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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

Texture Transition in Ordered CuAu, by E. A. Starke, Jr., J. C. Ogle, and C. J. Sparks, Jr., Trans. TMS-AIME, 1969, vol. 245, pp. 169-70. pole figures should have had two parts not one. On the Estimation of Oxygen Absorption by Continuous Molten Metal Streams, by J. Szekely, Trans. TMS-AIME, 1969, vol. 245, pp. 341-44.

Jan 1, 1970

By C. W. Spencer, J. T. Smith

GRAIN-BOUNDARY surfaces are penetrated by a liquid phase when the liquid-solid interfacial tension is less than one-half the tension of the grain-boundary surfaces. Grain growth may occur in the presence of this liquid phase. burke1 reports that grain growth of this nature has been observed in two-phase ceramic systems. He suggests that the presence of a grain-boundary liquid may accelerate or decelerate the

Jan 1, 1963

New York State Museum, Albany, N. Y. D H. Newland, State Geologist. A complete list of publications or the latest lists of available publications will be sent upon application. A series of Bulletins on The Mining and Quarry Industry of New York are available as follows: Bulletin 51 (1910), 15 cents; 161 (1911), 20 cents; 166 (1912), 20 cents, 174 (1913), 20 cents; 190 (1915), 15 cents; 277 (1925-26), 50 cents; 295 (1927-1929), 40 cents. Another series discusses the Geology of the State by Quad¬rangles, available as follows: Bulletin 153, Broadalbin Quad (1911), 25 cents; 154, Sche¬nectady Quad. (1911), 20 cents, 170, North Creek Quad . (1914)

Jan 1, 1933

Jan 1, 1969

Jan 1, 1967

Jan 1, 1967

ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, technical graduate, aged 36. Experienced copper metallurgist and mining geologist. Familiar also, through 15 years' broad practical experience, with mining, cyanidation, concentration (including oil flotation), metallurgical accounting, and mine and plant management. Best references. No. 237. Member, graduate engineer with 10 years' experience in malleable, gray -Iron, and steel, as chemist., metallographist, and metallurgist. Researches and investigations by laboratory methods and under works conditions. No objection to some routine. No. 243. Member, technical graduate, broad experience in coal, oil, and clay. Will go anywhere as mining geologist after Sept. 1, 1915. No. 244. Member, technical graduate, aged 30, married, with over 10 years' experience as chemist, engineer on construction, superintendent and general superintendent of bituminous coal and coke plants. SpeaksSpanish. References. No. 245. Member, open for engagement as mine safety inspector or as superintendent of bituminous coal mine. No. 246. Member, graduate mining engineer, with five years' experience in coal mining as mining engineer, construction engineer, pit boss, and superintendent, open for engagement. Best references. No. 247.

Jan 9, 1915

Map

Jan 1, 1939

Jan 1, 1967

By A. M. Gaudin

THE purpose of ore dressing is to separate the rough ore into one or several valuable concentrates and a discarded tailing. The first step is to crush the ore so that the resulting particles may be individually valuable or worthless. The next step generally has to be a sizing operation, because the property by which concentration is effected depends on the size of the in-dividual mineral particles as well as on their physical properties. These two effects may cancel each other if a preliminary sizing is not resorted to. Sizing is accomplished by screening or classifying. Screening depends almost solely on the dimensions of the particles; classifying depends also on the specific gravity of the particles and the viscosity of the settling medium in which the classifying operation is conducted. Classification, therefore, is to a certain extent a con-centrating operation as well as a sizing operation. Before the days of concentration by flotation, the available screens were mechanically poor. As a result classification was employed for sizing in the range. of comparatively coarse sands (table feeds). In recent years, the advent of stage-grinding to flotation size has brought about the development of good screens, which are more economical than classifiers down to about 20, -mesh. With decreasing size at which separation is to be made, screens become increasingly uneconomical, while classifiers become increasingly economical. The line of demarcation between the respective fields of screening .and classification is, therefore, fairly sharp. With the development of processes of concentrating finely comminuted ore, the need for classifiers or other sizing devices operating so as to make efficiently a split at a very fine size has become increasingly apparent. Such classifiers might be termed de-slimers, from the fact that they separate a material having a slimy ap-pearance from one having the characteristics of a sand. Sizing-tests are carried on by means of testing sieves, the finest of which have apertures of about 1/500 of an inch. The 200-mesh sieve, which has an average open-ing of 0.0029 linear inches is generally considered the limit of practical test-sizing. As a result, little is known of minus 200-mesh material and the advantages of classifying concentrator feeds within the minus 200-mesh range has been overlooked. An extension of the -present sieve scale beyond the 200-mesh screen is given in Table 1.

Jan 2, 1927

By C. A. Stetefeldt

FoR the convenience of those who do not care to enter into the details of this long essay, I begin with a summary of the most important results it presents. The extraction of silver by the lixiviation-process from ores which have been subjected to a chloridizing-roasting, is based upon the fact that silver chloride is easily soluble in solutions of sodium or calcium hyposulphite, and that silver is precipitated from such solutions by an alkaline sulphide, with regeneration of the hyposulphite salts. In case the ore contains lead a large portion of the latter is and dissolved, lead sulphate being soluble in hyposulphite solutions. If, at the same time, copper is present, the sulphides precipitated from the solution, contain silver, copper, and lead, a combination of metals not desirable for subsequent treatment. Mr. E. H. Russell, of Park City, Utah, is the inventor and the patentee in the United States and several foreign countries of a new lixiviation-process, based upon the chemical facts discussed in this paper. Mr. Russell has discovered that lead can be completely separated from a sodium hyposulphite solution, as lead carbonate, by sodium carbonate or purified soda-ash, without precipitating any copper or silver. After decanting the solution from the lead carbonate, silver and copper are obtained from it in the usual way. This method of separating lead prohibits the use of calcium poly-sulphide as a precipitant for the sulphides, because any calcium entering the regenerated lixiviationsolution would also be precipitated as a carbonate with the lead by soda-ash. Hence, a sodium sulphide must be employed. A full investigation has demonstrated that this is by no means detrimental. Sodium sulphide and hyposulphite are more advantageously used in the lixiviation-process than the corresponding calcium-salts. Another defect in the lixiviation-process consisted in the necessity of a very perfect chlorination of the silver in the ore, because silver in

Jan 1, 1885

By B. N. Das, P. A. Beck

THE o phases have a complex tetragonal structure with Lo/ao = 0.52 and 30 atoms per unit cell.1 A large number of such phases are now known to occur in various binary systems of the transition elements and they exhibit the following typical features: 2,3 The composition of binary o phases is variable, ranging from approximately A4B to ABI. With only a few exceptions, in the o phases the A-ele-ment comes from the V- or Cr- group of the periodic table, while the B-elements are from the Mn-, Fe-, Co-, or Ni- group. In the first long period the corresponding o phases of the V- and Cr-series have approximately the same compositions. However, as the B-element changes from Mn to Fe to Co to Ni, the mean composition shifts monotonously toward higher A-contents.2-4 For example, if the mean compositions of the various o phases with vanadium are compared with each other, the composition shift mentioned above becomes plainly visible: V 30Mn0 80 Vo.45Feo..,, Vo .,Coo. 45 and Vo.5Nio.3. Similiar composition shifts, although not the same composition values, were observed in u phases formed by second and by third long-period transition elements.3'4 This behavior, very characteristic of o phases, is in rather sharp contrast to the usually quite well-behaved stoichi-ometry of the Laves phases. In the latter, the AB2 stoichiometry predominates, with A the large atom and B the small atom.= The p phase occurs in the four binary systems of Mo or W with Fe or Co. On the basis of their crystal structure determination, Arnfelt and westgren6 ascribed to the p phase in the Co-W system the ideal composition W,Co7. Since all four binary pphases have nearly the same composition, it would seem quite plausible that some definite stoichiometry such as A6B7, might be characteristic of this phase, as AB2 is of the Laves phases. On the other hand, it has been noted,7 that the phases occur at average electron concentrations near to those at which the various cr phases are found. Also, it has been pointed out by Shoemaker and associates8 that structurally the a phases and the p phases are somewhat related to each other; both of these structures may be described in terms of suitable stackings of quasi-hexagonal layers'of atoms. By studying a suitably chosen ter- nary phase diagram, one might expect to be able to find out which one of the two conditions, the analogy with the o phase or the constant ratio between the number of large atoms and the number of small atoms in effect governs the behavior of the p phase. Several isothermal sections of ternary systems containing o phases have been investigated. In all cases where two binary o phases occur, these were found to be connected b a more or less straight ternary o phase field.7' '10 Such elongated o phase fields were also found in ternary systems in which only one of the limiting binaries is known to contain o phase. In this manner a latent o forming tendency could be detected and the virtual composition of a "binary o phase", which does not actually occur as such was approximately determined by extrapolation. The behavior of the phases, including their composition shift, is analogous to that of the classical electron compounds, as described by Hume-Rothery.11 In order to decide whether the p phase is essentially a "size compound" like the Laves phases, where a fixed stoichiometric ratio is quite generally maintained between the "large atoms" and the "small atoms", or whether the p phase is typically an "electron compound" in the same sense as ois, it was decided to investigate an isothermal section of the Mo-Mn-Co system. The Mo-Co system12 and the Mo-Mn system13 each are known to have a binary o phase. It could be therefore expected that a ternary o phase field will connect these two binary cr-phase fields. The p phase is known to occur in the Mo-Co system. If the p phase should turn out to form an elongated phase field extending deep into the ternary system, the following considerations mighto apply. The atomic radius of manganese (1.314for C.N.12) is between the va,lues for Mo (1.40Afor C.N.12) and for Co (1.26Afor C.N.12). If it is assumed that p is a "size compound", and that Mn is substituting for the smaller Co atoms in the p-structure in the ternary system, the y-phase field might be expected to extend parallel to the Mn-Co binary line. If Mn is substituting for the large Mo atoms in the p-structure, the p-phase field may be expected to extend parallel to the Mn-Mo binary line. On the other hand, if the p-phase turns out to be an "electron compound" like o, the ternary p-phase field should extend parallel to the ternary o -phase field connecting (Mo,Mn)owith (Mo, Co) a

Jan 1, 1961

By K. Heindlhofer

Estimates of the "plasticity" of a metal are commonly deduced from three types of test—tensile, torsion and impact. The several results have been more or less at variance, though this disparity has attracted little notice, largely perhaps because they have been expressed in different terms. The discrepancy between the results of the three tests becomes obvious when each is made at a series of low temperatures, for the temperature range within which the "plasticity" of iron largely disappears proves to be very different in the three types of test. The rather abrupt disappearance of "plasticity" of iron within a narrow temperature range cannot be due to any physicochemical change (such as a precipitation) taking place in the material at that time, because the original plasticity is immediately regained when the temperature of the material is brought above the sensitive range. Accordingly this difference in behavior shows that the "plasticity" of a metal depends upon the mode of action of the stresses which produce the deformation, and therefore upon the method of test. Analysis of the stresses leads to the conclusion that the observed plasticity of a metal is determined by the relation between its resistance to rupture by separation and its resistance to shear (slip), on the one hand, and between the effective normal and shearing stresses on the other; and that the relation between the two resistances does not in general remain constant with change of temperature, and may somehow be altered to some extent by the previous treatment of the specimen. This suggests the view that the results of none of the usual mechanical tests are directly comparable even for a single metal tested at a series of temperatures, or for a series of metals at one temperature, because the proportion of the total resistance of the metal to the test contributed by the

Jan 1, 1935

By K. Heindlhofer

Estimates of the "plasticity" of a metal are commonly deduced from three types of test—tensile, torsion and impact. The several results have been more or less at variance, though this disparity has attracted little notice, largely perhaps because they have been expressed in different terms. The discrepancy between the results of the three tests becomes obvious when each is made at a series of low temperatures, for the temperature range within which the "plasticity" of iron largely disappears proves to be very different in the three types of test. The rather abrupt disappearance of "plasticity" of iron within a narrow temperature range cannot be due to any physicochemical change (such as a precipitation) taking place in the material at that time, because the original plasticity is immediately regained when the temperature of the material is brought above the sensitive range. Accordingly this difference in behavior shows that the "plasticity" of a metal depends upon the mode of action of the stresses which produce the deformation, and therefore upon the method of test. Analysis of the stresses leads to the conclusion that the observed plasticity of a metal is determined by the relation between its resistance to rupture by separation and its resistance to shear (slip), on the one hand, and between the effective normal and shearing stresses on the other; and that the relation between the two resistances does not in general remain constant with change of temperature, and may somehow be altered to some extent by the previous treatment of the specimen. This suggests the view that the results of none of the usual mechanical tests are directly comparable even for a single metal tested at a series of temperatures, or for a series of metals at one temperature, because the proportion of the total resistance of the metal to the test contributed by the

Jan 1, 1935

Nominating Committee.-On the recommendation of the President, the Board of Directors, at their meeting on Apr. 25,1913, appointed the following Nominating, Committee to nominate officers and directors for next year: John Hays Hammond (Ex-President), Chairman. Robert H. Richards Chairman of Boston Local Section. Richard S. McCaffery, . . . . Chairman of Spokane Local Section. Chester F. Lee Chairman of Puget Sound Local Section. Frederick G. Cottrell, . . . . San Francisco, Cal. Charles W. Goodale Butte, Mont. James W. Maleolmson, . . . . Kansas City, Mo.

Jan 5, 1913

Jan 1, 1967

THE transformation, in a sample of levitation melted iodide titanium, has been studied with a Leitz hot-stage microscope. The specimen was etched in HF:HNO3: glycerine, (1:1:2) giving a structure shown in Fig. 1, and was then heated at approximately 5OC per min. At 870°C (±5OC) the etching product disappeared, the a-grain boundaries showed in relief, and some new grain boundaries (presumably of ß) appeared (Fig. 2, see arrow). Some evidence of ß-grain growth is indicated by the apparent longitudinal movement of a ß-grain boundary shown in Figs. 2 and 3 (see arrows). The specimen was later heated to 1000°C and then cooled at 2°C per min. At 845°C rumpling of the surface was first noticed, Fig. 4, and continued at constant temperature. The photomicrograph reproduced in Fig. 5 was taken 6 sec after Fig. 4, at 845°C. Fig. 6 shows the structure after cooling to room temperature. The room-temperature structure, showing a rumpled surface has been observed by previous investigators.' These structures presumably indicate a sheer transformation ß - a, athermally nucleated, but capable of isothermal progression.

Jan 1, 1960