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By Alec M. Crowell, C. H. Thigpen

Continuing the increase in production of crude oil and condensate started in 1937, the oil fields of South Arkansas reached a 13-year peak with 26,570,704 bbl. for the year 1942. The stability of the production branch of the industry in the area is demonstrated by Fig. I, which reflects the fact that although the number of producing wells in the state has declined from 3280 in 1931 to 2957 at the end of 1942, total production has continuously increased since the beginning of 1937. This is because all fields discovered since Jan. I, 1937, have observed spacing patterns up to one well to each 160 surface acres, the dual completion of wells where there is more than one producing horizon Eight new pools were brought into production in South Arkansas during 1942 (Fig. 2) They increased the state's crude oil and condensate reserve by 121,000,000 bbl., bringing the total recoverable reserve figure to 450,000,000 bbl. (Table 3) as of Jan. I, 1943. Abandonment of wells in the stripper areas of the state increased by 32 per cent over the preceding year, there having been 142 wells permanently abandoned in 1942. For economic reasons 279 wells were temporarily shut down as of Dec. 31, 1942. A price increase may start these wells to pumping again and also be the incentive toward the commencing of several secondary recovery projects in the fields discovered between 1922 and 1937. There were 149 wells brought into production in 1942 as against 119 for the

Jan 1, 1943

By C. H. Thigpen, Alec M. Crowell

Continuing the increase in production of crude oil and condensate started in 1937, the oil fields of South Arkansas reached a 13-year peak with 26,570,704 bbl. for the year 1942. The stability of the production branch of the industry in the area is demonstrated by Fig. I, which reflects the fact that although the number of producing wells in the state has declined from 3280 in 1931 to 2957 at the end of 1942, total production has continuously increased since the beginning of 1937. This is because all fields discovered since Jan. I, 1937, have observed spacing patterns up to one well to each 160 surface acres, the dual completion of wells where there is more than one producing horizon Eight new pools were brought into production in South Arkansas during 1942 (Fig. 2) They increased the state's crude oil and condensate reserve by 121,000,000 bbl., bringing the total recoverable reserve figure to 450,000,000 bbl. (Table 3) as of Jan. I, 1943. Abandonment of wells in the stripper areas of the state increased by 32 per cent over the preceding year, there having been 142 wells permanently abandoned in 1942. For economic reasons 279 wells were temporarily shut down as of Dec. 31, 1942. A price increase may start these wells to pumping again and also be the incentive toward the commencing of several secondary recovery projects in the fields discovered between 1922 and 1937. There were 149 wells brought into production in 1942 as against 119 for the

Jan 1, 1943

By Charles A. Kliche

INTRODUCTION The Northern Great Plains Coal Province which occupies approximately 36.6 ha contains about one-half of the nation's total coal resources. About one million ha are underlain by coal that is considered to be mineable from the surface. The topography of the province is predominately plains, rolling hills, and some badland areas characterized by breaks or sharply eroded hills. Elevations range from about 1500 m above sea level on the west to about 600 m above sea level on the eastern boundary. The average slope of the ground is approximately 2 m per km. Streams in the province drain generally easterly and southeasterly (1). In the United States, the Northern Great Plains Province lies within the states of North Dakota, South Dakota, Montana, Wyoming, Nebraska, and Colorado. The coal within the province is located almost entirely in the states of North Dakota, Montana, and Wyoming. Although it is relatively low rank, the coal within the province encompasses a large portion of the total remaining U. S. reserves. The U. S. Geological Survey estimates the total remaining coal resources of the United States to be 2.6 trillion mt within 1000 m of the surface, and 2.9 trillion tons within 1830 m of the surface. Of this total, only about 177 billion mt are classified as reserves meaning that they are (1) known in location, quantity and quality from geologic evidence supported by engineering measurements, and (2) economically recoverable based on currently available technologies and current market value (2).

Jan 1, 1983

By Jean A. Andre

In 1969 "Société des Mines et Fonderies de Zinc de la Vieille-Montagne" produced 221,000 tons zinc ingots and 22,000 tons zinc dust, thus rating highest on the world's zinc producer list. The Company's plant at Balen, Belgium, with an output of 135,000 tons electrolytic zinc is the most important one of this group; it is an integrated metallurgical zinc and lead unit with recovery of most by-products. The present paper describes the zinc production facilities. The roasting section includes four fluid bed roasters (total concentrates charged: 740 tpd) and two sulfuric acid having a corresponding capacity. Calcine is leached in a fully automated plant by a two-step continuous process. Leaching residues, mixed with lead furnace slag, are treated in a shaft furnace. The recovered zinc fume is leached separately. In the near future, the leaching residues are to be treated by a wet process, developed in the Company's own laboratories. Purification of solutions is accomplished in two steps: antimony and zinc dust are added in the first one, only zinc dust in the second one for removal of cadmium. Electrolysis cells are partly of a conventional type. A new type of cell configuration was put onstream in October, 1969, planned output 60,000 tpy. Main features of the new cell rooms are the fully automatic pulling, stripping and replacing of the jumbo-size cathodes (immersed area 2.6 m2). Zinc cathodes are remelted in induction furnaces followed by in-line automatic casting and stacking machines.

Jan 1, 1970

By Norman J. Sather

LOCATION AND HISTORY The Bunker Hill Mine is situated on the south side of the Coeur d’Alene River in Shoshone County of Northern Idaho near the City of Kellogg. Kellogg, the largest in the Coeur d’Alene District cities, is at an elevation of 2,300 feet and has a population of approximately 7,000 people. It can be reached by air, railway or highway. The history of the Bunker Hill Mine dates back to August 26, 1885, when Noah S . Kellogg found the outcrop of the Bunker Hill ore body on the hillside above the present town of Wardner, Idaho, in Milo Gulch. A small concentrator was erected in 1886. Before the railroad came, the mine output was transported by mule teams to the head of navigation on Coeur d’Alene Lake. After ten years of production, an interest was purchased in the Tacoma Smelter at Tacoma, Washington, to which the entire output was shipped. In 1916 and 1917 a modern lead smelting plant and refinery was erected and in 1927 and 1928, a modern Electrolytic Zinc Reduction Plant was built and put into operation by the Sullivan Mining Company which was 50% owned and now totally owned by The Bunker Hill Company. GEOLOGY AND MINERALOGY The Bunker Hill ore bodies are found in gray and greenish gray quartzite and argillaceous quartzite of Precambrian age and are known as the Revett and St. Regis formations. Most of the ore bodies are found in the St. Regis formation.

Jan 1, 1970

By W. L. Remick

The hydrotator coal-cleaning process was developed as an economic necessity to meet the ever-increasing demand for an inexpensive method of cleaning coal down to the sizes ordinarily referred to as "dust." As the most urgent demand seemed to be in the anthracite field, all experimental work has been conducted in that territory during the past two years, with the exception of a few months during the strike of 1925-26, when some experiments were performed in the Alabama bituminous fields. The first commercial plant was constructed at the Middle Creek Colliery of the Philadelphia & Reading Coal & Iron Co.,. Pottsville, Pa. This plant is now operating. Application The field of application of the process is: 1. Cleaning anthracite fines, ordinarily described as "slush" or "silt." Slush contains all sizes from 3/32 in. down to and including I(dust." (Anthracite passing a 3/32-in. mesh is also referred to as No. 2 Barley and No. 4 Buckwheat.) 2. Cleaning sizes too fine for recovery by other methods. 3. Removal of coal from sand circulated in the Chance sand-flotation process. 4. Cleaning of bituminous sizes from % in. down to "dust." 5. As equipment for the performance of the froth flotation process. 6. Other separating, extraction and washing processes which may be considered outside the realm of coal cleaning. Principle of Operation Fig. 1 shows the method of classification practiced under the Hydrotator patent.' In coal cleaning the machines are operated as "hindered settling" classifiers, the flow of solids and liquids being so controlled that the units may be combined in series.

Jan 1, 1927

By M. L. Fuller

IN connection with an investigation in this laboratory on the high-zinc side of the copper-zinc system, it was observed that well developed segre-gate structures of the Widmanstätten type were formed when a secondary phase precipitated from the solid solution of copper in zinc. This paper presents an analysis of the crystallographic relationship between the segregate and the solid solution matrix. The data to be presented are an interesting addition to the literature on segregate structures in that the plane of segregation is one of the less densely populated planes. In agreement with the generalization of C. H. Mathewson and D. W. Smith1 the plane of segregation in the matrix con-tains the direction of closest atomic packing of the lattice. Furthermore, the matrix and the segregate are both hexagonal close-packed, which has not been reported hitherto in the literature.2 The increasing com-mercial importance of zinc alloys containing copper makes this funda-mental study of value to the metallography of zinc alloys.

Jan 1, 1933

By Gerhard Derge

THE orientation relationships resulting from allotropic transforma-tions and the formation of segregate structures in metals and alloys have been the subject of the eight earlier papers in this series1. A brief summary of orientation studies has also been given by Sachs2. A survey of these papers discloses that the factors that determine the orientation relationship of a precipitated phase to its parent solid solution, as Well as the outward form and appearance of the new phase, are not completely understood. It is now evident that crystallographically analogous systems, as a rule, exhibit the same type of Widmanstätten figure and orientation relations, so that useful information is not to be expected from examination of a new alloy involving lattice combinations of which the orientation relationships are already known. Therefore, the determina-tion of the relations existing between lattice types that have not already been studied seems to be the most promising mode of attack upon the problem; both of the systems reported in this paper represent new com-binations of lattice types.

Jan 1, 1937

By Robert Glass Cleland

WALTER DOUGLAS succeeded his father, Dr. James Douglas, as president of Phelps Dodge in 1916. Before assuming office, the new president had been assayer at Bisbee, superintendent of the Copper Queen, general manager of all the Phelps Dodge mining interests, and altogether had spent a full quarter of a century in various phases of the company's business. Energetic and imaginative, experienced and courageous, he had need of all these qualities before he surrendered the direction of affairs into younger hands, fourteen years later. For the period of his administration was one of sudden ebb apd flow, flush production, drastic curtailment, quick recovery, and near-disaster. In 1917, soon after Walter Douglas became president, Phelps, Dodge & Co., Inc., which had been formed in 1908 as a holding company, went through an internal reorganization for the purpose of simplifying the structure and changing it from a holding company to an operating company. The Copper Queen Consolidated Mining Company, which had the necessary charter power and authority to carry on the business of any and all the subsidiary com-

Jan 1, 1952

By W. M. Corse

AT THE TURN of the century the nonferrous alloy industry was awakening to the value of scientific metallurgy, and brass foundries and rolling mills began to establish their own research laboratories for scientific research and control. As the industry grew and its scope broadened it became apparent that an organization was needed that would stand in the same relation to the nonferrous industry as the American Foundrymen's Association did to the iron foundry business. The brass founders' group of the foundrymen's association discussed the matter and it was finally decided to appoint a com- mittee to draw up a constitution for a new organization to be known as the American Brass Founders' Association. Charles J. Caley was chairman and Dr. Richard Moldenke secretary of this committee. The object of the organization as defined by the constitution was the study of the technological development of alloying and founding non- ferrous metals, and furthering the advance of nonferrous metallurgy and the standardization of materials and operations in cooperation with the Bureau of Standards and engineering societies.

Jan 1, 1932

By F. J. Plecity, J. T. Michalak, W. C. Leslie

W. M. Williams (McGill University)-The authors are to be congratulated on completing this detailed investigation of recrystallization behavior. The present writer has recently completed some research at the University of Toronto on the recrystallization and grain growth behavior of a number of "pure" irons, and he would like to take issue with the authors' contention that recrystallization cannot be followed by means of hardness measurements. Two series of specimens of Ferrovac E, a com- mercially available iron, were annealed to complete recrystallization at 525" and 620" C, measurements being made both of Rockwell hardness and of volume percent recrystallized as a function of annealing time. Good correlation was found between these two quantities and, following the earlier practice of Cook and Richards for copper, hardness measurements were used in an extensive investigation of recrystallization. No anomalous behavior was observed as a result of this practice. Specimens which showed complete softening always showed, (metallographically and by X-rays), completely re-crystallized structures. These observations do not, of course, detract in the least from the results of the work under discus-

Jan 1, 1962

By E. H. Bunce

CONTINUED progress in zinc metallurgy has been shown during 1933 by the adoption of new methods as well as the modernization of old processes and equipment, and by the initiation of new fields of activity for future advancement. The use of suspension roasting continued to grow as its advantages and adaptability became increasingly, apparent. The process developed by the National Smelting Co., Ltd., several years ago, of completely roasting on large sintering machines with utilization of the gas for acid manufacture has worked so successfully that an additional machine was installed during the year. At both the Swansea and the Avonmouth Works all of the ore for smelting is now roasted on the large sintering machines, thereby completely eliminating the old hearth-roasting furnaces. Work continued on obtaining partial purification of zinc ores from lead and cadmium by close control of conditions on the sintering machine, and in a few instances by chlorine additions to the ore before sintering. Ores so treated were either partially roasted or com-

Jan 1, 1934

Recent start-up of a new 3450 t/d (3800 stpd) copper-zinc concentrator complex in northern Manitoba, Canada, is expected to open new reserves and dramatically cut transportation costs for Hudson Bay Mining and Smelting Co.'s Snow Lake operations. The new $C33-million mill is located in Stall Lake, Manitoba, and includes a new crushing and grinding facility and two flotation circuits for the production of 23-25% copper and 55% zinc concentrates. A small amount of lead concentrate will also be recovered. The plant will produce some 145 000 t/y (160,000 stpy) of concentrates, to be shipped by rail to the firm's Flin Flon copper smelter and zinc refinery complex, located 177 km (110 miles) to the west on the Saskatchewan-Manitoba border.

Jan 9, 1979

NEW MEMBERS The following list comprises the names of those persons who became members during the period Aug. 1, 1916, to Sept. 10, 1916: ALLEN, Louis M., JR., Chief Mine Sampler, Old Dominion Min: & Smelt. Co., Globe, Ariz. ATKINSON, CHESTER, Min. Engr., Asst. Supt., Smelt. Dept., Cerro de Pasco Mining Co., La Fundicion, Peru, South America. BAKER, CLAIR LINCOLN, Genl. Mgr., Mexican Dept., Amer. Smelt. & Ref. Co., 1108 Mills Bldg., El Paso, Tex. BARROWS, WALTER A., 3d, Asst. Supt., Blast Furnaces, Thomas Iron Co., Hellertown, Pa. BARTHOLOMEW, GEORGE POMEROY, Asst. Cons. Engr., Guggenheim Bros., 120 Broadway, New York, N. Y. BILLOW, ELMER E., Pres., National Supply Co., 416 NN-rest Grand Ave., Chicago, 111. BROWN, SAMUEL ROLLINS, Mill Supt., The Plymouth Cons. Gold Mines, Ltd., Plymouth, Cal.

Jan 10, 1916

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of June, 1913: Members. ANGERER, VICTOR, Vice-Prest. and Genl. Mgr., Wm. Wharton, Jr. & Co., Inc., 25th St. and Washington Ave., Philadelphia, Pa. BULLOCK, ALLYN, Min. Engr Hazleton, Pa. CUNNINGHAM, NOEL, Met. Engr., Hollinger Gold Mines, Ltd., Timmins, Ont., Canada. ESTABROOK, EDWARD L., Supt. of Colliery 436 Center St., Ashland, Pa. GATES, A. 0., Instructor Purdue Univ., La Fayette, Ind. LUDLUM, ALBERT C., Prest., New York Engrg. Co., 2 Rector St., New York, N. Y. MILLER, HERBERT F., Met. Engr P. 0. Box 142, Verona, Pa MORTON, ELMER T., Min. Engr Clifton, Ariz. MURFIT, RICHARD H.. Fdv. Asst Hess Steel Castings Co., Bridgeton, N. J. QUAYLE, THEODORE W., Chief Sampler, Metcalf Mines, Arizona Copper Co., Metcalf, Ariz.

Jan 7, 1913

By J. A. Herbst, J. L. Sepulveda, J. D. Miller

Effective bismuth removal from flue dust residues has been accomplished for flue dusts from both zinc and copper smelters. Selective dissolution of bismuth, with respect to silver and lead, can be achieved by the proper manipulation of temperature, sulfuric acid addition and sodium chloride addition. Optimum levels of these variables were determined using a response surface technique to maximize the objective function: Y = %Bi/(1 + %Ag). In the case of the flue dust residue from a zinc smelter, which contains bismuth as an impurity (0.05%), 86% bismuth removal can be realized with less than 1% combined silver and lead dissolution. Similarly, in the case of flue dust from a copper smelter, which contains bismuth as a primary constituent (3.3%), 93% bismuth removal was obtained with little dissolution of silver and lead values.

Jan 1, 1977

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett' theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy's law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970

By M. Kitada, U. Kawabe, F. Ishida, T. Doi

The relations between micros tructures and critical current density in transverse magnetic field were experimentally investigated due to each transformation of the 0 to 0&apos; + P" phases at 700&apos; C for superconductmainly examined using replication electron microscopy. The ß&apos; or a precipitates were found to pin down magnetic flux lines in these alloys. The effects of precipitation upon the critical current density were discussed in relation with the size, spacing, and characler of these precipitates. HIGH magnetic field superconductors, such as Nb-Zr, Nb-Ti, and Nb-Zr-Ti alloys, have been recently put to extensive practical use as winding materials for superconducting magnets.13 The critical current density of these hard superconductors under an applied magnetic field is an important characteristic for magnet materials and is very sensitive to metallurgical structure. It is generally known that the critical current density is increased by introducing dislocations and precipitates into a superconductor; that is, dislocations and precipitates are presumed to be barriers that hinder quantized flux lines from moving.4&apos;5 Theoretical6&apos;7 and experimental analyses of the motion of flux lines and the interaction between flux lines and various defects have already been reported by many authors. Metallographic analysis of high magnetic field superconductors such as Nb-Zr and Nb-Ti is difficult, so that no quantitative relationship between microstruc-ture and critical current density has been established yet. In this paper, the effect of precipitation on the critical current density in magnetic field was investigated for two superconducting alloys, Nb-40Zr-10Ti and Nb-5Zr-60Ti. In these alloys the resistive critical field H, at 4.2oK was about 100 kG and the critical current density Jc at 80 kG was of the order of 104 amp per sq cm.13-l5 The superconducting properties were examined in relation to the microstructural changes due to transformation of i) the ß to ß&apos; + ß" phases at 700°C for Nb-40Zr-10Ti alloy and ii) the ß to a + ß phases at 500°C for Nb-5Zr-6OTi alloy. The effect of size, spacing, and character of precipitates on flux line pinning was in particular examined. The microstructures were studied by means of residual resistivity, microhardness, and tensile strength measurements as well as by X-ray diffraction, optical, and replication electron microscopies. I) EXPERIMENTAL PROCEDURE Pure niobium, zirconium, and titanium, in the form of rods 0.8 cm in diam, served as raw materials. Results of chemical analyses of these rods are given in Table I. Ingots of the alloys, 0.4 cm in diam and 3 cm in length, were prepared by means of levitation melting, utilizing a copper mold in an argon-gas atmosphere. Samples from the ingot then were cold-worked by grooved mill to 0.2 cm in diam, heat-treated homogeneously (in the ß phase region) for 5 hr at 1100° in a vacuum of 1 x 106 Torr, and finally cold-drawn to 0.025 cm in diam. For heat treatments, samples were wrapped in niobium foil and sealed in an argon-gas atmosphere in fused quartz capsules. Water quenching was done after each heat treatment. Subsequently H-J, were performed at 4.2° by slowly transporting the current through the samples 4 cm long, under transverse magnetic field, until the least detectable resistive terminal voltage was observed. The resistive critical field H, was taken as the field at which 100 pv appeared at 4.2°K across a sample 3 cm in length, with a current of 5 ma. The critical temperature T, was measured by means of a conventional four-probe resistivity technique and taken as the temperature at which the sample resistance reached one-half of full restoration of the normal-state resistance with a current l ma flowing through a sample 2 cm in length. Precipitates were observed by means of optical microscopy and carbon replication electron microscopy. The etching solution consisted of 5 ml HF, 10 ml H2SO4 10 ml H2O2, and 50 ml H2O, and shadowed carbon replicas were examined in a itachi HU-11 electron microscope operated at 50 kv. X-ray diffraction photographs were taken by a 11.46-cm-diam Debye-Scher-rer camera using copper Ka radiation. The micro-hardness was measured under a load of 200 g using

Jan 1, 1969