Search Documents

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,' ?-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's earlier model6 is that whereas Zener assumes tight coupling between atoms in a ring to establish a vibrational frequency, Pound'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

By R. E. Ogilvie, N. L. Peterson

Diffi-lsion measurements were conducted at all compositims in the bcc solid solution of the U-Nb system employing incremental couples at composition intemals of 10 at. pct. Diffusion coefficients were determined by the Matano method from concentration gradients obtained with the electron-probe microanalyzer. The activation energy for inter-diffi-lsion as a function of compositim shows three distinct regions: 1) 80 to 100 pct U.6= 30 kcal per mole; 2) 20 to 80 pct U, $ - 70 kcal per mole; 3) Oto 20 pet U, Q = i40 kcal per mole. The frequency factor, fi0 and the activation energy $ were found to be roughly related by the following equation: log Do ^9.7 X IO-5Q -6,6. The Kirkendall marker movement indicates that DU is larger than DNb between 16 and 100 pct U and DNb is larger than DU from 0 to 4 pct U. FOR practical as well as fundamental reasons, the rates of diffusion in alloys are of considerable consequence. Most solid-state reactions are largely dependent upon the diffusion of atoms through the lattice structure and along grain boundaries. The high-temperature strength and reasonable nuclear properties of niobium have prompted its use as a reactor material in contact with uranium fuel. Hence, diffusion data for the U-Nb system are of considerable importance. In the previous diffusion study1 on the U-Nb system using pure element couples, reliable data were obtained only in the range of 0 to 10 at. pct Nb due to the large variance of the diffusion coefficient with composition. Also, a large Kirkendall effect and considerable porosity in the uranium-rich areas of the specimen were reported, which suggests that the true diffusion coefficients are somewhat larger. The purpose of the present study was to obtain reliable diffusion coefficients at all compositions using incremental diffusion couples with intervals of 10 at. pct. In view of the abnormal self-diffusion be- havior of y uranium2-4 and some other bcc transition elements,&apos;-&apos; it was felt that a comparison of the interdiffusion coefficients in the bcc U-Nb system with those of Reynolds et al.9 for the fcc gold-nickel system might shed some light on the diffusion mechanism involved. Both systems have similar phase diagrams, in that complete solid solubility exists above a miscibility gap. EXPERIMENTAL PROCEDURE The uranium used in this investigation was obtained through the courtesy of Argonne National Laboratory. An analysis of this material detected only Si-30, A1-7, C-6, N < 10 and 0-18 ppm. The niobium was electron-beam melted material obtained from Stauffer-Temescal. The gaseous impurities were less than 50 ppm, and the spec troc hemical analysis showed Ta-500 and W-200 ppm. U-Nb alloys were prepared at composition intervals of 10 at. pct by melting the appropriate amounts of the pure elements in an arc furnace. The buttons were inverted and remelted 6 times to assure complete mixing. The buttons were then wrapped in molybdenum foil, canned in Zircaloy-2 or stainless steel, and hot rolled 30 pct reduction in thickness at temperatures between 850" and 1100°C. Alloys with 10, 20, 30, 40, and 90 at. pct Nb rolled quite easily under these conditions, but the 50, 60, 70, and 80 pct alloys remained brittle. After melting and rolling (when possible), the alloys were annealed for 24 hr at a temperature within 100°C of their melting point in a dynamic vacuum of better than 4 x 10-8 mm Hg. These treatments produced alloys which were homogeneous on a 1 p scale within the detectability limits of the electron probe. During fabrication, the alloys picked up as much as 100 ppm Mo and 100 ppm Zr. Other elements checked for but not found were Co, Cr, Fe, Mn, Ni, and Ti. The grain size of the annealed samples ranged from 3 mm for the uranium-rich alloys to 0.3 mm for the niobium-rich alloys. This permitted measurements of the concentration gradients in the diffusion samples without crossing more than one or two grains, thereby eliminating any grain boundary effects. The specimens were bonded by theU&apos;picture frame" technique as reported by Kittel.10 Specimens of composition b)U + (100 - x)Nb were sandwiched between two specimens of composition (x + 10)U + (90 - x)Nb after they were ground flat and parallel

Jan 1, 1963

By John Chipman, Helen Towers

DEVELOPMENT of a simple radioactive tracer technique for measurement of the diffusion coefficient of calcium ion in liquid slag has already been reported. The investigation was of a preliminary nature designed to explore the possibilities of using radioactive isotopes and to establish a method, and no great accuracy was claimed for the results. It was shown, however, that Ca15 could be used successfully, and the values obtained for the diffusion coefficient appeared to be of the right order of magnitude. However, it was considered that a better technique could be devised for carrying out the diffusion. The experiments were, therefore, continued to find a more accurate method, to check the calcium results, and to extend the investigation to include measurements of the diffusion coefficient of silicon in the same slag. There were two flaws in the original technique. Convection was the cause of too many failures, and the interface between the two slags in the diffusion cell was curved rather than plane, probably due to a surface tension effect caused by the addition of the tracer Ca45 in the form of chloride. Two methods of overcoming these defects were tried. Since it was planned to study diffusion of the short-lived isotope Si"&apos; also, the development of methods was restricted to those which gave promise of being reasonably rapid. Method 1—The principle was identical to that previously used with respect to the diffusion conditions, but there were three differences in technique. Temperature control was more rigid, the tracer was added to the slag as Ca45O rather than the chloride and, finally, an effort was made to translate to high temperatures the elegant method developed by Cohen and BruinV or bringing together the two liquid layers and beginning the diffusion. A master slag was melted in graphite, ground to a fine powder, and analyzed (38.5 pct Ca0-20.9 pct Al2O3-40.5 pct SiO2). The tracer was received as Ca45C12 in an aqueous solution of CaC12 + HC1. From this, calcium oxalate was precipitated, ignited to calcium oxide, and added as such to the slag to give an activity of approximately 5 µc per g. The mixture was then melted into the form of a cylinder 3/16 in. diam and about 1 in. long. A solution identical to the tracer solution without Ca45 was given exactly the same treatment. The resulting Ca40O was mixed with that slag which was to form the tracer-free half of the diffusion cell, and this was likewise melted into a cylinder of the same size. Slag cylinders, two with and two without Ca15, were set in graphite blocks as shown in Fig. 1, and the crucible was lowered into position in the fur-

Jan 1, 1958

By T. F. Archbold, W. H. King

THE diffusivities of gold in polycrystalline copper have been determined in the temperature range from 700° to 1000°C by the utilization of the neutron-activation method. Martin, Johnson, and ~saro&apos; used this method for their investigation of the diffusion of gold into copper at 375° and 550°C for 59 days in order to circumvent the experimental difficulties imposed by the 2.7-day half-life of Au-198. They employed the conventional technique of depositing Au-198 on copper specimens for short-time dif-

Jan 1, 1965

By T. S. Lundy, F. R. Winslow

DIFFUSION coefficients of Hf181 in the high-tem-perature bcc phase of reactor-grade hafnium were determined at temperatures of 1795° to 1995°C by standard lathe-sectioning techniques. The temperature dependence of the data may be described by an Arrhenius-type expression for this limited temperature interval. However, hafnium is classed with the "anomalous" bcc metals zirconium, titanium, and y uranium by the low values of Do and Q observed in this study. The hafnium metal was received as 1/2-in.-diameter crystal bar. Analyses by the Analytical Chemistry Division of Oak Ridge National Laboratory showed the major impurity to be zirconium— about 2.1 pct. The total interstitial content was about 225 ppm with 190 ppm of this oxygen. The Hf"&apos; was supplied as HfC12 in HC1 solution by the Isotopes Division of Oak Ridge National Laboratory. The hafnium bar was cut into disk-shaped specimens 3/8 in. long. One of the flat faces of each specimen was metallographically treated and then the isotope was deposited by vacuum evaporation from a tungsten filament. A 3 by 3 in. NaI (Tl) crystal with a single-channel analyzer was used for counting y rays with energies of 0.3 to 0.7 Mev. The as-deposited layers of isotope had counting rates of about 200 counts per sec. Specimens were annealed in argon in a tantalum resistance furnace. Temperatures were measured with a microoptical pyrometer calibrated for the particular furnace sighting conditions. All sectioning was done by standard lathe techniques. Section weights were determined on a semimicrobalance. A density of 12.5 g per cu cm was used in determinations of section thicknesses. Activities associated with the various sections were measured and the penetration data were treated using the computer code by winslow.&apos; In all cases, except for specimens annealed at temperatures below 1795°C, normal Gaussian penetration behavior resulted. At lower temperatures, plots of In A(x) vs x2 were nonlinear [~(x) = relative activity at a distance x from the

Jan 1, 1965

By R. A. Swalin

IN this paper, the results of an investigation concerning the diffusion of three elements, magnesium, silicon, and molybdenum, in nickel are presented. The work represents a continuation of a diffusion program relating to solute diffusion in nickel. The program has the dual aim of obtaining useful diffusion data and of yielding insight into the factors governing solute diffusion in close-packed metals. The first paper of this series has been published earlier? In both investigations, in agreement with recent results from other laboratories, the activation energies for solute diffusion were found to be close but not identical to that of self-diffusion in the pure solvent in question. In order to obtain valid diffusion data, certain experimental pitfalls recognized only in recent years had to be avoided. Chief among these were the necessity for minimizing short-circuiting diffusion paths such as grain boundaries and the necessity for using low solute concentration gradients. In this series of investigations the following precautions were taken in an attempt to minimize such errors. 1) Samples with large grain sizes, 0.5 to 10 mm, were prepared. 2) The diffusion coefficients were measured at relatively high temperatures, since imperfections such as dislocations play a less important role at such temperatures than at lower temperatures. 3) Alloys containing less than 1 atomic pct were chosen for study. Experimental Work Materials—A diffusion couple technique was employed in the experimental investigation. Briefly, this technique consisted of the following. A diffusion couple was fabricated by placing a flat face of a cylindrically shaped alloy disk against a similar face of a pure nickel disk, and a bond was formed at an intermediate temperature under pressure. The diffusion couple thus fabricated was subjected to a diffusion anneal at higher temperatures for a measured period of time and then sectioned perpendicular to the direction of diffusion. After analyzing the sections for solute concentration the diffusion coefficient was determined from a probability, plot of concentration vs distance from the diffusion interface. Vacuum melted Mond nickel was used in the experimental program. The chemical analysis of this nickel is listed in Table I. Alloys used were prepared

Jan 1, 1958

By T. S. Lundy, R. E. Pawel, F. R. Winslow, C. J. McHargue

The volume-diffusion coefficients of Nb-95 and Ta-182 in niobium have been measured over the temperature range 878° to 2400°C. High-temperature specimens (T 21500°C) were sectioned by conventional lathe and grinding techniques while low-temperature specimens were sectioned by an anodizing and stripping technique previously described. Over a range of more than ten orders of magnitude in diffusivity, the self-diffusion data is well-represented by the equation: D = (1.1+ 0.2) exp [- (96,000 * 900)/RT ] cm2/sec Upward deviations from this line are explained by short-circuit diffusion in combination with the loss of resolution of the sectioning techniques. Oxygen contamination within the range 100 to 450 ppm was found to have little or no effect on the self-diffusivitj 01 niobium. In a limited number of measurements, the diffusivity of Ta-182 in niobium was found to be about half that of Nb-95 in niobium. These data may be described by D = (I.0+0.90.5)exp [- (99,300 * 2400) /RT ] PREVIOUSLY reported studies of self-diffusion in niobium were by Resnick and Castleman1 and Peart, Graham, and Tomlin.2 The data of Resnick and Castleman over a temperature range 1585" to 2120°C show considerable scatter but. can be represented by D = (12.4 *0.8) exp [-(105,000+3OOO)/RT] cm2/sec The limited data of Peart, Graham, and Tomlin follow the equation D = 1.3 exp (-95,00O/RT) cm2/sec In view of recent diffusion data for ß zirconium3 and 0 titanium4 in which Arrhenius-type plots do not yield straight lines and of the potential high- temperature uses of niobium and its alloys, we thought it important to investigate the diffusion behavior of this bcc refractory metal over a large temperature range. This has recently been done for molybdenum,5 chromium,6 vanadium,"" and tantalum.9 Niobium was a particularly suitable material for this study largely because of the development of an anodizing and stripping sectioning technique which enables diffusivities as small as l0-19&apos; sq cm per sec to be determined accurately.10 In addition to self-diffusion data, data were obtained for the diffusion of Ta-182 in niobium and for the effect of varying oxygen content on self-diffusion. I) EXPERIMENTAL PROCEDURE Materials. The niobium was obtained from three sources: 1) melting stock from Shieldalloy Corp., 2) electron-beam melted single crystals, 1/2 in. diameter, from Semi-Elements, Inc., and 3) oxygen-doped, electron-beam melted single crystals from Materials Research Corp. The melting stock was electron-beam melted and specimens 5/8 in. diameter by 1/2 in. long were machined from the center of the bar. The analysis supplied by the vendor and an interstitial analysis of one of the specimens are given in Table I. The single crystals (type 2 above) were cut with a jeweler&apos;s saw to specimens about 3/8 in. long. The interstitial analysis of this material is given in Table 11. This material was used

Jan 1, 1965

By Cyril Wells, Paul E. Busby, Donald P. Hart

EARLY workers in the field have established that the diffusion of nitrogen follows normal diffusion laws. Concentration-penetration data from layer analyses of reasonably pure iron specimens nitrided in an atmosphere of CO-NH, are given in the literature,&apos; and were utilized to calculate diffusion constants for nitrogen. The diffusion of nitrogen in y-iron may be represented approximately by the equation D - 1.07x10-&apos; e-:".&apos;m&apos;"&apos;r The diflusion coefficients, D, given by this relation represent mean values, since carburization occurred simultaneously with nitriding. The rate of diffusion in a-iron has been determined from calculations based on data obtained by measuring the internal friction of samples at each of several frequencies and temperatures.&apos; The expression for the diffusion of nitrogen in a-iron derived from these experiments is D= 1.4x10-1 e-it tudent Increasing carbon content decreases the diffusion of nitrogen in a-iron.3 Oxygen, either dissolved or combined, has been shown&apos; to exert a marked influence on the diffusion of nitrogen from a nitriding atmosphere. D values increase rapidly with increasing amount of dissolved oxide in the metal, but diffusion is completely inhibited if preliminary oxidation has produced the slightest trace of iron oxide on the surface. Diffusion coefficients have also been calculated from permeability and solubility data,&apos; but these values are of questionable accuracy since the boundary conditions assumed may not actually exist. Experimental Method The method selected for determining the diffusion coefficient of nitrogen in a-iron in the present investigation was the so-called fractional saturation method. This method consists of heating the specimen in an atmosphere of H2-NH8 mixtures of known composition for a predetermined time. Following this treatment, the specimen is analyzed for nitrogen; and the diffusion coefficient is calculated from a known relationship of the fractional saturation, time of diffusion, and dimensions of the specimen. This relation is based on a solution of Fick&apos;s second law and assumes that the surface of the specimen immediately reaches a given concentration which remains constant during the diffusion anneal. Tabular solutions are available4-5 and provide the relationship between fractional saturation and the quantity \/Dt /a, where D is the diffusion coefficient in cm2 per sec, t is the time of the diffusion anneal in seconds, and a, in the present experiments, is the half-thickness of the slab specimen in cm. The method is adequately discussed elsewhere.9-10 Material The material for this study consisted of 3/32 in. thick (0.24 cm) carbonyl iron plate. The major impurities in this iron are oxygen and carbon, which are readily removed by long time high temperature treatment in an atmosphere of purified hydrogen. In order to reduce the diffusion anneal time for saturation runs, some of this material was rolled to a thickness of 0.015 in. (0.038 cm) prior to the hydrogen treatment. Hydrogen treatments were carried out in a hydrogen-purified Armco iron tube heated in a global

Jan 1, 1957

By George Mah, Charles Wert

Internal-friction peaks caused by diffusion of oxygen and nitrogen have been observed in ytterbium. They are thought to be caused by the redistribution, under stress, of strain dipoles around an interstitial oxygen or nitrogen and a neighboring substitutional impurity. With the use of a simple geometrical model, diffusion coefficients for oxygen and nitrogen between special interstitial sites have been calculated. a) APPLICATION OF INTERNAL FRICTION TO MEASUREMENT OF DIFFUSION RATES IN DISSOLVED INTERSTITIAL ATOMS In bcc metals, the interstitial atoms occupy the centers of cube faces (0, 1/2, 1/2), or their equivalents, the center of the cube edges (0, 0, 1/2). An interstitial atom in this position causes an aniso-tropic distortion in the lattice. When stress is applied, mechanical relaxation can take place by the movements of the interstitial atoms. This relaxation has been used to obtain information concerning the movements of the interstitial atoms in the bcc metals. Data for these alloys have been compiled by Stanley and Wert. Other researchers have extended the investigation of interstitial diffusion to the close-packed metals. Gupta and weinig2 found an oxygen peak in a titanium, the height of which is linearly dependent on the oxygen concentration. They assumed, therefore, that they were dealing with movement of atomic ally dispersed oxygen in titanium. KG and wang3 determined that the diffusion coefficients of carbon in fcc steels and in nickel obtained by internal-friction methods were consistent with those obtained by macrodiffusion methods at much higher temperatures. Bisogni found oxygen and nitrogen peaks in hafnium by use of which he deduced the diffusion coefficient of these gases in hafnium. He observed further that the half-widths of these peaks corresponded almost exactly with those of a single-relaxation process; he assumed it to be caused by movement of atomically dispersed oxygen and nitrogen. From these studies, the deduction can be drawn that, in general, diffusion data can also be obtained for the interstitial diffusion in close-packed metals (or more precisely, in slightly impure close-packed metals). One group of such metals for which little data exist for the diffusion of dissolved oxygen and nitrogen is the rare earths. They have great affinity for gases, which enter solution interstitially. In this investigation results were obtained for the Yb-O and Yb-N interstitial solid solutions with traces of substitutional impurities; these solid solutions are of fcc structure. b) MECHANISM OF THE RELAXATION IN FCC CRYSTALS In the fcc structure, an interstitial gas atom is usually situated in the octahedral position (1/2, 1/2,

Jan 1, 1964

By V. G. Leak, R. A. Swalin

The dilhsion of silver and trace concentrations of tin in liquid silver has been rrzeasured in the temperature range from about 975° to 1350°C. The difBsion dala. fil lhe following equations: fov self-diffusion of silver The ratio of DSn to DAg is found to be about 1.34. The higher diffusivity of tin is interpreted in terms of the coullombic repulsion which results from the fact that tin dissolved in silver has a valence of +3 relative to silver. THE phenomenon of diffusion has been well-described theoretically for hard-sphere gases and solids and found to be in good agreement with experimental data for certain gases and solids. Liquid-diffusion phenomena have not been well described theoretically and there is generally a lack of good experimental data. In this investigation self-diffusion and solute diffusion in liquid silver were studied. Silver was chosen as a solvent for two main reasons. First, silver is a noble metal and the atoms are considered to have a spherically symmetric charge field; hence the liquid may be considered to be a random array of approximate hard spheres. Mercury, gallium, and other lower-melting metals were eliminated from consideration since it appears possible that in their liquid states there is some residual long-range order and directional bonding. Second, silver behaves as a monovalent solvent and, while cadmium, indium, tin, and antimony all have nearly the same atomic size, they have chemical valences relative to that of silver of +1, +2, + 3, and +4, respectively. Slifkin, Lazarus, and coworkers1-5 investigated the diffusion of these solutes in solid silver and found that their diffusion rates increased with an increase of the excess valence of the solute. In the solid state the diffusion-rate increase was calculated to be due to a change in local modulus of the solvent caused by the excess valence of the solute.1"3 For the present investigation it was planned to determine the effect of valence upon solute diffusion in liquid silver. It was deduced that a coulombic repulsion between solute and solvent might be responsible for larger volume fluctuations in the vicinity of the solute thereby enhancing the diffusion of the solute atoms. Tin was the first solute investigated and was chosen for experimental convenience. If an excess-valence diffusion effect exists in the liquid state, the solute tin with its excess valence of + 3 might show a large enough effect to distinguish it from the self-diffusion of silver in silver. The silver self-diffusion data were obviously required as a base line for comparison. In addition silver self-diffusion was investigated with a view toward examining the data in connection with the Sutherland- Einstein: Coheen-Turnbull,7 and swalin8 theories of diffusion in liquids. I) EXPERIMENTAL TECHNIQUES The diffusion coefficients for tin and silver in liquid silver were determined in separate experiments using the capillary-reservoir method of Anderson and saddingtono but following closely the experimental techniques outlined by Ma and Swa1in. The radioactive alloy bath was prepared by plating either tin-113 or silver-110 m isotope* onto 99.999 *Isotopes obtained from Oak Ridge National Laboratory. pct Ag rods.* The silver and isotope were melted *Silver obtained from Cominco Co. and mixed in a graphite crucible under a purified argon atmosphere, then outgassed for capillary filling. Some of the fused-silica capillaries were filled individually as reported by Ma and Swalin, but most were filled in a different manner. A long piece of capillary tubing was sealed off on one end and held in the system so that the open end was just above the surface of the molten alloy. The system was evacuated, the open end submerged into the alloy, and argon was admitted into the system up to atmospheric pressure. The molten alloy was forced up the capillary several inches where it solidified and was subsequently cut into segments of the proper length for diffusion annealing. The apparatus for diffusion annealing was the same as that used for capillary filling except that a Pt—Pt, 10 pct Rh therinocouple was placed in the solvent bath in order to accurately measure the temperature during the run. A diagram of the dif-

Jan 1, 1964

By K. G. Davis, P. Fryzuk

The diffusivity of silver in liquid tin has been determined, using the capillavy-reservoir technique, over the temperature range 250° to 500°C. The new value, D = 2.5 x 10&apos;* exp(-2480/ RT) sq cm per sec, differs from that obtained by other workers in an earlier investigation. The analysis of data from the capillary-reservoir technique is discussed. In a recent investigation of the solidification of dilute alloys, values for the diffusion constant of silver in liquid tin were required in the analysis of the formation of impurity substructures. AS a result, measurements were made of the diffusion constants in the temperature range 250° to 500°C (melting point of tin 232°C), for the alloy concentrations used in the solidification experiments and at higher concentrations, to verify previous determinations.I)2 The capillary-reservoir method was adopted, using experimental procedures similar to those followed by Ma and Swalin,1 with the main exception that radioactive silver was used in the present investigation to facilitate solute-concentration measurements. EXPERIMENTAL PROCEDURE a) 100 ppm Samples. Glass capillary tubes of 2 mm inside diameter and approximately 5 cm- long were sealed at one end, evacuated, and filled with tin of 99.999 pct purity. The region of shrinkage near the mouth was cut off, and the tubes were then placed in a graphite holder and immersed, with the open end up, in an unstirred bath of alloy containing 100 ppm Ag 110, where they remained for periods of up to 30 hr. On removal from the bath they were cooled by an air blower. The bath was kept under a small positive pressure of argon, and the temperature controlled to within +1°C. A 10-hr diffusion period was used in the majority of the tests, scatter on runs of less than 5 hr being rather large. The procedure outlined above was chosen in preference to putting alloy in the capillary and pure tin in the bath, in order to avoid segregation when the tubes filled with alloy were first solidified. To minimize segregation when the diffusion period was complete and the capillaries again solidified, the earlier samples were held in thin-walled silica tubes which could be cooled very rapidly. Later tests were made in precision-bore Pyrex tubes, to eliminate effects caused by variations in the capillary diameter. No consistent differences in diffusivity as measured in the two types of tube were detected. After removal from the glass tubing, the samples were sectioned into 2.5 mm lengths and counted for y activity, using a scintillation counter with fixed geometry. Samples were also drawn directly from the bath and counted, so that values for C/C,, the ratio of the weight of Ag 110 in the sample to that in the bath, could be obtained. b) 5000 ppm Alloy. To check for possible effects of concentration, the silver content of the bath was increased to 5000 ppm. Complete mixing was found to have taken place in the capillary after a 10-hr period at 300°C. It appears that the greater density of the alloy was sufficient for buoyancy forces to cause instability in the alloy-tin interface, leading to rapid convective mixing. For the 5000 ppm alloy, therefore, the bath was of pure tin and the capillary tube was filled with alloy. With this arrangement, values of D consistent with those for the 100 ppm alloy were obtained, Fig. 1. CALCULATIONS OF DIFFUSIVITY The terminology used applies to a capillary of pure tin immersed in a bath of alloy. 1) Error-Function Method. under the present experimental conditions, the rod of liquid tin into which silver is penetrating may be considered semi-infinite. Assuming the concentration at the mouth of the tube to remain constant at Co, the concentration C at distance x from the mouth of the tube at time / is given by3 Plots of the inverse error function of (1 -C/Co) vs .v gave straight lines passing through the origin with slope 1/2-, x being corrected for shrinkage both on solidification and while cooling to the melting point (total correction about 6 pct at 500°C). Values for log D obtained in this manner are shown in Fig. 1. A least-squares fit to the relation D = Do exp(-Q/RT)

Jan 1, 1965

By F. E. Jaumot, A. Sawatzky

IT as long been recognized that there is a need for accurate systematic data on diffusion in solids. Originally, such data were needed to check existing theories but, more recently, it would appear that it could be used most advantageously as a guide to, or a check for, much needed extensions of the theory of diffusion. The awareness of the conditions which are important to experimental accuracy, the availability of the materials for accurate experiments, and the techniques have improved to the extent that it would now seem to an experimentalist that, unless extensions of the theory are made which take into account the fundamental parameters of the atoms, the electrons, and the lattice in some detail, the field of diffusion will rapidly become an empirical or semi-empirical field. The present series of experiments was designed to provide accurate data on the diffusion of the elements of the IB and IIB subgroups in silver; that is, to provide data on the diffusion in silver of three face-centered-cubic elements with roughly similar chemical properties, but with different atomic or ionic sizes and, similarly, for three noncubic elements. The elements of these two subgroups have different valences, so that the data will not give any significant information on differences due to the crystal structure of the solute. The present paper reports data on the diffusion of copper and mercury in single crystals of silver; the data for the other elements of the IB and IIB subgroups were reported previously by the authors1&apos;2 and by Tomizuka and Slifkin.8 Experiment The general technique used was identical to that previously described1,2 and will not be repeated here. In all cases, the sectioning technique and high specific activity isotopes" were used. The short half-life of Cu64 made decay corrections more important than for the other isotopes, and necessitated around the clock shifts while data were being taken. Each section was counted at least twice (as was true for all longer half-life isotopes) and a monitor was counted along with each sample. Data for the diffusion of mercury in silver are presented at a greater number of temperatures than for the other solutes. This is a result of two circumstances. First, six (of 30) samples had to be discarded because of pitting or recrystallization which occurred during the diffusion runs, even though the samples had sustained high temperature prediffusion anneals. Either of these was a very rare phenomenon in the other experiments, and their occurrence in this case is considered in more detail below. Second, the curves of the logarithm of the activity of the sections vs the square of the penetration deptht were, in general, quite good, but frequently seemed to show one point to have high activity and the next point to have slightly low activity in terms of the best straight line. When this occurred, there was remarkable regularity of the high-low sequence. In any event, the results, as far as diffusion coefficients are concerned, were not affected by this amalgam effect. In fact, the mercury data had the highest internal consistency of any of the data. Results Diffusion of Copper in Silver—-Diffusion runs were made at eight temperatures In the temperature range from 700° to 950°C, for times ranging from 5 to 45 hr. A linear curve of the logarithm or the activity vs the square of the penetration depth was obtained for all samples. Table I summarizes the results for individual samples and Fig. 1 gives a plot 02 the logarithm of the diffusion coefficients as

Jan 1, 1958

By R. L. Andelin, J. D. Knight, M. Kahn

Self-diffusion in single-crystal tungsten and diffusion of rhenium tracer in single-crystal tungsten have been measured over the temperature range 2660° to 3230°C by direct sectioning and radio-chemical analysis of W185 and Re183 and Re184 tracers. The initial radioactive layer was produced on the diffusion specimens by bombardment with 9.0-mev deuterons. Diffusion heating of the samples in high vacuum was accomplished by induction heating. Temperatures were measured by optical pyrometry, and the system was calibrated ALTHOUGH a considerable body of experimental information has been accumulated on self-diffusion in solids, the major part of the detailed work has by reference to the melting points of tantalum (2996°C), molybdenum (2620°C), niobium (2468°C), and rhodium (1966°C). The diffusion coefficients for the two systems, obtained by least-squares analyses of the data, are well-represented by the equations thus far dealt with relatively low-melting systems. Diffusion studies on the high-melting elements niobium,1 tantalum,2,3 and tungsten4&apos;5 have been limited to polycrystalline material, for which data interpretation and theoretical analysis are sometimes difficult. Only recently, a study has been made with single-crystal molybdenum.6 The present work deals with the measurement of self-diffusion in single-crystal tungsten at temperatures approaching the melting point (3410°c).7 Since the method chosen for producing the radioactive tracer layer-bombardment with deuterons—produced detectable isotopes of rhenium as well as of tungsten, the diffusion of rhenium was measured also.

Jan 1, 1965

By T. S. Lundy, C. J. McHargue

HE diffusion rate of v48 in single crystals of bee vanadium has been determined at temperatures from 1002° to 1888°C. Standard techniques of lathe sectioning were used for specimens annealed above 1500°C while sectioning by grinding was used for specimens annealed at lower temperatures. As will be seen, the lower-temperature data is enhanced on an Arrhenius-type plot relative to values expected by extrapolation of the high-temperature data. Single crystals were obtained from Linde Co. In Table I the analysis supplied by the vendor is compared with an analysis at Oak Ridge National Laboratory of a sample after a diffusion anneal. The isotope v4&apos; was prepared by the Isotopes Division of Oak Ridge National Laboratory. Proton bombardment of a titanium target in the 86-Inch ORNL Cyclotron was followed by a carrier-free chemical separation. Nineteen specimens, 1/2 in. diam and 3/8 in. long, were cut from the as-received vanadium single crystals. Each specimen was machined with the flat face perpendicular to the longitudinal axis. Specimens were polished through 1/0 emery paper and were etched with 25 pct HF-10 pct H2SO4-10 pct HNO3-55 pct H2O. The polishing and etching steps were repeated until a satisfactory surface finish was achieved. The isotope was electroplated onto the specimens from a neutral solution. Counting rates of the deposited layers were approximately 100 counts per sec. At temperatures above 1200°C specimens were annealed in a tantalum resistance furnace under an argon atmosphere. Temperatures were measured with a Pyro micro-optical pyrometer and a Pt-Pt 10 pct Rh thermocouple. At lower temperatures the specimens were sealed in evacuated quartz ampoules and annealed in Kanthal wire-wound horizontal tube furnaces. A severe reaction occurred at 1200°C between the quartz and the vanadium. This

Jan 1, 1965

By R. W. Balluffi, R. Resnick

NUMEROUS investigations of chemical diffusion in a brass have been made and the results are collected in several places.1-3 This work has been mainly concerned with the determination of the chemical diffusivity as a function of composition and temperature. In 1947 Smigelskas and Kirken-dall&apos; showed that zinc and copper diffuse at different rates in face-centered-cubic brass, and since then, a number of efforts have been made to determine the intrinsic diffusivities of zinc and copper in this alloy.1, 5-9 Horne and Mehl8 in particular have recently determined the intrinsic diffusivities as functions of temperature and composition using sandwich-type couples and inert markers. Inman et al." also have determined the intrinsic diffusivities in homogeneous alloys using tracer techniques. When the present work was started, no information of this type was available. Consequently, measurements of the intrinsic diffusivities were made as a function of temperature at a constant composition of 28 atomic pct Zn with vapor-solid diffusion couples where the zinc was diffused into the diffusion couple from the vapor phase. The application of these couples to the study of diffusion in a: brass has been described previously.0,7 The temperature dependence of the intrinsic diffusivities was found to follow the relation D, = A, exp(-Hi/RT) and the values of Hzn, and Hcu, were found to be closely the same. It is emphasized, however, that the chemical dif-fusivity (D = N1D2 + N2D1) is a composite diffusivity and does not necessarily follow this exponential form. It is usually found to do so within experimental error for substitutional alloys because the heats of activation of the intrinsic diffusivities generally are not greatly different.&apos;" Also, at the onset of this work, there was no information available concerning possible unequal diffusion rates of individual components and the existence of a Kirkendall effect in alloys with other than face-centered-cubic structures. Since then, two reports indicating a Kirkendall effect in body-centered-cubic ß brass have appeared. Landergren and Mehl" have published a note describing Kirkendall diffusion experiments with sandwich-type couples. Inman et a1.9 also find a Kirkendall effect in this alloy using the tracer technique. In the present work, several aspects of the Kirkendall effect in ß brass were further investigated using vapor-solid couples. Two different couples were used, one in which the zinc was diffused into the specimen from the vapor phase and the other in which the zinc was diffused out of the specimen into the vapor phase. Briefly, the existence of a Kirkendall effect is confirmed and it is found that Dzn/Dcu = 3 at about the 46 atomic pct composition in this alloy at 600°, 700°, and 800°C. As a result of the unequal diffusion rates of zinc and copper, volume changes occur and subgrain formation is observed in the diffusion zone. In addition, significant porosity is produced by the precipitation of supersaturated vacancies. Diffusion in this alloy is therefore outwardly similar to diffusion in a brass where these effects are also observed, a Brass Experimental Methods—The use of vapor-solid couples in studying diffusion in a brass has been described in previous articles.6,7 The method briefly consists of sealing a copper specimen with Kirkendall markers initially placed on its surface in an evacuated quartz capsule along with a large zinc source of fine a brass chips and then diffusing the zinc into the specimen through the vapor phase. The zinc concentration at the specimen surface rises rapidly enough to a value near that of the a brass source so that the surface concentration may be regarded as constant during diffusion. Under these boundary conditions, values of the chemical diffu-sivity may be obtained by applying the Boltzmann-Matano analysis to the concentration penetration curve, and the intrinsic diffusivities may be obtained from Darken&apos;s5 equations when the velocity of marker movement is known. The diffusion specimens were made from OFHC copper in the form of disks 3.2 cm diam and 0.5 cm thick with faces surface-ground parallel to within +0.001 cm. Markers in the form of fine alumina particles <0.0002 cm diam were placed on the specimen surface. These specimens were then sealed in quartz capsules along with enough a brass chips of a 30.0 atomic pct Zn composition to keep the source concentration from decreasing by more than 0.3 atomic pct Zn as a result of the loss of zinc to the specimen during diffusion. The quartz capsules which were initially evacuated to a pressure of

Jan 1, 1956

By A. G. Guy

Zinc vapor from a reservoir of liquid zinc maintained at lower temperatures was diffused into sets of copper-zinc alloys at 759° and 870° C and into sets of silver-zinc alloys at 650° and 700° C. Each set of ,four copper-zinc alloys consisted of pure copper and 90/10, 80/20, and 70/30 brass. Similarly the set of silver-base alloys consisted of specimens containing 0, 7, 15, and 20 pct Zn. Natural markers at the initial surfaces of the specimens ware "trapped" under a thin electroplate and their depth of burying was measured after diffusion. The ratio of diffusivities of the two components determined from these data and the chemical diffusion coefficient calculated by the Matano method agreed with previously reported results. The line of markers was irregular and was often discontinuous when a grain boundary was crossed. TECHNIQUES involving the vapor phase have been widely employed in studying diffusion phenomena in metals. Many investigators have evaporated the more volatile component from an alloy, but it is generally believed that the porosity created under these conditions interferes with adequate interpretation of the experimental results. The extensive work of Gertsriken6 has been criticized on this score. Accary1 found that the diffusion coefficient for de-zincification of brass is larger by a factor of five than that for zincification, although he attributed the difference to a higher vacancy concentration under conditions of dezincification. Balluffi and siegle2 thoroughly investigated the technique of adding a more volatile component to a less volatile base metal as a means for studying diffusion. They verified that no porosity forms in a brass under these conditions and that the diffusivities of the two components can be determined from observations of the motion of markers originally placed on the surface of the specimen. The mathematical analysis that they developed for treating the experimental data was modified in a later note, but essentially it involved using the graphical Boltzmann-Matano method that is customarily applied to solid-solid diffusion couples. The experimental method used in the present research was similar to that employed by Balluffi and Siegle except for two modifications. Balluffi and Siegle used alloy chips as the source of metal vapor. This procedure has the disadvantage that the concentration of solute at the surface of the specimen changes during the diffusion experiment as the alloy content of the chips is gradually decreased. This disadvantage was overcome by employing liquid zinc as the source of zinc vapor in a manner similar to that described by Herasymenko.9 There was then no limitation on the amount of solute usefully available, and several relatively large specimens could be diffused in a given experiment. The second modification was the use of natural markers on the surface of the specimen rather than larger, artificial markers, such as the alumina powder employed by Balluffi and Siegle. It was expected that the fine, natural markers would permit more precise measurement of the buried interface as in the case of ordinary sandwich specimens.10 EXPERIMENTAL The experiments were designed so that zinc from the vapor phase would maintain a constant zinc content at the surface of pure copper (or silver) and

Jan 1, 1960

By T. S. Lundy, J. I. Federer

Chemically purified Zr95and Cb95 have been used in determining self-diffusion coefficients in the bcc phase of iodide zirconium over the temperature range of 900o to 1750°C. The temperature dependence of the diffusion coefficients could not be described by the usual Arrhenius-type equation over the entire temperature range. Values of the apparent frequency factors (D0)a and activation energies (Q)A for ZR95 varied from 4.8 x 10-6 to 2.5 x 10-2 sq cm per sec and 20,700 to 46,900 cal per mole, respectively, between 900°and 1750°C. Similarly, for Cb95, values of (Do) a and (Q)A varied from about 2.4 x 10&apos;5 to 0.25 sq cm per sec and 26,500 to 56,800 cal per mole, respectively. The data may be described in terms of the a to ß transition temperature of 1136 °K and the absolute temperature of the diffusion anneals by the following eauations: SEVERAL studies on the diffusion of Zr95 in zirconium have been reported.1"5 The values of the constants contained in the usual Arrhenius-type equation for describing the temperature dependence of the diffusion coefficient, D = Do exp [- Q/(RT)], are summarized in Table I. The reported values of Do, the frequency factor, and Q, the activation energy, are seen to vary by factors of about 60 and 1.6, respectively. Examination of the data from any one study indicated reasonable consistency of measurements. The large discrepancies of over-all results, therefore, cannot be explained on the basis of experimental scatter. One possible explanation for the differences in results could be a varying impurity content of the zirconium. Another possibility is that the radioactive daughter, Cb95, influenced the values of some of the determined diffusion coefficients. Therefore, the first of the three purposes of this study was to reconcile the large differences in diffusion results that have been obtained. Several empirical relations have been proposed to relate the diffusion coefficients in solids with physical properties, such as the absolute melting point, the heat of fusion, and the heat of sublimation.

Jan 1, 1963

By M. H. Pilkuhn, H. Rupprecht

p layers on n-type substrates of GaAs were prepared by difhsion of zinc into these substrates. Experimental details about the diffusion technique will be presented. It will be shown that inhomogeneity in the substrate doping level and crystal shucture defects cause nonplanarity in the junction plane. These nonplanarities give rise to high threshold current densities. From incremental sheet-conductivity measurements the zinc profile is derived. Data about surface concentration and gradient of the zinc concentration at the junction are presented. Finally, some results of laser diodes, which were made of wafers with extremely planar diffusion fronts, are discussed. ThE investigations reported here are part of a program concerned with the materials aspect in the fabrication of GaAs laser diodes. This includes studies of the influence of crystal defects introduced both during the growth of the crystal and as a consequence of subsequent diffusion. Compared with the progress made in the investigation of structure defects, for instance by X-ray microscopy in materials like silicon, no similar results are known so far for the case of GaAs. The further progress in laser diodes will depend very much upon our knowledge of these structure defects and subsequently upon our ability to avoid them. Laser diodes of GaAs had been made mostly by diffusing an acceptor impurity, normally zinc, into an n-type substrate. This procedure was found more convenient than the inverse one for various technical reasons. We will follow this line and restrict ourselves to zinc diffusion only in this paper. DIFFUSION TECHNIQUES AND EXPERIMENTAL DETAIL In order to set a refgrence for our experiments, we used a standard procedure for the diffusion runs. The diffusions were carried out in a sealed quartz tube for 2-1/2 hr at 850°C. One milligram zinc arsenide (ZnAsz) per cu cm of the tube volume served as zinc source. Under these conditions the junction depth was between 25 and 30 p. It is assumed, according to the investigations of the zinc arsenide system by V. Lyons and V. ilvestri,&apos; that ZnAs2 dissociates completely at 850°C into ZnsAsz and Asg. Since there is a condensed phase of ZnsAs2 in the tube at 850°C, the partial pressure of zinc is controlled by the pressure of the arsenic formed by the dissociation of ZnAs2. Due to the fact that the zinc partial pressure resulting from the dissociation of ZnsAsz is only a weak function of the partial pressure of arsenic, the amount of the initial ZnAs2 is not very critical. Experimentally, we found that the junction depth, as well as the surface concentration, was practically the same, if the ingots of ZnAs2 varied between 0.2 and 5.0 mg per cu cm. The wafers were oriented with the main faces in (100). Surface damage due to cutting and lapping was removed by a chemical-etch treatment in a rotating beaker (etch solution: HzSOr, H202, and HzO in a ratio 3:l:l). The GaAs substrate material was n type and doped with tellurium, selenium, silicon, or germanium. It was grown by means of horizontal or Czochralski techniques. After the diffusion process, junction depth and planarity were checked either by grooving with a

Jan 1, 1964