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By M. Wittke

"In the course of the extension of the railway network in Israel, currently the two 4.6 km long tubes of the Gilon Tunnels on the line from Akko to Carmiel are being constructed. The tunnels run through the limestones of the Bina- and Yirka-formations, which locally are karstified. The maximum overburden amounts to 160 m.The limestones are mostly horizontally bedded and vertically jointed. Occasionally also inclined joints exist. The tunnels cross various fault zones, which mostly strike at an acute angle to the tunnel axis and are steeply inclined. The karstic cavities which were encountered during tunneling have partially been filled by clay. In the vicinity of the fault zones, the rock has often been strongly jointed and weathered respectively. The two single-track tubes have a cross section with vertical walls and an open invert. The tubes are connected by cross cuts with a spacing of approx. 250 m.During the tender phase, WBI has elaborated the tender design for a joint venture of a Chinese and an Israeli construction company. After the joint venture had been awarded the contract, the preliminary and the detailed design have been elaborated by WBI and the construction works have been guided. On the basis of the geological description, rock mechanical models have been elaborated, followed by stability analyses on the basis of the Finite Element method. The tunnels have been excavated according to the shotcrete method. The support in most areas only consisted of a very thin shotcrete lining and radial bolts in the area of the roof. Depending on the degree of jointing and weathering, locally advancing support by means of spiles has been applied.The internal lining of reinforced concrete has been constructed in parallel to the heading of the tubes. Mucking and delivery of materials was carried out through the cross cuts.The breakthrough was achieved in April 2014 and thus within schedule. The predicted distribution of the excavation and support classes along the tunnel has been in good agreement with reality."

Jan 1, 2015

Over the last 100 years in the Polish mining industry considerable work has been done to assess optimum slurry, develop flexible delivery systems and adjust the fill technology to a wide variety of mining and geological conditions. Sand or industrial mineral waste materials for the backfilling of underground voids are used to control ground movement and surface deformation. This paper discusses various criteria to be considered in the preparation of a fill, including slurry properties, mine infrastructure, mining geometry, placement methods and the purpose of the backfill. This paper presents laboratory and in situ test data on the influence of materials parameters on the slurry flow in a pipeline system, stiffness, permeability, binding time and strength of a backfill, on the distribution of mixture in underground voids or the penetration between roof fall materials.

Jan 1, 1998

By C. F. McCarroll

[Laboratory research and, control in the production an. utilization of petroleum and it 3 products have expanded greatly during the past decade, and much of the routine control and experimental equipment now rewires the constant daily use of liquid mercury. In spite of this ;;renter use, very little consideration has been given to the hazard that might be occasioned by the toxic vapors of mercury unavoidably spilled' of otherwise exposed to the atmosphere during the normal procedure of laboratory open at ions. A simple visual examination ).'.' son-,, r° the laboratories reveal the presence of a considerable quantity of mercury in the cracks of floors, on work tables, and on ark, around equipment stands. Usually this mercury is contaminated with oil3/ and dirt so that it remaining in a finely divided state and a ;mall amount pre presents a relatively large surface for evaporation. Since :mercury shows measurable volatility at a temperature v,.^ lo.! 5o F., mercury vapor will be present in, the mercury _3 exposed promiscuously.]

Jan 1, 1939

By G. Bartolacci, G. Couture, Levasseur. B., A. Lockhart, D. Nathan

"Pulp and froth zone characterization in a flotation circuit to improve transport of valuable minerals remains a challenge. Even though some significant breakthroughs have been made in the development of collectors in terms of selectivity, the control of gangue drainage is still the main bottleneck to achieve the production of a clean concentrate.Over the last decade, COREM’s team has been working on technologies to improve the selectivity of flotation circuits by tuning their hydrodynamic conditions using online instruments such as the bubble viewer, Jg sensor and gas hold-up. As part of its research program, COREM also developed the half-life column that establishes the relationship between the collection zone (bubble-particle attachment) and the cleaning zone (foam) of a flotation machine. In recent years, COREM has continued the development of the prototypes to make them more robust and improve the accuracy of their measurements.Recently, these hydrodynamic instruments were installed in an industrial process at Raglan Mine in order to diagnose and control the impact of hydrodynamic parameters versus the recovery and the quality of the Ni concentrate produced. Sampling campaigns of hydrodynamic parameters demonstrated that froth height could be optimized in order to increase recovery and quality of the concentrate at the same time. The specific effect of the froth height impacts both the pulp and the froth zones. Along with the impact on the drainage of the concentrate, it was observed that froth height also contributes to enhance the collection of particles in the pulp leading to an increase in metallic units.IntroductionOnce the particles of the minerals of interest are attached to the air bubbles injected in the pulp, the flotation process is driven by air dispersion parameters and froth properties. The pulp is usually responsible for the collision between air bubbles and hydrophobic particles of interest while the froth zone aims to upgrade the selectivity of the particles floated through drainage of the unwanted hydrophilic particles. Over the last four decades, flotation hydrodynamics has been extensively studied. Superficial gas velocity (Jg), gas hold-up (eg), Sauter mean bubble diameter measurements (d32) and bubble surface area flux (Sb) are among the most assessed parameters in flotation plants worldwide either to quantify the gas dispersion parameters or to optimize them (Fournier et al., 2015). McGill University has developed several sensors able to measure these parameters at industrial scale (Tavera et al., 1996; Finch et al., 1999; Chen et al. 2001)."

Jan 1, 2017

By Vaughan R. Voller

"Numerical methods for dealing with a temperature dependent conductivity are discussed. An approach based on a local application of a Kirchhoff transformation at the discrete level is presented. The application of this transformation - that does not require any inversion- is demonstrated on solving a two-dimensional test problem.IntroductionMuch is said in the recent literature on the modeling necessity of obtaining appropriate thermo-physical properties; in particular the requirement to account for properties that are ""strong"" functions of the depended variables, e.g., Temperature. Of course obtaining appropriate thermo-physical properties serves no purpose unless they can be accurately integrated into a discrete numerical calculation. The purpose of this paper is to examine how temperature dependent conductivities that exhibit discontinuities or rapid changes can be handled in a numerical code.The discussion will be made in the context of a control volume finite element method [1]. After a brief outline of control volume finite element fundamentals basic methods of dealing with discontinuous or rapidly changing thermal conductivity are discussed. This is followed by the presentation of the recently proposed local Kirchhoff method [2,3], The paper concludes with an investigation of the performance of the various conductivity schemes in solving two dimensional problems. This testing clearly shows the advantages (accuracy and implementation) in using the local Kirchhoff method."

Jan 1, 2001

By S. J. Pearce

The need for a simple, very sensitive, and accurate method for the determination of benzene in blood and urine vas evident throughout a recent study of chronic benzene (C6H6) poisoning conducted cooperatively by the United States Bureau of Mines, The Barrett Company, and the producers of benzene. A combustion method which will be described in a later publication, and a previously described/ adaptation of Smyth's method were developed and used during that investigation. The adaptation of Smyth's method gave satisfactory results when dealing with exposure conditions that produced chronic poisoning in a comparatively few days, but it was time-consuming; and lacked the accuracy necessary for a study of the absorption, distribution, and fate of benzene in the body during exposure to threshold concentrations of benzene vapor in air. The combustion procedure was satisfactory from the standpoint of sensitivity but was cumbersome, intricate, time-consuming, and required the use of special and somewhat expensive Physical and chemical apparatus. Following the termination of this study of chronic poisoning, possibilities ides for developing better methods occurred, and these have been investigated by the Bureau of Mines with the aid of Relief Works Division personnel microcolorimetric method for the determination of benzene in air has been described recently.6/ The present report deals rich the adaptation of this new colorimetric method to the determination

Jan 1, 1936

By Samuel Senanu, Benjamin Agyei-Tuffour, Lifeng Zhang, Eivind Øvrelid, Adegboyega Nathaniel Femi

"The solar grade silicon ingot produced from directional solidification process usually pushes the impurities to the top and finally cut off and discarded, which leads to material loss. The hard inclusions lead to wire breakages during the cutting of the ingot in wafers. The main kinds of inclusions found in solar grade silicon have been investigated using vacuum filtration: needle-like Si3N4 and lumpy SiC inclusions. Clusters of SiC inclusions and Si3N4 are also found. Surface observations of the scraps before polishing reveals that Si3N4 inclusions are usually bigger and in some cases can be about a few millimeters. SiC inclusions are usually smaller, ~200µm but can be ~500µm in some cases. Inclusions observed after filtration are mainly SiC with diameters ~10µm. Through the vacuum filtration, 99% inclusions can be removed 99%. The possible mechanisms of filtration are cake filtration for the larger sized Si3N4 and SiC inclusions and deep-bed filtration the SiC inclusions. For the directional solidified silicon ingot, an approximate distance of ~10mm gave an encouraging cutoff thickness. The inclusions sizes were below 10µm. Introduction The search for an alternative source of energy to fossil fuel has led to a dramatic increase in the demand for solar energy due to its high dependability (abundant in nature) and environmental friendliness 1). During the last 5 to 10 years, the annual worldwide production of solar cell by the photovoltaic industry has increased to an annual rate of 30 to 40 percent 2). A necessary condition for the maintenance and even an increase of this growth rate is a decrease in the cost of feedstock for the solar cell production 1). The total international production in 1997 was 130 MW worth more than $500 million. In 2004 the consolidated world total production of PV cells increased to 1146 MW or around. $7 billion (Figure 1) 3). Silicon is currently the most dominant semiconductor material used in the PV industry. As shown in Figure 2 3), solar cells consist of two types of material, often the p-type and n-type silicon. Light of certain wavelengths are able to ionize the atoms in the silicon (causing atoms to either gain or lose electrons) and the internal field produced by the junction separates some of the positive charges (“holes”) from the negative charges (electrons) within the photovoltaic device. The holes are swept into the positive or p-layer and the electrons are swept into the negative or n-layer. Although these opposite charges are attracted to each other, most of them can only recombine by passing through an external circuit outside the material because of the internal potential energy barrier. Therefore if a circuit is made, power can be produced from the cells under light because the free electrons pass through the load to recombine with the positive holes."

Jan 1, 2008

By Anderson Meireles, Vladimir Carrasco, Carlos Feliciano

Adopting new technology in drill and blast requires a structured implementation process, as it represents a significant change in a traditionally conservative industry. It involves addressing initially unknown implications. As the problem is not yet acutely felt, developing a market strategy must be approached from the customer’s perspective, considering how the product can optimize their activities or enhance flexibility. To achieve this, it is essential to have a comprehensive understanding of the context of the customers identified in the deployment process pipeline. This paper discusses aspects of introducing wireless initiation technology - the initiation of primers through a magnetic field without physical connections - in Brazil. Additionally, it presents a case study of the application of a structured process of sales with purpose in an underground mine. By identifying key opportunities that were highly profitable for the client, the necessary awareness was created, leading them to recognize the technology as an enabler for exploring their mineral deposits in a new way which allowed a successful change management process. Based on the applicable technique, a preloading project was developed to maintain inaccessible areas with high-grade precharged with the area loaded with wireless primers acting as a temporary pillar and controlling dilution throughout the orebody. Once the excavation of the stope was completed, the pillar was successfully blasted and the material - once considered lost in the original plan as a rib pillar - was recovered after serving its structural function. Through this method, the metallic recovery of the stope increased without dilution losses. Demonstrating economic viability and stablishing the previously unknown technology as a strategic tool for optimizing stope recovery.

Jan 21, 2025

By T. T. Chen, J. L. Jambor, J. E. Dutrizac

A reconnaissance study of the neutralization potential of 30 diverse minerals, 28 of which are silicates and aluminosilicates, has shown that most of these minerals contribute minimally to the neutralization potential (NP) in standard static tests. Feldspars in particular give low NP values and would not be expected to attenuate the acidity to any significant extent in acid rock drainage settings. The BET-determined surface areas of the minerals vary considerably, and the large surface areas of some of the pulverized samples have clearly affected the NP values even though the standard static-test protocol was used for the preparation of the samples. The low NP values of most silicates and aluminosilicates are in general agreement with the laboratory-determined slow dissolution rates for these minerals. The results suggest that, in the prediction of whether rocks will be acid-producing, the most realistic measure is that of the carbonate content. In mine wastes from metalliferous ore deposits, the contribution to the NP by the non-carbonate gangue assemblage is unlikely to be more than a token amount until well after the establishment of an acid rock drainage situation.

Jan 1, 2000

By M. P. D. Ingunza, Júnior Santos, F. S. D. Araújo, A. L. C. Araújo, J. Y. P. Leite

Wastewater sludge is a problem for environmental control and it is necessary alternative researches for its reuse. Industries can research the association of clay and sewage sludge as a source of ceramic mass. This procedure can contribute for the industry sustainability including in its raw materials, wastes of environmental concern. This paper presents the results of sewage sludge and clays characterization being analyzed particle size distribution (sedimentation), mineralogical (X-ray diffraction), chemical composition (X-ray fluorescence), thermal analysis, density, and Atterberg proprieties (liquid and plastic limit; plasticity index) and also their applications in ceramics. Results were used to determine moisture for mass of raw material and sewage sludge and there were realized tests of fired in kiln at temperatures used in ceramic industry for bricks production. In the test pieces were analyzed the properties for application as bricks.

Jan 1, 2005

By W. Mont Ferry

It is impossible to speak in exact terms of the effect that selective flotation has had, is having, and may have on the State of Utah. Its results enter into the economic structure of the state in so many ways and its ramifications are so widespread, that every line of industry is affectcd. Some effects can be definitely determined; others can be reasonably approximated; but the effect as a whole can not be set out in exact figures. Utah is essentially a mining state; mining is its basic industry and always will be. Agriculture, equally a basic industry, and of course, equally vital, can be practiced on only 6 per cent. of the 85,000 square miles of its area. It follows, therefore, that the economic future of this state depends upon a development of its natural resources. About 6 or 7 years ago, the mining industry in Utah was at a low ebb. This condition was caused partly by postwar conditions and other temporary causes, but prevailed also, which was most important, because the direet-smelting ores of the state were being rapidly exhausted and the cost of treatment of complex ores was almost prohibitive. Furthermore, the wet concentration of low-grade ores was unsatisfactory and did not result in producing a good smelting product. On visualizing this situation, one of the large smelting companies in the valley had the courage, ability and faith to develop and expand the principles involved in selective flotation of complex ores. This example has been followrd by other smelting and reduction companirs and the result has changed the entire aspect of the mining industry in Utah. The utilization of the zinc in the low-grade, lead-zinc-silvrr ores was the principal prob1t.m to be solvcd. The average yearly production from the State of Utah for the 10 years beginning 1914 and ending 1923, was something less than 10,000 tons of zinc corlcentrates. This period includes the world war, when abnormal priccs stimulated production. In 1924, selective flotation began to be practiced on a considerable scale, replacing concentration by gravity and bulk flotation which had been used generally until this time. Production and Value of Zinc Concentrates The production of zinc concentrates during 1924 was approximately 24,000 tons, or twice the average yearly production of the previous 10

Jan 1, 1928

By G. S. Hume

IN. THE autumn of 1922, British Petroleums Ltd. found oil of 14° Baumé in a sand 17 ft. thick in its. No. 2 well at Wainwright, 120 miles southeast of Edmonton. This greatly encouraged drilling in the Wainwright-Irma area and this past summer several wells were started, three of which are now completed and the others still being drilled. Of the three completed, No. 4 British Petroleums contains oil; No. 3 British Petroleums gave a show of oil but so far has not given much hope, of becoming a commercial producer; and No. 1 Maple Leaf Co., as now finished, is a. gas well with a daily flow of gas of about 2,500,000 cu. ft. at a closed pressure of 700 lb. An oil sand is reported to have been encountered below the producing gas horizon in the Maple Leaf well but has not been tested. Operations on this well have been suspended for the winter. The Geological Survey of Canada this past summer undertook a geological investigation of this area with the object of defining the structures with which the oil and gas are associated. The structure underlying this portion of the plains was supposed to be a terrace with the western edge dipping into the Alberta syncline and with a monoclinal structure to the east. By accurate leveling on known geological horizons on this terrace, a number of gentle folds were located and -it is in these folds that the oil and gas are found. At the British Petroleums Nos. 2 and 4 oil wells, the western flank of the fold has a gentle dip of only a few feet to the mile to the southwest whereas the strata on the eastern flank dip to the northeast about 40 ft. in ½ mile, the strike of the fold being northwest and southeast. How far oil will be found down the gentle southwest dip is unknown but probably the productive part of the fold will not exceed 1 mile in width, and possibly less. No. 3 British Petroleums well is on the strike of the fold 1 mile southeast of the two oil wells. The sand that was productive in Nos. 2 and 4 wells was not present in this well or, if present, was very thin and unproductive. Two other sand horizons, however, were encountered. The upper of these

Jan 3, 1925

By H. Wagner

The discovery of the gold-rich Main Reef Group of reefs on the farm Langlaagte in 1886 marked the opening of the richest and most extensive goldfield in history. Mining of the narrow reefs progressed from the outcrops to more than 3,5 km, and has made South Africa the foremost mining country in the world. Changes in the political and socio-economic climate create a new challenge to the gold-mining industry. The most significant of these is the emergence of Black trade unions, with their demands for higher wages, improved safety, job advancement, and abolition of discriminatory legislation. Industrial conflicts on gold mines have risen significantly in the past ten years, and are likely to continue in the future, although the causes of these conflicts may change. Events largely outside the control of the gold-mining industry, such as the improved dollar price for gold and the depreciation of the value of the rand relative to major currencies, have enabled the industry to meet the demands for higher wages and to narrow the wage gap. However, labour productivities have improved insignificantly and are a cause of major concern for the future development of the industry. Continued pressure in the industrial-relations area, the inflation of working costs, and the extension of mining operations to greater depths and more difficult areas create major challenges to mine managements and mining engineers. Significant improvements in mining technology, environmental control, and safety will have to be made to ensure the long-term survival of the industry. The unavoidable introduction in deep gold mines of mechanization on a larger scale to meet the requirements of higher labour productivities and a better and safer underground environment will have a major impact on the cost and management structure of these mines. Engineering will assume a more important role on deep gold mil1es, and management styles and structures will have to be adapted to accommodate these changes. The supply of suitably qualified engineers, technicians, and artisans will be a crucial factor controlling the rate of technological change. The industry is well-geared through its Group system to meet these challenges, and to benefit from the experience gained in the operation of highly mechanized mines. However, changes take time to implement and there is very little time left.

Jan 1, 1986

By Kazuki Morita

Dissolution mechanism and solubility of chlorine in the oxide melts, such as CaO-SiO2-Al2O3 (-Na2O), Na2O-SiO2-Al2O3 and CaO-SiO2-FeO systems, have been equilibrium technique was employed with controlled Po2 and PCl2, (Po2 = 10-6 -10 19 atm, PCl2 10-6 -10-13 atm at 1673-1748 K). The solubility of chlorine in the 40mass%CaO-40mass%SiO2- 20mass%Al2O3, slag was found to vary in proportion to Pb2/ w and pc/z/p' which proved that chlorine dissolved in the melts as C1 anion. Hence, the chloride capacity (CCI-), indicating the ability of molten oxide to absorb chlorine, has been defined as; The Ccl value was observed to increase with increasing slag basicity and temperature, and showed a reasonable relationship with that Of CS2-. Based on the result obtained in the present study, chlorine distribution during incineration with slags was predicted quantitatively.

Jan 1, 2003

The dissolution of gold in cyanide has been studied, using both chemical and electrochemical techniques. The electro-chemical studies have confirmed that gold may become passive in cyanide solution if its potential becomes more positive than -O· 5 V v. saturated calomel electrode (S.C.E.). The results of the conventional solution rate tests suggest that, although the solution rate is controlled by the rate of diffusion of oxygen at low oxygen and agitation levels, when these are increased the gold may become passive and its solution rate approach a steady value, or even decrease with increasing oxygen level. The passivity of gold has been shown to be of importance in the solution of small spheres of this metal, and in the extraction of gold from a calcined auriferous pyrite concentrate.INTRODUCTIONAlthough it has been appreciated for many years (McLaurin, 1893, 1895) that dissolved oxygen is a necessary adjunct to the solution of gold by the cyanide process, attempts to quantitatively assess its effect have led to conflicting results. For example, Barsky, Swainson, and Hedley (1934) reported that an increase in oxygen concentration improved the solution rate, but Beyers (1936) claimed that such an increase would reduce the rate at which the gold dissolved.By using an electrochemical approach Kudryk and Kellogg (1954) showed that the diffusion rate of either the cyanide or the oxygen was a controlling factor, and that, if the mole ratio of cyanide to oxygen concentration was greater than 10, the solution rate was proportional to oxygen concentration.These results, although they represent some of the most careful work available, were in direct contradiction to the findings of Mills (1951), who found that gold may become passive in cyanide solution, with a resultant decrease in solution rate.

Jan 1, 1963

By J. K. Szymanski, Val Srajer

In this decade mining companies in western Canada have searched for reliable and inexpensive ways to improve mine productivity. Truck dispatching systems, equipment vital sign monitoring and sensing, vehicle guidance systems, have all been considered. In this paper the off -highway vehicle monitoring systems used or planned to be installed at surface coal mines in western Canada are described. The monitoring systems are divided according to their function and application; installation and testing procedures are described, as well as the economic benefits to the mining operation.

Jan 1, 1989

By R. Lindsay Mundell

During the past 12 years, use of longwall methods to mine coal in the United States has continually in- creased. Although these methods offer several advantages, health hazards often exist because of unique and difficult problems in the control of respirable dust. This paper discusses the results of respirable dust studies conducted on United States longwall mining operations in 1972and 1978. Current engineering control methods (ventilation, water application and use of machine cutting parameters) and administrative controls for minimizing employees' respirable dust exposures are discussed.

Jan 1, 1980

By David Rees

Tomago Aluminium, a 400,OO tonnes per annum primary aluminium smelter in Australia, has installed Ozone for biological control of its process water. The system was designed in Australia by Ionics Watertec Engineering, whilst ANCO Australia monitors the water quality and provides technical support for the project. The motivation was initially to reduce operating costs, however investigations indicated that there were substantial environmental benefits to be achieved by the elimination of a part, or all of, the chemicals being used to control the system. Also the existing chemicals appeared to be losing their ability to control biological growth in the system, in particular, the legionella bacteria. Ozone water treatment commenced in January 1998 and after a short transition period has operated without chemical addition since. There appears to be no doubt that the biological control is effective, the clarity and purity of the water has improved and initial testing indicates that the corrosion control rate is acceptable, although some chemical corrosion control may be introduced after further testing around the total circuit to guarantee protection

Jan 1, 1999

By G J. Harbort, Z Pokra

It has been observed in several Jameson cell installations where the source for flotation feed is deslime screens, that the recovery of coal particles greater than 0.5 m is not as great as that of finer material. Consequently, a research project was undertaken at a CHPP in the Bowen Basin, Queensland, to assess the possibility of increasing the recovery of coarser particles (+0.5 mm) within the downcomer of the Jameson Cell. The effect of decreasing turbulence and agitation in a commercial-scale downcomer was investigated to assess the effect on the recovery of both coarse and fine coal particles. This paper details the findings of the testwork, summarising the results relating to differences in the operating parameters within the downcomer.

Jan 1, 2005

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener's anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,' the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.' THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.' Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969