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By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation' y = 100 (x/k)a [1] in which y — cumulative percent finer, x = particle size, a -= distribution modulus, and k = size modulus. Charles3 found that the energy consumption in comminution is usefully expressed by another empirical relation, E = Ak(1-D) [2] 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. Holmes3 has presented energy equations similar to Eq. 2. The constants a and n in Eqs. 1 and 2 have been shown to depend both on the nature of the material and on the comminuting device. Moreover, Charles showed that within experimental error a and n are a — n+1 = 0 [3] Combining Eqs. 2 and 3, E = A k-a [4] In the first sections of this article it is shown that the energy equation, Eq. 4, can be derived directly from the size distribution equation for the fine sizes, Eq. 1. The derivations are made without assuming any of the specific relationships between energy and particle size which have been common in previous literature. For comminution processes in which Eqs. 1 and 4 adequately represent the experimental data, the constant A in Eq. 4 is found to be a simple and useful inverse measure of grindability. That is, A is the energy consumption per unit volume of comminution product finer than unit size as determined from the straight line portion of the log-log plot of the size distribution. These considerations all lead to a unifying hypothesis of comminution mechanism from which both Eq. 1 and Eq. 4 can be derived. Finally, it is pointed out that this hypothesis raises serious questions as to the significance of the Rittinger hypothesis, the Kick hypothesis, and other theories in which energy numbers are systematically assigned to various size fractions of comminution products in order to calculate theoretical energy consumptions. Derivation of the Energy Equation from the Size Distribution Equation: For simplicity, consider the comminution of 100 volumes of a feed material of relatively uniform particle size. The comminution process may be considered as the summation of many individual and independent comminution events. The extent of comminution is most easily expressed as the number of comminution events, z. In the first derivation, the key assumption is that the characteristics of the comminution events in a given crushing or grinding process are substantially constant and do not vary with the progress of the comminution process. Accordingly the characteristics of an average comminution event may be defined. In one such event, a quantity of energy $E is applied to a single particle of size f and volume $v. The crushing of this particle produces fine particles with a size distribution similar to that given by Eq. 1: yw=100(x/ka)a0 [51 In this equation yo, a0, and k0 are used to characterize the product of an individual comminution event rather than the product of the comminution process as a whole. In using Eq. 5, we will not be concerned with values of x close to the feed size f and will therefore assume only that the equation is applicable to the finest sizes of the material. In 100 volumes of total product, the actual volume of product finer than x from a single comminution event, or dy, is given by The total volume of material below size x, resulting from z events, is then given by y = z(dy) =z(dv) (x/ka)a0 =" Eq. 7 reduces to Eq. 1 when we let a, = a and [8a] z =100/dv (ka/k )1 or k = ka (zdv/100)-1/a [8b] Eq. 8a shows that the distribution modulus of the comminution product is the same as for the product of an individual comminution event. Eq. 8b shows how the size modulus of the comminution product k varies with the extent of comminution as measured by the number of events, z, or as measured by the fraction of the feed actually subjected to com- minution1 zdv/100. The energy input to 100 volumes of total feed, or 100E, is the sum of the energy inputs for all the comminution events: 100E =z (dE) [9]

Jan 1, 1961

By J. P. Neumann, Y. A. Chang

Lattice parameter measurements of the hcp phase in the system Ag-A1 near the stoichiometric composition Ag2Al were carried out for specimens quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K. The three heat treatments resulted in the same lattice parameters at room temperature. None of the specimens showed any superlattice lines. The lattice parameters of this alloy were also measured at temperature from 77° to 750°K. An anomaly in the temperature variation of the lattice paramete.rs occurs in the region near 400°k, which may be associated with local ordering. FROM measurements of the diffuse scattering of X-rays, it is known that the [ phase in the system Ag-A1 near the stoichiometric composition Ag2A1 ex- hibits a considerable degree of short-range order at room temperature.' Moreover, based on the position of the short-range order peaks a superlattice model had been proposed in the same study and it was suggested that lowering the annealing temperature to 420°K might result in long-range order. In the present study, the diffraction patterns and the lattice parameters of three differently heat-treated specimens, i.e., quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K, were determined from 77" to 750°K. The purpose of these measurements was to investigate 1) whether long-range order could be established by prolonged annealing and 2) whether the lattice parameters at room temperature depended on the heat treatment, since it had been proposed earlier2 that the lattice parameters in this phase are related to the atomic arrangement. 1) EXPERIMENTAL TECHNIQUES Silver and aluminum, both 99.99 pct purity, were melted in a zirconium oxide crucible under helium in

Jan 1, 1969

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'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. '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's Reply) Dr. Fuerstenau's interesting comparison of rod milling and ball milling

Jan 1, 1961

By J. A. Hren, C. M. Wayman

RECENT investigators have noted anomalous behavior in the electrical resistivity of vanadium below room temperature. Rostoker and Yamamoto1 in studying the vanadium-oxygen system hypothesized that the body-centered-tetragonal phase existing from 15 to 34 at. pet O at approximately 800°K was really a low-temperature allotrope of vanadium that was stabilized by oxygen. In measuring the electrical resistance of cold-swaged vanadium rod over a range of temperatures, a small discontinuity was observed at approximately 240°K, supporting their notion of allotropy. However, the magnitude of the observed discontinuity was extremely small. Loomis and Carlson2 in studying the ductile-brittle transition in vanadium also made resistance measurements and reported a discontinuity near 200°K. More recently, White and Woods3 showed that the electrical resistivity from room temperature to approximately 100 °K was not linear and at variance with the Bloch-Griineisen law. Instead of finding a discontinuity, they observed a deviation from linearity below 200°K. In discussing their results they pointed

Jan 1, 1961

By M. J. Pool, R. K. Saxer, J. R. Myers, D. S. Dickson

ThE equilibrium phase diagram of the Mo-Cr system, described by anssen,' indicates that chromium and molybdenum form a continuous series of solid solutions above 1673K. The liquidus and solidus have been reported to have a minimum at about 12 at. pct Mo and 2133°K by Bloom and Grant2 and by Putnam, Potter, and Grant.3 X-ray studies by Trzebiatowski and ploszek4 and Baen and Duwez' revealed no indication of solid solution decomposition after long anneals at 1473", 1273", 923", and 873°K. However, Bloom and rant' by means of cooling and heating curve analysis of alloys containing up to 45 at. pct Mo found thermal effects at temperatures approximately 100" * 30°K below the liquidus. The only previous thermodynamic study of the Cr-Mo alloy system was made by Laffitte and Kuba-schewski6 who used the Knudsen effusion method at 1471°K. These investigators reported the possibility of a miscibility gap because they observed positive deviations from ideality in their chemical activity

Jan 1, 1970

By William E. Ford, Edward Salisbury Dana

The monoclinic Wolframite Group and the tetragonal Scheelite Group are included here. Wolframite Group WoIframite (Fe,Mn)W04 a : b : c = 0.8300 : 1 : 0.8678 B = 89' 22' Hiibnerite MnW04 048362 : 1 : 0.8668 89' 73' WOLFRAMITE. Monoclinic. Axes a : b : c = 0.8300 : 1 : 0.8678; B = 89' 22'. mm"', 110 A 1TO = 79" 23'. ay', 100 A 101 = 62' 54' at, 100 A 102 = 61" 54'. $', 011 A 011 = 81" 54'. Twins: (1) tw. axis c with a (100) as comp.-face; (2) tw. pl. k (023), Fig. 449, p. 171. Crystals commonly tabular (1 a (100); also prismatic. Faces in prismatic zone vertically striated. Often bladed, lamellar, coarse divergent columnar, granular. Cleavage: b (010) very perfect; also parting (1 a (100), and 11 t (102). Fract,ure uneven. Brittle. H. = 5-5.5. G. = 7.2-7.5. Luster submetallic. Color dark

Jan 1, 1922

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 J. Menashi, D. A. Douglas, A. S. Rappas

Aqueous solutions of Na2Cr04 are reduced with CO to produce hydrous Cr2O3 and NaHCO3/Na2CO3. CH3OH, HCOO- and HCHO in the presence of CO2 also reduce Cr(VI) and yield similar products. It is shown that the rate of Cr(VI) reduction can be represented by the expression -d [Cr(VI) ]/dt = k[Cr(VI)]0.5[R], where [R] is the aqueous phase concentration of CH3OH, HCOO- or CO. With these three reductants, the activation energies for the reduction processes are comparable and are of the order of 100 kJ/mol (43,000 Btu per lb mol). Rapid reduction rates are attained at temperatures in excess of 220°C (428°F). With these three reductants, a green acid-insoluble readily filterable hydrous Cr203, is formed. With HCHO, significant reduction of Cr(VI) occurs at about 80° to 100° C (176° to 212° F). The product is an acid-soluble violet modification of hydrous Cr203. Solutions of Na2CrO4 contaminated with Mo(VI) and W(VI) can be reduced to yield a Cr2O3 product with significantly reduced contaminant levels.

Jan 1, 1986

"Located in Madison River Canyon, about 14 miles by road from Norris, Mont. Built in 1907 by Madison River Power Co.DAM: Rock filled wooden crib structure, 183 ft. long, 34 ft. high or 44 ft. to top of flashboards.SPILLWAY: 140 ft. long, equipped with flashboards 10 ft. high.PIPE: One 10-foot and one 12-foot wood-stave pipe, 7,515 feet long.PRESSURE: One pressure chamber, 32 ft. high, 30 ft. wide and 81 ft.CHAMBER: long, built of concrete.PENSTOCKS: 4 9-foot steel penstocks about 200 ft. long, one for each wheel.WATER WHEELS: 4 double horizontal, center discharge, Sampson special 44-inch turbines, 3,600 h-p., at 100 ft. head. Speed 300 r. p. m„ direct connected to generators.GENERATORS: 4 G. E., W. C., 2,250 k-w., 4,000 volts, 300 r. p. m., 3 phase, 60 cycles, alternators, with exciters mounted on same shaft.TRANSFORMERS: 12 G. E., W. C., 900 k-w., 60 cycles. High tension voltage 23,100, 34,650, 46,200; low tension voltage 4,000, 3,800, 3,600. Now operating at 46,200, delta connected. They can be connected Y for 40,000, 60,000 or 80,000.OPERATION: This is the principal plant of the whole system and carries most of the load."

Jan 1, 1913

By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

By R. H. Jacoby, M. J. Rzasa

Experimental equilibrium vaporization ratios were obtained for nitrogen, methane, carbon dioxide, ethane, and hydrogen sulfide in natural gas-condensate systems. Two different overall mixture compositions were investigated over the pressure range 500 to 4,000 psia at 100°, 150°, and 200 °F. Partial phase diagrams of the mixtures were obtained; one of these showed a critical point at 204°F and 3,875 psia. These and earlier data' were compared with the Kellogg correlation' at! 100°F and 1,000 psia. INTRODUCTION The authors' have presented equilibrium vaporization ratios for nitrogen, methane, carbon dioxide, ethane, and hydrogen sulfide in complex mixtures, such as natural gas-crude oil and natural gas-absorber oil. Since mixtures of the natural gas-condensate type also occur widely in petroleum reservoirs and often contain the non-hydrocarbons mentioned, it would be useful to have appropriate K data for calculating equilibrium vaporization conditions. Roland, Smith, and Kave-ler' obtained K's for methane and the light hydrocarbons in gas-condensate mixtures; and Poettmann and Katz3 obtained K's for carbon dioxide in a gas-condensate system. The data presented in this paper extend this coverage to include K's for nitrogen and hydrogen sulfide and phase diagrams for the experimental mixtures. EXPERIMENTAL WORK The equipment and experimental procedure was essentially as described previously, except for analysis of the vapor samples. The vapor sample bombs were filled at the pressure and temperature of the run. Immediately after sampling, a portion of this sample was flushed from the bomb into a 650 cc glass bulb, filling it to near atmospheric pressure. The sample in the glass bulb was then analyzed by the mass spectrometer. Some checks were made on this analytical procedure to find the accuracy of measurement of the C + content of the vapor samples. The modifications tried were complete fractionation of the vapor sample and the use of several liquids (depropanized condensate and retrograde liquid from several vapor samples) as calibrating materials for the mass spectrometer. The results obtained from these various checks differed by about 10 per cent relative and this is believed to be the order of accuracy of the vapor C+ concentrations.

Jan 1, 1953

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener's anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,' the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.' THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.' Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969

By B. H. Bergstrom

The Gaudin-Meloy1 size distribution equation requires the evaluation of two constants, xo and r. The common log-log representation of a screen analysis as cumulative weight percentage passing versus size, readily yields the required constants as illustrated for curves A and B in Fig. 1. The 100% passing (y = 1.0) size is simply x,. If the straight portion of the curve be extrapolated to the 100% passing (y=1.0) abscissa, the intercept is the Schuhmann size modulus, k. The ratio of xo to the size modulus, k, is r as shown: The Gaudin-Meloy equation requires that the slope, a, of the size distribution approach unity in the finer sizes, as is the case for curves A and B. Often distributions are better characterized by slopes other than unity. The schuhmann2 equation is able to represent these distributions if the upper portions of the curves are ignored. Empirically, the Gaudin-Meloy equation can be modified to yield slopes other than unity by writing it as Here, a is the familiar Schuhmann slope, and xo is the 100% passing size. The value of r is still given by Eq. 2. Eq. 4 with its easily determined constants is more versatile than either the Schuhmann or the Gaudin-Meloy equations, since a wide variety of size distributions can be closely described. It is easier to fit than the Rosin-Rammler3 equation, and has the advantage that the top size, x,, is finite. REFERENCES A. M. Gaudin and T. P. Meloy: Model and a Comminution Distribution Equation for Single Fracture, AIME Transactions, 1962, Vol. 223, pp. 40 to 43. R. Schumann, Jr.: principles of comminution, I., size Distribution and Surface Calculations, AIME Technical Publication No. 1187, 1940. P. Rosin and E. Rammler: The Laws coverning the Fineness of Powdered Coal, J. Inst. Fuel, 1933. Vol. 7, p. 29.

Jan 1, 1967

By G. D. Rieck, G. H. G. Vaessen, D. L. Vogel

Both doped and undoped tungsten single crystals exhibit hardness anisotropy with respect to the direction of testing in each of the crystallographic phes investigated. The hardness anisotropy of undoped single-crystal tungsten is rather pronounced in (001) and (110) planes but very minor in (111) planes. The anisotropy in (122) planes of the doped and drawn tungsten after recrystallization is in accordance with a previously published concept of a stringlike distribution of the doping material in the metal. ANISOTROPY in mechanical properties of single-crystal tungsten was investigated by Rose et al., Garlick and Probst,2 and Beardmore and Hull. 3 Although data on the Vickers microhardness of tungsten have been published (see, e.g., Boosz 4 and the references cited by him), no data on the microhardness anisotropy are available. We report, therefore, some of our own results on the microhardness and its anisotropy. The microhardness has been determined of the following samples. A) Polycrystalline tungsten samples taken from: 1) powder metallurgical tungsten "normally" doped with potassium-silicon-aluminum oxides (final contents inppm: K, 100; Si, 100; Al, 20; Cr, 20; Fe, 50; Mo, 400; Ni, 10) and in the form of: a) a 10-mm-diam swaged ingot annealed at 1600°C, the grain sizes varying between 15 and 250 p; b) a sheet rolled at about 800°C and recrystallized at 2000°C7 the grain sizes varying between 15 and 150 p; c) a 2-mm-diam swaged rod, as-worked, with elongated grains (average diameter of about 25 , lengths up to 1 mm); 2) undoped electron-beam-melted tungsten with very large grains (contaminations in ppm: K < 10; Fe < 20; Cr < 10; Cu < 0.1; Ni not detectable; inter-stitial~ not determined). B) Single-crystal samples taken from: 1) pure tungsten grown on a Pintsch wire by the van Arkel procedure (main contaminations inppm: Mo, 100; Si < 10; Cu and Fe, 2; A1 < 2; interstitials not determined); 2) zone-melted undoped tungsten (analysis as under A2); 3) large crystals in secondary recrystallized tungsten

Jan 1, 1969

By D. G. Westlake

The electrical resistance of a series of V-H alloys (0 to 3.5 at. pct H) has been measured over the temperature range G° to 360°. Interstitial impurities made contributions to the residual resistivity, but not the ideal resistivity. The contribution of hydrogen in solid solution is expressed by Ap = 1.12 microhm-cm per at. pct H; but the contribution of precipitated hydride was negligible. A portion of the so1vu.s for the V-H phase diagram is presented. The solubility limit is given by In N (at. pct H) = (5.828 i 0.009) - (2933 i 44)/RT. Comparison of critical temperatures joy hydride precipitation and published critical temperatures for hydrogen embrittlement suggests the two are related. ThiS study was initiated as part of an investigation of the mechanism by which small concentrations of hydrogen embrittle the hydride-forming metals at low temperatures. It has already been shown that, in the case of hcp zirconium, a reduction in ductility accompanies the strengthening resulting from precipitation of a finely dispersed hydride phase.&apos;&apos;&apos; Our attempts to detect a similar precipitation of a second phase at low temperatures in V-H alloys by transmission electron microscopy have been thwarted because we have been unable to prepare thin foils that are representative of the bulk material with respect to hydrogen concentrati~n.~&apos;~ The present investigation establishes the solvus of the V-H system at subambient temperatures. Subsequently, we hope to be able to determine whether the embrittlement temperature is related to the critical temperature for precipitation of the hydride in a given V-H alloy. veleckis5 has proposed a partial phase diagram for the V-H system based on extrapolations of the pressure-composition relations he measured at higher temperatures. Kofstad and wallace&apos; conducted a similar study of single-phase alloys but did not attempt to establish the phase diagram. Zanowick and wallace&apos; and ~aeland&apos; have studied a portion of the phase diagram by X-ray diffraction, but they investigated no alloys in the hydrogen concentration range 0 to 3 at. pct, the range of interest to us. EXPERIMENTAL PROCEDURE The vanadium was obtained from the Bureau of Mines, Boulder City, Nev., in the form of electrolytic crystals. The analyses supplied with them listed 230 ppm by weight metallic impurities, 20 ppm C, 100 ppm N, and 290 ppm 0. The crystals were electron-beam-melted into an ingot that was rolled to 0.64 mm. Strips, 60 mm long and 4.2 mm wide, were cut from the sheet, and both rolled surfaces were ground on wet 600-grit Sic paper to produce specimens 0.4 mm thick. They were wrapped in molybdenum foil, vacuum-encapsulated in quartz, and annealed 4 hr at 1273°K. The specimens were annealed in a dynamic vacuum of 2X lo-&apos; Torr for 30 min at 1073°K for dehydrogenation, and charged with the desired quantity of hydrogen by allowing reaction with hydrogen gas at 1073°K for 2 hr and cooling at 100°K per hr. Purified hydrogen was obtained by thermal decomposition of UH3. Sixteen specimens were studied: two contained no hydrogen and the others had hydrogen concentrations between 0.5 and 3.5 at. pct (hydrogen analyses were done by vacuum extraction at 1073°K). Electrical resistances were measured by the four-terminal-resistor method on an apparatus similar to the one described by Horak.~ The specimen holder was designed so that both current and potential leads made spring-loaded mechanical contact with the specimen. The potential leads were 30 mm apart, and the current leads were 55 mm apart. The current was 0.10000 amp. We used the following baths for the indicated temperature ranges: liquid nitrogen, 77°K; Freon 12, 120" to 230°K; Freon 11, 230" to 290°K; and ethanol, 290" to 340°K. Temperatures lower than 77°K were achieved by allowing the specimen to warm up after removal from liquid helium. Temperatures above 77°K were measured by a calibrated copper-constantan thermocouple (soldered to the specimen holder) and below 77°K by a calibrated carbon resistor. The temperature of the bath changed less than 0.l0K between duplicate measurements of the resistance. RESULTS AND DISCUSSION Typical plots of resistivity p vs temperature T are shown in Fig. 1. In the interest of clarity, only five curves are presented and the data points have been

Jan 1, 1968

By Robert L. Fleischer

A well known but unexplained experimental fact is the observation1 that aluminum shows a pure <111> wire texture, in contrast with other fcc metals, which have a mixed <100> <111> texture at moderate reductions. A possibly related single crystal observation on aluminum is the following:2 under tensile deformation <111> single crystals are stable (maintain their original axial orientation), while <100> crystals are unstable at room temperature and become stable at lower temperatures. This suggests that at room temperature, as proposed by Yen and Hibbard,3 the single <111> texture obtains be- cause <100> orientations are unstable in the poly-crystal. It also implies that for wire drawing at lower temperature a <100> component of the texture might be expected since that orientation is then stable. This possibility has been examined by wire drawing at temperatures near 77°K. The apparatus was designed to be used with an existing draw-bench, a steel trough acting as die holder and containing sufficient liquid nitrogen to immerse the wire entering the die. The trough is insulated by a styrofoam container to prevent excessive boiling of the bath. The wire emerging from the die enters a polyethylene tube, into the far end of which the grips are inserted. Liquid nitrogen is funneled into the tube to maintain the low tem-

Jan 1, 1962

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 Henry Seltz, Cyril Wells, Hugh J. MacDonald

Several investigators have measured the heat capacity of cementite, using different methods of attack, but the agreement between the values obtained cannot be considered good. Naeserl has made measurements of "average heat capacities" of iron carbide between 1026" and 85" K., using a water calorimeter. His computed true specific heat at 78.1" K. is 11.22 cal. per gram-formula mass, which, if correct, is much too high for any reasonably accurate extrapolation to 0" K. The cementitc used by Naeser was obtained from a steel containing 0.9 per cent carbon, by electrolytically dissolving out the iron in a neutral bath of ferrous chloride. The cementite remained as a coarse, crystalline, gray powder. Andes2 has measured the specific heat of iron carbide, from 102" to 323" K., as it exists in steel. The specific heats of several slugs of steel of known iron carbide content were determined, and the specific heat of the iron carbide (Fe3C) calculated by plotting specific heat versus percentage of carbon, and extrapolating to pure Fe3C (6.7 per cent C). The heat-capacity values for temperatures below 100" K. were obtained by comparing the temperature-specific heat curve for Fe3C to that of Fe. Since the two were very similar in the range examined experimentally and approach more closely at low temperatures, it was assumed that near the absolute zero the form of the curve for Fe3C would be similar to that of Fe. Andes calculates for the entropy of Fe3 C,S298 = 23.55 e.u. The heat of formation of Fe3C has been studied by several workers. Kelley3 has reviewed these measurements and calculations, and selects those of Roth* and Naeser6 as worthy of most consideration. Roth has given AH = 5400 cal. + 30 per cent as a result of his own and other work. Naeser has determined the heat of formation from Fe and different forms of carbon, and for graphite (0) he finds AH = 5600 cal. Kelley accepts the rounded figure AH = 5500 as the heat of formation at 298.1" K., but this value is quite uncertain.

Jan 1, 1940

By Henry Seltz, Hugh J. MacDonald, Cyril Wells

Several investigators have measured the heat capacity of cementite, using different methods of attack, but the agreement between the values obtained cannot be considered good. Naeserl has made measurements of "average heat capacities" of iron carbide between 1026" and 85" K., using a water calorimeter. His computed true specific heat at 78.1" K. is 11.22 cal. per gram-formula mass, which, if correct, is much too high for any reasonably accurate extrapolation to 0" K. The cementitc used by Naeser was obtained from a steel containing 0.9 per cent carbon, by electrolytically dissolving out the iron in a neutral bath of ferrous chloride. The cementite remained as a coarse, crystalline, gray powder. Andes2 has measured the specific heat of iron carbide, from 102" to 323" K., as it exists in steel. The specific heats of several slugs of steel of known iron carbide content were determined, and the specific heat of the iron carbide (Fe3C) calculated by plotting specific heat versus percentage of carbon, and extrapolating to pure Fe3C (6.7 per cent C). The heat-capacity values for temperatures below 100" K. were obtained by comparing the temperature-specific heat curve for Fe3C to that of Fe. Since the two were very similar in the range examined experimentally and approach more closely at low temperatures, it was assumed that near the absolute zero the form of the curve for Fe3C would be similar to that of Fe. Andes calculates for the entropy of Fe3 C,S298 = 23.55 e.u. The heat of formation of Fe3C has been studied by several workers. Kelley3 has reviewed these measurements and calculations, and selects those of Roth* and Naeser6 as worthy of most consideration. Roth has given AH = 5400 cal. + 30 per cent as a result of his own and other work. Naeser has determined the heat of formation from Fe and different forms of carbon, and for graphite (0) he finds AH = 5600 cal. Kelley accepts the rounded figure AH = 5500 as the heat of formation at 298.1" K., but this value is quite uncertain.

Jan 1, 1940

By Harry Seltz

SEVERAL investigators have measured the heat capacity of cementite, using different methods of attack, but the agreement between the values obtained cannot be considered good. Naeser1 has made measurements of "average heat capacities" of iron carbide between 1026° and 85° K., using a water calorimeter. His computed true specific heat at 78.1° K. is 11.22 cal. per gram-formula mass, which, if correct, is much too high for any reasonably accurate extrapolation to 0° K. The cementite used by Naeser was obtained from a steel containing 0.9 per cent carbon, by electrolytically dissolving out the iron in a neutral bath of ferrous chloride. The cementite remained as a coarse, crystalline, gray powder. Andes" has measured the specific heat of iron carbide, from 102° to 323° K., as it exists in steel. The specific heats of several slugs of steel of known iron carbide content were determined, and the specific heat of the iron carbide (Fe3C) calculated by plotting specific heat versus percentage of carbon, and extrapolating to pure Fe3C (6.7 per cent C). The heat-capacity values for temperatures below 100° K. were obtained by comparing the temperature-specific heat curve for Fe3C to that of Fe. Since the two were very similar in the range examined experimentally and approach more closely at low temperatures, it was assumed that near the absolute zero the form of the curve for Fe3C would be similar to that of Fe. Andes calculates for the entropy of Fe3C, S298 = 23.55 e.u. The heat of formation of Fe3C has been studied by several workers. Kelley&apos; has reviewed these measurements and calculations, and selects those of Roth4 and Naeser5 as worthy of most consideration. Roth has given ?H = 5400 cal. ± 30 per cent as a result of his own and other work. Naeser has determined the heat of formation from Fe and different forms of carbon, and for graphite (ß) he finds OH = 5600 cal. Kelley accepts the rounded figure ?H = 5500 as the heat of formation at 298.1° K., but this value is quite uncertain.

Jan 1, 1939