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By Barbara A. Thompson

A previously reported high-resolution method for the location of boron-rich areas in metallurgical and biological specimens was been adapted for general use on a routine basis. The rnetlzod utilizes neutron activation and autoradiograpizy. Alpha-particles emitted by boron nuclei upon neutron capture are recorded on a photographic emulsion. The resulting a-particle tracks show the location of boron-rich areas. Experimental techniques, interferences, and limitations of the method are discussed in detail. The method is most useful where there is marked segregation of boron. In this type of sample, the segregation can be observed when the nominal boron concentration is as low as 0.0006 pct. THE positive identification and location of boron-rich areas in metals is frequently of great interest in metallurgical work. Unequivocal identification is often difficult to make by conventional metallo-graphic methods. Recently, a method has been described which accomplishes this objective by neutron activation and autoradiography.l-3 The method can be described briefly as follows. Upon neutron capture, a -particles are emitted by boron nuclei according to the following reaction: ,Blo + n - ,a4 + 3Li7 + 2.4 mev The energy is dissipated as kinetic energy of the products. By irradiating a boron-containing sample in contact with a photographic emulsion and subsequently developing this emulsion, a-particle tracks are obtained whose location corresponds to the location of boron-rich areas in the sample. Two factors combine to make the reaction extremely specific for boron. The first is the unusually high (755 barns) cross section of boron for thermal neutron capture. The second is the higher neutron energy required to produce (n, a ) reactions in essentially all other nuclei except lithium. These two factors make the method specific for boron by six to seven orders of magnitude when a predominantly thermal neutron source such as the Brookhaven reactor is used. The reported limit of detection of this method is of the order of 0.01 pct B., The present work was originally undertaken to determine whether this limit could be lowered by use of a thinner emulsion. However, initial experiments showed that in order to use the method at all, it was necessary to reestablish the optimum experimental conditions in terms of the available irradiation facilities. It is the purpose of this paper to describe these experimental conditions in detail, to discuss the factors influencing sensitivity, and to evaluate several techniques for increasing sensitivity. EXPERIMENTAL A) Preliminary Experiments—The first measure-ments were made using samples of crystal oriented silicon steel containing various concentrations of boron. In the later experiments, samples of various high-temperature alloys such as M-252, hcoloy 901, Nichrome V, and so forth, were used. Faraggi, et al.,2 reported that the lower limit of sensitivity in this type of sample was about 0.01 pct B using nuclear emulsions of 50- u thickness. but that it should be possible to extend this limit by the use of thinner emulsions. Accordingly, we first used Kodak Auto-radiographic Stripping Film (Permeable Base) which has an emulsion thickness of only 5 µ. This was mounted on the metallographic specimens according to the technique described by Boyd.4 The emulsion remained in contact with the metal surface throughout exposure and development. Since the emulsion is transparent after development, the autoradiograph and metal surface can be viewed simultaneously and any correlation between film blackening and structure of the metal can be made directly with no problems of realignment. Because the silicon steel is readily attacked by moisture alone, it was necessary to apply a protective coating to the metal surfaces before mounting the emulsion. The coating was made extremely thin in order to absorb as few a-particles as possible. Boyd4 and Gomberg5 have discussed various plastics used for this purpose; however, none was sufficiently impermeable to prevent chemical attack of the steel during the developing process. This attack resulted in the production of gross chemical artifacts in the emulsion. It was, therefore, necessary to use the method of Wolfsberg and John6 as follows. A very thin (approximately 1 µ) coating of Plexiglas II was applied by dipping the sample in a 2 pct solution of Plexiglas II in dichloroethylene. Then, because the emulsion will not adhere to Plexiglas 11, a thin coating of Parlodion was applied in a similar manner using 2 pct Parlodion in iso-amyl acetate. No protective coating was necessary with the high-tem-

Jan 1, 1961

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,' is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By Matti J. Saarivirta

Two new precipitation hardening copper-base alloys, Cu-1.5pct Ti-2.5 pct Sn and Cu-1.5 pct Ti-2.5 pct Sn-0.4 pct Cr were developed. High strength and medium conductivity are obtained by solution annealing and subsequent heat treatment. Combination of solution annealing, cold working, and heat treatment increases the strength further. Good elevated temperature strength and ductility makes these alloys superior to copper-beryllium-cobalt alloys. A considerable amount of research work is being done throughout the world to develop new and improved copper-base alloys. In many cases, the object is to develop alloys having a combination of high electrical and thermal conductivities, and high strength. The problem is complicated by the fact that any alloying element added to increase strength, invariably decreases conductivity. Among the few commercial precipitation hardening type copper-base alloys, the Cu-Be-Co alloys are best known. These alloys are used in many applications that require good spring characteristics cornbined with high strength and moderately high electrical conductivity. They can be formed readily after solution annealing, then heat treated to obtain high strength and conductivity. Because of the relatively high cost of the Cu-Be-Co alloys, considerable research has been aimed at developing new lower cost alloys having similar properties. As far as is known today, the binary Cu-Ti alloy is the only one whose properties are

Jan 1, 1962

By R. W. Fountain, J. F. Libsch

ONSIDERABLE time and effort have been ex- pended recently in research designed to provide a better understanding of the solid state transformations leading to the permanent magnet qualities of many commercial alloys. The knowledge derived from these investigations has resulted in the development of new magnetic materials as well as improvements in some of the older materials. The permanent magnet qualities of the newer alloys having high residual inductions and high coercive force values, have been attributed to the precipitation of a second phase or an order-disorder transformation in a solid solution. The ternary Co-Fe-V alloys provide an interesting group of magnetic materials having a wide range of magnetic properties. The low vanadium alloys' possess soft magnetic properties similar to the binary Co-Fe alloys, while at higher vanadium contents (about 10 pct) interesting permanent magnet properties are obtained.2,3 Previous work by Nesbitt' on the ternary Co-Fe-V permanent magnet materials, resulted in the conclusion that the precipitation of a second phase, ?, was responsible for the permanent magnet qualities of these alloys. However, unlike the conventional precipitation hardening alloys, the ? phase, which is stable at high temperatures, is precipitated in the low temperature a phase upon aging. Recent work by Geisler and Martin"." has established that the order-disorder reaction inherent in the binary Co-Fe alloys is also present in the ternary Co-Fe-V alloys. On the basis of their investigation, it was proposed that ordering of the a phase is also a possible explanation of the mechanical and magnetic hardening in these alloys. Thus, it appears that the Co-Fe-V alloys are rather unique in that two solid state transformations are taking place which may account for the properties of these alloys. In view of these facts, the present investigation was undertaken to study the mechanism of mechanical and magnetic hardening in the 10 pct V-Co-Fe alloy with particular reference to the role of the ? phase; and to correlate the results of this study with other magnetic properties. In addition, the influence of increasing vanadium contents on the transformation of Co-Fe alloys was also undertaken to supplement the main objective of the investigation. Experimental Procedure The Co-Fe-V alloys used for study consisted of: 1—a commercial lot of Vicalloy I, a 10 pct V alloy, and 2—alloys prepared by powder metallurgy and containing 52 pct Co and 0 to 14 pct V, balance iron. The commercial alloy was received in the cast and forged condition and was used primarily for the detailed study of hardness, electrical resistivity, and magnetic properties of the 10 pct V alloy. The powder metallurgy alloys were prepared from electrolytic iron, commercial cobalt, and ferro-vanadium powders. The processing cycle was as follows: 1—Elemental powders were weighed and mechanically mixed for 24 hr. 2—Mixed powders were pressed at 60,000 psi into the form of bars 5/8 x 5/8 x 5 in. 3—Bars were sintered in an atmosphere of purified dry hydrogen for 24 hr at temperatures ranging from 1380" to 1340°C, depending upon the vanadium content. The as-sintered bars were cut in half; and one half was machined to 7/16 in. diam for thermal analysis. The remainder of the bar was hot forged to approximately 0.050 in. for X-ray diffraction analysis. Additional details of sample preparation are presented subsequently according to the type of test performed. Thermal Analysis Measurements One of the simplest and most widely used tools for determining phase relations as they change with temperature and composition is to study the rate of change of temperature of a material as heat is supplied or extracted at a constant rate. The thermal analysis method used in this investigation is the inverse-rate method described by Smith.'

Jan 1, 1954

By Frances H. Clark

IN wartime, the fabrication and use of metals assumes increased importance, for a modern war of sizable proportions cannot be undertaken with- out a vast supply of this material. Light alloys of aluminum and magnesium, which were comparatively unknown in the last war, will play an important role in this one. Due to research on a vast scale in the interim of years, industry is today well equipped to fabricate metals on an enormous scale. Research for the past year has been most productive and a comprehensive survey in the space of this article would be impossible. It is hoped that the stressing of a few items here and there out of a great quantity of able work will indicate in a small way the advances made within recent times. Specific references to the literature will be omitted at the Editor's re- quest but some authors of papers that I have found of special interest are mentioned.

Jan 1, 1940

By W. C. Leslie, R. M. Fisher, K. G. Carroll

A nitride, believed to be Si3N, has been separated from three nitrided silicon steels. Germanium nitride, Ge3N4, has been prepared from pure germanium. Comparison of the diffraction patterns indicates that the two nitrides are isomorphous; on orthorhombic structure is suggested in place of the rhombohedral structure previously reported for Ge3N4. THE possibility that a nitride of silicon may, under appropriate conditions, precipitate in silicon steels or in steels killed with silicon makes it desirable to have some positive means of identifying such a compound. One such means is the X-ray or electron diffraction pattern of the nitride. A review of the meager data in the literature indicates that the nitride most likely to form is Si3N4, a conclusion supported by the results of a study of nitrided silicon steels to be published shortly by L. S. Darken and R. P. Smith, of this Laboratory. Unfortunately, there is available no diffraction pattern for this nitride. Data have been reported, however, for Ge3N4 which, judging from the similarity between germanium and silicon, might be expected to be isomorphous with Si3N4. An effort was made, therefore, to form such a silicon nitride, to determine its composition and diffraction pattern and, if possible, its structure. To this end a series of three silicon steels was nitrided under controlled conditions with the resultant formation of nitride particles which yielded an electron diffraction pattern in situ. The particles were then extracted from the steel and an attempt was made to determine their chemical composition. X-ray and electron diffraction patterns were also obtained from the extracted particles, which indicate that the nitride is isomorphous with Ge3N4, although a complete determination of the structure has not been possible. These results show that a silicon nitride with a well-defined diffraction pattern can form in silicon steels, and they suggest that this nitride is Si3N4. Materials and Procedures The sillicon steels investigated were In the form of thin sheet or strip and had the composition shown in Table I. The 0.58 and 1.21 pct Si steels were nitrided by holding them at 1110°F in an H2-NH3 atmosphere containing 3 pct ammonia for 48 hr. The nitride particle size was increased by subsequent heating at 1500°F for 13 1/2 hr in helium. The resulting microstructure is shown in Fig. 1. The steel containing 3.20 pct Si was nitrided at 1200°F for 16 1/2 hr after which it was held in helium at 1500°F for 4 hr. Its structure as seen under the electron microscope is illustrated by Fig. 2. As would be expected from the higher silicon content and the shorter holding time at 1500 °F, the nitride particles are smaller and more numerous than those in the 1.21 pct Si steel. The ammonia-hydrogen treatment reduced the carbon content of the steels to a very low level, so no interference was encountered from carbon or carbides. In the case of the 3.2 pct Si steel, the carbon was reduced to 0.003 pct before nitriding by heating in dry hydrogen. Attempts to obtain an X-ray diffraction pattern from polished and etched surfaces of the 1.21 and the 3.20 pct Si steels were unsuccessful. However, an electron diffraction pattern was obtained from the surface of the steels. The interplanar spacings obtained from these patterns arc shown in Table 11, col. 5. The nitride particles were then extracted from all three steels by dissolving the ferrite matrix in bromine-methyl acetate, the solution used in the Beeghly method for the extraction of aluminum nitride from steel. X-ray diffraction patterns of these residues, obtained by means of a spectrometer and by a 57 mm Debye-Scherrer powder camera using filtered cobalt or chromium radiation, are given in Table II along with the pattern obtained by

Jan 1, 1953

By Ulf S. Landergren

Diffusion coefficients and marker movements have been determined in brass using welded couples. Three different concentration ranges were employed at 750°C, while a fourth concentration range was measured at 500°, 600°, 700°, and 800°C. Marker displacements toward and porosity development in the high zinc side of the couple were observed in all cases. The results were interpreted as favoring a vacancy diffusion mechanism. IN the large amount of diffusion literature which has accumulated during the past half century, very few experimental data have been presented on body-centered-cubic metallic phases. The impressive combination of experimental and theoretical studies which has given the vacancy mechanism a fairly secure position as the preferred mechanism for most face-centered-cubic metals has no counterpart for body-centered-cubic phases, although the theoretical picture seems to be in a better state than the experimental work. The attempts to select diffusion mechanisms by the theoretical calculation of the activation energy for the various conceivable unit diffusion processes and the energy of formation of the type of lattice defect required have been based on models of two kinds. The first kind utilizes potential functions fitted for certain properties of pure crystalline copper; the second kind is fitted for sodium. The latter is an example of an open metal in which the metallic ion is small compared with interatomic distance,&apos; while the former is characteristic of the larger class of metals in which the ions have diameters about as large as the interatomic distance. brass should resemble copper in this fundamental property. It should be evident that results on the mechanism of diffusion obtained for one of these classes need not necessarily apply to the other. Huntington and Seitz, using a model of the copper type, showed that the activation energies to be expected for interstitial migration or a two-atom direct interchange were much higher than that for vacancy diffusion. Zener pointed out that a four-atom ring rotation would involve an activation energy considerably lower than the two unlikely mechanisms although still higher than the vacancy mechanism in the face-centered-cubic structure. Furthermore, he argued, the four-atom rotation would be relatively easier in a body-centered-cubic lattice and might be competitive with the vacancy mechanism. Paneth showed that a body-centered-cubic crystal-like sodium could form interstitial defects of special type, called a crowdion, by crowding an extra atom into < 111 > directions where the defects would affect a line of about eight atoms. The defect was constrained to move along the defining line. Unlike the face-centered-cubic case, therefore, the theoretical calculations for the body-centered-cubic mechanism do not provide a very clear-cut answer, and the absence of adequate experimental studies is the more serious. This investigation was undertaken for the purpose of obtaining useful information on diffusion in body-centered-cubic phases. brass was chosen for several reasons: 1—the phase field is sufficiently wide at high temperatures to permit the use of diffusion couples with adequate concentration ranges for satisfactory chemical analysis, 2-—thermodynamic activity data are available for the calculation of mobilities from diffusion coefficients, 3—the phase is as close to the theoretical model of the copper -type on which the calculations have been done as any body-centered-cubic metallic phase is likely to be. Measurements of the movements (if found) of inert markers during the diffusion process would indicate that a vacancy or Or mechanism played a major role in diffusion in brass. If no marker movement should be found, a ring mechanism would be indicated but not assured. Experimental Procedure The alloys used in these experiments, listed in Table I with analyses, were supplied by the Naval Research Laboratory. They were from ingots of 3x3 in. cross-section, heated to 760°C, reduced under a

Jan 1, 1957

By P. E. Busby, C. Wells, M. E. Warga

Fundamental data on the rate of diffusion of boron in austenite and solubility of boron in the a and y phases of iron and steel have been obtained from deboronizing experiments and provide partial explanations for some of the phenomena observed in boron steels. The rate of diffusion of boron is about the same as carbon in austenite. The solubility of boron in austenite at normal heat-treating temperatures is less than 0.001 pct. A partial tentative Fe-B phase diagram in the important low boron concentration ranges and an equation representing the diffusion of boron in austenite are presented. A LTHOUGH a search of the literature revealed ALTHOUGHthat boron diffusion had not been studied quantitatively and systematically prior to 1948, a few qualitative observations which were made by following the diffusion of boron into iron packed in ferro-boron1-3 suggest that boron obeys normal diffusion laws and that the rate of diffusion increases with increasing temperature. The claim of Cornelius and Bollenrath1 that boron does not appear to influence the rate of carbon diffusion has recently been substantiated by Wells, Batz, and Mehl.4 Calculations based on data from the paper by Campbell and Fayv indicated that the diffusion coefficient (D) for boron in iron at 900°C is approximately 3x10 sq cm per sec; a value of 2x10-7 sq cm per sec at 1038°C has been reported by Digges et al in connection with decarburizing experiments on a commercial boron steel containing 0.43 pct C. During the period 1948 to 1950 several diffusivity constant (D) values for the diffusion of boron in the y phase of iron and steel and a number of solubility values for boron in both a and y phases were reported. It was concluded tentatively as a result of Metals Research Laboratory studies that D values for boron in y and a phases are about the same as for carbon in the comparable phasesa and that carbon up to 0.4 pct did not affect the rate of diffusion of boron in y iron above 1000°C within the limits of experimental error. Whether saturation of the y or a phases with carbon would significantly affect rates of diffusion of boron through them was then and still remains in doubt. The best estimate of Q (activation energy) was reported to be about 25,000 cal, somewhat lower than that for carbon in y iron. The solubility of boron in y iron at 1000°C was thought to be higher than 0.004 pct B but not as high as a more recent analysis of available data shows it to be. The solubility of boron in a iron at 700°C was reported to be 0.0004 pct B, but it would not have surprised the authors if the true solubility value is actually lower than this. Breaks in diffusion curves which were not understood when first obtained prior to 1950 have now been recognized as indicating solubility limits, and these are included in the present paper. Experimental Procedure Two methods were employed in an effort to determine diffusion coefficients (D) for boron in austenite. Early experiments involved the use of welded couples prepared in accordance with the procedure of Wells and Mehl,&apos; but when the results of these experiments proved to be unsatisfactory for calculating D values, studies were continued by means of deboronizing experiments. In both cases, boron analyses following the diffusion anneal were carried out spectrographically and all D values were computed using the Grube solution of Fick&apos;s law. The precision of the spectrographic method used proved to be about equal to that reported by Corliss and Scribner" —average deviation from the mean about 5 pct of the amount present when the boron content is 0.003 pct. Concentration-penetration curves obtained from spectrographic analyses of welded couples generally indicated that practically no boron was transported across the weld interface during the diffusion anneal. Furthermore the concentration-penetration

Jan 1, 1954

By R. F. Mehl, W. Batz, C. Wells

Diffusion coefficient values for carbon in austenite covering a wide range of temperature and composition have been determined employing statistical methods. In addition, the relation between concentration and each of the following, D (diffusion coefficient), Q (activation heat of diffusion), and A (the constant in the diffusion equation), has been obtained. A study of the rates of diffusion of austenite was published in Metals Technology in 1940.&apos; The present investigation is an extension of the earlier work, undertaken (1) to obtain values of the coefficient of diffusion, D, over a much wider range of carbon concentration, and (2) to provide data in all ranges of concentration and temperature in such abundance that statistical methods could be employed to evaluate the accuracy of the data with unusual precision. Composition of Materials: Composition of materials used in this research program are listed in table I. These materials, all forged to about 1 1/4 in. rounds, consist of a high-purity iron, Armco iron, a large number of laboratory-made plain carbon steels containing amounts of impurities normally expected in high-quality commercial steels, and three silicon steels. Since it was known at the time these steels were being made that impurities in the amounts present were unlikely to affect carbon diffusion rates&apos; significantly, the effort made to obtain high-purity steels was not as persistent as it otherwise would have been. Procedure: In general, the procedure followed by Wells and Mehl and described&apos; in detail in an earlier publication&apos; is the one used by the present authors. However, certain modifications have been made which it is believed allow diffusion data to be interpreted more objectively and correctly. These are described completely under appropriate subheadings which follow. Experimental Procedure: Experimental procedure includes (1) the preparation of specimens by welding steels of different carbon contents, (2) the heating of these for certain times at selected temperatures in order to diffuse carbon along the specimens across the welded "interface," and (3) the determination of the carbon distribution across the diffusion zone. Preparation of Specimens: Prior to welding steel of one carbon content to iron or steel of another carbon content, surfaces to be welded are machined perpendicular to the longitudinal axis of cylinders which are about 3/4 in. in diam and 1 1/2 in. long. The prepared, flat, parallel surfaces are brought together and butt-welded electrically. Evidence of a good weld is given in fig. 1. Welding temperature

Jan 1, 1951

By R. F. Mehl, W. Batz, C. Wells

L. S. Darken—It is indeed gratifying to find that the results of the two different methods here reported are in substantial agreement with each other and with the earlier work1 of two of the authors. Dr. R. P. Smith, of our laboratory, has been conducting some experiments at 1000°C to determine the diffusivity of carbon in austenite by a third method— the steady state method. This work, which will soon be reported, is far enough advanced that we can say it is in substantial agreement with that of the present authors. The only disparity which might be considered significant is in the high-carbon region, where we find that the diffusivity rises a little less steeply than indicated in fig. 8. F. E. Harris—The authors have presented an impressive arrangement of data concerning the diffusion of carbon in austenite. Of particular interest is the compilation, table IV, which is repeated in col. B of table V for direct comparison with values (col. A. table V) from a formulation using a single Q value of 31,000 cal as the activation energy for diffusion. This comparatively simple formulation has been used quite successfully in the practical application of calculating the carbon added (or removed) through the face in carburizing and decarburizing experiments, where the face concentrations are held quite constant for known times and temperatures. Literally hundreds of tests have been so checked where the computed and experimental values have varied by less than 5 pct. For higher temperatures, where proper carburizing data are hard to obtain, the diffusion couple is treated as a decarburization of the high-concentration bar and as a carburization of the low-carbon member. The analysis has been limited to a maximum of 1.40 wt pct carbon. The agreement between cols. A and B in table V may be considered fair, if a liberal viewpoint is taken. The use of a diffusion couple has one serious drawback, in that comparatively small amounts of carbon pass through planes of concentration close to those of the initial high-carbon and low-carbon members, and hence small errors become important. In addition to the sensitivity at these high and low concentrations.

Jan 1, 1951

By Frank W. Clinard, Oleg D. Sherby

The effect of multiple an transformations on diffusion in a dilute iron alloy was studied. Inter-penetration between iron and an Fe-Co alloy was evaluated, under thermal-cycling conditions chosen so as to transform only the iron-rich side of the diffusion couple. It is shown that a small but consistent diffusion enhancement by a factor of two results when data from the transforming side of thermally cycled specimens are compared with predicted inter diffusion coefficients based on isothermal data. No enhancement is found when data from the mntransforming side of such couples are compared with predicted diffusivities. It is suggested that short-circuiting by moving pain boundaries is the most likely mechanism contributing to the observed diffusion enhancement from multiple phase transJormations in iron. Transformation-induced Point defects, dislocation-pifie short-circuiting, and point defects generated by dislocation motion are less effective in contributing to enhanced diffusion under the experimental conditions utilized. SO far as is known, no studies have been made of the effect of allotropic transformation on diffusion. previous to this investigation. Studies have been made, however, of the influence of transformation on the diffusion-controlled processes of spheroidization and sintering. Cullen1 has described a method of accelerating spheroidization in an AISI 1030 steel. Partial transformation between a and ? phases was uti-

Jan 1, 1965

By D. Y. F. Lai, R. J. Borg

Tracer diffusion of Fe59 has been measured in the a-stabilized Fe-1.8 at. pet V alloy from 700° to 1500°C. The activation energies are obtained in both the presence and absence of magnetic order. Furthermore, it is established that diffusion in the alloy is identical to that in pure iron and consequently the values of Do and Q accurately represent the temperature dependence for self-diffusion. The purpose of this investigation is to obtain an accurate estimate of the temperature dependence for self-diffusion in bee iron in both the presence and absence of magnetic order, and, in so doing, to establish the temperature range of the magnetic effect.&apos;" As the temperature interval suitable for diffusion measurements is severely limited in both bee phases of pure iron because of the intervening fee ? phase, the experiments were performed on an a-stabilized alloy containing 1.8 at. pet V. This alloy is bee over the entire range from room temperature to the melting point. Although there have been several independent investigations of self-diffusion of iron in a, iron,1, 3-6 there still exists considerable disagreement regarding the values of Do and Q for the paramagnetic region. The two systematic studies of diffusion in 6 iron6, 7 previously reported are also only in fair agreement; but in view of the extremely small temperature range available for diffusion studies, i.e., 1390o to 1535oC, this is not surprising. It is comparatively easy to obtain accurate values of Do and Q for the a-stabilized alloy inasmuch as measurements can be made over the entire temperature range -700o to 1500°C. However, in order to assume that these same values apply to pure iron requires careful comparison of the data in the a, and 6 regions in both the alloy and pure iron. We have made several measurements in the appropriate temperature ranges and are unable to establish any systematic difference between the diffusion coefficients of iron in pure iron and in the alloy. We therefore conclude that the values obtained for the alloy are truly applicable to pure iron; the complete evidence favoring this conclusion will be discussed later in this paper. EXPERIMENTAL The experimental methods will be given here only in barest detail since they have been thoroughly de- scribed elsewhere.l, 7 The alloy was prepared by induction melting and chill casting under argon. Diffusion samples were machined from the ingot and annealed in hydrogen for several days at 900°C to give an average grain diameter of 1 to 2 mm. The penetration profiles of the tracer were established by a sectioning technique, the residual activity being counted after the removal of each section. The tracer used is Fe59 which emits two high-energy ? rays of 1.098 and 1.289 Mev, respectively; these were detected by a ? scintillation counter equipped with a pulse-height analyzer. For the measurements in the temperature range -700o to 1130°C the samples were vapor-plated with Fe59, encapsulated in quartz under vacuo, and annealed in resistance-heated furnaces which are controlled to ±1°C. The specimens diffused at higher temperatures are prepared as edge-welded couples, the two halves being separated by a thin washer of the alloy to prevent sintering. The diffusion anneal is then carried out by inductive heating under a dynamic vacuum. The temperature is monitored pyrometrically. RESULTS The diffusion coefficients are obtained from the penetration profiles in the usual way using the error-function complement relationship. The results over the entire temperature range are shown in Fig. 1. In the linear region, 900o < t > 1500°C the least mean squares (lms) values of the diffusion coefficients are given by D = 1.39 exp[-(56.5 ± 1) x 103/Rt] cm2/sec [l] The average departure of the measured diffusion coefficients from the values given by Eq. [1]In order to determine whether or not the slope is truly constant over the entire range from 900" to 1500°C, the data are arbitrarily divided into two groups, the first containing values between -900" and 1133°C and the second between -1133o and 1500°C. The lms values for the two groups are given by Eqs. [2] and [3]: D = 0.519 exp[-55.7 x 103 /RT](900° to 1133°C) cm2/sec [2] D = 1.45 exp[-56.7x103/RT] (1133° to 1500=C) cm2/sec [3] Thus, there is no significant difference between the high- and low-temperature segments of the linear region. This not only assures us of the consistency of the values obtained by induction heating as compared to those obtained from the resistance-heated

Jan 1, 1965

By R. A. Wolfe, H. W. Paxton

Self-diffilsion coefficients for cr51 and Fe55 in 12 pct Cr-Fe and 17 pct Cr-Fe for Fe55 in chromium, and for Cr51 in vanadium have been measured. The results are compared with other values for the Fe-Cr system, and with the various theories of diffusion in hcc metals. Some empirical correlations are discussed between Do and Q in hcc systems, or, expressed differently, the constancy of ?G*/T solidus for seveval bcc metals and alloys is noted. It appears very probable that a vacancy mechanism is operative in bcc metals, hut this cannot he stated with certainty. THE great bulk of work on diffusion in metals, both experimental and theoretical, was for many years concentrated on those with close-packed and, in particular, fcc lattices.1,2 There appears to be little doubt that the mechanism of diffusion in these solids is vacancy migration, leading to mass transfer and in substitutional solid solutions to a Kirken-dall effect.3,4 For bcc metals, the picture is much less clear. The Kirkendall effect certainly occurs in several alloys.5-10 However, attempts to understand the factors contributing to the pre-exponential in the usual expression for the diffusion coefficient D =D, exp {-Q/RT) by extension of ideas useful in close-packed lattices have not always been successful. Zener,11 Leclaire,12 and Pound, Paxton, and Bitlerl3 have suggested that various forms of ring diffusion may be important in some bcc metals. For close-packed metals, Do is usually about 1 sq cm per sec and Q - 35Tm kcal per mole (Tm = melting temperature in OK). The theory of Pound et al. suggests for ring diffusion that Do may be about 10-4 and Q, although difficult to calculate with any precision, would be significantly less than 35 T,. The experimental results on self and solute diffusion in ? uranium14,15 and ß zirconium,10 and for solutes in 0 titanium,17 and possibly for self-diffu- sion in chromium below about 0.75 T,," gave some credence to this theory. However, not all bcc materials display low values of DO and Q, and the exceptions were not predicted by any theory. Furthermore, it has recently become apparent that, in bcc materials, log D is not always linear with T-l if a sufficiently wide range of temperature is studied.16,18 This variation may be such that Q may increase18,19 or decrease20 with increasing temperature. The present work was undertaken in an attempt to provide further diffusion data on bcc metals, and to try to understand the factors which contribute to differences in behavior between the various elements. For part of this work, the Fe-Cr system was chosen since it is of considerable technological importance, and data on 12 pct Cr and 17 pct Cr alloys appeared well worthwhile to supplement that existing for the remainder of the stern.18,22 The diffusion of Fe55 in chromium was studied as an example of a more or less "normal" tracer element in a possibly abnormal host lattice. Finally, no data were available for vanadium, the neighbor of chromium in the periodic table, because of lack of a suitable isotope so cr55 was used as a tracer in a few preliminary experiments. For convenience, we shall refer to elements whose Do and Q are low compared to those predicted by Zener&apos;s theory as "anomalous". PROCEDURE This investigation determined self-diffusion rates by means of radioactive tracers and the integral-activity method first utilized by Gruzin.23 In this method a thin layer of radioisotope of the diffusing element is plated or coated onto a planar surface of the diffusion sample, which is then given an isothermal-diffusion annealing treatment. The determination of an activity-penetration curve involves measuring the residual activity of the specimen after each successive layer or section has been removed parallel to the original planar surface. The method used here is essentially the same as that used by Gondolf18 and Kunitake.21 Two radioactive tracers, cr51 and Fe55, were used in this investigation. Diffusion coefficients were determined for the diffusion of one or both of these tracers in four different materials, viz., Fe-12 wt pct Cr alloy, Fe-17 wt pct Cr alloy, chromium, and vanadium. The diffusion samples had nominal dimensions of 1.5 cm diameter and 0.5 cm thickness. The grain size was several millimeters for the Fe-Cr alloys and at least 1 mm for the chromium and vanadium samples. Accurately planar surfaces

Jan 1, 1964

By Leonard R. Weisberg

The general properties of diffusion in GaAs are reviewed. A total of .fourteen atoms have been studied to date, and activation energies for eleven reported are (in ev): Ga (5.6), As (lo), Zn (2.49), Cd (2.43), Sn (2.5). Mn (2.75). S (4.0). Se (4.2). Ag (0.33), Cu (0.52). and Li (1.0). The dijfusion of the first eight atoms, as measured by Goldstein using radiotracer techniques, established the principle of sub lattice diffusion for both host and impurity atoms, since atoms substituting for gallium have lower activation energies than those substituting for arsenic. The diffusion constant of interstitial copper has been determined for the first time by Hall and Racette using heavily doped p-type samples in which interstitial copper predominates. The anomalous behavior of zinc, which has an abrupt diffusion front and a strong dependence on zinc concentration, has recently been quantitatively explained in terms of an interstitial-substi-tutional equilibrium-diffusion mechanism. Lithium and silver diffuse mainly interstitially, while the diffusion of phosphorus is complicated by the continual formation ofGap. Junction-migration measurements indicate diiferent results than radiotracer techniques, and this is one problem that still remains, together with discrepancies in cadmium-diffusion results, and an unexplained dependence of impurity diffusion on arsenic pressure. BESIDES the usual insights into the behavior of atoms in solids, studies of diffusion in semiconductors have additional importance for device applications. In fact, the amount of diffusion studies performed on a semiconductor might serve as a simple barometer of its technological importance. Thus, the information accumulated for GaAs is not yet quite comparable to that for germanium or silicon, but considerable knowledge is available. The diffusion of at least fourteen atoms has been investigated for GaAs, and the diffusion constants have been determined for eleven of these. Interesting results were found for GaAs that elucidated problems not previously solved for germanium or silicon. For example, the interstitial-diffusion constant for the very fast diffusant, copper, was first measured in GaAs. Also, solutions for interstitial-substitu-tional equilibrium diffusion in extrinsic material were provided first for GaAs, although they are ap- plicable to germanium, silicon, and other semiconductors. Studies in GaAs firmly established the concept of sublattice diffusion, which should have application in many different compound systems. The purpose of this paper is to review briefly the general state of knowledge concerning diffusion in GaAs. First some general aspects of diffusion will be covered, and next attention will be given to the results mentioned above. Diffusion in GaAs has been measured both by radiotracer and junction-penetration techniques, and some discussion will be given of differences in the two sets of results. The comprehensive work of oldsteinl-&apos; has served as the primary reference for the diffusion of well-behaved substitutional atoms in GaAs. Since a review has recently been presented of many of these reults, details of the diffusion data will not be repeated. Neither will any discussion be given of the experimental techniques of diffusion measurements, except to note here, in passing, the simplicity and effectiveness of the precision lapping device employed by Goldstein.&apos; I) EXPERIMENTAL RESULTS AND DISCUSSION A) Summary of Experimental Results. Diffusion constants D = Do exp(E/kT) have been determined for eleven atoms in GaAs: a,&apos; AS,&apos; n,&apos;" Cd,&apos;" n,&apos; n,8 s, e,&apos; Ag,O CU," and i." These results are summarized in Table I. In addition, diffusion was investigated for phosphorus,4&apos;12 germanium,I3 and ilicon,&apos; but Do and E were not determined. Radiotracer techniques were used for most of the studies except for lithium, where a combination of chemical and electrical techniques was employed, and germanium and silicon, where junction-migration techniques were applied. The diffusion of zinc, manganese, sulfur, and tin was also measured using junction migration.13&apos;14 Goldstein demon-

Jan 1, 1964

By Carl F. Lutz, Robert F. Mehl

A layer of brass was formed on 0 brass using a vapor-solid reaction technique. The variation in composition with distance within the phase layer and across the a -ß interface was determined by an electron probe. The diffusivities were calculated as a function of concentration; the diffusion coefficient in brass was found to change by a factor of twenty-five over a compositional range of 8 at. pct. An explanation is proposed to account for the large change in the diffusivity, based on possible stresses in the diffusion zone; it is suggested that the concentration dependence of the thermodynamic factor might decrease the activation energy with increasing zinc content. ALTHOUGH the body of data on diffusion coefficients (D- values) in terminal solid solutions and in isomorphous systems is quite large, there is but little quantitative information for intermediate alloy phases. This paper recounts measurements of D-values for the ? phase in the Cu-Zn system. The experimental method employed consists in the forming of alloy layers and determining and analyzing the concentration-distance (c-x) curve. The experimental method employed could have been applied to several systems; the Cu-Zn system was chosen because the D-values in the a and ß phases are well known, and can thus be used for purposes of comparison. The rates of growth, of intermediate alloy layers are known for a number of systems. In nearly all cases the thickness varies parabolically with time, as to be expected if the rate of growth is controlled by the D-values. In a few cases, nonparabolic behavior has been noted.1 Nonparabolic growth may be the result of a) a variation of the composition at the phase interface with time, b) interface-controlled kinetics, c) short diffusion times coupled with long vacancy lifetimes (in vacancy diffusion),2 and d) crystal reorientation during diffusion in anisotropic systems.3 In the Al-Ni system4 and in the Al-u5 system parabolic growth kinetics are slowly approached after an initial transient period. In general those phases stable at a given temperature in a system A-B appear as separate phase layers when A and B are put in contact and given a diffusion he at-treatment. In most cases the compositions at the interface of adjacent phase layers are those read from the phase diagrams for the termini of the respective phases. This discontinuity in concentration is taken as independent of time, and the growth of one phase at the expense of another is assumed to be independent of interface kinetics, i.e., the rate of interface movement is controlled by volume diffusion in the phases concerned. wagner6 has given many solutions for multi-phase diffusion processes, assuming that the chemical diffusion coefficient, D, is independent of concentration, as have others. Jost7 has pointed out that the familiar Boltzmann-Matano solution is as valid for a (c-x) curve exhibiting concentration discontinuities at phase boundaries as for the usual single-phase case. Heumann and associates8,9 have applied this solution to the multi-phase case, but lacking concentration data within the several layers were forced to assume linear concentration gradients, thus calculating only average D-values. The purposes of the present study were: 1) to determine the dependence of D on concentration, 2) to calculate the intrinsic diffusion coefficients D?Cu and D?Zn, 3) to establish the time-law for the movement of the interface, 4) to determine the concentration limits at the ß-? interface, and, 5) to attempt to clarify the mechanism of diffusion. EXPERIMENTAL PROCEDURE The ? phase is exceedingly brittle; conventional solid couples and conventional sectioning methods were thus inapplicable. Vapor-solid couples were accordingly employed. Unfortunately the equilibrium vapor pressures of Zn for the ? phase are unknown; to escape this awkwardness, samples were enclosed in a capsule containing powder of an alloy of known composition, sufficiently large in quantity as to be effectively an infinite source, maintaining the concentration of Zn at the sample surface constant with time. The sources of Zn-vapor which can be employed in reaction with Cu, or a brass, or ß brass, to form a layer of ? brass satisfactorily wide in concentration range, are alloys of the phases ?, or ? + E or ? + d (depending on the temperature).

Jan 1, 1962

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

By L. D. Hall, S. J. Rothman

The diffusion of lead and of trace amounts of bismuth in liquid lead have been investigated by the capillary method, using ROD and ROE as tracers. The results are compared with existing theories of diffusion in liquids, the agreement with theory being fair. The heat of activation for self-diffusion in lead is found experimentally to be close to the corresponding activation energy obtained from viscosity data. The pioneer data of Groh and von Hevesi for the self-diffusion of liquid lead, using ThB as a tracer, fit in with the present results. OMPARED with the volume of effort expended on solid state diffusion, there has been little attention paid to diffusion in liquid metals. A review of experimental work in this field, covering most of the studies up to 1951, was given by Jost.&apos; More recent papers include those by Hoffman2 on self-diffusion in mercury, Morgan and Kitchener" and Stark, Shchilishchev, and Kazachkev4 on the diffusion of various elements in liquid iron, and Grace and Derge on the diffusion of bismuth in bismuth-lead alloys. The need for more experimental data to aid in the evaluation of existing theories prompted the

Jan 1, 1957

By R. E. Ogilvie, J. I. Goldstein, R. E. Hanneman

The interdiffusion coefficients for the Fe-Ni system were determined as a function of composition in both the a and y phases at 1 atm pressure. The inter diffusion coefficients were also determined in the y phase at 40 kbar pressure. The concentration gradients were measured with an electron probe, and the diffusion coefficients were calculated by the Matano analysis. At 1 atm, Ey increases with nickel content up to 65 at. pct Ni. The relationship of Dy with temperature and nickel concentration, up to 50 at. pct Ni, is given by the equation DY-l atm = exp(.0519 CN~ +1.15) MANY of the transformations that occur in the solid state are diffusion-controlled, especially those involving precipitate growth in most metallurgical systems. Multicomponent diffusion is usually expressed in terms of a chemical or an inter diffusion The activation energy Q at 1 atm decreases from pure iron to 60 to 70 at. pct Ni and decreases from pztre nickel to 60 to 70 at. pct Ni. The Kirkendall marker movement indicates that DFe is greater than DNi zcp to about 60 at. pct Ni. Above 60 at. pct Ni, however, DNi becomes peater than DFe The inter diffusion coefficients were also compared with those calculated from self-diffusion data. A comparison between calculated and measured coefficients shows only rough agreement. The effect of 40 kbar pressure is to decrease DyPl atm by an order of magnitude. The activation volumes for high-pressure diffusion are in favorable agreement with theoretical models developed for self-diffusion. coefficient which determines the rate at which material is transferred from the matrix phase to the precipitate and hence determines the growth rate of the precipitate. Since the numerical values of the diffusion coefficients differ widely as a function of the metallic system, temperature, and pressure, the diffusion coefficients must be determined for each particular environmental condition. Of long-standing interest is the growth of the classic Widmanstatten pattern in metallic (Fe-Ni) meteorites. The growth rate of the pattern is controlled by the diffusion coefficients in the Fe-Ni system. Since these coefficients are essential to calculating the growth rate of the pattern, we found it necessary to determine the diffusion coefficients

Jan 1, 1965

By J. D. Braun, C. W. Powell

Diffusion between gold and indium at two temperatures below the melting point of indium (155.4oC) was investigated. The major, component of the diffusion zone was determined to be AuIn2; the other, intermediate phases in the system occur in much narrower layers In order of decreasing layer width these are: Au9In4, AuIn, Au4In. Inter diffusion coefficients of the four intermediate phases and the terminal solid solutions lie in the range of 2.4 x 10-l3 to 1.8 x 10-11 sq cm per sec. WHEN two metals which do not form a continuous series of solid solutions interdiffuse, each phase in equilibrium at the diffusion temperature should appear as a separate layer in the diffusion zone. In the Au-In system, diffusion plays a significant part in many commercial applications, particularly where indium alloys are used as solders for electrical contacts with very fine gold wire, for estab- lishing electrical contact to thin metallic films, and for mounting metal-coated piezoelectric crystals. A knowledge of the number, extent, and type of phases which form at diffusion temperatures below the melting point of indium, 155.4oC,1 and the diffusion constants for the system would be useful for these practical applications. Of more basic significance, additional information on polyphase diffusion in a system not previously investigated would be gained. The phase relationships in the Au-In system were determined primarily by Kubaschewski and Weibke1 and are based on thermal, microscopic, and X-ray analysis, Fig. 1. There are five intermediate phases in the system having approximate compositions corresponding to the formulas: Au4ln (ß)—80.0 at. pet Au; Au3In (?)— 75.0 at. pet Au; Au9In4 (d)—69.2 at. pet Au; AuIn—50.0 at. pet Au; AuIn2—33.3 at. pet Au. Solid solubility of indium in gold at 700°C is reported as 12.64 at. pet and at 406°C as 10.36 at. pet. No solid solubility of gold in indium is reported.

Jan 1, 1964

By T. Kunitake, H. W. Paxton

The self-diffusion coefficient of chromium in various alloys in the iron-chromium system has been measured. A variation in Dofrom 10-4 for pure chromium to a maximum of 102 near 60 pct Cr appears with a range of activation energy from about 50 to 80 kcal per mol. The general pattern of behavior observed is not consistent with present theories of diffusion by a vacancy mechanism. Suggestions are made for further clarifying experiments. RECENT work on the self-diffusion of chromium,&apos; ?-uranium2-4 and ß-zirconium,23, 26 has indicated that these elements have very low Do (10-3 to 10-4) compared to that conventionally expected for vacancy diffusion. Pound et al.5 have suggested that this may be due to ring diffusion being operative, and have proposed a model which gives Do of the correct order of magnitude. The essential difference between this model and Zener&apos;s earlier model6 is that whereas Zener assumes tight coupling between atoms in a ring to establish a vibrational frequency, Pound&apos;s model allows the atoms to vibrate essen- tially each in their own normal modes. The probability of each atom moving in the correct direction to cause a ring of n atoms to rotate by 2p/n must then be calculated as a "synchronal entropy" which may be -20 e.u. for a 4 atom ring. In iron, the latest determinations of self-diffusion yield Do in the range 18 to 522.7-9 The most accurate is probably that of Borg and Birchenall8 which is 118 ± 3. This value is not inconsistent with that expected for a vacancy mechanism. Since iron and chromium are very closely similar in size, are both transition metals, and their solution is thermodynamically ideal at temperatures of interest in diffusion, it appeared that a determination of self-diffusion coefficients, Do and Q as a function of composition would be of substantial interest to diffusion theory. The following measurements were made with this purpose in mind.

Jan 1, 1961