Search Documents

By R. J. Woody

DESIGN of the most economic continuous counter-current decantation (CCD) circuit is based on selection of the number of stages and the wash volume that will give the minimum summation of the following items: 1) Capital and operating costs of the CCD circuit. 2) Capital and operating costs of the precipitation circuit. 3) Value of the dissolved product lost.

Jan 7, 1958

By S. K. Kawatra

Many mineral oxide and multi-component oxide (basalt) specimens break down into powders upon expo-sure to sodium vapor at elevated temperatures for extended times. This paper examines several possible mechanisms of oxide breakage by sodium vapor, both experimentally and from a thermodynamic viewpoint. The oxides for which reduction by sodium was thermo-dynamically favorable all exhibited some degree of fragmentation. The oxides which were not favorable for reduction by sodium did not exhibit fragmentation, with the exception of rutile, a titanium oxide. The rutile fragmentation was caused by the reduction of iron that was in solid solution in the rutile crystal structure.

Jan 1, 1995

By L C. Taylor

Both the U. S. Navy and the U. S. Army are interested in knowing more about the loading applied to vehicles which are unfortunate enough to encounter a detonation of a buried mine in the course of performing their normal duties. The Dynamic Effects Laboratory at the University of Maryland has been involved in small scale testing for ten years to assist the Navy and the Army in understanding the loads that are applied to personnel carriers when a buried explosive detonates beneath them. This paper describes results from small scale tests conducted to determine the loading mechanisms on target plates when subjected to loading due to the detonation of a buried mine in saturated sand, dry sand, and water. Transparent target plates were utilized in order to determine the loading process beneath a floor board on armored vehicles. Various charge sizes were scaled in the laboratory accordingly to a standardized full size threat encountered in the battlefield. Tests were conducted in saturated sand, dry sand, and water keeping the stand-off distance of the target and the depth of burial of the charge constant. In the case of water impacting a transparent PMMA plate the crack propagation was recorded and the crack velocity is determined. Additional tests were performed in saturated sand by varying the stand-off distance of the target but keeping the depth of burial of the charge constant. The small-scale test results could be scaled to full scale by using verified scaling laws.

Jan 1, 2016

By Carolina Conter Elgert

A influência dos parâmetros termomecânicos e da adição de elementos microligantes na relação processo, microestrutura e propriedades de chapas laminadas, do aço DIN 20MnCr5 foi o objetivo de estudo deste trabalho. Os testes foram desenvolvidos em escala piloto, no laboratório de processos metalúrgicos do IPT. Foram testadas variações de composição química, condições de laminação e taxas de resfriamento. Ocorreu alongamento dos grãos austeníticos para os materiais processados por laminação termomecânica e refino de grão e aumento de limite de escoamento para os aços microligados, tanto na condição de laminação convencional, quanto na condição de laminação termomecânica.

Oct 30, 2017

By Raymond A. Binns

Exploration for undersea polymetallic sulfide mineral resources with high economic potential would be more effective given an ability to predict sites with particularly high gold contents (averaging say > 10 ppm Au). Herzig et al (1993) addressed this issue shortly after recognition that deposits in the back-arc Lau Basin (average 3.8 ppm Au) were enriched in gold relative to mid-ocean ridge sites (average 1.2 ppm Au). Small but significant numbers of hydrothermal sites with massive sulfide deposits averaging >10 ppm Au have since been discovered. The principal genetic factors underlying gold enrichment include depositional processes at and below the seabed, and the source of gold. It is timely to consider whether resolution of their relative importance can be translated into practical criteria for exploration strategies focused on especially gold-rich deposits. Comparing the ?grade? of seafloor deposits using analyses cited in research papers is fraught with difficulty, but there is no alternative at present to assuming that such averages provide an initial tenor guide. On this basis, four known polymetallic hydrothermal sites from convergent plate margins fit the exceptional-gold category with >10 ppm ?average? Au, while one from a divergent margin comes close: Sunrise (Myojin Knolls; 20 ppm ?average? Au) and Suiyo Seamount (28 ppm Au) in the Izu-Bonin Arc are frontal arc volcanoes dominated by rhyolite and dacite respectively, contrasting with more common mafic neighbor edifices (Iizasa et al., 1999). In both cases gold-rich massive sulfides occur in summit calderas with significant development of pumiceous volcaniclastic rocks, at depths around 1300 and 1370 m respectively. In the Eastern Manus Basin, PACMANUS (~1700 m; 14 ppm Au) and Suzette (~1550 m; 22 ppm Au) occur along the crests of volcanic ridges dominated by dacite/rhyodacite and andesite/mafic dacite respectively (Binns, 2004). Caldera structures are lacking. Although the Eastern Manus Basin is tectonically a rifted back-arc, its submarine volcanic edifices (picritic basalt to rhyodacite) have distinctly arc-style geochemical and isotopic affinities, differing from more typical back-arc basin basalts at the spreading axis further west (central Manus Basin). Probably as a consequence of transpression and a marked rupture in the New Britain subduction zone, submarine arc volcanism has here extended into the rifted back-arc region.

Jan 1, 2005

By Derek V. Ellis, Jack L. Littlepage

"Marine ecosystem effects ar1smg from the discharge of man-generated wastes to the sea can be schematized as: acute poisoning, chronic poisoning, enrichment, suffocation, temperature effects, salinity effects, toxin bio-concentration, changed production rates and changed species equilibria. A professionally designed site-specific monitoring program to check for such effects can not only safeguard the marine ecosystem from degradation, but it can also protect the industry involved from unanticipated remedial action after expensive construction has been undertaken. Monitoring programs should consist of three steps. Step 1 is an ecosystem survey which should be undertaken prior to final design of the discharge system and submission of applications for permission to discharge, because there can be considerable cost savings in obtaining information at an early stage in development. Step 2 involves location of the effluent field at the time of starting discharge, and analysing its dispersal behaviour. Step 3 consists of ecosystem monitoring with sampling stations and specific tests based on the accumulated prior information."

Jan 1, 1972

By John A. Meech

In many multiple-sulphide ore flotation processes, it is desirable to concentrate each of the various valuable minerals into separate products. Although there are a variety of techniques and chemicals which can be employed to produce efficient separation, two basic types of flotation circuits are used: The Differential Flotation Circuit and the Bulk/Selective Flotation Circuit. Figure I depicts these two circuits in their most simplified form for the production of two concentrates and one tailing product. If three or more valuable minerals are present in an ore, a variety of combinations or extensions of these two basic flowsheets may be used. There are many examples of the successful application of both circuit types with ores containing similar minerals. Each ore must be tested individually to decide on which circuit is best. However, the following general statements can be made: 1) The differential circuit will have higher capital and operating costs than will the bulk/selective circuit due to higher rougher capacity requirement. 2) The differential circuit will achieve better separation than will the bulk/selective circuit since it is usually easier to reactivate a depressed mineral than it is to depress an already active mineral. If the deactivation problem with the bulk/selective circuit . . in can be overcome, there is a clear economic argument for its use

Jan 1, 1977

By J. S. Fox

Major-element data for unaltered, unmineralized felsic host rocks from a number of stratigraphically simple, massive volcanogenic Zn-Cu(-Pb) sulphide deposits of low metamorphic grade have been compiled. The petrochemical affinities of these host rocks have been determined (by standard means and by discriminant analysis) and compared. This comparison indicates that volcanogenic deposits in felsic terrains are not restricted to the classical calc-alkaline rock association as previously thought, but can actually be hosted by rocks showing a range of iron content. There is a positive correlation between differentiation trend and are tenor. Zn-Cu ores usually have iron-rich felsic hosts (most Canadian Shield deposits); Pb-Zn -Cu ores have iron-poor felsic hosts (Japanese, Iberian and Tasmanian deposits). This parallels the antipathetic relationship between iron content and background lead levels evident in young, unmineralized, island arcs as well as in many older belts. Correlations between differentiation trend on one hand and massive ore mineralogy and the relative proportions of various rock type (including rhyolite, quartz-porphyry and coarse pyroclastic rocks) on the other are also evident. It is concluded that the recognition of a calc-alkaline differentiation trend cannot be used as a prospecting guide, as has previously been proposed. However, in view of the above correlations, the recognition of a given trend may aid in the formulation of an effective exploration philosophy.

Jan 1, 1979

By L. Rodd, C. Walker, T. Koehler

"The energy content of slag represents approximately 80% of the total energy inputs to a laterite nickel electric smelting furnace. Conventional slag handling methods produce only low grade heat and the entire thermal content of the slag is wasted. A heat recovery system proven on BOF slag in the mid 1980's can be adapted to a laterite nickel rotary kiln electric furnace (RKEF) plant. Slag is granulated using a high velocity air jet inside a waste heat boiler to produce slag granules. Granules are cooled during flight via radiation to water-cooled boiler walls and by convection to the granulation air. This system has the potential to recover 80% of the total slag energy in the form of hot air and steam.Integration of the recovered slag energy into the RKEF smelter can be achieved by a number of methods, including the use of preheated air at the ore dryers, kiln or existing power plant. Energy from the slag boiler may be used to reheat boiler feed water from the power plant or to produce superheated steam and generate electricity. The heat recovery system can provide up to 25 - 30% of the total electrical requirement of each RKEF line and a reduction in CO2 emissions of 234,000 tonnes per year.The total cost of slag heat recovery, including CAPEX and OPEX, is $2.5/GJ, which is competitive with using coal when CO2 credits are $18 per tonne. With Clean Development Mechanism (CDM) carbon credits currently selling at €13 ($20 USD) per tonne CO2, there is considerable opportunity for slag producers in regions including South America, Korea, Indonesia and Africa. Increasing fuel costs and more wide-spread legislation for GHG emissions will likely create conditions in which slag heat recovery could generate a favourable return on investment."

Jan 1, 2010

By Jalal Vakili

In designing very large excavated slopes which are becoming increasingly common in both mining and civil engineering projects, the most important decision of the engineer is the selection of a slope angle. The purpose of the geotechnical study of the slope is to ensure reasonable stability of the slope in the most economical way. Because the rock mass composing each slope is unique, there are no standard solutions for slope stability analysis. A practical solution is formulated from the basic geologic data, engineering properties of the rock, geometry of the slope, and ground water observations. Stability analysis consists of analyzing the forces causing and resisting slope failure. There are several methods of slope stability analysis. The limit equilibrium method evaluates the overall stability of the sliding mass just on the verge of slip, using some or all of the three equations of static equilibrium of a plane problem. The stress-strain relationships of the rock mass are not considered. Method of analysis include the assumption of the shape of the slip surface. Peterson (10) introduced the Swedish method of analysis in 1916, which is based on cylindrical sliding surfaces. Fellenius (4) in 1926 extended this method and introduced the method of slices. This method was refined by Bishop (I) in 1955 and later used by Morgenstern and Price (8) in 1965. In many cases layers of extremely soft strata or strata weakened by neutral stress cause failure to take place by translation along plane of weakness instead of by rotation on a circular surface. In this paper, a slope with a horizontal layer of weak meterial is selected for analysis. This is a usual case for open pit lignite mines where lignite seam may be non-cohesive and 'weaker than the overburden rock or a soft clay layer underlies the seam. It is also a common case of rock fill dams supported on a foundation stratum of clay where the strength of the clay layer is less than that of the rock fill. It is shown that utilizing this method, the location of potential failure surface and the value of the minimum factor of safety can be calculated directly and the trial computations of factors of safety for a number of assumed failure surfaces are not necessary.

Jan 1, 1982

By Georgy A. Cherkashov, Andrey V. Efimov, Yury S. Borodaev, Nadezhda N. Mozgova, Sergey G. Krasnov, Tamara V. Stepanova, Alexander M. Ashadze

"Abstract - A horizontal mineralogical-geochemical ore zonation with a southeast to northwest trending succession of Cu and Fe (Zn) main zones has been discovered in the Logatchev hydrothermal field (14°45??N Mid-Atlantic Ridge). The major minerals are pyrite, chalcopyrite, bornite, isocubanite, digenite and chalcocite. Zn-sulfide, marcasite and covellite are less abundant. Rare minerals are native copper, zincian copper and cobalt pentlandite (first found in oceanic massive sulfides), Cu and Cu-Co-bearing Fe-disulfides. Two groups of the main sulfide assemblages with different copper contents are recognized: Group I comprises assemblages with primary sulfides (isocubanite, chalcopyrite, pyrite and Zn-sulfide; Cu up to 35 wt% in Cu-bearing minerals); Group II contains assemblages with secondary Cu-rich sulfides (bornite, digenite, chalcocite; Cu ~60 wt%) as well as rare minerals (cobalt pentlandite, native copper and zincian copper). The assemblages of Group I formed at a temperature of about 300°C; the sulfur fugacity (log fs2 atm) at 300°C is probably 9.9. Relations between minerals of this group are contradictory, attributed to non-equilibrium environments, and no unified sequence of crystallization of minerals has been determined. Minerals of Group II replace, rim or cross the assemblages of Group I. Group II minerals crystallized in a distinct sequence (cobalt pentlandite-bornite-digenite- chalcocite-native copper), with increasing copper content from the start to the end of the depositional sequence. This may correspond to pH from 7 to 8 near Eh = -0.2 at 250°C. Minerals of this group were generally formed under hypergene alteration processes. Compositions of ore minerals were studied by means of electron microprobe analysis (EMPA) (150 analyses). Narrow composition fields were revealed in all main sulfides, which comprised known experimental data. ZnS contains 6.0 to 28.0 mol.% FeS, which is close to data known for other hydrothermal massive sulfides from the Mid-Atlantic Ridge (MAR). A common admixture in ZnS is Cu (0.16 to 1.32 wt%). Rare grains of unusual anisotropic Fe-disulfides, (Fe0.95Cu0.05)S2 and Cu(Fe,Co)9S20, were found among the ore minerals."

Jan 1, 1999

The Industrial Minerals Milling Section of the Mineral Processing Division has been engaged for the past three years in a study of the separation of minerals, by means of electronic sorting equipment, on the basis of their colour. Considerable knowledge of the subject has been built up. Because the object of this study is application as a means of beneficiation, a number of examples of the separations achieved are presented. Introduction T 0 the mineral collector, the colour of a mineral may be pleasing, even fascinating; to the mineralogist, student or professional, it may also be practical. It serves, to some extent, as a distinguishing feature in many minerals, and helps to fix with reasonable accuracy the identity of a few. It may now become a useful tool of the mineral dresser. The idea of using a difference in colour as a means of separation of one mineral from another is not new. Hand sorting dates back to ancient time. However, the means by which this can be done mechanically was developed only during the past decade. As far as the Mineral Processing Division is concerned, interest dates from March, 1960, when the following item was observed in the

Jan 1, 1965

By Mike Trovant, Stavros A. Argyropoulos

"A fixed grid numerical model for phase change problems is proposed. The model solves for heat transfer and fluid flow, via the coupled solution of the energy, continuity and momentum equations. In addition, the numerical scheme accounts for temperature varying thermophysical properties and determines the shrinkage profile resulting from phase and density change. Simulations are run to determine the effect of varying model parameters and wall cooling rates on the location and shape of the shrinkage void formation in cylindrical casts. Results are shown for both aluminum and magnesium.IntroductionThe mathematical modeling of phase change processes (be they solidification or melting problems) entails solving for many interrelated phenomena. A comprehensive numerical simulation of the casting of a metal, for example, would have to account for: (a) heat transfer in both the solid and liquid portions of the metal and in the mold, (b) the release of latent heat during phase change, (c) fluid flow behavior in the liquid portion of the metal, (d) temperature induced shrinkage caused by liquid contraction and solidification contraction, and (e) the development of thermal stresses with accompanying shrinkage in the solid portion of the cast and mold. A schematic of the relationships that exist between the coupled equations which govern solidification is shown in Figure 1."

Jan 1, 1994

By Youn-Bae Kang

Evaporation mechanism of S from liquid Fe–C–S alloys at 1873 K was proposed by analyzing available experimental data. It has been known that increasing C content in liquid alloy increases activity coefficient of S ðfSÞ, and it could raise driving force for the evaporation reaction S = S(g). However, experimental data of the evaporation of S in the Fe–C–S alloys could not be accounted for only by considering the increases of fS. In the present study, formation of carbosulfides, CS(g) and CS2(g), was additionally taken into account in order to explain role of C for the accelerated S evaporation. Surface adsorption of S was also taken into account, which retards the evaporation rate of S. An evaporation model equation was formulated. It can be applied to calculate the evaporation rate of S over wider C content (from zero to its saturation to liquid alloy).

By Kumar P. Dharmasena, Haydn N. G. Wadley, Bill W. Choi

"Non-contact eddy current sensing methods have been developed and applied to Cd0.955Zn0.045Te crystal growth to obtain a better understanding of the melt, solid nucleation, and the growth process. The application of this sensor approach relies on a large difference in liquid and solid electrical conductivities near the melting point and requires knowledge of the relationships between the electrical conductivity, melt composition, and temperature. Using a multifrequency encircling eddy current sensor, the electrical conductivities of three different Cd1-xZnxTe (x=0.00, 0.045, and 0.08) alloys were measured as a function of temperature in a laboratory-scale vertical Bridgman furnace. The measured solid and liquid electrical conductivities were then used in electromagnetic finite element models to analyze the multifrequency responses of eddy current sensor designs during the simulated growth of a crystal. These eddy current sensors were fabricated and installed in a vertical Bridgman furnace and used to monitor many Cd0.955Zn0.045 Te growth runs. One sensor was placed in the vicinity of the ampoule tip to detect undercooling/spontaneous nucleation and two other sensors (""absolute"" and ""differential"" designs) placed to monitor the movement/curvature of the liquid-solid interface during crystal growth. The sensor data was used to characterize the initial melt state, detect the onset of nucle-ation, determine the growth velocity, and identify the shape of the interface.IntroductionSingle crystal CdTe and its solid solution Cd1-xZnxTe alloys (0.03<x<0.05) are used as infrared transparent substrates for infrared focal plane array (IRFPA) detectors [1-6] and as solid state y- ray detectors [7-9j. Cd1-xZnxTe substrates are normally ""mined"" from large polycrystalline boules grown by the unseeded directional solidification of Cd1-xZnxTe melts using either a vertical or horizontal Bridgman process [10-14]. The vertical Bridgman method is particularly popular for growing CdTe and its related compounds. In this process, a Cd1-xZnxTe ingot is produced by first melting a charge in the hot zone of the furnace and then vertically translating the furnace (with its associated axial temperature profile) relative to the stationary crucible to cause directional solidification. In spite of many experimental efforts to investigate the relationships between material purity, stoichiometry, the controllable growth parameters (furnace temperature profiles, ampoule geometries/materials, furnace translation rates and starting position) and the resulting material characteristics (grain structure, dislocation densities, IR transmission, macro-segregation etc.), the yield of Cd1-xZnxTe of a quality suitable for large area (e.g. 4 cm x 6 cm) substrates remains low (<10%). Since much of this poor yield is directly associated with the crystal growth process (e.g. melt stoichiometry, solidification velocity, interface shape, temperature gradients, cooling rate, etc.) intensive efforts are under way to improve this technology."

Jan 1, 1997

By J. S. Lee, R. K. Massarsch

"A 3.2 km long immersed road tunnel forms part of the Busan-Geoje Fixed Link in South Korea, which connects Korea's second largest city Busan, with the island of Geoje. To ensure the water tightness of the joints of the segmental tunnel structure and to limit the forces in the shear keys, the differential settlements have to be limited. This was achieved by extensive soil improvement of the marine clay below the tunnel with cement deep mixing (CDM) and sand compaction piles (SCP). This paper focuses on the characteristics of the marine clay, the basic design principles, layout and constructional issues of the CDM soil improvement, and numerical and numerical analyses to predict settlement and stability.INTRODUCTIONThe Busan-Geoje Fixed Link consists of two short cut & cover tunnel access ramps, a 3.2 km long immersed tunnel (Figure 1) and two long span cable stayed bridges. The tunnel consists of eighteen concrete elements each of 180 m length having a rectangular cross section of 26.5 m in width and 10 m in height. The tunnel elements are cast in a dry dock on shore and floated out to the sea, immersed in their final positions on a gravel bed in pre-excavated trench and connected to each other by a dual gasket system. The water depth was up to 50 m making the tunnel of the deepest yet constructed. After immersion, the tunnel is protected by backfill material at the sides and rock armour on top. Each tunnel element consists of eight 22.5 m long segments. The joints between the segments and between the tunnel elements are equipped with EDPM water stops, Omega seals and concrete shear keys. The longitudinal displacement behaviour of the segmental tunnel structure in the varying ground conditions represents a complex soil-structure interaction problem which has been modelled with a FEM structural model representing the tunnel, the joints and with springs to represent the soil that are derived from the PLAXIS soil/foundation models. In order to ensure the water tightness of the joints which have limited opening capacity and to limit the forces in the shear keys, differential longitudinal settlements have to be limited. This is achieved by limiting the variations in subgrade modulus along the alignment and it in practice means that differential settlements are limited to a few tens of millimetres. Without soil improvement of the marine clay below the tunnel, long-term tunnel settlements of up to 400 mm were predicted when taking into account the likely variations in the trench profile, backfilling and uncertainties in the soil properties. Such large total settlements led to large variations in the sub-grade reaction along the alignment, which in turn resulted in significant differential settlements, unacceptable joint opening and large shear key loading. It was therefore decided to carry out extensive soil improvement with cement deep mixing (CDM) (CDIT, 1999) and sand compaction piles (SCP) (Kitazume, 2005) after studying a number of foundation alternatives."

Jan 1, 2015

By Madhu G. Ranade

A statistically designed pot grate- kiln test program was conducted to determine the agglomeration process variables necessary for increasing the low temperature disintegration resistance (LTD) and reducibility (R40) of magnetite-based Empire acid pellets. The ASTM tumble index and compression strength were to be maintained at an acceptable level. Six process variables, bentonite addition level, preheat time and temperature, firing time and temperature, and cooling rate, were investigated within the constraints of the Empire plant. The bentonite addition level and firing temperature had the largest effect on pellet properties. The results of this program were verified during a pl ant trial. The target firing temperature at the Empire Plant has been decreased for increasing the LTD and R40 of commercially produced Empire pellets

Jan 1, 1985

By S Whitton, W Wimmler, L Wimmler

“Given the increasing scrutiny of the mining industry and its relatively poor record with regards to mine tailings management, increased requirements to minimise water usage (often accompanied by very high costs of water) and the need to demonstrate achievable long-term closure strategies, it is likely that the option of a filtered tailings system will need to be considered in many operations in future.” (Australian Centre for Geomechanics, 2018). Given such a statement as a conference introduction, it is only appropriate that a range of potential technologies are investigated and compared, to create awareness for even underrated but appropriate technologies. The advantages and disadvantages of all technologies need to be considered and analysed. Suppliers are swift to promote their technologies advantages; however aspects of sustainability are not always fully understood. Perhaps a combination of two filtration technologies is appropriate. This paper delves into the technical details, good or bad, of four mechanical dewatering technologies in tailings dewatering and provides insight on an undervalued and, in the author’s opinion, young technology – the screw press.

Jul 1, 2021

By M D. Winning

The historical development of the elemental sulphur recovery industry in Western Canada is reviewed for the period 1952 to 1965. A brief technical description of a typical modified Claus sulphur recovery unit is presented. Some predictions are made concerning the future of the elemental sulphur recovery industry in Western Canada. THERE are evidences of sulphur or its compounds having been used for religious and medicinal purposes as far back as we have a recorded knowledge of history. As typical examples, sulphur was burned as a sort of inverse incense to drive away evil spirits at religious festivals, sulphur ointments were used by the early Egyptians to cure eye ailments, and hot sulphur-spring water was used as a cure for a variety of ailments. Thermopyle was called "Hot Gates" be-cause of its fame as a spa as well as a mountain pass. The Romans discovered the sulphur deposits in Sicily and mixed sulphur with bitumen for incendiaries; and, of course, anyone familiar with the travels of Marco Polo knows about the Chinese development of gunpowder, which contains sulphur. In some aspects things haven&apos;t changed much today. We still use sulphur-bearing ointments, and we still use the hot sulphur springs such as the one at Banff in Western

Jan 1, 1965

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969