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By J. W. Pugh, J. D. Nisbet

THIS study of the ternary has been made as one phase of a metallurgical investigation which began nearly four years ago in the General Electric Company's Research Laboratory in Schenectady, N. Y. The objective of this program is the discovery of new metallurgical information which will lead to the development of better high-temperature materials. Combinations of the four pure base elements—iron, chromium, nickel, and cobalt—are being studied at the present time. It is essential in an investigation such as this to know as much as possible about the constitutional diagrams involved. The study of the iron-chromium-nickel system has been made to this end. Preliminary Explanation of Experimental Procedure: In all, fifty-five alloys at steps of 10 at. pct were made for the investigation of this ternary. Several ternary alloys in the chromium rich corner had to be omitted because their extreme brittleness made testing impractical. All alloys were vacuum melted with hydrogen reduction and centrifugally cast. The apparatus and technique of this process has been described in detail by Nisbet.1,2 The purity of the alloys prepared in this way is considered to be quite good. Impurities are listed as follows: Pct Carbon.............................0.02 Oxygen................................0.02 Nitrogen.........................0.005 Magnesium..................0.03-0.05 Sulphur...........................trace Hydrogen....................trace Phosphorous..................trace Silicon........................ trace After casting, all samples were given a homo-genization treatment which consisted of holding them for 15 hr at 1150°C (2100°F) and water quenching. Testing was begun with the samples in this condition. The tests employed in the study of this system were (1) dilatometer, (2) hardness versus aging temperature, (3) tensile strength and elongation versus temperature, (4) microstructure analysis, and (5) electrical resistance versus temperature. Dilatometer tests were made at the rather rapid heating rate of 1093°C (2000°F) in one hour on a Bristol-Rockwell type instrument. Hardness data were taken on specimens cooled from 204", 427", 649°, 760°, 871°, 982°, and 1093°C under conditions which are thought sufficient to bring the specimens to equilibrium in all but the cases of the very sluggish transformations. Electrical resistance data for several specimens were taken for both heating and cooling conditions in a vacuum furnace especially designed for this work by D. W. Bainbridge, formerly of this laboratory. Provisions were made for heating and cooling standard specimens at a constant rate, while autographic records of resistance and temperature were made simultaneously. Micrographs of all the alloys were made in the quenched condition. Some question may exist as to how such physical values as hardness, tensile strength, and elongation were interpreted to indicate a change in phase. Original data were recorded on physical property versus temperature graphs, each of which was made from the data of a single alloy (fig. la). From these, another series of graphs were plotted with the physical property as a function of composition for constant temperatures (fig. 1b). Sharp deviations in the slope of these composition versus hardness curves often indicate a change in phase. The example of fig. 1 will serve to describe this experimental technique. The plotting of a single point from graph "a" to graph "b," and finally to the phase diagram "c," is illustrated. The location of the point on graph "b" is indicated as point (1). If all the alloys of the A-B binary system were solid solutions at temperature X, the hardness in this curve would be expected to rise at a fairly even rate as A is diluted with B to a maximum at some intermediate value between A and B, as

Jan 1, 1951

By AIME AIME

EVEN though most of the program of the joint meeting at Easton, Pa., on Oct. 30 to Nov. 1. was devoted to the interests of combustion engineers rather than to coal-mining engineers, nevertheless the A.I.M.E. Coal Division was well represented, with 83, or close to one third of those in attendance giving this as their affiliation. The fuels division of the American Society of Mechanical Engineers had 108 representatives, and an equal number reported no society affiliation. Added to the men's total registration was that of some twenty ladies so the total attendance was in the neighborhood of 325, exceeding that of the last two joint meetings, at Birmingham and Columbus, and equaling the 1938 crowd at Chicago.

Jan 1, 1941

By L. W. McKeehan

THE occurrence of twins in large ferrite crystals, made by a new process, was reported in a recent note. This paper describes a typical case of such twinning and suggests, on the basis of the observed facts, why smooth slip-planes are rarely observed in this metal. METHOD OF PREPARATION The material In which the crystals here dealt with were grown was made from 1/8 -in. Armco iron welding rod containing C, 0.04; S, 0.037; P, 0.003; Si, 0.008, and Mn, 0.02 per cent. This rod was cold drawn into wire about 1 mm. dia. A piece of this wire was supported vertically and was locally heated in hydrogen at atmospheric pressure to about 1400° C. by an alternating current (60 cycles per sec.) of about 35 amp., passed through it between a pair of travelling contacts about 8 cm. apart. The rate of travel for the case in hand was 12 cm. per hr. After some 30 cm. of the length of the wire had been heated and cooled in this manner the whole wire was immersed for a few seconds in dilute nitric acid, not restrained by alcohol. Etching was continued until, as nearly as could be judged by eye, the original smooth cylindrical surface of the wire was no longer capable of specular reflection.

Jan 1, 1927

By W. E. Ruder

It has been pointed out by Stead1 that grains of considerable coarseness may be developed in steels containing from 3 to 5 per cent. of silicon, and in a previous paper2 the present author has shown that under the proper conditions of annealing single grains having an area of 50 sq. cm. may be obtained. It is the purpose of this paper to discuss in more detail the conditions promoting the growth of these grains, in the hope that the experiments described may throw some additional light upon the general problem of grain growth in metals. These silicon steels lend themselves particularly' well to such experiments because of the ease with which the change in structure may be followed and because of the fact that the effect of the carbon present is largely obliterated by the high percentage of silicon. This forms a solid solution with the iron, which acts very much like a pure metal. This alloy has been found to have but one critical point, viz., Ar2. This point, determined by Roberts-Austen for Hadfield's 4 per cent. Si alloy, was found to lie at 703" C. Vigouroux3, in working with pure Fe-Si alloys, finds this point to rise from 750" C. for 0.5 per cent. Si to 860" for 6 per cent. alloy, with a flat region in the curve from 3 to 4 per cent. Si. No accurate determination of this point has been undertaken by the present author, but it has been roughly determined to lie between 730" and 750:. In the preliminary experiments, some of which have been described in a previous paper, it was found that practically all of these steels, when annealed to 1,200" C. or higher, showed grains of comparatively large size. These grains varied in size, however, from about 4 sq. mm. to 50 sq. cm. (see Figs. 1 and 2) under the same conditions of anneal, and it was for the purpose of determining the cause of this difference in size that the experiments herein described were undertaken. From a preliminary study of the chemical composition of the specimens

Jan 1, 1914

By Sallie McCabe Johnson

LIFE IN RUSSIA for the foreign woman is hard. It is up to her whether her days are spent in tearful longing for ironic or whether she :hakes the real effort to ferret out the interesting or amusing side of such exasperating conditions as ooh a Russian can conjure. So to begin Discard all promises.. This is perhaps the most difficult thins- to learn but promises in Russia are nut what they are at home. There are many reasons for ibis, sonic good and some bad but whatever the reason. the fact remains that they are usually worthless- as each of us must slowly learn In, disappointment after disappointment. Also we must learn that we cannot expect to get or to do a certain thing just because someone else has done so. What we did yesterday perhaps cannot be dune today. What we purchased air hour ago, oxen ten minutes ago- we cannot purchase now. What our neighbor did this morning we cannot do this afternoon. Changes arc continuous. Every person's experience is different from that of another aid this in a great measure accounts for the conflicting stories brought horns. In a land of chaos we live only from hour to hour and this is one of the exceedingly exasperating conditions to face. When I wished to visit Leningrad, an overnight nip from Moscow, more than a week's lime w as required to obtain a ticket, vi en through the efficiency of lntourist: alone I might have spent a month at it. Each day

Jan 1, 1932

THE Executive Board of The American Engineering Council met in Pittsburgh, May 26 and 27. Its actions on the licensing of engineers and on the Employment Bureau are printed at length elsewhere in this issue. The board announced plans purposing the solution of the national problems of water power and forestry, upon which "the industrial development of the nation and the standard of living of future generations largely depends. The whole Federal water-power situation is in so critical a condition that immediate constructive action by the Government to conserve the public interests, involving vast consequences of economic and Federal policy, is necessary. After a long discussion during which the water-power problem as it affects Government reorganization was reviewed and Henry Ford's Muscle Shoal's plan was discussed, the board decided to lay the entire question before President Harding. A national movement to conserve the nation's forests, in which engineers, the U. S. Forestry Service, the forestry services of the states, universities and technical schools, and other groups such as the farmers, the railroads, and lumbermen, shall pool their efforts, was set in motion by the engineers. The work will be in charge of a Reforestation Committee of the Council, headed by Charles H. MacDowell of Chicago. Mov-ing picture interests will be asked to aid. The board pledged its support to President Harding in his plan for Government reorganization. In adopting the report of its Committee on Public Affairs, headed by J. Parke Channing of New York, the Executive Board of the council determined, in the event of the failure of the President's efforts to bring about greater economy and ffieciency in national affairs by regrouping of Federal functions, to press independ-ently a nation-wide movement for the establishment of a Department of Public Works. Progress in a national survey of the two-shift day in American industries was reported by the Council's Committee on Work Periods in Continuous Industries. This survey, called the most extensive of its kind ever made, has been in progress for more than a year; and purposes an exposition of industrial conditions which shall form a basis for establishing the relative merits of three shifts of eight hours each and two shifts of twelve hours each.

Jan 7, 1922

By J. Mizrahi, A. M. Baniel, A. Mitzmager, S. Star

This article gives an account of the latest developments in the use of TBE for sink-float separation of silicate minerals. A number of minerals for which the process has been tested and found suitable are reviewed. Specific examples are discussed in relation to the particular problems of sink-float separation and recovery of TBE as compared with non-silicate minerals. The economic aspects are outlined. Silica and silicates comprise the most common and abundant group of minerals, and since they are present in variable amounts in most ores, they constitute an appropriate subject for the review and discussion of the recent developments in the use of TBE for mineral concentration. The silicates considered as a group have an extremely wide range of chemical and physical properties. Some of these properties, which are common to all minerals, are of importance to concentration by TBE and are discussed in some detail in this paper, as well as the development of methods and apparatus for concentration and recovery of TBE and several examples of concentration of silicates. PROPERTIES OF MINERALS WITH RESPECT TO CONCENTRATION BY TBE The properties considered as most important to concentration by TBE are specific gravity, structure, surface and shape. The specific gravity of a mineral is a fundamental property and is constant between very close limits for the same species of different sources if particles are pure and free from cavities or cracks. In many species, however, solid inclusions and changes in chemical composition due to replacement of elements cause variations in the specific gravity. The plagio-clase series of feldspars between albite and anorthite illustrate this point (specific gravity from 2.60 to 2.77). Fig. 1 shows the specific gravity distribution of some of the common silicate minerals.' The highest specific gravity is about 4.7 (zircon) and the lowest is 2.0 (sepiolite), with most of them ranging between 2.6 and 3.5. Although most of the silicates given in Fig. 1 are found as constituents of rocks, those generally considered as rock making minerals are comparatively few. They include quartz, feldspars, nephelite, sodalite, leucite, mica, pyroxenes, amphiboles, chrysolite, kaolin, talc and serpentine. These minerals may appear in igneous rocks as coarse crystals in granites, syenites and diorites or as very fine grained dispersions in basalt and felsite. When the latter rocks occur in an ore, their specific gravities depend on the minerals present and structure. The same is true for the sedimentary and metamorphic rocks (sandstones, shales, gneiss, slate, schists). A comparison of specific gravities for the minerals listed in Fig. 1 with that of TBE (see Table I) shows that the important rock-forming minerals, with the exception of pyroxenes, amphiboles and chrysolite (olivine), lie in the specific gravity range of less than 2.96 and can therefore be separated by TBE. The ore structure is important both in determining the apparent specific gravity and the efficiency of TBE recovery. The structure can be compact (as in

Jan 1, 1963

By H. O. Hofman

With the exception of the exhaustive paper on the Father de Smet mill, by its designer, Mr. A. J. Bowie, Jr. (Bans., x. 87), nothing, so far as the writer is aware, has as yet appeared on the stamp-mills of the Black Hills of Dakota, although they have been steady producers for the last ten years. Within the small area of about 6000 by 1600 feet, $2,271,341.14 was produced in 1887† from rock averaging $4 per ton in free gold. I. The Ores. Character of the Ores.—The gold of the district is found in quartz and pyrites finely distributed through vast bodies of mica- and amphibole-schists, argillites and phyllites, and also impregnating the schists themselves. The " Belt," embracing the section of Lead City, Terraville and Central City, is the only part worked at present. The principal associated mineral is iron pyrites, with some arsenopyrite and chalcopyrite, garnet and asbestos. The ores from open cuts and upper levels are more free-milling. than those from underground workings below water-line. Hence

Jan 1, 1889

By H. E. Elliott, R. S. Busk, A. T. Peters

One of the problems of the fabricator of metals and alloys is the propensity of some composition rarnges toward abnoermal grain growth during certain stages of fabrication. In this respect magnesium alloys are no exception among alloys. Fortunately, convenient foundry control methods have been developed by which the abnormal grain growth possible in certain magnesium-alloy castings can be suppressed. An unusual characteristic of magnesium alloys, however, is that castings of some composition ranges are subject to local grain growth during heat-treatment without the necessity of intentional mechanical stressing of the part prior to heat-treatment. This effect occurs only under certain critical casting conditions, and only in certain alloys of greater than about 8.5 per cent aluminum content, such as C alloy (Mg, 9 per cent A1, 2 Per cent Zn, 0.2 Per cent Mn) and G alloy (Mg, 10 per cent Al, 0.2 per cent Mn). The first observation of this phenomenon in cast magnesium alloys occasioned much surprise, since it is not observed in other meta1s- Jeffries and Archer1 have stated that "the grain size of cast metals, provided they have not been plastically deformed, cannot be changed by heating below the melting point." The study of the conditions leading to abnormal grain growth in cast magnesium alloys, and of the mechanism of this phenomenon, has led to some very interesting observations. Perhaps the most significant of these was the observation that stresses originating from cooling contraction in magnesium-alloy castings are the only stresses necessary, under certain conditions, to cause local recrystallization and subsequent grain growth in the casting during heat-treatment. Before recent developments, this phenomenon of abnormal local grain growth Was a definite problem in the production foundry on C alloy sand castings. Illustrated (Fig. I) is a picture of a casting scrapped because of this defect. A mottled effect is produced in coarse-grained areas by suitable etching solutions. The properties of metal in the affected area are much impaired by such grain coarsening. Ultimate tensile strengths of half the normal value have been measured in metal of this nature. In this paper are described the techniques that have been developed by The DOW Chemical Co. for studying, and in large measure solving, this production problem. Also discussed are studies of the mechanism by which excessive grain coarsening occurs, and the fundamental conditions that produce this effect. The abnormal grain growth discussed in this paper will be referred to as "germinasium since this term has been definedl as any process leading to an abnormally coarse grain size. This paper deals only with abnormal local grain growth that may occur during the solution heat-treatment of certain magnesium-alloy castings, as dis-

Jan 1, 1945

By L. C. Graton

At the Tenth International Geological Congress, Mexico, 1906, Waldemar Lindgren presented "The Relation of Ore Deposition to Physical Conditions." Retrospect ranks it as the outstanding offering at that Session and as the most fundamental contribution up to that date on the philosophy of ore deposition. Elaborating thereon in his text-book "Mineral Deposits," Lindgren analyzed ore-forming processes under conditions prevailing from great depth up to surface; explained the nature of deposition in each environment; and developed a comprehensive genetic ore classification, which brought wide acceptance and enriching contributions by many. Since Lindgren's latest edition (1933), have come wealths of material relevant to ore genesis, particularly through amazing renaissance and proliferation throughout science. Current publication regarding ores now emanates largely from a generation caught in pressures of the breathless modern tempo, which tempts scant reflection upon earlier truths. Consequently, today's thrilling output contains not a few offerings that need challenge because supplanting interrelationship and system by what seems, collectively, an assemblage of strange, ad hoc and often self-contradictory concepts. From these latter some merit may eventuate but at the probable cost of present confusion and delayed progress. The following pages, naming numerous post-Lindgren advances, record the conviction, held by many, that Lindgren's philosophy, progressively improved, remains the soundest approach to understanding ore genesis.

Jan 1, 1968

By Nathaniel Arbiter

There is a history in all men's lives, Figuring the nature of the times deceas'd, The which observ'd, a man may prophesy, With a near aim, of the main chance of things. W. Shakespeare, Henry IV; Part 2 Introduction This nation's first century embraced two stages of the Industrial Revolution. During one, what had been a colonial agricultural economy began to industrialize; water power, then steam after 1794, were the energy sources; coal and iron were the essential ingredients. The second stage started after 1850; aided by rich and diverse mineral resources, the country began its transition from the Iron Age to the Age of Metals. Early civilizations had been built on stone, and fairly high levels were sustained on iron. But the spectacular advances in the past century in communication, in construction, in transportation by sea, rail, land and air, and in much that characterizes modern civilization have depended increasingly on the use of the complete metallic and nonmetallic resources of the earth's crust. Thus it was appropriate to define the Industrial Revolution as “the period during which man's relationship to natural resources became utterly changed”, 1 with minerals playing a major and indispensable role. But we are now becoming aware that the relationship of man to natural resources must change again. On every hand the dangers inherent in the contamination of land, sea and air by the wastes of civilization are becoming apparent. And from the growing realization that mineral wealth is finite must eventually come other far reaching changes in mineral use and distribution. For on the scale of centuries we cannot continue to exploit mineral resources even at present rates, let alone at expanded rates, without eventual depletion of the more abundant resources, and early exhaustion of the less abundant. In the past our problems were relatively easily met by the development of new and improved machinery and processes. But the future will

Jan 1, 1971

By A. J. Mcintosh

PRICE changes in competing fuels in the last three decades have reflected the changes in the consuming habits of the people of the United States. Prior to World War 11 the importance of fuel oil and fuel gas increased almost constantly while the relative importance of both bituminous and anthracite coal decreased. During this same prewar period coal prices increased to a much greater extent than oil prices. In fact, in many years, oil prices declined and in most cases are now no higher than they were back in 1925-26. During the war natural economic trends were entirely upset because of the tremendous petroleum requirements of the Army and Navy. Under these conditions many industrial plants were converted to the use of coal and the new installations in home heating and industrial plants of all kinds which might have used oil were practically eliminated. Although petroleum prices were rigidly controlled by OPA coal prices increased several times during the war. An over-all statement as to the rela-

Jan 1, 1947

By Charles A. Stetefeldt

This treatise is the sequel of a paper on "Russell's Improved Process for the Lixiviation of Silver-ores," etc., read at the Chicago meeting, in May, 1884, and published in the Transactions, vol. xiii., page 47. The facts it presents are principally compiled from Mr. Russell's notes on his practical experience gained in various places where the Russell process has been introduced. For a complete understanding of this paper a perusal of my former one is desirable, as can be seen from the frequent references here made to it. All silver-ores that do not carry a large percentage of lead or copper can be treated by Russell's process with success and economy. I do not mean to create the impression that from ores containing considerable quantities of lead and copper a high percentage of the silver cannot be extracted by this process. Such ores, however, will, in many localities, be reduced to better advantage by smelting. In case lead-bearing silver-ores are suitable for concentration, it may be profitable to concentrate the ore by Krom's dry system, obtaining a smelting-product high in lead, and to lixiviate the tailings and the dust. This plan has been adopted in a mill recently erected in Cortez District, Nevada. The dry system of concentration deserves the preference because it delivers the tailings and the dust in a condition ready for chloridizing-roasting. In wet concentration the drying of the tail ings would be expensive, and there would be a considerable loss of silver in slimes. Oxidized ores, containing silver chloride and lead minerals, may be lixiviated after crushing, and the tailings may be concentrated for lead. In this case wet concentration would be most suitable. This has been done at the Old Telegraph Mine, Utah. I would give, however, the preference to dry concentration in all cases which, of course, requires that concentration should precede lixiviation. The Russell process is also adapted to the treatment of tailings resulting from ores which have been worked either by the old

Jan 1, 1887

By R. J. Wysor

Since the outbreak of the European war, few problems of raw-material supply have commanded more nation-wide attention than potash. It is well known that before the war the domestic production of potash was an insignificant percentage of the imports. The average annual importation of raw potash salts for several years prior to 1914 was slightly over 300,000 net tons, and of other potash manure salts about 700,000 tons. The sudden and almost total cessation of these imports created a unique and stringent situation. Methods of recovering potash from feldspar and other native mineral sources, and reclamation from hitherto waste products, have received a marked impetus. Soaring prices have been a keen incentive to research and industrial development. Although several brief articles concerning the possibilities of potash recovery have appeared in recent trade journals, it still may be a matter of some surprise to the average technical mind that potash might be reclaimed as a profitable byproduct in the manufacture of pig iron. At the present time it may be of special interest to present some data, largely of a technical nature, on this subject. A fairly thorough search of the literature reveals a number of articles concerning salts of the alkali metals in the blast furnace. Many of them deal with the theoretical rôle of alkali cyanides in the furnace. Several discuss the probable effect of the alkalies on the furnace brickwork. Two or three ambitious patents have been granted for reclaiming potash or other products from blast-furnace gas. However, we have heard nothing further as to the practical application of these patents. Little literature of importance has appeared during the last 10 years concerning alkalies in blast-furnace practice, and I have discovered no record whatsoever as to the actual sale or commercial disposal of flue dust for its potash content until this was inaugurated in our plant at Bethlehem. A bibliography of the most important articles discovered is appended. About 4 years ago, in the course of investigating blast-furnace stove efficiencies, I analyzed the fine, yellowish fume of which a considerable

Jan 1, 1917

By Emery R. Hayhurst

SILICOSIS has been described in a report of the American Public Health Association as a disease due to breathing air containing silica, characterized anatomically by generalized fibrotic changes and the development of miliary nodulations in both lungs, and clinically by shortness of breath, decreased chest expansion, lessened capacity for work, absence of fever, increased susceptibility to tuberculosis (some or all of which symptoms may be present), and by characteristic X-ray findings. ... The disease is divided arbitrarily into first, second, and third stages for convenience of description and possible compensation purposes. At least two distinct types of silicosis are recognized, acute and chronic. The acute form was reported as early as 1713, when a British patent for grinding flint by wet methods was granted because the dry powdered material "proved very destructive to mankind, so much that any person, ever so healthful, working in that business cannot possibly survive over two years."

Jan 1, 1936

By P. R. Bradley

NO thought had been given to deep level mining at the Alaska Juneau mine prior to 1930, but in that year a prospect winze was started and continued for 1000 ft. vertically below the main haulage or adit level. The point at which this winze was started was selected entirely by the prevailing physical conditions, such as proximity to established workings, convenience, and the presence overhead of a substantial pillar of dimensions sufficient to lo¬cate the sheave wheel and loading pocket. It was, therefore, with some surprise that the unusually high-grade ore found just below the collar of the winze persisted, with certain vari¬ations, to a full depth of 1000 ft. vertically. Likewise this unusually high-grade ore was found to persist on the various crosscuts driven on levels at 200-ft. vertical intervals. To be brief, this deep level work found richer ore than any yet found in the mine over like areas, and inasmuch as the area was sufficient to plan for extensive deep level mining, plans for such work were given extended consideration.

Jan 1, 1936

By J. J. Beeson

For the past fifty years or more, the structural features of the Cordil-leran mountain system of western United States have presented some most interesting problems. Any geologist or engineer living in this region, or even making occasional examinations of the mines, will lose much of interest and importance if he is not familiar with the literature. Some of the greatest works on geology have been the result of studies carried on in sections of this region. Among the more important of the earlier works are those of Dutton,l King,2 Gilbert3 and Powell;4 of the more recent Lindgren,5 Ransome,6 Spurr,7 Butler8 and others have contributed much. Many of the papers are largely of scientific interest but even these lay the foundation for the commercial application of the broader features of the geology. I have read many of these works with the keenest interest and pleasure; in fact, some have been read until some of the more important findings seem to be my own. In this paper, however, it is my aim to accept credit for little more than the labor of assembling some of the ideas of others. This is done with the hope that an interesting and valuable discussion will be the result. If some of the ideas presented should

Jan 1, 1927

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By David Sinclair

THE dimensions and shapes of mine structures may at present be determined by (1) field experience, (2) structural calculations, and (3) barodynamic tests.§ None of these, however, provide information as to the stresses, their direction and distribution in a mine structure. For the design of pillars, the placing of openings relative to working places such as gangways, haulage levels, etc., this information is desirable. Photoelastic methods provide this and, while relatively new, their appli-cation in all engineering fields is assuming increasing importance. This paper, therefore, will present the method with a few applications to mining, and with sufficient reference for further study by the reader. PART I THE PHOTOELASTIC METHOD The photoelastic method of stress measurement determines the stress distribution in a two-dimensional model by optical means. It makes use of the fact that when a piece of isotropic transparent material, such as glass, celluloid, or Bakelite, is stressed and viewed in polarized** light a picture is seen which indicates by its color bands of light, or fringes, the magnitude of the stresses, their direction and their distribution.

Jan 1, 1940

By George M. Fowler

DURING 1937 the subject of mining geology was probably given more attention and more mining geologists were usefully employed than at any previous time. Of the many contributing factors the most important were: (1) a higher degree of prosperity in many countries, (2) a. better understanding of geologic phenomena, and (3) the apparently diminishing reserves of several important minerals. Mining companies have come to look upon geology with a growing appreciation of its aid in the more effective exploration and exploitation of mineral deposits. Most of the larger and more active companies have one or more geologists permanently attached to their staffs and some have well organized and efficiently managed geological departments. Even the smaller companies, who feel they cannot afford to employ a geologist on a permanent basis, are seeking the advice of competent men in this field with increasing frequency. One of the most significant trends has been the growing tendency to base exploratory work on more thorough geologic studies instead of empirical "hunches,"on which so much off the work in the past has relied. Likewise, mining companies are apparently more willing to expend larger sums on the basis of geologic possibilities in a district.

Jan 1, 1938