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By Archer E., Wheeler

Producing copper companies were active during 1941 owing to the national defense program the United States and the requirements of the friendly belligerent nation. This activity extended to the American owned properties in South America, the major part of whose product was taken by the Metals Reserve Co., a U.S. Government agency. Anaconda Copper Mining Co. is building a new converter plant at Anaconda, with four units of the Peirce-Smith type. The addition is being built adjacent to the reverberatory plant so as to avoid the necessity of hauling matte and slag. It is expected to be completed this year.

Jan 1, 1942

By Edward H. Robie

THE registration badges gave out, there were not enough programs, the Pioneer Hotel's rooms were insufficient, and some hundred applicants for banquet tickets had to be turned down at the Institute's Regional Meeting in Tucson, Nov. 1-5. Minor inconveniences these, however, occasioned by the fact that, optimistic as they are in Arizona, about half again as many partook of the week's activities as were expected. For this, the local program committee can be blamed-both the technical and social features were too attractive in quantity and quality. Seriously speaking, though, the Institute has probably never had a more successful Regional Meeting than this one. It being the first that has been held in Arizona in 22 years, no effort was spared to make it the distinctive gathering that it was.

Jan 1, 1938

By R. E. Allen

THERE was once a time when a practical oil man would appraise or buy a producing property on the basis of from $200 to $500 per barrel of average daily settled production. Curtailment-has, for the present at least, caused a virtual abandonment of the "barrel -of settled production" as a yardstick of, oil property value and in its place has come the "barrel of allowable production," which, although an artificial thing, is nevertheless now the principal factor governing the rate of ?pay out? or investment return. The potential production of a well, settled or otherwise, is of less importance in determining the present worth of a well than is the rate at which it may be produced. Speaking only of true potential for the moment, it is obvious that of two similar wells having the same potential, the one having the highest rate of allowable production would be worth proportionately more than the one of lesser allowable. The discount factor for deferred return and risk can easily vary the present values of the two wells by as much as 20 per cent when allowable rates are not greatly different.

Jan 1, 1934

By Paul D. Martinka

Coal is the principal energy source for the American Electric Power System (AEP System), which generates and delivers more electric energy to its customers within a seven-state area than any other investor- owned electric public utility. The company expected to burn 21.5 million tons of coal in 1968 at its coal-fired, steam-electric generating stations. About 4.3 million tons, representing 20% of the firm's total annual requirement, was the expected yield of its captive coal mines; the other 17.2 million tons were to be purchased from commercial mines in Ohio, West Virginia, Virginia, Kentucky, Indiana, and Illinois. American Electric's largest captive coal mining operation is conducted by Central Ohio Coal Co., a subsidiary of Ohio Power Co., at the Muskingum mine in the Meigs Creek No. 9 coal field of southeastern Ohio. The mine was started in 1953 to produce the coal requirements of the Philo and Muskingum River generating plants of Ohio Power Co., and it has been supplying their annual requirements in the range of 2.5 to 3.5 million tons since that time. The Muskingum River plant is one of the major steam-electric generating stations on the AEP System. This plant began operation in 1953 with a 215-megawatt unit and now has five generating units with a total plant capacity of 1,495 megawatts. The addition of the 615-megawatt Unit 5 in the summer of 1968 increased the total annual coal requirement of the plant from 2.6 to 4.4 million tons. In order to produce the additional 1.8 million tons of coal for the Unit 5 addition and to exploit the remaining coal reserves at the Muskingum mine most economically, Central Ohio Coal Co. has undertaken a $41 million expansion and modernization program, involving the world's largest dragline and an electric railroad.

Jan 1, 1969

By R. S. Newlin

IN reality, the Butte district is the birthplace of the Anaconda Copper Mining Co., for it was here that strength was gathered and means provided for later expansions of the Company. The Butte district was organized at a miners' meeting on Aug. 20, 1866, primarily for gold placer-mining operations. Substantial amounts of placer gold were recovered from gulch gravels during the period 1862 to 1868. The earliest lode claim locations in the district were recorded in July and August 1864. Copper ore was first shipped, to Swansea, Wales, in 1866. In November 1866, according to the Montana Post, construction of a smelter was started to treat the silver

Jan 1, 1948

By Blandford C. Burgess

Mica is an orchid among minerals. It is formed in pegmatites, one of the most bizarre of igneous formations, and is exceeded by few other minerals in the perfection it may attain as to size, color, and cleavage. First used for window glazing, as an ornament and article of trade, it has become one of the most essential insulators of electricity, heat, and shock. Most internal combustion engines use mica condensers or capacitors and such machines of war as planes, tanks, and submarines are immobile without it. The original manuscript of this guide was written in April 1943 at the peak of war emergency. It was not used because shortly thereafter a decision was made to buy on a one price basis eliminating differentials for both quality and size. This is now presented with the thought that from the standpoint of preparedness we can only consider another war imminent and every effort should be made to set up in usable form the experience gained during the Second Morld War. Colonial Mica Corp. was set up by Metals Reserve Co. as a wholly owned government agency to encourage production of domestic mica and to purchase it. It soon became the exclusive buyimg agency for such mica. The writer as Southern Manager called on all the private agencies buying mica to assist in formulating buying policies, methods, and prices. A meeting was held for that purpose in Asheville, N. C., July 20, 1942. In the general discussion the first two hours of the meeting it was decided that the following factors should be considered in pricing strategic mica: clearness, flatness, trimming, color, classification (size and quality), free splitting, hardness, and air inclusions. Most of the mica miners have been buying strategic mica, according to the mine, as No. 1, No. 2, or Nos. 1 and 2 combined. In addition to these grades of strategic mica they have been buying three lower grades of mica, electric (vegetable-stained), black-spotted and black-stained. A number of mines were named one by one and the buyers present gave their opinions as to the basis they would use in buying the sheet mica from each. It was suggested that in addition to the prices already published, prices be posted up to 10 pct higher for special quality and preparation and prices be posted 25 pct lower than the published prices for the lowest acceptable grades of strategic mica, giving the buyers authority to make intermediate prices according to the quality and preparation. It was thought desirable at the same time to announce prices for nonstra-tegic mica where such quality is being obtained in mines producing strategic mica and where it would be necessary to take the output in order to get the strategic mica. It was also suggested that the price of electric and black-spotted mica be 50 pct below the price of the lowest grade of strategic mica and the price of black-stained mica be 60 pct below the price of lowest grade strategic mica. The few experienced buyers available were employed but they were inadequate for the job and others had to be trained. All needed a guide or primer of some kind to attain systematic procedure and consistent prices in their respective buying areas. The Mica Buyers Guide was formulated for that purpose based on experience gained in the first six months of buying. The Preface to the original guide was as follows: The purpose of this guide is to serve as a text in training beginners and as a handbook for experienced buyers of the instructions which have been issued up to this time. At the meeting of prospective buyers last summer, it developed that the first essential to attain uniformity must be some kind of check sheet. Our "Mica Buyers Report" was developed for this purpose and forms the backbone of this guide. Price is determined according to size, quality and preparation. Size can be measured, but no system of measurement or machine has been devised which can be substituted for the trained eye of the buyer to deterrnine quality and preparation. Although the "One Price" system was instituted and the "Guide" not used, the buyers were required to continue making out a "Mica Buyers Report" (Fig1) with each lot of mica purchased. The form proved its value and there is no doubt that in another such emergency some similar form should be

Jan 1, 1950

By John A. Gann

WITHIN a very few years magnesium has sprung from oblivion, from classification as a technically unknown, little appreciated, and expensive material to front-page importance in many fields of engineering. Bunsen may be considered the real founder of our present magnesium industry. In 1852; he prepared this metal by the electrolysis of fused magnesium chloride in a porcelain crucible. In the following years the electro¬lytic process became recognized as superior to chemical reduction methods and Germany became the world's chief producer, installing the first electrolytic magnesium plant in 1886. ' Thirty years later, national defense requirements, occasioned by the outbreak of the World War and the cutting off of imports, caused France, England, and the United States to begin production. Most of this magnesium was used for military purposes so the close of the war resulted in a large curtailment in production. A few companies, however, encouraged by the early success of the Germans and by the rapid developments taking place in aeronautics, and confident in the certain future and ultimate value of this metal, undertook extensive re¬searches in its production and utilization. A variety of production methods, both chemical and electrochemical, were investigated and some of them operated on a commercial scale. Reduction of the oxide with carbon at high temperatures and the electrolysis of the oxide in a fluoride

Jan 1, 1932

By E. R. Johnson

THE copper concentrator of the Braden Copper Co. is at Sewell, Chile, on the western flank of the main Cordillera of the Andes, at an air distance of approximately 50 miles southeast of Santiago, the capital of Chile. The region is mountainous and space is at a premium because of the rough terrain and the danger of snowslides. The ore, a porphyry copper, is mined by a block-caving method in the El Teniente mine. It is hauled to the crushing plant, a distance of 2.6 miles, through a tunnel because of the severe climatic conditions. The usual large, coarsely set, primary reduction machines found in many ore-treating plants are not required because of the mining method employed and the limiting 12-in. spacing of the grizzlies at the head of each ore pass in the mine. It is the purpose of this paper to describe the numerous improvements made in the crushing section of this large flotation concentrator during the past 15 years to increase the efficiency of the plant and to raise the daily output from around 20,000 to 30,000 tons. The reader should keep in mind that all changes were made within the existing building because of the limited space and the high cost of the heavy mill construction required to withstand the snow loads. The present plant, as well as the former, operates on a 24-hr, 7 days a week basis. FORMER PLANT The crushing plant commenced operations at its present site in 1921, the main equipment being No. 7 1/2 gyratories, followed by 48-in. horizontal Symons disk crushers. Fines were removed by 1-in. stationary grizzlies ahead of each unit. In 1924 a third stage of crushing was provided by the addition of 55 1/2-in. rolls in open circuit. During 1925, the Symons disks were replaced by 73 1/2-in. rolls. All the rolls were changed to closed circuit, with elevators and screens to give a final product of 9 pct plus 3-mesh. The flowsheet of a typical crushing section of this period is shown in Fig I. The ore was withdrawn from a common bin serving the five crushing sections in the plant by means of any number up to six 36-in. wide-apron feeders, which discharged onto a common conveyor belt. This conveyor was equipped with a magnetic head pulley and the crusher attendant was stationed near the discharge end to pick out pieces of mine timber that might be in the ore. The ore was discharged over a 1 3/4-in. spaced bar grizzly and the oversize of this grizzly was crushed by a No. 7 1/2 McCully gyratory crusher set at 1 3/4-in. opening on the closed side. The grizzly undersize joined the gyratory discharge and was conveyed to a set of 73 1/2 by 20-in. Garfield rolls set at I in. These rolls operated in closed circuit with a bucket elevator and two vibrating screens placed in parallel.

Jan 1, 1947

By John H. Schissler

INTRODUCTION AND SUMMARY Complex copper-lead-zinc ore is mined from underground workings high in the Western Cordillera of the Andes mountains about 100 km in a stralght line north of the city of Arequipa in southern Peru. The Madrigal mine is situated in a steep-walled canyon into which the six operating levels "daylight". Production is from cut-and-fill stopes currently producing approximately 740 dry metric tons per day. The Santa Rosa vein, the most important producer in the district, outcrops for a distance of about 4 km, bearing N 75º W and dipping about 70º NE. In places the vein splits into two or three branches; widths of each vary between 1 and 4 m and total mineralized widths of up to over 8 m occur. Principal ore minerals are chalcopyrite, galena and sphalerite. Ore reserve grades for the Madrigal mine average about 1.45% Cu, 2.6% Pb and 5.0% Zn, 2.9 ozAg per metric ton. [Compania] Minera del Madrigal is a California limited partnership; the general partner and operator is [Compania] Madrigal, a wholly-owned subsidiary of Homestake Mining Company. HISTORY Shallow workings found on the Santa Rosa vein were probably made by the Spaniards during colonial times in their search for

Jan 1, 1977

By Jim F. Lemons

INTRODUCTION A nickel doesn't buy much anymore. That's even true in the cost of recovering nickel -- the commodity. A 5[C] per pound (11 [c] per kilogram) increase in the nickel price won't cover a 10-percent increase in fuel costs for processing laterite ores, nor will it cover a 10- percent increase in wages for recovering nickel from a sulphide ore. It won't even cover a 5- percent increase in the capital cost necessary to mine and process ocean nodules. The basis for this statement and a quantitative analysis of the variations in costs to recover nickel from different types of nickel ores will be discussed in this paper. During the early part of the 1970's, the interest in nickel and its potential development was shifting from Canada to the Pacific Basin area. Canadian growth rate was slowing and each additional increase in nickel capacity was very expensive (Argall, G.O., 1970). Laterite ores were attractive to developers since they were easy to mine at a low labor cost, and technologies were being developed that would allow the recovery of nickel in marketable forms (Mohide, T.P., Warden, C.L., Mason, J.D., 1977). During the last decade, new laterite production was achieved in the Philippines and Botswana, and a significant increase in production from Indonesia and New Caledonia occurred. However, recent reports on nickel identify numerous problems plaguing the industry, i.e., high energy costs that are forcing shutdowns (INCO, 1980), (Mohide, T.P., Warden, C.L., Mason, J.D., 1977), high Canadian sulphide mining labor costs (Anon., 1976), and rapid inflation of nickel capital costs (Anon., 1981b). No definitive study has been made to determine how sensitive the total cost of production is to rising energy, labor, or capital costs, or to identify to what extent increased byproduct revenues could be used to offset these production costs. The purpose of this paper is to quantify the effects of increases in energy, labor, capital costs, and by-product credits on the future cost of production from nickel reserves and/or resources. METHODOLOGY OF ANALYSIS In order to evaluate the sensitivity of nickel production costs to changes in energy, labor, and capital costs, and in byproduct revenues, an analysis was made of existing and proposed nickel operations, their costs, and their sensitivity to change. The data for these analyses were obtained from numerous sources including international govern¬ment and university publications, professional journals, company reports, private communications, U.S. Bureau of Mines contracts, and estimates by Bureau of Mines personnel. These data were collected, in part, as an ongoing effort of the U.S. Bureau of Mines Minerals Availability System (MAS) to systematically measure and classify identified mineral resources according to their respective extraction technologies, economics, and commercial availability. The MAS Program is currently evaluating the present and potential availability of nickel to the United States in relation to mining, beneficiation, smelting, refining, leaching, transportation, infrastructure, environment, land use, labor, productivity, technology efficiencies, operating capacities, deposit life, and political factors. As a summary of this data, the following briefly describes nickel ore types as each relates to energy, labor, capital, and byproducts. Sulphide Operations Nickel is currently available from sulphide deposits. Roughly 55 percent of the current world nickel production in market economy countries is from sulphide ores, although only about 20 percent of the known land-based nickel reserves and/or resources are sulphides (INCO, 1981). In 1979, the Western World sulphide reserves were estimated at about 9.2 million metric tons of nickel (Little, A.D., 1979). Sulphide ores are typically mined underground, thus resulting in high mining costs; however, these ores can often be upgraded by flotation prior to final nickel recovery and require about one-third of the energy required to recover nickel from laterites (Anon., 1981c). In addition, nickel in sulphide ores may be associated with economically recoverable byproducts, which include copper, cobalt, gold, silver, and other precious metals. Laterite Operations Forty-five percent of current nickel production is from laterite deposits. Laterite deposits account for 80 percent of the known land-based nickel reserves and/or resources (INCO, 1981). In 1979, the Western World laterite reserves were estimated at over 35 million metric tons of nickel (Little, A.D., 1979). Nickeliferrous laterites are residual soils formed by weathering, typically under tropical or near tropical conditions. They can be easily mined by open-cut methods, but generally cannot be beneficiated; thus, recovery of nickel must entail processing of the total mined ore. Usually, these ores have high moisture content (20 to 30 percent by weight) that result in additional fuel costs to dry the ore. Nickel silicates, garnierites, are, processed by pyrometallurgical methods; limonite nickel oxides are normally leached. Byproduct cobalt is not recovered from most ferronickel operations, and is only recovered to a limited extent from many leach operations.

Jan 1, 1982

By IRVING H. WENTIVORTII

(New York Meeting, February, 1912.) THE little town of San Nicolás, Tamaulipas, Mexico, lies approximately 60 miles east of Linares, situated in the State of Nuevo Leon, and 150 miles SE. of Monterey, as shown in the sketch-map. Fig. 1. The place is reached from Monterey by the Tampico train as far as Linares, a distance of 92 miles, and then by coach the rest of the way. It is situated in a narrow valley between low hills, the houses forming one main street and a plaza. It is peopled by about 500 inhabitants. The climate is temperate, the thermometer ranging from 90° in summer to a few degrees below freezing-point in winter; but this severe weather only lasts a day or two at a time, when the " northers " blow. There are no streams in the vicinity, but water sufficient for the use of the people is obtained from wells. The rainfall is about the same as that in the rest of NE. Mexico. The rainy months are July, August, and September. The rest of the year is practically dry, with an occasional showery day or two during the winter, when a " norther " is blowing. Timber is abundant in many localities. There are two varieties of oak, besides mesquite, ebony, "maguira," "patol," and a number of other kinds of trees indigenous to this region. I. HISTORY. On the discovery of the silver-lead hearing veins occurring in this district, the mining-camp of San Nicolás was founded in 1767 by the Spaniards, and numerous mines were opened and worked for a distance of abort 3 miles east and 5 miles west of the town. At the western extremity and near the Carrolena mine, a small town called San Pedro was built. The ruined walls of the houses form a single street, and all is over-

Aug 1, 1912

By AIME AIME

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

Jan 1, 1945

By J. A. Retty

HOLLINGER CONSOLIDATED GOLD MINES LTD., through two subsidiary companies, has the exclusive right to prospect in two contiguous areas in central Labrador. This paper presents the results of the mineral exploration that has been conducted in these areas to date. One of the subsidiaries of Hollinger. the Labrador Mining and Exploration Co. Ltd., under an agreement with the Newfoundland Commission of Government, holds an area of approximately 20,000 sq.mi., which comprises the western portion of Newfoundland-Labrador and includes the upper basins of the Hamilton and Naskaupi Rivers. (The main area of the deposits so far discovered may be located on a map at about 67° west longitude and 55° north latitude.) The other subsidiary of Hollinger, Hollinger North Shore Exploration Co. Ltd., has licensed from the Province of Quebec an area of approximately 3900 sq.mi. lying directly north of the Newfoundland-controlled area at the headwaters of the George, Whale, and Swampy Bay Rivers. The M. A. Hanna Co., large iron-ore operators of the Lake Superior region, are participating in the project. With the exception of the years 1940 and 1941, field work has been conducted in the Newfoundland area since 1936, and in the Quebec area since 1939. Hollinger assumed the management in 1942. The field base is at Hollinger Lake, some 300 miles north of the tidewater base at Seven Islands, Quebec, which, in turn, is just west of the mouth of the Moisie River, on the Gulf of St. Lawrence. Air transportation is used exclusively to service the operation.

Jan 1, 1945

By P. D. I. Honeyman

DURING 1938 many copper companies again felt the economic pinch and smelter operations were often on a reduced basis which some- times resulted in intermittent operations and complete shutdowns. During the last half of the year production was stepped up and smelting operations resumed a more normal appearance. One of the present-day trends in reverberatory sme1ting is definitely toward high-tonnage operations. i\ t the Phelps Dodge Corporation's Douglas plant, the reconstructed 107 by 26- ft. reverberatory furnaces are operated at the rate of 1000 tons of solid charge per day. The arch, all of silica brick; is sufficiently high above the bath to give

Jan 1, 1939

By J. C. Bradley

THE relation of annealing temperature to conductivity of copper wire has been determined. Conductivity hard was 98.26 per cent. After a 10-min. heating at 200°C. it was 98.69. By annealing 10 min. at 300° C. a large increase, to 100.93, occurred. Maximum conductivity, 101.15, was attained after a 500° C. anneal; thereafter it decreased to 100.53 after a 950° C. anneal. If copper is gassed the decrease is much more than this. Materials and Methods The work was done on high grade electrolytic copper, 99.942 per cent. copper plus silver, silver 0.0008 per cent. It was hot-rolled to >/4 in., then cold drawn to 0.080 in. The wire was cut into 25 5-ft. lengths and numbered 1 to 25 as cut. Four samples were tested hard. The others were wound into 5-in. diameter coils. For the 100° C. heating a coil was put into water, the water brought to boiling, and the wire kept at this temperature for 10 min. For the higher temperatures the coils were placed in envelopes of sheet copper, a little water added, and the envelopes sealed by folding over the edges twice, and hammering them together. This kept the air out very well. The envelope and wire 'were brought to the desired temperature; this was maintained for 10 min., then the whole was water-quenched.

Jan 1, 1927

TO WE BOARD OF DIRECTORS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-The following report covers briefly some of the more important activities of the Institute during the year 1923. In my report for the year 1922, I drew attention to the falling off in membership of the Institute due to the depressed condition of the mining industry in several lines and the inability of many of our members to find profitable employment in mining or its associated branches. A number who were unemployed during 1922 established connections during 1923, but a still greater number have been forced to resign or drop their membership during 1923. Fortunately, the number dropped is not so great as in the previous year. The Employment Service conducted by the four Founder Societies bears witness to the trend in business. For the young men just out of college, there are plenty of opportunities at small salaries, there are plenty of opportunities for them as laborers; but for the mature members, those of experience, there are few calls. During the last eighteen months, our Employment Service has been able to place only six of our members out of every hundred engineers for whom it has found work. Another loss which this Society has suffered, but which is not felt so keenly by our sister societies, is in its foreign members. The A. I. M. E. has always had a large foreign membership, but of recent years exchange has been so heavily against many European and South American countries that a large number of members residing abroad have been compelled to relinquish their membership. Almost invariably these members express keen regret because of the necessity that confronts them, and almost invariably the writers express hope that present conditions will not last long and that they will soon be able to ask for reinstatement. Having stated the darkest side of the picture first, it may now be drawn to your attention that in spite of these losses the number of persons applying for membership was decidedly encouraging. From the quality point of view, the membership has not gone backward. The Membership Committee has declined to recommend many

Jan 1, 1925

By L. E. Young

IT has been said the British Empire was built on British Coal. In all the postwar planning for Great Britain the necessity for producing cheap coal and the prosperity of the coal industry are given first consideration. On Jan. 23, 1945, there was released in London a "Report to the Colliery Owners" which had been awaited with great interest. This was entitled "A Plan for Coal" and was the recommendation of Robert Foot, chairman of The Mining Association (Colliery Owners), prepared at their request. Presentation of the "Plan" at this time is particularly significant as it is an answer to the demand for nationalization of the coal industry by the Labour Party and at the same time is a carefully considered program for postwar reconstruction, prosperity, and stability. In the words of Mr. Foot, If the coal industry for the first ten years after this war is to find itself in a situation similar to the one it occupied for the ten years following the last war, with its record of disputes, strikes, stoppages, short-time working, unemployment, and, with it all, a completely insufficient margin of profit, and all the insecurity and instability in our basic industry that was brought with them, it is goodbye to any real prospect of full employment, social security, and high standard of living. To present an elaborate review of the conditions which have brought to a crisis the unfortunate situation in the British coal industry is here unnecessary, but certain of the salient points

Jan 1, 1945

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