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By Jamie Deuel

The a ad on Connection" For the purpose of this paper, we will concentrate on the ubquitous radon gas as the principle, low-level radiation effect from uranium tailings piles. Standards are also proposed for gamma radiations but, by most accounts, this is much less of a low level problem than is radon. I am also aware of some just completed research at Oak Ridge National Laboratories that suggest polonium may be a major concern in tailings, but those data are preliminary at this time. What is radon gas? In the first place it is not a gas in the accepted sense in that it has no driving pressure head. It might prove a more convenient description to call it radon vapor. Radon vapor, then, is 7-1/2 times heavier than air. Radiologically, it is an alpha emitter which means it spontaneously gives off high ionizing potential but low penetrating power particles. In fact, the alpha particle has such low penetrating power that this sheet of paper will completely shield a person. The problem, though, is breathing the radon decay products, called radon daughters. If radon daughter products are ingested into the lungs, their alpha emissions may cause cancer. The principle carcinoma associated with breathing radon, or more basically, associated with radiological effects is oat cell car- cinoma of the undifferentiated mall cell type. Radon has a 3.8 day half life which means in less than four days half of its initial radioactivity has decayed away. In less than a month it essentially becomes inert or non-radioactive. The Tailings Situation The NRC, in its April 1979 Generic Environmental Impact Statement

Jan 1, 1983

By F. C. Miller

THE metallurgical fuel of Colorado, Utah, and New Mexico has been a very tardy member in the caravan of western industrial progress. The history of western coke has naturally been closely related to the development of the metallurgy of iron and steel and the precious metals, in the State of Colorado. It was at Leadville, with a population of 300 in 1877, that the Sentinel was published by Richard S. Allen. The Sentinel gave very full accounts of the various mineral discoveries at the new town of Leadville, which found their, way to the more widely circulated journals of the East, and attracted the attention of many people. At the close of 1878, a census showed a total of 5040 persons. The first smelter was established in 1877, at Malta, two miles from Leadville, by A. R. Meyer, but was not successful. It was succeeded by the Harrison Reduction Works, in 1878. The La Plata began with one furnace in June, 1878, and in 1879 had four furnaces in active operation. These furnaces used charcoal for fuel, and, because of hot tops, suffered a tremendous loss in lead and silver. This difficulty was overcome by the erection of 50 single-bank 10-ft. beehive ovens at Crested Butte, Colo., in 1880. The slack coal sent to these ovens was very pure, and yielded a coke carrying as little as 4.5 per cent. ash. Among the pioneers in the Leadville district were Grant, Eddy, James, Billings, Eiler, and Dickson. To these men the West owes the present expansion of its mining industry, and the erection of metallurgical processes for the treatment of precious metals.

Jan 8, 1918

By Charles R. Keyes

During the past decade the genesis of the lead- and zincdeposits of the Mississippi valley has received special attention from many distinguished observers. But their united egorts, instead of settling all disputed questions, have, in many respects, involl-ed the general problem in greater uncertainty than would be thought possible under the circumstances. In place of the harmony of opinion that might be expected, there is unexpected disagreement, largely due to the fact that, instead of giving attention to a possible multiplicity of ore-producing conditions among the different deposits, the attempt has been made to bring all deposits under a single genetic head. To a new observer of the lead- and zinc-deposits of the Mississippi valley, it appears at the outset that all the deposits cannot possibly have had the same genesis. In fact, different modes of origin have been often asserted for the ore-bodies, but the difficulty has been that each writer has referred them either all to one category or all to another, and no intermediate ground has been considered possible. Such a position now appears to be clearly untenable. The opinion that, in the deposits of the region under consideration, the ore-materials represent original depositions, made at the time the rocks themselves were formed, is no longer held by any authority, and therefore need not be considered here. Of late years, a number of writers have attempted to account for the presence of the lead- and zinc-ores on the hypothesis that the metallic materials arose in heated solutions from the

Jan 1, 1902

WHEN Magma Copper Company in 1952 set about finding $100,000,000 to finance the project of developing and equipping the property of its lusty progeny, the San Manuel Copper Corporation, A. J. McNab, president and guiding genius for both companies (and incidentally a mining engineer by profession), determined that he would avoid the mistake frequently made in such circumstances, of underestimating the cost, and thereby running short of funds before the job was completed. The fear that this might happen was one of the reasons why insurance companies, one potent source of "big" money, were reluctant to finance the enterprise. How, they asked themselves, would Magma, a relatively small company, get additional money in such a contingency? Insurance officials' thumbs were turned down. Conditions Imposed by R.F.C. The upshot was the negotiation by Mr. McNab for San Manuel of a contract with the Reconstruction Finance Corporation, dated July 10, 1952, whereby needed monies in amount up to $94,000,000 would be advanced as a loan, bearing 5 per cent interest. Arrangements were made for the separate financing of the new $10,000,000 town, needed for the project, through the Del E. Webb Construction Company of Phoenix, Arizona, and M.O.W. Homes, Incorporated, of Los Angeles. Thus the $94,000,000 drawing account was believed ample to provide for building the railroad, the mine plant, the concentrator, and the smelter, as well as for the underground development of the mine needed to start production. As a matter of fact, only

Jan 1, 1957

By Robert Linton

The Sierra Consolidated Mines Co., organized in 1909, owns, together with other holdings, practically all of the productive mineral area in the Ocampo district. Lying within this area are 15 mines, large and small, that hid previously been worked and appear to have yielded, since the discovery of the camp, about 100 years ago, bullion of a total value of over $50,000,000. The deepest mine, the Santa Juliana, had been worked to 1,100 ft. below the outcrop. The reopening of the mines involved, first, extensive and thorough development to open up the known ore shoots at greater depth and explore the ledges for additional shoots, and, second, a revision of existing equipment and methods, so as to increase output and reduce cost of production. This paper will give some account of the metallurgical treatment and a description of the new mill to be built at El Salto. The Ore The ore is practically all argentite, Ag2S, with some associated gold, and carried in a siliceous gangue. The typical ledge matter is an ande-sitic breccia cemented with quartz, or quartz stockwork in andesite.l The proportion by weight of silver to gold averages about 60 to 1. The silver sulphides occur ordinarily in rather fine. dissemination, sometimes not being easily discernible with the naked eye, even in ores of very good grade. The ledges also contain considerable pyrites, which as a rule is barren. "Bronce" is the local term applied to such barren pyrites, and "Pasta" to such as carries values.

Jan 1, 1915

By Albert F. J. Bordeaux

This paper briefly describes the general outline of cyaniding silver-ores in Mexico, with special reference to personal experiments made in the Temascaltepec district. The most important papers on the subject deal with cyaniding gold-silver ores, the gold predominating in value, so that the treatment is nearly the same as for gold-ores, the losses of silver being considered of little importance. I describe here the treatment of silver-gold ores containing very little gold, which is more general in Mexico than elsewhere. The cyanide treatment, which was so successfully applied to gold-ores, did not succeed immediately with silver-ores on account of their varying composition. Gold occurs in nature usually in the native state, while silver occurs generally in combination with sulphur (argentite), and various combinations of sulphur, antimony, and arsenic. In former times there mas a complete difference in the treatment of gold-ores and silver-ores. Amalgamation, which was successful with gold-ores, was generally inadequate with silver-ores. The usual treatment in Mexico for silver was the patio process, the theory of which was satisfactorily explained only quite recently by Mr. Ortega and others. General Outline of the Cyanide Treatment. The general tendency of the present practice is to slime the silver-ore as much as possible, and in order to obtain a higher efficiency, with less loss of cyanide, and greater speed, the following lines are observed: 1. Crushing by stamps with 30- or 40-mesh screens, then crushing by Huntington or Chilean mills, through 60- or 80-mesh screens. 2. Concentration upon vanners.

Jan 1, 1910

By Giovanni Barla

In engineering analyses, rock is frequently treated as a homogeneous, isotropic, and linearly elastic medium. However, rock material exhibits, in most cases, physical nonlinearity, time-dependency, and anisotropy. In some instances, anelasticity due to nonmechanical effects, such as density and temperature changes, must also be taken into account. The influence of these different anomalies in the physical behavior of a rock material is often neglected. An estimate of the discrepancies which are introduced when classical theory of elasticity is used is consequently required. The easiest theoretical path by which these discrepancies can be analyzed is to vary the constitutive equations of the rock material. The constitutive equations, representing various physical experiences with different types of media, define a class of ideal substances. Assuming different constitutive equations for the description of the rock physical behavior, one can establish a sensitivity analysis to determine how much information is contained in elastic theory for reliable design purposes. The method may be applied also using numerical techniques (e.g., finite element or finite differences) which, because of the nature of the formulation, require one to assume in each case the rock constitutive equations. Theoretical and experimental work is needed to be able to perform such analyses with confidence. Adequate and practical procedures for the determination of the material functions which enter the various constitutive equations must be established. This paper presents such an attempt with respect to the simulation of some behavior patterns of rock material. It is felt worthwhile to stimulate activity in this field and it is hoped to contribute to this objective.

Jan 1, 1970

By P. Somasundaran, D. R. Nagaraj

Based on our finding that commercial copper chelating solvent extractants such as LIX65NR and LIX63R are excellent collectors for copper minerals, a detailed study was made using several water-soluble chelating agents belonging to the class of aromatic hydroxyoximes and having a gradual structural variation. A basic study of the system salicylaldoximetenorite was also carried out. Microflotation tests as a function of concentration of oxime, pH, addition of copper, etc., using oxidic copper minerals such as chrysocolla and tenorite, and batch laboratory flotation tests using synthetic mixtures of quartz and oxidic copper minerals were carried out. The results have demonstrated that the hydroxyoximes studied have comparable collector property, and in all cases the oxime was found to be partitioned between the mineral surface and the copper in the bulk aqueous phase in the form of a bulk copper chelate. The occurrence of the latter could be accounted for by formation in the bulk phase of a chelate between oxime and copper released from the mineral and/or by the detachment of the surface chelate. The role of surface and bulk chelates in flotation is discussed based on the results of partitioning of chelating agent into bulk and surface chelates in the salicylaldoxime-tenorite system. The effect of structural aspects such as isomerism and substitution in the molecule on the collector property of the oximes is also discussed. Substitution on oximic carbon by alkyl groups is found to promote collector activity. Only the anti-isomer has the ability to collect.

Jan 1, 1982

Discussion of the paper of C. A. HEBERLEIN, presented at the New York meeting. February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 497 to 504. H. D. PALLISTER, State College, Pa. (communication to the Secretary).-Mr. Heberlein gives some valuable information concerning a branch of mining and metallurgy which has been neglected during the last few years. His results with fine grinding and Deister tables suggest the possibility of the mining and concentration of a number of low-grade cinnabar deposits. Can Mr. Heberlein give us some idea as to the loss of quicksilver during this concentration? The advances in the metallurgy of quicksilver have been few and far between in recent years. Most miners prefer to go on in the old way with the Scott furnace and the large brick condensers. The large brick condensers are expensive to build and to keep in repair, and on account of the thick walls are extremely slow in cooling the gases; and further, the joints between the bricks offer passages for the quicksilver vapors unless great care is used in building the condensers.. The escape of vapor at the top of the furnace is another source of loss and I see the people at the Oceanic mine have overcome this in a very ingenious way. I recently returned from the Terlingua quicksilver district of Texas, where the only operating company, the Chisos Mining Co., is operating a 20-ton furnace of the Scott type. They had considerable difficulty with getting a good extraction, clue to too high heating in the furnace with its .resulting diffIculties. Recently they have been running with ashpit and fire doors closed and have been able to keep the heat lower, thus getting much better results and practically verifying the results obtained at the Oceanic mine.

Jan 5, 1915

By Frank Firmstone

IN 1871, two furnaces at the Glendon Iron Works, which had been blown out on account of the "coal strike," were altered from the open-top plan with side flues for collecting the gas, to closed tops with cup and cone. In one furnace the suppression of the side flues permitted a considerable alteration in the profile, but in the other (No. 5) no change in this respect was made; the side flues were simply bricked up and new ones cut through the sides close to the top. This furnace was in blast over four years, and we can, therefore, form a pretty good idea of the effect of the alterations on the furnace process. The principal dimensions are; Height 72'; greatest diameter, 18'; diameter at tuyeres, 8'; diameter of top, 10'; diameter at stock line (point at which the top of the materials is kept), 11'; cubic contents, 11,900 cubic feet. The table below shows the average results for periods of twenty-six weeks each. 1st, of the open-topped furnace; 2d, of the furnace with the first charger used, which was an ordinary cup and cone (diameter of cone 5' 2") 3d, with the charger used ever since, a "double" cone 7' 5" diameter outside, having a central opening 3' in diameter. The diagram (Plate II) shows the daily variations, in the grade of the irons for the same periods.* * In calculating the average grade of each day's iron, each twelve hours was taken by itself whenever more than two kinds of iron were made in the 24 hours, and the diagram drawn accordingly. By counting, it will be found that there were more such days with the single cone than with the "double" cone, and more with this than with the open top. † Anthracite.

Jan 1, 1876

By Arthur C. Spencer

In extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,' it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity, applied to an elastic brittle mass offering strung resistance to deformation, produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45' to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45. This general conclusion, resting upon analytical mechanics, is completely supported by the results obtained by DaubrBe2 in experiments upon the deformation of wax and resin prisms under compression. Let us then first consider one of Daubree's diagrams. In the case illustrated in Fig. 1, four sets of fractures in two approximately right-angled pairs (that is to say, in conjugate sets) were produced by endwise compression of a square cross-sectioned prism. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45o. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism, and place it between two fixed and

Jan 1, 1906

By T. H. Aldrich

This paper is intended only to give a preliminary account of experiments made, and conclusions reached, concerning the treatment of certain refractory low-grade gold-ores, the profitable reduction of which may furnish a useful guide to the solution of similar mining and metallurgical problems, not only in the gold-bearing belt of the Southern United States, but perhaps in other regions also. It must be regarded as simply a " report of progress," preceding a more elaborate and conclusive report of regular practice. The mines of the Hillabee Gold Mining Co. are located upon what is generally known locally as Hog Mountain, on the northern edge of Tallapoosa county, Ala., about 15 miles from Goodwater and 14 miles from Alexander City, stations on the Central of Georgia railway. Gold has been known since 1839 to exist on this property, where it was discovered in that year by a man named Johnston. The property was worked for placer-gold by the old miners, and there are now the remains of four attempts to operate it by stamp-mill and plate-amalgamation. The present owners purchasid it in 1896, and since that time they have experimented at frequent intervals, in order to devise a process that would satisfactorily recover the gold. In 1903 regular operations were begun. Geologically, the mountain consists of an intrusion of what has been pronounced true granite in altered sedimentary slates. The cooling of the granite produced shrinkage-cracks, which have become veins. There is considerable question as to the period of the slate formation; but it is undoubtedly, in my opinion, of Carboniferous age. The veins, about 50 in number, strike N. 60° to 80° E.; dip approximately 65' from the horizontal; vary from a few inches to 25 ft. (being in gen-

Jan 1, 1909

By J. E. Willson, N. K. Bohidar

An evaluation of internal stress distribution based on photoelastic studies and destructive testing of simulation models shows that pillar failure is a function of the internal stress distribution, and that stability can be changed by altering the internal stress pattern. Induced stresses in three-dimensional epoxy disks subjected to uniaxial forces were evaluated by photoelastic studies. Stress profiles across different sections perpendicular to the loading direction revealed two maxima for each profile. Based on the stress distribution for the entire column, an attempt was made to explain pillar spalling and the hour glass pattern of failure in a mine pillar. For maximum stability and optimum design of mine pillars, it is necessary to consider the external forces, the nature and distribution of induced stresses and the characteristics of the pillar material as determined in the laboratory. This paper summarizes the research done by N. K. Bohidarl and Ben L. seegrniller2 as partial fulfilment of the requirement for Master of Science degree in Mining Engineering, University of Utah. It is an evaluation of a study to determine the stress distribution in short columns in order that regions of high stress concentration in mine pillars may be found and their effect on pillar failure be ascertained. The ratios of the dimensions of the columns studied are representative of those found in mines located in flat-bedded deposits. The weight of the overburden generally constitutes the major external force. This force is calculated by taking into account specific weight and thickness of the cover. Determination of the distribution of this force on pillars may often require a complex analytical study. There have been many investigations of the strength

Jan 1, 1968

By John E. Udd

Introduction During the very long period in which man has mined minerals from the crust of the earth, falls of ground and collapes of under- ground workings have been the causes of a significant part of those accidents which have resulted in either death or in injury. At present, because of improvements in the approaches to the design of underground structures, in equipment, and in attitudes towards accident prevention, the proportion of accidents due to instability of rock is probably far less than it was historically. Nonetheless, in spite of the many advances which have been made, instabilities still account for about one-quarter of all fatalities, and one-tenth of all of the injuries, in the minerals industry. The means must be found whereby both the numbers of accidents and the accident rates due to falls of ground can be reduced to the lowest levels possible. At the outset it should be stated that, short of suspension of all mining activity, it will probably never be possible for us to eliminate accidents completely. Most human enterprise involves unknowns and risks, and mining is no exception. A certain number of accidents, then, must be viewed as the inevitable consequence of our attempting to work with unknowns and to make decisions that involve uncertainties. However, in retrospect, many instabilities can be attributed to factors which could have been within our control. The preventable accident must be eliminated. It should be our goal that we make every effort to direct our skills and technology to the creation of a safer working environment and should be constantly striving to

Jan 1, 1983

By Robert H. Richards

My first paper, read at the Cobalt Meeting of the Institute,' July, 1907, dealt with the behavior of a small Wilfley table when collceiltrating galena from quartz, the table being fed with natural products, with sized products, and with classified products. Since galena, having a specific gravity of 7.5, is among the heaviest minerals ordinarily concentrated by Wilfley table, it was desirable that a similar set of tests upon a mineral of lighter weight should be made. Chalcopyrite, of a specific gravity of 4, would have been the best mineral for this purpose, on account of its great importance as an economic mineral, but in carrying out the test I was obliged to content myself with a cupriferous pyrite, the specific gravity of which was 4.68 and the content in copper 8.80 per cent. Through the kindness of H. 0. Cummins, this material was obtained from Shasta, Cal., in very pure, clean, homogeneous condition. It was broken by rolls to 2 mm. in size, taking care to make a minimum of slimes. The quartz used to mix with it was pure, white, New England quartz, broken in the same way to the same size. In studying the accompanying tables, it should be borne in mind that the material concentrated was of low copper-content, and in many cases the quantity fed to the machine was 1 kg. or less. As a consequence of the smallness of the quantity treated it was very difficult to adjust the table and get it in condition to do its best work before the feed became exhausted, and for this reason many results were obtained which appear irregular.

Jan 1, 1909

By Eric K. Albert, J. Kiusalaas

The paper presents an overview of SPASID (Kiusalaas and Albert, 1983), a new computer program developed under U.S. Bureau of Mines funding for the prediction of surface subsidence caused by under- ground mining operations. The presentation, which is illustrated with two case studies, also re-evaluates the influence function method as a tool of subsidence prediction, arriving at some rather unconventional recommendations. SPASID consists of four modules that communicate through common data bases: (1) Preprocessor. This module prepares and maintains the database for the entire site. The database contains all the information about the site and the mine operation that is necessary for the computation of subsidence. (2) Subsidence Predictor. The influence function method is used to predict the surface displacements that occur in any portion of the site that occur between two given dates. The computations take into account the time lag between extraction and displacement, and the effects of pitching seams and incomplete compaction at the edges of panels. The program contains i not he's influence function and the Green's function of transversely isotropic elasticity theory. (3) System Identification. The purpose of System Identification is to determine the optimal values of the various parameters associated with the influence functions in the Subsidence Module. System Identification requires measurements of subsidence from a site with a sirnilar overburden structure. The values of the subsidence parameters are obtained by minimizing the discrepancy between the measured and computed surface displacements. (4) Postprocessor. The Postprocessor is a graphics facility for displaying the data generated by the other program modules.

Jan 1, 1984

By M. M. Neale

The pottery department has been aptly described as the "heart of the zinc plant," md every operator of a horizontal-retort plant is acquainted with the fact that good retort practice is the keystone of the smelting process. Since retorts and condensers are clay products, it is obvious that improvements in other branches of the ceramic industry should be observed for possible adoption in the pottery process for zinc smelting. Deaeration of clay bodies is one of the improvements that have become fully, established in many brick and pottery plants. Our investigation of a number of these installations always yielded the same answer—improved practice. Improvement in workability, elimination of laminations, less porosity, greater wet and dry strength, were among the claims put forth for this process. All of these features are exceedingly desirable characteristics in the manufacture of a zinc retort. A preliminary test, which involved truck transportation of deaired slugs over a relatively long distance, did show the value of many of these characteristics in forming the retort. Results from the standpoint of , longer retort life in the smelting furnace were not outstanding. The idea lay dormant for several years but was revived again in 1940, when it was decided to make whatever changes were necessary in the equipment for pottery manufacture to fully demonstrate the process. A number of the manu- facturers of machinery for clay work were asked to submit proposals, and the plan finally adopted was extremely simple and economical. Machine FOR DeaeRRATING Selection of the ''Straight-line'' principle for conversion of the "Wettengel" pug mill to a ''vacuum-extrusion" machine preserved some usable parts of the original equipment, such as the drive mechanism, and main shaft. The converted machine consists of a feed hopper, a compression and shredding zone, a vacuum chamber, and an extrusion barrel, as shown in Fig. I. In operation the clay mix travels from the feed hopper into the compression zone, where it is compressed and finally forced around the tapered cone into the vacuum chamber. As it enters this chamber the clay body is shredded into thin plates, for exFosure to the vacuum. The shredder consists of a hub mounted on the main shaft, to which are bolted segmental sections, each of which carries shredder knives. The compression zone and extrusion barrel function as seals for the vacuum chamber and the shredded clay mix is agitated thoroughly during its exposure to the vacuum. A vacuum pump, equipped with a 3-hp. motor, is attached to this chamber, and maintains 25 to 26 in. vacuum during operation of the mill. Changes in Practice Prior to the adoption of the deaeration process, our standard pottery practice called for double mixing in the combination 7

Jan 1, 1944

By Peter Allen, John R. Stuermer

COUNTRY RISK ANALYSIS A company operating in a foreign country assumes all the risks that it would at home. However, beyond these, it assumes risks that arise from the unique political economic, financial conditions of the foreign country which it operates. These risks are known as "country risks". The importance of these risks has grown appreciably in the recent past (particularly in the aftermath of Iran's revolution in the late 1970s and Mexico's debt rescheduling of 1982-83), and as a result, country risk analysis has become an increasingly useful management tool. Country risk analysis seeks to assess the probability that countries will service their aggregate foreign liabilities on time, as well as the probability that country conditions could inhibit the debt service capability of private sector debtors. This involves assessment of both the ability and the willingness of countries to meet their external liabilities in a timely fashion. "Ability" is linked economic and financial variables: principally, a country's economic structure, foreign exchange generating capacity and debt service burden. On the other hand, "willingness" is tied to political factors: mainly the economic/financial orientation of government policy and the stability of economic decision making. Ability: Economic, Financial Conditions and Prospects Judgement of a country's ability to meet foreign financial obligations begins with a detailed study of a country's external balance sheet which compares the country's foreign liabilities and assets. Table 1 below presents country balance sheets for Mexico, Korea and Indonesia. [TABLE 1 The External Balance 3-,-et 1983 (billions of dollars; Indonesia Mexico Korea Foreign Liabilities 31.1 67.6 40.5 By Source: Bank 13.1 75.5 26.3 Non-bank 18.0 12.114.2 Foreign Reserves 9.3 4.7 7.0] The large magnitude of Mexico's external debt (nearly $90 billion), compared to foreign assets of approximately $5 billion, illustrates the weakness of this country's external payments position, and the main reason that it has been unable to meet interest and principal payments and been forced to reschedule its foreign debt. On the other hand, the relationship between Korea's external liabilities and assets ($50.5 billion and $7 billion, respectively), is more favorable and helps explain why Korea has been able to meet debt service payments and maintain its access to the international capital markets. Indonesia has even a more favorable relationship between its foreign assets and liabilities, $31 billion and $9 billion, respectively, and its debt is mostly lower interest rate, non-bank debt, making for a less onerous debt service burden. After the balance sheet, the analysis turns to a comparison of the country's foreign exchange earning capacity and its prospective financing requirements, that is, the country's future earnings stream

Jan 1, 1985

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949