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By Pervez Patel, Martin G. Frohberg, Demetrios Papamantellos

Model experiments were carried out on the mass transfer of iodine between n-hexane and a 4 2 X 10-3 M aqueous sodium hydroxide solution. The influence of mechanical stirring by means of small gas bubbles (ca. 0.01 ml in volume) on mass transfer was examined in independent experiments. The results were described with the help of the penetration theory and in the case of bubble stirring with the help of a mathematical model based on this theory. S LAG-METAL reactions, especially those in steel-making processes, often occur under conditions where gas is evolved in the form of bubbles that break through the slag-metal interface. It is known that stirring by means of bubbles increases the mass transfer coefficient, but there has been very little quantitative work done in this field. Because of the difficulties that attach to experimental work at high temperatures this study was confined to model experiments at room temperature. EXPERIMENTAL APPARATUS The transport of iodine from an n-hexane layer into a weak sodium hydroxide solution was studied a) with stirring by means of bubbles and b) with mechanical stirring. The apparatus for the experiments with bubbles consisted of the cell, two Dreschel bottles filled with hexane in order to saturate the nitrogen flow, one flow meter, and a nitrogen gas cylinder fitted with a fine-regulating valve. Fig. 1 shows the cell consisting of a glass cylinder 33 cm in height with an overall diameter of 7.5 cm embedded in a copper flange. The flange is connected to a Plexiglas plate and to the gas inlet. The Plexiglas plate has holes of 0.2 mm diam bored into it which are spaced 1 cm from each other. For the experiments with mechanical stirring the bottom of the cell was sealed off by a Plexiglas plate. The upper layer was stirred by means of a glass stir-rer and the bottom layer with the help of a magnetic stirrer in a counter rotatory direction. Both stirrer speeds could be varied continuously. EXPERIMENTAL PROCEDURE Iodine dissolves in n-hexane producing a stable violet color thus enabling the iodine concentration in

Jan 1, 1970

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

TO THE. BOARD OF DIRECTORS AND MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS GENTLEMEN Submitted herewith are the report of the Treasurer for the year 1945 and reports for the same year of the following committees: Membership, Admissions, Papers and Publications, Mining and Metallury (Magazine), and Library. In this review of the year by the Secretary reference frequently will be made to the "Paul" Committee and to the "hotter" Committee. The first is the special committee on Divisional Relationships and the second the special Committee on Ways and Means. These two important committees, appointed by President Harvey S. Mudd under authorization of the Board of Directors on March 21, 1945, were composed as follows:

Jan 1, 1946

By J. L. Green

Virginia-Carolina Chemical Corp., in its Florida Operations, uses both roller mills and ball mills in dry grinding of phosphate rock. The roller mills have been in operation since 1954 in the Mining Department. The ball mills were installed and put in operation in 1960 in the Harding Concentrate Superphosphate Plant. The roller mills in the Mining Department are used to grind phosphate rock for outside customers. This involves short notice orders of varying grinds, grades and types of rock. The ball mills grind phosphate rock for use in V-C's own phosphoric acid and concentrated superphosphate plant. These mills grind generally two types of rock for one grind. In 1959, a 10% speed-up was made in the operating speed of the roller mills. This paper deals with the operational gains and resulting cost savings which evolved from this speed-up, and compares the present operations of the roller mills and of the ball mills in grinding phosphate rock. In January 1959 it was decided to determine the feasibility of reducing the grinding cost on the roller mills, per ton of rock ground, by speeding up the mill 10%. At this time, one mill was completely reconditioned so it would be in top condition. Extensive tests were then run both before and after the mill speed-up to determine the resultant cost savings. These tests showed that, due to this 10% speed-up, the mill capacity was increased approximately 20% and grinding power costs per ton were reduced approximately 10%. Table I shows the results of these tests. Each test run actually represents several of the same type rock and grind, averaged together. Each test run lasted approximately three hours. The validity of these runs has been confirmed by subsequent operation in grinding over 1,000,000 tons of phosphate rock. Accurate records have been kept on power consumption and repairs as well as tons produced. Two types of feed rock were used for the tests — pebble phosphate rock and flotation phosphate concentrate rock. The pebble phosphate rock size is approximately 80-90% plus 20 mesh. The flotation concentrate phosphate rock size is approximately 15% plus 20 mesh and 95% plus 100 mesh. The same two types of rock feed were used for all the test runs. Test Nos. 1, 2, and 3 were run at the original mill speed of 85.5 rpm on the vertical shaft. Test No. 1 was run with a feed of high grade flotation concentrates; the desired fineness attempted was 70% passing 200 mesh. Tests No. 2 and No. 3 were run with a feed of low grade pebble. Test No. 2 was run for a desired fineness of 70% passing 200 mesh. Test No. 3 was run for desired fineness of 50% passing 200 mesh.

Jan 1, 1963

By Sir Robert Hadfield

SINCE the writer has been intimately connected with the development of manganese steel for many years, some remarks upon the early work with regard to the rolling and forging of this material might he of interest, and particularly as to the question of rails of special quality and of superior wearing qualities. In a paper on Iron Alloys, with Special Deference to Manganese Steel, read before this Institute at the International Engineering Congress in Chicago in 1893,1 the writer mentioned that, about 20 years ago, his firm in Sheffield produced railroad material, such as tires and axles, of forged and rolled manganese steel, thus showing that this product could be manipulated and worked up into the various required forms. The tires illustrated in the paper referred to above formed a particularly difficult class of work to produce in a special steel, but no special obstacles were met with Although there was no difficulty at that time in making and producing manganese steel in various forms, forged, rolled or pressed; nevertheless, on account of its higher expense, sufficient encouragement

Jan 2, 1914

By A. W. Schlechten, R. P. Abendroth

Jan 1, 1960

By B. Wilshire, P. W. Davis

It has been shown that grain-boundary migration during high-temperature creep can reduce or even prevent the formation of intercrystalline voids, giving a considerable increase in ductility.' A similar observation has been made in a recent investigation of the creep properties of various grades of nickel and nickel alloys. The results can be illustrated by the observations made on: a) Pure vacuum-cast nickel (99.993 pct Ni) b) Impure vacuum-cast nickel (99.97 pct Ni) c) Pure nickel containing internal voids (produced by a process of intering). d) A substitutional solid solution alloy of pure nickel containing 1.16 pct Sn. All the materials were given a high-temperature anneal (>850°C) to produce a stable grain size of 7 to 10 grains per linear mm. The apparatus and techniques used to obtain the present results have been described elsewhere.' In this series, grain growth was observed only in the highest-purity, vacuum-cast metal. Thus we may consider that in the other materials grain-boundary migration was prevented by either preexisting voids or solute atoms. The effect of migration on the creep ductility of the above materials can be seen from Fig. 1, which

Jan 1, 1962

Jan 1, 1967

By H. Conrad

The strain hardening associated with the creep of magnesium single crystals at room temperatu.Je was investigated by shear tests in which the direction of stressing was reversed a number of times after creep in a <100> direction. The strain hardening was strongly anisotropic; the largest amount occurring in the direction of flow and the least 180 deg to this. The time law for creep changed from a parabolic type to logarithmic for the first and subsequent reversals of stress. For a given stress the creep strain decreased significantly for the first and second reversals and then only slightly for subsequent reversals. The logarithmic creep constant a changed in a similar manner. A linear relationship was observed between the creep strain for a given reversal and the stress. The slope for the third reversal yielded a strain hardening coefficient 12 to 16 times greater than that observed for unidirectional flow. Al-though no recovery was observed upon resting at room temperature, the hardening resulting from stress reversals could be completely removed by heating to 450" C. PREVIOUS work1.&apos; indicated that the creep rate of magnesium single crystals tested in the temperature range of 78" to 364°K decreased with time. This was attributed to an increase in internal stress resulting from an accumulation of dislocations at internal obstacles. The object of the present investigation was to further evaluate the nature of this hardening by conducting tests in which the direction of stressing is changed after previous creep in shear in a given slip direction. Previous to 1950 three investigations indicated that a Bauschinger effect3 occurred for single crystals as well as polycrystals brass in tension compression,

Jan 1, 1960

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall&apos;s statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall&apos;s statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Reno H. Sales

Our colleagues cannot in the future earn reputations and medals for achievements in milling and smelting ore and for successful management of mining companies, if some one doesn&apos;t keep finding and mining the ore to mill and smelt and to provide the basis for the good management. Good ore seems sometimes to be quite helpful to good management, and good ore is not as easy to find as it used to be. And there are still more reasons, why—when this honor had been decided upon and named for Mr. Daniel C. Jackling—it should be initially conferred on Reno H. Sales. . The terms of reference of the award are that it should be conferred upon an individual working in the fields of mining, geology, geophysics, who has made an outstanding contribution to the progress of technology in one or more of those fields. And in this initial year (the earlier years are the easiest) just that was done. I think I could get away with it amongst the old-timers of my generation if I say that this time they made the award to the individual, who made the outstanding contribution. But, as Al Smith used to say, "Let&apos;s look at the record." Really, the record is mixed up a little with extra-lateral litigation—the old-time "apex cases" under Section 2322 of the Revised Statutes. Reno Sales doesn&apos;t like such litigation, but there is little question that the urgency, generated by conflicting claims of intra-limital and extra-lateral rights, and consequent necessity for committing to records and maps the complications of Butte structure, did advance—and by several years—the first continuous, accurate, systematic, and scientific portrayal of the geological and mineralogical details of what is, after all, the most important and the most complicated copper district—at least in North America. Prior to Sales&apos; time, some of the most eminent of geologists often waived details. One geologist took the judge to the window to show him the Rarus fault going through a notch in the Continental Divide. The entertaining testimony in the Bluebird litigation was as perfect in literary style as it was innocent of the criteria by which faulting and lack of continuity of vein structure are now recognized. At any rate, this need for an accurate record of structure was in the background—to whatever extent it was, or was not, the etiological agent—for formation of the Geological Department of the Amalgamated Copper Co. in and about the year 1900. Charles W. Goodale was at that time the head of the Boston & Montana, and John D. Ryan succeeded William Scallon as the president of Anaconda Copper Mining Co. in 1905. Horace V. Winchell, for years a specialist in extra-lateral litigation, was perhaps the man who at that date had the vision, the persuasive weight with the management, and the willingness to defend the idea of large current expenditures (as then viewed) for a complete and sys-

Jan 1, 1955

Jan 1, 1963

By N. A. Gjostein

From their study of the anisotropy of grain boundary mobility in aluminum, the authors conclude that tilt boundaries have a higher mobility than twist boundaries because the atomic misfit at the pure-twist boundary is relatively small compared to the misfit at a tilt boundary for a given amount of misorientation. If this is true, then one would expect a twist boundary to have a lower grain boundary energy than the corresponding tilt boundary. Fig. 6, taken from the work of Gjostein and Rhines,10 shows that this is indeed the case for [001]-cu tilt and twist boundaries in the high-angle region, thus lending support to the authors&apos; conclusion.

Jan 1, 1968

By Ernest M. Spokes

For bituminous and lignite coals the economic picture continued to improve as it has each year since the low of 1961, with production at 480 mil- lion tons in 1964 compared with 1963&apos;s 459 million tons. The anthracite industry produced 16.3 million tons in 1964 and 18.3 million tons in 1963. The industry is looking toward a further expansion; among the new developments will be a mining wheel producing 3 million tons of lignite per year in South Dakota. It is expected that electric power generation will continue to provide the market for most of the increase in consumption, with exports second in importance in the expansion. Improvements in methods of mining and transporting coal underground and in strip mines, and the cooperation of carriers in finding ways to reduce transportation costs to distant markets, have made possible these expansions. Research continues to reduce costs of mining, transportation, steam generation of electric power and production of steam for space heating and manufacturing processes, to retain some markets and expand others. Other research seeks to expand markets by developing fuel from coal which will be more attractive than competing fuels, by reducing sulfur and other sources of air pollution. Public relations efforts of the industry are bearing fruit in a greater acceptance of coal as a modern fuel.

Jan 2, 1965

By Waldemar Lindgren

THE following pages present data accepted by many geochemists and geologists regarding the succession of minerals and the temperatures of formation in ore deposits affiliated with igneous rocks. They also present the individual views of the author on the composition of the solutions that were active and on the mode of deposition. He does not regard these views as speculations or hypotheses but as forming a well motivated and consistent theory. It is not certain, however, that all investigators will subscribe to them.

Jan 1, 1936

By H. J. de Haan, J. van Lookeren

In view of their size and favorable characteristics, Shell&apos;s heavy-oil fields on the eastern coast of Lake Maracaibo, Venezuela — known as the "Bolivar Coast" — are obvious candidates for the application of thermal recovery methods. During the last decade various methods have been tested, such as steam drive,&apos;, steam soak and in-situ combustion.3 Steam soak was discovered as a promising production method rather accidentally in 1969, during early steam drive testing in the Mene Grande Tar Sands1 When steam erupted at the surface due to breakdown of the overburden, the injection wells were back-flowed to relieve the reservoir pressure. This resulted in high oil production rates, all the more impressive because the reservoir is unproducible by primary means. It was concluded that injection of limited amounts of steam might be a very effective method for stimulation of heavy-oil wells. To obtain information that would be more widely applicable, testing of the process was continued in the eastern part of the Tia Juana field (Fig. 1). Here even more favorable results were obtained than in Mene Grande. This created sufficient confidence to prompt a large-scale project, which was considered essential for an adequate evaluation of ultimate recovery, steam requirements, mechanical problems and economic prospects. To obtain an early answer on the ultimate recovery a fairly depleted area was selected in the western part of the same field ("A" in Fig. 1). The first steam was injected in March, 1964. This paper describes the performance until the end of 1966. The production mechanism and well inflow performance are discussed in some detail. In view of the favorable results obtained so far, steam soak operations have expanded considerably since the start of this project. Presently, five other projects are under way, of which two are about the same size as the one under discussion, with further extensions being programmed. Description of the Project Reservoir Data Shell&apos;s part of the Main Tia Juana reservoir has a proven area of 8,800 acres and an average net oil sand thickness of 130 ft. It contained an initial quantity of 2,750 million bbl of stock tank oil (STOIIP), with an API gravity ranging from 10 to 15 API and a viscosity of 100 to 10,000 cp (at 122F). As a geological unit it is known locally as the Lower Lagun-illas member of the Lagunillas formation, which is early Miocene in age. The sand bodies are believed to be distributary channel sands deposited in a lower coastal plain. Most of the channel sands have lateral and some vertical communication. The field was developed mainly in the period from 1936 to 1950. The ultimate primary recovery is estimated at 18.1 percent of STOIIP, of which 12.5 percent STOIIP had been produced by the end of 1963 from some 540 wells. By then the average pressure had decreased from an initial value of 960 to 550

Jan 1, 1970

By M. Felsenthal

Engineers are frequently faced with the problem of having to predict oil recovery from a solution gas drive reservoir in the early life of a field. This is often the time when actual laboratory or field-derived gas-oil permeability (kg/k0) data are not yet available. Although excellent collections of k0/k0 data for various types of rocks may be found in the literature,1,2,3 a need exists for a more detailed correlation of k0/k0 data with core properties such as porosity, permeability, clay content or pore-size distribution. It is the purpose of this article to present this type of correlation for sandstone material. The correlation is based on laboratory tests performed on over 300 core samples from 19 reservoirs in the United States and Canada. EXPERIMENTAL Cores were analyzed by routine procedures, using samples of conventional size (7/8-in. diameter, 7/8-in long) cut parallel to the bedding planes. Air permeability was measured at 1.67 atm mean pressure in a Hassler-type apparatus. Porosity was determined with the aid of a Ruska bulk volume meter and a Boyle&apos;s Law rock volume meter, An evaporation method&apos; was used to evaluate irreducible water saturations. Core samples were saturated with 25,000 ppm NaCl brine. The brine was reduced to the irreducible saturation, and the remainder of the pore space was filled with kerosene. This was followed by multiphase flow tests using the so-called "dispersed feed" technique.5 n this technique, gas and oil (kerosene and kerosene-saturated air) were dispersed with the aid of a porous Alun-durn feed head, the face of which contained a waffle-shaped system of Lucite-lined grooves. Oil entered the back side of the feed head and emerged at the raised areas of the front face. Gas was introduced directly into the system of grooves at the front face. The gas-oil mixture then entered the test core which was kept in capillary contact with the feed head. Permeabilities were determined from rate and pressure measurements and saturations from weights. All determinations were performed at equilibrium or steady-state conditions. Pore-size distributions were determined on selected samples by a mercury injection technique.6 GENERAL CORRELATIVE TRENDS When examining data from a given reservoir, it was noted that k0/k0 vs saturation curves became generally less steep as specific air permeability increased, a development that has a favorable effect on oil displacement efficiency by solution gas drive. This trend has also been reported by others in the literature.&apos; An effect of porosity on k0/k0 data was also noted. This effect was not generally discernible in a study of relative permeability data for a given reservoir but became apparent when data for sandstone reservoirs of similar lithology but differing average porosity were compared. For instance, in a comparison of argillaceous and/or calcareous sandstones from 11 reservoirs ranging in average porosities from 14 to 28 per cent, a definite trend was noted, indicating that for a given permeability k0/k0 curves became less favorable (i.e., steeper) as porosity increased. A similar trend was observed for a group of comparatively clean sandstones from five reservoirs ranging in average porosities from 15 to 21 per cent. For a given permeability and porosity, comparatively clean sandstones gave more favorable k0/k0 curves than argillaceous and/or calcareous sandstone or chert reservoirs. The laboratory studies also showed that least favorable k0/k0 curves were exhibited by shaly sandstone, conglomerate, and sandstone containing carbon inclusions. Table 1 lists the various source reservoirs classified by lithology types. To facilitate a correlation of k0/k0 data with core characteristcis, it was found expedient to work with

By John Chipman, Wayne L. Worrell

Using recent thermodynamic data for the carbides and oxides of tantalum, columbium, and vanadium, the stable solid phases aboue 1300°K and at 1 atm CO(g) pressure in each M-C-O system have been determined. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures necessary to obtain these metals by carbothermic reduction under reduced pressures. TANTALUM, columbium, and vanadium react with carbon to form the M,C and MC carbide phases. The M,C carbides have narrow homogeneity ranges, but the MC phases possess considerable ranges of homogeneity.&apos; The free energies of formation of the MC carbides were recently measured, and those of MC and M2Ccarbides have been estimated., (The notations MC and MC denote, respectively, the carbide compositions at the carbon-rich and at the metal-rich boundaries of the homogeneous MC phase.) In this paper, these carbide data are combined with thermodynamic data for the oxides to predict the stable phases in the Ta-C-O, Cb-C-O, and V-C-O systems at specified temperatures and oxygen pressures. M-C-O PHASE DIAGRAMS The solid phases in equilibrium above 1300°K for each M-C-0 system are shown in Figs. 1, 2, and 3. Above 1300°K, the vapor would consist entirely of carbon monoxide; and these phase diagrams were obtained by specifying the vapor pressure of CO(g) to be 1 atm. The temperature at which any two solid phases become unstable is specified along the two-phase equilibrium lines in each diagram. To simplify the diagrams, all solid phases in the Ta-C-O and Cb-C-O systems are represented as stoichiometric compounds. However, the homogeneity ranges of VO and VC are indicated, because they form a complete series of solid solutions.3 It also should be noted that the homogeneity range of

Jan 1, 1964

By Edward I. Salkovitz

THE determination of the orientation of metal single crystals and the studies of plastic deformation are greatly facilitated by the use of the stereographic projection. To draw a standard projection of the crystal it is necessary to have a tabulation of the angles between the various crystal-lographic planes of the particular crystal studied. Bozorth&apos; has published such a table for the cubic system which can be found in many reference books; such convenient tabulation for the hexagonal metals, however, does not appear to be in the literature, although scores of workers have calculated these angles. Therefore, Table I of angles for magnesium, zinc, and cadmium has been compiled. Since the c/a ratio is different for each of these metals, three separate calculations are necessary. The angles 4 between (HKIL) and (hkil) were calculated by means of the formula: Hh+Kk+½(Hk + hK)1+~3aLl cos The c/a ratios were calculated from data given in the 1948 edition of Metals Handbook. Fig. 1 is a typical (0001) standard projection of zinc. For all practical purposes, it serves for cadmium as well, as can be seen from the table. For magnesium, however, it is necessary to construct another net. R. M. Bozorth: Physical Review. (1925) 26, 390.

Jan 1, 1952