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By R. V. Hughes, J. N. Breston

Conclusions drawn by previous research workers with reSPect to the relation between Pressure gradients and/or velocity and oil recovery obtained by laboratory water flood tests have been in disagreement probably due to variable procedures and unnatural conditions and materials. The Bradford Laboratory of the Pennsylvania Grade Crude Oil Association as part of its secondary recovery research program has conducted nineteen water floods on two long cores of widely differing characteristics in an attempt to clarify this relationship and make it an aid in predicting flooding pressures in the field. Unlike previous research procedures the present experiments were conducted with the aim of duplicating field conditions as closely as possible by using long unextracted consolidated cores, a live crude, and natural brines for both flooding and, connate water content. Also, the pressure gradients and flooding velocities were representative of field conditions where similar sands were being flooded. Eleven floods on one core and eight floods on the other core showed increased recoveries and lower residual oil saturation with increased flood pressure gradients and flood velocities. A marked decrease in recovery was obtained from both cores at very low flood velocities. This pressure versus recovery relationship is shown to hold up to the point of water breakthrough and also up to the 100 and 1 produced water to oil ratio point. INTRODUCTION The possibility of water flooding oil sands was suggested by Carl1 of the Pennsylvania Geological Survey in 1880. It is not known when the practice was tried intentionally for the first time, but its beneficial effects were noted in the annual production rate of the Bradford field as early as 1907. The practice was illegal in Pennsylvania until 1921. Early water floods in the Bradford field usually consisted of shooting or splitting the casing secretly to permit subsurface waters to enter the producing sands under hydrostatic head. As it was noted that the benefits of water flooding seemed to be proportional to the quantity of water dumped into the well many also began to utilize surface sources after the practice became legal. It was probably during the middle 20's before many producers realized that the pressurehead of the water upon the producing sand determined the rate and quantity of water that would enter the sand. Hence, rate and quantity of production appeared to be a direct function of input pressures. By 1927 a few producers had ventured the installation of pressure pumps in order to increase water-input rates and production through the combination of hydrostatic and hydraulic pressures. The adoption of pressure flooding and the "five-spot" drilling pattern in the Bradford field were essentially simultaneous. Water-input pressures in 1930 seldom exceeded 300 p.s.i. at the well head or 1100 p.s.i. at the sand face. Since that time, water-flood producers in the Bradford-Allegany fields have gone to higher and higher pressure until today 600 p.s.i. at the well heads is called a low pressure flood. Many high pressure floods now operate at 1300-1400 p.s.i. at the well head. The limiting and advisable pressure at the sand face has been pronounced as that pressure just under what is required to lift the overburden or to cause formation parting: According to this rule any water flood operation utilizing well-head pressures nearly equal in pounds per sq. in. to 1.1 times the average depth in feet to the top of the producing sand would be considered as a high-pressure flood. Despite the higher pressure trends in the Bradford-Allegany field operations and the results of early laboratory water flooding research, the desirability and benefits of high input pressures are still questioned by many operators, particularly in midwestern water flood operations. The present paper recounts a series of 19 laboratory water floods using two long, consolidated cores of widely differing characteristics saturated with live crude and flooded with oil field brines in an effort to simulate field conditions under • various pressure gradients and flooding velocities. For both cores, higher recoveries and lower residual oil saturations were obtained at higher pressure gradients and flood velocities. This relationship is shown to hold up to the water breakthrough point and also up to the 100 to 1 produced water to oil ratio point.

Jan 1, 1949

By C. WIFLARD HAYES

(New Haven Meeting, February, 1909.) I DESIRE to make it perfectly clear at the outset that I fully realize the hazardous nature of any attempt to estimate the quantity of iron-ore or any other mineral in the ground. I should not have had the temerity to venture upon an inventory of the iron-ore supplies of the United States except for the requirements of the Conservation Commission. During the preparation of this inventory I have been impressed by the wide diversity in estimates of those best qualified to. hold an opinion, and I am therefore prepared in advance for criticism of my figures. Inasmuch as this report was prepared in large part for unprofessional readers, I considered it necessary to classify and describe the commercial iron-ores in a somewhat elementary manner, in order to explain the reasons for the large element of uncertainty in the estimates. I have therefore given a chemical and a geological classification of iron-ores, which place the commercial deposits in six classes: (1) magmatic segregations in basic igneous rocks; (2) contact-deposits formed in connection with igneous intrusions; (3) concentration-deposits; (4) replacement-deposits; (5) bedded-deposits, and (6) gossan-deposits. The iron-ores are further distinguished under two classes available and not available. This classification is in large measure arbitrary, and it, is evident that it will vary front time to time. In the available class are placed those ores which can be worked at a profit under conditions essentially as they exist at present. Since it depends wholly on the question of costs, the various factors which affect cost will determine the classification of any particular deposit. Actual production, * Abstract of Report prepared for the Conservation Commission. t Chief Geologist, United States Geological Survey. .

Apr 1, 1909

By M. Kumral, Y. A. Sari

Underground mining operations tend to have higher operating costs than surface mines. When metal prices decrease, profitability is jeopardized due to the high costs. Therefore, mining management harnesses new practices that increase operational efficiency. One way to manage this challenge is to invest in new mine planning practices. Stope layout optimization as a part of underground mine planning aims to identify a portion of the orebody in the form of production volumes (stopes) to maximize profit under roadway and stope dimension constraints. In this paper we propose a novel approach based on identifying ore-rich areas of the deposit and prioritizing their extraction through an iterative heuristic clustering approach. The proposed approach is compared with and validated by an exact method through a small mining example. The heuristics produced nearly identical results in a very short time. Finally, a case study was carried out using a larger data-set. The cluster-based iterative approach generated nearoptimal stope layouts in a computationally effective manner.

Mar 1, 2021

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Jan 1, 1938

By Maurício Covcevich Bagatini, Maycon Athayde

Water consumption reduction in pellet feed operation is of paramount importance. Compared with traditional ball mills, high-pressure grinding rolls (HPGR) play an important role in Blaine surface area (BSA) generation to improve agglomeration properties, although stability is still a challenge. Grindability improvement of existing operation has a direct impact on the performance of the filtering and pelletizing operation. The results of this study, as a pregrinding operation, can be applied not only in new operations but also in existing ones, helping the operator control process variation in a more effective way while ore hardness increases. 

By L Bergin, D J. Williams, S Islam, T A. Vangsness

The flooding of open strip coal mines in the Bowen Basin and Hunter Valley Coalfields of Eastern Australia has the potential to soften the spoil and floor materials to produce “mud”. This mud can act as a slip plane or weak zone when spoil is dumped into it, resulting in geotechnical instabilities. Once mud has formed, typical handling techniques include its costly removal by mechanical means, or its isolation and capping.There are little data available on the moisture state and shear strength of the capped mud. To investigate the effectiveness of isolation and capping, research has been conducted using a large slurry consolidometer (150 mm in diameter by up to 410 mm in height) to simulate capping in situ. Once consolidated, the mud was subjected to shear strength testing in a direct shear box measuring 60 mm by 60 mm by about 20 mm high. The shear strength of the consolidated mud was compared to that of competent, fresh spoil, a mixture of spoil and mud, and to completely degraded spoil (mud alone).These results have been used as inputs in stability calculations using the commercial computer program Slide 7.0, which demonstrates the strong influence of consolidation of the mud on overall low wall slope stability. The results provide insight into the design and construction of capping to isolate in-pit mud.CITATION:Vangsness, T A, Williams, D J, Islam, S, Smith, A and Bergin, L, 2018. Consolidation and shear strength testing and stability analysis of coal mine spoil degraded to mud, in Proceedings Mine Waste and Tailings Stewardship Conference 2018, pp 97–109 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 23, 2018

By G. M. Card, K. D. Card, B. V. Sanford

Abstract-The Canadian Shield and its extensions are traversed by an orthogonal system of northwest and northeast trending arch-style uplifts. These basement arches were formed by repeated vertical movements along pre-existing structures during compressional and extensional tectonism connected with events in surrounding Proterozoic and Phanerozoic orogens and ocean basins. The arches influenced patterns of sedimentation and tectonism in the intervening epicratonic basins and marginal platforms throughout the Proterozoic and Phanerozoic. Movements on the arch structures also triggered minor magmatism and controlled the location and timing of alkalic rock-carbonatite, kimberlite, and related intrusions in the Canadian Shield, the Western Canada Sedimentary Basin, and West Greenland.

Jan 1, 1997

By G. M. Card, K. D. Card, B. V. Sanford

The Canadian Shield and its extensions are traversed by an orthogonal system of north-west and northeast trending arch-style uplifts. These basement arches were formed by repeated vertical movements along pre-existing structures during compressional and extensional tectonism connected with events in surrounding Proterozoic and Phanerozoic orogens and ocean basins. The arches in?uenced patterns of sedimentation and tectonism in the intervening epicratonic basins andmarginal platforms throughout the Proterozoic and Phanerozoic. Movements on the arch structuresalso triggered minor magmatism and controlled the location and timing of alkalic rock-carbonatite, kimberlite, and related intrusions in the Canadian Shield, the Western Canada Sedimentary Basin, and West Greenland.

Jan 1, 1997

By W. E. Coughlin, R. L. Faverty, F. H. Lightner

Introduction The intent of this paper is to present the general strategy and method of implementation to achieve a "fast-track" mine development. The major objectives of a "fast-track" or rapid development schedule are to minimize front-end development expenditures and to realize an early cash flow from operations. The Borealis project of Houston International Minerals Corp. (HIMCO) is used as the working example to illustrate the development schedule. Borealis is a 2.3 kt/d (2,500 stpd) gold-silver heap leach operation near Hawthorne, NV, Pre-Feasibility Planning Proper early planning and identification of priority items were necessary to expedite project progress. On April 1, 1978, HIMCO leased the rights to the Borealis prospect and initiated exploration activities almost immediately. Since Borealis was showing excellent potential for mine development, an effort to clear the way environmentally was initiated during the summer of 1979. With the Borealis properties located within the Toiyabe National Forest, the US Forest Service (USFS) was recognized as the "lead" or respon¬sible agency for addressing the environmental issues. Early scoping of the environmental issues by both HIMCO and the USFS allowed HIMCO to take the initiative and address two potentially critical issues-archaeological and biological. Third party consultants, agreed upon by HIMCO and the USFS, were contracted to conduct archaeological and biological surveys. Desert Research Institute of Reno, NV, provided archaeological services, and JFL & Associates of Boulder, CO, provided biological services. These efforts began in the fall of 1979 and continued through the summer of 1980. Conservative Design Criteria By adoption of conservation design criteria, flowsheets and processing data required for detail engineering were firmly established with a minimum of impact on schedule. On Oct. 21, 1980, HIMCO formally initiated a feasibility study to evaluate the Borealis project. Four organizations were contracted for particular scopes of work: • John T. Boyd Co.: Ore reserve estimation, preliminary mine plan, and mine capital and operating cost estimation. • Bechtel Civil and Minerals: Conceptual engineering, processing capital and operating cost estimation. • Hazen Research Inc.: Metallurgical testing. • Sierra Pacific Power: Cost estimation for power supply. Metallurgical testing and conceptual engineering of both heap and agitation leach flowsheets were investigated concurrently. Numerous economic evaluations were conducted for both heap and agitation leaching at varying production capacities. The results indicated a heap leaching flowsheet treating 454 kt/y (500,000 stpy) yielded the best economics and was compatible with the "fast-track" development goal. Conservative design criteria was established to provide operating flexibility and ensure plant productivities. A summary of major design criteria is presented in Table 1. HIMCO assembled the results of the studies of the various consultants along with internally generated studies to produce the feasibility document. The decision to supply 100% equity by HIMCO rather than arrange project financing help to expedite the project. Cooperation Between HIMCO and Regulatory Agencies With cooperation and mutual trust established between HIMCO and regulatory agencies, the time required for environmental permitting was streamlined as much as practical. To expedite the required construction permits, HIMCO proposed to the USFS that HIMCO fund the total cost of an Environmental Assessment Report (EAR) and that issues be addressed at the technical level of an Environmental Impact Statement (EIS). The previous studies on the critical issues of archaeology and biology provided HIMCO with the information to satisfy the proposed approach. Houston International Minerals and the USFS agreed to have Environmental Research and Technology (ERT) of Fort Collins, CO, prepare a draft EAR for the USFS.

Jan 11, 1983

INTRODUCTION From its beginnings in the first decade of this century, flotation has gradually moved to a predominant role in mineral separation. There are several reasons for this, the continuing trend toward treat¬ment of lower-grade and more finely disseminated ores being the major one. Not only has this been true for sulfide ores to which the process was first applied commercially, but also for most nonsulfide ores as well. A second factor has been the broad applicability of the process with respect to particle size; it is effective from 8 to 10 mesh to below 10m. Finally, more so than for any other separation process, flotation has almost no limitations in separating minerals. Gravity, magnetic, or electrostatic processes are either applicable to particular minerals, or to a restricted number of mineral combinations. Flotation, on the other hand, can utilize the wide range of surface chemical differences among minerals, and an equally wide range of reagents. The recent availability of selective flocculation capabilities on a commercial scale as an adjunct to flotation should remove one of the limitations to the process in the very fine particle range. History Although flotation was anticipated in a 19th century patent to Haynes, its first significant industrial uses were in the early 20th century in Australia. According to Hoover,' the Pottter-Del-prat pro¬cess had a "measure of success" at Broken Hill's Block 14 mine in 1905-1906, and was definitely successful at the BHP Mine, where it produced 80,000 tpy of zinc concentrates. Both the Mineral Separa¬tion and the Elmore processes had early trials in Australia also, with both successes and failures. The first application in the United States was in 1911, when the Hyde process was used by the Butte and Superior Copper Co. on a zinc ore in Montana. By 1916 Hoover could list 46 applications to copper, lead, and zinc ores, mainly in the United States. Ten years later Taggart2 listed almost a thousand patents covering processes and reagents which with few exceptions laid the foundations for modern practice. Included were: sulfidizing of oxides; leach-precip¬itation-flotation; cyanides, sulfites, sulfides, and oxidants for selective depression of sulfides; starch, tannin, and glue as depressants; and xanthates, dithiophosphates, and oleic acid as collectors. Within an¬other 20 years, all of these were in commercial use along with amines for floating silica from phosphates, and synthetic frothers were com¬peting with pine oil and cresylic acid. Flotation machine development followed a different course. Of the 170 patents listed by Taggart in 1927,1 those incorporating film and oil flotation-about a third of the total-were no longer then

Jan 1, 1985

By R. Blazej

Machinery Systems Division (MSD) in the Institute of Mining Engineering at Wroclaw University of Technology specializes in belt conveying systems analyzing, calculating and design. Within the division operates the certified Laboratory of Belt Transportation (LTT) and Laboratory of Rollers. Since few years, a group of several people have begun work on developing a comprehensive system for the automatic evaluation of condition of conveyor belts working in the mines. Group uses both magnetic devices developed by specialized companies servicing belts and its own machine vision system developed for assessment of belts covers and edges during belt movement (up to 7 m / s) on the specially designed for this purpose the test conveyor. Recently they have got the research grant funded by the National Centre for Research and Development (NCBiR) for development of the system for automatic diagnosing of conveyor belts? condition and aiding of rational belt management. On the basis of previously created diagnostic tool called ABCDE (Automatic Belt Condition Diagnostic Equipment) the five modules: vision-A magnetic-B, preventive-C, forecasting?D, and determining safety factor-E will be developed. They will automatically interpret data about conveyor belts? condition to indicate the extent and timing of repairs, to prevent failures and to select the optimum moments for their replacements. The system will use results of ongoing research & development and planned research concerning modeling of belt wear using evolutionary genetic algorithms. The reached stage of research can not yet allow to start the implementation work by potential users. It is therefore necessary to pursuit research in real scale, the development of new modules (C-E) and intensive testing of the system in working condition with system calibration to optimize the economic effects.

Aug 1, 2013

By Q Johnston

Since its inception in 1990, improved metallurgical processing technologies, coupled with mine planning enhancements and improved geological knowledge, have sequentially enabled better efficiencies and economies of scale at the Macraes Gold Project. Over a period of 11 years, processing enhancements have been achieved by: +        increasing mill throughput, from one million tonnes per year, to current throughput of 3.9 million tonnes per year; +        improving recovery rates, from 70 % to approx 84 %; and +        performance enhancement through innovation, eg the use of kerosene to combat ClL pregrobbing. Future processing improvements have been identified in optimising the ore feed and processing flowsheet. The introduction of the autoclave has transformed the process flow form a traditional 'mill headgrade and tonnes milled' operation, to a 'sulphur/gold ratio and sulphur tonnes oxidised' operation.

Jan 1, 2001

The Skorpion process comprises three processing steps, atmospheric leaching in sulphuric acid, zinc solvent extraction and electrowinning to produce special high grade zinc. The major mode of impurity transfer was attributed to crud runs in the solvent extraction circuit. Crud may be described as a heterogeneous, partly inorganic, partly organic mass of material which accumulates predominantly at the interface between organic and aqueous solutions. The paper describes the route causes of the crud formation in the solvent extraction circuit and optimisation strategies which are being followed to prevent impurity excursions in electrowinning. Keywords: zinc oxide, solvent extraction, crud formation, colloidal silica

Jan 1, 2007

By J. Vance Batty

The Permian Red Bed copper deposits of the South Central States are a potentially important resource. Only the higher grade, near-surface ores are now exploited because conventional froth flotation does not recover oxidized copper minerals which comprise 10 to 15 percent or more of the copper content of typical ore. Laboratory-scale beneficiation studies were initiated to devise a method capable of recovering both sulfide and oxidized copper mineral. Testing established that the high clay and gypsum content of typical ore prevented effective flotation of the oxide mineral using sulfidizing, fatty-acid, or oil emulsion techniques. A modified leach-precipitation-flotation (L-P-F) procedure recovered over 90 percent of the copper, compared to a recovery of 77 percent obtained by conventional sulfide flotation. The higher costs of the L-P-F method would reduce the increased revenue from higher copper recovery. An increase in copper price and/or an increase in oxide copper content of the ore would make the L-P-F process comparatively more attractive.

Jan 1, 1970

By Joseph W. Mullan

The today status of air pollution control legislation and regulations can best be described as an exaggerated state of environmental limbo. The '70's began but one and one-half months ago yet it already has been very appropriately named "the decade of the environment." This certainly will be the decade for new legislation - new regulations and hopefully "Clean Air." Already Washington is faced with legislators playing "pollution politics" to the crowds. Students have redirected their efforts from Vietnam to the cleansing of the environment and everyone including the man on the street has become an environ¬mental expert. This is the decade we all face, but where are we today? Pollution is not a new problem. It has been with us for centuries and while much is left to be done, much has already been accomplished. I will try to make some comparisons of what I believe to be the good and bad points in the national air pollution control picture and hopefully will generate within each of you sufficient concern as to which comparisons are sound.

Jan 1, 1970

By H. Y. Sohn, Hang Goo Kim

Computer simulations were carried out using calcium ferrite slags containing 25 wt% CaO, and the results compared with those obtained using fayalite slags. There was little difference in overall elimination of Pb and Bi, but elimination of Sb and As was much lower with calcium ferrite slag. When calcium ferrite slag is used only in the converting stage and fayalite slag in the smelting stage, as in the Mitsubishi process, the contents of Sb and As in the blister copper can be kept to reasonable levels. This allows advantage to be taken of the considerably higher iron oxide-holding capacity of calcium ferrite slag than of fayalite slag at the high oxygen potential under converting conditions, thus preventing precipitation of magnetite. Satisfactory agreement was obtained between predicted values and observed data from a Mitsubishi converter

Jun 18, 1905

By Lívia Silvestre Andrade

Uma das rotas mais importantes de produção do Fe-Nb para aplicações siderúrgicas é a aluminotermia. Para que o processo seja eficiente, é necessário projetar adequadamente a escória, para garantir a mínima retenção de metal na escória e reduzir as perdas, assim como determinar a carga da aluminotermia considerando os balanços de massa e de energia. Neste trabalho, os efeitos das adições de CaO e CaF2 sobre as características das escórias do processo são determinados através da termodinâmica computacional. Um balanço de massa e um balanço de entalpia são formulados, de modo a verificar se as quantidades dos diversos materiais adicionados são adequadas e se as temperaturas de fim de processo são razoáveis. Verifica-se que, a partir de uma carga hipotética formulada, há espaço para melhorias importantes balanceando-se corretamente as adições de CaO e CaF2. Além disto, verifica-se a influência do teor de Mg contido como impureza no Al empregado como redutor, observando-se que seu efeito é bem menos significativo do que inicialmente esperado por diversos operadores.

Oct 30, 2017

By N L. Turner, K Ehrig, V Liebezeit, D J. Robinson, L L. Kuhar, N Francis

Conventional industry tests used to determine leach recoveries are often fully monitored and may be time-consuming and expensive. Such tests may be limiting in geometallurgical applications where large numbers of samples are required to be processed for characterisation of an ore deposit. BHP Billiton currently use a fully instrumented leach test for characterisation of Olympic Dam uranium-rich samples. Researchers at the Commonwealth Scientific Research and Industrial Organisation (CSIRO) were approached to develop an alternative to these full-scale leach tests that could allow for the ranking of samples in terms of their leachability. The novel geometallurgical test was required to use samples of small mass and be affordable and rapid.Three leach test protocols were pursued in developing the small-scale tests. Kinetic leach tests were performed using mild conditions at higher pH, low temperature and low oxidation reduction potential, moderate conditions at intermediate pH, temperature and oxidation reduction potential and aggressive conditions at lower pH, higher temperature and higher reduction potential.This paper presents results from 44 leach tests on 11 samples with varying uranium mineralogy. The developed small-scale tests correlate well with data from the more costly conventional industry laboratory tests, indicating the possibility of using this alternative test as a geometallurgical leach proxy. Simple regression analysis confirmed the importance of pH, reduction potential and temperature on uranium extraction. Experimental data were fitted to published leach models to predict uranium leach extraction for a range of operating conditions.The ultimate aim of the test work is to combine a limited number of large-scale calibration tests, a large number of small-scale geometallurgical tests and leach models for geometallurgical sample characterisation and evaluation of a wide range of scenarios or processing options.CITATION:Turner, N L, Kuhar, L L, Francis, N, Liebezeit, V, Ehrig, K and Robinson, D J, 2013. Development and testing of a small-scale uranium leach for geometallurgical applications, in Proceedings The Second AusIMM International Geometallurgy Conference (GeoMet) 2013 , pp 345-350 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 29, 2013

A review is presented of developments in mill liners to improve performance in terms of wear, impact, as well as mill grind and throughput. These developments are in response to the growth in size of SAG mills and the use of larger ball loadings and ball sizes in modern SAG milling practice. Shell liner developments include specific mechanical design features such as special bolting, directed metal flow to prolong liner life and a focus on the process aspects of the mills to provide more effective grinding motion with reduced wasteful ball-on-liner impacts. Grate design developments aim to provide high throughput of material, especially in the larger size fractions, while providing good impact and wear life. Curved pulp lifters are designed to ensure, at high mill speeds, complete discharge of coarse solids from the mill.

Jan 1, 1999

By C. M. Wayman, R. Bullough

The selection rules fir twinning in fcc, bcc, and hcp lattices as established in Part I are used to predict the positions, relative to the matrix (untwinned) reciprocal lattice, of reflections due to double diffraction from the twins. These doubly diffracted reciprocal lattice points, which often coincide with ordinary matrix reciprocal lattice points, are deduced from kinematical considerations. 1. INTRODUCTION. A Bragg diffracted beam under certain conditions may be rediffracted to produce a third beam i .e., the incident beam, the first diffracted beam, and the rediffracted beam). In such a case an initial incident beam is diffracted by a set of planes; the diffracted beam may then be rediffracted by a second set of crystallographically different planes. The initially diffracted beam acts as an incident beam for the second set of planes, thus resulting in a twice-diffracted beam. This twice-diffracted beam may be regarded as a singly diffracted beam from a set of lattice planes whose structure factor is zero. In order to find the reciprocal lattice point corresponding to the doubly diffracted beam, it is customary1,2 to combine vectorially the component reciprocal lattice vectors which head to the extra reflections. For example, hcp metals may exhibit the forbidden (0001) reflections.* As Fig. 1 shows, the (0001) reciprocal lattice point results from: (1010) + (1011) = (0001) Similarly, combination of the beams (1011) and (1010) gives rise to: (1011)- (1010) = (0001) As Pashley and stowell2 have pointed out, even if in fact the double diffraction points lie on the Ewald sphere, they may not actually represent observed doubly diffracted beams because the initially diffracted primary beam, i.e., the source, must also correspond to a reciprocal lattice point which lies on the sphere of reflection; however, the reciprocal lattice point corresponding to the planes causing the rediffraction need not lie on the sphere. A little consideration of the Ewald construction in Fig. 2 makes this argument clear. In Fig. 2 the incident beam is represented by the wave vector ko. This beam is initially diffracted by the lattice planes (hkl) which are represented by the reciprocal lattice vector r(hk1) The reciprocal lattice point (hkl) of course lies on the Ewald sphere in order that the Bragg condition be satisfied. The initially diffracted beam is represented by the wave vector kl. If now kl is rediffracted by a second set of planes (h'k'l') resulting in k2 the lattice point (h"k"l") must lie on the Ewald sphere if the double diffracted beam k2 is to be observed. It is clear that (h"k"l") is the vector sum of (hkl) and (h'k'l'), and that (h'k'l') need not in fact lie on the Ewald sphere. In the usual1,2 analysis the origin (000) of the reciprocal lattice is shifted to the point (hkl). However the translation (000)— (hkl) automatically shifts the point (h'k'l') to the Ewald sphere, i.e., (h'k'l')— (h"k"1"). It is to be seen that (hkl), the source reflection, must lie on the Ewald sphere; if it does not the translation (000) — (hkl) places the "new" origin off the sphere, not satisfying the Ewald construction and hence the Bragg condition. The point (h"k"1") of course must lie on the sphere if it corresponds to an observed doubly diffracted beam. It is to be noted that crystals having the hcp structure, as just discussed, are intrinsically capable (i.e., without lattice defects such as twins) of double diffraction, as contrasted to fcc and bcc crystals which are extrinsically capable (requiring lattice defects or reoriented lattice regions). The "allowed" bcc reciprocal lattice points (which comprise an fcc lattice) are (110), (2001, (211), (220), (310), (2221, (321), (4001, and so forth. The combination

Jan 1, 1967