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By Ian MacKenzie

Over the past twelve years, professionals such as architects, engineers, accountants, and attorneys have not had to pay a great deal of attention to GST. The fees charged to clients (outputs) have not been subject to GST, but they have had to pay GST on al purchases of materials and taxable services relating to their activities.

Jan 1, 1990

By Michael D. Zuber

This paper discusses the use of a coalbed methane simulator that has been modified to account for the removal of grid blocks as a function of time to estimate gas emission and production for a variety of mine-associated problems. The specialized features of the simulator are presented. Example applications illustrate the models' use in estimating methane emission rates during mine roadway development, and estimation of longwall panel degasification by horizontal boreholes.

Jan 1, 1997

By S. P. Rivers

The stainless steel industry re1ies on nitric-hydrofluoric acid (HNO,/HF) pickling solutions to remove surface contaminants and maintain the corrosion resistance of the steel. More stringent environmental guide1ines are expected to be placed on the disposal of these solutions which could significantly increase processing costs. The U.S. Bureau of Mines has been conducting research to develop a process for recycling depleted pickling solutions, thus reducing the quantity of by product acids generated. Research has shown that F- can be liberated from the predominant iron fluoride species (FeF,') by using oxalic acid in an electrodialysis cell. Ion selective membranes allow dissolved metals in the depleted solution to be replaced with hydronium ions by metathesis, thereby regenerating the HF. The regenerated HN03/HF is then retained in the pick1ing solution. This paper reports on the research effort at the U.S. Bureau of Mines Rolla Research Center to apply electrodialytic recycling to HN03/HF pickling solutions.

Jan 1, 1993

By Adrian E. Scheidegger

Recently, a new theory of the subsidence of rock masses has been advanced by Litwiniszyn and coworkers, which is based on the notion that the individual rock particles perform random walks. It is shown in the present paper that the final equations of the random walk theory can be justified from general principles of statistical mechanics in which no specific theoretical model of particle behavior has to be made. The theory appears to account appropriately for subsidence phenomena.

Jan 1, 1966

By Atsushi Shibayama, Toyohisa Fujita, Luo Lin, Toshio Miyazaki

A novel process is developed in this study for separation of tungsten and vanadium from a leach solution of tungsten alloy scraps. Specifically, a magnesium salt combined ammonium solution is employed to precipitate vanadium and impurities in the purification of the leach solution. This separates vanadium from tungsten by rejecting tungsten in aqueous solution. Finally, tungsten is recovered as the form of ammonium para-tungstate (APT). Vanadium is recovered as the form of ammonium meta-vanadate(AMV).

Jan 1, 2003

By Jong-Jip Kim, J. G. Byrne, W. Kim, In-Ok Shim, John E. Flinn

"Two rapid solidification processes for 304 stainless steel were studied: centrifugal atomization (CA) in a helium atmosphere and atomization by exposing argon-containing melt to vacuum (VGA). Positron annihilation and x-ray line broadening measurements of explosively consolidated monoliths were used to clarify microhardness measurements as a function of annealing temperature. Interesting differences in positron response between CA and VGA materials are ascribed to more carbide formation in the CA material than in the VGA material in the 600 0C range. In addition, hot isostatic pressing of the CA material was examined as to the relations between mechanical behavior, pore shape, and relative density. A variable stress concentration factor is introduced into the theory to allow for changing pore shape as relative density increases.IntroductionThere are many potential advantages of rapid solidification processing (RSP), such as a high degree of matrix supersaturation, finely dispersed microstructures, improved chemical homogeneity, and retention of metastable phases, which have been studied extensively. To consolidate rapidly solidified material which is in powder form into useful shapes often requires subjecting the material to elevated temperature for extended periods of time under mechanical forces, as in hot isostatic pressing or hot extrusion. In such cases, some of the characteristics of the rapid-cooling step can be strongly affected. An alternative is dynamic consolidation (1), for example by explosive forming, where the time frame at least is extremely short.In the present work, effects of the consolidation processes of hot isostatic pressing (HIP) and explosive forming in a die are examined. The particular material is 304 stainless steel. The characteristics of both RS and VGA 304 stainless-steel powders were described by Wright, Flinn, and Korth (2) earlier."

Jan 1, 1988

By M. Nduna

Surface properties of metal sulphides have a great significance in various areas of engineering and science, such as acid mine drainage, contaminant sorption, and metal separation. In various attempts at producing metal sulphide particles from synthetic solutions, prodigious quantities of nuclei that grow only to colloidal dimensions have been frequently reported. This copious nucleation is promoted by the high levels of supersaturation that characterize most precipitation reactions. Colloidal particle formation in precipi¬tation-based separation processes results in sub-optimal solid-liquid separation, which is alleviated by the production of more highly crystalline particles or agglomerates. The current work approaches this challenge from an electrochemistry perspective, by measuring surface charge potential of precipitant particles during metal sulphide precipitation with respect to the concentration of metal sulphide lattice ions in solution. Electrophoresis was used to measure the metal sulphide particle zeta potential and the settling properties were obtained by performing settleability measurements using an Imhoff settling cone. A suspension of copper sulphide particles was precipitated from synthetic solutions of copper and sulphide ions at equimolar concentrations. Immediately after precipitation the copper sulphide particles had a zeta potential of -50 mV and a settleability of about 7 ml.l-1. With the addition of copper ions the settleability increased by a factor of nearly three times and the zeta potential also increased to a maximum of -40 mV. A decrease in zeta potential to a minimum of -60 mV was observed after the addition of sulphide ions and this was associated with a settleability of 0 ml.l-1.

Jan 1, 2013

By Rex B. McLellan, W. A. Oates

FROM a consideration of the application of the Gibbs-Duhem equation to multicomponent systems arken' derived the following equation applying to dilute solutions of a solute, 2, dissolved in a binary solution, 1-3:

Jan 1, 1969

By M. J. Pool, P. J. Spencer, R. V. Miner

The partial molar heat of solution of rhodiunz in liquid lin and Rh-Sn alloys has been measured as a function of rhodium concentration at 700" , 725" , 750" , and 775°K. The values at infinite dilution are very exo thermic, ranging from -29,950 to -28,260 cal per g-atom Rh at 700" and 775"K, respectively. At the solubility limit the heat of solution becomes sharply nzore exothermic and has permitted the liquidus boundary to be accurately established at each temperature. From the measurements in the two-phase region of liquid Plus RhSn, the heat of formation of RhSn,has been determined. A large increase in the heat of formation between 725" and 750°K suggests the possibility of a phase transformation in this compound. V ERY few measurements have been made of the heats of solution of transition metals in liquid tin; yet those values that are available are of great interest because of their very large exothermic nature. For example, the heat of solution at infinite dilution of palladium in tin has been measured as about -26,000 cal per g-atom (625" to 800°~),' while the heat of solution at infinite dilution of platinum is even more exothermic at -28,591 cal per g-atom (914°K).' These values are of the same order of magnitude as the heat of formation of many intermetallic compounds and as such clearly indicate that very strong bonding must exist between the solute and tin atoms in the liquid solutions. Rhodium might be expected to display similar solution characteristics in tin in view of its close electronic resemblance to palladium and platinum. Since no thermodynamic data are available for Rh-Sn alloys, rhodium was chosen as an appropriate solute for further investigation of transition-metal systems with highly exothermic heats of solution at infinite dilution. EXPERIMENTAL The heat of solution of rhodium in dilute Rh-Sn liquid solutions was measured as a functlon of rhodium concentration at 700°, 725", 750°, and 775°K. The liquid-metal solution calorimeter used in this work has been fully described elsewhere. At the start of each series of measurements, the solvent bath consisted of about 0.5 g-atoms of 99.9+ pct pure tin. To this was made a number of small rhodium additions, about 0.0005 g-atoms each, and the heat of solution was measured for each. Rhodium of 99.9+ pct purity in powder form was used in order to promote rapid dissolution in the liquid tin. The powder specimens were contained in tin foil stated to be purified (lead-free). This foil was found to have no measurable heat of solution in pure tin so the effect of any impurities could be neglected. The energy equivalent of the calorimeter was experi- mentally determined by dropping tungsten and/or tin specimens at intervals during each series of rhodium drops. The tungsten and tin used were 99.95 and 99.999+ pct pure, respectively. The only heat effect due to a tungsten drop, or a tin drop at low rhodium concentrations in the bath, is the sensible heat of the specimen. The heat content of these materials is well-established and is presented in the compilation of Hultgren et al. 4 As the rhodium concentration in the tin bath increases a small heat effect arises from the reaction: Sn (liquid, T) — & (soln, T) where T is the temperature of the tin bath. Where necessary, this heat of solution of tin was determined by Gibbs-Duhem integration, and corrections were made to the heat effect of the tin calibration specimens and the tin foil containing the rhodium specimens. RESULTS AND DISCUSSION The calculated values of the heat of solution of rhodium in dilute Rh-Sn alloys as a function of composition are shown graphically in Fig. 1. The values have been corrected for the sensible heat of the specimens, initially at 273"K, and apply to the reaction:

Jan 1, 1969

By D. B. Jugle, J. B. Darby, O. J. Kleppa

A systematic study has been made of the kinetics of solution under steady state, dynamic conditions of titanium, vanadium, chromium, iron, cobalt, and nickel in liquid aluminum. It was found that the temperature dependence of the solution rate obeyed an Arrhenius-type rate equation, and that at a given temperature the rate of solution of the various solutes correlates quantitatively with the equilibrium solubility of the solute in liquid aluminum. These results are consistent with a mechanism where the rate-controlling step is the diffusion of solute atoms through a liquid boundary layer. THE present study was initially started in order to explore the feasibility of liquid-metal solution calorimetry for transition metals and alloys. Previous work1 in this field employing liquid tin as a solvent at temperatures in the 500' to 600' range had indicated that the rates of solution of most transition metals in tin are very low. Under such conditions effective solution calorimetry is difficult. The objective of the present investigation was two-fold: a) To obtain, as far as possible, quantitative data on the rates of solution of a series of transition elements in liquid aluminum. b) To explore whether liquid aluminum might be a suitable solvent for liquid-metal calorimetry. In the course of this work a comprehensive set of data was obtained on the steady state rates of solution of transition metals in a common liquid-metal solvent. The results are consistent with the boundary layer model, which assumes that the rate-controlling step consists of diffusion of solute atoms through a viscous liquid layer. EXPERIMENTAL PROCEDURE A vacuum-tight stainless steel vessel was surrounded by a resistance furnace, as shown in Fig. 1. In all experiments the temperature of the liquid solvent was controlled to 2.5' by means of a Micromax controller. A high-vacuum manifold connected to the vessel maintained a vacuum of 1 x 105 mm of Hg or better. The vacuum vessel was equipped with a charging section isolated from the working chamber by a vacuum-tight gate valve. This arrangement allowed the specimen holder to be removed or inserted into the apparatus without removal of the liquid metal bath. The specimen holder was suspended from a closed end stainless steel tube, which also served as the thermocouple protection tube. The portion of the tube that was below the solvent level was surrounded by an alumina protection tube to isolate it from the liquid metal bath. The stainless steel tube was connected through a rotary vacuum seal and a gear train to a fractional horsepower motor. For most experiments the tube was rotated at a constant

Jan 1, 1963

By Árpád B. Palotás, Adel F. Sarofim, John B. Vander Sande, Lenore Rainey Christian, J. Feldermann

"Interest in the fine structure of soots and carbon blacks is motivated by a variety of possible applications. The structure provides information on the origins of the particles and on their adsorptive and reactive properties. This paper describes a method for quantification of the structure of soots and carbon blacks based on direct electron microscopic observation followed by image analysis of these materials. High-resolution transmission electron microscopy (HRTEM) provides a very detailed observation of particle structure. The differences in soot structure, because of its complexity, may not be easily quantifiable with the human eye; therefore, high-level computer software has been used to manipulate HRTEM images. This technique involves the application of fast Fourier transforms (FFT) to single particles and the measurement of characteristic parameters such as interplanar spacings and crystallite sizes from these particles. The methodology and application of this characterization technique are presented here. Results are shown for dif¬ferent samples obtained from soot and carbon black particles selected to illustrate the capabilities of the methodology. Quantitative information can be obtained on structural characteristics, e.g., interplanar spacing, circularity, orientation, elongation, and length distribution of lattice fringes, as well as on the fractional coverage of the extracted pattern. c 1996 Wiley-Liss, Inc.This paper presents a combination of techniques for recognizing and classifying different carbonaceous materials, using their structural morphology. A new method to assess and quantify the parameters which define such structures is proposed and discussed. The technique is based on the use of HRTEM (high-resolution transmission electron microscopy) and computational image analysis.It is well-known that carbonaceous materials like graphite, soots, coals, cokes, chars, etc. possess characteristic structural appearances which can vary from mostly random or amorphous to a perfectly ordered graphitic crystalline structure (Buseck and Bo-Jun, 1985; Buseck et al., 1987). The carbon structure has been variously described as turbostratic (Oberlin, 1989) or as crumpled sheets (Rouzaud et al., 1991) to indicate that parallel layering, reminiscent of graphite, is observed over dimensions of nanometers, but that these planes or crystallites show disorder over larger scales. The degree of order of such structures is strongly dependent on the thermal treatment of the material as well as on the composition of the source of the carbonaceous material. The value of the electron microscope in studying the morphology of such materials has been well-established, and abundant information is available (Ishiguro et al., 1991; Lahaye and Prado, 1978; Buseck, 1992).The use of HRTEM has brought further insight into this matter. Qualitative assessment of the structural order of such materials has been attempted over a long period of time in order to differentiate between various sources or treatments. There is, to date, no successful method available for quantifying the structural characteristics of various carbonaceous materials. This paper presents a technique which is able to recognize dif-ferent materials and to quantify the structural parameters of those materials using HRTEM and computational image analysis, including pattern recognition techniques.In the case of perfectly ordered graphitic crystals, electron diffraction is widely used for obtaining details on structure. Analysis of diffraction patterns can reveal parameters such as interplanar spacing, d002, crystallite size along the c-axis, Lc, crystal size in the plane of the layers, L., mean number of crystallites, Nc, etc.Complicated electron microscopy methods such as defocusing, tilted illumination, axial illumination, etc., often have to be used in order to characterize complex materials such as randomly oriented crystals in soots and carbons. Obtaining the right fo"

Jan 1, 1998

By Axel Preusse

For the last 150 years, subsidence damage to the surface has been an unavoidable phenomenon associated with underground coal mining. In particular, the mechanization of mining methods in multiple seam mining and the concentration of mining activities in densely populated European metropolitan areas (e.g., Ruhr, Upper Silesian industrial region) have led to mining having a very strong influence on the earth?s surface. In both these regions, surface subsidence of more than 20m has been reported up to now in comparison to the original state. Underground coal mining in these regions strongly impairs all kinds of surface use, such as urban and industrial development, infrastructure (roads, waterways, and railways) and pipelines?without restricting the functionality of those objects to a greater extent. Demanding and, in some cases, globally unique engineering solutions have been developed and implemented for this purpose. The previously mentioned mining and industrial regions are still very strongly characterized by the (increasingly declining) coal industry and will remain dependent to a large extent and for an indefinite period on artificial drainage measures because subsidence that has already occurred is irreversible. This paper will primarily discuss the prediction of subsidence that is caused by intensive multiple seam mining and its influence on surface objects (e.g., underground pipelines). However, an approach for predicting ground uplifts due to rising mine water as a consequence of mine closures will also be described.

Jan 1, 2012

Environmental and public concerns and the banned use of cyanide for the recovery of gold in some parts of the world have heightened the search for an alternative lixiviant to cyanide. Thiosulfate appears to be the most promising alternative to cyanide due to thiosulfate being non-toxic, relatively cheap compared to cyanide and generally gold recoveries are similar to those of cyanide. The most widely researched thiosulfate process is one where copper ions and ammonia are added to the solution. This paper reviews the leaching of gold in thiosulfate solutions and the contributions of the research at Monash University to the understanding of the gold oxidation reaction in thiosulfate solutions, the solution chemistry when copper ions, ammonia and oxygen are present, the influence of the changing solution chemistry on the gold leach kinetics, and the application of thiosulfate in the leaching of gold from ores. It is clearly shown that the gold oxidation rate is hindered in thiosulfate solutions. In the presence of copper ions the gold oxidation rate though is significantly enhanced and thus is why copper(II) is more effective than other oxidants in the thiosulfate leach system. The copper-ammonia-thiosulfate leach solution chemistry is shown to be very complex, especially in the presence of oxygen as the rate of thiosulfate oxidation increases and the majority of the copper ions are not maintained in the copper(II) oxidation state. The thiosulfate oxidation rate must also be maintained low as an intermediate thiosulfate oxidation product hinders gold leaching. In optimising the recovery of gold from ores with copper-ammonia-thiosulfate leach solutions it is important to evaluate and minimise any negative effect an ore may have on the leach solution chemistry and hence gold leaching.

Jan 1, 2003

By Earl L. H. Sackett

Barite, although not a glamour mineral and probably little known to many of those in the mining business, is produced in the US. in very respectable quantities and is an important factor in the mineral economy of this country. The scope of the various uses of this mineral is perhaps one of the most misunderstood things about it, for it is surprising how many of those with a casual knowledge of the subject speak of its primary utilization in terms of paint pigments and barium chemicals. The life blood of barite utilization, however, is the petroleum industry by virtue of its dependence on this high specific gravity, inert mineral as the weighting material in its drilling fluids. From 80 to 85% of barite usage in the U. S. is accounted for in this manner-in fact, its role in oil well drilling is the only excuse for some of the large-scale barite production facilities which have been developed. Other uses are important and widely varied, but comparatively they are of small scale. They include fine crushed barite of low iron content as a component in glass manufacture, barite as a source material for manufacture of barium chemicals, finely divided barite as a component of some rubbers and ground, bleached barite in pigments. The formerly substantial use of barite in lithopone, however, has declined markedly because of replacement of lithopone by titanium pigments

Jan 5, 1962

The sharp deterioration in Au~tralia'S ternn of trade in recent years and the accumulating national debt highlight the need for a restructuring of the economy which is highly dependent upon primary agricultural and mineral commodity exports (figure 1). Table I gives an indication of the value that can be added to raw material by mineral processing. Significantly higher value is added through downstream manufacturing. In 1987, the mining and rural sectors accounted for 47010 and 38010 respectively of total exports valued at $35,782 million (figure 2). The export contribution from minerals comprised $12,266 mil- lion from unprocessed ores and concentrates and $4,668 million from metals and processed minerals including some simple manufactures. Coal accounted for 450/s of total primary mineral exports. Iron ore and alumina are other important mineral exports, while gold and aluminium are major metal exports. (Figure 3) Australia's minerals are now traded in a much more competi- tive and oversupplied market in contrast to the 1960's and 1970's period which was characterised by increasing exports of largely unprocessed ores and concentrates. Since the early 1980's (I cI) resscd )ver~cas nutrkcts and km rununodlity liriccs ha~c hcen the product of excess capacity installed to satisfy a forecast high growth in demand which never eventuated due to the world reces- sion. During this period the emphasis on technology development was focussed on reducing costs through increased production effi- ciencies in order to maintain competitiveness.

Jan 1, 1988

By Gordan Marrs, O. Matwijenko

"The Kidd Creek metallurgical site has been highly integrated to maximize revenues from its base metals mines. The site's operations include a Concentrator processing 4.3 million tonnes per year of copper-zinc ore, a Copper complex producing 100,000 tonnes per year copper cathode and a Zinc Plant producing 130,000 tonnes per year of zinc metal. To improve operating efficiency with increasing emphasis on productivity, process control, process automation and process optimization have been augmented and expanded during the last decade.New microprocessor based control systems provided the opportunity for the capturing of an expanded number of process related measurements. As supervisory computers were already in place, databases could be generated with only increased disc space and database management programs required. Once the data had been accumulated and stored, a method was then required for handling, screening and sorting large volumes of information in relatively quick and easy terms in order that the stored information could be used. By 1984, a decision to use personal computers for accounting, engineering and management reporting provided the vehicle necessary to handle this data. Using commercially available software, large volumes of stored process data can be downloaded from existing databases, filtered, sorted, analyzed, graphed, displayed, projected, reported and distributed. All this can be performed in very little time."

Jan 1, 1989

By A. Hashempour, D. Javani

"Selection of an optimal bit is a critical issue in drilling engineering. Specific energy (SE) and Cost per Foot (CPF) are the most common methods for evaluation of bit efficiency and optimal bit selection. The major shortfall of both methods is that they do not directly account for geological and geomechanical parameters of formations being drilling. In this paper, results of using the two foregoing methods are compared using Formation Drillability (FD) method, which directly accounts for geological and geomechanical parameters of a formation. This method combines various geological and geomechanical parameters and yields a dimensionless parameter indicating the formation drilling hardness (drillability). Results of this study show that the amount of energy, cost and time spent for drilling a unit volume / length of an identical formation may vary in different wells. This is due to the fact that geological and geomechanical characteristics of a formation may vary among wells and even within short intervals of a single well. Therefore, an optimal bit may not be appropriately selected, if drilling and economical parameters are the only factors considered and the formation geological and geomechanical specifications are ignored.INTRODUCTIONMany authors such as Bilgesu, Al-Rashidi, Aminian, and Ameri (2000) and Clegg (2006) conducted research in the evaluation of bit performance and optimum bit selection. Almost all of them tried to establish a good relationship based on geomechanical parameters. Primary examples are the research done by Ubaldi (1999), Macini, Magagni, Da Dalt, and Valente (2007)."

Jan 1, 2015

Heap leaching has become one of the prime technologies used for the recovery of precious metals from low-grade ores over the past ten years. The recovery process involves mining and stacking the ore on engineered leach pads, with or without crushing and/or agglomeration, followed by leaching with a low concentration sodium cyanide solution. The metal-bearing, pregnant solution is then processed by zinc precipitation or activated carbon absorption to extract the precious metals. The leaching process continues until all economic metal values are removed at which time the spent heap leach pads, the leached materials and excess process solutions require decommissioning. The management of these solutions may present a potential challenge for successful and environmentally sound decommissioning due to their composition, volume or continuity of generation from the spent ore even though active leaching has been terminated. The principal objectives of solution management in decommissioning spent heap leach pads are to meet all operative environmental regulations in a cost-effective manner and to leave the pads in a condition where they do not present a long-term liability either to the operator or to the environment. This involves the reduction in volume of the residual process solutions and/or treatment of these solutions to where they meet applicable water quality criteria. In the past, the environmental and economic aspects of decommissioning and solution management have been overlooked or under-estimated during the planning of mining operations. As a result, there is a potential for long-term liabilities and costs to be recognized only at the end of active leaching, a time at which operating revenues and cash-flow are minimal. Therefore, the decommissioning process requires addressing at the mine planning stage and agencies now require that a plan for solution management after the cessation of operations be submitted prior to initiation of mining. This paper discusses aspects of process solution management during decommissioning, both in terms of quantity and quality, and how potential issues may be recognized and planned for in the initial stages of heap leach design.

Jan 1, 1992

By A. H. Winckers

"CAMIRO, The Canadian Mining Industry Research Organization, formerly known as MITEC, is a collaborative research organization of Canadian Mining Companies. It is comprised of Exploration, Metallurgical Processing and Mining Divisions.The Metallurgical Processing Division (MPD) has the mandate to contribute to the profitability, competitiveness, safety and growth of the Canadian mining industry by improving the efficiency and effectiveness of mineral processing and extractive metallurgy in an environmentally conscious manner through the development of innovative technology by managing cooperative industry focused research programs.Current membership includes about ten Canadian mining companies. Past research has largely focused on base metal mineral processing. The Division wants to expand its research base to include all areas of mineral processing and extractive metallurgy.Past performance and plans for the future will be highlighted in the presentation."

Jan 1, 1998

By M. Hoch

Equations are derived from statistical considerations to represent the activities of each component of an interstitial solution, and of a compound with a wide homogeneity range as a function of composition and temperature, based on the interaction energies between the various components, Eij. The equations are checked on the binary systems Fe-C, Ta-H, and Y-H, the ternary systems Ti-O-H, liquid Fe-C-0, and the compounds TiO, MnO, COO, and YH,. In all cases the present model represents the experimental data well. THE aim of this paper is to derive from statistical considerations the thermodynamic behavior of non-substitutional solid solutions. "Nonsubstitutional solid solution" means either an interstitial solid solution (carbon in iron, oxygen and hydrogen in hexagonal and bcc titanium, and so forth) or deviation from stoichiornetry in compounds (introduction of vacancies—removal of atoms in one or both lattice sites of compounds FeO, MnO, TiO, NbO, YH2). wagnerl and Fowler and Guggenheim considered the theory of compounds with small deviation from stoichiometry; Anderson includes larger deviations from stoichiometry, the defect being present in one component only, as vacancy and interstitial. Rees considers only vacancies in one of the components and introduces various kinds of sites for the component where the defect occurs; the various sites interact with different energies, thus giving isotherms with two or more plateaus. Both Rees and Anderson are mainly occupied in determining the limits of two-phase regions, and the defect interaction energy is determined from the critical point. Darken and Gurry5 gave a brief treatment of carbon solution in iron; Speiser and spretnak calculated the configurational entropy for binary interstitial solid solutions by assuming that each interstitial atom in the solution excludes a certain number of neighboring interstitial sites from occupancy. Use will be made of this concept later. Hoch et al treated transition metal oxides of the NaCl-type structure, and also oxygen solution in titanium.' The main aim was to determine the behavior of the activity of one of the components as a function of the composition in the single-phase region. In the present paper, the various interaction energies are discussed in detail and the similarity between interstitial solid solutions and deviation from stoichiometry in ionic compounds is shown. Both types of systems have in common that at least on one kind of lattice site only one kind of atom occurs; this gives a fixed frame to the system, permitting a much easier statistical treatment than for the substitu-tional solid solutions. (The theory is also applied to ternary systems.) The difference between an interstitial solution and deviation from stoichiometry can be explained as follows. In an interstitial solution in the pure or standard state the host atom or host structure is present alone and all the interstitial sites which are going to be filled when the interstitial atom is introduced are empty. The interstitial solution is now created by introducing atoms into this empty lattice. In the deviation from stoichiometry, both kinds of lattice sites are already occupied in a special fashion (all lattice sites occupied, or the same fraction of lattice sites empty, or one kind completely filled, the other only two-thirds). Deviation from stoichiometry removes atoms from lattice sites, adds them, or removes atoms from one kind of lattice site and introduces them on the other lattice site. Though both cases (interstitial solution and deviation from stoichiometry) lead almost to the same equations, they are treated separately. The treatment given below corresponds to the "regular solution"10 treatment of substitutional solid solutions. Speiser and spretnak's6 treatment is similar to the athermal solution in the substitutional use. a) INTERSTITIAL SOLID SOLUTIONS Theory. It will be assumed that there are N lat-tice sites occupied by the host atom (denoted by 1). Corresponding to those N lattice sites there are N octahedral and EN tetrahedral interstitial sites. If only one kind of interstitial atom is added, this in-

Jan 1, 1964