Diffusion and Oxidation of Metals - ACS Publications

Diffusion and Oxidation of Metals M. T. SIMNAD Mefals Research laboratory, Carnegie lnstifufe of Technology, Piftsburgh, Pa.

r\’ HIS valuable annual reviews of the past few years, Birchenall (3) has romnieiited upon the increasing number of labora-

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tories and investigators entering the field of diffusion in metals. The gathering inomentuin has now resulted in a veritable avalanche of publications on the subject. This can best be appreciated bv a comparison of the number of references listed in some former review articles on diffusion in metals. Mehl’s classic survey in 1936 ( I S ) , which covered the work of scveral decades, listed 302 papers. LeClaire’s ewellent reviews (IO, 11) included 132 references for the period to 1948 and 131 references for the years 1949 to 1952. Birchenall’s account of work published in 1954 referred to 75 papers, and this year the number of paprrs pul,lished total over 130. The interest in the subject shows no s i p s of abating and augurs well for pi’ogressin the near future.

Diffusion The principal factors that have led to a marked improvement in the undeistanding of diffusion have been, on the one hand, the close collaboration between many able so!id state phj sicists and metallurgists and, on the other hand, the marked improvements in the expcrimental techniques available for the study of diffusion. The gi rat interest in theory was especially manifest a t the Gordon Rrscarch Conference, American Association for the Advancenient of Science, held in July 1955 and devoted mainly to diffusion in met:& Unfortunately, the rules of this conference militate against the reporting of the discussions that toob place there. The theorim of diffusion are still in a state of flux, and their reappraisal b\ a more advanced critical approach has resulted in a re evaluation and modification of the original courepts. I n evpeiimentnl work several impoitant developments have tahen place in recent years, and the new techniques are being applied to an ever-increasing extent. These include the use of ultrapure metals prepared by zone-refining; oriented single and bicrystals of controlled relative orientation v i t h good structural homogeneity; radioactive isotopes for self-diffusion studies (Kuczynsbi’s ingenious method and the recently developed nuclear magnetic resonance techniques ( 6 B ) make it possible to measure self-diffusion without the use of radioisotopes); microbeam x-rays; displacement of p-n junctions in semiconductors ( Y K ) ; internal-friction measurements; advances in markermovement or Kirlrendall effect determination; porosity measurements in diffusion couples; field-emission microscopy [this method even has been able to show up dislocations in tungsten, tantalum, and nickel single crystals ( d F ) ]; and developments in radiation damage techniques. REVIEWS OF DIFFUSION

Several review papers and monographs on diffusion have appeared during the past year. Kleppa (8) has written a good summary of recent advances in diffusion in which he outlines

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the main developments in the theories and mechanism of diffusion. Two monographs published by The American Society for Metals continue the high standard and timeliness of the previous seminars arranged by the society. “Impurities and Imperfections” (1) includes a dozen up-to date contributions on subjects pertinent to the understanding of diffusion and “Theory of Alloy Phases” ( d ) is also useful in view of the interrelation between diffusion and phase structures. Other important reviem on alloy structures are by Fiiedel ( 6 ) and by HumeRothery and Coles (Y). The proceedings of a comprehensive conference on lattice defects in crystalline solids, held a t Bristoi in July 1954, have been published during the past year (15). A new edition of Cottiell’s book (4)entitled “Theoretical Structural Metallurgy” has appeared and includes a chapter on diffusion. The application of radioactive tracers in the study of diffusion in metals has been reviewed by Leymoiiie and Larombe (12). A staniiarci Russian test ( 5 ) on diffusion and heat exchange in chemical kinetics has been tianslated by Thon; and a contribution on diffusion and atomic interaction in metals by Kurdjumov (9) was included among the papers presented a t the Geneva Conference. A second edition of the W e t n l s Reference Book,” edited by Smithells (14), has been issued and should be of even greater value than the first edition. THEORY OF DIFFUSION

The task of interpreting the results of diffusion experiments has been attempted in several theories xrhich, in turn, have motivated fresh experiments designed to distinguish between these somewhat conflicting theories. In order to follow the advances in diffusion it is a prerequisite to keep abreast of recent developments in the concepts of vacancies, dislocations, and interstitials, and to acquire some familiarity ivith the methods employed to compute the energies involved in the various mechanisms postulated for the diffusion of atoms. It is beyond the scope of this review to describe these theories in any detail, but it is of inteiest t o draw attention to several important contributions that have been made during the past year. An outstanding paper by Fumi ( Q A )appeared late in the year under the modest title ”Vacancies in hlonovalent Metals.” Besides giving a concise treatment of the energy required to form a vacancy in a metal, and of the various factors that determine the energy and the variation from metal to metal, he also discusses a t length the energy required to move a vacancy. His theoretical calculations give results that agree n-ell with the experimental values. I n addition, he corrects the mistakes in some important previous calculations and points out the errors in several rerent theories. The outline of the method used by Fumi is as follom: The metal is represented as a large spherical box in which the positive charge of the ions is uniformly distributed and the electrons are free to move. When an ion is removed from the center of the sphere and spread over its surface, the cnergy of the frec elcctrons changes by A s c i , because the electron waves undergo phase shifts in order to screen the vacancy and the

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DIFFUSION IN METALS volume of the metal box changes. AEel is proportional to the Fermi energy of the metal, EF, and is cstiniated to be 1/6 EF. For the noble metals another relevant contribution t o the energy needed to create a vacancy is that of the closed-shell repulsion between ions. The application of Friedel’s theorem for the phase shifts a t the Fermi level, with the use of Born’s approximation, enables E’umi to describe AE’#L(the energy change of the free electrons upon removal of an ion from the center of the metal sphere) in a form independent of V ( r )(the perturbing potentiali.e., the potential field of the vacancy screened by the conduction electrons). A vacancy in a monovalent metal is depicted as an impurity atom nith an cxcess valence equal to -1. [In this connection, Kochendorfer (15d) considers a vacancy as equivalent to a section of two dislocations of opposite sign located at neighboring glide planes, and his calculations of the heat of formation of single vacariries are rather lower than Fumi’s values.] Upon removal of a metal ion from the interior thc nearest neighbors relax to new positions in such a n a y a8 to minimize the energy and, consequently, the repulsive energy decreases more than in a iigid lattice. (The shear constant calculations of Fuchs are upheld; apparently the repuluive potential attribiited by Zener to Huntington and Seitz is affertcd by niisprints in the original paper.) The complicated energy considerations involved in moving one of the nearest neighbois of a vacancy from its equilibrium position to the saddle-point configuration allow only a seniiquantitative treatnient of this problem. Recent experimental values reported by McDonald (81A),for the energies needed t o rreate thermal defects in alkali metals, make it possible to divide the activation energy for selfdiffusion into an energy of formation and a negligiblc energy of movement of vacancies. Fumi concludes that the thermal defects responsible for diffusion in alkali metals are vacancies. For copper, his results are in good agreement with the results of Huntington and Seitz after certain faulty calculations in their work are corrected. The new results indicate that the energy of movement for a vacancy in copper is larger than the energy of formation, since here the term due to closed-shell repulsion predominates. [The energies required to create thermal defects in several metals have been reported by Seeger (ZgA), Kauffman and Koehler ( I q A ) , and Meccham and Eggleston ( Z 3 d ) . The validity of the interpretation of Meecham and Egglestoii’s work has been questioned by Nicholas (LGA).] Fumi also criticizes sonic recent theories of diffusion in alkali metals: Paneth’s “crowdion” theory gives too low an energy since he neglects the f a c t that the electron gas is puehed o u t of the volume occupied by the interstitial ion. Other theories treat the lattice as a rigid framework bound by central forces and relate the energy t o form a vacancy to the heat of sublimation, but Fumi contends that the main contribution to the energy to form a vacancy in a metal comes from the change in energy of the conduction electrons, which is related to the Fermi energy level of the metal and not to the heat of sublimation.

MASSOUD T. SIMNAD has been a member of the staff of the Metals Research Laboratory, Carnegie Institute of Technology, Pittsburgh, Pa., since 1950. A native of Teheran, Iran, he obtained his B.S. at London University (Imperial College) and Ph.D. at Cambridge University in 1945. In 1949 Siinnad was Weston research fellow, American El e c t r oc h e m i c a1 Society, and guest fellow, Carnegie Institute of Technology. March 1956

The conclnsion regardhg vacancy diffusion in alkali metals contradicts a basic tenet of the theory of ring-diffusion in body centered cubic metals. Bufington and Cohcn ( 7 A )had concluded last year that recent data on self-diffusion in sodium did not rule out a vacancy mechanism for alkali metals. A truly crucial experiment to distinguisli betlveen these theoiies n-ould be to find whether a Kirdendall effect takes place during the interdiffusion of a potassium-rubidium couple. Such an experiment is being carried out by Ling Yang, Siiunad, and Melil. The Kirkendall effect actually has been observed 111 tn o body centered cubic systems-namely, in beta brass by Landergren and Llehl ( 1 6 A ) and by Resnick and Baluffi (28.4), and in n titaniummolybdenum couple by Shewmon and Bechtold (SOA). In these systems, however, the closed-shell core-repulsion term betn-een ions has to bc taken into consideration. Shewnion and Bechtold disriiss the anomalies that lead to the prediction of a ring mechanism and give an alternative eqdanation consistent with a vacancy mmhanism. The predictions of Zener and LeClaire had been based on a correlation bctv,een the entropy of activation for self-diffusion and the tenipcrnture dependence of the elastic constants. I n the light of Shewinon arid Rcchtold’s results, Zener (%$A) accounts for the anomalies in ternis of a revised hypothesis regarding the cntropy factor. He (haws attention to the factor that was overlooked in the development of his theory- namely, that the entropy associated nith the forination of a vacancy shoiild bc larger in a body centered cubic metal than in a face centered cubic metal, Pirice a greater relaxation of atoms around a vacancy is possible in a body centered cubic lattice The same explanation holds for LeClaire’s prediction of ring diffusion in body centered cubic metals. The ring mechanism is still upheld by RIaJ burg (%?A)as the mechanism of self-diffusion in germanium, and by Breen and Keertnian ( 3 J ) on the basis of creep experiments in polycrystalline tin. Rreen and Weeitnian find that the activation energy for thc creep of tin has t n o values, one for low temperatures and another for higher temperatures. There does not appear to be any correlation betxvecn these values and the activation energies for self-diffusion in tin, although in other metals the activation energy for creep is approuiniately equal to the activation energy for self-diffusion. They favor a ring mechanism for self-diffusion in tin, coupled n i t h a vacancy mechanism still operative in the creep process. This view is contradicted by Darn ( d J ) , who suspects eirois in the reported values for self-diffusion in tin, and by Nicholas (13B) in a theoretiral euamination of the possible diffusion mechanisms that may describe the data on self-diff usion in tin. A superb discussion of lattice vacancies and inteistitials has been presented by Brooks ( 6 A ) . I n this article a brief account of the types and nature of imperfections in cryst& precedes a description of the formal thermodynamic theory of atomic imperfections. The estimates of forniation energy in terms of macroscopic concepts are analyzed, followed by a discussion of thc quantum mechanical calculations of vacancy and interstitial energies. Finally, the experimental evidence concerning the energy of formation of atomic imperfections is critically summarized. Some of the salient points discussed in this papcr are as follows: Fumi’s comment regarding the relaxation process around a vacancy in a metal is elaborated by considering the result of “resonance,” which is responsible for a large part of metallic binding-the electrons in the metal are pictured adjusting their distribution to “shield out’’ any disturbance in the lattice so as to minimizc the energy. The calculated energies of formation of vacancies from surface energy and elastic contraction are presented in a tahle which includes values for silver, copper, gold, aluminum, lead, nickel, alpha iron, and tungsten. The data for sodium and copper agree with those estimated by Fumi, but for silver and gold they differ considerably. The thermodynamic theory indicates that pairs of vacancies can be of importmm only under conditions of considerable supersaturation of vacan-

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FUNDAMENTALS REVIEW

Radioactive tracer measurements in diffusion studies prove more reliable than those from chemical diffusion

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cies, which exist for common metals just below the melting point. This puts a limitation on a suggestion by Bartlett and Dienes that pairs of vacancies contribute to diffusion because of their higher mobility. h’achtrieb’s data on the effect of pressure on self-diffusion of sodium indicated a positive activation volume which strongly favors a vacancy mechanism in the alkali metals. The saddlepoint energy for body centered cubic metals is much lower than for face centered cubic metals. Broohs advances no theoretical justification for the empirical correlations discovered by Nachtrieb and others between the latent heat of fksion and activation energy for self-diffusion, or for the relation between the change with pressure of the activation energy in sodium and the change in melting properties. The entropy factor should be positive for vacancies since the relaxation effect results in a lonering of the vibration frequency of the neighboring atoms, but a negative entropy is associated Rith interstitials because of their increased vibration frequencies. I n order t o obtain the total entropy of self-diffusion, the entropy of formation of a vacancy is added to the entropy of activation a t the eaddle point, as postulated by 7xner. I n an appendix, Brooks sholvs that a correction has to be applied to Huntington’s quantum mechanical calculation of the energy of formation of a vacancy in copper, which brings the calculated value into much better agreement with other evidence. Calculations based on inacroscopic concepts such as surface energy and elastic constants predict only the relative magnitudes of different contributions to the activation energy of self-diffusion, and the actual magnitudes obtained are unreliable. Brooks also corrects the value for the “best” estimate of the saddle-point energy for the vacancy mechanism in copper, with the result that the best value for the total activation energy is about 2 e.v. There is a difference of opinion with Funii in regard to the relative contributions of the formation and migration energies to the activation energy for self-diffusion in copper. Brooks considers that the uncertainties in the calculations are in such a direction as to favor a greater formation than migration energy. He adds as an afterthought that pait of the good agreemcnt in the final results i s fortuitous. This view is based on his conclusion: The evidence for the identification of the vaiious typcs of defects involved in radiation damage, cold-work, and quenching experiments is inconclusive. It seems clear that the problem will only be resolved by experiments which make use of other properties introduced by vacancies and interstitials, especially changes in density, x-ray lattice spacing, and elastic moduli. I n the absence of clear identification of the migration processes, conclusions concerning the division between formation and migration energy of vacancies cannot be regarded as on a really firm foundation. Kleppa and others also have emphasized the urgent need for experimental techniques that allow an unambiguous distinction to be made between the different types of imperfections. Some recent Russian studies of this problem merit attention. Smirnov (SIA) has developed a theoretical treatment of the effect of holes on the electrical resistance of binary substitutional alloys and the effect of quenching from high temperatures. Lazarev and Ovcharenko (I‘i‘A) have reported values of the energy of formation of holes and their concentration in silver and platinum based on electrical resistance measurements. Gertsriken (11.4 ) has determined thermal expansion coefficients of metals and alloys to obtain a measure of the number of holes and of thc energy of hole formation.

Tho annealing of point defects in metals and alloys has been analyzed theoretically by Lomer and Cottrell (19A). They suggest that during a first stage in annealing the defects become trapped (for example, on impurity atoms), followed by a second stagc in which these defects “evaporate” from their traps. The theory is applied to some results of quenching experiments bj Roswell and Nonick. A further dctailed examination of the entropy of lattice defects has been carried out by Huntington, Shirn, and Wajda ( I S A ) They use a very simplified force model representing only thr closed-shell, ion-core repulsions of copper for evaluating tlir change of lattice vibrations with the introduction of each defect Since the change in entropy i s governed by the ratio of the original lattice frequency, V,,, to the final frequencies with defect, Vz,, as given by the relation A S = K 2 , In ( VI1j/Vzo), the entropy of a palticular defect is determined by evaluation of tho change in the resulting elastic spectrum by the introduction of the defect Their approach is to consider the localized vibrations in terms of three regions--the atoms in the immediate neighborhood of the defect, the region over which the defect sets up an elastic stress field, and, finally, the surface conditions and their influence They emphasize the qualitative nature of the calculated entropies in view of the oversimplified model used to represent atomic forces and the various arbitrary approximations that had to be introduced a t several points in the calculations. Their stated aim has been rather to draw attention to several interesting conclusions, and to indicate the manner in which various considerations might enter into a more precise evaluation. Lazarus (1BA) has summarized his commendable attempt to treat the role of impurities in metallic diffusion by a consideration of the electrostatic effects due to the excess valence of the impurity. IIe concludes, “The impurity is considered to be screened by a potential derived by a Thomas-Fermi approxiination. The interaction of the coulomb energy of the screening potential with that of the neighboring atoms is found to came measurable changes in diffusion rates for impurities relative t o self-diff usion in the pure lattice, and for diffusion in an impure material relative to that in a pure material.” He admits a possibly serious drawback in his analysis in the neglect of ternis arising from local lattice distortions in the immediate vicinity of the impurity. Jf these effects are present, the calculated values for the energy of migration will deviate considerably from measiirctl data. The effect of screening potential on solute diffusion is examined in a note by Blatt ( 4 A ) . He evaluates the correct screening radii for fulfilling the Friedel condition for the diffusion of impurities in silver. (Friedel has shown that the ThomasFermi approxiination is only a first-order approximation in which the screening radii18 is independent of the valence of the solute atom, contrary to recent experimental results. When the appropriate parameter is determined, the screening radius is also a function of the valence difference between the solutc and solvent atoms.) There is still a discrepancy between the calculated and experimental values, which is asci ibed to the semiquantitative nature of the Lazarus theory. A detailed experimental and theoretical study of self-diffusion in dilute binary solid sohitions has been reported by €€offman, Turnbull, and Hart ( I b A ) . I n order to interpret their results they develop a theory for thc interrelation of the solute and solvent atoms in diffusion. Previously, the theories of Overhauser and of Lazarus related t o the interatomic forces the exchange frequency of solvent atoms with vacancies in the vicinity of the solute atom. Hoffman, Turnbull, and Hart

DIFFUSION IN METALS by the void. The critical supersaturation a t grain boundaries point out that neither of these theories actually deals with the problem of relating the fundamental exchange frequencies t o the was estimated to be equal to or less than 1.006, compared to the observable dirfusion coefficients. In this paper the authors previous estimate of about 1.01 for the matrix. 9 more detailed provide a solution of the problem by assuming the lattice vacancy treatment of the effect of applied strcss has been performed by mechanism of diffusion, and then describe the modifications Brinkman (6A), which gives approximately the same results. that are required for other mechanisins of diffusion. Their Brinkman shows that a two-dimensional tensile stress is estabequation is strictly valid only for solutions so dilute that the lished in Kirkendall-type diffusion specimens on the side of the interface suffering a net loss of atoms. The tensile stress can probability that disturbed regions around solutes will impinge on each other is negligible. I t should also be noted that a t prenucleate voids of a critical size or larger, so that IGrkendall-type diffusion experiments can operate without the existence of an sent the theory can be compared with only a limited number of excess concentration of vacancies. His “fissuring” mechanism experiments, since few data on self-diffusion in dilute solid solutions are available. In their work the coefficient of self-diffusion for nucleation of voids does not depend on the presence of impurity particles and offers a mechanism for developnient of of silver was measurcd as a function of the atom fraction, X , of the substitutional solutes lead, copper, aluminum, or germanium. voids of sufficiently large radii for growth to continue. Accary The results could be described by an equation of the form D A ~ ( 1D ) has followed the kinetics of formation of microscopic porosities in the diffusion zone of an alpha brass by evaporation = Dho exp ( b X ) , where b is a temperature-dependent constant of zinc in vacuo a t 780” C. The formation of holes TT‘US related greater than zero. A more satisfactory relation for the silverparabolically to the time of diffusion. Geguzin ( 1 0 A ) examined (1 bX). lead and silver-copper solutions is given by D k = DA~O the voids in copper-brass-copper and nickel-copper couples and They suggest that the solvent atoms diffuse a t a rate diffcrent within disturbed regions, immediately surrounding solute atoms, found the shapes to be triangular, rectangular, pentagonal, and hexagonal. These results are explained on the basis of the Curiefrom that outside them. This is related by the equation D1 = (1-0rX)DI cuXD2, where 01 is the number of effective solventWulf coefficient of anisotropy of the surface tension a t the metalvacancy exchanges within the region during the period in which void boundary. The phenomenon of thermal diffusion has been examined by its center moves one lattice spacing, and D,and D, refei to solvent Darken and Oriani ( 8 A ) ,who obscrved this effect in three solid and solute, respectively. The self-diffusion of lead in silver was measured and the results were consistent with this theory with binary alloys, alpha iron--nitrogen, alpha iron-carbon, and goldcopper. The interstitial solutes migrate to the higher temperature 01-11. In conclusion, Hoffman and coworkers emphasize the fact that the simple strain energy theory of solid solutions canregion of the specimen, as does copper in copper-gold. The quantity “heat of transfer” appearing in the thermodynamic not cope with the diffusion behavior of all binary solid soluequations is interpreted as arising from the asymmetric dissipations because of unpredictable electronic disturbances which tion of activation energy after a unit step in diffusion. Thermal may accompany solution. At present no theoretical relationship is available that can relate, in terms of interatomic forces, the diffusivity is also treated theoretically by Vernotte ( M A ) a8 a effect of solute atoms on the self-diffusion coefficient of the solvent case in which the diffusivity is a function of concentration and is for all alloys. independent of the concentration gradient. The appreciable errors that arise a-hen a first-order approxiniaBabbitt (!?A)outlines the theoretical bases for the dependence tion of the Thomas-Fermi equation is employed lcd Alfred and of the diffusion coefficient upon concentration. Among Russian March ( 1 A ) to solve this equation numerically. They made contributions to diffusion theory, the \york of Smirnov (SIA ) and of Pines ( d T A ) deserves more attention than has been acdetailed calculations of the potential around impurily atoms with valence Z+1 dissolved in a monovalent metal. The results corded to them in recent puhlicntions. were always in the direction of a more effective shielding of the point charge, and the shielding depended appreciably on the VOLUME SELF-DIFFUSION IN PURE METALS valence of the dissolved impurity. When the calculations were extendcd to cover the case of a finite concentration of impurities, It is now a full decade since radioactive isotopes of metals by use of the model of Friedel, the use of the first-order approxihave become readily available from chain reacting piles, yet it is mation again gave results that were in error. only recently that their use has been xidespread in diffusion A method is described by Moon (,%$A)for calculation of the studies. The increasing knodedge of radiotracer techniques and size of octahedral solute atoms in close-packed interstitial an appreciation of the advantages and limitations involved in solutions from observed x-ray expansion data. Information on such work have encouraged many investigators to undertake the lattice volume of the metal in the presence of solutes such as experiments on self-diffusion in metals. The results of tracer carbon, oxygen, and nitrogen is summarized in graphic form. measurements in diffusion experiments have been more reliable The variation in axial ratios in hexagonal metal crystals is and reproducible than those of chemical diffusion, once the discussed theoretically by McClure (d0A). principles involved in such measurements are fully realized. An The reality of pore forniation during alloy diffusion is now instructive example of the corrections that have t o be applicd to gcnerally accepted and its study is of iniportance t o diffusion self-diffusion measurements is provided by Berkowitz ( I B ) . He theory. Baluffi and Seigle ( S A ) observed the diffusion of zinc determined the absorption of p-raj s from cobalt-60 in thin layers out of polycrystalline alpha brass sheet and concluded that the of nickel, aluminum, and cobalt in connection ~ i t thc h use of the results were consistent q i t h the viewpoint that the outward flux surface counting method of determining diffusion coefficients. of zinc atoms produces a supersaturation of vacancies that may I n all cases the activity actually increascd Kith thickness of abeither precipitate as porcs, or else be absorbed at sinks within the sorber up to 4 mg. per square cni. Also, a discrepancy was alloy, causing various dimensional changes. Drstruction of noted between data for foils and those for evaporated and electrovacancies at the boundaries tended to prevent nucleation of porosity near the grain boundaries and caused a contraction of plated layers. These effects could be explained on the basis of the specimen normal to the plane of the boundary. The problem simple scattering and absorption expressions. The results have wm analyzed by postulation of a quantitative relationship an important bearing on experiments in which the surface countbetween stress and the concentration of vacancies maintained a t ing method is used for measuring self-diffusion coefficients in mctals. the grain boundary, if the boundary acted as a perfect sink. The cffect of stress on the critical vacancy concentration for Nachtrieb (10B)and coworkers have continued their valuable nucleation of a void was estimated by the assumption that and extensive studies of self-diffusion in alkali metals. They elastic strain energy is relaxed throughout the volume occupied have reported measurements of self-diffusion in sodium near the

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FUNDAMENTALS REVIEW melting point in the solid and in the liquid state (IOB). Over the temperature range 98' to 226' C., the results are dcscribed The transition from the by D = 1.1 X 10-3 e-q (-2450/RT). rate of solid-state diffusion to the rate of liquid-state selfdiffusion was found to be as discontinuous in sodium as is the melting process. They redetermined the self-diffusion of lead (18B) in single crystals of high purity lead over the temperature range 174' to 322' C. The data fit D = 0.281 exp (-24,21O/ET). The reason for repeating the measurements was that the values reported previously for the activation energy for self-diff usion in lead exceeded the value predicted from the correlation with the The present result still latent heat of fusion ( A H = 16.5 L). exceeds the predictcd value by about 4500 calories per gram-atom, which is considerably larger than the experimental error. The technique of nuclear magnetic resonance incasurements has been emploved by Slichter ( 1 6 B ) and others to obtain selfdiffusion data in lithium and sodium. For the case of sodium, the results agree with the values obtained by Nachtrieb and coworkers. For lithium the trarer method cannot be applied, but the resonance data are subject to internal checks. Values reported are for sodium, I) = 0.36 eup ( - 10,40O/RT), and for lithium, D = 0.23 exp (-13,20O/l?T). Some unusual results have been found in the self-diffusion of liquid tin and indium by Careri and Paoletti ( S R ) . A preliminary experiment on indium (4B) in the temperature range exp (--135O/RT). Their 160' t o 480' C. gave D = 1.76 X more extensive experiments on liquid tin and on indium a t temperatures t o 700' C. showed, however, that the diffusion coefficient is not a linear function of 1/T. By use of the randomwalk treatment of diffusion and the assumption that evchange takes place only when two atoms move in the right phase with a n energy distributed on the system of two quantized harmonic oscillators, they derive an expression for D that fits the data within the error of measurement. The values reported for self-diffusion in solid tin are anomalous, and it has required some stretch of the imagination to follow the attempts to explain the anomaly theoretically. A new analysis by Nicholas ( I S B ) rules out the ring mechanism, but falls short in an attempt to assign any alternative from among four different possibilities. The recently discovered 21 &hour half-lived radionuclide magnesium-28 has again been used by Shewmon and Rhines (2513) t o measure self-diffusion in magnesium. This time they have carried out the experiments with single crj-stals of magnesium. Diffusion in single crystals whose e-axes made angles of 7" and 78" x-ith the diffusion dircction, in the temperature range 635" to 467" C., gave D l l = 1.01 exp (-32,30O/RT) and D1 = 1.47 exp ( -32,55O/RT). The relation for polycrystalline magnesium waa D = 1.2 exp (--32,00O/R2'). The ratio DI/D1l was found to range from 1.25 a t 630" C. to 1.13 a t 470" C. An analysis of the reason for this anisotropy of diffusion shoved that the entropy of activation for diffusion perpendicular to the c-axis is definitely larger than for diffusion parallel t o the e-axis. They could give no satisfactory explanation of this with present theories of self-diffusion. Close examination of the structure of single crystals of metals such as zinc gives information that is pertinent to the problem of self-diffusion. For example, Hulme ( I I F ) has discovered a systematic distribution of impurity in 99.99% pure zinc single crystals by use of the Berg-Barrctt form of x-ray microscopy technique. I n some cases the disoiientation boundaries and the impurity-rich regions coincided. Similarly, Gilnian ( 7 P ) has followed the structure and polygonization of bent zinc monocrystals. The bulk and grain boundary diffusion in 99.5% pure cadmium single crystals have been compared as a function of temperature by Wajda, Shirn, and Huntington (f7R). In a previous investigation they had carried out the same evperinients n-ith zinc

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single crystals and observed a definite anisotropy for the diffusion process along the e-&yis of the hexagonal zinc structure and perpendicular t o i t ; the grain boundary diffusion m s 61% of that for the bulk diffusion. For cadmium the diffusion constant is less anisotropic; in fact, no anisotropy is measuiablc, since i t lies within the experimental error, even though the c / a ratio is greater for cadmium. The activation energy for grain boundary diffusion is 7% higher for cadmium compared to zinc. The bulk diffusion cofistants for cadmium are given by D1, = 0.05 exp (-18,20O/RT) and D1 = 0.10 exp (--19,10O/RT), where Dll and D1 refer, respectively, to diffusion parallel and perpendicular to the hexagonal axis. The grain boundary diffusion gave Db = 10 exp ( - 13,00O/RT). Shirn (18R) continued this viork by measuring self-diffusion in thallium, another metal that has a hexagonal structure, with c / a ratio of 1.6, wlrich is mole ideally close-packed than zinc or cadmium. There was no difference between the activation energies parallel and perpendicular to the c-axis. There L V ~ R a tendcncy for the diffusion in the perpendicular direction to be greater than that in the parallel direction, which is the opposite of what was found for zinc and cadmium. This is attributed to the fact that in zinc and cadmium the c/a ratio is greater than ideal, whereas for thallium the reverse is true. The results are interpreted as satisfying either the two vacancy mechanisms or the two "ring of three" mechanisms discussed previously by them. The data were fitted by D = 0.4 esp (-22,90O/IZT), for tmiperatures below 230" C. Thallium undergoes a phase tiansition at about 230" C., abovc uliich it has a body centeled cubic structure. The data for the latter phase are given by D = 0.7 esp ( -20,000/

KT). The accuracy of the autoradiography technique for measuring self-diffusion was examined by Krueger and Ilersh ( 8 B )on silver. The results agreed well with previous data obtainrd by more conventional methods. The mathematical treatment of the corrections that may have to be applied in the autoradiographic technique is disrussed in detail by Shewmon, Gatos, and Kurtz (I@). Some relatively low temperature mcasurcmcnts of self-diffusion in tantalum have becn carried out by Gruzin and Xleshov ( 6 B ) . At these temperatures (1200" to 1300" C.) grain houndary diffusion predominates in tantalum, as shown previously, and the results are not reliable as a meamre of volume diffusion In a brief note on self-diffusion in nickel, Burgess and Smoluchowslii ( 2 B ) attiibute an activation energy of 61 to 65 kcal. per mole and a diffusion coefficient of 1.5 X lo-'* square cm. per second to the self-diffusion of nickel a t 1000" C. Hoffman, Pikus, and Ward ( 7 B ) recently have measured self-diffusion in solid nickel, and the results will be published soon. Mead and Birchenall ( 9 B )repeated self-diffusion measurements on cobalt by using the sectioning technique, in order t o check the accuracy of the decrcase-in-surface-activity method which had been emproyed previously. The new data show that the results with the latter method ivere too low when the surfaces of the specimens arere electropolished, whereas etched surfaces gave reasonably good results. The present work yields the equation for self-diffusion in cobalt, D = 0.83 exp ( -67,70O/RT)

VOLUME SELF-DIFFUSION IN ALLOYS

The diffusion of radioiron in dilute solutions in cobalt was measured by Birchenall and Mead (9B), who found D = 0.21 cxp (-62,'700/RT). The effect of manganese on the selfdifhsion of iron has been investigated by Gruziii, Noskov, and Shirokov (SC), mho observed B break in the plot of log D versus 1 / T a t 1150' C. They ascribe this to the predominance of grain boundary diffusion at temperatures below 1150" C. Gruzin ( I C ) exanlined the effect of chromium on the self-diffusion of iron. The valurs given for the activation energy for 8, 4, and

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0% chroniium are 90,75, and 68 kcal. per gram-atom, respectively. IIe draws the conclusion that chromium strengthens the interatomic bond strength in the gamma iron lattice and lowers the mobility of iron at temperatures belov 1000" C. A detailed descrilition of self-diffusion studies of iron in stainless steel has been given by Linnenbom, Tetenbaum, and Cheek (BC). They eniployed the decrease-in-surface-activity method. The volume srlf-cliffusion coefficieiit is given by D = 0.58 exp (-67,1001RT). The effect of variations in grain size was determined and indicated that when thc grain size was ?mall, grain boundary diffusion contributed appreciably l o the over-all diffusion PI ocess. this effect decreasing Rith increasing tcmperature. The effect of interstitial atoms on the self-diffusion of a metal is discussed by Krivoglaz and Smirnov (4C), sperificnlly for the case of carbon in ganinia iron. They calculated the equilibiium number of vnrancirs with zero to siu neiqhboring interstitial atoms 11) a statistical method. An expression n-as obtained for the self-diffusion roeffirirnt of iron in terms of its value in pure iron, the concentration of carbon, and the interaction energy of iron and carbon. D did not vary e\ponentinlly with 1/T, and the frequency facto1 decreased by a fartor of 100 n i t h increase of carlion content to 2.6 atom %. A novel approach was made by 1irisht:tl ( 3 C ) for estimation of the self-rliffiision of iron in l o r alloyed austenite, mthoiif use of radioiion, by following the rate of formation of an austenite layer during the decarburization of graphitic iron plates in hydrogen. Specimens containing 4% carbon and up to 1.2% silicon or up to 5% nickel y~eredecarhurizrtl a t 920" to 1050" C. The self-diffusion rate of iron was eetiniatrd to be about four orders of m a ~ i t u d egreater than that of pure iron, and these results are e\pl:tined in terms of vacancirs. Bii chenall and hlead (9C), using the conventional radiotracer techniques, have studied the effect of carbon concentration upon the self-diffusion of iron in austenite. They determined the self-diffusion over a temperature range 3oOOo to 1300' C. and up to 6.2 atom % carbon. .4 large increase in the diffusivity vith increasing carhon concentration was found. The results did not agree with Overhauser's equation, which leads Mead and 12irrhensll t o attribute the decrease in activation energy mairrlv t o a lonwed barrier for the diffusion of vacancies. Slifliin and Tomizuka ( I I C ) have proposed an interesting method nheiehy a distinction can be made between the possibilities of vacancy and interstitial diffueion b y study of selfdiffusion in ordered crystals. Preliminary measiirements of the self-diffusion of indium and antimony in indium-antimony indicate an apprecial)ly faster rate for indium than for antimony. The theory of the diffusion of interstilid atoms in ordered alloys has becn d e d t with by Krivoglaz and Sinirnov (5C, SC), who conclude that the transition ordered-disordered diffusion and activation encrgj- change discontinuously. They have studied the case of A4ucu3and FeVA41type alloys. The self-diffusion of gold in gold-nickel alloys has becn measured and discusscd in detail by Kurtz, Averhach, and Cohen ( 7 C ) . The chief aim of this work Tms to test the equation proposed lhv DarkPn and LeClairp, mliieh relates the self-diffusivities, 0 " : and 0$,,the int,erdiffusion coefficient, D,and the thermodynamic driving force for interdiffusion. They employed the autoradiographic technique to measure the self-diffusion of gold as a function of composition and temperature in the region of complete solid solubility. The data shoiwd maximum deviations from the h e a r averagw of the pure metal values in the composition range corresponding to the minimum in the solidus curve. The wlf-diffusion coefficients appeared t o correlate with the melting point variations as a function of composition. The values for the diffusion entropy calculated from D:,ku were all positive. The nevt step vi11 be to determine the self-diffusion of nickel in these alloys. [Tn their discufision of the theory of diffusion, Kurtz, Averbach, and Cohen have concluded that when the diffusing atom is jammed hetm-een the barrier atoms

March 1956

there is a negative contribution to the entropy arising from the reduced amplitude of vibration of the jumping atom and the barrier atoms. This effect is partially compensatcd by the increased amplitudes in the vacancy created by the diffusing atom. I n fact, as pointed out by Brooks ( S A ) and others, the entropy of formation of inkrstitials is negative since the vibration frequencies of the neighboring atoms will certainly be increased, whereas a positive entropy is associated with vacancies since the neighbois will be less constrained and can oscillate a t somewhat less than their normal frequency in the crystal.] The looscning of the lattice that accompanies formation of solid solutions in gold-nickel alloj s is discussed theoretically by Oriani (IOC) on the basis of the results of heat capacity measuremrnts. It may be recalled that in a measurement of the self-diffusion coefficient of one component in a binary alloy there are actually four identifiaI)Ie sixties-namely, inactive atoms A , active A * atoms, inactive R atoms, and vacancies. The thermodynamic equations of motion for such a system have bccn described by LeClaire (IO). CHEMICAL DIFFUSION IN SUBSTITUTIONAL ALLOYS

Continued studies of diffusion in brass make this the most intensively examined nonferrous alloy. Home and hfehl ( 6 0 ) discuss a t length a systematic determination of the Kirkendall effectin alpha brass, with the use of incremental diffusion couplw to nieasure the mobilities and diffusion cocfficients as functions of concentrations. The general diffusion coefficient was a singlevalued function of the concentration. Darken's analysis was used to calculate the individual diffusion coefficients of copper and zinc in the brass and their mobilities. The corffirient relating marker shift to hIatano area was found to be a constant independent of time, temperature, and the concentration range of the diffusion couple. The diffusion coefficients and mobilities were single-valued functions of the concentration; the forni of the functions was csscntially the same as the usual D versus C curve. The individual diffusion coefficient, Dcu, approached the selfdiffusion coefficient of copper a t low concentrationp of zinc; the effect of zinc was to increase Dc,, but Dzn decrcased with increasing copper conceni ration in the range of compositions used in this work. The difference between the individual diffusion coefficients increasps with temperature. These studies were extended to include beta brass by Landergren, Birchenall and Mehl(6L)), since in this case the lattice structure is hody centered cubic, and the results would contribute toward elucidating the mechanism of diffusion in such systems. They observed definite movement of marhers, ivhich ruled out the possibility of a ring niechanisni in this alloy. Only a few papers have appeared on chemical diffusion in ferrous alloys. Gruzin ( 4 0 ) has done further work using radioactive chromium, tungsten, and cobalt isotopes to determine the variations in the diffusion coefficients of these metals in iron and in steel of eutectoid composition. He concluded that the bonding of these elements with iron is stronger in the austenite lattice than the iron-iron bonds, and that their activation energies of diffusion are appreciably higher than the self-dirfusion activation energy of iron in austenite. Xeinien and Shinyaev (9D) adapted electropolishing to remove thin layers of metals and alloys for determination of diffusion coefficients. The diffusion coefficient of iron into nickel was 6.9 X 10-'0 square em. per second a t 1094" C. Lindner ( 7 0 ) gives a brief description of measurements of diffusion of radiocopper into steel. His results show D = 3 exp (-61,00O/RT). The diffusion of cobalt in niolybdmum was found by Bryon and Lambert ( 2 D ) to obey the relation D = 2.82 X exp (-34,8OO/RT). An electron diffraction technique was developed by Rfonch and Mohr ( 8 0 ) to carry out a very extensive study of the inter-

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FUNDAMENTALS REVIEW diffusion of thin silver and tellurium films prepared by evaporation on t o glass and other substrates. Optical and volume changes also were observed. Liquid alloy diffusion has not attracted much attention, possibly because of the experimental difficulties inherent in measurements of diffusion in liquids. Grace and Derge (SD) used the capillary reservoir technique t o carry out diffusion experiments in liquid lead-bismuth alloys. Their results indicate that the activation energies of diffusion and viscosity are approximately the same in dilute alloys. The diffusivity increased a t the melting point by a factor of about lo4, compared t o the values in the solid state. CHEMICAL DIFFUSION IN INTERSTITIAL ALLOYS

Dcspite the tremendous amount of past work on the diffusion of interstitials in metals, new xork on the subject continues unabated. Johnson and Hill ( 6 E ) have made valuable contributions to the problem of the diffusion of hydrogen in metals and have published a note on diffusion in iron and ferritic steels. Their conclusions are summarized as follows: Slody diffusing or "residual" hydrogen is a real component only after removal of the rapidly diffusing or "diffusible" hydrogen. The amount of residual hydrogen decreases as the specimen ternperaturc is increased from 400' to 900" C. and also depends on the thermal history of the specimen. Ewing and Ubbeholde ( 4 E ) describe the diffusion of hydrogen through metal septa by electrolysis. Their results do not conform to the relations given previously between permeation and square root of current density. Oxygen diffusion rates in iron a t high temperatures were estimated from subscale thicknesses by Meijering (1023). The activation energies for permeability of oxygen in variouR iron alloys range from 32 to 42 kcal. per mole. These are said to be equal to the sum of the diffusion activation energy and the heat of solution of ferrous oxide in the metals. The permeabilities of iion, nickel, copper, and silver for ovygen a t 85% of their meltsing temperatures are apparently of the same order of magnitude. Internal friction methods have been applied to a ternary alloy of iron, silicon, and nitrogen by Leak, Thomas, and Leak (RE) to establish the diffusion and solubility of nitrogen in a 3% silicon-iron alloy in the temperature range 250" to 1000° C. Busby and ITeIls (2B)used conventional methods to measure the diffusion of nitrogcn in iron and find D = 1.2 X 10-3 eup ( -15,60O/RT). Thomas and Leak ( 1 S E ) also applied the internal friction method t o reveal clearly the interstitial nature of boron in alphairon. The results indicate an activation energy for diffusion of the boron of 15 kcal. per mole, with Do = 10-6 square cm per second-'. The electrolytic migration of carbon in steel was further examined by Darken and Dayal ( S E ) . The rate of migration of the carbon under the influence of direct currents was detcrrnined at various temperatures between 920' and 1277" C. The carbon migrated from the anode t o the cathode. The rate of migration increased with carbon content and with temperature. They postulate that in austenite the carbon is quadrivalent and ionized, with a mean transport number of 4 X low6in a steel containing 0.46% carbon, and 13.4 X 10-6 in a steel with 1.11% carbon, in the temperature range 1175" to 1226" C. Under a thermal gradient, the carbon migrated from a cold to a hot zone in a direction opposite t o that of the direct current. It would be of interest if more experiments of this kind were carried. out on alloys, since the results of this work and the analogous observations of Seith and Wever ( I d E ) in other alloys are of great importance to the understanding of the diffusion and constitution of alloys. The growth rates of graphite nodules in cast irons have been calculated by Birchenall and Mead (123)from st model of a grow-

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ing graphite sphere surrounded by a shell of austeiiite through which carbon and iron are diffusing. They postulate that the carbon is supplied by a cementite-austenite mixture a t the outer edge of the shell. Their calculated rates from carbon diffusion agree fairly well with the measured values, but the rat,es based on iron self-diffusion are much too low. They suggest a plastic deformation mechanism to account for the removal of iron. This contradicts the theory of Krishtal (7E), who claims that, the rate of graphit,ization of cast iron depends on the diffusion rat,e of iron. Wagner, Rucur, and Steinberg ( 1 4 E ) have presented data on the rates of diffusion of carbon in alpha and beta titanium. The measuremente covered t,he temperature range 736" t o 1150" C., excluding the two-phase region between 882" and 920' C. The results for the alpha range gave D = 5.06 exp ( -43,5OO/R2'), and for the beta range D = 108 exp (--18,40O/RT). The effect, of carbon concent,ration T V ~ B negligible. The behavior and diffusion of sulfur in nickel have been investigated with the aid of radiosulfur by Pfeiffer (11E). I n this comprehensive work the effect, of sulfur on embrittlement and its distribution at grain boundaries are determined a t temperatures to 1200" C. From rates of diffusion of sulfur in nickel, the activation energy for diffusion is given as 900 kcal. per mole. An unusual experiment is described by LeClaire ( S E ) , who measured the diffusion of argon in silver. The argon was introduced into silver foil by bombardment of the latter with radioargon ions in a discharge tube. The rate a t which the argon was released from the foil when annealed a t elevated temperatures was determined by radiotracer methods. The dat'a gave

D = 0.12 exp (-33,60O/RT) GRAIN BOUNDARY A N D SURFACE DIFFUSION

For a proper understanding of grain boundary and surfacr diffusion it is essential to have an intimate knowledge of the properties of grain boundaries, suljstructures, and impurities. Excellent revims of these subjects have been written by Cahn ( 2 F ) and Chalmers ( S F ) , and a recent review by Forty ( 6 F ) , of direct observations of dislocations in crystals, is also of great interest. The study of the segregation of impurities to grain boundarics has been placed on a quantitative basis by the ingenious experimental technique devised by Thomas and Chalmcrs ( 1 9 F ) . They have shown that polonium segregates to grain boundaiiw in an alloy of lead and 5% bismuth. The extent of segregation was found to be a function of the orientation of the crystals adjacent t o the boundary and of the temperature a t whirh equilibrium was attained. Their results imply that the structure of the grain boundary changes abruptly as the oricntation difference increases through 15", and that above 25' the curve levels off "when all the single dislocations have lost their identity and the structure of the boundaiy is one of extreme disorder." Another asprct of this problem is reported by Tilkr and Winrgard (2027) in a note on the segrrgation of silver to grain boundaries of tin. I n this case the segregation appeared to have taken place during the solidification process, since the concentration of silver a t the boundary m m evident on an autoradiograph of the specimen soon after solidification. They explain the segregation in terms of the "distribution coefficicnt" of a solute in a solvent during solidification. Other papers on grain boundary segregation include copper in aluminum by Robert, Robillard, and T,acombe ( 1 7 F ) ; impurities in aluminum by Montariol ( 1 g F ) and Plumb ( l 4 F ) ; grain-boundary precipil ation in copper-nickel-manganpse and copper-beryllium by Gruhl and Ammann ( 8 F ) ; and in lead-silver by Heidenreich ( 1 0 F ) . There have been four papers reporting actual measurements of

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DIFFUSION IN METALS grain boundary diffusion rates. Haynes and Smoluchowski ( 9 F ) followed by autoradiography the penetration of radioiron at the grain boundaries of oriented bicrystals of a 3 % silicon-iron alloy. The grain boundary diffusion was found to be orientation dependent, with no preferential penetration for relative angles of disorientation below about lo", and an increased diffusion up to a disorientation of 86'. A broad minimum in the rcsults was noticed in the neighborhood of 50'. The interpretation of these observations was in terms of a model of the grain boundary based on density of atoms of misfit. Dunn and IIibbard ( 6 F ) observed some striking examples of dislocation sites in polygonized silicon-iron crystals, which were located by means of a special etching technique. These variable arrays of edge dislocations implied a variable angle between polygons, but they could be stabilized by migration along the boundary to form a uniform spacing. Recent work has indicated that preferential diffusion can take place along such dislocations. The study of the grain boundary diffusion of nickel in copper by Pukan-a and Sinnott ( 2 2 F )has been described thoroughly in an article v hich treats this problem quantitatively. Radionickel was used to follow its penetration by autoradiography into the grain boundaries. The extent of grain boundaiy diffusion was dependent upon the degree of crystallographic misfit, with the maximum pencti ation occurring a t the point of maximum disorientation. The ratio of grain boundary to lattice diffusion coefficients mas of the order of l o 4 to 106 for the temperature range 650" to 825' C. and for giain boundary angles from 10" to T O O . The activation energy for grain boundary diflusion of nickel into copper decreased with increasing boundary angle and varied from 64.8 kcal. per mole for volume diffusion t o 38.5 Itcal. per mole a t mauinium misorientation. The data for grain boundary diffusion were analyzed by use of the equations derived recently by Whipple ( 2 1 F ) for concentration contours in the neighborhood of a grain boundary. A method by which grain boundary self-diffugion is estimated from an analysis of diffusion-penetration curves has been employed by Okkerse, Tiedema, and Burgers (IS') to determine the self-diffusion of lead in oriented grain boundaries. They conclude that diffusion in grain boundaries is influenced strongly by the position of the dislocation lines Rith respect to the diffusion direction; the rate is much greater mhcn these lines are parallel to the diffusion direction. The autoradiographic technique has been used by Bokshtein, Gudkova, Kishlrin, and JIoroz (IF)in a series of experiments on segregation and grain boundary diffusion in alloys. The field of surface diffusion is still dormant. The reason for this inactivity and for the paucity of past work on the subject is evidently the great experimental difficulties associated nith surface studies. Recent advances in the attainment of ultrahigh vacua should facilitate such work. Some R-ork has been done on the related phenomenon of crystal groxtli from the vapor phase. The gron th mechanism of "whiskers" has been treated experimentally arid thcorctically by Sears (18F). A kinetic study of spiral grom th of cadmium crystals from the vaporphasehasbeen reported in a note by Pollock and Mehl (1527). The theory of hetrrogeneous nucleation from the vapor phase has been worked out by Pound, Simnad, and Yang (16F) who derived a rate equation on the basis of an adsorption, surface diffusion, and statistical fluctuation mechanism. I n all these cases, information on surface diffusion rates nould he of great importance.

A very valuable survey of the role of structural impurities in phasetransformationshasbeenmadebyTurnbull(4G). Thetheory of cellular precipitation has also been developed by Turnbull (9G), who describes the rate of cellular precipitation by parameters representing the diffusion coefficient of atoms in the cell boundary, the spacing of the precipitate lamellae in the cell, and the number of cells nucleated per unit volume. Heidenreich (8G) has attempted to interpret thermionic emission effects in plain carbon steels in terms of phase transformations a t temperatures above 625" C. IIe concludes from emission studies of the decomposition of austenite below the AB line that the transformation is of a diffusionless type rather than carbon diffusion controlled. IIis model for the transformation based on a diffusionless type reaction followed by a diffusion decomposition is criticized by Frank and l'uttick (1G).

SINTERING

The mechanism of sintering is still being studied intensely, and the importance of diffusion as a controlling factor is preeminent. Kiiigery and Berg ( b H ) report on the initial stages of sintering solids by viscous flox, evaporation-condensation, and self-diffusion. I n their model, volume diffusion occurs with grain boundaries and dislocations acting as vacancy sinks. Seigle and Pranatis (411)have considered the sintering of nonvolatile metals and oxides. Several detailed studies of sintering have been reported by Geguzin and coTyorkers ( I H ) , who treat the subject experimentally and theoretically.

MECHANICAL PROPERTIES

An excellent review of the effects of impurities and imperfections on niechanical properties has been written by Parkcr and Washburn ( 6 J ) . They survey recent fundamental work on work hardening, creep, and yield point phenomena. The processes accompanying the annealing of cold-worked metals are reviewed a t great length by Beck (2.T). The activation energies for creep are related t o self-diffusion activation energies by Frenkel, Sherby, and Dorn ( 4 J ) . They suggest that the rate controlling process for high temperature creep is that of self-diffusion. This lends partial support to Mott's theory which pictures a dislocation-climb model for high temperature creep. The anomalous behavior of tin (SJ)already has been mentioned. Recr tman ( 7 J ) has developed a theory of steady-state creep based on dislocation climl), using blott's mechanism. Here, too, the activation energy for self-diffusion is a controlling factor. I n this article the equation derived is of the form given by Dorn to describe creep rates. Anderson and Andreatch ( I J ) have shown that stress relauation in gold wire also is controlled by the same process as that of self-diffusion. Viscous flow studies of copper at high temperatures led Pranatis and Pound ( 6 J ) to interpret this phenomenon by means of the Herring theory of diffusional viscosity. They observed relationships between viscosity and grain size and viscosity and temperature that strongly supported the conclusion that deformation in this case takes place almost entirely by vacancy diffusion.

SEMICONDUCTORS PHASE TRANSFORMATIONS

The following are brief accounts of some recent work related to diffusion in metals, where diffusion is found to be a controlling factor. Information on diffusion rates can add to understanding of these phenomena and, in return, knowledge of these processes can throw light on the mechanism of diffusion.

March 1956

The effect of impurities and imperfections in semiconductors is described in a very interesting review by Burton ( 2 K ) . The concept of ionization and solubility in semiconductors is further developed by Reiss and Fuller ( S K ) . This approach is highly original and intriguing, and has led to extremely valuable predictions of the behavior of additives to semiconductors. I n this article the authors show how t,he formula agrees with data for

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FUNDAMENTALS REVIEW boron-doped silicon saturated with lithium by diffusion from a tin-lithium alloy. IRRADIATION DAMAGE

Rapid progress is being made in understanding of the damage in metals produced by nuclear particlcs. The results of an increasing number of these studies add greatly to the knowlcdge of the behavior of vacancies and of diffusion processes. Scvcral extensive, good revien-s of the subject have appeared during the past year, cspccially by Glen (bL), Kinchin and Pcasc ( S L ) , Seitz and Koehler (,$I,), and Broom ( I L ) .

Oxidation

It is nom 3 years since Kubaschewshi's book on o d a t i o n was published, and there is a decided need for a second edition or a new text to bring the subject up to date.

there are appreciable attractions betwecn impurity atoms and vacancies. His results indicate that nieasureinents of the diffusion of ions are capable of providing information ahout the degree of association with a directness which is not possible with ionic conductivity measurements. Ilschner ( 6 N ) has made a theoretical invcstigation of the diffusion of electrically charged lattice defects of difierent mobility. Katz ( O N ) has proposed a new criterion t o dccide whether ionic transport occurs interstitially or by vacancies. He bases his suggestion on an examination of self-diffusion and ionic conduction in crystals in which the Einstein relation is not obeyed exactly. His explanation of this deviation is based on a correction which must he applied to the usual dcrivation of this equation. IIe relatcs t h P "effective field" to the avrrage field by E* = E (1 & A ) . For vacancy transport, A is negligible, ahereas for intcistitial trans1)ort it has a large value. Expciimental confirmation of this assumption is provided by studies on sodium bromide (vacancy) and silver chloride (interstitial). As regards the types of experiments that may he expectcd to advance the understanding of oxidation, Bichardson and Carter ( 3 N ) cogently iemark:

REVIEWS OF OXIDATION

The proceedings of a highly successful symposiuin on metal surface reactions held in 1954 a t the New York Academy of Sciences has been published ( I M ) . I t is regrettable that the discussions of the papers presented a t that meeting are not included in this volume. Garner (731)has edited an interesting monograph on the chemistry of the solid state. Hauffe ( 8 M )has culminated his prolific publications on oxidation with a book that covers advances in this field in great detail. A monograph by Heavens (9.84) deals vith the optical properties of thin solid films. The volume, "Impurities and Imperfections," contains much information that is also of value in the field of oxidation, especially the chapters by Robertson (14A4) on the structure dependent chemistry of metal surfaces and by hfaurer ( I 2 M ) on vacancies in alkali halide crystals. A book by well-known Russian workers has appeared-Dankov, Ignatov, and Shishakov ( 5 M ) on the electron-diffraction examination of oxide and hydroxide films. Coughlin (4M)has listed the heats and free energies of formation of inorganic oxides. Review articles of general interest on oxidation have been written by Evans (6M)and Pfeil ( I S M ) ; by Smetzer ( I 5 M ) , with special reference to aluminum and its alloys; and by Betteridge ( $ A t ) , Levy ( I O M ) , and Long ( I I A f ) on alloys for high temperatures. A compilation of high temperature corrosion data has heen published in Corrosion ( S M ) .

THEORY OF OXIDATION Advances in oxidation during the past year have again been in the accumulation of experimental data rather than in theory. Although the number of papers on oxidation was more than double that of last ycar, the contributions have becn mainly towards elucidating the details of the processes upon which the mechanism of oxidation depends. The twin pillars of oxidation theory are still those associated with Wagner for thick films and with hlott and Cahrera for thin films. Birchenall ( I N ) recently has made an important contrilsution by deriving a quantitative description of hole formation in the oxidation of metals. Cabrera, Levine, and Plaskctt ( d N ) have given a very valuable mathematical treatment of hollow dislocations, n-hich has interesting possibilities for the description of many phenomena in oxidation and corrosion. Landsberg (7")has examined the logarithmic rate law found in certain cases in oxidation and has described it in terms of the effect of adsorbed molecules on surface sites. Lidiard ( 8 N , 9 N ) has applied elementary lattice kinetic theory to the problem of impurity diffusion by the vacancy mechanism in polar crystals. He pays special attention to the case where

The most important step now is to measure the relationships which exist between diffufiion coefficients, dcpartures from stoichiometry, and oxygen pressures for a number of oxides over good ranges of temperature and composition. Only in this way can the kinetic and thermodynamic properties of cation vacancies and electron holes be worked out and the basic data provided for the development, of theory. The wrong thing t o do is to pile up diffusion data alone or to work on substances for which it is impossible to measure the departures from nonstoichionietry by unequivocal chemical means. Uhlig ( I M ) has continued t o champion the electron-configuration theory. OXIDES AND RELATED CRYSTALS

The Kirkendall effect has been shown to take place in metal oxides by Fischer and Hoffmann ( 5 P ) , who placed a pure aluminum oxide specimen in contact with FeOA120, a t 1500' C. T h r y find that the diffusion of the components takes place principally as ions, with the aluminum ions having a higher mobility than the iron ions. Seith and Kruse ( 1 6 P )could detect no Kirkendall effect in a diffusion couple consisting of cuprous sulfide and silver sulfide. The diffusion v a s carried out a t 200" to 300" C., and only the cations were found t o move. The diffusion of zinc in zinc oxide has been measured by Secco and Moore (16P), from 900" to 1025" C. in an atmosphere of zinc vapor, by a radiotracer technique. At 1 atmosphere zinc pressure D = 4.8 exp (-73,00O/RT). From this they derive a value of -70 kcal. for AH and 8.1 calories pcr degrec for AS. The value of D was found to vary as Pz"Ps, which indicated that the diffusing species v-as the Zn+ ion. Since the D versus Pzn curve did not pass through the origin, they assume that there must, he some mechanism other than solution from the vapor for forniing exress zinc in zinc oxide crystals at low zinc pressures. Work along these lines is being continurd by Moore and others and should be of great interest. Lindner ( I S P ) has given valucs of D oand Q for a whole spate of oxides and spinels, in a short note. Electron-diffraction studics of Xi0 are reported by Libowitz and Bauer ( I S P ) . Hcikcs ( 7 P ) and Igalci ( 9 P )have studied the reIation between structure and electric and m a g n d c properties of nickel oxides of various compositions. The ionic conductance of some solid metallir azides has been reported by Jacobs and Tompkins (IOP).Variations in the composition of ferrous oxide have been measured by Aubry and Marion (BP), who find values of X = 0.88 to 0.946 for the formula Fe,O. The general features of the germanium-oxygen system have

DIFFUSION IN METALS been established by Candidus and Tuomi ( 4 P ) , by the heating of mixtures of germanium-geimanium dioxide a t 800" to 960" C. and quenching t o room temperature. The eutectic temperature was 870" C. Further studies of the oxides of uranium have been reported by Anderson and others ( I F ' ) , who have made very systematic contributions to this subject. Uranium dioxide is capable of absorbing oxygen at ion. temperatures, the extra oxygen entering interstitial positions in the fluorite lattice. Mixed crystals such as uranium-thorium-oxygen also were studied. Other work on the uranium-oxygen system has been done by Iloekstra, Siegel, Fuchs and Katz ( S P ) , who employed high temperature x-ray techniques. Winter (%UP)has continued his extensive studies of exchange reactions of solid oxides with gases. He has developed advanced experiniental techniques to follow such reactions by the use of mass spectrographic methods. We reports the results of work on the reactions of carbon monoxide, carbon dioxide, and oxygen on cuprous oxide, nickel oxide, and chromic oxide. The effect of proton irradiation on the properties of oxides is being studied by Simnad and Smoluchodci ( 1 7 P ) . They find that the solution rate of ferric oxide in acid is greatly increased follodng proton irradiation. l'olkenshtein and Orlov (18P) have observed increases in the electric conductivity of some ferritcs by irradiation n-ith gamma rays. Primak, Delbecq, and Yuster (14P) have measured expansion effects in alkali halides upon irradiation. They explain the results as the generation of vacancies associated n-ith color centers a t the jogs of edge dislocations during irradiation. An ohservation that may have important implications on oxidation theory is Johnston's findings ( 1 1 P ) in connection nith the effect of plastic deformation on the electrical conductivity of silver bromide. Plastic deformation increased the conductivity, the increase being greater parallel to slip planes than perpendicular t o them. The conductivity iacrease was attributed to regions of disorder that were introduced by the deformation. In view of the fact that most oxide films formed on metals are in a stressed condition, the effect of thia upon the growth rate may be appreciable. There are few data available on the plastic deformation of oxides as a function of temperature. Some progress has been made by Wachtman and Maxwell (19P), who found plastic deformation t o take place in periclase above llOOo C., in rutile above 600" C., and in sapphire above 900" C. They also noted that plastic deformation decreased the electrical conductivity of sapphire. The thermodynamic stabilities of refractory borides have been determined by Brewer and IIaraldson ( S P ) . The most stable borides were found to be those of tin, zinc, niobium, and tantalum. Garnei and Reeves ( 6 P ) have studied the decomposition of the alkaline earth azides. The results were interpreted in terms of a preiiucleation process, during d i i c h lattice vacancies were produced, with nucleation occurring when these reached a critical concentration. Nucleation most probably occurred a t the point of emergence of dislocations on the surface of the crystals. Culbransen (1M) has given an instructive account of the role of vacanries in oxides and of the entropy and free energy relationships involved in oxidation. METAL OXIDATION

Aluminum oxide layeis groniiig on aluminum have been examined by electron diffraction by Wilman ( d S Q ) , and electron micrographs of thick layers of the oxide have been obtained by Booker, Wood, 'and Walsh (6Q). The work of Wilman indirates that high surface temperatures may be attained during oxidation. The electron micrographs show a porous structure in the oxide. The gettaring action of barium nietal has been investigat,ed by Morrison and Zetterstrom (29Q). S o simple Ian, could describe the data. March 1956

The solubility of oxygen in chromium has been estimated to be

0.03'% at 1350' C. by Caplan and Burr ( 7 Q ) ,who also determined the diffusivity of oxygen in chromium. A systeniatic investigation of the oxidation of cobalt has been reported by Carter and Richardson (SQ), who also discuss the theory of oxiciation in the light of these results. In a n appendix to this article, Wagner prestnts the rate equations involved in such work. Carter and Richardson have measured the oxidation rates of cobalt a t various temperatures and oxygen pressures and have found these rates t o agree M-ith those calculated from Wagner's equation and the authors' previous values for the diffusion coefficient of cobalt in the oxide. By means of inert markers of radioplatinurn, they showed that cobalt metal oxidized by outward diffusion of cobalt atoms through the oxide. They also measured the distribution of radiocobalt in growing oxide layers and found it to be different froin that predicted from the Wagner oxidation theory. From the distribution measurements it appears that the concentration of vacancies varies in a complex manner across a groRing oxide layer. The lattice parameter of quenched cobalt oxide did not change with oxygen pressure obtaining a t the high temperatures at which it &-asprepared, because of rapid precipitation of the exress oxygen during cooling. The cobalt tracer distribution in the grox-ing oxide agreed closely with that given by a constant diffusion coefficient for approximately two thirds of the oxide thickness, and then fell towards zero a t the oxide-metal interface. Wagner asrribes the discrepancy to the possibility that the laws of ideal solution do not hold in this system. Copper has again been a favored nietal in oxidation studiea, as evidenced by the large number of articles concerning it that continue to appear each year. Schlier and Farnsworth (S?Q) have made a very careful low energy electron-diffraction investigation of chemisorbed gases on the (100) face of copper and nickel single crystals, employing high caliber experimeritsl techniques which should he an object lesson in themselves. -4t room temperatures, oxygen adsorbed into a complete, single~ of mpicury spaced square array a t a pressure of 2 X 1 0 - mm. in a 10-minute interval. At higher pressures, additional oxygen adsorbs into a thicker layer of no regular structure. Bernstcin ( 6 Q )has found an oxygen-isotope effect in the reaction of oxygen with copper. [Last year Dole and Lane ( 1 ) reported the fractionation of oxygen-18 during chenlisorptiori of oxygen on copper and steel: the oxygen-16 reacted preferentially.] Bernstein's work indicates that oxygen-16 reacts preferentially compared to oxygen-16-o\~.gen-l8. The magnitude of the fractionation 1va5 2% at 150' C , with a small negative temperature coefic-ient. He suggests an isotopic exchange equilibrium beta een gaseous oxygen molccwles and chemisoi bed oxyKen atoms which favors the concentration of oxygen-16 in the adSOrhed layer. Yo effect of an electric field (15,500 volts per cm.) on the oxidation of copper could be detected by Ijhlig and Brenner (44Q). The experiments were carricd out on films about 675 A. thick a t 150' C. The nucleation of copper oxide crystals a t preferential s i t t ~on ropper crystals w a ~observed by Gronlund and Benard ( I @ ) . They found this phenomenon to be dependent on oxygen pressure and time, and t o exist in the range of intermediate oxide thicknesses. An extensive study by Matyas (SSQ), reported on the merhanjsni of the oxidation of copper in the temperature range -197" to 1030' C., employed electrondiffraction techniques. The adsoiption of gases on a germanium surfacte has been f o i l o ~ ~ eby d Lax (SqQ), who used ultlahigh vacuum techniques and mass spectrometry to ineasure the adsorption. The structure of surface states at the germaniumgermanium oxide interface has bccn discussed by Statz, Davis, and Mars (bo&). The effect of oxygen on the surface conduction channel phenomenon in gernianium has been investigated by Christensen ( 5 Q ) and Clarke (I@). Channels of the n-type region were prepared by producing an oxygen rich surface, those

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FUNDAMENTALS REVIEW on the p-side by high humidity. Oxygen within the lattice of germanium could behave as an electron donor even though oxygen on the surface is known to act as an acceptor. There seems to be no end t o the possible studies of the oxidation of iron, despite the work of several decades that has been done on this metal. Gulbransen, McMillan, and Andrew (I?&) have carried out an electroc-microscope and electron-diffraction examination of the structure of oxide films formed on iron a t low temperatures from 650" to 850" C. They used Aimco iron and Puron specimens. There was a malked substrate-orientation dependent nucleation of the oxides. Among the structures observed was a fascinating series of unusual shapes and even "spirals." These results are in line n i t h the extensive and imporhant contributions made in previous years by Gulbrnnsen and coworkers. A microscopic examination of ovide nucleation on iron crystals has been made by Bardolle (@), who gives the nucleation rate on different crystal planes. The number inrreased in the order of the following crystal planes: (110), ( l l l ) , (211), and (100). Paidmsi (S2Q) has shown the process of precipitation of Fes04 in FeO in a new series of excellent micrographs. Pfeiffer and Laubmeyer (35Q)have made interesting investigations on the pressure dependence of the oxidatlon of iron a t 1000" C. I n thin layers and a t low pressures a linear rate law was obeyed, which indicated that the phase-boundary reaction rates determined the oxidation process; FeO w m the only phase formed in the oxide. For ovygen pressures above 1 mm. of mercury their results agree with those of Davies, Simnad, and Birchenall. They make a highly suggestive observation n-ith regard to hole formation in iron oxidation. A hollow area was found in thin wire8 after oxidation a t 1000" C., which had about the diameter of the unoxidized wire. In thicker wires the ovide layer broke down when it had reached a certain maximum thickness; oxygen then diffused in and a new' oxide layer formed on the metal. The kinetics and merhanism of the oxidation of inolybdenuin have been investigated by Simnad and Spilners (SSQ). The rates of formation of the different oxides on molybdenum in pure oxygen a t 1 atmosphere pressure have been determined in the temperature range 500" t o 770" C. The rate of vaporization of Mo03 was found to be linear with time, and the energy of activation for its vaporization was 53,000 calories per mole belon 650' C. and 89,600 calories per mole a t temperatures above 650" C. The ratio Moon (vapor)/RtoOa (surface) increased in a complicated manner Lsith time and temperature. There %as a maximumin the totalratcofovidationat600°C. Att below 600' C., an activation energy of 48,900 calor for the formation of total MoOp on molybdenum has been evaluated. The suboxide, hIo02, does not increase beyond a very snall critical thickness. At temperatures above 725' C., catastrophic oxidation of an autocatalytic nature was encountered. Pronounced pitting of the metal was found to occur in the tempeiature range 550' to 650" C. Marker movement evperiments, with radiosilver, indicated that the oxides on niolybdenum grow almost entirely by diffusion of oxygen anions. The nucleation of oxides on nickel has been determined by Jlartuis (86&),who heated pure nickel for 10 minutes to 2 hours. a t llOOo C. in an atmosphere of hydrogen containing a trace of moisture. The number and size of the oxide crystallites depended on the orientation of the nickel substrate. Some grain boundaries showed a string of oxide crystallites aligned along the houndaries; other boundaries, especially twin boundaries, exhibited no oxidation pattern of their own, Nitrogen fixation of nickel in a nuclear reactor was noticed by Primak and Fuchs (S6Q). They sealed nickel samples in silica ampoules containing dry oxygen, dry nitrogen, dry air, or moist air. The formation of reaction products on the irradiatcd nickel occurred only in the moist air. A discussion of the computation of the energy dissipated in R gas in nuclear reactor experiments is included.

596

The kinetics of nickel-sulfur and steel-sulfur reactions betwecn 205" and 445" C. have been followed by Dravnieks ( I I Q ) . The reactions followed the parabolic law. Thc activation energy for nickel changed at 300" C., which corresponded to the change from a lorn temperature form of nickel sulfide to a high temperature form. The activation energies had the valrrcs of 50 kcal. per mole below 300" C. and 20 kcal. per mole for higher temperatures. For iron the activation energy was found to be 41 kcal. per mole over the entire range of temperatures studied. The mechanism of formation of anodic oxide films on metals has been follomd in a somewhat controversial manner by several authors. Toung (51Q) has analyzed the rcsults of impedance measurements on oxide-coated electrodes of niobiuni. He concludes that thP ronductivity of the film is due to nonstoichiometry, the degree of nonstoirhiometry being controlled by local equilibria. Vermilyea (45&) has specialized even more in the field of the anodic oxidation of tantalum vith three notes on the subject. He has continued the detmte with Dewald regarding the mathematical treatment of the film growth (&'Q), and also has furnished information on the effect of ultraviolet illumination and of strong fields on the growth of the anodic f i l m on tantalum ( 4 7 Q ) . Torrisi (4ZQ)has found that the color of the anodic film defines the voltage and temperature conditions of formation of anodic films on tantalum. Demald ( 4 K ) has made a notable contribution to the theory of anodic oxides. An electron diffraction study of the ovidation of tin under reduced pressure has heen made by Trillat (4SQ). Filnis of tin 300 to 500 A. thick were heated in oxygen a t a pressure of 5 X 10-3 mm. of mercury. The oxide, SnO, was observed below 630" C. and SnOz was also present ahove this temperature. The amount of SnO decreased as the temperature increased. The oxidation of oxygen-saturated titanium has been shown to differ from that of the oxygen-free metal. Simnad, Spilners, and Katjz (59Q) have explained the unusual ovidation behavior of titaniuni in terms of the high solubility of oxygen in titanium. Part of the oxygen uptake during high temperature oxidation enters into solid solution in the metal and only a part is available for scale formation. The oxidation rates of oxygen-saturated and oxygen-free titanium were measured betmeen 800' and 1200" C. The initial rate8 of uptake of oxygen by both the oxygen-free and ouygen-saturated specimens were parabolic. The rate of uptake of oxygen was, however, appreciably lower for the oxygen-saturated titanium a t temperaf,urc.s ahove 950" C. The activation energips were estimated as 25 kcal per mole for the oxygen-saturated titanium, and 32 kcal. per mole for the oxygcnfree titanium. The results of this work corroborated the theory put forvard by Jenkins (21Q) that oxygen diffusion within the metal core is an accelerating fadlor in the oxidation of titanium. Stout and Gibbons (41Q) have measured the gelteiing of gases by titanium. Above 700" C. titanium nil1 getter oxygen, nitrogen, and carbon dioxide. The absorption of hydrogen takes placc in the range 25" to 400" C. The adsorption of oxygen on tungsten, as revealed in the field emission electron microscope, has heen followed by Becker and Rrandes (4Q). They conclude that oxygen i s adsorbed on tungsten in three stages. I n the first layer, the bond strength is about 5 e.v. and the oxygen cannot be removed below ahout 750" K., and these bond strengths depend somewhat on the crystallographic plane. In the second layer. the bond strcngth is about 2.5 c.v. and the oxygen cannot be removed below about 750" K. I n the third layer, the oxygen forms a variety of niolecular complexes with the substrate, which reveal t,heInselves as intensely bright, highly localized groups of spots. Each spot is said to be due to electrons emitted by individual atoms in a molecule. The adsorption of nitrogen on tungsten has been examined by Ehrlich ( I S Q ) , who concludes that there are a t least three distinct levels of interaction involved in the absorption of nitrogen on a sparsely covered tungsten surface.

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Vol. 48, No. 3

DIFFUSION IN METALS The oxidation of tungsten has been fully investigated by Webb, Norton, and Wagner (48Q). They report as follows: Two oxide layers form during the oxidation of tungsten between 700" and 1000" C. The outer layer is porous, powdery, yellow tungstic oxide, W03,and the inner layer is a dense, thin, dark-blue, tightly adherent oxide of uncertain composition. The oxidation reaction follows initially the parabolic rate law, but eventually there is a transition t o the linear rate law. The rate of formation of the inner oxide is presumably inversely proportional to its thickness. The inner oxide seems t o transform to the outer oxide a t a constant rate. Upon combining the rate laws of the two individual processes, an over-all rate equation covering the whole range is obtained. The thickness of the inner layer tends to a limiting value when the rate of its formation is equal to the rate of transformation t o the outer layer. Thcse authors (48Q)also have made an analysis of oxidation studies in metal-carbon systems. This is a very important new contribution to oxidation theory, and to the theory of oxidation of metal carbides. They summarize their work as follow:

A general analysis of the characteristics of the oxidation of alloys containing carbon or carbides is given. Evolution of gaseous carbon monoxide and carbon dioxide may rupture oxide films which in the absence of carbon are highly protective. On the other hand, if the base metal has a high affinity for oxygen, carbon may be retained in the alloy, or carbon may diffuse across the oxide layer. Experimental data are reported for the systems nickel-carbon, tungsten-carbon, manganese-carbon, and titanium-carbon. Sewkirk ( 3 I Q )has shown that finely divided tungsten carbide begins to ovidize rapidly in air a t 500" to 520" C. and can be burned completely at 529" C. For coarse tungsten carbide, rapid oxidation brgins a t higher temperatures. The reaction of nitrogen with uranium has been investigated by Mallet and Gerds ( 6 5 Q )in the temperature range 550" to 900' C. A parabolic rate law was observed, with some deviations initially and also after the period of parabolic reaction. Surface reaction products formed in the range 550" to 750' C. consisted principally of EN2. Between 775" and 900" C. three nitrides, UN, USN3, and UN2, were found. The activation energy in the range 550" to 750" C. W ~ R25 kcal. per mole, and bctwcen 775' and 900' C. it was 15 kcal. per mole. Henderson and Bernstein (ZOQ) have found a deuterium isotope exchange effect in the reaction of water vapor with zinc. The fractionation factor was 1.6 a t 400' C The zirconium-hydrogen-oxygen solid solution equilibrium was determined by Edwards and Levcsque (12Q),in the temperature range 600" to 900" C. Gulbransm and Andrew (I?'&) have made an elaborate thermodynamic analysis of the several equilibria involved ]\-hen hydrogen dissolves in the zirconium, They derived equal ions for the solubility, terminal solubility, and decomposition pressure of hydrogcn in terms of the heat, entropy, and frcc energy of solution of hydrogen in the given phase. Thr thcrrnodynaniic quantitirs were determined experimentally by the nieasurement of the decomposition pressures over a broad composition and temnpcrature range. They present two new methods of analyzing the experimental data for determining the terminal solubility. The standard partial molar free cnergies of solution of hydrogen in the alpha and delta phases weie used to explain the exothermic nature of the over-all solubilities and the endothermic nature of the terminal solubilities. A valuc of 14 kcal. per gram-atom was found for the standard and partial molar heat of solution of hydrogen for alpha zirconium, d i i l e a value of 22 kcal. per gram-atom was found for the delta hydride phasc. The formation of anodic oxide films on zirconium has been followed quantitatively by ildarns, Maraghini, and Van Rysselbergh (IQ). The results w r e correlatrd with illott's theory of oxidation.

March 1956

Electron-microscope studies on a number of metal oxides have been carried out by Halliday and Hirst (l9Q) and Pfefferkorn (34Q). They show the change in topography of the metals when they are oxidized, especially the shape of the needle-shaped oxides projecting from the surlaces. Muller (SOQ) has used his field cniission microscopy technique to measure the work function of tungsten single crystal planes. This information is of value for consideration of the effect of crystal orientation on rates of thin film formation. The room temperature electron emission by surfaces that have been abraded had been discovered by Kramer and others a few years ago. Grunberg and Wright (16Q) have carried out a detailed examination of this phenomenon on several abradrd metal surfaces. They ascribe the emission to lattice imperfections in the oxide formed during abrasion; oxygen ion vacancies occupied by two electrons, when returning to the ground state, cause emission from shallow centers near the surface. The interaction of oxygen with a large number of evaporated metal films has been investigated by Lanyou and Trapnell (SSQ). In this comprehensive study, the adsorption of hydrogen and carbon monoxide also was measured. On rhodium, molybdenum, and tungsten the rapid adsorption of oxygen and hydrogen at - 183" C. resulted in the forniation of monolayers with one atom per surface atom. On tantalum, platinum, palladium, copper, aluminum, and zinc, the oxygen formed a similar monolayer, but on iron formed several layers of oxide. On rhodium, molybdenum and possibly tantalum the fast carbon monoxide chemisorption corresponded to a two-site mechanism; on tungsten and iron it lay betwcen t h a t for a Bingle- and two-site mechanism; on platinum and palladium single-site adsorption may have taken place. The kinetics of slow oxygen uptake were followed, and with rhodium, molyhdenium, tungsten, tantalum, and zinc it va8 believed that the formation of the first oxide layer was observed. They postultite a rnechanism of slow oxygen uptake based on a penetration of the lattire a t the commencement of oxidation through interchange of adsorbed ouygen atoms with underlying mctal atoms. An extensive s-ries of experiments on the high temperature corrosion ratcs of several metals in nitric oxide has been reported by Farber, Darnell, and Ehrenberg (Id&). The reaction rates were determined in the temperature range 500' to 1700" C. and were found to increase in the order Incouel, 25-20 stainless steel, molybdenum, nickel, tantalum, 18-8 stainless, tungsten, iron, and copper. The high pressure oxidation of a great number of metals is being measured by Baur, Bridges, and Fassell (SQ), who employ a method called the linear temperatwe incre'we. In this technique, which is dcsigned to provide a quirk survey of ovidation behavior at high pressures, the gain in neight of a inetal is determined a t constant pressure xhile the temperature is increased in a linear manner. Measurements have been niade on tantalum, niobium, molybdenum, copper, zirconium, magnesium, titanium, and tungsten. The results were used t o evaluate values of the activation energy of the reaction and the enthalpy and entropy of adsorption by the solution of appropriatc rate equations n-hich the authors have developcd. ALLOY OXIDATION

The nature of thin oxide films formed on stainless steels has been elucidated by Rhodin (19R) in a very elegant series of experiments. The films wcre stripped chemically by a solution of brorninc in methanol and mechanically with a high purity adhesive tape. The compositions of the films were determined by microanalytical methods. The compositional and structural properties of the films reflected the capacity of the surface to protect itself against corrosion in certain media. The oxide film properties were uniquely dependent on alloy composition, corrosive medium, and surface treatment. The films associated

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FUNDAMENTALS REVIEW with passivity were not necessarily enriched in chromium or nickel, although these elements were important film constituents. In contrast., depletion in iron and enrichment in silicon was characterist,ic of ultrathin films. hIoreau and Renard ( 16 8 ) estended their valuable studies of oxide structures to include several alloy systems. I n a long paper they describe electron-diffraction examinations of t.he structure and composition of the oxide films. For example, with low chromium nickel-chromium alloys, the outer layer was NiO and the inner layer the spinel Ni CrzO1. With nickel-chromium alloys of 20% chromium there was an outer cuhic layer of N O followed by a spinel phase Ni Crz04and an inner layer of rhombohedral CrzOs. After 90 minutes of oxidation the NiO layer disappeared and the two other phases remained. The oxidation behavior of an iron-nickel alloy containing 42% nickel has been studied by Foley, Druck, and Fryxell (6%). Their objective \vas to formulate the mechanism of the reaction, and they employed metallographic, analytical, and electrondiffraction techniques. The rate measurenient,s showed that the parabolic rate constant folloxed the Arrhenius equation with the parameters dependent on the method of surface preparation. The oxide film possessed a two-phase structure consisting of a nickel ferrite (next to the alloy) and Fe203. Differences in activation energies and oxidation rates were explxined on the basis of diffusion through ferrite structures of a varying percent,age of nickel. Nickel-cobalt alloys were oxidized in air by Frederick and Cornet ( 7 R ) at temperatures ranging from 800" to 1400" C. The osidation rate of the pure nickel was found to be lower than reported previously in the literahre. The oxidation rat,e was found t o increase with increasing cobalt. content, but t,he effect was small until over 11% cobalt had been added. The activation energy for oxidation decreased Kith increasing cobalt content from a value of 51 kcal. per mole for pure nickel to about 28.8 kcal. per mole for pure cobalt. The development of alloys for atomic energy applications has been investigated by Saller, Stacy, and Eddy (20R). The good oxidation resistance combined with low absorption of thermal neutrons in iron-chromium-alumiriuni alloys made them attract,ive for such purposes. Aft.er exhaustive tests on a large number of these alloys with various other alloying elements, they concluded that the best addition to the 25 chromium-5 aluminum70 iron alloy was 10% tantalum (replacing 10% iron). This alloy had the same excellent oxidation resistance a t 2200' F. aa the ternary-base alloy with 100-hour rupture strength four times as great. However, the formability and dimensional stability during thermal cycling were impaired by the tantalum addition. The evaluation of the corrosion resistance of gas-turbine blade materials, and especially the effect of vanadium pentoxide and sodium sulfate, has been discussed in several papers. Young, Hershey, and Hussey (ISRj found that Inconel-X had the best resistance to vanadium attack, but had very poor resistance to sodium sulfate. Magnesium oxide in suitable proportions would reduce corrosion due to both of these agents. They emphasize the care and judgment that must be exercised in the selection of fuel additives, which show promise in laboratory or short-time tests, but may actually increase corrosion in operation owing to the formation of excessive deposits on blades (as xith calcium compounds). Lucas, Weddle, and Preace ( I S @ have determined the melting points of various mixtures of vanadium pentoxide with common high-melting metal oxides. Betteridge, Sachs, and Lewis (2E)have examined the effect of vanadium pentoxide on several heat-resisting alloys, both alone and mixed with sodium sulfate or calcium sulfate. They measured the effect on oxidation resistance and on stress-carrying capacity. I n many cases grain-boundary penetration caused severe reduction in strength without abnormally severe oxidation. Similar studies have been reported by Harris, Child, and Kerr (IOR). A specific attempt to explain the effects of sodium sulfate at high tempera-

598

tures has been made by Simons, Browning, and Liebhafsky ($In). They conclude that the presence of reducing agents triggers reactions that can become autocatalytic and destroy the alloy if sufficient sodium sulfate is present. The effects of cyclic heating on the oxidation behavior of metals and alloys have been surveyed in a symposium on the subject. The oxidation behavior of molybdenum alloys and the effect of various coatings on the resistance of molybdenum to high temperature oxidation have again received much attention. Gleiser, Larsen, Speiser, and Spretnak (8R) have made a rational approach to this problem in their extensive studies of the properties of oxidation-resistant scales formed on molybdenum-base alloys a t elevated temperatures. They summarize their findings aa follows:

(In)

Due to the limitations of externally applied claddings for protecting molybdenum-base alloys from oxidation a t elevated temperatures, a program of developing protective self-regenerative scales on molybdenum-base alloys was conducted. Various nlolyt,dates and niolybdenuin-containing oside complexes nxrc tested for stslility at elevated temperstures in order to ascertain if they would be stable a t operating temperatures and thus possibly present a barrier to further oxidation. Nickel and cobalt molybdates appeared promising and were further studied in terms of their properties and their ability to form as protective scales upon molybdenum alloys containing them. Results of oxidation tests show that molybdate scales will form on molybdenum-nickel and molybdenum-cobalt alloys are protective. Both nickel and cobalt molybdates spall upon thermal cycling. Spalling can be suppressed by the addition of certain third components which stabilize the molybdate crystal structure. The nature and suppression of spalling are discussed. The oxidation of iron-molybdenum and nickel-molybdenum allow and the mechanism of catastroDhic oxidation of some molybdenum-containing alloys have been investigatcd in great detail by Brenner ( S R ) . The binary alloys of iron and up to 12.5% molybdenum, and of nickel with up to 19.7% molybdenum did not exhibit catastrophic oxidation to 1000" C., either in stationary or in flowing atmospheres. In both systems, molybdenum dioxide and iron molybdate were formed in addition to iron oxides or nickel oxide. RIolybdenum was considered to decrease the oxidation rate of iron by preventing the formation of the cation deficient PeO normally formed on iron above 570' C. The effect on nickel was small, there beirig a slight increase due to the formation of additional vacancies in the K O , and a decrease beyond 12% molybdenum becawe of the densification of the A1002 subscale. When nickel or chromium m s added to ironmolybdenum alloys, catastrophic o.;idation occurred in certain concentration regions; chromium was more effective than nickel in promoting this effect. Brenner postdates the formation of liquid MOO, along the metal-oxide interface as the cause of catsstrophic oxidation. High nickel alloys, such as molybdenum-iron-nickel-chromium alloys with 40% nickel and 20% molybdenum, did not oxidize catastrophically, and may be of industrial use. The rate of oxidation of two zirconium-tin alloys was determined by Mallett and Albrecht (15R). A zirconium-1.5% tin alloy followed a cubic law in the temperature range 600" to 900" C. They found a change a t 800" C. in the rate constant dependence on temperature, which had values of 38 and 22 kcal. per mole below and above 800' C., respectively. An alloy of zirconium-2.5% tin gave quite different results. The rate of oxidation was parabolic, with an activation energy of 32 kcal. p e r mole. The effect of the tin was t o increase the porosity of the oxide f i l m and to decrease the time beforc breakdown of the protective properties of the films. Chatterjee (5R) has considered thc case of oxidation of some alloys when the addition of a third component changes the rate law from parabolic to logarithmic. These include copper-zinc

I N D U S T R I A L AND ENGINEERING CHEMISTRY

Vol. 48, No. 3

DIFFUSION IN METALS and copper-magnesium alloys to which aluminum or manganese is added. H e represents the experimental data in the form of an equation in which two or more functions, represcnting differcnt mechanisms of growth of film, are taken into considcration simultaneously. Smith, Steidlitz, and IIall (26R) have followed the reaction a t high temperatures between air and liquid metal solutions containing sodium. The composition limits of reaction of air with solutions of sodium with bismuth and mercury were established in the temperature range 600” to 800” C. For sodium-bismuth, the reaction was accompanied by a flame or a weak explosion a t high temperatures and high sodium concentrations. No reaction was observed a t mole fraction of sodium less than 0.45. For sodium-mercury, the critical sodium mole fraction was about 0.3. Saturation of the air with water vapor shifted the reaction limit to lower sodium concentrations. The systems sodium with cadmium, indium, lead, silver, and tin were tested in dry air at 700’ C. and a sodium mole fraction of 0.1 and were all found to be quite reactive. Pryor and Keir ( I 8 R ) have developed a method for the isolation of surface films from aluminum alloys and have made a detailed study of the mechanism of the reactions involved. The solution used for stripping the films consisted of iodine in warm methanol to which sulfosalicylic acid was added. A general review of high temperature metal-ceramic seals, by Palmour (17R), gives information that is of interest to the development of high temperature alloys, such as cermets.

Acknowledgment The preparation of this review was supported in part by the U. S. Atomic Energy Commission, the Office of Naval Research, and the Office of Scientific Research, W A F .

(1W Gegusin, Y A., Doklady Akad. Nauk S.S.S.R. 100,255 (1955). (11-4) Gertsriken, S. D., Ibid., 98, 2J1 (1954). (12-4) Hoffman, R. E., Turnbull, D., Hart, E. W., Acta Met. 3, 417 (1955). (13.1) Huntington, H. B., Shirn, G. A., Wajda, E. S.,Phys. Rev. 99, 1085 (1955). U4A) Kauffman, J. W., Koehler, J. S., Ibid., 97, 555 (1955). (15 9 ) Kochendbfer, A., Natvrwiasenschaften 41, 36 (1954). (16.4) Landergren, U. S., Mehl, R. F., J . Metals 5 , Trans. A I M E 197, 153 (1953). ( 17.4) Lasarev, B. G., Ovcharenko, 0. N., Doklady Akad. Nauk S.S.S.R. 100, 875 (1955). (18-1)Lararus, D., in “Impurities and Imperfections,” Am. SOC. Metals, Cleveland, Ohio, 1955. ( 1SA) Lorner, W. M., Cottrell, A. H., Phil. Mag. 46, 711 (1955). (20A) hlcClure, J. W., Phys. Rev. 98, 449 (1955). (21.4) McDonald, D. K. C., in “Report of Conference on Lattioo Defects in Crystalline Solids held at Bristol, July 1954,” Phys. Soc., London, England, 1955. (22-4) RIayburg, S., Phys. Reo. 98, 1134 (1955). (23.1) hIeecham, C. J., Eggleuton, R. R., ActQ Met. 2 , 680 (1954). (24.4.) Moon, K. A., J . Phys. Chem. 59, 71 (1955). ( 2 5 4 Nachtrieb, N. €I., Handler, G. S., Acta Met. 2, 797 (1954). (26A) Nicholas, J. P.,Ibid., 3, 411 (1955). ( 2 7 4 Pines, B. Y., Zhur. Tekh. Fiz. 24, 1521 (1954). (28-i) Resnick, R., Baluffi, R. W., J . Metals 7, Trans. A I M E 203, 1004 (1955). (29.4) Seeger. A., Phil. Mag. 46, 1194 (1955). (309) Shewmon, P. G., Bechtold, J. H., Acta Met. 3,452 (1955). ( 3 1 4 Smirnov, A. A., Dopovidi Akad. Nauk Ukr. R.S.R. 1954 No. 4, p. 250. (32.1) Smirnov, A. A., Zhur. Tekh. Fit. 23, 56 (1953). (33-4) Vernotte, P., Compt. rend. 240, 2522 (1955). (344) Zener, C., Acta Met. 3, 454 (1955). VOLUME SELF-DIFFUSION IN PURE METALS

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VOLUME SELF-DIFFUSION IN ALLOYS

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I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y

599

FUNDAMENT A LS R EVlEW CHEMICAL DIFFUSION IN SUBSTITUTIONAL ALLOYS

(1D) Accary, A., Compt. rend. 240, 519 (1955). (20) Bryon, E. S., Lambert, V. E., J . Electlochem. Soc. 102,38 (1955). (3D) Grace, 13. E., Derge, G., J . Xetals 7 , Trans. A I M E 203, 839 (1955). (4D) Gruzin, P. I,., Doklady Akad. Nauk B.S.S.R. 94, 681 (1954). (5D) Horne, G. T., hlehl, R. F., J . Metals 7, Trans. A I M E 203, 88 (1955). (6D) Landergren, U. S., Birchenall, C. E., Mehl, R. F., private communication. (7D) Lindner, R., Karnik, F., Acta M e t . 3, 297 (1955). (8D) Mohr, T., Monch, G. C., Ann. Physik 14, 363 (1954). (9D) Neiman, hI. B., Shinyaev, A. Y.,Doklady Akad. N a u k S.S.S.R. 96, 315 (1954). CHEMICAL DIFFUSION IN INTERSTITIAL ALLOYS

Birchenall, C. E., Mead, €I. W., private communication. Busby, P. E., Wells, C., private communication. Dayal, P., Darken, L. S., Trans. Indian I m t . Metals 7, 241 (1955). Ewing, V. C., Ubbeholde, A. R., Proc. Roy.SOC.(London)A230, 301 (1955). Grusin, P. L., Polokarpov, Y. 8.,Shumilov, M. A., %avo& skaga Lab. 21, 417 (1955). Johnson, E. W., Hill, M. L., Acta Met. 3, 99 (1955). Krishtal, hl. A., Doklady Alcad. N a v k S.S.S.R. 99, 983 (1954). Leak, D. A., Thomas, W. R., Leak, G. M., Acta Met. 3, 501 (1955). I,eClaire, A. D., Rowe, A. II., Rev. Met. 52, 94 (1955). Meijering, J. L., Acta M e t . 3, 157 (1955). Pfeiffer, I., Z . Metallkunde 46, 516 (1955). Seith, W.,Wever, H., Natuiwissenschaften 41, 447 (1954). Thomau, W. R., Leak, G. hI., Nature 176, 29 (1955). R’agne~,E’. C., Bucur, E:. J., Stcinberg, M. A., Trans. A m . SOC. Metals, preprint 32, 1955. GRAIN BOUNDARY AND SURFACE DIFFUSION

(1F) Bokhshtein, S. Z., Gudkova, T. I., others, Zavodskaya Lab. 21, 423 (1955). (2F) Cahn, R. W., in “Impurities and Imperfections,” Am. SOC. Metals, Cleveland, Ohio, 1955. (3F) Chalmers, B., Ibid. (4F) Drechsler, M., Pankow, G., Vansolow, R., 2. physik. Chem. 4, 249 (1955). (5F) Dunn, C. G., Hibbard, W. R., Acta Met. 3,409 (1955). (6F) Forty, A. J., Advances in Phys., No. 3, 1, 1955. (7F) Gilman, J. J., Acta Met. 3, 277 (1955). (8F) Gruhl, W., Ammann, D., Ibid., p. 347. (9F) Haynes, C. W., Smoluchowski, R., Ibid., p. 130. (10F) Heidenreich, R. D., Ibid., p. 79. (11F) Hulme, K. F., Ibid., 2,810 (1954). (12F) Montariol, F., Compt. rend. 240, 1087 (1955). (13F) Okkerse, B., Tiedema, 1’. J., Burgers, W. G., Acta M e t . 3, 300 (1955). (14F) Plumb, R. C., Rev. Sci. Instr. 26, 489 (1955). (15F) Pollock, W. I., Mehl, R. F., Acta Met. 3, 214 (1955). (16F) Pound, G. M., Simnad, M. T., Yang, L., J . C h e m Phys. 22, 1215 (1955). (17F) Robert, hf., Robillaid, A., Lacombe, P., Compt. rend. 240, 1089 (1955). (18F) Sears, G. W., Acta Met. 3, 361 (1955). (19F) Thomas, W. R., Chalniers, B., Ibid., p. 17. (20F) Tiller, W. A., Winegard, W. C., Ibid., p. 208. (21F) Whipple, R. T. P., Phil. Mag. 45, 1225 (1954). (22F) Yukawa, S., Sinnott, M. J., J . Metals 7 , Trans. A I M E 203, 996 (1955). PHASE TRANSFORMATIONS

(1G) (2G) (3G) (4G)

MECHANICAL PROPERTIES

(1J) Anderson, 0. L., Andreatch, P., J . Appl. Phys. 26, 1518 (1955). (25) Beck, P., Advances in Phys., No. 3, 245, 1954. (35) Breen, J. E., Weertman, J., J. Metals 7, Trans. A I M 8 203, 1230 (1955). (45) Frenkel, R. E., Sherby, 0. D., Dorn, J. E., Acta Met. 3, 470 (195.5). (55) Parker, E. R., Washburn, J., in “Impurities and Imperfections,” Am. SOC.Metals, Cleveland, Ohio, 1955. (6J) Pi-anatis, A. I,., Pound, G. JI., J . Metals 7, T r a m , A I M E 203, 664 (1955). (75) Weertman, J., J . A p p l . Phys. 10, 1213 (1955). SEMICONDUCTORS

(1K) Blodgett, K. B., J . A p p l . Phys. 26, 1520 (1955). (2K) Burton, J. A., in “Impurities and Imperfections,” Am. SOC. Metals, Cleveland, Ohio, 1955. (3K) Dunlap, W. C., Phys. Reo. 94, 1531 (1954). (4K) Ellis, S.G., J . A p p l . Phys. 26, 1140 (1955). (5K) Logan, R. A., Phys. Rev. 100, 615 (1955). J.I Appl. ., Phys. 26, 1287 (1955). (6K) Logan, R. A., Schwartz, % (7K) Maesen, F., Brenkman, J. A., J . Electrochem. SOC. 102, 229 (1955). (8K) Naesen, F., Brenkman, J. B . , Philips Research Repts. 9, 226 (1954). (9K) Reiss, H., Fuller, C. S., Phys. Rev. 97, 559 (1955). (10K) Vogel, F. L., Acta Met. 3, 245 (1955).

IRRADIATION DAMAGE

(1L) Broom, T., Advances in Phys., No. 3, 26, 1954. (2L) Glen, J. W., Ibid., No. 4,381, 1955. (3L) Kinchin, G., Pease, R. S.,Repts. Progr. in Phys. 18, 1 (1955). (4L) Seits, F., Koehler, J. S., in “Impurities and Imperfections,” Am. SOC.Metals, Cleveland, Ohio, 1955.

REVIEWS OF OXIDATION

(1M) (2M) (3M) (4M) (51cI)

Ann. N . Y. Acad. Sci. No. 58,1955. Betteridge, W., Brit. J . A p p l . Phys. 6, 301 (1955). Corrosion 11, No. 5, 59 (1955). Coughlin, J. P., U. S. Bur. Mines, Bull. 542, 1954. Dankov, P. D., Ignatov, D. V., Shishakov, N. A., “Electronographic Examination of Oxide and Hydroxide Coatings on hletals,” hloscow. 1953. (6bl) Evans, U. R., Rev. Pure A p p l . Chem. (Australia) 5 , 1 (1956). (7M) Garner, W. E., “Chemistry of the Solid State,” Academic Press, New York, 1955. (8h.I) Hauffe,K., “Reaktionen in und an Festen Stoffen,” SpringerVerlag, Berlin, 1955. (9M) Heavens, 0. S.,“Optical Properties of Thin Films,” Butterworths, London, 1955. (10M) Levy, A., Materials & Methods 41, 117 (1955). (11M) Long, R. A., Metal Progr. 68, No. 3, 123 (1955). (1231) Maurer, R., in “Impurities and Imperfections.” Am. SOC. Metals, Cleveland, Ohio, 1955. (13M) Pfeil, L. B., Chemistrg & Indw8trg 1955, p, 208. (14M) Robertson, W. D., in “Impurities and Imperfections.” Am. SOC. Metals, Cleveland, Ohio, 1955. (104) Smeltser, W. W., Corrosion 11, No. 9, 18 (1955). THEORY OF OXIDATION

Frank, E’. C., Puttick, K. E., J. A p p l . Phus. 26, 1522 (1955). Heidenreich, R. D., Ibid., p. 879. Turnbull, D., Acta Met. 3, 55 (1955). Turnbull, D., in “Impurities and Imperfections,” Am. SOC. Metals, Cleveland, Ohio, 1955.

SINTERING

(IH) Geguzin, Y. E., Pek-En-Gin, Zhur. Tekh. Fiz. 24, 1626 (1964). (2H) Kingery, W. D., Berg, M., J. Appl. Phys. 26, 1205 (1965).

600

(3H) Pines, B. Y., Gegusin, Y. E., Zhur. Tekh. Fiz. 23, 1559 (1953) (4H) Seigle, L. L.,Pranatis, A. L., J l f e t a l P ~ o g r 68, . No. 6. 86 (1965).

(1N) Birchenall, C. E., private communication. (2N) Cabrera, N., Levine, h1. hl., Plaskett, J. S., Phys. Rev. 96, 1153 (1954). (3N) Carter, R. E., Richardson, F. D., J . Metala 7 , Trans. A I M E 203, 700 (1955). (4N) Dowald, J. F., J. Electrochem. SOC.102, 1 (1955). (5N) Ilschner, B., 2.Elektrochem. 59, 542 (1955). (6N) Katz, E., Phys. Rev. 99, 1334 (1955). (7N) Landsberg, P. T., J . Chem. Phys. 23, 1079 (1955). (8N) Lidiard, A. B., Phil. Mag. 46, 815 (1955). (9N) Ibid., p. 1218.

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 48, No. 3

DIFFUSION IN METALS

(1P) Anderson, J. S , Edgington, D. N., others, J . Chem. SOC.1954, p. 3324. (2P) Aubry, J., Marion, F., Compt. rend. 240, 1770 (1955). (3P) Brewer, L., Haraldson, H., J . EZectrochem. SOC.102, 399 (1955). . 588 (1955). (4P) Candidus, E. S.,Tuomi, D., J . Chen. P h ~ s 23, (5P) Fischer, W. A., Hoffinann, A., i'?aturwissenschaften 41, 162 (1954). (6P) Garner, W. E., Reeves, L. E., Trans. Faraday SOC. 51, 694 (1955). (7P) Heikes, R. It., Phys. Rev. 99, 1232 (1955). (8P) Hoekstra, H. R., Siegel, S., others, J . Phys. Chem. 59, 136 (1955). (9P) Igaki, K., Bull. Nawina Uniu. A3, 113 (1955). (1OP) Jacobs, P. V. M., Tompkins, F. C., J . Chem. Phys. 23, 1445 (1955). (11P) Johnston, W. G., Phys. Rev. 98, 1777 (1955). (12P) Libowitz, G. G., Bauer, S. E., J . Phys. Chem. 59, 209 (1955). (13P) Lindner, R., J . Chem. Phys. 23,410 (1955). (14P) Priniak, W., Delbecq, C. J., Tuqter, P. H., P h w . Rev. 98, 1708 (1955). (15P) Secco, E:. A., Moore, W. J., J . Chem. Phys. 23, 1170 (1955). (16P) Seith, W., Kruse, R . , 2 anorg. u. atloem. Chem. 276, 141 (1954). (17P) Simnad, M. T., Smoluchowski, R , J . Chem. Phys. 23, 1961 (1955). (181') Volkenshtein, N. V., Orlov, A N.,Imest. Akad. Nauk S.S.S.R., Ser. Fiz. 18,494 (1954). (19P) Wachtman, J. B., Maxwell, L. €I., J . Am. Ceram. SOC.37, 291 (1954). (POP) ]Tinter, E. H . S..J . Chem. SOC. 1955, p. 2726

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METAL OXIDATION

ALLOY OXIDATION

(1Q) Adams, G. B., Maraghini, M., Rysselbergh, P. V., J . Electrochem. SOC.102, 502 (1955). (2Q) Bardolle, J., Rev. m8t. 51, 833 (1964). (3Q) Baur, J. P., Bridges, D. W.,Fassel, W. M., J . Electrochem. SOC.102, 490 (1955). (4Q) Recker, J. A,, Brandes, R. G., J . Chem. Phvs. 23,1323 (1955). (5Q) Bernstein, R. B., Ibid., p. 1797. (6Q) Booker, C. J. L., Wood, J. L., Walsh, A., Nature 176, 222 (1955). (7Q) Caplan, D., Burr, A. A., J . Mstala 7, Trans. A I M E 203, 1052 (1955). (8A) Carter, R. E., Richardson, F. D., Wagner, C., Ibid., p. 203. (98) Christensen, H., R o c . Inst. Radio Engrs. 42, 1371 (1954). (lOQ) Clarke, E. N., Ann. N . Y . Acad. Sci. 58, 937 (1954). (llQ) lhavnieks, A, J. Electrochem. SOC. 102,435 (1955). (12Q) Edwards, R. K., Levesque, P., J . Am. Chem. SOC.77, 1312 (1955). (136) Ehrlich, G., J. Chem. Phys. 23, 1543 (1955). (14Q) Farber, M., Darnell, J., Ehrenberg, D., J . Electlochem. SOC. 102, 446 (1955). (15Q) Gronlund, F., Benard, J., Compt. rend. 240, 624 (1955). Roy. SOC.(London) 232, (16Q) Grunberg, I,., Wright, K. I€. R., PTOC. 403 (1955). (17Q) Gulbransen,'E. A,, Andrew, K. F., J . Metals 7, Trans. -4I.MB 203, 136 (1955). (l8Q) Gulbranfien, E. A,, hfcMillan, . '%1 R., Andrew, K. F., Reu. mdt. 52, 509 (1955). (19Q) IIalliday, J. S.,Hirst, W.,Proc. Phys. SOC.(London) 68B, 178 (1955). (20Q) Henderson, W. G , Rernstein, R. R.,J . Am. Chem. SOC.76, 5344 (1954). (21Q) Jenkins, A. E., J.Inst. Metals 84, 9 (1955). (22Q) Kingston, R. If., Phys. Rev. 98, 1766 (1955). (23Q) Lanyon, M. A. H., Trapnell, R. M. W., Proc. Rog. SOC.(London) A227, 387 (1955). (24Q) Law, J. T., J . Phys. Chem. 59, 543 (1955)

(1R) Am. SOC.Testing Materials, Symposium on Effect of Cyclic Heating, Special Tech. Publ., 165, 1954. (2R) Betteridge, W., Sachs, K., Lewis, If., J . Inst. Petroleum 41, 170 (1955). (3R) Brenner, S.S.,J. Electrochem. SOC.102, 7 (1955). (4R) Ibid., p. 16. (5R) Chatterjec, G. P., J . AppE. Phfis. 26, 363 (1955). (6R) Foley, K. T.. Druck, J. U., Fryxell, R. E., J . Electrochem. SOC. 102, 440 (1955). (7R) Frederick, S. F., Cornet, I., Ibid., p, 285. (8R) Gleiser, M., Larsen, W. L., others, private communication. (9R) Grecne, R. J., Sefing, F. G., Corrosion 11, No. 7, 43 (1955). (10R) Harris, G. T..Child, IT. C., Kerr, J. A., J . Iron Steel Inat. (London) 179, 241 (1955). (11R) Heraig, A. J., Blanchard, J. R., Metal Progr. 68, No. 4, 109 (1955). (12R) Iitaka, I., Otsuka, R., Repts. Sci. Research Inst. (Japan) 30, 2G5 (1954). (13R) Lucas,'G., 'h'eddle, M., Preece, A, J . Iron SteelInut. (London) 179, 342 (1955). (14R) Malamand, F., Vidal, G., Compt. rend. 240, 186 (1955). (15121 Mallet, M. W.,Albrecht, W. AI., J . Electrochem. SOC. 102, 407 (1955). (16R) Moreau, J., Benard, J., Publs. inst. recherches siderurgie, No. 109, 3, 1955. (17R) Palmour, H., J . Electrochem. SOC.102, 160 (1955). (18R) Pryor, M. J., Keir, D. S., Ibid., p, 370. (19R) Rhodin, T. H., Ann. N . Y . Acad. Sci. 58,855 (1954). (20R) Saller. H. A., Stacy, J. T., Eddy, N. S., U. S.Atomic Energy Commission, BMI-922, June 1954. (21R) Simons, E. L., Browning, G. V., Liebhafsky, H. A., Corrosion 11. No. 12. 17 (1955). (22R) SrnitL, G. P., Ste(dlitz,'M. E., IIall, L. L., J. Am. Chenz. SOC. 77, 4533 (1955). (23R) Young, W. E., Hershey, A. E., Irussey, C. E., Trans. Am. SOC. Mech. Engrs. 77, 985 (1955).

OXIDES AND RELATED CRYSTALS

March 1956

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