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By P. Payson

INTERGRANULAR corrosion in corrosion-resistant chromium-nickel steels has been widely discussed in the last few years. So far as the author knows, nothing has been published which definitely shows that this tendency can be eliminated, although suggestions have been made that a remedy is possible if certain specifications are satisfied. Strauss, Schottky and Hinueber1 suggested an increase in chromium content to an extent that would prevent the impoverishment of chromium on carbide precipitation sufficient to cause impaired corrosion resistance in the matrix. Pilling2 suggested an increase in nickel, so that the stability of the austenite matrix would be increased. Aborn and Bain,3 say that "intergranular attack-may be eliminated by preventing carbide precipitation (e. g., by lowering the carbon content or somehow raising its solubility) or by precipitating it permanently under conditions which will not remove chromium from solid solution so drastically at any points." In a later paper Aborn and Bain4 state that many different metallic elements, tungsten, vanadium, copper, aluminum, molybdenum, titanium and zirconium, have been added in small per-centages to increase the stability of these alloys, but that it has been reported that according to the copper sulfate test these added elements act only to retard the intergranular corrosion, and that increased nickel and chromium contents have similar effects. Newell5 showed that the lower the quenching temperature before reheating, the less severe was the intergranular attack.

Jan 1, 1932

By Stephen Krickovic

THERE is today no proven continuous mining machine that can be used under all the varying conditions found in most bituminous coal mines. During the last five years, however, both the machines and methods of using them have been improved. Coal operators can now exercise a fair degree of selectivity, except those who must struggle with thick and hard partings and operate in seams less than 40 in. thick. It must be realized, then, that more than one type of continuous miner may be used advantageously in the same coal mine. Although this appears to violate the standardization generally sought after, the gain can more than offset added maintenance and, to a lesser degree, operating problems.

Jan 12, 1957

By M. B. Ramachandra Roa

This paper records the results of the earth resistivity surveys made in the Godavari River in connection with the Ramapadasagar project. After describing the topographical and geological features of the area, the results of the investigation at the several sites have been mentioned. Further, a detailed account has been given of the resistivity methods adopted, the apparatus used and the interpretation of the curves. The resistivity measurements carried out over the water course have been specially outlined, and a review of the verification of the electrical indications by drilling in a number of cases, has also been presented. Introduction The Government of Madras has under consideration the Ramapadasagar project which is estimated to cost some Rs.660,-000,000 (about two hundred million dollars). The most essential feature of this project is the construction of a high dam across the Godavari near Polavaram for impounding the waters of this great river of South India, whose maximum discharge is 2 million cu secs in flood time. It is estimated that when the proposed reservoir is constructed, about one million tons of rice could be produced annually under irrigation. To those who have had any acquaintance at all with the recent distressing famine conditions which India has passed through and is still undergoing, the Lounteous effects which this project will bring about to the country in the future, are obvious. In the region of the proposed reservoir, the river flows for several miles through a hilly tract, hemmed in between flanks of hard, solid rock; but the river bed is mostly sandy. A few bore holes put down in this sandy bed touched rock at a depth of 180 to 200 ft. The river bed is about jo ft above the mean sea level (m.s.l.) and the bedrock was found at —125 to —160 ft m.s.l. The crest of the dam is proposed at +162 ft m.s.l. The proposed dam mould therefore be about 120 to 130 ft above the river bed, and the foundations would have to reach down nearly zoo ft below the bed at the deepest part. A number of alternative sites were proposed for investigation, and it became necessary to quickly ascertain the bedrock topography at these sites. Dr. M. S. Krishnan,* who was consulted in the matter, furnished a detailed account of the geological features of the region and suggested a geophysical investigation which the writer carried out from February to April 1944, employing solely the electrical resistivity methods. The total length of the survey lines for the electrical measurements amounted to 62,600 ft and the number of resistivity determinations was about 2500. Altogether nine alignments for the dam were inten-

Jan 1, 1949

Jan 1, 1968

[A Aall, Christian H., M49 B VP, Dir of Smelt & Refin, Am. Metal Climax Inc., 1270 Ave. of the Americas, N.Y. Aaroe, Stanley L., A54 B VP, The W. S. Tyler Co. of Can. Ltd., St. Catharines, Ontario, Canada Abalos, Toodulo Q., J57 A Prod Foreman, Lepanto Cons. Mng. Co., Mt. Province, Philippines Abbass, G., M55 P. O. Box 680, Hong Kong, China Abbitt, James M., A54 770 Sole Blvd., Bartow, Fla. Abbott, Raymond C., J59 3442 Greenwich Ave., Columbus 24, Ohio Abdullah, N. Y., J53 Dept. of Mines, Res. Div., P. O. Box 1016, Tiger Lane, Ipoh Perak, Malaya Abel, John F., Jr., J53- 100 Maple, Littleton, Colo. Abell, Leo M., M31 B Conc Supt, Phelps Dodge Corp., Morenci, Ariz. Abendroth, Harry E., A57 A Geol, Union Carbide India, 183 Brabourne Rd.. Calcutta. India]

Jan 1, 1961

By M. R. Pickus

THE study of the plastic deformation and recrystallization of metals has been the subject of many investigations. In regard to the simple deformational processes, such as tension and compression, the early knowledge gained from studies of polycrystalline material has been supplemented by many significant researches on the behavior of single crystals. Unfortunately, this has not been true for more complicated deformational processes. As far back as 1927, G. I. Taylor1 wrote: It is impossible in the present state of knowledge to do more than give a possible reason why (face-centered cubic) crystals set themselves with a (110) direction in the plane of rolling, and at right angles to the direction of rolling. The explanation of why the orientation of the crystal axes round the transverse direction is what it is, must be left till the distortion of metals, and particularly single crystals of metals in the process of rolling, has been studied in greater detail. That this gap in the systematic study of deformation and recrystalliza-tion has not yet been filled was indicated by C. H. Samans,2 who wrote in 1934 that "only four investigations upon cold-rolled single crystals of any of the face-centered cubic metals have been reported in the literature." Of these four studies, only those of S. Tanaka3 and T. Sakao,4 both of whom worked with aluminum crystals, had quantitative significance. The other two, carried out by F. Wever5 and W. G. Burgers,6 were of a. qualitative nature. It is our hope that the present investigation may contribute some-thing to the knowledge necessary for a rationalization of the origin of rolling textures in terms of the known behavior of single crystals, and may add pertinent information concerning the recrystallization characteristics of deformed single crystals.

Jan 1, 1938

Sponsored by the Utah Section of AIME, the 1960 Annual Rocky Mountain Minerals Conference brought more than 500 members of the mineral industry to the conference rooms of the Newhouse Hotel in Salt Lake City during the period October 5 to October 7. Under the overall supervision of J. M. Ehrhorn, general chairman, and H. E. Wright, assistant general chairman, the Conference offered 14 papers of technical interest in four sessions during the first two days, and it culminated in the Exploration Symposium held on the morning of October 7. The opening session of the Conference, meeting on the morning of October 5, heard R. P. Work, utility engineer of the Mountain Fuel Supply Co., discuss the growth and economic factors related to the use of natural gas in Utah. In his paper entitled Natural Gas Market In Utah, Mr. Work emphasized the very good prospects of natural gas serving almost all parts of that state. He mentioned that recently the El Paso pipeline, built to serve the Pacific Northwest with gas from Texas, has permitted natural gas to be available to Eastern Utah, and a tentatively planned pipeline from Green River, Wyo. to Southern California will bring natural gas to the central and southeast areas of the state.

Jan 11, 1960

By Herbert Clark Hoover, Lou Henry Hoover

PREVIOUSLY I have given much information concerning the miners, also I have discussed the choice of localities for mining, for washing sands, and for evaporating waters; further, I described the method of searching for veins. With such matters I was occupied in the second book; now I come to the third book, which is about veins and stringers, and the seams in the rocks1. The term "vein" is sometimes used to indicate canales in the earth, but very often elsewhere by this name I have described that which may be put in vessels2; I now attach a second significance to these words, for by them I mean to designate any mineral substances which the earth keeps hidden within her own deep receptacles.

Jan 1, 1950

By J. H. Bucher

The effect oj strengthening by the precipitation of CbC on the toughness offerrilic steel (0.11 pct C, 0.74 pct Mn, 0.02 pct Cb) was stlrdierl. A g-veater degree of pvecij~itatiotz strengthning is ohtaznable by aging the so11ution-treated steel rtt velaticely Low temperature was (1050" to 1l0O3F) than at higher temperatures (I150" to 1200°F). Tlzis ),eslrlts because a finer dispersion of CbC is obtained. However, the ductile-brittle transition te~ripertltlo.e is raised approximately tlzjeee tirues as IFLIIC~ perv a given yield stress increase) by aging in the lower tempareture range, as opposer1 to the Irigher temperaturee range. This is proposed to result pl-iir~avily because different precipitation distributions ar-e associated with the different aging -treaments. For tile steel aged at 1050" and 1100 F, heavy: precipitation on disloccctions occurs resulting in a high degree of rlislocution pinningh tl~us lowevirzg- the toilguiess. in tll c(.rise of the steel aged at 1150 'a?zd 1300"F, Pvecipitatiol~ is irzove g-enerally distributed throughout the matrix rather limn preferentially on dislocations.; and Ike detlsitj, oj mobile dislocations is not sttyong-ly affected. THE most effective means of strengthening hot-rolled ferritic steels are grain refinement and precipitation hardening. It is well-known that grain refinement increases both the strength and the toughness. However, the upper limit of yield strength obtainable by grain refinement alone is about 60,000 psi,'12 i.e., without the formation of acicular structures of lower toughness. The most economical means of obtaining higher strengths is the addition of small amounts of elements such as columbium, vanadium, and titanium which form carbonitrides. These precipitates are very effective in increasing the strength, but the ductile-brittle transition temperature is is Although it is agreed upon that precipitation decreases the toughness, there has been little effort to isolate the causative aspects of embrittlement. The purposes of this research are to assess quantitatively the embrittlement associated with different precipitate distributions and morphologies, and to correlate the degree of the embrittlement with the microstruc-ture. In this manner, a more fundamental insight into the mechanism of embrittlement may be gained. The steel selected for this purpose was a low-carbon, columbium-bearing steel which, after solution treatment, was aged in various time-temperature cycles while attempting to hold all other microstructural variables constant. MATERIALS AND PROCEDURE The composition of the steel used in this investigation is given in Table I. Starting with commercially hot-rolled material 0.074 and 0.280 in. thick, tensile blanks were cut from the thinner material and sub-size Charpy blanks from the thicker stock. The steel had been rolled using a low finishing temperature and rapid cooling after hot rolling to produce grain refinement. Also, chemical-extraction analysis and electron-microscopic examination revealed that the cooling was rapid enough to suppress any significant precipitation of CbC. Therefore, the as-rolled steel is essentially in the solution-treated condition in terms of the precipitation reaction, and it was used as the base material in this investigation. The room-temperature tensile properties of the as-rolled steel aged at 1100", 1150", and 1200°F for various time intervals were determined, see Table 11. The ductile-brittle transition behavior was studied for smooth and notched tensile specimens, and longitudinal half-size (0.200 in. thick) Charpy V notch specimens aged at 1100" and 1150°F for various times, also Table 11. In addition, tensile specimens aged for single times at 1050" and 1200°F were evaluated with respect to their ductile-brittle transition. Only one 1050°F treatment was used because of the extremely slow kinetics of precipitation at this temperature and because no significant difference between 1100°F aging was observed. Only one treatment at 1200°F was used because aging at this temperature alters the shape of the grain boundary cementite particles present in this steel and complicates analysis. The design of the tensile specimens is given in Fig.1.

Jan 1, 1968

By John H. Walthall, Raymond L. Copson, Travis P. Hignett

In October 1942, the War Production Board requested the Tennessee Valley Authority to undertake investigations to determine the feasibility of producing alumina suitable for reduction in aluminum cells, from clays and other domestic materials, by a lime-sintering, soda-ash leaching process. The work was undertaken by the chemical engineering staff of the Authority under the general direction of the War Metallurgy Committee of the National Academy of Sciences. The investigation included small-scale tests to determine the most suitable conditions for the process, and construction and operation of a pilot plant to obtain data for evaluation of the process and for design of a plant. The results of this investigation are described in the present paper. Sources of Alumina Alumina for the commercial production of aluminum is obtained from bauxite by the Bayer process. The tremendous demand for aluminum for wartime uses is causing rapid exhaustion of the high-grade bauxite deposits in the United States. On the other hand, there is an abundance of aluminous materials such as clay and lower grades of bauxite, which are not suitable for treatment by the Bayer process because of their high silica content. The Tennessee Valley Authority has conducted research and pilot-plant work for more than 5 years on methods for the production of alumina from clay and low-grade bauxite. Particular attention has been given to the high-grade white kaolin found in Carroll County, Tennessee. Exploratory drilling has demonstrated that at least 4 1/2 million tons of kaolin containing in excess of 34 per cent AlzOI is available in this area by strip-mining methods. It has been estimated that hundreds of millions of tons of clay of similar quality occur in the Tennessee Valley region. The Process The process is illustrated in the flowsheet (Fig. I), and consists essentially of the following steps: I. Heating a mixture of clay and limestone to form a sinter containing calcium aluminate and dicalcium silicate. z. Leaching this sinter with a dilute sodium carbonate solution, to form a sodium aluminate solution and a calcium carbonate, calcium silicate residue, which is discarded. 3. Treating the sodium aluminate solution with carbon dioxide to precipitate aluminum trihydrate and regenerate the sodium carbonate solution, which is recycled. 4. Heating the aluminum trihydrate to produce alumina. The process was considered promising because of the abundance and cheapness of the two raw materials, clay and limestone; and because, as compared with an acid process, smaller amounts of critical

Jan 1, 1944

By J. R. Linney

THE Eastern Magnetite Industry produced approximately 7,850,000 long tons of crude ore in 1945 from which was obtained approximately 3,650,000 long tons of shipping product or a ratio of 2.10 to 1. Lack of skilled or experienced miners was the greatest handicap. Veterans returning to work improved the underground labor shortage in some localities but as a whole the labor shortage was keenly felt throughout the industry. One cannot now predict what may be accomplished in 1946 but barring major steel strikes a worthwhile improvement can be expected. At the Richard mine of the Richard Ore Co., the shipping product for the year amounted to approximately 124,650 long tons of concentrate and lump ore. Crude-ore production was 160,600 long tons. The average analysis for lump ore was 63 per cent iron and for concentrates 66.05 per cent. The Warren Foundry and Pipe Corp. at their Mt. Hope mine produced 73,000 long tons of lump ore averaging 59.5 per cent and 57,000 long tons of concentrate averaging 67 per cent. The total mine hoist was approximately 209,000 long tons. Operations were commenced through the new Leonard shaft on Jan. 18; the Brown shaft through which operations had been conducted since 1912 caved beyond repair on Sept. 26. No one was injured but pumping facilities were somewhat disrupted. In order to reach designed capacity a total of 400 men will be required with 300 underground. Due to shortage of labor all operations in 1945 were concentrated on the 1700 level. As fast as men can be hired and trained development of the 2100 and 2500 levels will commence. Mt. Hope has a consider-

Jan 1, 1946

By A. E. Bellis

ROBERT J. ANDERSON, Cleveland, Ohio (communication to the Secretary *).-The paper by Messrs. Bellis and Hardy was interesting to me and has led me to make a few remarks concerning some of the points brought out. The question of employing correct hardening temperatures is one that is sadly neglected, particularly in many large plants that forge and treat their machine tools for private use. As is most aptly remarked in this paper, "The custom of using one, high-speed temperature for all tools is very poor practice;" still, such practice is more common than otherwise. An instance came to my attention some time ago, in connection with some work with the standardization of high-speed steels for machine tools, where there were no less than six different brands of alloy steels being used for machine tools such as lathe, shaper, planer, boring mill and cutters of like nature. All of these different steels received identical heat and forging treatment-or at least that was the aim of the tool hardener. That the results were highly unsatisfactory goes without saying. That the hardening department of many plants is conducted on a rule-of-thumb fashion is the reason for a great deal of the trouble and disappointment which seems to be the lot of many tool-steel users. Exceedingly crude execution is the rule rather than the exception, and it is no small wonder that the results are as good as they sometimes happen to be. It would seem that at the present price of alloy steels the subject should receive a closer scrutiny by purchasers than it does. One not familiar with the workings of souse plants that disdain to lend an ear to scientific heat treatment would scarcely give credence to some of the methods employed, not only in the treatment of the steel but also in its selection and purchase. Heating for hardening should be conducted under close pyrometric control only after the correct hardening temperature has been determined.

Jan 3, 1917

By C. K. Donoho

SILICON is used in almost all commercial steels; up to about 0.20 pct in killed wrought steels and 0.50 pct in steel castings. Above about 0.50 pct in wrought steels and 0.70 pct in cast steels, silicon is considered an alloy. As an alloy, silicon is useful for several purposes: (I) for its effect on magnetic properties of parts for electrical apparatus; (2) for increasing the yield strength of carbon and low-alloy steels without too much sacrifice of ductility and weldability; (3) for adding hardness and toughness to spring and chisel steels; (4) for adding resistance to scaling and carburization to heat-resistant steels; and (5) for its graphitizing effect in graphitic steels. In acid electric steels for casting we are principally interested in the effect listed second; i.e., increase of strength with minimum sacrifice of ductility.

Jan 1, 1947

By E. B. Spice

Although much may be learned about the economics of cold weather operations by studying successful mining ventures in southern and central Canada, it is the purpose of this article to extend the study by considering only permafrost areas. Geographically this means most of the country north of the 60th parallel. In this area, at the present time, only five Canadian companies are carrying on routine and successful mining operations on a year-round basis. However, there have been some score of unsuccessful ventures, and a number of properties in the development stage show promise of being producers. Problems of cold weather are worthy of study. It may be pointed out that successful mines in this area face problems of isolation and costly transportation as well as cold weather. To reach valid conclusions, consider the development of a mythical mineral deposit located on the 65th parallel in the heart of the barren lands; problems of isolation and transportation will be ignored.

Jul 1, 1956

By Daryl R. Tweeton, Jerry R. Riding, Grant Buma, Frank J. Rosswog

In situ solution mining of uranium has environmental advantages over conventional mining. The leaching of uranium, however, alters the ground-water quality in the aquifer where the mining occurs. Currently, regulations require that the ground water be restored to approximately its original condition. This paper, a summary of a study funded by the Bureau of Mines, reviews the state of the art in restoring ground-water quality after in situ uranium leaching. Current restoration practices discussed include disposal of liquid wastes in deep disposal wells and evaporation ponds, producing from all wells during restoration, and recirculating water purified in surface plants. Methods for predicting the effectiveness and cost of current techniques are presented. Possible alternative techniques are also described. Two restoration operations are discussed.

Jan 1, 1979

ALTHOUGH the refining period of the heat is generally defined as starting after the charge has been completely melted, it may more properly be considered as beginning with the first efforts to facilitate the shaping up of the slag and the making of corrective additions for the control of slag or metal composition. Such actions may be initiated during the latter half of the lime boil. The early part of the refining period may, then, in essence overlap the latter part of the melting period. The primary aims of the refining period are: (1) to reduce phosphorus and sulfur from the steel bath to levels safely below the maximum contents specified; (2) to eliminate carbon to a specified level as rapidly as possible and still allow time for proper conditioning of the slag and attainment of the necessary bath temperature; and (3) to have the heat ready for tapping or furnace deoxidation, with slag in the proper physical and chemical condition, and with carbon and oxygen contents and the temperature of the steel at the proper levels for the composition and grade of steel being produced. The particular conditions that fulfill these aims are distinctly different, depending upon whether the steel is to be finished according to fully killed. semikilled, or rimming practice and also depending upon the carbon range specified. Regardless of the type of charging practice employed, the object of the refining period is to produce repeatedly the desired finishing and tapping conditions for the grade of steel being produced. The variations and proportions of raw materials used in the charge may cause some variations in the degree of control required during refining, but not in the method of control. The refining period can therefore be discussed from a viewpoint largely independent of charging and melting practice. SHAPING UP THE SLAG In the first helper's vocabulary, refining practice consists in

Jan 1, 1951

By G. W. P. Rengstorff, L. E. Olds

High purity molybdenum ingots containing controlled amounts of a single impurity element (oxygen, nitrogen, or carbon) were prepared. These ingots were tested for ductility by bending test specimens at various temperatures. The relationship between the plastic behavior of the ingots and their chemical composition has been determined. MANY proposed applications for molybdenum require ductility at or near room temperature. At the present time, it is possible to obtain wrought molybdenum with considerable ductility only if special fabrication techniques are used to control the grain structure. Starting with are-cast or powder metallurgy ingots, the usual methods for obtaining ductility rely on fabrication procedures that result in fibered microstructures in the finished product. Recently, it has been found that the ductility of either powder metallurgy or are-cast molybdenum can be improved by uniform recrystallization of the metal to a very fine equiaxed grain structure.' The need for a fibered or a fine grained structure may limit the practical usefulness of molybdenum. For example, welding. which may be used in fabricating the metal, generally produces coarse grained structures that lead to brittleness. This applies, certainly, to currently available commercial molybdenum. Although commercial molybdenum is brittle when the grains are coarse, it has been shown experimentally that fine grained structures are not always essential for ductility. For instance, as-cast molybdenum with a coarse columnar grain structure is ductile if it is sufficiently pure.' Because high purity cast molybdenum has good ductility even when coarse grained, it is probable that the brittleness in coarse grained commercial molybdenum is caused by the impurity content of the metal. Although the general effects of impurities on the cold ductility of molybdenum have been known in a qualitative manner for some time, no quantitative evaluation of these effects has been available. The present investigation was made in order to determine more accurately the effects of oxygen, nitrogen, and carbon on the cold ductility of cast molybdenum. Oxygen has long been known to be detrimental to ductility, although the minimum amount which will embrittle molybdenum has been open to speculation. Parke and Ham" showed that ingots with oxygen contents above 0.003 pct could not be forged. Maringer and Schwope have described the embrittle-ment of molybdenum wire by oxygen. A discussion on the effects of heat treatment on the distribution of oxygen in molybdenum has been given by Perry, Spacil, and Wulff." Although nitrogen would also be expected to have harmful effects on ductility, no extensive work has been done previously to determine whether this is so. However, Tury and Krausz" found that wires presumably with less than 0.007 pct N were brittle. Carbon is added to commercial cast molybdenum for deoxidation. Parke and Ham" have shown that molybdenum containing as much as 0.06 pct C could be forged if the oxygen was kept below 0.003 pct. Also, Bruckart and others' found that the room temperature ductility of sintered molybdenum improved with carbon contents up to 0.84 pct. However, Rengstorff and Fischer' found that residual carbide particles in cast molybdenum apparently had an unfavorable effect on room temperature ductility.

Jan 1, 1957

By DOOLITTLE E. M.

(Canal Zone Meeting, November, 1910.) The following notes are contributed, not with the idea of offering a complete history of the development of this very important process as applied to the Leadville district, but with the hope that the practice, as it was carried out in the Bi-Metallic Smelter, may still be of interest to others. The Bi-Metallic Smelter, at Leadville, Colo., was the first to make a commercial success of the process described in the following pages, which consisted essentially of smelting raw silver- and copper-bearing sulphide ores in blast-furnaces to form a matte, which was generally re-smelted with siliceous ores for a second high-grade matte. Robert Sticht, in his excellent monograph on the subject,1 has outlined briefly the plant belonging to this company. He says, in effect: The Boulder, Mont., enterprise set the example for others with whom the patentee (w. L. Austin) had been negotiating, and the old La Plata lead-smelter at Leadville, Colo., was fashioned into a crude, temporary experimental plant for the Bi-Metallic Company, and the feasibility of the process demonstrated by a trial run. Subsequently, the plant was considerably improved, and, being supplied with very favorable ores, continued to run without interruption from August, 1892, to June, 1893. In September, 1893, smelting was resumed in a completely remodeled establishment, some $200,000 having been expended upon the new work. Thus, aside from the Montana experiments, which, under the direction of W. L. Austin, began as early as- 1885 2 at Toston, and continued with indifferent success for six or seven years, the Bi-Metallic plant at Leadville may be said to have * Formerly Superintendent, Bi-Metallic Smelting Co. + Formerly Chief Assayer and Chemist, Bi-Metallic Smelting Co. 1 Modern Copper Smelting, E. D. Peters, 7th ed., p. 415 (1895). 2 Trans., xvi., p. 259 (1887-88).

Dec 1, 1910

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

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