The Reaction of Gases on the Surface of a Single Crystal of Copper. I

Chem. , 1942, 46 (8), pp 969–980. DOI: 10.1021/j150422a021. Publication Date: August 1942. ACS Legacy Archive. Cite this:J. Phys. Chem. 46, 8, 969-9...
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REACTION OF OXYGEN ON SINGLE CRYSTAL OF COPPER

969

THE REACTION OF GASES ON T H E SURFACE OF A SINGLE CRYSTAL OF COPPER. I OXYGEN ALLAN T. GWATHMEY

AND

ARTHUR F.

BENTON

Department of Chemistry, University of Virginia, Charlottesville, Virginia Received April 1.4, 1948

Many important processes, such as corrosion, contact catalysis, and powder metallurgy, depend in varying degrees on the reaction of gases on the surface of metals. The object of this investigation is to study the mechanism of this type of reaction on single crystals of copper. In this paper (Part I) experiments are described which show that the rate of reaction with oxygen varies greatly with the crystal plane along which the surface is prepared. In Part I1 experiments will be described which show that catalytic reactions between certain gases on the surface of a single crystal cause rearrangements of the metal atoms in the surface to develop special planes in a manner dependent on the nature of the reacting gases. There are two important methods of approach in the study of the reaction of gases on solid surfaces. The first, which is the more common, is the study of changes produced in the surrounding gas by the action of the surface. This includes measurements of the volume of gases adsorbed and studies of chemical changes produced catalytically in the surrounding gas. This method is limited in that it gives very little direct information about the nature of the surface, and thus a correlation between the changes produced in the gas and the nature of the surface which produces these changes is largely impossible. The second method is the study of the effect of the gas on the structure of the surface. The chief difficulty in this method in the past has been that the very small size and random orientation of the individual crystal grains have generally rendered impossible the identification and isolation of any one known type of surface on which specific measurements could be made. This difficulty has been especially pronounced in the study of catalysts. The development of the technique of growing large single crystals of metals and of preparing very smooth surfaces parallel to particular crystal planes offers new and relatively simple methods of studying the action of gases on the structure of known surfaces. In addition to measurements of changes produced in the surrounding gas two main effects may possibly be observed: ( I ) the variation in chemical reactivity of surfaces prepared parallel to different crystal planes, and (8)the rearrangements produced in the surface by the action of the gas. In using this method for interpreting the behavior of polycrystalline solids it should be emphasized that surfaces of single crystals may differ in some respects from those of polycrystalline solids. Study of single crystals should indicate whether such differences exist and furnish us with a reference standard for comparison of physically different surfaces. It seems reasonable to expect that

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there are certain fundamental properties which are common to surfaces of metals in any form. A single crystal of copper is used in the form of a sphere in order to have every possible crystal plane parallel to the surface a t some point on the sphere. It is first mechanically and then electrolytically polished so that only metal which is aa free as possible from contaminations and strains is exposed a t the surface. PREVIOUS EXPERIMENTAL WORK

It haa been previously shown that the rate of reaction of copper with liquid reagents and in electrolytic etching varies with the crystal plane along which the surface is prepared (12, 16, 26). It seems reasonable to expect that the rate of reaction with gases would also vary with the crystal plane, and a few experiments have been performed which indicate in varying degrees that this is so. Tammann (25), in studying crystallite orientation during rolling, drawing, and annealing of polycrystalline copper, reported that small crystals heated in air to 260°C. showed tarnish colors indicating that the (111) and (110) planes tarnished more rapidly than the cube. The details of this part of the study were not given, but apparently the crystals examined were a group of enlarged ones developed in a polycrystalline bar. Tammann suggested that the variation in rate may be due to variation in permeability to oxygen of the oxide layer on the various planes. Elam (7) heated in a vacuum to 950°C. single crystal rods the surfaces of which had been slightly oxidized and found that striations parallel to certain planes were produced. The development of striations was attributed to attack by oxygen along 'certain planes and subsequent volatilization of the cuprous oxide formed. Planes most readily attacked appeared t o be (100) and (110). Martin (19), in studying thermionic emission from a polished crystal sphere of tungsten, found that adsorption of barium and cesium waa a function of crystallographic direction. When the surface was clean, cesium waa adsorbed on the (110) and (211) planes in preference to others, and barium on the (100) plane. Very minute traces of gas completely altered the relative adsorptive powers of different planes. Gwathmey and Benton (13) obtained a symmetrical and highly colored pattern produced by the oxide film formed on heating a specially polished single crystal sphere of copper in 0.3 mm. of air at approximately l ~ o cThe . variation in colors was attributed to a variation in rate of oxidation of surfaces parallel to different crystal planes. The present paper is a detailed report of studies begun a t that time. Lustman and Mehl (18) studied the rate of oxidation from 80" t o 150C. of a number of single crystals of copper the surfaces of which were plane but were not prepared parallel to any particular crystal face. The surfaces were given a final finish, after mechanical polishing, by annealing in hydrogen above 900°C. At any one temperature the relative rates of the surfaces studied varied greatly with temperature changes of the order of 25°C. Finch, Murison, Stuart, and Thomson (9) studied the influence of method of

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formation on the structure and catalytic activity of sputtered films. Beeck, Smith, and Wheeler (2) in a similar study prepared films of nickel, iron, cobalt, palladium, and copper by condensation of their vapors on glass a t various temperatures. Xickel and iron films prepared in an inert gas a t 1 mm. pressure were completely oriented with the least dense of the planes, (110) for nickel and (111) for iron, lying parallel to the glass backing. Films prepared in a vacuum were unoriented. The catalytic activity of the oriented film for hydrogenation of ethylene was about five times that of the unoriented. The activity of the oriented films per unit weight was constant, indicating ready accessibility of the gas to the interior of the films. Many previous experiments have shown that a gas may promote rearrangements of various kinds in metal surfaces. Beilby (3) in studying the action of ammonia gas on tubes of copper, iron, nickel, platinum, and gold a t temperatures of about 80OoC,found that the tubes became spongy and lost their mechanical strength. He was led to the belief that the surfaee of the metal had been converted into a semifluid by decomposition of ammonia a t a temperature considerably below the melting point of the metal. Rearrangements in metal films or foils by heating in gases a t temperatures ranging from 25' to 350OC. have been studied by Beilby, Andrade ( l ) ,Edwards and Petersen (6), Preston and Bircumshaw (21), Finch, Quarrel, and Wilman (lo), and Finch and Wilman (11). Johnson (17) heated tungsten filaments to incandescence by means of an alternating or direct current in a mixture of argon and nitrogen, or by a direct current in a vacuum, and found that the surface atoms tended to rearrange and expose special crystal planes or step-like formations. Gwathmey and Benton (14) found that the catalytic interaction of hydrogen and oxygen on the surface of a specially prepared crystal of copper in the form of a sphere at 360°C. produced definite facets parallel to (111) planes. Details of this and similar experiments will be described in Part 11. EXPERIMEKTAL PROCEDURE

A single crystal of copper in the form of a sphere, 5/8 in. in diameter, with a shaft 3/16 in. in diameter by 1/2 in. long, was prepared and surfaced by the method previously described (15). The important feature of the surfacing process is the final electrolytic polishing, which removes all broken pieces of crystal and any strained layers a t the same time that the polishing takes place. Proof that the electrolytic polishing had removed undesirable layers was obtained from the fact that, on rrdi c'ng the current density below that required for polishing, a very striking etch pattern was obtained which revealed the symmetry of the single crystal; on reversing the current the electrodeposited copper continued the orientation of the single crystal. Finally the crystal was given a polish a t the high current density in order to remove the slight roughening produced in forming the etch pattern. This simple method of determining when the true structure of the underlying single crystal has been reached is one of the advantages of using the crystal in the form of a sphere. For the oxidation experiments the crystal was placed in a 100-cc.round-bottom

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flask with a neck, 1 in. in diameter by 15 in. long, extending vertically above the flask. The crystal was introduced into the flask through a ground-glass jbint sealed to the upper end of the neck. It was supported near the bottom of the flask with shaft pointing downward by means of a copper wire attached to the shaft. The gas entered from above and passed out a t the bottom. The flask could be heated to 575°C. by means of a portable electric furnace, and the temperature just outside the flask was read with a mercury thermometer. For pressures of less than lo-' mm. of mercury an all-glass system evacuated by a diffusion pump was used, and for temperatures above 600°C. the crystal was heated in a fused quartz tube. The crystal, after being removed from the electrolytic polishing bath, was rinsed thoroughly in water, dried on soft tissue paper, and placed immediately in the bulb. The system was then flushed out with dry hydrogen and the crystal heated in this gas a t 550'C. for a t least an hour. This treatment removes any slight film of oxide and also partially anneals the metal. The heating

FIG. 1. Photographs of patterns obtained by heating crystal a t 200OC. in air at atmos pheric pressure. Looking normal to the surface at the (100) pole. (a) 1 min.; (b) 30 min (c) 2 hr.; (d) 32 hr.; (e) sketch for identifying the important regions on the sphere.

hydrogen assures a uniform surface a t the beginning of each experiment. The crystal was next cooled in hydrogen to the temperature a t which the reaction was to take place, the hydrogen was pumped out for about 15 min., and dry reacting gas was admitted. The appearance of the crystal as the reaction proceeded was observed through a small opening in the top of the furnace illuminated by a flashlight. When an experiment was completed, the crystal was cooled, generally in a vacuum, then removed and examined by several different methods. In case of the oxidation experiments the crystal was examined by diffuse white light by placing over it in a well-lighted room a tube of white paper, about 2 in. in diameter and 4 in. long. The tube prevented images of the objects in the room from appearing on the surface of the crystal. The spurious black spot appearing in the center of the crystal in the photographs shown below is the reflected image of the open top of the paper tube. With this type of illumination oxide films on copper produce brilliant interference colors corresponding to differences in the thickness of the

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film, as critically discussed by Evans (8). Use is here made of the consistent results of Miley (20) and Constable (4) on the rela$on of color to film thicknes:. The films obtained vary in thickness from 370 A. to approximately 1300 A. The crystal was also examined in a dark room with a flashlight to identify by light reflection the presence of any new surfaces produced by rearrangement of the surface atoms. The surfaces were further examined under a microscope. For use in identifying the various regions the surfaces of which are approximately parallel to the principal crystal planes, a sketch is given in figure 1 (e) of the pattern formed by the intersection of these planes with the surface of the sphere. For convenience, only the areas which are nearly parallel to the four planes of highest reticular density are indicated, and their relative sizes are arbitrary. The various regions in the patterns obtained experimentally are designated by the planes the poles of which correspond most closely to the centers of these regions. I n order to facilitate description and discussion, regions having colors of approximately the same wave length are grouped together as one region, but actually most of them have a fine structure which should ultimately be considered in detail. In order to assure that heat alone would not cause a rearrangement of the surface atoms in these experiments, a freshly polished crystal was heated for 8 hr. a t about 500°C. in air a t a pressure of less than mm. No appreciable change in the surface could be noticed on examination with the unaided eye or the microscope. Heating for 12 hr. at 510OC. in hydrogen a t atmospheric pressure caused no appreciable change. In the present general survey of the oxidation process, the sphere.; were heated in air a t temperatures ranging from 200" to 1000"C., at pressures ranging from 0.3 mm. to atmospheric, and for periods ranging from 1 min. to 32 hr. RESVLTS

Photographs of the patterns obtained by heating a crystal a t 200'C. in air at atmospheric pressure for 1 min., 30 min., 2 hr., and 32 hr. are shown in figure 1. The various regions of the pattern may be identified by reference to the sketch in figure ] ( e ) . There are many interesting features of these patterns and the manner in which they change. When air was let into the bulb, no apparent change took place in the crystal until after about 15 sec., when reddish brown lines, which show as dark lines in figure l(a), began to appear. Thus, the regions covered by these dark lines are those which have the greatest early rate of oxidation. This effect is quite definite. The remaining areas, which include the regions surrounding the (311), (110), and (111) poles, retained their original copper color and did not appear to have oxidized appreciably. The (311) regions appear roughly as large hexagons, the (110) as smaller diamonds, and the (111) as still smaller triangles. At the end of about a minute, small bluish gray spots began to appear, first at the (100) pole position and then a t (210). The spots at the latter points may be faintly seen in figure 1(a), while that at the (100) pole is hidden by the spurious

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ALLAN T. GWATHMEY AND ARTHUR F. BENTON

black spot referred to above. Thus, in the more rapidly oxidizing regions shown by the dark lines or lanes in figure l(a), the above points have the greatest rate of oxidation. This will be borne out in the other photographs. The blue spots within the brown-red lanes grew in size until a t the end of about 10 min. they had joined one another, changing the red lanes to blue with anarrow red border. At this time the (311), (110),and (111) areas had oxidized appreciably, as shown by the appearance of a tan color. The points of maximum rate of color change, as shown by the blue spots, soon began to change to a straw color. The (311) and (110) regions also turned deeper red and the small (111) regions merged into the blue of the connecting lanes which slowly increased

FIG. 2. Micrograph a t the (100) pole after heating in air at atmospheric pressure and 200°C. for 32 hr. Magnification 135 diameters. FIG. 3. Crystal heated for 13 min. at 550°C. in air a t a pressure of 7 mm. of mercury. (a) specular reflection from the (311) area; (b) micrograph at the (311) pole, magnification 600 diameters. FIG.4. Crystal heated for 6 min. a t 550°C. in oxygen at a pressure of 5 mm. Looking normal to the (100) pole.

in width for about 2 hr., after which time their boundaries remained about constant. After 32 hr. the pattern had changed its colors considerably, but the important areas could still easily be identified and the relative rates of oxidation of some of the regions could be determined. The most striking feature was the small area near the (100) pole, which had oxidized sufficiently to begome quite rough and to force small particles of the oxide film to buckle and scale off, aa shown in the photomicrograph in figure 2. This can also be seen with the unaided eye. Contrasted with this was the (311) area, which had become purplish colored a t its center but remained quite smooth when examined under the microscope. Both the slow rate of color change and the continued smoothness of these (311) regions indicated very low rate of oxidation. The (110) areas appeared to be positions of low rate also. It is surprising that the regularity of the pattern wm preserved for such a great length of time, and it appeared

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that it might have continued for a much longer time. No rearrangement of the metal atoms to produce regular step-like formations took place a t 20OoC. In order to assure that the results obtained with spherical surfaces would also hold for plane surfaces, flat regions about 1/4 in. in diameter were filed on a sphere, one parallel to a (311) plane and another to a (100) plane. The surface was then polished in the usual way and oxidized a t 200°C. The colors on these plane surfaces followed accurately those a t the correfiponding pole positions on the spherical surface. A freshly polished crystal was heated at 550°C. in air at 7 mm. pressure for 13 min. to determine whether the higher temperature would give sufficient mobility to the metal atoms to allow a rearrangement of these atoms, or a formation of the oxide, into step-like layers along special crystal planes. Since the oxide layer formed in this case was too thick to produce color films and appeared as a reddish gray color showing only a faint pattern, the complete pattern could not be satisfactorily photographed. But several very striking features could be identified and photographed. If the crystal was examined in a closed room by means of a beam of light, a very striking specular reflection w&sobtained from any one of the twenty-four (311) regions when the beam w~tsdirected a t the pole position of that region. A photograph of one of these reflections, shown in figure 3(a), is a little more striking than the actual crystal appeared. The reason for the reflections from these regions may be seen in the photomicrograph of this area shown in figure 3(b). The oxide had formed in definite steps or facets parallel to the (311) plane. A crystal heated under approximately the same conditions a t 400°C. showed the same general type of pattern but fainter . The development of facets along these planes may be easily explained in terms of the information just described. I t was found that surfaces approximately parallel to the (311) plane were oxidized a t the minimum rate. I t has also been previously established (5) in the growth of crystals that the plane on which deposition takes place a t the slowest rate relative to the others is the plane which attains maximum development. It is therefore to be expected that surfaces parallel to the (311) plane will be developed, as is the case. Several experiments were conducted on heating a crystal under more drastic conditions. While no essentially different features were observed, the results will be briefly described in order to relate them to those previously obtained. When a freshly polished crystal was heated a t 550OC. in pure oxygen at 5 mm. for 5 min., the oxidation proceeded to a greater extent than with air. The crystal had a redder appearance and the regions of maximum oxidation were covered with a dull gray deposit which under the microscope showed greater roughness than the other regions. This type of pattern was difficult to photograph but an attempt is shown in figure 4. The lines connecting the square a t the (100) pole to the diamond-shaped region a t (110) showed high oxidation. The square a t the (100) pole was also a region of high oxidation. I t was somewhat larger than before but a t its center a small spot appeared which apparently had not reacted greatly. The connecting lines around the (110) region did not

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ALLAN T. GWATHMEY AND ARTHUR F. BENTON

appear, but four spots a t the corners of these regions showed a high oxidation. The (311) regions appeared brownish in color and relatively smooth, showing a low rate of oxidation. Faint specular reflections were obtained from these regions. A crystal, without preheating in hydrogen, was heated to 1OOO"C.in air a t 3 mm. pressure and allowed to cool in air a t the same pressure over a period of several hours. Specular reflections were obtained from the (311)regions. The square areas a t the (100)poles and the connecting lines running between these poles showed maximum rate of oxidation. The (111)regions showed .medium rate of oxidation. A number of experiments were carried out to determine the effect on the lattice of a number of alternate oxidations and reductions a t increasingly higher pressures of air. If a crystal, on which a definite pattern had been formed by heating a t 565°C.for 25 min. in air a t 3 mm., was heated in hydrogen a t about 350°C.,the colors due to the oxide were destroyed but a definite pattern composed of frosty-looking areas remained owing to a slightly roughened surface a t these positions. If the heating in hydrogen was continued for about 15 min. a t 550°C.,the surface of the crystal became quite smooth and shiny again. Thus, there seemed to be two effects. At 350OC.or lower the oxide was reduced but a t the higher temperatures a type of sintering took place, as shown by the rearrangement of the atoms in the roughened areas to produce a smooth surface. A second oxidation a t a pressure of 3 mm. produced a striking pattern similar to the first oxidation, and when the treatment was repeated three or four times without repolishing approximately the same result was obtained. Finally, the oxidations and reductions were continued, using higher pressures of air, until in the neighborhood of 200 mm. small particles began to flake off when the crystal was cooled to room temperature. In order to determine the dependence of oxidation pattern on smoothness and chemical treatment of the surface, several crystals were etched with different reagents which gave markedly different types of etch patterns. The reagents used were as follows: 2 parts of nitric acid to 1 part of water; 4 g. of cupric chloride in 100 cc. of concentrated hydrochloric acid, which largely develops (100)planes; 10 g. of ammonium persulfate in 35 cc. of concentrated ammonium hydroxide and 65 cc. of water, which largely develops (111)planes. Another crystal was electrolytically etched in phosphoric acid to give a definite pattern. When oxidized in air a t atmospheric pressure and 200'C., according to the usual procedure, all four of the crystals gave patterns of the same general type. The absolute rates of the various regions varied, but the relative rates on any one crystal remained approximately the same. The regions of minimum rate shifted slightly from the (311)towards the (522)positions and the regions which had corresponded to the (210)positions shifted slightly towards the (520). In order to determine the effect on the pattern of annealing a t a high temperature prior to oxidation, a crystal after electrolytic polishing was heated in hydrogen above 900°C.for 8 hr. It was then cooled to room temperature, exposed to the air, placed in the reaction chamber, heated in hydrogen a t 550"C.,and oxidized a t 200°C.according to the usual procedure. In general, the same type

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of pattern was obtained as with the usual procedure. The region of minlmum rate shifted slightly towards the (522) position and the (110) region was oxidized more rapidly than the (111). Ad crystal was electrolytically etched in phosphoric acid solution and then heated in hydrogen above 900°C. for about 3 hr. When the crystal was removed and examined, only a slight trace of the etch pattern remained and the surface was quite smooth and shiny. When the crystal was oxidized a t 200OC. according to the usual procedure, a pattern similar to the one just described wm obtained. A crystal was oxidized in air a t atmospheric pressure and 300OC. for 80 min. The (311) regions had a pinkish tan color and remained quite smooth, but the remaining areas were covered with a grayish black deposit which appeared warped and cracked when examined with a watchmaker's lens. The difference between the two types of regions is quite striking. The practical importance of the variation in rate is strikingly shown in this experiment by the fact that, when the sphere was rubbed with soft tissue paper, the (311) regions remained unchanged but the black deposit in the remaining areas scaled off quite easily, leaving bright copper exposed. Thus the same general type of oxidation pattern was obtained when the surface prior to oxidation wm treated with widely different reagents. This should not be understood to mean that all copper surfaces, regardless of how they are prepared, will necessarily give this same variation in rate of oxidation with crystal plane, for the rate will be influenced by foreign particles adsorbed on the surface. An attempt was made in these experiments, however, to remove such foreign particles. SUMMARY AND DISCUSSION OF RESULTS

The important results of experiments in which the surface was prepared by electrolytic polishing followed by annealing in hydrogen a t 550OC. may be briefly summarized. The relative rates of oxidation in air a t 200°C. and atmospheric pressure were, in the order of decreasing rates: (100) and (210) regions; boundary lines between two (311) regions; boundary lines between (311) and (110) regions; (111) regions; (110) regions; and (311) regions. These regions are shown in figure 5, those with the greater rates as black areas or heavy lines. KO appreciable shifts were found in the location of regions of maximum rates with temperature changes of 20" to 40"C., as were reported by Lustman and Mehl (18) for thinner films near 150OC. In the neighborhood of 500'C. there was some change in the order of relative rates but, judging from the color and relative roughness of the oxide film, the (100) and (210) regions continued to be the most reactive. Judged by the continued smoothness of the surface and by the development of definite crystal facets, the (311) regions remained the least reactive. When the surface, after being electrolytically polished, was treated with various reagents in order to give varying degrees of roughness prior to oxidation, the region of minimum rate a t 200°C. shifted slightly from the (311) position, and in some cases the (110) region became an area of high rate. With these

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exceptions the patterns were approximately the same as those obtained after electrolytic polishing. These results can be interpreted qualitatively in terms of simple concepts. During the initial stage of oxidation it would be expected, aa a first approximation, that the planes having the least residual affinity or the greatest reticular density would be the least reactive. In the case of copper the planes with greatest density are, in decreasing order: ( l l l ) , (loo), (110), (311), (331), (210), etc. Thus the planes near the beginning of the list would be expected to be the least reactive. With the exception of the (100) plane, this prediction in general seems to be confirmed, although the order does not follow strictly the above list. Also with the exception of the (100) plane, the regions having maximum rates were those which take the place of corners of edges on a polyhedron

FIG.5. Sketch showing regions of higher rates of oxidation in air at atmospheric pressure and 200°C. Regions of high rates shown by black areas and lines.

the faces of which would correspond to the least reactive planes. These boundary regions have low density, or high residual affinity, andwould beexpected to show greater activity. They may be seen in figure l(a) as the dark lines. This suggests that it is not just the apparent physical sharpness which may account for increased activity of edges and corners of crystals but the fact that planes of greater activity are exposed in these small regions. Edges which are sharp to the eye probably consist of a series of plane regions on an atomic scale. Stransky (24) has pointed out that these regions are crystallographically exceptional ones. Schwab and Rudolph (22) have found evidence for the increased catalytic activity of such regions. The mechanics of the reaction is probably not as simple as the above picture suggests. Quantum-mechanical considerations (23) indicate that the active part of a surface is dependent on a particular configuration of atoms such as would be obtained in a definite crystal plane. Also, variations in the rate of diffusion of oxygen through the oxide layer on the different crystal faces may play a controlling part aa the thickness of the layer becomes appreciable. The

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slight shift in position or change in size of some of the regions when the surface was previously roughened by various etching reagents may be due to variations in rate of diffusion of oxygen through the oxide layer formed on roughened surfaces. However, superficial roughness up to a certain point should exert only a minor influence; for, after oxidatian has taken place to a sufficient thickness to produce interference films, the boundary region between oxide and metal along which the reaction is taking place has probably lost its original roughness. The absolute rates, the exact location, and size of the various regions appear to be somewhat dependent on the roughness, and hence preparation, of the surface, but the relative rates and approximate location of the majority of regions seem to be largely independent of the surface roughness. The development of definite microscopic facets a t the higher temperatures showed that a t temperatures as low &s 40OOC. copper atoms migrated great distances, in terms of atomic dimensions, to take up their position in the oxide lattice above the underlying metal. Up to a certain point the underlying metal exerted an orientating influence on these facets, but under more drastic conditions, t w shown by alternate oxidations and reductions, the oxide formed was permanently disrupted from the underlying metal. The use of crystals in the shape of spheres has the advantage of making it possible to follow a t one time under the same conditions the oxidation of surfaces parallel to every possible crystal plane. The patterns obtained shduld serve as valuable guides in selecting for quantitative study on plane surfaces the regions which have the most striking oxidation characteristics. They also emphasize the necessity of studying surface reactions in terms of the individual properties of the various parts of the surface. REFERENCES ANDRADE, E . N . DAC.:Trans. Faraday Soc. 31, 1137 (1935). BEECK,O., SMITH,A. E., AND WHEELER, A,: Proc. Roy. Soc. (London) Al77, 62 (1940). BEILBY,G.: Aggregation and Flow ofSolids. The Macmillan Company, London (1921). CONSTABLE, F. H.: Proc. Roy. Soc. (London) Al17, 386 (1928). DESCH,C. H.: The Chemistry of Solids, Chap. 11. Cornell University Press, Ithaca, New York (1934). (6) EDWARDS, H. W., AND PETERSEN, R. P.: Phys. Rev. 42,407 (1936). (7) ELAM,C. F.: Trans. Faraday SOC. 32, 1604 (1936). (8) EVANS,U. R . : Metallic Corrosion, Passivity and Protection, p. 672. Edward Arnold, London (1937). (9) FINCH,G. I., MURISON,C. A,, STUART,N., A N D THOMSON, G. P.: Proc. Roy. SOC. (London) Ala,414 (1933). (10) FINCH,G. I., QUARRELL, A. G., A N D WILMAN, H.: Trans. Faraday SOC.S1, 1051 (1935). (11) FINCH,G.I., A N D WILMAN, H.: Ergeb. exakt. Naturw. 18,353 (1937). A. T., A N D RENTON, A. F . : Trans. Electrochem. SOC.TI, 211 (1940). (12) GWATHMEY, (13) GWATHMEY, A. T., AND BENTON, A. F.: J. Chem. Phys. 8,431 (1940). (14) GWATHMEY, A. T., A N D BENTON, A. F.: J. Chem. Phys. 8, 569 (1940). (15) GWATHMEY, A. T., AND BENTON, A. F.: J. Phys. Chem. 44.35 (1940); Trans. Electrochem. SOC.TI, 211 (1940). (16) HAUSSER, K. W., AND SCHOLZ,P.: Wiss. Veroffent. Siemens-Konzern 6, 144 (1927). (17) JOHNSON, R. P.: Phys. Rev. 64.459 (1938). (1) (2) (3) (4) (5)

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(IS) LOSTMAN, B . , AND MEHL,R. F . : Am. Inst. llining Met. Engrs., Tech. Pub. No. 1317 (1941). (19) ~ I A R T I S. N ,T: Phys. Rev. 63, 937 (1938); 46, 947 (1939). (20) MILEY,H . .4.: J . Am. Chem. S O C .69,2626 (1937). (21) PRESTON, G . D., AND BIRCUMSHAW, L . L.: Phil. Mag. 21,713 (1936); 20, 706 (1936). (22) ~ C H W A B ,G. M., A N D RUDOLPH, L . : Z. physik. Chem. Bl2,427 (1931). (23) SHERMAN, A . , AND EYRING, H . : J. 4111.Chem. SOC.64, 2661 (1932). (24) STR?LNFSKY, I . : z. physik. Chem. B11.342 (1931); Z. Krist. 78, 373 (1931); 88, 325 (1934). (25) TAMM4NN, G . :J. Inst. Metals 44,29 (1930). (26) T A M M A NG., N , AND S.4RTORIUS, F.: z. anorg. allgem. Chem. 176, 97 (1928).

O S T H E THEORY OF GALVANIC CELLS SUBJECT TO FIELDS O F FORCE. I1 THEELECTRIC AND F. 0. KOENIG

THE

AND

MAGNETIC FIELD^

S. W . GRINNELL

Department of Chemistry, Stanford University, California Received July 18, 1948 I . INTRODUCTION

In two previous papers (6, 7) we have analyzed the thermodynamics of galvanic cells subject to gravitational fields, Our object in the present paper is to extend this analysis to stationary electric and magnetic fields, respectively. We shall find that while the case of the electric field is unique, there is a high degree of formal resemblance between the magnetic and the gravitational cases, manifest on the one hand in the fact that the magnetic induction B (or its square, B’) plays a r81e analogous to that of the gravitational potential (o, and on the other hand in the conclusion-which we regard as the chief result of this study-that for the magnetic field the form of the condition for quasi-reversible conduction (“qrc. condition”) is the same as that previousljr established (6) for the gravitational field, namely

in which the integral extends over the solution in the cell. This conclusion is perhaps unexpected, in view of the fact that the transport of components through an electrolyte solution permeated by a magnetic field affects both the solution and the entire surrounding space, whereas in the gravitationalcase only the solution is affected. After proving this result we shall use it to deduce formulae for the E.M.F. of galvanic cells in magnetic fields. By means of some of these 1 Sections 111, IV, VIII, I X , and X of this paper were taken largely from the dissertittion submitted by S. W. Grinnell t o the Faculty of Stanford University in partial fulfillment of the requirements for the degree of Doctor of Philosophy, July, 1938.