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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

By Simon D. Strauss

What are future prospects for U.S. mining? In many quarters the assumption is made that this country has passed its zenith as a mineral producer -- that it is in a period of decline and that it is becoming a have-not nation like Japan and much of Western Europe. These industrial rivals of ours must depend almost entirely on others for their mineral supplies. In trying to answer this question one must of course distinguish between resources and productive capacity. In today's volatile and competitive markets, the definition of what are reserves and what are merely identified resources becomes ever more difficult. Many large deposits have been found that are unlikely to be viable in the marketplace under normal conditions but that can be of significance to the nation's military and industrial security in times of emergency. I should like to draw on personal experience from World War I1 for illustration. 4fter Pearl Harbor great concern developed over the availability of a long 1ist of strategic materials for which this country was largely dependent on imports. Included were a number of minerals of which domestic deposits had been identified. Among these were chromite, manganese ore, mercury, mica and tungsten.

Jan 1, 1982

By J. L. CAHUTHERS

MANY different methods are used for transporting coal from the working face to the tipple. The common methods are animal haulage, locomotive haulage, conveyor systems, and combinations of these three, supplemented, at times, by the miner pushing his own car. Haulage may also be classified into gathering and main line. Gathering haulage is the collecting of loaded cars to a point whence they are hauled to the tipple. In this there is perhaps more lost-time than on the main line because there are .more units in the operation to be synchronized. Also, conditions on the gathering haul- age, such as bad track, poor timbering, insufficient motive power, etc., cause delays; usually these are corrected on the main-line haulage.

Jan 1, 1931

By George M. Fowler, J. P. LYDEN

T HE relationship of geological structure to orebodies and to the great masses of chert in the Tri-State mining district is of such significance that it prompts a brief recital of the existing information regarding the various periods of structural deformation. We began to note a relationship between structure and orebodies early in our studies of the field, and further work revealed a like relationship of structure to the great masses of chert so commonly associated with the ore-

Jan 1, 1934

By H. O. Hofman

(Canal Zone Meeting, November, 19]0.) THE sudden decease, April 1, 1910, in Chicago, of Dr. Franklin R. Carpenter was a shock to his- many friends. He died in his sixty-second year, of heart paralysis. To most fellow-members of the Institute who have followed the progress of the. last twenty-five years in the mining and treatment of non-ferrous ores, the work of Dr. Carpenter in that line is familiar ; but very few, even of those who knew him well in the later years, are acquainted with his earlier struggles to satisfy an inborn hunger for knowledge. The story of his life resembles that of the pioneer who opens up new country; overcoming hardships with indomitable courage, meeting doubts and difficulties with an alert and open mind, and exercising in the face of reverses an unconquerable perseverance. It seems appropriate to place on record in the Transactions a brief outline of the life and work of this eminent engineer. During the past 15 years of his life Dr. Carpenter was much interested in genealogy. In the pursuit of this study as an avocation, he traced his own ancestry to the time when ?Hugh," called "le Charpentier" on account of the dexterity with which he had swung his battle-axe as a crusader, settled in Sussex on lands received from William the Conqueror. The Carpenters came to this country with William Penn. A prominent member of the family was Joshua Carpenter, the founder of Christ Church, Philadelphia. Dr. Carpenter's branch of -the family moved from Pennsylvania into that part of Virginia which is now West Virginia, where his grandfather settled in Harrison county, while the grand-uncle went further west, and built the first iron-furnace at Hanging Rock, Lawrence county, Ohio. In fact, since early times, the Carpenters appear to have been iron-masters. Franklin R.. Carpenter was born, Nov. 5, 1848, in Parkers-

Aug 1, 1910

By M. Smutz, C. J. Baroch, E. H. Olson

IN 1949 an orebody containing some 10 billion lb of recoverable rare earth metals was discovered in the Mountain Pass district of San Bernardino County, California.' The following year Molybdenum Corp. of America purchased a number of claims at the deposit and a mill on the property which had been constructed to process the district's gold ores. Average composition of ore from the San Bernardino deposit is less than 0.1 pct Tho2, 25 to 35 pct calcite, 10 pct rare earth oxides, 15 to 20 pct silica, and 30 to 40 pct barite.' Rare earth content of the ore analyzes 50.7 pct CeO2, 4.2 pct Pr6O11, 11.7 pct Nd2O3;, 1.3 pct Sm2O3,, and 34.3 pct La2O3 and others.' By floating the barite and depressing the bastna-site, Molybdenum Corp. of America produced a concentrate that contained 60 to 70 pct rare earth oxides. More than 25 pct of the rare earths, however, was lost in flotation. It seemed likely that a more economical method could be found. At the present time most of the rare earths in the concentrates are converted to rare earth chlorides, which are either fed to ion exchange columns for separation of the individual rare earths or reduced to misch metal. Current investigation shows that solvent extraction may achieve this separation more economically than ion exchange. The study reported here was undertaken to develop an economical method of preparing a pure rare earth nitrate mixture from California bastnasite ore. Results indicated that more than 98 pct of the rare earths could be recovered. Several possibilities were considered for processing bastnasite ore, but only the method outlined in Fig. 1 was investigated. This involved leaching the calcined ore with nitric acid. The nitric acid process is discussed under the following headings: 1) calcination of the ore, 2) leaching of calcine, 3) filtration studies, 4) solvent extraction, and 5) nitric acid recovery. Calcination: Since California bastnasite ore contains 25 to 35 pct calcite and about 10 pct bastnasite, calcination was needed to reduce the violence of reaction with nitric acid. Weight losses of 26 to 30 pct were obtained by calcining the ore at 900°C for I hr or at 800°C for 4 hr. Longer periods resulted in no further weight loss. Leaching the Calcine: When the bastnasite calcine was leached with 30 pct nitric acid for 8 to 10 days, rare earth recoveries of only 45 to 50 pct were

Jan 1, 1960

By R. M. Bird

FEW persons outside of the foundry trade have any conception of the great variety of sands now regularly specified and furnished, nor of the differences in foundry practice frequently resulting from apparently minor changes in sands. Conditions in each locality where the sands are mined and prepared necessitate special equipment designed to perform the work efficiently. The description that follows of the foundry sand producing operations is typical of the areas in New York and New Jersey, and particularly refers to the operations of the George F. Pettinos Co.

Jan 1, 1926

By E. M. Norris

Phosphate deposits are distributed widely over the earth's surface. Of the known areas of deposit, eight fields are of particular interest because of their vast reserves of high grade phosphatic material and the volume of their production that goes to the world's great consuming areas. These fields, in the order of their present economic importance, are situated respectively in Florida, French Morocco, Kola Peninsula of U.S.S.R., Tunisia and Algeria, Tennessee, Montana-Idaho-Wyoming-Utah, Ocean and Naru Islands in the Gilbert group, and in Egypt. The Rocky Mountain deposits have a comparatively low ranking in the phosphate trade of today, but this field contains one of the largest known reserves of phosphatic material, associated with which are recoverable trace minerals, which are of increasing importance in our national economy. The first discoveries of phosphate rock in the western states were recorded in Cache1 and Rich2 counties in Utah, respectively in 1889 and 1897. Mining operations were begun on these deposits near Montpelier, Idaho, in 1906. During the latter year geological studies of the phosphate beds were started by Weeks and Ferrier of the U. S. Geological Survey. These studies have been continued to the present day by a distinguished roster of the Survey's technicians. As a result of this systematic exploratory program, the Survey has published a series of bulletins, papers, and maps, which provide the mining public with a comprehensive study of the exposed

Jan 1, 1949

By S. H. Chauvenet

Jan 1, 1882

By C. E. LAWAL

WITH the object of adapting high-school vocational courses to the industrial needs of the community, a few high-school officials in West -Virginia working with the School of Mines of the State university decided to try an innovation this year. The purpose of this experiment was to teach coal mining in two high schools situated in mining communities. We thought that if a course in coal mining would be included in the list of optional courses offered in the high school, it might interest some of the boys, and if the course were properly taught it would undoubtedly be of inestimable value to those boys who later decided to take up mining work as their vocation. This coal-mining course was started last September in the Berwind and Gary high schools in West Virginia. The high-school officials in their conferences with' us decided that we should work up the outline of this course and they would assign the science teachers of the schools as instructors, with ,the understanding that we would help 'these instructors with this work. We consented to all this and submitted -an outline to the school officials which they are following this year.

Jan 1, 1929

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith's data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy's obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:'l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969

By Donald B. Gillies

TO me a graduating class of engineers constitutes one ' of the finest inspirations I can imagine. You have finished your four- year scholastic career and are starting out in competition with thou- sands of other young men from other universities to make your mark. Be- cause of your training you men are such an essential part of our present- day civilization that a great weight of responsibility rests on your shoulders, especially at this time, for this is an engineering era. Today, it is the engineer who dreams the dreams and makes our civilization better. It's the engineer who carries those dreams into realization and fulfillment. No matter where we go in business and industry, we find- engineers in key positions, charged with great responsibilities.

Jan 1, 1939

By M. C. LAKE

THE industrial development of the United States has been stimulated by the presence of high-grade iron ore in the Lake Superior district. These great deposits have been susceptible to economical extraction and are conveniently located for cheap lake vessel transportation to the great consuming centers. The district furnishes from 80 to 85 per cent of the iron ore annually consumed in the United States, and a full understanding of the available supply of this great commodity is so important that it is well to consider whether or not the industrial supremacy and national independence attained as a result of the abundance of cheap ore are permanent. The enormous deposits of high-grade ore available in the Lake Superior district have been the foundation upon which the vast industrial structure of the steel and allied industries has been built. It is extremely important to the country as a whole, and especially to those States and communities now dependent on Lake Superior ore for their prosperity, that their industries shall retain the particular advantages with which they are now endowed, and that a generous supply of high-grade raw material be available for their consumption at a satisfactory cost. The steel industry is so basic and fundamental that any fluctuation in the cost of its finished products as determined by the supply and cost of the raw materials involved in its manufacture will necessarily affect the business of a wide variety of industries which are dependent on it.

Jan 1, 1926

By A. KROENLEIN

THE Cromwell 'Pool has been the outstanding development in Oklahoma during the year 1924. . Tonkawa contributed the deep "Slick Sand" bit apparently its 'peak has been reached and like other pools producing from below the Mississippi lime its decline' mill be rapid. After reaching a daily production of 67,000 bbl., the Cromwell Pool is declining because of a lull in -new completions, but a mile extension has revived activity and an area equal to that of the present producing' area is under development and will cause an increase in the present production of 38,000 bbl. This pool is seven months old, has three dry holes in one hundred twenty completions and is actually defined only on the southern extremity. This area has been one of the chief contributors to the .over-production of high gravity oil in the Mid- continent fields and will be such' for the remainder of ' the year. 1924 and first part of 1925.

Jan 1, 1924

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

After the close of the Revolution, settlers began to pour over the mountains, to settle in the western parts of Pennsylvania, of Virginia, to move down the Ohio into Kentucky, and in the late seventeen-eighties to settle on "the Indian side" of the river, now Ohio. With the growth of population the interest in coal increased and it was not long before the production of coal west of the mountains was larger than that east of them. Foreign nations, too, became interested in the young republic and in 1783, at the instance of the Swedish government S. A. Hermelin, an engineer, visited this country to investigate its iron industry. He made a very interesting report, not published until 1931, in which he gave many details of the iron plants in the eastern United States; apparently he was not west of the mountains, but was well informed about conditions there. He says, "that some coal near the first branches of the Schuylkill River has been mined and utilized by the blacksmiths," referring, of course, to anthracite; again that "coal mines have also been worked for several years near Pittsburg," and that "great supplies of iron ore are available at the Ohio Falls and further to the west, at Coney Creek, a part of the Green River, where there is also coal."' In 1788, Dr. Johann David Schoepf, who came to this country with the Hessian troops, visited Pittsburgh. He was an intelligent man and acquainted to some extent with minerals and methods of working them. In speaking of Coal Hill on the south side of the Monongahela he mentioned several strata of marble in the lower part and that

Jan 1, 1942

By AIME AIME

ON Sept. 24, 1875, a remarkable deposit of silver ore was discovered by James Ryan and Samuel Hawkes at the east base of Grampian Hill in central Beaver County, Utah.. A shaft was begun and had been sunk about 30 ft. in ore when the claim was sold on Feb. 17, 1876, to A. G. Campbell, Matthew Cullen, Dennis Ryan, and A. Byram for $25,000. To them is due the credit of having developed the mine and started the district on the road to its present state of prosperity. Their development resulted in proving the vein to a depth of over 280 ft. and about 2500 tons of ore was extracted and turned into bullion. In February, 1879, the mine came into the possession of the Horn Silver Mining Co., and since then over $65,000,000 worth of ore has been taken from the mine. Two smelters were built in 1878, near the mine; 400 men were employed underground, and 1000 on the surface, burning charcoal, hauling wood from the surrounding hills, and freighting and hauling hay for the hundreds of horses used in the work. Ore was hauled thirty miles to the

Jan 1, 1936

By H. E. Criner, M. G. Driessen

Maurice Rey—The influence of cyclone diameter upon the fineness of separation is an important point which, however, cannot be discussed adequately if the injection pressure or the rate of flow are not specified. Perhaps some light can be thrown on the matter by using the formulas derived by Dahlstrom. Let us consider several geometrically similar cyclones where the apertures e and b are equal and proportional to the diameter D and which are operated with the same pressure drop. Eq 8 of Dahlstrom's paper can be written: Q Q = K D'. " or. if F is constant: Q = K D18 K is a constant of proportionality. Introducing this value of Q in eq 13 gives elimination efficiency = K D ,41 Elimination efficiency, in the terminology of Dahl-strom, means the diameter of particles, in microns, which divide equally between the underflow and the overflow. This denomination is regrettable and it would be preferable to call it diameter of separation or characteristic size or any other name connoting a size rather than an efficiency. Whatever the name used, the above equation shows a slow increase in the fineness of separation when the diameter of the cyclone decreases. For example, if a 14-in. cyclone gives a 400-mesh separation (37 microns), geometrically similar cyclones, having the same pressure drop will give separations at the sizes shown below.

Jan 1, 1951