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

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

Jan 1, 1964

PRESIDENT PHILIP N. MOORE, ST. Louis, Mo. PAST PRESIDENTS WILLIAM L. SAUNDERS NEW YORK, N. Y. L. D. RICKETTS NEW YORK, N. Y. FIRST VICE-PRESIDENT SIDNEY J. JENNINGS NEW YORK, N. Y. TREASURER GEORGE C. STONE NEW YORK, N. Y.

Jan 1, 1917

By M. Muskat R. D. Wyckoff

The phenomenon called "water-coning" is that, observed in many oil wells, in which bottom water gradually and frequently sudderlly displaces a part or all of the oil production when a certain rather critical production rate from the well is exceeded. To follow in detail the process of the formation of a water cone as it breaks through the oil zone and enters the well bore is a problem so complex as to make a theoretical analysis practically impossible. However, an analytical treatment of the flow system before the water has broken through and during the time that it lies statically beneath the oil zone with an elevated or "coned" surface can be carried through under certain approximations. To present an analysis which shows the essential characteristics of the coning mechanism is the purpose of the present discussion. Physical Basis of Theory and Meaning of Approximations As will always be true for flow systems where true water-coning is at all possible, the water will be supposed to lie beneath the oil zone because of its density contrast with respect to the oil. In fact, tinder the usual field conditions, when the pay horizon is reasonably homogeneous, the water most frequently enters the well through the lower zones, but even when it enters from intermediate zones it may, in the later life of the well, displace the bottom layers of oil, thus resulting in a system wherein the oil is effectively floating on the water.

Jan 1, 1935

By T. E. Scott, D. H. Sherman, C. V. Owen

Mechanical properties and optical metallographic characteristics of vanadium containing 53 ppm (wt) H were investigated from, 77° to 298°K. A sharp ductile to brittle transition induced by the presence of hydrogen was observed between 238° and 223°K and a mar-tensitically formed hydride appeared at 200°K. While there appears to be a subtle relationship between the hydride formation and the ductile-brittle transition, it was concluded that the hydride per se was not sufficietzt to cause the severe em brittletnent. On the basis of the metallographic experiments and the results of a Petch analysis it is suggested that the mechanism of the embrittlement involves a reduction of the true surface energy, or cohesion, of the uanadiunz. THAT hydrogen can severely embrittle vanadium is well-documented;'-5 however, the mechanism by which hydrogen induces the observed embrittlement has not been established. It is not known whether the embrittlement of vanadium is caused by the formation of vanadium hydride or by a more subtle role of hydrogen. Until very recently6>' the solid solubility of hydrogen in vanadium at temperatures in the,range of the embrittlement was not known to a useful accuracy. In general, a severe embrittlement of the type produced by the presence of hydrogen in vanadium can be caused by changes in either of two properties of a metal. Either the yield stress of the metal is raised to the extent that plastic deformation at the tip of a crack cannot occur or the cohesive properties of the metal are reduced, at least locally, to the point at which cleavage is the natural response to applied loads. Of course a combination of these is possible. It is not known which of these properties of vanadium is influenced most by the addition of hydrogen. The purpose of this investigation was to determine the role of hydrogen in the embrittlement of vanadium. Accordingly, the solubility of hydrogen in vanadium in the temperature range where embrittlement is most severe was determined, the appearance of vanadium hydride was examined in relation to the initial ductile to brittle transition temperature, and an attempt was made to evaluate the effect of hydrogen on the yield stress and cohesive properties of vanadium. MATERIAL AND PROCEDURES Sample Preparation. The vanadium used in this investigation was prepared by the iodide refining process described by Carlson and owen.' Three ingots, 3 in. diam by 6 in. long, were cold-swaged to 0.096 in. diam, cut into short lengths, and then arc-melted under purified argon into one ingot. This process was repeated to insure a uniform composition in the final ingot. Chemical analysis of the metal is given in Table I. On the basis of work of Loria et a/ .' the following sequence of treatments was performed in order to obtain a uniform equiaxed ultimate grain structure: a) cold swage q-in.-diam ingot to 0.230 in. diam; b) anneal 6 hr at 1000°C in vacuum; c) by cold swaging reduce 81 pct in area in three steps: 0.230 to 0.187 in. diam, 0.187 to 0.150 in. diam, 0.150 to 0.096 in. diam. This sequence provided the desired grain structure after subsequent annealing treatments. Because annealing in evacuated quartz capsules resulted in contamination by oxygen, all anneals in this investigation were performed in a 304 stainless-steel chamber under a dynamic vacuum of 10- I Torr with the vanadium wrapped in tantalum foil. Prior to all annealing treatments the wires were electropolished for 1 min at 16°C in an 80 pct methanol-20 pct sul-furic acid electrolyte at 12.5 v. Following the final reduction the 0.096-in.-diam wire was cut into 2-in. lengths. A 1-in. gage section was reduced to 0.090 in. diam by electropolishing as above. Five different grain sizes were obtained by annealing the 2-in. samples at different temperatures for 8 hr to insure uniform grain size and residual hydrogen removal. The annealing temperatures used and the resulting grain sizes are given in Table 11. The final step in sample preparation was to charge half of the specimens of each grain size with hydro-

Jan 1, 1969

Jan 1, 1970

By Ernest F. Burchard

MOST of the iron ore smelted in Alabama blast furnaces is mined within Alabama, although deposits in the neighboring States of Georgia and Tennessee may be drawn upon when occasion requires. Of the four commercial kinds of iron ore, the anhydrous ferric oxide, hematite (Fe2O3) ; the hydrous ferric oxide, mostly the type commonly known as limonite (2 Fe2O33H2O) ; the carbonate, siderite (FeCO3) ; and the magnetic oxide, magnetite (Fe:3O4) ; the first two are found in abundance in Alabama, the third in less than commercial quantities, and the fourth only rarely. Both the hematite and the hydroxide are found in somewhat different forms according to their geologic environment. The Red Mountain hematite, of Silurian age, that crops out in well¬defined beds for 1.50 miles northeast-southwest and 40 miles northwest-southeast is the predominant source of ore. Only a small part of this area carries ore of commercial value; Birmingham and Gadsden are now the only centers of production. The ore is of sedimentary origin, probably altered from vast deposits of greensand mixed with calcareous, fossiliferous. marine debris. Other types of hematite not vet mined commercially are in metamorphosed rocks-red ore in slates in Columbiana Mountain and specular hematite (gray ore) in quartzite in the Talladega Hills.

Jan 1, 1938

By M. T. Erickson, C. A. Rowland

Ball mills 5.5 m (18 ft) in diameter and larger tend to use energy delivered to the mill less efficiently than smaller diameter mills, particularly when the large mills carry 40% by volume ball charges. This paper will explore factors used in scaling up ball mills, showing where the advantages of one factor can possibly be negated by another factor. The paper will propose possible operating limits and areas for further study to establish selection and design limits.

Jan 1, 1985

By E. P. Pfleider, O. Rellensmann

For many years mine surveyors and exploration engineers have sought an accurate means of transferring meridian underground by using the gyro-compass. These efforts have generally failed, either because they were inaccurate or because the size and cost of the unit were prohibitive. During the past ten years, however, great strides have been made. Autonetics in California has developed a comparatively light-weight (100-lb) gyro-theodolite, and the Institute for Mine Surveying at Clausthal Mining Academy in Germany has developed an instrument that is accurate to within 20" to 30" of arc. Concurrently, Minneapolis-Honeywell has produced an astounding gyro, the size of a salt shaker, that weighs less than 0.5 lb and compares favorably in performance with the 50-lb gyros of conventional design. This unit, designed for missile guidance, should be adaptable for surveying small boreholes. Given the proper interest and approach from the engineering fraternity, excellent gyrocompasses could probably be available for accurate underground survey work at nominal cost within the next three years. Principles of the Gyro-Compass: The gyrocompass, used for 50 years as a navigational instrument in ships and aircraft, senses the turning axis of the earth and points out true polar north. It does this by employing the earth's rotation, the force of gravity, and the precession characteristics of a gyro. For further details the reader is referred to several excellent publications'"3 covering the principles and application of the gyroscope. The heart of the gyro-compass is the gyroscope, or rapidly spinning wheel, which rigidly maintains its angular orientation in inertial space. Free gyros employ universal joints to allow the wheel axle to maintain its rigid spatial orientation independent of base motion disturbances. Free gyros are independent of the earth's turning and are not north-seeking. Only as they might be initially oriented parallel to the earth's turning axis could any north indication be obtained. In practice, the free gyro tends to drift off its set position and lose its accuracy. The Sperry-Sun Well Surveying Co. instrument (5M in O. D.) is of this free gyro type. It is counterbalanced, however, against the rotational effects of the earth, so that orientation of the spinning axis will be maintained throughout the survey.

Jan 1, 1960

By C. O. Fairchild

THE meaning of temperature control can be extended to cover not only the control of temperatures' but also the control of processes through a knowledge of the temperatures involved. In this sense it has a very wide interest. A list of the industries in which temperature control is used in one way or another would cover nearly the entire industrial field. This discussion will be confined to the field of high temperatures. In practically all industries involving operations at high temperatures, pyrometers are used or men are paid for their ability either to estimate temperatures or gage an operation by some physical or chemical change or condition dependent on temperatures. As progress is made in the development of instruments and of methods for measuring temperature, some of these highly skilled artisans are learning the use of a new tool. Many processes have been, in recent years, improved by means of exact measurement thus substituted for estimation, but in a great many industries the pyrometer has had practically no opportunity to demonstrate its usefulness. The perfecting of instruments must be accompanied with a dissemination of the knowledge that new instruments are available and can be economically used. The demand at present, however, is ahead of the supply, and many industries are handicapped by the want of pyrometers. One of the highest paid skilled tradesmen of the present time is the man in the steel rolling mill who knows when proper working temperatures are attained. The metallurgist in his development of steels is continually demanding closer adherence to given temperature ranges in the processes, and the pyrometer is rapidly becoming indispensable. Properties of the finished products are being correlated with working temperatures and so closely that in some cases even the pyrometer is taxed to give the required accuracy. The greatest progress has been made in those industries in which the lower temperatures are used, particularly below 500° C. In this lower range automatic control has been highly developed.

Jan 9, 1919

By Michael Tenenbaum, T. L. Joseph

In a previous investigation1 the authors studied the effect of pressure on the reduction of iron ores by hydrogen. With hydrogen as a reducing agent, the rate of reduction was increased substantially by increasing the pressure from 1 to 2 atmospheres. The results with hydrogen prompted the present study of the effect of pressure on reduction with carbon monoxide and with mixtures of carbon monoxide and nitrogen. Features of Reduction Process The gas stream in the lower part of the blast furnace always contains sufficient concentrations of reducing gases to complete reduction provided sufficient time is allowed for the reaction to proceed. Reducing gases react immediately with the iron oxide on the surface of lumps of ore. However, as the unreduced surface recedes from the easily accessible exterior of the lump, the reaction proceeds by virtue of the diffusion of the gases into and out of individual pieces. The rate of diffusion of gases, which undoubtedly plays an important role in the reduction of iron ores, depends on several factors, most important of which are: (1) molecular weight or density, (2) pressure, (3) temperature, (4) concentration gradient. Thus, the rate of reduction of a lump of iron ore at any temperature will depend not only on the specific reaction rate but also upon: (1) available surface of unreduced iron oxide, (2) rate of diffusion of the reducing gas to the reacting surface, (3) rate of effusion of the gaseous products of the reaction from the reacting surface, (4) adsorption of the gases on the reacting surface. The various features of the reduction process were discussed in previous work and need not be reviewed. However, in order to explain

Jan 1, 1940

By Michael Tenenbaum, T. L. Joseph

In a previous investigation1 the authors studied the effect of pressure on the reduction of iron ores by hydrogen. With hydrogen as a reducing agent, the rate of reduction was increased substantially by increasing the pressure from 1 to 2 atmospheres. The results with hydrogen prompted the present study of the effect of pressure on reduction with carbon monoxide and with mixtures of carbon monoxide and nitrogen. Features of Reduction Process The gas stream in the lower part of the blast furnace always contains sufficient concentrations of reducing gases to complete reduction provided sufficient time is allowed for the reaction to proceed. Reducing gases react immediately with the iron oxide on the surface of lumps of ore. However, as the unreduced surface recedes from the easily accessible exterior of the lump, the reaction proceeds by virtue of the diffusion of the gases into and out of individual pieces. The rate of diffusion of gases, which undoubtedly plays an important role in the reduction of iron ores, depends on several factors, most important of which are: (1) molecular weight or density, (2) pressure, (3) temperature, (4) concentration gradient. Thus, the rate of reduction of a lump of iron ore at any temperature will depend not only on the specific reaction rate but also upon: (1) available surface of unreduced iron oxide, (2) rate of diffusion of the reducing gas to the reacting surface, (3) rate of effusion of the gaseous products of the reaction from the reacting surface, (4) adsorption of the gases on the reacting surface. The various features of the reduction process were discussed in previous work and need not be reviewed. However, in order to explain

Jan 1, 1940

By JESSE L. MAURY

DEVELOPMENT of new gold mines in Canada since the price of that metal was increased in 1932 and 1933 has been of interest and importance to many of us. The day-by-day story has given an impression of aggressive effort and enough good luck so that the spirit of enterprise has been encouraged. It is the purpose of this article to report the results of a statistical appraisal which give emphatic numerical confirmation to this impression, together with certain side lights on the costs of development and equipment of new mines. The data presented have been taken from all readily available published sources up to the close of 1938 and are representative of that year. A. B. Bower did a large part .of the spadework and Weston Thomas offered many helpful suggestions.

Jan 1, 1939

By W. C. PAGE

AS the pioneer operation treating the mixed lead- zinc-iron ores from the district tributary to the Salt Lake Valley, the International Smelting Co.'s plant has offered an extremely interesting and instructive opportunity to study some phases of this problem. Basically, there were two main reason for our attempting to work out a successful operation for the separation and concentration of the values contained in the rather widespread deposits of these so- called lead-zinc ores. In the first place, the time was ripe and demanded some method of curtailing the economic waste resulting from the costs of past and present practice of smelting ores of this character, or rather, those ores which could stand the charges inherent with smelting them. Secondly, but rather primarily with us, we believe that such a solution would greatly in- crease in general the production of lead in the district tributary to the Salt Lake Valley. It is generally known that there were and are three relatively large lead smelting plants in the Salt Lake Valley and the decreasing production of correspondingly clean lead ores was not efficient to justify the existence of all three. We could not hope for better lead smelting metallurgy nor more efficient business management than was being practised, so the only prospect was to at- tempt to work out some way to increase the primary production and thus widen the scope of operations.

Jan 1, 1926

By J. Doig, A. A. Bauer, F. A. Rough

AN investigation of the phase relationships between the 6 phases of the uranium-molybdenum and uranium-titanium systems was conducted by studying alloys ranging in composition from uranium-31.5 at. pct Mo to uranium-34 at. pct Ti. A ternary cut showing these phase relationships is presented upon the basis of thermal-analysis data obtained and upon the basis of metallographic and X-ray examination of heat-treated and quenched specimens. Isothermal ternary sections, inferred from phase relationships determined between the two 6 phases, are presented for the uranium-molybdenum-titanium system. In the compositional range investigated, a y-ura-nium solid solution exists at elevated temperatures. At about 900°C the 6-U2Ti phase, with limited molybdenum solubility, forms. Epsilon, a molybdenum-titanium-rich solid solution appears at the same temperature and appears in all phase regions that exist below this temperature except in the terminal 6-phase regions. The y phase is stable to approximately 660°C in titanium-rich alloys; the y and 6-U,Ti phases decompose at this temperature to a uranium in a peritectoid reaction. The y phase in molybdenum-rich alloys of the ternary cut studied decomposes in an apparent eutectoid reaction, at about 593°C, to the 6-uranium-molyb-denum and a-uranium phases. The e phase while present, presumably plays a negligible role in these reactions. Titanium was found to markedly decrease the stability of retained y in these alloys. Age-hardening characteristics developed in titanium-contain ing uranium-molybdenum alloys quenched from 900°C and aged at 500°C are ascribed to decomposition of Y to the a and E phases. INTRODUCTION Alloys of uranium with molybdenum, titanium, and zirconium, respectively, are of great interest because of their potential use as reactor fuels. As a result, this interest extends to the constitution of these alloys, particularly in view of their uniqueness of constitution. In these systems, alone, among known uranium-alloy systems, an intermediate phase forms by direct decomposition of the high-temperature y-uranium phase. As a prelude to possible future alloy development, an investigation has been undertaken of the phase relationships that occur between the intermediate phases of these systems. These phase relationships have already been reported for the intermediate 6 phases of the uranium-zirconium and uranium-titanium systems.' The results of an investigation of the phase relationships between the 6 phases of the uranium-molybdenum and uranium-titanium systems are reported here. The phase relationships that occur in the binary systems pertinent to this investigation are shown in Fig. 1. Phase nomenclature appearing throughout this report is as shown in these diagrams; the crystal structure of the phase is given in Table I. EXPERIMENTAL PROCEDURE Alloys were cast and fabricated to flat plate. Specimens were heat treated and examined metal-

Jan 1, 1959

By W. G. Sinclair

THE North Texas district presented in this paper includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Jack, Knox, Montague, Wichita, Wilbarger and Young. It corresponds with the Texas Railroad Commission's district No. 9. Table I conforms with the nomenclature of pools as designated by the Commission. Most of the oil and gas produced in this region, generally referred to as the Red River uplift, comes from the Pennsylvanian strata. In recent years, however, increasing amounts are being developed in both the Mississippian and Ordovician.

Jan 1, 1946

By W. G. Sinclair

The wartime momentum of exploration continued throughout the year 1945 despite the end of hostilities in mid-August. The table below illustrates drilling activity in the various categories: Completed wells. . . . . . . . . . . . . . . . . . . . . . . . 401 Wildcats.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104 Wildcat discoveries, oil.. . . . . . . . . . . . . . . . . . . 2 Wildcat discoveries, gas-condensate.. . . . . . . 4 Development wells.. . . . . . . . . . . . . . . . . . . . . .297

Jan 1, 1946

By J. L. Carne

ORE control is a matter of planning and supervision based on a foreknowledge of the content and distribution of ore. The Inspiration orebody is predominately a copper-sulphide blanket, overlain by an oxidized zone of copper silicates, copper carbonates, and barren capping. Most of the ore is treated by leaching, and the optimum requirement of this method is the goal toward which the mining schedule is aimed. Both open-pit operations and underground mining are used. The problems of ore control at Inspiration are: 1-maintenance of metallurgical balance, 2-conservation of oxide ore, and 3-mining out of the orebody at an average grade which parallels that of the reserve figure. Prior to the fall of 1926 all of the Inspiration division ores were treated by flotation, but the mixed ores of the Live Oak-Keystone section carried too large a proportion of copper in the form of chrysocolla for satisfactory flotation. For this type of mixed ore the leaching process now in use had been worked out, and the plant was put into operation in the fall of 1926. The process is known as the ferric sulphate leach, and the leaching solvents contain both ferric sulphate and free sulphuric acid. Sulphide copper in the form of chalcocite is leached by the ferric sulphate, and the oxidized copper minerals are dissolved by the sulphuric acid. From the beginning of operations to the present time the plant has treated some 67 thousand tons of ore having an average copper content of 1.142 pet, of which 0.605 pct has been in the form of oxidized copper minerals. The plant is currently being operated at the rate of 11,500 tons per day, 7 days per week. However, this tonnage is produced in 6 days of mine operation. The average current grade is approximately 1 pct copper, of which about 50 pct is present as oxidized or acid-soluble copper. Close control of metallurgical procedures is a vital factor in operation of the plant and is in turn dependent upon careful regulation of feed. An excess of sulphide copper requires the presence of more ferric sulphate in the leaching solvents. On the other hand, an excess of ferric sulphate in the presence of a low sulphide feed seriously reduces the efficiency of electrolytic precipitation in tank house operations. This condition must be avoided at all costs. An additional factor must be considered. It is known that the sulphide content is predominant in the ore which remains in the reserve. To maintain the necessary sulphide-oxide proportion, so that the entire reserve will mine out at both a grade and a sulphide-oxide ratio that will be permissible throughout the remaining life of the property, it is obvious that the oxide reserve must be currently preserved to as great an extent as possible. Fortunately much of the oxide reserve is found in the open-pit operation. This happy circumstance adds flexibility to the procedure and makes it possible to maintain the close regulation necessary to insure best overall results, both mining and metallurgical. The two ore streams from the pit and underground operations join at the coarse-crushing plant, and proper control must be exercised before the ore reaches this point. The open pit is currently providing about 55 pet of the ore and underground operations the balance of production. Both operations are under a single superintendent so that the closely interrelated problems may be more readily controlled. The least flexible of the two producing units is the underground mine, where the mining method is block caving. Although a block of ground may be undercut and developed, characteristics of the material determine its caving action. The ore in the chutes must be drawn. The area currently mined from underground is in a zone predominately sulphide and is generally

Jan 1, 1952

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By Frank Rieber

EVERYONE is familiar with the story of the poor Indian and his leaking tepee. He couldn't repair the leak while it was raining, naturally. And when it wasn't raining, where was the incentive? Even if this traditional Indian was apochryphal, his counterparts are certainly alive today, and operating on a world-wide scale. - A recent issue of the Wall Street Journal, for example, carried an impassioned letter from an old cocoa planter, who wants the world to know why the price of cocoa has gone skyrocketing. For years, he says, British and American interests have bought cocoa at the cheapest possible price and, incidentally, from growers willing to sell at that price. Between them, they didn't put enough money back into the business, either to fight disease in the cocoa groves or to plant new cocoa trees. Until new trees are planted and come into bearing, we will be paying exorbitant prices for our cocoa, and getting less of it.

Jan 1, 1948

By Jack M. Swales

Kermac Potash Co., the newest American entry in a rapidly expanding industry, has come on the scene with notable variations in conventional shaft-sinking and mining techniques. Located in the famed potash producing district east of Carlsbad, N. Mex., Kermac started up its mine in November, 1965, to supply ore to the company's 500,000-tpy potash crystallization refinery. In so doing, the company (1) drilled the first large diameter mine shaft in the potash industry and (2) has employed new continuous miners especially adapted for use in thin potash beds. REACHING THE ORE ZONE In its initial mine planning, Kermac, a partnership owned jointly by Kerr-McGee Corp. and the National Farmers Union Development Corp., considered it imperative that the shafts be sunk and equipped as soon as possible and that the mine be developed sufficiently to insure a constant ore feed to the mill when the unit was placed on stream. After examining the alternative sinking techniques available to it, the company decided to accept a proposal by Big Hole Drillers, Inc., to drill the shaft from the surface through various formations of sandstones, siltstone, shales, anhydrite, limestones, dolomite and salts to the potash ore zone.

Jan 12, 1966