Investigation of Thin Surface Films in Reflected Polarized Light*

Leif Tronstad

(Trondheim, Norway)

In classifying the properties of metals, one should keep in mind the distinction between internal and external properties. Thus, for example, thermal conductivity and electrical conductivity, as well as magnetism and elasticity, are internal properties, whereas such surface phenomena as etching, electrolytic, catalytic, photoelectric, thermionic, and optical properties are examples of external properties. Since, however, external properties are greatly influenced by external conditions, especially by the presence on the surface of non-metallic films, it proves very difficult to determine experimentally the true relation between the internal and external properties of metals unless the influence of the surface conditions is known. In almost all experimental work carried out with metallic surfaces that were apparently quite clean, one was in fact dealing with a thin, invisible oxide film formed owing to the presence of traces of oxygen. Therefore the study of the properties of these thin films and their influence on the properties of metals is extremely important for metallography.

The investigation of thin surface layers deserves attention also from a more general point of view, since it is often important to know the nature of the film itself; this is the case, for example, in the study of adsorption, surface migration, friction, and in investigations of monomolecular films.

Turning to metallic methods of investigation of invisible surface films, it must be pointed out that the study of almost all the external properties mentioned above may prove useful. Apart from methods based on the diffraction of electrons or X-rays, the most convenient for investigating surfaces at not very high temperatures should apparently be regarded as optical methods, especially those based on the study of polarized light** reflected from a metallic surface. Such methods, proposed by Jamson and Quincke, were improved by Förth and Drude², who developed their theory and performed the first experiments. In comparison with other methods the optical method has many advantages. Thus, investigations with electrons and X-rays are restricted to metals in vacuum or in gases, whereas measurements of the polarization of light can be carried out in any transparent medium, for example in solutions. For

* Trans. Faraday Soc. March 1933; translation by M. Sheshemintsev.
* As Langmuir and his coworkers have shown (cf., for example,¹), electron emission is an important means of studying properties and of determining the presence of surface films on metals at high temperatures. Measurement of the accommodation coefficient may also be used (Phys. Rev. 40*, 78, 1932).

of films with an average thickness of about \(10\)—\(50\ \mathring{\mathrm A}\) the sensitivity of the method is very good.

The principle of the method* is as follows: a beam of polarized light is reflected from a metallic surface; in this process the state of polarization of the beam changes. This change depends on the angle of incidence and the optical properties of the metal, as well as on the surface film present on it and on the surrounding medium. Consequently, if the angle of incidence and the optical properties of the clean metallic surface and of the surrounding medium are known, then from the change in polarization one can draw conclusions about the optical and other properties of any surface film. By using monochromatic light of different wavelengths, one can obtain information about the dispersion of the film.

The optical method can also be applied to nonabsorbing bodies (glass, water, etc.) covered with surface films,** but this is associated with difficulties depending on the low intensity of the reflected beam.

EXPERIMENTAL PART

The experimental part consists in investigating the change in polarization of monochromatic light reflected, at various angles of incidence, from a clean metallic surface and from a metallic surface covered with a thin film. The most convenient method consists in measuring two quantities: the phase difference \(\Delta\) and the absorption-coefficient ratio \(\operatorname{tg}\psi\). The electric vector of the incident light can be resolved into two components \(I_p\) and \(I_v\), one of which is parallel and the other perpendicular to the plane of incidence. From the optics of metals it is known that both components \(I_v\) and \(I_p\), after reflection, acquire different phases and amplitudes. If \(\delta_v\) and \(\delta_p\) are respectively the phases of \(I_v\) and \(I_p\), and \(R_v\) and \(R_p\) are the amplitudes of the electric vector after reflection, then \(\Delta\) and \(\psi\) will be equal to:

\[ \Delta = \delta_p - \delta_v, \]

\[ \operatorname{tg}\psi = \frac{I_v}{R_v} : \frac{I_p}{R_p}. \]

The scheme of the optical system is shown in Fig. 1. Instead of a monochromator, a mercury-cadmium light with filters was used; instead of slits, diaphragms of various diameters were used. The central stand of the new instrument constitutes a separate part; this was done so that no shocks which may arise during readings on the instrument limbs would be transmitted to the surface of the liquid under investigation.

The measurement method is as follows: by rotating the polarizer, the plane of polarization of the linearly polarized beam is set at a known azimuth relative to the plane of incidence. By rotating the compensator (a mica plate “a quarter wave”) the components \(I_v\) and \(I_p\) receive a phase difference which compensates each time the phase difference arising upon reflection. The positions of the polarizer and of the mica plate at exact compensation are determined with the aid of an elliptic half-shade compensator.

In this case \(\Delta\) can be found if the angles between the plane of incidence (the zero plane) and the directions of oscillation in the polarizer and in the mica plate are known; these angles are read on divided circles.

The reflected light will be plane-polarized; let its azimuth (with respect to the plane of incidence) be, on the assumption that both compo-

* A detailed description of the experimental and theoretical aspects of the method is given by Tronstad\(^3\). This work, cited below as \(^{t}\), contains a detailed bibliography.

** Cf., for example, Drude’s manual\(^4\).

STUDY OF THIN SURFACE FILMS

components have been equally diminished in intensity owing to absorption, is equal to \(\theta_2\); this azimuth can be calculated if the directions of oscillation in the polarizer and compensator are known. However, because the absorption coefficients of the two components are different, the azimuth found with the aid of the Lippich analyzer will differ from \(\theta_2\). It is easy to show that the ratio of the absorption coefficients for the two components, equal to \(\operatorname{tg}\psi\), can be obtained from the calculated azimuth \(\theta_2\) and the measured azimuth \(a\) in the following way:

\[ \operatorname{tg}\psi=\frac{\operatorname{tg}\theta_2}{\operatorname{tg}a}. \]

According to the electromagnetic theory of light, the quantities \(\Delta\) and \(\psi\) are determined by the optical constants of the metal \((n\)—the refractive index and \(k\)—the coefficient of absorption). To a first approximation we have the following equations:

Fig. 1. Optical system. 1. Light source. 2. Condenser. 3. Prism of total internal reflection. 4 and 5. Slits of the monochromator. 6. Lenses and prism of constant deviation of the monochromator. 7. Collimator lens. 8. Polarizer and its limb. 9. Diaphragms. 10. Mica quarter-wave plate (Senarmont compensator). 11. Central table. 12. Metallic mirror (serves as cathode or anode in the metallic bath). 13 and 14. Semishadow systems. 15. Analyzer and its limb. 16. Telescope.

\[ n=\frac{\sin\varphi\,\operatorname{tg}\varphi\cos 2\psi}{1+\cos\Delta\sin 2\psi}, \]

\[ k=\sin\Delta\,\operatorname{tg}2\psi, \]

where \(\varphi\) is the angle of incidence. Measurement of the quantities \(\Delta\) and \(\psi\) by the method described above constitutes an important method for determining the optical constants of a metal.

THEORETICAL PART

As indicated above, the optical properties of a metal can be investigated by studying polarized monochromatic light of various wavelengths reflected from the surface at various angles of incidence. The next step will be to establish the relation between changes in $\Delta$ and $\psi$ of reflected polarized light, caused by the presence of a nonabsorbing surface film, and the optical properties of this film.

Let the values of $\Delta$ and $\psi$ obtained on a clean metal surface and on a surface covered with a nonabsorbing film be, respectively, $\bar{\Delta}$, $\bar{\psi}$ and $\Delta$, $\psi$. Assuming that the film is a homogeneous isotropic layer of dielectric, one may write the equations, in first approximation, as follows$^{2,3,5}$:

\[ \Delta-\bar{\Delta} = -\frac{4\pi L}{\lambda} \frac{\cos\varphi\,\sin^{2}\varphi} {\left(\cos^{2}\varphi-n_{0}^{2}a\right)^{2}+n_{0}^{4}a'^{2}} \left(n_{1}^{2}-n_{0}^{2}\right) \]

\[ \left[ \left(\cos^{2}\varphi-n_{0}^{2}a\right) \left(\frac{1}{n_{1}^{2}}-a\right) +n_{0}^{2}a'^{2} \right], \]

\[ 2\psi-2\bar{\psi} = \sin 2\bar{\psi}\cdot \frac{4\pi L}{\lambda} \frac{\cos\varphi\,\sin^{2}\varphi} {\left(\cos^{2}\varphi-n_{0}^{2}a\right)^{2}+n_{0}^{4}a'^{2}} \left(n_{1}^{2}-n_{0}^{2}\right), \]

\[ \left[ n_{1}^{2}a' \left(\frac{1}{n_{1}^{2}}-a\right) - \left(\cos^{2}\varphi-n_{0}^{2}a\right)a' \right], \]

where

\[ a=\frac{1-k^{2}}{n^{2}(1+k^{2})^{2}}, \qquad a'=\frac{2k}{n'^{2}(1+k^{2})^{2}}. \]

Fig. 2. Iron in 0.5 N. NaOH, N. Na$_2$SO$_4$. Current density under stationary conditions: 0.2–0.4 mA/cm$^{2}$. From zero to A: cathode; A—B: anode; B—C: cathode; C—D: anode; D—E: cathode; E—F: anode; F—G: cathode; H—I: treatment in N. N. H$_2$SO$_4$; I—K: anode in acid solution, $D_A=15$ mA/cm$^{2}$.

Here $\lambda$ denotes the wavelength, $\varphi$ the angle of incidence, $n$ and $k$ the optical constants of the pure metal, $n_{0}$ the refractive index of the surrounding medium, $L$ the mean thickness, and $n_{1}$ the mean refractive index of the nonabsorbing film. In these equations all quantities except $L$ and $n_{1}$ are either known or can be measured, so that it proves possible approximately to calculate the unknown quantities $L$ and $n_{1}$.

It may be mentioned, incidentally, that C. Strachan, working with Faugère in Cambridge, derived equations similar to Drude’s equations, proceeding from other assumptions$^{6}$. Applying the method developed by Darwin, he regarded the layer as a volume distribution of Hertz oscillators. Thus the equations published by Drude, based on simpler assumptions, may be considered sufficiently accurate for the indicated purposes, especially if one takes into account that errors having their source in nonuniform thickness and optical nonuniformity—

...film thickness, are dominant. Drude also gave some experimental evidence for the correctness of his equations. It must be noted, however, that films whose optical properties differ little from the optical properties of the metal or of the surrounding medium are unsuitable for optical investigation.

APPLICATIONS OF THE OPTICAL METHOD

a) Passivity of metals

The field in which the optical method has so far been most fruitful is the study of the passivity of metals. As is known, metal passivation is achieved either by immersing it in oxidizing liquids or by anodic treatment at high current densities.^7

To evaluate the results obtained by optical means, it should be recalled that one hundred years ago Faraday published an explanation of this phenomenon, assuming that the cause of the effect is a surface film of oxygen or oxide which protects the metal from further action (“mechanical passivity”). Hittorf disputed this explanation and attributed passivity to changes inside the metal itself (“chemical passivity”). The question of which of the two theories of passivity corresponds to the truth can be solved by applying appropriate optical methods: if Faraday was right, then the metal in the passive state should have a lower reflecting power than in the active state. This question was investigated by Königsberger and Müller;^8 they found no noticeable difference, although the method they used, in their opinion, was suitable for detecting monomolecular films of oxygen. This result was cited in all handbooks as important evidence against Faraday’s theory.

Nevertheless, the most recent work on passivity and corrosion apparently shows that passivated metals are indeed covered with a thin oxide film. Thus it again becomes important to obtain optical evidence for the existence of such a film; for this purpose Drude’s method, owing to its sensitivity, seems the most suitable.

Fig. 3. Nickel in \(0.1\,N\ H_2SO_4\), \(0.3N\ Na_2SO_4\). Current density under stationary conditions: \(13\text{–}15\ \mathrm{mA}/\mathrm{cm}^2\).
\(a\) — cathode \(A—B\): anode \(B—C\): cathode \(C—D\): anode \(D—E\): cathode \(E—G\): anode \(G—H\): cathode \(H—K\): anode.

Using this method, Michel^9 and later Bernoulli^10 gave evidence for the existence of a surface film on iron and chromium passivated with nitric acid. However, in these works the metallic mirror was removed from the solution and the measurements were carried out in air; thus oxidation of the surface could have occurred after passivation of the metal, and the observed optical changes could have been caused precisely by this oxidation.

In the most recent optical investigations of this question, which were carried out by the author in the laboratory of Prof. Freundlich in Berlin,^11 the mirrors were subjected to anodic and cathodic treatments and, during the optical measurements, remained immersed in the solution.

As can be seen from the diagrams, large changes in the optical properties of iron and nickel occur precisely during the anodic treatment of these metals in alkaline and acidic solutions, respectively. The diagram in Fig. 3 gives the readings of the polarizer and analyzer, from which the values of \(\Delta\) and \(\psi\) can be obtained directly. The changes that took place during the first passivation correspond to the presence of an oxide film with an average thickness of \(20\text{–}40\) Å in the passive state. During the subsequent activation and passivation, the film became visible owing to interference colors.

Fig. 4.

Thus the attempt to establish the presence of a surface film in the case of anodic passivation proved successful.* The reason why Königsberger and Müller were unable to notice a film of the above-mentioned thickness is possibly that measurements of the intensity of the reflected light were strongly hindered by the luster of the metallic surface.^13

After the existence of the film had been established, the next step was to obtain quantitative data on the properties of this film, again using the same optical method. For this purpose, metallic mirrors of very high quality were required, free from scratches and thin oxide

* X-ray investigations were carried out by F. Krautgen and E. Nering^12 and yielded no results.

films or surface films formed during polishing. These investigations were carried out in the laboratory of Prof. Benedicks in Stockholm[^14].

Various specimens of iron and steel (including stainless steel) were polished on lead disks with diamond and then polished with aluminum oxide. It was found that polishing with crocus gives dense oxide films. After this the mirrors were used as cathodes and anodes in alkaline, neutral, and acid solutions at various current densities (18°C). Some of the results obtained in alkaline solutions are shown in Fig. 5.

Of interest is the fact that the value of \(\Delta\) increases by approximately \(2^\circ\) during the first cathodic treatment.

According to Freundlich, Patscheke, and Zocher, this change corresponds to the removal of the oxide film formed in air[^15]. It is, however, very

Fig. 5.

probable that the removal is incomplete; the optical change can equally well be explained by assuming the existence of a very porous or spongy film[^16]. After passivation of the metal the following changes were observed: \(\Delta\) about \(6^\circ\) and \(\psi\) about \(0.5^\circ\). Certain facts indicate that, for pure iron free of surface films, the value of \(\Delta\) is approximately \(148^\circ\); thus, from the equations given above it follows that the indicated change in \(\Delta\) corresponds to the presence of a film with an average thickness of about \(30\ \text{\AA}\) and an average refractive index of about 3.0. The refractive index of iron oxide in large pieces was found by Kundt[^17] to be equal to 2.6; consequently, the results obtained may be regarded as evidence in favor of the oxide theory of passivity. Prolonged anodic treatment does not cause noticeable changes. This fact indicates that the film is protective, i.e., impermeable to the ions contained in the solution. Reactivation causes a partial reversal of the optical properties, which indicates a change-

tion in the film or to partial removal of the surface film present in the anodic state. With alternating activation and passivation the average thickness of the oxide film gradually increases and, as the optical properties show, eventually becomes equal to 80–100 Å. A surface film of such thickness is invisible to the naked eye if viewed in normally incident light. In oblique light, however, interference colors of the first order should appear; this is indeed confirmed by observation.

The curves obtained in studying various iron specimens in alkaline, neutral, and acid solutions were similar to the curves shown in Fig. 4. Fig. 5, for example, shows the curve obtained with austenitic stainless steel in an acid solution. But the natural oxide film in this case, being very thin, is distinguished by stability and is removed with greater difficulty. The changes in optical properties obtained upon repeated passivation again correspond to a film about 30 Å thick and with a refractive index of about 3. These values for films formed during the first passivation were confirmed with sufficient accuracy by all the experiments performed.

The curves obtained also lead to several other important conclusions regarding the passivity of metals; but they should chiefly be referred to the author’s previous works 3, 5, 11, 16*. The results presented, however, are sufficient to show the application of the optical method to such objects. Much work still remains to be done, and the author hopes that he will be able to report new results in the near future.

b) Oxidation of metals and atmospheric corrosion. It is well known that iron and certain other metals, after being exposed for some time to air, change their behavior with respect to reagents that normally act upon them. It has been suggested that this change is due to the formation of a very thin invisible oxide film (the natural oxide film mentioned above), which protects the underlying metal from the reagent.

In 1927 Freundlich, Patscheke, and Zocher 15, using Drude’s optical method**, obtained evidence for the existence of such a film. They found that iron mirrors deposited on glass in vacuum dissolved rapidly in nitric acid of concentration 1:1. But after exposure to air at room temperature, the mirrors dissolved only very slowly, becoming covered with brown spots, which probably represent the natural oxide film. To obtain optical evidence for the formation of the natural film, the optical properties of mirrors prepared in vacuum were studied before and after their exposure to air. The measurements gave a difference in the value of Δ of about 2°, which corresponds to an oxide film about 10 Å in average thickness; that is, this film is thinner than the film present on passive iron before anodic treatment. Evacuation does not produce the reverse change; this indicates that genuine oxidation of the metal, and not merely adsorption of oxygen, is actually taking place here.

This method was also successfully used by Dutch investigators 21. Studying the action of air on mercury at room temperature, they found rapid formation of a film with an average thickness of about

* However, regarding the value of the optical method for these purposes, Müller and his collaborators (cf. Müller and May 9) apparently hold views different from those of the author.

** The existence of a natural oxide film on tungsten was also proved by electron diffraction 20. Electroemission likewise gave evidence for the existence of an oxide film 1.

15–20 Å, which protected the mercury from further oxidation. However, the double refraction in the “windows” of the layer (the so-called “Window effect”) apparently may have been satisfactorily taken into account in the calculation, so that the numerical values given cannot be criticized.

In this connection one should mention the work of Geinschild[^22]. He traced the change in the optical properties of iron mirrors during exposure to moist air containing carbon dioxide. The observed changes indicate the formation of porous surface films. Geinschild’s investigations lead to the problems of atmospheric corrosion—an area in which the optical method should be well mastered. As Vernon[^23], and also Evans[^24], have shown, protective films on metals can be obtained in various ways. These films usually cannot be seen by the eye and thus constitute an object suitable for optical investigation by Drude’s method.

c) Adsorption. In studying the adsorption of gases by metals this method may also prove valuable. The results mentioned in the discussion of metal oxidation can, of course, be understood as “chemical sorption” of oxygen. However, the investigations of Gershkovich[^25] deserve special consideration. The action of various gases on the clean surface of mercury at room temperature caused a marked change in the optical properties; the value of $\Delta$ changed by 1–2°. When the gases were pumped off, the change partly occurred in the reverse direction—a fact indicating that the process was partly adsorption. However, the gases used for the experiments were not entirely pure; traces of oxygen must have been present. Thus, in this way a certain part of the optical change may be attributed to the presence of an oxide film.

Although Gershkovich’s numerical results are unreliable, the work is of great interest, since it shows that the optical method can provide valuable information regarding the adsorbed phase. Thus, in studying the problem of adsorption, attention should be paid to optical methods.

d) Monomolecular films on metals. In the examples mentioned above, nothing was known beforehand about the surfaces of the film. To test the reliability of the method it is important to apply it to films with known properties. The most suitable for this purpose appear to be monomolecular films of long-chain fatty acids and alcohols, since X-ray analysis and the study of elastic properties by the Langmuir method have already given some information about the structure and dimensions of these films[^26]. However, in precise investigations these films must be regarded as optically anisotropic. A theoretical analysis of this case was given by Stranski[^9], who considered the effect of a monomolecular layer on light reflected from a surface.

Experimental work on this question was carried out by Phaezm and the author in Rayleigh’s laboratory in Cambridge; the purest mercury surface was used in an atmosphere of nitrogen, as far as possible free from oxygen. The results will be published in detail elsewhere. Here it may only be said that the method proved not only sufficiently sensitive to detect the optical changes produced by the film, but that with its help it was also possible to follow changes caused by contamination of the mercury surface and irregularities in the surface film. The optical properties of the fatty films, calculated from the measured changes in the values of $\Delta$ and $\Psi$ by means of the equations given above, agree fairly well with the actual properties of these films. Such agreement may be regarded as evidence of the approximate correctness of Drude’s equations.

Finally, it is necessary to mention some further possible applications of the optical method, which are still quite unexplored.

e) Heterogeneous catalysis. Although active centers are considered an essential component of the surface, it seems improbable—

that chemical reactions also occur over some distance beyond these centers, provided that contamination is absent. In addition to the destruction of active centers, the cessation of catalysis may also depend on the formation of an inactive or protective surface film. Knowing the causes of the cessation of catalysis makes it easier to take precautionary measures to preserve the catalyst from damage.

f) Surface migration. The fundamental work of Volmer^27 and his collaborators indicates that surface migration is a very important factor in all problems of surface chemistry. By focusing the eyepiece of the instrument described above on the surface itself, one can easily follow the slow motion of the surface phase over the metallic mirror (for example, iodine over copper, oxygen over mercury, etc.).

It would be possible to point to some further examples illustrating the application of the optical method (for example, lubrication and friction, metal casting, flotation of ores and minerals,^28 etc.). However, the examples already given are sufficient to make clear the importance of the method for the study of reactions occurring on metallic surfaces. The method is still in the first stage of development, and improvements may be expected both in technique and in the theoretical aspects. Nevertheless, the already existing facts establish the value of Drude’s method in various fields of investigation.

REFERENCES

1. Langmuir, I. Am. Chem. Soc. 53, 486, 1931.
2. P. Drude, Wied. Ann. 53, 481, 1890 (and preceding work).
3. T. Tronstad, Der Kongelige Norske Widenskabers Selskabs Skrifter 1, 248, 1931.
4. Drude, Lehrbuch der Optik, or Ch. Bouhet, Ann. Physique (10) 15, 5, 1931.
5. L. Tronstad, Z. Phys. Chem. A. 158, 387, 1932 (cited below as II).
6. C. Strachen, Proc. Camb. Physl. Soc. 29, 1, 1933.
7. I. Königsberger and W. J. Muller, Phys. Zs. 12, 606, 1911 (and preceding works).
8. See U. R. Evans, Nature 128, 1062, 1931.
9. F. J. Micheli, Archives der Sciences physiques et naturelles (Geneva) 10, 125, 27, 1900.
10. A. L. Bernoulli, Phys. Zs. 5, 632, 1904.
11. L. Tronstad, Z. phys. Chem. A. 142, 241, 1929 (cited below as III); Nature 124, 373, 1929.
12. F. Krügen and E. Nähring, Ann. d. Physik (IV) 84, 939, 1927.
13. Cf. references ^10 and ^3, pp. 27–28.
14. Cf. L. Tronstad, references ^3 and ^5, also Nature 127, 127, 1931.
15. H. Freundlich, G. Patscheke and H. Zocher, Z. Phys. Chem. 128, 321, 1927; 130, 289, 1927.
16. Cf. reference ^5, p. 383; cf. also L. Tronstad, Det Kongelige Norske Widenskabers Selskabs Forhandlinger 4, 161, 1931 (cited below as IV) and Z. phys. Chem. A. 161, 154, 1932.
17. A. Kundt, Wied. Ann. 34, 484, 1888.
18. Cf. U. R. Evans, Nature 125, 130, 1930.
19. W. Müller and W. Machu, Z. phys. Chem. A. 161, 150, 1932.
20. Cf. W. Boas and K. Rupp, Ann. d. Phys. 7, 983, 1930; ibid. (V) 13, 1, 1932.
21. Cf., for example, R. Sissing and J. J. Haak, Proc. Roy. Acad. Sci. (Amsterdam) 21, 678, 1919; C. A. Reeser, Physica 2, 135, 1922; Arch. Neirland. Sci. (3a) 6, 225, 1923; J. Ellerbrock, Arch. Neirland. Sci. (3a) 10, 42, 1927.

1. H. Hanschild, Ann. d. Phys. (IV) 10, 816, 1920.
2. W. H. J. Vernon, Trans. Far. Soc. 27, 225, 1931 (and the preceding paper).
3. U. R. Evans, J. Chem. Soc. 1020, 1927; ibid. 92 and 2651, 1929.
4. E. Herschkowitsch, Ann. d. Phys. (V) 10, 993, 1931.
5. Cf., for example, E. K. Rideal, Surface Chemistry, Cambridge 13, 1930.
6. M. Volmer and G. Adhikari, Zs. phys. Chem. 119, 46, 1926.
7. Preliminary communication by P. Bergsöe, Copenhagen.