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By B Saunders, J Carpenter

PanAust’s Phu Kham copper-gold operation (Phu Kham) in Laos is currently limited by throughput in the Semi Autogenous Grinding (SAG) mill. The ability to accurately predict SAG mill throughput (throughput) is therefore critical to accurately forecast copper and gold production. During the fourth quarter of 2016 the proportion of hard unweathered rocks in the mill feed increased, resulting in a period of lower than expected throughput. These low throughput rates prompted a study with the aim of identifying a practical solution for throughput predictions. The study identified an empirical modelling approach based on actual SAG mill throughput rates. The empirical model was then optimised by linear programming to identify the ideal feed blend of unweathered rocks to achieve a maximum SAG mill throughput.Rock strength was the initial focus of the throughput study at Phu Kham because previous studies had identified a strong link between rock strength and throughput. It was determined that there was insufficient valid data to adequately model but sufficient data to qualitatively characterise rock strength. The data identified that the weathering and lithology had a controlling influence on the rock strength. Complicating throughput predictions were operational improvements (changes to blasting and mill settings) implemented in response to the lower than expected throughput. This created uncertainty with the throughput equations. A self-learning empirical modelling method was developed to predict the throughput by incorporating fundamental rock properties with operational practices and improvements. The method is based on the proportion of mill feed with similar weathering and lithology (a proxy for comminution performance) and the actual mill throughput using the SAG mill as the analytical instrument. The modelling method simultaneously incorporated the sum and interaction of unmodelled influences including blasting, crushing and mill settings. The empirical modelling method worked at Phu Kham because the lithology and weathering has an intuitive and observable controlling influence on SAG mill throughput. The modelling method is described along with a worked example of feed blend optimisation using linear programming.CITATION:Carpenter, J and Saunders, B, 2017. Empirical mill throughput modelling and linear programming for blend optimisation at the Phu Kham copper-gold operation, Laos, in Proceedings Tenth International Mining Geology Conference 2017, pp 291–296 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 20, 2017

By Zdenek D. Hora

British Columbia is an important producer of a variety of industrial minerals for both domestic and export markets. Some commodities such as limestone, dolomite, gypsum, calcium carbonate, silica, barite and magnetite are raw materials for well-established industries located in British Columbia, Alberta and northwestern USA. Others, like magnesite, sulphur, jade, asbestos, dimension stone and clay products, are mainly exported in processed form to overseas customers. Companies are developing markets for relatively new mineral products, including pumice, volcanic cinder and zeolites. A number of attractive geological targets have been identified by industry while research by government geologists has outlined the potential for refractory minerals, gemstones, garnet, nepheline syenite, carbonatites, residual kaolin, igneous apatite and peat.

Jan 1, 2001

By Jane Li, Kevin Tom

"Research has shown that broken rock on conveyor transport systems can contribute upwards of 50% towards the overall heat load in underground mines. However, few studies have made significant efforts to predict the temperature distribution of the ore and air simultaneously, which can help implement heat management strategies. The present investigation explores a transient, analytical heat transfer model to track ore-pile temperature distributions, along conveyor systems in an example underground mine. Production rate, ambient conditions, ore pile thickness and belt velocity are adjusted to evaluate the effect on dry and wet bulb temperatures.INTRODUCTIONWith an ever increasing demand on Earth’s resources due to a multitude of factors like population growth and step changes in technology, pressure on the mining industry to bring out more ore with improved margins is a persistent challenge. Typically, high-volume producing mining methods (i.e., exceeding 5000 tons per day (tpd)) such as sublevel and block caving, room and pillar, and longwall shall utilize belt conveyors instead of trucks as the primary haulage method to surface to save on operational costs (de la Vergne, 2014). However, studies have shown that when such material transport systems are installed at mine depths with virgin rock temperatures (VRT) above 40oC, the heat dissipated by the conveyed ore can account for over 50% of the underground heat-load (Pareja, 2000; Bluhm, Jones, Moreby, & von Glehn, 2012; van den Berg, Moreby, & Kok, 2015).Unlike other types of heat sources encountered in underground mines, such as diesel machines, strata, electrical devices, and autocompression, heat transfer by conveyed broken rock is much more difficult to estimate. The seminal work of McPherson (1993) states that broken rock heat transfer is a function of its surface area, and the air’s psychrometric condition. It is additionally a function of the VRT, its specific heat, production rate, heat transfer coefficient and the residence time (Bossard, 1997; Ross, Tuck, Stokes, & Lowndes, 1997). Consequently, few studies have attempted to analytically quantify the significance of ore heat flow."

Jan 1, 2019

By Yongzhong Xiao, Tiejun Chun, Jian Pan, Zhen He, Deqing Zhu

"In this paper, the reduction kinetics of low grade hematite ore was calculated. Mineralogy shows that the ROM (run of mine) ore is of low grade hematite ore type, assaying 27.2 wt% Fetotal and with main valuable minerals of hematite. The reduction kinetics shows that the reduction reaction rates of pellets with additive and without additive are all controlled by diffusion through the product layer. The calculated apparent activation energy of pellets with 12 wt% complex additive is 8.55 KJ/mol, dropping 62.23% compared to that of pellets without additive.IntroductionWith the rapid development of iron and steel industry in China, there has been a soaring demand for iron ores in the past decade. The imports of iron ores have increased from 148 million ton in 2003 to 620 million ton in 2010[1]. Therefore, large quantities of low grade iron resources are necessary to utilize in China at the moment. During the past years, extensive research has been carried out on the low grade hematite ores [2-6], such as reverse floatation, gravity separation, high-gradient magnetic separation and direct reduction-magnetic separation. Direct reduction-magnetic separation is an innovation way to treat the low grade hematite [7]. However, the research of reduction kinetics of low grade hematite is few. Some research about the reduction kinetics of reducing iron oxides by CO was studied [8]. The results indicated that the apparent activation energy is 8.0-28 KJ/mol when the reducing reaction is controlled by internal diffusion. The apparent activation energy is 50-75 KJ/mol when the reducing reaction is controlled by chemical reaction. In this paper, the reduction kinetics of pellets was also been studied."

Jan 1, 2012

1. In 2003, a total of 1,972 coal mining operations reported employment to the Mine Safety and Health Administration (MSHA). Coal mines comprised 13.7% of all mining operations. • Bituminous mines comprised 92.5% (n = 1,825) and anthracite mines 7.5% (n = 147) of coal mining operations. • More than 70% of all coal mines were located in three states: Kentucky (29.0%), West Virginia (20.9%), and Pennsylvania (20.2%). • Bituminous coal mines reported the production of over 1 billion coal tons.

Feb 1, 2005

By D. F. Malan, P. J. Le Roux

Almost no work has been published on the strength of pillars in mines exploiting the LG6/LG6A chromitite bands in the Western Bushveld Complex. The strength of these pillars is unknown, and the hard rock industry still uses the Hedley and Grant formula. Numerical modelling, using inelastic constitutive models, may be of some value in estimating the pillar strength, but this approach is difficult and prone to errors as many assumptions are made. This paper explores the alternative approach of the back-analysis of actual LG6/LG6A mining layouts, using displacement discontinuity codes to simulate the average pillar stresses on a mine-wide scale. From this, and underground observations, a ‘minimum’ pillar strength (K-value in the pillar strength formula) can be estimated. The codes TEXAN and Map3D are both used in the paper to simulate the actual pillar shapes and sizes in an LG6/LG6A mine. The results are encouraging as the two codes produced similar APS values for a complex pillar geometry. An estimated K-value of 77 MPa was determined for the LG6/LG6A pillars in this particular area. This is more or less similar to earlier work done for the UG2 chromitite seam, but higher than the K-value of 39 MPa for a linear formula obtained by other workers for LG6/LG6A pillars. Caution should therefore be exercised before using this higher value for all areas. The effect of element sizes and explicitly simulating the effect of the surface for shallow pillars is illustrated in the manuscript using both codes. The need for actual pillar observations and an iterative design process, which cycles between modelling and observations, is also emphasized.

Nov 27, 2024

By AIME AIME

THE Committee on Elimination of Waste in industry came into existence from a speech in Washington by Mr. ,Hoover, in November, in which, he said: It is primary to mention the three-phase waste in production: first, from intermittent employment; second, from unemployment that arises in shifting of industrial currents; and third; from strikes and lockouts. Beyond this elimination of waste there is another field of progress in the adoption of measures for positive improvement in production.

Jan 1, 1921

By E. J. Bolitho

"The paper covers the activities of the Government Miners' Training-Schools. It argues that its success is proved by the steady demand for miners trained at the Schools; by the large numbers of ex-apprentices who hold responsible official positions in the industry; and bv the probable expansion of the organization in the near future to meet the never-ending call for trained personnel."

Jan 1, 1947

By Mahyera A, Sakashita B, Ahmed U, Abou-Sayed AS

Gas in U.S. coals is primarily composed of 90 to 99 percent methane and up to 10 per- cent carbon dioxide. In composition and heat- ing value, this coal-bed gas is similar to natural gas and can be introduced directly into commercial pipelines after standard condition- ing. The high permeability cleat system in the virgin coal can be exploited in order to drain the coal gas well in advance of mining. Two premining drainage methods have been extensive- ly evaluated in the U.S.; they are 1) horizon- tal boreholes collared from within the mine, and 2) vertical drilling from the surface with fracturing. Limited-size fracture treatments are advocated in order to prevent potential roof damage and the need for added support. An engineering approach to predicting gas flow for different drainage techniques near mining locations is presented. Results can be used in design, i.e. pipeline, compressor. Coal gas drainage from a horizontal borehole and a treated (contained fracture) vertical well for a 6 foot seam have been evaluated. Based on these results, it was concluded that selection of gas drainage techniques will depend primar

Jan 1, 1982

By Enrico Tosolini

O controle da massa linear dos arames CA60 vem sendo tratado com máxima prioridade, devido ao constante esforço da indústria nacional de reduzir os custos e melhorar a eficiência de produção. O trabalho é um estudo teórico dos fatores físicos que influenciam na variação da massa linear. Para desenvolver a análise, o problema foi simplificado para reconduzi-lo a um problema linear de fácil análise e com parâmetros intuitivos para fácil aplicação dos conceitos nos problemas diários da produção.

Aug 16, 2017

Colloquium And General Meeting - Trackless Mining in Underground Metal Mines A General Meeting and Mining Colloquium on the above topic was held on Wednesday, May 16th, 1973, at Kelvin House. Dr J. P. Hugo (President) was in the chair. The colloquium wasattended by approximately 200 delegates, and was opened by the President at 9.15 a.m. OBITUARIES The President: It is my sad duty to announce the death of the following: W. A. Schwezoff and L. G. S.

By Jue Kou, Lei Yu, Bern Klein, Lusheng Zhou, Chunbao Sun, Genzhuang Li, Reem Roufail, Amit Kumar

Magnetic liners can improve the performance of ball mills by increasing grinding efficiency, extending service life, and reducing maintenance costs. Despite their importance, the fundamental understanding and the quantitative investigation on the effects of the magnetic liners has not been addressed in the literature. This paper addresses this gap by studying charge motion, and how the use of a magnetic liner affects the breakage mechanism of the mill, using discrete element method (DEM) modeling and the Hertz-Mindlin contact model with relative velocity dependent (RVD) rolling friction. Charge motion was modeled under different mill speeds. Compared to conventional steel and rubber liners, the charge motion in the magnetic liner mill was predominantly cascading. Quantitative analysis of the energy dissipation within the mill was conducted to investigate mill breakage. Regardless of speed, over 50% of the total energy dissipation in the magnetic liner mill was in the form of abrasion and attrition. The results highlighted the appeal of magnetic liners in secondary and regrinding application, where abrasion and attrition are considered more efficient in the fine material breakage, and where impact is ideally minimized to reduce mill wear. A number of experiments were conducted to assess the effect of different model parameters on the performance of the magnetic liner mill. The highest abrasion/attrition intensity was observed with high values of the model parameters namely the restitution coefficient, static friction coefficient, and rolling friction coefficient.

By L. Voisin, E. Díaz, V. Montenegro, W. Kracht

Grinding media is of great concern in the mining industry mainly because its consumption represents an important part of the costs during mineral processing and consequently, of the total mining business OPEX. In addition, grinding media consumption impacts directly on flotation performance through negative contamination by corrosion, affecting the pulp chemical potential, complicating the understanding and control of the process, as galvanic interactions between mineral species also occur. In addition, during the process there is also a physical consumption of the grinding media through erosion and impact. In both cases, mineralogy has an important role because pulp abrasion power, chemical reactivity, rheology, hardness and other variables depend on the minerals contained in the pulp and their interactions. In the present study, a geometallurgical and phenomenological model, which describes the grinding media consumption and its relationship with mineral hardness expressed by Bond Work Index, was obtained based on advanced mineral characterization techniques such as Hylogger3TM, X-ray diffraction, X-ray fluorescence and experimental grinding tests using a laboratory mill applied on Chilean copper pulps. The results obtained show that pH has an important effect on grinding media consumption, because corrosion varies with hydrogen ions availability. Also, mineral hardness depends on mineralogical composition, but textural analysis must be performed to have a better description of this property. Finally, minerals present in a sample define the grinding media consumption mechanism, because a sample with harder minerals and a greater value of Bond Work index is capable of protecting grinding media from impact wear, while a sample with lower hardness but with a big sulfide minerals content would be more aggressive with grinding media because corrosion is more important in this case. The geometallurgical model obtained is capable to relate the grinding time, mineral hardness, content of sulfide minerals and grinding pH to estimate the grinding media consumption.

Jan 1, 2017

By R. Grau

"After commissioning and start-up of the first 500m3 TankCell® flotation cell in 2014, the over 300m3 mechanical flotation cells have earned their place in large-scale flotation operations. These 500 to 630m3 cells, designed for projects with large throughputs, are proven to provide savings in project capital and operational expenditure through savings in foot print, energy consumption, and less equipment to install and maintain. Addition to savings in different phases of a project, these cells provides operational flexibility and has shown improvements in metallurgical performance. In this paper a case study from Kevitsa TankCell® e500 installation and Buenavista del Cobre TankCell® e630 installations will be given.INTRODUCTION After development (Grönstrand and Bourke, 2008), characterization (Morales et al. 2009; Yanez et al. 2009; Grönstrand at al. 2009), validation (Elgueta et al. 2009; Coleman and Dixon, 2010), and more than 350 industrial installations of the Outotec TankCell® e300 flotation cell, the well proven energy efficient TankCell® product family introduced the TankCell® e500 forced-air flotation cell late June 2012 (Outotec.com, 2012). The introduction of the 500 m3 flotation cell followed by introduction of a 630 m3 flotation cell, TankCell® e630, in October 2014 (Outotec.com, 2014). These large flotation cells are designed for projects with high throughputs where the number of cells needed for operation with smaller equipment would become large. The benefits of this size of flotation cells comes from the lower capital expenditures due to lower equipment costs, savings in plant footprint, less installation work with less auxiliary equipment, lower energy consumption, and less units per installation resulting in less components, spare parts and maintenance.The first TankCell® e500 was commissioned and taken into operation in October 2014 at FQML Kevitsa Cu-Ni-PGE concentrator, nowadays owned by New Boliden. The first TankCell e630 was taken into operation in January 2018 at GrupoMexico’s Buenavista del Cobre Cu-Mo concentrator. The start-ups of the first TankCell® e500 and TankCell® e630 followed with test work where the hydrodynamic performances of the cells were characterized and metallurgical performance studied. The results of the TankCell® e500 test work were presented in detail by Mattsson et al (2015a; 2015b) and TankCell® e630 by Grau et al. 2018. In this paper the metallurgical improvements achieved with the large cell installations will be presented."

Jan 1, 2019

By Jurij Karlovšek, Wolfgang Angerer, Vojtech Ernst Gall, Jacob Grasmick

The International Tunneling Association (ITA) Working Group (WG) 22 “Information Modelling in Tunneling” has developed a guideline for the implementation of Building Information Modeling (BIM) concepts for Bored Tunneling Projects. The guideline primarily covers the use of BIM during the conceptual and delivery phases of a project. It provides Owners with an introduction to BIM, an overview of the current capabilities of BIM, and a guide for implementation for a Bored Tunnel. The document will be officially published at the World Tunnel Congress (WTC) in Copenhagen in 2022. This paper describes the need for the guideline and provides a preview of its contents.

Dec 1, 2022

By H. Scott-Russell

Ladies and Gentlemen. It is my great pleasure on behalf of The South African Institute of Mining and Metallurgy and The Geological Society of South Africa to welcome you to the 15th CMMI Congress and to Southern Africa. It is a great honour to be hosting this event and we have been looking forward to it for a long time. I am sure the technical discussions and visits will be of great value, and I am confident you will return with pleasant memories of places and people in South Africa and neighbouring countries. The theme of this Congress, Resources and Technology', is appropriate for discussions on the ways and means of going forward in the minerals industry to create the employment and wealth so sorely needed in this region. The technical programme will give mineral industry professionals from different parts of the world the opportunity to share experience and expertise for the purpose of making operations more productive, safer and environmentally acceptable to the world at large. Delegates will be exposed to current technical developments by means of 133 papers prepared for the congress: 30 on geological subjects, 45 on mining, 29 on extractive metallurgy, and 29 in the field of metals technology.

Jan 1, 1994

By Esterhuizen S. Gabriel, Su W. H. Daniel, Tulu B. Ihsan, Klemetti M. Ted, Mohammed M. Khaled, Gearhart F. Dave

"A numerical-model-based approach was recently developed for estimating the changes in both the horizontal and vertical loading conditions induced by an approaching longwall face. In this approach, a systematic procedure is used to estimate the model inputs. Shearing along the bedding planes is modeled with ubiquitous joint elements and interface elements. Coal is modeled with a newly developed coal mass model. The response of the gob is calibrated with back analysis of subsidence data and the results of previously published laboratory tests on rock fragments. The model results have been verified with the subsidence and stress data recently collected from a longwall mine in the eastern United States. INTRODUCTION In 2015, there were 40 longwall mines operating in the United States, each producing an average of 4.5 million tons of coal per year, and they supplied 60% of the U.S. underground coal production. This represents a substantial increase from 50% three years earlier (Sears, Tulu, and Esterhuizen, 2017). During this period, reportable roof fall rates in U.S. longwall mines also increased. Large roof falls that can block the gateroads are not only a ground-fall hazard, they can disrupt the ventilation system, block the escapeways, and increase the potential for elevated methane levels in the gob. To address these hazards, the National Institute for Occupational Safety and Health (NIOSH) Pittsburgh Mining Research Division (PMRD) is conducting research to improve the design of ground control systems in longwall gateroads. Gateroad stability is primarily determined by the longwall pillar design. Generally, the required dimensions of the pillars around a longwall panel are determined first, which then dictates the location of the gate entries relative to the mined panel. The Analysis of Longwall Pillar Stability (ALPS) method is the most accepted gateroad pillar design procedure in the United States (Mark, 1992). The ALPS method accounts for local roof geology in the gateroad stability assessment by including the Coal Mine Roof Rating as an input parameter (Mark, 1992). The key assumption in the ALPS method is that unstable pillars result in unstable gate entries. However, experience provides examples of mines where pillar stability and gateroad stability are only loosely correlated (Su, Draskovich, and Thomas, 2003)."

Jan 1, 2017

By J. Manchisi

This study has investigated the use of blast furnace slag as functional adsorbent for metal ions in acid mine drainage treatment. This opportunity has not yet been developed into a practical process partly because of limited understanding of rates and mechanisms of adsorption process and inconsistency in interpretations of adsorption data. The overall objectives were to determine the efficiency and mechanisms of sorption process of metal ions in a multiadsorbate system. We employed standard materials characterisation techniques to analyse composition, structure and surface morphology of the slag. Batch adsorption experiments were then conducted to study the mechanisms, kinetics and efficiency of metal sorption as a function of pH, phase ratio, mixing time, mass and particle sizes of slag. Both XRF and adsorption data suggested the slag to possess acid neutralising capacity. This slag is non-crystalline based on XRD pattern, has adequate porosity and pore volume comparable to similar commercial adsorbents but it has inferior pore structure, pore size distribution and BET surface area to be effective under wide applications. Metal sorption increased with decrease in slag particle diameter, decrease in initial metal concentration and increase in the mass of slag. Although slags have demonstrated to efficiently treat low concentrations of single and multiadsorbate effluents using fine particle sizes, they have limited capacity to treat multiadsorbate systems for some metal ions. This is probably due to low affinity, competitive adsorption or limitation in material?s adsorptive properties. Sorption mechanisms probably involve precipitation and ion exchange on the basis of alkaline pH and exchangeable slag surface ions. Sorption preference is proposed as Fe2+>Cu2+>>Cd2+>Co2+>Mn2+. Despite these limitations, deeper understanding of sorption behaviour of metal ions by slags for application in dilute and large volumes of effluents is necessary where precipitation and other standard techniques are either inefficient or uneconomic. Thus, this study has established that sorption capacity of slag to remove metal ions from acidic effluents is selective, limited to certain metal ions and for other ions only at low concentrations. Further adsorption studies in multiple solutes under various experimental conditions or those that can propose an economic slag activation process are needed that improves or widens adsorption window.

Aug 1, 2013

By N Guresin, M Rohde

A lead-zinc flotation tailings sample containing silver from BHP Billiton’s Cannington Mine has been characterised to understand occurrences of silver in the tailings by conventional elemental, X-ray diffraction (XRD) and size analyses followed by mineralogical analysis with a scanning electron microscope (SEM) equipped with mineral liberation analysis (MLA) software and the use of an adapted diagnostic leach process originally developed for gold containing materials.The tailings sample contained 67 g/t Ag, 1.8 per cent Pb and 0.52 per cent Zn. The XRD analysis showed that the sample consisted of 74 per cent silicates, nine per cent sulfides, 11 per cent magnetite and small amounts of other minerals such as fluorite, fluorapatite and rutile. The p80 and p50 of the sample were determined to be 106 µm and 38 µm, respectively. The silver distribution was high in the small size fraction with 52.1 per cent of the silver being in the -8 µm fraction. The silver minerals freibergite, acanthite, jamesonite, pyrargyrite and native silver were observed in the mineralogical analysis of the sample by SEM/MLA. The associations of the minerals were intricate and the occurrences of silver were complex. There were finely disseminated silver minerals and also coarser grains of silver minerals in composites with the host minerals. It was estimated that almost 50 per cent of the silver was contained in pyrargyrite, around 14 per cent as native silver and contained in acanthite, 12.5 per cent in galena and around ten per cent in freibergite and jamesonite.These composite particles and the type of the silver minerals present were expected to limit leaching efficiencies of the silver in hydrometallurgical processing. The diagnostic leach tests showed that around 50 per cent of the silver could be recovered by direct cyanidation and higher extractions could be achieved by more aggressive acidic systems.Cyanidation tests were conducted to confirm the findings of the diagnostic leach studies. The investigated cyanidation parameters were time (up to 48 hours), solid to liquid ratio (1:1 and 1:2), cyanide concentration (0.025 M, 0.5 M and 0.1 M) and particle size (p80 of 106 µm, 63 µm and 7.5 µm). The effects of oxygen and lead nitrate were also studied. The tests were conducted at atmospheric temperatures. The maximum silver recovery obtained was about 50 per cent for all the parameter ranges trialled except particle size. The decrease in particle size from 106 µm to 7.5 µm by fine grinding resulted in an increase in silver recoveries from 50 per cent up to approximately 82 per cent indicating that the liberation of the silver grains/minerals is one of the factors affecting the cyanidation recovery of silver in addition to the presence of refractory silver minerals not amenable to cyanidation.Low head grades of silver in the tailings and relatively low cyanidation recoveries of silver (without fine grinding) necessitate a thorough cost analysis for the cyanidation of the Cannington lead and zinc tailings to assess if cyanidation would be a suitable process option for the extraction of silver. It is clear that one of the most important factors in determining the cost feasibility will be the price of silver in the world metal market.CITATION:Rohde, M, Guresin, N and Johnson, N W, 2014. Characterisation of silver minerals in lead-zinc flotation tailings and their response to cyanidation, in Proceedings 12th AusIMM Mill Operators’ Conference 2014 , pp 163–172 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 1, 2014

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite 'aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou'e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.'" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, ''' and ativity'-' data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,'"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener''% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil'' (on the basis of a previous study by ohansson'), and subsequently rede-rived correctly by Speiser and retnak,' in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, ' in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener's method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967