Search Documents

By Z. B. Karshigina, Ye. G. Bochevskaya, E. A. Sargelova, Z. S. Abisheva

At the present time of depletion of reserves of high grade rare earth deposits, it has become necessary to involve low grade raw materials in the production. Among the rare-earth deposits in Kazakhstan, the most advanced one is Kundybai. The mineralogical composition of ore is represented by the minerals: a-quartz SiO2, kaolinite Al2(Si2O5)(OH)4, muscovite KAl2(AlSi3)O10(OH, F)2, albite Na(AlSi3O8), rutile TiO2, and hematite Fe2O3. It contains: 59.1–68.5% SiO2, 19.1–28.4% Al2O3, 7.2–10.3% Fe2O3, 0.51–0.84% TiO2, 0.10–2.32% CaO, 0.39–2.10% MgO, and some other elements. Rare earths are located in the clay part (kaolinite, goethite) in the ion-adsorbing form, and they are represented by the main ore mineral churchite - YPO4·2H2O. In the ore the amount of rare-earth elements (total REEs) varies from 210 to 600 ppm. Elements of the cerium group predominate (La, Nd, Ce, Sm, Pr) and the yttrium group is represented by Y, Gd and Dy. Extremely thin intergrowth and accumulation of REEs in clay minerals cause difficulties in their recovery using flotation and gravitation beneficiating methods. The purpose of this work is the development of an extraction method for the main mineral components of ore with transfer of the total REEs into the solution with high extractive efficiency. Results of the experimental work into high-temperature processing (hereinafter referred to as sulphatization) of ore by sulphuric acid with subsequent dual-mode water leaching of the sulphate product (sinter) are presented in this manuscript. The influence on the ore sulphatization process of some physical and chemical parameters: liquid-to-solid (L/S) ratio (0.36–0.86 cm3/g), temperature (100 – 500°?), concentration of sulphuric acid (3.0–18.62 mol/L) and duration (0.5–2.5 h) was studied. Optimal technological parameters of the process were determined to be: L/S ratio 0.36–0.46 cm3/g; temperature 500°?; concentration of H2SO4 9.0 mol/L; soaking time 1.5 h. Under these conditions it is possible to obtain extractions of ~ 85% REE, as well as 58% aluminium and 10% iron. XRD and IR-spectroscopy analyses were used to determine the material constitution of sulphated cakes obtained under optimal conditions. It was found that the primary minerals are quartz and muscovite; however different sodium aluminium silicates and albite minerals are present as well. In the future, it is proposed that the leach residue cakes are processed into precipitated silica (“white soot”).

Jan 1, 2016

Geological hazards such as faulting, basement ridges, and zones of "thin" (< 6 m) coal have a major impact on mining economics of underground operations in Huntly Coalfield. Experience has shown that drillhole-based investigations do not yield sufficiently detailed models of the coal seam to allow management of the planning risks associated with these hazards. Consequently, operational performance is affected by unplanned costs associated with lower productivity, loss of coal reserves, and expensive strata control remedies in problem ground conditions. Huntly Coalfield is a challenging environment for acquisition of good quality seismic reflection data due to the very thick (10-85m) weathering layer. Since 1994, successful acquisition of 2D and 3D data has been achieved through a combination of careful testing of technical parameters and experimental trials prior to committing to production recording. High resolution seismic reflection (HRSR) is proving to be an investigations technique which generates accurate and reliable models of the coal seam and associated structures, such as normal faults and topography of the surface on which the coal seam rests. The HRSR technique has been applied and developed in the Okowhao Sector where Huntly East Mine is developing and extracting coal reserves. Results of a recent 3D survey demonstrate that this technique is capable of revolutionising risk management in mine planning for underground mines in structurally complicated coal deposits.

Jan 1, 1997

In the early stages of opening up a mine, when there is some uncertainty as to its future career, necessitating caution in laying out works of a permanent character, the want is often felt of an assay furnace, easily built and easy of transportation, should the" mine " prove to be " no mine." Again, cases occur in which parties buy the right to treat comparatively small heaps of tailings, and then shift their plant to other localities. Under these circumstances it is necessary to restrict the plant to the barest necessaries, to suit, so to speak, the nomadic character of the work.An assay furnace that is really portable, easily transported, erected, taken down, of little weight, always ready for action on short notice, is indeed in these cases a desideratum which has long been wished for. The gasoline furnaces introduced intothe Australian market some time since practically fulfil these conditions; but they have the fatal drawback of being dependent on a constant supply of the liquid fuel, gasoline, which is seldom, if ever, obtainable locally in' any wayback mining township...

Jan 1, 1904

This study of the tin-tungsten ore of the Shepherd and Murphy Mine, in central northern Tasmania, was originally undertaken at the request of the Moina Tungsten-Tin Mining Co., N.L., as part of the research programme of the Mineragraphic Investigations Section of the C.S.I.R.O. It is based on the examination of a suite of specimens supplied by the management, supplemented by a more extensive collection and observations made by the author during a short visit to the mine in October, 1956.The Shepherd and Murphy Mine is at Moina, 36 miles S.W. of Devonport and 22 miles from Sheffield, the nearest railway station. It was worked almost· continuously from 1893 to 1919, when a fire destroyed the mill; to that date it had produced concentrates to the value of £141,000. After a long period of idleness, the mine was re-opened by the present company, but it has been announced recently that unfavourable market conditions have again forced closure.GENERAL GEOLOGYThe mine is on a deeply dissected plateau, about 2,500 ft. above sea level; it lies between the Iris and the Forth Rivers, whose valleys are deep gorges cut to about 400 to 600 ft. above sea level. From Moina westwards to the Iris River, a limestone regarded as part of the Gordon River Group, of Ordovician age, conformably overlies a sandstone containing tubicolar casts which are circular in cross section, half an inch in diameter and up to two feet long, and which resemble marine worm burrows (Elliston, 1953).

Jan 1, 1958

By D. G. Westlake

Polycrystalline tensile specimens of various Zr-0-H alloys have been tested at 298°, 178°, and 77°K. Solute oxygen and hydride precipitates in quenched alloys made individual contributions to the yield strength at 0.2 pct strain which combined to produce a resultant strength increment, a,., Ductility changes which were ohserved can he interpreted in terms of the various oxygen and hydrogen concentrations, testing tem -peratures, and dispositions of the hydride. ADDITIONS of oxygen in solid solution were known to increase the yield and tensile strengths of polycrystalline zirconium as early as 1951.' More recently, the critical resolved shear stress (CRSS) for prism slip in zirconium single crystals was also shown to be affected by the solute oxygen impurity.' This latter work also demonstrated that large increments of strength could be contributed by the finely dispersed zirconium hydride precipitates that are present in quenched Zr-H alloys.3 It was concluded that the combined strengthening due to alloying could be expressed by where to is the increase in the CRSS due to solute oxygen alone and TH is the increase due to finely dispersed hydride precipitates. Eq. [I] is analogous to one used to express the combined strengthening effects of work hardening and neutron radiation damage.4 Eq. [1] was verified only indirectly and for only small amounts of the impurities—up to 0.14 at. pct 0 and 0.63 at. pct H. The present investigation was undertaken to obtain a more direct verification of the validity of the form of Eq. [1] for this system and also to determine the combined effects of oxygen and finely dispersed hydride precipitates on the tensile strength and ductility of polycrystalline zirconium. EXPERIMENTAL PROCEDURE Tensile specimens were machined from the same rolled billet of Kroll zirconium used in the earlier study.' These measured 38 by 4.7 by 0.5 mm and had 10-mm gage lengths which were 2.8 by 0.5 mm. Each specimen was ß-annealed in vacuo at 1173°K for 15.5 hr and a-annealed at 1073°K for 4 hr to D. G. WESTLAKE, Member AIME, is Associate Metal l ur-gist, Metallurgy Division, Argonne National Laboratory, Argonne, III. Manuscript submitted July 17, 1964. IMD______________ give an equiaxed structure with grain diameters averaging 0.06 mm. Oxygen was added by allowing the metal to react with a known quantity of oxygen during the 0 anneal and known quantities of hydrogen were added during the a anneal. Each alloy was encapsulated in Pyrex under vacuum, annealed at 873°K for 4 hr, quenched into ice water, and polished by immersion in a solution of 46.75 vol pct H2O, 46.75 vol pct concentrated HNO3, and 6.5 vol pct HF (49 pct) at 298°K. Special heat treatments given to a few specimens are described in the results below. Tensile tests were done on an Instron machine and were begun within 20 min after the quench, except where specified otherwise. Tests at 298°K were in air, at 178°K in acetone, and at 77°K in liquid nitrogen. All tests were at a strain rate of 8x sec-1. RESULTS AND DISCUSSION Yield Stress at 298°K. The compositions of alloys and the corresponding yield stresses (0.2 pct strain) are given in Table I. A plot of the yield stresses of the oxygen alloys, A, B, C, and D, indicates that varies linearly with CO1/2, where Co is the oxygen concentration, Fig. 1. This is in accord with Fleischer's6 theory for solution strengthening if the oxygen atoms do not cluster, or the cluster size remains constant with increasing oxygen concentration. In Fig. 1, it appears that if one could prepare some oxygen-free zirconium its yield stress would be very low. Therefore, we shall assume that for the oxygen alloys is equivalent to O0, the strength increment contributed by the presence of oxygen. The relationship between0.2and Co is expressed by 0.2 = 31.3 CO1/2, when the yield stress is in kg per sq mm and the concentration is in at. pct. Each of the hydrogen alloys, Al, A2, A3, and A4, contained 0.081 at. pct 0 as an impurity. In Fig. 1, it appears that this small amount of oxygen makes a significant contribution to the strength which cannot be ignored when we evaluate the contribution of the finely dispersed hydride. Let us assume the validity of the following equation: a0.2 = (a2o+a2R)1/2 [2] which is analogous to Eq. [I] for single crystals, and calculate values of UH for the hydrogen alloys by using the experimental values of 0.2 and o (0.081 at. pct) = 8.9 kg per sq mm. For 0.36 at. pct H, oH = 6.47; for 0.72 at. pct H, OH = 11.30; for 2.16 at. pct H, OH = 19.4; and for 3.60 at. pct H,

Jan 1, 1965

By Jennifer Pell

Dunsmuir Ventures? Nanuq diamond project is located approximately 250 km northeast of Baker Lake and 170 km north of Chesterfield Inlet. It occurs at the intersection of the Wager Bay shear zone with the Keewatin Arch, a major long-lived crustal uplift. The newly discovered diamondiferous kimberlites at Rankin Inlet, Repulse Bay and on Melville Peninsula also occur along this arch. Kimberlite indicator mineral (KIM) sampling has outlined a distinct KIM train more than 35 km long and 6 km wide. Geomorphological studies, boulder displacements and dispersion of magnetite in tills suggest that glacial transport distances were on the order of 4 to 6 kms only. The presence of multiple sources within the main Nanuq indicator train would account for its length and breadth. A second train has been located on the west central part of the property and anomalous concentrations of KIM occur elsewhere. Pyrope garnets (G9?s and G10?s), diamond inclusion field (DI) eclogitic garnets and DI chromites were confirmed by microprobe analyses. Clinopyroxene thermobarometry indicates a cool geotherm, approximately 35 mW/m2, and that mantle within the diamond stability field was tapped. An aeromagnetic survey has identified a number of anomalies. Those with down ice KIM support will have ground geophysical follow-up and will be tested in a spring 2004 drill program. Dunsmuir is optimistic that this will lead to the discovery of a new kimberlite cluster on the Nanuq property.

May 1, 2004

By Derek T. Novotny

Blasting cap precision is of major importance to advanced blast design. New technologies have introduced the use of microchips within detonator casings in the hope that the electronic control of the timing element will increase the accuracy of the cap and therefore improve the results of perimeter control blasting applications. The electronic detonators have proven to be accurate in timing tests done to date. They boast cap scatter results to microsecond accuracy, but the question is, does this degree of accuracy actually prove to be beneficial during practical use in the industry, or are conventional technologies applicable.

Jan 1, 1998

By D. Scott Scovira, Ruilin Yang

Blast vibration in the highwall from a cast blast in open pit mines or in the hanging walls from a stope blast in underground mines is a common concern. Vibration in such cases is a typical near-field situation where the distance from a blasthole to a point of interest varies significantly compared to the distance between the blast as a whole and the point of interest. Most existing blast vibration models are designed for far-field vibration using a single seed wave to represent all blastholes within a blast and do not simulate wave shape change over the distance.

Jan 1, 2010

The processes by which particles and bubbles interact capture many of the central concepts of colloid science and hydrodynamics. This area of research embraces hydrodynamics, interfacial(including capillary) forces, particle and bubble behaviour and solution chemistry. In this review, we discuss collision, attachment and stability efficiencies. We deal with the identification of a flotation ?domain?, the deformation of a bubble surface upon interaction with a solid surface, the kinetics of three phase contact line expansion and the determination of attachment efficiencies through to the direct measurement of bubble-particle interaction forces. We have recently carried out a test of collision theory where the latter embraces both inertial and centrifugal forces. The real challenge is now to quantitatively describe the behaviour of real systems and to incorporate a reliable description of the behaviour of particles in flotation froths. The approach described is very robust when applied to flotation, both from qualitative and quantitative points of view, providing an intellectual foundation for understanding this complex process in separation science and technology.

Jan 1, 1999

By L. Vollert

In August 2018, the first full-scale HydroFloatTM cells for the recovery of coarse composited copper and gold were commissioned at Newcrest’s Cadia Valley operation in New South Wales, Australia. The primary objective of the installation is to recover coarse value-bearing composites that are lost to conventional flotation tailings, without the need for additional power input for particle size reduction to improve mineral liberation. This paper examines the application of Eriez HydroFloatTM technology for the recovery of coarse, poorly liberated copper sulphide particles drawing on recent experience from lab scale testwork through circuit design and commissioning of the full-scale installation at Cadia Valley. INTRODUCTION In the face of declining copper head grades and a tightening regulatory environment around the use of wet tailings dams, the processing of copper ores at coarser particle sizes has become a focal point for the industry. Sulphide flotation using the Eriez HydroFloatTM is one of the emergent technologies that sits under this umbrella of coarse pre-concentration. It has been demonstrated through numerous lab and pilot scale testwork programs carried out by Newcrest and others (Awatey, Kohmuench, Thanasekaran, Skinner & Zanin, 2013), to improve the flotation recovery of sulphide-rock composite particles with low surface liberation, relative to conventional flotation technology. The HydroFloatTM technology has been used widely for the recovery of coarse potash, phosphate, coal, vermiculite, spodumene and diamonds but has never been applied at full scale in either gold or sulphide flotation. In August 2018, the first full-scale 3.4 m diameter HydroFloatTM cells for the recovery of coarse composite copper and gold were commissioned at Newcrest’s Cadia Valley operation in New South Wales. The primary objective of the installation is to recover coarse value-bearing composite particles that are lost to conventional flotation tailings, without the need for additional upfront power input for particle size reduction to improve mineral liberation.

Jan 1, 2019

By M. K. Mohanty

Over the years, screen bowl centrifuges have been widely used for dewatering fine coal in coal preparation plants in the United States and elsewhere. Its popularity is attributed to its relatively low cost, its high capacity of providing low moisture content product and its relative ease of operation and maintenance. It is generally recognized in the engineering and scientific communities that screen bowl centrifuges provide some degree of particle size separation while dewatering fine coal in a common application. However, the extent of differential partitioning of coarse and fine particles achievable by a screen bowl centrifuge has not been systematically studied in the past. The present investigation was aimed at conducting a parametric study using a statistically designed experimental program to better understand and optimize the size classification performance of a screen bowl centrifuge. A continuously operating screen bowl centrifuge having a bowl diameter of 0.5 m was used for this study at the Illinois Coal Development Park. Three key operating parameters, i.e., feed flow rate, feed solid content and pool depth, were varied to conduct a total of 17 experiments using a three-level factorial test matrix. Some of the best size separation performances achieved in this study may be described as having an imperfection value of 0.13 at an effective separation size (d50c) of 38 µm and an imperfection value of 0.27 at an effective separation size (d50c) of 2.8 µm. Due to an effective separation of ultrafine high ash materials, the ash content of the screen bowl feed was reduced from 22.3% to a minimum of 8.84% with a combustible recovery of 84.1% and an ash rejection of 71.6%. A higher combustible recovery of 92.1% was achieved at a product ash content of 12.5% with a d50c of 2.8 µm and imperfection of 0.27.

Jan 1, 2008

By L. Bloomquist

This paper describes how Automated Mining Systems (AMS) is evolving the state-of-the-art in guidance systems for autonomous underground vehicles. The techniques, trade-offs, and lessons learned from these systems are described, including the safety regime that has been implemented. First generation autonomous guidance systems for underground vehicles relied on infrastructure for the vehicle to follow. However, there are additional costs associated with that approach. The current generation uses a pair of laser range finders as its only guidance sensors. This system uses a minimum of infrastructure, in the form of a redundant system of location referencing. Advanced steering and drive control algorithms are incorporated into this generation of system. The next generation of infrastructureless guidance systems will be based on a 3D vision sensor, which was originally developed for autonomous Mars rovers and is being adapted for underground mining use. Results of early underground field trials are presented, along with a description of this emerging technology.

Jan 1, 2004

By L. Bloomquist, C. Arnoldi

"This paper describes how Automated Mining Systems (AMS) is evolving the state-of the- art in guidance systems for autonomous underground vehicles. The techniques, tradeoffs, and lessons learned from these systems are described, including the safety regime that has been implemented.First generation autonomous guidance systems for underground vehicles relied on infrastructure for the vehicle to follow. However, there are additional costs associated with that approach.The current generation uses a pair of laser range finders as its only guidance sensors. This system uses a minimum of infrastructure, in the form of a redundant system of location referencing. Advanced steering and drive control algorithms are incorporated into this generation of system.The next generation of infrastructureless guidance systems will be based on a 3D vision sensor, which was originally developed for autonomous Mars rovers and is being adapted for underground mining use. Results of early underground field trials are presented, along with a description of this emerging technology."

Jan 1, 2004

By Thomas P. Mucho, Thomas M. Barczak, Dennis R. Dolinar

Maintaining ground stability in the gate roads, particularly the tailgate, has always been critical to the success of longwall mining, both in terms of safety and productivity. Several new support technologies have been developed in recent years to replace conventional wood and concrete cribbing for secondary roof support. Since their performance characteristics are unique, the best practices that have been developed with conventional wood cribbing may not be applicable for these alternative support technologies. Therefore, with so many options to consider and the importance of achieving adequate ground control at minimal cost, the trial-and-error approach to longwall gate road support is no longer prudent. This paper discusses a design methodology for standing secondary tailgate supports. This design technique requires in-mine measurements of tailgate support loading and convergence to establish a tailgate ground reaction behavior based on support and strata interaction. The methodology uses the performance characteristics generated in the National Institute of Occupational Safety and Health's (NIOSH) Mine Roof Simulator (MRS) to match the stiffness and load characteristics of various supports to the measured ground reaction behavior. It can be used to determine the appropriate application of alternative roof support systems or to design in-mine trials so that a fair and equitable comparison of different support systems can be made. A case study of the methodology at a western Pennsylvania mine site is presented in the paper, including a comparison of four alternative support technologies to the conventional wood and concrete cribbing historically used at this particular mine.

Jan 10, 2000

By Ali Jaberi Zamharir, Abolfazl Shoghian‐Alanaghi, Hossein Aghajani, Arvin Taghizadeh Tabrizi

In this study, the leaching rate of molybdenite concentrate was evaluated in sulfuric medium, and the influence of the diverse oxidants including hydrogen peroxide, manganese oxide, copper sulfate on the leaching rate was studied. Also, the effect of the addition of the ethylene glycol to the hydrogen peroxide was studied and results showed that with the addition of ethylene glycol, the leaching rate is increased 55% from 41% up to 80.3%. The optimum condition is achieved as 0.7 M of H2SO4, 4.4 M of H2O2, and 3.5 M of EG at 30 °C within 4 h of leaching time and 500 rpm. Also, inserting the oxygen with the pressure of 6 bar to the leaching autoclave, the leaching rate is increased more up to 86.4%. Finally, the leaching process was studied kinetically and the determined mode of controlling factor was specified based on the activation energy which equals 46.252 kJ/mole indicating the chemical reaction mode.

Jun 5, 2022

By Mann V. I

The Mount Isa property has been in operation since June, 1931; during this period operations have changed from the production and treatment of carbonate ores to the mining, milling, and smelting of sulphide ores. This change involved revision of ore-extraction methods.Stoping methods have been designed to apply to parallel lodes ranging from 10 ft. to over 100 ft. in width and dipping at 50° to 60°. The hardness and strength of the ore and enclosing wall rocks, together with the strength and thickness of the country rock between lodes, have permitted the selection of a sub-level stoping method for mining the sulphide ores.

Jan 1, 1938

By Christoph Mueller

Mining operations are characterized by cost pressure and cycling product prices. A high potential for enhancing efficiency is the integration of all single steps of the mining working chain into a production process structure to make advantage of an optimized flow of material and information through the ?moving ore factory?. As modern mining machinery today is controlled electronically and even already operated autonomously, a smooth and cost efficient flow of data in the mining process will be crucial for cost efficient future mine operations. Therefor, the International Rock Excavation Data Exchange Standard (IREDES) was launched by major players in the industry. The task of this initiative is to define a ?common electronic language? for easy and standardized data exchange between mining machines and central computer systems. As in other industries, this standard is expected to have significant impact on the use of automated equipment. It shall provide easy ways of using multi vendor machine installations in data controlled mining processes. At the same time it reduces cost for individual development of interfaces for all parties involved. Standardized data exchange is also a crucial precondition to integrate the mining process into enterprise level modeling, cost analysis and decision finding systems. The standard?s technical architecture is open and flexible for future applications. It uses modern XML technology enabling easy data exchange with commercial databases as well as open on line networking. The IREDES work is carried out by the initiative members working jointly together in the technical work groups. Prototyping implementations of the Drill rigs profile are currently going on. Further profiles under development cover LHD?s/Loaders/Trucks and Explosives Chargers. The first official release covering the Drill Rigs profile is planned for the end of 2002.

May 1, 2002

In general, the metallurgical industry has so far been slower than the chemical industry to adopt ion exchange materials for industrial processes. The atomic energy industry presents a marked exception to this general situation, and the literature shows a rapidly increasing use of ion exchange techniques for the recovery of atomic energy metals on scales ranging from the ultra micro up to that of the largest mining operations. In many cases, the processes used would be equally applicable to more common metals and it is hoped that this review will be of interest to metallurgists outside the specialised atomic energy field. The review is intended to describe developments of ion exchange processes made during the last three years. Earlier studies have been summarised by Kunin and Preuss (1956) and Roland (1957). In order to restrict the number of references discussed, purely analytical procedures have been omitted and only those processes which have been conducted on a reasonably large scale or which, from their nature, areclearly capable of being upscaled, have been considered. The paper is divided into five main sections concerning respectively:Water treatment and effluent disposal.Metal recovery and purification.New ion exchange materials.New ion exchange equipment.Membrane cells.WATER TREATMENT AND EFFLUENT DISPOSALA high proportion of atomic reactors, and particularly those of American design, are cooled by water which is...

Jan 1, 1961

By R. S. Handy

This paper describing the milling practices at tae concentrators of the Bunker Hill and Sullivan Mining and Concentrating Co. is one of a series being prepared by the United States Bureau of Mines on milling methods and costs in the United States. The possibility of useful comparisons has prompted the description of all five of the mills operated by the Bunker Hill and Sullivan Company in northern Idaho. The general features of these mills are tabulated below: [ ]

Jan 1, 1930

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