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By P. M. Robinson, M. B. Bever

THE heats of formation at 273°K of the compounds InBi, In2Bi, and TIBi2 have been determined by metal solution calorimetry with bismuth as solvent. The published information on the thermody-namic properties of these compounds is limited. The structure of the compound InBi (mp, 383°K) is tetragonal of the PbO (B10) type.1 The compounds In2Bi (mp, 362°K) and TIBi2 (mp of highest-melting composition, 486°K) are now believed to have structures of the NizIn (B8) type273 and not the A1B2 (C32) structures reported earlier.4, 5 The compounds In2Bi and TIBi2 have limited homogeneity ranges at room temperature, while the compound InBi has no detectable homogeneity range.' Samples of the compounds were prepared from 99.99 pet Bi (Mallinckrodt Chemical Works), 99.999 pet in (American Smelting and Refining Co.), and 99.99 pet Tl (Amend Drug and Chemical Co.) by melting the components in sealed, evacuated Vycor tubes. The compounds InBi and in2Bi were of the stoichiometric compositions. The compound TIBi2 contained 40 pet T1; this composition was chosen because at room temperature the alloy of stoichiometric composition does not lie within the homogeneity range.' The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The samples were homogenized for 48 hr at temperatures 20°C below the temperature of complete solidification. Metallographic examination of sections taken from the center and the ends of the ingots did not reveal second phases or segregation . The heats of formation were determined as the difference in the heat effects on solution of a compound and of a mechanical mixture of its components added from the reference temperature of 273°K to liquid bismuth at 623°K. The details of the calori-metric procedure and method of calculation have been described elsewhere? The calorimeter was calibrated by adding bismuth at 273°K to the bismuth bath at 623°K. The calculated values of the heats of formation of the compounds, listed in Table I, are based on a value of 4.96 keal per g-atom for the difference between the heat contents of bismuth at 273" and 623oK7 No published values are available for the heats of formation of the compounds InBi and In2Bi. Hultgren et a1.7 have calculated a value of -0.50 i 0.10 keal per g-atom for the heat of formation at 423°K of the compound TIBi2 containing 40 at. pet T1 from heat-content measurements in the range from 398" to 700°K and the heats of formation of the liquid alloy. The difference between this value and the value of -0.66 * 0.01 keal per g-atom at 273°K is too large to be attributed to a difference between the heat capacities of the compound and the components over the temperature range 273o to 423oK7 However, the direct determination of the heat of formation by a calorimetric method should give a more accurate value. The heats of formation at 273°K of the compounds InBi and In2Bi lie on a straight line when plotted as a function of composition, Fig. 1. The compound In2Bi, therefore, appears to be barely stable with respect to its neighboring phases. In order for the free energy vs composition curve to be concave towards the composition axis, the entropy change on formation of In2Bi must be more positive than that on formation of InBi. As the compounds are ordered,2, 3, 8 there is no configurational entropy change on formation. The difference between the entropy changes on formation of the two compounds, therefore, is probably associated with the vibrational entropies. In view of the low heats of formation, the changes in vibrational entropy, due to changes in bond strength on formation of the two compounds, are likely to be small. Owing to the volume contractions on formation of the two compounds,5 the vibrational entropies probably decrease slightly but the decrease of the vibrational entropy of InBi is expected to be larger than that of In2Bi.

Jan 1, 1965

By D. G. Westlake

Levine has concluded that prismatic slip in titanium is controlled by two distinct thermally activated processes in the temperature ranges O° to 220°K and 220" to 300°K. We feel that his evidence is not convincing. He has drawn a curve through the plot of activation volume u* vs temperature T with a break at 22WK, Fig. 2. We believe that considering the possible experimental error apd the fact that there are only four points between 4° and 196°K, one could be justified to represent these points by the smooth curve we show as a solid line in Fig. 12. Levine believes that (8rf/aT)+ is discontinuous at 220°K, but he hints that he recognizes the possible doubt. We doubt seriously that the results shown in Fig. 1 indicate a discontinuity at 220°K. Certainly if he were justified in drawing a straight line through only four points on Fig. 2, we are even more justified in drawing straight lines through the seven points between 77" and 297°K on Figs. 1 and 3, because a straight line touches all seven of his circles. If his measurements of t were so precise that his decision to draw two curves in Fig. 3 is valid, then the experimental technique is deserving of further mention. We have drawn a smooth curve through the results in Fig. 3 and used this and the curve in Fig. 12 to obtain the values of shown in Fig. 13. Finding continuous is a contradiction of Fig. 4, which deserves comment itself. Levine obtained the solid circles in Fig. 4 using Fig. 2 and a smooth curve through the points shown in Fig. 3. We have replotted these solid circles in Fig. 14. We submit that there is no basis for his two straight lines (dashed in Fig. 14), and therefore have superimposed the curve that we believe is indicated. Certainly, there is reasonable doubt that a discontinuity in dH/dT exists at 220°K, even when one accepts Fig, 2. Furthermore, if one draws the straight lines indicated by least-squares treatments of the results presented as open circles in Fig. 4, their intersection is at about 196°K, not at 220°K as shown. Thus the alleged agreement between Figs. 3 and 4 with respect to "break" temperatures is not apparent. In Fig. 9, Levine has drawn a straight line very much different from the one indicated by a least-squares treatment. Obviously, he has done this because he recognized that H = 0 when T = 0. He is consistent in drawing the low-temperature curves in

Jan 1, 1968

IRON AND STEEL DIVISION Established as a Division February 22, 1928 K C. McCutcheon, Chairman T. L. Joseph, Past Chairman J B Austin, Vice-Chairman E K Miller, Vice-Chairman T. J. McLoughlm, Vice-Chairman Ernest Kirkendall, Secretary-Treasurer CO M M I T T E E S EXECUTIVE J. A. Bowers '54 J. S. Marsh '55 R. W. Campbell '54 D. L. McBride '53 Walter Carroll '55 G. B. McMeans '53 K. L Fetters '53 F. L. Toy '54 H. M. Griffith '55

Jan 1, 1952

By M. E. Fine

THE electrical conductivity (a) and the thermal conductivity (K) of metallic conductors, as demonstrated by Smith and Palmer1 and Hume-Rothery,2 are to a good approximation related by an empirical equation, K = A s T + B, in which T is the absolute temperature, and A and B are constants, the Lorenz constant and the lattice con- ductivity. Strictly speaking, the lattice conductivity is not a constant, but to some extent depends upon the electronic conductivity.3 By plotting K as a function of sT, this equation has been proved to a

Jan 1, 1951

By S. E. Haszko

SEVERAL new XGa2 intermetallic compounds, Table 1, where X is a rare earth, having the AlB, structure were prepared as part of a continuing study of the magnetic and structural properties of rare-earth alloys.' In this note, the crystallographic results of these compounds are presented. Chart, Eq. 121 for the data in Fig. 1 can be adequately represented by The corresponding standard free-energy change is AF; = -4.576 T log K = -20,900 + 10.20T [5I At low nitrogen concentrations the ratio of mole fraction to weight percentage is a constant so that the mole fraction X of nitrogen is given by X = 0.0392 [%NJ. At low values of X, the activity and the concearation approach each other, hence K, = 0.0392 K,, where K, is expressed in terms of the mole fraction of nitrogen. Hence Eqs. [4]. and [5] become

Jan 1, 1962

By J. L. Huiatt, D. G. Foot

The Bureau of Mines, U.S. Department of the Interior, investigated methods of recovering potash values from process and waste brines. Laboratory pan evaporation of four chloride brines produced crude salts containing predominantly sylvite, halite and carnallite. Six sulfate- chloride brines produced crude salts containing primarily schoenite, kainite, leonite, sylvite, carnallite, and halite. Potash grades ranged from 7.2% to 22.2% K20, and recoveries by crystallization ranged from 85% to 99%. Sylvite flotation from chloride evaporites with amine collector, recovered 90% to 97% of the potash in a concentrate containing 54.3% to 60.3% K20. Fatty acid flotation of the high sulfate evaporite recovered 78% of the sulfate minerals in a 28%-K20 concentrate. Flotation of the remaining chloride minerals with amine collector recovered 80% of the potash in a 59.7%-K20 concentrate. Solar evaporation of 37 854 L (10,000 gal.) of brine recovered 99% of the potash in a crude evaporite containing 24.5% schoenite and 20% sylvite. Flotation in a 45-kglh (100-lblh) continuous flotation unit recovered over 95% of the potash in schoenite and sylvite concentrates, containing 28% and 62.3% K20, respectively. An economic evaluation is included.

Jan 1, 1985

By M. B. Bever, A. K. Jena

In the investigation reported here, calorimetric measurements have been made to determine the heat of formation of the compound AuSb2 and the partial gram-atomic enthalpies of antimony and gold in dilute solution in liquid tin and their enthalpy interaction coefficients. In order to interpret the behavior of antimony and gold in dilute solution in tin, nonzero values are assigned to the energies of bonds between like solute atoms relative to the pure solute state. Sa.mples of the compound AuSb2 were prepared by melting stoichiometric amounts of antimony and gold (99.999 pct pure) in evacuated and sealed Vycor tubes, which were shaken vigorously and quenched in water. The ingots were annealed in evacuated and sealed tubes at approximately 700°K for 2 weeks. Metallo-graphic and X-ray examinations gave no indication of second phases or microsegregation. The samples were added from 273°K to tin-rich solutions in a solution calorimeter1 maintained at 623°K. The calorimeter was calibrated with tin; the heat content of tin, H623°K- H273°K, was taken as 4.08 kcal per g-atom.2 In each calorimetric run at least four additions were made. The total concentration of solutes in the bath at the end of any run did not exceed 1 at. pct. The measured heat effect of an addition was plotted against the average of the atom fractions x of Sb + Au in solution before and after that addition. From this plot the heat effect at infinite dilution h,,, and the composition dependence of the heat effect dh/dx in the composition range 0 < x < 0.01 were obtained. The results for the additions of antimony, mixtures of antimony and gold, and the compound AuSb2 are listed in Table I. The heat effect h on addition of a sample of the compound AuSb2 or a mechanical mixture of antimony and gold at 273°K to a tin-rich solution at 623°K can be expressed as:

Jan 1, 1969

By A. S. Appleton, M. B. Bever

The stored and expended energies of an Au-Ag alloy deformed in torsion were investigated as functions of strain, strain rate, and temperature. At room temperature, the stored energy, measured by tin solution calorimetry, increased linearly up to an intermediate strain, above which it was nearly constant; at 78 °K the relation was linear up to fracture. Approximate values of the energy stored at 4 OK indicate a rapid increase below 78 OK. The energy stored by specimens deformed successively at 4o and 78oK changed slowly with increasing second strain from the curve for energy stored at 4 OK (measured after annealing at 78oK) to that for deformation at 78°K. The ratios of the stored to the expended energy at room temperature and 78 oK were unusually large. The additional amount of energy stored at the lower temperature is attributed mainly to an increase in the number and energy of dislocations. The stored energy as a function of strain rate at 4oK (measured after annealing at 78oK) increased to a sharp maximum over a narrow range of strain rates, whereas the expended energy changed only slightly. These effects are explained by the generation of point defects resulting from the enforced nonconservative movement of jogs in fast moving screw dislocations. The effect of straining successively at two strain rates at 4oK was also investigated. Stress-strain curves for 4o, 78oK, and room temperature and the results of micro examination of specimens deformed at these temperatures are also reported. THIS investigation is a continuation of a research program primarily concerned with the effects of variables on the energy relations involved in the deformation of metals. The variables investigated in earlier work have included strain, strain rate, temperature of deformation (room temperature and 78oK), and the type of deformation process. Most of this work has been carried out with Au-Ag alloys. In the investigation reported here, the deformation process was torsion, which had not been used previously in the program. The stored and expended energies involved in the deformation process were measured as functions of strain, strain rate and the temperature of deformation in the range 4" to 373" K. The microhardness and microstructure of deformed specimens were also investigated. The relation between stored energy and strain differs for different deformation processes.1,2 In general, the stored energy increases with strain and may attain a nearly constant value at large strains. This value and the rate at which it is reached, however, depend on the process of deformation. This dependence has been attributed, at least in part, to differences in the effective strain rate and rise in temperature of the specimen during deformation. The effects of the temperature of deformation on both the stored energy and the energy expended in the working process have been the subject of only a few investigations.3-6 Values of these quantities at low temperatures are of special interest as they yield information on point defects which, for many metals, is not obtainable at higher temperatures. The effect of the strain rate on the stored and expended energies has received little attention The strain rate has usually been measured only in relative terms, and hence the interpretation of its effect on the stored energy has been mainly comparative.

Jan 1, 1963

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann&apos;s hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. &apos;Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author&apos;s Reply) Dr. Fuerstenau&apos;s interesting comparison of rod milling and ball milling

Jan 1, 1961

By H. F. Gossenberger, J. J. Tietjen, J. J. Gannon, C. J. Nuese

External quantum efficiency measurements at 300" and 77°K are presented for vapor-grown GaAs and GaAs1-xPx electroluminescent diodes as a function of junction depth and doping. In GaAs, external efficiencies are found to decrease exponentially with increasing junction depth, defining an average absorption coefficient of 900 cm-1 at 300°K and 350 cm-1 at 77°Kfor epitaxial layers of p-type GaAs. It is shown that photon absorption losses dominate at room temperature and, in fact, account for most of the external efficiency degradation between 77° and 300°K. Healever, the internal (&apos;junction) quantum efficiency is also found to decrease by a factor of 3.5 between 77" ALTHOUGH rapid progress has been made in recent years with GaAs, Gap, and their alloys for use in electroluminescent diodes, there are still important unknown factors related to the performance of these de- and 300°K. The dependence of GaAs efficiencies on donor and acceptor concentrations is presented, illustrating best efficiencies at donor concentrations of 1.5 to 2x 1018 cm-3 . External efficiencies are found to be independent of acceptor concentrations less than 3 x 1019 cm-3 but to degrade at higher doping. The fabrication of GaAsi-xPx electroluminescent diodes is briefly discussed. External efficiencies here for planar uncoated diodes are about 0.035 pct at 300°K and 0.4 pct at 77°for x = 0.42. A brightness of about 8500 ft-Lamberts is attained at 77°K and of 315 ft-Lamberts at 300° K. for curvent densities of 10 amp per sq cm. vices. For example, although the external efficiency is known to decrease by factors of typically 10 to 30 between 77°K and room temperature, the exact causes of this are still uncertain. Experimental results of ill&apos; and carr2 with zinc-diffused electroluminescent diodes suggest that this external degradation is almost entirely due to increased absorption losses at room temperature, with a relatively temperature-independent internal efficiency; recent calculations by Gonda et al.3 corroborate this hypothesis. In contrast, Pilkuhn and Rupprecht4 find the internal efficiency of solution-grown GaAs laser diodes to degrade from 100 to 66 to 40 pct as the temperature is increased from

Jan 1, 1969

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By P. M. Robinson, J. S. LI. Leach

The heats of solution oj&apos; indiurrr, tin, lend, nrzd tellurium have been calculated from the measured heat effects when mechanical mixtres of indium and telLuium tin and tellurium, and lead and tellurium were added to liquid bismuth. The results are in good agreement xith publislzed values.s for the separate sollction of each eleltzent in bismuth. The heats oj solution of cadmium and tellurium calculated from the rneasuved heat effects on adding trechanical mixtures of these elements do not ugree zc,itl the published values jbv the separate solution of each element. It is shown that at 623°K Ile interaction between cadmium and tellurium dissolved in liquid bismuth is strong enough to led lo preciPitation of solid CdTc. The heats oj- jor-mation of CdTe at 273" nd 623°K (1)-c crilculated fi-or the measured heat ejlfecls. The calcnlaled az&apos;erage deviation from the Kopp-l\&apos;ez?,zunrz rule fov solid CdTe is less than 0.06 cat per g-atom- C over this lertzperalure range. Tlze importance 0.f these oDserl.ations to the determination of heals of formation hy metal solution calorimetry is considered. LIQUID metal solution calorimetry is a convenient method for determining the heats of formation of solid compounds. In this technique the heat of formation is the difference between the measured heat effects on dissolution of the compounds and of mechanical mixtures of the components in the liquid metal.&apos; The heat of solution of the mechanical mixture may be calculated from the measured heat effect. At infinite dilution of the solutes, this heat of solution is equal to the sum of the heats of solution of the separate components. If the heat of solution of one of the components is known, the value for the other can be derived; if both are known, they may be used to check the accuracy of the calorimetric technique. The heats of formation of the tellurides of cadmium, indium, tin, and lead have recently been measured by metal solution alorimetr. The heats of solution of indium, tin, lead, and tellurium at infinite dilution in liquid bismuth at 623"K, calculated from the measured heat effects on solution of the mechanical mixtures, are in good agreement with the published values. The heats of solution of cadmium and of tellurium calculated from the measured heat effect on solution in bismuth at 623&apos;K of mechanical mixtures of cadmium and tellurium, however, do not agree with values estimated from the literature. 1) EXPERIMENTAL PROCEDURE AND RESULTS The Heats of Solution of Indium, Tin, Lead, and Tellurium in Bismuth. The heat effects were measured when mechanical mixtures corresponding to the compounds In,Te, InTe, In2Te3, In2Te5, SnTe, and PbTe were dissolved in bismuth. The calorimetric procedure and the method of calculation have been described elsewhere.&apos; The heats of solution of the mechanical mixtures were obtained by subtracting the change in heat content per gram-atom of the sample between the addition temperature (273°K) and the bath temperature (623"K), (H623°K - H273°K)S, from the measured heat effects. The calorimeter was calibrated with pure bismuth. The reported values of the measured heat effects are based on (HGoK - ^273oK)Bi = 4.96 kcal per g-atom.3 The measured heat effects are found to be linear functions of the solute concentrations of the bath in the dilute solution range. The values, extrapolated to infinite dilution, are listed in Table I, together with the heats of solution of the mechanical mixtures calculated using the published values of (H 623°K - H273°k)s for indium, tin, lead,3 and tellrium. All the error limits quoted in this work represent the spread of values obtained. The heats of solution in liquid bismuth at 623°K of mechanical mixtures of indium and tellurium in four different proportions were determined. Values of the heats of solution of the two components were then calculated from the resulting four simultaneous equations: The heats of solution at infinite dilution of tin and lead in liquid bismuth at 623°K were calculated from the heats of solution of the mechanical mixtures of tin and tellurium and of lead and tellurium using the heat of solution of tellurium calculated above. These values of the heats of solution are listed in Table I1 together with some published values for comparison.

Jan 1, 1967

By P. Chaudhari, Michael B. Bever

The heat of solution at infinite dilution of selenium in bismuth, the heat of mixing of selenium and bismuth, and the limit of solubility of selenium in bis~rzuth have been determined at 573, 623; and 663°K by metal solution calorimetry. The heat of forrrzation of the compound Bi2Se at these temperatures has been determined from the heat effects associated with the precipitation of the compound from a saturated solution oj selenium and bismuth. The published information on the thermodynamic properties of the system Bi-Se is limited. The heat of solution at infinite dilution of selenium in bismuth at 623°K has been measured.&apos; The heat of formation at 273 K1 and room temperature2 and the heat capacity at 80 K3 of the compound Bi2Se3 have been reported. An estimate of the heat of formation of the compound BiSe at room temperature has been published.2 Information on the phase relations in the system Bi-Se is available.&apos; In the investigation reported here the following quantities have been determined at 573", 623", and 663°K: 1) the heat of solution at infinite dilution of selenium in bismuth, 2) the heat of mixing of selenium and bismuth in bismuth-rich solutions, 3) the limit of solubility of selenium in bismuth, and 4) the heat of formation of the compound BizSe. These quantities were determined by the addition of selenium to bismuth-rich solutions in a metal solution calorimeter. The determination of the heat of formation at the tem- perature of the calorimeter bath involved the precipitation of the compound from a saturated solution in the calorimeter. 5,6 This method differs from that commonly used which requires the addition of the compound and of a mechanical mixture of its components and yields the heat of formation at the temperature from which the additions are made (273 K EXPERIMENTAL PROCEDURE AND CALCULATIONS The solution calorimeter has been described in detail.&apos; Pure bismuth (99.999+ pct) was used as the bath at the start of a run. The calorimeter was calibrated with small amounts of bismuth added from 273°K; the differences of the heat contents of bismuth at 273°K and the temperatures of the baths are listed in Table I. After the calibration, additions of hexagonal selenium (99.999+ pct) were made. Loss of selenium by evaporation was negligible. No unusual experimental difficulties were encountered.9 The differences in the heat contents10 of selenium at 273°K and the temperature of the bath, listed in Table I, were subtracted from the measured heat effects to give the "adjusted heat effects". The methods by which the heat of solution at infinite dilution, the

Jan 1, 1968

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation [ ] in which y = cumulative percent finer, x = particle size, = distribution modulus, and k = size modulus. Charles found that the energy consumption in comminution is usefully expressed by another empirical relation, [ ] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; ( 1-n) is the slope of a plot of log E vs log k. Holmes has presented energy equations similar to Eq. 2.

Jan 2, 1960

By James A. McGurty, Walter J. Koshuba, Samuel G. Gordon, Gilbert E. Klein

ONE of the problems encountered in working with metals at elevated temperatures is the instability resulting from solid-solid diffusion at a -common interface. A determination of the nature and magnitude of this phenomenon is important as related to structural properties of materials potentially useful in high temperature applications. This paper is concerned with the solid state reaction between metallic molybdenum and beryllium at elevated temperatures. In the older literature,&apos; there were no known inter-metallic compounds in the system Be-Mo, and the list of beryllium intermetallics was rather small. New compilations have been made by Smithells&apos; and by Taylor," listing all the then known beryllium binary intermetallic compounds. In addition to these, some new phases have just been reported&apos; in the system Zr-Be and some further compounds of the type MBe,3 have been currently described. The new compound MoBe,, which is reported upon in this paper differs considerably from the above mentioned MBe13 group, and will be discussed in detail. Diffusion Study The nature of the solid diffusion at a Mo-Be interface was determined by sealing a beryllium rod inside a molybdenum capsule and heating at a temperature of 2000°F&apos; (1100°C) for 100 hr. The molybdenum capsule was fabricated from % in. swaged molybdenum rod obtained from the Fansteel Metallurgical Corp. The beryllium metal was obtained from Brush Beryllium Corp. as % in. cold-drawn rod. This material assayed 99.05 pct Be and contained as impurities 0.84 pct Be0 and 0.19 pct Be2C. The molybdenum capsule was % in. in OD x 2 in. long. To prepare it, a concentric hole 0.250 in. + 0.001 in. — 0.000 in. in diam was drilled and reamed in one end of a rod to a depth of 1 &apos;/2 in. A 1 in. long beryllium rod 0.250 in. + 0.000 in. — 0.001 in. in diam was pressed into the molybdenum capsule. A molybdenum plug 0.250 in. & 0.001 in. in diam x 9/16 in. long was then used to seal the beryllium in place. The capsules were placed in a molybdenum resistance furnace and heated at 2000°F (1100°C) for 100 hr. On cooling, the specimens were cut and examined metallographically. Fig. 1 is a micrograph at X250 of a portion of the interface from a transverse section. Four phases are clearly visible, with sharp boundaries between them. Phase A is a section of the molybdenum capsule; phase B is the molybdenum-rich intermetallic composition MoBe,; phase C is the beryllium-rich compound MoBe13; phase D is a section of the beryllium rod. All phases were readily polished to a high metallic luster. The molybdenum-rich phase has a pronounced purple tinge. The beryllium-rich phase (C) is only slightly darker than the pure beryllium. In polarized reflected light, however, it shows striking birefringence between crossed Nicols. The black areas represent flaws or pores in the material. A small representative amount of powdered material from each of the phases was carefully removed under the microscope with a diamond tool. With this material, powder X-ray diffraction patterns were made for the identification of each phase. Table I lists the X-ray diffraction spacings and corresponding indexes characteristic of these intermetallic compounds. Synthesis To establish the formula of the new intermetallic compound, X-ray diffraction patterns were made from powders obtained from solidified melts of known composition. The syntheses were made by

Jan 1, 1952

By W. D. Robertson, H. Conrad

Incremental loading creep tests were conducted on magnesium single crystals in tension and direct shear at 78" to 364°K. The creep curves were transient in character and exhibited waves or periodic behavior, especially at small strain rates. A sigmoidal curve was frequently observed following the first occurrence of creep. Repeating of segments of a master curve was observed at all temperatures indicating that identical conditions for flow existed after various stress and strain histories. A logarithmic time law with a independent of temperature whs observed at 78°and 203°K, while a parabolic (power) time law was approximated at 298" and 364°K. The departure from logarithmic creep was attributed. to recovery, which was observed at 298" and 364°K. The temperature independence of a represents a serious objection to the theory of low-temperature creep based on the intersection of dislocations. IN a previous paper1 it was found that the initial creep rate of magnesium single crystals, y, following the addition of a stress increment in the range of 78° to 364°K, was given by the expression ? = C exp - {?H/kT} exp {B(T- h ?)} [1] where B and C are constants, AH is an activation energy of 10,300 cal per mole, T is the applied stress, ? is the total strain at the time of the stress increment, and h is the strain-hardening coefficient. The present paper is concerned with certain other features of creep behavior observed during this investigation; namely, the form of the creep curves, time laws for creep, recovery, and microscopic and X-ray observations of the structural manifestations of the creep flow. To the authors&apos; knowledge the temperature range of the present investigation (0.08 Tm to 0.40 Tm) has not been covered previ-

Jan 1, 1959

By J. D. Mooney, D. L. Darnell

The accompanying chart has been drawn for the convenicncc of engineers as&apos; a means of quickly determining the correct number of plies of conveyor belts operating under specific conditions. The calculations are based on the average safe strength (factor of safety, 15) of the various standard rubber conveyor belts. The calculations assume maximum loading conditions; that is, the belt is considered as carrying the greatest load that it will handle without spillage at ordinary belt speeds. This not only produces the most economical operating conditions, but also the maximum tension in the belt. The chart is a graphical representation of the formula: Where, p = kg W(L + 10H) p = the correct number of plies k = a constant, depending on the type of drive g = the weight &apos;in pounds per cubic foot of material handled W = the width of the belt in inches L = the length of the belt in feet (approximately twice the center distance). H = the difference in elevation between the head and tail pulleys, in feet. For a simple drive, with a bare pulley, k = ----1 For a simple drive, with a rubber-lagged pulley, k = --- 1 For a, tandem drivej with bare pulleys, k = 1/375.000 For a tandem drive, with rubber-lagged pulleys, k = ---1 The chart is drawn for a simple drive, with a bare pulley (k — =e)1 ; therefore, the number of plies obtained from the chart should be multi- &apos; plied by the factor 0.83 or 5/6 for simple, lagged drive; the factor 0.67 or 2/3 for tandem, bare; and the factor 0.55 or 11/20, for tandem, lagged. The formula p = kgW(L + 10H) has been developed mathematically

Jan 1, 1916

By F. K. Spragins

Growing demand for conventional crude oil in North America in the face of diminishing sup- ply is bringing about increased interest in synthetic fuels. With one commercial plant already in full production, another in the planning and engineering stage and still others being seriously considered, the Athabasca tar sands are proving to be a leading center of interest. Here, and in the closely related deposits, reserves in place total over 700 billion barrels.&apos; When and if fully developed, Athabasca tar sands could make both Canada and the United States substantially independent of all off-shore supplies of crude for many years to come. Its product, a high-quality, low-sulfur synthetic crude, is beginning to enter the market place at a most favorable time. Oil Deposit The main body of Athabasca tar sands, about 250 miles northeast of the city of Edmonton, are centered in an area of something over 12,000 sq mi. The deposit runs as high as 250,000 bbl per acre and the average richness is placed at 100,000 bbl per acre. Of the over 700 billion bbl in place, 400 billion bbl of raw oil are considered recoverable from which 300 billion bbl of upgraded synthetic crude are expected to be produced.&apos; In the deeper zones, thermal stimulation is considered the best approach to recovery, while in the shallow areas several surface mining techniques are deemed practical.

Jan 10, 1972

By Leonard R. Weisberg

HE procedure of directional freezing by the Bridgman technique1 is frequently used in crystal preparation. On those occasions where the crystal is regrown, it can be advantageous to Crop part of the ingot before regrowth to achieve purification. This note describes some simple, yet interesting, observations concerning the effects of cropping an ingot between successive freezes. First, it is not effective to Crop the front end of an ingot, whether or not the distribution coefficient, k , of the impurities is greater or less than unity. This can be shown as follows. The concentration C, of an impurity in a directionally frozen ingot of length d with a uniform cross section is given by where x is the distance along the ingot, and C0 is the initial concentration per unit length. It is assumed in deriving this equation that diffusion is negligible in the solid, is complete in the melt, and that k is constant. Consider that a section of the ingot Ad is removed from the front end. Then the average impurity concentration in the remaining (d- Ad) section of the ingot can be shown by integration to be given by When the ingot is remelted and refrozen, the new impurity distribution is given by where xl is the distance along the refrozen ingot. Substituting the value of c into Eq. [3], one finds This is identical to Eq. [11 when x = (x, Ad), which represents the original impurity distribution in the (d - Ad) section of the ingot after the first directional freeze. Therefore, the cropping and re-freezing accomplished nothing. This can also be seen physically by realizing that the average impurity content in the melt after the first Ad section is frozen, is identical to that after the resulting ingot has been cropped and remelted. Hence, it is assumed in the following sections that only the tail end of the ingot is cropped. However, it must be realized that for impurities with k greater than one, the pieces cropped from the tail end are purer, and are therefore saved. After cropping an amount Ad from the tail end of an ingot, the average impurity concentration of impurities in the remaining portion of the ingot is given by wheref= d/d. For the case of k < 1, the purification is defined as c,/c. It is obvious from Eq. [5] that the purification increases asf increases, but the increase in purification is not large. For example, iff is doubled from 0.1 to 0.2, the purification increases by only 10 pct for k = 0.5, by only 24 pct for k = 0.1, and by 32 pct for k =0.01. Much smaller values off than 0.1 are not desirable since insufficient purification is achieved. These figures indicate that much larger values off do not lead to substantial improvement, especially considering that much of the original ingot is lost. Therefore, it is generally useful to Crop about 1/10 of the ingot to achieve purification. As compared to doubling the value off, it is much more helpful to remelt, refreeze, and crop the ingot twice. Using Eq. [51 reiteratively, and assuming f= 0.1, it is found that the purification after this process is found to be increased over the purification after a single freeze and cropping by 33 pct for k= 0.5, 450 pct for k = 0.1, and 4100 pct for k = 0.01. This indicates that considerable purification can be obtained by this procedure. However, if purification is the main goal, one should resort to zone refining,3

Jan 1, 1962