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By A. W. Fahrenwald

Flotation practice in Idaho is now about 13 years old. The advance has been steady during these 113 years. The operators have been alert to take advantage of the newest developments and they have themselves made a constant effort to improve their work. The metallurgical improvements are due to the development of (1) better equipment, (2) better reagents, and (3) better understanding and control of the process. During the eight years the writer has been in this district, there has been continuous experimentation by several companies to improve the ore dressing by flotation methods. Gravity concentration has fought hard to hold its place, and although it is true that gravity processes have been improved during this period, nevertheless, in several of the important mills of the district the few tables that managed to hang on have finally given way. On the straight-lead ores, tables and jigs are still used; and, due to better classification, their hold on this job has been strengthened. Ores of the District The ores of the district are of two general classes: (1) clean lead ores, such as those from the Bunker Hill and Hecla mines, and (2) complex lead-zinc ores. The general impression prevails that the clean lead ores, class 1, are simple and that it is easy to obtain high recoveries and good grade products. This, in a way, is a false impression; there is quite a high percentage of locked middling in these ores at 100 and' 150-mesh sizes. Improved classification preparatory to table treatment of this type of ore has made it possible to segregate effectively a high-grade middling which is further comminuted and floated. The complex lead-zinc ores of the district, of which the ore from the Morning mine of the Federal Mining & Smelting Co. is a typical example, always have presented a difficult problem. It always has been comparatively easy to make a clean lead concentrate, but it never has been possible to concentrate sphalerite with a specific gravity of 4.10 from siderite of gravity 3.88. Also, a large percentage of the galena and sphalerite of this class of ore refuses to separate out until the crushing has been carried

Jan 1, 1928

By Edwin Higgins

SINCE the "Days of Forty-nine" California has been the premier gold producing state of the union. The greatest production was recorded in 1.852, during which year the state's placer and lode deposits yielded over 81 millions. This peak was followed by a steady decline to about 12 millions during the years 1888 to 189.3, a period marked by the cessation of gravel mining. After 1893, production increased to a new peak of over 22 million in 1915, thereafter decreasing steadily to something over 13 million in 1923. Today; California's gold production shows a decrease of 84 per cent. as compared with the output of 1852, and a decrease of 41 per cent, as compared with 1915. It is not a difficult matter to find the causes of this more recent decline. In 1916 there began an upward swing in the cost of labor, which represents approximately 60 per cent. of the cost of mining, and in the price of supplies, representing the remaining, 40 per cent. This rise continued until 1922 and since that year there has been no decided tendency either upward or downward. The increase in the cost of mining since 1916 is variously estimated at from 50 to 75 per cent.; the price of gold has remained fixed at $20.67 per oz. This condition resulted in wiping out the profits of the low-grade operations which, in recent years, have constituted California's main source of supply of gold ore. It is now predicted that there will be renewed activity in California- gold mining. What are chances for the materialization of this forecast? A boom or even a revival of gold mining must of necessity be brought about or accompanied by one or more of the following factors: 1. A decrease in the cost of mining. 2. An increase in the price of gold. 3. New capital for development. 4. The discovery of new deposits. 5. The revival of hydraulic mining.

Jan 1, 1925

By Bruno KERL

THE list of deaths reported during the year 1905 comprises the following names (the figures in parentheses indicating the year in which the persons named were elected to membership:- Honorary Member.-Dr. Bruno Kerl. Members and Associates.-Charles Christy Adams (1903), John Wesley Anderson (1898), William Burton Barber (1901), Thomas A. Bennett (1900), Luke W. Bryan (1901), Edwin S. Daugherty (1905), William Scott de Camp (1875), George H. Eldridge (1889), B. W. Frazier (1871), John Broome Guinn, Jr. (1897), Dana C. Irish (1900), Harry Hugh Lee (1899), William Alfred Lindsay (1902), Roland C. Luther (1884), James MacNaughton (1890), Gordon McLean (1899), Herbert Holmes McNamara (1902), August R. Meyer (1886), William Orr (1897), William J. Parker, Jr. (1898), Joseph Phillips, Jr. (1895), Charles O. Ripley (1902), Emmerich J. Schmitz (1883), Ludwig Philip Seeger (1900), Jacob Johnston Sperry (1900), Gustavus H. Stoiber (1902), William L. Study (1905), Robert Macnair Wilson Swan (1900), Richard Henry Terhune (1886), Joseph Thiry (1892), John N. Tisdale (1903), Alfred Isham Totten (1897), Walter H. Virgoe (1902), Charles H. Wellman (1890), Harvey L. Williams (1903). Of these, Dr. Bruno Kerl and Prof. B. W. Frazier have been made the subjects of special Biographical Notices in the Bi-Monthly Bulletin 1 the former in No. 4, July, 1905, p. 743, and the latter in No. 5, September, 1905, p. 1097. Concerning the remainder of the list, the following paragraphs comprise such information as could be obtained by the Secretary. Charles Christy Adams, who had been a member of the Institute since 1903, died in Johannesburg, South Africa, August 31. 1905. He was born in New York City, July 13, 1849, and received his technical training at the Colorado State School of

May 1, 1906

Executive FREDERICK M. BECKET, Chairman HOWARD N. EAVENSON J. V. W. REYNDERS H. A. GUESS WILLIAM WRAITH Finance HENRY KRUMB, Chairman PAUL H. MERCER H. G. MOULTON Admissions JOHN M. LOVEJOY, Chairman GEORGE D. BARRON DONALD M. LIDDELI. E. V. DAVELER W. D. B. MOTTER, JR. Alternates AMOR F. KEENE L. F. STROBEL SAM TOUR Membership LEWIS B. LINDEMUTH, Chairman EDWARD H. ROBIE, Secretary Executive Committee NELSON DICKERMAN FREDERICK LAIST FRED H. KAY THOMAS T. READ H. A. KURSELL A. T. SHURICK SAM TOUR

Jan 1, 1932

By Charles R. Keyes

I. INTRODUCTION. FOR a period of several years, and in a large number of cases, the Metallurgical Laboratories of the New Mexico School of Mines were employed in umpire work. During this time many important local problems were solved. Against the results of careful chemical analyses of ores, assay-returns were often checked. In many cases the assay-methods of mine and custom-smelter were compared, and both often found faulty for the ore concerned. A wide range of ores was covered. Many of the chemical analyses and assays were made by Dr. F. C. Lincoln, Professor of Metallurgy, now of the Montana State School of Mines. A varied series of instructive assays was prepared by Prof. R. B. Brinsmade, now of the West Virginia State University. Single assays and given series of tests were undertaken by H. T. Goodjohn, now chief chemist to the Cia. Metalurgica de Torreon, Coahuila, Mexico; by H. J. Hubbard, now superintendent of the Butters Divisadero Mines, Jocoro,. San Salvador, C. A.; by E. D. Morton, now superintendent of the Arizona & Nevada Copper Mining Co., at Lunning, Nev. ; and by A. W. Edelen, now superintendent of the Angangueo Unit of the American Smelting & Refining Co., in Michoacan, Mexico. A critical comparison of assay-methods that were found to be followed in the case of certain gouge-ores mined in the Mimbres range in New Mexico, and about which there had been much controversy, was made by D. F. Riddell, then Acting Professor of Assaying, and now superintendent of the Providentia Mines Co. of Parral, in Chihuahua, Mexico. To him is due the credit of much that is contained in the following notes, which be has generously permitted -to be used in advance of the publication of the complete results.

Jul 1, 1911

By E. H. Rennhack

Phase equilibria of the zinc-rich portion of the Zn-Fe-A1 system containing up to 20.0 wt pct Fe and Al have been investigated at 600°C (1112°F), 450°C (842°F), and room temperature by metallographic and X-ray diffraction techniques. The phase relationships were found to involve only those phases present in the three binary systems. THE presence of small quantities of aluminum (approx. 0.2 wt pct*) in zinc galvanizing baths is known to suppress the formation of Zn-Fe alloy layers within the coating.' As part of an extended investigation of this suppression effect and the alloy reactions involved, the zinc-rich corner of the Zn-Fe-A1 equilibrium system containing up to 20.0 pct Fe and Al was determined at 600°C (1112°F), 450° F (842° F), and room temperature. The present paper reports the findings of this study. The constitution of the Zn-Fe system has been reported by Raynor2 based mainly on the work of Schramm3-3 and Truesdale et a1.6 The solid solubility of iron in zinc is extremely small and lies between 0.0009 and 0.0028 pct in the range 150° to 400°C (302°to752°F). Within the temperature and composition range of interest, a eutectic reaction involving nearly pure zinc, liquid = Zn+FeZn13, is observed at about 419°C (786° F) and 0.018 pct Fe along with a peritectic reaction, FeZn7+ liquid e FeZn13, at 530°C (986° F) and 6.2 pct Fe. The latter reaction is sluggish due to the large proportipn of solid phase involved in the transformation. Halla et al.,7 identified the compound FeZn13 as monoclinic with a = 13.68, b = 7.63, c = 5.07, and B = 128°44'. The structure of FeZn7 was reported by Bablik, et al.,8 to be of hexagonal symmetry, belonging to either the C6v = C6/m mc or D46h = C6/mc space group. Divensions of the unit cell are a = 12.81A and c = 57.6a. The Zn-A1 diagram as composed by Raynor9 and later Gebhardt10 is characterized by a eutectic decomposition, liquid 382°C (720°F) and 95.0 pct Zn and a eutectoid decomposition, at 275° (527°F) and 78.0 pct Zn. The eutectoid reaction cannot be suppressed permanently by quenching. Above 275° (527° F), a and a' co-exist in a closed miscibility gap between 31.6 and 78.0 pct Zn. Both phases are fcc and have nearly the same lattice parameter. The maximum solubility of aluminum in zinc (B) is approximately 1.0 pct at the eutectic temperature. PROCEDURE Materials. The experimental alloys were prepared from both massive and powdered material. Cast alloys were composed from three zinc-base master alloys containing 8.0 pct Fe, 16.0 pct Fe, and 50.0 pct Al which were made from C.P. zinc, Armco iron, and

Jan 1, 1962

By K. Leutwyler

The key to realistic casing stress analysis in thermal recovery installations is accurate knowledge of the temperatures involved. Much information leading to prediction of heat losses from tubing string to wellbore has been published. This .same information permits calculation of casing temperature under certain conditions. This paper reviews the basis for most of the published work, the line source solution to the diflusivity equation and examines some of its application criteria in the light of unsteady-state conditions. An alternate finite differences method is presented for correlation, and experimental data pertaining to the heat transfer mechanism in the annulus is reported. In the light of the information presented in the paper, it appears that the assumption of a line source for the tubing-wellbore system is valid even for reasonably short periods of heat flow, .such as "steam soak" operations. The empirically modified equation presented earlier matches computer derived results of the finite differences approach lor periods as short as 50 hours. Previously predicted cas ing temperatures and the associated stress levels are thus verified based on these correlative computations and the reported experimental information. Fall out from the computer output resulting in some studies of the influence of insulating cement properties on casing temperature, and experimentally studied effects of nitrogen placed in the annulus at various pressures., are described. INTRODUCTION Generally speaking, predictions of average casing temperatures have been based on an idealized model involving a centralized tubing string at uniform constant temperature radiating energy towards the casing under steady-state conditions.'. ' Heat is transferred away from the casing to the formation by unsteady-state conduction across thermal barriers consisting of cement and the mud sheath. Heat balances written on the casing permit prediction of instantaneous casing temperatures. During early periods of injection, casing temperature varies appreciably as a function of time; however, for long injection times this variation decays as heat flow from the wellbore to the formation stabilizes, and it becomes virtually negligible as conditions surrounding the wellbore become quasi-steady-state (Fig. 1). Carslaw and Jaeger -escribe a solution to the diffusivity equation for a line source (Fig. 2). A constant supply of heat is introduced into the medium from the line placed into the origin of the x-y coordinate system and parallel to the z-axis. Heat spreads outward in the infinite cylindrical solid and the temperature increase on a line going through point (x, y) parallel to the z-axis at a distance r can be predicted by: The following criterion must be considered: the Carslaw and Jaeger equation is obtained on the basis of a large

Jan 1, 1967

By Scott, Turner

MY whole life has been spent in the mining business, PO I naturally tend to address my remarks particularly to the newly-graduated mining and metallurgical engineers among you. To a certain extent, all forms of engineering principles are involved in the training of the mining engineer, and most sorts of engineering are certainly utilized by him, so every one of this graduatins class is concerned with the field I propose to discuss.

Jan 1, 1932

Executive SCOTT TURNER, Chairman FREDERICK M. BECKET JOHN A. MATHEWS H. A. GUESS WILLIAM WRAITH Finance HENRY KRUMB, Chairman PAUL D. MERICA ROBERT E. TALLY Admissions JOHN M. LovEJOY, Chairman GEORGE D. BARRON ERLE V. DAVELER WILLIAM H. BASSETT W. D. B. MOTTER, JR. Alternates HENRY B. FERNALD F. JULIUS Polls AMOR F. KEENE

Jan 1, 1932

By Charles R. Keyes, D. F. Riddell

For a period of several years, and in a large number of oases, the Metallurgical Laboratories of the New Mexico School of Mines were employed in umpire work. During this time many important local problems mere solved. Against the results of careful chemical analyses of ores, assay-returns mere often checked. In many cases the assay-methods of mine and custom-smelter were compared, and both often found faulty for the ore concerned. A wide range of ores was covered. Many of the chemical analyses and assays were made by Dr. F. C. Lincoln, Professor of Metallurgy, now of the Montana State School of Mines. A varied series of instructive assays was prepared by Prof. R. B. Brinsmade, now of the West Virginia State University. Single assays and given series of tests were undertaken by H. T. Goodjohn, now chief chemist to the Cia. Metalurgica de Torreon, Coahuila, Mexico; by H. J. Hub-bard, now superintendent of the Butters Divisadero Mines, Jocoro, San Salvador, C. A.; by E. D. Morton, now superintendent of the Arizona & Nevada Copper Mining Co., at Lunning, Nev.; and by A. W. Edelen, now superintendent of the Angangueo Unit of the American Smelting & Refining Co., in Michoacan, Mexico. A critical comparison of assay-methods that were found to be followed in the case of certain gouge-ores mined in the Mimbres range in New Mexico, and about which there had been much controversy, was made by D. F. Riddell, then Acting Professor of Assaying, and now superintendent of the Providentia Mines Co. of Parral, in Chihuahua, Mexico. To him is due the credit of much that is contained in the following notes, which he has generously permitted to be used in advance of the publication of the complete results.

Jan 1, 1912

By AIME AIME

Russell B. Paul, Chairman of the Special Committee on Divisional Relationships, presented the interim report of his Committee which was published in the September, 1945, issue of MINING AND METALLURGY and a copy of which is incorporated in the official minutes of this meeting. The following specific actions were taken by the Board of Directors in relation to the six recommendations in the Summary of the Report as published: (1) Mr. Haider, Chairman of the Petroleum Division, presented the formal request of his Executive Committee that the headquarters of the new Secretary of the Petroleum Division be established in Dallas, Texas. After lengthy discussion in which the point was made that the success of this program would depend upon effective co-operation between the Chairman of the Division, the Secretary of the Petroleum Division, and the Secretary of the Institute, the request was approved. The new secretary will be selected by the Division and will be employed by the Institute in the capacity of an Assistant Secretary. (2) The following item in the report was approved:

Jan 1, 1945

ALABAMA Anniston.-Bretz, J A Carnngton, F G Gerber, A B Ashland -Barton J Sturdevant, J C Bessemer -Abbott, C E Ball, T L Ferguson, V Salmon, H S Schaber, C F Thompson, N E Whatley, W J Birmingham.-Adams, J H -Aldrich, T H Aldrich, T H , Jr ALASKA Anchorage -Dyer, B W. Parker, H C Smith, S S Chichagof.-Baumann, H N , Jr Copper River.-Douglass, W C Cordova.-Hazelet, G C Fairbanks -Davis, J A Hyder -Pitt, D L Juneau -Jackson, G. T Murphy, R E R..11 ti At i

Jan 1, 1923

IN THE past, we have, perhaps, been somewhat careless in our furnace practice, in the use of high-grade material, lowering the production costs through demanding high-grade ores, increasing the size of units, and eliminating heat losses by collecting and returning unused heat to our furnaces. Further economies would seem to be possible through keeping out of the furnace those materials that appear to serve no useful purpose and carry with them heat that should be used in reduction operations. In the manufacture of pig iron, about three tons of inert nitrogen pass through the furnace for each ton of iron produced. This nitrogen serves no useful purpose in the chemical actions involved, but when discharged into the atmosphere it carries away a considerable quantity of heat. Can not this loss be eliminated, at least in part, through the use of more oxygen in the blast? Many metallurgical chemists, during the past 20 years, have stated that they thought it can and have urged that the plan be tried. Others have expressed doubt, not being able to visualize how more oxygen could be used in present practice; they have regarded it as impracticable, without trying to conceive of an entirely new practice based on a new reagent. That more experimental work has not been done is due to the fact that no cheap oxygen has been available, but the committee believes that there is strong reason to expect that, should a demand exist, 99 per cent. oxygen may be made at a cost not to exceed $3 per ton. The theoretical studies of the committee have indicated such marked economy by using oxygenated air in various operations that its members strongly recommend experimental work to verify the anticipated economies. The committee has developed plans for experimentally determining the effects of oxygen-enriched air on the operation of an iron, blast furnace. A furnace with a height of 30 ft. has been built and it is recommended that the plans be put in, effect as the first step in the research.

Jan 11, 1924

By William D. Southard, Joseph W. Schlitt, Bruce P. Ream, Lawrence J. Haug

The operation of Kennecott 's Bingham Canyon copper precipitation plant, one of the world's largest, is described. This description includes a brief historical review of precipitation at Bingham and the general layout and operation of the present cone cementation facility. Current practices are based on results of studies undertaken to define improvements needed in each unit operation. These improvements were required to meet changing plant conditions and were implemented primarily within the constraints of the existing facilities. Specific unit operations included were the cone precipitators, the cone discharge thickener, the cone effluent settling basins, and the plate and frame filter presses. As a result of these improvements, loss of precipitated copper decreased and the degree of precipitation increased, raising copper recovery by 9 t/d. At the same time, iron consumption was reduced by 22.5 t/d. Problems in drying the cement copper were also overcome so that a product containing 12-15% moisture could be consistently delivered for smelting.

Jan 1, 1980

By W. Joseph Schlitt, William D. Southard, Bruce P. Ream, Lawrence J. Haug

The operation of Kennecott's Bingham Canyon copper precipitation plant, one of the world's largest, is described. This description includes a brief historical review of precipitation at Bingham and the general layout and operation of the present cone cementation facility. Current practices are based on results of studies undertaken to define improvements needed in each unit operation. These improvements were required to meet changing plant conditions and were implemented primarily within the constraints of the existing facilities. Specific unit operations included were the cone precipitators, the cone discharge thickener, the cone effluent settling basins, and the plate and frame filter presses. As a result of these improvements, loss of precipitated copper decreased and the degree of precipitation increased, raising copper recovery by 9 t/d. At the same time, iron consumption was reduced by 22.5 t/d. Problems in drying the cement copper were also overcome so that a product containing 12 - 15% moisture could be consistently delivered for smelting.

Jan 6, 1979

By Thomas Lane Carter

THE history of mining in South Africa differs somewhat from that of other countries in the part taken by the aborigines in the development ?of the mineral deposits. The Spaniards in America, and the fortune-seekers of Australia and New Zealand, found large numbers of natives in these new countries, but the inhabitants did not become willing or efficient workers ill the mines which the white men started. The Kaffirs of South. Africa have not shown the same antipathy to labor, nor do they show any signs of dying out in the presence of the white man's civilization. They are a virile race, and so far the vices of civilization have not killed. them. While it is true that the brain and skill necessary for the exploitation of the mineral resources of this sub-continent-have been supplied by the white race, it is also a fact that most of the rough labor in the development of the mining industry of South Africa has been done by the Kaffirs. The Kaffir tribes differ greatly in their mental and physical capabilities. Compare, for instance, a Zulu of Natal with a Bechuana, or a Xosa of Cape Colony with some of the degenerate tribes of Central or East Africa, and you will find that they have little in common, save that their skin is black and that they do not believe in clothes. As a general rule, the tribe's in the milder, healthier climates are far superior, both in mind and body, to the Kaffirs brought up in the hot malarial sections of Central Africa; and it naturally follows that the black men from the temperate zones of the country, are much finer workmen than the degenerates from less favorable sections: It is universal in South Africa to speak. of the .Kaffirs as " boys." No matter if he is 90 years old, the Kaffir is always a " boy," and in this paper the word " boy " is synonymous with Kaffir.

Nov 1, 1908

By Hal T. Morris

The main Tintic mining district in central Utah has produced approximately 13,500,000 tons of ore, containing silver, lead, gold, copper, zinc, and other metals, valued at more than $315,000,000. More than 90 per cent of this ore has come from large, irregular ore bodies that have replaced folded and faulted limestone and dolomite strata. Of lesser importance are replacement veins that chiefly cut contact-pyrometasomatized carbonate rocks and fissure veins that cut altered intrμsive bodies and volcanic rocks. The district is in the west-central part of the East Tintic Mountains, a north-trending fault-block range near the eastern margin of the Great Basin. The consolidated sedimentary rocks exposed at the surface and in mine workings are miogeosynclinal deposits more than 10,000 feet thick that range in age from late Precambrian to Late Mississippian. They are folded and strongly faulted and are partly overlain by volcanic tuffs and agglomerates and by extensive flows of porphyritic and vitrophyric quartz latite, latite, and trachyandesite of Eocene age. All of these rocks are locally concealed beneath thick alluvial deposits of Pliocene and Quaternary age. The Eocene and older rocks are cut by dikes, sills, and small stocks of porphyritic quartz monzonite, monzonite, and latite, which are genetically related to the ore deposits. The district is inactive except for the production of halloysite clay and for minor leasing activity and exploration ventures. Several exploration targets remain untested.

Jan 1, 1968

By J. E. Lamar

THAT Illinois is an important mineral producing state is well known. A value of over $237,000,000 for the mineral products in 1926 indicates the magnitude of the industries. Coal mining is the largest mineral industry, and the value of its product was about 63 per cent of the total mineral production of the state. Oil and gas constituted about 8 per cent and the non-metallic minerals about 29 per cent. This 29 per cent represents the production of a varied group of mineral industries of wide geographic distribution through the state.

Jan 1, 1929

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who called at Institute headquarters during the period Apr. 10, 1916; to May 10, 1916: Philip P. Baily, New York, N. Y. George W. Otterson Seattle, Wash. John M. Brooks, Jr., Knoxville, Tenn. C. Q. Payne, New York, N. Y. C. A. Burdick, New York, N. Y. Charles F. Potter, Los Angeles, Cal. W. N. Crafts, Oberlin, Ohio. Albert E. Rhoads, Harrisburg, Pa. Andrew B. Crichton, Johnstown, Pa. M. F. Sayre, Schenectady, N. Y. 0. P. Hood, Pittsburgh, Pa. H. V. Smythe, Northpines, Ont., Canada. W. McA. Johnson, Tulsa Okla. W. 0. Snelling, Long Island City, N. Y. G. H. Morgan, New York, N. Y. W. H. Staver, Ophir, Colo. E. G. Norton, Chicago Ill., A. W. Tucker, Salisbury, N. C. M. L. O'Neale, Coal City, Ala. Andrew Weisenburg, Philadelphia, Pa. Arthur H. Brown has resigned his position with the Dome Lake Mining & Milling Co., South Porcupine, Ont., Canada. Robert Sterling has resigned his position as chief engineer of the Goldfield Consolidated Mines Co., Goldfield, Nev., to accept the position of assistant manager of the vanadium mines of the Primos Chemical Co., Vanadium, Colo.

Jan 6, 1916

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949