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By H. M. Day, C. H. Mathewson

THE constitution of the system silver-mercury has attracted the attention of many investigators during the last two decades, but since their results are for the most part in poor agreement, there is little need for a review of their individual contributions. It remained for the very careful thermal and microscopic investigation of Murphy' in 1931 to give the constitutional diagram in its present and unquestioned form, which is shown in Fig. 1. He devised methods for taking cooling curves on alloys under high pressures and for the microscopic observation of alloys which contained liquid mercury as a structural constituent at ordinary temperatures. The compositions of the intermediate phases were confirmed and supplemented through X-ray analyses by Preston2 and Stenbeck.3 According to Murphy, at 276° C. silver is able to dissolve 44 to 45 weight per cent of mercury, which may increase at lower temperatures to about 50 per cent. Preston concluded that the saturation boundary occurred at 46 ± 2 per cent at 100° C. From the values reported in the literature, these are the only ones that may be accepted as lying even in. the right region. PREPARATION OF ALLOYS The silver used in the present investigation was supplied by the United States Metals Refining Co. through the courtesy of the Committee on Industrial Uses of Silver and, since a complete spectrographic and chemical analysis was furnished, no attempt was made to purify it or to further establish the impurities present. The analyses reported by the company are shown in Table 1. Milligan4 has found that the magnesium content is probably less than 0.0005 per cent.

Jan 1, 1938

By K. Stout, L. Friel

Some rock mechanics theorists believe that if a hydraulically placed backfill can be introduced in a stoped out area, which will minimize wall closure by taking high stresses across the fill with minimum compaction, then heavy ground and rock burst phenomena will be minimized. The paper will discuss a large scale laboratory project when fill strength was increased over four times by the head vibrated method and up to well over 20 times by the double placed, cemented, vibrated head method when compared to conventionally placed fills. The only preconditioning of the 60% solids by weight slurry was the addition of cement in some tests.

Jan 1, 1983

By Robert B. Coleman

The recent surge in demand for uranium in the US, accompanied by a significant increase in price, has stimulated the search for and development of lower grade ore bodies. At the mill, this translates into much larger throughputs and-compounded by many recently enacted environmental considerations-has made the cost of milling a critical factor in today's uranium production economics. The three conventional milling methods employed in the extraction of uranium ores are reviewed in the following sections.

Jan 10, 1978

By A. T. Tye

REGARDING the results of preferential flotation at Cananea, Weinig has stated that "The concentrating mill of the Cananea Consolidated Copper Company at Cananea, Mexico, furnishes an excellent example of modern flotation practice. The complete figures are given because they present so forcibly the advantages of modern selective flotation."' L. 0. Howard notes that "Perhaps the outstanding example so far published of improvements in results through the use of selective flotation is that at Cananea, Mexico."2 The following notes indicate the conditions under which the results were obtained at Cananea; also the effect of preferential flotation at the concentrator and at the smelter. In the majority of cases the full benefit of selective flotation is not fully realized, as the concentrates are shipped from the mill to smelters owned by other companies. The saving made at a certain concentrator by this method of flotation may be well understood but the saving resulting at the smelter from the results of preferential flotation at the mill is not so apparent, as the data are contained in the smelting records of some other company. Even at the smelter the great gains following preferential flotation may not be noted, as a variety of ores and concentrates from various sources are received and the difference from the changed concentrator operations of a certain mill may be obscured. As noted by Professor Weinig and Professor Howard, the results obtained at Cananea brought about a veritable metallurgical revolution at the smelter.

Jan 1, 1927

By J. W. Snavely

WITH all the advantages of handling bulk materials by means of belt conveyor also go some problems, one of the most persistent being that of cleaning. When sticky materials are being carried; the build-up of material on the return idler rolls results in difficulty of belt training. Much attention has been given to the problem of cleaning conveyor belts, and a great variety of cleaning devices have been developed. Even the best involve troublesome maintenance, and none can completely remove the fine particles imbedded in the belt cover, which cause rapid wear of the return idler rolls, and at the same time, of the belt cover as well. One of the major rubber companies has been promoting a two-way belt system, in which the conveyor belt is given two successive 90" twists at each end to enable it to carry material in both directions simultaneously. For many years the flat belt transmission industry has installed quarter-turn and half-turn twists in countless numbers of instances. While quarter-turn and half-turn twists in transmission belts is a familiar application, the 180" twist apparently has never been previously attempted with a conveyor belt. About a year ago, two officials of the National Iron Co. of Duluth, Lester and Lewis Erickson, proposed twisting the return run of a conveyor belt on an installation that they were designing for one of the major iron ore producers. Since then the soundness of the idea has been demonstrated, both in theory and by practical test, with the result that the installation of two conveyor belts involving the twisting of the return run is now under way. These two installations are designed to have the return run of the conveyor belt twisted 180" as it leaves the snub pulley at the head drive. The clean underside of the belt is thus placed against the idlers on the return run as well as on the carrying run. Just before it enters the tail pulley, the belt will be twisted an additional 180°, restoring it to its normal position. Because this twisting of the return run of a conveyor belt is a radical departure from accepted practice, an elaborate and extensive test was conducted early in 1950 to demonstrate that this twisting of the return run could be done successfully, also to establish application data for accomplishing this twisting, and to determine if any special equipment would be required. In studying this concept of twisting the return run of a conveyor belt, a number of problems need to be solved, primarily the ones brought about by deliberately introducing an unequal distribution of stress across the conveyor belt and controlling that maldistribution of stress, while confining it to the return run portion. The tension conditions existing in the return run of a conveyor belt are clear to all designers. First, the return run carries the initial or slack side tension of the conveyor belt, the tension that must be supplied to the return run to provide proper frictional contact between the belt and the driving pulley so that the necessary power can be transmitted from the driving pulley to the belt without slippage. This slack side tension is supplied to the belt by means of takeups, either of the gravity type, which can be vertical or horizontal, or by means of the screw type. With inclined or declined belt conveyors the slope tension also must be considered, which is the tension imposed by the weight of the belt hanging from the top pulley. This slope tension frequently can furnish part or even all of the initial tension required. The maximum value of the slope tension will be at the top pulley, and it decreases in direct proportion to the length. In addition to the foregoing, it frequently is desirable to impose arbitrarily additional slack side tension to provide sufficient tension at the loading point at the tail, so that the belt will adequately support its load between the carrying idlers. Design Conditions for Twisting A number of design conditions exist, which must be satisfied successfully to accomplish the twisting of the return run without exceeding normal working limits in any portion of the conveyor belt. It is obvious that the belt edge, in its relation to the center of the belt, must stretch in making a twist, because as the twist is accomplished, the belt edge travels through a longer path than does the center of the belt. It is further obvious that if the edge of the belt is stretched, a redistribution of stress in the belt is required to allow this edge stretching. Moreover, this stress will be unequal across the width of the belt, having a maximum value at the edges, with a minimum value at the- center of the belt. With correct initial tension in the return run of a conveyor belt, the existing slack side tension will be unequally distributed when a twist is introduced. A condition then exists in which the edge stresses,

Jan 1, 1952

By Thys B. Johnson

Traditional mine planning concepts are discussed and suggestions for improvement through use of the developed model are proposed. The approach developed in this paper allows optimal planning of the complete mining-concentrating-refining system over the entire planning horizon and permits the system to dictate how and when to process a block of material, i. e., a dynamic cutoff.

Jan 1, 1969

NEW MEMBERS The following list comprises the names of those persons who became members during the period Dec. 10, 1915 to Jan. 10, 1916. ANDERSON, FRANK BASIL, Min. Engr., Sampler, Copper Queen Cons. Min. Co., Bisbee, Ariz. BAILEY, LEWIS NEWTON, Min. -Engr 4227 St. James Place, Sail Diego, Cal. BELL, JAMES E., Min. Engr., Care Chile Exploration Co., Chuquicamata, Chile, South America. BONILLAS, YGNACIO SAFFORD, Min. Geol., Copper Queen Cons. Min. Co., Bisbee, Ariz. BRADLEY, GEORGE OLIVER, Mech. Engr Hobart Bldg., San Francisco, Cal. CLARK, GEORGE L., Min. Engr Vipond Mine, Schumacher, Ont., Canada. CONKLING, RICHARD A., Geol., Roxana Petroleum Co. of Oklahoma, Tulsa, Okla. GOHRING, W. B.. Geol., Supt. of Mines, Calumet and Arizona Min. Co., Warren, Ariz.

Jan 2, 1916

By J. D. Hunt, R. J. McDonald

It is proposed that extensive fluid motion occurs between the dendrites of a Partially solid casting and it is suggested the A segregates in steel castings are a direct result of this motion. The fluid flow arises because of density differences between liquid ahead of the dendrites and the interdendritic liquid. Experiments are described on a model system investigating this fluid motion. The importance of interdendritic fluid flow is discussed with reference to longitudinal segregation. SERIOUS macro segregation is often found in large killed steel ingots. Among the most common segregates are those known as A and V, Fig. 1. The A segregates are arranged over the surface of cones, the wide parts being at the base of the ingot. The A segregates are pencil like in shape and extend from the columnar into the equiaxed region. The V segregates are distributed over inverted cones but have a less well defined shape. They occur at the center of the ingot. Because of the commercial importance of macro inhomogenities these segregates have attracted wide-scale attention. The segregates contain alloying elements and impurities which depress the freezing temperature and are thus the last liquid to freeze. A number of explanations have been proposed to explain their presence. It has been suggested1'' that the segregates are the result of the equiaxed zone growing towards the columnar region together with the interaction of convection within the bulk liquid. It has also been proposed that the segregates are the result of nucleation and rapid growth ahead of the dendritic front.3 Neither of these explanations is completely satisfactory because A segregates are pencil shaped and are not found as continuous cones. In this paper an alternative mechanism is proposed, and experiments are described on a model system to determine whether the mechanism occurs in practice. It is thought that A and V segregates are not peculiar to steels but should occur in many other large castings. Fluid motion within the bulk liquid region of a casting has been extensively discussed. Little attention has been paid to fluid motion within the partially solid regions. The work415 that has been done has been mainly concerned with the fluid motion which results from the volume contraction on freezing. The volume contraction is used to explain various types of macro segregation. The present authors suggest that in many cases the fluid flow resulting from volume contraction will be small compared with that due to other causes. When the columnar region is growing, the liquid still remaining between the dendrites has a much lower temperature near the ingot walls than at the dendrite tips. The composition of the liquid in contact with solid will vary with temperature. The density of the liquid will thus vary both because of changes in temperature and composition. The layers of different density liquid will give rise to a slow but steady liquid flow through the interdendritic regions. If there is no density change with composition, the temperature gradient within the dendritic region should give rise to a downward flow between the dendrites, shown schematically in Fig. 2. When the liquid density changes appreciably with alloy concentration this motion could either be en-

Jan 1, 1970

By Earl S. Greiner, Eric R. Jette

The literalure on the binary alloys of iron and silicon has been reviewed by Stoughton and Greiner.1 Another even more extensive and detailed survey of the present knowledge has been prepared under the auspices of the Alloys of Iron Research Committee by Greiner, Marsh and Stoughton. Since the latter surrey has already been issued in its preliminary form, it will be unnecessary to review the literature in the present article. However, in this connection there should be noted the important work on the crystal structures of the iron-silicon alloys by Phragmén,2 who investigated the entire system, identified the various phases and determined the homogeneity ranges of these phases. It was evident in the surveys cited above that in the range from 0 to 15 per cent silicon, which includes the commercially most important, alloys, the results obtained by thermal analysis, microscopic examination and the determination of electrical, magnetic and mechanical properties were extremely confusing. From time to time various compounds between iron and silicon have been postulated to account for the results yielded by the classical methods, and much argument has ensued. It was presumed that if compounds occurred which are sufficiently diverse in their properties to account for the characteristics of the alloys, they should be recognizable as separate phases but satisfactory proof of this sort has not been found by thermal or microscopic methods. Contributing to the confusion is the fact that the electrical, the magnetic and some of the mechanical properties are "structure sensit'ive"; i. e., they are influenced to a marked degree by the presence of minute amounts of impurities, the specific characters of these impurities, the grain size, the character of the grain boundaries, small general or local strains, etc. Thus interpretations of the discontinuities in the various property versus composition curves that identified these discontinuities with phase changes or compound formation have always been open to question.

Jan 1, 1933

By H. G. Doll

A new logging method, called induction logging, is described; it measures the conductivity, or resistivity, of the strata traversed by a bore hole. The apparatus, which is briefly described, comprises a coil system coupled with the ground by induction, so that there is no need for direct contact with the mud, or with the formations. For that reason, the method is particularly useful in oil base mud, and it was first applied to that case. A discussion concerning the respective contribution of each region of ground in the vicinity of the coil system is given. Through the concept of a geometrical factor, it is demonstrated that the total signal, which measures the apparent conductivity, is the summation of the partial products — geometrical factor by conductivity — for the different regions of the ground under consideration. It is thus possible to establish, for each type of coil arangement, investigation characteristic as well as departure curves and correction charts for beds of various thicknesses. This should greatly facilitate the quantative interpretation of the field logs, even in cases where such interpretation would have been difficult on electric logs taken with electrodes. It is also shown that focussing combinations of coils can be used, which give, directly on the recorded log, a value close to the true conductivity, even for fairly thin beds, thus eliminating in most cases the need for corrections. These focussing systems also give a sharper definition of the boundaries between successive strain.

Jan 1, 1949

By H. G. Doll

A new logging method, called induction logging, is described; it measures the conductivity, or resistivity, of the strata traversed by a bore hole. The apparatus, which is briefly described, comprises a coil system coupled with the ground by induction, so that there is no need for direct contact with the mud, or with the formations. For that reason, the method is particularly useful in oil base mud, and it was first applied to that case. A discussion concerning the respective contribution of each region of ground in the vicinity of the coil system is given. Through the concept of a geometrical factor, it is demonstrated that the total signal, which measures the apparent conductivity, is the summation of the partial products — geometrical factor by conductivity — for the different regions of the ground under consideration. It is thus possible to establish, for each type of coil arangement, investigation characteristic as well as departure curves and correction charts for beds of various thicknesses. This should greatly facilitate the quantative interpretation of the field logs, even in cases where such interpretation would have been difficult on electric logs taken with electrodes. It is also shown that focussing combinations of coils can be used, which give, directly on the recorded log, a value close to the true conductivity, even for fairly thin beds, thus eliminating in most cases the need for corrections. These focussing systems also give a sharper definition of the boundaries between successive strain.

Jan 1, 1949

By Milo Krejci

(Butte Meeting, August, 1913.) THE plant and quarries of the Inland Portland Cement Co. are located at Metaline Falls, Wash., about 128 miles north of Spokane, on the Pend Oreille river, and within 10 miles of the Canadian border. The plant is one of a chain of cement plants controlled by the Lehigh Portland Cement Co., of Allentown, Pa. Work on this plant was commenced in June, 1910, and was completed in April, 1911, but on account of some delays in 'the construction of the power plant, the works were not put into operation until August, 1911. Since then it has been in continuous operation and has furnished the Inland Empire with a high grade of cement. Fig. I is a view and Fig. 2 is a plan of the works. Water Power Development.-The source of the water supply for the hydro-electric plant of the Inland Portland Cement Co. is Sullivan lake, a body of water approximately 5.5 miles long and 0.5 mile wide, situated in the Kaniksu Forest Reserve. A wooden crib dam was installed so as to raise the elevation of the lake 25 ft., and the additional storage capacity was taken up by the diversion of Sullivan creek into the lake by means of a wooden flume, 0.25 mile long, 6 by S ft. in cross-section, and a ditch 1,200 ft. long. The water from the lake follows the natural water course to an intermediate storage reservoir, which was created by the construction of an earthen dam. This pond wits used in connection with the saw mill which was installed at this point. Besides the earth dam, there was also built a crib, at the point shown in the sketch map, Fig. 3. This crib dam is 35 ft. high. From this point the excess water follows the natural course of Sullivan creek to the Pend Oreille river.

Jan 7, 1913

By S. J. Green, R. D. Perkins

Little data exists on the high strain rate behavior of geologic materials. Uniaxial stress tests by Kumar1 and by Serdengecti and Boozer2 present some results to strain rates in the range 10 to 103 per sec. The two references cited are the only ones the authors found for high strain rates. Techniques for experiments at high strain rates are not well developed and, in general, leave questions with respect to interpretation of data when the material behaves in a brittle manner. The most reliable data at very high strain rates (104 to 106 per sec) are found in some recent flat-plate work3-5 where experimenters have impacted one plate into another, thereby creating a uniaxial strain loading. The standard uniaxial stress-strain curves cannot be obtained directly from these tests; however, yield (or fracture) may be studied by measuring the "elastic" wave magnitude. These data then may be compared to uniaxial stress data by resorting to some preassumed yield/fracture criteria. Even with the most liberal interpretation of existing data, little can be said of the effects of high strain rate on stiffness, yield/fracture, and post-fracture behavior of geologic materials. It is the purpose of this work to begin to add to the understanding. The data presented here are intended to provide material information for use in calculating the response of geologic materials to high rate deformations. These data can be applied directly to determine parameters such as the elastic modulus and Poisson ratio as a function of stress. Furthermore, these data can be used to derive an understanding of yield/fracture and the effect of rate on the yield/fracture surface. The work presented is a first step, and is

Jan 1, 1972

By H. F. A. Hergt, K. L. Sutherland, J. Rogers

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By R. C. Schmidt, B. E. Kennedy

The Mont Klahoyo magnetite deposit is located about 600 km (373 miles) northwest of Abidjan, Ivory Coast. During an exploration period ending in 1977 an international joint venture group investigated the deposit and proved reserves of 670 Mt (739 million short tons) grading 36% iron. The deposit occurs at the northeast end of the Baoubly-Kiriao chain of Precambrian iron formations with associated amphibolites, pyroxenites, and gneisses of the Liberian Shield. The ore body is represented by a highly metamorphosed banded quartz-magnetite iron formation with alternating beds of iron silicates and quartz-magnetite. Amphibolite-pyroxenites and sillimanite-cordierite-garnet gneisses form hanging and footwall rocks. The iron formation has been folded into an elongated, overturned 2-shaped major drag fold with axes trending and plunging approximately northeast. Beds are vertical or dip steeply to the southeast. The ore zone has an average thickness of 130 m (427 ft) and outcrops intermittently over a distance of approximately 5.5 km (3.4 miles). Based upon detailed studies of drill cores and the results of ore dressing test work, eight stratigraphic units, identified as K- 1 to K-8, are recognizable in the iron formation. Four interbedded units are low grade silicate zones (silicate facies) while the remaining quartz-magnetite units are oxide facies, representing the important Mont Klahoyo deposit ores. Ore-bearing "K" units are subdivided further into 11 ore types, based upon their specific lithologies, iron content, and concentration characteristics. Identification of these ore types proved particularly useful to mine planning and flowsheet design. A cap of oxidized material overlies the primary quartz- magnetite iron formation, but no enrichment has occurred. It is thought that the Mont Klahoyo iron formations were deposited chemically in a volcanic environment as a siliceous iron formation with volcanism the primary source of iron and silica. Metamorphism converted the siliceous iron formation to a coarse-grained, quartz-magnetite-silicate iron formation.

Jan 1, 1983

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By William B Price, Ralph W. Bailey

Arsenic, antimony and phosphorus are now used in the brass industry as standard inhibitors in preventing dezincification in condenser tubes. This subject has been thoroughly covered by Barry,l who de- scribed the testing procedure by total immersion of suitable specimens in a I per cent cupric chloride solution at definite temperatures. Effects of dezincification were then determined by loss in tensile strength and elongation of the test specimens after definite periods of immersion. In the crystallography of the chemical elements as tabulated by William Hume-Rothery,2 phosphorus (metallic), arsenic, antimony and bismuth are placed in group V-B and the type of crystal lattice for arsenic, antimony and bismuth is given as rhombohedral. The Metals Handbook3 lists them as 'rhobomhedral hexagonal," with the additional notation that for arsenic this is the ordinary form at 20°C.; other modifications known or probable at other temperatures. In view of these statements and of the fact that phosphorus, arsenic and antimony are effective in increasing the resistance to dezincification, it was natural to assume that bismuth would act in the same manner. A series of tests was therefore carried out employing the methods described by Barry. Much to our surprise, bismuth did not inhibit dezincification, but rather seemed to accelerate it. Tensile-test speci-

Jan 1, 1942

By Ralph W. Bailey, William B. Price

Arsenic, antimony and phosphorus are now used in the brass industry as standard inhibitors in preventing dezincification in condenser tubes. This subject has been thoroughly covered by Barry,l who de- scribed the testing procedure by total immersion of suitable specimens in a I per cent cupric chloride solution at definite temperatures. Effects of dezincification were then determined by loss in tensile strength and elongation of the test specimens after definite periods of immersion. In the crystallography of the chemical elements as tabulated by William Hume-Rothery,2 phosphorus (metallic), arsenic, antimony and bismuth are placed in group V-B and the type of crystal lattice for arsenic, antimony and bismuth is given as rhombohedral. The Metals Handbook3 lists them as 'rhobomhedral hexagonal," with the additional notation that for arsenic this is the ordinary form at 20°C.; other modifications known or probable at other temperatures. In view of these statements and of the fact that phosphorus, arsenic and antimony are effective in increasing the resistance to dezincification, it was natural to assume that bismuth would act in the same manner. A series of tests was therefore carried out employing the methods described by Barry. Much to our surprise, bismuth did not inhibit dezincification, but rather seemed to accelerate it. Tensile-test speci-

Jan 1, 1942

By G. B. Misra

Though resistance to flow offered by mine airways supported with timber sets has been an object of study over the last half century, no accurate relation has yet been established from which prediction of the resistance coefficient of a projected timbered airway can be made. Zenofontowa et al. developed an empirical relation, but this relation has not been found to satisfactorily correlate experimental data obtained by Sales and Hinsley. This led the author to develop a set of simple theoretical relations between the resistance coefficient of timbered airways and the various parameters affecting it, such as the type and spacing of sets as well as the shape and size of members forming the set. Experiments were designed with the help of a laboratory model airway to verify the validity of the relations developed. With the experiments conducted so far with 4, 3 and 1-piece sets of 3.4 x 3.4, 2..5 x 2.5, and 4.5 X 4.5-cm square-section timbers in a 45.8 x 38-cm model airway, the theoretical relations have been shown to hold.

Jan 1, 1972

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968