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By F. P. Bullen

Empirical relationships between fracture stress, orientation angle, and diameter of crystal have been determined at 77°K. Orientation ranges of markedly different behavior were found—a law of constant normal stress&apos; of value a (diameter)-1/2 for the fracture of ductile crystals, and a condition of shear stress (or strain) for more brittle crystals. The observations are not consistent with current theories. An interpretation is advanced which is also applicable to observations on the effect of prestrain at room temperature on the subsequent fracture stress at 77°K and to the effect of cyclic stressing on the cleavage strength.&apos;&apos; The law of constunt normal stress&apos; and the brittle ductile transition are also explained. The interpretation is more consistent with the initiation of cracks by intersecting dislocations than with theories based on stress -concentration by dislocation arrays. ZINC single crystals are particularly suited to the study of cleavage because fracture occurs on the basal plane over a wide range of crystal orientations. Analysis of the conditions of stress and strain at fracture in crystals of different orientations should indicate which parameters control the cleavage process. Unfortunately, controversy has arisen over the correct empirical relationship between tensile fracture stress and orientation. Schmid&apos;s observations1,2 favored a &apos;law of constant normal stress&apos;, as observed in other materials.2 For zinc, however, the observed values are far below the theoretical strength and cannot represent the true limit of cohesion between neighboring atomic planes. Hence, the interpretation of such a &apos;law&apos; is not straightforward. Deruyttere and Greenough3,4 found a complex variation between tensile fracture stress and orientation; this variation did not agree with a &apos;law of constant normal stress&apos;. Two theories have been advanced to account for their observations: a) the propagation of cracks from low-angle boundaries,5 and b) the release of energy from piled-up dislocations during crack-propagation.4 The present work resolves the apparent discrepancy between the observations and shows that neither of the above theories are applicable to the tensile fracture of zinc single crystals. A phenomenological explanation, along the lines suggested by Gilman,&apos; is advanced and successfully applied to previously unexplained effects. EXPERIMENTAL DETAILS &apos;Crown Special&apos; redistilled zinc was used, except for one comparison series op tests using &apos;Tadanac&apos; electrolytic zinc. Crystals of 1 mm diam, subsequently called &apos;1 mm crystals&apos;, were grown from the melt in vacuo in precision-bore Pyrex tubes internally coated with graphite. Several specimens 1 in. long were cut from each crystal and chemically polished. Jigs were used to minimize handling strains, and crystals were mounted in the Polanyi machine the day prior to testing to allow recovery from any such strains. One-mm crystals were chemically polished for long periods to obtain 0.1 mm (approx) crystals. One-mm crystals were cemented into miniature gimbals by &apos;Araldite&apos; casting resin. The Appendix gives the reasons for using gimbals and the results obtained by other methods. More complete details of all techniques are given elsewhere.7 The symbols and terminology used are as follows: X = orientation angle (angle between tensile axis and line of greatest slope in the basal plane). T = tensile stress (on true cross-section) S,N = shear and normal stress (components of T with respect to the basal plane) ? = shear strain D = crystal diameter. The subscript &apos;f&apos; will be used to denote values at fracture. PART I-ANNEALED CRYSTALS EXPERIMENTAL OBSERVATIONS One-mm crystals were used to establish the variation of fracture stress at 77°K with orientation at fracture (Xf), Fig. 1. For 18 deg = Xf = 55 deg, a &apos;law of constant normal stress&apos; was observed. For Xf > 55 deg, the fracture condition approximated to a constant shear stress. At Xf< 18 deg, twinning occurred before fracture so that the results were not typical of homogeneous single crystals,4,8— such specimens will not be considered herein. The dependences of fracture stress upon Xf were of similar type for 6 mm,* 1 mm, and 0.1 mm crystals,

Jan 1, 1963

By Francois E. Heuze

INTRODUCTION Rock slope stability typically is governed by the geological discontinuities. This stability can be improved by drainage, unloading, adjustment in slope orientation, adjustment in slope angle, and also by reinforcement such as bolts or tendons. This paper addresses the modeling of bolt reinforcement in rock slopes. Most geological discontinuities such as joints have rough surfaces; they dilate during shear displacement. Their shear strength is characterized by two envelopes (Fig. 1); the peak envelope is distinct from the residual envelope when the joints can dilate. If the dilation is restrained transversely, such as with bolts, the normal stress will increase and the joint strength also will increase. It has been demonstrated that this increase may be considerable (Obert et al., 1976). The new normal stress at peak strength is a com- posite function of the properties of the rock mass and of the steel (Heuze, 1979). Hence, the dilation and its resultant effects on joint shear strength must be included in the analysis and design of the reinforcement. We present a model which can be used to perform such an analysis. Early studies of rock reinforcement in mining and civil applications (Lang, 1957 - Panek, 1962 - Osen and Parsons, 1966 - Lang, 19721, did not consider the specific effects of bolts on joint shear strength. In 1973, Heuze and Goodman reported direct shear tests on rough sandstone joints with bolts perpendicular to the joint plane (Fig. 2). The peak shear strength of such joints was greatly in excess of the shear strength of the unbolted joints. The excess

Jan 1, 1983

By Keats, J. L.

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical charac- teristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained.

Jan 1, 1957

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By J. J. Arps

This paper is a study of the effect of temperature on the electrical resistivity of sodium chloride solutions based on the published resistivity and density data in the International Critical Tables. This temperature effect is of considerable importance in quantitative interpretation of electric logs, where it is frequently necessary to correct mud resistivities measured under surface conditions to temperatures existing at the bottom of the bore hole. An empirical approximation formula was developed for this conversion which has proved to be very useful and seems to provide results well within the range of accuracy of the data involved. This approximation formula states: sistivities of sodium chloride solutions at temperatures of t and t degrees Fahrenheit, respectively. INTRODUCTION Research by various investigators during the past 20 years has clarified the physical principles of the phenomena which cause the natural or spontaneous electric potential in rotary drilled bore holes. The basic relationship which is most commonly used reads: in which the SP deflection, as measured from the shale base line, is expressed in millivolts. K is a constant, which appears to vary between 50 and 110; the low value applying to shaly sands, whereas the higher values are more common in carbonate rocks. A good average value for K = 70. for which value there is considerable theoretical justification." In order to calculate the resistivity of the connate water R and to estimate its "equivalent salinity" (as NaCl) from an electric log by means of this SP relationship from a knowledge of the static self potential and of the resistiv- ity of the mud filtrate R it is necessary to first correct the resistivity of the mud filtrate measured under surface conditions to the resistivity of this same mud filtrate in the well bore at a different temperature. In order to make this temperature conversion for the mud filtrate the variation of the electrical resistivity of sodium chloride solutions with temperature is commonly used. Since some discrepancies were found in the charts ordinarily used for this purpose, it was felt desirable to make a new study of this relationship based on the published measurement data. Because of the fundamental nature of these relationships and as an aid to other workers in this field, an attempt has been made in this study to show every step in the calculations. CONDUCTIVITY VS MOL CONCENTRATION The most complete published reference on the temperature relationship of sodium chloride solutions of different concentrations is provided in the International Critical Tables.&apos; The basic measurement data on the electrical conductivity of aqueous sodium chloride solutions, at different temperatures, as given in these tables, are reproduced in Table 1. The electrical conductivity values in this Table 1 are expressed as 10&apos; times the specific conductivity k in ohm-&apos;cm&apos;l per unit of concentration in milligram mols per liter of solution C, or: RESISTIVITY VS MOL CONCENTRATION These conductivity values from Table 1 were first converted to the corresponding electrical resistivity values (R) , expressed in ohm-meters, as is conven-

Jan 1, 1953

By R. J. Borg, C. E. Birchenall

The self-diffusion coefficients for a iron have been deternzined between 980° and 1167° K using Fe55 as the tracer. With decreasing temperature the diffusivity was found to decrease more rapidly than predicted by the Arrhenius equation in the region of the Curie temperature. The diffusion coefficients obtained well above the temperature of the magnetic transformation are more precise ard differ substantially from all the previously reported values. In the temperature region beginning at least 50" above T,, the diffusion coefficient is given by D = 118 (±2) exp 1 HE self-diffusion coefficients for a iron have been reported previously as the result of four independent investigations The general lack of agreement and the poor precision of most of the previous work prompted the redetermination by the present authors. The possible effect of the onset of ferromagnetism upon the diffusivity5 provided an additional impetus for this investigation. The earlier measurements of Birchenall and Mehl1 gave low values for the diffusion coefficient at temperatures below the Curie temperature, Tc. However, the precision of these measurements is not sufficient to establish an indisputable correlation between the low values and the magnetic transformation. The results of this investigation along with all the previous ones are shown in Fig. 1. EXPERIMENTAL Small rectangular samples, approximately 1 by 0.5 by 0.3 cm, of high-purity iron (Vacuum Metals Corp., "Ferrovac") are first heated in hydrogen at 900°C for24hr in order to remove possible trace amounts of dissolved carbon and oxygen. The small

Jan 1, 1961

By K. R. Evans

The yield and fracture characteristics of a Ti-8 pct A1 alloy have been examined at room temperature as a function of exposure temperatures to 1700°F. Em-brittlenzent of the alloy is observed to occur following exposures below 1280°F, the critical temperature for formation of ordered Ti3Al particles. Presence of Ti3Al particles results in an increase in the yield and flout stresses which, for a given exposure time, are a maximum at the critical temperature. Embrittlement is attributed to the occurrence of plastically induced fracture controlled by the increase inflow stress. This interpretation is compatible with the decreasing ductility and increasing crack popagation rates observed with increasing exposure time below the critical temperature. Slip line observations and measurements of the gain size dependence of the yield stress indicate that the slip character of the alloy is not influenced by exposure treatments below the critical temperature. ThE potential usefulness of Ti-A1 alloys in structural applications has prompted considerable interest in studies of their microstructure and mechanical characteristics. The relatively recent surge of interest in the system and at the same time its complexities are indicated by the fact that despite numerous recent efforts14 there has not even been general agreement upon a phase diagram for the system. However, most of the Ti-A1 alloys of commercial interest range in aluminum content from 5.0 to 8.5 wt pct where most investigators achowledge the existence of the ordered Ti41 phase. Goldak and parrs confirmed the existence of Ti41 from X-ray diffraction analysis of the stoichiometric composition while Blackburn6 has determined its presence in commercial Ti-8 pct A1 alloys by electron diffraction analysis and dark field transmission microscopy. The embrittlement of Ti-8 pct A1 alloys was initially reported by Crossley and carew7 who showed that aging in the temperature range of 750" to 1110°F resulted in extreme brittleness. This behavior was later confirmed and correlated by Soltiss to the presence of long-range order in the commercial Ti-8 pct Al-1 pct Mo-1 pct V alloy (Ti-8-1-1) which exhibited anomalous creep and yield strength behavior at 950°F. This investigation was designed to study the mechanical characteristics of a binary Ti-8 pct A1 alloy in order to further examine the nature of the embrittlement behavior reported for the alloy system. EXPERIMENTAL PROCEDURE A Ti-8 pct A1 binary alloy was obtained from the Wah Chang Co. in the form of 0.050 in. sheet. The chemical composition of the alloy is given in Table I. Heat-treatment of the alloy was conducted in evacuated vycor capsules for the tensile sDecimens (1.25 bv 0.25 in. gage section) and in evacuated stainless steel jackets for the crack growth-rate panels. All specimens were annealed at 1700°F for 24 hr and water quenched before an exposure at elevated temperatures. Tensile testing was conducted at room temperature in an Instron testing machine equipped with a pushbutton control for instantaneous control of the cross-head motion. In this manner the change in stress, Aa, accompanying an increase in strain-rate by a factor of 10 was measured immediately after yielding. The crack growth-rate panels used were 3 by 18 in. with a precrack 0.33 in. long cut into the center of the panel. The panels were cycled at a maximum gross stress of 40,000 psi at a maximum to minimum tension stress ratio of 20. Cycling of the specimens was continued until the crack propagated the width of the panels. The crack length was intermittently measured during slow crack growth. EXPERIMENTAL RESULTS Correlation of Embrittlement to the Critical Temperature for Ordering. Blackburn6 has found that the critical temperature, T,, for the formation of Ti41 in a Ti-8 pct A1 alloy with an interstitial content on the order of that given in Table I is approximately 1245°F. The relationship between the ductility of the binary alloy used in this investigation and T, was estimated from tensile tests on specimens which were exposed for 24 hr at various temperatures followed

Jan 1, 1970

By B. H. Bergstrom

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

Jan 1, 1967

By B. K. Larkin

Solutions to the diffusion equation for a line source located anywhere in a region bounded by a circular discontinuity are presented. Such solutions follow automatically from the Green&apos;s function presented by Jaeger.4 Petroleum industry applications of this problem would include transient compressible fluid flow in porous media bounded by a discontinuity. Since several recent papers have treated the subject in less general form, it would appear that many workers in this area of the petroleum industry are not aware of Jaeger&apos;s work. STATEMENT OF THE PROBLEM In several trearments1,2,3 of the transient flow of compressible fluids in porous media it was convenient to consider a region to be bounded by a circular discontinuity. In such a region (Fig. I), the properties in Region 1, r < a, are constant but different from the properties in Region 2, r > a. Hurst, l using the Laplace transform, obtained solutions for a line source located in the center of such a porous medium. The purpose of this work is to point out that a much earlier paper by Jaeger4 presents the solution for a line source located anywhere inside the discontinuity. The assumption is made that a line source may be used to approximate a well. In the following material it is convenient to use the terms source and well as being equivalent; however, the reader should remember the distinction in applications. SOLUTIONS Jaeger presented the Green&apos;s function for a line source, or well, in the composite region shown in Fig. 1. In the most general form, the solution for a system of j wells in Region 1, each producing at a time varying rate, qi (t), is

By R. W. Diamond

THREE mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd:: (1) The Sullivan concentrator, Chapman, B. C. (near Kimberley, B. C.), (2) the St. Eugene concentrator, Moyie, B. C., and (3) the Tadanac (customs) concen-trator, Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Flotation equip-ment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sul-livan concentrator. Successful differential flotation of Sullivan ore com-menced in the spring of 1920, in the pilot concentrator at Trail. During 1920, 193,804 tons were treated by this process. This operation continued without interrup-tion and with steady growth. For the first 7 months of . 1923, which concluded the pilot plant operation, ap-proximately 1100 tons were treated daily. I believe the Sunnyside plant of the United States Smelting &. Refining Co. was the only successful and large scale operation practising differential flotation prior to 1920. in North America. The Sullivan ore, because of its high iron content, was quite a different problem from that at Sunnyside. The entire tonnage of Sullivan ore had to be separated into three sulfide concentrate products-lead concentrate, zinc concentrate and iron concentrate. The choice and arrangement of equipment, and the original flow sheet for the Sullivan concentrator were controlled by the results of the exhaustive pilot mill test. These covered a continuous period of 3 1/2 years and involved the treatment of 1,076,368 tons of Sullivan ore. Satisfactory recoveries are made from feed; 11.0 per cent lead and 7.5 per cent zinc in the form of lead concentrate containing 69 per cent lead, 4.5 per cent zinc, and zinc concentrate containing 3.0 per cent lead and 49 per cent zinc. (The pure zinc mineral in Sulli-van ore is marmatite, &apos;containing approximately 54.5 per cent zinc and 10 per cent iron. It is apparent, there-fore, that 49 percent concentrate is high grade for this particular ore.)

Jan 8, 1927

By W. C. Hardy, B. W. McArthur

The purpose of this work is to show application of laboratory data in calculating solution gas-drive performance of the Cisco K-I reservoir. Included herein is a diagram showing the graphical relationship between six variables common to all solution gas-drive mechanisms. With an iterative process one may assume existence of any of these six variables at a particular pressure and calculate the production performance likely to occur in a reservoir produced by solution gas drive. Four unique pressure values are described at which the material balance equation alone is sufficient to predict the cumulative volumes of gas produced. Information derived from these pressure points establishes a criterion for determining compatibility of the pressure-volume-temperature (PVT) analysis of the produced crude with the gas production history. Two averaging procedures are used to arrive at a relative permeability-saturation relationship which describes the field-wide performance. INTRODUCTION The Cisco K-1 reservoir is a lenticular-type sand structure lying at approximately 6,300-ft subsurface. It is located in the H. and T. C. Railroad Co. Block 97, SW 1/4 S 392 and NW 1/4 S 385, Scurry County, Tex. Correlation of data from logs indicated that the Cisco K-1 reservoir occupied approximately 3,218 acre-ft of space with a closure of from 15 to 20 ft. Analysis of the production data indicates that the initial formation pressure and temperature were 2,450 psig and 121°F, respectively. The bubble point occurred at 1,715 psig after production of 12,256 STB oil and 11,520 Mcf gas. Only traces of water have been produced since initiation of production. Successive material balance calculations from June, 1952, to June, 1957, showed that no initial gas cap or water influx has contributed to production of oil and that the Cisco K-1 reservoir originally contained approximately 1.44 X 10" STB of oil. THEORY Methods for calculating solution gas-drive perform-

By Arthur F. Johnson

Plant sites for the light metal industry must be located where ample low cost power is available. In the first half of the century hydroelectric development was the only source of this power-now the best sites have been exploited and those remaining do not promise enough water to permit year-round capacity power plant operation. In searching for economic plant sites engineers have concentrated on locations with vast water power potential. Olin Mathieson Chemical Corp. has been studying the economics of developing water power to make aluminum. However natural gas, lignite, and even atomic energy have also been considered as possible power sources for aluminum production. Economic studies have given consideration not merely to investment and production costs, but to total costs of delivering fabricated products to the market center of the U. S. When delivered costs are considered and when full account is taken of the newest techniques of mining bituminous coal and utilizing it to make electric power, one arrives at the inescapable conclusion that coal has emerged as the economic answer to American aluminum production.

Jan 4, 1955

By A. Totani, S. Nakajima, H. Okazaki

The phase diagram for the SnTe-SnSe system has been studied in the temperature range from 300° to 900°C by differential thermal and quenching techniques. The X-ray measurements were made on quenched specimens. High-temperature diffraction was also made to study the phase transition in SnSe. The system is proved to be of a eutectic type in which no intermetallic compound exists. The eutectic point is at the composition SnTeo.55 Seo.45. the eutectic temperature being 755°C. Solid solubility limits are SnTeo.6Seo.r and SnT eo. 3s Seo.6s at the eutectic temperature, and change almost linearly to SnTeo.aaSeo.lz and SnTeo.18 Seo.az as temperature decreases to 300°C. It was shown that the SnSe phase has a phase transition of the second order at about 540°C and that the transition temperature decreases with increase of the SnTe content. THERMOELECTRIC properties of tin telluride (SnTe) and tin selenide (SnSe) have been studied extensively in recent years. The variation of physical properties with composition could be of interest if these compounds form an appreciable crystalline solution. The purpose of present investigation is to confirm the formation of crystalline solution or intermetallic compound, if any, and to establish the phase diagram for this system. The crystal structure of SnTe is NaCl type with a cubic unit cell1 (a = 6.313A). The crystal of SnSe having an orthorh2mbic unit cellz (a = 11.496, b = 4.1510, and c = 4.4437A) is isomorphous with tin sulfide (SnS) which has a distorted sodium chloride structure. It has been known that SnSe has a phase at at 540°C; the transition has been assumed to be of the second order. As far as we know, only two studies on the SnTe-SnSe pseudobinary system have been reported. The conclusion obtained in these papers is that, in the composition regions near SnTe and SnSe, the system forms a crystalline solution of the SnTe structure and the SnSe structure, respectively, and that, in the intermediate region, both phases coexist. However, neither the variation of the solid solubility vs the temperature nor the liquidus and solidus were investigated. Hence present writers have attempted to determine the phase diagram of the system by differential thermal analysis (D.T.A.) and X-ray diffraction. EXPERIMENTAL Sample Preparation. Starting materials, SnTe and SnSe, were prepared by the direct fusion of commercially available high-purity (99.999 pct) elements. Stoichiometric amounts of each couple Sn-Te or Sn-Se were weighed into a clear fused silica ampule. After evacuation to a pressure below 10-3 mm Hg, the am- pule was sealed, and annealed at 900°C for 5 hr. The melt was quenched in water. X-ray analysis confirmed the formation of a single phase of SnTe or SnSe. The other samples, SnTel-,Sex were synthesized from these SnTe and SnSe by mixing them in the required ratio, followed by annealing at 900°C and quenching. These samples were used directly for D.T.A. For X-ray measurements, samples were annealed at 700°, 600°, or 500°C for 100 hr or at 300°C for 150 hr, and then quenched in water. It was found that the lattice constants of the SnTe phase annealed for 150 hr at temperatures above 500°C did not differ from those annealed for 100 hr at the same temperatures. However the X-ray phase analysis showed that at 300°C the annealing for 150 hr was necessary to attain a true equilibrium state. D.T.A. The solid-liquid equilibrium temperature was determined from D.T.A. measurements. The sample was sealed in an evacuated silica tube and molybdenum powders sealed in an another tube were used as a reference material. The sample and the reference tube were placed in a nickel block and were heated from room temperature to 900°C at a rate of 3°C per min and then cooled down at the same rate to 600°C. Thermocouples for these measurements were Pt-Pt. Rh (10 pct) and the error of temperature measurements was within + l0C. D.T.A. curves were obtained on a two-pen recorder and an automatic controller (PID type) was used for the program of heating and cooling. When temperature reaches the solidus from the low-temperature side, there appears an endothermic peak. The solidus temperature was determined by extrapolation of the straight portion of the starting flank of this peak to the base line. In a similar way, the liquidus temperature was determined from an exothermic peak on D.T.A. cooling curve. In the case of supercooling, if any, its degree can be estimated from the magnitude of the abrupt temperature rise. X-Ray . X-ray powder patterns were taken by a diffractometer using CuK, radiation. Since the SnSe crystal is cleaved easily, the powders become flaky when SnSe-rich samples are ground in an agate

Jan 1, 1969

By P. D. Zemany, G. W. Sear, B. W. Roberts

Vanadium metal is embrittled by hydrogen at a temperature as low as 250°C when held in the presence of manganese metal and water vapor in a rough vacuum. It is established that the property changes are caused by the catalytic decomposition of water vapor at the vanadium surface and the diffusion into and solution in the vanadium of the resultant hydrogen. It is found that manganese is a necessary component of the catalyst. The manganese is transported in the vapor phase by an unknown molecule. A deuterium tracer experiment demonstates the role of water vapor in the embrittle-ment process. VANADIUM metal foils were observed to become embrittled&apos; at a temperature of about 300 °C when held in the presence of manganese metal and a small amount of moist air, This paper describes the investigation to find the embrittling agent and an understanding of the relatively low temperature reactions that are involved. Experimental The vanadium metal foil used was prepared by cold-rolling and pack-rolling 32 mil sheet" in a series of steps down to 1 mil foil. The original observation was confirmed by sealing vanadium foils of 3 x 10 sq cm into individual Pyrex tubes with manganese powder† and a con- trol tube containing only the vanadium foil. These tubes were evacuated to 10 -5 mm Hg without baking and sealed. After heat treatment for 200 hr at 300°C, the control foil showed no change in duetility, whereas the foil contained in the manganese— containing tube was embrittled. The visual appearance of each was unchanged. A series of Pyrex sample tubes, about 2.5 cm diam and 25 cm long, were prepared, each containing a 3 x 10 sq cm piece of foil and 5 g manganese powder at the lower end of the tube. By reducing the time of anneal and the temperature of these samples, it was found that embrittlement could be created at 250°C in a time as short as 1 hr. Since the vanadium metal used here has been drastically cold-worked by rolling, it is assumed that it contains a maximum number of dislocations. To check the possible necessity of dislocations in this low temperature reaction, a vanadium foil sample was annealed in Vycor for 2 hr at 800°C to re crystallize and reduce the dislocation concentration. Metallographic examination showed grains which were not visible before annealing. The embrittlement procedure was carried out at 300°C and 3 hr. Upon checking the foil no embrittlement was observed. Further experiments demonstrated that about 6 hr at 300°C are required to create embrittlement in the foil. This delay in the onset of embrittlement in the vanadium foil suggests but does not prove that dislocation channels play a role in the embrittlement phenomena. If manganese metal is necessary for this low temperature embrittlement, do other elements in the transition metals group yield the same result? To check this qualitatively, a group of elements of similar atomic radii were obtained and sealed as before into Pyrex tubes with a sheet of vanadium foil. These tubes were annealed at 250°C for 6 hr and included (with radii)-2 A1 (1.4A), As (1.25A), Be (1.2A), Co (1.25A), Cr (1.45A), Cu (1.25A), Fe (1.25A), Ga (1.2A), Ge (1.25L%), Mn (1.3A), Ni (1.25A), Si (1.2A), Ti (1.45A), Zn (1.3A), air, H,O, 10 cm Hg of dry hydrogen, and MnO, powder. Upon testing the above sample foils for brittleness, only the manganese-containing tube yielded a brittle foil. Manganese Transport—To eliminate contact of manganese metal powder and vanadium foil, sample tubes were prepared with fritted glass barriers. The embrittlement reaction was still found to occur. Thus, the mode of transfer of manganese is certainly vapor transport. A vanadium foil was embrittled by this mechanism in an evacuated Pyrex tube for 8 hr at 300°C. By means of X-ray fluorescence analysis,&apos; the amount of manganese added to the surface was established at 5 ±2 x 10 -6 g per sq cm. Since the average rate of manganese deposition is known, an effective average pressure of an assumed carrier compound can be computed. ___ P = M/T v2p mkT

Jan 1, 1959

By E. S. Machlin

The possibility that formation of voids under creep-rupture conditions may take place by the condensation of vacancies has been investigated theoretically. It has been concluded that nucleation of voids under creep-rupture conditions by vacancy condensation is highly improbable. However, growth of pre-existant voids by vacancy condensation is probable. A number of predictions made in this theory have been verified by the data. It has been predicted and checked that the product of rupture life and steady-state creep rate for preannealed metals and single phase alloys is an approximately invariant quantity, independent of stress, temperature, and atomic number for a given type structure. The direction of the effect of cold work on this product has been predicted and found in agreement with experiment. A number of experiments to evaluate the vacancy condensation mechanism further are described. SEVERAL papers have appeared recently which speculate on the origin of voids formed at grain boundaries under stress.&apos; &apos; The object of this paper is to examine quantitatively the proposition that the voids produced in a creep test are a result of vacancy condensation. A result of this paper is a theory of creep-rupture. Void Nucleation Application of standard nucleation theory" to the problem of void nucleation leads to the following conclusions: 1—Homogeneous nucleation of voids requires a supersaturation ratio (concentration of vacancies in supersaturated to that in saturated solution) of 400 for a reasonable surface energy of 1000 erg per cm-and 1.4 for the improbably low surface energy of 10 erg per cm. 2—Heterogeneous nucleation of voids at plane interfaces between two phases requires a supersaturation ratio of 2.5 for a typical contact angle of 145 3-—Void nucleation about a solid particle may be accomplished at a supersaturation ratio of 1.17 for a typical value of work of adhesion? of 60 erg per The work of adhesion is the surface work 10 replace two solid-vauor surfaces by a solid-solid interface. enr &apos; between an oxide and a metal in the presence of a surface active element such as sulphur. Estimates of the supersaturation ratio at which voids are produced in diffusion experiments yield a maximum of 1.01. Inasmuch as the foregoing mechanisms of void nucleation probably will not operate at this level—too low a surface energy is required—the investigatol. is led to the conclusion that voids must already exist. That is, nucleation of voids probably does not occur. Rather, existing submicroscopic voids grow out to visible size. Already existing voids might be produced during solidification or working. Supercritical sized parlicles which contain cracks may act as heterogeneous void nuclei. Gas pockets may act as void nuclei. Experiments are desired to determine the nature of the heterogeneous void nuclei which grow out to voids in both diffusion and creep experiments. Void Growth Void growth might occur in at least two possible ways, depending upon whether the already existing void nuclei are at grain boundaries or within the grains. In the case of a spherical void far from a crystal boundary, vacancies are generated during creep as a consequence of the migration of suitable dislocation jogs&apos; and are also annihilated at sinks. Under these conditions, a steady-state concentration of vacancies is built up in the crystal, defined by the condition that for any differential volume the rate of generation of vacancies in that volume equals the rate of annihilation of those vacancies." This equality would lead to the development of a gradient of vacancy concentration radially outward from the void surface up to a radius where the vacancy lifetime becomes equal for all directions of vacancy migration. The distance over which this vacancy concentration gradient extends equals about 2vD,T* where D, is the vacancy diffusivity and T:&apos; the vacancy lifetime in a crystal outside the gradient in a zone of constant vacancy concentration. The vacancies generated in the region over which the gradient exists will annihilate more often at the void than elsewhere. Approximately a little over one-half the vacancies generated in the gradient zone will annihilate at the void. Hence, the growth rate of the void is given by on where R is the radius of void in centimeters, is the atomic volume, and R is the rate of generation of vacancies, number per centimeter" per second. R D and T* may be estimated in terms of other physical parameters." In particular, R = n.j e/b [3] where n is the average number of vacancy produc-

Jan 1, 1957

By S. F. Frederick, W. A. Bailey

The relationship between microstructure and mechanical properties of cast 356-type aluminum alloys was studied to determine the cause of the variations in properties resulting from differences in solidification rate. It was found that variations in strength are a consequence of variations in ductility and that ductility is inversely proportional to the dendrite cell size. A mechanism is proposed to account for this correlation based on the fracture strain of the inter-dendritic silicon particles and the differential strain across dendrite cell boundaries. IT has long been assumed that permanent mold castings of aluminum are superior to sand castings because of their finer grain structure and reduced porosity.&apos; A systematic variation of static properties was noted during unpublished studies of fatigue-strength variations with solidification rate of A356-T6. Of particular interest was the observation that for a given composition and heat-treatment, both ductility and the ultimate strength increased with higher solidification rate. Because the A1-Si system forms the basis of many alloys used for castings and welding wire, a study was initiated to determine the details of how higher cooling rates improved mechanical properties of these alloys. The results of this study are presented here. EXPERIMENTAL PROCEDURE Specimens were prepared from 356-T6 to supplement the A365-T6 alloy data from earlier studies. This allowed a comparison of behavior of alloys with substantially different strengths but with only small differences in alloy composition. The composition and heat treatment of both alloys are given in Table I. The specimens were cut from a chill plate casting,&apos; which is a 6 by 9-in. plate, 1 in. thick, which has one end heavily chilled, and a large riser at the other so that solidification is essentially unidirectional from the chill end to the riser. Although not measured here, solidification times measured on similar specimens by embedded thermocouples are a few seconds at the chill end and up to 5 min near the riser. Specimens were obtained by cutting slabs from the plate, parallel to the chill; these represented different cooling rates, with essentially the same composition. For the tests, either 0.125 or 0.250-in. thick slabs were cut for standard 2-in. gage length specimens. The thicker specimens were tested to failure at 2000 lb per min while the thinner specimens were tested in an Instron machine at a constant cross-head speed of 0.02 in. per min. These thin specimens were intended for trans- mission electron microscopy. Some thin specimens were tested to failure while the remainder were given various amounts of prestrain. Dendrite cell sizes were measured by the linear intercept method on photomicrographs at either X100 or X50, depending on the cell size. It was assumed that the dendrite cells were outlined by the silicon particles. Determinations were made on two mutually perpendicular planes and an rms average taken. Electron fractographs of representative tensile specimens were made in the conventional manner using the two-stage replica technique.3 Samples for transmission electron microscopy were prepared by chemical milling followed by electropolishing. RESULTS AND DISCUSSION The results of the tensile tests and the dendrite cell-size determinations are given in Figs. 1 and 2. All data show the same trends, namely, a decrease in ultimate strength and elongation with increasing distance from the chill (and solidification time), and a corresponding increase in dendrite cell size. The yield strength remains essentially constant. The constancy of the yield strength was particularly significant since it indicated that variation in the solidification rate does not affect the stress required to initiate plastic flow. By plotting true stress-true strain curves as in Fig. 3, it can be seen that both

Jan 1, 1969

By Oscar Weiss

STILFONTEIN and surrounding areas gave nega-tive results in all prospecting attempts since about 1904 when Goerz and Co., a forerunner of Union Corporation Ltd., first drilled in the region and on the farm Stilfontein. Subsequent efforts by African and European Investments Co. and Anglo American Corp. from 1934-37 were completely unsuccessful. Holes drilled by these companies on the farms Riet-fontein, Hessie, and Palmietfontein were stopped in the Lower Witwatersrand system without finding payable reefs. The results of gravimeter, ground magnetometer, and aerial magnetometer surveys are presented in the area, in and around the new Stilfontein Gold Mine, in the Klerksdorp District of the Transvaal in the Union of South Africa. The gravimeter and ground magnetic surveys were completed in 1947—48. The gravity anomalies suggested a block of Upper Witwatersrand quartzites faulted-up between denser rocks of dolomite and Ventersdorp lava. Boreholes S.T. 1, 2, and 3 were drilled in 1948 and, after penetrating the dolomite and Ventersdorp lava, entered Upper Witwatersrand quartzites and intersected the Gold Estates Reef and Vaal Reef. Subsequent drilling delineated the suboutcrop of the Vaal Reef and determined the main structure of this horizon. The gold content of the Vaal Reef was highly payable and shaft sinking is now in progress. The Stilfontein Gold Mining Co. has been formed and, up to date, f5,000,000 capital has been raised for plant, shaft sinking, and development. The payable Vaal Reef horizon extends further south from Stilfontein, the reef occurring at increasing depths. It is possible that at least another mine may be established on these deeper horizons. The farm Stilfontein 39 is situated in the Klerksdorp District of the Transvaal. This farm and the surrounding areas have been subjected to repeated programs of prospecting dating back to about 1904, when Goerz and Co., the forerunner of Union Corporation, Ltd., first drilled on the farm and in the surrounding areas. From 1934-37, numerous boreholes were drilled on the neighboring farms, Riet-fontein. Hessie. and Palmietfontein, by African and European Investment Co. and Anglo American Corp. All these efforts were completely unsuccessful, and nobody suspected any possible gold-bearing area on Stilfontein until about 1947, when a gravity traverse run by B. D. Maree on the main road, showed a negative gravity anomaly. During 1947-48, the writer&apos;s organization completed gravimeter and magnetic surveys on Stilfontein and Rieffontein. An area of negative gravity anomalies was mapped, and it was suggested that this could be caused by blocks of Upper Witwatersrand quartzites, of the average density of 2.65, faulted up between dolomites and Ventersdorp lavas, the density of both of these rocks being 2.8. Fig. 1 shows the geology of the area as mapped by L. T. Nel of the Geological Survey of South Africa. The boreholes on Stilfontein, with the exception of a single hole of Goerz and Co., were drilled after the completion of the geophysical survey. The grouping of the first boreholes S.T. 1, 2, 3, 4, 5, and 6, clearly shows that these were located in the zone of negative gravity anomalies. Fig. 2 shows the gravity anomaly contours. Fig. 3 shows two sections across the gravity anomaly, together with the corresponding geological sections as obtained from boreholes. The close relation between gravity values and thickness of dolomite plus Ventersdorp lavas is striking. The two latter formations having the same density (2.8), act as one mass as far as gravity effects are concerned. Fig. 4 shows the magnetic anomalies observed on the ground by vertical magnetometers and at 500 ft abbve mean ground level by aerial magnetometer. The latter are anomalies of the total magnetic intensity. The magnetic results show that, on the farm Rietfontein and on the northern half of Stilfontein. Lower Witwatersrand magnetic shales were to be expected at relatively shallow depths. As the strongly

Jan 1, 1952

By P. Chiotti, J. T. Mason

Metallographic, thermal, X-ray, and vapor-pressure data were employed in establishing the Ce-Zn phase diagram. Nine compounds and three eutectics were observed. The eutectic compositions in weight percent zinc and temperatures are 10 pct and 495"C, 37 pct and 795°C, and 56 pct and 810°C. Three of the compounds, CeZn, CeZnn, and CeZne.5, melt congru-ently at 825°, 87.505°, and 980°C, respectively; the other six compounds, CeZns, CeZns.67, CeZn4.5, CeZn5.25, CeZn,, and CeZnll, decompose peritectically at 820°, 840°, 870°, 885", 960°, and 795"C, respectively. The compound CeZn5.25 is an AB5 type with a small range of composition which lies on the zinc-rich side of the 1 to 5 stoichiometry. Zinc vapor-pressure data obtained by the dewpoint method were employed in calczilating the thermodynamic properties of both the liquid alloys and solid compounds. The data for the A critical review of the information available on the Ce-Zn system up to 1960 has been given by K. Gschneidner, Jr.&apos; Of particular interest is the work by J. schramm2 who investigated the region between 55 and 100 wt pct Zn and reported a CeZn,, compound which decomposes peritectically at 785"C, a CeZn, compound which melts congruently at 972"C, and five temperature horizontals at 79@, 817", 840", liquid alloys were fitted to the relation from which the relation was obtained by integration. In these relations F XS is the excess partial molal free energy, N is atom fraction, and the constants c and d have the values c = (-22,000 + 7.0T) and d = 6171,000 + 74.0T). Relations for the standard free energy of formation for the solid compounds were derived from the data. At 973°K the enthalpy in kilocalories per gram-atom z)aries from —11.3 for CeZnz to —8.21 for CeZn~l and the free energy in the same units varies from —7.1 joy CeZn, to -3.82 for CeZn11. and 942°C in the region between 55 and 75 wt pct Zn. No attempt was made to identify other features of the system. I. Johnson and R. yonko3 used a fused-salt cell to measure the electromotive force between pure cerium and an alloy consisting of zinc-rich liquid in equilibrium with CeZnll. Solubility data for cerium in zinc has been reported by J. Knighton et u1 .4 Johnson and Yonko give the following equa-. tions for the mole fraction of cerium in zinc and the standard free energy of formation of CeZnll:

Jan 1, 1965

By J. E. Hanlon, S. R. Butler, R. J. Wasilewski

The temperature, orientation, and strain-rate dependence of tensile flow in single-crystal NiA1 of equiatomic composition have been investigated up to 800°C. Compression tests at room temperature have also been carried out. Optical and replica electron microscopy and X-ray diffraction methods were used to investigate the slip mechanisms. NiAl exhibits {110)(001) slip and cube slip {l00)(010) was also observed. This results in very high strength of single crystals in cube orientation. The implications of this slip mode, with the resultant small number of possible slip systems and three mutually perpendicular slip vectors, are discussed. ThE CsCl structure compounds represent a class related to the bcc elements, but their behavior is affected by three additional variables: composition (within the stability range of the compound), extent of long-range order perfection, and bonding energy. Very little data are available on the effects of these variables on mechanical properties. Rachinger and ~ottrell&apos; suggested slip to occur along (111) in compounds of low ordering energy; in compounds of higher bond strength (>0.06 ev), they observed (110) (001) slip. As pointed out by copley,&apos; only three in- dependent slip systems are available in the latter case; hence general deformation is impossible. Brown3 carried out a theoretical calculation of the yield-point variation with the degree of long-range order in the CsCl structure, based on the assumption of superdislocations. More general approaches, based on considerations of superlattice dislocations and antiphase domain boundaries in ordered structures, were carried out by Flinn~ and by Vidoz and Brown.&apos; These, however, give no information on changes in the slip structure—if any—between the ordered and the disordered compounds. This aspect was investigated experimentally and theoretically by Stoloff and Davies&apos; and by Marcinkowski and chessin7 in FeCo. The latter workers proposed the deformation behavior of the ordered FeCo to be essentially the same as that in many other bcc metals. Investigations of polycrystalline A~M~&apos;-&apos;O indicate considerable variation in mechanical properties with composition and test temperature. The existence of {123)(111) slip was reported in AgMg.&apos;9&apos;9&apos;0 (The formation energy of this compound, presumed to be ordered at all temperatures below melting, is 4.38 cal per g-atom," i.e., 0.024 ev per bond.) The yield strength has been reported as relatively independent of temperature below 0.45 T, (where T, is the absolute melting temperature). Tensile deformation of single-crystal AgMg was also investigated by Kurf-man," who observed marked tendency to single glide on{112}(111) and {110)(111). From observations of slip lines in deformed poly-crystalline NiA1, Westbrook et a1.I3 suggested the

Jan 1, 1968

By B. Fazan, O. D. Sherby, J. E. Dorn

McLean&apos;s technique was employed to determine the effect of temperature on the contribution of grain boundary shearing to the total creep strain in pure aluminum over the range of 610° to 747°K. The contribution of grain boundary shearing at the same stress was found to depend upon a temperature-compensated time, where the activation energy AH was practically identical with that for total high temperature creep. SEVERAL outstanding investigations by McLeanl-&apos; have demonstrated that the total creep strain in polycrystalline aluminum at 473°K arises from microscopically detectable slip, subgrain tilting, and grain boundary shearing. Whereas microscopically detectable slip arises from dislocations that move out of the grains, subgrain tilting is due to entrapment of dislocations of like sign in subgrain bound-arles. Consequently, creep in polycrystalline aggregates appears to be the resultant of two mechanisms, namely, migration of dislocations and grain boundary shearing. This suggests that an appropriate law for creep should contain two additive terms ?1 = ?d + ?yb where the total creep strain, ?1, depends on the sums of the creep strains arising from motion of dislocations, ?d, and from grain boundary shearing, ?yb. But extensive investigations5 over wide ranges of alloys, grain sizes, temperatures, and stresses have shown that the total creep strain is quite accurately dependent on the single term functional relationship ?1 = f (?), s = constant where s is the stress (constant),* ? = te-?H/RT, t is the time under stress, AH is the activation energy, R is gas constant, and T is absolute temperature. Since Eq. 2 was found to be valid over those ranges where appreciable grain boundary shearing is observed, it appears probable that the activation energy for grain boundary shearing might be identical with the activation energy for migration of dislocations. Thus, under a given stress, it could be thought that where fd and fgb represent the appropriate functions for each mechanism of creep. The primary objective of this investigation was to obtain a direct check on the accuracy of this hypothesis. Experimental Procedure and Results Rolled aluminum sheet (99.987 pct Al), 0.100 in. thick, was used in this investigation. Creep specimens having a 0.25 in. wide, 3 in. long gage section were so machined that their axes were in the rolling direction. All specimens were annealed for 9 hr at 894°K before testing to produce a mean grain diameter of about 0.1 in. One face of each specimen was polished electrolytically in 10 pct HBF4. In order to permit accurate measurements of grain boundary shearing, the polished surface was lightly scribed with a ruling machine accurate to ±0.0001 in. to give a uniform grid of lines which were 0.01 in. apart. Although it was thought that surface working might modify the creep behavior in the vicinity of the scribed grid lines, this technique nonetheless was employed because such local differences in creep properties should not modify seriously the fractions of the total creep strain due to grain boundary shearing or to migration of dislocations. All creep tests were conducted under constant load with an initial stress of 250 psi. The specimen tem-

Jan 1, 1955