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By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

The United States has never been a large coal exporting nation, and normally such shipments, aside from those to Canada, have been relatively small. Since the first railroad was built across the Allegheny Mountains, the imports have been quite small also, although fairly large tonnages of Canadian coal have moved into the extreme northeastern and northwestern states at times. In Table 21 are shown all data available about these shipments from 1790 to 1939, inclusive.

Jan 1, 1942

By Howard H. Fields

Any mining engineer with a desire to operate independently, with some financial backing, and with no fear of heavy responsibility and long hours, should be able to make a comfortable living in Mexico. Barring a few inconveniences such as a lack of satisfactory liability or accident insurance, the difficulty of obtaining repair parts or vehicles, and the length of time required to receive returns from shipments, the operation of small mine is not at all difficult. It is, in fact, a little easier to find a good prospect in Mexico than in the U.S.

Jan 1, 1950

By James E. Adler, Timothy C. Richmond

The Stillwater District is located in south central Montana approximately 75 miles southwest of Billings, the state's largest city. It lies along the northeast front of the Beartooth Mountains and is within the boundaries of the Custer and Galatin National Forests. The first white visitors in the district were the early trappers, who were soon followed by the prospectors. These early prospectors were drawn to the area by gold and silver discoveries at Cooke City in 1870 as well as by the large gossan formation in Verdigris Creek near the west bank of the Stillwater River and by several scattered smaller gossan exposures throughout the area. The first patented mining claims were recorded in September, 1886.

Jan 3, 1974

By W. S. CAYPLESS, H. O. Hofman, E. E. HARRINGTON

I. INTRODUCTION. LIME-ROASTING is a term proposed by Ingalls 1 for the operation of forcing air under pressure through a mixture of galena and lime at the kindling-temperature with the object of oxidizing lead and sulphur and of fritting or fusing the charge. If, finely-divided galena were treated in this manner without the addition of lime, the heat set free by the oxidation of part of the lead and the sulphur would be sufficiently great to fuse undecomposed sulphide, and thus stop desulphurization. Besides the chemical action that the addition of lime, limestone or gypsum to the charge may have, the admixture has the physical effect that it keeps the particles of galena separated from one another and accessible to the oxidizing effect of the air. At present, three methods of lime-roasting are carried out on a working-scale, the Huntington-Heberlein, the Carmichael-Bradford and the Savelsberg2 processes. In the last, which interests us here, an 8-ton charge is made up of galena, limestone and perhaps some siliceous or ferruginous flux; the whole is crushed to pass a screen with 3-mm. holes and moistened with 5 per cent of water. It is fed gradually into a bowl-shaped converter, 6.56 ft. in diameter, supported by trunnions attached to a truck. On the .bottom the converter has a grate with blast-inlet beneath. In starting, the truck with the converter

Jan 1, 1907

By Arthur F. Taggart, Herbert H. Kellogg, Nathaniel Arbiter

The experimental work herein described is presented in support of the following broad hypothesis: Conditioning of metals and metallic sulphides by amine collectors involves metathetic reaction at the solid surface between the collector and an oxidized metallic compound, to produce a coating comprising an amine-bearing compound of low solubility in the system. The type of reaction is different in acid and in basic solutions; both types may occur simultaneously in near-neutral pulps. Experimental The experiments comprise contact-angle tests with a variety of metals and metallic sulphides and extraction teats on ground chalcocite. Contact-angle tests were made principally on metals. Covellite paralleled metallic copper in amine solution at pH 8.8 (Table 3) and in alkaline water, but maintained an angle of about 70° in Io-3 HCl solution, where metallic copper lost its angle. The tests with anionic collectors (Table I) indicate that the behavior of metals in general is parallel to that of their minerals in anionic solutions. It is believed that this is generally true with cationic collectors also, but the covellite test is a warning against a broad assumption to this effect. All test specimens were mounted in Transoptic.* All tests in conditioning solution were preceded by a test in distilled water; cleaning and polishing were continued in every case until the angle in water was zero. Subsequent transfers into and out of solutions and test cells were made in such a way as to prevent exposure of the surface to air.1 The amine used was primary laurylamine, Armour and Co., AM-1120. It was used in the form of the hydrochloride, obtained by precipitation with gaseous hydrochloric acid from an ether solution of the amine, and purified by two recrystallizations from ether-alcoho1.2 Inorganic and other test reagents were standard laboratory grades. Temperatures were not controlled; the probable range of test-solution temperatures is 650 to 80°F.

Jan 1, 1943

By Herbert H. Kellogg, Nathaniel Arbiter, Arthur F. Taggart

The experimental work herein described is presented in support of the following broad hypothesis: Conditioning of metals and metallic sulphides by amine collectors involves metathetic reaction at the solid surface between the collector and an oxidized metallic compound, to produce a coating comprising an amine-bearing compound of low solubility in the system. The type of reaction is different in acid and in basic solutions; both types may occur simultaneously in near-neutral pulps. Experimental The experiments comprise contact-angle tests with a variety of metals and metallic sulphides and extraction teats on ground chalcocite. Contact-angle tests were made principally on metals. Covellite paralleled metallic copper in amine solution at pH 8.8 (Table 3) and in alkaline water, but maintained an angle of about 70° in Io-3 HCl solution, where metallic copper lost its angle. The tests with anionic collectors (Table I) indicate that the behavior of metals in general is parallel to that of their minerals in anionic solutions. It is believed that this is generally true with cationic collectors also, but the covellite test is a warning against a broad assumption to this effect. All test specimens were mounted in Transoptic.* All tests in conditioning solution were preceded by a test in distilled water; cleaning and polishing were continued in every case until the angle in water was zero. Subsequent transfers into and out of solutions and test cells were made in such a way as to prevent exposure of the surface to air.1 The amine used was primary laurylamine, Armour and Co., AM-1120. It was used in the form of the hydrochloride, obtained by precipitation with gaseous hydrochloric acid from an ether solution of the amine, and purified by two recrystallizations from ether-alcoho1.2 Inorganic and other test reagents were standard laboratory grades. Temperatures were not controlled; the probable range of test-solution temperatures is 650 to 80°F.

Jan 1, 1943

By Lawrence K. Nordell

This paper reviews practices used In the selection and sizing of belt conveyors and stacker systems commonly used in crushing and grinding plant facilities. Historical and modern methods of sizing this equipment are presented. The new methods Include: 1) probability theory applications for establishing component reliability, 2) "Monte Carlo" simulation techniques used in evaluating alternative system designs and in establishing service factors and corresponding availability Indices of each system, 3) quantifying the system and component operating characteristics using computer assisted modeling tools simulating rigid body and elasto-mechanic behavior for starting and stopping large and/or complex belt conveyors.

Jan 1, 1982

By L. G. Austin

The procedure for scaling breakage parameters determined in a laboratory mill to values for a full-scale mill is briefly presented. A simulation model of a closed circuit mill also requires a model of residence time distribution, a mass transfer law to predict over-filling as a function of flow rate through the mill, and a model to describe classification action. For fine dry grinding, or viscous slurry grinding, it is necessary to allow for slowing-down of breakage rates for a fine mill charge. Four examples of comparing simulation models to actual plant data are presented. The first is wet grinding of copper ore in normal closed circuit at 50 tph (metric) production, under conditions where the mill does not overfill. The second is the wet grinding of copper ore in reversed closed circuit at production of 87, 102 and 108 tph, with flow through the mill of approximately 150, 200 and 300 tph. The third is dry grinding of coal with a hot air sweeping stream to remove all of the coal as air-borne material, in open and normal closed circuit. The fourth is grinding of cement clinker in a two-compartment, air-swept tube mill in normal closed circuit with two different classifiers, producing 120 tph of 3250 Blaine cement. In all cases the simulated capacities and product size distributions were in reasonable agreement with actual plant performance.

Jan 1, 1984

By D. R. Shoemaker

BACKGROUND AND PROJECT DESCRIPTION A 16.5 kt per day underground molybdenum mine is being developed at Questa in northern New Mexico by Molycorp, Inc., a wholly-owned subsidiary of Union Oil Company of California. Small scale underground mining first began in 1920 and large scale open-pit mining was initiated in 1965, but because of the high stripping ratio, surface mining is being phased out. Construction of the underground mine began in 1979, and first production is scheduled for 1983. Full production of 9 Gg of molybdenum per year will be reached in 1984. Access to the mine will be through a service shaft, development shaft, and a conveyor decline. 'The service shaft, 7.3 m in diameter and 396 m deep, will be used for personnel, supplies, development muck, and fresh air intake. It will be equipped with a large, double-deck man and material cage. A double-drum hoist will be used for cage hoisting and will handle up to a 27-t load in balance with a counterweight. Development muck will be loaded into skips in balance and a single-drum auxiliary hoist will provide secondary access. The 396-m-deep, 4.3-m-diameter development shaft will be used for initial mine development, mine exhaust air, and a slick line pass for concrete entering the mine. The development shaft is located 400 m north of the service shaft. Run-of-mine ore will be transported from one of two 1.4-kt storage pockets by a 1.2-m-wide conveyor belt located in the 10°, 1980-m-long, 5.0-m-wide, and 4.6-m-high decline. The decline conveyor belt has a centerline length of 2229 m and a vertical rise of 363 m. It will be powered by four 448 kw motors driving a single drive pulley. There will be two 1.2 m transfer belts on the surface with centerline lengths of 322 m and 542 m. All three conveyor belts will be reinforced with steel cables. On the surface, in addition to the headframes and hoist houses for the two vertical shafts, a large maintenance shop, warehouse, compressor house, change house, main office building and timber framing building have been constructed.

Jan 1, 1981

By R. H. Tien

This paper presents an analytical solution of the problem of freezing of a semi-infinite slab with constant surface temperature; in this analysis accoz~nt is taken of the heat evolution during the solid-state transformations in the frozen skin. The regions where transformations occur are treated as plane isothermal heat sources; i.e., the rates of transformations are assumed to be infinite. In the model considered, three plane heat sources are assumed to be present in the frozen solid. The solution yields the temperature distribution in the solid, the rates of movement of the heat sources , and the rate of movement of the solidification front. It is shown that, although the sum of the heats of transformations in the solid is about 20 or 43 pct of the heat of fusion of iron or manganese, respectively, the effect of the heat evolution in solid-state transformations on the rate of solidification is insignzficant. IN several recent mathematical studies of solidification of liquid metals'-3 no account was taken of the heat evolution accompanying the solid-state transformations. In the case of, for example, steel, there are several phase transformations 6 -y, y -a, and the magnetic transformation. Whether or not a significant error is introduced into the mathematical simulation of solidification processes by the omission of the heat effects associated with these phase transformations is not known. The purpose of the present study is to investigate the effect of these phase transformations on the temperature distribution and the rate of solidification based solely on the heat transfer point of view. That is, for the sake of simplicity, freezing of a pure metal with solid-state transformations will be considered. The mathematical model which represents the present problem includes four moving heat sources representing freezing and phase transformations, 6— y — a — ferromagnetic. The thermal properties such as conductivity and specific heat, and so forth, are different from one phase to the other. But they are considered to be uniform over any particular phase. The usual Fourier heat flow law is employed. The concept of conservation of energy is applied at every heat source in order to estimate their rate of movement. The temperature distribution in the solid and the positions where transformations occur are expressed analytically in terms of error function solutions and four coefficients which are determined from four nonlinear algebraic equations. These coefficients can be calculated either by trial and error or by any numerical method. MATHEMATICAL ANALYSIS Fig. 1 is a schematic diagram showing the zones of different phases 1, 2, 3, and 4 in the solidified portion of a semi-infinite pure liquid metal. The heat is subtracted from the system at x = 0 which is maintained

Jan 1, 1968

By P. A. Young

The historical background of on-strand cooling is given, together with a resume of recent practical developments. Laboratory test procedures are then considered in detail, for both productivity and quality parameters, with particular reference to the design of the Ravenscraig No 3 machine (Scotland). A heat transfer model is presented for a porous sinter with propagating cracks. The influence of cooling/sintering area ratio, sinter strength, granulometry, return fines, coke consumption and FeO levels are examined in relation to economics. A detailed comparison of capital and running costs for two different strands, designed for identical duties, but with off or on-strand cooling, is then given.

Jan 1, 1977

By George Otis Smith

In the utilization of natural resources owner, operator, and consumer* should share the attendant benefits. Development needs to be planned under terms recognizing fully the interests of all concerned, for ally undue advantage given to any one of these participants is apt to involve even greater and disproportionate injury to one or both of the others. For this reason it is well to preface any consideration of needed reforms in legislation affecting the disposition of public land with a survey of certain fundamental principles that determine the general conditions of a11 land transfers preliminary to development, utilization, and production. The disposition of any undeveloped natural resource, whether timber, oil, coal, or water power, as a transaction to which land owner and prospective developer are parties, must be based in theory upon a division of expected returns.' Whatever the terms of such disposition, neither party can reasonably ask for anything other than an equitable division of the returns. Under this analysis three and only three questions need to be discussed; namely, what are those profits, how is this division to be accomplished, and what is the equitable basis of division ? The answer to the third question should probably be found by applying to the problem the principles of theoretical sociology, and the question need not be mentioned further at this time, inasmuch as it does not involve the practical considerations to be kept in mind in connection with the other questions, which are concerned with only the measure of returns and their division. That is to say, whether the land owner's equity is to be stated as 95 per cent, ox as 6 per cent, of the profits attending the development of the particular resource, no change would be necessary in the method to be adopted of arriving at the closest approximation of the prospective total profit. If on this basis we now compare the two methods of disposing of

Jan 1, 1915

By E. P. Pfleider, C. A. Dufresne

The problem of mooing open-pit ores over large vertical distances is increasing in importance because of the immense deposits being mined. Gravity fall of ore through transfer raises to central haulage points underground has advantages for certain open-pit operations, and this method is being seriously considered for the Carol Project now underway in Canada.

Jan 6, 1961

By Robert W. Fullerton, Donald T. King

INTRODUCTION AND THEORY by Robert W. Fullerton In coal preparation plants, as in any industrial operation where raw materials are handled, nuisance problems arising from the generation of dust are inevitable. Devices for the control or collection of dust are there- fore essential components of the plant process equipment. The general term "aerosol" is applied to small particles suspended in a gaseous medium, usually air, whose velocity under the force of gravity is small enough that the particles remain suspended for a reasonable length of time. Aerosols can be classified as dust, smokes, fumes, mists or fogs. Dust includes particles originally formed by pulverization of materials by such processes as crushing, grinding, drilling, blasting and abrasion. Smoke includes particles formed from the burning of organic materials. Fumes are particles formed by processes such as condensation and sublimation, usually at high temperatures. Mists or fogs are particles formed by the condensation of water or other vapors on some nuclei. The size of aerosol particles is generally designated in units of microns, there being 1000 microns to a millimeter and 25,400 microns to an inch. Particles of about 10 microns or above are visible to the naked eye. Table 14-1 shows size characteristics of the general classifications of particles discussed above and includes typical examples of particles commonly en- countered. Table 14-1 also shows the relationship between micron size and standard screen mesh sizes. Smoke and fume are usually in the range of 0.01 to one micron, dusts are in the range of one to 400 microns, mists are in the range of 0.1 to 100 microns, and fogs are in the range of one to 100 microns. For purposes of dust control, particles greater than 10 or 20 microns in size are considered large, particles one to 10 microns are considered fine and particles below one micron are ultrafine. Sources of Dust Because coal is relatively friable, the mining and subsequent handling operations break part of the coal into dust that can be readily carried by currents of air. In a coal preparation plant mechanical handling operations such as unloading, transferring from one belt to another, screening, cleaning, and crushing in a dry state result in the generation and release of varying amounts of additional dust. The dust problem, of course, is much less serious in plants employing entirely wet processing. In addition to dust from handling operations, thermal drying of the fine coal product frequently presents another dust collection problem. Most coal driers are

Jan 1, 1968

By G. T. Pruitt, T. L. Irby, P. B. Crawford, H. Ferrell

In water flooding peripheral, center-to-edge, line-drive or water-encroachment patterns the question has arisen, "when should a producing well be converted to a water-injection well?". It is realized that, if the producing well is shut in when water breakthrough occurs, some oil could be left in an unswept area. Yet, operation to high water-oil ratios may require processing much additional water. If a well is shut in, "where should the allowable be transferred?". A review of the literature indicates that very few data are available to the engineer to assist him in answering these questions. It is the purpose of this paper to present information which may be of value in selecting the flooding technique and the injection and producing wells and in scheduling injection and production rates. Certain phases of these problems can be studied in the laboratory. The Potentiometric model is well suited for studying many waterflooding problems. This model assumes that steady-state flow exists, that the mobility ratio is equal to one and that gravitational effects are neglected.'-' The three-phase sand model also has been recognized as an effective means for studying certain reservoir problems. Both models were used in making the study reported here. This paper discusses seven cases utilizing various waterflooding techniques. Data for the first five cases were obtained on the potentiometric model. Data for Cases VI and VII were obtained by constructing and flooding an unconsolidated sand pack (a three-fluid-phase system) and by determining the swept area and cumulative oil recovery for various types of operations. APPARATUS AND PROCEDURE The potentiometric model reservoir was 30 in. long X 10 in. wide by about 1/2 in. deep. Four wells were equally spaced in a line array along the lateral center line. (See Fig. 1.) Well No. 1 initially was an injection well for each of the patterns reported. The cases studied with the potentiometric model and sand model are described herein. The laboratory sand model reservoir was a 30- 10-in. rectangular Lucite vessel packed with sand to a depth of about 0.65 in. Four wells were equally spaced in a line array along the lateral center line. The reservoir material was an unconsolidated sand into which the reservoir fluids were mixed to yield fluid saturations of 55 per cent oil, 25 per cent water and 20 per cent gas. The water was added to the sand and the material mixed, after which the oil was added. Kerosene and water, the fluids used, gave a viscosity ratio of 1.64:1. In packing the reservoir, care was taken to assure constant fluid saturations and constant porosities. A new mixture was prepared for each run. During water flooding, a colored water was injected by a constant rate pump. The injection rate was 1.1 B/D/ft of sand thickness. For this series of tests, each of the producing wells was open to the atmosphere and, as in the potentiometric model study, Well No. 1 initially was an injection well for each of the patterns. KESULTS OF POTENTIOMETKIC MODEL STUDlES Two cases (Cases I and 11) involving equal pressure injections were studied, with the following results. Case Water injection was initiated at Well No. 1; the producing wells (Nos. 2, 3 and 4) were operated at constant and equal bottom-hole pressures. When water broke through at Well No. 2 and achieved the selected water-oil ratio, Well 2 was converted to a water injection well, resulting in two injection and two producing wells. The injection pressures at Wells 1 and 2 were maintained equal and constant; pressures at the producing wells were held equal, but they were lower than those at the injecting wells. A similar process was repeated when water broke through at Well No. 3. The flood was terminated when

By H. O. Hofman

The sudden decease, April 1, 1910, in Chicago, of Dr. Franklin R. Carpenter was a shock to his many friends. He died in his sixty-second year, of heart paralysis. To most fellow-members of the Institute who have followed the progress of the last twenty-five years in the mining and treatment of non-ferrous ores, the work of Dr. Carpenter in that line is familiar; but very few, even of those who knew hinl well in the later years, are acquainted with his earlier struggles to satisfy an inborn hunger for knowledge. The story of his life resembles that of the pioneer who opens up new country; overcoming hardships with indomitable courage, meeting doubts and difficulties with an alert and open mind, and exercising in the face of reverses an unconquerable perseverance. It seems appropriate to place on record in the Transactions a brief outline of the life and work of this eminent engineer. During the past 15 years of his life Dr. Carpenter was much interested in genealogy. In the pursuit of this study as an avocation, he traced his own ancestry to the time when ((Hugh," called "le Charpentier" on account of the dexterity with which he had swung his battle-axe as a crusader, settled in Sussex on lands received from William the Conqueror. The Carpenters came to this country with William Penn. A prominent member of the family was Joshua Carpenter, the founder of Christ Church, Philadelphia. Dr. Carpenter's branch of the family moved from Pennsylvania into that part of Virginia which is now West Virginia, where his grandfather settled in Harrison county, while the grand-uncle went further west, and built the first iron-furnace at Hanging Rock, Lawrence county, Ohio. In fact, since early times, the Carpenters appear to have been iron-masters. Franklin R. Carpenter mas born, Nov. 5, 1848, in Parkers-

Jan 1, 1911

By J. A. Putnam, A. D. K. Laird

In laboratory research on the behavior of oil, gas and water in porous materials, no direct method has been devised to measure saturation without disturbing the flow. Indirect methods involving various forms of radiation have been developed for measuring one or two components. The X-ray absorption method for two components has been described previously1-3. The possibility of three component measurement has also been mentioned1. Since two component measurement still requires considerable care to insure accuracy, the fact that three components can be measured satisfactorily is not generally appreciated. The fraction of the energy of an X-ray beam of one wavelength transmitted through a material is given by the transmission factor. in which 1 is the beam's path length through the fluid. p is the fluid density, and 1,. is its mass absorption coefficient. Eq. 1 implies that all parts of the beam pass through equal amounts of the fluid. Practical applications are, therefore, limited to systems in which the fluid is distributed so that I varies negligibly over the cross-section of the beam. Typical variations of the transmission factor with X-ray tube potential arc shown in Fig. 2 from which experimental points have been omitted for clarity. The X-ray absorption of low pressure gases in a core is practically zero so it cannot he distinguished from that a vacuum by instruments that will differentiate between liquids. The transmission factor of a gas in a core is. therefore, unity. Consequently, the saturation of only one gaseous component can be found. If two fluids completely fill a core, their two saturations add to unity and, therefore, only one value of the transmission factor, T, is needed to determine both of them. When two liquids do not completely fill the core, their saturations do not add to unity and transmission factors at two wavelengths must be measured. At one of these wavelengths, 7 for one liquid must be different from T or the other liquid. The change of T for one liquid us the wavelength is changed between the two values must be different from the corresponding change of T in the other liquid. The two values of fluid saturation will also give that of the gas because the three saturations must add to unity. In Fig. 2 it can be seen that there are many large differences of T between various oil solutions and water solutions at any one potential, and between potentials for any one solution. Consequently, conditions for optimum accuracy of measurement of the saturations of a gas and two liquids can be chosen. Once the operating potentials have been selected, however. it is more convenient to cross plot the data from Fig. 2 on transmission factor-solution concentration coordinates for the chosen potentials, as shown in Fig. 3. Fig. 3 was used to plan the experimental procedure for Core N-38-1. Since the voltage control at 45 kv was good, the slopes of the curves in Fig. 2 at this potential would cause little error. At low potentials, however, the voltage control was not good, so 33 kv was chosen because the small slopes of the curves made voltage control less critical. The lowest strength beam that could be measured reasonably at 33 kv corresponded to a minimum T factor of 0.385. Fig. 3 shows that both 4.80 weight per cent of cadmium chloride in water and 24.0 per cent of iodobenzene in crystal oil had this T value, and, consequently, were indistinguishable to the X-rays at 33 kv. Thus, at 33 kv, the liquid saturation was given by the same curve regardless of the relative amounts of oil and water solutions present. This simple calibration curve from which the gas and liquid saturation can be read, is shown in Fig. 4. Fig. 3 also shows that at 45 kv, T for the aqueous solution is 0.610. and that T for the oil solution is 0.220. These values were transferred to Fig. 4 to give the triangular calibration plot from which the brine and oil saturations can be found, after the gas saturation has been determined at 33 kv.

By Pradeep K. Rohatgi, Clyde M. Adams

An analysis of heal conduction in the freezing of a solution has been performed. The case considered is the semi-infinite mass of solution, bounded by a con-stant-temperature plane with one-dimensional heat flow, Numerical cooling rate and freezing rate distributions hare been calcutated for the particular case of unidirectional freezing of aqueous solutions against. a cold copper chill. The solution at each level parallel to the chill surface is subjected to a spectra of frcezing rates; the freezing rate is inilially lour., passes through a maximum, and then decreases until solidification is camplete. Arange and maximum freeeing rates are inversely proportional to the square of distance from the chill surface. The temperature of the chill surface in contact with the solution remains constant during solidification. Experimentally, it is observed that deudrite sparing increases linearly with distance from the chill surface; in the light of heat -flow analysis this means that the dendrile spacing is imersely proportional to the square root of the maximum freezing rate. SOLIDIFICATION of liquids is accompanied by rejection of latent heat at the solid-liquid interface. The over-all rate of liquid to solid transformation is governed by the rate of heat extraction. Analysis of the heat transfer in the liquid during freezing is important since it determines the freezing rate and resulting structure. A considerable amount of work has been done on metallic systems since solidification is frequently a major step in processing metals. Unidirectional freezing from heat sinks has been treated by several investigators.1-4 Much of the work has been limited to the simpler case of substances such as pure metals which freeze isothermally at a unique transformation temperature. In this case the thickness of the solid zone y, next to a chill surface. is a parabolic function of the time. 8. where a and b are constants. Eq. |1| is a close approximation giving the progress of solidification for the case in which there is a small but finite thermal contact resistance at the interface between the freezing liquid and the chill.' It has been used with some success in connection with large steel ingots4 when the therma1 contact resistance is negligibly small (as is the case when water is brought into contact with the metal chill). The constant, b. becomes zero and Eq. [l] is then exact. even when the thermal properties of the chill and the freezing liquid depend on temperature. Analysis of unidirectional solidification of solutions is more complicated since the latent heat is evolved over a range of temperatures. Next to the all-solid zone in contact with the chill surface there is a solid plus liquid zone in which solidification takes place. Although the equations presented are considered quite general the numerical and experimental results are for freezing of aqueous solutions from a copper chill. I) EXPERIMENTAL PROCEDURE Solutions of potassium chloride, sodium chloride. and lithium chloride have been used. These solutions form a eutectic: a typical phase diagram is shown in Fig. 1. A solution at its liquid us temperature is poured into a tygon tube mounted on a relatively large copper chill. The chill is immersed in a freezing mixture of dry ice and acetone at -70°C. A thermocouple connected to a high-speed recorder was mounted near the top of the chill to measure the fluctuation in the temperature of chill surface in contact with the solution. In this system the progress of solidification can be visually observed through the tygon tube. After the specimens freeze to a desired height they are removed from the copper chill and stripped from the tygon tube. Longitudinal and transverse sections are cut from the specimen for micrographic examination. Specimens in the form of a thin slice are mounted on a transparent glass slide by freezing small drops of water around the periphery. They are then polished on a series of emery papers; the final finishing is done on a soft tissue paper. A Leitz Biological microscope was used for structural observations; photography was

Jan 1, 1968

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969