an
I I/=c]Chemical Engineering Fundamentals Review
Diffusion in Metals by P. G. Shewmon and G. R. love, Metallurgy Department, Carnegie Institute of Technology, Pittsburgh, Pa. The study of defects in pure metals has become one of the most active areas of research in metallurgy and solid state physics
T,E
GREAT MAJORITY of the diffusion work reported during the past year was aimed at studying the atomic processes in, and structures of, metals. The question: How fast does diffusion occur? has been largely replaced by : How does it occur on an atomic scale? I n pure metals, an absolute value of the number of vacancies in a metal near its melting point has been determined for the first time. A more detailed, more plausible, and more complicated model of the activation process has been studied. In alloys, interesting work was done on the effect of solute-dislocation interaction on the diffusion coefficient. Another study indicated the relative effectiveness of various types of grain and twin boundaries as sources and “conductors” of vacancies. The older question : How fast does element A diffuse in element B? was studied infrequently, and when it was, the authors often made a systematic study of the variation of the solute diffusion coefficient with atomic diameter or valence. A large amount of work has been done on the formation, diffusion, and interaction of point defects. Much of this work has been done by physicists who are interested in the structure of solids. T h e active study results partly from the importance of these defects but more from the fact that annealing and diffusion studies provide a means of studying these entities, since other, more important defects such as dislocations cannot be as easily isolated and studied. This review covers the literature published between Nov. 1, 1959, and Nov. 1, 1960.
Reviews Three reviews on diffusion have been published in the last year. Lazarus ( 7 A ) covered the entire field in 20 pages. The review is advanced, brief, and written more for the specialist. Van Bueren ( 3 A ) has also covered the entire field, but has used slightly more space and has written more of a n introduction for the nonspecialist. T h e study of defects in pure metals has become one of the most active areas of research in metallurgy and solid state physics. Lomer ( 2 A ) has written a n excellent, comprehensive review of
this growing field with an emphasis on point defects, the validity of the theoretical calculations made to date, and the bearing of experimental observations on the models used.
Pure Metals The activation process in diffusion is not well understood. The model used primarily in the past was the quasithermodynamic picture of reaction rate theory. Last year, Rice supplied a new approach to the problem by studying the probability that in a large group of oscillating atoms one next to a vacant site would achieve a critical displacement at the same time that all particles which might impede its motion had oscillated out of the way. Manley has now generalized the calculation and made it more explicit (98, 7023). H e also shows that, to a first approximation, the activation energy obtained from this newer procedure is equal to the strain energy in the lattice a t the saddle point, as Zener inferred several years ago. Another detailed calculation of the activation process using lattice waves was given by Plesner (788). H e used a onedimensional lattice to make the problem tractable. His results indicate a much larger variation of the diffusion coefficient D with the mass of the diffusing atom than is indicated by the older studies. I n spite of the large amount of work that has been done on the formation and annealing kinetics of vacancies in metals, before last year there were no experimental results which gave an absolute value of the fraction of sites vacant, Nu, a t any given temperature. I t was always much easier and adequate to work with some property which was proportional to N , . Simmons and Balluffi (24B, 25B) have now made the first measurement of the absolute value of N , by simultaneously measuring the lattice parameter, ao, and the macroscopic length, I , of a bar of metal from room temperature to the melting point. The quantity a,, gives the mean interplanar spacing even if many sites are vacant. If vacancies are added, new planes are added so that by comparing Aao/ao and A l / l the number of new sites (i.e,, vacancies) can be de-
termined.
T h e maximum values of
N , at the melting point were about for aluminum (25B) and for silver (24B). T h e experimental problems involved are awesome, but the work was well done. The entropy of formation of a vacancy in aluminum was found to be 2.4k (Boltzman constant) per atom [equivalent to 2.4R (gas constant) per mole]. This is the first time this quantity has been measured in any metal. I t is within a factor of 2 of that calculated for a vacancy in copper, which indicates that the calculation is satisfactory. Formation energies of vacancies in both silver and aluminum were obtained which agreed well with values previously obtained from the variation of quenchedin resistance with quenching temperature. I t has been pointed out by Lomer ( 2 A ) that the term “vacancy” or “an interstitial atom” does not mean a vacant lattice site or one atom not on a normal lattice site, but only signifies a n extra atom or a deficit of one atom, respectively, in a given region. This approach prepares one for the type of “interstitial~’’ now being discussed for pure face-centered-cubic metals. Seeger and Mann (22B) have made a new calculation of the formation energy and concluded, as have others, that the extra atom is not “inserted” at the midpoint of a cube edge but shares a site with a facecentered atom. T h a t is, both atoms line up in a direction in a (010)-type plane, with the lattice site midway between the two. This type of configuration introduces a tetragonal distortion and, if present in sufficient quantity, should give rise to a n internal friction peak when the applied frequency approximates the j u m p frequency of the interstitial. Seeger and others (238) have found a resonance peak in cold worked nickel which has the activation energy they calculate (0.8 e.v.) for the reorientation of such an interstitial atom. Unfortunately, this does not prove their model, since a n interstitial atom inserted on a cube edge would give the same type of resonance peak. Another interesting example of a relaxed group of atoms is a trivacancy in a face-centered-cubic lattice. Damask and others (7B)have pointed out that the VOL. 53, NO. 4
APRIL 1961
325
an
Chemical Engineering Fundamentals Review
Table I.
Pure Metals
Subject
Quenched-in defects Au
Ag Lattice relaxation near vacancy Dynamics of diffusion Point defect migration (W) Effect of torsion on diffusion Point defect migration (Cu) Diffusion mechanism (2-Fe) Self-diffusion (Ni) Equilibrium vacancy concentration (Al) Point defects in Pt Self-diffusion (Nb) Self-diffusion (y-U) Vacancy-vacancy interaction (Cu) Grain boundary grooving Theory of diffusion
lowest energy configuration for the three vacancies of a trivacancy is a triangular arrangement on a close-packed plane. There will be a n atom in the middle of this triangle on the close-packed plane immediately above or below, and it will “fall into” this triangular hole. This gives one atom in the middle of a tetrahedron. T h e ’ composite is quite stable and has a high activation energy for movement. I t is generally accepted that divacancies are quite mobile and can contribute appreciably to the annealing of vacancies in quenched samples. However, from the abo\e, it would appear that aggregates of three or more vacancies contribute to annealing only by acting as stationary sinks. Several years ago Fensham reported that, for self-diffusion in p-tin, DO10-4 in the equation D = DO exp( - A H / R T ) . Thus The entropy of activation would be quite negative. This was inconsistent with Zener’s analysis and most of the other data on self-diffusion in pure metals. Meakin and Klocholm ( 7 7B)have remeasured self-diffusion in P-tin and found D Oto be between 1 and 10, as would be expected from Zener’s model and the data on other metals. These new values also fit in with the activation energies obtained by De Sorbo (3B) from creep studies and quenching experiments on tin. A4dditionalstudies on pure metals are listed in Table I .
Alloy Diffusion ,4t low temperatures, the apparent diffusivity of solute atoms and tracer atoms in single crystals is frequently appreciably higher than would be predicted by extrapolating from the high temperature data. According to a theory advanced by Hart, this enhanced diffusivity may be explained, for tracer diffusion in pure metal, by- chance
326
encounters of a diffusing atom wiih a random array of high-diffusivity “pipes” -e.g., dislocations-in metal. This theory has now been extended by Mortlock (26C) to the case of alloy diffusion, and he has shown that the apparent lattice diffusivity of solute may h e further enhanced if the solute is attracted to the dislocations. When such attraction exists, the solute atom spends more time in the high diffusivity region than Tvould be expected Gom chance encounters. Since the segregation to dislocations and the ratio of dislocation diffusivity to lattice diffusivity each increase with decreasing temperature, the apparent low temperature diffusivity is doubly exaggerated. The author discussed the low temperature diffusivity of iron, cobalt, and nickel in copper and obtained reasonable values for the binding energy between solute atom and dislocation. H e also showed that it is no longer necessary to assume unreasonable dislocation densities to rationalize the observed low temperature diffusivity of anrimony in silver. I t was observed by Garstone and Nileshwar (75C)that the rate of solution of CuAlz particles in aluminum is reduced by simultaneous high temperature creep. The observation is in contrast to the general observation that mechanical deformation accelerates diffusion and thus, one would believe, diffusion-controlled processes. They proposed that the solution rate is retarded because dislocation loops around the CuA12particles, introduced by the creep, act as copper sinks and barriers to copper diffusion. They cited several other observations that diffusion-controlled processes may be slowed by deformation. The effect of pressure on the growth rate of intermetallic phases in binary diffusion couples has been discussed by Castleman (73C). H e pointed out that pressure may influence the growth rate in two ways: through its influence on the diffusivity (in general, diffusivity decreases with increasing pressure) and through its influence on the equilibrium phase boundary concentrations. He established critical parameters for determining the relative influence of the two contributions and discussed the applicability of his model to the observed growth rate of intermetallic layers in the systems uranium-aluminum and nickel-aluminum. The energies of formation and motion of vacancies are of considerable interest for a theoretical understanding of diffusion processes. A number of recent experimental attempts to determine these quantities have yielded anomalous data. A detailed discussion of the kinetics of the annealing of quenched-in vacancies in dilute alloys has been pre-
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
sented by Damask and Dienes (74C), and their discussion allows quantitative interpretation of the supposed anomalies in such data. They consider that the vacancy may participate in two reactions during annealing after quenching or after ion bombardment: I t may be absorbed a t a sink, or it may be more or less tightly bound to an impurity atom in a “complex.” Solutions obtained from a n analog computer suggested simplifying assumptions Mhich allowed an analytic solution of the differential equations for these reactions. For a wide range of physically interesring parameters, the solutions predict: that measured activation energies may not be equal to the energy of motion of the vacancy, even at solute concentrations of the order 10-6; that the pre-exponent of the rate constant is temperature dependent ; and that, if the vacancy/impurity atom binding energy is high or if the impurity Concentration is appreciable, large transients appear in the decay curves of vacancy concentration us. time, independent of the formation of divacancies. The treatment suggests experimental methods for determining both the energy of motion and the binding energy. It also stresses the necessity for using very pure material for vacancy annealing studies. Two major attempts have been made LO test the validity of existing general theories or alloy diffusion. Inman and Barr 178C‘) reported a summary of the best data for the diffusion of nickel, cobalt, iron? copper, zinc, cadmium, and antimony in copper and compared the observed activation energies with the predictions of Lazarus (who considered the influence of excess valence) and the modification of the Lazarus theory proposed by 41fred and March. T o afford a n approximate comparison to the relative size of the solute and solvent atoms, they also presented the Guldschmidt radii of the solute atoms. Although a qualitative correlation exists between diffusivity and either the excess valence or the difference in radius, no quantitative relationship is apparent. Quite similar work comparing the relative diffusivity of silicon, chromium, iron, nickel, strontium, and lanthanum in yuranium has been carried out by Mosse and others (3C, 25C) with somewhat greater success. Again, they observed only a qualitative correlation between activation energies and the nominal excess valence. However, they found that, a t all temperatures investigated, a plot of the logarithm of the solute diffusivity a t a given temperature us. the solute Goldschmidt radius yielded a smooth, inflection-free curve. If a homogeneous binary alloy is placed in a temperature gradient, there
.
an will be a n unmixing which will make the hot end richer in one component. This is called thermal diffusion. Shewmon (35C) has measured this unmixing for carbon in a-iron, where the carbon segregates strongly to the hot end, and in y-iron, where no unmixing occurs. T h e model used to rationaliie the results suggests that this type of experiment can be used to determine the region along the jump path where most of the activation energy must be absorbed before a jump can occur. Table I1 lists other work in this area.
Surface Diffusion A detailed investigation of the surface self-diffusion of tungsten has been carried out by Barbour and others ( I D ) using the field emission microscope. Quantitative determinations of the diffusion constants could be made for the first time, since very high fields could be used to make individual atomic steps in the surface visible, and the motion of the steps could be related to the diffusion flux. The surface was quite clean, since the ambient pressure was of the order mm. of mercury; the constants obtained were applicable for diffusion in the absence of a field, since the field was pulsed and was on only O.O030j, of the time. The diffusion expression obtained in this manner was :
D
=
4 exp (-72,00O/RT) sq. cm./second
I n this investigation an effective electrostatic pressure could be placed
Table 11.
Alloy Diffusion
Subject Sr in U Cu, Ni, and A1 in U (influence of pressure) Nb in U Au in U Ti in U Na, K, and Ca in Pt AI, Sn, V, Mo, and Mn in Ti Cu, Mg, and Zn in AI (influence of impurities) Pt in Au Cr in Fe Fe in Fe(V) S i n Fe(Si) and Fe(Si, Mn) Li in W Cd in Ge B in Si P in Si and S i 0 X e in Ag He, Ne, NP,and H g in glass HPin metals (especially Fe) H Ppermeation in metals HPin Ni (effect of deformation) HPin a-Fe C in y-Fe (Mn, Si) HZin Zircaloy-2 H2 permeability in Fe H2permeabilit, in Pd Correlation effects Thermal diffusion in a-Fe Dynamical theory Precipitation (equations)
Kef. (2C) (iC) (SOC) (S2C)
(4C) UiC)
(16C)
(8C) (I7C) (29C)
(SQC)
(6C) (2SC)
UQC) (2W (6C (S8C)
(2lC) (1OC)
(QC) (i7C) (28C, Sf C )
(56C) (SsCt
@4C) (37C) (22C) U2C) (70
(24Q
r dChemlical Engineering Fundamentals Review
on the emitter surface by introducing a d.c. bias field. This pressure reduced the effective chemical potential gradient in the emitter surface and hence the diffusion flux. The bias field a t which the flux became zero was used to calculate the surface free energy of the tungsten emitter, y = 2900 ergs per sq. cm. T h e values of Do,the activation energy Q, and y are average values since diffusion took place over a hemispherical cap. Significant deviations from the average values occurred only for emitter axes near (110) and (211). The influence of the applied d.c. field on the activation energy for surface diffusion, though not significant for this work, was investigated in greater detail by Bettler and Charbonnier (30). Prior to last year, two significant attempts to describe the influence of a grain boundary on observed diffusivity have been made. I n each of these the grain boundary was considered to be a slab of high diffusivity material imbedded in a semi-infinite low-diffusivity medium. Each attempt made a number of limiting assumptions, and neither was ideally suited to the range of parameters in which diffusion data were easily obtained. Last year Levine and MacCallum ( 5 D ) proposed an extension of these models to describe the diffusion penetration in fine-grained polycrystalline samples. I n this case the low diffusivity region was assumed to be bounded on all sides by high diffusivity regions, and this assumption led to marked deviations from the penetration us. time predictions of the earlier theories. The authors avoided the necessity for oversimplification by relving on computer solutions and thus obtained an approximation applicable throughout the experimentally interesting range of parameters. They recalculated the ratio of grain boundary to lattice diffusivity, on the basis of their model, for the several investigations which have been reported, and obtained values roughly a factor of 4 larger than the values previously reported. They also developed a number of parameters for describing the diffusion conditions and used these parameters to outline the correct choice of experimental conditions for studying grain boundary diffusion. If a fully annealed copper sample is irradiated with a 38 m.e.v. beam of alpha particles, an extreme supersaturation of helium in solution in the copper is produced in a 3-mil-thick layer 40 mils below the irradiated surface. On heating, this supersaturation is relieved by precipitation of the helium. In order that the precipitating helium bubbles may nucleate and grow, there must be an appreciable flux of vacancies into the helium-supersaturated region ; hence bubbles will nucleate and grow only in the vicinity of bacancy sources.
The method of alpha-particle bombardment was used by Barnes ( 2 0 )to investigate sources of vacancies in metals. H e observed that sufficient quantities of vacancies for bubble formation may originate from high angle grain boundaries, internal voids, and free surfaces, but not from coherent twin boundaries or, apparently, from isolated dislocations or dislocation arrays such as sub-boundaries. Since a vacancy flux away €rom a source produces a metal-atom flux toward that source, active sources are distinguished from transmitting paths by a central portion containing dense metal. This difference verified that incoherent twin boundaries transmit, but do not produce, vacancies. I n Table I11 are listed other reports on surface diffusion. liquids Prior to last year theories of diffusion in liquids were based on models which calculated the frequency with which a “hole” of some minimum size occurred next to the diffusing atom and the probability the atom would j u m p into it. The calculation and results w-ere quite similar to that for diffusion by a vacancy mechanism in crystals. Swalin ( 6 E ) has presented an alternate model. His main contribution is the assumption that there is no minimum “hole” size or activation barrier for a “jump” but that the changes in the position of the atom are uncorrelated and thus they all contribute to the diffusion of the atom. H e calculated a mean square displacement from a density fluctuation model and obtained a closed expression for D. The most striking result is that D increases as T 2 , not as exp ( - Q / R T ) . The combination of low accuracy, low Q, and the small temperature range investigated made it difficult to distinguish between these two types of temperature dependence with the diffusion data available. A modified “hole theory” was used by Cohen and Turnbull ( I E ) to treat diffusion in liquids in the temperature range where a liquid turns to glass. The problem of frames of reference in liquids has bothered many since the Kirkendall effect showed the importance of the reference frame in diffusion in crystals. Kirkwood and others (2E) have given a detailed discussion of the various possible frames for liquids and
Table 111.
Surface Diffusion Ref.
Subject
Fe‘in a-Fe grain boundaries Dzin Cu H20(on ice)
VOL. 53. NO. 4
0
(GD) (7D)
(40)
APRIL 1961
327
an
Chemical Engineering Fundamentals Review
Table IV.
Liquids
Subject
Ref.
Solutes in liquid Sn Na in liquid Pb Ag in liquid Pb In in liquid Sn Sn in liquid In
(3E)
(CE) @E) (7.9 (7E)
the interrelation between the diffusion coefficients in the different frames for multicomponent systems. Additional rzports on this subject are contained in Table IV.
Nonmetals
(7B) Koo, R. C., “Reactive hfetals,” Vol. 11, pp, 265-73, Interscience Publishers, New York, 1959. (8B) Lee, Ch., Maddin, R., Weertman, J., Trans. A m . Inst. Mining, .Met., Petrol. Engrs. 218, 364 (1960). (9B) Manley, 0. P., J . Phys. Chem. Solids 13, 244 (1960). (10B) Manley, 0. P., Rice, S. A,, Phys. Reu. 117, 632 (1960). (11B) hfeakin, J. D.; Klokholm, E.?Trans. A m . Znst. itlining, Met., Petrol. Engrs. 218, 463 11960). (12i3) Meechan, C. J.: Phys. Rw. L m r s 4, 284 (1960). (13B) Meechan, C. .J., Sosin, A,, Brinkman, J. A,, Phys. R e v . 120, 411 (1960). (14B) Messner, A , ? Benson, R., Dorn, J. E..Trans. Am. Soc. Metals 53, Preprint No. 193 (1961). (l5B) Mullins, W’. W., Trans. Am. Znst. Minine. M e t . , Petrol. Eners. 218. 354 (1960y.’ (16B) Nenno, S., Kaufman. J. W.,Phil. Mag. 4, 1382 (1959). (17B) Piercy, G. R . , Phil. M a g . 5, 201 (1960). (18B) Plesner, I. W.: J . Chem. Phys. 33, 652 (1960), (19B) Resnick, R., Castleman, L. S., Trans. Am. Znst. Mining, Met., Petrol. Engrs. 218, 307 (1960). (20B) Rice, S. A , , Frisch, H. L., J . Chem. Pliys. 32, 1026 (1960). (21B) Rothman, S. J., Lloyd, L. T., Harkness, A. L., Trans. Am. Inst. Mining. Met., Petrol. Engrs. 218, 605 (1960). (22B) Seeger, A, Mann, E., J . Phys. Chem. Solids 12, 326-40 (1960). (23B) Seeger, A.: Schiller, P.? Kronmuller, H., Phil. M a g . 5 , 853 (1960). (24B) Simmons, R. 0.: Balluffi, R. W., Phys. Rev. 119, 980 (1960). (25B) Ibid., 117, 52 (1960). (26B) Mrcizer, V. G., Girifalco: L. A , Zbid.: 120, 837 (1960). Y
Internal friction is nojv used almost exclusively to measure D for interstitial atoms in body-centered-cubic metals. A similar effect has been suggested b y Haas ( I F ) for the case of interstitial oxygen in diamond-cubic siiicon or germanium. His model fits the prevjously available data and should be applicable to interstitial impurities in a n y diamond-cubic alloy. T h e determination of D for intcrstitial lithium in silicon was made by Pell ( 4 F ) using lithium4 and lithium-7. He found that D varied inversely with the square root of the mass of the diffusing isotope. From time to time one hears of diffusion experiments in which the j u m p frequency does not vary inversely as the squarc root of thc mass of the diffusing atom. However, there seem to be no well substantiated examples of this. Table V includes other studies of diffusion in nonmetals.
Table
V.
Nonmetals
Subject Thermal diffusion theory Li in Si Vacancy concentration in G e
Ref. (2F) (3F) (6.9
Literature Cifed Reviews (1A) Lazarus, D., “Solid State Physics,” Vol. X, p. 71, Seitz, F., Turnbull, D., ed.,
Academic Press, New York, 1960. (2A) Lomer, W. M., Progress in Metal Phjsics 8, 255 (1959). (3+) Van Bueren, H. G., “Imperfections
Crystals,” Tiorth Holland, Xmsterdam, Interscience, New York, 1960.
in
Pure Metals
(1B) Damask, A., Dienes, G., Weizer, V.: Phys. Ken. 113, 781 (1959). (2B) DeSorbo, W., Zbid., 117, 444 (1960). J . Phys. Chem. Solids 15, (3B) DeSorbo, W., 7 7 (~c)hn\ (1960). ,L, .,”,. (4B) Doyarna, M., Koehler, J. S., Phys. Rea. 119, 939 (1960). (5B) Girafalco. L. A., Wiezer. B. G..‘ J . ‘ Phys. Chem. Solids 12, 260 (1960). (6B) Kikuchi, R., Ann. Phys., 11, 306 (1960).
328
Alloy Diffusion (1C) Adda, Y . , Beyeler, M., others, l!dhm. sci. reu. ndt. 57, 423 (1960). (2C) Adda, Y . , Levy, V., others, Comfli. rend. : . 5 , 536 (1760). 13C) Adda. Y.. Levv. V.. others. Me‘m. ‘ sci. rev. me‘f:,5 7 ; 278 (1960). (4C) Adda, Y., Philibert; J., Acta M e t . 8, 700 11960\. N. G., Seybolt, A. U., J . Iron (5C) Steel Inst. (London) 194, 341 (1960). (6C) Alien, R. B., Bernstein, H.; Kurtz, A. D.: J . Appl. Phys. 31, 334 (1960). (7C) Allnatt. A. R., Rice, S.A,, J . Chem. ‘ Phys. 33, 573 (1960). (8C) Amitani, T., Sumitomo Lizht iVfetal Tech. R e p s . 1, 53 (1960). (9C) Ash, R., Barrer, R. M., Phil. Mag. 4, 1197 (1959). (10C) Banege-Nia, A , , Conipt. rend. 250, 524 (1960). (l?C) Bradley, R . C . ; Phy.r. Reu. 117, 1204 (1960). (12C) Brammer, W. G., Acta M e t . 8 , 630 (1960). (13C) Castleman, L. S., Ibid., 8, 137 (1960). (14C) Damask, A. C., Dienes, G. J . , Phys. Rev. 120, 99 (1960). (15C) Garstone, J., Nileshwar, V. B., J. h s t . iw8tQlS 88, 476 (1960). (16C) Goold, D.? Zbid., 88, 444 (1960). (17C) Grimes, H. H., Acta Met. 7, 782 (1959). (18C) Inman, M. C., Barr, L. W., Ibid.,8, 112 (1960). (19C) Kosenko, F. E., Sou& Phys.-Solid State 1, 1481 (1960). (2OC) Kurtz, A. D., Yee, R., J.A$$. Phys. 31, 303 (1960).
INDUSTRIAL AND ENOINEERING CHEMISTRY
~
(21C) Leiby, C. C.: Jr., Chen, C . I-.., Ibid., 31, 268 (1960). (22C) Manning, J. R.: Phys. Reu. 116, 819 / I ncn\ (1737).
(23C) McCracken, G. M., Love, H. M., Phys. Re&.Letters 5 , 201 (1960). (24C) Morrison, J. A,, Frisch, H. L., J Apfll. Phis. 31, 1621 (1960). (25C) Mosse, M., Levy, V., Adda, Y., Comfit. rend. 250, 3171 (1960). (26C) Mortlock, -4.J.. Acta Mef. 8, 132 I1 960). (2?C) Mortlock, A . J., Rowc, A. H.. LeClaire, A. D., Phd. M a g . 5, 803 (1960). (28C) Parlee, N. -4..Carmichael, D., others, Trans. Am. inst. Mining, .Met., Petrol. Engrs. 218, 826 (1960). (29C) Paxton, H. W., Pasierb, E. J., Zbid., 218, 794 (1960). (30C) Peterson, ii. L., Ogiivie, R. E., Zbid., 218, 439 (1960). (31C) Plusquellec, J., M i m . sci. rev. mtt. 57, 263 (1960). (32C) Rothman, S. J., U. S. Atomic Energy Commission ANL-6127, 1960. J . Nuclear Materials 2, (33C) Sawatzky, 4.: 62 (1960). (34C) Schenk, H., Taxhet, H., Arch. Eisenhiiltenw. 30, 661 (1960). (35C) Shewmon, P. G., Acta M e t . 8, 605 (1960). (36C) Steiner: W.,Krisement, O., Arch. Eisenhiittenw. 30, 637 (1959). (37C) van Swaay, M., Birchenall, C. E., Trans. Am. Inst. Mining, M e t . , Petrol. Engrs. 218, 285 (1960). (38C) Tobin, J. M., Acta M t t . 7, 701 (1959). (39C) Zelinsky, M. S., Noskov, B. M., others, Fit. M e t . i Metalloced. 8, 725 (1959). Surface Diffusion
(1D) Barbour, J. P., Charbonnier, F. M., others, Phys. Reo. 117, 1452 (1960). (2D) Barnes, R. S., Phil. Mag. 5, 635 (I 960). \ - - --,.
(3D) Bettler, P. C., Charbonnier, F. hl., Phys. Rev. 119, 85 (1960). (4D) Kingery, W.D., J . Afifd. Phys. 31, 833 (1960). (5D) Levine, H. S.. MacCallum. C. .J., ’ Zbid.: 31, 595 (1960). (6D). Leymonie, C., Lacombe, P., ’L4e‘rn. sc7. rea. mtt. 57, 285 (1960). (7D) Robinson, M. T., Southern, A . I>., Wills, W. R., J . Aflfll. Phys. 31, 1474 (1960). Liquids
(1E) Cohen, h5. H., Turnbull, D., J . Chem. Phvs. 31. 1164 (1959). 12E) -~~~~~ Kirkwood. J. G.: Baidwin (2E) Kirkwood, Baidwin,’ R. L.. L., .. others, Zbid., Zbzd., 33, 1505 11960). (1960). (3E) Ma, C. H., Swalin, R . A., Acta M e t . 8 , 388 (1960). (4E) Morachevsky, A. G., Cherespanova. E. A., Alabysher, A. F., Itvest. VL’ZTsLetnaja Metallurgiya Tscetnaja Metallurgzya 1960, p. 70. (5E) Preckshot, G. W.,Hudrik, R. E., Trans. Am. Znst. Mzninp, Minine, - M e t . , Petrol. Engrs. 218, 516 (1960). (6E) Swalin, R. A., Acta ‘Met. 7,736 (1959). (7E) Vicentini. M., Paoletti, A., iVuouooo ‘ c/mento 14, 1373 (1959). ,
\
~
~
,
I
~
~
Nonmetals
(IF) Haas, C., J . Phys. Chem. Solids 15, 108 (1 960). (2F) Ham, J . S., J . Apfil. Phys. 31, 1853 (1960) (3F) Pell, E. M., Phjjs. Reo. 119, 1222 (1960). (4F) Zbid.,p. 1014. (5F) Tweet, A. G., J . Appl. Phys. 30, 2002 (1959).
