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By Walter C. Lawson

The primary objective in laying track in panel sections is to reduce the number of track laborers required. This is possible because the work is mechanized. Moreover, because the work is mechanized and each of the operations needs only a few men, and each is self-contained, the work can be carried on at night as well as in daylight; therefore, the method provides a means of preparing tracks on more than one shift. The laying of tracks in open pits and quarries in panel sections is not new but new methods have been made possible by the introduction of new types of equipment. The purpose of this paper is to describe the methods that are followed in the Morenci open pit. General Mining Operations Full-scale ore production at Morenci is about 50,000 tons daily. The normal yearly output of ore and waste is 32,000,000 tons, of which 30,000,000 tons is handled by rail haulage. This requires the building of approximately 47 miles of loading and other temporary tracks during a 12 months' period (Fig I). Broken ore and waste is loaded into 90-ton capacity dump cars with 5-cu-yd full-revolving electric shovels. Shovel banks are uniformly 50 ft high. They are blasted with churn drill holes and the broken material from a blast is loaded out with two shovel cuts, the first one being called (locally) the "splatter" cut and the second one the "clean-up" or "face-up" cut. When a shovel is making its clean-up cut, the loading track is about 70 ft from the toe of the bank and, under normal conditions, a bank is blasted against it without removing the track. It is thus evident that each track is used for two shovel cuts before relocation is necessary, inasmuch as a single position serves for both the clean-up cut prior to blasting and for the splatter cut following the blast. The normal advance of a solid bench by a single blast is 40 ft (Fig 2). Preparation OF Panel Grade In preparation of panel grades bulldozers and rooters are used for the bulk of the work and an auto-patrol road grader for the final stage. At Morenci, bulldozers have always been used for track-grade preparation, but before the introduction of the other two types of equipment grades were uneven and irregular at best, and always necessitated a big gang of track laborers to hand-block under the ties with rocks after a track was laid into place. High blocking also made poor track because of instability and caused frequent derailments. Under these conditions derailments were generally bad as re-railing became difficult. Much track was torn up and many tics broken in the process. The inadequacy of the hand-blocked track, together with the inefficiency of hand blocking, constantly pointed, to the desirability of reducing the amount of labor required, so various means were tried to improve conditions, such as wood

Jan 1, 1949

By Hernan Fernandez, Khalid Saif F S Al- Khayareen, Volkan Salepciler, Jacek B. Stypulkowski

Wakrah and Wukair Drainage Tunnel, WWDT is 13 km long with a 4.5 m ID sewer water tunnel about 50 to 60 m below ground surface. Integral to the project are several adits with provisions for future connections as well as four work shafts, four intermediate access shafts, ancillary hydraulic structures, and an Odor Control Facility. The shaft depths range from 50 to 60 m. The project is constructed in aggressive ground with aggressive ground water. The construction activities require years of pumping and disposal of the ground water during tunneling operations as well as construction of permanent structures in shafts. Grouting of the corrosive rock mass in corrosive groundwater for the WWDT has been described in detail.

Jun 23, 2024

By A. L. Hinde, P. J. D. Lloyd, A. R. Atkins, J. G. MacKay

The control of milling circuits by A. R. ATKINS, M.Se. (Elee. Eng.) (Visitor), A. L. HINDE, S.Se., Ph.D. (London) (Visitor), P. J. D. LLOYD, S.Se. (Chem. Eng.), Ph.D. (Cape) (Fellow) and J. G. MACKA Y, S.Se. (Chem. Eng.) (Visitor). The general behaviour of mills is described in an attempt to find a control philosophy that will permit milling circuits to produce a constant particle size. Although the experimental work has been confined to a single section of the milling circuit of one mine, it is felt that the findings are applicable to other milling circuits.

Jan 6, 1974

La central de Paucartambo pertenece a la Cerro de Pasco Corporation, cuya fuerza generada es transmitida a La Oroya mediante una línea de transmisión para 138. 000 voltios. Las partes más importantes de la central son: las obras de captación, el túnel, la tubería de precisión, Casa de fuerza en Yaupi, línea de transmisión, subestaciones y obras complementarias y las obras complementarias como la carretera y los campamentos. Es a partir de la descripción de estas obras componentes, que el objeto del texto señala los métodos de construcción empleados en la perforación y revestimiento del túnel de Paucartambo. El procedimiento utilizado para la perforación de túneles depende de su magnitud y diámetro, encontrándose que el empleo de jumbos para túneles mayores de 3 metros de diámetro es recomendable ya que acelera el proceso de perforación. Mientras que el empleo de cercas de acero es más factible en túneles que tengan mayor tiempo sin revestimiento. En el caso de revestimiento de túneles se sugiere el uso de un equipo moderno que acelere el proceso y mejore la calidad del proyecto. Finalmente, en túneles que requieran grandes volúmenes de concreto, es recomendable el uso de plantas de concreto y laboratorios de campo que los controlen ya que su costo de precio es bajo y la concentración del volumen es mayor.

Jul 20, 1959

By Edward Judd

CANADA'S mining industry is rapidly recovering from the depression through which it passed in 1921. Its total output of $183,029,600 in 1922 was 6.4 per cent. greater than that of 1921, and was exceeded by only three previous years, 1917, 1918, and 1920. Table 1 compares the output of a few of 'the more important items selected from preliminary data published' by the Dominion Bureau of Statistics. TABLE 1.-OUTPUT OF CERTAIN MINERAL PRODUCTS IN CANADA PER CENT. 1921 1922 CHANGE Cobalt, metal and in compounds, lb 252,000 443,800 +76.1; Copper contents of blister, matte, and exported ores, lb 47,620,820 43,321,400 - 9.0 Refined copper, lb 4,286,000 730,000 -83.0 Gold, fine oz 926,329 1,230,985 +32.8 Pig iron, sh. tons 665,676 429,024 -35.5 Lead, sh. tons 33,340 47,085 +41.2 Nickel contents of matte, etc., lb. 19,293,060 17,496,490 - 9.3 Silver, including that in base bullion, gold bullion, etc., fine, oz. 13,543,198 17,611,646 +30.0 Zinc (nearly all refined), sh. tons. 26,545 28,199 + 6.2 Asbestos shipments, sh. tons 92,761 136,657 +47.3 Coal, all grades, sh. tons 15,057,500 15,045,300 Gypsum shipments, sh. tons 386,550 441,160 +14.1 Natural gas, M. cu. ft 14,077,600 14,954,100 + 6.2 Petroleum, bbl : 187,540 178,570 - 4.8 Cement, bbl 5,752,885 6,943,968 +21.0 Brick, structural, all kinds, M. , , 109,009 127,137 +17.0 On the basis of estimated market values, the whole output of 1922 was contributed as follows: Metals, 33.4 per cent.; non-metallic minerals, 45.1 per cent.; structural materials and clay products, 21.5 percent.; this distribution indicates a return of the metal mining. industry nearly to the position of relative importance that it occupied. before 1921, in which year metals contributed only 28.7 per cent. to the total value. of output while non-metallics gave 51.1 per cent. Canadian cobalt originates entirely in the ores of the Cobalt district, which are mainly treated at smelters in southern Ontario, although some quantities of residues have been exported to England and Europe. Exports during 1922 increased even more than production, consisting of about four-fifths . cobalt oxides and salts, and one-fifth of cobalt alloys and other metal combinations.

Jan 8, 1923

By John Gross

THE method of measurement of surface on quartz particles was given in a previous paper.1 With such a method the relation of surface produced in crushing quartz can be compared to the work in crushing without recourse to sieve sizing or microscopic measurement. In crushing, the work input must be known with a fair degree of accuracy. With crushers, rolls, ball mills, and similar apparatus the measurement of the work in crushing is subject to possible errors, due to friction in .the transmission as well as in the machine itself. Moreover, relatively large quantities of material must be crushed to get an average figure. In the selection of a method of crushing, simplicity in design and operation was desired and this was most readily obtained by the use of a free-falling body. A description of the apparatus embodying this principle is given herewith. THE CRUSHING DEVICE The apparatus used is shown in Fig. 1 and in cross-section in Fig. 2. The material to be crushed is placed in the crushing chamber C in the steel mortar M. The mortar is 3 in. dia. by 3 in. high. Two mortars are used, one having a crushing chamber 1-in. dia. by 1/2 in. deep, with a capacity of 4 g. of quartz, the other having a crushing chamber 1 ½ in. dia. by 3/4 in. deep, with a capacity of 12 g. of quartz. The position of the mortar is adjusted by means of three centering screws A. The steel plunger P, which fits neatly into the chamber, is placed on top of the material to be crushed. Plungers of different lengths were tried and as they were found to give practically identical results the length adopted was equal to the depth of the chamber.

Jan 1, 1928

By D. T. White

Pressure acid leaching of nickel laterite ores typically involves the production of an intermediate product that is releached and refined to pure nickel and cobalt products. BHP Billiton is developing the Ravensthorpe Nickel Project to produce up to 50,000 t/y of nickel via a mixed hydroxide intermediate, which will be refined at its Queensland Nickel (QNI) Yabulu Refinery near Townsville, Queensland. The hydroxide precipitation flowsheet has been adapted to process high magnesium ores through an atmospheric leach stage, eliminate iron(III) as jarosite and oxidise iron(II) during neutralisation. The neutralisation conditions are controlled to precipitate aluminium, chromium and silicon, and to ensure good solid-liquid separation. Soluble impurities such as magnesium are purged with the tailings stream and will be managed over the long term by crystallisation in evaporation ponds.

Jan 1, 2006

By Anderson Rosa Pereira

A constante busca pela excelência na qualidade do material produzido tem gerado demanda para métodos precisos e de determinação on-line das características do material. Os métodos hoje utilizados para coleta de dados de rugosidade superficial geram amostras randômicas ou concentradas no início ou fim da bobina, o que não necessariamente mostra com precisão a rugosidade de todo o material produzido, e impossibilitam uma intervenção mais direta, precisa e automática nos parâmetros de laminação, objetivando um melhor aproveitamento dos cilindros, redução de custos e controle sobre este importante parâmetro de qualidade. Esta publicação descreve o funcionamento e a aplicação do sistema de medição de rugosidade on-line EMGSORM 3plus no controle automático de rugosidade desenvolvido para um skin pass mill. Assim, a linha principal deste artigo mostra através de um exemplo prático a aplicação de um sistema de medição de rugosidade on-line e seus benefícios.

Aug 16, 2017

By Eric Toh, Michel David

"Geo-statistics was born from mining problems: grades not being what was expected; more tons of waste than expected; in other words, dilution. Geo-statisticians now claim to have solved many of these problems, but the solutions seem to have a hard time being picked up by practitionners. One of the reasons may be the jargon which geo-statisticians are using. The reason for jargon is that obtaining solutions required a strict formulation in a statistical framework. Practicing mining engineers and geologists are not used to such a framework, and they are not familiar with the jargon. In this paper, the authors re-examine dilution in operating mines and answer two extremely practical problems, using practical language as much as possible. Can dilution be reduced by improving the quality of blast hole samples? How many samples are needed to obtain a good ore-waste discrimination, i.e. to reduce dilution to acceptable levels? Citing real situations, this paper will try to show how fairly simple concepts can be used to answer both problems. It will try to present the solut ions using a minimum of jargon, even if the theoretical solution could be obtained in a few precisely worded paragraphs.The two problems considered are the following: the first one was encountered in the Panguna deposit of Bougainville Copper Limited, P.N .G., but it occurs in every open pit operation where selective mining is required. As the cut-off is lowered, more and more mining occurs in marginal areas. Grade control is mostly based on the grades obtained from blast holes, hence, it is essential that the quality of the blast hole samples be as good as possible in order to reduce dilution, waste being sent to the mill and ore being sent to the waste dump.The second example stemmed from the grade control technique used in many gold open-pit operations in Western Australia: channels are cut on lines 5 m apart and assays are taken every metre. The pattern in the same regardless of rock type, whether one is in the oxidized zone or not. The number of samples to be treated is enormous, hence, the question arises how to find an acceptable sampling grid, and whether changing it can reduce dilution at an acceptable cost.A solution will be given to each problem separately, although in fact it could be seen that the formal framework is the same in both situations."

Jan 1, 1989

By D. C. Lynch

While a sizable amount of data exist as to the activity and distribution of minor elements between matte and metal, there has been no unifying theory presented delineating the form of dissolution of these elements in molten sulfides. In order to alleviate that deficiency the literature concerning the behavior of As, Sb, Bi and Pb in mattes is reviewed. Models present in the literature, regarding the thermochemical behavior of minor elements, are tested, and new models are presented and evaluated using thermodynamic theory. The results of those analyses are used to predict optimum conditions for the volatilization of minor elements. The dearth of data on the behavior of minor elements in nickel mattes requires that this review focus on copper- iron mattes. An effort is made, however, to utilize basic knowledge regarding nickel sulfides and the interaction of nickel with the minor elements to predict the behavior of those elements in nickel-copper and nickel-iron mattes.

Jan 1, 1993

By M. G. F. Söhnlein

In the earlier clays, these ores were treated by chloridizing-roasting followed by amalgamation, with satisfactory results, according to the information now available. Material from old tailing dumps from ore treated by this process, which are found at several places in the vicinity of Oruro, seldom contains more than 5 to 6 oz. of silver per ton. As ore with less than 100 oz. per ton was not treated, the extraction of silver must have been good. Reports of the operating companies published about 1890 asserted that over 90 per cent. of the silver was recovered, but in these calculations, as a rule, no allowance was made for silver lost during roasting and the figure referred only to the extraction of silvcr by amalgamation from the roasted ore.

Jan 1, 1921

By Joshua Hoffman, Braden Lusk, David McLane, John Rathbun

The dynamics of explosive detonations are understood; however recreating a real-world, to-scale scenario is costly. The use of a shock-tunnel allows testing to be done on a smaller scale, with the simulated effect of a large explosion. Analyzing explosive waveforms using this method can greatly reduce cost in testing blast-resistant products, such as anti-terrorism devices, mine safety products, and military equipment. The purpose of this project is to better the understanding of how the waveform dynamics of an explosive detonated within a shock-tunnel differ from those in an open-air arena test.

Jan 1, 2011

By Jessica M. Wempen

"Differential Interferometric Synthetic Aperture Radar (DInSAR), a satellite-based remote sensing technique, has application for monitoring subsidence with high resolution over short periods. DInSAR uses radar images to measure centimeter-level surface displacements. In the images, ground resolution can be relatively high, with each data point (pixel) representing the average displacement over an area of several square meters. The image data are acquired regularly which allows subsidence to be monitored sequentially over short periods; imaging periods typically range from weeks to months.Monitoring subsidence over short periods with high spatial resolution has potential to provide insight into the dynamics of subsidence and into relationships between mine advance and subsidence. In this study, for three longwall mines in the western United States, initial subsidence occurring at the start of longwall advance is quantified over short periods (12 to 72 days). C-band interferometric wide swath Synthetic Aperture Radar (SAR) images from the Sentinel satellites are used to quantify the subsidence. Overall, the data show initial development of subsidence, expansion of the subsidence trough, and the advance of subsidence in the direction of mining.INTRODUCTIONApplied Differential Interferometric Synthetic Aperture Radar (DInSAR)Differential Interferometric Synthetic Aperture Radar (DInSAR) is a satellite-based remote sensing technique that can be used to quantify small displacements of the Earth’s surface. Using data from the Seasat satellite, which was launched in 1978 (Jet Propulsion Laboratory, 2018), studies by Goldstein, Zebker, and Werner (1988) and by Gabriel, Goldstein, and Zebker (1989) applied Synthetic Aperture Radar (SAR) interferometry to topographic mapping and displacement monitoring. These studies established the potential for broader applications of radar interferometry. Studies by Foxall, Sweeney, and Walter (1998), Wright and Stow (1999), and Carnec and Delacourt (2000) represent some of the earliest evaluations of DInSAR for mine subsidence monitoring. All three of the studies demonstrated the application of DInSAR for quantifying mine subsidence. They also demonstrated difficulty accurately measuring subsidence over long periods due to data decorrelation. DInSAR continues to be evaluated as a tool to quantify surface deformation related to active and historic mining. For example, see Vervoort and Declercq (2018), Wempen and McCarter (2017a), Chen et al. (2013), and Liu et al. (2013). Technologies associated with SAR interferometry continue to develop. Recently launched satellites have relatively high spatial and temporal resolutions, and data processing methods and data accessibility are improving."

Jan 1, 2019

By James F. McConnell

Federal and State sulfur oxide emission and ambient air quality regulations have been implemented to fulfill the requirements of the Federal Clean Air Act Amendments of 1970. Primary and secondary air quality standards have been established at levels considered necessary to assure the protection of the health and welfare of the public. Standards of performance under this Act have been established to control the rate of sulfur oxide emissions from individual sources so as to protect and to improve the quality of the Nation's air. The new source standards of performance were made rigorous for large coal burning stationary sources. This has had a severe impact on the electric utilities that operate the coal fired steam electric plants which are the largest consumers of the Nation's coal production. States have taken different approaches in State Implementation Plans (SIPS) as approved by the Federal Environmental Protection Agency. Some states, such as Pennsylvania, have chosen to permit moderate SO2 emission rates from existing sources which are not in critical air basins. All are required to meet primary and secondary air quality standards and to limit sulfur oxide emissions from new large stationary sources to a minimum of 1.2 LBS of S02/MMBTU fired. This re- quires a fuel sulfur percentage of about 0.7 for a 12,000 BTU/lb coal. In an effort to develop strategies and technologies to conform to performance standards while continuing and hopefully expanding the utilization of the Nation's coal supply, the electric utilities, the Federal and State regulatory agencies, and other industries and government agencies are considering several alternatives. 1. Natural low sulfur coal 2. Flue gas desulfurization - (FGD) non-regenerative and regenerative 3. Coal gasification 4. Liquefaction and solvent refined coal 5. Fluidized bed combustion 6. Chemical coal cleaning 7. Physical coal cleaning Of these options, only the first and the last can be considered to be widely used in full commercial practice at this time. FGD has certainly demonstrated technical and operating feasibility and is close to being in full commercial practice but it remains to be seen if the large systems under construction are economically and environmentally optimum.

Jan 1, 1975

By Carl F. Dietz

(New York Meeting, February, 1912.) THE problem of drying ores is one that most mill-engineers are sooner or later called upon to meet, and it may be timely to point out sortie of the difficulties resulting from such operations from purely a metallurgical and economic stand-point. We mean, in the following pages, to discuss primarily the effect of such operations on. the ore itself, without particular reference to the mechanical or cost features of the subject; That an appreciable tonnage of the ore fed to the usual form of drier, either rotary or stack, is lost, is fairly well appreciated, but we believe that only a few mill-managers know just. what their drier-losses amount to, and we have found that in most cases they console themselves with the fact that the drier-smoke is not very much discolored, and it is generally believed that the draft is not sufficient to carry away more than a. negligible percentage of the values. The drying of ores is becoming an important factor. since the more general application of magnetic, static, and dry-table treatment. Its importance in the field of metallurgical operations warrants a close examination into its effects. This subject has been repeatedly brought hone to us, and while the drier-losses, in every case examined, have considerably exceeded even the most generous estimate, an attempt at a recovery of these values is rarely made. We have found that the losses resulting from drying-operations can be effectively recovered, at a low cost, and believe that the publication of the results of a number of investigations along these lines will be of interest and benefit to the profession at large. To dry an ore quickly and effectively, it must be brought into actual contact with hot gases or air. The rapid drying is effected by the fact that the hotter the gas the hungrier it is

Jul 1, 1912

By Alex Rown

"THE SYDNEY COAL FIELD has long been afflicted by high costs and low productivities. However, a distinct possibility now exists that improvements can be made in costs, productivities and revenues. If these hopes materialize, the Sydney coal field will once again be regarded as a valuable asset in our national inventory of energy and metallurgical coals. The economic possibilities for the Sydney collieries depend on performance at the pits and in the market place. Because this audience is already well informed about colliery planning, I would like to start with an assessment of the modern coal market insofar as it may relate to the Sydney field. Since 1950 we have seen a vast growth in the population and industrial empires of the western world which has resulted in an enormous and escalating demand for energy. If the energy supply pattern of the first 50 years of this century had been followed, this would have led to an immense demand for coal."

Jan 1, 1972

By P. C. van Aswegen

Owing to the strategic value of organic solvents, an investigation was conducted on the reduction of solvent losses at the Buffelsfontein solvent-extraction plant. It was established that the major cause of the high solvent losses was the high content of suspended solids in the uranium pregnant solution. To improve the clarification of the pregnant solution, it was decided to replace the conventional sand clarifiers that were being used at that stage. After pilot-plant tests had been conducted, a circulatorclarifier 16 m in diameter was installed to treat 9000 m3 per day of pregnant solution containing approximately 500p.p.m. of suspended solids. The clarifier was commissioned successfully, and yielded an overflow containing approximately 80 p.p.m. of suspended solids compared to the previous value of 250 p.p.m. This reduction in suspended solids immediately resulted in a decreasing trend In losses of organic solvent, finally yielding a reduction in these losses of approximately 50 per cent.

Jan 1, 1983

By Calvert D. Iles

Open-pit mines in the US and throughout the world are typically characterized by increasing operating costs and decreasing ore grades. Thus, companies must continue to improve their use of human and technological resources to remain competitive in the marketplace. Duval Corp. has historically been very sensitive to mining costs, in part because of relatively low grade copper-molybdenum ore bodies. These concerns have resulted in three haulage system generations at the 218 kt/d (240,000 stpd) Sierrita-Esperanza open-pit mine south of Tucson, AZ. Each generation has exceeded the performance of the one replaced. The latest system of portable crushers and conveyors reduces hauling costs by combining both hardware and technique. Savings are achieved not only bysubstituting conveyors for haul trucks, but also by permitting the crusher-convey or system to closely follow mining as the pit deepens and/or mining areas change location. The Duval system is capable of easy and inexpensive relocation in varying site configurations in relatively short time periods. Its implementation in active mining areas results in minimum disruption to both the mine operation and mine design. This haulage concept allows the mining engineer maximum freedom to design an open pit for profit rather than for equipment. Maximum savings with a portable system are achieved by minimizing truck haulage costs. At Sierrita, for example, the yearly estimated operating cost savings for each thousand feet of +10% truck ramp replaced by conveyors is about $1 million per portable crusher. A savings of $30 million could be achieved fora three-portable system overa 10 year period simply by reducing the average truck Iiftto the crusher by 30 m (100 ft), There is also the added capital expense of buying trucks to cover the additional 30 m (100 ft) of lift. Relocation costs are an important consideration in a portable system. Direct costs can become a significant operating expense if frequent relocations are necessary to take full advantage of potential haulage cost savings. A site preparation cost of $375,000, for example, would add an additional operating cost of 2.8¢/t(2.5¢/st) for a system handling 13.6 Mt/a (15 million stpy), assuming one move a year, In addition to the direct cost of site preparation, such as installation of retaining walls, apron feeder slots, and equipment pads, there is the cost of site renovation after abandonment. Indirect relocation costs, while less tangible and more dependent on specific mine design and scheduling, can be of significance. A slowdown in the mining rate or a less efficient mining plan can result from a site not being immediately available for mining after abandonment. Conversely, mining in narrow areas can be adversely affected if two or three month lead times are required for site preparation.

Jan 4, 1983

By Jim Morris, Davin Ishii

The major source of water for Southern Nevada is Lake Mead. However, the existing pump station located on Lake Mead is inadequate for one of the fastest growing areas in the United States. In order to keep up with the increasing demand for water in Las Vegas, a parallel system is being constructed. The intake for this system is being constructed approximately 68.58m (225ft) below the surface of Lake Mead. The lake tap consists of installing casing and secant piles to support the shaft collar, excavating a 21.34m (70ft) deep intake shaft, and installing a3.66m (12ft) diameter steel liner.

Jan 1, 1999

By P. S. Rudman

The allotropic volume changes of the ,metallic elements are reviezoed with the conclusion that in general atomic volume is conserved to better than 1 pct in such transformations. A table of the atomic volumes of the metallic elements is given and its use in considering the size factor in alloys is discussed. The importance of the concept of atomic-size factor, due to Hume-Rothery and coworkers,' is firmly established. Most attempts at quantitative formulations of this concept have employed the atomic radius (half some interatomic distance) as the measure of size and innumerable tables of such radii exist. This is probably, however, an unfortunate choice of parameter. Firstly, discussion in terms of interatomic distances requires a knowledge of the crystal structure. While this is known, except for a few cases, for the elemental structures, there are still many undetermined alloy structures. Secondly, except for the simpler structures, face-centered cubic (Al),* body-centered cubic (A2),* and hexagonal-close-packed (A3).* with ideal axial ratio, there is no unique in- teratomic distance, an m y decision must be made as to which distance, or which average of the distances, should be used. However, the most important point is that for metals the dominant bonding parameter can generally be expected to be atomic volume and not interatomic distance. This is perhaps most explicitly stated in the Wigner-Seitz cellular method.' In this approximation, cellular polyhedra of atomic volume v are replaced by spheres of radius Y,: 4/3 ?rs3 = v. That is, there is no reference to the interatomic distances. If atomic volume is in fact the dominant parameter, then in allotropic transformations we might expect to find atomic volume approximately conserved. For example, in the A1 ? A2 transformation we would thus have

Jan 1, 1965