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By W. A. Vine

When a hole is made in a stressed solid, such as rock pierced by mine openings, equilibrium of the solid is destroyed. To restablish that equilibrium the stress condition in the rock surrounding the opening becomes rearranged. This rearrangement may or may not develop local stresses in the vicinity of the opening which exceed the elastic strength of the rock. Since stability of the opening depends, therefore, on the strength of the naturally occurring rock surrounding the opening, this rock is an engineering material of construction, and all rock affected by the associated opening or system of openings may be considered a structure. The term invert is chosen to describe the formation of the structure built from the inside, as it were, and a consequence of mining rather than an entity built for a purpose. By definition, an invert structure is formed when openings are made underground and is com- posed of that material on the solid side of a rock-air interface wherein the stress condition is affected by the associated opening or system of openings. The shape of an invert structure is never clearly defined; the skin of the structure may be mapped, and even described, but the boundary of the structure within the solid rock mass must be arbitrarily set.

Nov 1, 1955

By R. F. Hollis, C. K. McArthur

PRIOR to the application of anion exchange, all recovery of uranium from acid leach liquors precipitated an impure product requiring further upgrading before it could be refined. The ion exchange process, on the other hand, provides excellent selectivity for extracting soluble uranium from leach liquors, so that high grade concentrates can be produced directly. The discovery that uranium is readily adsorbed by anion exchange resins, together with the experience of resin and equipment manufacturers in water treatment, led to rapid development of ion exchange in a multiple column operation. Many processing plants using fixed bed ion exchange are in operation or under construction in Africa, Australia, and Canada. There are a limited number in the U. S. Although the fixed bed process has been highly successful, the feed to the ion exchange columns must be a clear solution, which is obtained by filtration or by countercurrent decantation of leached pulps. With some ores, poor filtration or settling characteristics make production of a clear solution difficult. Most processing plants in the U. S. receive their ores from a number of small mines, and there is considerable variation in the settling and filtering behavior of the ores. An ion exchange process was therefore desirable in which the uranium could be recovered directly for the leached pulp by adding ion exchange resin, which could be then separated from the pulp by a screening operation. The process would thus resemble the cyanide-charcoal process in which gold is adsorbed from cyanide pulp by means of activated charcoal. Preliminary tests in which leached pulps were directly contacted with resin beads led to the development of the RIP process.

Jan 4, 1957

By David B. Reger

The value of carbon ratios in determining the boundaries of possible oil deposits appears to have passed the hypothetical stage. The theory that the ratio of fixed carbon in pure coals is an invariable index of incipient metamorphism in both surface and underground rocks and that it may be applied in defining the limits of petroleum, advanced by David White,' has been received with keen interest by many petroleum geologists. Detailed isocarb maps have been prepared of the Pennsylvanian area of North Texas and Eastern Oklahoma by M. L. Fuller.² A similar map of the coal-bearing area of West Virginia is given here. An isocarb3 is a line showing an equal fixed-carbon percentage, pure coal basis; the term has been proposed by David White to supersede a less expressive nomenclature. The term carbon ratio is applied to the pereentage of carbon in pure coal after water and ash have been eliminated. As a comparatively small number of analyses have been made on this basis, it is usually necessary to compute the ratio by dividing the fixed carbon of the proximate analysis by the sum of the fixed carbon and volatile matter of the same analysis. Many thousands of proximate analyses have been made by the West Virginia Geological Survey, covering nearly every county in which coal is found. Numerous others have been made by the U. S. Geological Survey and the U. S. Bureau of Mines, but as uniformity of results is best secured by adhering to one set of analyses, the tests of the West Virginia Survey have been cxclusively used.

Jan 1, 1921

By Walter S. Weeks

The process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case I If compressed air is allowed to expand to the atmospheric pressure through an orifice in an air line that is supplied by a running compressor, no cooling results except the negligible one due to the JouleThompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. C, Specific heat of air at constant volume, B.t.u. per lb. per deg. F. C, Specific heat at constant pressure, B.t.u. per lb, per deg. F. T1 Absolute temperature of air in pipe, deg. F. T8 Absolute temperature of air outside after expansion and mixing and coming to rest. j Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

By F. F. Aplan

INTRODUCTION Coal is a solid combustible mineral substance resulting from the alteration of vegetable matter largely in the absence of air. It occurs in nature with varying percentages of mineral matter associated with and incorporated into the coalified material. If the amount of this inorganic mineral matter is sufficiently small, and if selective mining can be practiced so as to avoid the incorporation of ash- bearing material from adjacent strata and/or parting seams, the coal can be used as-mined. Otherwise, it must be given a preparation treatment. In 1980 the bulk of the approximately 525 coal preparation plants were located in the eastern half of the U.S., largely in the Appalachian and to a lesser extent in the midwest coal fields (1). Only 17 of these preparation plants were located in the west; these were in Colorado, New Mexico, Utah, Washington and Wyoming. In the past, however, a great many more preparation plants were operated in these and other western states. The upsurge in both the domestic and world- wide demand for quality coking and steam coal will certainly lead to an increase in the number of preparation plants in the west. In fact, there has been a massive development of coal mines and their associated preparation plants across our northern border in Alberta and British Columbia, largely to serve the export coking and steam coal market. Most of the tremendous increase in newly-mined coal in the western U.S. has come from thick seams of inherently low-sulfur, low- ash coal, easy to mine selectively without significant contamination with ash-forming minerals and requiring no preparation. Because of

Jan 1, 1983

By A. L. Mular

lnput energy-size modulus relation at small reduc-tion ratios is expressed by Et = (M, -Mt) k;. In some cases 13 is close to Schuhmann's distribution modulus a in value. Experimental results in conjunc-tion with the equation demonstrate the fact that energy input which produced fracture is not expended on unbroken starting material inside the mill at any time. Recently, schuhmann1 derived the Charles equation2 using the postulate that complex com-minution operations can be considered as a summa- tion of many comminution events. The fragments resulting from each event are assumed to follow the Gaudin-Schuhmamn distribution. In his derivation, Schuhmann implies that the size distribution of the total mass of a material is determined by the fraction of that mass actually subjected to comminution. Consider a feed to contain a volume, Vo, of uni- formly sized homogeneous material. After t seconds of grinding, let the volume of broken material be Vo - Vt where Vt is the volume of starting material not yet broken. The size distribution of the broken material is given by: where V is the cumulative volume less than size X, and k, is the size modulus of the broken material at time t. The distribution for the total volume at this

Jan 1, 1962

By Joseph Chalmers

The Petroleum Experiment Station of the U. S. Bureau of Mines at Bartlesville, Okla., has for the past three and a half years maintained a laboratory with the necessary personnel for conducting research on methods of increasing the recovery of oil. Some of the preliminary problems encountered in starting this work, with the data obtained, were discussed in A. I. M. E. Technical Publication No. 144, "Oil Recovery Investigations of the Petroleum Experiment Station of the U. S. Bureau of Mines," which was presented at the October meeting of the Institute at Tulsa, Okla., in 1928. Scope of Paper The following discussion gives some of the results of the more recent work at the Oil Recovery Laboratory. These experiments were conducted to obtain laboratory data pertaining to the relative merits or efficiencies of various pressure media in the recovery of oil from a sand reservoir. Two general types of experiments were conducted. In one the various pressure media were passed through an artificial body of sand partly saturated with oil at a constant input pressure; in the other the pressure media were passed through the body of sand partly saturated with oil at a constant volume rate. No attempt will be made to discuss the ramifications of economic problems which enter into the choice of a pressure medium. Apparatus and Materials The two 6-in. by 6-ft. flow tubes described in Technical Publication 144 were used in these experiments. They consist of 6-ft. sections of 6-in. casing with a blind flange at each end. There are three 1-in. well openings in each tube, spaced 2 ft. 4 in. apart, the end wells being

Jan 1, 1930

By Walter S. Weeks

THE process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case 1 If compressed air is allowed to expand to the atmospheric pressure through an orifice in an sir line that is supplied by a running compressor, no cooling results except the negligible one due to the Joule-Thompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. Cv Specific heat of air at constant volume, B.t.u. per lb. per deg. F. Cp Specific heat at constant pressure, B.t.u. per lb. per deg. F. T1 Absolute temperature of air in pipe, deg. F. T3 Absolute temperature of air outside after expansion and mixing and coming to rest. J Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

One of the newest and most modern surface mining operations in the East is gathering steam at Mapco Inc.'s Martiki mine in anticipation of yielding 2.7 million tons (3 million st) of coal annually.

Jan 10, 1977

By James Boyd

REACTIVE metals are not only those sufficiently radioactive to be used as fuels, such as uranium and thorium, but all metals that will find application in power reactors. It is required of such metals that they be relatively inert or chemically unreactive, dimensionally stable at high temperatures and pressures, and either very absorbent of radioactivity or transparent to it. To gain the right perspective concerning these metals it is necessary at this point to explode some erroneous concepts propounded so often they have become accepted as fact. The first of these is that the great industrial nations, especially the U. S., have reached their pre-eminent position chiefly because they possess abundant mineral resources. Some U. S. mineral economists, echoed by the politicians, have taken this position so often that many of their theories and policies are based on the presence of developed mineral resources as a sine qua non to the country's greatness. Actually the reverse is true- under a social and political system granting free rein to the initiative and creativeness of its people, many hidden mineral resources that otherwise would have lain fallow have been developed into productive enterprises to the benefit of the national industrial economy. Again, once the proper incentive was furnished, other countries have also been able to establish valuable mineral enterprises in recent years; resources long dormant for lack of a proper economic environment suddenly have become valuable and productive. It is possible to name immediately several nations where such domestic economic developments have had favorable repercussions within the last decade. The absence of productive mines in any country is no indication that workable deposits do not exist within its territory.

Jan 11, 1957

By Paul Averitt

In spite of recent trends in the United States toward construction of steam generating plants near mine mouths, and toward use of high-voltage direct current for long-distance transmission of electricity, coal in substantial amounts is being transported over relatively long distances to serve specific needs. As coal is a low-cost bulk commodity which is more suitable for use near the point of origin, some of these long hauls are of considerable interest because they show what can be done under the pressure for more and more coal to support industrial and economic growth. Japan has an Insatiable Appetite for Coal Perhaps the longest U.S. coal journey begins in the east Appalachian Basin of southern Pennsylvania, eastern West Virginia, and southwestern Virginia. High-quality coking coal mined in these areas is shipped by rail to Baltimore, Md., and to Hampton Roads, Va., where the coal is reloaded on freighters for shipment primarily to western Europe and Japan. In 1967, shipments of coal to western Europe totaled 19 million tons, and shipments to Japan totaled 12 million tons. Japan also imports coal from Australia, the U.S.S.R., Canada, Poland, the People's Republic of China, and to a lesser ex- tent from several other countries. In an effort to solve long-term needs, Japanese steel interests have contracted for the purchase from the Kaiser Steel Corp. of 51 million long tons of coking coal over the period 1970 to 1985. The coal will come from the Kaiser Steel Corp. mine near Fernie, British Columbia. This arrangement will reduce Japan's future dependence on Appalachian Basin coal.

Jan 10, 1969

THE foundation established by the partners of the late Robert W. Hunt provides for both a medal and a prize. The latter has not been given before this year, and the first award is to C. H. Herty, Jr., for his several papers on the physical chemistry of the open-hearth process.. He is the son of the well known chemist of the same name. He was born at Athens, Ga., on Oct. G 1896, graduated from the University of North Carolina in 1918, and went into war service as foreman of U. S. Chemical Plant No. 4, at Saltsville, Va. In 1919 he went to Massachusetts Institute of Technology, where he was successively instructor, research assistant, and research associate in the School of Chemical En-gineering practice receiving his master's degree in 1921 and his Ph.D. in 1924. He continued his brilliant work on the physical chemistry of the open-hearth process, much of it being done in cooperation with the Bethlehem Steel Co. at its Lackawanna plant, and dealing with the elimination of sulfur. In 1926 he joined the staff of the U. S. Bureau of Mines, in charge of its ferrous metallur-gical work at Pittsburgh, and continues to be active in research work on the physical chemistry and metallurgy of the open-hearth process. His Institute publications are: Some Factors Affecting the Elimination of Sulfur in the Basic Open-hearth Process," "Chemical Equilibrium of Manganese, Carbon and Phosphorus in the Basic Open-hearth Process" and "Desulfurizing Action of Manganese and Iron," and he will present a paper on ?Effect of Temperature on the Solubility of Iron Oxide in Iron" at the annual meeting.

Jan 2, 1928

By R. W. Newcomb

THE constancy of calibration, and to a great extent the life, of a thermoelement is dependent on the suitability of the primary protecting tube in which the wires are mounted, particularly when used at high temperatures. An ideal thermocouple protecting tube would be com-posed of materials that would not contaminate the thermoelement wires contained in it-one that would remain absolutely gas-tight ,it all temperatures of usage, that will not be attacked by gases, or other surrounding agencies, that is not destroyed by heat, that withstands sudden and extreme temperature changes, that affords a high degree of mechanical protection and does not deform at high temperatures, that is a good heat conductor and obtainable in small diameters so as to keep down lag factors. It has not yet been possible to produce tubes of any known mate-rials that will meet all of these conditions. In selecting protecting tubes, therefore, one should be chosen the characteristics of which best fit it to the particular conditions of usage. Frequently conditions are such that two tubes have to be used, a primary gas-tight protecting tube inside of a secondary protecting tube, because certain agencies will attack the primary gas-tight tube unless it is guarded by the outside tube.

Jan 9, 1919

By Garland R. Dever, Preston McGrain, George W. Ellsworth

Limestone resources for industrial, constructional, and agricultural uses occur on the surface and at minable depths in several areas along the Ohio River and its navigable tributaries in Kentucky. High calcium and high carbonate limestones suitable for use in cement and lime production, steel manufacture, environmental control measures, and other special uses are present in the High Bridge Group (Ordovician) and Warsaw and Ste. Genevieve Limestones (Mississippian). Deposits with thicknesses of 7.3 to 20.7 m,(24 to 68 feet) have been documented by the analysis of samples taken at 0.3-m (1ft) intervals. Active and potential mine and quarry sites afford access to water transporation and proximity to a number of industrial and metropolitan centers. Geologic factors affecting the distribution of deposits include the Cincinnati arch, regional dip into the Appalachian and Eastern Interior basins, complex faulting in and near the western Kentucky fluorspar mining district, and late Paleozoic erosional unconformities in northeastern Kentucky.

Jan 1, 1979

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

We would like to thank Mr. Mandolesi for his informative paper on rails from strand cast steel. The chemical and structural properties of the strand cast steel were of particular interest to us. We would like to supplement his excellent report with some of Inland's findings from our Caster with submerged nozzles and strands reduced in line from 7" x 7" to 5-5/8" square cross section. Inland has conducted extensive segregation studies on AISI 1049 steel - Fine Grain 0.50% carbon and 0.75% manganese. Based on approximately 80 heats, our normal segregation pattern results in analyses of .49% carbon in the center, and 0.50% carbon at the midway and edge position. The sulfur analysis averages .025% in the center, .027% midway, and .026% at the edge. Note the slight negative segregation between the center and midway position. This steel, being lower carbon and probably cast nearer the liquidus, resulted in less segregation than the 0.80% carbon rail steel.

Jan 1, 1972

By Garland R. Dever, Preston McGrain, George W. Ellsworth

Abstract-Limestone resources for industrial, constructional, and agricultural uses occur on the surface and at minable depths in several areas along the Ohio River and its navigable tributaries in Kentucky. High calcium and high carbonate limestones suitable for use in cement and lime production, steel manufacture, environment control measures, and other special uses are present in the High Bridge Group (Ordovician) and Warsaw and Ste. Genevieve Limestones (Mississippian). Deposits with thicknesses of 7.3 to 20.7 m, (24 to 68 feet) have been documented by the analysis of samples taken at 0.3-m (1- ft) intervals. Active and potential mine and quarry sites afford access to water transporation and proximity to a number of industrial and metropolitan centers. Geologic factors affecting the distribution of deposits include the Cincinnati arch, regional dip into the Appalachian and Eastern Interior basins, complex faulting in and near the western Kentucky Fluorspar mining district, and late Paleozoic, erosional unconformities in northeastern Kentucky.

Jan 4, 1978

By A. T. Aldred

HIS note reports the existence of several new scandium intermetallic compounds of the A2B and AB stoichiometries where the A element is scandium and the B element is from group VIII or IB of the periodic table. Alloys were arc melted from high-purity materials using 2-g charges. Typical lot analyses for the materials used are given in Table I. Chemical analyses were not made on the alloys as there was little or no weight loss on melting. After annealing the specimens for 14 days at 600°C and water quenching, metallographic and X-ray techniques were used to determine the occurrence of the various phases. Table II lists the relevant data for the A2B phases. The Ti2Ni structure,2 has ninety-six atoms in a face-centered cubic cell, whilst the Al2Cu structure is body-centered tetragonal.3 The occurrence and stability of the various A2B type phases in transition metal alloy systems has recently been considered by Nevitt.4 The Ti2 Ni-type phases occur over a relatively narrow range of radius ratios from 1.14-1.26 with A partners mainly from the titanium group and B partners predominantly from the cobalt group. This suggests that both a favorable relative size of the atoms and a favorable electron concentration are necessary conditions for the existence of this structure type. A12Cu-type phases involving Ti group elements as A partners are formed with B partners from the cobalt and nickel groups, predominantly the latter, and have a higher radius ratio (1.27-1.29) than the Ti2Ni-type phases. The occurrence of both Sc2Pd and Sc2Co can be rationalized in terms of these considerations but SczNi is anomalous because of its high radius ratio. The radius ratios are calculated from the Goldschmidt CN12 radii and it might be postulated that the scandium atom is reduced in size in the compound. Unfortunately the apparent atomic size of scandium in the compound cannot be calculated from a knowledge of the structure and lattice dimensions. The crystal structure of the Sc2Au compound could not be identified from the powder diffraction pattern, but it is interesting to note that it is isostructural with a series of A2Au phases where A is a rare earth element.5 Pertinent information concerning the AB phases found in this investigation is given in Table 111. All the phases have the ordered bcc CsCl structure. The occurrence and stability of CsC1-type phases have recently been discussed by Dwight,7 who concludes that the relative sizes of the atoms do not appear to be a controlling factor (the radius ratios of all the known phases vary between 0.985 and 1.439) but that the occurrence of the phase is predominantly dependent on the relative positions of the A and B partners in the periodic table. As a measure of the stability of a given CsCl phase it has been customary to define a lattice contraction on alloying, DAB — dAB, where DAB is the AB interatomic spacing as calculated from the Goldschmidt CN8 radii and dAB is the AB interatomic distance in the compound (= v3/2 ao). Values of the parameter DscB -dScB for the compounds found in this investigation are given in column 5 of Table III and are plotted in Fig. 1. If the lattice contraction does in fact reflect the stability of a phase then Fig. 1 shows two very interesting trends when the position of the B partner in the periodic table is considered. Firstly, within any given group the stability increases in order on going from the first to third long period. Secondly, within any given period the stability increases in order as the B partner is taken from the copper, nickel, and cobalt groups. In the case of the second long period, the lattice contraction reaches a maximum at ScRh and then decreases to ScRu. The same trend could

Jan 1, 1962

By H. N. Treaftis, J. W. Cahn

THE previous determinations of the solvus of tin in solid lead disagree with one another by as much as 40°C or almost 10 at. pct. Even determinations that appear to be careful differ considerably in both the solubility and its temperature coefficient. Recent kinetic workl -3 on the rate of precipitation of tin from lead-tin alloys and thermodynamic work4 on the heat of solution of tin in lead have given some insight into the time necessary to reach equilibrium in this system. As this time is longer than that used in almost all previous determinations of the solvus, these determinations are questionable. Since the interpretation of recent kinetic results requires accurate values of the equilibrium solubility the present work was undertaken. DISCUSSION OF PREVIOUS RESULTS The methods used in previous studies may be placed into three classes: 1) Several alloys covering a range of compositions are allowed to reach "equilibrium" at a certain temperature.5-7 Some property, such as the X-ray lattice parameter of the lead-rich phase or the re- sistivity of the alloy, is then measured as a function of composition. The solubility limit for that temperature is taken to be that composition at which a discontinuity in the property occurs. However, the recent kinetic work has shown that tin precipitates in two stages. The first stage is rapid but leaves the lead still supersaturated. The second stage is very slow, and it seems from the equilibration times quoted by the investigators of the solvus that the end of the first stage of precipitation was usually mistaken for equilibrium. This is especially true at temperatures below 100°C where the first reaction is still quite rapid (from minutes to months), but where the second stage is so slow that very long holding times are required to reach equilibrium. Alternatively micrographic work8 on several alloys of different compositions seems to have given good results if done carefully. 2) The beginning of precipitation in a homogenized alloy is measured as it cools slowly8-10. Since reactions in solids undercool easily, such determinations will always give too low a temperature for the solvus. 3) Some property of an alloy is measured as a function of temperature while the alloy is above the solvus.5,9,11 The range of temperature can usually be extended slightly into the two phase region. Then the alloy is precipitated at a much lower temperature and slowly reheated. The solvus is taken to be the lowest temperature where the property of the reheated alloy is equal to that previously determined for the homogeneous alloy. Usually one also expects a discontinuity at the solvus in the temperature variation of the property for the reheated alloy. The difficulty in this method is the sluggishness of the dissolution process, and this method may give too high a solvus temperature. EXPERIMENTAL The phase boundary or solvus temperature was determined by a modification of method 3 for a series of chemically analyzed high-purity alloys, ranging from 5.1 to 26.4 at. pct Sn. The resistance, as a function of temperature, of a sample of homogenized alloy (which could easily be undercooled) was compared with the equilibrium resistance which that alloy sample attained after precipitation at room temperature followed by long isothermal anneals at various temperatures. Before each anneal the sample was rehomogenized and reprecipitated. The solvus temperature could be located to within 1°C as the intersection of the resistance vs temperature curves for the homogenized and equilibrium alloys. No attempt was made to locate the phase boundary more accurately since the limiting factor was the precision with which the alloys could be analyzed. This precision was ±0.1 wt pct Sn and corresponds to an error of 1 deg in temperature. This use of isothermal anneals differs from some of the previous investigations in which method 3 was used with baths of slowly rising temperatures. It was found early in the investigation that solvus temperatures tended to be high if the latter method was used even at extremely slow heating rates. For example a

Jan 1, 1961