Search Documents

By H. C. Fowler, G. B. Shea

MODERN industry's incessant demands for increased operating efficiency and lower costs require that hazards attending all occupations be reduced to a minimum. Reduction of the inevitable losses that result from accidents and injury to the worker is one of the important economic problems confronting industry today and is the basis for the widespread safety movement. Dr. Charles E. Munroe, chief explosive chemist of the U. S. Bureau of Mines, is father of the statement, "The existence of a nuisance is evidence of an economic waste." This pointed expression of the internationally recognized scholar and explosives engineer has a direct relation to the prevention of accidents. Every injury and death in industry is a waste in human endeavor and a lessening of productive gain. Dr. Munroe has aptly paraphrased his previous summation with reference to wastes as follows: "A lost-time accident is evidence of an economic waste." That the economic waste entailed by occupational accidents is chargeable to industry is well substantiated by the fact that all but four states (Mississippi, South Carolina, Florida and Arkansas) now have workingmen's liability and compensation laws.

Jan 1, 1933

By Eugene McAuliffe

AS anthracite is no longer used to a marked extent by the rail- ways of the United States (1,513,000 tons in 1933), that portion of the mining industry engaged in the production of bituminous coal is, and will continue to be, the one chiefly concerned with the future use of its product by the railways. In a period such as the present, when all enter- prise is unsettled, when fundamental principles of industrial management and control are being swept aside or else changed overnight, it is difficult to predict what will happen. The relation between the total production of bituminous coal and the volume consumed by the steam rail- ways of the United States, Classes I,

Jan 1, 1936

By Howard N. Eavenson

AN analysis of the bituminous coal situation by an authority who traces the production, mining, safety, markets and labor trends in comparison with other fuels. BEFORE 1918 the production of coal experienced a steady growth, with slight recessions in ouput in only twelve years (1837, 1841, 1852, 1855, 1861, 1874, 1876, 1889, 1894, 1905, 1909, 1914), and in each of these cases the loss was recovered in the following year and the increase continued. In each decade the output was doubled. Prices, while not high, allowed some profit. In 1918 during World War I, an output of 580 million tons was reached and with the exception of 1923 this total was not again reached until 1942, in World War 11. Losses of output in this period were much greater than ever before; in 1932 the total was 270 million tons less than in 1918 or 1923, and the loss after 1923 was not recovered until 1942. The greatest output was 631 million tons in 1947.

Jan 1, 1950

By Alan M. Bateman

Before World War II we proudly considered that we were the nation of all the world most richly endowed in mineral resources. We knew it was no accident that those countries abundantly supplied with mineral resources became the great manufacturing nations, and the politically and militarily strong ones; and that our own great industrial cities sprang up where coal and iron met. We all reallized, especially we of the mining profession, that the energy of fuels and the solidity of metals spelled industrial growth and in turn industrial might and that other nations came to regard mineral self-sufficiency as one of the chief goalsof economic nationalism.

Jan 1, 1949

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 Scott Turner

MY YEAR OF SERVICE as president of the A.I.M.E. came at a time when the mineral industry had suffered severely because of disturbed economic conditions throughout the world. The Institute, an integral part of this industry, had been similarly affected. Its membership and revenues decreased; it was confronted by problems of retrenchment at a time when its vigorous operation was especially important to its members, of some moment to the mining industry, and of value to the nation. Throughout the last year, the recession of activity in our industry continued with slight abatement. Your Board accordingly exercised such economy within the Institute as was possible without impairment of essential functions. It endeavored to aid in sustaining the morale of members, their sense of professional unity, and their interest in maintaining research and the interchange of scientific and technologic data upon which the progress of our industry depends. Effort was made to assist in the difficult task of finding employment for needy members; our endeavors have met with some success.

Jan 1, 1933

By W. B. Plank

RETURNS already received from a current survey of the enrolment of students in the mineral technology schools indicate a degree of activity and prosperity in those schools never before equalled. The returns are as yet too meager for accurate analysis, but those at hand point LO considerable increase in the metallurgical and petroleum engineering groups, and indicate that the total of 5011 two years ago in the United States schools will be substantially increased. Generally speaking, the enrolment is not only maximum in quantity but optimum in quality. Better income has sent the boys back to school, but the improved employment conditions have somewhat reduced the number of graduate students. Laboratories are commonly filled to capacity, in some instances overcrowded. Increased enrolment of foreign students from both Canada and South America is noticeable.

Jan 1, 1937

By L. Leibowitz, M. G. Chasanov, L. W. Mishler

A drop calorimeter system is described for use in measuring enthalpies to 3600°K. Data are presented for tungsten between 2800" and 3600°K. The enthalpy of tungsten in cal per mole between 2000° and 3600°K can be represented by the equation HºT- Hº298 = - 1.7622 X 103 + 5.7772T + 8.9861 where T is in degrees Kelvin. A tabulation of com -puted values is presented for heat capacity, entropy, and free energy function. A drop calorimeter has been constructed to carry out enthalpy measurements at temperatures to 3600°K. Samples are heated by induction1 and dropped into a commercial adiabatic calorimeter, modified for this purpose. The experimental temperature is limited by the melting point of container materials and compatibility of the container and its contents. Several high-temperature drop calorimeters have been described in the literature1-5 but none has been used at temperatures as high as those in the present work; our measurements of the enthalpy of tungsten range from 2800" to 3600°K. DESCRIPTION OF EQUIPMENT An overall schematic view of the equipment is shown in Fig. 1. Power for the induction coil is supplied by a 25-kw 250 kHz Ther-Monic generator coupled to an iron core RF transformer. The Sample capsule is suspended in the work coil by 10-mil diam tungsten wires which are wrapped around a horizontal 5-mil diam tungsten wire. The horizontal suspension wire is clamped between two massive copper electrodes which are fixed in an x-y motion device that allows adjustment of the position of the heated capsule from outside the vacuum chamber. The copper electrodes are connected by flexible copper straps to a 1250-joule (5 kv, 100 pfarad) condenser bank. When it is desired to release the capsule, the condensers are discharged through the horizontal suspension wire causing it to vaporize rapidly. Very reliable and precise release of the capsule is achieved in this manner. Experiments have shown that no heat correction is required for this discharge energy. As part of the temperature measuring system, two prism holders have been incorporated in the apparatus. The upper prism holder is in the main vacuum chamber itself, whereas the lower one is in a side arm attached to the drop tube below the gate valve. The upper prism is mounted on a rotary vacuum feed-through, and may be moved under a protective shield when not in use. This prevents deposition of vapors on the prism surfaces when temperature measurements are not being made. Similarly, the lower prism is mounted on a push-pull vacuum feed-through, and when not in use may be pulled into its side tube. The prism mountings are fitted with guides and stops so that they may be moved precisely into the desired position. The aim throughout is to minimize the time the prisms are exposed to vapors from the hot samples. At the high temperatures reported in this paper, only the lower prism was used. The upper prism holder in these cases was fitted with an additional radiation shield. By using a prism and viewport, the lower surface of the samples can be observed by an optical pyrometer. The measurements discussed in this paper were obtained with a Leeds and Northrup 8622-C-S series manual pyrometer which is estimated to be accurate to 0.5 pct. Pyrometer calibrations and prism and window corrections were carried out in the conventional manner6 using tungsten strip lamps calibrated by the National Physical Laboratory, Teddington, England. Prism corrections were rechecked after each use. All work to date has been done in vacuum, and no measurable change has been observed in the prism correction below -2300°K for the upper prism and below -2800°K for the lower one. The total time of exposure of the prisms is about 50 sec per run. At high temperature, the final temperature reading is corrected by using the final A value for the prism; see Ref. 6 for details of this procedure. The calorimeter is a modified Parr Instrument Co. (Moline, lll.), Series 1230 adiabatic calorimeter with automatic jacket control. Other authors5 have used a similar calorimeter with good results. The calorimeter jacket cover and calorimeter cover are attached to the drop tube which contains a radiation shield. This shield is a gold-plated copper disc which can be operated manually from outside the calorimeter. The receiver is attached below the radiation shield and is lined with tungsten. In a typical experiment, the calorimeter and its jacket water temperatures were adjusted to 0.000°K temperature difference. The sample was allowed to equilibrate in the furnace at the desired temperature for about 20 min. The initial calorimeter temperature was then recorded, the sample dropped, and appropriate shutters closed. After about 3 min, the drop tube and receiver were filled with helium to 60 torr. The final calorimeter temperature was recorded after it had remained constant over a 5-min period. The equilibration time in the calorimeter was about 25 min. Thermistor probes are used to operate a hot and cold water supply system to maintain the jacket temperature equal to the calorimeter temperature. For actual measurements of the calorimeter temperatures, a quartz thermometer was used (Hewlett Packard Dymec Thermometer, Model #2801A). This thermome-

Jan 1, 1970

By R. S. Archibald

THE Blueberry mine is about 10 miles west of Ishpeming, Marquette County, Michigan. The property consists of about 2000 acres in sets. 3, 4 and 5, T. 47, N.R. 28W. and sets. 32, 33 and 34, T. 48, N.R. 28W., and, excepting one intervening 80-acre tract, contains the iron formation for a length of about 2 1/4 miles. The property is traversed by State Highway M-28 and is served by three railways, the Chicago & Northwestern, the Duluth, South Shore & Atlantic, and the Lake Superior & Ishpeming. The Northwestern transports the ore to a dock at Escanaba; the other railways, to Mar¬quette. Ore for Chicago goes via Escanaba and that for Lower Lake ports, as Detroit, Cleveland, and Buffalo, via Marquette.

Jan 1, 1935

By Krahmann, Rudolf

THE following is an account of a survey undertaken to test the possibility of outlining a kimberlite pipe by magnetouietric methods. Kimberlite is a basic igneous rock closely related to melilite-basalt or alnoite, which occurs either in the form of volcanic plugs or as dikes intruded into rocks of various types and geological ages up to and includ¬ing the Lower Cretaceous. The famous diamond mines of South Africa are all in kimberlite pipes and these pipes are probably the original source as well of the vast alluvial deposits found in various parts of the country. The pipe chosen for this experiment is one that ' occurs on the farm Goedgevonden No. 20, about sixteen miles north of the village of Klerksdorp and ninety miles southwest of Johannesburg. Some prospecting has been done on this pipe and diamonds were produced from it but not in paying quantities. The magnetometric survey was made in June, 1932, by R. Krahmann and H. Wallisch and the results are shown on the accompanying plan. On the plan are shown also the boundaries of the pipe as exposed at the surface and details in regard to the surrounding foundations. These are taken from a geological survey made at a later date by W. Beetz, of Johannesburg.

Jan 1, 1935

By Oliver Bololes

UNDER the able leadership of Samuel H. Dolbear, the Committee on Nonmetallic Minerals furnished a program of sixteen papers comprising three sessions. An outstanding accomplishment in technology presented at the first session by Benjamin L. Miller and C. H. Breerwood is the application of flotation to the purification of limestone used in cement manufacture. In place of selective quarrying to provide high-grade raw material, the quarry-run stone is pulverized and treated in froth flotation cells for removal of free silica and mica. Some advantages are cheaper quarrying, more complete utilization of quarry rock, avoidance of purchasing high calcium stone, lower fuel cost and improvement in the finished cement. Paul M. Tyler presented the general subject of milling methods as applied to nonmetal lies. He pointed out the importance of some of the more recent refinements in ore dressing, and urged the need of a wider appreciation of their possibilities. The gypsum industry of Canada was described by L. H. Cole. Crystal growth during the setting process was illustrated by moving pictures. The Coastal Plain and interior salt

Jan 1, 1935

Henry LOUIS, London, England (communication to the Secretary) : Prof. Richards's paper has impressed me as highly valuable. Without entering upon any discussion of it as careful and thorough as it deserves, I venture to mention one or two points which a perusal of it has recalled to my mind in connection with my own study and practice of ore-dressing. I always mentally divide jigging into two phases: 1. A particle at rest on the jig-bed is lifted and carried upwards by the rising current of water, at an increasing velocity, which tends to a maximum. When the upward current is stopped, the particle continues to rise with rapidly diminishing velocity until it comes to rest. This completes the first phase. 2. In the second phase, the particle falls from its position of rest with an increasing velocity which tends again to a maximum, and continues to fall until the rising current of water has reduced its velocity to zero. This completes the second phase. The second phase will evidently be greatly modified by the effect of suction, as Prof. Richards shows; but I do not see that his experiments very clearly imitate the action of the second phase. And the brief intervals at the end of each phase, when the mineral particle, by reason of its acquired velocity, is still moving, though in opposition to the water-current, yet remain to be investigated. I feel especially, in Prof. Richards's paper, a difficulty which I have felt with regard to all similar previous investigations, namely, that the experiments deal with particles falling a long distance, when the velocity becomes uniform. I question whether this uniform maximum velocity is attained in actual jigging-practice. If so, it is certainly for a comparatively very small proportion only of each stroke. It seems to me that an investigation like that of Prof. Richards, but confined to the first 6 or 8 inches of fall only, and carried out with suitably delicate recording-apparatus, is what we

Jan 1, 1895

By J. W. Spretnak, J. N. Cordea

The gain boundary relaxation in high-purity aluminum, nickel, copper, and silver was studied by means of a low-frequency torsion pendulum. Both internal friction and creep at constant stress tests were conducted. A lognormal distribution in relaxation times was found to account for the relatively wide experimental internal friction peaks and the gradual relaxation behavior during the creep tests. This distribution was separated further into a lognormal distribution of relaxation time constants and a normal distribution in activation energies. A spread of up to ±6 kcal per mole in the activation energies accounted for the major part of the distribution. A "double-peak" internal friction phenomenon was observed in silver. The activation energies in kcal per mole derived from the grain boundary relaxation phenomena are 34.5 for aluminum, 73.5 for nickel, 31.5 for copper, and 41.5 for silver. It was found that the rain boundary relaxation strength in these metals increases with the reported stacking-fault energy. GRAIN boundary relaxation phenomena have been observed in a large number of polycrystalline metals and alloys. Numerous investigations have been conducted to study the structure of the grain boundary through this relaxation process. One of the first investigators was Ke1-4 who observed that the activation energy for grain boundary relaxation in aluminum, a brass, and a iron was about the same as that for volume diffusion. He concluded that the grain boundary behaved as if it were a thin liquid layer with neighboring grains sliding over one another. Leak5 conducted experiments on iron of a higher purity and observed that the grain boundary activation energy is comparable with that of grain boundary diffusion. He suggested that, in metals where this relationship holds, the damping may be caused by a reversible migration of grain boundaries into adjoining grains. Nowick6 has presented an interesting view of inter-facial relaxation with his "sphere of relaxation" model. A relaxed interface is represented as one where the shear stress is greater than the normal value along the edges and zero in the interior of the interface. The region of the stress relaxation is pictured as a sphere surrounding the interface. From his calculations Nowick concluded that the slip along an interface is directly proportional to its length. Therefore, the time of relaxation, T, depends on the size of the relaxation interface. This means that in the Arrhenius relationship, t = TO exp[H/RT], valid for atom movements, the relaxation time T is predicted to be proportional to the grain diameter through the pre-exponential term, TO. Since the internal friction can be given as Q-1 = ?j wt/(1 + w2r2), where ?J is the relaxation strength and w is the angular frequency, an increase in grain size at a constant frequency will shift the peak to a higher temperature. A great deal of work has been done to determine the exact relationship between the internal friction and grain size.1,5,7,8 In metals, the grain boundary peaks are found to be lower and broader than predicted theoretically.' The above model can explain this by a distribution in the size of the interface areas, represented by a distribution in the parameter tO, and an overlap of spheres of relaxation, represented by a distribution in activation energies. Both these phenomena result in an over-all distribution in the relaxation time, which could affect the internal friction peak height, breadth, and also position. This relationship between the experimental data and theoretical calculations appears very promising in the study of interfacial relaxation mechanisms. THEORY A lognormal distribution in t can sometimes be used to adequately describe the spectrum of relaxation times governing an anelastic relaxation. wiechert9 originally suggested such a distribution to explain the elastic after-effect in solids. This choice is particularly applicable to grain boundary relaxation when considering Saltykov's work.'' He found a lognormal distribution in the grain sizes within a metal. Recently Nowick and Berry11 have introduced a log-normal distribution in T into the theoretical internal friction equations. The form of the distribution function is where z = In(r/rm), and Tm is the mean value of t. The parameter ß is a measure of the distribution and is the half-width of the distribution when is l/e of its maximum, IC/(O). Nowick and Berry have described the methods to obtain the parameters Tm, ß, and ?,J from experimental internal friction and creep test data. In the idealized case, where only one relaxation event occurs with one relaxation time, only ?J and T are necessary to completely describe the event, and 0 = 0. For the broader internal friction curves 6 is some positive number greater than zero. The larger the 6, the greater is the half-width of the distribution in In t.

Jan 1, 1967

By P. K. STRONG

AS an evidence of the fact that mines safety is not being neglected even in the remote district of the Philippines, a short account is appended of the organization and activities of the Mambulao-Paracale District First Aid and Mine, Rescue Association, whose headquarters are at Jose Panganiban Cam, Norte P. I. The second annual miner?s safety celebration which is sponsored by the Association was held in Paracale on Sept. 2, 1940. The event is the big occasion of the year when the thousands of employees of the mines in the district meet to compete for prizes and has become a great social function as well.=

Jan 1, 1941

By A. Blake Caldwell

Tyrone-a complete mining and concentrating facility built by Phelps Dodge Corp.-straddles the Continental Divide where surface water on either side flows in opposite directions although all water is taken from and returned on the northwest side of the Divide. At the outset, Tyrone was saddled with a problem of an adequate water supply, and the Gila River some 23 miles distant appeared to be the logical source. This in itself presented a major obstacle to Phelps Dodge because of the distance water had to be pumped and because of an adverse head which had to be overcome between the Gila River and the two 4-million-gal-capacity terminal water supply tanks at the mill. Having acquired water rights on the Gila River and in order to control the seasonal fluctuations in water volume, the company built the Bill Evans, off stream, earth-filled dam. This reservoir will contain 2100 acre-ft of water when full and it was constructed by the Hamilton Construction Co. for Phelps Dodge. The dam impounds fresh water for the Tyrone plant's use and four vertical turbine pumps (4500 gpm each) lift the water 275 ft from the Gila River into the reservoir. Since construction, Phelps Dodge has optioned the lake to the New Mexico State Game Commission for recreational purposes. In addition to the lake, land around the reservoir has been optioned to the State Game Commission for public use. The lake has already been stocked with trout and by next summer some keepers should be available for the taking.

Jan 12, 1969

By AIME AIME

A REQUEST for information as to the details of activities of the Engineering Council was made by the Joint Conference Committee for the benefit of the new American Engineering Council. , This request was complied with, and the scheduled reply so succinctly sets forth the activities of the old Council as well as the scope of possible activities of ,the new Council, about whose efforts there has been much discussion, .that it' is given herewith in full, except the 'budget which is summarized.

Jan 1, 1920

By A. B. Parsons

LECTURE, it appears, is a discourse that is supposed to be instructive. I am quite sure that you will derive no instruction from what I have to say. I will be satisfied if my remarks provoke thought along one or two mental paths that have not been traveled so fre¬quently as to be devoid of interest. I have no particular message apropos of professional engineers or professional engineering, and any conclusions that I may seem to reach will be purely tentative and incidental. Probably at times you have wondered, in a casual way at least, why so many people who are not, never have been, and never will be engineers, want to use the title. For example, I recently received a communication from a life insurance broker or salesman, whose chaste letterhead bore the legend "Estate Engineer." He was perfectly serious about it, as is also the expert accountant who assumes the imposing name of cost-analysis engineer. Dozens of equally amazing titles might be cited. Then there is that class of individuals who have been engineers, in the true sense of the word; who have gone into some other kind of occupation; but who cling tenaciously to the name engineer, usually prefixing some word or other which at once gives them away by telling what their work really is. For example, we have such pseudomorphs as the management engineer, and the sales engineer. It is quite evident that engineer is a word to conjure with. Evidently both the man who appro¬priates the designation without any justification and the ex-engineer who persists in calling himself an engineer even after he has abandoned engineer-

Jan 1, 1933

By F. R. Brotzen, D. L. Davidson

ALTHOUGH much effort has been devoted to the problem, the nature of plastic flow in bcc metals is still not fully understood. Some of the difficulties encountered stem from the scarcity of information on orientation effects and the uncertainty as to the glide system in these metals. In an attempt to provide some of this information, the present investigation was carried out, using zone-refined molybdenum single crystals deformed in tension and in direct shear. Considerable evidence exists to indicate that the primary slip system for molybdenum is (110) <111>.1,2 Figs. 1 and 2 indicate that this is, indeed, the case for direct shear at room temperature (see Ref. 3 for a description of the shear-testing equipment and procedure). Moreover, from Fig. 2, the shear stress on the (123) is lower than that on the (112). This would be the case if, as has been suggested,4,5 slip on these two planes is in reality com-

Jan 1, 1965

By J. W. Buch

IN THE FIELD of track haulage, interest has seemed to center on the question of larger mine cars both for handling material from loading point to shaft bottom or surface, and for shuttle service. Saving of time in car changing is obvious if larger cars are used. In addition, shorter trips result where car transportation is from face to opening without transfer. This also brings about side-track and equipment savings. Track shuttle service, using large automatic-dump cars (10 tons) between loading machines and trip loading point, has been a satisfactory solution for the operator who mechanizes a working mine regularly equipped with a large number of small mine cars. This development in track shuttle haulage, has made track installation and maintenance increasingly important, requiring closer supervision.

Jan 1, 1942

By Kenneth A. Moon

An exact statistical treatment of a one-dimensional model is used as a basis for evoluating the reliability of certain simplified expressions for the activity of the solute in interstitial solutions, including one obtained from the exact expression by setting the repulsive interaction equal to infinity. The latter approximation is found to be satisfactory at low and moderate concentration if the repulsive interaction is large, even though not infinite. A similar expression (identical if the co-odination number is two) is derived from the quasichemical expression of Lacher, and is recommended as the best available expression for the excess configurational entropy of interstitial solutions with excluded sites. Some reasonable models are discussed, and the nature of the saturated solutions is determined by inspection. Some of the models reduce to the one -dimensional case. An analysis is given of the excess partial entropy of hydrogen in V-H; Nb-H; and To-H solutions. MOST treatments of the statistical thermodynamics of interstitial solid solutions have followed the classic paper1 of Lacher in making the simplifying assumption that the configurational entropy of the solution is ideal. However, it is becoming increasingly apparent that there are many interstitial solutions with very large so lute-solute repulsions, and for these the assumption of ideal entropy is not valid or useful. It is important to realize that with substitutional solutions large repulsions between the component atoms must lead to phase separation, whereas in interstitial solutions the free energy of the solution is not drastically increased by large solute-solute repulsions until intrinsic saturation is reached at the concentration where further solute would be forced to enter a site in which it would experience the repulsive effect of one or more solute atoms already present. In the limiting case of an infinitely large repulsive interaction, the excess free energy would be attributable entirely to excess entropy, the enthalpy of mixing being zero. AS will be shown below, even if the repulsions are less than infinite, a treatment based on an assumption of infinite repulsions may be very satisfactory up to moderately high concentrations of the interstitial component. Often in solutions where large repulsive interactions exist, there are also small interactions — often attractive—between solute atoms in configurations other than that corresponding to the large repulsion. In such cases the excess free energy will consist of an excess entropy term attributable to the large repulsive interactions, and an enthalpy term corresponding to the other small interactions. Nomenclature to differentiate succinctly between important cases would be a convenience. In this paper the nomenclature shown in Table I will be used. In Table I, and in the preceeding discussion, excess quantities are defined in terms of standard states which are pure solid solvent and pure (possibly hypothetical) solid saturated phase of the structure in question. In practice, it is more convenient to choose the interstitial element as a component, and its conventional standard state. This will add a composition-independent term to the excess entropy and the enthalpy. The earliest paper known to the present author which treats the thermodynamics of athermal interstitial solutions was given by schei12 in 1951, but the statistical derivations in that paper are open to criticism. Speiser and Spretnak were the first to give a correct statistical treatment,3 limited, however, to concentrations sufficiently low that the number of empty sites excluded from occupancy by more than one filled site is negligible. The purpose of the present paper is to extend the statistical treatment to more concentrated solutions, and to examine the magnitude of the errors introduced by assuming that the repulsive interactions are infinite when in fact they must be finite. THE QUASICHEMICAL APPROXIMATION Fortunately, a standard method already exists for taking into account the effect of large interactions upon the entropy of mixing. This is the quasi-chemical method, in which the probability of existence of a given pair of solute atoms in a certain proximate configuration is assumed to be proportional to exp(-w/kT), where w is the energy increase of the solution when the two atoms are moved from isolated locations in the solution to the configuration in question. A quasichemical treatment of interstitial solutions was given in 1937 in a widely neglected paper by Lacher.4 The result comes out

Jan 1, 1963