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By D. H. Fleming

DURING 1950 the jet-piercing process was used commercially in the piercing of primary blast- holes in magnetic taconite at the preliminary taconite plant of the Erie Mining Co., Aurora, Minn. The Erie Mining Co. purchased a jet-piercing ma- chine and associated equipment in 1949, and the machine has been in operation since its installation in the summer of that year. An overall view of the pit with the JPM-1 jet-piercing machine in operation is shown in Fig. 1.

Jan 7, 1951

Jan 1, 1961

By Nicholas J. Grant, Noboru Komatsu

Electron-micrographic studies and hardness tests were made of an internally oxidized dispersion-strengthened Cu-12 vol pct SiO2 alloy follozuing longtime annealing at elevated temperatures. The rate of coarsening of SiO2 particles and the relationship between hardness and interpavticle spacing were Dispersion -strengthened alloys exhibit a remarkable stability of structure and properties at elevated temperatures compared with conventional alloys; nevertheless, when they are exposed to high measured. The rate of coarsening of SiO2 particles is controlled by the decomposition of SiO, rather than by the diffusion rates of silicon or oxygen through the copper matrix. The mechanism of coarsening was also studied by using a diffusion-couple technique. temperatures, weakening takes place as a result of coarsening of the dispersed phase. The theoretical treatment of the coarsening of dispersed phases has been treated by Greenwood,1 wagner,, and others3 by considering the interfacial energy of dispersions and the diffusion of solute atoms. Recently, experimental work on the coarsening of relatively insoluble, finely dispersed cobalt particles in copper was reported by Livingston,4 and on aluminum oxide in nickel by Dromsky, Lenel, and Ansell;5 according to these investigations, the rate

Jan 1, 1964

By S. S. Clarke

THE sheet-ground deposits of the TriState district, because they are fairly uniform in thickness (7 to 11 ft.)-rather flat, with an easy dip to the west-and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. DEVELOPING TRACTORS AND TRAILERS A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Fig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½ -in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the springs could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dual. After four months of use, the tires are beginning to show signs of failure.* In

Jan 1, 1942

Jan 1, 1922

By W. A. Thomas

STEAM is, and doubtless always will be, the basic power in the anthracite industry, either directly applied through engines and pumps or electrically. The rapidity with which electric power is being applied to the mining and preparation of anthracite leaves little doubt as to its utility and economy. There is practically no operation, except possibly the drilling of hard rock, that has not been successfully electrified and the matter of drilling is handled economically with electrically driven compressors and the standard compressed-air drills. Conservation and the seemingly ever-increasing cost of production, justify careful consideration of the possible results of the more extensive use of electric power in the industry. It is not planned to discuss, herein, the relative economies of individual applications but to consider the relative economy and flexibility of steam and electric power. The reports available for the year 1920 indicate a production of slightly over 80,000,000 tons of anthracite, of which 8,843,500 tons were used for power and heating purposes; in other words, over 11 per cent. of the production was used at the mines. Some of this was used to generate electric power at the mines, about 160,000,000 kw-hr., while 150,000,000 kw.-hr. was purchased from the public utility companies. One large producer, who is buying some electric power and generating some, used over 13 per cent. of the production for power and heating at the mines. Another producer, where considerable electric power is generated on the properties, is using less than 9 per cent. of the output for power and heating. One of the largest producers has a fuel consumption of over 15 per cent. of the output, besides which considerable power is purchased. A careful study of the field indicates that steam-operated plants use upwards of 13 per cent. of the production for power and heating, while electrically operated plants use about 1 per cent. for heating; so that, for steam-power purposes at least 12 per cent., or 268.8 lb., are used for power out of each ton produced.

Jan 9, 1921

By Len Ramp

CHROMITE deposits in southwestern Oregon occur along definite zones or horizons in sill-like ultramafic intrusions. These horizons are here referred to as ore zones and are distinguishable only by relatively Shin and scattered, discontinuous chromite occurrences. The zones are tabular in shape but are usually folded and faulted by the intensive post-intrusion deformation the ultramafic rocks have undergone. A single zone may contain disseminated, nodular, banded, or pods of massive chromite. The typical chromite deposit is composed of a series of thin lens-shaped bodies that lie along a definite plane and generally show evidence of magmatic flow with their long dimensions aligned in the direction of flow. A body of chromite often pinches down to a narrow wisp only a fraction of an inch thick. This thin streak of chromite may point to or be connected with another body of chromite. In some deposits the orebodies have a definite rake. The depth at which chromite may be found can be predicted by its position in a folded intrusive, provided that adequate structural evidence is available. Although the ore shoots are characteristically discontinuous, there is theoretically no limit to the depth at which chromite may be found. Origin: All the chromite deposits examined in southwestern Oregon are of magmatic origin, that is, the chromite was an original constituent of the peridotite magma and became segregated in varying degree from the magma to form the ore de- posits. Examples of early, intermediate, and late magmatic chromite have been recognized in the area. Crystallization of the principal minerals (olivine, pyroxene, and chromite) was apparently near completion at the time of intrusion of the peridotite magma. The magma acted as a viscous crystal mush stringing out aggregates of pyroxene and chromite in the direction of flow. These streaky accumulations are termed schlieren.

Jan 8, 1957

No records have been found of coal in the old Spanish documents, although some mention of it probably exists in manuscripts. Coal was found in Mt. Diablo, in Contra Costa County, about five miles south of the San Joaquin River in 1852, but the first mine, the Teutonia, was located in 1858. The deposits are located on both sides of a high ridge, and vessels of 1,000 tons burden could ascend the river to the nearest point to the mines.1 In 1854, coal was found about four miles from Oroville, on the Feather River, in Butte County. Development work was started and in 1856 a mine was opened. From the description the coal was likely a variety of lignite and probably never amounted to anything commercially, as it does not appear again in the records 2 The more valuable mines at Mt. Diablo were opened in 1859 and 1860. By 1867 there had been 11 mines started and at that time five were in operation. The seam conditions were much disturbed and lack of knowledge of them caused much waste of effort and money. All of the coal excepting that used locally and in nearby towns, was shipped to San Francisco, and largely used for steam purposes. The first receipts were in 1861-6,620 tons. A railroad to the river had been constructed and opened in February 1866. The Corral Hollow field in Alameda County was found and prospected to a small extent in 1862. Two mines were opened but little work was done and the field was then abandoned. Good exposures were rare and the cost of underground exploration was then prohibitive. The Commercial mine produced coal in 1869 and 1870, but a fire in the latter year destroyed the tipple and communications to the mine. The Livermore mine was abandoned after 18 months operation in 1875 and 1876 and no other work was done here until the nineties. In 1867 Hyne reported the presence of coal in workable thickness, and of good quality, on the property of the Pacific Coast Petroleum Company,

Jan 1, 1942

By J. W. Spretnak, G. Sachs

The: iron-rich iron-nickel alloys have attracted considerable academic interest in recent years. The carbon-free alloys are of minor practical importance, but they are the base of many alloys with various outstanding properties. The iron-nickel alloys, therefore, have been investigated extensively regarding both their structures and their properties. The researches on these alloys up to 1938 have been collected and critically reviewed by J. S. Marsh,l and will be discussed in some detail in the sections of this paper dealing with specific subjects. These numerous investigations have not succeeded in establishing the equilibrium conditions in this system. Alloys containing more than a certain amount of nickel (8 to 10 per cent Ni) undergo the allotropic transformation extremely sluggishly, both on heating and cooling, showing a large hysteresis," which is not dependent upon the rate of cooling and persists even with very slow rates of cooling.3 Honda4 and Merica4 have therefore resigned themselves to proposing a diagram (Fig. I) for practical use, illustrating the structural relations under commercial conditions instead of attempting to establish the true equilibrium diagram. Marsh is less pessimistic and suggests an equilibrium diagram (Fig. 2) which conforms approximately to the facts known about this system. Recent X-ray investigations by Owen-Sully5 and Bradley-Gold-schmidt6 on powdered alloys indicate that the previous work on the iron-nickel system yielded very incomplete results. These investigators agree (Figs. 3 and ,+) that alloys in the powdered form containing more than 8 per cent and up to about 35 per cent Ni decompose into a stable heterogeneous mix-

Jan 1, 1941

By G. Sachs, J. W. Spretnak

The: iron-rich iron-nickel alloys have attracted considerable academic interest in recent years. The carbon-free alloys are of minor practical importance, but they are the base of many alloys with various outstanding properties. The iron-nickel alloys, therefore, have been investigated extensively regarding both their structures and their properties. The researches on these alloys up to 1938 have been collected and critically reviewed by J. S. Marsh,l and will be discussed in some detail in the sections of this paper dealing with specific subjects. These numerous investigations have not succeeded in establishing the equilibrium conditions in this system. Alloys containing more than a certain amount of nickel (8 to 10 per cent Ni) undergo the allotropic transformation extremely sluggishly, both on heating and cooling, showing a large hysteresis," which is not dependent upon the rate of cooling and persists even with very slow rates of cooling.3 Honda4 and Merica4 have therefore resigned themselves to proposing a diagram (Fig. I) for practical use, illustrating the structural relations under commercial conditions instead of attempting to establish the true equilibrium diagram. Marsh is less pessimistic and suggests an equilibrium diagram (Fig. 2) which conforms approximately to the facts known about this system. Recent X-ray investigations by Owen-Sully5 and Bradley-Gold-schmidt6 on powdered alloys indicate that the previous work on the iron-nickel system yielded very incomplete results. These investigators agree (Figs. 3 and ,+) that alloys in the powdered form containing more than 8 per cent and up to about 35 per cent Ni decompose into a stable heterogeneous mix-

Jan 1, 1941

By J. R. Long, T. R. Graham, R. G. Feustel, R. S. Dean

THE comprehensive study of the copper-manganese-zinc alloy system in the Bureau of Mines Laboratories has so far been principally concerned with alloys that lie within the alpha solid solution field of the system. Two regions, one centering about 65 per cent copper, 10 manganese and 25 zinc, and the other centering about 70 per cent copper, 20 manganese, 10 zinc, have been carefully examined.1,2 These have indicated that when the alloys are made with electrolytic manganese considerable amounts may be readily introduced and that the strength and hardness are increased without excessive losses in ductility. In the course of the work of establishing the limits of the alpha solid solution range,3 enough of certain of the alloys was prepared to permit determination of their physical properties at a future date. The 60 per cent copper alloys concerned here are part of that series. They cross through the alpha field and into the adjacent alpha plus beta and alpha plus X fields, and are of interest because they offer some information on the effects of manganese on alloys lying in these fields. COMPOSITION AND FABRICATION OF ALLOYS The chemical composition of the alloys involved is given in Table I. They were intended to contain 60 per cent copper with manganese increasing from 5 to 25 per cent in 5 per cent steps and zinc decreasing [ ] from 35 to 15 per cent. The analyses are so close to the intended composition that the alloys will be referred to hereafter by their nominal compositions. They were finished into sheet by cold-rolling and intermediate annealing procedures calculated to produce sheet 1/16 in. thick, cold-reduced by 20, 40, 60, and 80 per cent in thickness. Physical properties were determined on standard flat tensile specimens with 4-in. gauge length, although the test gauge section used was 2 in. The properties were obtained on cold-worked material and on material annealed at temperatures ranging from l00° to 1500°F. after 60 per cent cold reduction. Since an annealing temperature of 1200°F.

Jan 1, 1946

By Jed H. Mosgrove, Paul M. Budzak

INTRODUCTION Good mine ventilation starts at the drawing board. A coal mine will either be adequately ventilated or not, depending upon how good a job was done in the planning. Poor planning will not only result in inadequate ventilation, but may also lead to low productivity. A mine foreman cannot achieve high productivity while trying to maintain 4.2 m3/s (9000 cfm) of air at his last open crosscut. PLANNING What will provide adequate ventilation? A rule of thumb in laying out a coal mine is to provide enough entries in the main entry system to keep air velocities at 2.5 m/s (500 fpm) or less; at this rate of flow, good ventilation may be expected. The intake and return air courses of a coal mine do not improve with age. Entries will deteriorate, ribs will slough, roof will fall, and clutter will accumulate. The resistance offered to air travel will continue to increase with each passing year. Providing enough airways for the present and the future cannot be emphasized too strongly. In order to better appreciate good planning and bring it into better focus, assume a hypothetical mine has the following features: entries 1.5 m (5 ft) high and 6.1 m (20 ft) wide; one intake and one return entry; the mine development is 4.8 km (3 miles) from the intake and upcast ventilation shafts; and the ventilation requirement is 141.6 m3/s (300,000 cfm). Air travel of 4.8 km (3 miles) into a mine and the same distance back to the fan is not unusual. However, to do so with one intake and one

Jan 1, 1981

By W. J. Keep

Manganese is a nearly white metal, having about the same appearance when fractured as white cast-iron. Its specific gravity is about 8, while that of white cast-iron, reasonably free from impurities, is but a little above 7.5. As produced commercially, it is combined with iron, and with small percentages of silicon, phosphorus, and sulphur. It is generally produced in the blast-furnace. If the silicon is under 0.50 per cent., the product will be white. If the manganese is under 40 per cent., with the remainder mostly iron, and silicon not high enough to make the product gray, the alloy is called spiegeleisen, and the fracture will show flat reflecting surfaces, from which it takes its name. With manganese above 50 per cent., the iron alloy is called ferromanganese. As manganese increases beyond 50 per cent., the mass cracks in cooling, and when it approaches 98 per cent. the mass crumbles or falls in small pieces. When the percentage of manganese is high, the planes of the fracture are not so bright as when it is lower. The ferro-manganese which we have used in the experiments reported in this paper, contains Mn, 81.62; Si, 0.256 ; and combined carbon, 6.153 per cent. We have not been able to make test-bars from this, because the alloy cracks in small pieces in cooling. Manganese combines with iron in almost any proportion, but if an iron containing manganese is remelted, more or less of the manganese will escape by volatilization, and by oxidation with other elements present in the iron. If sulphur be present, some of the manganese will be likely to unite with it and escape, thus reducing the amount of both elements in the casting. Hence, in remelting irons, some of the sulphur which has entered from the fuel with which the iron is melted will very likely unite with some of the manganese in irons which make up the mixture and escape. Remelting, therefore,' reduces the percentage of manganese in cast-iron.

Jan 1, 1892

By Edward C. Mack, Ronald G. Stovash

INTRODUCTION Ronald G. Stovash General Superintendent Consolidation Coal Company Shoemaker Mine Moundsville, West Virginia Consolidation Coal Company's Shoemaker Mine is located in West Virginia's Northern panhandle near Wheeling, adjacent to the Ohio River. Steam coal is mined from the Pittsburgh #8 seam which averages 65 in. in thickness. The 10 in. of draw rock directly above the coal is taken on advancement, but remains when longwalled. The top consists of up to 12 in. of lower quality coal, and immediately over that, up to 10 ft of multi layered shales, coal, and bone. The cover ranges from 300 to 800 ft of shales and limestone. Two longwalls operate in the mine. The first longwall started in April 1975 and is retreating its eighth panel. This wall was the first to use shield supports in the United States. The second longwall started in September 1979 and is currently retreating its first 7,000 ft panel.

Jan 1, 1981

Engineers who are in charge of industrial operations, and their number is legion, sense as much as anyone the present feeling of unrest in the' country and more than anyone else realize the present inefficiency of labor. Undoubtedly the two phenomena are closely correlated and no doubt are due to a multitude of causes which it will be impossible to enumerate. From my experience in mining I estimate that the present efficiency of labor is only about two-thirds of what it was under pre-war conditions. In the mining industry, at least, we have not a large surplus of men looking for work and usually under these conditions men are rather more independent and will not work as efficiently and faithfully as if they felt there were plenty of men ready to take their places. Wages in metal mining have advanced more than the increased cost of normal and sane living. The result is that the men often work fewer days in a month and do not seem to have very much interest in their work while actually engaged in it. Then again, they have been listening to the more or less vague propaganda of the I. W. W. and the radical wing of the socialists, who are harping on the fact that the distribution of newly created wealth is unfair and that the laborer really is not working for himself or his fellow laborers but is carrying on his exertions for the benefit of a small and lim-ited class of exploiters. A continued harping on this view is bound to influence the judgment of even a conservative workman who is not a student of economics and who hears little or nothing upon the other side. I am a great believer in the common sense of the American people and in the long run I do not think that they will be carried away by unsafe doctrines. The trouble with so many of these propagandists of industrial in-equality is that they do not differentiate between production and dis-tribution. Even if we admit that distribution is unfair, unless goods are produced there will be nothing to distribute. A great many unthinking people seem to feel that wages are paid out of a pot which is inexhaustible and do not realize that eventually what comes out of the pot can never exceed what is put into it. The workman is not paid in money but is paid in goods, money as we all know being used simply as a measure of value and a medium of exchange, and that all that can be used to pay the laborer is what he produces.

Jan 11, 1919

By Jed H. Mosgrove, Paul M. Budzak

INTRODUCTION Good mine ventilation starts at the drawing board. A coal mine will either be adequately ventilated or not, depending upon how good a job was done in the planning. Poor planning will not only result in inadequate ventilation, but may also lead to low productivity. A mine foreman cannot achieve high productivity while trying to maintain 4.2 m3/s (9000 cfm) of air at his last open crosscut. PLANNING What will provide adequate ventilation? A rule of thumb in laying out a coal mine is to provide enough entries in the main entry system to keep air velocities at 2.5 m/s (500 fpm) or less; at this rate of flow, good ventilation may be expected. The intake and return air courses of a coal mine do not improve with age. Entries will deteriorate, ribs will slough, roof will fall, and clutter will accumulate. The resistance offered to air travel will continue to increase with each passing year. Providing enough airways for the present and the future cannot be emphasized too strongly. In order to better appreciate good planning and bring it into better focus, assume a hypothetical mine has the following features: entries 1.5 m (5 ft) high and 6.1 m (20 ft) wide; one intake and one return entry; the mine development is 4.8 km (3 miles) from the intake and upcast ventilation shafts; and the ventilation requirement is 141.6 m3/s (300,000 cfm) . Air travel of 4.8 km (3 miles) into a mine and the same distance back to the fan is not unusual. However, to do so with one intake and one

Jan 1, 1981

By R. Taggart, R. H. Ericksen, D. H. Polonis

MarTENSITIC a has been observed to form spontaneously from the retained ß phase during the preparation of thin foil specimens of metastable Ti-Cr alloys containing from 6.9 to 20 wt pet Cr. Similar spontaneous martensite reactions have been reported in thin foils of 0 brass' and other alloys.2 4 The absence of retained austenite in iron-based alloys has also been attributed to spontaneous decomposition during thinning.5 The present work indicates that a unique situation occurs during which the spontaneous transformation takes place when the transitional ? phase is present in the as-quenched or partially aged ß phase. Alloys containing 6.9, 7.0, 8.0, 12.0, and 20.0 wt pet Cr were prepared by the levitation melting of "io-chrome" chromium and iodide titanium. The 0.5-in.-diam ingots were vacuum-annealed at 1000oC, and wafers 0.020 in. thick were then cut from the ingots. These wafers were wrapped in molybdenum foil, encapsulated in Vycor under a reduced pressure of purified helium, and then held for 30 min at 1000°C. The specimens were quenched in water to retain the metastable high-temperature ß phase. The quenched alloys were thinned by mechanical grinding to about 0.005 in. thick, then electropolished in a solution of 300 ml methyl alcohol, 175 ml n-butyl alcohol, and 30 ml perchloric acid at a temperature of -40°C. Needle specimens 0.005 to 0.010 in. diam were taken from each ingot and heat-treated with the foil specimens. X-ray diffraction patterns indicated the structure of the 6.9, 7.0, and 8 wt pet alloys to be a

Jan 1, 1968

By L. G. Austin, P. T. Luckie, R. R. Klimpel

Application of the Charles and Bond Laws to batch grinding can be deduced as a special case of solution of the first-order batch grinding equation. With additional limitations on the feed size distribution, this special case also gives Rosin-Rammler distributions of constant slope, with the 36.79% retained point a simple function of time. In general, the assumptions concerning the breakage parameters S and B which are necessary to get Charles' and Bond's laws, are not valid except as a crude approximation. With less restrictive assumptions, it is still possible to get approximate Rosin-Rammler distributions, but the slopes change with time of grinding, and the 36.79% retained point is a more complicated function of time. An alternative form to Charles' law is suggested, which accomplishes the same result and has the same errors, but avoids the use of energy of grinding and deals with specific rate of grinding.

Jan 1, 1973

By W. F. Cloud

The data and information compiled under Part I of this report are the results of experiments performed in the petroleum engineering laboratory under the supervision of W. F. Cloud, Associate Professor of Petroleum Engineering and William Schriever, Professor of Physics, University of Oklahoma. Problems Being Studied Most of the time has been spent in trying to determine the rate of flow and pressure gradient in a 4-in. flow tube 10 ft. long, which was packed with sand of various grain sizes. To date, only two kinds of sand have been packed in this tube: 60 to 80-mesh Canadian river sand, 60 to 80-mesh and 80 to 100-mesh Simpson sand. The original intention was to follow the same procedure and use the same types of crude under identical saturation pressures of both air and gas, as well as unsaturated (dead) oil, flowing the various crudes through several different sizes of both Canadian river and Simpson (Wilcox) sands, but lack of time has prevented such an intensive study of the problem. Some additional time has been spent flowing saturated and unsaturated crudes, similar to those used in the 4-in. tube, through 1-in. tubes, one of which was 2 ft. long and one 5 ft. long. The results obtained have been checked against those obtained by using the 4-in. tube, to obtain the relation of diameter and length of tube to rate of flow in similar sands. Laboratory Equipment Saturation Tank.—A heavy steel cylindrical saturation tank, capacity about 42 gal. was mounted on a platform of bricks, then a galvanized tin temperature bath was built around the saturation tank. This contained

Jan 1, 1930

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 thermo-dynamic 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 called 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 formulae 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. AuCu3; 4. AuCu. When the temperature is so high that no long-range order exists, these formulae reduce to the same form for all lattice types, namely: [ ] Here the symbols have the following meanings: [F-Helmholtz free energy E-energy S-entropy k-the gas constant per molecule z-coordination number, (e.g. 12 in. a-brass). N-total number of atoms c-atomic fraction of A] VAA, VBB, VAB-energy per bond of the corresponding bonds log means log, throughout The superscript 0 denotes the thermo- dynamic function 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 [ ] The free energy may also be written in terms of µA and µB, the chemical potentials or partial free energies per atom:

Jan 1, 1948