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By B. D. Cullity

Gold and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,' this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low-temperature beta form will be considered in this paper. Experimental Procedure The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be prepared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsym-metrically in the camera in order to afford a basis for film-shrinkage corrections. A sample homogenized at 500°C gave the same diffraction pattern as a sample taken from the as-melted ingot. General Results The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 + 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the diffraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an LCaverage" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing sornewhat more and somewhat less than so at' pet gold, indicating a fixed composition for AuBe.

Jan 1, 1947

By B. D. Cullity

Gold and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,' this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low-temperature beta form will be considered in this paper. Experimental Procedure The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be prepared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsym-metrically in the camera in order to afford a basis for film-shrinkage corrections. A sample homogenized at 500°C gave the same diffraction pattern as a sample taken from the as-melted ingot. General Results The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 + 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the diffraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an LCaverage" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing sornewhat more and somewhat less than so at' pet gold, indicating a fixed composition for AuBe.

Jan 1, 1947

By G. W. Preckshot, N. G. DeLisle, C. E. Cottrell, D. L. Katz

MOST crude oils contain asphaltic substances that may be naturally or artificially precipitated. In the Greeley field, California, this asphaltic bitumen is precipitated during the flow of the oil from the reservoir to the stock tank. The mechanism of such precipitation is not well understood. This paper presents the progress that has been made by using the electron microscope as a new tool and by observing the effects of the streaming potential on the formation of bitumen particles. Crude oils at atmospheric pressure viewed in the electron microscope in very thin films under a vacuum showed no asphaltic particles. A technique of preparing slides of thin films by dilution of the oil with benzene and washing in petroleum ether was used at first, and these observations showed that the solvents caused the formation of the particles, varying from 0.01 to 0.2 micron in diameter. The electrical effects of fluids flowing through porous solid were studied, with emphasis on the formation of colloidal particles by the streaming potential. The streaming potential of crude oil flowing through sand was measured and was shown to be responsible for the formation of bitumen particles. These results bring out a new phenomenon, which may occur when crude oil flows through the porous oil reservoir.

Jan 1, 1942

By H. Hansen, A. U. Seybolt, P. Yurcisin, B. W. Roberts

The Bi-Mn phase diagram in the region near BiMn was investigated, using principally thermal analysis and changes in magnetization with temperature. Of chief interest are the findings related to the magnetic transformation in Bi-Mn. THE Bi-Mn system is of both theoretical and practical interest because of the occurrence of the compound BiMn which exhibits unusual ferromagnetic properties. Because the Bi-Mn phase diagram reviewed by Hansen' (see Fig. 1) in 1936 is based on work done by BekierY in 1914 and by Siebe" in 1919, which left considerable doubt about the nature of the diagram. it appeared desirable as an aid in understanding the alloying characteristics and magnetic behavior to examine the pertinent regions of the phase diagram. The most interesting reaction is the peritectic at 445°C which forms BiMn by the reaction: Liquid + Mn(sulfield) ? BiMn(sol field) There is also a eutectic at 262° C between pure bismuth and BiMn. Hansen draws in BiMn dotted, since in 1936 evidence for its existence was uncertain. Experimental Materials—Preparation of Alloys Electrolytic manganese of about 99.97 pet purity and bismuth of 99.99 + pet purity were used as starting materials.

Jan 1, 1957

By Michael H. Kuryla, Galen H. Clevenger

Some years after Nobel made his epoch-making contribution to the knowledge of high explosives, Sprengell described a new class of detonating explosives consisting of mixtures, made immediately before use, of an oxidizing agent and a combustible substance.2 The novel feature of the Sprengel explosives is that the constituents alone are non-explosive during manufacture, storage and transport. Despite this advantage, and although some of these have been used in important work, they are now little used, possibly on account of the greater inconvenience to the user, compared with explosives supplied by the manufacturer in final form. Liquid-oxygen explosives are a type of Sprengel explosive in that the oxidizing agent (liquid oxygen) and the combustible substance or substances (solid carbonaceous matter alone or in combination with liquid hydrocarbons or even metallic powders and, at times inert absorbents) are brought together immediately before use. The components separately are non-explosive. The possibility of using liquid oxygen as one of the components of an explosive was perhaps first suggested by Sprengel, who stated that the beau ideal of a detonating explosive was a mixture of eight parts of liquid oxygen with one part of liquid hydrogen. Although the liquefaction of air3 had been accomplished in the laboratory as early

Jan 1, 1923

By Michael H. Kuryla, Galen H. Clevenger

Some years after Nobel made his epoch-making contribution to the knowledge of high explosives, Sprengell described a new class of detonating explosives consisting of mixtures, made immediately before use, of an oxidizing agent and a combustible substance.2 The novel feature of the Sprengel explosives is that the constituents alone are non-explosive during manufacture, storage and transport. Despite this advantage, and although some of these have been used in important work, they are now little used, possibly on account of the greater inconvenience to the user, compared with explosives supplied by the manufacturer in final form. Liquid-oxygen explosives are a type of Sprengel explosive in that the oxidizing agent (liquid oxygen) and the combustible substance or substances (solid carbonaceous matter alone or in combination with liquid hydrocarbons or even metallic powders and, at times inert absorbents) are brought together immediately before use. The components separately are non-explosive. The possibility of using liquid oxygen as one of the components of an explosive was perhaps first suggested by Sprengel, who stated that the beau ideal of a detonating explosive was a mixture of eight parts of liquid oxygen with one part of liquid hydrogen. Although the liquefaction of air3 had been accomplished in the laboratory as early

Jan 1, 1923

By Hugh Neill, O&apos

In previous papers,' the author has reported the results of experiments on the straining in tension of a single-crystal test piece, about 0.6 in. long, of vacuum-melted electrolytic iron containing 1.8 per cent. of silicon. The crystal was originally in the "as cast" condition, and was stressed slowly along a tetragonal axis so that slipping along conjugate gliding planes finally transformed the original cylindrical portion into a pair of fracture wedges. One of these fracture wedges was sectioned along the stress axis in a plane at right angles to the edge of the wedge. A metallographic study of this plane of section led to the conclusion that slip had taken place in the (111) direction along (112) planes making a V shape with the stress axis. The present paper describes the results of scratch-hardness tests conducted on the same section, in order to determine the distribution of strain hardness therein, followed by annealing, and considers the resulting variations in hardness. These observations supplement those made by Krivobok2 on similar material reduced 25 per cent. by hammering (i. e., by impact) in the cold. In order to investigate ageing effects, two small crystals of the same alloy were also tested. The Specimens Employed The principal specimen, A, was prepared for the metallographic examination leading to the determination of the slip planes of the crystal. Therefore the work described in this paper was conducted on metal which had been repeatedly etched and had been allowed to rest for about 30 months after straining. It consisted of a section of the fracture wedge and contiguous unstrained head of the test piece taken along a tetragonal axis parallel to the direction of stressing, the plane of section originally being not far removed from the (011). Several subsequent grindings

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By Henry M. Howe

Jan 1, 1909

By Frederic Dewey

IT IS common to blame irregular assay results upon volatilization and much has been written upon the subject, but there is no. real evidence that, in a properly conducted assay, the loss of either gold or silver by volatilization is sufficient to affect appreciably the result, even when, arsenic or antimony may be present. Bulk assays of flue dust from assay muffles have been published, but the data given are totally insufficient to even approximate the volatilization from a single assay; and such figures as we have indicate the volatilization to be extremely small. Diligent search in the literature and wide inquiry among assayers and instructors have failed to produce a single case where the litharge volatilized in making an assay has been collected and assayed for gold and silver. Having attempted to do this, with most indifferent success, I am not surprised that this has not been done. While various textbooks give volatilization as a cause of loss in cupellation, it may safely be said that in the rare cases where this volatilization is sufficient to affect appreciably the result it is due to excessive temperature. Percy1 says "The loss of silver by volatilization during cupellation is very slight (unless the temperature has been much too high), and may be disregarded." This statement is repeated by the Beringers2 and Smith,3 who includes gold with silver. Mitchell4 says the litharge fume rarely contains over one ten-thousandth of silver. Campredon5 says that at a proper temperature no silver is lost by volatilization.

Jan 2, 1920

By Chandler Morse

RENEWABLE VS. NONRENEWABLE NATURAL RESOURCES Nonrenewable resources, such as minerals, are the inevitable center of attention in discussions of depletion and exhaustion. Nevertheless, it may well be proper to regard some nonrenewable resources as not subject to exhaustion, and renewable resources may sometimes be treated as if they were finite stocks. Thus, the availability of nonrenewable resources is not and probably never will be known completely Chap. 2.5A, and therefore is not subject to firm predictions concerning exhaustibility. Moreover, because exploration and discovery are more or less continuous processes it is often appropriate to regard mineral supplies as flows, and to treat the estimated reserves as working capital, an inventory, continually depleted by use and augmented by discoveries.23 The aggregate economically exploitable stocks of a given mineral are seldom estimated (or estimatable) with precision, as Chap. 2.5A shows, and even when they are, forecasts concerning years of remaining life can be and often are falsified by changes in one or more of the multidimensional conditions of supply and demand; or the productive services formerly derived from an exhausted stock may continue to provided without material impairment by one or more substitutes b Conversely, the renewable resources are all subject to depletion when the rate of use exceeds the natural or induced rate of replenishment, and cases of exhaustion or near exhaustion, as through soil erosion, overcuttmg of forest lands, and overfishing, are rather common c Where exhaustion is a clear possibility the resource may either be exploited on a consciously adopted "sustainable yield" basis or be treated as an exhausting asset." In some cases, conscious treatment

Jan 1, 1976

By George E. Thackray

In December, 1894, the Cambria Iron Company made a number of heats of Bessemer steel to be used in structures by one of its customers, subject to inspection and tests by a firm of consulting engineers, one of the requirements being that the material should riot exceed .08 per cent. of phosphorus. In other respects the requirements were such that they could only be met by material of good quality; but the general spe cification is not introduced here, as it is not the purpose of this paper to deal with anything except certain difficulties encoun tered in determining the phosphorus-content of the material in a manner satisfactory to both seller and buyer. Preliminary determinations of phosphorus were made in sample-ingots from each of the heats from which material was rolled for the order in question, and these preliminary chemical tests, made in the laboratory of the Cambria Iron Company, showed that, with very few exceptions, every heat was within the prescribed limit of phosphorus. After the material had been rolled, sample-drilling8 of finished material were taken from the various heats in the regular manner in use at the works, these samples being thoroughly mixed and divided into two parts, one of which was analyzed at the works' laboratory and the other sent to the inspecting engineer. Several hundred determinations were made from this mate rial without reaching an agreement between the work of the inspector's chemist and that of the works' chemist; but as it is not the object of this memorandum to treat of this part of the subject at length, it is considered sufficient to present herewith only a few of these first determinations. The analyses given in Table I. are those of the original series made on the heats which were afterwards resampled for final determination by an arbitrator; and they are selected for this reason, as the entire " comparison is thus rendered more complete.

Jan 1, 1896

By R. R. Unterberger

Three different physical techniques have been used to see through or probe into rocks, so miners might know what is ahead or overhead. These are radar, sonar, and a unique type of sonar called nonlinear sonar. Five radar systems have been developed. The highest frequency used is 4300 MHz for detecting small fractures at close range. This gives the best resolution. For longest range (over 2000 m, or 6560 ft) we use the 30 MHz radar for finding faults ahead of mining or ranging to salt dome flanks. Two types of salt, dome and bedded, are recognized. Radar works well in dry (dome) salt, but not in bedded salt which contains small amounts of water. The dipole moment of water absorbs energy from the radar. Thus was born the 30 MHz radar system and sonar probing systems. These can probe to 100 m (328 ft) even into wet salt. All probing systems measure data in time, which are converted to distance by measuring the time of travel of radar or sonar through salt pillars of known thickness. Ranges of probing in salt are from less than 1 m (3.3 ft) to more than 2000 m (6560 ft). Uses of radar and sonar probing in mines include mapping the top of salt above a mine; mapping salt dome flanks; finding impurities in salt such as anhydrite, sandstone, or potash stringers; locating old boreholes in salt pillars; locating fractures in salt; and finding faults or water zones ahead of mining.

Jan 1, 1985

By Roy A. Lindgren

SINCE the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced', at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces'. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a supe¬rior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1937

By Howard Reiss, C. S. Fuller

A theoretical and experimental study has been made of those interactions between holes and electrons which influence the solubilities of donors and acceptors in semiconductors. The major portion of the work concerns the solubility of lithium in silicon doped to varying degrees with boron. This solubility increases with increasing boron content in a manner predicted by theory and exhibits the expected temperature dependence. A qualitative experiment in germanium is described which demonstrates, in accordance with theory, that doping with a donor decreases the solubility of another donor. SEVERAL authors have discussed the possibility that holes and electrons behave like chemical entities and influence the solubilities of ionized impurities, Wagner was the first to invoke this concept in connection with his studies on nonstoichio-metric oxides. He used it again in explaining the solubility of hydrogen in molten binary alloys. In a theoretical paper,' Reiss drew attention to the fact that solutions of impurities in semiconductors

Jan 1, 1957

By J. Rourke, F. S. Minshall, E. G. Zukas, C. M. Fowler, O&apos

The Hugoniot curves were determined for Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si. The pressure of the transition increased as the silicon content of the alloy increased. Single crystals of 2.9 wt pct Si-Fe were also studied. The pressure of the transition was not dependent on crystallo-graphic orientation. All of the Neumann bands (mechanical twins) were attributable to (112) planes but not all of the {112} planes showed twin markings. A thorough study of the iron Hugoniot (the relationship between specific volume and pressure) under plane wave shock loading revealed a pressure transition at about 130 kbar shock pressure. The results of this investigation were reported by Bancroft, Peterson, and inshall1 in 1956. At the time of this discovery, it was felt that this was probably the a, to y transition normally found in iron and many of its alloys. Subsequently a number of iron alloy systems were surveyed in which the alloying element has a considerable effect on the normal a, to y transformation. The influence of carbon and nickel and/or chromium have already been reported.2,3 At the present time, there appears to be some doubt that this pressure transition is the usual a, to y transition In this study, Fe-Si alloys containing up to 7 wt pct (13 at. pct) Si were chosen for several reasons. To the present, the transition has been found only in iron-base alloys which were originally in the a, phase (bcc). Secondly, the y loop at atmospheric pressure extends to only about 2.5 wt pct Si. If the transition were a, to y, then one might expect a rather drastic pressure effect for alloys containing more than 2.5 wt pct Si. Finally, single crystals of Fe-Si alloys large enough for shock loading studies are readily available thereby making it quite easy to determine the effect of crystal orientation on the transition pressure and on the twinning behavior of the alloy. EXPERIMENTAL PROCEDURE Fe-Si alloys containing up to 7 wt pct Si were produced by normal vacuum casting procedures. Single crystals of Fe-2.9 wt pct Si were purchased from Monocrystals Co., Cleveland, Ohio. The orientations of these crystals were determined and samples cut so that the shock wave would be parallel (to within 1.5 deg) to either the (loo), (Ill), or (112) principal orientations. Three distinct experimental testing techniques were used. First, the pin technique, described elsewhere,4 was used to determine the transition pressure for the polycrystalline alloys as well as for the (111) and (112) orientations of the 2.9 wt pct Si single crystals. Secondly, the recovery studies, described in detail in an earlier paper,2 were used for determining the effect of alloy composition and crystal orientation on the plastic II compression-plastic I rarefaction interaction zone for several specific shock pressures. Finally, measurements of pressures above the two-wave threshold were made on the polycrystalline alloys so that more complete Hugoniot curves could be constructed for this alloy system. The optical techniques described by Rice et al.5 were used to measure the shock and free surface velocities of the samples from which the Hugoniot data were obtained. This method is applicable only in the single wave region, since velocities are obtained from the measured total transit times of the disturbances through measured sample thicknesses.

Jan 1, 1963

By A. F. Melcher

The present paper is a progress report on an investigation of the physical factors of oil and gas and especially of their sands,' such as pore space, size of pores or permeability, retentivity, viscosity of the oil, temperature, pressure, thickness and area of the pay sand, water relations, and capillarity. The purpose is to determine as many of these physical factors as possible, and to ascertain the relations existing, directly or indirectly, between these physical factors and the production of oil and gas. As yet only pore space2 and size of grains of pay sands have been investigated, although an apparatus has been designed to determine the permeability of a sand to oil, water, or gas under definite drops of pressure between the entrance face and exit face of the sample. Messrs. E. W. Shaw, R. Van A. Mills, D. Dale Condit, G. B. Richardson, G. C. Matson, and C. H. Wegemann collected the samples upon which the physical determinations were made. Acknowledgment is made to my colleagues of the United States Geological Survey for many suggestions and criticisms; to Mr. Mills for the production data given of the oil wells from which some of the samples were collected; to Mr. A. W. McCoy of the Empire Gas and Fuel Co., Bartlesville, Okla., for many ideas. Determining Pore Space of Oil and Gas Sands In selecting a method for the determination of pore space, two objects were kept in mind: First, the method must not only be sufficiently

Jan 1, 1921

By C. L. Meyers, J. L. Lytton, T. E. Tietz

The recovery of tensile flow stress of 99.995-pct Al and Al-1 pct Mg alloy was investigated using a fractional recovery parameter. Tensile strainirg was conducted at room temperature, and recovery treatments were made in the range from 80° to 200°C. Equal values of fractional flow stress recovery were found to result in equivalent structural states. Identical recovery treatments were found to produce constant values of fractional flow stress re covery, independent of prestrain. The activation energy for recovery of the 99.995-pct A1 between 80" and 200°C was found to be 23,000 +2000 cal per mole, and the activation energy for the Al-1 pct Mg alloy was 27,500 cal per mole. 1 HE degree of recovery of a cold-worked metal may be studied by measuring the changes which take place in any of a number of properties. Some of the properties which have been used by past investigators include X-ray diffraction phenomena, electrical resistivity, hardness, creep strength, elastic limit, and flow stress. Despite the apparent preponderance of such studies, little is known concerning the effect of recovery on the strength of metals except as deduced from changes in various types of hardness measurements. Furthermore, little information is avail- able concerning the effects which specific solute atoms have on the recovery process. Limited studies have indicated that in some cases solid-solution additions greatly decrease the rate of recovery,' whereas in at least the case of magnesium additions to alluminum an increase in the rate has been reported.2 The purpose of this investigation was to determine the effect of a 1 pct Mg addition on the recovery of high-purity aluminum. Because of the particular interest in the effect of solute additions on the recovery behavior as related to mechanical properties, the degree of recovery was evaluated in terms of tensile flow stress. For the purposes of this study, a recovery process shall be defined as any process, short of recrystallization, whereby the properties, of work-hardened metals tend toward their values ill the unstrained state. EXPERIMENTAL PROCEDURE Test Materials. The materials used in this study were a 99.995-3 A1 and an Al-1 pct Mg alloy made from high-purity base metal. The high-purity aluminum contained the following wt pct impurities: 0.001 pct Cu, 0.002 pct Fe, 0.001 pct Si, and 0.0004 pct Mg. The Pil-1 pct Mg alloy contained 0.001 pct Cu, 0.002 pct Fe, 0.003 pct Si, and 0.99 pct Mg. Both materials were obtained in the form of as-rolled 0.125-in.-thick sheets, from the Alcoa Research Laboratories, New Kensington, Penn. Tensile specimens were cut from these sheets with the longitudinal axis in the rolling direction. Both materials were recrystallized in a molten salt bath; the high-purity aluminum at 450° C for 20 min and

Jan 1, 1962

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

By T. Egleston

FOR a great part of the progress of the world we are indebted to the works of engineers. It is to them that we owe our means of rapid transportation, our canals, our railroads, our bridges, many of our automatic machines, and most of those appliances which, by facili tating or decreasing the amount of human labor to be expended and by utilizing the great forces of nature, have made the present progress of the world possible. Their education is a matter of momentous interest to the whole civilized world. I have, therefore, thought that some discussion of the theory upon which their education should be based would be of interest to this body, and have ventured a few reflections and suggestions upon the subject. The word education, in its original signification, meant the draw ing out of a man what there was in him. In our common schools the practical work of education consists in putting into the brain a larger number of facts than can be retained, which are consequently more or less understood and digested. It ordinarily consists simply of teaching a round of abstractions or facts which when not assim ilated are not only useless to the individual, but generate careless habits of thought and make more or less untruthful, unfaithful or unsuccessful men. In most of our schools a procrustean system is adopted; all are made to advance upon one general plan, the quick being kept back and the slow dragged on at a rate too great for their power of comprehension. Until within a very few years it has been a theory in common school education that the brain alone should be developed, and that little or no attention need be paid to the train-

Jan 1, 1888