X-ray Diffraction in Liquids

M. Korsunsky, Tomsk

The phenomenon of X-ray diffraction, discovered by Laue and subsequently developed by the Braggs, made it possible to determine the spatial arrangement of atoms and molecules in a crystal lattice, in the case when we are dealing with a crystal of sufficiently large dimensions. A modification of Laue’s method, made by Debye and Scherrer, made it possible to extend the methods of X-ray analysis to the study of the structure of substances forming a finely crystalline aggregate. Scherrer showed that this method is applicable to the study of the structure of colloidal particles having dimensions of \(10^{-9}\)—\(10^{-7}\) cm and, in addition, makes it possible to determine the sizes of these particles.

A perfectly natural continuation of work in this direction was the attempt to determine the spatial arrangement of atoms in the molecules of liquids—an attempt undertaken by Debye and Scherrer \((^{1})\) in 1916. The substance studied was benzene. It turned out that, when X-rays pass through benzene, a diffraction maximum is indeed observed; its appearance was attributed to the presence of a definite spatial arrangement of atoms in the benzene molecule. Debye derived a formula establishing the dependence of the intensity of scattered X-rays on the arrangement of the scattering centers (atoms), which, in the case where these centers are arranged on one circumference (as was assumed for the benzene molecule), takes a compar-

...a comparatively simple form, making it possible to determine, from the position of the observed maximum, the diameter of the circle on which the scattering centers are located. The appearance of diffraction maxima when X-rays pass through a liquid was subsequently confirmed by a number of other investigators [Oebirne (²) on methyl iodide, methylene iodide, bromobenzene, benzene; Hewlett (³) on octane, mesitylene, and benzene, etc.]. Keesom and Smit (⁴), who studied the phenomenon of X-ray scattering in a series of liquids differing in molecular structure—such as water, ethyl ether, ethyl alcohol, benzene, liquid nitrogen, liquid oxygen, liquid argon, and mercury—found the appearance of diffraction maxima for all the liquids mentioned. This result led the authors to conclude that diffraction maxima may appear not only as a result of the spatial arrangement of atoms in a molecule, but also as a consequence of the scattering of X-rays by molecules oriented at random, yet situated at distances from one another differing little from a certain mean intermolecular distance. The appearance of a diffraction maximum in liquid argon, whose molecule is certainly monatomic, especially clearly emphasizes the correctness of the principal conclusion of the work of Keesom and Smit.

Determination of the mean distance between molecules from the value of the angle of the diffraction maximum \(\theta\), and comparison of it with the value of the mean distance between molecules determined from the density of the substance and the molecular weight, showed that here it is necessary to use not Bragg’s formula

\[ 2d \sin \frac{\theta}{2} = \lambda \tag{1} \]

(\(d\) is the mean molecular distance, \(\theta\) is the angle of maximum intensity of the scattered rays, \(\lambda\) is the wavelength), but the formula first proposed by Ehrenfest for the case of scattering by a diatomic gas:

\[ 2d \times 0.8 \times \sin \frac{\theta}{2} = \lambda . \tag{2} \]

The applicability of this formula not only to liquid argon, but also to all liquids for which Keesom and Smith observed the appearance of diffraction maxima, made it very probable that, for liquids whose molecules contain several atoms, the appearance of diffraction maxima is also an effect of the mean molecular distance. Despite the fact that some data obtained in the study of the scattering of X-rays by liquids do not agree with the results obtained by Keesom and Smith (thus Waikov\(^{5}\), studying the diffraction of X-rays in mixtures of two liquids, came to the conviction that the pattern he observed corresponds rather to an intramolecular than to an intermolecular effect), the latter seem so convincing that they have received almost universal recognition. Theoretical works on the study of the scattering of X-rays in liquids all proceed from the assumption that the observed effect is an intermolecular effect. Thus Raman and Ramanathan\(^{6}\) developed a theory of the scattering of X-rays by liquids in which the latter was considered as a continuous medium with local changes in density determined by thermodynamic considerations. Debye\(^{7}\) developed a theory of the scattering of X-rays in a liquid, taking as the basis of the calculation the assumption that the molecules of the liquid are scattering centers. Prins\(^{8}\) considered a liquid as a microcrystalline powder whose lattice, hexagonal or cubic and closely packed, possesses an extremely strong thermal motion.

Debye\(^{9}\) and Waller\(^{10}\) showed that extremely strong thermal motion causes not only a decrease in the intensity of the diffraction maximum, but also a broadening of the lines. All the theories mentioned give similar results for the position of the intensity maximum, differing only by a certain coefficient.

Recently published works by Debye on the study of the phenomenon of X-ray scattering by gases showed that in this case, too, one can observe the appearance of maxima—

atoms in the distribution of the intensity of rays scattered at different angles. In a gas these maxima can appear only as a result of the spatial arrangement of atoms in the molecule, and there is no doubt, of course, that the spatial arrangement of atoms in the molecule of a liquid may be the cause of those anomalies which individual investigators [Uikov\(^5\) and others] have succeeded in observing. Stuart and Skinner\((^{11})\) also observed, in the scattering of X-rays by fatty acids, the appearance of maxima which are difficult to explain otherwise than as an effect of the spatial arrangement of atoms in the molecule (see below). Along with this, Stuart and his students were able to show that the scattering pattern of X-rays by organic liquids observed by them cannot be explained either by the effect of the mean molecular distance or by the effect of the spatial arrangement of atoms in the molecule. Stuart’s works, which led him to a new view of the structure of liquids, are of great interest, and their exposition is the aim of the present article.

EXPERIMENTAL CONDITIONS

The experimental conditions under which the work of Stuart and his students was carried out were as follows. A beam of X-rays emitted by a Coolidge tube with a molybdenum anticathode passed through a system of slits limiting its dimensions and fell upon a liquid, which was placed in a closed glass tube. The walls of the tube, in order to avoid appreciable absorption of X-rays in them, were made very thin. The intensity of the X-rays scattered by the liquid at different angles was measured with the aid of an ionization chamber, for which purpose the tube with the liquid was placed on the table of an ionization spectrometer. Both the collimator and the ionization chamber carried a set of 8 slits, placed at a distance of 20 cm [according to Soller]. The size of the slits was \(0.079 \times 1.6\) cm.

To eliminate KβMo, Stuart first passed prelimi-

...a beam of X-rays through a zirconium filter and thus in his work dealt with only one (more precisely, a doublet) characteristic line, Mo Kα, and with some part of the continuous spectrum. Under such conditions, Stewart, in his curves giving the dependence of the intensity of scattered X-rays on the scattering angle, observed three maxima. What causes the observed maxima? Trillat and Tabo (12), in a recently published paper, showed that in a liquid, under certain conditions, one can always observe, alongside one maximum characterizing the mean distance between molecules, another maximum as well. The authors of the paper, by a number of ingenious experiments, showed with certainty and convincingly that the second diffraction maximum is due to the continuous spectrum accompanying the characteristic radiation. When X-rays pass through a liquid, the latter serves as a filter that filters out the soft part of the spectrum; and, for a sufficiently great thickness of the liquid, the latter will transmit a comparatively small portion of the spectrum—the hardest part of it, containing also the portion with maximum intensity. As a result a second maximum appears, the position of which is determined, on the one hand, by the mean molecular distance, and on the other by the wavelength of the maximum intensity of the continuous spectrum. Trillat and Tabo believe that the secondary maxima observed by some investigators should be explained precisely by the considerations indicated above. What, then, gives rise to the maxima observed by Stewart and his collaborators? To decide this question, Stewart and Morrow (13) (three years before the appearance of the paper by Trillat and Tabo) carried out the following control experiments.

1. A measurement was made of the positions of the intensity maxima of the scattered X-rays at various voltages applied to the X-ray tube. Since the region of maximum intensity of the continuous spectrum is thereby shifted, the position of the diffraction maximum caused by this part of the spectrum should also...

should change. This is what Stuart and Morrow observed. One of the three diffraction maxima observed by them shifted toward smaller angles when the voltage was increased. Figure 1 gives the curves obtained by Stuart and Morrow for nonyl alcohol \((\mathrm{C}_9\mathrm{H}_{19}\mathrm{OH})\) at various voltages on the tube. In the diagram the magnitude of the ionization current is plotted along the ordinate axis, and the scattering angle along the abscissa axis. The origin of the coordinates of the second curve relative to the first and of the third relative to the second is shifted by one division along the ordinate axis.

Fig. 1

The curves were taken at voltages in the primary circuit of the transformer: curve 1 — 70 V, 2 — 80 V, and 3 — 103 V (103 V in the primary circuit give 46.3 kV in the secondary). The position of the maxima of the ionization-current curve at \(2^\circ\) and \(9^\circ\) remains unchanged; the position of the middle maximum, located at \(5^\circ\) at a voltage of 103 V in the primary circuit of the transformer, changes, shifting toward softer wavelengths as the voltage is decreased. From this Stuart concludes that the maxima on the ionization-current curves at 2 and 9 degrees are due to the wavelength \(K\alpha_{\mathrm{Mo}}\), while the middle maximum belongs to the continuous spectrum.

1. If it is assumed that the maximum at \(9^\circ\) is due to a wavelength of \(0.71\ \text{\AA}\), then the maximum at \(5^\circ\) must be caused by a wavelength of \(0.4\ \text{\AA}\), which agrees very well with the wavelength of the maximum intensity of the continuous spectrum at 46 kV.

2. The X-rays scattered by the liquid were passed through an aluminum filter \(2\ \mathrm{mm}\) thick, and the attenuation of the X-ray intensity on passing through the filter was measured. It turned out that the maxima at \(2^\circ\) and \(9^\circ\) and the maxima at \(5^\circ\) (at a voltage of 46.3 kV)

they are attenuated differently by the filter. Whereas the former lost 95% of their intensity, the maximum at 5° was weakened only by half. This change in intensity agrees very well with the change in the absorption coefficient which occurs in going from the wavelength 0.71 Å to the wavelength 0.4 Å.

Thus, all the control experiments carried out by Stuart and Morrow confirm Stuart’s conclusion already mentioned above. Two out of the three observed maxima undoubtedly belong to the characteristic radiation of Mo (in the present case \(K\alpha\)). This conclusion is extremely important, since the presence of two maxima already serves as a sufficient guarantee that the observed pattern is not merely an effect of the mean molecular distance. In our case this is especially convincing, since the maxima, by their positions (two and nine degrees), cannot be one and the same maximum of different order.

In what follows we shall be concerned precisely with these two maxima; for brevity we shall call the maximum at \(2^\circ\) the first maximum, and that at \(9^\circ\) the second.

Main results of Stuart’s work and conclusions

The liquids with which Stuart and his collaborators worked were predominantly organic compounds with a long chain. In Fig. 2 are given the ionization-current curves obtained by Stuart and Morrow with normal alcohols. Here, as in Fig. 1, along the ordinate axis is plotted the strength of the ionization current, along the abscissa axis—the scattering angle, and the origin of coordinates of each curve is shifted relative to the preceding one by one division (in the direction of the ordinate axis). Curve 1 corresponds to methyl alcohol (\(\mathrm{CH_3OH}\)), the second to ethyl alcohol (\(\mathrm{C_2H_5OH}\)), the third to propyl alcohol (\(\mathrm{C_3H_7OH}\)), etc. The last curve corresponds to lauryl alcohol (\(\mathrm{C_{11}H_{23}OH}\)). From comparison of the curves in Fig. 2 it may be noted that the position of the second maxi-

…remains almost unchanged for all the alcohols studied. In Fig. 3, curve II gives the dependence of the position of the second maximum on the number of carbon atoms in the alcohol molecule. (On the ordinate axis is plotted the angle at which the diffraction maximum is observed; on the abscissa axis, the number of carbon atoms in the molecule.) This curve illustrates the stated proposition very convincingly. In subsequent work carried out by Stewart and his co-workers with paraffins, fatty acids, etc., the position of the second maximum remains the same—\(8.8^\circ\). From this second maximum alone it can no longer be determined by the mean molecular distance, which would have to change in passing from one substance to another, since the length of the molecules must depend on the number of carbon atoms. Moreover, if, using Bragg’s formula with Keesom’s correction, one calculates the quantity \(d\), and from it the density of the substances, it proves to be several times greater than its true value. Thus, the quantity \(d\), calculated by Bragg’s formula from the position of the second maximum—which, in what follows, in contrast to the quantity \(d_1\) calculated from the position of the first maximum, we shall denote by \(d_2\)—is not the mean molecular distance. What is it? Stewart suggested that \(d_2\) is the distance between the centers of two molecules standing side by side. The following data confirm this assumption.

Fig. 2

1. The numerical value of the quantity \(d_2\), calculated by Bragg’s formula from the position of the second maximum, is equal to \(4.6\ \text{Å}\). Adam \(^{(14)}\) from his own

experiments on the study of films of saturated fatty acids formed on the surface of water, came to the conclusion that the area per molecule is equal to \(21.0 \times 10^{-16}\), which gives for the transverse dimension of the molecule or, what is the same, for the distance between the centers of molecules standing side by side, the value \(4.58\ \text{\AA}\)—in very good agreement with the number \(4.6\ \text{\AA}\), found by Stewart.

Fig. 3

Fig. 4

1. When the group \(\mathrm{CH}_3\) or \(\mathrm{OH}\) is attached to the side of the chain molecule (see below, the experiments with isomers of alcohols), the position of the second maximum shifts. At the same time the magnitude \(d_2\) changes and, moreover, increases.

If the second maximum is due to the transverse dimensions of the molecules, then what determines the position of the first maximum? What is the magnitude \(d_1\)? If the curves of Fig. 2 are compared with one another, it is immediately evident that the position of the first maximum, in contrast to the second maximum, is not constant; it shifts toward smaller angles in passing from a substance with a small content of carbon atoms in the molecule to substances with a larger content of carbon atoms. Curve 1 of Fig. 3 shows the change in the position of the first maximum with the content of carbon atoms in the molecule, and curve 2

in Fig. 4 gives the dependence of the quantity \(d_1\) on the number of carbon atoms in the molecule (along the abscissa axis there is still plotted the number of carbon atoms in the molecule of the substance, and along the ordinate axis the values of \(d_1\) and \(d_2\)). It turns out that the quantity \(d_1\) varies linearly with an increase in the number of carbon atoms. In passing from one substance to another, in which the content of carbon atoms in the molecules differs by one, the quantity \(d_1\) changes by \(1.54\ \text{Å}\).

With regard to the quantity \(d_1\), just as with regard to the quantity \(d_2\), it may be asserted that it is not the mean molecular distance. The density calculated by the formula

\[ \rho=\frac{M\cdot m_H}{d_1^3}, \tag{3} \]

where \(M\) is the molecular weight, \(m_H\) is the mass of a hydrogen atom, gives an extremely small value. Here it is necessary to make the reservation that for molecules of long chains, in general, it is very difficult to speak of an average distance between molecules. In this respect organic liquids with a long chain may be likened to a gas, where the distance between the centers of molecules varies within very wide limits and for which the effect of the mean molecular distance with respect to the scattering of X-rays does not occur at all.

Therefore Stewart’s supposition that the quantity \(d_1\) characterizes the length of the molecule proved quite natural, and then the linear course of the quantity \(d_1\) with respect to the number of carbon atoms in the molecule becomes understandable, since the length of the molecule, with an increase in the number of carbon atoms in the chain, must vary linearly. Let us make the assumption that the quantity \(d_1\) is equal to the length of the molecule; then by the formula

\[ \rho=\frac{M m_H}{d_1 d_2^2} \tag{4} \]

one can calculate the value for the density of the substance. Calculations carried out for decyl alcohol \((\mathrm{C}_{10}\mathrm{H}_{21}\mathrm{OH})\),

give for the density the value 0.60, whereas the true density is equal to 0.83. Since the quantity \(d_2\) gives the correct value of the transverse dimensions of the molecules, it follows from this that the only conclusion is that \(d_1\) is not the length of the molecule and, since the calculated value of the density is less than the true one, consequently the quantity \(d_1\) is numerically greater than the length of the molecule.

Before giving a final answer concerning the physical significance of the quantity \(d_1\), it is necessary to consider the question of how, in general, such maxima can appear in the scattering of X-rays by liquids. According to the preceding, these maxima are not an effect of the mean molecular distance, but then they must be the result of some oriented arrangement of the molecules in space, in which the quantities \(d_1\) and \(d_2\) must be repeated several times.

Fig. 5

This is an extremely important conclusion: in a liquid which is not a liquid crystal, at temperatures differing from the melting temperature by several degrees (sometimes tens of degrees), there exist regions in which the molecules of the liquid occupy a certain oriented position in space.

The following experiments led Stewart to the assumption that the regions of oriented arrangement of the molecules cannot be pieces of crystals.

1. Measurements were made of the intensity of scattered X-rays for lauryl alcohol \((\mathrm{C}_{11}\mathrm{H}_{23}\mathrm{OH})\) both in the liquid and in the solid phases. Fig. 5 shows the dependence of the current in the ionization chamber (the ordinate axis—

is the angle of scattering (the axis of abscissas). The curve indicated by a dashed line refers to the solid phase, and the curve indicated by a solid line to the liquid. The two curves are undoubtedly similar to one another, but not identical. Whereas the first maximum on the curve referring to the solid phase is shifted, relative to the first maximum of the curve of the liquid phase, toward smaller angles, the second maximum is shifted, on the contrary, toward larger angles.

Fig. 6

Analogous data were obtained by Morrow \(^{(15)}\) for capric acid (Fig. 6). Krishnamurti \(^{(16)}\) made similar comparisons for eight different substances. His conclusions are the same as those of Stewart and Morrow. The scattering of X-rays produced by a solid crystalline phase is similar to scattering from the liquid phase, but, despite the similarity, the diffraction patterns of the two phases are not identical and, consequently, the structures of the two phases also differ from one another.

1. If one measures the width of the diffraction maximum and calculates, by Scherrer’s formula \(^{(17)}\),

\[ h=\frac{2\left(\ln \frac{2}{\pi}\right)^{1/2}\lambda}{\Omega \cos \frac{\theta}{2}}, \tag{5} \]

where \(\lambda\) is the wavelength, \(h\) is the width of the maximum, and \(\Omega\) is the linear size of the crystallites, it turns out that \(\Omega\) has a value smaller than one molecular length, i.e. the diffraction maxima are so broad that they cannot be ascribed to the crystalline state, however small the crystallites may be.

To these data one must, of course, add the fact that the existence in a liquid, at temperatures above the melting temperature, of crystallites, i.e. regions of the solid phase, even of small dimensions, appears extremely improbable.

The considerations indicated make it extremely difficult to give a simple explanation of the observed picture of the scattering of X-rays by liquids. The only way out that Stewart finds consists in ascribing to the liquids he investigated a special state, for which he proposes the name “cybotaxis” (meaning “spatially arranged”). The peculiarity of such a structure of liquids consists in the fact that in it (the liquid) there exist groups of molecules possessing a certain mutual orientation and at the same time not losing their mobility.

In favor of the supposition that oriented groups of molecules exist in the liquids studied by Stewart speaks the course of the intensity of the scattered rays near zero. Whereas for amorphous substances the intensity of X-rays scattered near zero should be very great, the intensity of X-rays scattered by a crystalline substance is great only at zero itself and falls very rapidly with distance from zero. Something analogous also occurs for scattering by the liquids investigated by Stewart. Stewart showed (see the curves of diagram 2) that, as zero is approached, the intensity of the scattered X-rays falls (as is also the case for crystals) down to \(24'\)—the limit beyond which Stewart could not go.

Unfortunately, the accumulated experimental data do not yet make it possible to give a more exact description of this special state of the liquid.

Let us now return to the determination of the value \(d_1\). Since \(d_1\) is greater than the length of the molecule, Stewart assumes that we are dealing here with two associated molecules. This assumption of Stewart’s may be justified by chemical considerations, since the alcohol molecule possesses the polar group \(\mathrm{CH_2OH}\). If we now

\(^1\) Stewart is inclined to regard this state as characteristic of all liquids, with only the reservation that in organic liquids with a long chain it manifests itself more sharply.

let us assume that the quantity \(d_1\) represents the doubled length of the molecule and calculate the density of the liquid by formula (4); then it turns out that the calculated density is considerably greater than the true one (1.20 instead of 0.83 for decyl alcohol).

Better agreement of the experimental density with the calculated one is obtained on the assumption that \(d_1\) is the distance between planes cutting off equal segments on three mutually perpendicular axes, along which the double associated molecules of the liquid are arranged.^1 If this is so, then from the value of \(d_1\) we can determine the length of the molecule, and also the change that occurs in the length of the molecule when the number of carbon atoms in it changes by one. We already know that in this case the quantity \(d_1\) changes by \(1.54\) Å. According to the adopted scheme, the change in the length of the molecule \(\Delta l\), corresponding to 1 carbon atom, will be

\[ \Delta l = \frac{1.54}{2}\sqrt{3} = \frac{1.54 \times 1.7}{2} = 1.33\ \text{Å}. \]

Möller and Sävill \((^{18})\), from their experiments on the study of long hydrocarbon chains (in the solid crystalline phase), found that the change in chain length corresponding to 1 carbon atom is equal to \(1.3\) Å (in some cases \(1.24\) Å), i.e. it is close to the value obtained by Stuart from his assumption about the structure of molecular groups. If one takes into account that the segment cut off on the ordinate axis by the straight line expressing the dependence of the quantity \(d_1\) on the number of carbon atoms contained in the molecule is equal to \(5\) Å, then the length of the molecule may be expressed by the following formula:

\[ l = 4.32 + 1.33\,n, \tag{6} \]

^1 It is quite obvious that this assumption is an assumption about the structure of “molecular groups.” The orientation of the molecules of the liquid along three mutually perpendicular directions must substantially distinguish such a liquid from a liquid crystal.

where \(n\) is the number of carbon atoms in the molecule. The molecular length calculated from this formula agrees well with the value for the molecular length determined by the formula

\[ d_1=\frac{M\cdot m_{\mathrm H}}{P\cdot d_2^2}. \tag{7} \]

Thus, the meaning of the parameters \(d_2\) and \(d_1\)—the nature of the first and second diffraction maxima—is clear. These parameters characterize the longitudinal and transverse dimensions of the molecules. The further direction of Stuart’s work consisted in studying those changes undergone by the quantities \(d_1\) and \(d_2\) in passing from one chain to another. Table I gives the values of the quantities \(d_1\) and \(d_2\), obtained by Stuart and Skinner for various isomers of alcohols. From these data the following conclusions may be drawn:

TABLE I

1. The addition of a CH₃ group to the side of the chain increases the transverse size of the molecule \((d_2)\) by approximately 0.6 Å.

2. The addition of an OH group to the side of the chain increases the transverse size of the molecules by a smaller amount, approximately equal to 0.4 Å.

3. The addition of CH₃ and OH groups (simultaneously) to the side of the chain increases the transverse size of the molecule as if only the CH₃ group had been added to the side of the chain.

In the course of studying alcohol isomers, Stuart \((^{19})\) found that alcohol molecules associate in two ways. Molecules having OH groups at the end of the chain, and molecules in which the OH group is attached to the second carbon atom, counting from the end of the chain, associate in such a way that the directions of the chain lengths form one straight line. Molecules in which the OH group is attached to middle atoms associate side-to-side. I shall not dwell here on the proofs and the persuasiveness of these proofs, which Stuart gives in support of this very interesting conclusion, although this may have some significance for determining the structure of molecular groups. I shall note only two further facts observed by Stuart and Skinner.

1. For triethylcarbinol, in addition to the 1st and 2nd maxima, two more were found—at angles of \(20^\circ\) and \(37.5^\circ\). Two explanations are possible: either the observed maxima are higher orders of one of the two previously observed maxima, or they are genuinely new additional maxima. In their value they may be maxima of the third and fifth orders from the second maximum, which for triethylcarbinol occurs at an angle of \(7.1^\circ\). The corresponding values in the third and fifth orders will be \(21.3^\circ\) and \(36.1^\circ\), which agrees quite well with the angles found for the new maxima. The disappearance of maxima of even order can be explained, according to Scherrer \((^{20})\), by the arrangement of electrons in the association of two molecules.

The independent significance of these maxima appears no less probable. In this case they will corre-

to give values of \(d\) equal to \(2.05\ \text{\AA}\) and \(1.11\ \text{\AA}\), which agrees rather well with the distances between carbon atoms in the chain, \(2.0\ \text{\AA}\) and \(1.24\ \text{\AA}\). Confirmation of this conclusion would be of extremely important significance for resolving the question of whether the scattering of X-rays by liquids can make it possible to determine the structure of the molecule. After Debye’s work this seems quite probable, especially for substances whose molecules are long chains.

1. In the investigation of paraffins that give only one second maximum, it turned out that for all the paraffins investigated, with the exception of pentane and decane, the angle at which this maximum is observed is constant and equal to \(8.8^\circ\), i.e. to the value observed for the cases of other chains. Pentane and decane gave another value for this angle. It was assumed that this displacement was caused by an impurity in the objects used. Synthetic pentane and decane were prepared. The investigation of these substances gave the correct value of the angle at which the maximum of the scattered radiation is observed. Fig. 7 shows the ionization-current curve for synthetic pentane and decane (solid curves) and for ordinary pentane and decane (dotted curve). This fact shows what a great influence an impurity in the objects under investigation can have.

Fig. 7

In conclusion, I will allow myself once again to enumerate the main facts which compel one to suppose the existence in liquids of that special ordered state which Stewart called “Cybotaxis.” These facts are as follows:

1. The existence of two maxima, connected in a definite way with the dimensions of the molecule, suggests the presence in the liquid of planes in the Bragg sense. 2. The course of the intensity of the scattered X-rays near zero differs sharply from the course of the intensity for an amorphous substance.

and resembles the course of the intensity in crystalline bodies. 3. A comparison of the intensity curves of the scattered rays for the solid and liquid phases shows that the structure of solid organic substances differs somewhat from the structure of those regions of the liquid where internal reflecting planes exist. 4. The dimensions of the crystallites, calculated from the width of the diffraction maxima, are smaller than one molecule; consequently, the substance under investigation is noncrystalline (there is no regularity in the arrangement of the scattering centers). 5. The numerical value of the parameters $d_1$ and $d_2$, calculated by Bragg’s formula, gives, under a definite assumption about the structure of the molecular groups, values for the transverse and longitudinal dimensions of the molecule that agree well with the data of other investigators.

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