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By D. W. Mitchell

While pure magnesium does not corrode rapidly the presence of even very small quantities of certain other metals accelerates corrosion remarkably. Because magnesium is such an electropositive metal (E° = +2.34 volts)' the presence of substances that permit galvanic activity is extremely undesirable. It is stated that as little as 0.017 pct of iron in magnesium causes a marked increase in the corrosion rate.2 Magnesium and its alloys are commonly melted in iron or steel pots; consequently the commercial metal has the opportunity to pick up iron if it has that tendency. Quantitative data on the solubility of iron in magnesium are of practical as well as of academic interest. Some magnesium alloy castings tend to have large grain size unless suitable treatment is given to the liquid metal just prior to casting. One method of grain refinement consists of "superheating" the metal just prior to casting. "Superhcating" is heating to a temperature 100 to 200°C above the casting temperature and holding for a short period of time. Superheated metal has a much finer grain than unsuperheated metal. A satisfactory explanation of this phenomenon has not been forthcoming. One hypothesis attributes the grain refinement in the superheated metal to precipitation of some phase that is mis-cible at the temperature of superheat but not miscible just below the casting temperature and which is thought to provide nucleating centers for crystallization. This phase, if the foregoing hypothesis is correct, would probably be a metal or an intermetal-lic compound. Of the metals likely to be found in magnesium alloys, iron is one of the most likely candidates for the role of grain refiner for iron occurs in small quantities in all commercial magnesium and magnesium alloys. A. Beck³ states that magnesium, in either the liquid or the solid state, cannot dissolve iron and that iron exists as a finely divided suspension which does not settle out because of its extreme fineness. Beck also presents a micrograph showing a large iron dendrite in magnesium but does not comment on the crystallization of iron from a solution supposed to contain none. It is doubtful that dendrite formation from suspended iron -would be possible. This suspension theory is the basis of patents4 covering the removal of iron from magnesium by allowing the iron particles to act as nuclei for the formation of primary magnesium crystals which can be separated by segregation. Also covered by patents is the removal of iron by the addition of another metal to form an intermetallic compound with the iron which, because of its increased particle size, is able to settle out of the molten metal. Here, too, quantitative information on the extent of iron solubility in liquid magnesium is of more than theoretical interest. M. Hansen,5 in his critical collection of the data on binary alloys, states that iron is not soluble in liquid magnesium. W. R. D. Jones% ho studied the physical properties of low iron magnesium alloys observed a 57°

Jan 1, 1949

By D. R. Parrish, T. M. Geffen, R. A. Morse, W. W. Owens

Laboratory studies of several factors affecting measurements of relative permeability were made using the three-section plastic-covered core technique. Results show that the core assembly, properly constructed, will perform as a single unit, and that the testing technique will, under suitable conditions of pressure gradient, gas expansion, and migration of partial water saturation, permit measurement of flow characteristics not affected by technique. Wettability equilibrium is readily established in cores exhibiting strong wetting preference to water or oil when initially saturated with water. Laboratory tests must be conducted so that saturation changes represent those that occur in the reservoir. Immediate implications of saturation history are (1:) that the possibility exists of increasing the displacement efficiency of solution gas drive reservoirs over the natural process, and (2) residual gas saturations following water flooding in gas or gas condensate reservoirs will be 15 to 50 per cent pore space rather than 1 to 11 per cent as generally believed. INTRODUCTION Solutions of petroleum reservoir problems pertaining to production performance require the use of true relative permeability characteristics. 'This relationship of fluid conductivity and saturation has been obtained by reservoir engineers in four ways, namely: 1. From past gross reservoir performance and the extrapolation of this data based on experience,1,2 2. By using published fluid flow relationships obtained in laboratory studies on general type porous materials,3, 4, 5 3. By attempting a mathematical derivation of flow behavior," using some experimentally obtained characteristics of reservoir rocks, and 4. By laboratory flow tests using representative rock samples of a reservoir. The first three methods listed above have shortcomings which make their use limited or questionable. Production characteristics of only certain processes are obtained from field data and these are not available at the beginning of a reservoir's producing life, at which time they are desirable. It is fortuitous if general fluid flow characteristics obtained experimentally have accurate application to specific field problems. Also, it is felt that at this time there is not sufficient knowledge of the flow behavior of oil, water, and gas in porous materials to enable applicable analytical description of this to be made based on other measured rock characteristics. Measurement of relative permeability in the laboratory offers the only direct method subject to adequate checking for determination of flow characteristics applicable to field problems. Primarily, this paper deals with laboratory experiments to establish the effects of several factors on the measurement of relative permeability and the practical significance of this knowledge. Laboratory flow tests are essentially model studies; the gross reservoir being represented by a small rock sample. It is necessary to simulate in experiments all the factors of importance which influence flow in the reservoir, as well a.; to eliminate effects peculiar to the model studied to assure measurement of valid flow behavior. Factors which affect the measurement and behavior of fluid flow in porous materials have been studied by other investigators.3,7,8,9,10,11 This analysis is not intended to evaluate fully all factors involved, but to establish first the validity of measurements by the technique used and then study flow behavior under various conditions. The studies reported are as follows: 1. Effects of pressure gradient, 2. Effects of gas expansion in tests conducted at near atmospheric pressure, 3. Effects of migration of a partial water saturation in oil-gas-water systems, 4. Effects If wettability characteristics of the system. and 5. Effects of the fluid saturation history. The first three are important only in laboratory measure-

Jan 1, 1951

By Forbes Wilson

IN February 1952 Freeport Sulphur Company started exploration work on a group of lateritic deposits at Moa Bay, Cuba. As a result of successful exploration work and a vast amount of metallurgical research over the past five years, these deposits will soon become a new Free World source of nickel and cobalt. Moa Bay lies on the north coast of Oriente Province, the easternmost part of the island, about 600 miles east of Havana and about 40 miles east of the U. S. Government nickel plant at Nicaro.

Jan 5, 1958

By J. S. Levine, M. Prats

Several methods are available for calculating the performance of solution-gas-drive reservoirs from the PVT properties of the oil and from the relative permeability and other properties of the formation. These methods require a number of simplifying assumptions. The present method of computation has made use of a high-speed computer to solve simultaneously the nonlinear partial differential equations that describe two-phase flow by solution-gas drive in order to calculate the performance of a reservoir. Some of the results obtained by the nonlinear partial differential equation solution are compared with those obtained with an approximate method, which has been called the semisteady-state solution. The pressure and saturation profiles from the wellbore to outer boundary calculated by the two methods are compared for one constant-terminal-rate case and two constant-teminal-pressure cases. The agreement in these profiles, as well as in the values of average reservoir pressure and cumulative recovery, leads to the conclusion that, for most engineering calculations, the semisteady-state method will give a reasonable approximation to the numerical solution of the differential equations describing solution-gas drive. An unfavorable (as regards ultimate oil production) set of relative permeability curves was used in the calculations in the belief that the effect of the parameters which were studied would be emphasized to a greater degree. Furthermore, the reservoir was assumed to be completely homogeneous, and these results should not be considered applicable to any other type of reservoir. Gravity effects are not considered. The absolute permeability was varied from 25 to 0.5 md. At an economic limit of 2 B/D, the recovery for a 25-md reservoir is about 1.8 times as great as that for a 0.5-md reservoir. The effect of permeability on the producing gas-oil ratio is minor. Once PVT properties of the oil and the relative penneability properties of the reservoir are fixed, the pro- during gas-oil ratio is found to be a function of the fraction of oil recovered. Well spacings of 10, 40 and 80 acres were considered. For the assumed homogeneous-reservoir properties, the effect of spacing on recovery at an economic limit of 2 B/D was very slight. Certain dimensionless groups can be used to extend the results to other fields having different penneabilities, spacings, reservoir thicknesses, well radii and porosities, so long as the PVT and relative permeability properties are similar to those used in this paper. INTRODUCTION An important aspect of reservoir engineering is the prediction of the performance of the reservoir based on the limited information normally available early in the life of a field. Usually, soon after a field has been discovered, it is necessary to decide upon the spacing to be employed and the production program to be used for most efficient utilization of reservoir energy. Where these decisions have not been dictated by legal or political considerations, they have frequently been based on experience factors which indicate that two fields with similar characteristics will probably have similar performances. To the extent that the industry has been successful in economically exploiting oil reservoirs, this rule-of-thumb method has been found to have merit. A large amount of theory has been developed with which it is possible to predict the performance of a reservoir by using certain known properties of the oil and the formation. Because of the difficulties of the mathematics involved for a drainage area having square or rectangular boundaries, the problem usually has been simplified and idealized by assuming each drainage area to have radial symmetry and the field to be represented by a number of these drainage areas. Muskatl was one of the first to formulate the theory for two-phase flow and to solve the equations for a few cases by numerical integration, using the relatively slow means of computing available at that time. His equations describing

By L. P. Teas

The main facts brought out by the study of the blende-bearing ores examined are as follows: 1. Chalcopyrite as minute triangular or rectangular dots, or as

Jan 1, 1918

By W. A. LaVenue, W. M. Houston

Pebble phosphate mines of Florida have been established from south of Hardee County to north of the Georgia state line, a distance of over 200 miles. Mining has been carried out on an ever-increasing scale since 1885, but phosphate deposits that can be mined on the economical standards of today, are confined in a roughly circular area about 30 miles in diameter, generally within Polk and Hillsborough Counties, in the central part of the State. The phosphate deposit, which is in the Bone Valley formation of Pliocene age, is covered by Pleistocene terrace deposits of unconsolidated quartz sand. The matrix is composed of approximately 1/3 clay slimes, 1/3 silica sand and 1/3 phosphate pebbles. The phosphate usually occurs as rounded pebbles, ranging in size from about 1 in. down to approximately 400 mesh. The phosphate may vary from well-defined hard pebbles to soft weathered rock. The color and character of the phosphate will range from smooth buff pebbles to black and white "salt-and- pepper rock." The screen size distribution varies considerably between locations; the recoverable phosphate may extend down to the 400-mesh size in some areas, while in others the phosphate may cut off sharply at about 35 mesh.

Jan 11, 1962

By John Birkinbine

The press, trade publications, and special circulars, some elaborately illustrated, have been liberally employed within recent years in this country, to set forth the advantages of various locations as industrial centers, having as a basis the possibility of profitably producing pig-iron at these proposed centers: and special stress has been placed upon opportunities believed to exist at certain points for making iron of a quality suitable for the manufacture of Bessemer steel. The remarkable statements and prophecies made in some of these publications, have suggested the present paper, treating of the influence which location exerts upon the special industries named.

Jan 1, 1893

By L. A. Hanson

Jan 1, 1964

By C. B. Gillson, Henry Fay

For several years past, investigations on the chemistry of tellurium have been carried on in the laboratory of this institution. The methods of preparation of pure telluriumf and the estimation of tellurium‡ have been studied, and an attempt to determine the atomic weight of tellurium is now in progress. All these problems had been investigated, however, along purely theoretical lines; and it was thought desirable to study the more practical application of the metal, which can now be had in considerable quantities as a waste product in the refining of copper-ores. In its physical and chemical properties tellurium is very similar to antimony, and it was thought

Jan 1, 1902

By E. C. Weichel

THERE have been many attempts at permanent roof support in anthracite mines, in some cases brick arches, in others concrete, and also combinations of brick or concrete walls with steel beams. These supposedly permanent roof supports have frequently failed when heavy pressure is brought to bear upon the structure, because they are so rigid that failure occurs because the structure is unable to adjust itself to the increased load. Roof pressure exerts a tremendous weight, and it is at times difficult to find any means of support which is strong enough to bear the entire pressure, unless this supporting structure has in itself the element of some flexibility which will enable the structure to hold the moving mass until it "arches" itself. If the supporting medium has flexibility enough so that it can adjust itself to the heavy initial loads, and so give the overlying material an opportunity to form a self-supporting arch, then such a roof support will be more useful than any rigid roof support. There has recently been introduced into the anthracite region a new form of gangway lining that is flexible enough to slightly adjust itself under heavy pressures, and so give the loosened material which is being supported a chance to form into an "arched" mass. This lining, manufactured under patents granted to Hans Schaefer of Essen, Germany, was introduced in the United States in the summer of 1928, at which time the Amercan licensee, Richard Howells of

Jan 1, 1930

By R. A. Pasternak, B. Evans

A dynamic technique for the determination of solubilities of gases in metals has been explored, using the N-Nb system as a test case. An initially clean sample, maintained at constant high temperature, is exposed to the gas at low pressure: the rate of sorp-tion and the corresponding change in sample resistance are measured continuously. A pronounced decrease in the slope of the resistance concentration curve is observed at the terminal solubility. The rate of gas uptake by the sample was determined in an ultrahigh-vacuum flow system equipped with a servo-control which maintains constant pressure in the sample chamber; the system and the technique have been described in detail elsewhere. 1,2 The sample was held at constant temperature during sorption by maintaining approximately constant power input into it; this results in constant temperature, since the emissivity of a metal is independent of moderate concentrations of dissolved gas. The simple electrical circuit used both for heating and for resistance measurement is shown in Fig. 1. The power input into the filament is where R is the filament resistance, RL is an adjustable resistance in series with the filament, and VT is the constant dc potential of the power source. If RL is set equal to R at the beginning of an absorption run, the power input becomes insensitive to subsequent resistance changes; for example, an increase of 20 pct in sample resistance is accompanied by a decrease in power input of less than 0.8 pct; i.e., the

Jan 1, 1967

Falconbridge Nickel, the one-time subsidiary that grew up to swallow its own parent, Ventures Limited, in 1962, is not about to be left behind by rising nickel consumption. At a cost of several hundred million dollars, this Canadian firm has undertaken a series of new projects that will not only ensure its present share of the market, but also lead it into new areas of the nickel business. Although Falconbridge Nickel Mines Ltd. was not formed until 1928, it actually had its start in 1917- 18 with the discovery of a large, good grade nickel- copper deposit in Falconbridge, near Sudbury, Ontario. However, due to several factors, financing could not be obtained and the orebody lay fallow. It was not until 1928, when the Thayer Lindsley interests bought the property from the original owner, that it was developed.

Jan 10, 1968

By R. W. Diamond

THREE mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd.: (1) The Sullivan Concentrator, Chapman Camp, B. C. (near Kimberley, B. C.), (2) the, St. Eugene Concentrator, Moyie, B. C., and (3) the. Tadanac (Customs) Concentrator,Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Values in all ores treated are as minerals of some or all of the metals -lead, zinc, gold or silver. Occasional customs ores contain small amounts of copper. Sulfide iron content of ores treated varies from a FIG. 1.-THE SULLIVAN CONCENTRATOR, CHAPMAN CAMP, B. C. (NEAR KIMBERLEY, B. C.). low figure in some ores to 38 per cent. iron in Sullivan ore. Gangue minerals vary considerably. A few customs ores are somewhat oxidized and as a result present difficulties. Flotation equipment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sullivan Concentrator. In this paper I will not detail treatment nor equipment in any of our plants but will describe special features in, or in connection with, all of them. I will then deal with flotation reagents, describing our use of each of them, particularly where differing from general practice. I will conclude with comments on special subjects related to differential-flotation.

Jan 1, 1927

By R. I. Jaffee, F. C. Holden, H. R. Ogden

The mechanical properties of Ti-C and Ti-C-0 alloys can be altered by heat treatments to dissolve or reject carbon from solid solutions. The maximum strength is obtained by annealing just below the peritectoid temperature. Quenching from the ß-carbide field results in softening. Impact behavior is influenced by the extent of solution of interstitials CARBON is not as important in titanium alloys as it was in earlier years when graphite induction melting was more prevalent. With induction melting, carbon pickup is about 0.5 to 0.8 pct. Cold-mold arc melting with graphite electrodes, which is among the more current methods, results in carbon pickup of 0.1 to 0.2 pct. The titanium-sponge melting stock itself contains about 0.02 to 0.07 pct C, picked up from the magnesium used in the reduction process. Thus, carbon is still one of the more important contaminants in titanium and needs careful study and evaluation in order to understand titanium and titanium alloys. Moreover, it is equally proper to consider carbon as an alloying addition because, in controlled amounts in titanium alloys, it may serve a most useful function. This is particularly the case where the ultimate in toughness is not required. The addition of carbon to titanium results in a peritectoid-type system as illustrated in Fig. 1. The solubility of carbon is seen to be higher in the a phase than in the ß phase in the temperature range of interest. Below the peritectoid temperature, the solubility of carbon in a titanium decreases with decreasing temperature. This type of system permits many microstructural and heat-treatment variations which may influence the properties of the alloys. The study of how the microstructure variations affect mechanical properties is described in this paper. Experimental Procedures The experimental techniques and testing methods used in this work were the same as those described in detail in a previous paper.' No further descriptions will be given except where changes have been made. High purity iodide titanium, produced by the New Jersey Zinc Co., was used in all of the alloys. Carbon additions were made using high purity spectro-graphic carbon electrodes in order to obtain the highest purity carbon available. The alloys were prepared by double arc melting to reduce the possibility of segregation. The alloys were forged at 875°C to ¾ in. round, descaled, vacuum annealed for 5 hr at 900°C to remove the residual hydrogen, and swaged to ¼ in. round at 750°C. All heat treatments were made on material in this initial condition. Two of the early Ti-C ingots were found to have been contaminated in melting. Vacuum-fusion analyses showed that the two contaminated alloys had picked up oxygen, so the test results on these two alloys permitted an evaluation of ternary Ti-C-0 alloys. A list of the alloys and their compositions are given in Table I. Properties of Ti-C Alloys In a peritectoid-type system, such as the Ti-C system, the chief microstructural variable which influences the properties is solid-solution strengthening. For a given composition, it is possible to control the disposition of carbon, either in solid solution or as the compound Tic, by suitable heat treatments. When in solid solution, the carbon present in the alloy makes a definite contribution to the strength of the alloy. However, when present as Tic, it has very little effect on the strength. Other microstructural variables considered in this investigation were transformation structures and grain size. As discussed in subsequent sections, these variables have only a minor effect on properties as compared to the solid-solution effect. Solid-Solution Strengthening: The principal strengthening mechanism for Ti-C alloys has been found to be solid-solution strengthening. Carbon in interstitial solid solution strengthens titanium, but has very little strengthening effect if present as the compound. Since carbon has a higher solubility in

Jan 1, 1956

By James C. M. Li

The Petch relation between the flow stress and the gain size is derived from a consideration of gain boundary sources of dislocations without the need of dislocation Pile-ups. Three mechanisms for inierpreting the yield stress: the gain boundary strength, the unpinning of Frank-Read source near a grain boundary, and the generation of dislocations from the grain boundary are compared and the condition of their equivalence is shown. The effect of the average angle of misfit of pain boundaries is found to be sma11 and so is that of the average angle of misfit of subboundaries having impurities. The effect of impurities on the ledge density in the grain boundary is treated thermodynamically and a relatwn is proposed for the variation of Petch slope with impurity activity. The effect of temperature on the Petch slope is interpreted as due to the change of ledge structure in the grain boundary. It is indicated that the effect of annealing temperature may be more important than that of the test temperature and therefore should be studied. The effect of plastic strain on the Petch analysis is deduced from a work-hardening equation in which the generation of dislocations has first-order kinetics and the annihilation of dislocations has second-order kinetics. It is concluded that the Petch slope will decrease with plustic strain if the rate of annihilation of dislocations is sufficiently large. Critical experiments which may shed light on the mechanism for the Petch relation are suggested. THE relation between the yield or flow stress, 0, and the grain size, l, was first proposed by all' and later studied more extensively by Petch and co-workers, who also proposed a similar relation for the fracture stress and deduced from these a grain-size effect of the ductile-brittle transition temperature. The microscopic mechanism used by all' and petch2 involves a pile-up of dislocations of like sign generated from a Frank-Read source. The yielding or flow takes place when the pile-up exerts sufficient stress at the grain boundary so that the plastic deformation can propagate from one grain to another. If the average strength of the grain boundary is ai and the average length of the pileup is lp, the Petch slope, k, is given by" where p is the shear modulus, b the Burgers vector, and v the Poisson ratio. This slope will be independent of the grain size if l/lp is a constant. This is possible, since, if the Frank-Reed source is situated near the grain boundary, lp = 1, and if it is situated in the middle of the grain, Ip = 1/2. cottrell,12 also using the pile-up mechanism, proposed that the stress concentration at the grain boundary will initiate Frank-Read sources near the grain boundary and in this manner a Lüders band can propagate from one grain to another. Assuming that the average distance between the Frank-Read sources and the grain boundary is 1, and the unpinning stress of the Frank-Read sources is op, Cottrell obtained the following Petch slope: This slope will be independent of the grain size if ls is independent of the same, which is not as obvious as the condition, Ip = I for Eq. [2]. In addition to this assumption, the direct relation between the Petch slope k and the unpinning stress, up, was recently questioned by Johnsonon grounds that it is inconsistent with the following observations: the independence of k with temperature and strain rate, and the small k in columbium, which, like iron, has a sharp yield point. As pointed out by ohnson," the most important objection both to the Hall-Petch mechanism, in which the strength of the grain boundary plays the role in yielding, and to the Cottrell mechanism, in which the unpinning of Frank-Read sources plays the role in yielding, is the lack of direct observation of the pile-ups. The dislocation structure in deformed iron has been examined recently in the electron microsope.'-' Dislocations appear to be generated from grain boundaries or other interfaces; they form clusters and tangles within the grain at very early stages of deformation, even in the Lüders band, if the deformation is slow or at normal and elevated temperatures. Although it is still too early to interpret bulk properties from thin-film observations, it does seem worthwhile to look for a mechanism for the Petch relation which does not require dislocation pileup. SUBBOUNDARY SOURCES In order to show that a consideration of grain boundary sources can lead to the same Petch relation as does the consideration of the strength of the grain boundary, we shall first discuss the case of a simple tilt boundary whose elastic properties have been studied in detail.17 The strength of a partially

Jan 1, 1963

By Alan K. Burton

Having estimated fleet size and productivity, the next and final step in this analysis is to introduce cost. Total cost of the system is a combination of capital, operating, and any other external costs that may be incurred. The last item, external costs, can be particularly important when comparing one size or type of truck fleet with another. Once costs are calculated, it is possible to compare systems on a total cost, cost per hour, cost per ton, or any other basis that is required. Methods used vary from simple owning and operating costs to sophisticated discounted cash flow analyses involving optional fleet replacements over the project life.

Jan 1, 1976

By Jack A. Caldwell

Jan 1, 1985

Jan 1, 1892

By Elmer W., Pehrson

NOT much serious consideration was liven to the military aspects of raw materials before World War 1. Following the outbreak of war in Europe in 1914, however. this situation was promptly changed. Disruption of allied shipping and German submarine warfare soon cut off a substantial part of the material the United Staten was accustomed to receiving from overseas. At the same time, raw material requirements rose rapidly as the tempo of industrial preparedness was stepped up in anticipation of war. By April 1917, when we entered the war, serious shortages threatened and consideralde attention was being given to our "deficcient" raw materials. The term "war mineral," began to appear after we became active combatants. But there is no evidence that "strategics" and "critical." as now used, had entered the lexicon of our raw materials experts during the last war nor were there apparently any officially recog¬nized list or definitions of what con¬stituted war materials. According to G. A. Roush in his book, `'Strategic Mineral Supplies," C. K. Leith, while serving as mineral advisor to the War Industries Board. compiled the first unofficial list of deficient minerals in 1917.

Jan 1, 1944

By J. C. Uy, A. A. Burr

A quantitative relationship between the allotropic phase boundaries of zirconium-base binary systenzs and the solute metallic valence is shown through an intermediate thermodynamic parameter. A simplified equation relating this parameter to the phase boundaries is briefly reviewed, and data from the literature are used to show the relationship of this parameter to the solute metallic valence. It has been reported that the solute metallic valence can be used as an index of phase stabilization in zirconium-base binary alloys.' It was shown that the algebraic sign of the slopes of the hcp/bcc phase boundaries of zirconium alloys correspond to the algebraic sign of the metallic valence of zirconium minus the metallic valence of the solute, or, in other words, a solute whose metallic valence is higher than that of the solvent tends to stabilize the high-temperature phase while one whose metallic valence is lower than that of the solvent tends to stabilize the low-temperature phase. Further analysis of the zirconium binary systems has revealed a quantitative relationship between the solute metallic valence and the relative slopes of the two-phase allotropic boundaries. This relationship involves a thermodynamic quantity whose significance can be seen in the following section. PHASE-STABILIZATION PARAMETER Let Qb be the difference between the partial molar heats of mixing of a given solute in the two allotropic phases of the solvent which are in equilibrium with each other at a given temperature, thus A relationship between this term Qb and allotropic phase boundaries has been employed by several au-thors'-= in the evaluation of phase diagrams, and can be briefly derived as follows. Referring to Fig. 1, consider the general case of two allotropic phases, each having a small mole fraction (Xa,Xb) of the solute, in equilibrium at temperature T and atmospheric pressure as represented by the reaction. solute in ß phase =solute in a phase If now a reaction occurs such that an infinitesimal amount of the solute is removed from the ß phase and added to the a phase, there would be a partial molar

Jan 1, 1967