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By Nichols J. Grant, Bill C. Geissen

In low temperature phase diagrams, liquidus curves below about 1500°C are relatively easily established, e.g., by thermal analysis or separation of coexisting solid and liquid phases, followed by chemical analysis. Experimental difficulties increase considerably at higher temperatures and in systems involving more reactive metals. Although there are now thermocouples available for use from 1600" to 2400°c, as summarized by Caldwell,' the need for frequent calibration, aging, and contamination problems, and unavailability of suitable protection tubes has sharply limited their use at higher temperatures. Many of the high melt- ing metals are found to react with refractory oxides. TO avoid such problems, a frequently used procedure is the diffusion and saturation method, as described by Spedding et a1.' for the system La-C. This technique involves the annealing of one metal or a suitable alloy in a crucible of the other element at a temperature above the melting point, followed by chemical analysis of the center of the melt, after equilibrium is established. Further, if an alloy system is to be investigated employing the electron microbeam probe, and calibration charts have been established, it may be possible to measure the alloy concentration at the center of a cored as-cast structure, and to conclude from this points on the liquidus curve in a manner similar to the one to be described. It is known that in phases with a broad homogeneity range the rapidly cooled, cored, as-cast structure of an alloy presents concentrations having different lattice constants; this spread of lattice constant values contributes to the broadened lines of a powder pattern for the as-cast condition. The region of the crystal which is first to solidify will then correspond to the edge of the lines if the change of the lattice parameters with concentration is monotonous. In the course of the determination of the Ta-Tr phase diagram,3 it became evident that such behavior made it possible to construct the

Jan 1, 1963

By W. N. Carr, J. R. Biard, B. S. Reed

An analysis of the semiconductor injection laser is presented which is based on a phenomenological model using device and material parameters. The intent of the laser threshold analysis is not to predict from theory the actual threshold current density but rather to provide a logical means of interpreting experimental results. The device and material parameters have been selected such that they describe both the threshold conditions and quantum efficiency of the lasev. A technique is proposed whereby the current required to obtain a population inversion is predicted from device 1-V characteristics. Experimental data are presented which support the analysis. THIS investigation is concerned with the characteristics of GaAs lasers fabricated in this laboratory. However, the assumptions used in these calculations should not limit their application to GaAs alone. It is felt that the analysis is sufficiently general to be useful in describing the operation of other semiconductor-laser materials. ANALYSIS heavily doped semiconductors to be considered. The absorption and/or generation of optical radiation may be completely specified in terms of q(E) and the probability functions f,,(E) and f,(E) which define the occupancy of the valence-band and conduction-band levels, respectively. The symbols used in this analysis are listed at the end. Following the approach of all' it can be shown that the effective gain coefficient, g, in the plane of a forward-biased P -N junction is g(E)=-ai@)[1-fv(E)-fc(E)] [1I In particular Eq. [I] holds for the photon energy at which lasing occurs, Ep. Throughout the following discussion Eq. [I] is considered only for the lasing transition E = Ep. For simplicity the functional energy dependence of the various factors is omitted in subsequent equations. Unless otherwise stated the symbols used represent the values at Ep. If the analysis is limited to the P-type side of the laser junction, the function q(l -f,,) is recognized as the band-to-band absorption in the P-type material at thermal equilibrium. Under forward-bias conditions the function f, is determined by the electron quasi Fermi level in P-type material. For sufficiently large forward bias the second term in Eq. [3] will become dominant and net gain will result; i.e., g will become positive. In order to simplify the subsequent analysis several assumptions are in order at this point. a) No conductivity modulation occurs. /„ is independent of f, and therefore go is a constant. b) The P-type material is heavily doped such that the degeneracy of the valence band permits popu-

Jan 1, 1964

By A. G. Guy

Thermodynamic activity rather than chemical composition is basic to the analysis of diffusion. This is the essential conclusion reached by Darken1-3 and by Birchenall and Mehl.4 If so, it is reasonable to expect that diffusion calculations should be carried out using activities. This paper will illustrate a method of employing activities in analyzing interstitial diffusion. For interstitial diffusion (of carbon in iron and probably generally) the diffusion of the solvent atoms, volume changes, and other such complexities not explicitly provided for in the usual diffusion equations cause a negligible error of the order of 1 pct. Therefore it is relatively easy to test the validity of an analysis based on activities in the instance of interstitial diffusion. The mathematical treatment of the more complex substitutional diffusion could be simplified once the adequacy of the activity method had been established for substitutional diffusion. Thus the present work has the purpose not only of providing a superior analysis of interstitial diffusion but also of indicating a possible approach to the more important question of an adequate treatment of substitutional diffusion. Development of the Diffusion Equation Although activities are convenient quantities to determine experimentally, they are derived from the more fundamental fugacities.9 Possible confusion in using activities can be avoided by basing equations involving their use on the relationship, dP = -D1d/ax dt [I] where, dP = the number of grams of solute crossing one cm2 in the time dt sec. D, = the diffusion constant for use with fugacities; it is assumed to be constant at a given temperature, and has units of secs. f = the fugacity of the solute in the solid solution; the units are those of pressure, dynes per cm2. x = the distance in cm. Eq 1 can be considered to be the basic form of the first Fick Law for one-dimensional diffusion. In order to convert Eq 1 into an equation involving activities, a choice of a standard or reference fugacity, f°, must be made: then. a = f [2] where a is the activity corresponding to the fugacity f. However, the value of a is also determined by the relation, a = a\c [3] where a is the activity coefficient and c is the concentration. For a given value of a (such as a = 1) it is evident that the units used for expressing concentration will affect the numerical value of a corresponding to a given amount of carbon dissolved in y-iron. Since weight per cent concentration is so widely used, this unit will be adopted as the standard in this paper. When the value off given by Eq 2 is substituted in Eq 1, the first Fick Law becomes, dP= -D,f°dl [4] Since D,f° is constant (at a given temperature), the second form of Fick's Law can be obtained in the usual manner, -dt D'f° dx [5] where c' is the concentration in g per cm3. In terms of weight per cent concentration, c, Eq 5 becomes, dc _ 100 d2a Tt = T /f w [6] where p is the density of the solid solution and will be assumed to be constant. In order to simplify Eq6, it is necessary to consider the standard state, f°. Standard states are chosen for convenience. There appears to be one especially convenient choice for the analysis of interstitial diffusion. If the activity coefficient, a, is set equal to unity at infinite dilution of the solute, 100 then — 100D1fl° is approximately equal P to the usual diffusion constant in dilute solutions. This is true since the activity, a, in Eq 6 can be replaced by the concentration, c, with little error in an infinitely dilute solution.* Here f1° is the standard fugacity necessary to achieve this standard state. It is proposed that a diffusion constant Da' be defined, Da1=100/pD1f1° [7] where A is the metal whose diffusion is * The second derivative of a is equal to the second derivative of c in dilute solution only if -da/dr- is. zero. Although theory does not require this condition, in the systems C in Fe, and Zn in Cu, dc is in fact found to be essentially zero.

Jan 1, 1950

By N. W. Lord

The process of molten-zone refining is analyzed for long ingots and many zone passages. Formulas are derived which give the resultant impurity distribution in terms of finite series. A comparison with the approximate procedure of Hamming is given. HE physical principles and applications of an extremely physicalprinciple efficient form of metallurgical refinement has been described by Pfann. The purpose of the present paper is to describe a method of analyzing exactly the particular program used which enables the segregation effect to be predicted for any number of molten-zone passages in a long ingot. The method is applied to the particular case of refinement of an ingot whose impurity initially is uniformly distributed throughout its length. A number of molten zones of equal length are passed through the ingot effecting a radical redistribution of impurity. Pfann has indicated an approximate method, due to R. W. Hamming, of calculating the resultant concentration after each successive zone pass for a particular value of the segregation constant defined in his paper. Here a solution will be presented in terms of the number of zone passes and the segregation constant. The expression, though cumbersome, is exact and susceptible to ordinary numerical computation procedures. The results of a similar computation using the procedure of Hamming are presented in a table together with the exact results of the present method. The discrepancy in terms of absolute concentrations is tabulated for the first eight zone-lengths. To establish the notation (which follows that of Pfann1 as closely as possible) and physical basis of the analytical equations, the physical model and principal assumptions may be reviewed. An alloy of two elements, where there is formed a continuous range of solid solutions, usually does not melt as a simple compound. Rather, a temperature is reached where the solid solution is in heterogeneous phase equilibrium with a liquid solution of different composition. The temperature dependence of these equilibrium compositions forms part of the phase diagram. For very small concentrations of a solute B in a solvent A, this usually takes the form of Fig. 1. Sometimes the solidus and liquidus slope upward. This corresponds to a segregation constant (defined below) which is greater than unity. The segregation constant is now defined as k = Cn(x)/CnI(x) [1] where C,,(x) is the impurity concentration in the solid ingot at distance x during the nth passing of a molten zone and Cnl (x) is the impurity concentration of the liquid zone from which the solid at dis- tance x is formed (see Fig. 4 of ref. 1.) C (x) remains the same after passage of the zone. The constant k may be either greater or less than unity in general. Purification in the former case is effected only in a finite ingot and in the portion that is melted last. For k less than unity purification is effected even in an infinite ingot. The method which follows gives, in the former case, the successive increases in impurity concentration and, in the latter case, the successive decreases in concentration. The general case of impurity redistribution will be considered first, and purification will be discussed later on. The analysis rests on the following assumption: The movement of the zone is too rapid to allow appreciable atomic rearrangement in the solid sections and too slow to disturb the uniform impurity distribution in the liquid zone characteristic of equilibrium. Hence, the composition in the solid at the left solidifying interface will be determined by Eq. 1 while the impurity concentration of the liquid zone will be uniform throughout its length. The reasoning which follows closely parallels that of Appendix 11 in Pfann&apos;s paper. It is reviewed here for the case of the nth zone pass in order to make clear the meaning of an operator essential to the present method. Fig. 4 of ref. 1 shows the movement of a molten zone of length 1 in an ingot of total length d. Each Cn(x) can be determined from the condition that the amount of solute added to the zone during an incremental advance, dx, is due to the melting in of a solid portion C(x)dx and the freezing out of kCnl(x), that is d I —r- CnL (x) dx = Cn-1 (x+l)- kCnL (x) dx or, in terms of Cn(x) d k k —— C,(x) +—c.(x) =— Cn-1 (x + l). [2] dx l l This, of course, is derived from the main assumption, the fact that 1 is constant, and that the total impurity content previously present up to x + 1 is constant . A correction has to be made for the region (d — nl) < x < d. This is due to the zone length changing during the passage of the solidifying interface beyond x = d — 1. Since the general solution would be too complicated otherwise, only the region 0 < x < d — nl is considered. The general solution of Eq. 2 is

Jan 1, 1954

By D. L. McDanels, J. W. Weeton, R. W. Jech

An investigation was conducted to determine the stress-strain behavior and tensile properties of metallic composites and to relate them to the properties of the base materials. Tungsten fibers in a copper matrix were chosen as the model sys-tem to investigate these properties. Room-temp-atzcre tensile and dynamic -modulus tests were used To meet the demand for improved structural materials, considerable effort is being directed toward the creation of composite materials. One such material under investigation is the fiber-reinforced composite, in which a ductile, relatively weak matrix is reinforced with high-strength fibers. Some work has been done on the reinforcement of metallic matrices with metallic fibers1"5 as well as with ceramic-whisker reinforcement. Summaries of much of this work have been published by Mach-lin7 and Baske~.&apos; Work done at the Lewis Research Center of NASA-" has involved the making and testing of composites composed of a fiber, tungsten, and a matrix, copper, which were insoluble in each other. An equation was presented that showed the relation between the ultimate tensile strength of the composites and the strengths and relative volume percents of the components. This relation was verified experimentally for composites containing fibers extending the full length of the specimen as well as for composites reinforced with short-length or discontinuous fibers. Since the publication of the preliminary results,9&apos;10 additional data have been obtained. This paper presents these data as well as analyses of the stress-strain behavior and the mechanics of deformation of uni-axially oriented, fiber-reinforced metallic composites, in which both components are mutually insoluble. EXPERIMENTAL PROCEDURE Composites were made with high-purity copper as the matrix and 3-, 5-, and 7-mil-diam tungsten wire as the reinforcing fiber. Some specimens were made in which the reinforcing fiber extended completely through the full length of the composite test section. The fibers were placed in ceramic to determine these properties. The composites were reinforced with either continuous or discontinuos tungsten fibers. The tensile properties and stress-strain behavior of composites reinforced with either type of reinforcement were similar, and in both cases the full strength of the fiber was utilized. tubes to insure axial orientation and infiltrated with copper at 2200°F for 1 hr. Composites were also made with short-length (3/8 in. long) 5-mil-diam tungsten fibers as discontinuous reinforcement and infiltrated under the same conditions. The reinforcing fibers in both cases were longitudinally oriented in the direction parallel to the tensile axis. Room-temperature tensile tests were conducted on the composites, stress-strain curves were obtained, and ultimate tensile strength and elongation were measured. Dynamic modulus of elasticity, based upon the resonant frequency induced in the flexural mode of vibration, was also determined for the composites and the components. A more detailed discussion of the experimental procedure employed in this investigation may be found in Ref. 11. RESULTS Room-temperature tensile tests were conducted on 3-, 5-, and 7-mil-diam tungsten wires which had been annealed for 1 hr at 2200°F and show the tensile strength of the wires to be 331,000, 327,000, and 290,000 psi, respectively. Since all the composites were infiltrated under these conditions, the strengths were considered to represent the strength of the fibers in the composites throughout this study. The average tensile strength of the annealed copper used as the matrix in this investigation was 27,800 psi. Results of room-temperature tensile tests on composites reinforced with 3-, 5-, or 7-mil-diam tungsten fibers are plotted as functions of composition in Fig. 1. These data represent previously reported datag,l0 as well as data more recently obtained. The line shown on each curve represents a prediction of tensile strength as a function of composition; the calculation of this line was explained in Refs. 9 and 10. A similar plot is presented in Fig. l(d) for composites reinforced with short-length, discontinuous 5-mil-diam tungsten fibers. Again, both the previously reported and the recent data are presented, and the line shown is identical to that shown for

Jan 1, 1965

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby&apos;, it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes&apos; which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,&apos; the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young&apos;s modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By W. Rosotoker

Using an expression for the free energy of a homogeneous phase as a function of composition, a relationship is derived which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. Comparisons between observed and calculated phase boundaries in the systems Fe-Ni, Fe-Mn, Fe-W, Ti-Mo, and Ti-Cb are presented. IT is the purpose of this paper to illustrate how the general free energy equations for two phases in equilibrium may be used to derive an expression which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. The free energy per gram atom of a disordered solid solution may, for many purposes, be represented by the equation:&apos; F = ½NZ [C-V,, + (1-C) VbB + 2C (l-C)V] + K(T) +RT[C-lnC+ (l-C)ln(l-C) ] [1] where N is Avogadro&apos;s number; Z, the coordination number; C, the concentration of the solute element in atomic percent; the subscripts refer to concentrations at phase mixture boundaries; VAA, VBB, and V,, are the bond energies between like and unlike adjacent atoms, respectively, at the interatomic spacing characteristic of the phase. The bond energies are usually assumed to be independent of small changes in the lattice parameter occasioned by solute additions and variations in temperature; V = VAB ---------------—— ; K(T) is the sum of the heat con- tent and heat entropy; R, the molar gas constant; and T, the temperature in degrees Kelvin. The free energy of a homogeneous phase is there- fore the sum of an internal energy, a specific heat, and a configurational entropy term, respectively. The compositions of two phases in equilibrium at a given temperature are governed by the minimum total free energy principle. Graphically, this is represented by the points of tangency of the tangent common to the free energy vs. concentration curves of the two phases. Analytically, this may be expressed as: ( df) = (df) [2] dc dc Expanding both sides using eq 1, the following equation is obtained after convenient readjustment of the terms: RT In[(ca)(1-c)]-½N (Vaa-Vbb)(Za-Zb) +NV [Za(l-2Ca)-Z,(l-2C,)] [3] The following assumptions have been made at this point: 1—The specific heats of the two phases are independent of composition variations within the range under consideration. Accordingly, the K(T) terms disappear on differentiation. 2— (Vaa)o = (VAA); (VBB). = (VBB); Va = V, Theyjustification for these assumptions can lie only in the successful application of the resultant equation. It may be noted that Zener2 has used assumption 1 in the calculation of the boundaries limiting the (a+j3) phase mixture in the Cu-Zn system.

Jan 1, 1952

By L. D. Hall, D. R. Mash

The paper presents the results of experiments on the anelastic. behavior of gold, as manifested by grain boundary relaxation. Two grain boundary internal friction peaks are found for 99.9998 pct Au. It is found that the peaks are associated with primary and secondary recrystallization. However, the existence of two discrete peaks cannot be explained on the basis of grain size and shape alone. It is suggested that grain boundary stability, as determined by orientation, plays a role in the observed effects. EVIDENCE for the viscous behavior of grain boundaries in metals has been presented in recent years by several investigators, based upon studies of various anelastic effects, especially internal friction. KG1 has contributed greatly to this field, having put forward a coherent body of evidence for stress relaxation by the viscous intercrystalline flow mechanism. In this connection, he has made extensive use of pure aluminum (99.991 pct) as the test material, although he has also studied other metals and alloys, including pure iron (Puron).² Rotherham, Smith, and Greenough³ have studied the internal friction of pure tin, interpreting their results in a manner similar to that of KG. In view of the importance of such studies in shedding light upon the fundamental structure and behavior of the grain boundaries in pure metals, it appears that the use of a very pure test material which is inert to its environment should provide useful information on anelastic properties and the source of such behavior in pure metals. The present work was carried out on spectrograph-ically pure, 99.9998 pct Au, free of all impurities except for a trace of silver, estimated to be present to the extent of about 0.0002 pct. The term "pure gold" will hereafter refer to this very pure material. Gold of commercial purity, 99.98 pct, was also studied to observe the effects of small amounts of impurities. A pure gold "single crystal" specimen was also tested for comparison. The variation of the internal friction and rigidity modulus as a function of temperature was determined by means of a torsion pendulum apparatus employing extremely low stress amplitudes and a frequency of vibration of the order of 1 cycle per sec. A 12 in. length of 0.031 in. (20 gage) gold wire formed the suspension element. The apparatus was similar to that described by Ke.l The test procedure and the basic requirements to be met for obtaining useful experimental data by this method have been given elsewhere.1,2 It should be made clear that in all of the experiments to be described, the internal friction and rigidity were independent of the amplitude of torsional vibration. The semilog plot of amplitude of vibration vs ordinal number of vibration was a straight line. This was carefully verified for each internal friction measurement. The linear variation shows that the internal friction was independent of stress; i.e., that the specimens were not being cold-worked during testing. The reproducibility of the internal friction curves, which were obtained by cyclic heating and cooling, indicates that the gold was unaffected by its environment during the tests. The measure of internal friction adopted in the present study is the conventional "logarithmic decrement," defined as follows: log. dec. = l/n In A0/An [I] where n is the number of cycles or vibrations; A,, the initial amplitude of vibration; and An, the amplitude after the nth cycle. When the logarithmic decrement is small, the shear modulus, G, of the wire is proportional to the square of the frequency of vibration provided the length and radius of the wire are kept constant. A plot of frequency squared vs temperature gives the following ratio:&apos; This expresses the fraction of the stress which has not been relaxed at a given temperature. Gr and Gv are the relaxed and unrelaxed moduli, respectively. The frequency of vibration in the polycrys-talline specimen is fp, and the frequency of vibration of a single crystal is f8. This latter quantity is obtained simply by extrapolating the linear, low temperature portion of the curve of frequency squared vs temperature for the polycrystalline specimens. The theory of viscous grain boundary stress relaxation as demonstrated by the anelastic behavior of metals has been discussed in detail by Zener4 and need not be reproduced here. Experimental Results Initial measurements of the internal friction of pure gold were carried out on specimens which had been drawn with no intermediate annealing, resulting in a material which had undergone approximately 99 pct reduction of area in final processing. Annealing was then carried out at successively higher temperatures starting at 400°F for 1 hr and proceeding in this manner to as high as 1600°F in 100°F intervals. After each annealing treatment an internal friction and rigidity vs temperature curve was obtained over the range from room temperature to the particular annealing temperature. The resulting internal friction curves did not exhibit well defined maxima (peaks), but rather several fairly flat

Jan 1, 1954

By D. P. Seraphim

Single crystals of bee Li-Mg solid solution were grown and their internal friction was measured as a function of temperature, A peak of the Zener type was found in the damping spectrum. The activation energy for the relaxation process is 21.5 ± 1 kcal per mole and the frequency factor is 1015.7 ± 0.7 sec-1. ZENER internal-friction peaks which are observed for a wide range of solid solutions are attributed to stress-induced changes in local order.&apos; In the present work a Zener internal-friction peak, the first reported for a solid solution of an alkali metal, is

Jan 1, 1961

By P. W. Bakarian, John C. McDonald

Three magnesium alloys were processed in various ways to exhibit a wide variation in the ratios of yield strength and tensile strength in the rolling direction compared to the cross-rolling direction. Basal-plane pole figures were prepared from several specimens. A fair correlation was observed between the property ratios and the ratio of percent of poles oriented in the cross-direction quadrants compared to the percent oriented in the rolling-direction quadrants of the pole figures. THE modes by which magnesium crystals deform are such as to lead to marked preferred orientations in all forms of wrought products. The effect of the active modes at room temperature, coupled with these orientations, is often to produce a lower compressive yield stress compared to the tensile yield stress. The phenomenon is due to easy twinning in compression, and has been well-related to the preferred orientations as described by basal-plane pole figures of the hcp magnesium single crystal. The literature contains some information on the variation with test direction of the tensile properties of sheet, but no quantitative relationship to the observed pole figures has been established. These effects have been reviewed in the few com- prehensive treatises in English which have been written on magnesium technology and metallurgy.1°3 Roberts presents several pole figures, but no tensile-property data in the plane of the sheet. Raynor has no pole figures, but quotes Frommer&apos;s4 results. The information in Beck&apos;s compendium more or less parallels the results of Jones and powell.5 In both a Mg + 1.5 Mn alloy and a Mg + 4.6 A1 alloy, cold rolling was found not to change the general situation of higher properties in the cross-rolling direction,* than in the rolling direction. Thomas&apos;6 X-ray studies of Jones and Powell&apos;s specimens did not permit correlation of properties and preferred orientation. Ansel and Betterton7 report tensile and compressive properties on three other alloys as a function of degree of cold rolling, plus a recrystallizing anneal. As rolled, there was a change in anisotropy with degree of reduction, but all alloys were reasonably isotropic in tension when annealed. X-ray diffraction photograms illustrated the kinds of orientations present, but were not correlated with the properties. Bakarian8 has described a method of determining quantitatively a preferred orientation, and illustrated the method by applying it to pure magnesium and two of its alloys. This method was used in the present work as a basis for correlating the strength properties with the texture.

Jan 1, 1965

By Jei Y. Choi, P. G. Shewmon

Using a scratch smoothing technique, the magnitude and the ratio of the surface diffusion coefficients (D,) in two orthogonal directions have been measured on copper for over 100 different surface orientations. Anisotropy was found for all surface orientations except those lying near the (100) and (111); however, these anisotropies were rarely greater than 2.0. The direction of maximum D, appears to coincide with the direction of step edges on any given surface, and if no such steps exist, no anisotropy is found. Thus the jump frequency along a step edge is shown to be faster than the frequency of a jump over the step. The values of Ds and AH for the (100) and the (111) orientations agree quite well with those obtained earlier by the grain boundary grooving technique. It is proven that the directions of maximum and minimum D, (the principal axes) for any surface orientation are known if the perfectly ordered plane corresponding to the given surface orientation possesses a plane of mirror symmetry. Thus the principal axes of D, for orientations lying along the sides of the unit stereo-graphic triangle are always known independent of the extent of thermal disorder or impurity adsorption. The merits and shortcomings of King and Mullins&apos; recently published equations relating Ds to the rate of scratch smoothing are discussed. 1N an earlier paper the authors have reported the variation of the surface diffusion coefficient (Ds) with surface orientation on copper.&apos; In that study Ds was determined from the rate of growth of grain boundary grooves on symmetric bicrystals. This gave values of Ds from 850° to 1070°C in a given direction on each of the six surfaces. It was found that the activation energy for surface diffusion was essentially the same for all six surfaces. The theory developed to explain these data assumed that the free energy of any given type of surface site depends only on the number of nearest neighbors the atom has. This same theory predicted that on any given surface Ds should be independent of direction. The primary aim of this study was to check the validity of this prediction for a wide range of surface orientations on copper. The growth of grain boundary grooves is ideal for studying Ds in a given direction on a given surface over a range of temperatures, because the same specimen can be repolished and used again. However, there is considerable work involved in growing a symmetric bicrystal, and for a survey of Ds in two or more directions on many surface orientations, the technique would be arduous. A better technique appeared to be the scratch method used primarily by Mykura. 2 If a scratch is placed in a surface whose surface tension is independent of orientation, the surface will smooth out in time under the influence of surface tension. To determine D, from this flattening, Blakely and Mykura2 used an approximate solution which was assumed to describe the rate of flattening. Recently King and Mullins3 (hereinafter K and M) have given a more exact analysis of the flattening of an isolated scratch. A second aim of this paper was to check the validity of this newer analysis and compare the values of Ds determined thereby with the values obtained from grain boundary grooving techniques. EXPERIMENTAL PROCEDURE In an effort to work with a particular predetermined surface orientation, light orthogonal scratches

Jan 1, 1963

By R. L. Grunes, F. K. Kies, C. D&apos, Antonio

THE several studies concerned with the annealing of thin nickel films have largely been restricted to films of a single thickness.1-4 It is well-known, however, that both physical and mechanical properties depend upon film thickness.5, 6 The strength-thickness relations found in vapor-deposited nickel films in the annealed and as-deposited states, as an example, are at least partially due to the density and arrangement of imperfections within the films.7, 8 For these reasons, the annealing characteristics of thin nickel films as a function of thickness were investigated. Electrical resistance was chosen to monitor annealing behavior since resistance changes are partially dependent upon defect structure. In addition, the equations predicting film resistivity as a function of thickness are already available.9, 10 Further advantages afforded by electrical-resistance measurements are its adaption to continuous readings during annealing and its relative simplicity. Nickel films were vapor-deposited, at average rates of 60Å per sec, on Vycor substrates held at room temperature in vacuums of about 10-5 torr. Afterwards, deposition-thickness measurements were made using a multiple-beam interferometric technique. A more detailed description of deposition procedures and the interferometer appear elsewhere.7, 8 The four-probe method was employed in measuring electrical resistance since this technique measures film resistance without contributions from lead wires and contacts. Resistance measurements were made before, during, and after annealing to temperatures of 700°C under vacuums of approximately 10-4 torr. Measurements were made every 25°C or more often when necessitated by unusual resistance changes. Cooling and heating rates were maintained at approximately 5°C per min. Typical resistivity vs temperature curves are shown in Figs. 1 through 4. It is apparent from these

Jan 1, 1965

By P. A. Beck, A. H. Lutts

IN the classical picture of recrystallization the growth of strain-free grains at the expense of a strained and work hardened matrix is responsible for the softening of cold worked metals on annealing. It has been commonly assumed that the release of the stored energy of cold work, softening, and re-orientation take place simultaneously, as the high angle boundaries of the new recrystallized grains sweep over the cold worked matrix. However, recent evidence indicates&apos;,&apos; that, at least in some cases, considerable or even complete soften- ing may take place essentially without reorientation (i.e., without the migration of ordinary high angle grain boundaries, or "recrystallization&apos;&apos;) and the release of most of the stored energy of cold work may precede softening. These cases suggest that the property changes, taking place during the annealing of cold worked metals, may be associated with various distinct processes. The study of such situations is of considerable interest, since quantitative data are still scarce. In the present work, isothermal softening curves were determined for a heavily rolled aluminum single crystal, under such conditions that no "recrystallization" occurred until after complete softening. The hardness data were correlated with X-ray diffraction pinhole patterns in order to detect any reorientation that may occur and with measure-

Jan 1, 1955

By R. A. Swalin, L. A. Neimark

The research work presented in this paper had initially a two-fold goal. First, further data concerning the low-temperature recovery of cold work was desired. Recovery phenomena have been extensively studied in face-centered-cubic metals but at the time of initiation of this research, no investigation concerning the low-temperature recovery in body-centered-cubic metals had been made. During the course of the investigation a paper by Martin on the recovery of point defects in molybdenum appeared.&apos; Comparison of our results on tungsten with Martin&apos;s results on molybdenum will be made. Secondly, knowledge concerning the influence of a particular type of impurity addition on the recovery kinetics was desired. It has been known for a long time that extremely small amounts of certain impurity additions exert a profound influence on the recrystallization behavior and the resulting microstructure of tungsten. Small amounts of potassium silicate and aluminum chloride added prior to the reduction of tungsten oxide to the metal have been found by Smithells to raise the recrystallization temperature markedly,2 and yield an ultimate microstructure in which grains several millimeters long are produced in fine wires of say 10 mil diam. If the impurities are added singly, ordinary secondary recrystallization results with none of the spectacular properties of the wire to which special additions were made. Swalin and Geisler3 and Rieck4 have studied the recrystallization behavior of such doped wire in some detail. The former workers found that small amounts of these impurities raised the recrystallization temperature over 400°C and electron microscopic examination revealed no obvious inclusions in the microstructures. In fact. chemical analysis showed that there was <0.001 pct K, <0.002 pct Al, trace of Si, and <0.0003 pct 0 in the wire studied. The possibility that the role of the special impurities is to keep the structure open by void formation and that submicroscopic porosity acts as the inhibiting agent has been discussed.2&apos;3 Meijering and Rieck5 have suggested that the impurities are strung out as second-phase particles in a direction parallel to the drawing direction. It was thought that a kinetic study of recovery could perhaps elucidate the role of the impurities to some extent. When a metal is deformed by cold work three basic types of defects are thought to be introduced into the crystal lattice, namely, interstitials, vacancies, and dislocations. Van Bueren6 has proposed that recovery of cold-worked metal is a four-stage process, each step being the result of the annealing of a primary defect or a combination of defects and having a unique activation energy. The steps in order of increasing activation energy are attributed to a) the diffusion of interstitials recombining with vacancies, b) diffusion of vacancy pairs, c) the diffusion of single vacancies, and d) climb of dislocations. In metals with relatively low- or medium-range melting points the temperatures for recovery are low enough so that the first three steps may occur during room-temperature deformation. For tungsten, because of the high melting point and subsequently high recovery temperature, it was calculated, using Nowick&apos;s approach7 that this recovery would occur in the temperature range 200" to 600°C. It is also known that recovery of X-ray line broadening, presumably due to dislocation climb, occurs at about 600°C.8 EXPERIMENTAL METHOD Two types of cold-rolled 10-mil-diam tungsten wire were used in the investigation; a) pure tungsten, (called undoped) and b) G. E. No. 218 wire (called

Jan 1, 1961

By D. T. Novick, M. B. Bever, B. Roessler

Ordered and disordered specimens of the alloy CusAu were cold worked and then annealed at 2880, 310°, and 340°C, together with disordered unworked specimens. me resistivity decreased during annealing mainly as a result of ordering; the resistivity measurements suggest that in cold-worked specimens the growth of antiphase domains is impeded. The strength properties increased during annealing at 288 "C; in cold-worked specimens this increase was lo a level above that for cold-worked specimens which had not been annealed. X-ray diffraction showed that after annealing for a few hours at 288ºC, the long-range order increased to a constant value; additional annealing at 288ºC resulted in the growth of antiphase domains in which the degree of order was constant. Changes in peak breadth and particle size confirmed that in cold-worked specimens the major effects of cold work were not eliminated during annealing at 288 "C, although a slight recovery process occurred. When a specimen of the alloy Cu3Au is heated to a temperature below the critical temperature (388ºC), long-range ordering tends to occur in a specimen containing less than the equilibrium amount of order characteristic of that temperature Ideally, a specimen of Cu3Au contains no long-range order if it has been quenched from above the critical temperature. Long-range order is reduced by cold work. If cold-worked specimens are heated, restoration processes such as recovery and recrystallization may occur,

Jan 1, 1963

By S. R. Goodman, Hsun Hu

A study has hem made of the formation of annealing textures in an 18-8 austenitic stainless steel (Type 304L) from various deformation textures obtained by rolling at different temperatures. When the deformation texture is a mixture of the ferritic type and the brass type owing to the pres -ence of both martensitic ferrite and retained aus-tenite in the specimen, recrystallization takes place by the growth of the existing austenite phase. In a previous report,&apos; it was shown that the rolling texture of austenitic stainless steel (Type 304L) changed gradually from the brass type to the copper type with increasing temperature of deformation above 200°C. These changes are similar to those in high-purity silver2,3 and electrolytic copper;4 a brass-type texture is favored at low rolling temperatures, whereas a copper-type texture is favored During the course of rolling -texture transition from the brass type to the copper type, the subsequent recrystallization textures change accordingly. The orientation relationship between the annealing textures and the various rolling textures, being consistent with previous observations on various fcc metals, can be described as [Ill] rotations of approximately 25 to 40 deg. Carhide precipitation may influence the annealing textures. at high rolling temperatures. Furthermore, the annealing textures in high-purity silver5 and electrolytic copper4 were found to depend entirely on the prior deformation texture. From a copper-type rolling texture a strong cube texture will form upon recrystallization, whereas from a brass-type rolling texture the annealing texture will be quite different from the cube orientation. In an earlier comm~nication,6 the formation of a strong cube texture in 18-8 austenite stainless steels (Types 304 and 304L) was reported briefly by the authors. The present paper constitutes the results of a complete study of the annealing textures obtained from a

Jan 1, 1965

By Hsun Hu

The formation of annealing textures in high-purity silver, from the various rolling textures obtanled in the course of texture transition, was studied. It was found that from a brass-type rolling texture the recrystallization texture is mainly (120) [211] type, which is quite different from the recrystallization texture of brass. From a predominantly copper-type rolling texture, the reclystallization texture is mainly (100) [001]. The recrystallization texture of silver- varies also with the degree of purity. In each case, however, the reorientation can be expressed as [Ill] rotations of 30° to 40°, which is consistent with the oriented growth theory of the formation of annealing textures. ThE recrystallization textures of rolled silver were studied long ago by Glocker and co-workers (1924-27) and were reported to be (113) [iil] upon annealing at low temperatures.1 Since that time, no further study of the recrystallization textures of silver, particularly with the modern techniques of quantitative texture determinations, has been reported in the literature. In a previous study2y3 it was found that the rolling texture of high-purity silver (99.999 +pct pure) is changed gradually from the common silver- or brass-type to the copper-type by raising the temperature of rolling from 0" to 200°C. The formation of annealing textures from the various rolling textures in the same material is, therefore, of considerable interest. The present paper constitutes the results of such a study. MATERIAL AND METHOD Specimens were taken from the same strips of high-purity silver* that were used previously for

Jan 1, 1962

By P. A. Beck, Hsun Hu

As described by means of quantitative pole figures, the annealing texture of highly rolled aluminum consists of the four retained components of the rolling texture near (123) [121], rather more sharply developed, and of a cube texture component. Local reorientation corresponds fairly well to 40 rotation around a [111] axis. In copper strip rolled 96 pct, the annealing texture is mainly the cube texture, with the four twin orientations as minor components. The annealing texture of highly rolled brass strip consists of four components of the (225) [734] type. REVIEWS by Wassermann,&apos; Barrett,&apos; Dunn,3 and Richards&apos; give detailed accounts of the numerous publications dealing with annealing textures in rolled polycrystalline metals. Although a considerable amount of information of an empirical nature has been available for many years, even relatively recently the state of recrystallization-texture theory was considered uncertain. The reviews referred to above deal mainly with the description of experimental results, without developing generally applicable principles, suitable for explaining the observed annealing textures. The investigations of Burgers and Louwerse5 and Barrett6 showed that in deformed single crystals of aluminum the orientation of the recrystallized grains deviates drastically from that of the deformed matrix. According to Barrett and to Beck and Hu,7 the relationship between the two orientations can be best described as a rotation of about 40° around a [111] axis. Recent investigations led to similar orientation relationships for various face-centered cubic metals with a simple texture, regardless of whether the annealing process was recrystallization (strain-free grains growing in a highly deformed large crystal of aluminum&apos; or copper: or in deformed cube texture copper") or coarsening (strain-free grains growing at the expense of an essentially strain-free, fine grained, polycrystalline matrix of single orientation texture copper,&apos;" aluminum,&apos; or nickel-iron). Barrett" pointed out the possibility that this orientation relationship may be a result of the orientation dependence of the rate of grain boundary migration. More recently, considerable evidence became available in favor of this view.12,13 In apparent contradiction to the above results, it has been known for a long time that the recrystallization texture of polycrystalline metals is often similar to the deformation texture. This was found, in particular, for the fiber textures obtained by wire drawing, compression, or compression rolling.&apos; Following a suggestion by Barrett,2 Kronberg and Wilson and Beck and Hu7 described a mechanism by which a [Ill] fiber texture, resulting from plastic deformation, may be retained upon recrystallization, even though the orientation of individual recrystallized grains differs from that of the local area of the matrix in which they grow. This mechanism assumes that the reorientation corresponds to a rotation around the [1ll] axis, which is also the fiber axis. The present investigation was undertaken to examine in detail the orientation relationship between deformation texture and recrystallization texture in rolled face-centered cubic metals, using the quantitative methods of texture determination that have recently become available.", &apos;" Quantitative pole figures for the rolling textures of such metals were reported recently." Quantitative pole figures for annealing textures are given in the present paper. It was planned to investigate whether or not the orientation relationship previously found for the recrystallization of deformed single crystals, and for coarsening of single-orientation texture material, is capable of accounting for the observed, often complex, annealing textures in rolled polycrystalline metals. The question whether local reorientation is predominant, even in the early phases of the annealing process, was to be studied with high purity aluminum. by making use of an oxide film and sensitive tint illum-

Jan 1, 1953

By J. W. Rutter, K. T. Aust

Observations are presented of the formation of annealing twins during the growth of a recrystallized grain into a striated, melt-grown crystal of high-purity lead. The formation of an annealing twin resulted in replacement of the original migrating boundary by a large-angle grain boundary of the caincidence-site type or by a near-twin boundary. The results support the Fullman-Fisher theory of annealing twins and demonstrate the usefulness of the coincidence-site model. FULLMAN and Fisher1 have advanced the following theory to account for the formation of annealing twins during grain growth. Whenever a grain A grows into a matrix of grains S1 and S2, a twin A&apos; of grain A may form, as shown in Fig. 1, if the following energetic condition is satisfied: where "E" and "a" refer to the specific interfacial free energy and the area, respectively, of the boundaries indicated by the subscripts. In effect, the twinned grain will persist when the energy of the boundary between the twin(A&apos;) and the matrix grain (S, or S,) is less than that of the boundary between the original growing grain (A) and the matrix grain by an amount which exceeds the energy of the coherent twin boundary between A and A&apos;. Experimental observations on the changes in grain boundary free energy accompanying the formation of twins1 are in agreement with the theory outlined in Eq.[l]. Direct observations of the formation of annealing twins at moving grain corners1"3 and the depend-

Jan 1, 1961

By K. T. Aust

The occurrence of annealing twins in high-purity aluminum resulted in the formation of grain boundaries having orientation relationships which correspond to a high density of coincidence sites. The results provide support for the coincidence site model and indicate that large-angle coincidence boundaries have lower free energies than large-angle noncoincidence boundaries. Observations are presented concerning the coherent structure of twin interfaces in aluminum and the importance of inter-facial energy in preferred orientation. RECENT experiments1 have shown that when an annealing twin is formed during grain boundary migration in zone-refined lead, a large-angle random boundary is replaced at the growth front by a large-angle coincidence site boundary. The coincidence site orientation relationships obtained by twinning were of the type considered by Kronberg and Wilson,2 Frank,3 and Dunn.4 On the basis of the theory of annealing twins advanced by Fullman and Fisher,5 these observations indicate that the energy of a coincidence site boundary is less than the energy of a random boundary by an amount which exceeds the energy of the coherent twin boundary. This energy difference between the coincidence and random boundaries must be at least about 5 pct since the ratio of twin boundary energy to grain boundary energy in zone-refined lead is 0.05 * .014.6 Fullman7 has found that the twin boundary energy in aluminum is about 21 i 5 pct that of a large-angle grain boundary. A twin boundary energy as large as this would be expected to exclude the formation of many coincidence site grain boundaries, especially those which have a relatively low density of coin- cidence sites. Therefore, if the coincidence site model is a useful interpretation of certain large-angle boundaries, then it would be predicted that only coincidence boundaries which separate adjacent crystals with a relatively high density of coincidence sites may be obtained as a result of twinning in aluminum. The present experiments provided a means of testing this prediction since annealing twins occurred during the growth of recrystallized grains into striated, melt-grown single crystals of zone-refined aluminum. EXPERJMENTAL PROCEDURE A striated single crystal of zone-refined aluminum, about 1 cm sq and 37 cm in length, was obtained during zone melting of aluminum of 99.996 wt pct starting purity in a graphite boat under helium atmosphere.8 A molten zone of 2 to 3 cm in length, which was maintained by induction heating. was passed along the length of the bar for eleven passes at a rate of 0.9 mm per min. An additional final pass was given at a rate of 0.2 mm per min. The center portion of the zone-melted bar was characterized by an electrical resistivity ratio between room temperature and 4.2° K of 8000 to 9000. Single crystals of 1 to 2 cm in length were removed from the center section of the zone-refined bar and electrolytic ally polished in a 2:l solution of methyl alcohol and concentrated nitric acid. The specimens were then chemically polished in Alcoa R-5 solution. X-ray analysis of the single crystals indicated the presence of striations or lineage substructure having misorientations as high as 2 deg. New, recrystallized grains were introduced into each striated crystal by the technique of artificial nucleation and growth, previously described.9 During the growth of the recrystallized grains at 300&apos; to 600°C in argon, it was sometimes found that a

Jan 1, 1962