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By Cecil H. Desch

THE progress of metallurgical practice and the demands made by the engineering industry on our foundries and mills have made the crystalline structure of metals a subject of far more than academic interest. Metals and alloys are made up of crystals. Even if we accept the view, so ably maintained by some metallurgists, that the crystals are separated from one another by an amorphous layer, it remains true that all but a very minute fraction of any metallic mass is crystalline. The conditions which affect the growth of crystals are therefore of importance in metallurgy. It is not only castings whose properties depend on the arrangement of their crystals, for the more we learn of the behavior of forged, rolled and drawn metals, the more certain it becomes that it is profoundly influenced by the size and arrangement of the crystals in the original ingot, deter- mining a structure which may persist in a modified form through a long series of mechanical operations and annealings. This is mainly due to the concentration of much of the impurities in the last portions of the liquid to freeze, so that the boundaries between single crystals or groups of crystals are marked out by a zone of segregated material, differing in properties from the mass, and offering a barrier to diffusion and equalization of composition throughout the whole. The importance of this fact has been fully recognized by steel manufacturers, who have to deal with ingots which are sometimes very large, and are cast at a high temperature, containing impurities which have a marked effect on the properties even when present in very small quantity. For this reason the Iron and Steel Institute has set up a committee to examine the whole question of the heterogeneity of steel ingots,(l)f and a report has been issued, containing an account of the structure of 16 ingots, ranging in weight from 15 cwt. to 172 tons, each of which was sectioned and examined by chemical analysis and by etching. A valuable body of data concerning segregation has thus been collected. The work of the committee is being prosecuted with great activity, and at the same time researches are in progress to determine the physical

Jan 1, 1927

By Scott Tzcrner

WITHIN recent years people have begun to realize the importance and significance of the mining and allied industries. The leading part the engineer plays in civilization is becoming recognized. However accurate quantitative knowledge of the industrial importance of mining is still seldom possessed except by those close to this business. It is true that there are a few who go to the extreme and represent the whole progress of civilization as a reflection of man's gradual mastery of mineral utilization, but on the whole, the magnitude of the-industry is underestimated. In this paper I shall call attention briefly to the importance of mining in the United States, in Canada, and in the world. Ordinarily, the annual primary mineral production of the United States is about $5,500,000,000. The average for the last 5 years has been a little over that, but last year, sadly enough, it was less than 31/4 billion. Just now, we are on the decline, and have been for the last two years. In Canada, the 5-year average was about $268,000,000, and last year it was 227 million. Due in part to gold mines (in 1930, for the first time, Canada's gold production exceeded that of the United States), the Canadian average is holding up better than ours. Average world mineral production over the last -5 years has been estimated at about $12,000,000;000 whereas in 1931 it was less than than 8 billion.

Jan 1, 1932

By Zay Jeffries

Rearmament superimposed on buying sprees by the public, caused a general shortage of metals in 1911. and the rare metals were no exception; they also shared with the more common metals the uncertainty of future demand. In general, the apparent undersupply of metals is a favorable condition for the realization of sleeping possibilities of the rare metals, especially if the supply can he made sufficient to take care of the possible new demand. Many changes in metal usage in 1941 were forced because of shortages. When such changes are in the direction of the economic trend there is a speeding up in the tempo of the inevitable change, but when the forced changes are against the economic trend they are likely to be shortlived. In any event, the latter is not a solid foundation on which to build a future business.

Jan 1, 1942

By Michael Tenenbaum

Selected characteristics of nonmetallic phases were determined in low-carbon sheet steels which had been produced by various refining; deoxidizing, and casting procedures. The results showed little influence of the refining process on the quantity, distribution, size, and character of the nonmetallic phases. The quantity of inclusions was governed by the deoxidation procedures. While the mode of casting influenced the internal structure and the pattern of inclusion distribution, it had little effect on the quantity of nonmetallics. The vast majority of inclusions were under 30 µ in diam, and there was little change in size distribution during hot and cold rolling. The composition and structure of the inclusions were expained an the basis of known equilibrium phase diagrams for the appropriate systems. Additional work is needed to explain some of the observations of this paper. HENRY Marion Howe's contributions to the metallurgical profession include his many writings, the wisdom that he imparted to his students, and the inspiration that he gave to the many scholars, teachers, and industrialists who knew him personally. It was Professor Howe's intimate colleague, Albert Sauveur,1 who, in the first Howe Memorial Lecture, could have been speaking for the metallurgist of our generation as well as his own when he wrote, "...how many of us on the point of going astray were called back to the right path by Howe's guiding torch?" More than a quarter of a century later, Francis Foley,2 one of the last in the Howe Lecture series who worked directly with the great man, delivered the ultimate tribute, "...truth, in its time is so hard to identify." While Professor Howe strove to be right, "he was content if he provoked the reader to take the next step along the path to greater knowledge." Like so many of my predecessors, I sought guidance for this lecture by referring to Professor Howe's two classic texts, Metallurgy of steel,3 and Metallography of Steel and Cast Iron: the former book interpreting the facts as he saw them near the start of his career, and the latter—published 26 years later—pointing to many fertile fields for metallurgical investigation. Those of us who harvest the fruits of Henry Marion Howe's contributions to the metallurgical profession now look with wonder at the tremendous legacy he has provided. It is rewarding to study his writings and to recognize the anticipation of such aspects of modern ferrous metallurgy as: 1) Direct reduction 2) Steelmaking reactions 3) The approaches and benefits of degassing 4) Solidification mechanisms 5) Habits and behavior of nonmetallic inclusions 6) Recrystallization phenomena 7) Slip and slip propagation 8) Dislocations 9) Discontinuous deformation 10) Microscopic and macroscopic segregation

Jan 1, 1970

By J. V. Gluck

In the present paper," as in earlier publications, V1'2"1 the authors present experimentally obtained relations for the free energy of solution of oxygen in various metals as a function of temperature. The relations are linear and given in slope-intercept form. The authors give values for the "probable error" of the slope and intercept, citing Birge's method17 for obtaining these quantities. Birge discussed these methods as early as the period 1929-32.25726 In Ref. 25 the probable error is defined as "the numerical value which the true error is as likely to exceed as not", i.e., 50 pct probability. Ref. 26 is even more detailed and includes a lengthy discussion of the applicability of the Gaussian distribution to experimental data. However, the use of the "probable error" has come under some question. For example, Ezekiel'~ states that "the use of the probable error tends to make the results appear rather more accurate than the standard error". Moroney28 stated (in 1951) that "the term 'probable error' was used in former times to denote 0.67450 (50 pct confidence using the normal distribution)....the term, a poor one, is now very much obsolescent. It has been said that 'it is neither an error nor probable' ". Bennett and Franklin in 1954" in discussing statistical confidence levels mentioned that "the customary use of the 5 and 1 pct levels is not completely a matter of chance; these levels probably represent a balance between the desire to be correct and the desire to be specific. Also in most people's minds the borderline between something that could possibly happen and something that is not likely to happen is somewhere in this region. Certainly 5 or 1 pct confidence limits are to be preferred to limits such as the 'probable error' which has only a 50/50 chance of including the correct value." It may readily be seen that the 95 pct confidence level, which is given by 1.960 (assuming large sample size), thus corresponds to approximately three times the "probable error". Indeed, limits of one standard deviation correspond only to about 68 pct probability. Even if we triple the tolerances given by the authors in the equations of their Table 111, the deviations do not become excessive and would not detract from their excellent results. It could then be said with a high degree of confidence (95%) that the precision of the slope and intercept values is about *3-5 percent of their absolute levels rather than the 1-2 percent implied in Table 111. This is then compatible with an earlier suggestion of Gokcen~' of a probable accuracy of 5 pct in dissolved oxygen measurements by the technique employed. Alternatively, the authors could have

Jan 1, 1967

By A. P. Cohen, D. W. Fuerstenau

Methods of accounting for the feed size in analyzing the size distribution shift during comminution have been discussed in a number of papers.1,2,3 Based on experiments which charles2 performed with single Pyrex specimens, Schuhmann4 pointed out that the size modulus of an assembly of particles should be determined by the energy expended per unit volume (or mass), independent of the size of particle being comminuted. In this same paper, Schuhmann derived the Charles energy-size reduction relationship by considering that complex comminution operations can be considered to be the summation of many individual comminution events, each of which must be governed by Were 6wi is the mass of a particle receiving the impact, 6Ei is the energy delivered to the particle, ki is the size modulus of the product resulting from the impact, a is the distribution modulus of the assembly of particles, and A is a constant. Recent experiments on the compression loading of Pyrex spheres ranging in size from 1/8 to l-in. diam have shown that the size modulus of the fragments is determined by the strain energy at fracture per unit mass, independent of sphere diameter.' The objective of the present investigation has been to determine experimentally whether the size distribution of the product from such a complex comminution process as rod milling is determined only by the energy expended per unit mass independent of feed size. Samples of each Tyler sieve fraction ranging from 4x6 to 48x65 mesh were prepared from crushed Brazilian quartz crystals. One kilogram of each fraction was ground at 60 pct solids in an 8x9 1/4-in. mill containing 17.5 kg of rods (26 rods, 5/8-in.; 10 rods, 3/4-in.; and 5 rods, 7/8-in. diam). In each test, the mill was run at 77 rpm for 15 min. Size distributions were determined by a wet-dry sieving technique. Table I presents the size distribution of the products obtained by grinding each of the size fractions. Because the size distributions are so nearly alike, they are plotted in Fig. 1 by shifting each size distribution for the different feed sizes one screen fraction to the right. Thus, the lowest point in each size distribution represents 400 mesh and each of the other sieve sizes must be shifted accordingly. A single regression line was calculated by combining the data for the six tests, excluding the coarsest feed and the two finest feed fractions. 6 This regression line, which is given by (Y \0.88 where y is the cumulative percentage of material

Jan 1, 1962

By F. B. Plummer

PROGRESS during 1940 in oil-production technology has been confined largely to a steady advancement in practices inaugurated in previous years, rather than the introduction of any new startling process or technique. The usual changes, improvements and additions in production equipment have been introduced. An increased attention to, and interest in, research has been noteworthy, resulting in improved efficiency in operation of oil wells. control, utilization of reservoir energies and reduction of production costs.

Jan 1, 1941

By G. R. Speich, L. Zwell, H. A. Wriedt

HORNBOGEN1 has recently shown that it is possible to measure the degree of segregation accompanying cellular precipitation in ferritic Fe-Zn alloys by measuring the lattice parameter of the ferrite phase within the cell. In extending this work to study a wider range of composition and to evaluate the free-energy change accompanying the growth of the cells, the lattice parameter and the boundary of the a! phase in Fe-Zn alloys were redetermined to check the earlier work of Schramm.2 This appeared to be necessary since the Fe-Zn diagram has been drastically revised since the work of Schramm. Stadelmaier and Bridgers3 have recently shown that, contrary to prior belief: the y iron field is closed and the a phase boundary extends to an a + T + L peritectic at 782°C where peritectic a contains 42 at, pet Zn. The phase T in equilibrium with the a solid solution has a composition near Fe3Zn10 and a cubic 081 type structure.' The alloys were prepared by two different methods. In the first method carbonyl iron powder (400 mesh, 99.8 pet pure) and high-purity zinc powder (200 mesh, 99.99 pet pure) were mixed in a ball mill and then pressed in a die at 40,000 psi pressure to make compacts with a diameter of 5/8 in. and a thickness of l/4 in. These were sealed in evacuated quartz capsules, gradually heated to 1100°C over a period of 1 week (3 days at 600°C) 3 days at 800°C, 1 day at (1100°C), and then quenched in iced brine. For the alloys containing 23.4 and 30.1 at. pet Zn, the final homogenization anneals were performed at 1000" and 850°C) respectively, to prevent melting. In the second method, alloys were prepared by saturating high-purity iron millings (0.001 in. thick, 99.9 pet pure) in zinc vapor. For each alloy the impregnation was conducted at a fixed vapor pressure of zinc and a fixed temperature between 750' and 800°C. When saturated, the millings were quenched in water. The compositions of the alloys prepared by both methods are shown in Table I. The lattice parameters of the ferritic solid solutions were determined by comparing the 26 values of their 310, peaks (using Co Ka) or of their 211 , peaks (using Cr Ka) with those of corresponding peaks for high-purity a iron. The 20 values were measured at room temperature with an X-ray dif-fractometer (G.E.-XRD5). By using a fiducial value of 2.8664Å for the lattice parameter of pure a iron at 25oC,5 the lattice parameters of the zinc-bearing

Jan 1, 1964

By John Johnston

THIS necessarily brief sketch will attempt to summarize the high lights of perhaps the best meeting so far held by the Iron and Steel Division. All sessions were well attended and the discussion was vigorous and of a high order. The technical sessions opened. on Tuesday morning. "Precipitation Hardening of Copper Steels" was discussed by Cyril S. Smith and Earl W. Palmer, and dealt with steel with a 1 per cent copper content. Discussion brought out that there were no fabricating difficulties, but that the surface might be somewhat checked due to intergranular penetration of copper which could be easily taken care of. Probable advantages of steels of this type for high temperatures were pointed out. "An Improved Nickel-chromium Hardened Chilled Cast Iron," by J. S. Vanick, described a wear-resistant cast iron and evoked a lively discussion.

Jan 1, 1933

"World Mining and Metals Technology" is the title of this year's SME-AIME Fall Meeting and Exhibit in Denver, Sept. 1-3, where a record number of exhibits are scheduled for display. The international theme is particularly appropriate, for in addition to the annual SME session, the Third MMIJ-AIME Joint Meeting will be held.

Jan 8, 1976

THE Boston meeting, August 29-31, was in many ways one of the pleasantest the Institute has enjoyed in years. Much hard work had been done by the committee, and with excellent results. The program had been purposely restricted with the idea that a smaller, more homogeneous audience formed the best basis for a regional meeting, and the event fully justified the plan. The one hundred and sixty-three members and guests attending were dominantly interested in geophysical methods or their application, and, despite the highly technical character of the papers and the unusual heat, attendance and interest in the technical sessions were well sustained. The exhibition of geophysical instruments and aerial maps added greatly to the meeting.

Jan 1, 1928

By C. A. Gibbons

AFTER nine years of extremely de- pressed business, marked mostly A with red ink on the balance sheets of most coal companies and with an increasing internal competitive struggle for diminishing markets, somewhat of a change appeared during 1939. Shipments increased and prices generally firmed, giving the coal industry increasing optimism and encouragement for the future. Specifically, it now appears that bituminous coal production for 1939 will approximate 378,000,000 tons, and anthracite production will approximate 47,500,000 tons, bituminous production being around 14 per cent ahead of 1938 and anthracite production 12 per cent better. The curve on p. 31, showing both bituminous and anthracite production, furnished by the bituminous coal division of the Department of the Interior, shows graphically most of the 1939 monthly production and clearly illustrates the increased production.

Jan 1, 1940

By M. D. Curran

AS applied to coal, the term processing is subject to many interpretations. To some it means preparation of coal for the market by mechanical means such as crushing, sizing, washing, or treating with oil or chemicals to eliminate dust or improve combustion quality. To others it means conversion of the coal to other commodities as in carbonization to produce coke and by- products, or to liquids by application of the hydrogenation process. I prefer to classify the various forms of mechanical treatment under the heading of beneficiation and apply the term processing to those methods of treatment that destroy the coal sub- stance through distillation or hydrogenation.

Jan 1, 1939

By P. F. Kinyoun

MANY interesting new features are embodied in the latest extension to the open-hearth department of the Bethlehem Steel Co., at Lackawanna, N. Y. Automatic control of the important factors in furnace operation-fuel, air, draft, pressure, slag composition, and of the temperature in various regions of the furnace-has been carried out to a remarkable degree; the human factor is minimized, and the chances for mishaps and irregularities in operation are greatly reduced.

Jan 1, 1937

By M. D. Hassialis

THE object of a technical paper is to communicate new technical knowledge, the paper being the vehicle of communication and the existence of new knowledge its reason for being. It follows that the development of information worthy of communication, the criterion being novelty, is prerequisite to exercising the privilege of communication. The act of communication is achieved when the reader perceives the nature of the new knowledge, i.e., when he understands it. A paper achieving this objective is an acceptable technical paper. Development of new knowledge has as one of its purposes the increase of the existing state of knowledge and the enjoyment of the benefits derived therefrom. Technical knowledge is a collection of facts so ordered as to make apparent, relations existing between the facts. When the interrelations have been exposed the facts have been interpreted or explained Three broad, overlapping categories of technical papers may be recognized: papers consisting of (a) a report of facts, (b) an explanation of facts, or (c) a combination of a report and an interpretation. Ideally a technical paper should belong to one of the last two categories but current practice is to accept papers belonging to any of the three categories. Based on a small sample drawn from the scientific and engineering literature, the relative frequency of the three types is a: b: c:: 20:1:14. If the sample be limited to engineering literature, the ratios become a:c::2:1; type (b) being nonexistent. This large departure from the ideal is a consequent of the

Jan 1, 1948

By Herty, C. H.

Iron oxide (FeO) plays an extremely important part in the manufacture of iron and steel. In the three major processes- blast-furnace, open-hearth, and Bessemer converter-iron oxide is the chemically predominant compound and controls to a large ex- tent the operation of the furnaces and the composition and quality of their respective products. In order to emphasize the importance of iron oxide in each process, they will be considered individually in some detail. THE OPEN-HEARTH FURNACE. Iron oxide is introduced into the open-hearth furnace in four ways : 1. The scrap charged into the open hearth is oxidized by the furnace gases, the amount of oxide formed depending primarily on the amount and type of scrap charged. It has been found' that with large scrap, 1.7 Ib. of FeO is formed per 100 Ib. of scrap charged, whereas with scrap of medium size about 5.3 Ib. of FeO is formed per 100 Ib. of scrap charged, when the period between the charging of the scrap and the addition of hot metal is 3 hours. 2. The decomposition of the limestone sets free CO, by the reaction

Jan 1, 1957

Howard N. Eavenson, Gary, W. Va. (communication to the Secretary*):—For some time before the publication of Mr. Scholz's paper, I had been collecting data bearing upon its subject, and I now take pleasure in presenting to the Institute my results in the form of a discussion. It has long been a matter of common opinion among mining-men that mine-explosions are more frequent during the colder, or winter months, than during the warmer ones, and it is a matter of common knowledge among them that the air-ways and road-ways in most mines are much drier and are more inclined to be dusty during the winter than during the summer. In many mines, places which are wet and sloppy in the summer are dry and sometimes dusty during the winter. These changes, of course, can only be due to atmospheric conditions, and are caused by differences in temperature and humidity. Until recently, however, very little attention has been paid to the part that atmospheric conditions may play in mine-explosions, or, rather, to the effect they may have in rendering mine-conditions peculiarly dangerous, and in spreading and rendering more disastrous the effects of what otherwise probably would have been small explosions. To show the difference in mine-conditions during summer and winter months, I have tabulated in Table I. the results of 24 observations of hygrometric conditions in several different mines at different times of the year. Mines Nos. 1, 2, and 6 are located in the Pocahontas coal-region, in McDowell county,w.Va., the first one being a shaft-mine and the others drift. Mines 1A and 2A are drift-mines located in Logan county, W. Va. All of these are mines of fair size, but none of them has been in operation more than six years,

Jan 1, 1910

By E. A. Gulbransen, W. S. Wysong

The behavior of molybdenum and its surface oxides in oxidizing and reducing gas atmospheres and in high vacua at elevated temperatures is a question of scientific and technical importance. The use of molybdenum as a metal or as an important component in alloys in oxidizing atmospheres at elevated temperatures has been limited because of the unprotec-tive nature of its oxide film and the volatility of this oxide at moderate temperatures. This communication will present results of a vacuum microbalance studyl, 2 of the following problems: (I) the oxidation kinetics in the temperature range of 250°to 450°C; (2) the reduction with pure hydrogen of thin oxide films formed on molybdenum; (3) the volatility of the thin oxide films; and (4) the vacuum oxidation of molybdenum at high temperatures. Molybdenum is an interesting metal to study for the following reasons: (I) although the oxide-to-metal-volume ratio is greater than one, the metal is not considered protective; (2) the metal oxidizes readily at temperatures of 2 50°C and higher; (3) the oxides of the metal are reduced at temperatures as low as 500°C by pure hydrogen; (4) the oxide Moo3 melts at 795°C; and (5) the oxides of molybdenum are volatile at moderate temperatures. The following variables are studied in the oxidation kinetics: time, temperature, pressure, surface preparation, surface area, concentration of inert gas in the lattice, cycling procedures in temperature, vacuum effect and high temperature vacuum oxidation. The general interpretation of many of these factors has been previously discussed. Literature The oxidation of molybdenum has not been studied critically. Although many studies have probably been made on the kinetics of the oxidation process, none has been reported in the literature available to us. The crystal structures found in the oxidation of molybdenum have been studied by Hickman and Gulbransen." Their results showed that Moo2 is the oxide which is stable in contact with the metallic substrate throughout the temperature range 300 to 700°C. As the film thickens in the low temperature range, MoO3 becomes predominant on the surface. Above 400°C, Moos is no longer observed, MoO2 being the only oxide found. Hagg and Magneli6 have shown from an X ray study that the a-phase, orthor-hombic Moo3 is stable up to 1050°C. Two other phases, ß and ß with compositions close to MoO2.90 are also obtained. The formula for the 0 phase is not given but that of the ß phase is defined as Mo9O26 The 0' phase is found to be built upon a monoclinic unit cell. A ?-phase is isolated from a preparation MoO2.75 heated for 17 hrs at 670°C. This phase is

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

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