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By Morris Muskat

In preparing a well for pumping, observations are often made of the fluid level in the well bore or bottom-hole pressures at various times before equilibrium has set in. From a qualitative point of view one may immediately infer that if the rise in the bottom-hole pressure or fluid level is rapid the permeability of the sand about the well bore is large, and converse conclusions may be drawn if the rise is slow. However, a more quantitative estimate will give additional information of value, as will be shown in this paper. To derive such an estimate we may proceed as follows. Let h be the fluid height, above the sand face, at time t, and let yo be the average density of the fluid that enters the bore. The bottom-hole pressure, for a fluid height h will therefore be p = rogh, neglecting, of course, the friction drop in the well bore, while the fluid is rising, as may be justifiably done for most pumping wells. If a is the free area of the open-flow string—assumed to be uniform— the rate of production from the sand during the rise of fluid will be: where the last part of the equation merely indicates that, in general, the production rate Q must be considered as a function of the back pressure, and is determined by it alone. In fact, equation 1 shows that if the rate of rise of the pressure or fluid level is determined as a function of the height of rise, or p, for a number of values of the latter, this functional relation between Q and p will be immediately given. Conversely, if we know this functional relation, the rate of increase of p or h may be predicted, or, by observing the rate of rise of p or h some of the constants of the sand may be determined. Thus we may approximate the production from a well in a pumping state by that of a dead

Jan 1, 1937

By AIME AIME

IN ORDER to carry on its work most effectively, the Committee on Industrial Organization (now known as the Committee on Industrial Relations) consists, of .a number of sub-committees, each composed of a chairman and members who are especially fitted to carry out the work designated by its title. With only one or two exceptions, all of these committees made reports at the New York meeting of the Institute, in February of this year, abstracts of which follow.

Jan 1, 1920

By R. M. Brick, R. G. Treuting

DESPITE the basic importance of slip in the plastic deformation of metals, and the considerable experimental investigation, thought, and speculation that have been devoted to the fundamental nature of these processes, surprisingly few data have been reported regarding the microscopic appear- [ ] ance and distribution of slip lines,[$] the external manifestation of the slip process. Photographs hitherto reproduced in the literature are in general at low or unspecified magnifications with no correlation to the prior shear. A single-crystal cylindrical tensile specimen of alpha brass about ½ in. in diameter, one of many previously prepared by H. L. Burghoff,1 was available for study. A plane about 3/16 in. wide, parallel to the specimen axis and normal to the plane containing the slip direction and the specimen axis, was ground and metallographically polished along the entire 5-in. gauge length. Heavy etching produced a surface free of both scratches and flow. The specimen was strained in tension until slip markings first became visible on the polished surface (Figs. I and 2). Restressing the crystal caused additional markings to appear at an initially lower [ ] stress than previously was required. Stretching the specimen to produce a dense concentration of slip lines caused such variations in level in the polished surface (normal to the slip direction) that microscopic study at higher magnifications became impossible. After annealing 15 hr. at 850°C., the specimen recrystallized to form two grains with a boundary approximately normal to the specimen axis and about midway along its length. Each was X-rayed, and two planes were again polished along the length of the specimen, in this case each parallel to the slip direction in one of the two crystals. A light longitudinal scratch parallel to the specimen axis was drawn down the center of each plane. A Huggenberger extensometer was attached to the crystal A, whose slip plane would have the higher resolved shear stress of the two, and the specimen was again strained in tension.

Jan 1, 1941

By E. H. Rose

IN these days of the spectacular in research and technological accomplishment, it is easy and natural to overlook some of the applications to everyday life of recent developments of a more pedestrian kind, or to fail to realize that sometimes two or three of the latter may be combined to serve a novel purpose in fields other than those in which they grew. The present remarks are to point out three such developments which might be combined to apply to an everyday function of the A.I.M.E. as an organization. By its Constitution, the A.I.M.E. is organized "to promote the arts and sciences connected with . . . minerals and metals, and the welfare of those employed in these industries . . .; to hold meetings for social intercourse and the reading and discussion of professional papers, and to circulate . . . among its members the information thus obtained . . .; and to . . . maintain . . . a library." By these words of Article I the profession of mining and metallurgy is recognized to involve many arts and sciences, of which the art and science of exchanging information is a leading one. As to methods of preparing or securing papers, the Constitution is silent.

Jan 1, 1944

By Walter Renton Ingalls

Metallurgical literature has no record of any ore beneficiated for cadmium alone, and the cadmium of commerce is derived from zinc ore, with which cadmium is generally associated. Zinc ores free from cadmium—e.g., the ores of the Franklin and Stirling mines, New Jersey, and of Broken Hill in Rhodesia—are rare. Blende concentrates of 50 to 60 per cent grade have contained (in production of important tonnage) as much as I per cent Cd, which is unusually high. The concentrates from the Tri-State district average from 0.3 to 0.4 per cent Cd, which is high. The concentrates from mines west of the Rocky Mountains seldom are higher than 0.2 per cent. In the periodic system of the elements, cadmium is in the same group with zinc. Its properties and compounds are similar. Its metallurgy is also similar. Cadmium has a melting point of 320°C. and a boiling point of 778"C., while the melting point of zinc is 415'C. and the boiling point gos°C. These conditions, together with the lower reduction temperature of cadmium oxide, indicate means for. separating cadmium from zinc. Cadmium in spelter is viewed, if not as an impurity, at least as an alloying element that may be objectionable, its special effect being hardening. However, for some purposes, a little cadmium in spelter is desired, and 0.4 per cent may be permissible, even in spelter for rolling. Cadmium in spelter for brassmaking is completely volatilized at the temperature of that process, and in bygone days an immense quantity of cadmium must have been lost in the fumes from these furnaces. Pyrometalltjrgy—Early Cadmium compounds, sulphide and oxide, being more volatile than the corresponding compounds of zinc, loss of cadmium begins to occur from the first furnace operation. In normal roasting, even with Tri-State ore, this loss may not be very high. Raw ore, assaying 0.4 per cent Cd, may be expected to give a roasted product of the same assay, which would imply a cadmium loss of about 15 per cent. Roasted ore, assaying 0.4 per cent Cd when distilled at ordinary furnace temperature, yielded spelter containing about half of that in the ore charged. The first draw of spelter under these conditions may assay 0.8 per cent Cd (accounting for 22 per cent of the cadmium recovery) and after the several draws of spelter have been equalized the cadmium content may average 0.35 per cent. If, therefore, 2000 lb. of blende averaging 0.35 to 0.4 per cent Cd is roasted and distilled, there may be obtained 1000 lb. of spelter, assaying 0.35 per cent Cd or 3.5 lb. content, which entering into Prime Western spelter will be sold at the spelter price. It will be observed from the outline hereinbefore (summarizing conditions prior to the introduction of sintering) that the main loss of cadmium occurred in the distillation process and by failure to condense, which could be ameliorated by attaching a prolong to the condenser, thus collecting

Jan 1, 1944

By Ernest R. Lilley

THOSE acquainted with the fundamental differences between the, educational .systems of Great Britain and. the United States would hardly expect .the training of men for the petroleum industry to proceed along the same lines- in the two countries. The youth entering an English university is, except in the case of-the student from some of the British colonies or from foreign countries, almost invariably a product of the English "public school." This is in no sense comparable .with the American public school. It is a private institution, frequently of considerable age and heavily endowed. In many aspects it seems to be comparable with the American preparatory school. Yet to some extent its activities remind one of the first years of the undergraduate: course in the American college. Certainly it takes to-itself many of the social, functions of the American college.

Jan 1, 1931

By John Tyssowski

IN 1925, Harry Howard Stout, then metallurgist for Phelps Dodge Corporation, while investigating the cleaning of cathode copper by various gases at elevated temper-atures below the melting point of the metal, observed in the laboratory that particles of pure copper heated in a closed tube filled with hydrogen seemingly "stuck together." By further investigation he found that there was actual crystal growth across the boundaries of the particles of pure metal; in other words, there was a complete new crystal realignment and growth throughout the newly formed copper mass. It was coalescence, not adhesion; the several parti-cles had become one unit. From this dis-covery has been developed the coalescence process, whereby copper of cathode purity is squirted out in semifabricated form from an extrusion press, by the appli-cation of about 3000 tons pressure on a 10-in. piston. Stout decided that cathode copper pro-duced by electrolytic deposition was the logical source of the pure copper required for the coalescence process, but as there was no way of reducing the ordinary tough commercial cathodes to the small particles required he was confronted by a serious problem at the outset. Under his direction, this problem was solved by William H. Osborn and Harry Howard Stout, Jr. They developed the process and technique for producing cathode copper in brittle, friable

Jan 1, 1940

By W. F. Stowasser

downdraft traveling grate process to agglomerate pelletized iron ore concentrates has been successfully demonstrated in a pilot plant at Carrollville, Wis. Work there followed several years of development in the Allis-Chalmers Mfg. Co. laboratories, and the pilot plant phase was carried out in cooperation with Arthur G. McKee & Co., consultants and engineers to the iron and steel industry. End result of the process is conversion of iron ore concentrates into a form which can easily be transported and smelted in the blast furnace. Process Description The first of two process steps incorporates the art of balling and prepares the concentrates for burning. The second step consists of burning the green balls on the grate machine to the hardness required for shipping and handling purposes and for reduction in blast furnaces, see Fig. 1. Facilities are provided at the pilot plant to receive carload quantities of concentrate. The concentrates are loaded into a 50-ton bin direct from railroad cars. Because of the variable moisture content of the concentrates after shipment in an open railroad car it is necessary to repulp and refilter the concentrates to maintain a uniform and proper moisture content for the balling operation. Concentrates are conveyed to slurry tanks, and the slurry, at 50 to 60 pct solids, is pumped to a 4x4-ft drum filter. The filter provides feed of uniform moisture to the plant. Magnetite concentrates are normally filtered to produce a cake containing about 10 pct moisture, a necessary requirement for the following balling operation. The filtered concentrate is conveyed to a rotary bin table feeder which acts as a surge bin for the filter cake and delivers a steady flow of concentrates to the balling drum. It is often desirable to make additions to the concentrates as they are fed to the balling drum. These additives, such as bentonite, increase the strength of the finished green pellet and improve ballability of the concentrate. A vibrating feeder supplies additive to the feed belt, and the additive is mixed with the concentrate in the balling drum. The balling drum, shown in Fig. 3, is 8x3-ft diam. An oscillating cutting bar maintains the lining in the drum by trimming off the buildup of excess concentrate as it forms. The drum is operated in closed circuit with a lx4-ft rod-deck vibrating screen. Undersize pellets or seed pellets from the screen are returned to the balling drum until they grow to the desired size. Size of pellets is controlled by the opening in the screen deck. The formation of pellets in the balling drum is affected by many variables. Some of these are: the size distribution of the feed, the particle shape of the concentrate, the feed rate to the drum, the moisture in the concentrate, the speed of rotation of the drum, the slope of the drum, and the type of trimming obtained with the cutting bar. In this process, attempts are made to control the pellet size within the limits of % to 5/8 in. diam. The screened oversize pellets are conveyed under a coal feeder where sufficient powdered coal is added to the belt to produce desired results in the burning process. The top size of the coal successfully used has been 20 mesh, and anthracite was used in the test program. Fig. 4 illustrates the vibrating screen and the coal feeder. The pellets and free coal are conveyed together to the 5x3-ft diam- reroll drum that rolls the coal onto the surface of the pellets. This drum is also equipped with a cutting bar. The prepared pellets, containing bentonite, water, and surface coal, are elevated to the traveling grate, which consists of a continuous strand of 37 pallets. Each pallet, with a grate bar area 2 ft wide by 1 1/2 ft long, has 14-in. high side plates, Fig. 5. Feeding and distribution of the green balls to the grate is handled by a short conveyor which oscillates back and forth across the 2-ft width of the grate. An adjustable vertical plate located several inches in front of the head pulley of the oscillating conveyor controls the height of the bed and levels the moving bed of pellets. This method of feeding prevents segregation of various size pellets as well as fines and produces a uniform, permeable bed. The pallet train moves under the furnace and across four windboxes, located beneath the pallet frames, see Fig. 2. As the green pellets are deposited on the grate, partial drying of the pellets begins over a 2-ft long updraft windbox. The low temperature air reduces the moisture in the pellets in the lower level of the bed and this operation is essential to prevent sagging of the bed during later stages of the Process. The air used for this drying is recuperated from cooling the pellets on the grate, and supplemental heat, required for starting the Process, is obtained from an auxiliary burner. The pellets are then moved by the grate into the furnace and over an 8-ft windbox, designated as the downdraft waste windbox. Products of combustion are exhausted from this windbox to atmosphere. The furnace, shown in Fig. 6, is constructed with three chambers to provide downdraft drying, preheating, and ignition, respectively, to the pellet bed as it passes through. Overall length of the furnace is 5.57 ft; however, the exterior wall ends may be moved to reduce the length and also adjusted to Obtain the bed height desired, The drying, preheating, and ignition sections of the furnace are supplied with medium temperature

Jan 1, 1956

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 Fred J. Miller

FRED J. MILLER was born in Ohio, in 1857. He had a common and high school education, supplemented by personal study and special instruction. After serving a 4-year apprenticeship and working in various capacities in machine shops, he became a contributor to mechanical journals and finally a member of the editorial staff of The American Machinist, where he remained for twenty years, the last ten years as editor-in-chief of the magazine, and vice-president of the publishing company. On retiring from journalism, he was for nine years general manager of a group of typewriter factories, and was then commissioned Major of Ordnance in the U. S. Army, being stationed during most of his service at Rock Island Arsenal, where he organized the Civilian Service Division of the Arsenal. He is now a member of the Technical Advisory Committee of the War Claims Board at Washington. Major Miller became a member of the American Society of Mechanical Engineers in 1890, and has always taken an active interest in its affairs, having served on a number of important committees, and as a member of Council from 1904 to 1907, inclusive. He was elected President in December, 1919.

Jan 1, 1920

By Richard J. Lund

Stock piling-and by that I mean well-organized stock piling on a substantial scale-is almost as old as the hills themselves. It was back in early Biblical times, as recounted in the Book of Genesis, that Joseph was charged by Pharaoh with the responsibility of stock piling food during the seven years of plenty to guard against the seven subsequent years of famine that were revealed by the Pharaoh's dream. And this same policy of storing up food or materials to provide for future anticipated emergencies can be traced repeatedly down through the ages. So our own efforts are anything but new. Our modern concept of stock piling-the purchase and storage of strategic materials to assure supplies needed in time of some future war- stems from our experience in World War I. In 1920, the War Department was charged by Congress with the responsibility of procuring all War Department supplies and mobilizing industry in the event of another war. During the two decades that followed there were many authoritative studies made of our deficient mineral problem, all of which pointed out the urgent necessity of stock piling certain strategic materials as a reserve against future war. One such study, made in 1925 through the combined efforts of the Mining and Metallurgical Society and the AIME, was done at the ex- press request of the War Department. Eight years later another more de-

Jan 1, 1949

By A. C. Watts

FOR several years, a mine in Colorado experienced considerable trouble from small fires caused by the blasting of coal. Although a well-known make of permissible powder was used, it was first thought that the powder ignited gas that might be present and that this, in turn, set fire to line brattices or to the coal. Experiments were, therefore, conducted with another make of powder, but the results convinced the superintendent of the mine, Robt. Williams, Jr., that the fires were not caused by the powder but by the high-voltage electric current used for detonating the shots. The mine "makes" gas very freely, giving off from three-fourths to a million cubic feet of methane per 24 hours. The coal is a good grade bituminous of a very free burning quality. Electric shot-firing from the outside after all men and animals were outside had been practiced for a number of years. The shooting circuit was connected with the main power circuit at the mouth of each entry. Shooting circuit switches were mounted in boxes, which were kept locked with the handle of the switch, in open position, showing through the bottom of the box. The door of the box could not be shut and locked when the shooting switch was closed. At the entrance to each room, or working place, a small switch, called the miner's switch, was placed on the shooting line. It was the duty of the miner, when entering his place at the beginning of the shift, to see that this switch was open and that it was kept open until he left the place at the end of the shift to go out of the mine. Grounded return was used for main power lines. The current was 500 volts, direct current, with 100 to 300 amp. The nearest working face was 9600 ft. from the shot-firers' switch outside the mine and the most remote working face was 2 ½ miles. The various working faces were scattered over a wide area between these two points.

Jan 9, 1925

By PERCY E. BARBOUR

SECONDARY copper1 has &come more or less of a bugbear generally. What is its influence is often the subject of heated argument. The inedapable fact usually quoted is that since in 1929 primary production of copper in the United States was 1,026,348 tons and secondary production was 626,550 tons, there- fore, 0.6 lb. of secondary is produced for every pound of primary, and "How can you get around that?" The matter seems very plain, now that I have reached my conclusions, but they are the result of much laborious study and research. I shall show that' the production of secondary copper is not 0.6 per lb. of primary, in spite of statistical appearances; that the production of secondary is a function of primary production rather than of price; that secondary production has 'only a sub-. ordinate influence on the price of copper and then only in abnormal times; that there is not an accumulating reservoir of secondary from which the country is some- time to be drowned in copper, as is believed by some, or a reservoir from which we are going to draw much needed and more or less inexhaustible stores in the future, as is believed by others; and finally, that the United States always produces more copper than it uses and exports the surplus. These are all controversial points, and for that reason and to anticipate argument I have set forth my reasoning in considerable detail.

Jan 1, 1931

By B. A. Stainton, John D. Gill

OUR combined economic activities have as their goal the maximum of individual well-being and national security. In this age of intense international competition the two objectives are closely related. For many decades, the maximum of well-being and ability to maintain national security have moved generally upward. The best single measure-perhaps the only adequate measure -of the level of the rising goal is the per capita real national income (national income corrected for price changes). For centuries before the industrial revolution the income of the world's population changed little from generation to generation. In our country prior to 1800 the growth of national income was hardly measurable from decade to decade. Since 1850, perhaps since the "industrial revolution," the growth of per capita real income has been increasing geometrically. Of major importance is the accelerative growth of the productive ability of our economy. Inadequate consideration of its implications is partly responsible for periodic delays in solving our princi-

Jan 1, 1946

By F. N. Rhines, A. H. Grobe

At elevated temperatures the oxide of silver is unstable in the air at atmospheric pressure, consequently no external oxide scale forms upon pure silver under conditions of high-temperature annealing. When small quantities of certain alloying elements are present in the silver, the formation of a thin external scale is possible1 and in addition there may form a subscale composed of the oxide of the solute element precipitated within the body of the silver. Norbury2 and Leroux and Raub3 have reported internal oxidation (subscaleiormation) in alloys of silver with 2, 7.5, and 30 per cent of copper. The presence of the subscale is believed to be responsible, at least in part, for the objectionable "fire mark" in Sterling silver.4 Several other alloys of silver, after oxidizing heat-treatments, are known to exhibit undesirable polishing characteristics that may be the result of internal oxidation. Except for the absence of an external scale of silver oxide, it is to be anticipated that silver alloys will prove to be very similar in their oxidation behavior to the alloys of copper, the oxidation characteristics of which have been studied in some detai1.5,6 The present research confirms this anticipation. The oxidation of a series of 20 dilute alloys of silver has been studied metallographically; some types of subscale not encountered among the copper alloys have been found. Instances of internal oxidation in alloys of most of the metals of the 1-6 and VIII groups of the periodic system are on record, but evidence of this type of oxidation in alloys of the metals of the intermediate groups is lacking. A number of the metals of the intermediate group, among them cadmium, lead, tin, and zinc, appear to provide the conditions essential to subscale formation; i.e., they form oxides with a relatively low negative free energy of formation, they dissolve other metals that form more stable oxides, and, presumably, oxygen will diffuse through them. In a study of 40 alloys of these white metals only a few cases of internal oxidation have been found. The probable reasons for this difference in behavior will be discussed presently. Experimental Procedure Silver.—The silver alloys employed in the oxidation studies were prepared in heats of 30 grams each from high-purity silver (99.993 per cent Ag)* and the purest avail-

Jan 1, 1942

By A. H. Grobe, F. N. Rhines

At elevated temperatures the oxide of silver is unstable in the air at atmospheric pressure, consequently no external oxide scale forms upon pure silver under conditions of high-temperature annealing. When small quantities of certain alloying elements are present in the silver, the formation of a thin external scale is possible1 and in addition there may form a subscale composed of the oxide of the solute element precipitated within the body of the silver. Norbury2 and Leroux and Raub3 have reported internal oxidation (subscaleiormation) in alloys of silver with 2, 7.5, and 30 per cent of copper. The presence of the subscale is believed to be responsible, at least in part, for the objectionable "fire mark" in Sterling silver.4 Several other alloys of silver, after oxidizing heat-treatments, are known to exhibit undesirable polishing characteristics that may be the result of internal oxidation. Except for the absence of an external scale of silver oxide, it is to be anticipated that silver alloys will prove to be very similar in their oxidation behavior to the alloys of copper, the oxidation characteristics of which have been studied in some detai1.5,6 The present research confirms this anticipation. The oxidation of a series of 20 dilute alloys of silver has been studied metallographically; some types of subscale not encountered among the copper alloys have been found. Instances of internal oxidation in alloys of most of the metals of the 1-6 and VIII groups of the periodic system are on record, but evidence of this type of oxidation in alloys of the metals of the intermediate groups is lacking. A number of the metals of the intermediate group, among them cadmium, lead, tin, and zinc, appear to provide the conditions essential to subscale formation; i.e., they form oxides with a relatively low negative free energy of formation, they dissolve other metals that form more stable oxides, and, presumably, oxygen will diffuse through them. In a study of 40 alloys of these white metals only a few cases of internal oxidation have been found. The probable reasons for this difference in behavior will be discussed presently. Experimental Procedure Silver.—The silver alloys employed in the oxidation studies were prepared in heats of 30 grams each from high-purity silver (99.993 per cent Ag)* and the purest avail-

Jan 1, 1942

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

Jan 4, 1950

Jan 5, 1953

Jan 4, 1953