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By Joseph E. Pogue

NEW economic forces are at work in the petroleum industry.. In order to visualize these forces and clearly see their bearing on the producer, refiner and marketer, it is necessary to see in perspective the economic evolution of the business. For several decades prior to 1913 the outstanding feature of the petroleum industry was a trend toward integration, culminating in a huge combine, the Standard Oil Co. An important aspect of this integrative trend, however, was its concentration on the combination aid control of refining and marketing, leaving crude oil production, for the most part, to the exigencies. of small-unit competition. It is a noteworthy coincidence that during this era the law of oil and gas was formulated and applied, whereby these substances had to be reduced to possession to establish ownership; and the forces of competition in crude oil production were thereby intensified. It was to the interest of an industry, safeguarded in its control of manufacturing and markets, to have supply stimulated by legal convention as well as by individual initiative in order that the growing demand could be met without interruption. And so over-production of crude oil during this era was no handicap, but rather an aid, to the progress of the industry.

Jan 1, 1929

By John D. Sullivan

ALUMINUM and magnesium plants in the United States underwent enormous wartime expansion which made many wonder if ghost plants would result when industry swung back to a peacetime basis. Production capacity of primary aluminum ingots was stepped up from 150,000 tons annually to about 1,150,000 tons; magnesium production increased from 2500 tons in 1936 to nearly 200,000 in 1943, with a production capacity of some 300,000 tons. Not only was primary metal production enlarged but also the capacity of prime fabrications such as castings, forgings, extrusions, and sheets was correspondingly increased. In mid-December it was estimated that production of primary aluminum ingots in the United States in 1946 will be about 410,000 tons while consumption will be about 500,000, close to half of the wartime consumption. The 1946 estimated consumption of secondary aluminum is 200,000 tons. The critical shortage of soda ash is hindering production of primary metal, and the outlook for an early relief of this shortage is dark.

Jan 1, 1947

By Harlowe Hardinge

AN extensive recent trip throughout the mining districts of the Southwest, Central West, an Northwest,' reveals a numbes of interesting conditions that have influenced operators, in both large and small mills, to modify their flow sheets insofar as they pertain to crushing and grinding. The changes made and planned for the future should be of interest. It is interesting to note when traveling through the country, how ideas change and practice is modified, and it is rather amusing to see how milling methods seem to run, more or less, in cycles. New ideas and developments are brought about which run through the industry and are taken up by many of the best and most well informed operators. Some of them will change, sooner or later, back to their old practice; for, like everything .else, what will work well in one place will not necessarily be suited to another. On the other hand, it is often difficult to establish. other practices known to be of value, owing to the natural resistance to make a change, but on the whole, the western mill men seem to be more alive to possible benefits of various modifications than any other engineers with whom I have come in contact in all parts of the world. Mill men in other parts of the world always keep in con- tact with what is being done in the western part of the United States, but it does not necessarily follow that those in the western part of the United States are always right. Some of these changes that have been made and afterward abandoned will be referred to later.

Jan 1, 1929

By A. S. Malicsi, I. Iwasaki

Differential flotation of bulk sulfide concentrates from Duluth gabbro into copper and nickel concentrates could be implemented by first destroying the hydrophobic coating with ozone and then by recovering the copper concentrate with a copper-selective collector. A number of parameters involved in the use of ozone, such as the sequence and the conditioning time of ozone treatment, the pulp pH, and the level of xanthate addition, were investigated.

Jan 1, 1986

BECAUSE of the impetus given to placer mining since the price of gold was advanced to $35, several types of small dredges have made their appearance, especially in the Lincoln and Oroville areas of California. Some of these are known as "doodle bugs," and have been given considerable publicity, though many believe their performance has been overrated and that complete costs of construction and operation, if known would not put them in so favorable a light. Fig. 1 is a doodle bug owned by E. M. Clark and operated near Lincoln, Calif. It is understood that it was abandoned because of inability to handle deep ground. A similar machine that has been operated-profitably by Comstock Placers is shown in Fig. 2.

Jan 1, 1938

By AIME

Compiled by Mary Ann Gross, Department of Energy. Bruceton. PA. Supplemental data from Coal Age indicated by (*). Reprinted by permission from CoalAge magazine.

Jan 1, 1981

Jan 1, 1947

By J. A. Herbst, R. Mackelprang, J. D. Miller

Droplet size distributions were determined by stabilizing in gelatin and measurement of the distributions by means of computerized image analysis Several variables that affect droplet sizes were studied and the resulting size distributions were modeled via a population balance equation Key parameters in the model were related to the physical properties and operating conditions of the systems examined using a multiple linear approach

Jan 1, 1981

By R. W. Raymond

THE death of Privy Councilor Bruno Kerl, on March 25, 1905, terminated a distinguished and useful career. Bruno Kerl was born March 24, 1824, at St. Andreasberg in the Harz, and entered in 1840 the mining school of Clausthal, where he studied for three years, working at the same time in the mines and stamp-mills. After an additional year of practice in the silver-reduction and iron-works of the Upper Harz, he passed his examination as a metallurgical graduate, and studied for a year at Göttingen under WV filer in chemistry, Hausmann in mineralogy, and eminent teachers in other branches. In 1846 he was employed at the Oker works, but very soon left this post, to become a tutor in chemistry, metallurgy, etc., at Clausthal, where he continued to labor until 1867. During this period the Clausthal school became a completely equipped Mining Academy, and Kerl was made in 1862 a full professor. Meanwhile, in addition to the work of instruction, he discharged, simultaneously or successively, the duties of many responsible official positions in the Royal Hanoverian administration of mines and smelting-works, and also published many valuable books and treatises. Among these were professional guide-books to the Upper and Lower Harz, and their characteristic metallurgical processes; a manual of qualitative and quantitative blow-pipe analysis; another of metallurgical assaying ; and, most important of all, a Handbook of Metallurgy in four volumes, the second edition of which was issued in Leipzig, 1861-1865. This book was speedily recognized as the leading authority in its field. In this country, the English translation and revision, by Crookes and Röhrig, published about 1869, had a large circulation. In addition to these literary labors, Prof. Kerl became in

Jul 1, 1905

By Russell C., Fleming

FOK, many years the officials of the Magma Copper Co. mine at Superior, Ariz., have had to contend with adverse conditions underground in the form of high rock temperatures, hot water, and high relative humidity. These conditions in the mine have been such that working the mine would have been impossible were it not for the constantly expanding and improved sys- tem of ventilation to produce bearable conditions in the working places. Results that have already been achieved make an interesting study of what can be done along those lines. From the time the mine was first opened in 1910 it has been hot. An idea of the conditions that have persistently been encountered can be obtained from parts of the mine that are not being worked at present or that do not yet have sufficient ventilation. Virgin rock temperatures as determined in drill holes at the faces range from 104° to 116°*. An observation made at the face of No. 5 West footwall drift on the 2800-ft. level.

Jan 1, 1930

By John D. Roach

DURING an investigation of the yttrium-hydrogen system aimed at producing solid yttrium hydride specimens containing various amounts of hydrogen, it was observed that yttrium containing approximately 2 wt pct H exhibited a tendency to crack and crumble to a powder on standing in air at room temperature. It was also observed that longer hydriding times, at a given temperature, increased this susceptibility to powdering without an increase in hydrogen content, also that moisture in the air is necessary for the observed effects to occur. Even if cracking did not occur, there was a continual formation of a light gray powder on the as-treated surface of the hydrided yttrium and this reaction continues until the entire hydrided piece has been reduced to a powder. Storing the hydrided specimens in the absence of air or removing the surface either by machining or grinding were effective means of preventing this disintegration of hydrided yttrium. In an attempt to determine the reason for this powdering phenomenon, the surfaces of a number of as-hydrided yttrium specimens were examined by X-ray techniques. In all cases the X-ray pattern obtained showed the major phase to be yttrium hydride (YH2) as would be expected since the specimens contained 2 to 2.2 wt pct H. In some cases a trace of yttrium oxide was observed. There was also a third phase present on the surface of these hydrided specimens which could not immediately be identified. This unknown phase was a face-centered cubic material, NaC1-type structure, with a lattice parameter of 4.855 and a calculated density of 5.914 g per cc. Very slight hand polishing of the surface of the hydrided yttrium specimens completely removed both the unknown phase and the traces of oxide so that only the yttrium hydride pattern remained. Based on the X-ray patterns the quantity of the unknown phase on the surface of the hydrided yttrium appeared to be directly related to the susceptibility of the material to powdering. Work at the Denver Research Institute on the yttrium-nitrogen binary system showed that yttrium nitride (YN) is a face-centered cubic material with a lattice parameter of 4.878A and a density of 5.890 g per cc. They also noted that this compound rapidly disintegrated to a powder on standing in air. The unknown pattern observed in the above specimens corresponds very closely to that of the nitride—fcc structure, 4.885 parameter, and density of 5.914 g per cc. The presence of this thin film of nitride on the surface of the hydrided specimens probably accounts for the observed powder formation and crumbling. The nitride reacts with the water vapor in the air (verified by private communication from Dr. C. Huffine, General Electric Co.) to yield yttrium oxide and ammonia. Ammonia is readily detected when hydrided yttrium specimens were allowed to stand in bottled moist air. The powder formed on the surface of the hydrided specimens was shown by X-ray analysis to be yttrium oxide. This reaction appears to occur primarily at the grain boundaries since discrete particles of yttrium hydride separate from the specimens during this powdering process. The reaction of yttrium nitride with water vapor is believed to be as follows: 2YN + 3H2O - Y203 + 2NH3. Despite the fact that this nitride is present only as an extremely thin surface film, if the above reaction is not prevented by removing this film from the surface either by machining or grinding, the reaction continues until the entire hydrided piece has been reduced to a powder. To account for this continuation of the reaction, it is believed that the following reactionalsooccurs: 2YH2 + 2NH3 -2YN + 5H2. The nitride produced by the latter reaction reacts in turn with water vapor. The reaction therefore becomes autocatalytic and continues until the hydride has been consumed and the entire piece reduced to oxide powder. The amount of nitride required to initiate this reaction is quite small and this nitrogen contamination can occur from a number of sources—hydrogen gas employed, minute leak in the hydriding apparatus or even from degassing of the reaction vessel itself. Longer hydriding times increase the possibility of nitrogen contamination and this is especially true when a dynamic gas system is employed in the hydriding process. The production of stable, solid hydrided yttrium is dependent on the complete absence of nitrogen contamination during processing. If such contamination does occur, powdering of the hydrided product can be prevented by removing the nitride from the surface e.g. grinding or by preventing access of air to the pieces e.g. sealing in wax or plastic. The author wishes to express his appreciation to General Electric Co. for sponsoring this research and for permission to publish the results of work under Subcontract AT-93.

Jan 1, 1962

By F. R. Wadleigh

There are in commercial use today in the United States various classifications of coal, each based on one or more characteristics. The bases of these classifications may be described as follows: GeNeRaL Basis Examples 1. Geological By seams and basins (local). 2. Chemical By constituents, as determined by analysis—ash, volatilc, slilfur and hcating value. 3. Combustion Characteristics As frce-burning, smokeless, character of ash. 4. Carbonization Characteristics Coking, noncoking. 5. Physical Characteristics Splint, soft, hard, block. 6. Geographical States, Fields, Counties, Districts. 7. Sizes By dimension or name. 8. Company Names Producing or sales company names, as "C. C. B. Pocahontas," etc. 9. Trade Names, copyrighted or not 10. Uses Gas, steam, coking, locomotive, fuel, bunkers, etc. 11. Use Methods Stoker coal. 12. Pools (Tidewater Exchanges) Analyses Size Seams Railroads Uses Structure Districts There are also classifications founded on more than one basis, as follows: 1. Geographical and Geological. By locality of mines (State, District, County) and seam. Examples: Cambria County, Miller Seam, New River, Sewell Seam. 2. Geographical and Chemical. Alabama medium volatile. 3. Combustion Characteristics and Ash Content. Free-burning, red ash (anthra- cite). 4. Carbonization Characteristics and Analysis. Noncoking, high-volatile, low sulfur. 5. Physical and Carbonization Characteristics. Splint, noncoking. 6. Size and Use. ¾-in. gas coal; domestic sizes (prepared sizcs); stcam sizcs. 7. Company Name and Seam. Consolidation Co., Elkhorn. 8. Size and Analysis. Low-volatile run-of-mine; low-volatilc slack. 9. Sizes—size of screen and name. 6 by sin. lump. 10. Chemical and USP. High-volatile steam. 11. Geographical and Use. Youghiogheny gas. 12. District, Size and Use. Pittsburgh gas l¼-in. lump. ,

Jan 1, 1930

By Ralph K. Foster

During five underground mine fires which occurred in Arizona during 1980 and 1981, sealing the fire area became necessary. To minimize leakage into the fire area, ventilation control measures were instituted to balance pressure across the bulkheads. Problems en- countered in sealing the fire areas and measures taken to improve these conditions are discussed. The routing of the ventilation and ventilation control to en- sure the workers' safety were also important considerations in reopening the mines. The use of continuous CO monitors is discussed. One important consideration was the condition of the fire, and chromatographic analysis was used to establish this. Graphs comparing the Trickett ratio, carbon monoxide, carbon dioxide, and oxygen concentrations are given. The Trickett ratio was useful but needed to be augmented by the comparison of CO, C02, and 02. Problems with getting good samples from sealed areas and recommended procedures that were developed during these fires are discussed.

Jan 1, 1982

By L., Ormsby

DRILLING and blasting practices in the Morenci open pit have undergone considerable modification in recent years. Changes in the character of the ground being mined, modifications of working conditions, and continuous experimentation have been the contributing factors.

Jan 1, 1950

Institute of Metals - Iron and Steel - Mineral Industry - Industrial Minerals Year ?Division - Petroleum Division ? Division - Coal Division - Education Division -Division 1918 W M CORSE 1919 1920 W. H BASSETT 1921 1922 W B PRICE RALPH ARNOLD 1923 E DEGOLYER 1924 G K ELLIOTT 1925 F JULIUS FOHS 1926 PAUL D MERICA 1927 JOHN M LOvEJOY 1928 S SKOWRONSKI A W AMBROSE RALPH H SWEETSER

Jan 1, 1952

By C. Chamberlain

The Telfer Project, Australia's newest, largest, and most remote gold mine treats 480 kt of ore grading 9.33 g/t derived from open pit mining operations. Coarse gold is recovered by gravity concentration with jigs and further upgraded wing a continuous strake launder table, and by amalgamation. Remaining gold is recovered in a cyanide circuit and incorporates flat bottom air agitators, counter current decantation (CCD) and stellar filters for clarification and precipitate removal. Overall recovery into a bullion averages 98%. The mill incorporates a number of design features that allow for maximum efficiency and security wing a minimum number of operation personnel.

Jan 1, 1983

By M. G. Nicholas

The influence of deformation, relative movement and surface cleanliness on the strength of room -temperature "interparticle" bonds between copper surfaces has been studied. No bonding resulted when clean surfaces were merely pressed together, even under pressures of 50,000 psi. Bonding resulted, however, when clean surfaces were simultaneously pressed and moved relative to each other, some bonding occurring no matter how small the pressure or relative movement. Exposure of the clean surfaces to various chemicals inhibited bonding, none at all being produced by small relative movements. The size of the movements which first produce bonding between exposed surfaces depends on the nature of the chemical, being less than 0.002 in. for cleansing reagents and greater than 0.004 in. for lubricants, water and hydrogen sulfide. It is concluded from the experimental data that the prime requirement for bonding is the dispersal of surface films such as oxides and adsorbed contaminants. THE formation of interparticle bonds during the room-temperature compaction of powder metallurgy components greatly increases the ease of handling in subsequent production operations prior to sintering. The strength of unsintered compacts follows the same general trends as their density and hardness, but quantitative data are extremely Scarce. Quantitative correlation of the data on the overall strength of a compact with that of the individual interparticle bonds is virtually impossible due to the extremely complex geometry of powder compacts. Qualitatively, however, the strengths of unsintered compacts can be correlated with variations in parameters known to influence the extent of cold bonding, and hence interparticle bonding, such as surface cleanliness, relative movement, and deformation of the mating surfaces. Kuzmic and seelig4 found that contamination of powder particle surfaces with lubricants reduced the strength of unsintered iron and copper compacts. Interparticle shear has been shown to promote bonding by Train and Hersey7 while Gregory has shown that die rotation is beneficial. Eilender and schwalbe6 concluded that most bonding occurred during the early stages of pressing iron powder compacts when interparticle shear is one of the principal processes occurring. mile there can be little doubt that these and other factors, such as particle size and shape, affect the extent of interparticle bonding produced by compaction, evaluation of the influence of individual factors is not easy. Particle deformation and relative movement, for example, occur simultaneously during compaction, making any precise measurement of their relative influences difficult. Because of these and other difficulties encountered in studying interparticle bonding in actual powder compacts, the approach adopted in this study was to

Jan 1, 1963

By Strathmore R. B. Cooke, Iwao Iwasaki, C. S. Chang

The effects of aeration on an aqueous suspension of pyrrhotite were studied and their results correlated with flotation tests using xanthates as collectors. The effects of copper activation and of pH variation were determined and possible mechanisms postulated. PYRRHOTITE has long been considered a gangue mineral to be eliminated as tailing in the treatment of various sulphide ores. However, in recent years the world-wide lack of sulphur resources has called attention to this mineral as a potential source of both sulphur and iron. Its importance as an economic mineral, however, has not been particularly emphasized. For this reason very little is known about its response to flotation, except that it can be depressed easily in alkaline circuit, by long aeration,1,2 addition of oxidizing agents,3 or by starch.' The object of this work was to study the floatabil-ity of pyrrhotite. This includes the effect of oxidation by aeration, of copper activation, and of change in pH. Preparation of the Pyrrhotite Sample: It was desirable that the highest grade of pyrrhotite obtainable be used for this experiment, since the presence of other minerals could affect the surface properties.5 However, no pyrrhotite was available as crystals, and massive deposits of hydrothermal origin commonly contain considerable amounts of chalcopyrite. Pyrrhotite concentrate was, therefore, prepared from a sulphide deposit occurring near Aitkin, Minn. The deposit is of pyrometamorphic nature consistirlg mainly of pyrrhotite and pyrite with graphite, silicates, and carbonates as gangue. The ore, already crushed through 3 mesh when received, was screened at 65 mesh and the undersize discarded. The oversize was crushed through rolls, and then stage-ground dry in an Abbe porcelain mill, the —65 mesh portion being screened out after every 15 min of grinding until all the material passed through this size. The ground product was then concentrated with a drum-type dry magnetic separator. The rougher concentrate was cleaned twice and then demagnetized. The final product was split in a Jones splitter and stored in air-tight bottles. Microscopic examination of the concentrate showed that it was relatively clean and free of pyrite, locked particles, and gangue. By means of the krypton gas adsorption method," the specific surface was determined to be 3000 cm2 per g. The chemical and screen analyses of the final concentrate are given in Tables I and II respectively. It is a well-recognized fact that the oxidation of some sulphide ores during stockpiling, grinding, and conditioning affects their flotation behavior. The problem of oxidation may become serious in the case of pyrrhotite, since this is known to be more easily oxidized than many other sulphides. To ascertain the extent of oxidation, an experiment was carried out by aerating an aqueous suspension of pyrrhotite with air, oxygen, and nitrogen as follows. A 300-g sample of pyrrhotite in 2700 ml of water was agitated and simultaneously aerated in a Fager-gren-type laboratory flotation machine. A Precision wet test meter was connected to the air inlet valve, the flow rate of the gas being kept constant at 0.3 cu ft per min throughout the experiment. Samples of approximately 30 ml each were taken from the cell at 0, 4, 10, 20, 35, 60, and 90 min. After the pH was taken, each sample was filtered and the filtrate was analyzed for total iron and sulphur. The iron was determined colorimetrically by the thioglycolate method using a green filter.' The filtrate was oxidized with bromine to convert all of the soluble sulphur compounds into sulphate and this was determined with a Parr turbidimeter." When aeration tests were made in alkaline circuit, calcium hydroxide or sodium hydroxide was added at regular intervals to maintain a constant pH. A similar procedure was followed in an experiment to determine the abstraction of copper. ion by pyrrhotite. In this case various quantities of cupric chloride were added. The filtrate from each sample taken was analyzed for copper, total iron, and sulphur. The carbamate method with a green filter was used for the copper analysis,' since this method could tolerate a considerable amount of iron in the solution. A pneumatic cell, made from a 350-ml fritted glass Buechner funnel, was used for this experiment. The detail of the assemblage has been described elsewhere." In the present work a stainless steel baffle was inserted in the cell. This baffle overcame the tendency for the coarse pyrrhotite particles to be swirled around the wall of the cell and thus fail to collect in the froth. A 50-g sample of pyrrhotite was added to the cell which contained 260 ml of water. When pretreat-ment of the sample was desired, reagents, such as activator and pH regulator, were then added and the pulp was conditioned for a specified conditioning time. Prior to the addition of the collector approximately 15 ml of the solution were removed for pH measurement and for iron and sulphur analyses. Copper when used as activator was also determined. Collector and frother were then added and the pulp was conditioned for an additional 2 min. Air was admitted to the cell and the froth removed. The separation required from 4 to 6 min, depending on the characteristics of the froth. The float and non-float products were filtered, dried, weighed, and assayed for iron.

Jan 1, 1955

Discussion of the paper of F. C. LANGENBERG and R. G. WEBBER, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 291 to 300. HENRY M. HOWE, Bedford Hills, N. Y.-The results here given are of great interest and are welcome as forming another rivet to increase the stability of our present theories of the constitution and properties of steel. The important discovery is that the hysteresis increases with the fineness of the structure, that is to say with the extent of contact between the particles of ferrite and cementite. All of the specimens except No. 4 consist of ferrite and cementite of different degrees of intimacy of admixture. If hysteresis represents something akin to surface friction, which retards the rotation of the ferrite on the application and release of the magnetizing force, then it is only natural that it should increase as it does with the intimacy of admixture, because it is at the surface of contact of a given particle of ferrite with the neighboring particles of cementite that this friction is to be expected, and of course the extent of surface must in¬crease with the intimacy of admixture. The somewhat greater hardness of specimen 4 than of the others may perhaps he referred to the principle discussed in my paper, Why Does Lag Increase with the Temperature from Which Cooling Starts?' The furnace-cooled specimens were cooled so slowly that the influence of the initial temperature of heating is effaced. But in the air-cooled specimens we have the suggestion that the high temperature, 1,000°, from which the cooling of No. 4 started has prevented the completion of the transformation, with the result that the metal is slightly harder than any of the others. The difference is not to be explained by difference in the fineness of structure, because the whole range of fineness from No. 1 to No. 6 is accompanied by no change in hardness, the only change being an appreciable increase of hardness following the air cooling from 1,000°.

Jan 5, 1915

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967