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By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of liquid Mg-Ge alloys have been determined between 1000°and 1500°K by an isopiestic method. Germanium specimens, heated in a temperature gradient and contained in covered graphite crucibles of special geometry, were equilibrated with magrtesium vapor in closed titanium tubes. The crucible design allowed free access of magnesium vapor to the samples during the equilibration to form alloys of magnesium and germanium, but prevented magnesium losses from the crucibles on quenching the titaniuin tubes to terminate the experimental runs, thus preserving the equilibrium alloy compositions. The activities and partial molar enthalpies of magnesium and the integral thermodynamic properties of the system were calculated from the experimental data. THE Mg-Ge phase diagram' shows one congruent melting compound, Mg2Ge, of essentially stoichio-metric composition, two eutectics, and very limited terminal solid solubilities. Very little information is available on the thermodynamic properties of the Mg-Ge system. The free energy of formation of Mg,Ge was recently deter-mined2 by a Knudsen cell technique in the temperature range 610° to 760°C. The standard enthalpy of formation of Mg,Ge was measured calorimetrically by Bever and coworkers.3 The present study was undertaken as part of a general investigation of the thermodynamic properties of the homologous series of Mg-Group IVB systems, i.e., Mg-Pb,4 Mg-Sn,5 Mg-Ge, and Mg-Si. An isopiestic technique was used which was developed by the authors5 for investigating the thermodynamic properties of liquid Mg-Sn alloys. Specimens of the nonvolatile component, contained in covered graphite crucibles, are heated in a temperature gradient in an evacuated and sealed titanium reaction tube, and equilibrated with magnesium vapor of known pressure. The method employs crucibles of special geometry which preserve the high-temperature equilibrium composition of liquid alloys having a highly volatile component such as magnesium on termination of the experimental runs by quenching the crucibles to room temperature. EXPERIMENTAL PROCEDURE First reduction germanium of 99.999+ pct purity (Eagle-Pitcher Co., Cincinnati, Ohio) and 99.99+ pct magnesium metal (Dominion Magnesium Ltd., Toronto, Canada) were used. The graphite crucibles were machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non-reactivity of graphite with germanium at the temperatures used in this study had been previously established by Scace and Sleck.6 The experimental procedure has been previously described in detail.5 The selection of a particular crucible geometry for a run was determined by a combination of imposed experimental conditions, the principle being that more tightly covered crucibles were required to preserve alloy compositions during quenching when higher magnesium pressures and higher specimen temperatures were used. Depending upon the composition range of the equilibrated alloys the source of the magnesium vapor was either pure magnesium or a two-phase mixture of Mg2Ge + Ge-rich liquid of known magnesium pressure. The experimental runs can be divided into the following three groups on the basis of crucible geometry and magnesium source material. Crucibles with Small Holes and Pure Magnesium Reservoirs. The crucible dimensions were identical to those of the Mg-Sn investigation5 except that the hole diameters were reduced to 0.010 in. because of the higher temperatures and higher magnesium pressures involved in the Mg-Ge system. During an equilibration run, magnesium vapor diffused from the reservoir to each specimen through the small holes, one drilled through the crucible lid and two others drilled through graphite baffles positioned vertically inside the crucible between the lid hole and the specimen. Since the magnesium pressure was high, i.e., in the range 117 to 277 Torr, during the equilibration time of approximately 24 hr, equilibration was not impeded by these holes. A specimen composition at equilibrium was fixed by the relative temperatures of the specimen and the reservoir, and by the thermodynamic properties of the system. Upon brine quenching the titanium reaction tube to end a run the vapor pressure of magnesium above the liquid alloys decreased exponentially with decreasing temperature, and the small cross-sectional areas of the holes (4.9 x 10"* sq cm) drastically reduced magnesium losses from the crucibles. Because of its low vapor pressure, germanium losses from crucibles during a run were at most 0.2 mg for pure germanium and correspondingly less for the alloys. This crucible geometry satisfactorily retained the equilibrium alloy compositions on quenching for magnesium-rich (from 3 to 33 at. pct Ge) alloys provided their temperatures were below the melting

Jan 1, 1967

By T. A. Pollard, C. R. Sandberg, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By C. R. Sandberg, T. A. Pollard, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By James W. Halley

"Fine-grained" steels have been standard products for many years. This paper describes an investigation of the effects of some of the more common grain-growth inhibitors used to produce these steels. The properties, response to heat-treatment, and the deoxidation practice necessary to produce "fine-grained" steels have been the subjects of numerous papers. It has been shown that a substantial quantity of aluminum is necessary to produce this type of steel, and it has been indicated that titanium and zirconium produce a similar result. For some time there was a lively argument between those who felt that aluminum refined the grain and those who felt that aluminum oxide was the effective agent. This argument subsided with an apparent victory for those promoting aluminum oxide. Most of the work on grain size has divided steels into two broad classifications based upon McQuaid and Ehn's original carburizing test at 1700°F or some similar test at this temperature. If the steel coarsened at this temperature, it was coarse grained, while if it did not it was he grained. Quantitative data concerning how much a certain amount of aluminum raised the coarsening temperature and affected the properties, all other factors being constant, are very meager. Similar information regarding titanium and zirconium is practically nonexistent. The published information on aluminum yields some quantitative information. Epstein, Nead and Washburn' gave the first quantitative information on the amount of aluminum necessary to prevent grain growth at 1700°F. They showed that the addition of a pound to a pound and a half of aluminum per ton (0.05 to 0.075 per cent) would assure steel that would not coarsen during a McQuaid-Ehn test at 1700°F. Herty, McBride and Houghg reported that a steel containing 0.020 per cent acid-soluble aluminum coarsened between 1742° and 1832°F., while steels containing 0.016 per cent and 0.017 per cent acid-soluble aluminum coarsened between 1652° and 1742°F. compared with similar aluminum-free steels that started to coarsen at 1580°F. Herty3 also showed a marked improvebent in low-temperature notched impact resistance with increasing acid-soluble aluminum up to 0.030 per cent. McQuaid4 compared the coarsening of steels containing 0.011 to 0.204 per cent total aluminum and found a maximum coarsening temperature at 0.098 per cent aluminum. He had no samples between 0.015 and 0.098 per cent aluminum. Houdrement6 found a marked decrease in coarsening temperature with aluminum contents above 0.50 per cent. Kinzel, Crafts and Egan6 found that aluminum and zirconium improved the low-temperature impact resistance of a low-alloy steel, while titanium was detrimental. Sims7 shows that sulphur increases the coarsening temperature and that the maximum coarsening temperature is between 0.04 and 0.06 per cent added aluminum. The fact that the coarsening temperature passes through a maximum with increasing aluminum content appears to be well established. The aluminum content that

Jan 1, 1947

By James W. Halley

"Fine-grained" steels have been standard products for many years. This paper describes an investigation of the effects of some of the more common grain-growth inhibitors used to produce these steels. The properties, response to heat-treatment, and the deoxidation practice necessary to produce "fine-grained" steels have been the subjects of numerous papers. It has been shown that a substantial quantity of aluminum is necessary to produce this type of steel, and it has been indicated that titanium and zirconium produce a similar result. For some time there was a lively argument between those who felt that aluminum refined the grain and those who felt that aluminum oxide was the effective agent. This argument subsided with an apparent victory for those promoting aluminum oxide. Most of the work on grain size has divided steels into two broad classifications based upon McQuaid and Ehn's original carburizing test at 1700°F or some similar test at this temperature. If the steel coarsened at this temperature, it was coarse grained, while if it did not it was he grained. Quantitative data concerning how much a certain amount of aluminum raised the coarsening temperature and affected the properties, all other factors being constant, are very meager. Similar information regarding titanium and zirconium is practically nonexistent. The published information on aluminum yields some quantitative information. Epstein, Nead and Washburn' gave the first quantitative information on the amount of aluminum necessary to prevent grain growth at 1700°F. They showed that the addition of a pound to a pound and a half of aluminum per ton (0.05 to 0.075 per cent) would assure steel that would not coarsen during a McQuaid-Ehn test at 1700°F. Herty, McBride and Houghg reported that a steel containing 0.020 per cent acid-soluble aluminum coarsened between 1742° and 1832°F., while steels containing 0.016 per cent and 0.017 per cent acid-soluble aluminum coarsened between 1652° and 1742°F. compared with similar aluminum-free steels that started to coarsen at 1580°F. Herty3 also showed a marked improvebent in low-temperature notched impact resistance with increasing acid-soluble aluminum up to 0.030 per cent. McQuaid4 compared the coarsening of steels containing 0.011 to 0.204 per cent total aluminum and found a maximum coarsening temperature at 0.098 per cent aluminum. He had no samples between 0.015 and 0.098 per cent aluminum. Houdrement6 found a marked decrease in coarsening temperature with aluminum contents above 0.50 per cent. Kinzel, Crafts and Egan6 found that aluminum and zirconium improved the low-temperature impact resistance of a low-alloy steel, while titanium was detrimental. Sims7 shows that sulphur increases the coarsening temperature and that the maximum coarsening temperature is between 0.04 and 0.06 per cent added aluminum. The fact that the coarsening temperature passes through a maximum with increasing aluminum content appears to be well established. The aluminum content that

Jan 1, 1947

By G. S. Ansell, J. Weertman

The creep behavior of an aluminum alloy hardened with a finely dispersed phase of aluminum oxide was investigated. The as-extruded alloy shows an approximate steady-state creep in which the creed rate depends exponentially on the applied stress. The activation energy of creeb is abbroximately 150,000 cal per mole. The recrystallized alloy shows no steady-state creep. ONE method of improving the creep resistance of a metal is to introduce a finely dispersed second phase into the metal matrix. The improvement of the creep resistance has been qualitatively explained by assuming that the dispersed second-phase particles act as obstacles to dislocation motion. If the main effect of second-phase particles is simply to hinder dislocation motion then it is possible to derive a high-temperature creep equation for a dispersion-hardened alloy in a straightforward manner. In the Appendix of this paper such an equation is derived from a creep model which works very well for pure metals. Recently, F. V. Lenel has fabricated, for the first time, powder extrusions of aluminum-aluminum oxide in a large-grained recrystallized form. This alloy, designated as MD 2100, consists of a fine dispersion of aluminum oxide plates in a matrix of commercial purity aluminum. A considerable amount of investigation has been carried out concerning the microstructure and physical properties of this alloy.&apos; ) The aluminum oxide is present in the form of flakes 130A units thick and 0.3 u on edge. They are dispersed in the aluminum matrix with an average spacing of approximately 0.5 jx. The spacing varies in the range of 0.05 to 1.5 µ. The alloy structure is extremely stable at high temperatures. For this reason the alloy offers a unique opportunity for a fundamental study of creep of a very finely dispersed two-phase alloy. Lenel supplied specimens in both the unrecrystallized and recrystallized condition. This paper reports high-temperature creep experiments carried out on these specimens. The results obtained were rather unexpected. No steady-state creep was observed in the recrys-tallized material. In fact, after some transient creep which takes place upon loading, the creep rate is essentially zero ( < 10-8per min). If the second-phase particles acted solely as obstacles to the motion of dislocations, measurable steady-state creep would be expected. Since none is observed it appears that the main effect of the fine dispersion in the recrystallized material is to inactivate the dislocation sources themselves, rather than hinder the motion of dislocation loops created at these sources. EXPERIMENTAL DETAILS Specimens were tested in wire form, 0.087 in. in diam for the as-extruded alloy, and 0.035 in. in diam for the recrystallized alloy. These samples were held in friction-type wire grips; a gage length of 2.5 cm was used for all the creep tests. The specimens were held at 600°C in the test apparatus for at least 15 hr prior to each test. The tests were run under the condition of constant loading and, since the creep strains were small, can be considered as constant stress tests. The temperature of testing was held constant within 3°C. Elongations were measured with an optical cathetometer which was capable of measuring strains as smaIl as 0.00012. This allowed the measurement of strain rates as low as l0-8&apos;per rnin. In addition to the creep tests optical micrographs were made in order to determine both the grain size and microstructure of these materials. RESULTS Fig. 1 shows a few typical creep curves obtained from the as-extruded material. The elongations were somewhat erratic, but each curve shows a region of quasi-steady-state creep from which an approximate steady-state creep rate can be obtained. In general the higher the stress at a given temperature, the greater the total elongation before fracture. The lower the applied stress, the longer is the region where the creep rate is almost constant. Summary data from the creep tests of the as-extruded material are listed in Table I. The steady-state creep data of the as-extruded material for a range of stresses at a constant temperature follow a creep equation of the type creep rate = K&apos; = A exp (&) [11 where A and B are constants, k is Boltzmann&apos;s constant, T is the absolute temperature, and a the stress. The standard error of estimate of the data received is less than one order of magnitude. As shown in Fig. 2, if one compensates the creep-rate data for the effect of temperature over the range of test temperature, the steady-state creep data roughly follow a creep equation of the type Temperature compensated creep rate = K* = A exp

Jan 1, 1960

NEW MEMBERS The following list comprises the names of those persons who became members during the period of June 10, 1917, to July 10, 1917. BANKS, LEON MAXWELL Agent 3. Supt., Grant Leasing Co. Metcalf Ariz. BEAUCHAMP, HENRY CLAY : Mine Operator, Sisson, Siskiyou Co., Cal. BOCKING, CHARLES, Asst. Mgr., Butte & Superior ,Mining Co., Rialto Bldg., Butte, Mont. BEYER, HERMAN E., Chief Engr., Condenser Dept., Ingersoll-Rand Co., 11 Broadway, New York, N. Y. BLACK, HERBERT F 1512 Oliver Bldg., Pittsburgh, Pa. BRENNAN, PATRICK J., Gen&apos;l. Supt., Elkhorn Division, Consolidation Coal Co., Jenkins, Ky. BUTNER, DANIEL W., Chem. & Supt., Underground Min., Spanish American Iron Co., Daiquiri, Santiago de Cuba, Cuba. CARLTON, DAVE P Nevada-Douglas Cons. Copper Co., Ludwig, Nev. DE AROZENA, JOE Min. Engr., 321 Preusser St., San Angelo, Texas. DICKIE, CHARLES HERBERT, Pres., Georgia River Min. Co., Duncan, Vancouver Island, B. C., Canada. DOBBINS, WALTER Mill Foreman, Chino Copper Co., Hurley, New Mexico. DRURY, CHARLES W., Asst. Professor of Met., Queen&apos;s University, Kingston Out. Canada.

Jan 8, 1917

By A. U. Seybolt

Since the time this topic was originally treated in 1954, more recent French3,1 work has been published making it advisable to repeat the earlier oxygen solubility experiments, but using iron of a higher purity. Upon repeating oxygen saturation experiments with zone-refined iron, it was found that the oxygen solid solubility was at least an order of magnitude less than previously observed. SINCE the publication of an earlier paper1 (1954) on this subject by the present author, several contributions on this topic have appeared. Meijering2 in 1955 attempted to reconcile recent conflicting solubility data, without reaching any definite conclusion. sifferlen3 (1955) found that iron of high purity appeared to absorb a quantity of oxygen (0.005 to 0.025 pct) approximately proportional to the structural imperfections present, such as polygonization and grain boundary area. However, he also indicated that purity itself was a significant factor. He concluded that very pure iron nearly free of lattice imperfections would have essentially zero oxygen solubility. His second paper4 (1957) supported this contention since a zone-melted iron containing initially 0.0007 pct O analyzed only 0.0006 pct 0 after prolonged soaking at 850°C with an FeO layer on the surface. Because of the discrepancy between the results of Ref. 1 and those of Sifferlen, it seemed desirable to attempt to resolve this disagreement. EXPERIMENTAL PROCEDURE AND MATERIALS The experimental method used by sifferlen3,1 was essentially the same as that of Ref. 1. In this technique thin iron strip with a surface layer of FeO is soaked for prolonged periods at an elevated temperature in order to saturate the iron with oxygen. After two days at temperatures near 800° to 900° C, one would expect that the iron would be in equilibrium with the surface FeO. In the work reported in Ref. 1 there was evidence that two days holding at 8000to 900°C was more than sufficiently long for saturation. Sifferlen used 48 hr at 850°C. Because of the evidence presented by Sifferlen that the apparent oxygen solubility is a function of iron purity, three grades of iron were used as indicated in Table 1. The Bureau of Standards wire was used only for resistivity tests, while the other two irons were used for saturation-analysis tests of the type described above.

Jan 1, 1960

By B. M. Larsen, T. E. Brower

For some years we have been carrying on a rather comprehensive investigation of the occurrence of oxygen in liquid open-hearth steel. This investigation was interrupted by the war emergency and is therefore incomplete, with many questions still answered only partially, if at all; yet it seemed worth while to present a report of progress on this difficult field of research, if for no other reason than to promote discussion and further investigation of this important problem. The significance of such studies depends in large measure upon the accuracy of measurements of oxygen content in liquid steel while it is still in the furnace or as it flows into the ladle, or thence into the mold and there is, as we shall show, good reason for believing that the main source of uncertainty is in the sampling, not in the analytical method as such. The difficulty arises from the fact that any method of sampling is of itself apt to alter the amount of oxygen in solution in the liquid steel, because this oxygen is in a readily reactive condition. On the one hand, being usually present at a concentration appreciably in excess of that corresponding to equilibrium with the carbon then present, it may decrease rapidly in percentage by reaction with carbon and evolution of CO, especially if the liquid metal is in any way shaken or brought in contact with a cooler solid surface. On the other hand, it may increase rapidly by ab- sorption of oxygen from a slag, a furnace atmosphere, or from air. These circumstances, which are inherent in the problem, as well as our conclusion that, despite the considerable amount of careful work already done, there is still no method of sampling liquid steel acceptable as an unquestioned standard, ed us to undertake systematic comparisons of oxygen content of large numbers of samples taken: (I) by a single method at different positions and levels in the bath; (2) at the same place by different sampling methods; and (3) from bath, tapping stream and pouring stream. The different sampling methods yield somewhat different values and there is as yet no way to tell with certainty which is the most accurate. But the general reproducibility and consistency of the results give us some confidence in certain inferences we draw from them: namely, that the "spoon" method of sampling, properly carried out, gives somewhat more consistent results than the "bomb" method, as it has usually been practiced; that, in the bomb method, an aluminum cap is preferable to a steel cap; that the oxygen content of liquid steel in a finished heat is substantially the same all over the bath at the same level, and tends to decrease at lower levels further from the slag interface; also that it tends to decrease, and to decrease erratically, from furnace bath to tapping stream entering the ladle. Accordingly it seemed desirable to report these observations in detail as a first step, so that the reader may judge their significance as a contribution towards solution of the main problem, which is to find a means of pre-2

Jan 1, 1945

By S. W. Hazen

The use of operations research and computer techniques continued to expand during 1967. A number of mining companies either obtained computers or were experimenting with their use through service bureaus. This trend was also evident in the Canadian mining industry. Although the annual Symposium and Short Course on Computers and Operations Research in Mineral Industries was not held in 1967, technical periodicals like MINING ENGINEERING, Mining Congress Journal and Engineering and Mining Journal stepped up their coverage on the subject. The annual AIME meeting had eight papers in two sessions and one session on Operations Research was held at the SME Fall Meeting in Las Vegas.

Jan 2, 1968

The St. Lawrence Seaway and power project has received the support of the Canadian Parliament, with the House of Commons approving a bill that authorizes the Government to proceed with construction of the seaway, with or without U. S. cooperation. Itogan Mining Co., third largest gold mine in the Philippines, reopened in December under the management of Marsman and. Co. The &apos;mine was almost totally destroyed during the occupation. The International Materials Conference committee on copper, lead, and zinc has recommended against stockpiling during the: first quarter of 1952 because of the current demands for defense needs. The General Services Administration has told producers who have contracts calling for delivery of copper to the stockpile during the first quarter of 1952 that they do not need to make those deliveries.

Jan 1, 1952

By J. B. Cheatham

Applications of the mathematical theory of plasticity promises to lead to the solution of many drilling and rock mechanics problems. ,Because of mathematical considerations, the inelastic behavior of rock has frequently been represented by a perfectly plastic model in conjunction with a yield criteria of the Coulomb or Mohr type. The totality of all stress states for which a solid ceases to behave elastically can be represented as a limit surface in stress space. ,Probing of such limit surfaces indicates details of strain hardening which are not provided by the standard triaxial testing procedure. Probing tests of the limit surfaces have been performed on Cardova Cream limestone to provide data for extending plasticity theory to cover situations in which consolidation and strain hardening are present. Test results indicate that this highly porous limestone undergoes a permanent volume decrease when it is subjected to hydrostatic pressures in excess of 3,500 psi. A virgin sample tested under a confining pressure of 1,500 psi has a yield strength of 1,700 psi; however, if the sample is subjected to a consolidation pressure of 5,000 psi, before testing at 1,500 psi, the yield strength is raised to 2,300 psi. Thus, both consolidation and strain hardening are important considerations in describing the mechanical behavior of this limestone. Tests conducted with the axis of the core having different orientations indicate that this rock is also anisotropic. Portions of the initial and subsequent limit surfaces are determined for samples loaded either perpendicular or parallel to the bedding planes. INTRODUCTION Previous experimental work in rock mechanics indicates that no mathematically tractable constitutive theory is inclusive enough to describe the mechanical behavior exhibited by all types of rocks under all conditions of stress and temperature. Indeed, the type of deformation encountered in a single type of rock is known to depend upon the stress and temperature conditions in the rock during deformation.l-5 Certain rocks and minerals, notably those minerals composed of ionic salts, have been shown to exhibit plastic deformation when tested under conditions of high confining pressure.2 Since the mathematical theory of plasticity provides simplifications over the theory of elasticity in certain types of problems, such as those in which limit analysis can be applied, it is of interest to know under what conditions plasticity theory may be applied to rock mechanics problems. The following factors determine the nature of the deformation a particular specimen will undergo: (1) the microscopic structure of the rock, i.e., the structure visible under an optical microscope, including number of phases, porosity, distribution of phases, (2) the mineralogical structure of the solid phases, (3) the conditions of stress and the rate of change of stress and (4) the temperature. Extensive experiments on Yule marble, Carthage marble, Solenhofen limestone and other calcerous rocks indicate that these relatively nonporous rocks deform plastically under certain conditions of loading, and creep under other conditions of loading.l-3 This study is concerned with the behavior of Cordova Cream limestone (Austin chalk) which is also composed almost entirely of calcite and thus has the same mineralogical composition but, because of a rather large porosity, it possesses a different microscopic structure. This investigation was undertaken to learn if Cordova Cream limestone deforms plastically despite the embrittling effect of the pore spaces, and to provide data which can be used to determine whether the mathematical theory of plasticity can describe the mechanical behavior of Cordova Cream limestone. A brief discussion is given of some of the underlying principles of plasticity theory concerning stress space and limit surfaces. Strain hardening is defined and a discussion is given of how the mechanical behavior of a material can depend on the previous history of the loading. This is followed by a description of the experimental procedures

By Earl Bardwell

THE determination of suitable and safe annealing temperatures is one of the most important problems arising in the operation of a copper rolling mill. Certain of the larger mills have worked this problem out for themselves and in these mills the operation has become more or less standardized. In some of the mills pyrometers are used to measure the temperature of the annealing furnaces and careful watch is kept to see that overheating does not take place. In a considerable number of the mills, however, dependence is placed entirely on the judgment of the operator. The almost total lack of literature bearing on this subject seems sufficient warrant for the publication of this paper. The discussion of this subject naturally divides itself into two parts: (1) The effect of annealing temperature on physical properties; and (2) changes in the microstructure of refined copper due to cold rolling and annealing. I. THE EFFECT OF ANNEALING TEMPERATURE ON PHYSICAL PROPERTIES For the purpose of investigating this phase of the subject six test bars were selected, varying in oxygen content between the limits of 0.036 and 0.070 per cent. The chemical composition of each of these test bars was as follows:

Jan 8, 1914

By B. H. Kear, B. J. Piearcey

The orientation and temperature dependence of the tensile and creep propevties oj Mav-M200 crystals halle been determined. Crystals oriented for single slip exhibit ,maximum ductility, minimum work hardening, and least creep resistance, whereas crystals in multiple slip orientations show nzinimu~n ductility, strongest work hardening, and greatest creep resistance. At 1400" and 1600°F there is a marked improzlenzent in creep strength for orientations approaching [001] and [111], indicating that interactions between dislocations gliding in intersecting octahedral slip systems play an important role in creep resistance. At 1800°F the creep strength is much less dependent on orientation, which is rationalized in terms of slip in cube planes as well as octahedral A frequent mode of failure in high-strength cast nickel-base superalloys is by intergranular fracture, particularly along those grain boundaries oriented transverse to the major stress axis. VerSnyder and ~uard&apos; demonstrated that this problem could be overcome by eliminating transverse grain boundaries through unidirectional solidification. Piearcey and versnyder2 made use of this principle in the development of unidirectionally solidified gas turbine blades and vanes, where the growth direction of the columnar grain structure coincides with the axis of principal stress under operating conditions. The present investigation was undertaken to determine if further improvement in properties may be obtained by eliminating grain boundaries altogether, so as to take advantage of the well-known dependence of mechanical properties of single crystals upon the orientation. 1) EXPERIMENTAL PROCEDURE Single crystals of Mar-M200* were grown from the melt under vacuum by a modified Bridgman method. The melt was poured into a preheated alumina mold, and crystal growth was promoted from one end by appropriate gradient cooling. Tensile and creep specimens (2 in. diam by $ in. gage length) were prepared by a series of operations involving electrical discharge machining, precision grinding, and electropolishing. The orientations of the specimens were determined by the Laue X-ray back-reflection method. Tensile tests were carried out in aWiedemann machine with furnace attachment, using a strain rate planes. In all orientations imzpvouement in the strength charactevistics of the material can be induced by heat treatment. Creep ad stress rupture data for (001) oriented crystals are compared with similar data obtailted previously joy random polycvystalline material, and also columnar grained material having a prejevved (001) orientation. The single-crystal )material exhibits both longer rupture life and lower minimum creep rate at all temperatuves, and the rupture elongation is comparable with that in the columnar grained material. From these results it is concluded that single crystals should and useful application in gas-turbine blades and tanes. The optimum orientation for a blade is considered to be with its axis of principal stvess parallel to (001) ou (111). of 0.0001 sec-&apos;. Load and extension were recorded directly on an X-Y recorder. The strain measuring device consisted of extension arms attached to the grips at one end and leading out of the furnace to an LVDT (linear variable differential transformer) at the other. Creep tests were performed using a standard constant load creep frame. 2) DISCUSSION OF RESULTS 2.1) Structure of Alloy. The structure and segregation in as-cast and heat-treated Mar-M200 has been described in detail else where.~ The main features are as follows: the as-cast material is heavily cored, due to pronounced dendritic segregation during solidification; the dendrites are rich in tungsten and cobalt whereas the interdendritic regions are rich in chromium, titanium, nickel, and carbon. The structure consists of -60 vol pct coherent precipitate of y&apos;, basically Ni3(A1,Ti), in a matrix of y (nickel-base solid solution), interspersed in the interdendritic regions with minor MC carbides and -y&apos; eutectic. The y&apos; particles, and y-y&apos; eutectic, contain more titanium, aluminum, and nickel, and less tungsten, cobalt, and chromium than the y matrix. Heat treatment partially removes segregation, eliminates the eutectic, refines the y&apos; dispersion in y, and gives additional partially coherent M23Cs carbide. An as-cast crystal, therefore, is composed primarily of two oriented phases (y + y&apos;), whereas the normally heat-treated crystal consists of three oriented phases (y + y&apos; + MZ3Cs). Typical electron transmission micrographs of the y + y&apos; structure are shown in Fig. 1. Crystals grown in the (100) orientation develop a simple unidirectional dendritic structure, Fig. 2, since (100) happens to be the preferred direction of growth for dendrites in this material. Crystals grown in the {110) and (111) orientations, however, tend to promote equal growth, generally in separate colonies, in the two and three geometrically favored (100) growth directions, respectively. In other orientations of growth, a single (100) dendrite direction generally pre-

Jan 1, 1968

By C. W. Binckley, F. R. Burgess, E. R. Haymaker

A method of establishing stabilized back-pressure curves for gas wells producing from formations of extremely low permeability is presented. Actual well performance under many different operating conditions is shown by the stabilized back-pressure curve. By use of the method. it is possible to conduct back-pressure tests with a critical-flow prover on wells that stabilize slowly, and save approximately 88% of the gas ordinarily vented to obtain satisfactory test data, with a great reduction in time required for testing. INTRODUCTION The reasons for establishing dependable back-pressure curves on gas wells have been pointed out by previous publications. The publication most referred to. of course, is the United States Bureau of Mines Monograph 7, titled "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices". The technique generally established therein has been accepted and used by many engineers; and, when proper tests are conducted, the results can be used for the analysis and solution of several practical problems concerning field operation and development. Even where formations of low specific permeability are encountered, the determination of a well&apos;s actual performance by the back-pressure test method permits the engineer to analyze many problems in individual well operation and also to predict necessary future field development. Such problems as the determination of the ability of a well to produce into a pipe line at a predetermined line pressure, the design of gas gathering systems and meter settings, and the determination of the time and the number of wells required to be drilled to meet future market obligations, can be solved, in part., by the use of a reliable back-~ressure curve. In addition, the computed well delivery rates determined by data from backpressure tests ordered by state regtilatory bodies, when compared with the true back-Pressure curve, permit the operator to ascertain whether such data represent unstable or relatively stabilized delivery rates for given pressure conditions of the well. The technique of back-pressure testing, as described in this report, was developed by Phillips Petroleum Company engineers from data obtained during a testing program that started in 1944 and has been continued to date. Three hundred and eleven back-pressure tests were conducted on 299 wells located in the southern part of the Hugoton Field. The gas-bearing zone is composed of several dolomitic formations of the Permian Age; the important ones are the Herington, Upper Krider, Lower Krider, and Winfield. The average bottom-hole temperature is approximately 91 °F.. and the initial wellhead shut-in pressures range from 400 to 440 psig. The spacing pattern is 640 acres per well with each well located near the center of the section. The range of back-pressure potentials on wells tested was from 500 to 23,000 Mcfd. All gas wells were acidized, and the quantity of acid used, expressed in 1574 hydrocloric acid, varied from 12,000 to 22,000 gallons per well. The quantity and concentration of each treatment depended on the stage, the formation being treated, and experience gained from previously completed wells. The gas in the Hugoton Feld is a "dry" gas. It has a gasoline content of approximately 0.25 gallons per thousand cubic feet, as determined by charcoal test, and its specific gravity averages about 0.71 as compared to air (air = 1.00 at 60°F.). Of the wells tested, 71 were completed with 7" casing, 3 with 9 5/8" casing, and 1 with 6%" casing set on top of the upper producing formation with the well bore through the gas bearing formations being open hole. Two hundred and twenty-four were completed with 5 1/2&apos;&apos; O.D. casing set through the gas bearing formations and perforated. For the purpose of establishing reliable back-pressure curves in the area, Phillips Petroleum Company personnel has computed data on the basis of 24-hour flows per point. Early in the program, many tests were actually permitted to flow 24 hours to obtain data for each plotting point, at great expense in man power and time. Presently, however, such tests have been replaced by tests of short duration flows which can be made to effect results that correspond to the tests obtained by flows of much longer duration. METHOD When a gas well producing from a reservoir of low permeability is opened for production through a constant size orifice, both the rate of flow and working pressure decline. first at a high rate and later at a lower rate until after several hours the decline becomes difficult to ascertain. In this paper the rae of flow and working pressure are considered to be stabilized when it becomes difficult to observe changes in working pressure during a period of three hours by the use of a deadweight pressure gage. Stalibization of pressure in the literal sense is never obtained in a producing gas well. In formations of low permeability. such as those in the Hugo-ton Field, most wellhead working pressures approach stabilization closely enough to be used satisfactorily in the determination of a back-Pressure potential curve after flow periods of 24 hours. We shall therefore describe the backpressure curve calculated from ohserved rates of flow and working pressure at the end of 24-hour flow periods.

Jan 1, 1949

By E. R. Haymaker, C. W. Binckley, F. R. Burgess

A method of establishing stabilized back-pressure curves for gas wells producing from formations of extremely low permeability is presented. Actual well performance under many different operating conditions is shown by the stabilized back-pressure curve. By use of the method. it is possible to conduct back-pressure tests with a critical-flow prover on wells that stabilize slowly, and save approximately 88% of the gas ordinarily vented to obtain satisfactory test data, with a great reduction in time required for testing. INTRODUCTION The reasons for establishing dependable back-pressure curves on gas wells have been pointed out by previous publications. The publication most referred to. of course, is the United States Bureau of Mines Monograph 7, titled "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices". The technique generally established therein has been accepted and used by many engineers; and, when proper tests are conducted, the results can be used for the analysis and solution of several practical problems concerning field operation and development. Even where formations of low specific permeability are encountered, the determination of a well&apos;s actual performance by the back-pressure test method permits the engineer to analyze many problems in individual well operation and also to predict necessary future field development. Such problems as the determination of the ability of a well to produce into a pipe line at a predetermined line pressure, the design of gas gathering systems and meter settings, and the determination of the time and the number of wells required to be drilled to meet future market obligations, can be solved, in part., by the use of a reliable back-~ressure curve. In addition, the computed well delivery rates determined by data from backpressure tests ordered by state regtilatory bodies, when compared with the true back-Pressure curve, permit the operator to ascertain whether such data represent unstable or relatively stabilized delivery rates for given pressure conditions of the well. The technique of back-pressure testing, as described in this report, was developed by Phillips Petroleum Company engineers from data obtained during a testing program that started in 1944 and has been continued to date. Three hundred and eleven back-pressure tests were conducted on 299 wells located in the southern part of the Hugoton Field. The gas-bearing zone is composed of several dolomitic formations of the Permian Age; the important ones are the Herington, Upper Krider, Lower Krider, and Winfield. The average bottom-hole temperature is approximately 91 °F.. and the initial wellhead shut-in pressures range from 400 to 440 psig. The spacing pattern is 640 acres per well with each well located near the center of the section. The range of back-pressure potentials on wells tested was from 500 to 23,000 Mcfd. All gas wells were acidized, and the quantity of acid used, expressed in 1574 hydrocloric acid, varied from 12,000 to 22,000 gallons per well. The quantity and concentration of each treatment depended on the stage, the formation being treated, and experience gained from previously completed wells. The gas in the Hugoton Feld is a "dry" gas. It has a gasoline content of approximately 0.25 gallons per thousand cubic feet, as determined by charcoal test, and its specific gravity averages about 0.71 as compared to air (air = 1.00 at 60°F.). Of the wells tested, 71 were completed with 7" casing, 3 with 9 5/8" casing, and 1 with 6%" casing set on top of the upper producing formation with the well bore through the gas bearing formations being open hole. Two hundred and twenty-four were completed with 5 1/2&apos;&apos; O.D. casing set through the gas bearing formations and perforated. For the purpose of establishing reliable back-pressure curves in the area, Phillips Petroleum Company personnel has computed data on the basis of 24-hour flows per point. Early in the program, many tests were actually permitted to flow 24 hours to obtain data for each plotting point, at great expense in man power and time. Presently, however, such tests have been replaced by tests of short duration flows which can be made to effect results that correspond to the tests obtained by flows of much longer duration. METHOD When a gas well producing from a reservoir of low permeability is opened for production through a constant size orifice, both the rate of flow and working pressure decline. first at a high rate and later at a lower rate until after several hours the decline becomes difficult to ascertain. In this paper the rae of flow and working pressure are considered to be stabilized when it becomes difficult to observe changes in working pressure during a period of three hours by the use of a deadweight pressure gage. Stalibization of pressure in the literal sense is never obtained in a producing gas well. In formations of low permeability. such as those in the Hugo-ton Field, most wellhead working pressures approach stabilization closely enough to be used satisfactorily in the determination of a back-Pressure potential curve after flow periods of 24 hours. We shall therefore describe the backpressure curve calculated from ohserved rates of flow and working pressure at the end of 24-hour flow periods.

Jan 1, 1949

By P. Greenfield, P. A. Beck

RECENT work by J. Darby, Jr. in this laboratory has shown that the reported vanadium-rich limit of the s phase in the Co-V system at 1200°C is in error. The appearance of a second phase in s actually is restricted to alloys containing over 68 atomic pct V. The error in the original value is due apparently to a reaction that takes place along the numerous cracks in the s specimens between the alloy and the impurities present in the He + 8 pct H atmosphere in the annealing furnace. Such a reaction and the consequent appearance of a second phase can be suppressed if the alloys are sealed under vacuum in Vycor tubing. The new value of 68 atomic pct V for the vana-dium-rich limit of the s phase in the Co-V system effects slightly the s compositions calculated from average values of N, and N,. for various s phases. The standard deviation between experimental mean compositions and those calculated from the assumption that s is characterized by a constant number of 3d + 4s electrons per atom (N,), is slightly reduced from 9.1 to 8.8 pct. The maximum divergence for the V-Mn s phase is reduced from 15.5 to 14 atomic pct. The standard deviation calculated from constant electron vacancy numbers given by N.. = 4.66 (Mo + Cr + V) + 3.2 (Mn) + 2.2(Fe) + 1.71(Co) + 1.6(Ni) is now greatly reduced, as the maximum divergence for this correlation previously occurred in the V-Co system. This maximum divergence is reduced from 7.6 to 2.3 pct, and the standard deviation for all s- phases is reduced from 4.1 to only 2.9 pct. The correlation for electron vacancy numbers given by N. 5.66 (V when with Ni or Co) + 4.88 (V when with Mn or Fe) + 4.66 (Cr + Mn) + 3.3 (Mn) + 2.66 (Fe) + 1.71 (Co) + 0.61 (Ni) is made slightly worse, and the standard deviation increases from 2.8 to 3.9 pct. These changes, however, do not affect the conclusions of the paper.&apos; The deviation between calculated and experimental s compositions is much less for either one of the electron vacancy correlations than for the correlation with the number of 3d + 4s electrons.

Jan 1, 1955

By J. V. N. Dorr

DEADWOOD and the Black Hills were familiar names to me from childhood, for. I had an uncle who was among the earliest eastern investors there and I used to hear of the Uncle Sam mine and its rich ore back in the eighties. The spring of my junior year at college, in 1893, brought me an offer of summer work at the Deadwood & Delaware smelter, in Deadwood, and full of the thrill of the long journey from New Jersey, I went out as chemist and stayed four months. Within a week or two of my arrival, I went through the tragic experience of seeing an associate drink cyanide by mistake and die within a few moments. I shall never forget the horror of feeling that my lack of knowledge of an antidote might be responsible for his death, but I found later that the solution he drank was so strong that nothing could have been done. A year after graduation, when I had settled down to chemical research work in New York, an offer came to go back to the smelter in Deadwood, and within a few days I was again tramping down "the Gulch" with my lunch bucket and putting in the standard assay office shift of that day, from 7 a.m. to 6 p.m., with a half-day off on Sundays. During my absence East, the D. & D. smelter had been changed from a pyritic smelter, using native pyrite, and Homestake concentrate to matte the siliceous gold ores, into a copper-matting smelter using copper ores brought from Butte, over the newly-completed Burlington rail-road. The work was interesting, and the laboratory offered many opportunities for making improvements. I remember also undertaking experiments at home on a new method of gold precipitation for the chlorination process and leasing a mine in Strawberry Gulch that promised great things, but soon petered out.

Jan 8, 1927

By Samuel Shallcross

THE principal function of the Bell limestone mine, of the American Lime & Stone Co., at Bellefonte, Pa., is to supply raw material to the company&apos;s modern rotary kiln plant at Bellefonte. Because mining costs are naturally higher than many open quarries with more favorably lying strata, it cannot compete, except to a limited extent, in the markets for road material and fluxing stone. In the broad sense, mining does have an advantage over the average open quarry when the end products are designed for and controlled by process and final inspection for the exacting demands of the industrial and chemical markets. Approximately 80 per cent of the output of the Bell mine is sold in the industrial and chemical markets. And as higher standards are set each year for construction and agricultural work, the remainder of the mine output goes to these two classes. Mining produces more fines than open quarries, and these fines are difficult to market; on the other hand, owing to absence of contaminating clay and impure rock, a greater percentage of the output of a mine is marketable. Because of the great production of fines, rotary kilns for lime burning are necessary when the stone must be mined. In 1921 the American Lime & Stone Co. operated 19 quarries and 72 lime shaft kilns spread over an area of 40 miles between Bellefonte and Altoona, Pa. At that time the line-production capacity of the 72 kilns amounted to approximately 700 tons per day. After 15 years the company operates three rotary kilns and six shaft kilns, with a combined output of approximately 500 tons of lime per day, concentrated in its single Bellefonte plant (Fig. 1). Its only stone-producing plants are now the limestone mine at Bellefonte and a construction-stone open quarry at Union Furnace, near Tyrone, Pennsylvania.

Jan 1, 1936

By Richard R. Zupp, David A. Stevenson

A theoretical treatment of austenitic Fe-C-Z solutions (where Z represents a substitutional solute) was developed by extending a solution model which was previously applied to austenitic Fe-C alloys. The model assumes that each carbon atom in the solution excludes H interstitial sites from occupancy by other carbon atoms rmd thai otherwise the assembly of carbon atoms is equivalent to a modified Langmuir lattice gas. The results of the treatment provide theoretical justification for a phenomenological expression previously developed to represent the influence of substitutional solutes on the thernlodynamics of carbon in austenitic Fe-C-Z alloys. The expression is: where Kz is a parameter which characterizes the Fe-C-Z system at a given temperature and Xz and xj are the concentrations of substitutional solute and interstitial carbon expressed as atom ratios. The parameter, Kz, was associated with the differ- A number of investigators have measured the influence of various substitutional solutes on the carbon activity in austenitic Fe-C-Z alloys, where Z represents any substitutional solute. Experimental information is available for alloys containing the following substitutional solutes: Mn,&apos; Si,&apos; Ni,2-5 CO,&apos;-&apos;, Cr,5, 9-11 CU,4 Al,= v,11, 12 and Ti.13 This information is essential for studying many phenomena in Fe-C-Z alloys, particularly diffusion and diffusion-controlled phase transformations For example the pffprts nf various ence between the interaction energies between carbon atorns and host-lattice atoms in the Fe-C-Z solution and the corresponding energies for the Fe-C solution. The carbon activity in a ternary Fe-C-Z alloy, ac, was obtained in terms of the composition of the alloy and the single parameter, Kz: where y° is the Henry&apos;s law constant for the binary Fe-C solution. Both y° and H crm be determined from the data for Fe-C solutions, without recourse to any experimental data for Fe-C-Z solutions. The theoretical treatment was extended to alloys containing several substitutional solutes. By neglecting interactions between the substitutional solutes, an expression for the carbon activity in multicomponent alloys was obtained in terms of the Kz values characterizing ternary Fe-C-Z systems. substitutional solutes on the rate of pearlite growth is explained14 on the basis of their effects on carbon diffusion, which result from their influences on the carbon activity in the solid phases. In addition, recent studies have emphasized the dependence of the pro-eutectoid ferrite transformation15 and other diffusional processes in austenite16 on the influence of substitutional solutes on the carbon activity in austenite. They have indicated the need for suitable analytical expressions to represent such influences. The present authors previously developed general phenomenological expressions to represent the equilibrium partitioning of carbon between Fe-C alloys and Fe-C-Z alloys.&apos;2 The expressions are applicable to all the austenitic Fe-C-Z alloys for which experimental data are available, and are sufficiently simple to recommend their general application. For alloys in

Jan 1, 1969