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By Charles M. McCulloch

This Bureau of Mines report discusses the principles of using computers to draw maps and plot geologic data of mining areas. The types of maps that can be drawn by a computer are reviewed, using as examples two separate areas where poor roof and gas emissions caused mining problems. Such maps can be used not only to help identify problem areas, but also to predict areas where problems could occur, thus giving mine operators time to work out solutions prior to mining. The average cost of a computer-drawn map for a mine property is less than $100, including computer time and man-hours for data preparation.

Jan 1, 1976

By J. E. Hamak

This publication contains analyses and related source data for 151 natural gas samples from 19 States. Of the total samples, 138 were collected calendar year 1989. The remainder were collected earlier, but releases to were not received until 1989. All samples were obtained and analyzed as part of U.S. Bureau of Mines investigations of the occurrences of helium in natural gases of countries with free market economies. This survey has been conducted since 1917. The analyses published herein were made by mass spectrometer and chromatograph.

Jan 1, 1990

By T. D. Yensen

Discussion of the paper of T. D. YENSEN, presented at the New York meeting, February, 1916, and printed in Bulletin No. 110, February, 1916, pp. 483 to 512. JOHN A. MATHEWS, Syracuse, N. Y.-Concerning the critical composition of the steel containing 2.50 per cent. of silicon, I may say that 12 or 13 years ago we made some of these alloys. They. were not as pure as the alloys made by Mr. Yensen, nor were they melted in vacuo, but one of them contained exactly 2.50 per cent. silicon, and about 0.25 per cent. carbon. It gave us no trouble whatever in hammering to a billet or rolling into bars, nor even when rolling into ¼ -in. wire rods. The steel in question was practically free from everything except carbon or silicon and contained no manganese sulphur or phosphorus worth mention. The alloy containing 2.50 per cent. of silicon worked perfectly well, as well as one containing 0.5 per cent. silicon, and it seems to me that further work should be done by Mr. Yensen on the physical properties of alloys at this seemingly critical change point. W. E. -RUDER, Schenectady, N. Y.-We -have made silicon steels of practically every composition and have never obtained any material under 5 or 6 per cent. of silicon which was brittle. This may be due, of course, to the presence of carbon, in some of the 'commercial materials, and I presume that Mr. Yensen would argue that the: presence of this carbon might prevent inter-granular brittleness. However, all of our silicon steels, up to 5 per cent. of silicon, by treatment in hydrogen at temperatures near the melting point, can be made to show inter-granular brittleness. Furthermore, the material made brittle in this way could be restored by treating at the same temperature in hydrogen containing a hydrocarbon vapor. I discussed this matter some years ago in a paper on inter-granular cement. It therefore appears likely to me that Mr.

Jan 5, 1916

By S. H. Lorain

Shortly after the Strategic Minerals Act of 1939 we passed by Congress, the Bureau of Mines was authorized to begin a program of investigation of domestic sources of strategic minerals. Since World War I, the Philipsburg district had been virtually the only one in the United States that was producing manganese on a commercial scale. Consequently, the district was among the first to he investigated. During the summer of 1939, the Geological Survey mapped the geology and ore deposits of the district. In late July 1939 the writer examined the district for the Bureau of Mines. On the basis of this examination and of the work performed by the Geological Survey, the Bureau of Mines diamond-drilled at several properties in the district during the summer of 1940. This report reviews the mining history and geology of the district, and presents the factual data obtained by diamond drilling.

Jan 1, 1950

By N Clarke, A Barros

Preconcentration of run-of-mine subgrade and marginal ore by screening has the potential to substantially improve the economics of mining, particularly for large, low-grade orebodies, and to reduce environmental impacts. It has recently been the subject of a major research effort by a joint public-private research body, CRCORE. Yet despite this, there appears to have been only one fully commercial installation, at Bougainville Copper Limited in the late 1980s. Two reasons for the limited application are that not all ores have suitable properties and the economics of all pre-concentration processes on low-grade materials are highly sensitive to the precise balance of mass and value recovery and to the pre-concentration process cost, including materials handling. These factors make it imperative to have good test data on the process response of feedstock across the orebody. Collecting that data presents major challenges, which differ for green and brownfields operations. This paper first discusses the approach to preliminary evaluation developed by CRCORE, which relies on testing of coarse rejects or drill chips available from exploration drilling programs. This method is an efficient first step in evaluating an orebody which is deemed geologically to be potentially amenable to screen upgrading, but it does have limitations and must be followed by larger scale work. A suite of methods have been developed by the authors as a result of test work since the 1990s on several projects, supplemented by published data, which aim to provide statistically robust data at lower cost than large scale bulk sampling tests. For greenfields projects, the upgrade response measured on material crushed to -53 mm has been found to correlate closely with ROM ore, with no scale-up required for material with upgrade responses in the range of commercial interest. Large diameter whole drill core, such as PQ, is expected to be suitable for this method. As drilling such core is costly, the aim should be to establish relationships between upgrade performance and proxy measurements such as multi-element chemical or hyperspectral analyses. This approach was successful at the Gramalote gold project in Colombia. The method is not applicable for ores with thick vein material comparable with the crush size, but such material is not suitable for upgrading by screening and would be eliminated by the preliminary testing. For brownfields projects where blasted material can be sampled, the upgrade response can be accurately measured by sampling only the finer fraction of the ore, selecting a top size which represents 30–50 per cent or more of the ROM size distribution. This is likely to be between 50 and 100 mm. The much finer size compared with the full ROM ore greatly reduces the sample mass required to achieve a given intrinsic sampling error and enables sample preparation to be undertaken with large-scale laboratory equipment rather than mobile crushing plant. The accuracy of the method can be improved by measuring the approximate mass of oversize rejected during sampling. Some ores do show a systematic deviation from the assumed model fit which results in this method slightly underestimating the upgrade response, and it would therefore still be recommended to take one or two full bulk samples to confirm results before a final investment decision.

Aug 24, 2022

The mineral chromate is the sole current source of commercial chromium Chromite varies compositionally within limits permitted by the formula ((Mg,Fe,Zn,Mn)(A1,Cr)2O4) No chromate has been mined in the United States since 1961 In the past, almost all the chromate mined in the United States came from Alaska, California, Maryland, Montana, Oregon, and Pennsylvania, with about one-half of all production coming from Montana Primary chromate deposits occur only in certain kinds of ultramafic or closely related anorthositic rocks The two major types are stratiform (layered) and pod-shaped The Stillwater Complex of Montana is the largest known United States resource It is a stratiform deposit where several exposed zones of high-iron chromiferous material extend in length Since there is no commercial chromate mining in the United States, there are no environmental problems related to underground mining

Jan 1, 1975

By N. E. Hanna

As part of a program for improving, the safety of permissible explosives, the Federal Bureau of Mines has undertaken an investigation to establish the ability of sodium chloride to reduce the incendivity of permissible explosives to firedamp atmospheres. A motivating influence for this investigation has been the comparatively extensive experience of British and other European investigators, who used sodium chloride as a component of their permitted explosives (1, 5, 6 7).5/ In the United States research and development work of this type has been less extensive, although sodium chloride has been added to permissible explosives as a cooling agent (9) for many years. The results of the first phase of this investigation were presented in a previous paper (8), which established that adding up to 10 percent sodium chloride to permissible explosives reduces the likelihood of ignition of firedamp in the gallery test; however, the results were somewhat inconsistent, and the conclusions were qualified. Accordingly, the investigation was continued with a study of the effect of added sodium chloride as a function of the quantity added and of the particle size of the salt.

Jan 1, 1960

By E. R. Weltevreden, C. Klauber, C. Vernon

"In this paper a review of the current status in recycling technologies for cathode ray tubes is given for both the glass and phosphors. Particular emphasis is placed on the opportunities for the recovery of the rare earth elements (REE) from the phosphor coatings. This is placed in the market context of alternative virgin sources and some of the advantages and disadvantages for REE waste recovery. Future opportunities are explored and also some experimental detail on a low cost leach system is presented. INTRODUCTIONThe disposal of cathode ray tube (CRT) based colour televisions has accelerated world-wide with the development of high definition flat screen panels. The total number of colour CRT televisions that have been sold in the United States in the mid-20th century is estimated to have been over 2 billion (U.S. Environmental Protection Agency, 2007), with high current rates of disposal. It is estimated that of the 20 million televisions annually discarded, 78% are send to landfill (Nnorom, Osibanjo & Ogwuegbu, 2011). However, this easily accessible item of electronics cannot only be turned into a valuable resource using the right recovery procedures, it can also prevent the substantial environmental contamination arising from improper disposal. In this review we focus on previous and current work performed on the recycling of CRT based televisions. Due to the increasing demand for rare earth metals, the main focus will be on the possibilities and challenges of recycling the fluorescent phosphor powders on the CRT’s panel glass.CATHODE RAY TUBE’S GLASS RECYCLINGConventional cathode ray tubes consist of three main parts, the panel, the funnel and the neck (Figure 1). To produce the different colours on the screen, the inside of the panel is coated with a matrix of hundreds of thousands of small phosphor dots. Each dot is one of three types of coloured phosphors, emitting either red, green or blue light. These emit light when excited by a beam of electrons generated by electron guns located in the neck of the CRT. These beams pass through holes in the shadow mask and excite the phosphor coating on the inside of the panel, to give light of variable RGB composition, see Figure 1."

Jan 1, 2012

By T. A. Sullivan

The Bureau of Mines investigated modified sulfur concretes as one part of a program for utilizing sulfur in construction materials. The use of modified sulfur was studied as a means of preventing the stressing action in the concretes caused by the allotropic transformation of sulfur on solidification. Unmodified sulfur concretes have been prepared that have compression, flexural, and tensile strengths equivalent or better than Portland concretes. However, most of these concretes have been vulnerable to deterioration by weathering, temperature fluctuations, and freeze-thaw cycling. The sulfur was modified by reaction with dicyclopentadiene or dipentene before use as an aggregate binder. Sulfur concretes and modified sulfur concretes were pre-pared from acidic and basic type aggregates. Physical properties of the optimum mixtures were determined and compared with each other and with Portland cement concretes. The best results were obtained by reacting sulfur with 5 pct dicyclopentadiene to prepare modified sulfur concretes. Field testing of the concretes are in progress. Present results show that modified sulfur concretes are superior to unmodified sulfur concretes and equal or better than Portland concretes in compressive, flexural, and tensile strengths. Long-term aging characteristics of both modified and unmodified sulfur concretes are being determined.

Jan 1, 1976

By R. Lapcevic, P. Lokin

"Among other components, ore body „T“ was discovered in the Bor pit copper mine at a depth of app. 500m. The ore body is relatively small: 60-65m long, 40-45m wide and up to 50m high, but with an extremely high content of copper and accompanying metals. The rock mass containing the ore body is composed of altered andesite of relatively poor physical-mechanical characteristics. The exploitation of this ore body by way of conventional mining methods was associated with high risk, cost, and potential losses of the rich ore. Due to everything specified hereinbefore, the adopted solution involved ore exploitation with complete ensuring of excavation stability, thus forming an extremely large underground opening. The excavation and supporting were performed according to the NATM principles along with applying shotcrete, 9-25 m long cables, and horizontal and vertical lattice girders. The excavation of the ore body was completed in app. 2.5 years, all the while ensuring complete stability and security of people and equipment; construction works were constantly monitored. The proposed solution for ore excavation enabled more than 95% exploitation of ore as requested by the Investor, while depletion due to waste-rock excavation was less than the allowed 5%. INTRODUCTIONThe Bor copper deposit is located in Eastern Serbia. Copper exploitation in Bor commenced as far back as 1902. A total of 26 ore bodies varying in size and valuable mineral content have been excavated so far. One of the most recent excavated ore bodies is ore body „T“, which is one of the smallest bodies by volume, but also a body with one of the largest content of copper and accompanying metals. An important fact regarding its exploitation is that it is located at a depth of app. 500 m; that its shape is irregular: 60-65 m long; 40-45 m wide and app. 50 m high; and that it lays within a rock mass of relatively poor physical-mechanical characteristics. In addition, above it, in its immediate vicinity, ore body „F“ was previously excavated and its room was refilled with backfill and water. Excavation methods common in mining practice (excavation with caving, excavation with backfilling, excavation with protective pillars) were inadequate in this case for various reasons:• The immediate vicinity of the previous ore body „F“ room could cause expansion of the caving zone also to that room, along with penetration of groundwater and flotation sludge;• Possibility of deformation expansion caused by caving as far up as the surface of the terrain, including the urban area;• Difficulties in maintaining the stability of excavation sidewalls having steep slopes and great height;• Significant loss of ore mass with a relatively high content of metals etc."

Jan 1, 2015

By Brenton Fletcher, Yongjun Peng, Wonder Chimonyo

As a cheap, renewable and non-toxic material, starch can contribute to the sustainability of the flotation process, albeit in a minor way as one type of reagent in systems involving materials with far greater impact. But the physical and chemical versatility of starch can help address another issue, namely, that of processing complex ores with decreasing grades of valuable minerals and increasing mixtures of gangue. This paper compares the results of two lab scale flotation studies where starches (native wheat starch (NWS), dextrin and two oxidised wheat starches) were used to depress two common gangue minerals, copper-activated pyrite and carbon (graphite), over a range of dosages. The oxidised starch with the larger molecular weight structures depressed copper-activated pyrite best, and the oxidised starch with lower molecular weight structures was better at depressing graphite. In both cases, the oxidised starches allowed greater recovery of chalcopyrite, pointing to selectivity potential. The extent to which the carbonyl and carboxyl moieties of the oxidised starches contribute to depressant performance is difficult to quantify, but it should not be discounted. Importantly, the results demonstrate relatively simple modifications of native starch by oxidation can yield structures suitable for depressing gangue minerals with diverse surface properties. The challenge remaining for greater application of modified starch depressants is being able to replicate the desired structures at scale in cold-water-soluble form.

Jan 18, 2021

By E. Oshima

In May 1991, a New Mitsubishi Continuous Copper Smelter Line started operation at Naoshima. Recently, it has been continuing steady operation and one and a half year campaign life has been achieved. In 1996, new records of on line time, the amount of copper concentrate treated and copper anode production were achieved. 1t proves the superiority of the process with respect to pollution control, energy efficiency, flexibility and easiness of the operation and over all economy including off gas handling cost. Furthermore, .plans are underway to prolong the campaign life for two years and to improve the process efficiency. This paper describes recent operation, improvements, and a future capability study.

Jan 1, 1998

By A. L. Engel

This report is a compilation of results of preliminary concentration tests of nine manganese-ore samples in 1953-1954. Three samples were from Nevada and the other six from California. These samples represent marginal or low-grade ores from deposits that have been mined selectively in the past. The present interest lies chiefly in the possibilities of concentration of the remaining low-grade ores for economical exploitation. The treatment methods included gravity concentration and flotation in most cases. Results were sometimes unsatisfactory, particularly when the ore was too fine grained for liberation of the minerals within economical grinding range. The contaminating gangue minerals, such as quartz and iron oxides, were locked with the manganese to an extent that prevented separation of high-grade concentrates with satisfactory recovery. In cases where fairly good concentrates were made, it was at the expense of recovery, a condition typical of low-grade ores.

Jan 1, 1955

By João Filipe Cavalcanti Leal

São apresentados e discutidos os resultados da caracterização de concretos nanoestruturados do sistema Al2O3-SiC-C para canal de corrida. Foram avaliadas três composições, denominadas A, B e C, ligadas por sílica coloidal. Os corpos de prova para determinação das propriedades físicas e químicas foram moldados em escala laboratorial com auxílio de forma metálica. O concreto A foi desenvolvido por um fabricante nacional. O concreto B é o concreto A modificado, ou seja, contém uma fase extra. O ajuste da composição A visou adequar as propriedades desse concreto às variáveis de processos da Usiminas. Os resultados de testes laboratoriais indicaram que o concreto modificado (B) apresentou desempenho compatível ao do concreto C, tradicionalmente utilizado na Usiminas. As principais vantagens dessa geração de concretos ligados por sílica coloidal são bombeamento estável e reduzido tempo de secagem.

Aug 1, 2018

By J. W. Watkins

This report describes in detail methods of making corrosion tests and chemical analyses that have been used extensively and satisfactorily in a study of plants in which various surface, waters and brines are conditioned and used for water flooding, brine disposal, and reservoir-pressure maintenance in Kansas, Oklahoma, and North Texas. The tests and analyses described were designed and adapted for use in the field in determining the relative corrosive and plugging tendencies of waters from various sources conditioned by different methods. Although the described methods were developed and used in testing oil-field waters in the Midcontinent oil-producing area of the United States, these same methods should be equally applicable to testing oil-field or highly mineralized waters throughout the world. Many of the methods used have been discussed by the writer (1)2/ previously, and some of them have been used for similar work in other laboratories. Early in the development of the practice of the subsurface injection of brines for disposal and increasing the recovery of oil, it became evident that different methods of chemical treatment and conditioning equipment would have to be devised to sustain desired injection rates into water-input wells. These changes became necessary because the highly mineralized waters produced with petroleum from deep formations became chemically unstable when pumped to the surface, owing to loss of dissolved gases as pressure and temperature dropped to atmospheric and to the contact with atmospheric oxygen at the surface.

Jan 1, 1954

By F. N. Rhines, A. S. Nemy

The mode of high-temperature tertiary creep of 523-0 aluminum alloy was found to be strongly stress dependent. The occurrence of necking and/or fissures during tertiary creep exhibited a sequence with varying stress, wherein fissures with no necking occur at a minimum stress and necking with no fissures occur at a maximum stress. At an intermediate stress, tertiary creep begins without necking but with fissures in a region just beneath the external surface, followed by necking and the development of fissures along the axis of the specimen. The results are interpreted in terms of grain boundary gliding and the hydrostatic stresses produced by restraints to grain boundary gliding. THERE appear to be two possible reasons for the existence of a period of accelerating elongation prior to rupture during high-temperature creep in metals; namely, 1) a change in the structure of the metal itself, leading to a change in its response to loading, and 2) a reduction in the cross section of the metal resulting in a higher unit loading. Howe,' by annealing and retesting broken low-temperature creep specimens, found that irreparable damage is done once a metal is subjected to creep. Andrade2 first pointed out the association between the reduction in cross section and the increase in creep rate. The present research was designed to investigate both of these factors by retesting specimens machined from material which had been subjected to high-temperature creep testing short of rupture. EXPERIMENTAL METHOD An aluminum alloy, 52s-0, was selected for these studies because it is constitutionally simple, is strong enough to be relatively insensitive to mechanical damage during machining,3 and undergoes accelerating creep in a convenient temperature range. This alloy is hardened by 2.6 wt pct Mg in solid solution and is not subject to overaging effects; it has a very small quantity of an insoluble impurity phase, Mg2Si, finely dispersed throughout its micro-structure. Creep specimens, similar in design to ASTM 0.252-in. tensile specimens, were machined from 3/4-in. round stock and the surfaces were electro-polished. A 24-hr anneal at 500°C was then applied to stabilize the grain size to an average diameier of 0.27 mm. Subsequent heating for as long as 700 hr at the intended test temperatures produced no change in the tensile properties, indicating a well-stabilized state of the material. Corresponding to each of the typical testing conditions listed in Table I, one creep specimen was tested to destruction and this test was employed as a guide in the selection of times for subsequent tests. Duplicate creep tests were then run to various points along the creep curve to produce specimens which were used to determine changes in mechanical properties and microstructures. The latter were examined at the midsections of the specimens. Other specimens were tested to various stages of tertiary creep, after which they were remachined to new cylindrical test specimens, electropolished and re-tested in creep. RESULTS The major findings of this investigation may be illustrated by a comparison of the results of three sets of creep tests. These were run at 400°C at three stress levels, namely 750, 1000, and 1500 psi. In presenting these results in Figs. 1, 5, and 8, the creep curves are given in pairs: That curve of each pair which is drawn through filled circles corresponds to the initial test, and the curve drawn through open circles (and designated by - R) represents the result of retesting the same specimen after machining to a new cylindrical surface. The load was readjusted to the original unit stress at the beginning of each retest.

Jan 1, 1960

By Mónica P. Arenas

Aços austeníticos resistentes ao calor apresentam propriedades mecânicas que permitem seu uso em altas temperaturas e pressão, sendo frequentemente utilizados em fornos de reforma e pirolise. Devido às severas condições de operação danos de carburização podem ser induzidos. No presente trabalho foram analisados corpos de prova provenientes de fornos de reforma que apresentaram baixos níveis carburização. Com a finalidade de desenvolver uma metodologia que permita detectar e separar diferentes níveis de carburização, foi projetado, simulado e construído um sensor magnético constituído por um yoke e um sensor Hall. De acordo aos resultados obtidos, concluiu-se que o sensor permitiu determinar confiavelmente o nível de carburização em ligas austeníticas que estiveram expostas a diferentes temperaturas de operação.

Oct 30, 2017

By G. S. Austin

Soil next to an abandoned smelter near Socorro, New Mexico, has the highest Pb concentration in the clay-size fraction, although this fraction accounted for only 1 to 3 wt. % of the soil. The depth of contamination was determined in areas relatively undisturbed since the smelter was abandoned about 98 years ago. Lead concentration drops to background levels below a depth of 3 inches. A mineralogical examination of the fine-size fraction of Pb-contaminated soils revealed an absence of crystalline Pb compounds. We conclude that Pb is present either as amorphous phases or adsorbed on the surfaces of soil particles. Yet, because of the alkalinity of the soil, the movement of Pb-bearing particles controls Pb mobility, not chemical transport in solution. Plant material from the site contained elevated Pb levels that increased as the amount of Pb in the soil increased. Of the types of material tested, rabbit bush showed the greatest increase of Pb levels. Lead levels were highest in rabbit bush roots, whereas levels in creosote were highest in foliage. Levels in cactus varied. The amount of Pb due to dust incorporated in plant tissue is almost negligible compared to the amount absorbed through the plant vascular system.

Jan 1, 1992

By P. S. Jacobsen

In 1960 over 93 percent of the coal cleaned mechanically in the United States was cleaned in processes that utilized water or dense-medium suspensions of fine solids in water. Thus, in the process of removing deleterious ash-forming and sulfur-bearing minerals, another deleterious substance--water-- is added to the coal. The subsequent removal of the water from the coal, and the concomitant recovery of the coal from the water, is not troublesome in the sizes coarser than 1/4-inch. In the finer sizes, however, it is a difficult procedure that often costs more than the original washing operation. Because of the importance of liquid-solids separation in coal preparation, the Bureau of Mines has a continuing program of research in this field. The objective is to make available information on the performance characteristics of various types of equipment available for liquid-solids separations, thus promoting the wise selection of equipment for specific applications, and, thereby, more effective processing of coal. Results of work on flocculation as an aid to filtration5 and the sieve bend screen6 have been published. The present investigation of the screw-type classifier operating in combination with the cyclone was undertaken primarily because such classifiers are comparatively new to coal preparation and information on their performance is not available. The cyclone has become well-known since its introduction in this country by the Bureau of Mines in 1948.7 Use of the cyclone in conjunction with the screw-type classifier represents an attempt to provide the maximum recovery of solids at minimum moisture content.

Jan 1, 1962

By William J. Gillich, Gerald L. Moss

PREVIOUS studies of the shock loading of randomly oriented polycrystalline aggregates have firmly established that, after rather short load duration, hydrostatic compression closely approximates the shocked state.' However, McQueen deduced from pressure measurements with good time resolution that, during shock loading, metals begin to undergo a stress relaxation at the yield stress. He suggested that the relaxation is due to plastic deformation accompanying the change from a one-dimensional compression to a three-dimensional, hydrostatic, compression.' Stress relaxation may occur faster as stress is increased above the yield stress, but the existence of unidirectionally compressed states for finite times suggests that the concept of a unidirectionally distorted lattice should furnish considerable insight into the mechanical behavior of materials subjected to shock loading. Here, a crystallographic analysis is presented for the hypothetical situation where atom motion may be considered as unidirectional which, as indicated above, is a useful extension of the macroscopic concept of shock loading to the microscopic domain. Only motion caused by the com-pressive forces is treated; i.e., lattice vibrations upon which this motion is superimposed, as discussed by Fitzgerald, are ignored.3 The purpose of the analysis to be presented is to develop a description for single crystals of the lattice rotations that occur for idealized uniaxial strain deformation. The usefulness of such an analysis in realistic deformation is to give a method of specification of those properties of an initially distorted lattice which would affect the subsequent deformation. Non-axial complications that arise experimentally, such as off-axis rarefaction waves, must be treated in proper context. Consider the material element shown in Fig. 1 and let the compression be uniform at all regions of the element. Then, any interior point of the element is displaced in proportion to its distance from the base of the element. Accordingly, if the top of a unit element is displaced by an amount, (-K), with respect to the base, a point P(X, Y) will be displaced by (-KY). Crystal planes are, therefore, rotated by the compression. Analysis of this rotation may be accomplished from the geometry shown in Fig. 1 where the line OP is the edge of the plane {hkl} and N is its normal. The orientation of the crystal plane with respect to the shock direction is specified by the angle, before deformation. After deformation the edge of plane {hkl}

Jan 1, 1969