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` LAWRENCE ADDICKS, New York, N. Y.-We have really two competitive processes for the production of electrolytic zinc. In the process used at Great Falls, the ore is roasted and the calcines leached, leaving a residue which has to be smelted; in the other method, the ore is burned, the zinc and lead fumed off, and the condensed fumes are leached. I do not think that we can yet come to any decision as to which is the better way to attack the problem. Of course if we roast first and then leach, various substances remain in the calcines which may consume sulphuric acid; whereas if we do the burning first, we obtain simply the zinc and lead oxides, with considerable sulphate, in the fume, and there is no shortage of acid. It also depends partly on the complexity of the ore. The one that Mr. Hall is treating and the ore they are treating at Great Falls are not quite alike, but I think they are sufficiently similar to make a comparison of the two methods, working in competition, on different parts of the country, very interesting. C. E. SCHWARTZ, Miami, Okla.-Mr. Hall states that the Joplin conditions are not suitable for the manufacture of electrolytic zinc. When we speak of Joplin ore in general, we consider, of course, a 60-per cent: concentrate with comparatively low iron, but if a low-grade concentrate could be made from tailings and so-called chats, then the problem would be quite different. A Joplin ore is comparatively simple to treat electrolytically, and I believe the electrolytic process would open a field for the treatment of such ores as would not be ordinarily smeltable; that is,

Jan 1, 1918

By Robert V. Whitman

INTRODUCTION Ideally, this paper should start by citing examples of slope failures in open pit mines during earthquakes. I do not know of any such examples, although - since my search of the literature has not been exhaustive - such examples may well exist. However, there certainly are many examples of devastating earthquake-induced landslides, and there is no reason why such landslides cannot occur at large open pits. Moreover, many of the actual earthquake-induced landslides have seriously affected mining operations in one way or another. Hence, this paper will treat earthquake-induced landslide phenomena in general, in the hope and expectation that the reader can apply this general knowledge to the specific problems associated with open pit mining. Ultimately, of course, the aim is to predict the likelihood of the occurrence of earthquake-induced landslides, and to delineate steps which can be taken to minimize the possibility of their occurrence. These aims can be achieved only imperfectly at the present time, for our knowledge concerning earthquake-induced landslides is still in an embryonic stage. Nonetheless, much useful knowledge does exist. In order to understand and apply this knowledge, it is necessary to: 1. Review the nature and extent of actual earthquake-induced landslides; 2. Have a grasp of the basic terminology and concepts of seismology; 3. Study the fundamentals of probability-based seismic risk analysis; 4. Appreciate the way in which earth materials behave during earthquake loadings; and 5. Have a general knowledge of the methods currently available for analyzing the dynamic response of slopes. Much of this paper is devoted to this necessary background. Information of practical use in connection with various classes of slope stability problems is assembled in the final sections. LANDSLIDES DURING PAST EARTHQUAKES Almost every earthquake in mountainous country, strong enough to be reported in the literature, has caused at least some landslides and rockfalls. Unless these slides or falls damage

Jan 1, 1971

Jan 1, 1967

By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.' If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The

By Rudolph G. Wuerker

The scarcity of values of tensile strength of rocks has been explained by the lack of successful testing procedures. In the case of mine rock a description is given' of the difficulties encountered in testing a cylindrical specimen, such as a core, by conventional methods. Over a period of years the following method has given definite and reproducible results with the weakest as well as with the strongest rocks. It does not completely supersede the use of cores with special fixtures but is a supplement in all cases where cores cannot be obtained, as from soft rocks, or in cases where it is less expensive to prepare test specimens by cutting them out of the rock instead of drilling cores.

Jan 2, 1955

By E. L. Bruce

Gold occurs in many mineral deposits in the rocks of the Canadian Shield. It is present in the ores of many base metals and a considerable quantity is recovered as a by-product from the production of copper at Noranda, of nickel and copper at Sudbury and of copper and zinc at Flinflon. But the greater part of the gold production of Canada is from deposits in which gold is the only metal of value. No gold is obtained from placer deposits within the borders of the Canadian Shield. A brief review of the geological relations of some of the gold deposits of the Canadian Shield will be presented in an attempt to explain certain associations. Only those which are being worked for their gold content will be considered and descriptions will be confined to representative types of deposits, chiefly those of major importance; a few others, differing in certain features from those of the older and larger mines, will be included in order to illustrate the general conditions in which gold occurs in these ancient rocks. Brief summaries will be given of the geological relations of the Beattie and Siscoe mines of northern Quebec, of the mines of the Porcupine and Kirkland Lake areas of northeastern Ontario and of the Howey, Central Patricia and Little Long Lac mines of northwestern Ontario. Genetic relations to igneous rocks of granitic composition, outcropping in the vicinity, have been assumed for many of these deposits. Undoubtedly the ore minerals have been derived from igneous sources and, for some occurrences, there is evidence suggestive of genetic relationship between the ore bodies and neighbouring intrusive rocks. During the past few years, however, many investigators have expressed doubt of the genetic relationship of certain ore bodies to igneous masses near which they occur. As will be seen from .references in the following descriptions the importance of the structural conditions in localizing deposition has been realized. This is pointed out for Canadian pre-Cambrian gold deposits by E. T. Dougherty, who also refers to the

Jan 1, 1937

By Vincent Carlsson

A comprehensive investigation has been undertaken to clarify how pellets are affected by alkali circulating in the blast furnace. The investigation has been performed with acid and basic pellets in a special furnace. Experiments were carried out to ascertain the influence of potassium on swelling and reducibility when added at different stages of reduction. After that, the significance of the quantity of potassium added in the hematite stage was studied. A parallel experiment with sodium as the alkali component was also con- ducted. Besides these vaporization experiments the effect of alkali on softening and reduction characteristics at high temperatures was investigated. The results showed that alkali always increases swelling, especially when added in the hematite stage. The addition of alkali increases reducibility of acid pellets during reduction from wustite to 70 % reduction. The softening temperature is significantly lowered by the addition of alkali and is, in any case, lower for acid pellets than for basic pellets. The microscopic studies showed that alkali ferrites can be formed irrespective of the influence of alkali on the slag phase.

Jan 1, 1977

By C. M. Young

The following paper has been prepared with the object of placing on record in the Transactions some facts concerning the present condition and future prospects of the coal industry of Illinois. In presenting it, the writer wishes to say that a considerable amount of the material contained is taken from the publications and records of the Illinois Coal Mining Investigations, the annual Coal Report of the State Mining Board, and the work of the State Geological Survey. Coal Beds and Mining Methods According to the latest maps of the State Geological Survey, there are only 19 of the 102 counties of the State some portion of whose territory is not within the borders of the coal measures. If outlying areas in Calhoun and Whiteside Counties are considered, the number is reduced to 17. This does not mean that all of the 85 counties that are partly or wholly underlain by coal measures will become producers, as there are some portions of the State in which the coal does not occur in beds of such thickness as to warrant the hope that it can be mined. The mining of coal is widespread, however, for in 1916 there was production from 61 of the 102 counties of the State, There seem to be no cases in which operations will be limited by depth, as none of the coal measures lie at depths much greater than those at which it has been proved that coal may be profitably mined in this field. In fact, the deepest shaft reaching a bed of bituminous coal in the United States is located in this State at Assumption, where coal only 3 ½ ft. (1.07 m.) thick is worked at a depth of 1004 ft. (306 m.). The coal beds occur in the form of a basin which is deepest along a line extending through the central part of the State and bearing a little west of north. The northern, western and southern borders of this basin lie within the boundaries of the State, but on the eastern side the Illinois field is continuous with the Indiana field. The glacial drift covers all except the extreme southern end of the State and the visible outcropping

Jan 1, 1918

By W. O Hotchkiss

An essential mental equipment for planning exploration is the fullest possible knowledge of the way in which the orebodies occur in the region to be explored, also the realization that in no mining district is this knowledge complete, and that new facts of importance will be revealed to the explorer in every exploration if he is in the proper frame of mind to grasp them. The geology of the ore deposits of the Gogebic Range for a long time was thought to be relatively simple, but work in recent years, by several men, has proved that this is not the case. We now realize that we are far from knowing all the factors that have resulted in the localization of ore deposits. For example, we have long known that the intersections of the dikes and the foot wall were favorable places to look for ore, but only within the last few years have we learned that there are several horizons in the various members, well north of the foot wall, that are likely to carry ore. The influence of the numerous cross faults on orebodies is not known or appreciated beyond a general realization that they are important. Just how they may be favorable or unfavorable to the localization of ore is not known. Such elementary information as the positions of these faults is just beginning to appear on the mine maps. Such being the condition, one can hardly overestimate the importance to the various operators and fee owners of careful studies of conditions in their properties for the purpose of assuring themselves that they are not missing valuable ore—that they are doing all the exploration that their situation demands in order to secure maximum returns. Valuable ores have been missed in the past and will be missed in the future. Only with a complete knowledge of all the factors that have united to produce ore could anything else be expected. The purpose of this paper is to call attention to these facts briefly and to suggest a few of the principles that should guide effective exploration. The foremost principle is that the man who starts out with the idea that he knows all about the mine geology of the Gogebic Range is starting with a heavy handicap.

Jan 1, 1923

By W. O. Hotchkiss

An essential mental equipment for planning exploration is the fullest possible knowledge of the way in which the orebodies occur in the region to be explored, also the realization that in no mining district is this knowledge complete, and that new facts of importance will be revealed to the explorer in every exploration if he is in the proper frame of mind to grasp them. The geology of the ore deposits of the Gogebic Range for a long time was thought to be relatively simple, but work in recent years, by several men, has proved that this is not the case. We now realize that we are far from knowing all the factors that have resulted in the localization of ore deposits. For example, we have long known that the intersections of the dikes and the foot wall were favorable places to look for ore, but only within the last few years have we learned that there are several horizons in the various members, well north of the foot wall, that are likely to carry ore. The influence of the numerous cross faults on orebodies is not known or appreciated beyond a general realization that they are important. Just how they may be favorable or unfavorable to the localization of ore is not known. Such elementary information as the positions of these faults is just beginning to appear on the mine maps. Such being the condition, one can hardly overestimate the importance to the various operators and fee owners of careful studies of conditions in their properties for the purpose of assuring themselves that they are not missing valuable ore—that they are doing all the exploration that their situation demands in order to secure maximum returns. Valuable ores have been missed in the past and will be missed in the future. Only with a complete knowledge of all the factors that have united to produce ore could anything else be expected. The purpose of this paper is to call attention to these facts briefly and to suggest a few of the principles that should guide effective exploration. The foremost principle is that the man who starts out with the idea that he knows all about the mine geology of the Gogebic Range is starting with a heavy handicap.

Jan 1, 1923

By Thomas D. Henderson, Donald E. Crowell

INTRODUCTION This paper presents a "case history" of the steps taken to estimate capital and operating costs for a typical porphyry copper concentrator of ±9,070 metric tons (10,000 short tons) per day capacity. The concentrator described herein is hypothetical, but is based on experience and is, in effect, a composite of several actual projects. The numbers used are illustrative only and do not represent actual costs at any particular concentrator. These numbers are, however, representative of typical milling costs at one point in time, and. are sufficiently accurate to illustrate the cost estimating procedures described in this paper. It is not possible to publish actual, current milling costs and, in any event, actual cost figures quickly become meaningless in today's economic situation with various costs all rising at different rates. The paper is divided into three parts: (1) order-of-magnitude estimate, (2) feasibility study estimate, and (3) discussion of differences between estimated and actual costs.

Jan 1, 1978

By Alden B. Greninger

Although the crystallography of lattice transformations has been studied extensively during the past few years, these studies have been limited, with few exceptions1'2, to specimens in which the transformed lattice appears as a segregate phase. A realization of the technical importance of the segregation mechanism, especially in the formation of martensitic structures and in age-hardening phenomena, has undoubtedly stimulated research in this direction. In the crystallographic studies of segregation, the general problem has been to relate the orientation of the parent crystal to that of the segregate crystals. The technique has been complicated by the fact that it has been necessary to deal with the presence of as many as 24 ideal segregate orientations within one parent lattice; furthermore, the segregate lattices are invariably scattered (seldom less than ±2º, often as much as 15" or 20') about these ideal positions. It is probable that a more complete picture of phase transformations may result from a study in which complete lattice relationships between individual grains are evaluated, thereby providing an additional parameter which when it is necessary to work with multiple segregate orientations, cannot be evaluated. The present paper presents the results of such a study, ? wherein a peritectic reaction is made use of to produce the transformed lattices. Matebials and Methods Pem'tectic Reaction.—In Fig. 1 is reproduced a portion of the copper-zinc equilibrium diagram, which includes the peritectic reaction a + liq. —ß. A liquid of composition between B and D upon solidifying will

Jan 1, 1937

Bethlehem Steel Co. has just brought an all-new iron ore mine into production at Marmora, Canada, about 120 miles east of Toronto. High grade pellets produced at the mine from open-pit magnetite ore travel 64 miles by rail to the port at Picton, then go by Lake boat to help supply Bethlehem's Lackawanna, N. Y., plant. At full production about half a million tons of pellets a year will be shipped, and mining will be at a scale of more than a million tons per year of ore. Aeromagnetic surveys carried out in 1949 by the Ontario Dept. of Mines and the Canadian Geological Survey revealed an anomaly that interested Bethlehem geologists. By 1951 the company had put down some 40 diamond drillholes ranging from 460 to 1800 ft to block out the magnetite replacement deposit which lies in pre-Cambrian limestone below about 130 ft of Paleozoic limestone. The orebody, roughly 2100 ft long and up to 400 ft wide, averages about 37 pct iron, too low for direct shipment. Not only construction of concentrating and pelletizing facilities, but 20 million tons of stripping lay ahead before production could start

Jul 1, 1955

By Albert Burch

AN analysis of this subject demands a study of the theory and practice of the present system, conclusions as to its merits, and recommendations for remedying its defects if any be found. Theory of the Present Law The theory of the present law with reference to lode locations contemplates the existence upon the surface of mineral-bearing veins which have clearly marked boundaries, and which can be so readily traced that a locator may immediately mark the boundaries of his 600 by 1,500 ft. claim in such a way that the vein will pass through both of its end-lines. It also supposes that, having discovered such a mineral-bearing vein, the locator will at once post a notice upon such discovery, mark the boundaries of his location in such a manner that they can be readily traced, and from that time forward have absolute title to the ground embraced within such boundaries, as against every person except the United States. For initiating title to placer ground, the law presupposes the discovery of a valuable mineral deposit; but not necessarily in place, as in the case of lode claims; and the location must be made to conform "as nearly as may be" to the legal subdivisions of the United States public land survey. When the placer law was extended to include the acquisition of title to oil lands, no exception was made as to the necessity for the discovery of valuable mineral in advance of location!

Jan 6, 1914

By Millard K. Shaler, Sydney H. Ball

During the past 50 years the attention of mining-men has been turned to Africa, and within the past decade prospecting-expeditions sent into Central Africa have resulted in the open-ing-up of several mines. Having recently spent two years in the Belgian Congo for the Societe Internationale Forestiere et Miniere du Congo, it is our purpose to outline briefly the mining-conditions in that part of Central Africa. Before it became, in 1908, a Belgian colony, this region was known as the Congo Free State. 11. Location and Area. The Belgian Congo lies in southwestern Central Africa, west of the continental divide, as illustrated in Fig. 1. It has a coastline of but 20 miles on the Atlantic, but widens rapidly eastward to points 5 north and 14 south of the equator. Its area is 908,000 sq. miles, which is almost one-quarter that of the United States and Alaska, or more than one and one-half times that of Alaska. Stated in other terms, its area is nearly one-third that of the United States, exclusive of Alaska and the insular possessions, or more than that of all the United States east of the Mississippi river. III. Topography and Drainage. From north to south, Africa is made up of three topographic elements: 1, the Atlas mountains, a highly-accentuated region

Jan 1, 1911

By W. G. Fischer

This paper attempts to close the gap between extensive rock testing with field measurements and the mine operator's need for safe mine layouts and alternatives. It was found that many of the variables that influence mine geometry and worker safety are relatively unimportant while others are critical. The development of empirical relationships that tie the critical variables to the safe useful life of a trona mine layout and observations made in 140 production areas where the variables were researched over a 15-year period are discussed. The concepts presented may have applicability in mine design for other bedded deposits.

Jan 1, 1986

By W. H. Craigue

THE scope of this article covers only the mathematical principles involved in discounting to present worth future expected profits and it is believed answers definitely two questions, which were raised at a recent meeting of the Committee on Methods of Valuing Coal Properties, as follows: 1. The accumulative effect of carrying charges on the value of coal mines showing definitely the number of years beyond which the coal may not be mined at a profit and subsequent to which the possession of any unmined coal will be a liability rather than an asset. 2. The effect on the valuation of coal mines, in the presence of the carrying charges described in question 1, of an increase in plant capacity and production. In general, in considering these questions, it may be stated that the consideration of an increase in plant capacity and production follows as a matter of course after a determination has been made of the year beyond which no profits are to be realized (giving the carrying. charges accumulative effect, or in other words capitalizing the carrying charges, as shown hereinafter). For example, if it is determined that any coal that is unmined after 45 years will have no value or less than no value, the question immediately arises as to whether or not a plant should be constructed that would result in a yearly production great enough to extract the entire tonnage in a time less than 45 years, and if so the number 'of years less than 45 years that would, from a financial stand-point, be the most desirable, all under the assumption that the market for the product or the transportation facilities are such that the yearly production can be increased to the desired amount.

Jan 1, 1933

By J. E. Burke

THE origin of so-called annealing or recrystalli-zation twins in face-centered-cubic metals continues to be a matter for speculation, and in the present report an attempt is made to explain their origin and to account for at least a majority of the observations concerning their behavior. The fact that annealing twins are prominent only The speelmen was deformed 8 pet in compression and then indented over the lower left-hand corner in a Rockwell in-denter, and then annealed to cause partial recrystallization. Note intense twinning in heavily deformed part and slight twinning in less deformed part. The upper right-hand corner is unrecrystalized. Area reduced approximately 25 pot for reproduction. after recrystallization suggests that deformation may be necessary for their formation. In 1926, Mathewson1 reported the observation by Phillips that annealing twins are frequently parallel to strain markings which delineate octahedral planes in the deformed (and partially recrystallized) matrix, and suggested that strain markings are mechanical twins which grow into annealing twins during recrystallization. Later work by Burke and Barrett' has shown that strain markings are traces of planes upon which slip has occurred, and that there is no evidence for the formation of mechanical twins of microscopically resolvable width in face-centered-cubic metals. Mathewson3 has pointed out, however, that slip may produce twin faults, and later modifications of this hypothesis have assumed that twin faults rather than true mechanical twins serve as the nuclei for annealing twins. Carpenter and Tamura5 suggested, also in 1926, that annealing twins might form by accidents of growth. A close-packed layer of atoms can be added to the octahedral plane of a face-centered-cubic metal in two possible positions, the right position

Jan 1, 1951

By H. D. Williams, R. A. Scriven

The distribution of elevation angle of finite plane facets distributed symmetrically about a given axis is derived in terms of the angular distribution of lines which these facets produce in a plane section parallel to the axis. It is assumed that the facets are not markedly elongated in preferential directions. The theory is intended for application to the angular distribution in polycrystalline metals of slip planes and of particular grain boundaries on which certain phenomena such as cavitation can occuv. Illustrative examples are given in closed form and simple numerical techniques are de-ueloped for practical application. The results are applied to the distribution of cavitated boundaries in a copper specimen after fatigue at 400°C and it is found that voids form on the boundaries that exper~enced maximum shear stress. When investigating the distribution of elevation angle between a given axis and planes symmetrically distributed about this axis the angular distribution observed in a plane section parallel to the axis is not necessarily the same as the required distribution. Consequently a technique for processing the results obtained by sectioning methods is required. An example where such a technique would find application is in the problem of intercrystalline void formation during uniaxial tensile creep. Two theories have been proposed to explain this cavitation in terms of the normal and the shear components of stress, respectively. Hull and Rimmer (1959) postulate that the growth of intercrystalline voids is controlled by the rate of supply of vacancies from the grain boundary, the local vacancy concentration being proportional to the normal stress on the boundary. Gifkins (1956) considers that slip arising within a grain causes a ledge to be formed at the grain boundary which is subsequently opened up into a cavity by grain boundary sliding. It might be possible to differentiate between these mechanisms by determining the angular distribution of grain boundaries containing cavities since the former theory predicts a predominance of cavitated facets normal to the stress direction whereas the latter should favor an angle of 45 deg to this direction. In a similar manner an indication may be obtained of the type of mechanism responsible for intercrystalline cavitation during high-temperature fatigue. Davies and Wilshire (1962) have analyzed the slip-plane distribution in a nickel specimen but the problem was not treated in any detail nor was any account taken of the finite extent of the planes being sectioned. Hilliard (1962) has given a very general account of how anisotropy in the microstruciure can be related to measurements taken in one or more plane sections by expressing both the measured and the true angular distributions as expansions in spherical harmonics.* The present analysis is con-

Jan 1, 1965

By W. A. Tiller

The conventional techniques1 for determining the liquidus and solidus surfaces of an alloy system containing more than two components are extremely tedious to use and do not provide a complete picture of the equilibrium relations between solid and liquid alloys. These techniques are unable to yield "tie-line" information concerning solid and liquid phase equilibrium, a very important parameter in the solidification description of the liquid alloy and a very necessary parameter in the preparation of "zone-levelled" alloy crystals. The tie-line in a polycomponent system is analogous to the partition coefficient, k, in a binary system, it gives the composition of the solid, Cs, in equilibrium with a liquid of composition CL. That is, CS = kCL, where CL = [CO, c1,...Cn] denotes the concentrations of the n + 1 constituents, and k = [ko, kb ,...kon] denotes the gross partition coefficient for the elements between the two phases; thus, k is the tie-line in this system. To provide complete information concerning the two-phase equilibrium in a polycomponent system it is necessary to know both the liquidus surface and the gross partition coefficient. From these two the solidus surface is obtainable. The conventional techniques are unable to provide this information in other than a binary system so we must look elsewhere. In recent years considerable insight has been gained into the correct description of the liquid-solid transformation, 2,3 and controlled solidification experiments may now be designed to both facilitate and enhance equilibrium diagram studies. In the present paper consideration is given to two methods for obtaining the liquidus surface and the tie-lines in polycomponent systems. The methods to be described below deal with the solidification of an n + 1 constituent liquid alloy of initial composition [co, Co ,...Con], where the superscripts refer to the elements present and the Oth element is considered as the solvent in which the n solutes are dissolved. The general assumptions made in the treatment are the following: (i) the solid and the liquid at their interface are in equilibrium during the growth of the solid phase, (ii) there is no diffusion in the solid phase, and (iii) the liquid phase is completely mixed and is therefore homogeneous in concentration. METHOD I In this section a general experimental method will be described which, in principle, is capable of giving an exact description of the liquidus surface and tie-lines. Consider the unidirectional solidification of the liquid alloy specimens L cm in length (freezing either horizontally or vertically). Allow the sample to be frozen very slowly from one end, as indicated in Fig. 1, with complete mixing in the liquid, and then analyze the solid bar to determine its chemical constitution as a function of position, x, along the bar. Let Fig. 2 represent a possible distribution of the ith constituent along the bar. At the point x' the concentration of the ith constituent is C1/5(x'), and the average concentration of the rest of the bar between x' and L is given by C:(X' - L) where [ A(x) c1s(x)dx c1/s(x'-L) = f A(x) dx x * and A(X) is the cross-sectional area at x. In a similar manner. all the Cf(x' - L) may be determined. Thus, the gross artition coefficient k for liquid of composition [Cs(x - L),...Cs(X' - L)] is given by -ko= CUs')/Cos(x' - L)" k0 = csn{x')/cs(x'- L) During the freezing of a charge of length L, the liquid composition may vary over a wide segment of the phase diagram and the gross partition coefficient over this segment of the phase diagram may be determined from one, bar. Fig. 3 illustrates the magnitude of Cs(g)/C,' as a function of the fraction g of the bar which has Solidified.2 We can see that the concentration in the bar will vary over a range of about 15 wt pct for C,' = 10 wt pct and k0 = 0.5. It appears that 4 or 5 specimens would be adequate to study a simple binary eutectic phase diagram.

Jan 1, 1960