Search Documents

By Jürg Schlumpf

Concrete is one of the decisive construction materials, also for the AlpTransit Gotthard Tunnel. The client has many requirements, and many are the solution possibilities that concrete systems can offer. Cement producers and concrete admixture manufacturers have been challenged to design and test jointly concrete systems for cast and sprayed concrete. The testing operation followed the scenario laid out by the Gotthard AlpTransit Project management?s instructions ?Testing system for concrete mixes.? Various supplier teams have applied for the concrete systems for sections Amsteg/Erstfeld, section Sedrun and/or sections Bodio/Faido and have also followed through with the tests. As was to be expected, the rate of failed mixes matched the level of the requirements. Thanks to this system, it was nevertheless possible to test complete concrete systems for all sections and to get them approved. The joint ventures tendering for the contracts were allowed to include only approved mix designs in their bids. Workability and durability are of paramount importance for cast and sprayed concrete mixes. Durability is influenced by the chosen mix design where binder concept and well-defined water content, i.e., impermeability, are determinant. Aggregates for AlpTransit are to be considered as given. The concrete mix design also determines workability. Because ambient conditions and also requirements with respect to workability are subjected to change, it is necessary that the mix designs include control measures. The choice and number of components for the concrete systems (cement, additives and admixtures) allow adaptation to changing conditions. For AlpTransit such adaptive measures must meet very strict requirements.

Jan 1, 2008

By Jonas Olsson

"The picture of China as an antiquated continent is changing rapidly and fast-forwarding progress is a fact in most infrastructural fields. Mining is not an exception. China is today the largest producer of aluminum, coal, steel, zinc, tin, lead and manganese and the country’s mineral resources comprising approximately 12% of the global reserves ranks them number three in the world after US and Russia.In order to feed the growth industry is needed to take extra ordinary strides to improve supply of raw material and Chinese mines are continuously being upgraded with the latest western technology to meet the increasing domestic demand of base metals.In Anshan located in China’s northeast province Liaoning we find one of the fastest developing mining companies, Angang Iron & Steel Group Co. Ltd. With their six mines that together process approximately 60 M ton iron ore/year Angang Iron & Steel Group Co. Ltd is the largest iron ore company in China. The group’s thorough pre-studies and technical evaluations over the past five years have made them very successful in both plant upgrades of existing operations and green field projects.INTRODUCTIONWe live in a time when the world market is gradually acclimatising to the global consequences of “The China effect”. An effect caused by a formerly sleeping giant nation that during the last years has awakened and developed beyond comparison, primarily because of booming infrastructure projects and demand for capital and consumer goods"

Jan 1, 2006

By R. E. Head

At the microscopic laboratory of the Bureau of Mines Intermountain Experiment Station, Salt Lake City, Utah, efforts are being made to devise methods of differentially coloring finely crashed minerals as a means for their identification. Staining would facilitate sight recognition of minerals under the microscope and would be of great value in the study of crushed ores, concentrates, and tailings. Since the treatment of ores for their beneficiation is primarily based on the recovery of the minerals containing the clements of value, it is extremely important that these minerals should be known and that a method for quickly determining them when in minute fragments should be available. Herein lies one of the greatest uses for color methods. In many cases it is a difficult matter for even the trained petrographer and mineralogist to identify finely crushed minerals quickly. Although ordinary petrographic methods are accurate, they are often time--consuming and are not suitable to the needs of millmen who require, especially in the examination of tailings a method for determining minerals by inspection.

Jan 1, 1929

In the past few years the Rietveld method emerged as a routine tool for quantitative phase analysis (QPA) from X-ray diffraction data. Fast and reliable results became possible by combining modern computer technology and optimised mathematical algorithms with the fundamental parameters approach in the Bruker AXS TOPAS software. Here the routine analysis of bauxite raw material and of aluminium bath electrolyte is presented. The accuracy of bauxite quantification was tested by analysing the IUCr round robin sample. An agreement of better than one per cent was obtained for minor constituents and a maximum deviation of 2.5 per cent for the major phases. This is excellent agreement with expected results from weighting. Ten different phases were quantified in natural samples from Turkey with a precision better 0.5 per cent for the major phases and one per cent for the minor phases. Additionally, crystallite sizes were obtained from the peak profiles that give valuable information for the processability of the material. XRD data from solidified aluminium electrolytes were rapidly measured using silicon strip detector technology. With the LynxEyeTM detector full patterns were collected in 90 seconds and analysed with TOPAS. It is shown how to derive well-established measures such as bath ratio and excess AlF3 from the Rietveld results. These measures are widely used in aluminium production and readily available with very high precision. The excellent agreement with ALCAN reference data demonstrates the outstanding accuracy of the method. The mean deviation between here presented results and reference data is below 0.5 per cent for total CaF2, below 0.25 per cent for excess AlF3 and 0.02 for the bath ratio. The precision of the method was evaluated by repeated measurements.

Jan 1, 2008

By S M. C Verryn

Through the application of the Rietveld method, X-ray diffraction analysis has developed into a fully quantitative method for phase analysis of metallurgical products. The Rietveld method itself has progressed from an unstable method that required constant operator intervention to a stable and robust method suited even for routine process control. Knowledge of the crystal structures of the major phases is essential for Rietveld analysis, and these are well known for most minerals and major phases in metallurgical products. It provides the basic structural information necessary for the determination of mineral stoichiometry and for elucidating solid solution behaviour. Modern methods, such as simulated annealing and charge flipping, permits the determination of crystal structures from powder data. Unit cell data can be used where conventional microchemical analysis is unable to provide an answer to the extent of solid solution in ilmenite roasting. Unit cell data (by XRD) is used to determine the amount of roasting necessary for the development of magnetisation to be able to separate chromite from an ilmenite concentrate. Phase quantification is probably the most widely used application of XRD analysis. It is used for materials balance in the minerals and cement industries, and it is finding novel applications in the iron and steel industry. Applications of XRD in high-temperature metallurgical processes are increasing. In this paper the phase chemistry of iron ore sinters, the evaluation of subsolidus reactions in titania slags and the identification of furnace accretions are discussed. Despite the success of the Rietveld method in phase quantification, the method still needs further development in the quantification of closely related or polytypic phases. The quantification of pyrrhotite phases using various Rietveld programs still gives ambiguous results. This is also true for the different SFCA phases in iron ore sinters. Clearly the analysis of similar phases, differing only in the presence of weak superlattice reflections is still problematic.

Jan 1, 2008

By R. V. Ramani

This volume is the third of a four-volume final report on research carried out under a contract from the U.S. Bureau of Mines on the development of a computer simulation model for surface mine reclamation planning. The other volumes are titled as follows: Volume I: Ore Reserve Estimation, Volume II: Dragline Model, and Volume IV: User's Manual for OPMHS/2. The Mine Coordinate Generator System serves as an interface between the Geology and Reserves System (Volume I, final report) and OPMHS/2 (Volume IV, final report) to provide local mine grid information which is used as input to the decision making process and dynamic simulation routines of OPMHS/2. After the Geology and Reserves System has been successfully run for a property, a data base containing values for each grid cell covering the property is created at the end of execution, if chosen as an option by the user. The Mine Coordinate Generator reads this information and creates a special direct access data set from the sequential data input. When information defining the mine grid is read, the values present in the property grid are for the interpolation of values for each mine block.

Jan 1, 1985

By A. C. Emery

The physical and chemical properties for the metalliferrous feed materials to the Imperial Smelting Process blast furnace are defined and the means of achieving these properties by the sintering or briquetting routes discussed. Modern sinter plant performance data is included with a plant flow sheet showing draughting patterns. The necessity for ensuring an adequate SO2 content in sinter machine gases when roasting sulphide materials to enable conversion to sulphuric acid in a contact acid plant is described. The ability of the process to consume limited quantities of oxide materials, residues from other processes and other secondary sources is discussed. The argument for a briquetting route is developed out of this limitation and the merits of cold and hot briquetting examined. Development work on the hot briquetting route for this purpose is briefly described and several flow sheets outlining possible applications for hot briquetting to different raw material situations including the preparation of low lead charges for the furnace are presented.

Jan 1, 1977

By B McCreath

Industrial process water for the Commodore Coal Mine and the adjoining Millmerran Power Station is provided by pumping secondary treated sewage effluent 100 km from the Wetalla Sewage Treatment Plant near Toowoomba. (A separate source is used for potable water.) The effluent is not of sufficient quality for discharge to a watercourse, but it is suitable, with further treatment, for the mine and power station. In designing and constructing the pipeline, special emphasis was placed on preventing accidental spills or planned releases to the environment. The pipeline and associated works can transfer 1000 ML/annum for reuse in the coal mine and power station.

Jan 1, 2003

By S. P. Liebenberg

During the past fifteen years significant progress has been made on carbon-in-pulp (CIP) technology for the extraction of gold. While most research on the mechanisms and kinetics of CIP sub-processes has focused on the adsorption step only, auxiliary unit operations such as elution have received less attention. The mathematical models which have been developed for elution at the University of Stellenbosch can be used for design as well as process optimisation by incorporation into an overall CIP simulation program. Except for these models, no other comprehensive models for the complex elution process are available. It is the aim of this paper to review recent modelling work on competitive elution from activated carbon.

Jan 1, 1995

By Gino Vogt

In mechanized tunnelling operations performance, consumption and safety are main factors for jobsites. One of the most important components effecting these factors, especially in slurry TBM operations, are Slurry Treatment Plants (STPs). Inadequate/ suboptimally dimensioned and designed STPs create bottlenecks for tunnelling operation and jeopardize time schedules and performance. Inefficiently planned STPs could drastically increase consumption figures such as electrical power, bentonite, water and polymers, etc. Inaccurately selected and treated suspension properties can cause a high-risk potential for the whole job. This paper debates the relevant key parameters for STPs from start to finish of a project and its results in influencing factors from the manufacturer´s point of view.

Jun 13, 2021

By Gino Vogt

In mechanized tunnelling operations, performance, consumption and safety are main factors for jobsites. One of the most important components effecting these factors, especially in slurry TBM operations, are Slurry Treatment Plants (STPs). Inadequately dimensioned and designed STPs create bottlenecks for tunnelling operation and jeopardize time schedules and performance. Inefficiently planned STPs could drastically increase consumption figures such as electrical power, bentonite, water polymers, etc. Inaccurately selected and treated suspension properties can cause a high-risk potential for the whole project. This paper debates the relevant key parameters for STPs from start to finish of a project and its results in influencing factors from the manufacturer’s point of view.

Dec 1, 2022

By L. C. IlsLey

[In 1922 a conference of representative coal-mine operators, cable manufacturers, mining-machine manufacturers, and representatives of the United States Bur eau of Mines vas held at the Pittsburgh Experiment Station, regarding suitable cables for use with permissible raining machines. This conference recommended that the Bureau investigate rubber-sheathed trailing cables in order to obtain specifications for tests leading to approval for rise with mining machines. Effective until such time as an investigation could be made, the bureau asked the several manufacturers of approved mining machines to recommend cables for wise with their machines. In general the Cables recommended tentatively approved. Arrangements for the tests were completed in 1927. Concentric-type cables were investigated first, and Reports of Investigations, Serial No. 2909, covering the tests, was issued in January, 1929.]

Jan 1, 1929

A kinetic model for leaching of various metals with different lixiviants in a batch system has been developed. Material balances for reactants and products at the solid/liquid interface were formulated and solutions to these balances were obtained in view of practical conditions. Special emphasis has been given to examine mixed controlled reaction systems where both heterogenous reaction and mass transfer play important role on the overall rate expression. The resulting kinetic expressions for either powder or rotating disc are discussed in light of experimental findings for various metals. Examples of the metal dissolution systems considered in this study include cobalt, nickel, copper and gold in acid, cyanide or ammoniacal solutions.

Jan 1, 1992

By Jack O?Hearn

A liquid and solid waste management plan for an operating uranium ore processing mill was developed to efficiently and effectively dispose of existing solid wastes and related, affected surface and ground water resources. The goal of this management plan was to achieve satisfactory clean up of these existing wastes ad their by-products as well as to prevent similar situations from occurring in the future. An existing, modern system of synthetically lined tailings ponds, constructed after many years of mill operations, now provides an approved site for the disposal and containment of waste streams currently generated by the mill. This system was thought to be readily adaptable to serve as a key element of the waste management plan. The potential presence of extra capacity in these ponds could eliminate or reduce expenditures for new facilities required solely for proper management of liquid and solid wastes generated by operations prior to construction of the modern tailings ponds as well as for a range of anticipated future operations.

Jan 1, 1984

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l'wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade' in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965

By A. C. Fieldner

The Bureau of Mires in its investigations of gas masks for use in mines and allied industries has studied and developed various types of masks for protection against noxious uses and furies that may be present in atmospheres encountered in mines, metallurgical works, chemical and other industries. As a result of these investigations, the Bureau issued a schedule5 of tests under which manufacturer who voluntarily submit masks for examination and test, are issued an approval certificate for masks that meet the Bureau's specifications. In the Bureau's schedule, masks arc classified by types of gases removed, as type A masks for protection against acid gases; B; organic vapor; C, ammonia; D, carbon monoxide; E, smoke, dust, and mist; F, special gases; combination types, and type N, for protection in air against all gases, vapors, and smokes. The purpose of this paper is to describe the physical and chemical tests that were conducted on a type N mask, the protective principles and construction of the essential elements of the canister and attachments, and the uses and limitations of this type of mask. The mask tested is known as the all-service mask, manufactured by the Mine Safety Appliances Co., Pittsburgh, Pa;, and was approved (approval No. 1403) by the Bureau on July 1, 1924, for protection from all classes of poisonous vapors, gases and smokes in air.

Jan 1, 1925

By R. F. Krueger, L. C. Vogel

A design is presented for an electrical analog computer which can solve non-steady state heat transfer problems in an extensive radial forrnation containing a moving cylindrical source. The computer is used to simulate a .simplified thermal oil recovery process in which heat transfer from a moving, constant temperature source takes place radially by conduction only. Temperature distribution curves are .shown for several different assumed modes of travel for the heat source. The data are used to estimate the residual fuel requirements necessary to maintain a self-propagating isotherma1 front for the particular system being studied. Although the computer is designed to represent an unique system. conversion factors can he adjusted to show the effects of changing the assumed values of system constants, such as thermal conductivity of the formation and temperature of the source isotherm. Examples are given to illustrate the relative influence the assumed values of these variab1es will have upon the quantity of fuel required to maintain the source. The maximum effect of heat transfer by the flowing air stream is estimated mathematically, and full requirements for this system are shown to he markedly reduced. Inasmuch as the examples discussrd refer to a simplified process, the results are not directly applicable to a practical field operation. It is believed, however, that the data il1ustr-ate some general trends which are important in thermal recovery processes. Data from laboratory and field experimentation can he used to modify the computer to take into account the influence of heat transfer by various mechanisms, for example, by injected air and by fluids ahead of the hot zone. With .such refinements it would be possible to estimate more accurately the limiting values for the rate of travel of the high temperature front and for the required air- injection rates. Use of this computer should aid in evaluating the economic feasibility of oil recovery by various thermal processes. It is hoped this paper will stimulate further work by others to help accomplish this objective. As the costs of exploration for and development of new oil fields rise. increasing the recovery of oil from established fields becomes more and more important. In fields containing low gravity crude oil, ultimate recoveries by primary means are sometimes less than 10 per cent and often total only 10 to 20 per cent of the oil in place. Conventional secondary recovery methods are not always effective in increasing this total. Methods which have been proposed for increasing the recovery of viscous oils include thermal processes for increasing the mobility of the oil. One method is to provide a moving heat source generated within the formation to heat the oil and a flowing gaseous medium (for example, air) to sweep the oil to the producing wells. The possibility of such a process has intrigued engineers for many years.'. '." but little or no information has been available in the literature relative to the technical or economic feasibility of this method. Recently, however, interest has been revived by publication of laboratory and field test results indicating the feasibility of maintaining

Jan 1, 1956

By Javier Ramirez

"Recent R&D pilot plant testing was done to validate a full industrial scale system for recovering residual magnetite from the tails of an iron ore concentration plant. The recovery system is based on an autogenous heavy media separator treating a tailings slurry at 0.45% solids by weight. A 3,100 m3/h capacity concentrator was installed based on the testing findings. Excellent metallurgical results have been observed in two years of continuous operation. This experience is the basis for the proposal of a novel process consisting of the preconcentration of base metals ores; the idea being to obtain a heavy bulk concentrate of the polymetallic minerals and discarding in one step the light gangue mineral components. The bulk concentrate then proceeds to conventional froth flotation. The reduced volumetric flow of the bulk concentrate allows a reduction in the size of the subsequent flotation circuit. A prerequisite for the heavy media separation is a fine size grinding of the ore and a correspondingly high degree of liberation of the mineral species to be recovered. A process scheme is also presented in which the gravity concentrator works in conjunction with a companion tailings thickener for process water recovery. The underflow from this thickener, having paste consistency, can be sent to a tailings dam or mixed with Portland cement for mine backfill. The process water in the system is managed at an estimated recovery in excess of 98%. Additional R&D work using this novel approach is being considered by a large iron ore concentrator for removal of liberated silica from the final concentrate; and for upgrading 3.5 million tons of a marginal hematite reserve owned by the mining company.INTRODUCTIONGravity preconcentration (static and dynamic) of sulphides prior to froth flotation has been and is being practiced at various concentrator plants (Asarco´s Young Mill: heavy media cone; Mount Isa: DSM cyclone; Afton Mines: Denver jigs; Tsumeb Mine: Reichert cone) (Burt, 1984). The idea behind installing preconcentration equipment is to reduce the volume of feed processed on flotation, thus requiring smaller flotation plants although other advantages may be of importance, such as obtaining richer concentrates due to higher grade feed, better process water and energy management, and reduced flotation reagent consumption.The SedconTM solid/liquid separator is a versatile process unit patented in Mexico (MX/u/2007/000305). As a gravity device, it may be classified as an autogenous heavy media dynamic concentrator. Figure 1 depicts the Sedcon (Sedimentador de conos) separator. The four main components are as follows: the feedwell for efficient mixing of the pulp with dilution water and flocculant (and coagulant for water clarification); the inner cones (passive elements for solid/liquid separation); the discharge underflow cone; and the scraper mechanism. The standard discharge cone is a 60° inclined cone for general applications. For paste tailings thickening applications, a deep cone with a 69° inclined cone is used."

Jan 1, 2016

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?') is described. Essentially it involves the 'floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?' and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?' is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,' or foil,' specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.' Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?') is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?'/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?'/? or the absolute value of ?' for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?' for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?'/? is large; that is, for cases where no other technique is available for measuring ?'. Aside from trying to learn more about surfaces through measuring ? and ?', the primary reason for wanting values of ? or ?' is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.' where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?' vs ki, it is thus possible

Jan 1, 1963