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By B. M. Larsen, L. S. Darken

Some years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general, our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2) by a high concentration of active (or "free") lime and of manganese oxide dissolved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. Distribution 02 Manganese between Slag and Metal at Equilibrium On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction FeO + Mn -& MnO + Fe [A] slag metal slag metal the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as K,, _ aMnO' afe aFeO ' aMn where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term afe may be combined with K" to give a new constant K'. Making these changes, 7

Jan 1, 1942

By B. M. Larsen, L. S. Darken

Some years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general, our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2) by a high concentration of active (or "free") lime and of manganese oxide dissolved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. Distribution 02 Manganese between Slag and Metal at Equilibrium On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction FeO + Mn -& MnO + Fe [A] slag metal slag metal the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as K,, _ aMnO' afe aFeO ' aMn where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term afe may be combined with K" to give a new constant K'. Making these changes, 7

Jan 1, 1942

By W. J. Romanow

RECENT papers by Williams, Sherwood, and Boothby,1 Seybolt et al.2 Heikes; and Roberts4 attest to the increasing importance of the hexagonal ferromagnetic compound MnBi. Since the magnetic properties of MnBi crystals are highly anisotropic, it is useful and necessary to have appropriate aids for determining their orientations—a (00.1) standard stereographic projection and a corresponding table of crystallographic angles for this structure. The tables of crystallographic angles for the hexagonal system available in the literature5 are computed for c/a ratios greater than that of MnBi and cannot satisfactorily be used to find the crystallographic angles of MnBi. A table of angles between the crystallographic planes (HK.L) and (hk.1) was calculated for MnBi from the formula0 F=are cos Hh+Kk+ 1/2(Hk+hK) + 3/4 (a/c)2Ll/v(H2 + K2 + HK + 3/4 (a/c)2L2) (h2+ k2+hk + 3/4 (a/c)2l2) on an IBM Type 650 Magnetic Drum Data Processing machine. The lattice constants used are listed in Table I and are those determined by Willis and Rooksby7 at 20°C. More recently published values obtained by both X-ray and neutron diffraction"' show no difference from these significant to the calculation. From the crystallographic angles between the basal plane (00.1) and the general plane (hk.1) in Table I, an (00.1) standard stereographic projection was made for MnBi which is shown in Fig. 1. Acknowledgments The author wishes to thank R. G. Treuting and J. N. Hobstetter for their technical assistance, and Miss D. P. Booth for programing the IBM machine for the calculations. He appreciates the opportunity to read the paper of B. W. Roberts of General Electric Co. prior to its publication. References 1H. J. Williams, R. C. Sherwood, and 0. L. Boothby: Bulletin Amer. Physical Soc., 1956 vol. 1, p. 132. 2 A. U. Seybolt, H. Hangen, B. W. Roberts, and P. Yurcisin: AIME Trans., 1956, vol. 206, p. 605: Journal oF Metals, May 1956. 3R. R. Heikes: Physical Review, 1955, vol. 99, p. 446. .B. W. Roberts: A Neutron Diffraction Study of the Structures of Manganese B.W.Roberts:ANeutronDiffractionBismuthide, Physical. Review, 1956, vol. 104, p. 607. 5 A. Taylor and S. Leber: AIME Trans., 1954, vol. 200, p. 190; JouRNal of Metals February 1954. « C. S. Barrett: Structure of Metals, 2nd Ed., p. 635. McGraw-Hill Book Co. New York and London, 1952. 7B. T. M. Willis and H. P. Rooksby: Proceedings Physical Soc., London, 1954, vol. 67B, p. 290.

Jan 1, 1958

By W. Rosotoker

Using an expression for the free energy of a homogeneous phase as a function of composition, a relationship is derived which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. Comparisons between observed and calculated phase boundaries in the systems Fe-Ni, Fe-Mn, Fe-W, Ti-Mo, and Ti-Cb are presented. IT is the purpose of this paper to illustrate how the general free energy equations for two phases in equilibrium may be used to derive an expression which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. The free energy per gram atom of a disordered solid solution may, for many purposes, be represented by the equation:' F = ½NZ [C-V,, + (1-C) VbB + 2C (l-C)V] + K(T) +RT[C-lnC+ (l-C)ln(l-C) ] [1] where N is Avogadro's number; Z, the coordination number; C, the concentration of the solute element in atomic percent; the subscripts refer to concentrations at phase mixture boundaries; VAA, VBB, and V,, are the bond energies between like and unlike adjacent atoms, respectively, at the interatomic spacing characteristic of the phase. The bond energies are usually assumed to be independent of small changes in the lattice parameter occasioned by solute additions and variations in temperature; V = VAB ---------------—— ; K(T) is the sum of the heat con- tent and heat entropy; R, the molar gas constant; and T, the temperature in degrees Kelvin. The free energy of a homogeneous phase is there- fore the sum of an internal energy, a specific heat, and a configurational entropy term, respectively. The compositions of two phases in equilibrium at a given temperature are governed by the minimum total free energy principle. Graphically, this is represented by the points of tangency of the tangent common to the free energy vs. concentration curves of the two phases. Analytically, this may be expressed as: ( df) = (df) [2] dc dc Expanding both sides using eq 1, the following equation is obtained after convenient readjustment of the terms: RT In[(ca)(1-c)]-½N (Vaa-Vbb)(Za-Zb) +NV [Za(l-2Ca)-Z,(l-2C,)] [3] The following assumptions have been made at this point: 1—The specific heats of the two phases are independent of composition variations within the range under consideration. Accordingly, the K(T) terms disappear on differentiation. 2— (Vaa)o = (VAA); (VBB). = (VBB); Va = V, Theyjustification for these assumptions can lie only in the successful application of the resultant equation. It may be noted that Zener2 has used assumption 1 in the calculation of the boundaries limiting the (a+j3) phase mixture in the Cu-Zn system.

Jan 1, 1952

By O. L. Culberson, J. J. McKetta

INTRODUCTION The equilibrium constants for methane and for water, and for ethane and water have been calculated from experimental data for the two binary systems.2,3,11,12 These constants are for the two-phase systems for the temperature range of 100" to 340°F and the pressure range of 200 to 10,000 psia. The constants for ethane are greater than those for methane. Equilibrium constants for a natural gas from a natural gas-water system6 are about the same as those for methane. Equilibrium constants for water in all three systems are very nearly the same over the greater part of the range of temperatures and pressures studied. In ideal solutions, the vapor-liquid equilibrium constants for a component should be the same in all such solutions at a given temperature and pressure.5 Few solutions are ideal, and consequently the use of generalized constants often leads to error in situations where they do not actually apply. In decidedly non-ideal systems, it is desirable to have equilibrium constant data for the specific system. Vaporization equilibrium constants may be calculated either by thermodynamic methods or from experimental vapor-liquid equilibrium data. In the thermodynamic calculation. the equilibrium constant K may be shown to be" K = fP,/fl'..........(1) where fPi is the fugacity of the pure component i at the given temperature and at the vapor pressure of the pure component, and fp is the fugacity of pure i in the gaseous state at the temperature and total pressure of the system. At best the thermodynamic calculation results in a K applicable to ideal solutions. Equilibrium constants calculated from Equation (1) have been found to have only limited agreement with experimental values, even though the solutions for which they were calculated approached ideality."'" If the more volatile component is at a temperature above its critical, the accuracy of the equilibrium constant for the component is made more doubtful by the use of the vapor pressure term under such conditions. In order to make the thermodynamic calculation on a component above its critical temperature, one must resort to one of the empirical methods of extrapolation of the vapor pressure to conditions above its critical point.13 Application of the thermodynamic equilibrium constant then to the methane-water or the ethane-water systems would be risky since the systems are non-ideal, and the methane and ethane are above their critical in most petroleum operations. ETHANE-WATER SYSTEM In the temperature range of from 100° to 340°F and for pressures up to 10,000 psia, the vapor-liquid equilibrium data 'References given at end of paper. Manuscript received in the office of the Petroleum Branch March 16, 1951.

Jan 1, 1951

By R. B. Gilmore, Lewis W. MacNauhgton

The North Texas district, as' herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wilbarger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, usually are modified by stratigraphic changes in the sediments. Excepting those in southeastern Baylor, southern Archer, and southwestern Clay counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsyl-vanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1942 Approximately 500 wells were drilled in the district during 1942, in contrast with some 1600 wells drilled during 1941, and only some goo oil wells were completed, a decrease from 1941 of more than 10 per cent in the number of successful drilling operations of the total wells drilled. Production increased slightly over the previous year in spite of a decrease in the number of producing wells. The average depth of discovery wells was some 600 ft. deeper than in 1941. Although more discoveries produced from horizons above the base of the Strawn series than those below the Strawn, the deeper horizons, including the Bend series of the Pennsylvanian, the Mississippian limestone, and the Simpson and Ellenburger of the Ordovician, furnished most of the addition to oil reserves. The largest single addition to the reserves was again in the Ellenburger formation in the K. M. A. field. During the year 47 wells were completed, bringing the total developed acreage in this horizon to some 5450 acres. The most active area was Montague County, in which eight fields, or potential fields, were discovered although only 39 oil wells were completed. K. M. A: Pressure Maintenance Satisfactory progress was made by the K. M. A. Pressure Maintenance Association in 1942, At the end of the year, 100 wells were being used for input and total monthly volume of gas returned to the reservoir reached a high of 430,971 M cu. ft. in December, with an input ratio of 587 cu. ft. of gas returned for each barrel of oil produced during the month. This represents a utilization of 50 per cent of the gas available for return during that month. Comparison of the present average bottom-hole pressure by means of a decline

Jan 1, 1943

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

By J. J. McKetta, O. L. Culberson

INTRODUCTION The equilibrium constants for methane and for water, and for ethane and water have been calculated from experimental data for the two binary systems.2,3,11,12 These constants are for the two-phase systems for the temperature range of 100" to 340°F and the pressure range of 200 to 10,000 psia. The constants for ethane are greater than those for methane. Equilibrium constants for a natural gas from a natural gas-water system6 are about the same as those for methane. Equilibrium constants for water in all three systems are very nearly the same over the greater part of the range of temperatures and pressures studied. In ideal solutions, the vapor-liquid equilibrium constants for a component should be the same in all such solutions at a given temperature and pressure.5 Few solutions are ideal, and consequently the use of generalized constants often leads to error in situations where they do not actually apply. In decidedly non-ideal systems, it is desirable to have equilibrium constant data for the specific system. Vaporization equilibrium constants may be calculated either by thermodynamic methods or from experimental vapor-liquid equilibrium data. In the thermodynamic calculation. the equilibrium constant K may be shown to be" K = fP,/fl'..........(1) where fPi is the fugacity of the pure component i at the given temperature and at the vapor pressure of the pure component, and fp is the fugacity of pure i in the gaseous state at the temperature and total pressure of the system. At best the thermodynamic calculation results in a K applicable to ideal solutions. Equilibrium constants calculated from Equation (1) have been found to have only limited agreement with experimental values, even though the solutions for which they were calculated approached ideality."'" If the more volatile component is at a temperature above its critical, the accuracy of the equilibrium constant for the component is made more doubtful by the use of the vapor pressure term under such conditions. In order to make the thermodynamic calculation on a component above its critical temperature, one must resort to one of the empirical methods of extrapolation of the vapor pressure to conditions above its critical point.13 Application of the thermodynamic equilibrium constant then to the methane-water or the ethane-water systems would be risky since the systems are non-ideal, and the methane and ethane are above their critical in most petroleum operations. ETHANE-WATER SYSTEM In the temperature range of from 100° to 340°F and for pressures up to 10,000 psia, the vapor-liquid equilibrium data 'References given at end of paper. Manuscript received in the office of the Petroleum Branch March 16, 1951.

Jan 1, 1951

By R. B. Gilmore, Lewis W. MacNauhgton

The North Texas district, as' herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wilbarger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, usually are modified by stratigraphic changes in the sediments. Excepting those in southeastern Baylor, southern Archer, and southwestern Clay counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsyl-vanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1942 Approximately 500 wells were drilled in the district during 1942, in contrast with some 1600 wells drilled during 1941, and only some goo oil wells were completed, a decrease from 1941 of more than 10 per cent in the number of successful drilling operations of the total wells drilled. Production increased slightly over the previous year in spite of a decrease in the number of producing wells. The average depth of discovery wells was some 600 ft. deeper than in 1941. Although more discoveries produced from horizons above the base of the Strawn series than those below the Strawn, the deeper horizons, including the Bend series of the Pennsylvanian, the Mississippian limestone, and the Simpson and Ellenburger of the Ordovician, furnished most of the addition to oil reserves. The largest single addition to the reserves was again in the Ellenburger formation in the K. M. A. field. During the year 47 wells were completed, bringing the total developed acreage in this horizon to some 5450 acres. The most active area was Montague County, in which eight fields, or potential fields, were discovered although only 39 oil wells were completed. K. M. A: Pressure Maintenance Satisfactory progress was made by the K. M. A. Pressure Maintenance Association in 1942, At the end of the year, 100 wells were being used for input and total monthly volume of gas returned to the reservoir reached a high of 430,971 M cu. ft. in December, with an input ratio of 587 cu. ft. of gas returned for each barrel of oil produced during the month. This represents a utilization of 50 per cent of the gas available for return during that month. Comparison of the present average bottom-hole pressure by means of a decline

Jan 1, 1943

By B. M. Larsen, L. S. Darken

SOME years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general. our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2-by a high concentration of active (or "free") lime and of manganese oxide dis) solved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. DISTRIBUTION OF MANGANESE BETWEEN SLAG AND METAL AT EQUILIBRIUM On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction [FeO + Mn ;7± MnO + Fe [A] slag metal slag metal] the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as [K" aFPI OFeO ? aMn] where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term aFe may he combined with K" to give a new constant K'. Making these changes.

Jan 1, 1942

By Toshiyuki Hashida, Victor M. Lopez-Hirata

"Small-punch tests and determination of fracture toughness JIC were conducted at 4 and 77 K on new cryogenic JN1, JJ1 and JK2 austenitic stainless steels, after isothermal aging. Equivalent fracture strain ?qf determined by measuring the reduction of thickness in the small-punch test specimen. A linear dependence of JIC on ?qf was found in these new materials. Regression analysis of experimental data produced the following linear relation JIC = 1304.1 ?qf + 8.09 [kJm-2]. An analysis of present work relation was pursued on the basis of material properties and evaluation method of he. Results showed that the slope value has a strong dependence on material yield strength and JIC evaluation method. This linear relation is useful for the evaluation of fracture toughness JIC, measuring the equivalent fracture strain ?qf by means of small-punch test. Thus it can be useful for assessing the degradation of fracture toughness in small areas such as, the heat-affected zone in welded components.IntroductionCryogenic structural materials for superconducting magnets of fusion nuclear reactor are required to possess a good combination of strength and toughness. The mechanical properties are required beyond the capability of conventional austenitic stainless steels [1]. New cryogenic JN1, JJ1 and JK2 austenitic stainless steels were developed by the Japan Atomic Energy Research Institute (JAERI) [1]. The structure of superconducting magnets is constructed by welding of 200 = thick plates of these steels, which are solution treated at high temperatures and then water-quenched to avoid intergranular precipitation. However, the welding process involves heating and cooling [2], which cause microstructural changes in both base metal and weld. In this heterogeneous microstructure, it is important to estimate the fracture toughness of these materials at cryogenic temperatures. Therefore, it is necessary to evaluate the effect of aging process on the fracture toughness behavior of these new steels. To determine the cryogenic fracture toughness, the elastic-plastic JIC value has been co=only used [2]; however, the specimen size is much larger than heat-affected zones in welded components. Small-punch (SP) testing method, employing miniature specimens, has permitted to evaluate the fracture toughness behavior at different temperatures in different nuclear reactor materials [3,4]. Mao et al. [5,6] and Misawa et al. [7] found a linear relation between JIC value and equivalent fracture strain ?qf, determined by SP method in non-ferrous alloys and ferritic steels at room temperature and austenitic stainless steels at 4 and 77 K, respectively. So that, this kind of correlation would be very useful to assess the fracture toughness JICe values by means of SP test in small zones of welded components."

Jan 1, 2012

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By R. S. French, W. R. Hibbard

FOR tensile deformation, if the stress value is defined by the ratio of the load to the actual area, and the strain value by the natural logarithm of the ratio of the immediate length to the original gauge length of the sample, the resulting data when plotted with logarithmic coordinates result in a linear relation extending from the initial plastic yielding through the maximum load and in some cases, such as for copper and brass, to fracture'.'. The normal form of the curve, therefore, is a parabola, satisfying the following equation: S = Kem [1] where S and e represent true stress and strain, K is a constant, and m is a coefficient evaluating the slope of the curve and designated therefore as the strain hardening coefficient. Hollomon² has reported that this coefficient is a function of the yield strength as effected by grain size in alpha brass, and the carbon content and heat treatment of steel. In the case of steel, the value of the proportionality constant is a function of the carbon content. It was further shown in that paper2 and also by Low and Prater -hat, if the power relation between stress and strain remains valid, the strain hardening coefficient m, is equal to the strain at the maximum or necking load. Thus, an added significant feature is that this coefficient may serve as an index of the capacity for deformation prior to localized necking and subsequent fracture, e.g. drawability. The constant K may be defined as the strength of the material at unit strain. Together the K constant and the m coefficient describe an alloy's physical properties as far as strength and ductility are concerned for a particular yield strength and, in the case of steel, a particular carbon content. The work of Lacy and Gensamer4 gives data on alloy ferrites from which very close estimates of the strength of ternary and higher iron alloys have been made. It was the purpose of this investigation to develop similar data for commercial copper base alpha solid solution alloys. Preparation of Specimens Commercial binary alloys of copper with aluminum, beryllium, cadmium, nickel, silicon, tin and zinc were investigated. In addition, laboratory castings were made of a 1 pct silicon alloy and a 2 pct aluminum alloy to complete these particular series. Two types of copper were used, oxygen free OFHC and tough pitch FC. The analyses of these alloys are shown in table I. Standard ASTM sheet tensile specimens were used to determine the usual physical properties of each alloy and to obtain stress data at strains from 0.0005 to 0.01. Small (1/4 in. x 3 in. x tk.) samples

Jan 1, 1951

By E. G. King

Heat of formation values for mercuric sulfide appear in all the comprehensive listings of thermodynamic data, but experimentally determined entropy values have been lacking. Consequently, all free energy calculations involving mercuric sulfide have been based upon estimated entropy values. This paper reports Bureau of Mines measurements of the low-temperature heat capacity of red mercuric sulfide (cinnabar) and the entropy value at 298.15° K. derived therefrom. The entropy value was combined with heat data to obtain free energy values for the formation of red mercuric sulfide from liquid or gaseous mercury and from rhombic or gaseous diatomic sulfur.

Jan 1, 1962

By Austin Whillier

INTRODUCTION Use of air-cooling or refrigeration equipment in underground mines is needed when conventional ventila¬tion techniques do not maintain acceptable environ¬mental temperatures in working areas. Because refrig¬eration can be very expensive, it should be implemented only after all possible and practical steps have been taken to eliminate or reduce heat sources in the mine. As an example, to prevent the main ventilation fans from contributing heat to mine air, they should be located in the air return and not in the air intake. It is particularly important to prevent any direct contact between hot water and ventilation air, especially in mines which encounter large flows of hot fissure water. Any water hotter than the prevailing wet-bulb temperature of the ambient air must be removed by pipes located as close as possible to the water source. This hot water must not be allowed free contact with the incoming ventilation air at any time during the water's passage out of the mine. Although insulation of the pipes carrying the hot water is seldom necessary, direct contact between the air and the water must be prevented so the warm water cannot evaporate. REVIEW OF COOLING PRACTICES Spot Coolers vs. Centralized Refrigeration To eliminate a few specific hot places in an otherwise cool mine, it is possible to use devices known as "spot coolers." A typical spot cooler that uses chilled water is shown in Fig. 1. These devices consist of self-contained refrigeration units that are often mounted on rail cars for haulage to hot spots. The cooling capacities of such spot coolers usually are limited to about 100 kW or 30 "refrigeration tons." A refrigeration ton represents a cooling rate that produces 1.0 st of ice in 24 hr; that is a cooling rate of 3.517 kW (200 Btu per min). Typically, the electric-power consumption to drive the compressor motor of the refrigeration plant in mines is 1.0 kW per refrigeration ton, corresponding to a coefficient of per¬formance of about 3.5. The principal difference between spot coolers and centralized refrigeration plants is the method of re¬jecting heat from the refrigeration system. Centralized refrigeration plants always discharge heat into the reject or return airflow of the mine; often that is the primary influence in selecting the location for the underground refrigeration plant. Heat from spot coolers usually is rejected into drain water or into air that is not flowing to the location requiring the cooling. As a result, spot coolers remove heat from troublesome hot spots in the mine, injecting that heat-plus the electrical energy used by the cooling unit itself-into other working areas where the ambient conditions are cooler. In effect, this is "robbing Peter to pay Paul." In deep, extensive mines, spot coolers usually pro¬vide only temporary and, over the long term, expensive solutions to localized cooling problems. Centralized re¬frigeration plants are preferred for such mines, with cooling distributed throughout the mine as required. Fig. 2 illustrates a typical underground centralized re¬frigeration plant. Centralized plants lend themselves to improved maintenance at reduced costs while offering the economy of size. Refrigeration plants of larger unit sizes have considerably lower initial costs than smaller unit sizes. The remainder of this chapter is devoted to large refrigeration plants, with no further consideration of spot coolers. Cost of Refrigeration Total Cost: The total cost of refrigeration amounts to about $200/kW of cooling per year (1981 US $). This total cost breaks down into approximately three equal parts: 1) Financial charges, which include the interest and amortization on the capital cost of the initial installation, and the cost of necessary underground excavations. 2) Operating and maintenance costs which include the cost of the electric power to drive the refrigeration plant's compressors. 3) Distribution costs which include costs for pump¬ing, insulated piping, and air-to-water heat exchangers. The local cost of electric power, the number of operating months per year, and the method of refrigera¬tion distribution all contribute to the actual costs in¬curred in a given application. However, the variations usually are limited to no more than ±30% of the $200/ kW per year total cost figure. Cost Per Ton: Refrigeration cost per ton of mineral production can be calculated if the annual production tonnage from the refrigerated section of the mine is known. In most cases, this cost will be less than $1 .00/t. However, in deep mines with high rock temperatures, such as those found in South Africa, the total cost of refrigeration can increase to several dollars per ton of broken rock. Distribution In deep extensive mines, distributing refrigeration often accounts for about half the total cooling costs. As a result, careful consideration and planning must be

Jan 1, 1982

By Carl J. McHargue

Mechanical twins were produced in electron-beam melted columbium by high-speed impact at room temperature and by slow or fast compression at -196°C. The composition plane of the twins was { 112} and the shear direction was <111>. Notches in the twin bands often corresponded to traces of {110) of the matrix and appeared to be untwinned regions. Markings within the twin bands were interpreted as resulting from {110} slip in the twins. THERE has been much work in recent years concerning plastic deformation by glide, and the dislocation theory relating to glide has reached a relatively high degree of development. On the other hand, there have been fewer studies of deformation by mechanical twinning, and understanding of this process is far from satisfactory. This method of deformation is of interest for at least two reasons. First, it provides a mechanism in addition to glide for the relief of stresses, and, in the bcc and hexagonal close-packed metals may result in significant amounts of plastic flow. Secondly, there is the possibility that twins may act as barriers for dislocation movement, resulting in pile-ups which could nucleate cracks. As might be expected, the bulk of the literature on mechanical twinning in the bcc metals is concerned with iron. A good summary of the work done prior to 1954 is contained in the book by all.&apos; Recently the refractory bcc metals have become increasingly important. Limited studies have shown that tantalum,2,3 molybdenum,4,5 vanadium,6,7 tungsten,&apos; and columbium9-11 deform by mechanical twinning under some conditions. Alloys of molybdenum with rhenium and tungsten with rhenium show extensive deformation by twinning at room temperature.I2-l4 Most of these studies have dealt primarily with mechanical properties at low temperatures or have shown the existence of twins, and there is only a small amount of information concerning the conditions under which they form. The subject of the present paper is the formation of twins under stress in columbium with a consideration of their morphology. EXPERIMENTAL PROCEDURE The material used for these studies was taken from an ingot of columbium which had been melted twice by the electron-be am-method. The analysis of the ingot was (in ppm): B < 1, C = 10, Fe < 100, The cast ingot contained very large grains, and it was possible to obtain single-crystal prisms which measured from ¼ to 3/4 in. on a side. A few experiments were conducted on polycrystalline plate which was prepared by rolling material from the same ingot at room temperature and annealing at 1000 in a dynamic vacuum of 10-6 mm Hg. This gave a plate in which the grains had an average diameter of 3 mm. After the specimens were cut from the ingot, the six faces were metallographically polished and elec-tropolished to remove all traces of cold work. Most of the observations were made on the surfaces of the deformed specirllens without further treatment. Occasionally, etching after deformation was desirable. In these cases, an etchant of the composition 50 parts H2O, 5 parts HNO3 25 parts HF, and 10 parts H2SO4 was found to delineate the twins very well. Unless considerable care was taken to ensure the removal of all disturbed metal left by the mechanical polishing, etching failed to reveal many of the features discussed in this; paper. The specimen&apos;s were deformed either by impact or slow compression at 77°K (liquid-nitrogen coolant), 198°K (dry ice and acetone coolant), and 298°K. The impact load was delivered by a hammer except in one case where the load was delivered by a bullet. Slow compression was carried out on a hydraulic testing machine equipped with a chamber to hold the coolant. EXPERIMENTAL RESULTS It has been generally believed that the conditions favoring the formation of deformation twins are large grains, low temperature, and impact loading. In fact, Barrett and Bakish2 found twins in tantalum only after impact deformation at 77°K, and Adams, Roberts, and Smallman10 observed twins in columbium only at 20 For these reasons, the initial experiments of this study used impact loading. Hammer blows caused many bands resembling twins in single crystals a.t 77" but not at 198°K. Only a few slip lines were observed on any of the single-crystal specimens of this study—essentially all the deformation occurred by twinning. The appearance of the twins on the as-deformed surface is shown in Fig. 1. Although both Figs. 1(a) and l(b) are photomicrographs of twins taken at the same magnification and from the same crystal, they are startlingly different in appearance. Fig. 1(a) was taken from the crystal face approximately perpendicular to the shear direction, whereas Fig. 1(b) was taken from

Jan 1, 1962

By K. J. Liles

The Bureau of Mines conducted laboratory semicontinuous and continuous heavy liquid tests to determine the feasibility of producing commercial-grade products from the high-clay sylvinite ores of the Permian Basin in New Mexico. Continuous test operations demonstrated that concentrates containing 59.9 percent K2O and recoveries of over 75 percent of the contained potash can be obtained. The organic heavy liquid was effectively recovered by vaporization, condensation, and absorption methods. Less than 5 parts per million of heavy liquid vapors were released to the atmosphere. This loss represents only 0.02 pound of heavy liquid per ton of ore treated.

Jan 1, 1973

By G. Chi, W. J. Davis, S. Watters, D. Hoy, S. Castonguay

"The Poplar Mountain gold occurrence in western New Brunswick is hosted in the Poplar Mountain volcanic complex (PMVC), which is located along the southern segment of the regional Woodstock fault zone. The PMVC consists of three principal units including, in ascending order, a porphyritic felsic volcanic unit, a volcaniclastic unit, and a mafic volcanic unit. U-Pb dating of zircon indicates that the age of the volcanic rocks is younger than 459 ± 3 Ma, and 40Ar/39Ar dating of mineralization-associated sericite indicates that the age of mineralization is 411 ± 3.7 Ma. Gold-mineralized zones occur in all the lithologic units but mainly in the porphyritic felsic volcanic unit. Gold zones are not controlled by individual faults but are characterized by high-density brittle fracturing, thin carbonate-quartz veining, and intensive ankerite-sericite alteration, superimposed on an earlier chlorite-calcite- quartz alteration. Gold is associated with arsenopyrite, which mostly occurs as disseminations in the host rocks, and to a lesser extent with quartz-carbonate-sericite veins and quartz-cemented breccias.Geochemical data indicate that mineralization-associated alteration is characterized by enrichment of K, Rb, Cs, Ca, Sr, Ba, As, Sb, W, C, and S. Fluid inclusion data indicate that the mineralizing fluids are composed of H2O, salts, and CO2 with variable amounts of N2 and CH4; salinities range from 2.3 to 10.6 eq. wt.% NaCl, but mainly from 2.3 to 5.6 eq. wt.% NaCl, and homogenization temperatures lie mainly between 220° and 270°C. Fluid pressures at the site of mineralization are estimated to have been 770 to 1200 bars, corresponding to a depth of 2.9 to 4.6 km at lithostatic pressure. The d18OSMOW and d13CPDB values of mineralization-related ankerite range from +14.5‰ to +16.5‰, and -6.8‰ to -8.3‰, respectively. The d18O values of the ore-forming fluids are estimated to be 6.4‰ to 8.3‰ at a temperature of 250°C. These carbon and oxygen isotope data fall in the field of magmatic fluids and in part the field of metamorphic fluids.Considering the geological setting of the region, abundant granitic intrusions, the similarity between the age of mineralization (411 ± 3.7 Ma) and the nearby Pokiok batholith (402-415 Ma), and the enrichment of granophile elements in mineralization-related alteration, the ore-forming fluids were probably derived from a granitic intrusion underneath the PMVC. These fluids were focused along structures related to the Woodstock fault. The Poplar Mountain gold occurrence might be compared to some granitic intrusion-related gold systems based on the geochemical data presented herein. L’indice aurifère de Poplar Mountain dans l’ouest du Nouveau Brunswick est contenu dans le complexe volcanique de Poplar Mountain (CVPM), lequel est situé le long du segment sud de la zone de faille régionale de Woodstock. Les trois unités principales du CVPM sont, de la base au sommet, une unité volcanique felsique porphyrique, une unité volcaniclastique et une unité volcanique mafique. La datation U-Pb de zircons indique que les roches volcaniques sont plus jeunes que 459 ± 3 Ma, et la datation par la méthode 40Ar/39Ar de séricite associée à la minéralisation assigne à la minéralisation un age de 411 ± 3.7 Ma. Bien que les zones minéralisées en or soient présentes dans toutes les unités lithologiques, on les retrouve surtout dans l’unité felsique porphyrique. Les zones aurifères ne sont pas contrôlées par des failles individuelles mais sont caractérisées par une grande densité de fractures cassantes, de minces veines de quartz-carbonate, et par une altération en ankérite-séricite intense qui se superpose à une altération antérieure en chlorite-calcite-quartz. L’or est associé à l’arsénopyrite, laquelle est principalement présente à l’état de disséminations dans la roche hôte, et à un moindre degré avec des veines de quartz-carbonate-séricite et des brèches à ciment de quartz.Les données de géochimie indiquent que l’alté"

Jan 1, 2008

By Kenric C. Owen

INTRODUCTION Situated 23 miles east of Pretoria the Premier Mine started diamond production in 1903. Two years later it produced the largest diamond yet discovered, the 3 106 carat Cullinan stone. For the period to 1932 when the mine was closed down due to economic circumstances, open cast mining was practised using inclined rope haulage traction and by this time had produced 48.5 million carats of predominantly industrial quality diamonds from 148 million tons of ore. In 1945 it was decided to re-open the mine using underground mining methods. A system using long hole benching was devised (Hodgson and Sewel 1960). This system was later modified but still forms the basis for approximately fifty percent of production. Following the successful introduction of block caving on associated diamond mines in the Kimberley area (Gallagher and Loftus 1960) this mining method was introduced to the Premier Mine in the late 60&apos;s and now accounts for nearly 50% of production. This paper will discuss block caving at Premier Mine in the light of our experience and discussion will be directed to the main geological and structural features of the orebody and host rocks and the related constraints imposed on the mining methods. Reference is made to the long hole benching mining method for comparative purposes. GENERAL DESCRIPTION OF OPERATIONS The ore from the block caving and bench mining areas gravitates via ore passes to a twin haulage, 500m below surface. Electric 13 tonne locomotives, each hauling a train of 10 Granby type cars, deliver the ore to two 42" x 48" (1.06m x 1.22m) jaw crushers. The ore is reduced in size to minus 0.15m before being hoisted to the treatment plant on surface. Hoisting is done with 12.5 tonne bottom discharge skips in a five compartment rectangular shaft using two 3 240 H.P. semi automatic Ward Leonard winders. A small single drum service winder operates in the other compartment. Men and materials travel in a separate shaft in a 5,4m x 2,8m cage operated by a Koepi winder. These two shafts are also the main intake airways to the mine. The two main extraction fans capable of 250 m3/s at 3,2 kPa are situated on surface and are connected to the underground workings by an incline and a network of air passes and return airways. GEOLOGY Although there are numerous occurrences of kimberlite bodies in the district, the Premier Mine kimberlite pipe is the only economic orebody. It is roughly oval in shape with surface dimensions of 900m on the long axis and 450monthe short axis. The surface area is 320 000 m2. The kimberlite has intruded a massive body of felsite and norite which is intersected by a number of faults. The contact between the kimberlite and host rock is clear cut and dips inward at an average angle of 80°. Cutting across the pipe and the country rock is a 75 metre thick gabbro sill, the top of which intersects the pipe below the 347m level and dips at 15&apos; to the north west. The kimberlite has been metamorphosed a distance of some 20m both above and below the sill contacts. Age measurements on biotite from the gabbro date the sill as 1 115 million years, thereby providing a minimum age of the pipe. (Pre Cambrian). All other pipes in South Africa are of Cretaceous age (60 million years). A simplified geological plan and section of the Premier Mine orebody is shown in Figure 1. It is thought that the kimberlite intruded in at least three distinct phases. The kimberlites of these different phases can be distinguished most easily by their characteristic colour. BROWN KIMBERLITE. This is the oldest kimberlite and forms a crescent shape in plan on the south eastern side of the pipe. In depth it increases in relative area. Although the brown kimberlite carries the highest diamond grade in terms of carats per ton all the various kimberlites in the Premier pipe are economic to mine.

Jan 1, 1981