\) of incident energy.

The intensity of the radiation at the detector of the spectrometer, with good resolution, is \(0.05\text{—}0.2\ \mu\mathrm{W}\).

The principal inconvenience of the thermocouple—galvanometer system is zero displacement associated with changes in the temperature of the receiver. This drawback can be weakened to some extent by using a compensating junction, but it cannot be reduced to zero, since it is impossible to make two identical thermocouples. This drawback is not very troublesome in point-by-point measurements (as was done earlier), but the use of a photorelay or automatic recording of the spectrum requires strict constancy of the zero.

To get around this difficulty, interrupted illumination began to be used (5—15 interruptions per second), measuring precisely the alternating, i.e. true, signal. The alternating-current signal requires the use of a transformer in the receiver circuit in order to create an impedance such that electronic amplification can replace the galvano-

meters. The indicated circumstances, as well as the successful work on infrared signaling carried out during the war period, have led to the fact that at present this technique rests on good, stable receiving and recording systems of various types; however, as regards sensitivity, here we still do not have a significant gain in comparison with what was already available in 1930.

Since a large part of this work on improving receivers of infrared radiation proceeded independently of spectrometric problems, it is useful here to consider the principles for standardizing detector design. The most important point is the absolute sensitivity of the receiver, which is equal to the relative sensitivity \((\mu V/\mu W\) of radiant energy incident on the sensitive area of the receiver), divided by the noise level. This criterion may be replaced by the concept of “minimum detectable energy,” which corresponds to the reciprocal of the absolute sensitivity. It is assumed that for modern receivers the limiting factor is Johnson noise, for which we have the exact expression:

\[ (e_J)^2_{\mathrm{av}} = 4kRT\Delta f, \tag{13} \]

where \(R\) is the resistance of the receiver, \(T\) the absolute temperature, and \(\Delta f\) the transmitted frequency band (inversely proportional to the response time) of the receiving system. The bandwidth factor in equation (13) establishes qualitatively that the faster one tries to measure a signal, the less accurate the measurement will be. Even if the Johnson-noise level of the receiver is lowered, the limit is set by thermal noises caused by temperature fluctuations in the element. For modern receivers (bolometers and thermopiles) the thermal noise is 5–20 times below the Johnson-noise level.

From all that has been said above it follows that, in order to characterize modern thermopiles and bolometers, the following data are needed: relative sensitivity, noise level, area, resistance, the time constant of the element itself (the time during which the element gives \(1/e\) of the full response under continuous exposure to constant radiation), and the passband of the system for which the sensitivity is measured. A convenient characteristic of the time constant is the percentage deviation under direct current as a function of the frequency of the interrupted radiation. In some cases these data can be found for modern receivers; however, as will be shown below, the design and the conditions of measurement are so varied that it is difficult to make an absolute comparison.

Let us turn to a description of the development of modern receivers. One of the first was the work of Harris and co-workers\(^{99–101}\) with low-inertia thin (deposited) thermopiles for re-

...of alternating current, although initially they were not intended for spectrometric applications. Lehrer\(^{102}\), in 1937, used a platinum bolometer (0.5 \(\mu\) thick, 0.1 mm wide, and 5 mm long, with a resistance of 16 \(\Omega\)) with intermittent illumination (68 cycles per second) and electronic amplification for spectral recording. After these works, a large number of reports appeared concerning the use of thermocouples and bolometers in combination with intermittent illumination and alternating-current amplification. Bolometers made of rolled strips and thin nickel wires with low resistance have been described\(^{79,103—105}\). Aiken\(^{106}\) and his co-workers described a bolometer made of gold film obtained by evaporation in vacuum; Billings and co-workers\(^{107,108}\) gave a detailed theory of similar bolometers. Uelts\(^{109}\) developed an interesting idea of a dielectric bolometer consisting of a methyl methacrylate film impregnated with nitrobenzene. He established a sensitivity in air of 300 V/W and a 60% response in 0.2 sec., but the resistance of such a bolometer is not mentioned. Ress and Dakus\(^{110}\) made a thermocouple of bismuth with antimony, obtained by evaporation; it had the following characteristic: resistance 20–25 \(\Omega\), steady sensitivity \(6—7\ \mu\text{V}/10^{-4}\) W per cm\(^2\), and 50% response at 7 cycles per second. Their sensitivity is difficult to compare with the sensitivity of wire thermocouples, owing to the fact that in the control tests the authors illuminate the entire thermocouple, from the hot to the cold junction, whereas wire thermocouples in similar tests “see” radiation falling only on the receiver itself. The sensitivity of such a thermocouple will always be lower than that of a wire thermocouple because of large heat losses.

Hornig and O’Keeffe\(^{111}\) gave a summary of the theory of wire thermocouples. They characterize the quality of a thermoelectric material by the following quantity: \(\dfrac{Q}{(k\rho)^{1/2}}\), where \(Q\) is the thermoelectric coefficient, \(k\) is the thermal conductivity, and \(\rho\) is the electrical conductivity. A list is also given of materials most suitable for making thermocouples; from this list it is evident that semiconductor alloys have the best figures of merit, although the properties of such materials are difficult to control because of their extreme sensitivity to the slightest traces of impurities. The authors described a thermocouple made of Gatchins alloy with the following characteristics: area 0.5 mm\(^2\), time constant 0.036 sec., sensitivity under steady illumination 6.5 \(\mu\)V/\(\mu\)W, 88% response at 5 cycles per second, minimum recorded signal \(5\cdot10^{-5}\) W at 5 cycles/sec.

Liston\(^{112}\) described a new type of low-inertia thermocouple, similar to Schwarz’s thermocouple (Hilger), consisting of two heavy rods (1 mm in diameter and 2 mm long), mounted side by side so that a gap of 2 mm remains between them. Lead wires are attached to the ends of the rods, and their other ends

sharpened. The receiver \((2\ \mathrm{mm} \times 0.2\ \mathrm{mm})\) lies on two points and is welded to them. A double thermopile is obtained: the first thermoelement with the receiver, connected with a receiver attached to the second thermoelement. Liston does not report the composition of the substances forming the whole thermopile, mentioning only that these are semiconductors in which the thermoelectromotive force gives \(800\text{—}900\ \mu\mathrm{V}/{}^\circ\mathrm{C}\), but this gain is partly reduced owing to an increase in the Wiedemann–Franz coefficient. It is known that the Perkin–Elmer thermopile gives a constant sensitivity of \(8\text{—}10\ \mu\mathrm{V}/\mu\mathrm{W}\) and 70% response at 15 cycles per second, while for the Schwarz thermopile the firm gives \(60\ \mu\mathrm{V}/\mu\mathrm{W}\). However, measurement of two or three Schwarz thermopiles with the smallest area, tested in the USA, showed a sensitivity of \(8\text{—}12\ \mu\mathrm{V}/\mu\mathrm{W}\).

Let us dwell on four other of the most interesting thermal receivers that have appeared recently: the spectrophone\(^{113}\), the thermistor\(^{114}\) (a semiconductor bolometer), Andrews’ superconducting bolometer\(^{115}\), and Golay’s pneumatic element\(^{116}\). In Weingerov’s spectrophone a gas is illuminated by a beam of infrared light interrupted mechanically (by a sector) at an audio frequency (200 cycles). If the radiation is absorbed by the gas, a sound will be heard and the intensity of absorption can be measured by a microphone and an amplifier*).

The thermistor (Western Electric Company) is a solid bolometer, operating in air, consisting of fused nickel, cobalt, and magnesium oxides. A typical characteristic of a thermistor: dimensions \(3 \times 0.2 \times 0.01\ \mathrm{mm}\), resistance \(4 \cdot 10^6\ \Omega\), time constant \(0.003\ \mathrm{sec}\), noise level \(2 \times 10^{-8}\ \mathrm{W}\) for illumination in \(0.003\ \mathrm{sec}\) with a bandwidth of 30 cycles. The thermistor is not yet widely used in infrared spectrometry, although its sensitivity, operation in air, and ruggedness are convenient for applications. The first specimens had a “gray” region near \(2000\ \mathrm{cm}^{-1}\) \((5\ \mu)\).

The superconducting bolometer is an attempt to improve the efficiency of detectors by the use of low temperatures. A thin strip of columbium nitride operates at \(15^\circ\ \mathrm{K}\) in the region of its superconductivity, where its resistance is \(\sim 0.2\ \Omega\).

Golay’s pneumatic element is a three-millimeter cube filled with air or a nonabsorbing gas. The interrupted radiation enters the cube through a KBr window and falls on a thin (semitransparent) diaphragm of soot in the center of the element. The intermittent heating of the diaphragm and of the gas leads to fluctuating pressures, which are transmitted through a capillary tube into—

) It should be emphasized that a substantial innovation in this ingenious device is the resonant tuning, which increases the sensitivity of the instrument by a factor of 1000. The instrument makes it possible to carry out rapid analysis of gas mixtures or to maintain continuous registration of the concentration of one or another impurity in a gas (see, for example, UFN*, 21, issue 4, 482 (1939)). (Translator’s note.)

second small reservoir. One of the walls of this reservoir is a thin curved diaphragm. This diaphragm plays the role of a mirror for the beam of light incident on it. As a result of periodic changes in pressure, the collodion or metallized diaphragm (made of plastic) deflects the light beam so that it either falls on, or does not fall on, the photocell; the alternating current arising in the photocell is proportional to the intensity of the incident radiation.

The author reports that such an element has a time constant of 0.003 sec and an equivalent noise output of \(1.4\cdot 10^{-9}\) watt.

Let us incidentally give two typical formulas for the absolute sensitivity of a receiver on alternating current in the case of a bolometer consisting of a metallic strip\(^{108}\) and for a wire thermocouple\(^{111}\), operating in vacuum:

\[ S_{\text{bolometer}}= \frac{\alpha}{2(kT\Delta f)^{1/2}} \left[\frac{\varphi}{(\gamma lw)}\right]^{1/2} \cdot \left[\frac{\gamma^2}{4\pi^2\nu^2 a^2 l^2+\gamma^2}\right]^{1/2}, \tag{14} \]

where \(\alpha\) is the temperature coefficient of resistance, \(k\) is Boltzmann’s constant, \(T\) is the absolute temperature, \(\Delta f\) is the pass band of the system, \(\varphi\) is the maximum temperature at which the bolometer can operate, \(\gamma\) is the loss of heat per unit surface (radiation), \(l\), \(w\), and \(a\) are the length, width, and thickness of the strip, \(C\) is the heat capacity, and \(\nu\) is the frequency of interruption of the beam. This rather complicated formula is only an approximate solution. Moreover, it is obtained under the assumption that the bolometer operates at the highest voltage (i.e., temperature), that losses due to conductivity may be neglected, and that no correction has been made for the heat capacity of the blackened layer. It should be noted that this expression does not depend on the resistance of the bolometer.

\[ S_{\text{thermocouple}}= \frac{Q}{2(kTR\Delta f)^{1/2}} \cdot \frac{1}{\left[4\pi^2\nu^2 C^2+L^2\right]^{1/2}}; \tag{15} \]

\(Q\) is the thermoelectric coefficient of the element, \(R\) is the resistance of the thermocouple, \(L\) is the total heat loss, equal to

\[ 4\sigma AT^3+\left[K_1\left(\frac{a_1}{l_1}\right)+K_2\left(\frac{a_2}{l_2}\right)\right], \]

where \(\sigma\) is the radiation constant, \(A\) is the area of the receiver, \(K_1\) and \(K_2\) are the thermal conductivities of the wires, \(a_1\), \(a_2\), \(l_1\), and \(l_2\) are the cross sections and lengths of the wires; \(C\) is the total heat capacity, equal to

\[ \left(\frac{a_1l_1C_1+a_2l_2C_2}{2}\right)_{\text{wires}} + C_{\text{receiver}} + C_{\text{blackening}}. \]

In each case the time constant of the element is equal to \(C/L\). A decrease in this quantity is achieved by reducing the heat capacity of the entire

of the system \(C\). The optimum characteristic can be found by seeking the maximum \(S\) with respect to the variables on which this quantity depends.

These formulas are given only to illustrate the difficulty of comparing thermal receivers described in the literature. In each case one seeks to achieve a definite ultimate purpose, which imposes a number of requirements on some of the constants of the instrument. Thus, for example, for spectrometric purposes the area of the receiver must correspond to the dimensions of the image of the exit slit; for military applications (signaling or aerial reconnaissance) a small time constant is required. Since some parameters in the design are fixed, the remaining ones are computed so as to obtain the most advantageous design. A spectroscopist who wants to choose the best receiver for his instrument must recompute the sensitivity for the conditions he wishes to realize, or he may take only the minimum number of variables and compute the maximum sensitivity on the assumption that the other variables can be changed at will. Billing carried out

Table IVA

Comparison of thermal receivers under various conditions

(it should be noted that for these computations certain assumptions were required, and the conditions are not quite identical)

Element	Time constant	Minimum recorded power in watts
Polaroid bolometer	0.02	\(5\cdot 10^{-10}\)
Baird bolometer	0.05	\(2\cdot 10^{-10}\)
Golay receiver	—	\(2\cdot 10^{-10}\)
Gorning thermocouple	0.035	\(7\cdot 10^{-11}\)

a similar comparison, and its results are given in Tables IVA and IVB. This comparison is very interesting, but there are many assumptions here, and it is dangerous to base the choice of a receiver only on this material.

Bell and co-workers \(^{117}\) assembled various receivers and tested their noise level and the decrease of sensitivity with illumination frequency. They estimate the noise level of the Andrews bolometer at \(6\cdot 10^{-4}\ \mu\mathrm{W}\), that of the Golay receiver at \(1.4\cdot 10^{-3}\ \mu\mathrm{W}\), and that of other thermopiles and bolometers at about \(10^{-2}\ \mu\mathrm{W}\). These tests were carried out with spe-

cial purpose and were not sufficiently general to provide all the necessary information. Moreover, since then new detectors have appeared, and the old ones have been improved.

Another uncertainty in determining sensitivity is connected with the character of the radiation used for the test. This is rarely mentioned in reports containing data on detectors. A frequently used source is the tungsten-filament lamp calibrated by the Bureau of Standards; however, its radiation has

Table IV B*)

Element	Threshold under conditions reported by the authors	Time constant	Minimum registered power under conditions \(A\), in watts	Minimum registered power under conditions \(B\), in watts
Thermistor . . . . .	\(2\cdot 10^{-8}\)	0.003	\(7.2\cdot 10^{-8}\)	\(7.2\cdot 10^{-8}\)
Harris thermocouple .	\(2.2\cdot 10^{-10}\)	0.2	\(3.0\cdot 10^{-6}\)	\(6.9\cdot 10^{-7}\)
Polaroid bolometer	\(3.3\cdot 10^{-8}\)	0.004	\(3.3\cdot 10^{-8}\)	\(3.3\cdot 10^{-8}\)

Conditions \(A\): calculated threshold for an area of \(0.06\ \mathrm{cm}^2\), modulation at 30 cycles, bandwidth 100 cycles. The time constant is the same.

Conditions \(B\): the same, except that the element is redesigned and the calculation is made under the condition of maximum cooling at 30 cycles.

*) Borrowed from 106.

a very high frequency \((\sim 5000\ \mathrm{cm}^{-1})\). In order to extend the results thus obtained to lower frequencies, where the sensitivity is more desirable, the detector must be uniformly “black.”

It is difficult to obtain a detector equally “black” at both low and high frequencies, especially in the case of fast detectors, where the amount of blackening material is reduced to a minimum in order to decrease the heat capacity of the detector.

In short, at present it is difficult to survey the situation with detectors. But those who work in this field need the establishment of standard criteria of measurement, test conditions, and complete experimental data that must be obtained for an absolute comparison of detectors. Such data should contain values of sensitivity as a function

of the frequency (i.e., wavelength) of the radiation. It would then also be necessary to include a method of comparing equivalent areas for such elements, for example, as a thermocouple deposited in vacuum or a Golay detector, where the area used for spectral reception is not so sharply delineated as it is in the case of receivers designed for a slit source. Clark Jones \(^{118}\) laid the beginning for work in this direction by setting forth a set of conditions that could be used as standard ones; however, he did not include other conditions, such as, for example, the nature of the radiant energy.

Much time will be required to establish a complete set of standards and to give them official status, but this should be done so that full comparison will be possible, or so that some group of workers will be able to carry out authoritative tests of the various elements, in such a way that these tests are satisfactory and instructive for organizations producing the elements.

Amplifiers and recording. Before 1925 the standard method of measuring the infrared spectrum consisted in setting the spectrometer by hand to the desired frequency and visually observing the deflection of a galvanometer with and without the specimen. In 1925 Moll and Burger \(^{119}\) developed a “thermorelay,” in which the deflection of a primary galvanometer receiving the signal from a thermocouple causes a powerful light beam to act on a second thermoelement, whose current is measured by a second galvanometer. Barnes and Matossi \(^{120}\) modified this method so that the mirrors of the first galvanometer reflected the image of one slit onto another slit, placed in front of a photocell with a blocking layer, connected to the second galvanometer. The deflections of the first galvanometer shifted the image of the first slit relative to the empty intervals of the other slit. This system gave an amplification by a factor of 50–200, and the Brownian limit of the primary galvanometer was readily reached. Ellis \(^{121}\) and Veninger \(^{122}\) introduced automatic photographic recording; the Littrow prism or mirror rotated automatically, and the galvanometer pointer fell on a continuously moving film, giving a continuous spectral curve. To obtain the percent transmission, the ordinates of the curves corresponding to measurements with and without the specimen were measured by hand and divided one by the other, point by point. Thus, a saving of time and greater convenience of measurements were obtained. The main difficulty in this method was connected with the need somehow to control the zero position, which, owing to shifts of the zero of the thermoelement or galvanometer, usually changed. To eliminate this shortcoming, resonance methods \(^{123,124}\) were applied, in which a slowly interrupted beam of radiation was combined with an undamped galvanometer and a photo- or thermorelay, so that a complete oscillation of the galvanometer was obtained

from one extreme position to the other. The deviations obtained in this way are independent of the position of the zero and are insensitive to small displacements of it. At first it even seemed that by means of this method one could reach the Brownian limit; however, Firestone \(^{125}\) showed that the earlier method gives a gain in accuracy at the expense of the time required to establish equilibrium. Firestone was one of the first to begin using electronic amplification. In his apparatus the periodically varying light flux, reflected by the primary galvanometer, falls on a photoelement which, through a capacitor for blocking direct-current signals, feeds an amplifier with an FP-54 tube. The amplified alternating current actuates a secondary galvanometer, whose deflection is recorded photographically. Although Firestone’s method gave good accuracy and a negligible zero displacement, it was still, of necessity, slow, and in the period 1930–1940 many preferred to use amplification by means of a photorelay. In 1937, Lehrer \(^{126}\) applied complete electronic amplification of the primary alternating current produced by a bolometer under the action of intermittent radiation, and at the output recorded the result with an ordinary self-recorder. However, up to the present the advantages of this technique have been little used.

Mac-Alister et al. \(^{50}\) divided the light beam from the primary galvanometer, directing it onto the edge of a prism, with both beams falling on two CE-2 photoelements, and a direct-current amplifier actuated the recording instrument. They used, to some extent, feedback from the amplifier to the galvanometer in order to increase the speed at the cost of some loss in sensitivity.

Pompeo and Penter \(^{127}\) avoided the inconveniences of photographic recording by applying the following method: a photoelement with a double cathode (for example, RCA-920) was mounted on a carriage to which a pen moving over a rotating drum was attached. When the beam of light coming from the galvanometer is displaced so that more light falls on one cathode than on the other, the unbalanced response of the photoelement is amplified by means of a thyratron and actuates a motor which moves the carriage until the carriage has taken up a position in which the intensities of the light beams falling on both cathodes are again balanced.

These automatic methods are gradually displacing galvanometers and photographic recording, and at the present time in most instruments direct amplification of the receiver signal and recording by means of ordinary recording devices such as the Leeds and Northrup “Speedomax” or the “Electric Recorder” are used. Two methods of amplification are employed. Alternating-current signals are fed directly to a transformer \(^{79,128}\), amplified by an electronic amplifier, and, after rectification, recorded. Alternating signals of low frequency or direct-current signals may be modula-

mechanically modulated\(^{129}\) by means of a vibrator up to a high frequency (80 cycles per second, for example), transformed, amplified, and rectified by a commutator in order to use direct-current recording.

The second method is more flexible than the first, since it can be used both for direct and for alternating currents; however, it requires more careful construction and maintenance of the noise level below the detector level.

The low inertia of receivers of the new type, especially bolometers, makes it possible to use oscillographs for recording infrared spectra. Baker and Robb\(^{81}\) described a new type of spectrometer in which two beams of radiation, one passing through the specimen under study and the other bypassing it, alternately (\(T = 0.4\) sec.) enter a double monochromator, and each of them is then directed, by means of an oscillating mirror (\(T = 0.2\) sec.), onto the corresponding bolometer. The bolometers are connected to a primary galvanometer (\(T = 0.2\) sec.), whose mirror sends the light beam alternately to one photoelement and to the other. The current of these photoelements, after amplification, is fed to an oscillograph recording 300 points per minute. Half of this number of points corresponds to the zero line, one quarter of them corresponds to the energy of the radiation that has passed the specimen, and the remainder to the transmission of the specimen. In this way it is possible to mark, in 1 minute, 75 absorption figures in the given frequency interval.

The latest advances in this direction have been made\(^{130,131}\) with discontinuous radiation and a thermistor as receiver at 15–20 cycles per second. The signal is amplified, rectified, amplified again, and recorded by an oscillograph with a long-persistence screen. Both groups of investigators published excellent spectra and were able to measure a frequency interval of \(300\ \text{cm}^{-1}\) in the course of 15 sec. With corresponding movement of the wavelength drum in this method, it is possible to pass continuously through the whole spectrum in such intervals. These methods open broad prospects in the direct investigation of rapidly occurring processes, such as, for example, chemical reactions with intermediate products, etc.

d) Cuvettes and specimens

As we have seen in the preceding sections, the methods and apparatus for infrared measurements have undergone considerable improvements, but alongside this the technique of preparing specimens has improved very little. Indeed, with the introduction of spectrometers with modulated radiation and of instruments directly giving the percentage transmission, the lack of exactly reproducible specimens (liquid and solid) is one of the greatest experimental limitations on further development.

At the present time the accuracy of radiation measurements exceeds the accuracy with which the thickness of the sample or the transmission of the absorption cell is known. Partly as a result of these difficulties, data on infrared absorption cannot be expressed in the form of an extinction coefficient as a function of frequency or wavelength; instead, data are usually published as percent transmission as a function of frequency or wavelength, and only the best estimates of sample thickness are reported. In general, the thickness is chosen so that the most intense absorption bands reach 80–95% of the characteristic radiation. It has been found that the thickness of the sample must contain from \(10^{18}\) to \(10^{20}\) molecules/\(\mathrm{cm}^2\) in order for this requirement to be satisfied.

Typical conditions for preparing samples are given below, together with the subsequent discussion of the difficulties encountered here and the possibilities for future development.

A cell for studies in the infrared spectrum is placed between the source and the entrance slit. In this position small changes in the temperature of the cell do not noticeably affect the receiver, and since the source is usually wider than the entrance slit, no especially high optical requirements are imposed on the cell. If, however, the cell is placed in the monochromatic beam between the exit slit and the receiver, temperature fluctuations may lead to large errors; in addition, the cell must have high optical quality, since the slightest irregularities or inaccuracies in its mounting displace the focused beam from the surface of the receiver. By using intermittent illumination one can get rid of temperature distortions, but the requirement concerning the accuracy of focusing remains in force for instruments with thermocouples or bolometers. The latter may be disregarded only in the case of a Golay receiver, where exact focusing is not needed. Placing the cell in front of the spectral instrument, in turn, has the disadvantage that the temperature of the substance being studied increases as a result of absorption of light. With such an arrangement of the cell, a photochemical action of the near-infrared radiation is also possible.

Absorption cells for studying gases are made of metal or Pyrex glass with windows cemented on with suitable cements (glyptal, apiezon, etc.) or pressed against rubber, and sometimes against amalgamated, gaskets. Mercury amalgam is more desirable, since chemical inertness is required, but cements are nevertheless used more often because they are simpler. The length of the cell varies from 1 to 20 cm, and for cells with \(d = 10\) cm the pressure may vary from several millimeters Hg for intense absorption bands up to atmospheric pressure for weak absorption. When a very long path of the ray in a weakly absorbing medium is required, one can use the method of multiple reflection \(^{132}\). Gases represent the simplest case—

gas, since both the length of the absorbing layer and the pressure can be measured precisely.

Liquids can be studied in two ways. If the liquid is not volatile and only an approximate spectrum is required, it may be placed on a transmitting plate and covered with another plate. All this is placed in an ordinary cuvette holder. Crude variations in thickness can be obtained by inserting U-shaped metal spacers between the plates. More often, however, a set of cuvettes with different layer thicknesses is used, calibrated in advance.

Fig. 14A. Infrared gas-absorption cuvette.

Usually they are made demountable and consist of plates transparent to infrared light, separated by spacers made of mercury amalgam, lead, or tin; the cuvette assembled in this way is fastened in a holder. Such cuvettes are filled and emptied by means of a hypodermic syringe needle inserted into a hole drilled in one of the plates. Various modifications of this type of cuvette may be found in the literature \(^{133—139}\). The thickness of the gap is either determined by the thickness of the spacer or measured with a cathetometer or by interferometric methods \(^{35}\). Even in cases where the thickness is not known exactly, samples can be studied under comparable measurement conditions in the same cuvette. Unfortunately, filling and washing fixed cuvettes with thicknesses less than \(0.01\) mm is extremely difficult. Since the thickness of liquid samples varies from \(0.15\) mm for nonpolar substances (such as aliphatic hydrocarbons) to \(0.001\) mm for polar ones (such as amides or esters), the use of fixed cuvettes is impossible without the use of a transparent solvent.

Owing to the requirements imposed on the thickness of cells, and the nonuniformity of the material of the windows, cells of variable thickness are used little, although methods for their manufacture have been described \(^{135,140,141}\). A typical gas cell and a series of calibrated cells are shown in Figs. 14A and B.

Fig. 14B. Series of calibrated cells for liquids.

Solids are studied either in the form of molten films, or by evaporating a solution onto a transparent window; the film thicknesses are of the same order as in the case of liquids. Here, however, there is the inconvenience that the films often lie down nonuniformly and in essence constitute a finely dispersed powder, strongly scattering the incident radiation. To avoid this effect, the following procedure is now used: the substance under study is smeared or ground with mineral oil (as, for example, Nujol) and applied in the form of a paste onto a plate. The absorption bands

of the oil itself interfere at 2900, 1450, and 1375 cm\(^{-1}\), but in the remaining parts of the spectrum this method is conveniently applied.

For some investigations unusual temperature conditions are needed. High temperatures are necessary in studying the spectra of substances in the vapor state, for the decomposition of complexes, or in studying reactions proceeding at high temperatures. Spectra at low temperatures are often used for studying hindered rotation. Since the half-width of absorption bands decreases with decreasing temperature, this method is convenient for studying bands that overlap at room temperatures\(^{142}\). On the other hand, use of the whole temperature interval may be needed for determining the bond energy and the energy difference between two isomeric forms of one and the same molecule. For these cases special cuvettes have been designed: Cohn et al.\(^{143}\) and Avery and Ellis\(^{142}\) described a cuvette for work at liquid-air temperatures, Smith\(^{144}\) a gas cuvette for the range from \(-100^\circ\)C to \(+200^\circ\)C, and Szymard and Steger\(^{145}\) a gas cuvette for higher temperatures (from 200°C to 500°C).

For windows, NaCl and KBr are most often used because of their exceptional transparency and accessibility. However, they are too soft and fragile and are affected by water vapor. Clouding of the surface does not have a very strong effect on infrared transmission\(^{146}\), but it is undesirable in precise work. Both substances are readily polished by using emery papers of different grades and are finally polished with a fine powder of aluminum oxide or titanium oxide on a slightly moistened linen disk. This is done quickly, but a sufficiently good optical surface is not obtained. When higher optical quality is required, other methods\(^{147}\) must be used, although plane-parallel cuvettes or specimens sometimes show interference bands that may be superposed on the true spectrum. Because of the indicated shortcomings of NaCl and KBr, other substances are often used as well. Table V gives a list of some substances, with approximate values of the limits of applicability on the low-frequency side and the properties of these substances.

The preceding discussion points to two principal difficulties in preparing liquid or solid specimens for infrared spectrometry: the thickness of the specimens is so small that it cannot be measured accurately, and windows that have a broad region of transmission possess, in other respects, unfavorable properties. To eliminate the first difficulty it would have been necessary to dissolve or dilute the substance under investigation, so that work could be carried out in thicker layers. This attempt leads to a third and greatest difficulty: it is impossible to select a solvent transparent in the infrared region. Only a very small number of solvents have sufficient transparency in one or another region of the infra-

Table V

Transparency of various solid substances in the infrared region
The indicated values of the lower boundary of frequencies are approximate: they represent transmission from 20 to 50% for a thickness of 1–3 mm (except mica)

Substance	Lower limit of transparency	Remarks
Glass	\(4000\ \mathrm{cm}^{-1}\) \((2.5\mu)\)	Convenient to handle
Quartz	\(2300\ \mathrm{cm}^{-1}\) \((4.4\mu)\)	Convenient to handle
Mica	\(1900\ \mathrm{cm}^{-1}\) \((5.3\mu)\)	Scratches; easily cleaves
Spinel	\(1800\ \mathrm{cm}^{-1}\) \((5.5\mu)\)	Convenient, except for an absorption band in the region \(3600\text{–}3200\ \mathrm{cm}^{-1}\)
Sapphire	\(1600\ \mathrm{cm}^{-1}\) \((6.5\mu)\)
LiF	\(1400\ \mathrm{cm}^{-1}\) \((7.0\mu)\)	Good, but slightly hygroscopic
CaF\(_2\)	\(950\ \mathrm{cm}^{-1}\) \((10.5\mu)\)	Gives a good surface, but is sensitive to mechanical and thermal action
SrF\(_2\)	\(800\ \mathrm{cm}^{-1}\) \((12\mu)\)	Same
BaF\(_2\)	\(750\ \mathrm{cm}^{-1}\) \((12\mu)\)	Same
NaCl	\(650\ \mathrm{cm}^{-1}\) \((13\mu)\)	Soft, easily contaminated, hygroscopic
KBr	\(350\ \mathrm{cm}^{-1}\) \((28\mu)\)	Even more hygroscopic than NaCl
AgCl	\(350\ \mathrm{cm}^{-1}\) \((28\mu)\)	Very soft and plastic. Large reflection losses. Loss of transparency under the action of ultraviolet rays
Tl(B + J)	\(200\ \mathrm{cm}^{-1}\) \((50\text{–}60\mu)\)	Same

of the infrared spectrum (“windows”). The most transparent solvents are nonpolar substances with simple molecules, such as, for example, CS\(_2\) and CCl\(_4\); they are most often used in practice. Unfortunately, solvents or diluents are especially needed for strongly polar substances, which usually are not compatible with CS\(_2\) and CCl\(_4\). A suitable substance itself must likewise be polar and therefore will absorb strongly. Thompson and Torkington\(^{22}\) investigated the absorption spectra of common solvents, and it turned out that none of these substances can be considered good with respect to transparency in the infrared spectrum. The advantage of infrared spectrometry consists in the fact that almost every type of compound has a characteristic spectrum in this region, but the price paid for this is that,

that samples cannot be prepared with sufficient accuracy. This circumstance especially affects qualitative analysis. In the case of quantitative analysis, one is dealing with measurements of characteristic bands, for which solvents can always be selected that have “windows” at the appropriate places. For qualitative analysis, however, it is necessary to determine rapidly and accurately the extinction coefficients of characteristic atomic groups. Using the scheme of Fig. 6, attention must chiefly be paid to the relation between the values of the frequencies; that is, for example, one can say that a hydroxyl group is present in the compound under investigation, but it is impossible to specify the number of groups present. Information obtained from the ratio of frequencies is much more specific if the values of the absorption intensities are also found.

As we showed in Section IVв, spectrometers with a “double beam” or recording spectrometers are best suited for this purpose. These instruments, which automatically record the ratio of the transmission of the solution under investigation to the transmission of the solvent, provide the necessary information for an accurately known concentration of the dissolved substance and layer thickness, except for those regions of the spectrum where the solvent absorbs too strongly. In many cases, however, the whole spectrum can be obtained by using two or three solvents and recording in each case only those parts of the spectrum in which the given solvent is transparent.

Of course, such a method does not eliminate another difficulty—the absence of permanently transparent materials for cells. In fact, this method increases the difficulty. A double-beam instrument requires two accurately calibrated cells, while for a recording spectrometer one cell must remain unchanged for a long time, or else several measurements with different solvents must be made. At present there are very weighty reasons for using artificially produced crystals of BaF₂ or KRS-5 \([Tl(Br + J)]\), or for applying some thin films to KBr, which would improve its surface characteristics without lowering its transmission. If such a material, sufficiently good for making windows, became available, the trouble and expense connected with making cells of fixed or variable thickness would be justified.

е) Instruments and apparatus

In the preceding sections a sufficient number of individual spectrometers has been described, and thereby a picture has been given of the apparatus currently in use. A large part of spectroscopic work is still carried out by the method of “direct deflection.” The spectrometer is set to some initial frequency,

INFRARED SPECTROMETRY

the widths of the slits and the amplifying system are set, and an automatic recording is obtained of the energy distribution of the black body, upon which the absorption bands of the material under investigation are superimposed. If the recording proceeds toward low frequencies, then it continues until

Text in the figure:
Upper curves—atmosphere. Lower curves—p-methylstyrene.
4.3 μ CO₂. Organic matter in the windows. CO₂ and LiF. LiF prism. Slit—0.1 mm.
Frequency in cm⁻¹.
Ordinates arbitrary. NaCl prism. Slit—0.250 mm. NaCl prism. Slit—0.160 mm. NaCl prism. Slit—0.117 mm. 6.26 μ H₂O. NaCl prism. Slit—0.077 mm.
Frequency in cm⁻¹.
KBr prism. Slit—0.950 mm. KBr prism. Slit—0.600 mm. KBr prism. Slit—0.360 mm. 15 μ CO₂. NaCl prism. Slit—0.450 mm.
Frequency in cm⁻¹.

Fig. 15. Direct recording of infrared spectra. The upper curve is the spectrum of the source; the lower curve is the absorption spectrum of p-methylstyrene.

until the radiation energy has decreased to one half of its initial value; then the slit width is increased, and the same process is repeated. If it is necessary to obtain an energy curve, the same recording is made without an absorbing substance in the path of the beam. In the simplest cases the Littrow mirror is rotated with constant angular velocity, and the calibration marks are indicated on the

recorded automatically. Calibration is carried out beforehand by plotting calibration marks on the graph against absorption frequencies obtained in the study of ordinary gases with the aid of a grating6. In order to avoid changes in the graduation with temperature, the spectrometer is either placed in a room with constant temperature, or in a thermostat box with running water at constant temperature. In another method one of the mirrors is rotated by means of a bimetallic strip, compensating for changes in the dispersion of the prism with temperature. These precautions are important when using a method in which, for each frequency, measurements are made first with the cell and then without it; in the “direct-deflection” method

Fig. 16. Infrared transmission spectrum of p-methylstyrene, obtained by dividing the ordinates of the curves in Fig. 15.

the absorption bands of atmospheric air give, in each case, marks for checking the graduation. This is not obtained in the case of instruments that give percent transmission. The pattern of recording spectra by the “direct-deflection” method is shown in Fig. 15, where the energy curve and the spectrum of the substance under investigation are given together. Dividing the ordinates of one curve by the ordinates of the other for each frequency makes it possible to construct the absorption-spectrum curve (Fig. 16), although often the appropriate conclusions can already be drawn from the original record. As indicated in the literature, some spectrometers have a special transmission to the slit, regulating its width in such a way that \(I_0\) is obtained the same, without changing with frequency. These devices are very useful, but for the most part they were only temporary measures until instruments appeared that record percent transmission.

With the introduction of proven designs of commercial instruments, individual prism instruments are no longer built, although prism–grating instruments are still sometimes assembled in laboratories. Since 400–500 ready-made spectrometers are in use, and many published works contain indications of the type of spectrometer used, it is advisable to consider their characteristics briefly.

The original task of this section was to discuss the designs, advantages, and applications of the commercially manufactured instruments currently available. However, the attempt to do this showed that the difficulty of the task makes it impracticable.

In considering various types of instruments, it is important to know the response speed of the instrument for large and small deflections, the speed of recording spectra, the resolving power in comparison with the signal-to-noise ratio, the stability of the zero signals, the constancy of the source (i.e., the degree of agreement of spectra obtained under identical conditions), the constancy of calibration, the simplicity of operation, the convenience of changing cells and dispersing media, etc. Cost is also of great importance. The difficulty of evaluation is connected with the fact that many of these characteristics are not independent of one another, and it is impossible to obtain maximally favorable qualities simultaneously in all these characteristics. For example, any combination of recording speed, resolving power, and signal-to-noise ratio must represent some compromise, and different combinations are desirable for flexibility of applications. For quantitative analysis, resolving power is less important than speed and stability, whereas in qualitative work one may sacrifice the signal-to-noise ratio in favor of speed and resolving power, while for comparison spectra stability and resolution are more desirable than rapid recording. For these reasons, in some instruments it is possible to vary the response time, recording speed, sensitivity, and slit width, so that the operator can select the measurement conditions most advantageous for the solution of the given problem. Different combinations of variables may yield different spectra, although each of them will be characteristic of the instrument. Another important characteristic of a spectral instrument is the limit of the instrument’s spectral resolving power, which is a function of the quality of its optics. This quantity can usually be determined under conditions of very slow, stable operation when recording the corresponding rotational spectrum in the high-frequency region, with ever narrower slits. When conditions are reached such that further reduction of the slit gives no gain in resolving power, and the diffraction limit has not yet been reached, then these conditions correspond to the aberration limit of the given instrument. Knowledge of this quantity, together with knowledge of the optical

systems make it possible to express the limit of spectral resolution as a function of the frequency and of the dispersion of the prism material. This may not be of especially great importance at the present time, but if improved receivers are used in the future, they nevertheless cannot be employed for greater resolution in the high-frequency region if the optics are the limiting factor.

With the exception of the Hardy spectrophotometer for the visible part of the spectrum, commercial instruments, including everything from the source to the recording device, have appeared quite recently. In descriptions of instruments, more attention is sometimes paid to physical data than to design characteristics, although this situation is rapidly improving. The chief task of such descriptions is the selection and presentation of all the necessary information. At the present moment this is especially important, since instruments are being continuously improved and an established characteristic rapidly becomes obsolete. However, as the situation becomes more stable and the instruments more flexible, manufacturers will have to provide extensive monographs—descriptions.

We give a list of commercial instruments with their brief characteristics.

The Perkin-Elmer infrared spectrometer, model 12C: a small, all-purpose automatically recording spectrometer with interchangeable prisms. This model operates on alternating current and has superseded the earlier models 12A and 12B[^55][^56], which operated on direct current.

The Beckman IR-2 infrared spectrophotometer: also a small but multipurpose instrument, operating on alternating current, with interchangeable prisms. The Beckman and Perkin-Elmer instruments are the most widely used.

The Baird recording percent-transmittance spectrometer: an instrument of medium size, recording the percent transmittance on a chart with a linear wavelength scale. A description may be found in the literature[^80]; the instrument is of the same type as those of Wright and Herscher[^79].

The Hilger spectrometers: two instruments—one a small, non-recording technical instrument with a galvanometer, the other a large spectrometer recording the percent transmittance with a double beam and a double thermocouple. Both types have interchangeable prisms.

A small infrared monochromator and a large Gerthner spectrometer; only the spectrometers themselves with the corresponding thermocouple are sold. For a description, see[^50].

V. THE NEAR INFRARED REGION, OR THE OVERTONE REGION: 13,000 cm\(^{-1}\) (0.75 \(\mu\))—4000 cm\(^{-1}\) (2.5 \(\mu\)); INFRARED PHOTOSENSITIVE RECEIVERS

The chief applications in the overtone region are connected with the study of emission lines of excited atoms as a supplement to ultraviolet and visible spectra, and also of bands corresponding to overtones and combination frequencies of the near infrared.

spectra. In theoretical work these data are important for completing the scheme of energy levels and for identifying the fundamental frequencies. Fundamental frequencies that do not manifest themselves can be established from active overtones or combination bands, and additional information about the upper energy levels makes it possible to estimate the anharmonicity constant in the potential-energy function. The region from \(10\,000\ \mathrm{cm}^{-1}\) \((1\mu)\) to \(5000\ \mathrm{cm}^{-1}\) \((2\mu)\) attracts considerable attention, since here lie the first harmonics of the hydrogen-bond frequencies from 3600 to \(2800\ \mathrm{cm}^{-1}\). Since the absorption coefficients in this region are small, large layer thicknesses can be used (up to \(10\ \mathrm{cm}\); \(\mathrm{CCl}_4\) is completely transparent), which makes easier and more accurate work possible. In addition, the spacing of the vibrational bands here is twice as large, so that band overlap is less than in the region of the fundamental frequencies.

From the experimental point of view, in this region one may single out the interval down to \(8300\ \mathrm{cm}^{-1}\) \((1.2\mu)\), where the use of specially sensitized plates is possible. The high sensitivity of the photographic method makes it possible to attain greater resolution (down to \(0.3\ \mathrm{cm}^{-1}\)) than in the region of the fundamental frequencies (where thermal detectors are used), so that the rotational constants of large vapor molecules can be studied, although considerable thicknesses are necessary. Below \(8300\ \mathrm{cm}^{-1}\) it is already necessary to pass to thermal detectors. The source may be the tungsten filament of an incandescent lamp, and both prisms and gratings may be used. Brackett and Mac Alister\(^{53}\) described a photographically recording instrument in which there are two \(60^\circ\) prisms and one \(30^\circ\) prism in a Littrow arrangement, giving a resolution of \(2\ \mathrm{cm}^{-1}\) at \(5000\ \mathrm{cm}^{-1}\). Hardy\(^{148}\), using a grating, the Pfund-Barnes optical system, and resonant radiometric amplification from a thermocouple, achieved a resolution of \(1\ \mathrm{cm}^{-1}\) at \(10\,000\ \mathrm{cm}^{-1}\) \((1\mu)\). In general, the attainable resolution of wave numbers is almost as good as that possible in the region of the fundamental frequencies. The relative resolution \(\frac{\Delta \nu}{\nu}\) is better because of the higher energies. However, in the region above \(3800\ \mathrm{cm}^{-1}\) there are only a few industrial applications.

Quite recently, infrared phosphors and infrared photoresistors have appeared, which has increased interest in the near-infrared region. Work with phosphors during the war was conducted under secrecy. When the ban was lifted, several reviews appeared, for example by O. Brien\(^{149}\) and by Urbakh et al.\(^{150}\). Fonda\(^{151}\) described ZnS substances; Ellickson and Parker\(^{152}\) considered the kinetics and theory of decay; Smith\(^{153}\) et al. reported on a method for preparing screens from strontium selenide. Most of the phosphors described are sulfides or selenides of alkaline-earth metals (\(\mathrm{SrS}\), \(\mathrm{SrSe}\), \(\mathrm{ZnS}\), etc.), containing the principal activator

and an additional activator (samarium, cerium, europium, copper, lead, etc.). These phosphors have the property of accumulating energy when irradiated by visible and ultraviolet light, X-rays, and α-particles. After irradiation, natural phosphorescence is obtained, which falls to very low values. When illuminated by infrared rays, even after several hours of afterglow, the phosphor can still emit relatively bright visible light. In general, the main activator determines the spectral characteristics of the phosphorescence, while the additional activator gives sensitivity to infrared light. For a phosphor at room temperature the sensitivity threshold is located at about \(6000\ \text{cm}^{-1}\) (\(1.6\,\mu\)), but at the temperature of liquid nitrogen some sensitivity is detected even beyond \(3300\ \text{cm}^{-1}\) (\(3\,\mu\)). During the war these phosphors found application in the reception of “black-light” signals and in the nighttime detection of objects emitting infrared rays. This technique has the advantage that, during operation, no supply of energy is required, since the energy can be stored beforehand, several hours in advance, using, for example, sunlight. Another advantage is also that the enemy cannot detect the use of this device. Reports on spectral applications of this technique are still few in number. Paul\({}^{154}\) described spectra of an Hg arc obtained by focusing the image of the spectrum onto a phosphor-coated plate in contact with a photographic plate. Sometimes the spectrum was focused directly onto a plate coated with a suspension of the phosphor in glycerin. These results showed the possibility of photographing up to \(10\,000\ \text{cm}^{-1}\) and still better results in the region of \(6500\ \text{cm}^{-1}\) (\(1.53\,\mu\)). However, in this work the possible resolution and sensitivity were not studied in detail. Berg and Kaiser\({}^{155}\) published an interesting possibility of obtaining radiographs by irradiating with X-rays objects situated in front of a phosphor screen, followed by photographing the afterglow of the screen under the action of infrared radiation.

This method makes it possible to overcome the difficulties of X-ray photography: the need for trials to find the proper exposure is eliminated, since exposure errors are easily corrected here. An overexposed phosphor plate can be weakened by irradiation with infrared radiation until the density becomes correct, while an underexposed one can be strengthened by intensive irradiation. Undoubtedly, this technique should find wide application in nuclear physics, X-ray technology, ultraviolet and infrared photography; however, its applications in infrared spectroscopy are nevertheless somewhat limited. The region of the infrared spectrum in which photography can be used is somewhat extended, but the suitability of the method still has to be demonstrated*).

*) See also UFN 12, 726 (1932). (Translator’s note.)

Much greater prospects have been opened up for the infrared spectroscopist by recent achievements ^156–158 in the field of photoelements and photoresistances sensitive to the infrared spectrum; stable photoresistances and photoelements made of lead sulfide and thallium sulfide have been developed*). They are manufactured by evaporating the sulfides in vacuum onto glass. These films are sensitized by introducing oxygen at elevated temperatures. Gippel and Rittner ^159 developed a theory of the conductivity mechanism of thallium-sulfide photoelements. Oksin ^160 described some experiments with German lead-sulfide photoelements obtained by chemical precipitation. Working at dry-ice temperatures, he found a noise level equivalent to \(3 \cdot 10^{-11}\) W of radiation at \(4000 \text{ cm}^{-1}\), falling on an area of \(3 \text{ mm}^2\).

The applications of English and American photoelements to spectrometric measurements in the infrared region of the spectrum have been discussed little. \(\mathrm{Tl}_2\mathrm{S}\) has a sensitivity maximum at \(11000 \text{ cm}^{-1}\) (\(0.9\,\mu\)) and can be used down to \(7700 \text{ cm}^{-1}\) (\(1.3\,\mu\)). PbS gives a maximum at \(3900 \text{ cm}^{-1}\) (\(2.6\,\mu\)), after which its sensitivity rapidly decreases, although it still extends as far as \(2800 \text{ cm}^{-1}\) (\(3.6\,\mu\)). A voltage of 50–200 V is applied to the photoelement; the resistance is of the order of megohms. Such a characteristic and the rapid response time (\(\sim 1\) millisecond) make it possible to use amplification. Ketman ^156 established that the maximum sensitivity of these and other photoelements is almost 1000 times greater than that of a thermopile for the same wavelength. Severland, Bleakwell, and Felgett ^161 established that the signal-to-noise ratio for their PbS photoresistances at dry-ice temperature is 100 times greater than for the Hilger–Schwarz thermopile, which permits the slit width to be reduced by a factor of 10 at \(4000 \text{ cm}^{-1}\). Using an ordinary grating with 14,000 lines per inch, they resolved the \(\mathrm{H}_2\mathrm{O}\) bands at \(3900 \text{ cm}^{-1}\), separated from one another by \(0.14 \text{ cm}^{-1}\). Further resolution was hindered by aberration phenomena in the instrument, but not by lack of energy. The best resolution obtained in this region with thermopiles is \(0.5\)—\(0.6 \text{ cm}^{-1}\), so that the photoelectric methods described already represent an improvement by a factor of 4–5, with the possibility of a further twofold improvement.

This success in the development of photoresistances sensitive to infrared light gives great hope, especially if it is necessary—

) It should be mentioned that these types of photoelements, having high sensitivity in the near infrared region, were first developed in the USSR. In 1937 Yu. P. Maslakovets and B. G. Kolomyets (Leningrad Physico-Technical Institute of the Academy of Sciences of the USSR) developed germanium-valve photoelements with a “positive” photoeffect, a sensitivity maximum at \(1\,\mu\), and an integral sensitivity of 5000–7000 mA/lm. In 1940 D. S. Geikhman and M. E. Soroka (Institute of Physics, Academy of Sciences of the Ukrainian SSR) developed silver-sulfide photoelements of the same type with a sensitivity up to 3500–4500 mA/lm and a maximum at \(0.9\,\mu\) (see a brief review and literature on this question in UFN 36, issue 1, p. 83, 1948) (Translator’s note*).

the need for operation at low temperatures will be eliminated. The diagram in Fig. 6 shows that O-, N-, and C—H deformation vibrations, as well as overtones of these fundamental frequencies, fall within the sensitivity range of photoelements. Modern instruments with a LiF prism give a resolution down to \(3—10\ \text{cm}^{-1}\), which is already quite sufficient for industrial applications; however, this can be achieved at a high signal-to-noise ratio (1–2%). The rotational structure of these hydrogen-vibrational bands, especially NH and OH, is very interesting for the spectroscopist using a grating, since they overlap less than the lower fundamental frequencies. Moreover, photoresistances should prove useful in industrial analysis, especially in the overtone region, since their signal is easier to use than in the case of thermocouples, and glass or quartz optics can be used.

There are only a few reports in the literature on photosensitivity at lower frequencies. Fink and Mackey\(^{163}\) described a photoelement with a barrier layer made of a pressed layer of bismuth sulfide or selenide located between two metal contacts. They report sensitivity down to \(1400\ \text{cm}^{-1}\) (\(7\ \mu\)); however, this photosensitive layer gives poorer results than a thermocouple. Nevertheless, there may well be possibilities here for improving the design or for the appearance of new materials with increased sensitivity.

VI. FAR INFRARED REGION:

\(400\ \text{cm}^{-1}\ (25\ \mu)—30\ \text{cm}^{-1}\ (350\ \mu)\)

In this region lie purely rotational bands of light gases\(^{163,164}\), fundamental vibrations (proper frequencies) of inorganic crystals such as metal halide compounds\(^{165,166}\), and low fundamental frequencies of organic substances. However, the number of works devoted to investigations in this region is very small, since here the experimenter encounters enormous difficulties; a limited number of systems has been studied, and only incomplete information has been obtained. Perhaps the most fruitful will be the study of the rotational structure of molecules possessing a permanent dipole moment. Although, it would seem, the same could also be obtained in the near infrared spectrum from vibration-rotational bands, the far infrared portion of the infrared spectrum has the advantage that here the vibrational bands do not overlap and there is less perturbing influence from vibration-rotational interaction. In addition, the limiting width of a rotational line is determined chiefly by Doppler broadening, which is linearly related to the frequency. Therefore, considerably better theoretical resolution can be obtained precisely in the region of low frequencies, although in order to take advantage of this it is necessary to work at low pressures.

Unfortunately, energy limitations do not permit these advantages to be used, and indeed only one paper with a spectrometer for the far infrared spectrum^167 can be cited as having appeared in the literature. In that work a resolution of \((0.5—1\ \mathrm{cm}^{-1})\) was achieved, comparable with what is ordinarily obtained in the near infrared region with standard spectrometers. A second drawback is also that only very light molecules should give many rotational lines here. Owing to the inverse dependence of the distances between lines on the moments of inertia, the spectra of heavier molecules should lie still farther away.

The experimental difficulties in this region are the same as in the near infrared region, but they are still considerably greater. The source is again a black body, whose energy rapidly decreases at low frequencies, and still greater effort must be expended here to get rid of interfering high-frequency radiation. The same detectors are used, but the problem of obtaining a “black” receiver becomes more difficult at low frequencies. The best means of spectral decomposition here is the echelette. Energy losses here can be reduced only by switching to spectrometers with large aperture, using gratings of larger size and higher slits; however, if a strong reduction of the image of the exit slit on the receiver cannot be achieved, there is a loss in detection sensitivity. Let us dwell on some additional methods of isolating frequencies in the far infrared spectrum. Rubens and Wood^168 used quartz lenses, which transmit far infrared energy, and isolated wavelengths up to \(200\ \mu\) by diaphragming the focused image of the source for any specified wavelength. A second lens with a diaphragm concentrates the isolated wavelength on a thermal detector. This method does not give strict monochromaticity, but it is simple and useful in cases of approximate measurements of transmission and reflection.

The second method is the method of residual rays^169, based on the fact that crystals specularly reflect frequencies corresponding to the fundamental vibrations of the crystal lattice. Therefore, by successive reflection from a series of polished crystalline surfaces one can isolate a narrow frequency interval. The instrument in which this method of monochromatization was used is described by Strong^147 and shown schematically in Fig. 17. The construction of the instrument is simple, but it can yield only separate intervals of the infrared spectrum.

The most useful in this part of the spectrum proves to be a spectrometer with a grating. On the manufacture of lamellar gratings see^170. Wire gratings^171 are made of thin wires wound around two carefully grooved rods. The length of the rods and the distance between them determine the area of the grating. The wires are soldered

to the rods, and half of the wires on one side is removed altogether. The rulings of echelette gratings are cut with a sharp steel cutter of special shape on a soft metallic surface.

The Michigan spectrometer for the far infrared region has given the best data on rotational frequencies. This is a vacuum instrument with an insertable parabolic mirror of \(f=36\) inches and a grating \(10\times 22\) inches. It employs the Firestone\({}^{125}\) amplification system, and the spectra are recorded photographically. Because of the absence of substances suitable for making prisms for preliminary dispersion, in order to reduce the influence of spectra of higher orders it is necessary to use suitably chosen windows, filters, and residual-ray plates. Windows are made of quartz or paraffin, which do not transmit high frequencies. For some regions residual rays obtained from KBr or KJ plates, which selectively reflect the required frequencies, are used. Since the Firestone method uses an alternating signal obtained by periodically interrupting the beam, thin KBr and KJ screens can be used which transmit radiation of higher frequencies and stop the lower frequencies. With this apparatus one can obtain absorption spectra rapidly, continuously, and accurately, with a resolution of the order of \(0.5—1\ \text{cm}^{-1}\).

Fig. 17. Diagram of an installation for selecting a band of the infrared spectrum by the residual-ray method; \(S_0\)—source, \(M\)—mirrors, \(Re\)—crystals, \(D\)—receiver.

Taking into account the enormous experimental difficulties in this region, such spectral resolution is a definite achievement. For a good review of this material, see Randall\({}^{173}\).

VII. MICROWAVE REGION: \(\sim 1\ \text{cm}^{-1}\) \((1\ \text{cm},\ 10000\ \mu)\)

In 1923\({}^{174}\), and then also in 1924\({}^{175}\), the region of thermal radiation and the region of radio waves met\({}^{*}\). In 1923 Nichols and Tear, using—

* The Soviet physicist A. Glagoleva-Arkad’eva, as early as 1922, developed the so-called “mass radiator”—an apparatus making it possible to obtain short electromagnetic waves with wavelengths from several centimeters down to \(0.08\ \text{mm}\). Thus radiation was obtained that filled the gap between long-wave infrared radiation (Rubens waves, \(343\ \mu\)) and the shortest electromagnetic waves (Lebedev waves, \(6\ \text{mm}\), 1895). Literature: Proceedings of the Third Congress of the Russian Association of Physicists in Nizhny Novgorod, 1922; DAN SSSR, 3, No. 6, 1934, etc. (Translator’s note.)

by using a Hertz oscillator, a radiometer as receiver, and interferometric methods of wavelength measurement, were able to work at frequencies above \(45\ \mathrm{cm}^{-1}\) (\(220\ \mu\)). In 1934, Cleeton and Williams \(^{176}\) studied the spectrum of inversion doublets at \(0.8\ \mathrm{cm}^{-1}\) (\(1.25\ \mathrm{cm}\)), using a magnetron and an echelette. These experiments were not continued, and only in 1945 did interest in this region grow strongly in connection with the development and use of radar. Since then many works on this subject have appeared. The exceptionally high resolution and accuracy of measuring frequency differences \((10^{-5}—10^{-6}\ \mathrm{cm}^{-1})\), as well as the simplicity of using long waveguides (up to 100 feet) as absorption cells, give this region considerable potential value. These long cells make it possible to work at very low pressures \((5\cdot 10^{-3}\ \mathrm{mm\ Hg})\), when the broadening of spectral lines due to collisions is very small, and effects of second-order perturbations can be observed. An example of a typical investigation that became possible under these conditions is the study of line broadening under the influence of pressure, carried out by Bleaney and Penrose \(^{177}\), who showed that the line-width constant (half-width at half-maximum) of the NH\(_3\) band at \(0.5\ \mathrm{mm\ Hg}\) varies from \(2\cdot 10^{-4}\) to \(5\cdot 10^{-4}\ \mathrm{cm}^{-1}\), and that the width factor changes with pressure according to the formula

\[ \Delta \nu\ (\mathrm{cm}^{-1}) = 1\times 10^{-2}p\ (\mathrm{cm\ Hg})\cdot \left(\frac{K^2}{J^2+J}\right)^{1/3}, \tag{16} \]

where \(K\) and \(J\) are the rotational quantum numbers corresponding to the given line. With such resolution it is possible to measure accurately the contour of a line and the absorption coefficient, which makes it possible to calculate the dipole moment \((\mu)\) of a gas molecule according to the formula

\[ \int \frac{\alpha_\nu}{\nu^2}\,d\nu = \frac{8\pi^3}{3ckT}\,N_{JK}\, \frac{K^2}{J^2+J}\,\mu^2, \tag{17} \]

where \(\alpha_\nu\) is the absorption coefficient for frequency \(\nu\), and \(N_{JK}\) is the number of molecules on the \(JK\)-rotational level. Daikin, Good, and Coles \(^{178}\), studying the rotational structure of O\(^{16}\), C\(^{12}\), S\(^{32}\) and O\(^{16}\), C\(^{12}\), S\(^{34}\), indicated that the accuracy of determining the molecular moment of inertia should provide exceptional accuracy in calculating internuclear distances. They estimate an error of \(0.005\ \text{Å}\), associated with the uncertainty in the difference of the atomic masses S\(^{32}\) and S\(^{34}\). Townes, Holden, and Merritt \(^{179}\) continued this discussion, pointing out that the inaccuracy in measuring internuclear distances by this method also increases owing to the variation of the zero-point vibrational energy in nuclear isomerism. Good \(^{180}\), studying the inversion spectrum of NH\(_3\) at very low pressures, discovered a fine structure in the rotational lines caused by the interaction of the electric quadrupole moment of the N\(^{14}\) nucleus with the electric field of the remaining parts of the molecule. These investiga-

...studies were continued by Gordy and Kessler\(^{182}\) and by Townes et al.,\(^{179}\) who used the magnitude of the quadrupole coupling to determine the values of the nuclear spins of atoms in certain linear molecules. Stark and Zeeman splittings of the rotational levels of linear molecules were also studied. Hershberger\(^{185}\) considered the thermal and acoustic effects accompanying the absorption of microwaves in gases.

There have as yet been no reports on the application of the microwave region to industrial analyses. One may doubt the feasibility of this, since the advantages of resolution and, consequently, successful separation of components are achieved only at pressures that are too low for technical processes. However, such analytical conditions may occur in which it will be necessary to analyze a gas composed of heavy polar molecules in the presence of lighter molecules, the gaps in the rotational structure of which can be used as transmission “windows.” From the experimental point of view, the work of Klyton and Williams\(^{176}\) is very interesting, even though the method was not subsequently used. They constructed a magnetron oscillator lamp giving continuous radiation in an interval of \(\pm 30\%\) from the mean frequency. In order to cover the region from \(0.95\) to \(0.26\ \mathrm{cm}^{-1}\), a set of four tubes was used. The oscillator was placed at the focus of a copper parabolic mirror 3 feet in diameter, which gave a parallel beam incident on an echelette grating of 18 elements, with a grating constant of \(7.49\ \mathrm{cm}\). The diffracted beam was focused by another parabolic mirror onto a crystal detector made of iron pyrite–phosphor bronze, connected to a galvanometer. When the grating was rotated, the individual elements also turned, so as to obtain grazing incidence. The cell was of rubberized fabric, 16 inches long and \(36 \times 45\) inches in cross section. With this instrument it was possible to obtain inversion vibrational bands of \(\mathrm{NH}_3\) and to measure their absorption with good accuracy. Since the time of this investigation, measuring technique for waveguides has been developed.\(^{186\text{--}188}\) One of the first investigators to apply this technique to the study of microwave absorption in organic vapors was Hershberger.\(^{189}\) His apparatus consisted of a klystron, a variable-length waveguide (from 1 to 10 m), and a crystal detector. The waveguides were closed with mica windows and could be evacuated and filled with the vapors or gases under investigation. The absorption coefficients of various vapors were measured by plotting the transmitted power as a function of vapor pressure. Good used a balanced system in which the signal from a klystron oscillator was attenuated and, being split in a T-shaped section, passed along two waveguide channels to two crystal detectors (Fig. 18). In one arm there was an absorption chamber, and in the other—a variable attenuator and a calibrated attenuator. The signals from the crystal...

…of the crystal detector were grounded through equal resistances, and the galvanometer was connected between them. Absorption was measured by equalizing the two signals with an empty absorption chamber and then, after filling the chamber to the desired pressure, bringing the galvanometer back to the zero position with the aid of a calibrated attenuator. Hurd also used recording by means of an oscillograph, since the klystron frequency can vary over wide limits when the voltage applied to one of its electrodes is changed. The sweep generator supplies this varying voltage to the klystron and to the horizontal plates of the oscilloscope. The signal from the unbalanced galvanometer is amplified and fed to the vertical plates. Wavelength calibration is carried out on the screen with the aid of a hollow wavemeter—an endovibrator. Hurd obtained an accuracy of ±5 megacycles \((1.6 \cdot 10^{-4}\ \mathrm{cm}^{-1})\) in determining the frequency and ±10% in the attenuation.

Fig. 18. Radio equipment for studying the absorption of vapors. 1—generator, 2—variable attenuator, 3—waveguide, 4—wavemeter, 5—to the vacuum system, 6—gas cuvette, 7—fixed attenuator, 8—variable attenuator, 9—calibrated attenuator, 10—crystal detector, 11—sweep generator, 12—oscilloscope, 13—balance amplifier, 14—galvanometer.

The elements of the described installation are quite standard, although Blenney and Penrose used a bolometer as the receiver.

Becker and Autler^190 and Lamb^191 considered a system consisting of a magnetron oscillator and an endovibrator connected to a thermocouple. Dicke et al.^192 described a tunable radiometer consisting of an antenna and a receiver whose sensitivity \((10^{-16}\ \text{watt})\) made it possible to study the emission of water vapor in the microwave region. Hughes and Wilson^193 described a high-sensitivity spectrometer in which the signal (80 kilocycles) propagated along an insulated strip at the center of a waveguide in order to produce the Stark effect in the gas under study. If the frequency of the klystron signal coincided with an absorption line in the gas, then the variable absorption caused by the periodic Stark splitting modulated the amplitude of the klystron signal. This modulated signal was rectified by a crystal detector and received by a broadcast-type receiver tuned to 80 kilocycles. In this case it was possible to detect very weak absorption, but the form of the resulting signal was a complicated function of the nature of the Stark effect of the molecule. Experimental technique in the microwave region is limited maxi-

with a low frequency, obtainable in modern klystrons (\(1.5\ \mathrm{cm}^{-1}\)—the highest frequency according to the literature), and by the fact that continuous spectra can be obtained with only one tube over a relatively narrow range, so that a series of tubes is necessary. Some information has been reported\(^{194}\) on obtaining radiation from \(4\ \mathrm{cm}^{-1}\) (\(2.2\ \mathrm{mm}\)) to \(50\ \mathrm{cm}^{-1}\) (\(0.2\ \mathrm{mm}\)) by means of a spark discharge through a jet of oil containing small aluminum particles, but the method is inconvenient and has not been further developed. As was indicated in Section VI, there are enormous possibilities for purely rotational studies of heavy molecules (with a permanent dipole), if the narrow frequency band and the power of microwave radiation make it possible to obtain a portion of the spectrum from 10 to \(20\ \mathrm{cm}^{-1}\). Substances with low vapor pressure also become accessible to study, since long beam paths can be used here.

VIII. INFRARED FILTERS; INFRARED GAS ANALYZER

Simplified spectrophotometers with filters for the infrared spectrum have not been sufficiently developed. Such instruments cannot be cheap because of the high cost of stable signal amplification. Moreover, bands in the infrared region overlap more than in the visible part of the spectrum, so that narrower monochromatization by means of filters is required. And, finally, infrared techniques are still too new in industry for there to have arisen a great need for simple routine analysis in production or in the laboratory. However, this need will grow and must be satisfied. First of all, a fast thermocouple with a sufficiently accurate output voltage under intermittent irradiation is needed, in order to obtain an alternating-current signal and record it without amplification.

One of the methods of filtration is Christiansen’s method\(^{195}\), by means of which filters can be obtained with a transparency of 40–60% at the transmission maximum and a band width of \(1\)–\(2\ \mu\). In these filters, small particles with a relatively high refractive index are suspended in a transparent liquid with a lower refractive index, or are present as a powder on a plate, in air. If the incident wavelength approaches \(\lambda_0\)—the principal absorption frequency of the particles—the refractive index of the particles begins to fall, and for some wavelength \(\lambda_{\mathrm{cr}}\) the refractive indices of the particles and of the medium become identical. At this point the mixture should be relatively transparent; at shorter wavelengths the particles will scatter light, and at longer wavelengths they will absorb it.

Another possibility is connected with the use of powder filters or echelette-type gratings (Fig. 11), especially in those cases where it is necessary to cut off the higher frequencies. If it is necessary to remove the lower frequencies, absorbing materials are used.

(see Table V). Both methods have the disadvantage that the choice of materials is somewhat limited, so that the construction of a filter for an arbitrary frequency may prove impracticable. A further disadvantage of Christiansen filters is their temperature sensitivity.

A very flexible device has appeared comparatively recently—the “infrared gas analyzer”\(^{196—201}\), which is described as an instrument of zero dispersion and infinitely great resolving power. Since it promises to be especially valuable for the analysis of vapor-like and liquid streams in the laboratory and in industry, it is necessary to give a brief description of this method.

Fig. 19.
a) Scheme of a gas analyzer with a positive filter. \(S_0\)—source, \(M\) and \(M'\)—mirrors, \(S\) and \(S'\)—cuvettes for the samples under investigation, \(F\)—cuvette-filter, \(D\) and \(D'\)—selective receivers.
b) Gas analyzer with a negative filter; \(S\)—cuvette for the sample, \(Se\) and \(Se'\)—sensitized cuvettes, \(D\) and \(D'\)—nonselective receivers.

The instrument can be constructed with filters of two types (Fig. 19, \(a\) and \(b\)). In case \(a\) (positive filter), the radiation from an infrared source (usually a nichrome spiral, like the electric lighter for papirosy) is split into two parallel beams by means of a lens or two concave mirrors and passes through cuvettes \(S\) and \(S'\), filter \(F\), and two detector cuvettes \(D\) and \(D'\). Suppose we wish to find the content of some gas, for example \(CO_2\); \(D\) and \(D'\) are filled with \(CO_2\) under a certain pressure and play the role of gas thermometers, indicating a temperature difference, since the pressure difference between them is determined. It is measured by means of a thin metal diaphragm connected as one of the plates of a variable capacitor. \(CO_2\) in both

the cuvettes \(D\) and \(D'\) must absorb one and the same energy from the source, and specifically at those frequencies that are characteristic of the absorbing molecule. If the gas under investigation, introduced into \(S\) (\(S'\) being an empty cuvette), contains \(\mathrm{CO}_2\), the detector \(D\) will be cooled, and the resulting displacement of the diaphragm can be calibrated in terms of the \(\mathrm{CO}_2\) content in the gas filling the cuvette \(S\). Conversely, into the cuvette \(S'\) one can introduce different concentrations of \(\mathrm{CO}_2\) and obtain compensation—the zero position of the diaphragm. If some other gas is present in the sample under investigation, then it should not produce any effect, since it has other characteristic frequencies. If any bands overlap, the cuvette \(F\) must be filled with such a substance as will absorb the interfering frequencies. Liquid samples can also be analyzed by this method, although the larger number of absorption bands, possible overlaps, and the necessity of working in thin layers make the application of this technique difficult. The radiation may be mechanically interrupted, which opens up the possibility of using an alternating-current amplifier arising in the capacitor, in order to avoid zero drift, to which the instrument is very sensitive.

In another type of instrument (Fig. 19, \(b\)) two beams pass together through the sample, which is in the cuvette \(S\), the filter \(F\), and, after passing through two cuvettes \(Se\) and \(Se'\), fall on the receivers \(D\) and \(D'\). As receivers here thermopiles connected in opposition are usually used, or bolometers connected to a Wheatstone bridge. If it is necessary to determine \(\mathrm{CO}_2\), then the cuvette \(Se\) is filled with this gas (i.e. \(D\) must not sense radiation of the frequencies characteristic of \(\mathrm{CO}_2\)), while \(Se'\) is filled with an inert gas, \(\mathrm{N}_2\), or air without \(\mathrm{CO}_2\). If the gas stream passing through \(S\) contains \(\mathrm{CO}_2\), then the receiver \(D\) will not respond, whereas \(D'\) will be cooled, and from the difference in the responses obtained the concentration of \(\mathrm{CO}_2\) can be determined. The presence of another gas in \(S\) cannot cause changes, since it will act on \(D\) and \(D'\) to the same degree.

The first type of instrument with the so-called “positive” filter was put on sale and was widely used during the war in Germany under the name “Uras”\({}^{202}\) (Ultrarotabsorption-schreiber) and also in England. The second type with the “negative” filter was produced in the USA. As yet there are no data for comparing the merits of the instruments of these two types, especially since the question of the experimental difficulties associated with the use of both of these methods has not been discussed in the literature. In principle, the instrument with the negative filter seems somewhat worse, since it measures the unknown concentration as a small difference between two intense signals, and a slight shift of equilibrium in the transmission of the windows must be interpreted as a significant change in the concentration of the component. Moreover, in this method the radiation is delayed in the detectors, whereas in the instrument of the first type the entire

beam after removal only of those frequencies that are absorbed in \(D\) and \(D'\). Therefore it is possible to make interchangeable detectors from a pair \(D\) and \(D'\), which can be exchanged one for the other for multicomponent analysis.

In any case, these instruments are exceptionally sensitive, capable of registering several thousandths of a strong absorber, such as, for example, \(\mathrm{CO_2}\). The possibilities for industrial application are extremely broad—analysis of explosive gases, determination of \(\mathrm{NO}\), \(\mathrm{NO_2}\), \(\mathrm{NH_3}\), butadiene, etc. This should also be extremely useful in laboratory practice—microanalysis of hydrocarbons, etc., since this method would provide greater sensitivity and speed than modern gravimetric measurements.

IX. VARIOUS APPLICATIONS OF INFRARED RADIATION

Numerous applications of infrared radiation are known that fall outside the scope of the present review. Applications in photography, camouflage detection, medical applications (diathermy), industrial heating and drying of varnishes, radiation pyrometry, etc., are well known. However, we must nevertheless briefly dwell on certain cases.

Working with powder filters (see part IVb), Camble[^203] and Barnett[^204] developed methods for determining particle sizes and the particle-size distribution in suspensions of pigments and rubber fillers. The transmission of a particle suspension in oil or in rubber is obtained from \(0.4\) to \(4.0\,\mu\). From the shape of the curve, i.e., from the sharpness of the transition from low transmission to high, the distribution can be determined, and from the wavelength of the transition—the particle sizes.

Strong[^205] described a sensitive pyrometer with quartz plates that isolate (by the residual-rays method) radiation at \(1140\ \mathrm{cm}^{-1}\) \((8.8\,\mu)\). This region corresponds to a “window” in the atmosphere, so that the instrument can be used for distant objects without correction factors. The accuracy of this instrument is \(\pm 0.1^\circ\mathrm{C}\) in the interval \(0\text{–}100^\circ\mathrm{C}\). In another type of instrument, the residual rays of calcite in the region \(1500\ \mathrm{cm}^{-1}\) \((6.7\,\mu)\) are used for measuring absolute humidity, i.e., the amount of water vapor in the atmosphere.

Hardy and Soderstrom[^206] described a radiation pyrometer giving an accuracy of \(\pm 0.01^\circ\mathrm{C}\) for measuring skin temperature. They showed that skin radiates almost like a black body (within two percent). Hardy et al.[^207], who developed various applications of infrared radiation for physiological problems, described the use of this instrument for measuring the pain threshold and the level of pain. A flux of infrared radiation of known intensity is focused on the blackened forehead of the subject. The latter establishes the minimum amount of intensity that he can feel—

measure, or compares the sensation of pain produced by a given flow with the sensation from other sources. Despite the subjective method of comparison, surprising agreement and uniformity of results have been obtained. This technique has been used successfully in studying the effectiveness of various medicines and in measuring pain associated with certain physiological disorders.

Also of interest are military applications208, although they are little used in the practice of spectroscopists in their present form. In Germany, the production of image converters209, or devices that convert an infrared image into a visible one, was developed on a large scale; this is of importance for nighttime driving by automobile. Objects are illuminated with infrared rays from a projector with a tungsten lamp covered by a filter that does not transmit visible rays, and the reflected light is focused onto a photosensitive cesium compound surface at one end of an electron converter tube. The electrons, emitted with varying intensity from different points of the image-screen, are focused by an electrostatic lens onto a fluorescent screen at the other end of the tube. This image is observed by the eye. The portable device is equipped with batteries for the lamp and for powering the lens (5000–15,000 V) and with a source for the vibrator. This device can “illuminate” a highway quite satisfactorily at a distance of 90 m, and objects can be observed at much greater distances. A similar instrument is called a “sniperscope.”

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* Uspekhi Fizicheskikh Nauk, vol. XXXVII, issue 2.

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1. Visible reference marker in the source. ↩

2. Visible reference marker in the source. ↩

3. Visible reference marker in the source. ↩

4. Visible reference marker in the source. ↩

5. Visible reference marker in the source. ↩

6. As cited in the original text. ↩