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By A. U. Seybolt

DURING the course of experiments involving oxygen equilibrations with a high-purity Pd-5 at. pct Rh alloy, the appearance of a subscale was noted. Most of the heat treatments in a pure oxygen atmosphere were performed at 900°C. The presence of the subscale was noted when the oxygen partial pressure was in excess of approximately 95 mm, up to 1 atm, the highest pressure used. According to available thermodynamic information' on the free energy of formation of Rh2O3 (the only reliably reported solid oxide of rhodium), this oxide should not be stable under these conditions, nor, of course, any oxide of palladium. Extraction of the subscale from the matrix was affected by treatment with aqua regia, and the resulting X-ray diffraction powder pattern is shown in Table I. This pattern is not that of Rh2O3, nor that of any known rhodium or palladium oxide. It can be indexed on a hexagonal lattice with a. = 5.22Å and co = 6.0Å. In addition to this unknown material, there was a weak Rh2O3 pattern. An X-ray fluorescence analysis of the powder gave 3214 palladium counts per sec and 5381 rhodium counts per sec, thus indicating the likelihood of a double oxide of palladium and rhodium. In view of the fact that the above result was obtained on a single sample, it is perhaps best not to insist upon the above ratio of about 0.6, but possibly to tentatively assume 0.5 or 1/1. The small amount of Rh2O3 in the X-ray pattern might have occurred on cooling, and it seems possible that the double oxide, below some temperature level, is not as stable as Rh2O3. To examine this point, some of the extracted double oxide was heated on a sheet of pure palladium in air at 900°C, and allowed to furnace-cool over a period of several hours. The X-ray diffraction pattern of the powder showed approximately the same intensity of Rh2O3 and the "hexagonal" oxide as before, but, in addition, a rather faint pattern of another crystalline species made its appearance. This finding again suggests partial transformation of the major (double) oxide to other oxides on cooling from 900°C. Application of the phase rule shows that only one equilibrium oxide (subscale) could have been present at temperature. Vacuum-fusion, oxygen analysis of the extracted subscale showed 7.7 ± 0.7 pct O. Combining this information with that of the X-ray fluorescence analysis suggests the formula PdRhO. This compound should have an oxygen content of 7.07 pct, which is within the range of error of the oxygen analysis. However, until a more careful stoichiometric study is made, it is suggested that the formula be written

Jan 1, 1965

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?') is described. Essentially it involves the 'floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?' and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?' is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,' or foil,' specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.' Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?') is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?'/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?'/? or the absolute value of ?' for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?' for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?'/? is large; that is, for cases where no other technique is available for measuring ?'. Aside from trying to learn more about surfaces through measuring ? and ?', the primary reason for wanting values of ? or ?' is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.' where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?' vs ki, it is thus possible

Jan 1, 1963

By Mark J. Klein

An internal-friction profile induced by nitrogen in Cr-35 at. pet Re was studied as a function of nitrogen concentration and heat treatment. From these studies, the solubility of nitrogen in this alloy was deduced. The equilibrium solubility of nitrogen in chromium does not appear to be substantially changed by the addition of 35 at. pet Re to chromium. However the precipitation kinetics of nitrogen from solution are significantly decreased. IT has been found that rhenium has a beneficial effect on the low-temperature ductility of Group VI-A metals. As part of a study to investigate the mechanism of this increased ductility, it was of interest to compare the concentration of interstitials retained in solution in one of these ductile bee alloys with the concentration retained in solution in its base metal. In this regard, a study of the solubility of nitrogen in ductile Cr-35 at. pet Re was selected for this phase of the investigation because the solubility of nitrogen in the base metal, chromium, has been determined over a fairly large temperature span.1-3 In addition, nitrogen is known to have an embrittling effect on chromium,4 but does not appear to have a comparable embrittling effect on Cr-35 at. pet Re.5 The experimental method selected for this study was the measurement of internal friction. This technique allows interstitial-concentration measurements to be made in bee metals that are sensitive to small changes in the concentration of a particular interstitial, even when other interstitials are present. When subjected to a cyclic stress, interstitial atoms in solid solution give rise to an internal-friction peak whose origin is the stress-induced ordering of interstitials into preferred lat- tice sites. These internal-friction peaks signify a dissipation of elastic energy which is greatest when the period of oscillation is comparable with the relaxation time for the attainment of an equilibrium interstitial distribution. For dilute interstitial binary alloys, the height of the internal-friction peak is proportional to the concentration of interstitial atoms in solid solutions. snoek8 has shown that the internal friction, Q-1, may be expressed by the equation where A is the relaxation strength, ? is the angular frequency, and 7 is the relaxation time. The relaxation strength, A, is proportional to the concentration of interstitials taking part in the relaxation if no interaction occurs between solute atoms. Thus values of peak height, which can be determined as a function of temperature, give a measure of the relative concentration of interstitial atoms in solution at various temperatures. If equilibrium has been attained, the peak heights will be proportional to the interstitial solubilities. The constant that relates A to the interstitial concentration can be determined experimentally from peak-height measurements as a function of concentration for specimens of constant crystallographic orientation. When this has been done, Q-1 measurements can be used to determine solubilities according to the equation C - KQ-1 where C is the soluble interstitial concentration and K is a constant that can be experimentally determined. It is possible, however, that lattice imperfections may bind interstitials to certain lattice sites. Internal friction does not measure these interstitial~, but does measure interstitials which are free to move in the normal lattice sites when subjected to an applied oscillating stress. On alloying the pure metal with a substitutional

Jan 1, 1965

By Stanley Rajnak, John E. Dorn

The saddle-point activation energy for the nu-cleation of a pair of kinks is estimated as a function of the applied stress, the lattice constants, and the height and shape of the Peierls' hill by employing the line-energy model of a dislocation. The kinetics of disloration motion by the Peierls' mechanism are discussed and the microscopic dislocation velocities and macroscopic strain rates are formulated by the Arrkenius type of approach in terms of the activation energy for the formation of pairs of PEIERLS was the first to illustrate that a straight-dislocation line has its lowest energy when it lies in a potential valley parallel to lines of closest packing kinks. The log of the dislocation velocity is found to be approximately proportional to the log of the local applied stress. It is also shown that the low-temperature mechmical properties of several bcc metals might be explained in terms of the Peierls mechanism, good agreement being obtained between theory and experiment for the flow stress us ternperature, activation energy vs stress, and activation volume us stress curves for these metals. of atoms on the slip plane. When such a straight dislocation is moved rigidly from one valley toward the next, the atoms in the vicinity of the core of the dislocation change their positions and bond angles, causing the energy of the dislocation to increase. Midway between two adjacent valleys, the disloca-tion energy reaches a maximum value and any additional small displacement will cause the dislocation to fall down the hill into the next valley. The maximum shear stress necessary to promote such

Jan 1, 1964

By C. G. Durdaller, W. H. Robinson, G. M. Pound

The nucleation rate of the a (pay) to 0 (white) tin transformation was measured as a function of temperature and a tin particle size using an X-ray diffraction technique. The powder specimens of a tin were essentially monodisperse and the small dinzension of the particles of these specimens was varied from 13 to 75 p. Several types of nucleation sites of differing potency were fbund to be operative in the nucleation process, but it could not be determined whether these sites were on the free surface of the tin particles or within the volume. Assuming that they were on the free surface, the average density of the most potent sites was calculated to be 2.5 to 5.3 x 10' sites per sq cnz through the application of a Poisson distribztion finction to the isothermal data. Analysis of the temperature dependence' of the rate constmts at a given fraction transformed suggests that the active sites are regions of higher free energy and not catalytic interfaces. Appreciable induction periods were observed at the lower temperatures of transformation. Experimental studies1 of solid-solid phase transformations have led to the belief that the new phase nucleates at structural imperfections. The purpose of the present work was to learn more about the mechanism of nucleation in solids and the nature of the singularities at which nucleation occurs. In this investigation nucleation rates in the isothermal transformation of gray to white tin were measured by an X-ray diffraction technique using essentially monodisperse powders of gray tin. This particular phase transformation was chosen for study because it presented fewer experimental difficulties than most others. The experimental temperature-control problems were minimal because the two phases coexist in equilibrium at 13.3"C, and measurable transformation rates occur at temperatures only slightly above room temperature. The growth rate of the P phase into the a2 is sufficiently fast to make the measured transformation rate equivalent to the nucleation rate, provided that the particle size of the samples is small enough; for the experimental temperatures used in this study, the particle diameter must be less than 100 p. EXPERIMENTAL TECHNIQUE The P tin used in this study was obtained from Capper Pass and Son Ltd., North Ferriby, Yorkshire, England, and was of 99.999 pct purity. It was transformedS to the a phase and ground into a fine powder in an agate mortar. This powder was separated by a Roller air classifier into seven fractions whose dimensions, as determined by microscopic measurement of many thousands of particles, are given in Table I and whose distribution of size within each fraction is given in Figs. 1 and 2. The shape of the particles was roughly that of an oblate spheroid,

Jan 1, 1964

By P. E. Doherty, R. S. Davis

Sub boundaries and micropores, as well as certain other imperfections, may be revealed in aluminum by the formation of pits on the surface during cooling from elevated temperatures. The pits are attributed to the condensation of vacancies from supersaturated solution. This "vacancy pit" phenomenon has been used as an etching technique for studying the structure of aluminum specimens grown from the melt. Three fundamental structures were studied: stria-tions, cells, and dendrites. Two types of striations, as well as a crosswise structure are reported. Mic-roporosity is observed to occur in the cell walls on freezing. Subboundaries between primary, secondary, and tertiary branches are observed in dendritic growth. A special case is cited in which cellular growth suppresses the formation of striations. SMALL, well-defined pits have been observed to form on the surfaces of electropolished aluminum specimens during cooling from elevated temperatures.' This phenomenon was attributed to the condensation, from supersaturated solution, of vacancies at particular points on the surface. It was shown that the amount of cooling required for the formation of pits increased exponentially with decreasing holding temperatures in a way that was consistent with the thesis that a critical supersaturation of vacancies was required for the pits to form. Pits do not form in the vicinity of certain imperfections, namely, subgrain or normal graind boundaries, phase boundaries, certain surface irregularities, and pores. The width of the pit-free region increases with decreasing cooling rate. This observation suggests that the imperfections in question are effective sinks for vacancies and that the pit-free region around them is material that is not sufficiently supersaturated with respect to vacancies to nucleate the surface pits during cooling.

Jan 1, 1962

By J. L. Walter

Extra-low carbon iron sheet, when deformed and annealed, undergoes exaggerated or abnormal grain growth in the critically deformed regions of the sheet. This exaggerated pmth occurs, for low strains (3 to 6 pct), only in sheet which has a fine dispersion of precipitates in the subsurface region of the sheet and fewer and coarser precipitates in the sheet interior. These particles have been identified as manganese sulfides. Wing the anneal, grains near the surface are gvowth-inhibited by the fine particles but the grains in the interior are free to grow normally. With the additional driving force provided by the strain energy, the interior grains first grow into the small subsurface pains. Eventually, these growing grains grow completely through the sheet. Calculations of limiting grain sizes at various values of strain indicate that a volume fraction of precipitates in excess of 10-' would be required to eliminate exaggerated growth in material strained to 10 pct. OPEN-COIL annealing has made decarburization of sheet steel both efficient and economically practical. Use of such material for porcelain-enameling stock is one of many possible applications of low-carbon iron since carbon in steel is deleterious to porcelain-enameling properties.' However, the extra-low carbon iron presently available presents another problem, that of exaggerated grain growth in regions where the sheet has been deformed as by bending or stretching. In exaggerated grain growth a few grains start to absorb their neighbors and these may become very much larger than the average grains of the sheet. Other names for exaggerated grain growth are coarsening, critical grain growth, secondary recrystallization, abnormal grain growth, or discontinuous grain growth. While this grain growth does not affect the enameling qualities of the low-carbon iron sheet, their presence results in a marked reduction of tensile-yield strength in the region of the sheet containing the large grains. The loss of tensile yield strength may render the material unsuitable for many applications . This report describes the results of a study undertaken to determine the cause of the exaggerated grab growth in extra-1ow carbon iron and, if possi- ble, to prescribe practical procedures for its prevention. GENERAL THEORY The driving force for exaggerated grain growth is the grain boundary free energy. This driving force is proportional to (l/rl + l/r2) where rl and r2 are the mutually perpendicular radii of curvature of the boundary between the growing grain and the grain being consumed. Thus, the greater the difference in size between the growing grain and the matrix grains, the higher the driving force for grain growth. If, however, the matrix grains are free to grow simultaneously, the driving force for exaggerated growth will be diminished. Stability toward growth of the matrix grains may be caused by a) a strong single orientation texture (texture inhibition),' b) a dispersed second phase,3"5 c) the thickness effect,' or d) intergranular segregation.7"9 As exaggerated growth occurs when growth of the matrix grains has been slowed by the stabilizing processes mentioned above, there must be an additional factor acting to promote growth of a few of the grains to the point where they are enough larger than the matrix grains that boundary energy driving forces are sufficient to cause continued growth. For instance, at the annealing temperature, growth-inhibiting inclusions may slowly dissolve and coalesce. Eventually, a grain boundary becomes unlocked and migration occurs at the expense of neighboring grains. Or, an additional driving force may be supplied to some of the grains if the material is strained. Then, since some grains will be strained less than others, the difference in strain energy between adjacent grains may be sufficient to overcome boundary locking and allow growth of the grains with lower strain energies. In the present study, therefore, such factors as the presence or absence of dispersed phases, the nature of the exaggerated growth, and the effect of strain have been considered. EXPERIMENTAL PROCEDURE I) Material and Processing. Three types of low-carbon iron were used in this study; types A and B were commercial grades, each from a different supplier.* The precise details of the processing of

Jan 1, 1963

By R. D. Nelson, D. H. Polonis

ThE eutectoid decomposition of 6 phase in the Cu-Sn system (32.53 wt pct Sn) has been studied by several investigators.1-6 On the basis of X-ray work, Iball and 0wen1 reported complete decomposition of 6 in powder specimens after 7 days at 300°C. Wang and Hansen followed the micro-structural changes during heat treatment of lump specimens and estimated 5 pct decomposition after 63 days at 300°C. Wang and Hansen suggested that the discrepancy between the decomposition rates of powder and lump specimens might be due to the excess surface free energy of powders. The present work involved 6 decomposition in copper-tin alloy powders containing 32.6 wt pct Sn. Alloy lump specimens exhibited entirely 6 phase after fairly slow cooling (air cooling) from above 350°C and were so brittle that they could be easily crushed to-200 mesh in a percussion mortar. X-ray diffraction study of the as-crushed powders (-200 mesh) revealed 100 pct 6 phase with very slight line broadening effects due to strain introduced by crushing. Only 6 phase was detected by X-ray diffraction in powders which were heat treated 4 hr at 450°C and air cooled to room tem-

Jan 1, 1960

By J. Gurland

THE microstructure of sintered carbides consists of particles of metal carbides, such as WC and TiC, embedded in a metallic binder which is usually a cobalt—or nickel-rich solid solution. One of the important factors influencing the strength of the alloys is the degree of dispersion of the carbide particles in the binder matrix. While it is generally accepted

Jan 1, 1960

By H. B. Probst

Mechanical twins were produced in zone-refined tungsten single crystals by explosive working at room temperature. These twins are parallel to (112) planes and have irregular boundaries rather than the classical plane twin boundaries. These boundaries aye grooved surfaces in which the grooves themselves are parallel to a <111> direction and the sides of the grooves appear to be par-allel to (110) planes. TWINS were produced in tungsten single crystals by explosive working at room temperature. These twins differ in character from any previously reported for tungsten; however, they are similar to those found in molybdenum after compression at -196°C.1 Deformation twins "resembling Neumann bands in ingot iron" have been observed in tungsten by Bech-told and Shewmon.2 This observation was made with sintered polycrystalline tungsten pulled in tension to fracture at 100°C and using a strain rate of 2.8 x 10-4 sec-1. More recently Schadler3 found deformation twins in zone-refined tungsten single crystals pulled in tension at -196"&apos; and -253°C. These tests were conducted using a strain rate of 3.3 x l0-4 sec-1, and the twin bands were found to be parallel to a (112) plane. Deformation twins in tungsten&apos;s sister metal, molybdenum, were observed by Cahn.4 These twins were produced by compressing small (0.7 mm) vapor-deproducedposited molybdenum single crystals at -183°C. The compression was performed &apos;by impact." By the use of precession X-ray techniques, Cahn was able to identify the twin plane as {112} and the shear direction as <1ll>. Mueller and Parker1 produced deformation twins in polycrystalline electron-beam-melted molybdenum by compression at -196°C. Their "loading rate" was 5000 psi per min which, judging from their stress-strain curve, corresponds to a strain rate of approximately 0.3 x 10-4 sec-1. These twin bands were found to be parallel to (1 12) planes; however, they differed in appearance from previously observed twins. In place of straight and parallel twin boundaries they were found to be irregular, jagged, and sawtoothed. The sides of the saw teeth were identified as (110) planes and irrational planes of a (111) zone. The twins observed in the present work in tungsten single crystals are similar in appearance to those of Mueller and Parker in polycrystalline molybdenum. The starting material used in this investigation was 3/16-in. diam commercial tungsten rod produced by powder-metallurgy techniques. This material was converted to a single crystal by the electron-bombardment floating-zone technique.= The process was carried out in a vacuum of 10-5 mm of Hg using a traversing speed of 4 mm per min. Segments (=2 in. long and 3/16 in. in diam) of two crystals (A and B) produced in this manner were studied. Crystal A received one zoning pass, while crystal B received two passes. The two crystals were explosively worked at Bat-telle Memorial Institute in the following manner. A 1/2-in.-thick layer of plastic was applied to the crystals to serve as a buffer in an attempt to prevent cracking. The composite, crystal and buffer, was then wrapped with 1/8-in.-thick DuPont sheet explosive EL506A2 and detonated in water at room temperature. Metallographic samples of the worked crystals were prepared, and back-reflection Laue X-ray patterns were obtained using unfiltered molybdenum radiation. RESULTS AND DISCUSSION Blasting the crystals as described above failed to prevent cracking. The crystals fractured into several fragments about 3/16 to 1/2 in. long; however, the fragments were of sufficient size to be useful for the subsequent study. The diamond pyramid hardness of the crystals after blasting was in the range 430 to 450 as compared with 340 for the as-melted material, which shows a definite hardening resulting from plastic deformation. These hardness values were obtained using a 1000-g load and taking readings only in sound portions of the crystals free of cracks. The crystals exhibited profuse twinning as shown in Fig. 1. No such structure is present in the as-melted condition. Most of these twins have jagged twin boundaries and are similar in appearance to those found in molybdenum by Mueller and Parker. The twins in both crystals were found to be parallel to {112} planes. This identification was made by using the conventional two-trace method. Subsequent efforts to describe these twins more fully were carried out on crystal A. If the longitudinal axis of crystal A is placed in the (001)-(011)-(Il l) basic triangle of the standard cubic stereographic projection, as in Fig. 2, then the two sets of twins shown in Fig. 1 are parallel to the (112) and (121) planes. Fig. 3 shows a schematic representation of a twin with jagged boundaries. This type of twin with a <111>

Jan 1, 1962

By M. E. Nicholson

IN order to understand how alloying elements influence hardenability through their effect on the rate of pearlite nucleation, it is advantageous to use a model to describe the mechanism of pearlite nucleation. The model which currently is most widely accepted has been described, among others, by Mehl et a1.1-3 and by Hultgren.4 Pearlite nucleation involves both the nucleation of ferrite and cementite.4,5 Cementite nucleates first, followed rapidly by the formation of ferrite at the cementite-austenite interface. The conclusion that cementite is the first phase to form during the process of pearlite nucleation is based, in part, on the observation that proeutectoid cementite is continuous with pearlitic cementite and that the orientation relationship between proeutectoid ferrite and austenite is not the same as that between pearlitic: ferrite and austenite.6,7 Recently, Smith" has suggested that the dissimilarity in orientation relations, instead of indicating the pearlite nucleation sequence, may be evidence that pearlite is nucleated in a grain adjacent to the one in which it is growing. Also, Modin9 as shown that ferrite in pearlite may be continuous with proeutectoid ferrite, and he has also shown that proeutectoid cementite is not always continuous with pearlitic cementite. Thus, it appears that the conclusion that cementite always initiates the pearlite nucleation process is open to serious question. The author believes that important evidence on the question of how pearlite is nucleated exists in the rates of pearlite nucleation of different steels. The following is a review and analysis of this evidence. If the nucleation of pearlite is considered as requiring the nucleation of both cementite and ferrite, then the time to nucleate pearlite consists of the time to nucleate the first phase to form, plus the time to nucleate the second phase at the advancing interface of the first. In the absence of a visible proeutectoid constituent, the second phase must be nucleated very soon after the first. If cementite is the first phase to form, the time to nucleate pearlite will be approximately equal to the time to nucleate cementite. Since the nucleation rate of a phase precipitating from solid solution increases with the degree of supersaturation, it would be expected that the rate of pearlite nucleation should increase with increasing carbon content. Digges10 has shown that the reverse is true. He determined the quenching velocity necessary to suppress pearlite formation in plain carbon steels as a function of carbon content. His results showed that pearlite formation could be suppressed with lower quenching velocities as the carbon content of the steel increased, at least up to 1.25 pct C, the highest carbon content he studied. Thus, it would appear that in plain carbon steels, in which pearlite is formed at the nose of the C-curve, the hypothesis that cementite nucleates first does not predict the observed change in nucleation rate. The validity of the current model of pearlite nucleation may be tested also by determining whether or not it predicts the relative influence of alloying elements on the nucleation of ferrite and pearlite. This can be done best by a consideration of the changes in a TTT diagram produced by a change in alloy content. Hultgren4 suggests that the general shape of a TTT diagram, as well as what constituents will form from austenite, can be predicted from the relative nucleation rates of ferrite and cementite. This is illustrated in the schematic diagram for a hypoeutectoid low alloy or plain carbon steel shown in Fig. 1. The C-curves for ferrite nucleation and for cementite nucleation are represented by AA&apos; and CC&apos;, respectively, and the start of ferrite formation and pearlite formation are represented by AX and BC respectively. Adopting the current theory, Hultgren suggests that between X and C pearlite forms directly from austenite, since cementite nucleates more rapidly than ferrite in this temperature range. Conversely, at temperatures above Tx, ferrite is the first to nucleate and proeutectoid ferrite is formed. As proeutectoid ferrite grows, austenite becomes enriched in carbon, so that the cementite nucleation rate is increased. As a result, pearlite nucleation above temperature Tx is accelerated, beginning along BX and not along C&apos;X. Temperature T, represents the temperature at which the nucleation rate of ferrite equals that of cementite. By extending this type of reasoning, using the principle that the nucleation rates of ferrite and cementite increase with increasing supersaturation of austenite with respect to these phases, it should be possible to predict the influence of carbon content on the shape of the isothermal transformation diagram. For a slightly higher carbon content than that of Fig. 1, the curve A A&apos; representing the beginning of ferrite formation should be moved to the right, whereas the curve CC&apos; representing the beginning of cementite formation should be moved to the left. For hypoeutectoid plain carbon and low alloy steels, this prediction does not agree with existing data. Instead, as the carbon content is increased, the pearlite curve moves to the right along with the ferrite curve and always appears to join it tangen-tially. This behavior is demonstrated by the TTT-curves of a series of manganese steels" shown in Fig. 2. In this figure, TTT-curves for four alloys containing 0.20, 0.40, 0.60, and 1.20 pct C are superimposed. The curves are identified in the figure legend. The letters F, P, and C are used to indicate the start of ferrite, pearlite, and cementite formation, respectively. In these steels, it appears that the nucleation of ferrite and of pearlite are related processes. As a result of the foregoing evidence, it is proposed that the formation of pearlite be considered as follows: Either ferrite or cementite may nucleate from austenite, then grow until the remaining phase is nucleated at the interface between the growing phase and austenite. (The growth of the first phase to form is assumed to be accompanied by a composition change in the adjoining austenite.) According to this model there are two modes of nucleating pearlite: 1—where cementite initiates the succession

Jan 1, 1955

By H. W. Paxton, G. M. Pound

A method is outlined for taking into account variation in chemical potential of both components in evaluating capillary effects at growing interfaces. The results are compared with experiment, and seem to be in reasonably good accord for Widman-statten ferrite growing in austenite. ENERY pointed out that during the steady-state growth of phases with a rather small radius of curvature at their advancing edge capillarity cannot be neglected. By proper application of the Laplace equation a correction must be made to the activity gradients down which diffusion occurs. Subsequent workers have concerned themselves with attempts to evaluate specific cases by the use and modification of the principles laid down by Zener.2-5 To solve the problem in its simplest form it is necessary to assume thermodynamic equilibrium at the interface and to select some criterion which will allocate the available free energy between reversible and irreversible processes. Zener chose to assume that the division should be made such that the new phase grew at the maximum rate. Other workers have used the same2,3 or different assumptions, e.g., maximum rate of free-energy dissipation,4 minimum rate of entropy production.5 Li6 has proposed that the "thermokinetic potential" should be a minimum at steady state. The purpose of this presentation is to note that most prior treatments have considered variations due to capillarity only in the chemical potential of the mobile constituent, and that a more consistent treatment must involve a consideration of the variation of chemical potentials of both solute -and sol- vent in a binary system.* As an example, the way in which this arises for ferrite growing from austenite may be illustrated by reference to Fig. l(a). The line OABC shows a typical variation of carbon activity with composition at one atmosphere pressure (at a transformation temperature below A3). In the tip of a growing ferrite plate with a hemi-cylindricab leading edge of radius ?, the pressure due to capillarity is*

Jan 1, 1963

By B. W. Howlett, M. B. Bever, Somnath Misra

The heats oj- formation at 0°C of the compounds AuSn,, AuSn2, AuSn, and the £ phase were measured in a metal -solution calorimeter with liquid tin or a liquid Sn-Bi alloy as solvent. The melting point, heat of fusion, and heat capacities near the melting point of- the compound AuSn in the solid and liquid state were measured in a constant temperature gradient calorimeter. The free energy and entropy of formation of the compound AuSn at its melting point and at 298 °K were calculated from the experimental results and published data. The heats of formation are discussed in relation to the nature of the compounds. The heat capacity below the melting point, heat of fusion, and entropy of fusion of AuSn are interpreted in terms of processes oc-curring before melting. The atomic arrangement in liquid Au-Sn alloys and the bonding in the intermediate phases of. the Au-Sn system are discussed in the light of the measured thermodynamic properties. THE available thermodynamic information on the intermediate phases in the Au-Sn system consists of the heats of formation of the compounds AuSn4, AuSn2, and AuSnly2 and of one composition of the < phase2 besides values of the heat content of the compound AuSn from 0" to 635".&apos; However, the heats of formation refer to different temperatures ringing from 90" to 450°C. Also, the reported error limits of some of the values are large and several inconsistencies are apparent. In the investigation reported here the heats of formation of the compounds AuS-, AuSnz, and AuSn and of three compositions of the < phase were determined for a single reference temperature of 0°C by liquid metal-solution calorimetry. The compound AuSn, which is the only congruently melting intermediate phase in this system, was further investigated in a constant temperature gradient calorimeter by measuring its heat of fusion, melting point, and heat capacity in the solid and liquid states near the melting point. From these data and published free energies of the liquid of composition Au~n,&apos; the free energies of formation of the compound AuSn at the melting point and at 298°K were calculated. The results shed light on the solid-liquid transition of AuSn and on the atomic bonding and state of association of gold and tin in the solid and liquid phases. 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Samples. Stoichiometric amounts of gold and tin, each 99.99+ pct pure, were melted in evacuated Vycor capsules (12 mm ID). The melts were maintained approximately 150°C above the liquidus for about 12 hr and shaken repeatedly. Samples of the compound AuSn were cooled slowly to room temperature. Melts of the other phases, all of which solidify by peritectic reactions, were transferred to the narrow end (5 mm ID) of the capsule, which was then quenched into iced brine. The solidified samples were annealed in the unopened capsules for 10 days at 30" to 50° C below the respective solidus temperatures. The absence of microsegregation and second phases was confirmed by metallographic examination. At least two batches of each composition were prepared. 1.2) Solution Calorimetry. The heats of formation were determined by liquid metal-solution calorimetry. In this technique, the difference between the heat effects on dissolution in a liquid metal, or alloy bath, of the compound and a mechanical mixture of its annealed components, adjusted for changes in composition of the bath, is the heat of formation of the compound at the temperature from which the samples are added. Details of the equipment and technique have been described."&apos; A tin bath at 300" or 350°C was used with the compounds AuSn,, AuSnz, and AuSn. The high gold content of the £ phase would have caused it to dissolve with an appreciable exothermic heat effect. In order to achieve thermal compensation, the samples were added from 0°C to a bath at 350°C consisting of 66.2 wt pct Bi (99.999+ pct pure), balance Sn (99.99+ pct pure). This solvent gives thermal compensation because gold dissolves exothermically in tin and endothermically in bismuth. The calorimeter was calibrated by adding from 0°C approximately 0.015 g-atom of the solvent.

Jan 1, 1965

By N. S. Stoloff, R. G. Davies

A study has been made of the efject oj different dislocation-precipitate interactions upon the temperature dependence of the flow stress of aged Ni-14 at. pct A1 alloy. It is observed that when the dislocations bow between widely spaced (-20004 coherent Ni3Al particles the flow stress decreases with increasing temperature in the normal way. However, when the dislocations cut closely spaced (-5004 particles the flow stress is independent of temperature from -100 to 600°C, due to a balance between softening of the matrix and an increase in strength of the particles with increasing temperature. The retention of strength at high tempera-tures of commercial nickel-base alloys, which are strengthened by the precipitation of a phase based upon Ni3Al, is thought to be due to the unusual strength properties of Ni3Al. The flow stress of Ni3Al increases continuous1y from -196"C to a maximum at -600"C. It is concluded from a series of thermal-mechanical tests that the sevenfold increase in flow stress over this temperature interval is due to a lattice effect and is not diffusion-controlled. The flow stress of precipitation- or dispersion-hardened materials depends on the resistance to dislocation motion within the matrix and the extra energy required for dislocations to bow between or to cut particles. If the dislocations bow between the particles or if the strength of the cut particles is constant with temperature, then the flow stress of the precipitation-hardened alloy must decrease with increasing temperature due at least to the decrease in elastic modulus of the material. There will be softening also from thermally activated cross-slip or climb, offering an additional degree of freedom for dislocations to avoid particles. For example, in the case of nickel containing a dispersion of thoria,&apos; which most probably deforms by dislocations bowing between particles, the flow stress decreases by about 50 pct between 25" and 650°C. In A1-Cu alloys2 aged to produce the 8" precipitate, dislocations cut the particles, and the flow stress decreases by about 20 pct between -269" and 25°C. However, many commercial high-temperature nickel-base alloys, for example Inconel-X and Udimet-700, exhibit little or no decrease in flow stress with increasing temperature up to about 700°C. A characteristic feature of these alloys is that they are strengthened by the precipitation of a phase based upon Ni3A1. Guard and westbrook4 and flinn&apos; have shown that Ni3Al (and alloys in which a third element such as molybdenum or iron is substituted for part of the aluminum) is unusual in that the hardness and flow stress increase with temperature to a maximum at about 600°C. For the flow stress of a precipitation-hardened alloy to be independent of temperature we propose that the particles must be cut by dislocations moving through the matrix and that the strength of the particle must increase with increasing temperature. Theories of precipitation hardening do not take into account the flow stress of the dispersed particles that are cut during deformation; the only dissipative process usually considered7 is the creation of interface within the particle and between the precipitate and matrix. The purpose of the present investigation has been to study in detail the temperature dependence of the flow stress of a nickel-base alloy strengthened by the precipitation of Ni3Al in two structural conditions such that when deformation occurs it does so by dislocations a) bowing between the particles and b) cutting the particles, respectively. A simple binary Ni-14 at. pct A1 alloy was chosen because considerable information is already available for this system concerning phase equilibria and precipitation reactions and rates.&apos; Dislocation-precipitate interactions in the binary alloy should be similar to those in the more complex commercial alloys. In addition, the mechanical and physical properties of NisAl were studied in detail in the hope of elucidating the mechanism by which the strength increases with increasing temperature up to 600°C. EXPERIMENTAL PROCEDURE For the study of the effect of precipitation of Ni3A1 upon the temperature dependence of the flow stress, an alloy containing 14 at. pct A1 was utilized; a Ni-8 at. pct A1 solid-solution alloy was employed as a comparison material. Vacuum-cast ingots were hot-rolled at 1000°C and cylindrical compression samples, 0.20 in. diam by 0.40 in. high, were prepared from the 1/4-in.-diam rod. Specimens were recrystallized and solution-treated at 1000°C for 1/2 hr and then water-quenched. A preliminary study revealed that, when the Ni-14 at. pct A1 alloy was aged for 1 hr at 700°C, significant precipitation hardening was obtained, and that the structure was free from grain boundary discontinuous precipitation; an overaged condition was produced by annealing the aged specimens at 850°C for 1 hr. To circumvent the difficulties involved in the hot rolling and swaging of Ni3A1, compression samples,

Jan 1, 1965

By H. J. McQueen, G. C. Kuczynski

ThE useful properties of k6-Alfenol and the thermenol alloys (summarized by J. E. Nachman and W. J. Buehler&apos;) have encouraged research into those alloys which, having compositions near 25 at. pct Al, 75 at. pct Fe, undergo an ordering transformation between 500° and 550°C. The equilibrium diagram of the iron-rich iron-aluminum alloys was first determined by Bradley and Jay.2,3 They distinguished three structures: the disordered, which is bcc; FeAl, which is simple cubic with one Fe atom and one Al atom per lattice site; and Fe3Al, which is fcc with three Fe atoms and one Al atom per lattice site. This last structure may be conceived as eight body-centered cubes with Al atoms at the centers of alternate ones, so that Al atoms have only Fe as first and second nearest neighbors. Later, Osawa and Murata4 determined the boundaries of the different superlattice regions in the iron-rich Fe-Al solid solution by dilatometric and X-ray methods. Two of the six phases, which they found between 0 and 50 at. pct Al, were never identified by other workers. A. Taylor and R. M. ones,&apos; concurrently with and independently of this research, redetermined this diagram by measuring lattice parameters at temperature. Further reference will be made to their results. EQUILIBRIUM DIAGRAM A) Experimental Procedure—The alloys were prepared from NRC gas-free iron (99.9 pct Fe) and 99.99 pct Al. They were melted in alumina&apos; crucubles under vacuum in an induction furnace. If the ingots were unsound or showed more than a 3 pct weight loss, they were rejected. The ingots were homogenized at 1100°C for 24 hr before hot-rolling at 700" to 900°C from 1 in. to 0.25 in. thick. It is interesting to note that alloys containing more than 28 at. pct Al were able to take an 80 pct reduction of area in the ordered FeAl region. The dilatometer specimens and specimens for chemical analysis were cut from these plates. A Leitz dilatometer was used to measure the coefficient of linear expansion as a function of temperature. The specimens were slowly cooled from 900" to 300°C where they were annealed for 10 hr before slowly cooling to room temperature. The expansion was recorded photographically as the alloys were heated and cooled at 1.5oC per min between 100" and 1000°C. The magnetic measurements determining the Curie points were performed on the dilatometer specimens in the dilatometer, by using direct current in the furnace windings both to heat the specimen at 1.5°C per min and to serve as the primary coil. The regular specimen holder was replaced by a thin alundum tube on which was wound, as a secondary, a closely spaced coil of fine copper wire. A reversal of current in the furnace windings produced, in the secondary, an emf which was proportional to the induction in the specimen, and which could be detected on a galvanometer. In this way, it was possible to determine the Curie points of alloys to within * 5°C. B) Results and Discussion—The coefficients of linear expansion, as obtained from the dilatometer curves, are plotted as a function of temperature and composition in Fig. 1. Since in many cases the heating and cooling curves were superimposed, it was decided to measure slopes of heating curves only. Definite high peaks, due to the transformations, were observed on each curve between 400" and 520°C, and, for alloys containing more than 23 at. pct Al, a second set of smaller peaks at temperatures above 660°C. The sharpness of the peaks indicates that ordering to Fe3Al is a first-order reaction. The compositions and the temperatures of these peaks are listed in Table I. When these temperatures are plotted as a function of the composition, the result is the constitution diagram presented in

Jan 1, 1960

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 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 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 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