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Discussion of the paper of George C. Stone, presented at the New York Meeting, October, 1913, and printed in Bulletin No. 82, October, 1913, pp. 2401 to 2402. D. S. JACOBUS,* New York, N. Y.:-The engineers of the country are waking up to the possibilities of waste-heat boilers. As the cost of fuel increases, and as more attention is given to economies, it is evident that a great deal may lie gained by utilizing heat that has ordinarily been wasted. The art in the manufacture of' waste-heat boilers has. advanced so that it will now pay to install them under certain conditions where it would not have paid to install boilers constructed in accordance with older methods. In using boilers where the gases are at a comparatively low temperature, a great deal depends on the method of baffling the boiler in securing good results. The Babcock & Wilcox Co. has made a careful investigation of the laws of heat transfer and has applied the same to waste-heat boilers, which have been carefully tested under operating conditions, with the result that we now know what to expect with different arrangements of baffles and heating surfaces. The old idea of installing waste-heat boilers was to provide an arrangement where the draft loss would be a minimum, and little or no attention was paid to the effect of different systems of baffling on the steaming capacity of the boiler. In some instances, to secure a minimum draft loss no baffles were placed in the boilers. After making a most careful study of the subject it developed that this practice was bad, and that to obtain the best commercial economy, in place of endeavoring to obtain a minimum draft loss, an arrangement should be used that would lead to the maximum amount of heat transmission with a comparatively high draft loss. In nearly every case the amount of resistance of the gases fussing through the boiler involves the use of an induced-draft ,fan, but the additional capacity developed by the boiler over that which could be secured with the older designs, through arranging the heating surface properly and using proper baffles, much more than pays for the increase in the steam required to drive the fan.

Jan 12, 1913

By S. J. Hubbard, S. D. Michaelson, A. W. Last, B. H. Ensign

Of the seventeen western states, five-Arizona, Utah, New Mexico, Montana, and Nevada-produce about 90 pct of this country's primary copper. All seventeen of these states occupy 60 pct of the nation's land area but receive only 25 pct of the country's total precipitation. Seventy percent of this precipitation returns directly to the atmosphere through evaporation and transpiration, leaving very little for ground reservoir recharge or immediate domestic, agricultural, or industrial use. With so limited a supply available for all, competition for water rights among users is severe. The result does not always permit using the limited supply to produce the most valuable end product. Most of industry and much of agriculture can shop around for suitable operating locations. Where water is critical to their purposes, they can and do locate in areas where the needed amounts are available. Such is not the ordinary lot of the mining industry, which must locate in the area of the deposit it is planning to mine and concentrate. In the case of copper this happens to be, for the most part, right in the heart of the semi-arid regions of the West.

Jan 7, 1960

By Norman B. Braly

The following is not offered as an extended paper on the subject of shaft sinking, but more as a description of the present practice of shaft sinking in the Butte district. The Anaconda company is sinking at present the following shafts: Badger State, Moose, Mountain Consolidated, Mountain View, Pennsylvania and Tropic. At the High Ore and Leonard mines the shafts are being deepened by sinking two compartments and will subsequently be enlarged to the full working size by raising alongside the compartments which are now being sunk. The following other companies are also sinking shafts: Butte-Alex Scott, Butte and Zenith City, Boston and Corbin, North Butte Mining Co. (at the Granite Mountain shaft), East Butte Co. (at the Pittsmont shaft), and the Rainbow Lode Development Co. Shaft Timbering. The shafts of the Butte district, generally speaking, are of three compartments arranged in a straight line, and the pump compartment is usually arranged for the use of an auxiliary hoisting cage, as well as for carrying pipe lines and electric wires. The Rainbow shaft is practically square, and of three compartments. The length of the shafts outside of timber will vary from 17 to 22 ft., and the width from 6 ft. 6 in. to 7 ft. Fir timber is used in all shaft work. This may be obtained from the Coast, when it is known as Coast fir, or from Idaho or Montana, when it is known as native fir. The native fir seems to be the tougher wood, but it is hard to obtain clear lumber in the lengths and sizes necessary for shaft work. Some of the shaft timber of the Anaconda company has been treated with creosote as a preservative, but this practice has not come into general use, as the ground of the camp is so heavy that the timbers usually crush before they rot. The size of timber most used for shaft work is 12 by 12 in., while 10 by 12 in., 10 by 14 in. and 12 by 14 in. are used for some of the special pieces around the shaft. The new Leonard shaft is timbered with 14 by 14 in. wall plates throughout.

Jan 1, 1914

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By Thomas Egleston

The adoption of the regenerative principle for burning fire-bricks, pottery, etc., has been delayed beyond what would naturally have been expected, because there bas been until recently little necessity for high heat in burning such material. But the introduction of pro-

Jan 1, 1887

By Richard F. Moe

INTEREST in developing White Pine, considered since 1942, was renewed by the Korean conflict and its shortage of domestic sources of copper. In view of this Morris F. La Croix, president of Copper Range Co. of Boston, and of its wholly owned subsidiary, White Pine Copper Co., worked an agreement out with Government officials. Essentially the contract called for a construction loan of $57,185,000 at 5 pct interest, with $13 million additional supplied by Copper Range. Defense Materials Procurement Agency contracted for 243,750 tons of copper from the first 275,000 tons produced, at a base price of 25.5& per lb, the contract to expire Dec. 31, 1961.

Jan 4, 1954

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By M. J. Scoble, N. Rowlands, L. Piciacchia

Pronounced non-linear behaviour of mine backfill arises from the influence of confining pressure, cementing agent content, curing time, void ratio and water content. Past research into backfill behaviour under stress is reviewed and related to the needs for constitutive laws which can be integrated into numerical modelling for mine design where structures employ backfill support. A method for representing non-linear backfill behaviour is proposed, which is based upon numerical regression treatment of triaxial laboratory data. The non-linear behaviour observed from a program of laboratory triaxial testing of cemented hydraulic backfill is presented. The particular influence of confining stress and curing duration is high- lighted. The paper concludes by considering the alternative means of accounting for such behaviour in mine design.

Jan 1, 1984

By T. W. Peterson, J. W. White, E. E. Krist

In developing a minicomputer application for an industrial grinding circuit, the control program is usually coded and the compilation is debugged on a remote access computing system. Final debugging must wait for installation of the minicomputer. This work reports on an alternative. Here both compilation and execution bugs are eliminated before the hardware is installed by testing the control program against a dynamic simulation. Attention is directed toward development of a particular real-time control program for an industrial wet grinding circuit in a copper concentrator. Specific data were supplied by the Anamax Mining Co. for a grinding division consisting of a rod mill followed by two ball mills in parallel. This information was used to set up a plausible model structure.

Jan 1, 1977

By J. Stringer, I. W. Edington, C. R. Rarey

THE geometrical interpretation of transmission electron micrographs of hcp metals is more complicated than the equivalent interpretation of cubic metal for two reasons: firstly, prominent zone axes are not in general normal to prominent planes, so that a simple diffraction pattern often corresponds to a nonra-tional foil plane; and secondly, the Miller-Bravais sys-tem of indexing directions is not easy to visualize. In this, the indexing is referred to the Bravais four-axis system, and the direction is labeled [hkil], chosen so that and I are shown in Fig. 1. Some geometrical relationships useful for the interpretation of transmission micrographs have been calculated and are tabulated below: 6) Direction of the intersection of two planes; this is easily calculated by applying Condition 4 to both planes: a direction that lies in both planes is clearly their direction of intersection. Some of the above expressions have also recently been given by Otte and Crocker;' Expression 5 is of course in most standard crystallographic texts. It is generally considered easier and quicker to use graphical methods for the interpretation of electron micrographs than analytical methods. For this purpose, it is most convenient to use a "double stereo-gram" in which both the poles alzd the rational directions are plotted. It is, of course, necessary to orient

Jan 1, 1967

By Fred Witt, Milton Schwartz

ESTABLISHED methods for obtaining quantitative pole figures for flat sheets1"5 can be extended to apply to thin films on a substrate. The mode of scanning the sample is exactly the same as described in the references? but consideration is given to the fact that the scattered X-ray intensities are due to both the thin film and its substrate with appropriate attenuation factors. The purpose of this paper is to describe a method to obtain the scattered intensities from the film alone for subsequent pole-figure determinations. Fig. 1 shows the four possible general positions of the film (f) and its substrate (s) with respect to the incident X-ray beam (I,). In this paper it will be assumed that the plane of the sample is normal to the plane of the diffractometer. In the diagrams the line jV is the normal to the flat sample and the line P is the trace of the diffracting crystallographic planes in the plane of the diffractometer. The angle of tilt, a, is the positive acute angle measured from the line N to the line P; if this angle is measured clockwise then a is said to be in the positive a region; if this angle is measured counterclockwise then a is said to be in the negative a region. For the reflection cases, the total scattered intensity, at the proper Bragg angle for a particular set of planes, is due to that scattered by the film Vf) and that scattered by the substrate. The beam incident on

Jan 1, 1967

By Thomas D. West

The occasional reports of progressive furnace-men, giving the results of physical tests to prove the superior qualities of their pig-irons, have encouraged the writer to believe that the time is ripe for the discussion of such work, and the inauguration of some correct system by which the furnace-man and the founder could make intelligent comparison of the elements of strength, deflection, contraction, and chill presented in pigmetal. In most cases the physical tests now made by furnace-men define but one quality in the iron, and are generally too vague to permit any true comparison. For example, one furnaceman tells us he can punch holes in his cast-iron, wishing it to be inferred that the iron is very soft and strong. Another furnace casts a long wedge, the thin end running to a knife's edge, which is supposed to prove the fluidity of the iron, for the founder's benefit. Another casts in square-cornered " chills," to define the hardness or softness of the metal. To the writer's knowledge these tests are not advocated by their originators as suitable for standards; and they are, to his mind, but evidence of unrest on the part of progressive furnace-men, who feel that something should be done in the line of physical tests. The writer knows of no furnace-men who make and keep records of the strength of their iron obtained by means of tests made on recognized standard testing-scales ; but he does know of a prominent furnace-salesman, who, not long ago, came into possession of a 1-inch square bar that stood 1400 pounds

Jan 1, 1897

By Robert M. Lewis

Silica sand deposits are usually contaminated with various heavy minerals which must be removed to make the silica useful for flat-glass production. Research was undertaken to develop a better procedure for producing flat-glass-grade silica. Batch tests revealed that anionic detergent-type reagents had considerable promise. Pilot plant tests were run to compare the effectiveness of anionic detergent-type reagents with petroleum sulfonate in the removal of heavy minerals from a potential glass sand. Another slightly modified commercial procedure also was evaluated for comparison. In the pilot plant trials, utilization of the anionic detergent potation reagents did not produce quite as good results as petroleum sulfonate. It is likely that flat glass-grade sand could be produced with the anionic detergent reagents if more extensive pilot plant tests were conducted.

Jan 1, 1977

By Leigh J. Wardle

SUMMARY This paper describes a numerical method for calculating the three- dimensional stresses and displacements induced by tabular excavations in a rock mass consisting of parallel layers of distinct material properties. The method is based on the superposition of numerical solutions for elementary displacement discontinuities in a parallel layered rock mass. The method can be used to analyse complicated excavation layouts such as those encountered in room-and-pillar or longwall mining. The method can automatically take into account the effect of the earth's surface. The method offers an economic and efficient solution to stress analysis problems which cannot be adequately modelled using two- dimensional methods and for which the expense of three-dimensional finite element or general boundary element analysis cannot be justified. INTRODUCTION Underground mining often takes place in tabular or lenticular orebodies. In many cases, for example room-and-pillar and longwall mining, the excavation geometry cannot be adequately modelled by two- dimensional methods of analysis. In these cases resort must be made to three-dimensional methods of analysis. Although in principle three-dimensional finite element models can be used for these geometries, cost limitations have restricted their application to a small number of cases. For example, room-and-pillar systems of regular pattern have been analysed by numerically modelling

Jan 1, 1984

By P. W. Ramsey, D. P. Kedzie

INCREASING demand for improved strength-weight ratios made on aircraft structures has resulted in a gradual increase in the tensile strength requirements for steels used in such applications. As the cyclic loads often are more critical than static loads, and the fatigue properties are generally the design criteria, the question arises as to whether an improvement in fatigue properties accompanies the increased tensile strength. The present investigation was undertaken to determine the relationship between fatigue and tensile properties for an aircraft quality steel in the 155 to 280 ksi (1000 psi) tensile strength range, using the Prot method of fatigue testing. Procedure and Results After preliminary work to establish proper heat treating procedures for this heat of aircraft quality electric furnace steel (a Ni-Cr-Mo-V steel," AMS- Prot Fatigue Testing Method—The determination of the endurance limit by the conventional Wohler method can be time-consuming and easily require 20 specimens when statistical variance is to be established. This is also true when endurance limit loads are determined on actual parts or subassem-blies, and the desirability of a reliable accelerated method has been evident for some time. The primary advantage of the Prot method of fatigue testing is in reducing the number of specimens and the time required for each test. Unlike the Wohler method, every Prot specimen tested con- tributes to the determination of the endurance limit, and the authors have been able to duplicate Wohler results obtained with 20 specimens with only half the specimens and a fourth of the total cycles. This new technique for defining the endurance limit was proposed in 1948' by Marcel Prot and consists of progressively increasing cyclic stress until fatigue failure occurs. By varying the load rate, a, a useful relationship is found to exist with failure stress, so that for steel the failure stress appears to

Jan 1, 1958

W. 0. HOTCHKISS,* Madison, Wis.-When we began to do geological field work in the Lake Superior region, we found a correlation in existence, and, as youngsters, accepted all that as settled. Both Mr. Allen and I, since that time, have seen a great many things that were not apparent nor visible to Van Hise, and those who worked with him; we realize now that the correlation was not final and that much remains to be determined concerning geology of the Lake Superior region. My attitude on this matter is that we should not publish an amended correlation as a final thing. We should avoid, in every way possible, foreclosing the minds of those who follow us in working in the geology of this region. As a matter of fact, no correlation can be final at present, because facts and data are accumulating so rapidly that every classification must be immediately modified to fit further observation. Consequently, my attitude in this matter would be, instead of saying that the iron formations of the Lake Superior region are all Middle Huronian, to say that there may be three Huronians-or four or five- we do not know. I believe it is better policy to hold to our present correlation. I do not believe there is any economic benefit to the mining man or the geologist working on problems relating to explorations for iron ore, that cannot be just as well solved by maintaining our present correlation, with a. wholesome idea of our lack of knowledge and the necessity for further detailed work. Then, if any new horizons are discovered in any particular range, the minds of the investigators will not be foreclosed because some one has said that all the iron formation is in the Middle so that there is no use looking elsewhere for it. There is use looking elsewhere, in many cases, as the ore deposits become exhausted.

Jan 1, 1920

By Raymond D. Daniels, Frank E. Rizzo, James D. Gerber

ThIS discussion describes a method for the addition of small amounts of oxygen to columbium (niobium) in an accurate and reproducible manner. The method is based on the complete reduction by columbium of a carefully weighed amount of another metal oxide. The equilibrium Pq associated with Cb-CbO mixtures is extremely low, e.g., 10"25 atm at 100O°C, and the pressures over Cb-0 solutions are even lower. The equilibrium Pq associated with a given metal-metal oxide mixture can be easily obtained, with the aid of a Richardson-Jeffes chart.' Although columbium should effectively reduce almost any metal-metal oxide combination, the proper choice of a metal-metal oxide system is complicated by the low rate of oxygen transport in the gas phase at low oxygen pressures and the difficulty in reducing any columbium suboxide formed during the reduction of the oxygen source material. Thermodynamically, oxide formation on columbium will be avoided so long as the oxygen partial pressure over the columbium is below the equilibrium pressure associated with the mixture Cb-CbO. The logical choice of a source for oxygen would appear to be a mixture of Cb-CbO, since oxide formation would be precluded by nucleation difficulty. But calculations using the kinetic theory of gasses indicate that, for a temperature of 900°C, the reaction would proceed too JAMES D. GERBER, formerly Research Assistant, University of Oklahoma, Norman, Okla., is Research Metallurgist, Air Force Weapons Test Laboratory, Kirtland Air Force Base, N. Mex. FRANK E. RIZZO, Junior Member AIME, formerly Assistant Professor of Metallurgy, University of Oklahoma, is Associate Professor of Metallurgy, University of Texas at El Paso, El Paso, Tex. RAYMOND D. DANIELS, Member AIME, Professor of Metallurgical Engineering, University of Oklahoma, is an NSF Fellow, Institute de MBtallurgie Structurale, Universite de euch:tel, Neuchitel, Switzerland. Manuscript submitted October 28, 1968. IMD

Jan 1, 1970