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By W. G. Pfann

In zone-melting, a small molten zone or zones traverse a long charge of alloy or impure metal. Consequences of this manner of freezing are examined with impurerespect to solute distribution in the ingot, with particular reference to purification and to prevention of segregation. Results are expressed in terms of the number, size, and direction of travel of the zones, the initial intermsofsolute distribution, and the distribution coefficient. IF a charge of binary solid-solution alloy is melted and then frozen slowly from one end, as for example in the Bridgman method of making single crystals,' coring usually occurs, with a resulting end-to-end variation in concentration. Such coring, or normal segregation, is undesirable where uniformity is an object. On the other hand, for certain systems, it can be utilized to refine a material by concentrating impurities at one end of the ingot.'. ' In the present paper a different manner of freezing will be examined with respect to the distribution of solute in the ingot. A number of procedures will be indicated which have in common the traversal of a relatively long charge of solid alloy by a small molten zone. Such methods will be denoted by the general term zone-,melting, while the process described in the preceding paragraph will be called normal freezing. It will be shown that, in contrast to normal freezing, zone-melting affords wide latitude in possible distributions of solute. Segregation can either be almost entirely eliminated or it can be enhanced so as to provide a high degree of sttparation of solute and solvent. A number of simplifying assumptions will be invoked which, while not entirely realizable in practice, nevertheless provide a suitable point of departure for more refined treatments. Moreover, our own experience with zone-melting has shown that, for certain systems at least, the analysis holds quite well. The present paper will be confined to a discussion of principles and a general description of procedures. Comparison with experiment is planned for later publication. Normal Freezing Before considering zone-melting, segregation during normal freezing will be reviewed briefly. If a cylinder of molten binary alloy is made to freeze from one end as in Fig. 1, there usually will be a segregating action which will concentrate the solute in one or the other end of the ingot. If the constitutional diagram for the system is like that of Fig. 2, then the distribution coefficient k, defined as the ratio of the concentration in the solid to that in the liquid at equilibrium, will be less than one and the solute will be concentrated in the last regions to freeze. If the solute raises the freezing point, then k will be greater than one and the solute will be concentrated in the first regions to freeze. The concentration in the solid as a function of g, the fraction which has solidified, can be expressed by the relation: C = kC0 (1-g)k-1 [I] where C, is the initial solute concentration in the melt. Eq 1 is based on the following assumptions: 1—Diffusion in the solid is negligible. 2—Diffusion in the liquid is complete (i.e., concentration in the liquid is uniform). 3—k is constant. Concentration curves representing eq 1 for k's from 0.01 to 5.0 are plotted in Fig. 3. This equation, in one form or another, has been treated by Gulliver,³ Scheuer,4 Hayes and Chipman5 for alloys and by McFee2 for NaCl crystals. It is derived in Appendix I. It should be pointed out that the k which is calculated from the phase diagram will be valid only in the ideal case for which the stated assumptions are correct. In all actual cases, the effective k will be larger than this value for solutes which lower the melting point, smaller for solutes which raise the melting point, and will probably vary during the beginning of the freezing process. For simplification it will be assumed that the ideal k is valid. Zone-Leveling Processes The processes of this part are designed to produce a uniform, or level, distribution of solute in the ingot. Single Pass: Consider a rod or charge of alloy whose cross-section is constant and whose composition, C2, is constant, although permissibly varying on a microscopic scale." Such a charge might be a rapidly frozen casting or a mixture of crushed or powdered constituents. Cause a molten zone of

Jan 1, 1953

By J. J. Gilman

Rates of prisnzatic plastic glide ( {1010}<2110>) in pure Cd crystals have been measured at temperatures from 158° to 276°C. The glide rate is proportional to the 2.75 power of the applied shear-stress. The activation energy is 29.2 kcal per mol. It is suggested that the rates of prismatic glide in Cd and Zn crystals are determined by the strengths of the atomic bonds across the prism planes. ALTHOUGH zinc and cadmium crystals both have hexagonal structures with nearly the same c/o ratios, their mechanical behaviors are quite different. Whereas zinc becomes quite brittle below room temperature, and cleaves readily on (0001) planes, cadmium is very ductile even at 4.2°K, and cannot be cleaved at any temperature. As part of a search for the explanation of this difference in behavior, a study has been made of prismatic glide in cadmium. It complements a previous study of the same phenomenon in zinc.1 The primary glide plane in cadmium is the basal (0001) plane, and the primary glide direction is the direction of atomic close-packing <2110>. However, if a tensile stress is applied parallel to the basal plane, then the shear stress on the basal plane equals zero so basal glide cannot occur. At low temperatures, deformation by twinning occurs; but at high temperatures, it has been found in this study that gliding on prismatic planes (1010) occurs in the close-packed direction. This is completely analogous with the case of zinc, except that lower temperatures are required. EXPERIMENTAL The experiments were done in nearly the same way as for zinc.&apos; Therefore, only the differences in the two sets of experiments will be described here; for other details the reader is referred to the previous paper. Crystals 6 by 6 mm sq were used that were grown from "Super Purity" 99.999 + pct Cd purchased from the New Jersey Zinc Co. The crystals were grown with their basal planes parallel to both the rod axis and one of the flat sides of the square cross section, A close-packed direction in the basal plane was oriented parallel to the rod axis. Gage sections were carefully machined into the crystals, and the surface damage caused by machining was removed with the same chemical polishing reagent as had been used for zinc. Thus, specimens of the same form and size as the previous zinc ones were produced. The crystals were heated to the test temperatures in a silicone oil bath (fused salts were tried first, but they reacted badly with the cadmium). An Instron tensile-testing machine was used for applying stresses to the crystals at various constant strain-rates. RESULTS The general behavior of cadmium crystals is much the same as for zinc. Only the constants that measure specific properties are different. Just as

Jan 1, 1962

By D. F. Kaufman, E. D. Levine, L. R. Aronin

ThE primary slip plane in hcp metal crystals can usually be inferred from the c/a ratio. Basal slip is the primary system at room temperature for zinc, cadmium, magnesium, cobalt, and rhenium, all of which have a c/a ratio greater than 1.60. Zirconium and titanium, on the other hand, each with a c/a ratio of 1.59, deform primarily by (1010) [ll20] prismatic slip. The increasing tendency toward prismatic slip in these materials is generally thought to be associated with the increase in atomic density on (10i0) as c/a is reduced. Beryllium, with a c/a ratio of 1.57, would, according to the above scheme, be expected to exhibit prismatic slip. However, in beryllium of commercial purity, the primary deformation mode at room temperature is basal slip.&apos; The ratio of critical shear stress for prismatic to that for basal slip at room temperature is approximately 5:l. The critical shear stress for prismatic slip decreases quite rapidly with increasing temperature, however, and at 500°C the ratio is approximately unity. The apparently anomalous behavior of beryllium has led to speculation that prismatic slip in this material may be restricted by an anisotropic effect of impurities,&apos; and that, if beryllium could be purified to a sufficient extent, prismatic slip might predominate at room temperature. In such a case, the conditions under which basal cleavage can occur would be suppressed, and enhanced low-temperature ductility might result. With the advent of the floating-zone method for purification of beryllium,3 it has become possible to determine experimentally the effects of purification on basal and prismatic slip. Tensile tests were performed at room temperature on single crystals oriented favorably either for basal or prismatic slip. The crystals had been purified to various extents by zone-refining, employing procedures that have been described elsewhere.4 Relative purities of the crystals were estimated by measuring the ratio of electrical resistance at 4.2"K to that at 298°K. Typical values ranged from 0.40 for commercial-purity material to 7.7 X 10"4 for crystals prepared from vacuum-distilled beryllium and subjected to six zone-refining passes. The purity dependence of the critical shear stresses for basal and prismatic slip is shown in Fig. 1. In the purity range studied, the critical shear stress for basal slip is decreased from 1.4 to 0.14 kg per sq mm. The critical shear stress for prismatic slip is decreased from 6.7 to 5.3 kg per sq mm. The decreases in critical shear stress for each deformation mode, therefore, are approximately equivalent. No purification anisotropy is observed. Because of the absolute magnitudes of the critical stresses, the ratio of the critical shear stress for prismatic slip to that for basal slip actually increases from 5:l to 38:l at the highest purity level studied. It is evident, therefore, that basal slip is the primary deformation mode in high-purity beryllium. This fact must be accounted for in any rationalization of the deformation behavior of hcp metals. This work was performed at Nuclear Metals, Inc., under the sponsorship of the U.S. Atomic Energy Commission.

Jan 1, 1964

By D. C. Jillson

BRIDGMAN1,2 melted metals in a graphite or hard glass tube and lowered the tube through a furnace to make it cool from one end only. Because of the difficulty of eliminating all vibration of the mold, others have raised the furnace instead. Neither way seems as desirable as a setup with no motion of either the mold or the furnace. A furnace in which both the shape and the slope of the temperature gradient could be controlled and varied over a wide range and in which such a gradient could be moved from one end of the furnace to the other, freezing the specimen from one end to the other, at any desired rate, all by means of isolated external control, seemed to offer definite advantages. In addition to eliminating the possibility of vibration due to moving parts, it might also give better control over the direction and rate of heat flow. Such an apparatus was assembled and is shown schematically in fig. 1. Equipment Furnace: A clay-carborundum tube of 3 1/2 in. ID with a % in. wall thickness was used as the core. This had a main winding of No. 12 B.&S. gauge Nichrome V with some compensation for heat loss at the ends. Taps to this winding were made at points 12 in. from each end. Fig. 2 shows details of this winding and of the two end windings. Each end winding was wound over Micanite over the main winding. No. 15 B.&S. gauge Nichrome V was used for these, and again taps were supplied at two inter-mediat,e points on each. The tube was supported in an 18 in. OD black iron shell with brick insulation. The input to each of the windings was regulated by means of a variable transformer. Temperature Regulation: A chromel-alumel thermocouple located near the furnace wall in the center of the furnace was connected with a Celec-tray controller, type PIC, 300" to 900°C range, which opened and closed a shunt across an external variable resistance in the main winding circuit. An "anticipatory response" device also was incorporated to minimize the cyclic effect of the control mechanism. Eleven survey couples in a common pyrex glass protection tube were located near the furnace wall and spaced 2 in. apart. The couple leads went to a common reference junction box where they were connected to copper leads from a selector switch which, in turn, was connected to a type K potentio-meter. This arrangement permitted rapid temperature surveys. The knob on the controller dial was replaced with a threaded brass spool turned at a controlled rate by a thin iron wire one end of which was attached to a gear train and the other to a small weight heavy enough to prevent slipping of the wire on the spool. The gear train, driven by a 1-rpm Telechron motor, contained a series of different sized interchangeable gears and threaded drums permitting a range of travel speeds from 0.10 in. per hr up to a hypo-

Jan 1, 1951

By H. P. Leighly, F. C. Perkins

THERE have been several statements in the literature about the difficulty of producing single crystals of high-purity (99.99pct) by the strain-anneal method. Consequently, investigators tend to employ low-purity aluminum for their single-crystal experiments, or else resort to the Bridgman or other techniques which depend on solidification for the production of single crystals. The following paragraphs describe a solid-state method for the manufacture of single crystals of high-purity aluminum which should provide crystals with greater perfection than those formed by solidification. The starting material for this method of producing single crystals was secured from the Aluminum Corp. of America and has a purity of 99.99 pct, the balance being trace amounts of impurities. Specimens approximately 1 by 4 in. are sheared from sheet having a nominal 0.050 in. thickness. The specimens are given a preliminary anneal at 640°C for approximately 3 hr in order to remove fabrication strains and to produce an average grain size of about 1/4-in. diam. The specimens are then etched in Tucker&apos;s etchant (45 pct HC1, 15 pct HNO3, 15 pct HF and 25 pct H2O) to remove the oxide film. Critical strain is applied by wrapping each specimen about a 1 3/4 in. round and subsequently straightening it against a flat surface. The high-purity aluminum sheet is sufficiently soft that this operation can be accomplished by ordinary finger pressure. The specimens are immediately annealed again at 640°C for 3 hr and reetched for examination. Ordinarily, considerable growth of certain of the grains will have occurred, and occasionally a single crystal will be produced on the first attempt. The procedure of alternately straining, annealing and etching is repeated until the majority of a batch of specimens contains usable crystal sizes. Typical examples are illustrated in Fig. 1. The greatest changes in crystal sizes are produced in the initial treatments. As the average crystal sizes get coarser in the later treatments, the sever- ity of the strain must be increased in order to produce grain boundary- migration. This increase in severity is effected by decreasing the diameter of the round used for straining (to 1 1/2 in., for example) and/or wrapping the specimens about the round twice, with opposite faces in contact with the round, before flattening. Usually the strain treatments described are not severe enough to produce nucleation in coarse grain high-purity aluminum. The growth of grains occurs by strain-induced grain-boundary migration. It has been observed that the grain boundaries move most readily during the first hour or so of each annealing treatment and that the rate of movement decreases with extended holding times at temperature. Prolonged annealing treatments are therefore not usually beneficial. Similarly, the rate of growth of each crystal appears to depend upon the orientation of the crystal with relation to those of its neighbors. Frequently island grains are formed after the initial heat treatment as the result of slow grain-boundary migration. These sometime become stationary during later heat treatments. Twin orientation interfaces are frequently developed during annealing. These imperfections can usually be removed by increasing the severity of strain to produce actual nucleation of new grains of more favorable orientation at the imperfection interfaces. The largest single crystals produced in our laboratory by the above method measured 4 by 1 by 0.050 in. Examination of Laue back-reflection patterns from a limited area of the specimens, gave no evidence of polygonization. Probably there is some indication of polygonization in the original grain area provided a more sensitive technique is used for detection. Experiments to produce wider specimens were less successful, possibly because wider sheets increase the complexity of the strains induced by deformation and promote widespread nucleation. Grain boundary migration occurs preferentially in a direction parallel to the longitudinal axis of the specimen. The choice of specimen geometry with respect to the rolling direction of the sheet appears to be immaterial in regard to the production of single crystals.

Jan 1, 1961

By Charles Smeal, Robert J. Schafer, Max Quantinetz

Normally metal powders cannot be ground to sub-micron sizes because of welding and agglomeration phenomena. Through the use of selected grinding aids and grinding fluids, nickel and other metal powders have been ball-milled as fine as 0.1 It was found that certain inorganic salts are more effective grinding aids for metal powders than conventionally used surfactants. METAL and alloy powders are used to produce reagents, pigments, coatings, solders, brazes, and parts for industry by powder metallurgy techniques. They are also combined with refractory compounds to produce cermets and dispersion-hardened products. One of the interests at the Lewis Research Center has been to explore the potentialities of the dispersion strengthening process. Since the work of Ir-mann, many investigators have shown that the strength of dispersion-hardened products may increase with decreasing interparticle spacing.24 One approach to achieving small interparticle spacing is to combine fine refractory compounds and metal powders, preferably below 1 in size. In attempting to obtain fine metal powders, it was found that until very recently the best that could be obtained from commercial suppliers, particularly of ductile metals, was about 1.0 . Interest was therefore developed in providing finer metal powders for dispersion-hardening studies. Information obtained from the literature, from others working in the field, and from prior experimental work performed at NASA, led to a consideration of ball-milling as a technique to produce the desired materials. Some of the variables associated with ball-milling are the size, material, and nature of construction of the grinding container; the nature and amount of the grinding material and material to be ground; and the nature and amount of the grinding liquid and grinding aid, if employed, and the grinding time. In all ball-milling, welding and agglomeration can oc- cur as well as grinding. Because of the tendency of ductile metals to weld together, they are difficult to grind.5 The ultimate particle size obtained on grinding is generally the one at which the rate of grinding becomes equal to the rate of welding. To help delay welding and thus obtain smaller particle sizes, grinding aids are often employed. The principal objective of this investigation was to produce submicron metal powders by ball-milling the powders with selected grinding aids and grinding fluids. A secondary objective has been to attempt to explain the variations observed in grinding behavior by considering possible grinding mechanisms and correlating various parameters with grinding effectiveness. Three groups of ball-milling experiments were run; one in which the grinding aid was varied, a second in which the grinding fluid was varied, and a third in which the material being ground was varied MATERIALS, APPARATUS, AND PROCEDURE In the first group of experiments in which the grinding aid was varied Inco Carbonyl Grade B nickel powder initially 2.5 (all sizes refer to average particle size as measured by Fisher Sub -sieve Sizer) was used as the material being ground and 200-proof ethyl-alcohol as the grinding fluid. Surfactants, representative of typical organic structures, were selected as grinding aids. Inorganic salts used as grinding aids were chosen on the basis of the size and valence of their ions. Water soluble salts were used in order to facilitate their removal from the slurry after grinding. In the second set of experiments, grinding of the 2.5- Ni powder was tried in four different grinding liquids; water, cyclohexane, n -heptane, and methy-lene chloride. In this study seven grinding aids selected from those tried in the first group of experiments were employed. In the third group of experiments 200-proof ethyl alcohol was again used as the grinding fluid to mill Cu, Cr, Fe, Ag, and Ni powders of various initial particle sizes&apos; All mill charges contained 300 ml of grinding liquid and 3000 g of 1/2 in. stainless steel balls. When inorganic salts were used as the grinding aid, 70 g of salt and 210 g of metal powder were employed, and with surfactants 6 g of grinding aid and 300 g of

Jan 1, 1962

By O. N. Cole, R. E. Davis, T. D. Brotherton

Pvfoperties of rubidium and cesium are compared with those of other alkali metals. Methods for the preparation of rubidium and cesium metal are reviewed briefly, ad hazards and safety precautions required in handling rubidium and cesium metal are described. SimPle methods for handling laboratory quantities of elemental rubidium ad cesium under oil and under argon are illustrated. CESIUM and rubidium were both discovered by Bunsen and Kirchoff in the years 1860 and 1861. Cesium was discovered while Bunsen and Kirchoff were making a spectrographic study of spring water from Durkheim, Germany. It was the first element discovered by this technique. The element was given the Latin name "caesius" for sky blue because of the color it imparted to flames. Elemental cesium was first prepared by Setterberg in 1881 through electrolysis of a molten mixture of cesium and barium cyanides.&apos; In 1861, Bunsen and Mirchoff discovered rubidium while making a spectrographic study of the alkali content of lepidolite ore from Saxony. Two prominent dark red lines appeared in the spectrum and so the element was named "rubidius" or dark red. In 1861 Bunsen and Kirchoff first prepared elemental rubidium through the electrolysis of molten rubidium chl~ride.~ The alkali metals are very similar in their chemical and physical properties. They are the most active metals, and all exhibit a single oxidation state of one. They are so reactive that they are never found in nature in the elemental state. The reactivity of he metals increases with atomic number. Rubidiurn and cesium ignite spontaneously in air and react explosively with water. This extreme reactivity makes necessary special equipment and techniques for the safe preparation and use of the metals. The cation: of Group IA can be separated from the metallic cations of other groups with relative ease, but the separation of the individual alkali cations is much more difficult because of their close chemical similarity. This close chemical and physical similarity of alkali metals can be inferred from the atomic radii, oxidation numbers, and ioni-zation potentials shown in Table I. A difficult but the most practical physical method of separating the elemental alkali metals from one another is by distillation. Only lithium has a boiling point sufficiently far-removed from the boiling points of the other alkali metals to make this method of separation feasible without elaborate and expensive equipment. This method is not used, however, for lithium because it possesses sufficient chemical dissimilarity from the other alkalies for it to be separated relatively easily as lithium hydroxide monohydrate or as lithium carbonate. Francium, the last member of the group, has no known stable isotopes. The naturally occurring

Jan 1, 1962

By F. V. Lenel, M. V. Rose, A. B. Backensto

WHEN aluminum-flake powders are compacted and hot pressed and the resulting compacts are extruded or hot forged, a group of materials with unique properties is obtained. Not only do they exhibit high room-temperature strength of the order of some of the aluminum alloys, but they maintain this strength even after prolonged heat treatment at temperatures up to 900°F. Moreover, their strength decreases much less with increasing temperature than that of aluminum alloys of comparable room-temperature properties. Irmann,&apos;" who discovered and first described this group of materials, which was called SAP, showed that the room-temperature mechanical properties of the extrusions are a function of the oxide content of the powders and therefore the oxide content of the extrusions. The higher the oxide content, the higher are their tensile strength, yield strength, and hardness, and the lower their ductility. Lyle" investigated the relationship between mechanical properties at elevated temperature and oxide content in the course of the development work of the Aluminum Co. of America on materials, called APMP, similar to those developed in Switzerland. He found that at 600 °F, just as at room temperatures, tensile strength and yield strength increase and elongation decreases with oxide content. A careful study of his data (Fig. 3, loc. cit.) shows, however, that the scatter is more pronounced than at room temperature. Gregory and Grant&apos;s data on the creep5 and stress-ruptureb roperties of the one commercial grade of the Swiss SAP and the various grades of APMP indicate that creep strength and stress to rupture also generally increase with increasing oxide .content. Ever since this new group of materials was discovered, attempts have been made to explain the mechanism by which they obtain their high room-temperature and particularly their elevated-temperature strength. In most of the attempts the new material was considered as a dispersion of aluminum oxide particles in a matrix of aluminum. Ir-mann, Von Zeerleder, and Rohner&apos; applied a theory on dispersion strengthening developed by Rohners to the flake-powder extrusions. According to this theory the elastic limit S, of a dispersion would depend upon the average distance between the dispersed particles L according to the equation: 2 E ¦ a where E is the modulus of elasticity and a the distance between nearest neighbors in the lattice of the matrix material. Irmann and co-workers assumed

Jan 1, 1958

By S. J. Sindeband

Prior to discussing the metallurgy of sintered chromium borides, it is pertinent to outline some of the reasoning behind this investigation and the purposes underlying the work. This study was initiated as an aproach to the ubiquitous problem of a material for service at high temperatures under oxidizing atmospheres, and it was undertaken with a view to raising the 1500°F (816°C) ceiling to 2000°F (1093°C) or better. For the reason that no small, but rather a major, lifting of the high temperature working limit was being attempted, it was felt appropriate that a completely new approach be taken to this problem. A summary of the thinking behind this approach was published recently by Schwarzkopf.&apos; In briefest terms, it was postulated that the following requirements could be set up for a material which would have high strength at high temperatures. 1. The individual crystals of the material must exhibit high strength interatomic bonds. This automatically leads to consideration of highly refractory materials, since their high energy requirements for melting are related to the strength of their atom-to-atom bonds. 2. On the polycrystalline basis, high boundary strength, superimposed on the above consideration, would also be a necessity. Since this implies control of boundary conditions, the powder metallurgy approach would hold considerable promise. Such materials actually had been fabricated for a number of years, and the cemented carbide is the best example of these. Here a highly refractory crystal was carefully bonded and resulted in a material of extremely high strength. That this strength was maintained at high temperature is exhibited by the ability of the cemented carbide tool to hold an edge for extended periods of heavy service. Nowick and Machlin2,3 have analytically approached the problem of creep and stress-rupture properties at high temperature and developed procedures whereby these properties can be approximately predicted from the room temperature physical constants of a material. The most important single constant in the provision of high temperature strength and creep resistance is shown to be the Modulus of Rigidity. On this basis, they proposed that a fertile field for investigation would be that of materials similar to cemented carbides, which have Moduli of Rigidity that are among the highest recorded. The cemented carbide, however, does not have good corrosion resistance in oxidizing atmospheres and without protection could not be used in gas turbines and similar pieces of equipment. It would be necessary then to attempt the fabrication of an allied material based upon a hard crystal which had good corrosion resistance as well. It was upon these premises that the subject study was undertaken and at an early stage it was sponsored by the U.S. Navy, Office of Naval Research. Since then, it has been carried on under contract with this agency. Chromium boride provided a logical starting point for such research, since it was relatively hard, exhibited good corrosion resistance, and, in addition, was commercially available, since it had found application in hard-surfacing alloys with iron and nickel. That chromium boride did not provide a material that met the ultimate aim of the study results from factors which are subsequently discussed. This, however, does not detract from the basis on which the study was conceived, nor from the value of reporting the results which follow. Chromium Boride While work on chromium boride proper dates back to Moissan,4 there has been a dearth of literature on borides since 1906. Subsequent to Moissan, principal investigators of chromium boride were Tucker and Moody,5 Wede-kind and Fetzer,6 du Jassoneix,7,8,9 and Andrieux." These investigators were generally limited to studies of methods of producing chromium boride and detennining its properties. Some study, however, was devoted to the chromium-boron system by du Jassoneix,7 who did this chemically and metal-lographically. This system is not amenable to normal methods of analysis by virtue of the refractory nature of the alloys involved, and the difficulties of measurement and control of temperature conditions in their range. Dilatometric apparatus is nonexistent for operation at these temperatures. Du Jassoneix made use of apparent chemical differences between two phases observed under the microscope and reported the existence of two definite compounds, namely: Cr3B2 and CrB. These two compounds, he reported, had quite similar chemical characteristics, but were sufficiently different to enable him to separate them. The easiest method for producing chromium boride is apparently the thermite process, first applied by Wede-

Jan 1, 1950

By S. J. Sindeband

J. WULFF*—It seems to me that the author could improve the quality of his high temperature material by using less nickel as a cementing agent in hot pressing. Furthermore, to avoid the presence of undilfused nickel which would not be oxidation resistant, permit me to suggest that he use a nickel-chromium powder containing a small percentage of boron. This would give him a liquid phase at a lower temperature and accelerate both sintering and homogenization. The commercial alloy known ascolrnonoy contains sufficient chromium to be heat resistant and sufficient boron to be of low melting point. Such an alloy may be applicable as a cementing agent in increasing the quality of Mr. Sindeband&apos;s alloys. Finally 1 believe the author unfair to himself in expecting a porous material to have properties equivalent to one of 100 pet density. S. J. SINDEBAND—Dr. Wulff&apos;s point is well taken. Early in the program we realized the fact that we were having difficulty with these low-melting alloys, and we had hoped, since the colmonoy alloys of which you speak are at the nickel-rich end of the diagram, that by going to the other end of the diagram (chromium boride-rich) we would not have this difficulty. Thus we tried to use very small percentages of binder; but for reasons which are not exactly apparent we found that when we did this it was necessary to raise the pressing temperature to a point which we were unable to attain. For all compositions which we tried using nickel, or for that matter any nickel iron or cobalt containing material as a binder, we found that we would get low melting boride phases, which as you point out are the commercial "strength" of the hard-facing materials. 1 personally believe these owe a great deal of their behavior and even hardness to the nickel boride which is considerable evidence when an alloy of chromium boride is made with nickel. Nickel boride itself is very hard. We did try pure chromium as a binder and found there was considerable difficulty in handling it, particularly since we could not just hot press under

Jan 1, 1950

By Irving B. Cadoff, Stojan M. Zalar

AgInTe2, CuInTe2, and all Proportions of CuxAg1-xInTe, forMed homogeneous single phase alloys after direct solidification from the nielt. X-ray analysis indicated a zinc-blel~de strzccture typical of the chalcopyrite compounds, and the electrical resistivity and Sccbeck coefficient values were in the semiconducting range. AuInTe, and AuxA4g,-, InTe, formed by what appeared to be a peritectic reaction (the thermal analysis curves showing more than one arrest) and were conseyue~ztly polyphase. Substitution of copper into AgIrzTe, resulted in a continuous transition in the room tenzperature Seebeck coefficient from the negative AgIzTe, to the positive CuInTe,. A zero coefficient was obtained at about Cuo.55 Ago.45 InTe, . The temperatzire variation was similar to that observed for the stoichiometric compounds, that zs, tendency towards "p" concEuction at elevated temperatures. The thernzoelectric figure of merit for the compo~uzds, as determined by the Putley -Harmnn method were in the range 10- to 10-7 "K-l; the thermal conductivities in the order of 0.15 cal per sec-cm-oK. INCREASED interest in semiconducting intermetallic substances is expanding much of recent research from simple binary compounds into polyatomic systems and solid solutions. Ternary compounds A&apos; represent a covalent extension of the binary semiconductors Within the a tin isoelec-tronic series, Ag-Cd-In-Sn-Sb-Te-I, divalent cadmium atoms in CdTe are being substituted for by monovalent silver and trivalent indium atoms to form the compound AgInTe, . By cross-substitution with elements of other isoelectronic series, a great number of ternary compounds A &apos;B"&apos;c? is possible. In all of them, however, a necessary though not sufficient condition for the covalent, semiconducting bond—that there be four sharing orbital electrons per atom—must be fulfilled. In AgInTe,, each silver or indium atom is tetrahedrally surrounded by four tellurium atoms, while each tellurium atom is co-valently bound to two silver and two indium atoms. Synthetic chalcopyrites A&apos;B"&apos;c~ were first recognized as potential semiconduct&rs by Goodman and Douglas.&apos; Austin, Goodman, and Pengelly discuss preparation difficulties and some electronic measurements on AgInS, , AgInSe, CuInSe, , AgInTe, , and CuInTe,. Chalcopyrites A B c2v are mentioned in papers attempting to classify and predict semiconducting behavior of intermetallic compounds; on the basis of saturated tetrahedral sp3 bonds,3 by specific selection criteria,&apos; and by crystallographic considerations."

Jan 1, 1962

By T. E. Leontis

ONLY a limited amount of information has been published on the effect of thorium as an alloying ingredient in magnesium. McDonald13&apos;2 showed that the addition of thorium in amounts up to 3 pct increases significantly both the ductility and the strength of rolled magnesium sheet. A recent publication by Sauerwald" indicates that thorium contributes strength and creep resistance at elevated temperatures to magnesium in both the cast and wrought states. The observations of Sauerwald are confirmed in this paper, which presents the results of a systematic study of the effects of compositional variation on the tensile properties, creep resistance, conductivity, density, and metallography of Mg-Th alloys containing up to 50 pct Th both in the sand-cast and in the extruded states. The effect of the addition of cerium to Mg-Th alloys is also reported. Experimental Methods The alloys studied in this investigation were pre.pared in small laboratory melts according to the melting practice described by Nelson4 as the crucible method. Electrolytic magnesium was used as the starting material to which the thorium* was introduced in metallic form. It was observed that the behavior of thorium in molten magnesium with respect to reaction with protective fluxes is similar to that of rare-earth metals. In order to obtain the highest possible alloying efficiency, it is necessary to use non-MgC1, fluxes and to apply all the precautions described by Marande6 for melting, alloying, and casting magnesium-rare-earth alloys. .Under these conditions it is possible to obtain an alloying efficiency in the range of 85 to 95 pct. The Mg-Th-Ce alloys were made with cerium of the highest purity available, not with the commercial product "misch-metal" which contains approximately 50 pct Ce. The total rare-earth content of this material was 97.1 pct, of which 0.3 pct was rare-earth metals other than cerium; the major impurities comprising the balance were iron and magnesium. The thorium and cerium contents of each alloy were determined chemically. Test bars 6% in. long with a 2% in. long reduced section of % in. diam were cast in sand molds using a four-baf pattern. In most cases, a 3 in. diam extrusion billet 10 in. long was cast in a steel mold from the same melt used for making the sand-cast test bars. For the higher thorium alloys, it was necessary to remelt the foundry scrap from the test bars in order to make the extrusion billets. The billets were scalped to a diameter of 2 15/16 in. and the ends faced to a length of 9% in. as limited by the size of the extrusion container. The alloys were extruded into % in. diam rod on a 500-ton direct-extrusion press. The details of the extrusion process are as follows: Billet preheat 925°F (2 to 16 hr) Container temperature 900 °F Die temperature 900°F Extrusion speed 10 ft per min Reduction ratio 36:1 Percent reduction 97.3 Alloys containing up to 10.2 pct Th were preheated at 925°F for 2 hr; all alloys with higher thorium contents were preheated for 16 hr. In order to establish the effect of extrusion temperature, billets of

Jan 1, 1953

By P. W. Ramsey, D. P. Kedzie

INCREASING demand for improved strength-weight ratios made on aircraft structures has resulted in a gradual increase in the tensile strength requirements for steels used in such applications. As the cyclic loads often are more critical than static loads, and the fatigue properties are generally the design criteria, the question arises as to whether an improvement in fatigue properties accompanies the increased tensile strength. The present investigation was undertaken to determine the relationship between fatigue and tensile properties for an aircraft quality steel in the 155 to 280 ksi (1000 psi) tensile strength range, using the Prot method of fatigue testing. Procedure and Results After preliminary work to establish proper heat treating procedures for this heat of aircraft quality electric furnace steel (a Ni-Cr-Mo-V steel," AMS- Prot Fatigue Testing Method—The determination of the endurance limit by the conventional Wohler method can be time-consuming and easily require 20 specimens when statistical variance is to be established. This is also true when endurance limit loads are determined on actual parts or subassem-blies, and the desirability of a reliable accelerated method has been evident for some time. The primary advantage of the Prot method of fatigue testing is in reducing the number of specimens and the time required for each test. Unlike the Wohler method, every Prot specimen tested con- tributes to the determination of the endurance limit, and the authors have been able to duplicate Wohler results obtained with 20 specimens with only half the specimens and a fourth of the total cycles. This new technique for defining the endurance limit was proposed in 1948&apos; by Marcel Prot and consists of progressively increasing cyclic stress until fatigue failure occurs. By varying the load rate, a, a useful relationship is found to exist with failure stress, so that for steel the failure stress appears to

Jan 1, 1958

By Robert M. Yonco, Irving Johnson, Martin G. Chasanov

The thermodynamics of the cadmium-rich portion of the Pu-Cd system has been studied with a high-temperature galvanic-cell method. The partial phase diagram of the Pu-Cd system was determined. The existence of the intermediate phases PuCd11 (cubic BaHg11 structure, ao= 9.282) and PuCd6 (cubic, CeCd6 structure, a, = 15.59) was established. The existence of at least one other intermediate phase richer in plutonium was indicated. PuCd11 was found to peritectically decompose into PuCd6 and liquid at 406" * 2°C. The solubility of plutonium in liquid cadmium may be represented by the equations: (355&apos; to 399°C) log (at. pct Pu) = 6.223 -4282T-1 (399° to 632°C) log (al. pct Pu) - 5.148 - 5277T-1 > 1.156 x 106 T-2 The free energy of formation values (kcal per mole) of the two intermetallic phases are given by the equations: (PuCd11), ?Gf= -45.9 + 35.7 x 10-3 T (PuCd6), ?Gf0- -39.27 + 25.86 X 10-3T The excess free energy (kcal per mole) of plutonium in liquid cadmium may be represented by the equation: -(-16.72 * 29.54 NPu) 10-3T in which Npu and Ned are the atom fractions of plutonium and cadmium. The thermodyanamics of the U- Cd and Pu-Cd systems are compared. THERMODYNAMIC information on systems of the actinide metals with low-melting metals, such as zinc and cadmium, is useful in the design of pyro-metallurgical processes for the purification of nuclear reactor fuels. The thermodynamics of the Pu-Zn,1 Th-Zn.2,3 U-Zn,4-5 and U-Cd6 systems have been reported. The present report on the Pu-Cd system concerns the liquidus composition in the cadmium-rich region, the characterization of the two most cadmium-rich intermetallic phases, and the thermodynamic properties of these intermetallic phases and dilute liquid solutions of plutonium in cadmium. EXPERIMENTAL Phase Studies. The liquidus composition was determined by analysis of filtered samples of the liquid phase withdrawn at a series of temperatures. The apparatus and procedure were identical to that used in the previous study of the Pu-Zn system.&apos; Briefly. a sample of the melt was withdrawn into a tantalum tube fitted with a porous tantalum filter (30-µ pore). the entire sample dissolved in hydrochloric acid (to avoid errors due to segregation

Jan 1, 1965

By N. S. Stoloff, M. Gensamer

Pyramidal (1122) slip was observed in cadmium single crystals deformed in compression and bending at room temperature and —196°C. Crystals tested in tension twinned with no evidence of pyramidal slip. A critical resolved shear stress law for the propagation of twin nuclei appears probable. Twinning and low-stress kinking are believed to inhibit the appearance of pyramidal slip under ordinary experimental conditions. SEVERAL reports of nonbasal slip in cadmium have appeared in the literature recently, two of the reports having appeared after work on this project was in progress. Brown1 reported cross slip on electron micrographs, but did not identify the cross-slip plane. Wernick and Thomas2 observed nonbasal slip traces parallel to [1123] on a crystal bent with a pair of tweezers, but this too was an isolated observation, with no confirmation of the glide plane. The critical stress for pyramidal glide, and the temperature and strain rate dependence of glide on this system were not discussed. price3 has reported some observations of nonbasal slip in thin films of cadmium with the aid of transmission electron microscopy, but a full publication of these observations was not available at this writing. Pyramidal (1122) <1123> slip also has been observed on zinc single crystals4, 5 and (1122) <1010> slip on magnesium single crystals,6 all oriented with the basal plane nearly parallel to the specimen axis. Since the choice of slip system in the hexa- gonal metals is generally believed to depend on the axial ratio, with basal slip predominating for high-axial ratios, the occurrence of pyramidal slip in zinc and cadmium is unexpected. The objectives of the present investigation were to confirm the existence of nonbasal slip in cadmium, to identify the slip system, and to obtain an estimate of the critical resolved shear stress, assuming that the resolved shear stress law is applicable. EXPERIMENTAL PROCEDURE Two purities of cadmium, 99.95 pet and 99.99+ pet, were employed. As received bars were cold swaged to 3/16 in. rounds. Bicrystals and tricrystals were prepared by passing the polycrystalline rods through a gradient without seeds. It was desired to obtain a large yield of single crystals oriented xo* < 5 deg, in order to be able to suppress basal slip during deformation by keeping the resolved shear stress on the basal plane to a minimum. Cylindrical single crystals of cadmium were prepared by a seeding technique developed by Weiner,7 to obtain a predetermined orientation. The single-crystal rods were sectioned to specimen size by an acid-cutting technique originally developed for zinc crystals.&apos; An aqueous solution of nitric acid was the cutting agent. The acid was picked up by a plexiglass disc spinning at an optimum cutting speed through the acid, which was contained in a sump-like arrangement. The section to be cut, the acid bath, and the spinning disc were enclosed in a plexiglass case. The rod to be sectioned was coated with a thick layer of collodion. At the points at which sectioning was to be effected, the collodion was removed over a length of about 1/8 in. by dissolving it in acetone. To prepare a surface suitable for microscopic exam-

Jan 1, 1962

By R. D. Reiswig

An increasing amount of high-temperature metall~?~gical research is carried out in resistively heated tube furnaces in which a bare specimen is suspended by a fine wire at the midpoint of the tube. It is shown that the assumption of near-blackbody conditions on the surface of the sample may give rise to errors in optical pyrometry of 50°C or more. A number of papers published in the metallurgical literature in recent years have described the use of high-temperature tube furnaces for heat treatments, melting-point determinations, and other work. Typically, the tube is of a refractory metal with open ends, is heated by the passage of an electric current, and has concentric cylindrical radiation shields outside it. In at least one of these,&apos; the specimen is contained within a crucible having a small hole in its lid through which optical-pyrometer measurements are made under essentially blackbody conditions. In another design,* the specimen is inside a muffle which is concentric with the heater tube and which contains a number of washerlike longitudinal radi- ation shields to reduce axial temperature gradients and to give conditions near the specimen closer to those of a black cavity. Yet another design3 employs a wire specimen coaxial with the heater tube. Blackbody conditions are simulated by passing current from a separate supply through the wire until it "disappears" against the background (the inside of the heater tube) as seen through a radial spy hole in the tube. Good agreement with known melting points is achieved when an optical pyrometer is used under such disappearance conditions as the melting point is approached. That this latter method works so well is due, evidently, to considerations such as those mentioned by Dike4 and others.5-8 A more common method than the above, however, has been the suspension of an uncovered specimen by a fine wire in a resistively heated tube with open ends. A radial spy hole about midway between the ends of the tube permits optical-pyrometer observations on the specimen, the inside of the tube, or both. So observed, the specimen typically appears to differ but little in brightness temperature from the inside of the tube. According to De vos9 the radiation from such a spy hole in an empty tube of reasonable 1ength:diameter ratio (e.g., 10 or greater) should be essentially blackbody radiation. For these reasons, apparently, descriptions of work carried out in such furnaces usually include a statement to the effect that conditions surrounding

Jan 1, 1964

By D. H. Shaffer, W. F. Harris, W. M. Hickam, M. H. Loeffler

Experiments have been performed on the quantitative addition to niobium of enriched isotopes 018 and 017 at the 0.1 - 40 micro-gram level and their subsequent recovery. A measured quantity of molecular oxygen of known isotopic concentration is added to niobium metal by oxidation. Recovery of the enriched isotopes as carbon monoxide is by the vacuum fusion technique. Quantitative determinations of the enriched isotopes are made in standard volumes at constant temperature using accurately calibrated micromanometers and the mass spectrometer as pressure measuring instruments. THE presence of low concentrations of nonmetallic impurities in metals can often adversely affect the physical properties of the metal. The increase in hardness and the embrittlement of refractory metals due to oxygen is well known. In metallurgical studies dealing with the diffusion rates or the effect of oxygen on the physical properties of refractory metals, it is often necessary to add small quantities of oxygen to the metal and later recover the total quantity present. It is desirable, therefore, to establish the accuracy with which microgram quantities of oxygen can be added to niobium and recovered by vacuum fusion. The successful addition of microgram quantities of oxygen to metals by the usual manometric techniques and the subsequent recovery by vacuum fusion is difficult because of the uncertainty in the accurate determination of the quantity of oxygen originally present in the metal and because of the chance of contamination by atmospheric oxygen. In order to minimize these uncertainties earlier workers have added quantities of O16 at levels much higher than the oxygen concentrations that are of interest.&apos;-3 In order to eliminate the uncertainty associated with the O16 additions to metals at low microgram levels, experiments have been performed on the quantitative addition of oxygen highly enriched in O17 and O18 at the 0.1 to 40 pg level to niobium and the subsequent quantitative recovery of the isotopes by vacuum fusion. Since the natural abundance of O17 is 0.04 pct and of 0" is 0.2 pct this enriched oxygen provides a uniqueness from interference not achieved in earlier work.&apos;-= A measured quantity of molecular oxygen of known isotopic concentration is diffused into the metal. Recovery of the isotopes in the form of carbon monoxide is by vacuum fusion. The total quantity of gas is determined in standard volumes at constant tempera- ture using accurately calibrated Consolidated Electrodynamics micromanometers and the mass spectrometer for pressure measurements. The molecular and isotopic composition is determined mass spectrometrically. APPARATUS A schematic of the oxygen addition apparatus is shown in Fig. 1. Take-offs are provided for the attachment of the isotope container and for sample bulbs which are used to transfer samples to the mass spectrometer. Metal valves are used throughout the system including the sample bulbs in order to achieve a vacuum of 10"6 mm Hg. Evacuation is accomplished with a 3-stage oil-diffusion pump backed by a mechanical pump. A liquid nitrogen trap is used to remove condensables and to prevent oil vapor from entering the system. A micromano-meter is used for pressure measurements. The furnace assembly is shown in Fig. 2. It consists of a quartz tube joined to the apparatus through a 40/W joint with Apiezon W low-pressure wax. The furnace cap, also a 40/W pyrex joint, is provided with a pyrex hook. The sample is suspended from this hook with a platinum wire. The total volume of the furnace section is 435 ml. All volumes were determined by expanding a known volume of gas at a known pressure into the evacuated system and re-measuring the pressure. Both the micromanometer used on the oxygen addition system and the micromanometer used on the mass spectrometer were compared to a precision

Jan 1, 1961

By B. D. Cullity, A. Freda

It is well known that deformation by cold drawing or swaging produces a kind of preferred orientation called fiber texture in metal wires. Such textures have been extensively studied by means of X-ray diffraction, chiefly by techniques in which the diffracted X-rays are recorded photographically. This paper describes some results obtained with a new method, involving the use of a diffractometer. X-RAY METHOD Since the pole figure of a material having a fiber texture is symmetrical about the fiber axis, there is no need to present the entire pole figure. Instead, texture data can be summarized by means of a curve showing the variation of pole density along any meridian of the pole figure, if the north-south axis of the latter is made parallel to the fiber axis. The position of a pole on the meridian is specified by the angle 9 between the pole and the fiber axis (wire axis). The X-ray method1 used here to measure pole density as a function of 9 actually consists of two methods, referred to as A and B. In method a, X-rays are reflected from the wire surface. Pole densities can be measured by this method from O = 90 deg down to a limiting value which is dependent on the Bragg angle 8 and is typically of the order of 30 to 40 deg. Method B involves diffraction from the wire cross section and covers a range of 0 values from 0 up to an angle sufficient to overlap the measurements made by method A. By a combination of the two methods, a complete pole-density curve can be obtained. However, method A alone, which requires no specimen preparation other than etching, can often reveal enough of the pole-density curve to provide complete information about texture components. Both methods require that the measured diffracted intensities be corrected for changes in absorption and diffracting volume with changes in 9. A11 intensities I reported in this paper are corrected diffracted intensities; they are propor-

Jan 1, 1960

By R. W. Kraft, F. D. George, F. D. Lemkey

From a conszderation of the geometrically possible ways in which an array of lines or linear features in three-dimensional space can depart from a statistically random arrangement, a system was developed to describe and measure different types of anisotrypic arrangements of lines in opaque solids. The technique was applied to a specimen of unidirectionally solidified Al-Cwll, eutectic which contained microstructural imperfections termed lamellar faults. Experimental data obtained from photomicrographs of different facets of a grain of this alloy were then analyzed using this system. It was deduced that the defects, which are essentially linear in natuve, were predominantly parallel to one another but not parallel to the nominal growth direction probably because of some lateral heat flow during solidification. InGOTS of lamellar eutectic alloys which have been unidirectionally solidified under growth conditions which prevent colony formation consist of large elongated grains in which the lamellae are approximately parallel to one another. Deviations from a parallel lamellar structure within a grain are caused by extra lamellae which form occasionally during the solidification process. Three-dimensional analyses of such specimens have revealed that one extra platelet produces two defects, termed 1amellar faults, which can and do grow more or less independently of one another.&apos; The faults are analogous in many ways to edge dislocations in crystals. If a lamella of one phase is considered to be basically two-dimensional, e.g., a surface, then a fault can be defined as the locus of points which delineates an edge (or half the periphery) of one extra lamella as it grows and forms bridges and saddles in an otherwise parallel arrangement oi lamellae, Fig. 1. Were it not for the fact that bridges and saddles occur in the structure, the extra platelet could be defined as the unit defect and the concept of linear faults of positive and negative character around the periphery of the extra platelet would be unnecessary. If an extra platelet is merely inserted (actually it is grown in) between other parallel platelets, the fault line around the periphery of the extra platelet would circumscribe one and only one platelet, namely the extra one, and the faults would lie in a plane parallel to the lamellae. But when an extra platelet merges with adjacent ones and each side grows independently of the other, it is no longer topologically possible to delineate "the extra plate." A fault circuit which either closes on itself or passes out of the specimen still occurs although it no longer will be coplanar with the lamellae. In fact, it is usually not even Planar even if the lamellae are. Under these conditions a concept that a specimen contains N extra platelets of a given size per unit volume would be very artificial and consequently meaningless. Therefore, because of the topological complexity of the alloys, it was deemed necessary to define one-dimensional

Jan 1, 1962

By Stanley L. Lopata, Eric B. Kula

The problem of preferred orientation has been considered in quantitative phase analysis by X-ray diffraction techniques. The average intensity of a diffraction peak can be obtained by integration over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. For rod or wire, where the pole figure shows rotational symmetry, the intensity is measured along a radius of the pole figure. Where no symmetry is present, rotational symmetry is imparted by rapid rotation of the sheet around its surface normal during measurement. These methods are applied to the determination of aus-tenite in an Fe-31 pct Ni rod and Fe-28 pct Ni sheet. X-RAY diffraction techniques are frequently used for quantitatively determining the relative amounts of two or more phases present in a structure.1,2 Briefly, the method requires a measurement of the intensity of a Bragg reflection for each phase. The method is based on the principle that the intensity of a Bragg reflection, IA, is directly proportional to the volume fraction of the given phase present, CA: T KRACA/2µ [1] where K is a constant independent of the diffracting phase, RA can be calculated and depends on the Bragg angle ? and the particular reflection measured, and µ is the linear absorption coefficient of the mixture.&apos; For a mixture of two phases A and B, IA = RAcA [2] IA/IB=RAcA/Rbcb and CA+ CB = 1 [3] This allows the volume fraction of a phase to be calculated directly from the measured integrated intensities of the two phases present. This method is frequently used for quantitatively determining retained austenite in steels, but can be used for the quantitative determination of in titanium alloys, as well as phases in other alloy systems. The intensities are generally measured by diffracting only from planes whose normals are perpendicular to the specimen surface, with the implicit assumption being made that this intensity is typical of reflections from planes whose normals lie at other angles to the surface. If the specimen contains a texture or preferred orientation of the crys- tallographic planes by virtue of previous mechanical working, however, this measured intensity is correct only if the intensity level fortuitously is one times random. Examination of pole figures for actual rolled sheet shows that the intensity level at the center of the figure is seldom at the random level, and can very easily differ by a factor of five or more, leading to a commensurate error in the calculated amount of the phases. Textures have been commonly found in materials which are cold-rolled or recrystallized after cold rolling. This problem is becoming of greater importance since structural materials in use today, such as the high-strength stainless steels, frequently are further strengthened by cold rolling, and hence contain textures. Although high-strength carbon-containing alloy steels generally do not contain textures, some of the newer thermomechani-cal treatments will impart a texture even in these cases. In the case of hexagonal metals, such as titanium, probably every wrought sample will show some anisotropy. Since the standard X-ray techniques are inapplicable in all these cases, there is a clear need for some method of taking this anisotropy into account. The specific problem is to obtain the integrated intensity of a Bragg reflection for each phase, averaged over all orientations of the sample with respect to the X-ray beam. This can be done either by purely mechanical means or by a mathematical averaging. Mechanically, a small spherical speci-

Jan 1, 1965