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By M. J. Pool, J. R. Guadagno

THE relative partial molar heats of solution in liquid tin have been determined for phosphorous, arsenic, and antimony at 750°K. This work was carried out as part of an over-all program to determine the heats of formation of the III-V semiconducting compounds. A differential twin-type liquid tin solution calorimeter was used in the investigation. All three elements are endothermic upon solution in tin. The relative partial molar heats of solution go through a minimum value at arsenic. No concentration dependence of the heat of solution was found in the dilute (0 to 2 at. pct solute) solution range investigated. The measured heat effects and the calculated relative partial molar heats of solution at infinite dilution are listed in Table I along with the relative heat contents of the solutes calculated from the data of kelley.1 All of the values are referred to 750°K even though the calorimeter temperature fluctuated by *1°K during the course of the experiments. In this range of temperature change no variations were found which were outside the experimental error. This would be expected since the partial molar heat of solution is in general a very insensitive function of temperature. The limits of error given in Table I represent the standard deviation from the mean. The reported error estimates only apply to the estimated precision of the data and not the accuracy. Systematic errors could be present which would affect the absolute values given. This is especially true in the case of phosphorous and arsenic where vaporization could occur. If this were true, the experimental values reported here would be too high and the true partial molar heat of solution would be less than that given in Table I. Moreover, the heat-content data could be in error and this would also affect the calculated values. The relative partial molar heat of solution of phosphorous at infinite dilution in liquid tin is given in Table I. This value is based on eight drops at

Jan 1, 1965

By H. Guyod

The response of the Guard Electrode sonde (LL3) and the Laterolog (LL7) can be mathematically computed only for cases that do not represent realistic conditions. A resistance network analogue that simulates a number of typical—although idealized—formations was used instead to obtain, for both devices, a large number of resistivity logs and current distribution maps. From these data, charts were prepared for estimating true resistivities under a number of conditions. Some of these charts and current distribution maps are presented. INTRODUCTION Two main benefits are expected from a resistivity log: (1) obtaining geological information for mapping and other purposes, and (2) obtaining petrophysical data, based on true rock resistivity. The geological information can be derived from any resistivity curve having sufficient vertical detail, but true rock resistivities frequently are difficult to determine with desired accuracy because we do not have sufficient interpretation data. This is particularly true for the records given by the Laterolog tools. The object of this paper is to throw some light on the factors affecting the responses of these tools so that better resistivity data can be obtained from Laterologs. LATEROLOGS Laterolog measuring systems are of two types: the LL3 sonde, frequently called "Guard", and the LL7 sonde. Both measure the resistance between a single exploring electrode placed in the borehole and a faraway return electrode whose influence will be assumed here to be negligible. Although the principles of these tools have already been outlined,1-3 it is desirable to review them briefly in this article. LL3 Fig. 1, left side, represents a long cylindrical, vertical current electrode placed in a medium of uniform resistivity. The current leaving the center section of the electrode flows essentially along horizontal lines, delineating a surface having the shape of a biconcave lens. It is the elec- trical resistance offered to this particular group of current lines that is measured by the Guard tool. This is done in practice by having a long cylindrical electrode consisting of three sections physically and electrically separated by thin insulating washers, as shown in the center of the figure, and keeping the three sections at the same potential. It is obvious, for all practical purposes, that the current and potential distributions about this electrode are the same, as if we had a continuous electrode of same dimensions. Because the three sections are electrically separated, the resistance seen by the center section E can be independently measured. This section will be called the exploring electrbde, or E electrode. Its height generally is from a few inches to 1 ft. The outer sections are the guards G, which are several feet long. The combined length of the three sections is from 10 to 12 ft for the tools currently used in the petroleum industry. Let V denote the potential difference between E and the faraway return electrode, and I be the current flowing between these two electrodes. The resistance (Re) seen by the exploring electrode is VII, and the corresponding apparent resistivity is Ra = k(Re),............(1) where k is the tool calibration factor. The previous description establishes that the Guard tool uses that central portion of the sonde from which, in a uniform medium, the current follows essentially horizontal paths. When the formation being logged is fairly uniform, and when its resistivity is of the same order as

Jan 1, 1965

By L. Burris, G. A. Bennett, P. A. Nelson

Staznless steels ave rrzuch less seuel-ely attacketl by zinc lapov than by molten zinc systems. To determine the applicubility of stainless steels fov equipment items which would be exposed only to zinc vapor, the corvosion resistance of several stainless steels to zinc vapor was investigated in 500-hr- exposuves at 900° C. Two austenilic stainless steels, Types 304 and 3-17, suffered severe intergranular attack. Loss of nickel from these steels and micro-probe crnalyses indicated the probable formation of low-melting zinc-rich phases. Good vesistance to attack by zinc vapor, as determined by metallo-9-rpaphic excr)rtination and physical testing, Loas exhibited by Type 405 stainless steel, a jevvitic steel. Type 440C stainless steel, a tnartensitic steel, although suffering considevable loss in weight, was not structurally weakened. At Argonne National Laboratory liquid zinc and zinc-rich alloys are being employed as solvent media in pyrometallurgical processes under development for recovering and purifying discharged reactor-fuel materials.' Because of the high solubility of most metals in liquid zinc,' there are few metals which can serve as container materials for liquid zinc at temperatures much above the melting point. The poor corrosion resistance of the common metals and alloys to molten zinc has been discussed by Eldred.3 DeKany, Lavendel, and Burris4 tested some of the less-common alloys of the nonrefractory metals and found that they also have poor resistance to attack by liquid zinc and Zn-Mg solutions. Of the metallic materials, only some of the refractory metals such as tantalum, tungsten, and molybdenum and their alloys have shown resistance to attack by liquid zinc.4-7 In the process-development work at Argonne National Laboratory, tantalum and tungsten vessels have been used to hold liquid-zinc alloys. These vessels are housed in stainless-steel equipment, principally to permit maintenance of an inert atmosphere and operation at various pressures. In this experimental work, it has often been observed that Type 304 stainless steel suffers little attack by zinc vapor at temperatures up to about 800 °C. In contrast, severe attack occurs in areas where zinc condenses as a liquid. The extent of attack by zinc vapor on several stainless steels was investigated because there are possible useful applications of stainless steel for equipment items which would be exposed only to attack by zinc vapor. These applications include, for example, housings around processing equipment as indicated above and vapor lines leading from zinc stillpots or retorts to condensers. EXPERIMENTAL EQUIPMENT AND PROCEDURE The experimental procedure consisted in exposing stainless-steel test coupons to static zinc vapor for 500 hr at a temperature of about 900°C. The apparatus, shown in Fig. 1, consisted of a 12-in.-long closed tantalum tube jacketed in Type 304 stainless steel to prevent oxidation of the tantalum. A Zn-10 wtpct Mg* alloy charge of 293 g in the bottom of the

Jan 1, 1965

By P. W. Bennett, E. M. Elkin

A new technique for the recovery of palladium and platinum and sludge from go12 electrolyte eliminates many of the drawbacks of the zinc-dust cementation process. In the electrolytic refining of gold by the Wohwill method, the electrolyte contains about 100 gpl gold as AuCl, and 100 gpl free hydrochloric acid. Any palladium and platinum contained in impure gold dissolve and accumulate in the electrolyte. When their concentration approaches that of gold, it becomes desirable to discard the electrolyte and to recover the gold and the palladium and platinum. As practiced at Canadian Copper Refiners until recently, discarded electrolyte was treated with sulfur dioxide to precipitate the gold. 2AuCl3 + 6H2O + 3SO2 —2Au + 6HC1 + 3H2SO4 The gold precipitate was filtered off, washed with water, and melted with scrap anodes. The wash water was added to the gold-free filtrate and treated with zinc dust to cement the palladium and platinum. PdCl2 + Zn — Pd + ZnCl2 PtCl4 + 2Zn—Pt + 2ZnCl2 The precipitate was separated and sold as Pd-Pt concentrate, and the barren filtrate and wash water were discarded. The receipts of palladium and platinum at this company were too small to warrant their refining. The process suffered from a number of disadvantages. Handling the gold-free solution was disagreeable, as it was laden with sulfur dioxide even after blowing with air overnight. Subsequent treatment with zinc dust was also troublesome. A large excess of zinc dust was required. Spray, acid mist, and vigorous evolution of hydrogen accompanied the reaction. The Pd-Pt precipitate was grossly contaminated with occluded unreacted zinc and with yellow granules of sulfur, thought to be formed by the reduction of sulfur dioxide and its derivatives. Repeated boiling of the precipitate with hydrochloric acid and washing with water decreased somewhat, but did not eliminate, the zinc. After drying overnight, the precipitate hardened to a clinkerlike mass that was difficult to grind. Grinding, handling, and packing created heavy dusting. Even weighing in an analytical balance generated dust, indicating that the powder was easily charged with static electricity. The total palladium and platinum content of the powder varied from 56 to 72 pct, with an average of 65 pct. The powder dissolved in aqua regia with difficulty, leaving a small amount of insoluble residue. However, the main drawback of the process was the strongly hygroscopic Pd-Pt product. The powder showed a marked though erratic increase in weight and a corresponding decrease in assay on exposure to air, even during the course of laboratory analysis. Such changes were the source of disagreement between Canadian Copper Refiners and the buyers of concentrate. The cause of the change in weight is believed to be hydrogen, liberated by the action of zinc dust on hydrochloric acid. Some of this hydrogen was adsorbed so strongly by the precipitate that it could not be driven off during the drying. On exposure to air it oxidized catalytically, forming water. Experiments soon showed that the entire process of treatment of discarded electrolyte then in use would have to be changed. A small quantity of apparatus was moved into the gold room, and experimentation was held to a minimum compatible with the development of a new process. PALLADIUM AND PLATINUM PRECIPITATION It was thought that zinc could be replaced with a reagent other than a hydrogen-evolving metal. Semiquantitative experiments showed that platinum and palladium could be precipitated completely from the gold-free solutions with such well-known reagents as sodium formate, formic acid, formaldehyde, and paraformaldehyde. Sodium formate was the preferred reagent, since the other three are volatile and somewhat toxic. The gold-free solutions used were those saturated with sulfur dioxide, partly freed of sulfur dioxide by aerating overnight, completely freed by boiling, as well as strongly and weakly acidic, neutral, and alkaline solutions. The reactions are complex and can be represented by these over-all equations: PdC1, + HCOONa — Pd + NaCl + HC1 + Co2 PtCl4 + 2HCOONa — Pt + 2NaCl + 2HC1 + 2CCX, Strongly acidic solutions required as much as five times the theoretical amount of sodium formate as did solutions neutralized to pH 4.5. Increasing the pH decreased the consumption of

Jan 1, 1965

By F. O. Jones

The capabilities of small proportions of divalent cations, such as calcium or magnesium, for controlling clay blocking are reported. Potentially sensitive formations can be exposed to fresh water if at least one-tenth of the salts dissolved in both the native water and invading fresh water are calcium and magnesium salts. Often, even less suffices. The behavior evidently depends upon the cation exchange properties of the clays, which favor adsorption of calcium and magnesium over sodium. Clays having sufficient adsorbed calcium and magnesium resist dispersion by water and consequent blocking of permeability. An allied phenomenon, the dependency of clay blocking on salinity contrast, is also reported. Abrupt change from highly saline to fresh water can cause blocking which may not occur if salinity is lowered slowly. A process related to osmosis is thought responsible for this behavior. Applications of findings to drilling, fracturing and water flooding are discussed. INTRODUCTION Many formations, when exposed to fresh water, can lose permeability through clay effects.',' For example, drilling-mud filtrate can cause oil permeability decreases, which persist long enough to interfere with drill-stem testing and well completion.3 Ultimate productivity may suffer when clay damage is severe, especially if drawdown pressures are low.' The injection pressures and the time required for water flooding can increase if clay blocking occurs. Earlier work indicates that clay blocking is caused by obstruction of flow channels by clays or other mineral fines dispersed by fresh water.'!" It is well known that increasing salt concentrations in water tends to prevent clay blocking. Also it is well established, although perhaps not as widely known, that the nature of the dissolved solids is also important. If, for instance, formation clays are exposed to calcium chloride solution and then exposed to weaker solutions of calcium chloride or distilled water, considerably less permeability damage results than if the clays had been exposed instead to sodium chloride solutions. The reasons for this behavior are: (1) clays are cation-exchange, or base-exchange, materials similar in this respect to zeolites or exchange resins, and (2) clays in the calcium form do not disperse easily in fresh water, whereas clays in the sodium form do. The base-exchange form of a clay is easily altered by flowing a solution through it. For example, a sodium clay can be changed to a calcium clay simply by passing a calcium chloride solution through the clay bed. There is general agreement that the reason calcium and magnesium clays do not disperse easily in fresh water is because the calcium ions do not ionize easily from the clay surfaces.' Sodium clays, however, are believed to allow the sodium ions to ionize from the clay particle surfaces. In fresh water, this allows the particle to accumulate a net negative electrical charge great enough for the particles to repel one another and, therefore, disperse more easily. The foregoing suggests that, even in the presence of a large excess of sodium, a relatively small ratio of divalent cation, such as calcium or magnesium, might serve to prevent clay dispersion. The divalent ion probably adsorbs to a disproportionately large extent, because of being adsorbed more tightly, with the result that the proportion of divalent cation on the exchange positions of the clay might then be great enough for the clays to resist dispersion. Consequently, an investigation was conducted to find how mixtures of salts in solution influence clay blocking. APPARATUS AND PROCEDURE Water permeability tests were conducted using conventional techniques. The equipment is illustrated schematically in Fig. 1. Flow rates of solutions driven through small core samples at known temperatures and pressures were measured. Regulated compressed air, usually at 10 to 15 psig, was used to drive the solutions. Core samples 0.75 in. in diameter and 1 in. long were used for the most part. Cores were saturated by evacuating and then admitting a de-aerated solution. Tight core samples were first saturated with carbon dioxide gas and then evacuated and saturated with the test solution. After saturation, 140 psig pressure was imposed for several hours. Cores were tested to insure absence of gas saturation by a Boyle's

Jan 1, 1965

By J. E. Sandor, P. F. Schmidt

A general review of the present knowledge of the semiconductor/oxide interface is given, with emphasis on silicon and germanium. The electrical properties of clean surfaces and the changes that occur upon oxidation are described. A brief disczcssion of the methods and mechanisms of oxidation of silicon is given, and the interaction between the semiconductor substrate and the oxide phase is considered. Physical properties of the oxide film, charge storage effects due to the dielectric, and some device applications of oxide films on semiconductors are discussed. THIS paper will be heavily preoccupied with the elemental semiconductors germanium and silicon. Undoubtedly some injustice is done thereby to other semiconductor-oxide systems, but it is not readily possible to cover all aspects of so vast a field in the present review. In considering the semiconductor/oxide interface, we may start out by discussing briefly an idealized clean semiconductor surface, and may then follow the changes brought about by oxidation, as the oxide is allowed to grow progressively thicker. The references given are not a complete list, but are to be taken as guides to the literature. Tamml suggested in 1933, based upon the study of a one-dimensional asymmetrical potential model, that localized surface states may appear at the surface of a crystalline lattice; it was pointed out by Fowler that these states should occur in pairs. shockley3 examined the origin of such surface states on the basis of a more general one-dimensional model and found that surface states may appear in the forbidden region between the highest filled and the lowest vacant band. This happens when the two bands overlap, as, for instance, the "s" and ('p" bands of the diamond structure. In a three-dimensional model these levels would produce a surface band which is half-filled for diamond, and the number of surface states should be approximately equal to the number of surface atoms. This picture of the surface has been refined by more recent theoretical work, like Handler's4 and Koutecky and Tomasek's~ without introducing essential modifications. When these concepts were applied to semiconduc-

Jan 1, 1965

By J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young's modulus and a value of approximately 0.5 for Poisson's ratio. A value of % for Poison's ratio with finite Young's modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By P. R. Gage, R. W. Bartlett

At high temperatues and reduced oxygen pressuves, molybdenum silicicles oxidize to form SiO(g) vathev than a passivating SiO2 film. This is a sevious problem for low-pressure applications of sili-cide-coated rejvactory tnetals. As oxiclalion pvoceeds, the higher oxidntion potential of silicon initially suppresses oxidation of molybdenum and silicon is depleted near the surface. Eventually, silicon depletion causes secondary passivation (SiO2) mid an active to passiue transition in oxidntion behavior at moderately low pressures. At very low pressures, silicon depletion continues until steady-state oxidation of both silicon and rnolyhdenum can proceed at rates propovtional to their initial stoicliiorrzetvies. Ohsel-vations of 'oxidatiou-rate belzcriliov at temperatures from 1101° to 1700°C and oxygen pressures from 10-7 to 1 at in were made using thermogravimetn'c, X-ray diffraction, and elect?*on-rtric?ro/,vobe techniqrres. The experimental results are in good agreement with calculated lirnits for the various types of behavior that were based on tlievtnochernicnl atzd dffusion rate data for the Mo-Si system. A protective oxide film normally forms during the oxidation of elemental silicon. However, at elevated temperatures and reduced pressures this film is not present and oxidation is rapid. wagnerl has shown that this behavior occurs because SiO(g) is more stable than SiO2. The behavior of the silicides at high temperatures is similar but more complicated. Molybdenum and several silicide compounds are involved and the chemical activity of silicon, or the equivalent silicon vapor pressure, can vary considerably in these phases. Also, diffusion in the silicides resulting from reactions in which a higher silicide is reduced to a lower silicide, or molybdenum containing dissolved silicon, must be considered. EXPERIMENTAL AND ANALYTICAL METHODS Isothermal oxidation experiments were conducted using hot-pressed MoSi2 and Mo5Si3 wafers. Each experiment was conducted at a fixed oxygen pressure by controlling the flow of oxygen in and out of the furnace chamber. Most of the experiments were conducted in a molybdenum-wound tube furnace. Special construction features, including use of a high-purity dense A12O3 refractory tube, permitted operation in high vacuum to 1500°C. Higher temperatures could be obtained at higher working pressures and with a sacrifice of tube lifetime. Temperature was measured with three Pt 6 pct Rh/Pt 30 pct Rh thermocouples and controlled with a proportional controller. Weight changes were monitored with a quartz spring balance. The few experiments, at higher temperatures and low pressures, were conducted in a cold wall vacuum chamber using induction heating with direct susceptance of the sample. Because of the variable levitation effect of the induction coil on the sample, weight changes could not be monitored continuously in these experiments. All samples representing both experimental methods were weighed before and after oxidiation and examined with a microscope and analyzed by X-ray diffraction. The analytical treatment assumes equilibrium at interfaces and uses existing thermodynamic data. For convenience, equilibria are expressed as chemical potentials or as vapor pressures of the gases involved. The resulting differences in equilibrium vapor pressure between adjacent interfaces and between the surface and external atmosphere drive diffusion processes in the solid and gas boundary film, respectively. These diffusion processes govern the rate of oxidation. A bibliography of the sources of thermochemical data for the reactions pertinent to the Mo-Si-O system is given in Table I. Reactions are listed with the sources of free-energy data referenced. Since all of these reactions involve one or more gas species, usually oxygen, a plot of the product-gas chemical potential, -RT In Pg, vs absolute temperature for each reaction is given in Fig. 1. These curves can be used to determine equilibrium vapor pressures or to compare the stability of different compounds in the various gases: O2, Si, SiO, and Moo3,. The data of Table I and Fig. 1 were used to determine the analytical results presented in this paper. EXPERIMENTAL RESULTS The weight changes for three MoSi, samples oxidized at 1500°C are plotted against time in Fig. 2. The treatments were identical except for the indicated variance of oxygen pressure and each curve represents one of three characteristic types of behavior that were observed. The upper curve is an example of passive oxidation, which is defined as

Jan 1, 1965

By Y. C. Liu, R. H. Richman

From rolling textures of polycrystalline AgCl determined as a function of temperature, changes in the amounts of the individual textural components are correlated with temperature-dependent changes in glide geometry. The preferred orientations are influenced by the slip behavior as follows: 1) pencil glide, characterized by (110) slip directions and a greater participation in the deformation the higher the temperature, leads to a(012) fiber texture; 2) low-temperature deformation, primarily on (110) (110) systems, generates the {237}-(11, 9, 7) component; and 3) slip on {111}(110), comprising a significant portion of the room-temperature deformation, generates the {135}(211) and {110}(112) components. Typical re crystallization textures are also presented and briefly discussed. SPECIFIC relations between flow mechanisms in crystals and the individual orientations or components in deformation textures are necessary for a thorough understanding of the origin of such textures. Within each ordinary class of crystal struc- tures there is insufficient variety in the observed preferred orientations to permit direct and unambiguous correlation between flow mechanism and texture. A second approach to this problem is the correlation of textural changes with some known variation in glide geometry within one substance,1 In this paper, the latter approach is applied directly to a material in which there are distinct changes in the character of glide with changes in temperature. Silver chloride, although a nonmetal, is reported to exhibit slip,2,3 fiber textures,4 and rolling textures5,6 crystallographically similar to those of the well-studied fcc metals;7,8 in addition, there is a marked temperature sensitivity of the glide planes upon which flow occurs.3 Previous investigations of textures in AgCl unfortunately did not employ methods sufficiently sensitive to define possibly important minor components in the texture, nor did they utilize the temperature dependence of the glide systems. Thus, in order to clarify the effects of changes in slip mechanism, this paper reports a survey, using semiquantitative methods, of preferred orientations in rolled AgC1. Inasmuch as the influence of prior deformation texture upon preferred orientations after annealing is also of interest, some representative annealing textures are presented.

Jan 1, 1965

By W. B. Gogarty

The reported decreases in water mobility do not seem unusual in view of non-Newtonian fluid properties. Shear stress vs shear rate diagrams have been reported for other solutions of water-soluble polymers. Some of these polymers are similar to the type mentioned by the author. Generally, the shear stress-shear rate is a non-linear function for these solutions. Data for plotting apparent viscosity vs shear rate can be obtained from this function. Apparent viscosity is defined as the ratio of shear stress to shear rate at a given shear rate. When plotted, the apparent viscosity decreases with increasing shear rate. This behavior is typical of a pseudoplastic fluid. For some water-soluble polymer solutions, the apparent viscosity decreases more than 50 times while the shear rate increases 1,000 times. Thus, viscosity of a pseudoplastic fluid only has meaning at a specified shear rate. Results of Fig. 1 could be explained in these terms. Viscosities measured in the Ostwald viscometer represent values at a given shear rate. Some average shear rate is affecting the polymer solutions while flowing through the core. This average value fixes the apparent viscosity as long as the flow rate remains constant. Viscosities measured by the two methods will be equal if shear rates are the same. The results indicate that shear rate in the core is lower (higher apparent viscosity) than in the viscometer. In the paper by Johnson, Bossler and Naumann, the relative permeability is independent of viscosity ratio. Thus, the relative permeability with respect to water flow at residual oil should be independent of the flowing phase viscosity. Polymer solutions will appear as Newtonian fluids The discussion emphasizes the nature of the "resistance factor effect" as discussed in the paper. Repeated anomalies arising in hundreds of experiments led us to the conclusion that non-Newtonian flow is not the only factor. Several of the key anomalies are as follows: 1. Measured viscosities over a range of shear rates from <1 sec-&apos; to 1,000 sec-&apos; do not account for but a minor fraction of the R observed in cores when compared in similar shear-rate ranges. 2. The slope of R vs flow rates in cores is always different from that expected from viscometer shear-rate measurements as shown in Fig. 2. in a core, the level of viscosity being fixed at a given flow rate. With these conditions, the definition of resistance factor R by Eq. 2 is simplified to Since , is constant with rate, R becomes a measure of the apparent viscosity in a core at a given flow rate. Variation in flow rate could easily account for the changes of R shown in Fig. 5. Also, this points to the fallacy of assuming R to be a unique parameter. The constant resistance factors at different flooding velocities appear to be in disagreement with the above discussion. The author furnishes Fig. 2 to support his arguments. As shown, the resistance factors remained substantially constant in the two cores over a considerable range of flooding velocities. However, in the 73-md core, the factor increases at lower rates. This behavior agrees with known characteristics of some pseudoplastic material. These materials act both as Newtonian and as non-Newtonian fluids in different regions of shear rate. Some exhibit first Newtonian, then non-Newtonian, finally, Newtonian character. Others are first non-Newtonian and then Newtonian. This latter type would explain the results with the 73-md core. The Fann-instrument results are not significant since shear rates in the core may be much different than with the viscometer. The higher resistance factor at high rates in the 150-md core is more difficult to explain. The greater resistance at increased flow rates could be attributed to what might be termed temporary bridging. As envisioned, changes in polymer configuration occur at the higher energy associated with the increased flow rate. These changes could cause less effective passage of polymer through the core. Correspondingly, increases in pressure drop will occur. These will be interpreted as higher resistance factors. 3. Most polymer solutions are non-Newtonian and many are more shear-rate sensitive than the polymers in question, yet only a very few polymers demonstrate useful R values. Gogarty&apos;s assumption that viscosities in cores and vis-cometers will be the same if measured at the same shear rate is only valid if non-Newtonian rheology is the only parameter. The experimental evidence does not validate this assumption. The anomalies observed in the equilibrium displacement experiment shown in Fig. 5 are not explained on the basis of varying flow rates since the rates were held constant. M

Jan 1, 1965

By M. J. Pool

The partial molar heats of solution in liquid tin of cadmium, silver, tellurium, and zinc have been measured at 655°. 700°, and 750°K by liquid-metal solution calorimetry. Silver, cadmium, and zinc are endothermic at these temperatures while tellurium is exothermic. Only the heat of solution of silver depends on composition while all four elements show a temperature-de pendent heat of solution. The heat of solution of tellurium is constant up to 0.6 g-at. pct, becomes increasingly more exothermic, and reaches a limiting value at 1 g-at. pct Te. The limiting value has been used to calculate the heat of formation of SnTe at 750°K. The heat effects associated with the dissolution of the compounds Ag2 Te, CdTe, and ZnTe in liquid tin were measured at 750°K. These values are cotnOined with the measured hat effects at 750°Kfor silver, cadmium, tellurium, and zinc to detertrline the heats of formation of the telluride compounds. Cadmium lelluride exhibits a heat of dissolution which has a compositional dependence. THERE is a considerable amount of interest in the compounds of tellurium because of their electronic properties. Both cadmium and zinc tellurides are thermoelectric materials and considerable work has been done on their electronic properties but a limited amount of data is available on their ther-modynamic properties. This work was undertaken to elucidate the heat of formation data on cadmium and zinc telluride. Since both cadmium and zinc are in Group II it seemed to be of interest to compare the values obtained for them with the heat of formation of a Group I telluride. Silver telluride was selected for this comparison. In the course of the work it was also possible to determine the heat of formation of tin telluride and therefore to make a comparison of some of the Group I, 11, and lV tellurides with the metallic elements silver, cadmium, and tin being in the same period. There is also a great deal of interest in the energetic changes which occur upon addition of solute elements to a common solvent. This investigation provided an opportunity to study the partial molar heats of solution of silver, cadmium, tellurium, and zinc in liquid tin. The partial molar heats of solution are of theoretical interest because solute-solute interactions are a minimum in dilute solutions and application of solution models is simpli- fied. In order to complete the analysis of solute-solute and solute-solvent interactions the temperature dependence of the partial molar heats of solution was also measured. MATERIALS AND EXPERIMENTAL PROCEDURE All materials were of the highest purity available. The silver, zinc, cadmium, and tellurium were obtained from American Smelting and Refining Co. and were reported to be 99.999 pct pure. The silver telluride, zinc telluride, and cadmium telluride were obtained from Atomergic Chemetals Co., a division of Gallard-Schlesinger Chemical Manufacturing Corp., and were electronic-grade material of 99.999 pct purity. Tin used for the solvent bath and for calibration was obtained from the Vulcan Manufacturing Co. and was reported as being 99.99 pct pure. The liquid-tin solution calorimeter used in this work is similar in principle to the differential twin-type calorimeter described by K1eppa.l Two of three identical calorimeter wells are used together during any set of experiments, one well being active and the other being passive. The wells are positioned 120 deg apart in an aluminum calorimeter block. Each well contains a multijunction thermopile and a Pyrex test tube to hold the liquid metal bath. Forty-eight of the thermopile junctions are distributed over the surface of each calorimeter well adjacent to the test tube and serve to integrate the heat effects occurring. The other forty-eight are next to the aluminum calorimeter block. The thermopiles for the three wells are connected differentially so that any change in temperature at the outer junctions (which will be the same for both wells because of the high conductivity of the aluminum block) will oppose for the two wells and result in no shift of the zero. The electrical output represents the true temperature difference between the two reaction vessels. A reaction occurring in the active well gives a comparison with another body of very similar thermal properties. In this way, any spurious heat effects due to slight temperature drifts within the entire calorimeter block are eliminated. The output of the differential thermopile goes to a dc amplifier with multiple ranges of from * 10 pv to 1 30 mv. The output of the amplifier is then fed into a Leeds and Northrup strip-chart recorder. The adiabatic temperature change is then calculated using the technique of Howlett, Leach, Ticknor, and ever.&apos; The aluminum calorimeter block is contained in a cylindrical furnace with main and control heaters

Jan 1, 1965

By R. R. Joseph, K. A. Gschneidner

The solid solubility of magnesium in the close-packed modifications of lanthanum, cerium, praseodymium, neodymium, gadolinium, dysprosium, and lutetium was determined from approximately 250°C to the eutectoid temperature by the X-ray parametric technique. The maximum solubility at the eutectoid temperature was found to be 9.4 at. pet in La, 8.2 in Ce, 9.2 in Pr, 8.2 in Nd, 14.1 in Gd, 13.5 in Dy, and 11.5 in Lu. The solubility when compared at a homologous temperature was found to increase in a smooth manner with decreasing size factor from lanthanum to lutetium. It was found that the apparent atomic radius of magnesium when dissolved in the lanthanide solvent was constant and could be accounted for by consideration of several models dealing with departures from Vegard&apos;s law. The eutectoid temperatures for the lanthanide-rich La-Mg, Ce-Mg, and Nd-Mg systems were found to be 544", 505°, and 551°c, respectively. A study of the solid solubility of magnesium in the lanthanide metals was initiated because the valency and electron egativity difference are essentially constant and favorable for solid-solution formation, and thus one could examine the effect of size on terminal solid solutions. The size factors based on metal radii range from 14.6 pet for lanthanum to 7.5 pet for lutetium. Since the electronegativity difference is small, 0.06 unit or less, application of the Hume-~othery&apos; and Darken and Gurry2 criteria for solid-solution formation indicates that the solubility of magnesium would be expected to be small for lanthanum (between 5 and 10 at. pet) and to increase as we proceed along the lanthanide series. A search of the literature revealed no data on the solubility of magnesium in the lanthanide metals except for the solubility of magnesium in cerium at 450oCA typical phase diagram for the lanthanide-rich end of the lanthanide-magnesium phase diagram is shown in Fig. 1. EXPERIMENTAL PROCEDURES Preparation of Alloys. The lanthanide metals used in the preparation of alloys for this investigation were prepared from the corresponding fluoride by metallothermic reduction techniques previously described by Daane.4 The chemical analyses of the metals used are listed in Table I.

Jan 1, 1965

By R. E. Tate, L. J. Herman

We have had occasion to produce wire of Np-237 in small diameters for use in some chemical experiments. Since the mechanical metallurgy of neptunium has not been investigated extensively, it seems desirable to report our successful extrusion technique. Because of the neptunium activity and its attendant health hazard the experimental work was done in glove boxes and related equipment also used for Pu-239. At room temperature a phase neptunium&apos; is a hard (Dph -355) orthorhombic metal of high density (p = 20.45 g per cu cm). a neptunium transforms2 to tetragonal ß neptunium at about 280°C and this in turn transforms to bcc y neptunium at about 577°C. The y phase melts at about 637°C. A temperature of 340° to 345°C was selected for the extrusion, this temperature being a compromise be- tween a possible advantage of working with the presumably more plastic cubic y phase above 577°C and the risk of having the neptunium react with the alloy steel die to form the low-melting Fe-Np eutectic. A 0.75-in.-long, 0.26-in.-diameter ingot of good-purity* Np-237 was extruded by the direct *C = 230 ppm, Pu = 200 ppm, thirty-five metallic elements below limit of detection by spectrographic methods. process through flat-face orifices to form several sizes of wire ranging from 0.010 to 0.030 in. in diameter. Molybdenum disulfide was used as the die lubricant. The extrusion was done in a vacuum of about 10-4 torr to reduce reaction of the neptunium with atmospheric gases. British workers3 at Harwell have extruded neptunium under similar conditions. The force required to extrude 0.010-in.-diameter wire at the rate of 4 in. per min was 6000 lb, as measured with an electrical load cell. Wire 0.020 in. in diameter was extruded with a force of 4700 lb at a rate of 2 in. per min, and wire 0.030 in. in diameter was extruded with a force of 4000 lb at a rate of 1.3 in. per min. An extrusion constant, c, can be computed from the measured forces, P, for the equation4 P = c log-A/a where A/a is the extrusion ratio or the ratio of the cross-sectional areas of the container and the

Jan 1, 1965

By F. W. Osterwald, C. R. Dunrud

A continuously recording seismic network was constructed in 1962 by the U.S. Geological Survey to locate epicenters and record incidence of bumps (bounces, rock bursts) that occur in the bituminous coal mines of the Book Cliffs coal field near Sunny-side, Utah. The coal is mined because of its value as coking coal, although these bumps may be a hazard to life and property. Daily records of tremors caused by bumps for 1 3/4 years indicate that a seasonal pattern, as well as a daily pattern, exists for the number of bumps that occur in a given period. Maxima occur in May and June and November and December. Marked increases at 5-day to 9-day intervals are superimposed on these seasonal maxima. The largest bumps commonly occur during seasonal maxima when the rate of occurrence suddenly decreases and the amplitude of the individual bumps increases. Knowledge of this pattern may lead to prediction of general locations and periods of increased hazard from bumps. Experience to date has shown that prediction of precise times and locations of hazardous bumps is not possible, and may never be; primarily because even a small bump can be a hazard to life and property. Some bumps or bump sequences are actually composites, consisting or two or more discrete bumps a few tenths of a second to a few seconds apart. Violent and spontaneous releases of coal and rock from faces, ribs and roofs of mines (termed bumps or bounces by miners) are a common hazard to life and property in the coal mines located in the Book Cliffs near Sunnyside, Utah (Fig. 1). These bumps

Jan 1, 1965

Jan 1, 1965

By B. Ramaswami, U. F. Kocks, B. Chalmers

The latent hardening of silver and an Ag-Au alloy was investigated by lateral compression, overshoot in tension and cormpression, and the stability of multiple-slib orientations. The latent hardening of a secondary slip systenz depends on its relation to the primary slip system. For most secondary slip systems the latent hardening is larger for Ag-10 at. pct Au than for pure silver. The maximum increase in. flow stress on a secondary slip system over that of the primary slip system was 40 pct. The work hardening during the lateral-compression test on the latent system after prestress on the primary system is iuterbreted in terms of the preferential distribution of barriers to dislocation movement with respect to the active slip system in work-lzardened fcc crystals. The work-hardening in fcc crystals is mainly due to the dislocation interactions and the barriers to dislocation movement formed as a result of reactions between dislocations of different slip systems. The operation of sources on the latent system depends on the flow stress of those systems; hence, the increase in flow stress of a latent system due to glide on an active system, which is called latent hardening, is an important element in understanding the phenomenon of work hardening. The problem of latent hardening has attracted the attention of many investigators in the past. For example, a theoretical study of the elastic latent hardening of the latent systems due to glide on an operative system has been made by Haasen&apos; and ~troh. These calculations, however, neglect the stress required for the intersection of forest dislocations by the glide dislocations, a factor which would be important for producing macroscopic strains on the secondary slip systems. The importance of this factor will become evident from the results presented here. Attempts have also been made to determine the latent hardening of different slip systems by experimental means by the methods summarized in Table I.3-9 The experimental methods used have been subject to certain limitations. For instance, in the method used by Hauser,9 frictional constraints between the specimen and the compression platen were not eliminated by proper lubrication (see Hos- ford10). Secondly, with the exception of Kocks,6 Hauser,9 and Rohm and Kochendorfer,11 latent-hardening studies have been made on only one of the slip systems, i.e., on either the conjugate or the coplanar slip system; hence, extensive results are not available on the latent hardening of different slip systems in the same materials, with the exception of aluminum.6 It was therefore decided to study the latent hardening of the conjugate, critical and half-related slip systems in silver. Similar experiments were done in Ag-10 at. pct Au to study the effect of solute (gold) on the latent hardening of silver. Lastly, indirect evidence can be obtained by a study of the orientation stability of crystals of multiple-slip orientations in tension and compression. This method has been used by Kocks6 to supplement his studies of latent hardening in aluminum. Similar studies were made at room temperature in single crystals of silver. EXPERIMENTAL PROCEDURE The single crystals of the desired orientations were grown and the tensile test specimens were prepared as described in Ref. 12. The compression tests were made on 1/4-in.-cube specimens. The specimens were cut from single crystals, in the Servomet spark-erosion machine.13 The two cut surfaces were planed using the lowest available planing rate in the machine to minimize the deformation layer. A brass strip was used as the planing tool. This method of preparation ensured plane parallel faces for the compression tests. The deformed material was removed by prolonged etching in a weak etching solution. A weak etching solution was used to prevent pitting of the surfaces and to ensure uniform etching. About 25 to 50 µ of material were removed from all faces by the etching treatment. The specimens were then annealed for 24 hr at 940°C in oxygen-free helium and cooled in the furnace to room temperature over a period of 7 hr. After annealing, the orientation of the specimens was determined by Laue back-reflection technique to make sure that no recrystallization had occurred on annealing. The compression-test technique and setup are described in Ref. 14. The Laue back-reflection technique was used to study the overshoot in tension, the overshoot in compression, and the stability of the axial orientation in tension and compression. The tests were interrupted after every few percent strain to determine the axial orientation. In investigating the overshoot in compression, the operative system was determined by studying the asterism of the Laue spots.

Jan 1, 1965

By R. W. Hertzberg, F. D. Lemkey, J. A. Ford

The technique of unidirectional solidification has been applied to the A1-AI3Ni and A1-CuAl2 ezltectic alloy systems; the controlled microstructure of A1-A3Ni consists of parallel A13Ni whiskers emhedded in an aluminum matrix while the Al-CuAl2, system solidifies as parallel alternate lamellae of aluminm and CuAl2. Mechanical tests (tension and flexure) have shown that the particle-matrix interface bond formed during unidirectional solidification allowes for efficient load transfer from the matrix to the reinforcing phase. Strength and fracture characterstics of the alloys were studied as a function of phase orientation; the tensile strength of controlled Al-Al3Ni samples was 43,000 psi (three times greater than that of as-cast specime~s). The strength of the Al-CIA2, cutectic was studied as a function of lamellae-flexure stress-axis orientation using a microbend apparatus. A twofold increase in outer fiber stress was observed as the lamellae were rotated from a position of no reinforcing (perpendicular to the stress axis) to one of maximum reinforcing (parallel to the stress axis), The brittle reinforcing constituent in each alloy (A13Ni and CuAl2) was observed to he the nucleating phase for fracture. It is to be concluded from this investigation that unidirectionally solidified eutectic alloys have a potential use as reinforcing coniposite) materials. In a recent review article, Chadwick1 has described the work of many investigators in the area of controlled solidification of binary eutectic alloys. Thus far, more than twenty eutectic alloys have been unidirectionally solidified to produce structures consisting of two phases in the form of alternating lamellae or as whiskers embedded within a continuous matrix; in either case, the phases are aligned parallel to the growth direction. In particular, Kraft and Albright2 have shown that the Al-CuA1, eutectic alloy exhibits a lamellar microstruc- ture as a result of unidirectional solidification while Lemkey, Hertzberg, and Ford3 have studied the A13Ni whisker-aluminum matrix morphology in the A1-A13Ni system. Whether these alloys could exhibit reinforcing behavior would have to depend upon the strength and volume fraction of the reinforcing phase (AI3Ni and CuA12) and the nature of the bond between the reinforcing phase and the matrix. Hertzberg and Kraft4 have shown that the interface bond between chromium whiskers and a copper matrix in unidirectionally solidified Cu-Cr is particularly good while Lemkey and Kraft5 have reported chromium-whisker tensile strengths in excess of 1,000,000 psi. However, with the chromium volume fraction being less than 2 pct, no reinforcing behavior was displayed by the Cu-Cr alloy.6 In view of the encouraging results concerning the good interfacial bond and high strength of the reinforcing phase in the Cu-Cr system and preliminary mechanical test data reported by Lemkey et al.3 for the A1-A13Ni system, the A1-CuA1, and A1-A13Ni eutectic alloys containing 50 and 10 vol pct, respectively, of the reinforcing phase give promise of possessing mechanical reinforcing behavior. Based on this premise, the objective of the investigation was to study the strength and fracture behavior exhibited by these anisotropic microstructures. EXPERIMENTAL PROCEDURE Controlled Solidification Procedure. An extensive description of the technique of unidirectional solidification has been presented elsewhere.&apos; However, the pertinent details for each eutectic system studied are discussed below. Al-A13Ni System. Several master heats of this alloy were prepared by vacuum-induction melting in an A12O3crucible and casting in SiO2 mold or by induction melting in alumina crucibles under argon. The initial heats were prepared from 99.99 pct A1 and 99.99+ pct Ni, while later heats used 99.999+ pct A1 and 99.99+ pct Ni. Specimens of these master heats were unidirectionally solidified using induction and resistance heating sources and argon atmospheres at growth rates from 1.1 to 28.7 cm per hr. The thermal gradients in the liquid were controlled in the range of 26" to 36°C per cm for these runs. Al-CuA12 System. The master heat and controlled

Jan 1, 1965

By D. S. Tomalin, D. F. Stein

The effect of reducing oxygen to low concentrations on the fracture of high-purity iron single crystals has been examined at 78° and 20°K. It is found that iron single crystals grown by the strain-anneal method usually contain a few occluded grain boundaries which may become embittled in the presence of oxygen, thereby nucleating cleavage fractures. High purity with respect to interstitial elements was found to inhibit twinning and evidence is presented for an orientation dependence of the resolved yield stress. Deformation occurred by slip rather than twinning at both temperatures of testing with elongations of as much as 9 pct at 20°K. THE fracture properties of iron single crystals have been observedl-3 to be a function of temperature, orientation, and purity. Allen, Hopkins, and McLennan1 demonstrated that at 78°K iron single crystals became increasingly brittle as the tensile axis approached the (001) pole of the stereographic unit triangle. Iron crystals with the tension axis near a (001) pole were completely brittle and orientations near the (011)-(111) boundary were very ductile, achieving a 100 pct reduction in area prior to fracture. Later work of Biggs and pratt2 and of Edmondson3 demonstrated that by reducing the carbon content of the single crystals the transition between brittle and ductile failure at 78°K could be shifted to orientations nearer the (001) pole. Ed-mondson went further and pointed out that any mechanism which tended to increase the yield strength of the iron (i.e., carbon addition, pre-strain) also increased the tendency for brittle behavior at 78°K. Thus by a reduction of carbon content Biggs and Pratt were able to obtain ductile behavior to within 20 deg of the (001) pole, and Ed-mondson was able to obtain ductile behavior to within 26 deg of the (001) pole. Edmondson&apos;s material had a total interstitial content (carbon, oxygen, and nitrogen) of approximately 60 ppm and, although Biggs and Pratt reported no analysis, indications were that their iron contained comparable impurities. Stein, Low, and seybolt4 purified iron single crystals to a total carbon, oxygen, and nitrogen content of approximately 20 ppm. They observed a lowering of the yield stress with this increased purity, and thus one might have expected an observation of increased ductility. Although they tested specimens of orientations which the previous workers had indicated should be ductile, the crystals failed at a 78°K in a brittle manner with little elongation. Stein noted,&apos; however, that about 90 pet of the failures could be traced in origin to occluded grains. Allen et al.1 and Edmondson3 do not report examination of their cleavage surfaces, but Biggs and pratt2 reported that microscopic examination of the cleavage surfaces of many of their specimens revealed the presence of small occluded grains. Honda and cohen6 and Keh7 have also observed the initiation of fracture at occluded grains in iron single crystals. Therefore, the additional complication of occluded grains must be considered in studying the properties of iron single crystals and the origin of fractures determined if the ductility exhibited by the crystals is to be considered meaningful. Various investigators8-12 have studied the effects of impurities on grain boundaries in high-purity polycrystalline iron. Rees and Hopkins10 showed that the addition of oxygen to low-carbon (0.002 pet) iron weakened the grain boundaries, causing a shift from transcrystalline to intercrystalline fracture and a progressive decrease on the brittle-fracture stress with increasing oxygen content. In addition, it has been shown by Low and Feustel11 that the addition of carbon to polycrystalline iron containing oxygen eliminated grain boundary brittleness. Thus, oxygen can embrittle grain boundaries in high-purity polycrystalline iron, but the addition of an appropriate amount of carbon can eliminate the oxygen-induced brittleness. The oxygen content (19 ppm) of the iron "single crystals" employed by Stein el al. was large enough to suspect impurity effects at the occluded grain boundaries. Allen et al.1 Biggs and pratt,2 and Edmondson3 may have masked any occluded grain problem in their specimens considering the relatively high carbon levels they employed. stein13 demonstrated that the addition of as little as 0.9 ppm C to previously purified (less than 5 x 10-3 ppm C) "single crystals" would increase the elongation from a few percent to more than 20 pet at 78°K and the fracture was not associated with grade boundary initiation.

Jan 1, 1965

By P. M. Kelly

TWO analytical methods for calculating the positions of matrix and twin reflections on electron-diffraction patterns of a twinned cubic crystal have recently been published.1,2 Meieran and Richman1 considered the case of twinning on (1 12) in a bcc structure, while a more general treatment, capable of analyzing twinning on any plane in a cubic crystal, was developed by Johari and Thomas.2 The latter authors applied their general rotation matrix to both (111) twinning in face-centered crystals and {112} twinning in body-centered crystals and they derived separate expressions for these two cases. This separate treatment masks the fact that in a holosymmetric cubic crystal a (111) twin is crys-tallographically equivalent to a {112} twin.3 This is analogous to the crystallographic equivalence of rotation and reflection twins in centrosymmetric crys tals. A particularly simple example of this equivalence occurs when the two twin planes are perpendicular to each other—for example (111) and (112). Then, if twinning on (111) moves a point P to a new position P1, and twinning on (112) moves P to P2, P1 and P2 will be related to each other by a 180-deg rotation about [110]— the direction normal to both (111) and (112). Since there are diad axis axis along (110) direction in a holosymmetric cubic crys tal the two positions P1 and P2 must be crystallo-graphically equivalent. In other words if a particular pole (hk l) is in a position P1 after twinning on (Ill), then after twinning on (112) a pole of the type {hkl}—but not the particular pole (hk1)—will also be in the position P1. As a result, when only the general (as opposed to the particular) indices of poles after twinning are required, twinning on (111) gives the same results as twinning on (112). To convert the results for a (111) twin to those applicable to a (112) twin, when the particular (as opposed to the general) indices of poles after twinning are required, all that is necessary is to multiply the indices of the twin poles by the matrix for 180-deg rotation about [lie], i.e., The analytical methods suffer the disadvantage that a new set of calculations must be performed for each different diffraction pattern or, as is done in the Meieran and Richman treatment,1 a lengthy list of the location of the twin spots in reciprocal space must be prepared. All the tedious computation involved in these analytical approaches can be avoided by simply plotting, on tracing paper, a stereographic projection of a crystal twinned on say (112). By superimposing this twin stereogram on a standard (001) projection (preferably with the points and indices in a different color from those on the twin stereogram) the relative positions of both matrix and twin reflections can be determined by inspection. Alternatively, a composite projection can be

Jan 1, 1965

By D. J. Sellmyer

In order to orient single crystals by the back-reflection method it is necessary to know the angles between the various crystallographic planes. These angles have already been published for the hexagonal close-packed metals magnesium, zinc, and cadmium.&apos;

Jan 1, 1965