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By A. W. McReynolds

E. OROWAN*—I observed the phenomenon of jerky yielding many years ago with zinc25 and cadmium single crystals. A significant point was that the jerks occurred not only when the stress was raised but also (sometimes, after a pause of many minutes during which no trace of creep was observable) at constant stress. The phenomenon may be closely linked with the inertia of the testing machine and of the specimen, although the inertia alone cannot account for it. If, during the test, the resistance of the material to plastic deformation suddenly diminishes while the applied force remains constant, a sudden deformation follows until the yield stress has risen, by strain hardening, to the level of the applied stress (= the value of the previous "upper yield point."). When this is reached, the rate of deformation has attained a maximum value because, up to this moment, the applied force was higher than the plastic resistance of the specimen, and the difference was used for accelerating the moving parts of machine and specimen. The kinetic energy accumulated is now transformed into plastic work by further deformation; that is. the deformation overshoots the point at which the plastic resistance equals the applied static force. When the kinetic energy has been used up, therefore, we are left with a specimen the yield stress of which is higher than the applied stress, and no further deformation can occur (apart from a little creep) until either the applied stress has been raised to the new yield stress level, or the yield stress has fallen by thermal recovery to the level of the applied stress. While this occurs, a new upper yield point can develop, for example, by precipitation.26

Jan 1, 1950

By P. Barnes

The sums given in the accompanying table are those actually paid for material and labor up to about August, 1875; but, as some parts of the machinery were not wholly completed at the starting of the works in September, 1875, the statement cannot be taken as an absolutely correct note of the total cost. A complete description, with engravings of the building and machinery, was given in Engineering, April 26th, 1878, in a paper by Messrs. A. L. Holley and Lenox Smith, to which convenient reference may be made. A detailed list of the construction accounts has been given in a paper, by the present writer, in vol. vi, Transactions of the Institute. A summary is given in the table of the items in each class which enter into the total cost, and also a note of the proportion which each of these items forms of the whole. A concise view may thus he obtained of the facts embodied in the statement as a whole, even though it cannot lay claim to completeness in showing the entire or final cost. An urgent suggestion has reached the writer from a distant country that such statements of cost to be really most serviceable should give the details in days of labor, in weight of iron, and in number of brick, and to this an assent is most cordially yielded. It is true, however, that the mere labor of copying arid compiling these details to such a degree of minuteness, would be very great, and, in any event, the probable difference between the plans of an existing establishment and one projected, would be so wide as to render even so complete a statement of cost of little more real service than the approximate notes given herewith.

Jan 1, 1879

By P. Barnes

THE sums given in the accompanying table are those actually paid for material and labor up to about August, 1875; but, as some parts of the machinery were not wholly completed at the starting of the works in September, 1875, the statement cannot be taken as an absolutely correct note of the total cost. A complete description, with engravings of the building and machinery, was given in Engineering, April 26th, 1878, in a paper by Messrs. A. L. Holley and Lenox Smith, to which convenient reference may be made. A detailed list of the construction accounts has been given in a paper, by the present writer, in vol. vi, Transactions of the Institute. A summary is given in the table of the items in each class which enter into the total cost, and also a note of the proportion which each of these items forms of the whole. A concise view may thus be obtained of the facts embodied in the statement, as a whole, even though it cannot lay claim to completeness in showing the entire or final cost. An urgent suggestion has reached the writer from a distant country that such statements of cost to be really most serviceable should give the details in days of labor, in weight of iron, and in number of brick, and to this an assent is most cordially yielded. It is true, however, that the mere labor of copying and compiling these details to such a degree of minuteness, would be very great, and, in any event, the probable difference between the plans of an existing establishment and one projected, would be so wide as to render even so complete a statement of cost of little more real service than the approximate notes given herewith.

Jan 1, 1879

By John Branner

FIVE of the geologic horizons that yield oil in other parts of the world are represented in Brazil; namely, the Devonian, Carboniferous, Permian, Cretaceous, and Tertiary. Thus far, the first two have shown no, evidences of being oil bearing within Brazilian territory. Not enough exploring has been done to permit trustworthy comparisons of the relative importance of the Permian, Cretaceous, and Tertiary as oil-bearing horizons in this country. The most important, indeed almost the only, information available relates to the locations of the areas and to the structural features of the several horizons. The theories regarding the physical conditions under which these rocks were laid down, however, I regard of the utmost importance. PERMIAN Rocks of Permian age cover an enormous area in Brazil, extending from Rio Grande do Sul to Maranhão on the north, and to Matto Grosso on the west. These Permian rocks in many places are known to include oil-bearing shales and in some locations contain small veins of gilsonite. The geologic map of Brazil shows that the Permian area is widely distributed, but there is considerable doubt about 'the origin of some of the rocks:. Some of the lower Permian beds in southern Brazil contain marine fossils, but in Minas no fossils have as yet been found in them, and in Bahia, at only one locality have a few Permian plants been found. Indications of oil have been found in the states of São-Paulo, Paraná, and elsewhere farther south, but wells drilled in the Permian of São Paulo near the Morro do Bofete did not find oil. One well has been started, by the Brazilian government, in the Permian of Paraná near Marechal Mallet, close to latitude 26° south, but thus far oil has not been found.

Jan 6, 1922

By E. W. Henderson

Development work in the state of Utah in 1935 consisted of additional work done on wildcat tests started in previous years and on a number of new wildcat tests started during the year. No effort was made to extend areas or to discover deeper productive horizons in proven fields. Principal areas of development were in Daggett County, northeastern Utah; Grand and Emery counties, east-central Utah; and in Washington County, southwestern Utah. Daggett County Clay Basin.—The Mountain Fuel Supply Co. deepened Murphy No. 2, sec. 21, T.3N., R.24E., from 6030 to 6790 ft. for a test of the Sundance formation. Two sandstone members at 6520 to 6644 ft. and 6737 to 6790 ft. contained water. The hole was plugged back to 5860 ft. and left as a future gas supply for the Salt Lake City-Ogden pipe line. The failure of the Sundance formation to produce in this test, in view of the recent Sundance discoveries in Colorado arid Wyoming, was disappointing Emery County Last Chance.—-Thc wildcat test of the Rainsey Petroleum Corporn-tion, Well No. 1-X, sec. 18, T.26S., R.7E., completed plugging back from total depth of 3168 ft. to 2771 ft. and was shut in as a gas well. A gas sand at 2724 to 2771 ft. produced approximately 21 million cubic fert. A deep test of the structure will be started upon approval of a wit plan of development. Grand County Cisco.—-The wildcat test of the Utah Southern Oil Co., sec. 33, T.22S., R.22E., of which the total depth was 1720 ft. on Dec. 31, 1935, is the most interesting operation ill the state. Location of the test was deter-

Jan 1, 1936

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Mining Engineer. Graduate of Colorado School of Mines, 1912, experienced in coal, lead manganese and limestone mining, wishes execu¬tive position. A-2146. Graduate Mining Engineer.-Discharged, reserve officer, age 32, single, 7 years' experience holding responsible executive positions, in iron, copper, and talc mining. Well recommended. A-4913. Mine Manager, Superintendent or Engineer. Age 41, graduate of Michigan College of Mines; 20 years' experience in responsible positions in connection with large operations; in iron, copper, pyrites, lead and zinc mines; successful in finding and developing orebodies, increasing production, and reducing costs. Desires a position with a future. A-4081. Mining Engineer.-Graduate from Polytechnicum, Stockholm; 14 years' practical experience in Sweden, United States, Belgium, and Spain, in iron-ore development, mining, and milling; thorough knowledge of English, French and Spanish; desires position as superintendent or assistant manager. Good references; member; now in Sweden. A-4914. Research Engineer. Now in Chile on the erection of a 50-ton mill with modern machinery for the treatment of Chilean nitrate. Desires connection from the first of next year; with firm operating in South or Central America. A-4915. Metallurgical Engineer. Junior member, age 26, single, graduate Columbia School of Mines; recently discharged as lieutenant in the heavy artillery. A-4916. General Superintendent. Technical graduate, age 35, desires position over a group of four or five mines or as assistant general superintendent for a large. company. Has had experience in superintending mines, construction work, opening new and abandoned mines, safety and effi-ciency engineering and handling organized labor. At present employed by a coal company in the middle West. A-4917.

Jan 11, 1919

By E. W. Henderson

Development work in the state of Utah in 1935 consisted of additional work done on wildcat tests started in previous years and on a number of new wildcat tests started during the year. No effort was made to extend areas or to discover deeper productive horizons in proven fields. Principal areas of development were in Daggett County, northeastern Utah; Grand and Emery counties, east-central Utah; and in Washington County, southwestern Utah. Daggett County Clay Basin.—The Mountain Fuel Supply Co. deepened Murphy No. 2, sec. 21, T.3N., R.24E., from 6030 to 6790 ft. for a test of the Sundance formation. Two sandstone members at 6520 to 6644 ft. and 6737 to 6790 ft. contained water. The hole was plugged back to 5860 ft. and left as a future gas supply for the Salt Lake City-Ogden pipe line. The failure of the Sundance formation to produce in this test, in view of the recent Sundance discoveries in Colorado arid Wyoming, was disappointing Emery County Last Chance.—-Thc wildcat test of the Rainsey Petroleum Corporn-tion, Well No. 1-X, sec. 18, T.26S., R.7E., completed plugging back from total depth of 3168 ft. to 2771 ft. and was shut in as a gas well. A gas sand at 2724 to 2771 ft. produced approximately 21 million cubic fert. A deep test of the structure will be started upon approval of a wit plan of development. Grand County Cisco.—-The wildcat test of the Utah Southern Oil Co., sec. 33, T.22S., R.22E., of which the total depth was 1720 ft. on Dec. 31, 1935, is the most interesting operation ill the state. Location of the test was deter-

Jan 1, 1936

By Harold F. Unger, Byron S. Snowden, William H. Engelmann

The effects of using surfactant solutions while diamond drilling in amygdaloidal basalt of the Upper Michigan copper mining district were investigated. Nonionic, anionic, and cationic surfactant solutions, all biodegradable, were tested with size AX surface-set bits mounted on a drill instrumented for continuous recording of thrust, rotational speed, and torque levels. Water flow and penetrations rates were also recorded. A drilling study was carried out, testing two rotational speed levels, two diamond bit grade levels, and four flushing agents (including water as a control). Comparison of all low-speed/high-thrust groups of tests shows that the non-ionic surfactant produced a 35% overall average increase in penetration rate over water, the anionic a 29% increase, and the cationic a 28% increase. These increases in, penetration rates resulted in a 22 to 26% reduction in cost over flushing with water alone. With the high-speed/low-thrust combination, the surfactants produced less benefits in penetration rate increases over water (14% increase for nonionic, 14% decrease for anionic, and 2% decrease for cationic type). Particle size analyses were run on drill cuttings produced by the three surfactant solutions and by water. All surfactant solutions showed a 20 to 50% increase in solids content over that of water alone. Since flushing rates were constant, these increases in solids content agree well with the penetration rate changes. The diamonds were recovered from each bit by matrix dissolution, and bit wear was measured in terms of total loss of weight. Flushing with surfactant solutions showed a savings in bit wear in most cases. The drill team noted also that surfactant flushing improved recovery of drill core by allowing easier removal of the core from the barrel.

Jan 1, 1976

Jan 1, 1891

By S. W. MEALS

TWENTY million people in this country and Canada in nearly four million homes can give thanks to our Creator for natural gas, that most wonderful natural fuel with which Dame Nature has so bountifully blessed us. It is a clean, healthy and cheerful fuel, made up almost entirely of carbon and hydrogen. There is no residue, no waste and there are no objectionable constituents; an ideal fuel for the home. It operates like magic, open the valve and it is there for your needs, winter or summer, night or day. You are not required to place your order 30 to 90 days in advance and you do not need to pay for your winter's supply in advance. No ashes to worry about, no flues or chimneys to clean, nor kindling wood to store or bother the housekeeper. We who have been so blessed do not realize what it would mean to be without it. If in place of opening a valve we had to go to the woodshed or coalhouse and then build our fire-carry out the ashes-well, some of us I am afraid would be late reaching our offices and perhaps would miss our hot cakes for breakfast. One cubic foot of gas produced from the White Sand formation contains 1130 B.t.u. and weighs 47/1000 lb.; there are about 24,000 B.t.u. in 1 lb. of gas. Temperatures of over 3400 deg. Fahr. have been obtained with natural gas. Not only is it a superior fuel for the home but it has no equal for use in many large manufacturing industries, especially with the making of glass, pottery and open-hearth steel. In an open-hearth furnace, properly constructed, 5000 cu. ft. will melt one ton of steel. It requires 1/3 ton of bituminous coal gasified in a producer to do the same work, or about 40 gal. of tar or fuel oil, or 11,000 cu. ft. of by-product gas.

Jan 1, 1926

By AIME AIME

T. E. PURCELL, general chairman . of the local committee, opened the seventh meeting of the Fuels Division A.S.M.E. and the Coal Division A.I.M.E., at the William Penn Hotel, Pittsburgh, Oct. 28-29, by introducing Harry M. Moses, president, H. C. Frick Coke Co., who welcomed the 500 registrants to "our town." Mr. Moses, in his brief talk, declared that in the postwar period each of the new centers must have a reason for existence. Pittsburgh, he said, has no iron ore, or bauxite, and limestone is scattered and not near by; but Pittsburgh does have low-cost fuel within reasonable distance. Its problem is the economical utilization of the low-cost fuels that remain, as the high-quality fuels are gone. Mr. Moses expressed confidence in this group in the solution of the problem and looked forward to what they would do. Harold V. Coes, the first A.S.M.E. president to attend one of these conferences, responded. He thoroughly believed in these joint meetings - in the cross-fertilization of ideas. Each Division learns from the other. Mr. Purcell then turned the meeting over to J. E. Tobey who presided over the coal research session that followed.

Jan 1, 1943

By H. T. Hildage

Although Greater New York does not bear any resemblance to a great mining district, the mining operations that are being conducted in and about the city are both extensive and interesting in character. With regard to the extent, it may be mentioned that, at present, there is more dynamite used in New York than in any mining district in the United States; that there are under construction about 38 miles of tunnel, and that 66 miles more are projected, most of which must be constructed .in the near future; that since 1903 at least 2,000,000 tons of earth has been removed in underground work, in addition to about 3,500,000 tons that has been removed in open-cut in connection with tunnel-work, and many times this quantity that has been removed in excavating foundations for buildings not connected with tunnel-work; and that there are to-day probably more than 5,000 men engaged in mining-work in and about New lrork City. These undertakings include almost every operation connected with underground work, from exploration by means of trench and boring, to the sinking of large shafts and the driving of large tunnels through every kind of ground from hard rock to soft, semi-fluid silt and quicksand. It is proposed in this paper to give a general description of some of the methods and appliances used in the opening-up of a " mine " in a large city, and a brief description of some of the &'mines" now being developed in New York, connecting as far as possible the methods described with the particular work for which they were designed, in order to give a general idea of the

Jan 1, 1908

By W. L. Dumoulin

A RATHER detailed description of the entire plant and leaching process was given in a paper recently presented to the Institute,1 so this paper will cover briefly only the crushing practice of the New Cornelia Copper Co. for the year, 1918. The ore, which is mined by steam shovels and loaded in side-dump cars, passes through two crushing plants. These crushing plants were constructed to crush the ore required by a leaching plant of 5000 tons daily, capacity, during a crushing period of 16 hours. The primary plant reduces to less than 3 in. (76 mm.) and the secondary plant, to ¼ in. (6.35 mm.), which is sufficiently fine for satisfactory percolation of solution through the ore in the leaching tanks, and to give good extraction. The ore is then conveyed to the leaching tanks by a system of 28-in.. (71-cm.) belt conveyors. On the way to the leaching tanks, it passes through an automatic sampling plant, where a 1-per cent. sample is taken. From the primary crushing plant, the ore is conveyed by two 36-in. (91-cm.) belt conveyors to a 10,000-ton steel storage bin, with a reinforced-concrete flat bottom. The ore discharges from the bottom of this bin onto four 20-in. belt conveyors, which deliver it to the four units of crushers in the secondary crushing plant. There is no storage bin between the mine and the primary crushing plant. The ore breaks very coarse, is very hard, and contains a great many boulders, some as large as 4 ½ by 4 1/2 by 10 ft. (1.3 by 1.3 by 3 m.). Jams form in the bowl of the coarse crusher in the primary crushing plant, as a consequence, and are freed by means of an immense steel hook operated from a 40-ton electric traveling crane.

Jan 8, 1919

Jan 1, 1970

By Thomas Varley

IN THE congressional act establishing the Bureau of Mines one of the functions outlined was "to assist I the industry in the prevention of mineral waste." This had not only to do with the waste in mining but in milling and metallurgical practices, including smelting. The organization of the Bureau of 'Mines includes many divisions, each working in a particular field and charged with certain investigative work. The metallurgical division has the above duties under its immediate supervision, and the station located at Salt Lake City is directed by the chief of this division: There are ten experiment stations of the Bureau of Mines, located in various parts of the country, most of them being housed at state universities under cooperative agreements. Considerable care was exercised in locating the stations and in choosing the particular type of work to be investigated at each place. Inasmuch as the Bureau was designed to serve and cooperate with the industry it is only natural that the investigative work be of interest and importance to the territory immediately adjacent to the respective stations.

Jan 1, 1925

By P. G. Winchell, J. K. Jackson

The strtcture of body-centered Fe-Ni-C alloys (0 to 16.5 wt pct Ni) containing less than 0.015 wt pct C was investigated by measuring the carbon-diffusion peak at low frequencies with a torsion pendulurrr. By determining the Snoek damping in ferrite and in quenched alloys of identical composition, the effects of nickel content and heat treatment were separated, and the existence of a structure in which Snoek damping is greatly reduced was revealed in the quenched ternary alloys. The relative amount of this structure increases with increased nickel content and cooling rate. It is proposed that this structure may be highly imperfect or tetragonal. In Fe-Ni-C alloys containing only ferrite the addition of nickel (0 to 5.1 wt pet) decreases tke area of the carbon-diffusion peak and shifts its position to lower temperatures but broadens the peak only slightljl. The decrease in peak area with increasing nickel implies that short-range interactions with the nickel atoms prevent some of the carbon atoms from participating in the relaxation process. The shift in the peak position indicates a long-range effect of nickel on the movement of carbon atoms so that at 300°K the diffisivity of carbon in -ferrite is increased by about 35 pct by the addition of 5.1 tut pct Ni. The results are presented as distributions of relaxation strength 072 the activation energy under the assumption that the frequency factor is invariant. BODY-CENTERED iron-base solid solutions dissolve carbon interstitially in the octahedral sites. The occupation of an octahedral site produces a tetragonal distortion of the surrounding lattice. These sites fall into three sets according to the orientation of the tegragonal distortion associated with each and may be identified by their lattice coordinates as: type 1/2 0 0, type 0 1/2 0, type 0 0 1/2. At low carbon levels in cubic ferrite the carbon atoms are distributed at random1 among these sites. In high-carbon body-centered iron-base solid solutions, which are unstable with respect to several two-phase mixtures, a tetragonal structure occurs as the product of the diffusionless transformation of austenite. This transformation is commonly accompanied by appreciable microstrain and its product is called martensite. The tetragonality of martensite, a supersaturated solution of carbon in a iron, is maintained prior to decomposition even though local diffusion of carbon occurs as evidenced by carbide precipitation. The tetragonality is taken as evidence that one set of octahedral sites is preferentially occupied by carbon. (This preferential occupation is called ordering below.) Support for this view is presented by the absence of strain-induced carbon-atom diffusion in high-carbon solid solutions (martensite). Such diffusion occurs in ferrite and produces the 40°C internal-friction peak observed at 1 cps frequencies.' Thus, there appears to be qualitative evidence favoring the view that at sufficiently high carbon levels tetragonality arises spontaneously as a result of the ordering of the carbon atoms; however, no experimental evidence exists concerning an equilibrium between cubic and tetragonal body-centered solid solutions. Moreover, attempts to estimate the energy of ordering7-' predict a value too low to maintain the tetragonality observed at medium carbon levels, 0.3 to 0.6 wt pct C. In the present work an attempt using internal-friction measurements is made to establish the presence or absence of tetragonality in low-carbon body-centered solid solutions formed by quenching austenite. Fe-Ni alloys containing about 0.01 wt pct and 0 to 15 wt pct Ni were selected for the study. While the work was in progress Gilbert and Owen10 reported that the transformation which occurs in these alloys during quenching at rates up to 5000°C per sec is not martensitic but is more properly categorized as massive. Thus, the solid solution

Jan 1, 1964

By T. G. Decker, A. F. Witt, A. M. Gaudin

The historical development of the concept of contact angle hysteresis is reviewed. The measurements of contact angles reported in literature have all been made under static conditions. For the measurement of dynamic advancing and receding contact angles, four methods are described together with an evaluation of their precision. Three of these methods were adapted from devices already used for the measurement of static contact angles. The fourth method uses a new principle and apparatus and is the most accurate. While the relationship between surface tensions and the contact angle was extablished as early as 1805 by T. Young,' it was only in 1890 that the existence of contact angle hysteresis was reported by Lord Rayleigh. His observations, however, remained almost unnoticed. With the invention of froth flotation, the contact angle and its behavior became the subject of investigation. In 1907, L. Sulman and collaborators investigated the cause of discrepancies between recorded values of contact angles. They found that certain variations existed in most cases, but that definite maximum and minimum values of contact angles are obtainable. The difference between the maximum and the minimum contact angle in a given system was termed "hysteresis" by Sulman. First attempts to explain hysteresis were made by E. Edser. In the following years extensive studies of contact angles in various three-phase systems

Jan 1, 1963

By Marie Kinzel

LOS ALAMOS, New Mexico, the birthplace f the atomic bomb, is one of the most famous-and mysterious-places in the world. It leaped into fame on Aug. 6, 1945, when the first atomic bomb burst over Hiroshima. Unheard of until that day, its present life is as hidden from most people as was its very existence in pre-Hiroshima days. Then, those who did know of it dared not breathe their knowledge. "What do you tell your wife when you go to Shangri La?" was the favorite quip of the few consultants who made regular trips from east or west to Los Alamos during the tense months when the bomb was in the making. Security regulations made it impossible even to hint at the rigid secrecy surrounding the project. The puzzled wives in question knew only that their husbands had top priority on airplane flights to Albuquerque. When they had verified the safe arrival of the flight, they undoubtedly breathed a sigh of relief. If they could have visualized the rest of the trip, the sigh of relief would have been replaced by a state of tizzy, until a telegram came saying "Arriving home on Flight X" (on a nice safe airplane).

Jan 1, 1946

By Dell P. Williams, Howard G. Nelson

The tensile behavior of magnesium single crystals at a temperature of 26º ± 2ºC was investigated at varying pressure levels from 760 to 8 X 10-8 tow. For crystals deformed at a constant linear strain rate of 0.061 min-1. there was no apparent effect of the vacuum environment down to 10-8 torr. However, from a vacuum of 10-5 torr down to the lowest pressure attained (8 x 10-8 tor,), the effect of the vacuum environment was to increase the strain at the end of the first linear (or easy-glide) stage and to decrease the slope of this stage; the magnitude of this effect was found to be dependent on pressure. The slope of the second linear stage was also decreased at the lower pressure levels; however, this effect appears to be caused primarity by the vacuum effect on the first linear stage. The magnitude of the vacuum-environmrnt effect was also found to be dependent upon strain rate. The reduction in flow stress at 5 x 10-8 torr, as compared to the stress in air, was obserced to be about 10 pct for a strain rate of 0.0250 min-' and 70 pct for a strain rate of 0.67 min-1. No systematic effect of pressure on the critical resolvled shear stress was observed. The data interpreted in terms of a modified form of Mott's work-hardening mechanism for hexagonal metals. It has long been known that surface conditions influence the mechanical behavior of materials. Roscoe 1 demonstrated the importance of surface conditions on mechanical behavior by testing cadmium crystals with oxide layers. He found that the "apparent" critical resolved shear stress for cadmium was increased approximately 2.5 times by the presence of an oxide layer 1000 atoms thick. The magnitude of this effect was dependent on film thickness with crystals having films less than 20 atoms thick still showing a definite increase. This observed strengthening could not be attributed to any strength of the oxide film because of 1) the thinness of the films and 2) an observed increase in the flow stress as deformation proceeded. Harper and cottrel12 obtained similar results on zinc crystals which had been etched and steamed to give artificially thick oxide films. However, in the course of this study, they also carefully examined the very early stages of plastic flow for zinc crystals which in one case had been electrolytically polished and in the other had been lightly etched to produce a thin film. They then found that the critical resolved shear stress for both surface treatments of the crystals was actually identical but that the etched crystal exhibited a much more rapid initial hardening rate. This had not been noted previously. This result indicated that, in fact, the film caused an increase in the stress for continuation of slip, rather than for the initiation of slip. Lipsett and King3 investigated the effect of evaporated gold films on the plastic behavior of cadmium single crystals. For large angles (=75 deg) between the specimen axis and the normal to the slip plane, they found that the stress-strain curve of the coated specimen always lies above that for a clean specimen. The shear strain at the end of the first linear stage was greater in clean specimens than in coated specimens and the slope of the second linear stage was

Jan 1, 1965

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