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By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

The effect of such variables as feed size, particle shape, cleavage, and hardness on the relative proportion of impact, abrasion, and chipping events in a tumbling mill is demonstrated. The concept of an average event, which is a combination of the three comminution mechanisms, is introduced. It is postulated that the average event in a particular mill determines not only the size distribution but also the energy-size reduction relationship for the comminution process. Fragmentation of particles in tumbling mills appears to result from a combination of impact, abrasion, and chipping grinding.' The relative rates of size reduction attributable to any of the basic grinding mechanisms must depend upon a number of variables, such as feed size, particle shape, hardness, and the number and kind of particles in the mill. The purpose of this paper is to show experimentally how these variables in the properties of materials affect the size distributions obtained by grinding the material's in a laboratory tumbling mill. The resulting size distributions will be intetpreted in terms of a combination of three comminution mechanisms. METHODS AND MATERIALS In this study, minerals of widely differing properties were ground either separately or as mixtures in laboratory mills using rods or balls for grinding media. The materials used include quartz, Tuolomne, limestone (99.8% CaCO3), barite, corundum, galena, pyrite, glass beads, and crushed glass. The mill used was 8 in. in diam. and 9-1/4 in. long. For the ball milling tests, 17.6 kg of steel balls (36: 7/8 in. balls, 178: 1 in. balls, and 44: 1-1/8 to 1-1/4 in. balls) were used. For the rod milling experiments, 17.6 kg of steel rods 9-1/16 in. long (25: 5/8 in., 10: 3/4 in., and 5: 7/8 in. in diam.) were used. In each test, 1 kg of solids were ground wet at 60% solids at 77 rpm. In all cases except where otherwise specified, the feed to the mill was 4 x 8 mesh material. Size distributions of the ground products were determined by a wet-dry sieving procedure with Tyler series sieves. Size distributions of mixed products containing limestone were determined by dissolving the limestone with acid and sizing the residue. EXPERIMENTAL RESULTS AND DISCUSSION If the size distribution of the product from a tumbling mill depends upon the relative proportion of impact and attrition (abrasion and chipping) events, altering the grinding conditions may change these proportions and consequently alter the size distribution of the product. Data to illustrate this point can be taken from Gaudin's classic 1926 paper.2 In one series of experiments, Gaudin ground quartz of different initial sizes for four hours in a laboratory ball mill with 7/8-in. balls. In Fig. 1, his data are reproduced as the cumulative fraction finer than the stated size for the following initial feed sizes: 13.3 x 9.4 mm, 6.7 x 4.7 mm, 2.6 x 1.6 mm, and 0.83 x 0.59 mm. As the feed size was decreased, a dramatic change in the shape of the size distribution curves took place, even though the amount of minus 100-mesh

Jan 1, 1964

By Cleveland Dodge

THE present organization of Copper Queen employ-ees, known as the Employees' Conference Com-mittee, is really an outgrowth of the former Grievance Committee, which, in turn, had developed from the original Hospital Committee. The relatively small membership of these older organizations, the practical limitation of their activities to the presenting of grievances, and their lack of initiating powers, were the principal defects which the plan now in operation seeks to overcome. A somewhat parallel scheme was instituted in our Sacramento Hill division about four years ago; this gradually developed into the Ways and Means Committee, which, in addition to providing a forum for the discussion of operating problems, was instrumental in establishing an excellent and mutually satisfactory bonus system. Before recommending adoption of the plan now in force, we made extensive inquiries among those who have had any experience in such matters, and ended by proposing a modification of a scheme developed by John Leitch,1 which was characterized by its similarity to the constitution of the Federal Government. As finally remodeled, the. plan was submitted to vote of the entire working forces at the Copper Queen mines, and was adopted by them in May, 1920. Mining opera-tions since that date have been so interrupted that it is scarcely possible to state exactly what the results have been. The following quotations are from a printed pamphlet containing the constitution of the organization, as finally adopted. The first extract is from a letter addressed by the management to the employees: The plan submitted for your approval and adoption is modeled after the constitution of our own country, under which every individual is given an opportunity for advancement, according to his ability and determination, and every citizen is given a voice in the laws that shall govern him. So it is to encourage the individual employee in advancement, and to give him a voice in making the rules that shall govern his conduct, that we favor the adoption of the proposed constitution.

Jan 1, 1923

By F. F. Hintze

Petroleum production in the Rocky Mountain district during 1929 registered a small decline from that of the previous year, conforming with a gradual decrease in the amount of oil produced during the last few years. A number of causes may be mentioned to account for this result, chiefly overproduction in other regions and the apparent desire of operators in this territory to conform to the policy of proration and retrenchment adopted by special agreement among operators in many of the fields. Unit operation has been adopted to control oil production from the Sundance sands in the Salt Creek field, Wyoming, in line with the general effort to stabilize this phase of the industry and prevent excessive drilling of new wells. Another factor which greatly retarded development in the Rocky Mountain region was the executive order of President Hoover issued in March refusing the award of new prospecting permits to future applicants and threatening cancellation of all existing permits upon which actual drilling had not been done as specified by law. Only four states in the Rocky Mountain region are important oil producers. In 1929 Wyoming led with an average daily output of 52,600 bbl., followed by Montana, with 10,730 bbl.; Colorado, with 6500 bbl., and New Mexico with 2700 bbl. daily average. These states bear the following percentage relation to total production in the Rocky Mountain district: Wyoming, 72; Montana, 15; Colorado, 9; New Mexico, 4., (Table 1.) The total average daily production was approximately 73,000 bbl. and the total production of all four states during the year was 26,534,606 bbl. This is 2.7 per cent. of the total oil production of the United States during this period. Colorado Although Colorado is not a large producer of oil and natural gas, its oil operations are widely distributed over the state. The Florence field is one of the oldest oil fields in the country, and there are good reasons for believing that the state will retain its place for many years to

Jan 1, 1930

By D. L. Katz

The Oklahoma City Wilcox sand, discovered on March 26, 1930, has produced 394 million barrels of crude oil and 819 billion cubic feet of natural gas as of July I, 1941. The 100,000-bbl. wells, pressures of 2600 lb. per sq. in., and flows of "Wilcox" sand caused exciting moments in the early life of the field. Today the reservoir is substantially at atmospheric pressure and produccs 75,000 bbl. of crude oil daily through 466 pumping wells. Early estimates of the initial crude-oil content of the "Wilcox" sand1 indicated that about 600 million barrels of crude oil would remain after the pumping wells ceased to produce economically. The Oklahoma City Wilcox Secondary Recovery Association was organized in March 1939, to study the possibilities of recovering a portion of this oil. Only a very brief summary of the information available can be presented in a paper of this nature. Some simplifications and generalizations are necessary to give the over-all picture in SO short a space and statements made may not apply to a specific well or small area. Since the area under consideration by the Association is that north of the south line of section 22-11-3, some information will be presented for areas A, B, C, 1, 2, 3 and part of 4 of Fig. 2, and some will be for the entire Wilcox zone west of the fault. This paper is essentially an abstract of an engineering report made by A. D. Small, B. T. Murphree, M. C. Sons and the author for the Oklahoma City Wilcox Secondary Recovery Association on Sept. 5, 1940. Some information is taken from a report to the Association by C. V. Sidwell on March I, 1940, and some data are from a recent report by A. D. Small. It gives a brief history of the Wilcox zone, estimates of the initial oil contents of the reservoir, present conditions in the reservoir, and probable results from several programs of "secondary recovery." History of Wilcox Zone The Wilcox sand lies on the flank of the general structure, as shown by cross section of Fig. I2,3,4 and areal map of Fig. 2. The sand is of Ordovician age and is composed of well assorted, rounded sand grains with no apparent cementing material. The loose texture of the sand is shown by the enormous quantities of sand production from the wells and from the soft cores. The productive sand varies from zero thickness on the east to 220 ft. maximum and to zero thickness on the west because of water. The development of the pool4 as dependent upon drilling restrictions within the city limits, which accounts for the spacing of drilling operations listed in Table I by years. In 1931, areas I through 7 of Fig. 2 were open for drilling with the exception of some west-edge properties, and all wells drilled before Feb. I, 1935, were in this portion of the field. Nearly all wells drilled from 1933 to 1037 were in areas A, B and C. Since 1939, the newly drilled wells have gradually enlarged the producing area toward the west in the northern portion.

Jan 1, 1942

By D. L. Katz

The Oklahoma City Wilcox sand, discovered on March 26, 1930, has produced 394 million barrels of crude oil and 819 billion cubic feet of natural gas as of July I, 1941. The 100,000-bbl. wells, pressures of 2600 lb. per sq. in., and flows of "Wilcox" sand caused exciting moments in the early life of the field. Today the reservoir is substantially at atmospheric pressure and produccs 75,000 bbl. of crude oil daily through 466 pumping wells. Early estimates of the initial crude-oil content of the "Wilcox" sand1 indicated that about 600 million barrels of crude oil would remain after the pumping wells ceased to produce economically. The Oklahoma City Wilcox Secondary Recovery Association was organized in March 1939, to study the possibilities of recovering a portion of this oil. Only a very brief summary of the information available can be presented in a paper of this nature. Some simplifications and generalizations are necessary to give the over-all picture in SO short a space and statements made may not apply to a specific well or small area. Since the area under consideration by the Association is that north of the south line of section 22-11-3, some information will be presented for areas A, B, C, 1, 2, 3 and part of 4 of Fig. 2, and some will be for the entire Wilcox zone west of the fault. This paper is essentially an abstract of an engineering report made by A. D. Small, B. T. Murphree, M. C. Sons and the author for the Oklahoma City Wilcox Secondary Recovery Association on Sept. 5, 1940. Some information is taken from a report to the Association by C. V. Sidwell on March I, 1940, and some data are from a recent report by A. D. Small. It gives a brief history of the Wilcox zone, estimates of the initial oil contents of the reservoir, present conditions in the reservoir, and probable results from several programs of "secondary recovery." History of Wilcox Zone The Wilcox sand lies on the flank of the general structure, as shown by cross section of Fig. I2,3,4 and areal map of Fig. 2. The sand is of Ordovician age and is composed of well assorted, rounded sand grains with no apparent cementing material. The loose texture of the sand is shown by the enormous quantities of sand production from the wells and from the soft cores. The productive sand varies from zero thickness on the east to 220 ft. maximum and to zero thickness on the west because of water. The development of the pool4 as dependent upon drilling restrictions within the city limits, which accounts for the spacing of drilling operations listed in Table I by years. In 1931, areas I through 7 of Fig. 2 were open for drilling with the exception of some west-edge properties, and all wells drilled before Feb. I, 1935, were in this portion of the field. Nearly all wells drilled from 1933 to 1037 were in areas A, B and C. Since 1939, the newly drilled wells have gradually enlarged the producing area toward the west in the northern portion.

Jan 1, 1942

By J. L. Humphrey

The origin of roof bolting is obscure, but is believed to have begun some 40 years ago in the mines of St. Joseph Lead Co. in southern Missouri. It was not until after World War II, and more particularly after 1949, as a result of the concentrated effort of the USBM, that roof bolting attracted widespread interest. It is estimated that at the end of 1954, 26 pct of all bituminous coal mining in the U. S. was being done under roof bolts. Those mines alone use nearly 2,000,000 roof bolts per month, according to USBM statistics. Uses in metal mines are increasing rapidly, as confidence and knowledge grow. The application has found equal success in other fields, such as tunneling work for dam and waterway construction and right of way maintenance on highways and railroads.

May 1, 1956

By Walter Harvey Weed

In a previous paper upon the enrichment of mineral veins by later metallic sulphides,? the writer has shown that certain masses of rich ores, such as are found in many mines, either near the water-line or as bonanzas in depth, are of secondary origin, and are due to a leaching of lean ore and the concentration of the material by reaction between the solution and the unaltered ore below. The geological and mineralogical evidence is believed to form an adequate basis for a chemical and physical explanation of the phenomenon. In the present paper the writer will give a brief synopsis of this theory, and will apply it more particularly to deposits of the precious metals, laying special emphasis upon the dependence of such enrichments upon the presence of iron sulphide (as pyrite, etc.) in the primary ore, and upon structural features which control the circulation of the enriching solutions below the water-level. It is believed that many, though not all, of the bonanzas arid pay-shoots of rich sulphide ores, especially those carrying gold and silver, which are encountered in ore-deposits, are of such secondary origin. Apparently it is essential that the occurrence and structural relations of such ore-masses should be understood, as the success of the mine is often dependent upon the finding and extraction of these ores. A legitimate deduction, too, is that such ore-deposits decrease in value With depth. As my own studies have been mainly in Montana, my illustrations must be drawn from the ore-deposits of this and adjacent States, with such as I have noted in hurried visits else-

Jan 1, 1901

By Robert R. Walden, LaMont West

KENTUCKY'S first acid-grade fluorspar flotation mill, shown in Fig. 1, was placed in operation Aug. 1, 1952, by the Pennsylvania Salt Manufacturing Co. at Mexico, Ky. During 1951 a critical shortage of acid-grade fluorspar developed and it became necessary for the company to produce part of its fluorspar requirements. In 1951 the company purchased the Crider and Lennen metallurgical fluorspar mill and an adjacent stockpile of tailing at Mexico, Ky. The tailing, assaying about 26 pct calcium fluoride, originated from log washer and jig mill concentrators in the area. As the mill did not have a fluorspar dryer or convenient rail facilities, the company leased the Burleson concentrator at Marion, Ky., where these facilities were available. At Marion, Ky., on the Illinois Central Railroad, dry acid-grade fluorspar is transported direct to the company's Calvert City, Ky., hydrofluoric acid plant.

Jan 5, 1954

By F. R. Koeberlin

ABOUT thirty miles south of the port of Coquimbo, Chile, nestling in one of the western outliers of the main Andes range, lies the little mining town of Andacollo, a place whose history and traditions make up one of the most romantic pages in the life story of this southern republic. The beginning of Andacollo is shrouded in the penumbra of the pre-Columbian era, but its first mining activity probably dates from about the years 1440 to 1460. It was in the middle of the fifteenth century that the Inca Tupac-Yupanqui, grandfather of Atahualpa, conquered this part of Chile. His domain extended even as far south as the present site of Santiago, and perhaps farther, but was maintained with increasing difficulty against the fiercely independent and indomitable tribes of Araucanian Indians of the South.

Jan 1, 1938

By E. L. Tucker

PREVIOUS investigations of E. L. Tucker and R. E. Head' related in particular to the effect of cyanogen compounds on galena, sphalerite, and pyrite, and their behavior in the presence of such com- pounds. The present contribution deals with the float- ability of the copper minerals and of pyrite. All experiments were performed on minus 200-mesh material, the method of preparation being the same as that described in the previous article. Flotation tests were made in a small mechanically agitated machine of 50-g. capacity designed in this laboratory by Gates and Jacobsen." General Naval Stores pine oil No. 5 and potassium xanthate were used in constant amount in all of the experiments; these agents were selected because of their present wide use in the flotation of copper minerals. Lime additions were varied to secure four 'final hydrogen ion concentrations, namely, neutral, 0.0005 per cent CaO, 0.003 per cent CaO, and 0.02 per cent CaO. The variation in lime addition was introduced to include the range of alkalinities employed in actual flotation practice.

Jan 1, 1926

By E. S. Wheeler, M. W. Murphy

A LARGE part of the molybdenum produced in Colorado is converted and consumed in the Eastern States. As the raw materials and the power needed for the conversion of the Colorado concentrate are also accessible in the Eastern States, the conversion plant has been installed some 1500 miles east of where the ore is mined and milled. When concentrate was first produced at Climax in 1918, a custom smelter converted the product into ferromolybdenum. By 1924, the Company had decided to produce calcium molybdate and rented a building and installed equipment for that purpose at Langeloth, near Burgettstown, Pa., about thirty miles west of Pittsburgh. For the first few years the plant was a simple one of small capacity. A small hand-rabbled roaster was used, the product of which was made iota calcium molybdate by a conventional method; then an eight hearth mechanically rabbled roaster was installed to increase and speed up production. The output was considerably less than a million pounds of contained molybdenum annually until 1928, when a small part of the produc-

Jan 1, 1946

By V. D. Perry

Carlisle: Reno, let's start off by asking "When was the first day that you began working in your profession?" Sales: I began in Butte, Montana, on August 22, 1900 as an assistant engineer for the Boston & Montana Consolidated Copper and Silver Mining Co., and continued at that job for about a year. The general manager was C. S. Batterman, and the mines- Mountain View, Pennsylvania, Leonard, East Colusa, and one or two others-were part of Boston & Montana.

Jan 5, 1966

By Paul Foote

MOST of the treatises on metallurgy intimate that simultaneously with the development by the atomic physicist of a really satisfactory theory of the atom will be inaugurated a new epoch in the science of metals. Metallurgically and metaphorically, we shall dwell in the Utopia of Sir Thomas More. It is my privilege this afternoon to demonstrate that this state has not arrived. An atom is a miniature planetary system consisting of a positively charged nuclear sun about which revolve electrons each carrying the negative charge e. The charge on the nucleus is + Ze where Z is the atomic number and the number of planetary electrons in a neutral atom is equal to Z. These electrons are arranged in several groups having different binding energies. Ordinary x-ray phenomena relate to processes occurring deep within the atom, usually with electrons in the so-called K or L shells. Such electrons in the heavier atoms are so closely bound to the nucleus that the forces exerted by neighboring atoms in a solid are relatively inappreciable. For most practical x-ray investigation, the atom may, be considered as in the gaseous phase completely isolated from its neighbors. The K radiation from an element in the gaseous state, in the solid or liquid phase, or even in combination with other elements in all its possible valences, is almost identical. ? Visual and ultraviolet spectroscopy is concerned with disturbances of the most loosely, bound outer or valence electrons of the atom, always in the vapor state. The remarkable progress of the last year in both theo-

Jan 2, 1926

By E. L. Bruce

The district of Patricia, in the province of Ontario, lies northwest of the Albany River and extends northward to Hudson Bay. Formerly this was the unorganized district of Keewatin, the southern part of which was divided in 1912 between the provinces of Manitoba and Ontario. The interprovincial boundary now runs north from Lake of the Woods for 275 miles and thence northeast 375 miles to Hudson Bay. This district is comparable in size to all the older part of Ontario south of the Canadian Pacific Railway east of Lake Huron—thus it is roughly one-third of the whole of the present provincial area. The central part of this great triangle is one of the least accessible parts of Canada. From it streams flow southward to the English River, southeastward to the Albany, northward to Hudson Bay and the Hayes River, and westward to Lake Winnipeg. None of the streams is large and canoe travel is not easy. The only industry it has ever had is the trade in furs. Until the development of the airplane on a commercial basis, the only means of travel was by canoe or dog-train. There is not a mile of railway in the whole district. The two areas to be dealt with lie in the southwestern part of Patricia. Red Lake is 50 miles east of the Manitoba boundary and 75 miles north of the transcontinental railway from Cochrane to Winnipeg. Woman Lake is 50 miles farther east and slightly farther north. The late Dr. D. B. Dowling, of the Geological Survey of Canada, visited Red Lake and spent some time there during his exploration survey from Lac Seul to Berens River in 1893. He also visited the Woman Lake basin during the same journey, but his examination of it was much less detailed, the great area covered by him during the one field season making it impossible to make more than a hurried reconnaissance. Some prospecting in the Red Lake district followed Dowling's exploration, but the distance from railway was too great for any systematic work to be done. In 1922, following the usual plan, the Ontario Department of Mines made a geological reconnaissance of the English River, following :in instrumental survey of that river and its lakes by the Department of Lands. A side trip was taken to examine the rocks of Red Lake described

Jan 1, 1928

By Samuel D. Warriner

(Wilkes-Barre Meeting, June, 1911.) THE dealings between concentrated capital invested in the conduct of our various industries and the combinations of labor known as "trade union organizations," have produced not only in the United States, but abroad, many novel methods of negotiation between employers and wage-workers. The size and strength of these organizations have destroyed the personal elements formerly governing the dealings between employer and employee and have produced various forms of trade-agreements now in more or less successful operation. The difficulty, however, has- been to secure consent of both parties to an equitable agreement. For this purpose there have been devised various forms of arbitration, either compulsory under the shadow of governmental legislation, or voluntary by mutual agreement. But these have not been altogether successful from a technical stand-point, for the reason that a compromise has generally been necessary, and in an effort to reach an agreement, terms have been made which have been neither fair nor satisfactory to either of the contending parties. The Anthracite Board of Conciliation represents one of the few thoroughly successful courts for the settlement of trade-disputes, if not the only one which has yet been evolved. The prestige of this board rests upon its successful treatment of the labor-troubles of the anthracite region for a period of more than eight years, and upon the fact that it has been able not only to reach decisions based upon the merits of the controversies, but to enforce its decisions upon both the employees and the employers. It has never been obliged to shape its conduct to secure the consent of the contending parties, and its decisions have been strictly and, in the main, cheerfully observed. The remarkable feature of this board has been that it has

Aug 1, 1911

By F. E. Bedale

STUDY of several severe mine explosions that occurred during the winter of 1907 led to the belief that coal dust was a definite explosion hazard. The Consolidation Coal Co. was a pioneer in the early work to' eliminate this hazard and to combat the dangers incident to poor ventilation and the presence of methane. Maintenance of high humidity throughout the mines was one of the first measures adopted, later to be superseded by rock-dusting. In the twenty years from 1907 on, many safety measures were developed and adopted, and several prizes were won, though the practice was crude by present-day standards. But in 1927, the company went to work in earnest, and organized a Department of Safety with adequate personnel and with authority to enforce all approved rules for the prevention of accidents and the preservation of company property. All plans for new construction work, changes in mining systems, and proposals for the purchase of new mining equipment had to receive the approval of this Department. A set of operating- and safety standards was written to govern the activities of all employees, and physical examinations for them were required.

Jan 1, 1938

By Gilbert Soler

PRODUCERS of alloy steels recognize the importance of chemical composition in rela-tion to the hot-working properties and the typical surface defects found in their prod-uct. Each analysis of steel has its own peculiar characteristics. Under conditions of standard mill practice each analysis is susceptible to certain types of defects. Mill practice must be varied to obtain the best combination of surface and internal quality in the product. Chemical composition influences the cast structure and crystallization character-istics of the ingot. It also determines the rate of heating and cooling, the plastic hot-working range, and the phase structure of the steel at various temperatures as well as the tendency toward scale formation and decarburization, This paper endeavors to emphasize the manner in which chemical composition affects the various properties of steel, and to indicate the relative impor-tance of these factors in relation to the hot-working properties and surface charac-teristics of killed steel. The influence of chemical composition may be outlined as follows: I. Effect on the cast structure of steel, including: A. State of deoxidation, and type of inclusions. B. Gas content of steel. C. Freezing point and melting point of steel.

Jan 1, 1940

By Herbert Hoover

YOUR committee asks that I speak today on the relations of the engineering profession to public affairs. That takes in a lot of ground. This being a cheerful occasion, I will assume that I should exclude the engineer's function as a taxpayer. This being a nonpartisan occasion, I will assume that I should not refer to his voting emotions in 1940. Perhaps what was in the minds of your committee was the application of engineering thought to the confusions of the times. That is also a lot of ground. I fear, however, its boundaries disappear in mirages and rainbows on all sides. Now any entry of the engineer into public affairs involves his breaking into the fields of the sociologists, the economists, and the politicians. However I don't know why, seeing the difficulties these professions are having, they should not welcome a little help.

Jan 1, 1939

THE research and policy committee of the Committee for Economic Development, a non-profit research organization composed of leaders in industry and the professions, including such prominent figures as Dwight D. Eisenhower, Paul G. Hoffman, and Charles E. Wilson, recently published a report entitled "How to Raise Real Wages." Since its founding in 1942 the CED has initiated many objective studies on matters of national economic policy, and has gained a fair measure of prestige from its activities. The CED's latest report cites the more than three- fold rise in real wages in the United States in the past 50 years and attributes the accompanying improvement in the standard of living to the great in- crease in production per man hour. The report states that in order for production to continue rising in the future with the attendant increase in real wages four basic conditions must be manifest: (1) better methods, (2) more capital, (3) better training of workers, and (4) better management. The report cautions that although prospects for increases in output per man hour are good "it is desirable that steps be taken to encourage such a rise."

Jan 8, 1950

By Thomas L. Garrard, James A. Sprague, Rex B. McLellan, Samuel J. Horowitz

A simple rnodel for interstitial solid solutions has been devised in which each solute atom interacts with the solzlent lattice in such a way as to exclude an integral number of nearest-neighbor sites from being occupied by solute atoms. The vemaining interstitial sites ave not affected. In calculating the entropy of such a solution the increase in the number of interstitial sites available to solute atoms due to the ozlerlap of blocked sites is taken into account. The ther-modynamic functions and the solute activity fov the solution rnodel are calculated. It is shown that considevation of the overlap sues vise to a correction term of the order 8' ( where 0 is the ratio of solute to solvent atoms) in the thevmodynamic functions of the solution and the solute activity. The theo,uetical equation for the solute activity was used to analyze the available data for the activity of carbon in austenite at three different temperatures. The use of a computer enabled many comparisons to be made between the experimental activity data and those predicted by both the complex blocking model and the simple, widely used blocking model in which the ozierlapping of blocked sites is not taken into consideration. Even though at the highest concentvations oj carbon the value of 0 is small it is shown that the best fit to the experimental data is found with the complex blocking model. RECENTLY it has been shown by analysis of gas-solid equilibriums that many interstitial solid solutions can be described by the quasi-regular solution model in which the partial energy of solution E, is independent of composition and, apart from a composition-independent term due to nonconfigurational factors, the partial entropy is that of an ideal solution. Dilute solutions of nitrogen in both bcc and fcc iron,' dilute solutions of oxygen and silver,' carbon in a Fe,' and dilute solutions of carbon in ? Fe2 are all quasi-regular. In addition many hydrogen-metal solutions, both dilute and concentrated (with the notable exceptions of the H-Ni and H-Pd systems), can be described by this model.3 However, it has been shown that, at various temperatures, solutions of carbon in ? Fe begin to depart strongly from quasi-regular behavior at low concentrations. A plot of the activity of carbon in ? Fe relative to pure graphite vs atom fraction of carbon (Cc) calculated from Smith's data4 begins to depart from the (nonlinear) plot for a quasi-regular solution at about Cc = 0.02. Several statistical models have been proposed to account for the thermodynamic behavior of carbon in y Fe. Darken and smith4 set up a model in which a carbon atom in its octahedral site in the fcc lattice has either one or no neighboring carbon atoms in the twelve nearest-neighbor octahedral sites. It is assumed that the number of carbon atoms having more than one nearest neighbor is negligibly small and that a solute atom does not interact with another solute atom located at a greater distance than the first shell of interstitial sites. Thus this model contains two characteristic interaction energies. Darken and Smith showed that this model gives reasonable agreement with the measured variation of carbon activity ac with composition. It is noteworthy that Darken and Smith concluded from their analysis of the activity data using this model that there was a repulsive force between carbon atoms in austenite which reduces the concentration of C-C pairs below that corresponding to random mixing. Recently Aaronson, Domian, and pound5 have considered in detail the statistical model developed by Lachere and by Fowler and Guggenheim7 and have shown that it is compatible with the activity data for carbon in austenite. In Darken's model the energy of solution of carbon in austenite is dependent on temperature and concentration; the departure from Henry's law arises from the concentration dependence of the energy of solution. In Aaronson, Domian, and Pound's discussion of the Lacher, Fowler, Guggenheim model the interaction energy wy between adjacent carbon atoms in austenite is strongly temperature-dependent. Aaronson et al . suggested that this temperature dependence of wy and hence the energy of solution of carbon could be explained either by the formation of clusters of carbon atoms (despite the repulsive nature of wy) or by the dual occupancy of the octahedral and tetrahedral sites by the carbon atoms. However, a temperature-dependent heat of solution

Jan 1, 1968