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PERSONAL (Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during. the period May 10 to June 10, 1915: Robert M. Keeney, Somersville, Conn. C. A. Moffett, Birmingham, Ala. Emilio Mosonyi, San Salvador, C. A: A. W. G. Wilson, Ottawa, Canada. Junjiro Nagazumi, Fukuoka, Japan. G. H. Glover, Jr., Short Hills, N. J. Francis R. Pyne, Elizabeth, N. J. R. W. Brock, Vancouver, B. C. F. C. Alsdorf, Los Angeles, Cal. J. L. W. Birkinbine, Philadelphia, Pa. W. J. Loring, London, England. Roy H. Allen, Jamesburg, N. J. R. A. Bull, Granite City; 111. Francis Andrew Thomson received the degree of Master of Science from the Colorado School of Mines at the recent commencement exercises. The subject of his thesis was Stamp Milling and Cyaniding.

Jan 7, 1915

By Richard Mainiero, Donald A. Hurd, James H. Rowland

In previous conferences the authors have reported on toxic fumes generated by the detonation of ANFO. The research reported here extends the earlier work to include an emulsion blasting agent and ANFO/emulsion blends. Explosive mixtures were shot in 4-inch Schedule 80 steel pipe in a chamber in the experimental mine at the Pittsburgh Research Laboratory (PRL). Following each shot, the fumes in the chamber were analyzed using on-line instrumentation. A major goal of the research was to gain a better understanding of the factors that lead to the generation of toxic fumes in blasting operations. Earlier studies have suggested that the high nitrogen dioxide and nitric oxide concentrations in product clouds might be the result of the poor confinement provided by relatively weak ground strata or the exposure of the explosive to ground water prior to shooting the shot. Various mixtures of ANFO and emulsion were detonated in schedule 80 steel pipe and galvanized sheet metal pipe to evaluate the effect of confinement. Explosive mixtures were also allowed to soak in water for less than one day, one week, one month, and two months to determine which explosive mixtures would be degraded and observe what effect this degradation had on fume production. Results indicated that the production of nitrogen dioxide increased with low confinement of the detonating explosive and with exposure of the explosive to water.

By J. R. Thoenen

In June 1929 the Bureau of Mines issued a 13-page Information Circular entitled "Mineral wool." This was one of the first publications to present to the public some technical aspects of the mineral-wool industry. Since that time several articles have appeared on the subject in the technical press as well as publications by State organizations. Inquiries for information on mineral wool have continued to be received by the Bureau of Mines in large numbers, and in 1935 it was decided, with the cooperation of the is industry, to make a field survey of the plants then producing and to collect therefrom technical data to be compiled in a paper for public distribution. As a first step, a brief questionnaire was mailed to the known producers asking if they would cooperate for publication. Favorable replies were received from of percent of the manufacturers, and the field work was started. As the study progressed and tie number of plants visited grew, it became more and more apparent that the industry had made rapid strides in technical operation and control of their product, as well as in increasing production during the mast decade.

Jan 1, 1938

By Brian Fulcher

In April 1997, Kiewit/Parsons Brinckerhoff (K/PB) completed the 7,600-m (25,000-ft) primary access tunnel for the Yucca Mountain, NV proposed high-level nuclear waste site. K/PB then began boring an exploratory east-west cross drift tunnel at the site. The 2,681-m (8,796-linear ft)East-West Cross Drift Tunnel was excavated through volcanic tuffs having zones of incompetent rock using a rebuilt Robbins 5-m (16.4-ft)hard-rock tunnel boring machine(TBM) with a special arrangement of supporting equipment. This portion of the Yucca Mountain project was completed in eight months.

Jan 1, 2000

How did you get into mining; were you from a mining town or mining family? Not at all. I grew up in northwest Kansas. I liked to hunt and fish, so I thought it would be fun to work for a company that made knives or guns. It seemed like metallurgical engineers would be something those companies could use, so I started in physical metallurgy. I got a summer job at the great Climax molybdenum mine near Leadville, CO shoveling muck onto conveyors. I was hooked. I loved everything about mining, so in the fall, I changed majors from physical metallurgy to mineral processing. For many years you actually discouraged young people from studying the mining disciplines. Could that be right? That’s true.

Jan 1, 2007

By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

By Holdgate G. R, Thompson B. R, Webster R. L, Bolger P. F

The Gippsland Basin in south-eastern Australia has an area of approximately 46 000 sq km. It is one of the world's major coal and petroleum bearing basins, with most of the former occurring in the smaller one fifth on-shore part. The stratigraphy, structure and economic resources of the Tertiary sedimentary pile is now well known through extensive drilling for coal and petroleum. In contrast, the older Cretaceous sequences through their lesser economic importance are relatively less explored. The sedimentational history of the Gippsland Basin has largely followed along similar lines of development to the many other southern Australian basins since the Cretaceous break-up of Gondwanaland. However, the scale of accumulation of coal and hydrocarbon source rocks is unprecedented and differentiates this basin, for reasons less well understood, from the others. Large scale open cut brown coal mining since the late-1920s has been carried out in the western extremities of the basin, while vigorous extraction of some two thirds of Australian petroleum products taken place in the offshore part. Brown coal seam thicknesses and economically winnable reserves are huge and outrank most other brown coal basins of the world. Development of the resource currently meets the need for electricity generation throughout the State of Victoria, but other future developments such as conversion to oil, being investigated.

Jan 1, 1992

By M. J. Scoble, L. M. Daneshmend, C. Hendricks

Paper presented at a meeting on: Artificial intelligence in the minerals sector, held in Nottingham, UK, 20 April 1993. An attempt is made to relate emerging technologies to education and training requirements by examining the nature of the Canadian mining industry's human resources. Particular attention is given to the trends evident in mine automation and their likely impact on instructional needs. The characteristics of "computer-aided instruction" systems are reviewed and related to the implementation and support of mine-wide monitoring and communication networks, which are seen as fundamental to the eventual automation of underground hardrock mines

Apr 1, 1994

By R. J. Kuczynski

The U.S. Bureau of Mines Reno Research Center operated a batch pilot plant to demonstrate high-temperature cyanide leaching for recovering platinum group metals (PGM) from automobile catalysts. Approximately 1,600 kg of used pellet, monolith, and metal support catalyst containing 1,680 g (54 tr oz) of PGM were processed. Forty-five-kilogram batches of used catalyst were leached with sodium cyanide solution at 160° C for 1 h under basic conditions in a countercurrent processing sequence to dissolve the PGM. Extractions from the used pellet catalyst ranged from 94 to 95 pct for Pd, 95 to 97 pct for Pt, and 64 to 81 pct for Rh. Extractions from the used monolith catalyst ranged from 7B to BB pct for Pd, 75 to 90 pct for Pt, and 43 to 71 pct for Rh. Heating the pregnant leach solutions to 275' C for 4 h destroyed the PGM-cyanide complexes, resulting in over 99.7 pct of the PGM precipitating from solution. The PGM precipitate was predominantly a powder metallic concentrate, typically analyzing greater than 50 pct PGM. Heating destroyed cyanide to less than 0.2 mg/L. Both the pellet and monolith residues were evaluated for disposal using the EPA Toxicity Characteristic Leaching Procedure.

Jan 1, 1995

By Delahant A. B, Dworski M

From the Saranac Laboratory for the Study of Tuberculosis of the Edward L., Trudeau Foundation, Saranac Lake, New York:We are assembled to honor the memory of our friend and colleague, Donald Cummings, one of the founders and a past president of the American Industrial Hygiene Association. I deem it an Unusual privilege to have been asked to give this first memorial lecture and hope that what shall have to say may be worthy of the occasion. It is fitting that we should discuss here the subject of Silicosis to which he devoted such a large part of his life and it is doubly fitting, I think, that I should report to you an extended series of investigations carried on by his associates at the Saranac Laboratory.The subject of silicosis may seem hackneyed to this audience which is so familiar with the tried and accepted methods of prevention and control.But in spite of our efforts, the condition is still with us and unfortunately is still being produced in many places. In industries that now maintain good control of dust, fresh cases are appearing on annual re-examination, whose major exposure date back to the days before the hazard was recognized.A few new employees, with apparently ineffective upper respiratory protection against inhaled dust, develop silicosis precociously in environments that are comparatively harmless to their fellows. In plants that have relaxed their vigilance under the urgency of war production schedules, conditions again prevail that will produce, disease in the future.Silicosis acquired new interest with the announcement by Denny, Robson and Irwin(1) in 1937 that it could be prevented by the inhalation of powdered metallic aluminium. It so happened that without knowledge of their work, we at the Saranac Laboratory had for some months been conducting similar experiments with one of the hydroxides of aluminium.Quite independently we discovered that hydrated alumina would also protect animals against quartz. Our approach to the problem had been empirical; we were trying to neutralize quartz particles by coating their surfaces with an insoluble material following the lead of Kettle who in 1932 had shown that this could be accomplished with iron. He neglected to describe his method and the chemist who prepared his coated...

Jan 1, 1945

By Tamara Caroline Guimarães Vilela

Neste trabalho foi avaliado o comportamento de propagação de trinca por fadiga de cinco aços utilizados na fabricação de trilhos empregados na construção e manutenção de vias permanentes brasileiras, por meio da realização de ensaios de propagação de trinca por fadiga (da/dN x ?K), utilizando-se a razão de tensões de carregamento R = 0,7 e comparação com os resultados obtidos com R = 0,1. Vários modelos de previsão do comportamento em fadiga foram avaliados. Observou-se a influência de R nos valores mais próximos ao limiar ?KTH, com diminuição considerável no valor de ?KTH para R = 0,7. Dentre os modelos matemáticos usados no ajuste das curvas sigmoidais da/dN x ?K, o que forneceu melhor ajuste foi o ajuste de Hartman e Schijve. O parâmetro K? proposto por Kujawski reduziu os efeitos de R na tentativa de unificar os dados em uma única e estreita banda de dispersão, porém, na Região I da curva, os dados ainda ficaram bastante dispersos.

Aug 17, 2017

By J L. Mauk

The Sovereign, Jubilee, Scotia and Jasper Creek prospects occur in an area of ~3.0 km by 2.5 km (~7.5 km2) in the Hauraki goldfield. The prospects are hosted by andesitic to dacitic flows, autoclastic breccias and localised pyroclastic and air fall deposits. Jubilee and Sovereign prospects lie along the northern and southern parts of the Waitekauri Fault, respectively, whereas Scotia is located ~1 km to the E, and Jasper Creek a further ~1.2 km to the ENE. Wall rocks are typically intensely altered, although the degree of alteration becomes more variable east of Scotia and at Jasper Creek. Alteration minerals include quartz, adularia, albite, chlorite, pyrite, illite, interstratified illite-smectite, smectite and calcite. Several of these minerals have distributions that show distinct zonation with adularia most abundant at Sovereign and Jasper Creek, but restricted to shallow levels at Scotia. Illite occurs throughout Sovereign and Jubilee plus the western margin of Scotia where it grades into interstratified illite-smectite; smectite predominates at Jasper Creek. Veins are uncommon and typically narrow, but show distinct zonations. Quartz veins are more abundant at Sovereign and Jubilee, whereas calcite veins are more abundant at Scotia and Jasper Creek. Laumontite veins occur at Scotia, and rare clinoptilolite, mordenite and stilbite veinlets with calcite occur at Jasper Creek. Fluid inclusion in quartz and calcite homogenised between 141¦ to 272¦C and trapped a dilute solution with an apparent salinity of less than 2.6 weight percent NaCl equivalent. Homogenisation temperatures are hottest at Sovereign (average 241¦C) and Jubilee (average 239¦C), cooler at Scotia (average 204¦C) and coolest at Jasper Creek (average 162¦C). Calculated paleowater table elevations suggest the water table was 680 m to 750 m above sea level at Sovereign and Jubilee, 450 m at Scotia and 225 m at Jasper Creek. The current data suggest three scenarios that can explain why Sovereign and Jubilee are deep and hot, whereas Jasper Creek is cool, shallow and marginal; 1.   some or all of the prospects may represent separate overlapping hydrothermal system, 2.   a high-relief hydrothermal system on the side of volcano with an inclined water table and outflow towards Jasper Creek, and 3.   a low-relief hydrothermal system that has been either tilted or block faulted with greatest uplift and erosion to the west.

Jan 1, 2005

ALABAMA Altoona -Cain, J Anniston-Cowie, L K Hermrod, A A White, H E Bessemer -Abbott, C E Ball, E M Mitchell, F R Thompson, N E Birmingham -Adler, J E Aldrich, T H Aldrich, T H, Jr Blackburn, A R Bush, M W Clark, G H Cowrn, P G Crane, W R Crawford, G G Crockard. F H

Jan 1, 1923

Council Members 1988/1989, left to right: Row 1 (seated): H.E. James, P.W.J. van Rensburg, Dr H. Wagner, B.C. Alberts, C.E. Flvaz (President), H.G. Mosenthal, R.D. Beck, Professor A.N. Brown, Dr P.R. Jochens Row 2 (standing): P.C. van Aswegen, J.P. Hoftman, D. Wllson, P.M.T. White, K.A. van Gessel, Dr LA. Cramer, J.S. Freer, V.J. Moore, G.A. Brown, R.A. Snodgrass, J.D. Austin Row 3 (standing): Dr G.A. Fourle, Dr J. Lurle, A.M.P. Henderson, R.P. Mohring, J.A. Cruise, J.L. Nel, H. Scott Russell, J.P. Deetlefs, D.A.J. Ross-Watt Inserts, top row: K.R. Beard, N.J. De~ine, R.J. Dlppenaar, G.T.G. Emere, Dr J-P. Franzidls, Professor R.P. King, J.G. McCallum. Bottom row: G.Y. Nisblt, Professor R.P. Plewman, Dr R.E. Roblnson, Dr O.K.H. Steften, P.A. van Wlelllgh

Jan 1, 1989

By H. W. Gillett, E. L. Mack

Prior to 1911 the literature on melting brass by electricity consisted entirely-save for some suggestions made in patent literature but not actually worked out-of a few observations by farseeing men ' on the theoretical advantages of melting brass and other nonferrous alloys in electric furnaces. Roeber was the first to see and clearly state the possible advantages of the electric furnace in brass melting. The same factors tha.t make it desirable to manufacture special steels in the electric furnace rather than in crucibles, he declared, apply to brass as well. He pointed out the possibility of using larger melting units, of eliminating crucible cost, of readily controlling the purity of the product. and of nearly eliminating the loss of zinc. "The replacement of the • old crucible process is sure to come," he said; "perhaps it will come in two years, but it will, necessarily, in ten years .... The inevitable advance along this industrial line will have great influence in the metal world and will also provide, in large cities, a new kind of load for the central station." The years 1905 to 1910 may be termed the purely theoretical period of the development of the electric brass furnace, though the Conley furnace was tried out e:xperimenta.lly about 1910 and a few heats were made in an induction furnace. 2 In December, 1911, the American Chemical Society held a symposium on mineral wastes, at which Bassett s discussed the zinc· losses that attend making brass in fuel-fired furnaces.

Jan 1, 1922

By B. Wilshire, W. J. Evans

W. J. Evans and 8. Wilshire SEVERAL recent investigations1-6 have shown that the strain, c, during transient and steady-state creep is well-represented by the expression: € = e0 + et(l - e-mt) + Esl [l] where Eo is the instantaneous strain on loading, ET the total transient strain, C, the steady creep rate! and m a constant relating to the rate of exhaustion of transient creep. However, it has been noted6 that deviations from this equation occur over the first 10 to 15 pct of the transient stage, when the creep rate, (. decreases more rapidly than is predicted by this equation. This rapid decrease has been attributed to a large change in work-hardening coefficient. It 1s widely accepted that steady-state creep results from a balance between the rate of strain hardcning h and the rate of recovery r (=-s(st) as: dE/dt = Es = r/h [2] Comparison of values obtained for h at the end of the initial extension and during steady creep suggests that h increases several fold during the transient stage. which has the effect of reducing the creep rate proportionally.7 To examine the dependence, on r and h, of the deformation behavior during transient and steady-state creep. a series of constant-stress creep tests was carried out at 413°C at 6000 psi using 70-30 a brass. Prelinlinary investigation showed that. with this material. the transient stage constituted a significant portion of the total creep life (-0.4tf. where tf is the time to fracture). The alloy. obtained from Metals Research Limited. was made from high-purity copper, 99.999 pct. and zinc. 99.99 pct. Heat treatment at 675°C for 4 1/2 gave a uniform grain size of 5 mm-1. Details of specimen preparation and creep testing procedures have been given previously.6 Values of h (?s/?E) were determined by measuring the instantaneous strain. ?E. which occurred on increasing the stress during creep by a small amount. ?s. Similarly. v (= -?s/ ?t) was derived from the incubation period. At, after a small decrease in stress.' Several values of v and h were obtained throughout duplicate creep tests. using different stress increments in the range 300 to 800 psi. The accuracy with which Eq. [I] represents the present creep curves was established by determining the best value of the constants Es, Et, m , and 6, using a digital computer program based essentially on the graphical solution for this equation devised by Conway and Mullikan.9 About 40 strain/time readings were taken during transient and steady-state creep. Over most of the creep curve, the average difference between the measured reading and the calculated strain at the appropriate time was less than 0.0001. However.

Jan 1, 1969

By Rick Coleman, Chelvan (Chevy) Veloo

"P.T. Freeport Indonesia's lrian Jaya Operation has been producing copper concentrate continuously since 1972. Numerous ore discoveries and five mill expansion programs have seen the initial milling rate of 7,200 MTPD escalate to the present rate of 125,000 MTPD, producing 2.5 million pounds of copper and 3,500 troy ounces of gold per day. The latest expansion, commissioned in February 1995, incorporates a 34 foot Semi- Autogenous Grinding (SAG) Mill, two 20'x30' Ball Mills, conventional roughing, cleaner column flotation, and attendant upgrades to the existing concentrate pumping and dewatering facilities. This paper will describe the SAG Plant flowsheet, and focus on the key training issues which contributed to a successful plant start-up.IntroductionP.T. Freeport Indonesia's operations in the Ertsberg mining district are located in the Jayawijaya Mountains of Irian Jaya, the easternmost province of the Republic of Indonesia. P.T. Freeport Indonesia (PTFI), the operator, is owned by Freeport MacMoRan Copper and Gold (81.3%), the Government of Indonesia (9.4%), and private Indonesian investors (9.4%). Geographical location, and sailing distances are provided on the attached location map.The operation stretches over 7 4 miles ( 114 km) from the dewatering and concentrate shipping facility at the Port of Amamapare on the Arafura Sea to the Grasberg open pit located at 3400m. The regional geology is covered in detail by Van Nort et al (1991 ), with current proven and probable reserves estimated at 1.13 billion metric tonnes grading 1.30% Copper, 1.42 ppm Gold, and 4.06 ppm Silver. The Grasberg open pit mining operation provides 92% of the mill feed, and is described in detail by Hickson (1991). The remainder of the mill feed is derived from several underground block caving operations. Current production rates provide a mine life in excess of 25 years. However, very favorable geology in the area leads to expectations that additional reserves will extend the life of the operation considerably."

Jan 1, 1996

By McLeod RL

The Tolukuma gold-silver prospect is located approximately 100km N of Port Moresby in the Central Province of Papua New Guinea (PNG). Epithermal "adularia-sericite" style mineralisation crops out over 1200m within an en echelon quartz veined zone 1 to lOm wide. At a 4g/t cut-off grade, a geological resource of approximately 1.47Mt @ 13.77g/t Au is indicated from 38 diamond drill holes completed since discovery by Newmont Pty Ltd in September 1986. At a regional scale, Tolukuma miner- alisation appears localised in a dilatant zone at the intersection of a 1150 magnetic structure, and the western margin of a N-S trending graben which is filled by a Pliocene volcanic complex contemporaneous with the Mt Davidson Volcanics 30km to the W. A l0km diameter circular Landsat feature, which may reflect magma emplacement at depth, occurs immediately N of Tolukuma and nearby mineralisation. Mineralisation at Tolukuma occurs in sub-vertical quartz veins at, or adjacent to the faulted contact between Pliocene basic and intermediate volcanics/intrusives, and quartz mica schists and phyllites of the Cretaceous Kagi Metamorphics. Most veins display evidence of multiple episodes of brecciation and textures indicative of cyclic boiling, including crustiform rhythmic banding and quartz pseudomorphs after platy calcite.

Jan 1, 1991

By Johnson T, Huynh D

The State Electricity Commission of Victoria is conducting a program of research and development into alternatives to the use of conventional boilers for the generation of electricity from brown coal. The objectives of the program are to reduce the cost of electricity generation and also to improve the thermal efficiency so as to reduce the emission of greenhouse gases and other pollutants. The program presently includes the following four technologies: Hydro-thermal Drying, Direct Coal Fired Gas Turbine, Integrated Gasification Combined Cycle, and Steam Fluidised Bed Drying. The Hydro-thermal Drying process produces a combustible coal-water-slurry fuel which is suitable for use in a coal fired gas turbine. The coal fired gas turbine has the potential to produce electricity at a lower cost than conventional power stations and when combined with a steam cycle, it will also use significantly less coal. The Integrated Gasification Combined Cycle process gasifies the coal, cleans the gas, and then bums it in a gas turbine/combined cycle. This process is being developed in Europe and the USA in order to meet their stringent emission regulations. It offers Victoria cleaner more efficient and cheaper electricity.

Jan 1, 1992

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954