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By Frederic Benard

Recovery of selenium and tellurium at Copper Cliff by the Ontario Refining Co. has been previously described by the writer.l During 1935 a new building was erected to house this operation and description of the new plant and process form the subject of this paper. The building, of modern steel and tile construction, covers an area of 5900 sq. ft. with a volume of approximately 166,000 cu. ft. The large monitored center bay is flanked by two smaller outside bays, one of which is devoted to the tellurium section. All equipment, ceilings and upper walls, are treated with aluminum paint, giving good illumination and facilitating good housekeeping, essential from a health standpoint in handling material of this nature. Equipment Layout and type of equipment conforms to the requirements of the process as described below. In the selenium section, storage tanks, neutralizing tanks and precipitators are of steel construction, lead-lined and arranged for gravity flow (Fig. 1). The neutralizing tanks are equipped with water-cooled lead coils for controlling solution temperature, agitation being accomplished with compressed air. The precipitators are provided with mechanical agitators, and sulphur dioxide is introduced into the solution through 1/2-in. lead pipes leading from a manifold attached to the cover of the precipitator. Each precipitator has internal cooling coils and an air-jet exhauster to carry off fumes. Neutralized solutions are filtered in a 29-plate wooden filter press using heavy cotton duck as a filter medium, forced feed being maintained by a Welmet centrifugal pump. Dilute solutions are concentrated by evaporation in a vacuum evaporator, constructed of cast hard lead. Heat is supplied by an outside steam chest operating under 15 Ib. steam pressure. The solution is circulated through the steam chest by a pump of antimonial lead at a rate approximating 400 cu. ft. per min. The evaporator is evacuated by a water-jet condenser that creates a vacuum of 26 in. of mercury under normal operating conditions. The capacity of the vessel is 60 cu. ft. and the rate of evaporation 25 cu. ft. per hour.

Jan 1, 1943

By Frederic Benard

Recovery of selenium and tellurium at Copper Cliff by the Ontario Refining Co. has been previously described by the writer.l During 1935 a new building was erected to house this operation and description of the new plant and process form the subject of this paper. The building, of modern steel and tile construction, covers an area of 5900 sq. ft. with a volume of approximately 166,000 cu. ft. The large monitored center bay is flanked by two smaller outside bays, one of which is devoted to the tellurium section. All equipment, ceilings and upper walls, are treated with aluminum paint, giving good illumination and facilitating good housekeeping, essential from a health standpoint in handling material of this nature. Equipment Layout and type of equipment conforms to the requirements of the process as described below. In the selenium section, storage tanks, neutralizing tanks and precipitators are of steel construction, lead-lined and arranged for gravity flow (Fig. 1). The neutralizing tanks are equipped with water-cooled lead coils for controlling solution temperature, agitation being accomplished with compressed air. The precipitators are provided with mechanical agitators, and sulphur dioxide is introduced into the solution through 1/2-in. lead pipes leading from a manifold attached to the cover of the precipitator. Each precipitator has internal cooling coils and an air-jet exhauster to carry off fumes. Neutralized solutions are filtered in a 29-plate wooden filter press using heavy cotton duck as a filter medium, forced feed being maintained by a Welmet centrifugal pump. Dilute solutions are concentrated by evaporation in a vacuum evaporator, constructed of cast hard lead. Heat is supplied by an outside steam chest operating under 15 Ib. steam pressure. The solution is circulated through the steam chest by a pump of antimonial lead at a rate approximating 400 cu. ft. per min. The evaporator is evacuated by a water-jet condenser that creates a vacuum of 26 in. of mercury under normal operating conditions. The capacity of the vessel is 60 cu. ft. and the rate of evaporation 25 cu. ft. per hour.

Jan 1, 1943

Jan 1, 1903

By James M. Riddle

INTRODUCTION Block-caving mines are generally large operations. Calculating the quantity and value of mineral present and determining the economic limits to mining are complicated processes requiring much time and effort. If these processes are to be worthwhile, they must be accurate and reliable. Success in planning may increase the economic returns significantly. Since capital investments in block-caving mines are generally quite large, and development may span several years, quicker and more accurate methods of mine layout are very worthwhile to the mining industry. The purpose of this study is to develop an approach to the evaluation and layout of block-caving mines. The study included development of a simple approach to modelling ore reserves and a rapid, dynamic programming solution for optimum ultimate mining limits. TRADITIONAL APPROACHES TO BLOCK-CAVING MINE LAYOUT General discussion of techniques of calculating and valuing ore reserves can be found in the literature, (1-4). Mining limit approaches have been investigated by many and follow five general methods: 1, Moving cone method (5) 2. Graphroriented technique (6,7) 3. Dynamic programming technique (7,8,9) 4. Network flow method (10,11) 5. Pillar method (12) Of these investigations, only two were developed for underground mining applications, those of Sharp (9) and Riddle (11).

Jan 1, 1977

By J. W. Schroeder

SEAMLESS pipe, the product produced from piercing a solid round billet of steel by the Mannesmann process, was first produced in the latter half of the 19th century, the Mannesmann machine having been patented in 1885. The products of other processes also have been termed seamless pipe; for example, the cylindrical section produced by "cupping," which consists of forming a cup from a flat plate or disk and further elongating the cup into a tube by passing it through a set of reducing dies. The purpose of this paper is to discuss some of the more important metallurgical factors and their relationship to the economical production of seamless pipe produced by the Mannesmann piercing process. The first seamless tube plant in America was established at Shelby, Ohio, in 1891, and was employed in the manufacture of bicycle tubing. For a number of years the bicycle industry was the only user of seamless tubing, and this tubing was produced by hot-rolling pierced billets imported from Europe and finishing on the cold drawbench. At the turn of the century, the automotive industry was responsible for an increase in the demand for seamless tubing. The growth of this industry was the dominant factor leading to the phenomenal growth of the petroleum industry, which in turn created a tremendous demand for seamless pipe. In addition; the old lapweld iron boiler tubes for stationary and locomotive boilers were replaced gradually by seamless tubes. Since 1929, the production of seamless steel pipe and tubes has increased over loo pct. In 1929, 1,459,9031 net tons of seamless pipe was produced, including both hot-finished and cold-drawn material, as compared with 3,087,3122 net [ ] tons in 1948. Table I gives the distribution of seamless pipe by classes for 1948. METALLURGICAL PROBLEMS From a metallurgical standpoint, the production of seamless pipe has presented many problems. Practically every type of steel, carbon and alloy, with the exception of the superalloys developed during World War II, has been pierced and rolled successfully into tubing. This includes bessemer, open hearth, by the stationary and duplex processes, and electric steels. The range of sizes produced is no less staggering to the imagination, when it is considered that the hypodermic needle, which is 0.016 in. diam with a wall thickness of 0.004 in., and pipe for gas or oil transmission lines, with a 26 in. OD, are both seamless tubes. Between these extremes, the range of diameters and wall thicknesses meets most present-day demands for seam-

Jan 1, 1951

No. 349.-A Canadian university wishes to engage a man to teach non-ferrous metallurgy and ore-dressing as well as to direct research work. The instruction work covers 7 months but the research work is continued throughout the year. To a suitable man the rank of professor will be granted. Applicants are requested to state education, experience, salary desired and any other particulars that might assist in selecting a man for this position. No. 354.-Wanted, for Northern Nigeria, one chief and two assistant mining engineers, competent surveyors, with good knowledge of alluvial tin mining and dressing of tin concentrate. Preferably with previous Nigerian experience, and exempted or able to. secure passport. Apply in writing, stating qualifications, experience and salary required.

Jan 12, 1918

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

Jan 1, 1967

Jan 1, 1967

By Eugene Coste

Although some of the observers who first paid especial attention to the occurrences of oil and gas in the strata (such as Hunt in 1859, Andrews in 1861; Winchell in 1865, Mendelejeff in 1876, Höfer in 1876, Minshall in 1881, and I. C. White in 1883) seem to have been impressed with the fact that oil and gas deposits were connected with the disturbances in the rocks caused by their upheavalll yet, with the exception of Mendelejeff, and possibly Andrews, these observers do not appear to have understood what is really the one essential factor in the occurrence of oil and gas in the strata: viz., the faulting, uplifting, fracturing, fis-suring, and jointing always accompanying even slight rock disturbances, and in certain districts (petroliferous provinces)2 allowing solfataric hydrocarbon emanations to force their way up from the interior and to reach and impregnate the porous portions of sediments subjected to the disturbances. Instead of this simple explanation to account -for the observed connection between petroleum deposits and rock disturbances, most of the observers mentioned above, and many others who have foliowed them on the same lines since, have entirely reversed the problem. To them, instead of the dissemination of gases from fissures into the sediments, it presented the accumulation and concentration, according to anticlinal or other geologic structures, of oil and gas originally present throughout the whole mass of the strata where they were produced by the decomposition or distillation of organic remains. Whether this important problem involves accumulation from sources within the strata themselves, or infiltration and dissemination from outside sources, may be easily determined if all preconceived ideas are put aside and the established facts only are considered. Physical Facts Sedimentary strata are composed of alternate beds of shales, sandstones, and limestones, most of which are sufficiently close-grained to

Jan 1, 1915

Jan 1, 1959

By C. Richard Honeycutt, Frederick C. Langenberg, Guenter Pestel

Otto Schaaber (Institut für Harterei-Technik, Bremen-Schönebeck, Germany)— Langenberg, Pestel, and Honeycutt gave an interesting example of the grain refining effect nonstationary magnetic fields may execute on a solidifying metal. Probably some additional comments, based on more than a decade of experience with this method of influencing crystallization, may be useful. They refer to an attempt to explain the mechanism of grain refinement by such fields, and to recent European developments which have not been mentioned in the paper. I. During studies of the temperature distribution in a metal body near the phase boundary solid/liquid, an anomaly was observed under certain special conditions: a) direction of heat transfer as horizontal as possible, b) steady state (equilibrium, i.e,, solidification resp. melting rate exactly zero). In the liquid phase, immediately adjacent to the phase boundary, the temperature was found to be constant over an appreciable distance in spite of a high value of heat transfer (40.000 to 70.000 keal/ m2h).3 Convection, which might explain this phenomenon, could not be observed. Therefore another explanation had to be sought. The assumption that a metallic melt, especially at temperatures near the point of solidification, contains some sort of atomic arrangement with a higher degree of order than the surrounding liquid, now is generally accepted. Considering the differences in energy between such an arrangement and its environs, a transport of heat even in absence of any temperature gradient is conceivable by continued formation and redissolution of regions with a higher degree of order, i.e., with lower energy level.3 At this stage, it was not necessary to postulate any special condition as to the form or size of these regions or the distance between arrangements to be newly formed and those to be redissolved. However, a simple consideration shows that an energy transfer from one region to another will only be possible without loss of energy, if the distance between will be equal to the lattice parameters, and if, secondly, crystallographic axis or planes will be parallel.4 By the way, this assumption might give a reasonable explanation of the well known orientation effect of the heat flow during solidification. Any measures to prevent columnar crystallization should act upon this ordering mechanism: a) the regions with a lower energy (higher order) should not be allowed to arrange themselves parallel to the direction of heat flow, and their growth should be disturbed; b) all conditions leading to an appreciable heat flow of uniform direction should be avoided or removed. Condition a) may be satisfied by a physical force preferably under 90 deg to the main axis of the columnar crystals (i.e., parallel to the solidification front) acting on the ordered regions; condition b) by equalizing any differences in

Jan 1, 1962

By H. W. Schreiber, H. R. Babitzke, R. E. Rodriquez, Patterson J. A., C. D. Masters, J. J. Schanz, R. B. McCammon, E. A. Noble, P. M. Krishna

A five-year effort by the ASTM subcommittee E10.14 on uranium resource evaluation has culminated in the approval of E901-82, Classification System for Uranium Resources (ASTM Standard E901-82, April 1983). The standard classification was prepared with participation of representatives from the US Department of Energy, the US Department of Interior's Geological Survey and Bureau Mines, utilities, and consultants. The classification a resource is based on level of knowledge and the economic producibility of the resource at a given time. Alphanumeric identifiers are used rather than words to avoid confusion with existing terms, definitions, and classifications. An example demonstrates the dynamic nature of the process of classification and attests to the necessity of addressing both the aggregate needs of broad-scale resource planning and the specific needs of individual property evaluation. Problems that remain infixing the classification a given uranium resource include uncertainty in estimating the quantity of undiscovered resources and resolving differences that may exist in deciding when the drill-hole spacing is adequate to determine the tonnage and grade of discovered resources.

Jan 1, 1985

By Staff

Concentrates at the rate of 1000 tons a day are being smelted by International Nickel Co.'s new commercial flash smelting furnace. Developed by Inco, the process is a radical departure from the former practice which involved conventional smelting in coal-fired reverberatory furnaces. In the new process copper flotation concentrate and flux are injected horizontally with oxygen into a specially designed reverberatory furnace, and smelting temperature is maintained solely by the flash combustion of iron and sulphur while the particles are in suspension. The major benefits of this new process stem from two sources: 1)-Substitution of energy from local resources for imported coal; and 2)-Production of liquid sulphur dioxide, replacing equivalent imported sulphur. A measure of these benefits is afforded by considering the saving, in 1954, of 60,000 tons of coal and the production of 70,000 tons of liquid sulphur dioxide, equivalent to 35,000 tons of sulphur.

Jun 1, 1955

By H. H. Kellogg

A model of the slag-fuming process for recovery of zinc oxide fume from lead blast furnace slags, adapted to solution by a digital computer, is presented. The model incorporates the variaticm with time of the following: the fuming of zinc and lead, the change in the ferrous-ferric ratio in the slag, the transfer of sulfur to and from the slag, the temperature of the liquid slag, the temperature of the gases and fume which exit to the flue, the heat losses to the water jackets, and the amount of frozen slag on the water jackets. The assumptions which underlie the model-some of which are but crude approximations—are discussed. Despite some obvious shortcomings, the model simulates faithfully many of the important features of practical slag-fuming operations. The behavior of the model is compared with the operation of the American Smelting and Refining Co. fumzace at El Paso, Tex. The model is used to predict the effects on performance of changes in the coal rate, the temperature of the secondary air, and the composition of the coal. THE fuming of lead blast furnace slag for recovery of zinc oxide is standard practice today, and it has been the subject of several previous attempts at mathematical process analysis.'-' The mathematical process model described in this paper incorporates many of the features from the earlier studies, but it is a far more complete and realistic representation of the commercial process in that the following additional features have been included: the fuming of lead as well as zinc; the transfer of sulfur between slag and gas; the addition of slag feed in batches, over a period of time; tapping of the final slag over a period of time; the change of slag temperature with time. The additional features of the present model add greatly to the mathematical complexity, but this difficulty has been obviated by programming the model for solution by a digital computer. The IBM 7094 computer solves the model for one operating cycle of the fuming furnace in less than 1 min. It is doubtful if the same calculations could be completed with the aid of a desk calculator in less than a month. The computer program, written in the Fortran IV language, is too lengthy for presentation here.* Instead, this paper As shown in the sections which follow, it does simulate with remarkable faithfulness most of the known behavior of the industrial process. On the other hand, the model contains several gross simplifications of both the chemistry and heat balance, necessitated by the lack of more exact knowledge. In addition to these known weaknesses, it is not unlikely that those more intimately acquainted with industrial practice than the author will find other additions to or modifications of the model which will improve its utility and reliability. CHEMISTRY In brief outline, the present model treats the fuming furnace as two units, A and B, in series. In A the batch of slag reacts with the continuous stream of air (primary and secondary) and fuel injected at the tuyeres, to produce a stream of hot, reduced gases containing zinc vapor. The zinc content of both the slag and the product gas changes with time because of the batch nature of the process. Unit A is called the "lower furnace" in this paper; physically, it is considered to be that part of the fuming furnace which lies below the charge port. In B, the "upper furnace", the product gas from A is burned with the stream of "tertiary" air, to produce zinc oxide fume. The performance of B also depends on time because of the time dependence inherited from the product gas of A. The rate behavior in the lower furnace determines the important features of the process—the rate of elimination of zinc and lead from the slag, and the amount of fuel required for this purpose. Bell, Turner, and peters' published the first useful model of the lower furnace. They employed the assumption that, at any instant of time, the slag and reduced gas reach a state of equilibrium, according to the reactions: They cited only indirect evidence in support of their assumption of slag-gas equilibrium, yet several more recent laboratory studies of the activity of zinc oxide in slags4-8 have produced evidence which supports their view. On first acquaintance it seems unlikely that a high-output "rate" process like slag fuming would even approach an equilibrium state. The author, in an earlier study,' established, however, that the gas-slag interface in a fuming furnace was capable of such high mass-transfer rates that a close approach to equilibrium between gas and slag was quite probable. In devising the present model it was decided to assume a state of equilibrium between slag and gas at the outset, and then to modify this assumption as necessary in order to make the model agree with the be -havior of the actual process. Up to this time the assumption remains a part of the model, since no behavior

Jan 1, 1968

By J. T. Norton, H. Blumenthal, S. J. Sindeband

The interstitial phases formed by the transition elements with carbon, nitrogen and boron constitute a unique class of substances which are of considerable technical interest because of their well developed metallic properties and their high hardness and melting points. They are also of interest from the point of view of structure. It was pointed out by Hagg1 some years ago that the principal factor determining these structures was the relative sizes of metal and metalloid atoms. He predicted that if the ratio of the radii of metalloid to metal atoms was less than 0.59, the metal atoms would be arranged in a close-packed fashion of relatively simple type. This prediction has been amply confirmed. It appears, however, that this specification applies most generally to those structures in which the metalloid atoms occupy isolated positions in the lattice and there is no tendency for strong binding between the metalloid atoms themselves. The series of borides of the type MeB2 formed from the transition elements of the fourth (Ti, Zr) and fifth (V, Cb, Ta) groups of the periodic table provide an opportunity to investigate this situation further. If one takes as a basis the radius of 0.87 A for the boron radius and the Goldschmidt values for the metal atoms in 12 coordination, then the radius ratio varies from 0.54 for zirconium to 0.64 for vanadium, which latter is considerably greater than Hagg's limit of 0.59. It was of interest, therefore, to see if these five elements would form borides of the MeB2 type and have simple isomorphous structures. When this investigation was initiated, relatively little information had been published on the structure of this group of borides. McKenna2 reported the preparation of ZrB2 by a carbon reduction process. Its structure was hexagonal and the approximate lattice constants were given as a = 3.15 A, c = 3.53 A. Ehrlich3 reported the structure of TiB2 as being of the C 32 type with a = 3.02, c = 3.21 and c/a = 1.06 A. Recently, Kiessling4 published the results on ZrB2, showing it to be one in which the metal atoms are arranged in a simple hexagonal lattice with the boron atoms in flat sheets, midway between the layers of metal atoms. The structure is C 32 type with a = 3.169, c = 3.530 and an axial ratio =1.11 A. He also states that CbB2 and TaB2 are isomorphous with ZrB2. Preparation of Borides The borides of titanium, zirconium, columbium and tantalum were made by the electrolysis of fused salt baths after the method described by Andrieux.5 The bath, totalling about 6500 g in each case had the following general composition: Metal Oxide + B2O3 + CaO + CaF2. The actual proportions of the ingredients were determined for each individual case. Although Andrieux reports the preparation of vanadium boride by the same electrolytic method, several attempts proved unsuccessful. However, it was possible to prepare VB2 by the carbon reduction method used by McKenna to produce ZrB2. The mixture consisted of V2O5 + 6B2O3 + 11C and the reduction was carried out in an induction heated graphite crucible. This method proved satisfactory for ZrB2 and TiB2 and undoubtedly the others could be made in the same way. The borides, which were all in the form of fine gray metallic crystals from the electrolytic bath or gray powders from the reduction process, were carefully separated from other constituents and analyzed chemically for metal and boron content. The densities of the boride powders were measured using a standard 10 cc pyenometer at 18°C and ethyl benzene proved to be the most satisfactory liquid for this purpose. X Ray Technique The boride crystals, as prepared, were too small for single crystal examination so that powder techniques were employed. Patterns of the finely ground borides were prepared, using the Norelco recording X ray spectrometer. The lines on these patterns were indexed with the aid of Hull-Davy charts and the approximate dimensions

Jan 1, 1950

By H. Merton Ruth

THE northern anthracite fields, although facing the same economic problems as the southern fields, are confronted with the additional problem of fast dwindling reserves of anthracite which can be conventionally and economically won. The mining of coal which remains in thin beds and the recovery of pillars from areas heretofore considered unrecoverable, either by reason of cost or surface restriction, pose problems of in- creasing importance to the economic life of the northern field operations. Successful approaches have Been made to this problem and other work is being performed that holds promise. There exists in the northern anthracite field millions of tons of solid coal, the recovery of which has not been too successful due to the following inherent operating faults: inability to concentrate producing areas; the great quantities of rock to be cut and handled, lack of consideration of proper sequence and speed of second mining, and the continued use of the mine car as the basis of payment. A mining system that has successfully solved these major problems has been in operation in the Scranton area since 1944. Over 1% million tons have been produced from veins varying from 3 to 4% ft thick by this method, which is known as the multiple panel-triangular system-conveyor mining.

Jan 1, 1950

By Charles Barrett

SINCE 1925, when the preferred orientations in compressed aluminum were first determined1, 2 the orientations have been described as a fiber texture in which a face diagonal, [110], of the face-centered cubic lattice is parallel to the compression axis. Subsequent experiments have seemed to confirm this texture,3-5 and a number of theories (recently summarized in references 6 and 7) have been proposed to explain it and to relate it to the behavior of single crystals during compression. 3,8-11 The experiments reported in this paper prove that the orientations are not adequately described as quoted above-i.e., as a [110] fiber texture-although this is a first approximation to the actual texture. They also show that the texture cannot be thought of as a stable orienta-tion that is reached and maintained after a sufficient amount of deforma-tion. The actual texture, when studied in detail at successive stages of compression, indicates that a hitherto unsuspected range of orientations is present, both in the polycrystalline metal as a whole and in various individual grains in its interior, and that a state of dynamic equilibrium exists within this range. The reasons for the failure of previous theories to predict the actual texture become obvious when the heterogeneous nature of the flow is considered. In addition to the deformation texture, the manner of its develop-ment, and its theory, this paper presents data on the following related subjects: the identity of strain markings in aluminum; the orientation changes in aluminum single crystals during compression and a com-parison of these with the conditions in individual grains of a polycrystal-line specimen; the origin of asterism in deformed single crystals, which heretofore has been regarded as a distortion localized at the surfaces of slip planes; and the relation of plastic strain in individual grains in an aggregate to the strain of the whole.

Jan 1, 1939