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By J. B. Newkirk, D. L. Martin, A. H. Geisler, R. Smoluchowski

A FUNDAMENTAL investigation of the mecha-nism of the ordering reaction and of the accompanying changes in properties has been undertaken, since an extensive study of this process could well contribute to the knowledge of phase transitions in alloys. Cobalt-platinum alloys were chosen for the study since they exhibit interesting and unusual permanent magnet properties.1,2. In addition, the ordering reaction in cobalt-platinum alloys is a convenient one to study experimentally because of the high maximum ordering temperature, the large difference in the X-ray scattering power of cobalt and platinum atoms, and the relative ease with which the alloys can be plastically worked into wire and strip. In the early stages of this study, it became apparent that the published phase diagrams&apos;, &apos; of the cobalt-platinum system contained questionable features, in the region of 40 to 60 atomic pct Co, which were considered in another publication by the authors.4 That portion of the research reported elsewhere on the equilibrium states of cobalt-platinum alloys does not confirm the presence of a previously reported, high temperature disordered tetragonal phase and a low temperature body-centered cubic phase. On the other hand, the structure of the ordered phase is face-centered tetragonal with an atomic distribution analogous to that of CuAu.4 This lattice forms from the disordered face-centered cubic phase in such an orientation that the <100> directions are parallel to the <100> direc-tions of the disordered phase. At compositions other than the ideal 50 atomic pct the ordered phase can exist in equilibrium at high temperatures with the disordered phase. A Widmanstatten pattern of plate-like particles of the ordered phase parallel to (110) planes of the disordered matrix is observed when an initially disordered alloy is held at these temperatures. The temperature range of the two-phase region has been determined for three alloys by X-ray diffraction analyses, microscopic examination, and electrical resistivity measurements, and these results are incorporated with some of those of Gebhardt and Köster in the revised phase diagram of fig. 1. The purpose of the investigation reported here was to examine the mechanism of ordering in co-balt-platinum alloys by X-ray diffraction and metal-

Jan 1, 1951

By J. B. Newkirk, A. H. Geisler

The alloy Cu4Pd has a disordered face-centered-cubic structure when quenched from temperatures between 478ºC and the melting point (about 1100°C). Below 478ºC an ordered phase is stable. The results of a Debye-Scherrer X-ray analysis indicate that the ordered phase has a tetragonal unit cell described by the space group C24h — P42/mt with 2 Cu in 2a, 2 Cu in 2f, 4 Cu in 4j (x = 0.2, y = 0.6), 4Pd in 4j (x = 0.4, y = 0.2), and 8 Cu in 8k (x = 0.1, y = 0.3). The orientation relationship between the face-centered-cubic phase and the ordered tetragonal phase is given by: [100],,. // [130]al,. COO1Ia.d.//COO1I,,.. • The behavior of Cu,Pd is typical of ordering alloys except that the transformation is very sluggish. The increase in hardness and the microstructural and X-ray diffraction effects are interpreted in terms of coherency strains caused by the ordering. AN anomalous construction in the Cu-Pd phase diagram (Fig. 1) was reported in 1939 and has been allowed to stand without further published attention since that time. The odd figuration about the composition 10 to 27 atomic pct Pd is derived mostly from the work of Jones and Sykes.1 Evidently several features of this binary system require further study if the constitutional forms are to be well understood. The present paper includes a study of one of these features, that is, the crystal structure of a single ordered alloy containing nominally 20 atomic pct Pd. This choice of composition was suggested by the work of Harker and associates who determined the structure of Ni4Mo2 and Ni4W.3 The nature of the ordering process in Cu4Pd was studied also by observing the hardness, microstructure, and Debye-Scherrer patterns of specimens which had been aged at various temperatures after quenching from an initial disordering treatment. Experimental Methods A 20 gram ingot of Cu4Pd was made by melting spectrographically standardized copper from Johnson, Matthey, and Co., and commercially pure (99.5 + ) palladium in an argon-filled quartz tube. Chemical analysis showed that the ingot contained 80.0 atomic pct Cu. The ingot was rolled about 60 pct to a strip 0.060 in. thick and was homogenized for 16 hr at 950°C in low pressure argon. Rods cut from the rolled strip were worked into wire 0.015 in. in diameter, and specimens for hardness and microscopic examination were cut from the remaining strip. All specimens, with the exception of some of the wire, were given an initial disordering treatment by heating for 16 hr at 950°C, followed by water quenching. A 10 cm length of as-drawn wire was water quenched after being held in a temperature-gradient furnace4 for 89 days. Room-temperature Debye-Scherrer photograms were then made at points along the wire to determine the temperature below which the ordered phase was stable. Although the accuracy of temperature determination in the gradient was only about ±10 °C, the temperature gradient was sufficiently gradual that the sensitivity was much better and locations which had differed by as little as 1°C could be distinguished. An analysis of the crystal structure of the well ordered alloy was made by X-ray diffraction using a specimen cut from this wire. The change of Debye-Scherrer pattern as ordering progressed was studied by using isothermally aged samples of initially disordered wires. The wires were sealed under low-pressure argon in small quartz tubes for heat treatment. After the aging treatment, the tubes were quenched in water and photograms were made at room temperature in a 10 cm diam camera using filtered Cu kX. (A = 1.540511) Hardness was measured on a Vickers hardness tester using a 10 kg load and 2/3 in. objective lens. Reported values are the average of at least three impressions made on flat specimens 0.060 in. thick. After the hardness of a heat-treated sample had been measured, it was resealed in low-pressure argon and returned to the furnace for continued aging at the same temperature. In this way, two samples served for all aging times at each temperature. Hardness specimens which had been aged 500 hr or more were used for metallographic examination after the final aging treatment. A dilute potassium-dichromate etching solution was used.

Jan 1, 1955

By P. G. Shewmon, F. R. Winslow

An experimental method is describedfor Ihe determination of the derivative of the surface free energy (y,) with surface orientation using symmetric bicrystals. The method measures the equilibrium root-angle of grain boundary grooves for the same grain boundary on two different surfaces. In contrast to previous methods, the presence of annealing twins is not necessary. Results on silver at 900°C indicate that ??s/?3 is 0.014y, on the (loo), 0.075y, on the (111), and < 0.004?s on the (110). DURING an investigation of the kinetics of grain-boundary grooving on silver&apos; values of the derivative of the surface free energy ?s with respect to orientation were needed. Previous investigations of these so-called torque terms show that, for low-index planes in copper2 and nickel,&apos; a finite derivative exists even near the melting point. These two studies give the only previously published values of the torque on low-index metal surfaces. These investigators measured the equilibrium root angles, both greater than and less than 180 deg, along the lines where a twin boundary intersects a free surface. The technique described here is suitable for materials which do not have annealing twins, and enables the surface for study to be chosen instead of having to work in a direction normal to the twin trace on the surface. The purpose of this paper is to describe this new technique and to report the values found for the (111): (100), and (110) surfaces of silver. To check the technique proposed above, a series of 99.99 pct Ag bicrystals were used. These bicrystals were grown from the melt by a modified Bridge-man technique so that a low-index direction was parallel to the growth direction. Two orthogonal faces were studied on each bicrystal. One of these contained the low index or simple plane normal to

Jan 1, 1963

By F. R. Brotzen, D. L. Davidson

ALTHOUGH much effort has been devoted to the problem, the nature of plastic flow in bcc metals is still not fully understood. Some of the difficulties encountered stem from the scarcity of information on orientation effects and the uncertainty as to the glide system in these metals. In an attempt to provide some of this information, the present investigation was carried out, using zone-refined molybdenum single crystals deformed in tension and in direct shear. Considerable evidence exists to indicate that the primary slip system for molybdenum is (110) <111>.1,2 Figs. 1 and 2 indicate that this is, indeed, the case for direct shear at room temperature (see Ref. 3 for a description of the shear-testing equipment and procedure). Moreover, from Fig. 2, the shear stress on the (123) is lower than that on the (112). This would be the case if, as has been suggested,4,5 slip on these two planes is in reality com-

Jan 1, 1965

By A. G. Metcalfe, R. P. Elliott, F. A. Crossley

THE texture method (utilizing monochromatic copper radiation) was applied to determine the orientation of the columnar grains of two vacuum cast beryllium ingots of 3 in. diam. Samples were mounted in a fixture as illustrated in Fig. 1, which permitted rotation and translation in order to approximate the method used for wires. The specimens were aligned so that the major axes of the columnar grains were parallel. Rotation was around the growth direction. After each translation the specimen holder was rotated 2 deg (1 deg for the samples from the second ingot) until a range of 30 deg on either side of the vertical was covered. The speed of translation was 1 mm per sec. A representative Debye pattern is shown in Fig. 2. The pattern was compared with theoretical patterns for various orientations. Also shown in Fig. 2 is the disposition of reflections on the (10i0), (0002), and (1011) Debye rings for the two possibilities that growth is either in the <10i0> or <ll30> direction. It is apparent that no significant preference for the direction of columnar growth is indicated. It is considered that the lack of a preferred orientation is due to the occurrence of the phase transformation (reported by Martin and oore&apos; to occur above 1250 "C) which masked the original solidification orientation. This research was supported by the United States Air Force under Contract No. AF 33(616)-5911, monitored by the Materials Central, WADD, Wright-Patterson Air Force Base.

Jan 1, 1962

By Y. C. Liu

The orientation relationship between the dejormation and recrystallization textztres of binary Cu-P alloys of high phosphorus content was observed to he a ± 14-deg (110) rotation. According to the ori-ented-gvowth hypothesis, the same relationship should exist between a successfully flowing pain and the strained single-crystal matrix of alloys of corresponding composition. The orientations of thirty successfully growing grains were obtained in a Cu-1.0 at. pct P alloy. Both a conventional analysis and the more detailed analysis advanced in the present study demonstrate that the observed orientation relationship is not comparahle to that predicted by the oriented growth hypothesis. IT has been shown experimentally that the formation of recrystallization textures in metals may be explained on the basis of the oriented-growth hypothesis. This conclusion is based primarily on the results of cooperative experiments carried out by various investigators in aluminum. Beck and HU&apos; suggested that the orientation relationship between the recrystallization and deformation textures of aluminum is a 38-deg(111) rotation. A similar relationship, i.e., a 40-deg(111) rotation, was observed between the primary and secondary recrys-tallization textures.&apos; Since the secondary grains result from a process of selective growth, this naturally implies that the same mechanism is also responsible for the formation of the primary re-crystallization texture from the deformed matrix. Further evidence was provided by the experiments of Liebmann, Liicke, and Massing3 and Yoshida, Liebmann, and Lucke.4 They observed that grains which could successfully grow into strained aluminum single crystals invariably exhibited the same orientation relationships with their matrix. Thus, regardless of other opinions,5&apos;9 these results offered good evidence in favor of the oriented-growth hypothesis. In order to examine broader applications of this oriented-growth hypothesis, experiments should be carried out in metals other than aluminum. In a recent investigation on the recrystallization textures of binary copper alloys with phosphorus, arsenic, and antimony,7 it was found that the predominant recrystallization components were related to the deformation textures by a (110) rotation. The (110) rotational relationship is different from the (111) relationship generally proposed between the recrystallization and deformation components of other binary copper alloys. 1,8,9 Applying the observations made for aluminum, the oriented-growth hypothesis predicts that the orientation relationship of grains successfully growing into the strained single crystals of either one of these copper alloys should correspond to that observed in the textural study. Verification of this prediction would provide a critical test of general applicability of the oriented-growth hypothesis to the formation of recrystallization textures in fcc metals other than aluminum. The Cu-1.0 at. pct P alloy was selected in the

Jan 1, 1964

By J. Fageant, W. C. Ellis

All major regions in a progressively solidified germanium ingot were related through successive orders of octahedral twinning. The occurrence of lineage structure and the generation and survival of orientations are discussed. WHEN metals solidify in a temperature gradient a preferred orientation, or casting texture, usually develops. For example, in face-centered and body-centered cubic metals, most of the solidifying crystals have a cube axis, <loo>, aligned approximately in the freezing direction.&apos; In the solidification of diamond cubic metals this is not the case, since there is a natural tendency to form twin orientations.&apos; . In this paper, twinning relationships in cast germanium are described; some conclusions with respect to nucleation and survival of new orientations are discussed. In the first experiment, an ingot of high purity germanium, % in. in diameter and 1 % in. in length, was formed by progressive solidification4 from the bottom. The ingot was cut into 21 slices, each circular and about 0.030 in. thick. The top surface of each slice was polished and etched to reveal the regions of different orientations. Orientations were determined by the Laue X-ray back-reflection method. The uncertainty in the determined orientation relationships was l" or 2" when separate slices and films were involved. Frequently, however, advantage was taken of illuminating across a boundary when the patterns of the two orientations were recorded on the same film. The uncertainty then was less than 1". Often the twin relation was evident from common zones or individual reflections. Twin relationships were recognized through comparison of the values of the nine angles between cube poles of the two orientations with those calculated for successive orders of octahedral twinning. The birth and survival of each region can be reconstructed by visual examination of the etched slices shown in Fig. 1. In slice 21, where solidification began, many regions are present; these regions were found to be twin-related. Solidification appears to have started from one nucleus formed probably at the wall of the crucible.* Subsequent ori- entations were developed by nucleation on existing solid surfaces, and only in the twin relationship. This is an example of a general process of nucleation on a surface of existing solid and may be descriptively termed oriented nuc1eation.t In germanium, and other diamond cubic substances, the orienting habit is that of twinning on an octahedral plane.&apos; " The prevalence of straight traces in the polished surfaces of succeeding slices (Fig. 1) suggests that the twinning observed in the first slice persisted throughout solidification. This was confirmed by X-ray determinations. The schematic diagram of Fig. 2 shows the twinning relationships of the major regions throughout the ingot. Since all observed relationships are describable as twinning, it is reasonable to conclude that no random nucleation occurred in the freezing of the ingot. An alternative possibility would be that nucleation of a random nature occurred, but only those nuclei in twin orientations survived in subsequent growth. This is unlikely for there would be as good a reason for the growth of randomly oriented nuclei as for the growth of the many different orientations present after several orders of twinning. The many twin components contain a wide distribution of orientations, and did grow. In fact, they are the only ones found in the solid. The conditions of solidification of this ingot were such as to discourage nucleation of crystals wholly in the liquid. The rate of solidification was 0.125 in. per min. This slow rate of heat removal afforded but small opportunity for supercooling within the liquid —a condition needed to provide enough decrease in free energy for such nucleation. When nucleation occurs on an existing solid surface, the interfacial energy between the existing and forming regions is important in determining the new stable orientation. The new orientation is expected to be one which minimizes this energy. In the diamond cubic structure, the interface for the

Jan 1, 1955

By L. F. Mondolfo, B. E. Sundquist

The crystallographic orientation relationships resulting when lead is nucleated from the liquid by Ni, Cu, Ag, and Ge were determined. For each nucleating agent several definite orientatioz relationships were found. These relationships seemed to be controlled by good symmetry relations and low crystallographic disregistry between mating planes. For any given nucleating agent the under colling for nucleation was found fairly constant and independent of the orientation relationship and consequent disregistry. It was also found that, upon re melting and refreezing the Pb, the orientation relationship was changed. These findings prove that crystallographic disregistry is not the controlling factor in heterogeneous nucleation from the liquid. The results of this investigation tend to confirm the theory presented in a preceding paper that heterogeneous nucleation starts with the formation of an adsorbed layer of nucleated metal on the nucleat-ing impurity. Evidence is given that cavities in the nucleating agent act as centers of nucleation. IT has long been known&apos; that solid extraneous particles are active in catalyzing phase transformations that occur in a system, particularly condensation and crystallization. It is well established that these heterogeneities act as catalysts by providing surfaces upon which nuclei of the precipitating phase can form with activation energies smaller than those required for homogeneous nucleation. Numerous investigations have shown that in this process of heterogeneous nucleation: a) the nucleus forms with one, or several, definite crystallographic orientation relationships with the nucleating phase2-4 and b) that there is a small range of undercoolings or super saturations characteristic of the nucleation of a given solid on a given Substrate.5-10 Turnbull and vonnegut11 have developed a theory based on theories developed by Volmer12 and Turn-bull and Fisher1= for heterogeneous nucleation from gases and liquids, that relates the super saturation or undercooling required for nucleation to the dis-registry between the lattices of the nucleus and the nucleating agent. This theory predicts that nucleation should occur with the orientation relationship between the nucleus and nucleating agent that minimizes the disregistry. Further, it predicts that the undercooling or super saturation necessary for nucleation should be a function of the disregistry. Numerous investigations have dealt with the orientation relationships resulting from the condensation of vapors onto crystalline solid substrates2,3 and a few with the nucleation of one phase by a second phase in solidification4,14. Others have dealt with the supersaturation8-10 and undercooling5-7 associated with nucleation in condensation and solidification respectively. However, there is virtually no report that gives both of these factors for the same system. In this investigation a study was made of the undercoolings and orientation relationships resulting when Pb is nucleated from the liquid by Ni, Cu, Ag, and Ge. It was the purpose of this investigation to check the Turnbull-Vonnegut theory, i.e., the importance of crystallographic disregistry between nucleating catalyst and nucleated metal. The results indicate that disregistry is not an important factor in nucleation and that the nucleation process is probably somewhat more complex than current theories suggest. EXPERMENTAL PROCEDURE Small single crystals of nickel, copper, silver, and germanium were prepared from materials of four to five nines purity, and the Pb used was also 99.999+ pet pure. Cu and Ag single crystals were prepared by sealing small chips of Cu or Ag in an evacuated quartz capsule and heating the capsule at 2000°F for 1 hr before cooling. Nickel crystals of 200 diam were also prepared in evacuated quartz capsules, but melting was done by heating the capsules in an oxy-acetylene flame for a few minutes. These spheres were invariably polycrystalline so

Jan 1, 1962

By J. N. Hobstetter, J. J. Becker

Deformed copper single crystals exhibited, upon annealing, a recrystallized twinned grain with a twin plane parallel to an active deformation plane, rotated approximately 22" about its pole, or else did not recrystallize at all. If extraneous deformation was not carefully removed, no simple orientation relationship was found. RECRYSTALLIZATION textures have been a subject of practical interest for many years, but any real understanding of their formation will have to start with a study of the recrystallization of carefully deformed single crystals. Some efforts have been made in this direction,&apos;-&apos; but much more experimental information is needed before a satisfactory picture of the crystallography of recrystallization can be formed. This paper reports a few results in copper single crystals. The crystals studied in this investigation were grown by the Bridgman method," and their orientations determined by the back-reflection Laue technique." Some specimens were simply deformed in compression, others were sheared, and still others tested in a rotating-grip device, in attempts to remove end constraints. The details of their deformation behavior are described elsewhere.&apos; The deformed specimens were annealed and the orientations of the recrystallized grains were determined optically, as described by Barrett and Levenson.8 Compressed Specimens Specimen 17-A, whose orientation is given in Fig. 1, was compressed to a total of 19 pct. As observed before,&apos; increasing deformation took place by increasing density of slip lines in initially formed clusters, with little if any formation of new slip clusters in unslipped areas. The specimen was then etched in nitric acid until its length had been reduced from 0.766 to 0.735 in. It was annealed at 1000°C, in increments of a few minutes. After 63 min, two small grains had appeared in the center, Fig. 2. They were found to be twinned with respect to each other (AB, Fig. 4). After 30 min more, the specimen was completely recrystallized. A typical view of it is given in Fig. 3. A summary of all orientations found is given in Fig. 4, in which the prominent grain G is in (001) standard projection, and the poles of the active slip planes after deformation are indicated by SP (primary slip plane), CrSP (cross-slip plane), and CnSP (conjugate slip plane). All the orientations found were related through seven orders of twinning. A "family tree" of these twins is given in Fig. 5. Furthermore, the BG twin composition plane lies close to the cross-slip plane

Jan 1, 1954

By R. H. Hiltz, R. W. Douglass

Large-grain specimens of iodide titanium prepared metal-lographically were stain etched using the technique of New York University as modified by Watertown Arsenal Laboratories. Orientations of grains showing an abnormal response to stain etching were determined by back-reflection X-ray techniques. X-ray results showed that a-titanium grains, oriented such that their basal planes were parallel to the polished surface, have a slower reactivity to stain etching than any other orientation. Grains oriented such that their basal planes made small angles with the polished surface exhibited reaction rates between that of the true basal orientation and the normal rate. As the angle with the surface increases the reactivity increases up to a maximum angle of 14 deg. Basal planes making an angle with the surface of greater than 14 deg show normal reactivity to stain etching. These data, plus work on polycrystalline specimens, indicate that the oxidation rate of titanium might be reduced by correct alignment of crystal planes. ThE earliest observed phenomenon in the micrography of titanium was the occurrence of a grains which exhibited no birefringency. Even though a titanium possesses a hexagonal-close-packed structure and should be optically anisotropic, it can appear optically isotropic, when the crystal is so oriented that its intersection with the polished surface is perpendicular to the axis of symmetry. During the develoment of color staining techniques for titanium: it was noted that the a phase did not stain uniformly. Staining of specimens of commercially pure titanium resulted in a micro-structure of blue-colored grains, among which were randomly oriented a few grains exhibiting colors between the initial yellow and the final blue color. Under polarized light, these off-colored grains appeared to be optically isotropic. More intense study with polarized light, however, showed only the yellow grains to be isotropic. The intermediate colored grains exhibited weak birefringency, which at first glance is not detectable due to the strong birefringency of the surrounding structure. Aminoff2 and Straumanis3 have previously shown that in zinc the basal orientation is less reactive than other orientations. Leidheiser4 showed the same thing to be true for the hexagonal-close -packed configuration of cobalt. Thus, it would appear that the basal-plane orientation is responsible for the abnormality in stained titanium. Later work by Leidheiser5 on cobalt has shown that other planes besides the basal plane exhibited reaction rates slower than the normal rate. Reported planes were the (100), the (1011) and several planes making small angles with the basal plane. The last observance appears not to be due to the reactivity of the reported plane but due to the reactivity of the basal plane which is very close to being parallel to the surface. There are, then, two possible explanations for the range of colors observed in stain-etched a titanium. Since extensive research on the effect of orientation on surface reaction has failed to provide any definite trend, these two explanations are not adequate in themselves. Planes showing the retarded reactivity differ not only for different crystal structures but for metals of the same crystal structure and even for different reactions of the same metal. Tragert,6 Leidheiser,7 Tammann,6 and wagner9 have shown copper to exhibit retarded reactivity on the (111) plane. However, Leidheiser10 has shown that under other conditions the retarded reactivity of copper is associated with the (100)

Jan 1, 1960

By A. J. Opinsky, J. L. Orehotsky, L. L. Seigle

TUNGSTEN incandescent lamp filaments possess a typical structure of elongated crystals generated upon heating the silica-alumina doped wire rapidly to 2200°C or above.&apos; It is known that these very long grains exhibit a preferred orientation, but there is disagreement in the literature about the direction. Rosi,2 and later Rieck; reported that the <135> direction of the large grains in doped wire tends to be parallel to the wire axis, but other investigators have reported that <110> is the preferred direction. Some further investigation of the orientations of large grains in tungsten wire is reported in the following. In the first series of experiments, 6-in. lengths of wire were heated rapidly in a bell jar. Current was passed through the wires and within 15 sec the wires had reached the grain coarsening temperature. 2 min was the annealing time. Wires were heated in hydrogen, nitrogen, and vacuum. Later, wires were heated in an evacuated tube furnace in which the tube was brought from 1000°C to the operating temperature within 25 sec and held 5 min at temperature. Temperatures were measured with an optical pyrometer. After heating, the wires were electro polished and etched, and the orientations of the large grains determined by the Laue back-reflection technique. Most of the experiments were carried out on a single spool of 5-mil silica-alumina doped wire, but a few tests were made with 5-mil thoriated tungsten wire and 10-mil undoped wire. 5-mil silica-alumina doped wires were reduced to smaller diameters by electropolishing for one series of experiments. Orientations of the large grains in silica-alumina doped wire heated in various atmospheres are presented in Figs. 1 and 2 as plots of the direction of the wire axis relative to the cube axes of the crystals. For most of the conditions studied, the preferred orientation cannot be described as a single direction, but the points might be said to group themselves about the arc passing through <110> and <113>. This arc is the trace of the (211) planes and contains the <135> and <124 as well as <011> directions previously observed by other investigators. The preferred orientation of large crystals in silica-alumina doped tungsten wire might be most generally described, therefore, by stating that a (211 ) tends to be parallel to the wire axis. This is true also for wires reduced in diameter by etching and furnace heated, Fig. 2, i.e., the recrystallization texture is apparently unchanged upon removal of the outer layers and substantially independent of the temperature gradient within the wire.

Jan 1, 1962

By T. N. Rhodin

There can be two types of films on solids, those which are stable in mono-layers and those which tend to aggregate into three dimensional structures. A great number of metal films formed by condensation onto a solid base are unstable in the sense that they will aggregate into crystals providing the atoms possess sufficient surface mobility. The crystalline structure of the film is strongly influenced by the base in many systems and, in some cases, a single orientation prevails when the force fields around the atoms in the supporting crystal are sufficiently strong.&apos; Relatively little is available in the literature about the nature of these forces and the role they play in promoting a preferred orientation of the atoms arriving at the substrate surface. An understanding of their periodicity and magnitude relative to the surface forces characteristic of the film itself should provide insight into the critical dependence of film orientation on the nature and temperature of the substrate. In addition, this effect may be very useful in preparing samples for surface studies. The study of the physical and chemical characteristics of pure metal surfaces has been severely handicapped by the presence of strongly adherent foreign films. Furthermore, the randomness of the surface orientation has obscured interpretation of experimental results. Evaporation of metals in high vacuum onto carefully selected substrates under ideal conditions for preferred orientation appears suited to the preparation of flat, oxide-free, oriented films for surface reaction studies. Many factors influence their structure and some understanding of the mechanism of their formation is a necessary prerequisite for obtaining satisfactory surfaces for study. The dominant factors in defining film structure are film thickness and growth rate and the nature, condition, and temperature of the substrate. GENERAL ASSEMBLY The system was enclosed in an 18 in. bell jar which rested on an L-shaped neoprene gasket on a ground steel plate as indicated in Fig 1. Rapid evacuation of the system to 10-6 mm mercury was facilitated by a 4 in. manifold, 2 in. packless valve, and an extra large diffusion pump. Suitable arrangement of valves on a secondary manifold readily permitted introduction of purified gases

Jan 1, 1950

By E. J. Whittenberger, F. N. Rhines

The formation of casting porosity is viewed as a nucleation and growth process with solidification shrinkage and gas precipitation as cooperative driving forces. Experimental evidence evaluating the individual contribution of each force confirms the major premise that microporosity is nucleated by gas precipitation. Additional data disclose the effects of the identity and quantity of gas, the temperature range of freezing, and the freezing rate upon the amount and distribution of porosity in light metal castings. POROSITY, as it commonly occurs in metal castings, has been ascribed to the contraction that accompanies the freezing of the metal, to the evolution of dissolved gases from the liquid during cooling and freezing, and, most frequently, to a combination of the two.&apos;" "Pipe" formation is universally associated with solidification shrinkage; spherical "gas holes" are understood to be retained bubbles of gas; but the origin of microporosity, which usually exhibits an irregular or scalloped outline when viewed in cross-section, remains a subject of continuing debate.", &apos; The present research constitutes an endeavor to show what parts are played respectively by shrinkage and gas evolution in the initiation and growth of micropores and what factors determine their number, size, shape, and distribution. A preliminary outline of the mechanism of cavity formation in castings will serve to coordinate the experimental findings that will be reported and will at the same time provide a general theory of the origin of casting porosity. Basic to the mechanism of cavity formation that will be proposed are the following established facts: 1—that liquid metals and alloys contract gradually during cooling down to the freezing range, where a relatively large contraction, known as the "solidification shrinkage," takes place (exceptions in bismuth and gallium being noted);&apos; 2—that the capacity of liquid metals and alloys for dissolving gases diminishes with cooling until, in the freezing interval, a large decrease takes place (various exceptions being noted and excluded from present consideration) ;.: and 3—that freezing proceeds counter to the direction of heat flow, the freezing front most commonly being composed of a system of tapering dendrite stalks and side arms which are coarser the lower the freezing rate and which protrude into the liquid for a distance that is greater the longer the freezing temperature interval of the alloy and the smaller the thermal gradient.&apos; The mechanism by which voids are generated

Jan 1, 1953

By M. E. Wadsworth, K. J. Richards

The oxidation rates of tantalum in various partial pressures of carbon dioxide in the temperature range 700°to 950°C were measured with a thermo-gravimetric balance. Oxidation involved a surface -controlled reaction associated with the formation of a nonprotective layer of Ta2O5. Below about 720°C, there was a change in the rate-determining mechanism, and above 830°C the linear rate was preceded by a complex region of nonlinear oxidation behavior. The linear oxidation of tantalum has been explained quantitatively in terms of carbon dioxide adsorption, followed by a rate-controlling surface reaction. The initial adsorption has been expressed both as an equilibrium process and as a steady-state reaction. The enthalpy for chemisorption of CO, was determined to be -17.3 kcal per mole. The surface-controlled reaction had an activation enthalpy of 40.4 kcal per mole. A considerable amount of interest has been shown in recent years in the oxidation of tantalum and the nature of the oxide film produced. This interest is associated with the increasing demand in our technology for structural materials to withstand high temperatures and corrosive atmospheres. The low oxidation resistance of tantalum has severely restricted its application as a high-strength, high-temperature material. As a fundamental approach to the realization of the full poten- tials of this metal, the kinetics of the oxidation of tantalum in oxygen and air have been extensively studied; however, very little work has been reported on the effect of other gases, including carbon dioxide. According to Miller,&apos; the only reported study of the reaction between tantalum and dry carbon dioxide is a restricted observation by O&apos;Driscoll et al.2 at 8 atm absolute pressure and 500°C. Therefore, this study was made to investigate the reaction of tantalum with carbon dioxide. EXPERIMENTAL MATERIALS AND METHODS The vacuum-annealed tantalum used in this study was obtained from Fansteel Metallurgical Corp. as 0.025-mm-thick sheet stock. This material had less than 0.1 pct total impurities, and the maximum individual impurity concentrations were

Jan 1, 1964

By R. E. Carter, C. Wagner, F. D. Richardson

By means of inert markers of radio-platinum, it has been shown that cobalt metal oxidizes by out-ward diffusion of cobalt atoms through the oxide. Oxidation rates have been measured at various temperatures and oxygen pressures and have been found to agree with the rates calculated from the Wagner equation and the authors&apos; values for the diffusion coefficient of cobalt in the oxide. The distribution of radio-cobalt in growing oxide loyers has been accurately measured and found to be different from that predicted from the Wagner oxidation theory. Attempts have been made to measure the change of lattice parameter of the oxide with composition. SEVERAL investigators have shown that cobalt metal oxidizes according to the parabolic law,1-3 but no detailed study has been made of the oxidation mechanism. Cobaltous oxide has a metal-deficient lattice, but the defect concentration which is dependent on the oxygen pressure is only approximately known.&apos; From the similarities in the structures of "CoO" and "FeO" and the rate laws governing the oxidation of cobalt and iron, Gulbransen- as suggested that cobalt, like iron," oxidizes by diffusion of cobaltous ions through the oxide layer. To substantiate this hypothesis, he has attempted to measure the oxidation rate of cobalt as a function of the oxygen pressure but has been able to report only that the rate depends on a "small" power of the pressure. On the other hand, Preece," Valensi,&apos; and Arkharov&apos; all have suggested from indirect evidence that oxygen diffuses through the COO to the metal-oxide interface. The present authors, in a previous paper,&apos; have shown that the rate of diffusion of cobalt in cobaltous oxide is dependent on the oxygen pressure. In that investigation, they also found that cobaltous oxide disks made by complete oxidation of cobalt metal were porous at their centers (Fig. 5L, ref. 4). Both these facts strongly suggest that oxidation of the metal proceeds via outward diffusion of cations. In order to establish the mechanism unequivocally, oxidation experiments were made with inert radioactive platinum markers, and the dependence of oxidation rate on oxygen pressure was measured. In addition, an attempt was made to determine the form of the cation vacancy gradient, which the marker experiment showed must exist across a growing oxide layer. This was done by depositing radioactive Co on the surface of a cobalt disk and then measuring the tracer distribution across the oxide layer produced by partial oxidation of the metal. Finally, an X-ray examination was made in an attempt to find the expected change of lattice parameter of COO with oxygen pressure. Experimental The apparatus and materials used were substantially the same as those previously described by the authors.4 Marker Studies: The use of inert markers to follow oxidation reactions was first attempted by Pfeil" in 1929, and radioactive markers have recently been used by Davies et al.&apos; In the investigation reported here, the markers were applied as an (NH4)2PtCI6 slurry in several thin streaks across both faces of four disks of cobalt metal 1 mm thick and 14 mm in diameter. The disks were then oxidized almost to completion at 1200°C in pure oxygen. After oxidation, they were mounted and sectioned and auto-radiographs were taken to locate the markers. Oxidation Rate: The oxidation rate of cobalt was measured at 1148°C at oxygen pressures ranging from 0.0055 to 1.0 atm and at 1000°, 1148", and 1350°C under 1 atm of oxygen. The rate was deter-

Jan 1, 1956

By P. R. Gage, R. W. Bartlett

At high temperatues and reduced oxygen pressuves, molybdenum silicicles oxidize to form SiO(g) vathev than a passivating SiO2 film. This is a sevious problem for low-pressure applications of sili-cide-coated rejvactory tnetals. As oxiclalion pvoceeds, the higher oxidntion potential of silicon initially suppresses oxidation of molybdenum and silicon is depleted near the surface. Eventually, silicon depletion causes secondary passivation (SiO2) mid an active to passiue transition in oxidntion behavior at moderately low pressures. At very low pressures, silicon depletion continues until steady-state oxidation of both silicon and rnolyhdenum can proceed at rates propovtional to their initial stoicliiorrzetvies. Ohsel-vations of &apos;oxidatiou-rate belzcriliov at temperatures from 1101° to 1700°C and oxygen pressures from 10-7 to 1 at in were made using thermogravimetn&apos;c, X-ray diffraction, and elect?*on-rtric?ro/,vobe techniqrres. The experimental results are in good agreement with calculated lirnits for the various types of behavior that were based on tlievtnochernicnl atzd dffusion rate data for the Mo-Si system. A protective oxide film normally forms during the oxidation of elemental silicon. However, at elevated temperatures and reduced pressures this film is not present and oxidation is rapid. wagnerl has shown that this behavior occurs because SiO(g) is more stable than SiO2. The behavior of the silicides at high temperatures is similar but more complicated. Molybdenum and several silicide compounds are involved and the chemical activity of silicon, or the equivalent silicon vapor pressure, can vary considerably in these phases. Also, diffusion in the silicides resulting from reactions in which a higher silicide is reduced to a lower silicide, or molybdenum containing dissolved silicon, must be considered. EXPERIMENTAL AND ANALYTICAL METHODS Isothermal oxidation experiments were conducted using hot-pressed MoSi2 and Mo5Si3 wafers. Each experiment was conducted at a fixed oxygen pressure by controlling the flow of oxygen in and out of the furnace chamber. Most of the experiments were conducted in a molybdenum-wound tube furnace. Special construction features, including use of a high-purity dense A12O3 refractory tube, permitted operation in high vacuum to 1500°C. Higher temperatures could be obtained at higher working pressures and with a sacrifice of tube lifetime. Temperature was measured with three Pt 6 pct Rh/Pt 30 pct Rh thermocouples and controlled with a proportional controller. Weight changes were monitored with a quartz spring balance. The few experiments, at higher temperatures and low pressures, were conducted in a cold wall vacuum chamber using induction heating with direct susceptance of the sample. Because of the variable levitation effect of the induction coil on the sample, weight changes could not be monitored continuously in these experiments. All samples representing both experimental methods were weighed before and after oxidiation and examined with a microscope and analyzed by X-ray diffraction. The analytical treatment assumes equilibrium at interfaces and uses existing thermodynamic data. For convenience, equilibria are expressed as chemical potentials or as vapor pressures of the gases involved. The resulting differences in equilibrium vapor pressure between adjacent interfaces and between the surface and external atmosphere drive diffusion processes in the solid and gas boundary film, respectively. These diffusion processes govern the rate of oxidation. A bibliography of the sources of thermochemical data for the reactions pertinent to the Mo-Si-O system is given in Table I. Reactions are listed with the sources of free-energy data referenced. Since all of these reactions involve one or more gas species, usually oxygen, a plot of the product-gas chemical potential, -RT In Pg, vs absolute temperature for each reaction is given in Fig. 1. These curves can be used to determine equilibrium vapor pressures or to compare the stability of different compounds in the various gases: O2, Si, SiO, and Moo3,. The data of Table I and Fig. 1 were used to determine the analytical results presented in this paper. EXPERIMENTAL RESULTS The weight changes for three MoSi, samples oxidized at 1500°C are plotted against time in Fig. 2. The treatments were identical except for the indicated variance of oxygen pressure and each curve represents one of three characteristic types of behavior that were observed. The upper curve is an example of passive oxidation, which is defined as

Jan 1, 1965

By J. N. Ong

The oxidation of tantalum is assumed to occur by four simultaneous first-order chain reactions; solution of oxygen in the metal, nucleation and growth of a suboxide phase at the metal surface and two phase boundary processes which give rise to two different modifications of Ta2O5. A rate equation is then formulated which accounts for all principal details of oxidation behavior, unifies and correlatss the results of the principal investigations, and expresses the rate as a function of pressure, temperature, and time. For purposes of practical application, the expressions: may be used below and above 700T respectively to determine the regression rate of tantalum in cm per hr, where T is to be expressed in "K and P in atmospheres pressure of oxygm. The equations will reproduce within a factor of two all reported experimental rates in the temperature range 475" to 1400°C and pressure range 0.000026 to 40.8 atm 0. 1 HE oxidation kinetics of tantalum have been investigated thoroughly in the temperature range 50" to 1400 and pressure range 1.32 x l0-&apos; to 40.8 atm pressure of 0,and as a result, the principal features of the oxidation of tantalum are known and have been described in considerable detail. The exposition of the characteristics of the behavior of tantalum in oxygen has been largely descriptive, with considerable attention being devoted to elucidating the structure, composition, and morphology of the resulting oxide products. The weight change vs time results have usually been reported graphically. With the exception of the linear rate below 700 C and the process of diffusion of interstitial oxygen into the metal,6&apos;9 no effort has been made to characterize the reaction rates in functional form. It is the purpose of this paper to demonstrate that when the fundamental principles of chemical kinetics are rigorously followed, the results of the principal investigations will be correlated and unified and the oxidation rale may be expressed as an analytic function of pressure, temperature, and time. In addition to accounting for the temperature and pressure dependency of the oxidation rate, the following minor features will be accounted for as a result of the basic analysis: the initial period of nonline-arity in rate at low temperatures, which decreases with increasing temperature;3&apos;5&apos;7 the rate vs temperature cusps obtained at constant pressure"5 the concentration gradient of oxygen interstitially dissolved in the metal.5&apos;7 The analysis will also be consistent with the overall chemistry of reaction and with all visual, microscopic, and X-ray observations. DEVELOPMENT OF RATE EQUATION As a fundamental basis for the treatment of metal-oxygen reaction kinetics, it will be regarded that the rate of reaction is determined by the concentration and not the activity or chemical potential. It is further assumed that all metal-oxygen reactions are first order complex chain reactions" whose rate is dependent on the concentration of an intermediate species which is a complex function of the oxygen concentration, or oxygen pressure, only. The basic rate equation is therefore: is the weight of oxygen consumed by the reaction, A is that portion of the area of the metal over which the reaction is occurring (cm2), t the time (sec), kf the rate constant for forward reaction, C the intermediate species concentration and f &apos;([Oz]) and f (Po,) are complex functions of oxygen concentration and Oxygen pressure respectively. Reverse reactions may usually be neglected in metal-oxygen systems since a large negative free energy generally accompanies these reactions. Eq. [I] takes different forms when the rate of reaction is controlled by diffusion into or through a phase or at a phase boundary. For diffusion into the metal phase, the rate is given by1&apos; Di is the diffusion coefficient of species diffusing into the metal phase (cm2/sec), and Q is the corre-

Jan 1, 1962

By T. L. MacKay

Oxidation rates of single-crystal and poly crystalline zirconium in oxygen at temperatures from 307° to 815°C obey the parabolic rate law for short ex-posure time, 4 to 6 hr. The activation energy for the oxidation of single-crystal zirconium between 420° and 790°C is 42.6 ± 0.7 kcal per mole, and in the temperature range 307" to 600°C the activation energy for oxidation of poly crystalline zirconium is approximately the same. The high-activation energy is indicative that diffusion through the bulk oxide film is the primary mode of mass transport for both types of metal. The higher oxidation rates for poly -crystalline zirconium in this temperature range were attributed to differences in the orientation of the grains in the metal with respect to the oxidizing surfaces. Above 600°C, vain growth was observed in polycrystalline zirconium, and the oxidation rates approached those of single-crystal zirconium. ThE kinetic data of previous oxidation studies1-&apos; of zirconium in oxygen have been interpreted by both parabolic and cubic rate laws. There is some evidence that there is a transition from the parabolic to the cubic rate law at prolonged exposures, but the question is still controversial. For the parabolic rate law activation energies are reported in the range 18.6 to 35 kcal per mole, and for the cubic rate law in the range 38 to 47 kcal per mole. So far as the mechanism of zirconium oxidation is concerned, inert marker studies10,11 have indicated that the oxidation proceeds by oxygen (anion) diffusion through the oxide film toward the metal-metal oxide interface. Pemslerl2 observed that the orientation of the grains in the zirconium metal substrate affected the rate of formation of the oxide film on the surfaces of the grains and that the orientation dependence of the corrosion rate persisted beyond the initial stages of reaction. The rate of oxidation was a minimum when the c axis of the grain was parallel to the surface of the sample, and rose to a maximum when the c axis was inclined at about 20 deg to the plane of sample surface, and decreased again at higher inclinations. cox13 observed that in 300°C steam a thin oxide film was formed initially on zirconium and that this oxide film, which exhibited interference colors, became dark first along the grain boundaries and then over the whole surface in an inhomogeneous manner as the film thickened. Cox proposed a mechanism in which oxygen diffused along preferred paths created by grain boundaries in the metal and formed a much thicker film at or near the grain boundary than on the central zone of the grain. In the present study, the oxidation rates of single crystals of zirconium were measured in oxygen and compared with the oxidation rates of polycrystalline zirconium of the same bar stock. It was felt that such a comparison would elucidate the role of grain boundaries in the metal substrate. SAMPLE PREPARATION Single crystals of zirconium were prepared by following the procedure of I3apperport,14 starting with 1/4-in. rod purchased as crystal-bar zirconium. Zirconium rods 2 in. long were wrapped in tungsten foil and sealed in quartz tubes at pressures of less than 10-6 mm of mercury. Large single crystals were grown by thermal cycling above and below the a-/3 transformation temperature, 862°C. Several specimens were simultaneously subjected to the same cycling procedure, heating to 1200°C, holding for 4 hr, then cooling in the furnace and holding at a temperature of 840°C for 5 to 10 days. This cycle was repeated five or six times for each set of specimens. The grain size of the crystal-bar zirconium before thermal cycling was between 10 and 30 p. Fig. 1 shows the microstructure of an end section of as-received crystal-bar zirconium. A longitudinal section of each zirconium rod after thermal cycling was polished and examined under polarized light, see Fig. 2, and the largest single crystals were selected for this study. Zirconium rods 1/8 in. in diameter and 1/2 in. long with spherical ends were machined from the single crystals and from the as-received bar stock. An X-ray examination showed that the c axis of the single crystals made either a 34-deg or an 89-deg angle with the rod axis. The specimens were chemically etched for 2 min in solution consisting of 15 parts hydrofluoric acid (48 pct), 80 parts nitric acid, and 80 parts water. The chemical polish removed 1 to 2 mils from the surface. EXPERIMENTAL The Sartorius vacuum microbalance used in this study has a sensitivity of 0.5 pg and a capacity of

Jan 1, 1963

By S. W. Kennedy, M. Cohen, L. D. Calvert

A high-temperature X-ray diffraction method has been used to study the composition and the kinetics of formation of oxide scales at 800 °C on iron and pure iron-nickel alloys containing 25.6, 75, and 84 pct Ni. This technique has been combined with chemical analysis, and metallographic examination, and determination of weight-gain time curves. The 75 and 84 pct Ni alloys form a three-layer scale consisting of porous NiO next to the metal, a spinel layer, and a -Fe203 on the outside. The 25 pct Ni alloy produces a scale of spinel and Fe,O,, in which, however, traces of FeO and NiO are observed near to the metal. On all the nickel alloys the Fe20, is orieqted with the (107) plane parallel to the surfaces. The exposed surface of the Fe20, is in the form of needles whose axis is perpendicular to the specimen surface. Although the alloys show nonuniform oxidation rates as determined from weight-gain measurements, the X-ray data indicate that the total scale and individml scale layers grow uniformly and parabolically. Deep subscale formation is observed in the 25 pct Ni alloy only. This appeared to be associated with cracking of the scale and penetration of the oxygen along the grain boundaries. ALTHOUGH film formation has been investigated by high-temperature electron-diffraction techniques, for example by Gulbransenl and Hickman,&apos; there have apparently been no investigations of scaling by methods permitting study of the scale during formation at the reaction temperature. Methods involving quenching of scales are based on the working assumption that no significant changes take place on cooling. In general, however, compounds may disproportionate, and the different thermal expansions of constituents may cause disruption of the scale on cooling. In particular, some scales cannot be quenched without spalling. These difficulties are avoided by X-ray diffraction examination at the temperature of formation. High-temperature diffraction procedures also provide a method of determining the kinetics of formation of each phase separately in a multicom-ponent scale. The scaling of binary iron-nickel alloys Containing up to 30 pct Ni at a temperature of 800°C has been studied by Benard and Moreau using cooled specimen~,~ whilst Foley, Druck, and Fryxel14 made an electron-diffraction study of cooled oxide films formed on an iron 42 pci Ni alloy. In the present work the scaling of three iron-nickel alloys containing 25.6, 75, and 84 pct by weight of nickel, at 800°C in oxygen at atmospheric pressure was investigated by X-ray diffraction techniques using a Norelco Geiger-counter diffrac-tometer. The oxidation of iron was investigated for comparison. In addition normal metallographic examinations and chemical and X-ray analyses were made, and weight-gain time curves obtained. EXPERIMENTAL Materials Used—The analyses of the alloys were as follows: Percent by Weight Nickel 25.6 pct 75.4 pct 83.2 pct Aluminum 0.004 None found 0.002 Cobalt — 0.05 0.05 Chromium — — — Silicon — 0.01 None found Carbon All less than 0.05 pct The chemical analysis of the iron was: Al— 0.002 i 0.001 pct, C—0.007 pct, Cr less than 0.001 pct, Cu—0.002 ± 0.001 pct, Mn—0.003 ± 0.001 pct, N—0.0002 pct, 0-0.013 pct, P—less than 0.0002 pct, Pb—not detected, S—0.0017 pct, Si—0.0095 pct, Sn—none detected. This iron was the same as that used to make the alloys and was obtained from the same source-Vacuum Metals Corp. One specimen of pure iron from The British Iron and Steel Research Association was used for preliminary investigation. Specimens were machined to shape from cast rod, polished (the final polish being with 600 Sic paper), degreased in trichlorethylene, washed, and etched. The etching and neutralizing procedure adopted by

Jan 1, 1960

By Charles Luner

ALTHOUGH the kinetics of the atmospheric oxidation of tin have been studied,1-3 the kinetics in pure oxygen have not been reported. This note presents some results of the kinetics of the oxidation of tin foil in pure oxygen. The tin foil used in this investigation was 99.78 pct pure, the two major impurities being Pb (0.17 pct) and Sb (0.024 pct). The foil was degreased and air-dried prior to oxidation. The air-formed film was estimated by coulometric reduction4 of the surface oxides to be about 25A. The samples, which were in strip form and had a total geometric surface area of about 300 sq cm, were first evacuated at room temperature in an oxidation bulb to 1 X 10 -5 mm Hg and subsequently degassed for 1 hr at the temperature of the experiment. Spectroscopically pure oxygen was then introduced into the bulb. The rates of oxidation were measured by following the rate of pressure change due to oxygen consumption in a closed system, the volume of which was sufficiently large so that the pressure change during an experiment was 10 to 15 per cent of the total pressure. An oil-mercury manometer,5 with a sensitivity of 3 X x mm Hg (which corresponds approximately to 5 X 10 -7 gm of oxygen) was used to measure the pressure change. The oxidation bulb was heated by an oil-bath and controlled to within -10.3 C. The reproducibility of the rates was good, as determined by the coincidence of rates at 190oC for duplicate experiments. Fig. 1 shows the oxidation curves in the temperature range 168 to 211.5oC at 8 mm Hg pressure. The effect of pressure on the rate of oxidation at 190°C is also shown. The rate of oxidation was not markedly affected by changes in pressure in the range 4 to 9 mm Hg, except perhaps at the lowest pressure, 4 mm Hg, where after about 70 min there appeared to be a decline in the rate, as compared with the rate at the higher pressures. At the lower tem- perature, 168oC, and for short reaction times, it is difficult to distinguish between a linear relationship and a slight curvature in the oxidation rate. However, for longer times, there was a somewhat larger indication of curvature. The samples after oxidation were gold-colored in appearance. The oxide that was formed at 170°C was identified as a-SnO by reflection electron diffraction. This is in agreement with results obtained by other workers.6, 7 The rate data best fitted the logarithmic-oxidation rate law, w = K1n ln(1 + -t/to) [1] where w is the weight of oxygen consumed, t is the time, and K In, and to are constants. First estimates to were obtained according to the method of Taylor Thon8 and were then employed to obtain the best simuItaneous estimates of to and K In, that would fit the logarithmic expression. These estimates were found numerically, so that the residual variance could be minimized. The calculations were performed on an

Jan 1, 1961