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PRESIDENT W E WRATHER Washington, D C PAST PRESIDENTS Louis S CATES, New York, N Y CLYDE WILLIAMS, Columbus, Ohio VICE PRESIDENTS ' HOLCOMBE J BROWN,' Boston, Mass ROBERT W THOMAS, Ray, Ariz RLE V DAVELER, New York, N Y C HARRY BENEDICT Lake Linden, Mich DONALD H MCLAUCHLIN, San Fiancisco, Calif VICE PRESIDENT AND TREASURER ANDREW FLETCHER New York, N Y

Jan 1, 1952

By R. E. Miner, J. K. Jackson, D. F. Gibbons

Internal-friction measurements were made during isothermal aging treatments of 18 pct Ni maraging-steel wires between 420° and 612°C. A sharp initial drop in the internal-friction level was interpreted in terms of a rapid dislocation recovery reaction. The rate of the recovery was found to be independent of temperature. Truncation of the recovery reaction was apparent in those systems that exhibited the rapid age-hardening characteristics of the maraging steels. It is proposed that this initial hardening response is the result of a low activation energy preprecipitation reaction involving molybdenum. A gradual rise in the internal-friction level at longer aging times was associated with the precipitation of a molybdenum-containing precipitate. CONSIDERABLE research effort has recently been devoted to the mechanisms responsible for the high strength and toughness of 18 pct Ni maraging steels. These bcc martensitic alloys are found to harden during aging at temperatures between 400° and 600°C. The aging response is very rapid with more than half the total hardness increase occurring within the first few minutes of aging, Fig. 1. Precipitate particles have been observed in the later stages of aging by a number of investigators.'-' While the identity of the precipitates remains the subject of some controversy, one or more of the intermetallic compounds, Ni3Mo, Ni3Ti, and Fe2Mo, are almost certainly involved. Heterogeneous nucleation of precipitates at dislocations has been noted8 and cobalt is believed to enhance the formation of fine, homogeneously distributed particles by lowering the solubility of the alloying elements in the martensitic matrix.3,7 Transmission electron microscopy studies of the initial hardening behavior have not been fruitful. Strengthening mechanisms based on atomic ordering have not been generally supported by X-ray and neutron-diffraction experiments.9 In the present investigation, the aging reaction was studied using isothermal-aging internal-friction measurements. The marked sensitivity of internal friction to short-range diffusion and precipitation processes has provided a convenient tool for the elucidation of the strengthening mechanisms operative in the maraging steels. EXPERIMENTAL PROCEDURE An upright torsion pendulum was used to measure the internal friction of several maraging steels during isothermal aging. The pendulum was placed in an atmosphere of helium at a pressure slightly less than atmospheric. To permit measurement of internal friction during the first minutes of aging, the specimens were rapidly heated by passing a current through them in a manner similar to that described by Ang and Wert.10 Thermal gradients in the specimen were largely eliminated by using specially designed specimen grips11 which produced temperature variations of less than 1 pct over 90 pct of the specimen length and less than 3 pct over the entire length at aging temperatures up to 620°C. A proportioning strip-chart program controller was employed to maintain constant specimen temperature during treatments of up to 36 hr duration. A number of vacuum-melted laboratory heats having compositions near that of a typical commercial 18Ni-7Co-5Mo-0.4Ti alloy were investigated. The amount of cobalt was varied from 0 to 7 wt pct in five of the heats. Either molybdenum or titanium was omitted in the remaining two heats. The alloy desig-

Jan 1, 1967

PRESIDENT L. D. RICKETTS,1 NEW YORK, N. Y. PAST PRESIDENTS BENJAMIN B. THAYER,1 NEW YORK, N, Y. WILLIAM L. SAUNDERS,2 NEW YORK, N. Y. FIRST VICE-PRESIDENT SIDNEY J. JENNINGS,1 NEW YORK, N. Y. TREASURER GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER W.. RAYMOND NEW YORK, N. Y SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 6, 1916

By C. G. Brehm

THE anthracite-producing region is in the northeastern section of Pennsylvania, and has an area of approximately 484 square miles. It is divided geographically into three separate fields, known as the Northern, Middle and Southern. The Northern field, with Wilkes-Barre approximately at its center, is a basin about 60 miles long and almost 6 miles wide at its greatest distance across. Generally speaking, it may be said that the coal meas-ures in this field lie horizontally, or on slight pitches, and consist of from 11 to 19 veins of coal, varying in thickness from several inches to several feet. The intervening strata between veins may be composed of slate, clay, rock or shale, or a combination of several, and are sometimes very thin. This condition often causes a treacherous roof, therefore roof sup-port and the attending hazard of mining are problems of concern. The Middle field is made up of a number of small basins of not very great depth, and the measures, which are in like number to those of the Northern field, are varying inclinations running from nearly flat to steep pitches.

Jan 1, 1938

By J. Morgan Clements

PETROLEUM has been known in Japan since at least 668 A. D., for a picture shows the presentation, during that year, to the Emperor Tenchi (Tenji) of "burning water" and." burning earth" by his subjects from Echigo Province, which today is the largest producer of petroleum in Japan. The burning water was doubtless petroleum and the burning earth either bituminous shale or oil-soaked earth or rock from near the oil seepages. The early methods of getting the oil were simple and similar to methods used today in Japan and in China. Where the seepages occurred, trenches or shallow wells were dug along the seepages and allowed to fill with oil which was then bailed out; in some cases, they filled with oil and water and overflowed. During the 300 years following 1500 A. D:, the use of petroleum in Echigo Province seems to have increased considerably, as compared with earlier centuries, and records show that in 1818 the depth of the wells had been greatly increased. Doubtless, they passed through the seepages and tapped the shallow oil-bearing strata; probably some of these deeper wells were dug before that time. The real value of petroleum was not recognized until early in the Meiji era, which began in 1868, when the Japanese learned that the kerosene that was being imported was derived from petroleum. Guided solely by information obtained from books, they refined the oil and increased the depth of their wells in order to increase the production. The deepest well, dug by hand, about this time was 894 ft.1 (273 m.) and by 1874 the recorded production reached 3499 barrels. In 1876, Benjamin Smith Lyman prepared geological maps of the Echigo oil field, which were the first. of such geological maps made in Japan, and based on these a more enlightened development of the oil fields began; the. Japanese, however, still dug the wells by hand. Toward the end of the '80s, an American well-drilling outfit was secured, but the efforts to use it failed from lack of experience by the operators. In 1888, a complete well-drilling outfit was, purchased and American oil-well

Jan 7, 1922

By A. L. Galpin

INTRODUCTION For many tailings ponds, particularly those having substantial watershed areas, the control of pond water levels will be a major factor influencing the operation of the pond and the design and construction of the dam retaining the pond. This paper summarizes the basic factors affecting the control of water in tailings ponds, methods of water control, and methods of estimating the variables involved. The influences that pond water levels can have on the design, construction, and stability of tailings dams are explained in order to emphasize the importance of water control in the overall planning of mine tailings disposal systems. Two examples of pond water control planning conclude the paper. BASIC FACTORS The principal factors influencing the control of water in tailings ponds are illustrated on Fig. 1. Fig. 1 (a) shows the general disposition of the tailings solids and water in the pond; the solids settle from the slurry to form "slimes", deposits sloping down into the pond from the points of discharge; these slimes hold volumes of water in the voids between solid particles; water in excess of this "retained" water forms a pool of "free" water laying over the slimes deposits. In some cases, tailings solids (and water) go to the tailings dam for its construction. Fig. 1 (b) indicates those ways additional to tailings disposal in which the pond gains or loses water. These include surface and sub-surface runoff from the pond watershed, water reclaimed from the pond for ore processing, evaporation, and seepage. Seepage losses sometimes include water draining from tailings sand placed in the dam, but a portion of the total seepage flow is often collected and returned to the pond in order to avoid downstream pollution and to recover water for re-use. PRINCIPAL REQUIREMENTS In relation to the control of water in a tailings pond, the first requirement is usually to maintain a pool sufficiently large to ensure adequate clarification of the free water prior to its reclaim for use in the mill, or its discharge from the pond.

Jan 1, 1972

By J. M. McDowell

A study has been made to deter~r~irre how the behavior of a water drivee reservoir changes as a function of the permeability of the formation and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rote of nat11rn1 water influx is also studied, (IS well as the influence on the influx of the position of water injection we1ls with reference to the oil-water contact. The results are determined by the use of an electrical reservoir analyzer and are plotted as families of curves of pressure, natural water influx, and water injection vs time or cumulalive production. Two size aquifers are studided. One is limited with a 36-inile radius, and the, other approximates an infinite reservoir. The field remains the same in all respects for the completed. study except that the permeability is changed to agree with that assumed for the aquifer. 1 N TR ODUCTI ON this study was undertaken in -dcr to determine how the pres- sure decline and water influx of a water drive field would change as a function of the rate of fluid withdrawals, as a function of the permeability of the formation, and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rate of natural water influx was also studied as was the position of water injection wells with reference to the oil-water contact. The information has been determined by the use of an electrical reservoir analyzer1, sometimes referred to as a Carter type analyzer. This instrument is an analog type computer which can be set up to represent a water-drive oil field. It can reproduce the past performance of the field in terms of analogous electrical quantities when the proper circuit analog of resistors and condensers has been determined, also, it can determine the future behavior for any method of production which may be selected, or permit the comparison among several different methods. Although most applications of the reservoir analyzer"" have been to thc study of specific field performance, it is intended to use the analyzer here to help understand how various reservoir characteristics effect the final performance of the field and to sec under what conditions water injection will be of benefit and to what extent. Within the oil industry the performance of water-drive reservoirs was first described analytically by LV. Hurst' and M. Muskat2 for certain types of boundary conditions. The solutions of the equations developed involved products of exponential functions and Bessel functions. Later publications by Hurst4 and van Ever-clingen" and the hooks of Muskat6 gave further information on reservoirs with other boundary conditions. They also presented rather extensive curves and tables to help evaluate the analytical expressions involved. A rccent series of publications by Chatas. bascd on the work of Hurst and van Everdingen, gives quite complete charts and tables of data to evaluate the pressure decline or water influx in infinite or limited radial reservoirs. and in linear reservoirs. The curves in all of these publications are given in dimensionless form

Jan 1, 1956

By Walter Bradley

MINING by hydraulic process of the important gold-bearing gravels of the Sacramento Valley in the basins of the Yuba, Bear and American rivers began in 1853, and continued at an ever-increasing rate for 30 years. In its most active days it reached an annual production of $15,000,000, and averaged $10,000,000 per year over the 30 years. During that period no provisions were made to prevent the debris from being dis-charged into the water courses, and ultimately large quantities of silt, sand and gravel were washed down to the lower valleys; filling channels, causing overflow of agricultural lands and difficulty in maintaining navigable depths in the Sacramento River. Agitation and suits filed because of these damages finally resulted in the injunction decision of Judge L. B. Sawyer,1 in the U.S. Circuit Court, Jan. 23, 1884, which closed down practically all hydraulic mining operations not having means to restrain their debris. In 1893 (approved March 1, 1893), Congress passed the act introduced by Representative Anthony Caminetti, of California, creating the California Debris Com-mission, composed of three officers assigned from the Engineer Corps of the U.S. Army, and since that time it has been legal and possible within the drainage systems of Sacramento and San Joaquin rivers to conduct hydraulic mining of gold-bearing gravels behind dams built under this commission's permit and supervision. In the watersheds of the Trinity and Klamath rivers, which flow directly to the Pacific Ocean and do not affect navigation or agriculture, operating permits from the California Debris Commission are not required. There is a measure of restriction there, however,. through what is known as the Trinity and Klamath River Fish and Game Dis-trict. Chap. 215, Stat. 1931, in order to secure relatively clear water for the fishing season, provides that between July 15 and October 15 each year there must not be discharged into these rivers debris that will cause a turbidity greater than a content of 50 parts per million in the

Jan 1, 1936

EXECUTIVE COMMITTEES OF LOCAL SECTIONS New York L. W. FRANCIS, Chairman, WILLARD S. MORSE, Vice-Chairman. THOMAS -T. READ, Secretary, Woolworth Bldg., New York: N. Y. P. A. MOSMAN, Treasurer. LOUIS D: HUNTOON. Boston HENRY L. SMYTH, Chairman. ALFRED C. LANE, Vice-Chairman. AUGUSTUS H. EUSTIS, Secretary-Treasurer, 131 State St., Boston, Mass. TIMOTHY W. SPRAGUE, HENRY A. WENTWORTH. Columbia F. A. THOMSON, Chairman. GEORGE W. RODDEWIG, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. R. S. McCAFFERY, S. H. RICHARDSON.

Jan 10, 1914

By J. A. Jr. Church

I. EARLY FURNACES. COPPER blast-furnace construction in America has long recognized a general standard in the rectangular mater jacketed shaft with separate forehearth. The details, however, and especially those relating to shaft dimensions, have had to meet a great variety of conditions, and show no uniformity whatever. Selecting a few of the present day Western plants, we find furnace lengths varying from 12.5 to 87 ft., widths at tuyere level from 42 to 84 in., and heights above tuyeres from 5 ft. 4 in. to 22 ft. 4 in. ; and comparing present designs with those of the past, we meet contrasts no less striking. Unlike its transverse section, the length of a furnace has come to depend rather on the size of unit desired than on the requirements of smelting ; and if the question of length be ignored, several of the various existing designs can be grouped together on the basis of a common transverse section. This section, having a width at tuyere level of 56 in. and a height above tuyeres of 18 ft., was developed at Great Falls, and the story of its development contains some interesting features. Ground was broken for the Great Falls works in the spring of 1891. About a year later, the concentrator was able to begin operation, followed within the next few mouths by the Brueckner, reverberatory, and converter departments, and in April, 1893, by the first blast fur-

Jan 7, 1913

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of September, 1913: Members. ANDERSON, ANDREW P., Min. Engr 908 Story Bldg., Los Angeles, Cal. ANDROS, STEPHEN 0., Min. Engr University of Illinois, Urbana, Ill. BECKETT, PERCY G., Min. Engr Globe, Ariz. BLAIR, THOMAS S., JR., Prest. Blair Engrg. Co 343 S. Dearborn St., Chicago, Ill. BOYLE, HARRY, Min. Engr S07 Lowman Bldg., Seattle, Wash. BRADEN, EUGENE B., Vice-Prest., Selby Smelting & Lead Co., Merchants Exchange Bldg., San Francisco, Cal. CHALMERS, JOHN W., Min. and Elec. Engr., Morro Velho, Villa Nova de Lima, Honorio Becalho Minas Geraes, Brazil, So. America.

Jan 10, 1913

By Albert Ledoux

SEVERAL years ago my firm was representing the Mt. Lyell Co. of Australia, which was shipping its blister copper to a refining works in the United States. After the contract had been running for many months, the superintendent of these works discovered that if water was poured upon the surface of the bars much of it would disappear into the interior through blow holes. -Some experiments made by him showed that this could be a considerable amount, so that copper which had been rained on before it was weighed, although the surface appeared dry, nevertheless would contain water. It had frequently occurred in our experience-as samp-lers that the drillings from a lot taken by boring would come out quite wet, and in some cases, indeed, water would drip into the sample pan placed below the bars, due to the fact that the drill had penetrated a cavity or cavities containing water, which presumably got into the cavities at the time the copper was water-cooled after casting, there being, perhaps, no outlet to the surface. So far as I know, until this discovery at the refining works, no. one had thought that rain could penetrate into the interior of blister copper; at least in any quantity sufficient to be considered.

Jan 10, 1922

By H. W. Camp

ALTHOUGH the situation in the oil industry during the past year has. not been conducive to large expenditures for development and research, there is little indication that such expenditures have been curtailed. While few outstanding achievements have been reported, considerable progress has been made in the development of new products and the adaptation of petroleum derivatives to new uses. The most important question facing the refiner today is the anti-knock quality of his gasoline. This year has seen the widespread adoption of the term "octane number" as a measure for anti-knock values, and in the latter months of the year the public has been made acutely aware of this condition through competitive advertising. Gaso-line is no longer priced on volatility and gravity alone, but on octane number as well; and premiums are being paid for material of relatively high octane rating. The situation has grown more and more competitive and has forced refiners continually to raise the octane rating of their regular and com-petitive grades, and at this writing the same situation exists for premium grades which have possessed relatively high anti-knock properties for some time. Straight-run gasoline produced from paraffin-base or semiparaffin-base crudes has an inherently low anti-knock value, and in order to convert this material to a higher quality it has been found necessary to crack an increasing percentage of the crude oil charge. By completely cracking the heavier portions of the crude, and blending back with the straight-run gasoline, it has been possible to produce an average of 63 to 65 octane number gasoline' on average Mid-Continent crude. This operation carried to the fullest extent does not suffice, however, and the recent and rapid development of the so-called "re-forming unit," has resulted. The straight-run gasoline fraction is cut into two parts: a light, low boiling point gasoline; and a heavy gasoline or naphtha. The latter containing the low anti-knock portions of the gasoline, is sent through a re-forming unit and subjected either to high temperature ,or pressure, or both, which materially increases its octane number. On average Mid-Continent the blend of low boiling point straight-run,

Jan 1, 1932

NEW MEMBERS The following list comprises the names of those persons who became members during the period Apr. 10 to May 10, 1915: Members ADMAN, WILLIAM, Supt., Susquehanna Coal Co Lykens, Pa. BARTH, CARL G., JR., Min. Engr 6151 Columbia Ave., Philadelphia, Pa. BOOTH, ERIC EDWIN, Min. Engr., Mount Elliott Mine, Selwyn via Cloncurry, North Queensland, Australia. BOYDELL, HARRY CYRIL, Asst. Mgr., Randfontein Central Gold Min. Co., Box 42, Randfontein, Transvaal, South Africa. BRADY, SAMUEL HOWARD, Mine Supt Bohemian Club, .San Francisco, Cal. Buses, HARRY EDWARD, Mine Supt., Engels Copper MiningCo Keddie, Cal.

Jan 6, 1915

President MRS. FREDERICK LAIST 24 Tompkins Road Scarsdale, N. Y. First Vice-president MRS. LOUIS D. HUNTOON Pleasantville New York Second Vice-president MRS. REED W. HYDE 84 Mountain Avenue Summit, N. J. Third Vice-president MISS MADELINE P. STONE 49 West 11th St. New York, N. Y. Fourth Vice-president MRS. JOHN J. LINCOLN Elkhorn, McDowell Co. West Virginia

Jan 1, 1932

By E. S. Machlin

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

Jan 1, 1957

Members whose deaths were reported from Mar. 5, 1919, to Apr. 5. 1920 [Elected Died 1895 ANDERSON, ROBERT HAY 1920 1916 ATWATER, M. W 1919 1905 BARD, D. C. 1920 1893 BECKER, GEORGE F 1919 1914 BIGELOW, BRAXTON 1917 1917 BLACK, HERBERT F 1919 1911 BOWLER, ROBERT P 1919 1902 BROWN, ARTHUR H 1919 1913 BURNHAM, WILLIAM 1918 1905 Carnegie. Andrew 1919] [ ]

Jan 1, 1925

By W. G. Scott

Since devising the incline top-slicing method in use at the Coronado mine,l I have had numerous inquiries as to how the same system could be adapted to larger orebodies. Based upon our experience here, I have outlined below some suggestions for its application to orebodies of larger size. Modifications and extensions, of course, would have to be made to take care of different dimensions and irregularities. In order that one may have a better understanding of the scheme, a brief description of the Coronado method will be given first. CORONADO METHOD The portion of the Coronado vein that is worked by the slicing system ranges from 20 to 40 ft. (6 to 12 m.) in width. Preparatory work in this orebody consists of driving sub-levels every 55 ft. (1 6.77 m.) vertically, or in multiples of 11 ft. (3.36 m.) (which is the height of a slice). These levels are usually driven along the hanging wall until the end of the orebody is reached. Crosscuts, at right angles to the strike, 50 ft. (15.24 m.) apart, are then run from wall to wall, or until the lean ore is reached. They are run in the middle of the block, which is 50 ft. in length and the width of the vein. The crosscut on the hanging-wall side is extended in the wall a short distance for a manway and timberway raise. This raise is carried up in the wall to the sub-level above, leaving a pillar about 5 ft. in thickness between it and the vein. Connections are made every 11

Jan 1, 1918

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