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By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

Addicks, L Ambler, J O Anderson, F B Armstrong, T Allen, L M, Jr Arnold, C E Adams, C E Adams, R E Anderson, A J Booth, E L Bernhardt, D I Boyd, W S Browning, W C Blake, D E Black, T B Bergman, Julius Bowen, H P Beckett, P G Blickensdefer, F C Bond, Josiah Butler, P P Bondlas. Y

Jan 1, 1923

Aamot, Olav Crone, (M'29) Chem. Engr., Elektro¬kcmisk, Raadhusgt. 32, Oslo. Norway. . Aase. Glenn D., (J'40) Jr. Met., American Smelt. & Refin. Co., Selby, Calif. Abadie, Henry G., (J'43) Petr. Engrg., Avenal, Calif. Abadilla, Quirico A., (M'38) Min. Engr., Dir., Bureau of Mines, Manila, P. I. Abbott, Agatin Townsend, (J'40) Jr. Engr., Phelps Dodge Corp., Morenci Branch. Morenci. Ariz. Abbott, Clarence E., (M'04) Civ. Engr. V.P., Tennessee Coal Iron & R.R. Co., 1542. Brown Mars Bldg. Birmingham. Ala. Abel, Raymond L.. (M'23) Chem. Engr., Com¬manding Officer, Pittsburgh Chem. Warfare urement Dist., American Bank Bldg.. Pittsburgh. Pa. Abel, Walter D., (M'32) Min. Engr., Supvr. Engr.. R.F.C., Los Angeles, Calif. Abele, Louis T., (M'31) 423 3rd Ave., Decatur. Ga. Abell, Leo M.: (M'31) Mill Supt. & Met.. Em¬ peror Gold Min. Co., Ltd., Vatukoula. Fiji Islands. Abernathy, G. E., (M'38) Geol., Kansas State Geol. Survey, Pittsburg, Fan. Abernathy, Jack H., (M'40) Cons. Petr. Engr., First National Bldg.. Oklahoma City, Okla.

Jan 1, 1943

By G. A. Deitz, J. Halpren

The kinetics of dissolution of silver in cyanide solutions under oxygen pressure have been investigated over a wide range of conditions with a view to establishing the reactions involved and the factors which influence the rate. The results indicate that the rate is determined principally by the transport of reactants in solution to the silver surface. The thermodynamic features of the reaction with particular reference to the influence of pH and CN- are also discussed and summarized in the form of potential-pH diagrams. METALLIC silver is readily attacked and dissolved by cyanide solutions in the presence of oxygen. This reaction has long been recognized and extensively applied1 in the well-known cyanide process for the extraction of silver from its ores. While this process has been subjected in the past to a number of investigations2,3 both of a practical and fundamental nature, some features relating to the chemistry of the reactions involved, the role of oxygen, the nature of the rate-controlling step, and the effects of pH and certain reagents such as lime, are still not fully understood. It was felt that this situation justified a further investigation of the reaction, made with a view to obtaining a better understanding of its kinetics and mechanism. In the present investigation rate curves for the dissolution of silver were determined over an extensive range of carefully controlled reaction conditions. By carrying out the reactions in a pressure vessel, the partial pressure of oxygen, and hence its concentration, could be varied widely. The influence on the reaction of other variables including temperature, pH, and the concentrations of cyanide, peroxide, and other salts was also examined. The results of these kinetic studies are presented and discussed in this paper, together with a summary of available thermodynamic information relating to the possible reactions which can accompany the attack on silver by aqueous solutions of cyanide and oxygen. Chemistry and Thermodynamics of the Reaction The chemistry of the reactions of gold and silver with aqueous cyanide solutions has been the subject of several recent reviews.'." It has been proposed' that the following reaction occurs when silver dissolves in cyanide solutions in the presence of oxygen: 4Ag + 8CN- + 0, + 2H.0 -t 4Ag(CN); + 40H- [la] An equation of this form, for the corresponding dissolution of gold, was first suggested by Elsner." Bodlaender5 proposed a similar overall reaction, but suggested that it took place in two steps, 2Ag + 4CN- + O2 + 2H2O ? 2Ag(CN),- + 2OH- + H2O2 [2a] followed by 2Ag + 4CN- + H2O2? 2Ag(CN); + 20H- [3a] On the other hand, Janin- suggested that the dissolution of gold can occur with the liberation of hydrogen, rather than by reduction of oxygen. The corresponding equation for the dissolution of silver is 2Ag + 4CN- + 2H20 -t 2Ag(CN); + 20H + H2 [4a] All these reactions represent oxidation-reduction processes and may be resolved into the corresponding separate oxidation and reduction components. The oxidation step involves the formation of the argentocyanide ion and is the same for all the reactions, i.e., Ag + 2CN? Ag(CN)2 + e [51 However, reactions la, 2a, 3a, and 4a differ in the nature of the reduction steps which are, respectively, O2 + 2H2O + 4e ? 4OH- [lb] O2 + 2H2O + 2e ? H2O2 + 2OH- [2b] H2O2 + 2e ? 2OH- [3b] 2H2O + 2e? 20H- + H2 [4b]

Jan 1, 1954

By Charles Austin

IT has been known for several years1 that certain alloys of the Konal type, containing commercial cobalt (99.32 per cent C0 and 0.42 per cent Ni) and varying amounts of ferrotitanium, exhibit very high tensile strengths at 600°C. However, their pro-portional limits and yield points are rela-tively low. Published data1 for the alloys quenched in water from 950°C. and then tested at 600°C. are summarized in the upper section of Fig. I. Similar specimens that were aged at 650°C. for 72 hr., after quench and prior to testing at 600°C., gave the results shown in the lower section of Fig. I. TABLE I.-Analysis of Material I Percentages Constituent Sample Sample Sample 3125 3124 3123 Si 0.25 0.51 o.6o Fe 4.15 10.70 13.17 Ti I.15 3.58 4.70 Mn 0.30 0.41 0.42 Co (by difference)^ 94.15 84.80 81.71 The cobalt from all three samples, united and tested for nickel, gave 0.54 per cent Ni based on the weight of cobalt. In the present work the investigation of the properties of these materials has been extended by a study of the tensile deforma- tion characteristics in moderately long-time tests at 600°, 700° and 800°C. after quenching from various solution tempera-tures. In addition, some metallographic studies have been made to correlate with the deformation tests, and to obtain in- FIG. 1.-EFFECT OF VARYING AMOUNTS OF FERROTITANIUM (FE2TI) ON PHYSICAL PROPER-TIES OF COMMERCIAL COBALT. (C. R. Austin.1) Upper section. Tested at 600°C. after water-quenching from 950°C. Lower section. Tested at 600°C. after water-quenching from 950°C. and aging 72 hr. at 650°C. FIG. 2.-PORTION OF QUASI-BINARY DIAGRAM COBALT-FE2TI AS DETERMINED METALLOGRAPH-ICALLY. formation on the quasi-binary system Cobalt-Fe2Ti. The material, very kindly furnished by the Westinghouse Electric and Manufac-turing Co. in the form of hot-swaged rods of 3/16-in. diameter, analyzed as shown in Table I. The alloys, when originally made up,1 were based upon an iron-titanium com-pound, Fe3Ti, as indicated by the work of

Jan 1, 1940

By Frederick Laist

The ores received at the Washoe Smelter come almost entirely from the mines in Butte and contain the following minerals : Chalcocite, Cu2S; covellite, CuS; chalcopyrite, CuFeS2, (trace); bornite, Cu3FeS3; enargite, Cu3AsS4; malachite, Cu2CO4 + H2O (trace); pyrite, FeS2; sphalerite, ZnS; rhodo-chrosite, MnCO3, (less than 1 per cent.); rhodonite, MnSiO3, (less than I per cent.). The country-rock of Butte is of the granite family and is a quartz-monzonite containing a little less silica than typical granite. It is made up of the following rock-minerals in approximately the proportions indicated: Minerals. Composition. Per Cent. Quartz SiO2 20 Andesine 1/2 NaAlSi3O8; 4 CaAI2Si2O8 42 Orthoclase KA1Si308 23 Hornblende 1/2 Ca(MgFe)3Si4O12; & (MgFe)2(AlFe)4Si2O12 6 Biotite (HK)2(MgFe)2A12Si3O12 9 Titanite CaTiSiO5 0.1 Apatite (CaF)Ca4(PO4)3 0.05 Magnetite (FeO)(Fe2O3 0.15 Pyrite FeS2 0.02 99.32 The main country-rock (quartz-monzonite) is cut by dikes of aplite, a granite having the following composition: Quartz, 30; andesine, 20; orthoclase, 45; ferro-rnagnesian minerals, 3; pyrite, 0.1; total, 98.1 per cent. Closely associated with the copper-deposits are dikes and bodies of " Modoe" porphyry, technically known as quartz-

Jan 1, 1913

By Bernt Ellingsaeter, Terkel Rosenqvist

IN the silicothermic reduction of magnesia, burned dolomite is treated with high grade ferrosilicon in an evacuated steel retort at temperatures between 1150° and 1200°C. The following reaction is assumed to occur MgO + CaO + 1/2 Si (Fe) - Mg(g) +- & Ca,SiO, + Fe with the equilibrium constant on the basis of thermodynamic data for the substances involved and assuming unit activity for all solid constituents, Kubaschewski and Evans' calculated the magnesium pressure as a function of temperature logp,, (mmHg) = 15.06-1.61 T- log T- 13,16O/T. Pidgeon and King," who measured the magnesium pressure by means of a flow method, found values about three times the calculated ones. This may be caused by uncertainties in the thermodynamic data, but may also be caused by the formation of other reaction products, such as Ca,SiO,, which is known to be the stable silicate in equilibrium with lime. Whatever the exact reaction may be, it is evident that as long as all other factors are maintained constant the magnesium pressure will vary with the silicon activity, viz: p,, = &,. (p,,) ", where (p,,)" is the magnesium pressure by the reduction with silicon of unit activity. In the present investigation, p,,, was therefore measured for various grades of ferrosilicon and their silicon activities were calculated. The experimental method was similar to that used by Pidgeon and King. Briquettes of burned dolomite and Fe-Si alloys were placed in a 1 in. heat resistant steel tube and were heated to 1200°C. By means of a flow of purified hydrogen, the magnesium vapor was swept into a condenser filled with steel wool. From the amounts of hydrogen used and magnesium condensed the magnesium partial pressure was calculated. First a tube of 28 pct Cr steel, and later a tube of Kanthal D (a ferrous alloy with 22.6 pct Cr, 2 pct Co, and 4.5 pct Al), was used as a heat resistant tube. The latter tube showed the best heat resistance. The dolomite used had the following composition: 43.6 pct MgO, 55.5 pct CaO, 0.2 pct K,O + NalO, 0.2 pct Fe,O,, and 0.3 pct insoluble. The ferrosilicons were prepared from 98 pct Si of technical grade (0.7 pct Al, 0.3 pct Ca, and 1 pct Fe) by melting with various amounts of electrolytic iron of high purity. The alloys thus obtained were analyzed on their iron and silicon contents, which added up to between 99 and 100 pct. The amounts of reactants were chosen so that there would always be an excess of the oxides, and the average decrease in silicon content during the experiments would be about 1 pct. Most of the reaction occurred in the part of the reaction mixture facing the gas flow. The change in the silicon concentration in the part facing the condenser was, therefore, negligible. To facilitate the reaction, about 1 pct fluorspar was added to the briquette mixture. Fluorspar does not enter the reaction, but is known to act as a

Jan 1, 1957

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts'1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By C. M. Moncrief, B C. Craft

A bentonite-clay drilling mud when treated with tetrasodium pyroarsenate underwent substantially the same reduction in viscosity and water loss as when treated with the complex phosphates. The complex arsenate showed a slightly higher reversion after heating; the other arsenates showed poor viscosity-reducing properties. Introduction During the past 10 years the chemical control of drilling mud has become of major importance in affecting the successful drilling and working over of wells. The desired properties of drilling mud have been well established, and in obtaining these characteristics there has developed a large market for viscosity-reducing chemicals. Viscosity reduction produced by humic acid, tannic acid, sodium silicate, sodium tannate, Calgon, and the complex phosphates has been described by Loomis, Ford, and Fidiam.l The effects Of treatment with complex phosphates and ammonium PolyPhosPhates on the rheological properties of muds were investigated by Fancher2 and the alkali vanadates have been described by Williams.3 Laboratory Investigations It is the purpose of this paper to point out the effects of arsenates in controlling the viscosity and gelling characteristics of a drilling mud. Viscosities and gel strengths were measured at room temperatures with a Stormer viscosimeter calibrated in centipoises and operated at 600 r.p.m. Water loss was determined at 80°F. with the Baroid low-pressure wall-building tester at a pressure of I00 lb. per sq. in. for 30 min. The hydrogen-ion concentration was measured with a glass electrode. The bentonite-clay suspensions were prepared in the laboratory and allowed to age several days before testing. Members of the Arsenic Group in the periodic Table include arsenic, antimony and bismuth, but this investigation was limited to arsenic. Phosphorus also occurs in Group V of the Periodic system and phosphorus and arsenic form many closely related compounds such as pH3 and AsH3, P2O5 and As2O5, H3PO4 and H3AS04 Samples of tetrasodium pyroarsenate were prepared by fusing c.p. disodium arsenate (Na2HA5O4.7H2O). According to Friend,' this re-forms the ortho-arsenate on dissolution in water. Sodium trihydrodiorthoarsenate was prepared as described by Mellor,5 from arsenic pen-toxide as follows: As2O5 + 3H20 -> 2H3AsO4 2H3AS04 + 3NaOH Na3H3(AsO4)2 .3H20 Sodium dihydrogen orthoarsenateWaHz-As04) was obtained by fusing together equivalent quantities of arsenious Oxide and sodium nitrate, dissolving the residue in water and allowing it to crystallize.

Jan 1, 1946

By C. M. Moncrief

A bentonite-clay drilling mud when treated with tetrasodium pyroarsenate underwent substantially the same reduction in viscosity and water loss as when treated with the complex phosphates. The complex arsenate showed a slightly higher reversion after heating; the other arsenates showed poor viscosity-reducing properties. Introduction During the past 10 years the chemical control of drilling mud has become of major importance in affecting the successful drilling and working over of wells. The desired properties of drilling mud have been well established, and in obtaining these characteristics there has developed a large market for viscosity-reducing chemicals. Viscosity reduction produced by humic acid, tannic acid, sodium silicate, sodium tannate, Calgon, and the complex phosphates has been described by Loomis, Ford, and Fidiam.l The effects Of treatment with complex phosphates and ammonium PolyPhosPhates on the rheological properties of muds were investigated by Fancher2 and the alkali vanadates have been described by Williams.3 Laboratory Investigations It is the purpose of this paper to point out the effects of arsenates in controlling the viscosity and gelling characteristics of a drilling mud. Viscosities and gel strengths were measured at room temperatures with a Stormer viscosimeter calibrated in centipoises and operated at 600 r.p.m. Water loss was determined at 80°F. with the Baroid low-pressure wall-building tester at a pressure of I00 lb. per sq. in. for 30 min. The hydrogen-ion concentration was measured with a glass electrode. The bentonite-clay suspensions were prepared in the laboratory and allowed to age several days before testing. Members of the Arsenic Group in the periodic Table include arsenic, antimony and bismuth, but this investigation was limited to arsenic. Phosphorus also occurs in Group V of the Periodic system and phosphorus and arsenic form many closely related compounds such as pH3 and AsH3, P2O5 and As2O5, H3PO4 and H3AS04 Samples of tetrasodium pyroarsenate were prepared by fusing c.p. disodium arsenate (Na2HA5O4.7H2O). According to Friend,' this re-forms the ortho-arsenate on dissolution in water. Sodium trihydrodiorthoarsenate was prepared as described by Mellor,5 from arsenic pen-toxide as follows: As2O5 + 3H20 -> 2H3AsO4 2H3AS04 + 3NaOH Na3H3(AsO4)2 .3H20 Sodium dihydrogen orthoarsenateWaHz-As04) was obtained by fusing together equivalent quantities of arsenious Oxide and sodium nitrate, dissolving the residue in water and allowing it to crystallize.

Jan 1, 1946

By Frank Milliken

IN September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1007 to 1019. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was dissemi-nated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was prob-ably less than 6o per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a com-plete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof com-prised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. 1, which gives percentages of tonnage and copper content.

Jan 1, 1940

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By Joseph M. Jacisin

Fatigue tests were conducted on 2017-T4 alumium in alloy in an u1lrcthig.h vacuum of 2 x 10-lo Torr and in air. The vatio of vacuum-to-air faligue life for this ~malerial varied Jrom 3.5:1 at a strain of 2.5 X 1O-3 ill. pegr in. to 8:l at a strum of 3.3 x X ill. per 171. Sotlze pvelivtlinary data were also obtained on the faligue life of the alumirnum alloy in a dvy-nitrogen atmosphere. A dark deposit observed on the fracture surfaces of the aiv-tested specimens was identified as oxides of tr~angarzese and magnesium This observalion, and the close correlalion betaveen results obtained in vaCuum and dry-nitrogen environtments, tend to confirm that air stvongly influences the fatigue mechanism by a covrosion process. THE fatigue life of certain metals is known to increase when the atmospheric pressure is reduced. Gough and Sopwith1-2 postulated that this is due to a joint chemical and mechanical process operating in air at the surface of the metal with oxygen and water vapor playing significant roles. Wadsworth and Hutchings3 observed that aluminum is mainly affected by the presence of water vapor. Very little information is available on the fatigue properties of structural aluminum alloys in a vacuum environment. This report describes work performed on 2017-T4 aluminum alloy in an ultrahigh vacuum (2 x 10-loTorr) and in air. Some preliminary data are also presented on the fatigue life of the alloy in a dry-nitrogen environment. 1) EXPERIMENT 1.1) Test Material. The material tested was commerciaT 2017-T4 aluminum alloy which, in addition to aluminum, has an approximate composition of 4 pct Cu, 1 pct Fe, 0.8 pct Si, 0.5 pct Mg, 0.5 pct Mn, plus smaller amounts of other elements.* Some typical naturally age to a substantially stable condition. Specimens were then machined from these rods and ground to a No. 8 microfinish. In order to minimize variation in material characteristics, specimens were made from rods procured from the same lot. 1.2) Apparatus. The apparatus and test specimen used in the fatigue tests are shown in Fig. 1. The device utilized a single-cantilever beam with rotating-bending loading. Bending stress was applied to the fatigue test specimen by placing a spacer beneath the bearing support, thereby providing a constant deflec-

Jan 1, 1968

By E. S. Machlin

THE function of this paper is to present certain results based on the fact that the strain energy arising from the solution of out-of-size solute atoms into the solid matrix is free energy and not internal energy, and that this strain energy is almost wholly shear strain energy as Zener1 pointed out. One natural consequence of this fact is an expression for the excess entropy of mixing due to the strain energy. Also, a derivation of the integral molar free energy of mixing partitioned to strain energy will be made using the model of Lawson2 and thermodynamics. This derivation has the advantage of showing in a simple way the assumptions involved in Lawson's treatment. The excess entropy of mixing partitioned to strain energy can be derived in two ways. The first way makes use of the fact that the strain energy is almost wholly in the form of shear strain energy. In this case, as Zener1 pointed out, the change in entropy due to the addition of shear strain energy is to a first approximation given by ?S/?? p,T = - ?lnµ/?T p,? Hence, the excess entropy of mixing partitioned to strain energy will be given by Sx ? = ?S/?? p,T Gx ? = - ?lnµ/?T p,? Gx ? where, Gx ? is the relative integral molar free en- ergy partitioned to strain energy; S is the entropy; is the shear strain energy; µ is the shear modulus; T is the absolute temperature; p is the pressure; and ? is the shear strain. Zener,1 as well as others, has pointed out that the shear strain energy stored in a compressible isotropic solid due to the insertion of an off-size incompres-sible sphere into a spherical hole in the solid, is approximately given by 2/3 µ/O (O°I - O)2 where a is the volume of spherical hole and no , is the volume of sphere. If we now consider the introduction of one mol of such spheres into an infinite volume of solid, then the relative partial molar free energy excess due to strain energy alone is GM ? = 2/3 µ/v (v ° 1 - v)2 where v is the molar volume of solvent and v°1, is the molar volume of pure solute type 1. Let us consider that these spheres are the two types of atoms in a binary solution, then there will be a similar relation for solute 2. The total relative integral molar free energy excess due to strain is then, to the approximations stated above GM ? = GM ? x1 + GM2 ? x2 = 2/3 µ/v [(v ° 1 - v)2 x1 + (v ° 1 - v)2 x2]. Lawson's relation for the strain energy can be de-

Jan 1, 1955

By R. G. Wheeler, J. W. Goffard

The Larson-Miller parameter was used to correlate time, temperature, and indentation creep of magnesium, aluminum, and some of their alloys. In the temperature range 300" to 450°C, the short-time Meyer hardness of pure magnesium was less than that of the magnesium alloys tested, but for long times the pure magnesium has greater indentation creep resistance. Aluminum (1100 alloy) had 1.5 to 2.5 times more indentation creep resistance than magnesium at 300" and 450oC, respectively. Hardening of aluminum with a dispersion of Al2O3 was effective in the time and temperature ranges studied. New technologies have required the development of new materials and the utilization of the more familiar materials for new and unusual applications. The use of magnesium and aluminum and some of their alloys, because of their desirable nuclear characteristics, light weight, low cost, and ready availability, has been extended to the 300" to 450°C temperature range. In this temperature range the basic consideration of these materials must be their rate of plastic flow rather than offset yield strengths. The indentation testing reported here arose from a need for design data for the load-holding ability of supports made of these materials. Test Procedure—Hardness indents were made with a 0.275-in.-diam quartz indentor and a 10.65-lb load. The indentor was made by fire-polishing a spherical surface on the end of a fused quartz rod. The samples were held at temperature in a graphite crucible controlled to ±2°C. A thermocouple was attached to the sample and test temperatures were recorded. The diameter of the spherical indentation was measured at the end of a test period and the compression stress (Meyer Hardness) was determined by: H___________load__________ m = projected area of indent Samples were 1 in. in diam and at least 1/4 in. thick. It was observed that at the higher temperatures and longer times, the quartz indentor would stick to the magnesium sample. The quartz indentor was, therefore, frequently inspected and fire-polishing repeated when necessary. The area of sticking was always a small fraction of the area of indent and was therefore considered to have an insignificant effect on results. Correlation of Hot-Indentation Test Data with Time-Temperature Parameter—Sherby and Dorn' have correlated creep or tensile data of a' solid solutions of aluminum with a temperature and strain-rate parameter suggested by Zener and Holloman. underwood2 used this parameter to correlate creep properties of some steels with hot hardness, and upon the basis of this correlation a means of obtaining creep properties from short-time (and inexpensive) hot hardness tests has been demonstrated. Since the validity of the correlation of creep properties with a time-temperature parameter and the correlation of creep properties with hot hardness have been shown, it follows that hot hardness may correlate with the time-temperature parameter. The hot-indentation data obtained was expressed as Meyer hardness, and was shown to be time and temperature dependent. Correlation of Meyer hardness, time, and temperature with the parameter was made using the relationship: Hm = Meyer hardness t = time, hours T = absolute temperature, OK K = constant A value for the constant K was calculated by equating In l/t + K/T at different temperatures and times but at the same hardness. The correlation was tested by plotting Hm vs the parameter, In 1/t +K/T. Since materials are being sought which have high hardness at low indentation creep, i.e., a high Meyer hardness for long time at high temperatures, low values of the parameter are ofthe most interest. TEST RESULTS Magnesium—Pure magnesium (99.98 pct) cut from extruded rod was indentation tested perpendicular to the rod axis at temperatures of 300°, 350°, 400°, and 450°C for times ranging from 6 sec to 112 hr. Fig. 1 shows the time dependency of Meyer hardness at the four constant temperatures. Fig. 2 shows the correlation of the Meyer hardness of pure magnesium with the time-temperature parameter using a K of 22,720 in Eq. [I]. At the bottom of Fig. 2, the effect of doubling the time of indentation t2 = 2(t1), on the abscissa for any time is shown graphically. This effect is of constant magnitude. Also shown graphically are the magnitudes of the effects on the

Jan 1, 1960

By N. A. Gokcen, J. Chipman

A revised treatment of the authors' published data eliminates the complex relation previously proposed between concentration of silicon and activity coefficient of oxygen in liquid iron. Revised values of the thermodynamic properties of the liquid solution are presented. IN a recent experimental study of the reaction SiO2 (s) = Si+ 2O; Kf, = [% Si] [% O]² [1] the authors' found a substantially constant equilibrium product in liquid iron at 1600°C of 2.8x10-5 They also reported extensive data on the reactions: SiO2 (s) + 2H2 (8) = Si- + 2H2O (g); K'2= [% Si] (H2O/H2 [2] and H, (g) + 0 = H2O (g); K'3 =( H2 O [31 (H2) [%O] From the results on reaction 3 and earlier data of Dastur² on this same reaction in the absence of silicon, they determined the activity coefficient of oxygen, f0, on the basis of the definition K3 = (H2O)/ (H2)f0 [% 0] where K, is the equilibrium constant and f0, is taken as unity in the pure Fe-0 system. Similarly values of fsi were deduced from results on reaction 2. In a more recent study" of analogous reactions in the system Fe-A1-0, it was found impossible to reconcile the results on reaction 3 with Dastur's data; accordingly the latter were ignored and the equilibrium results were extrapolated to find a value of K, at zero concentration of aluminum. This procedure failed to locate the cause of the discrepancy but it did yield reasonable values of activity coefficients. It also avoided introduction of the complex empirical relation between the oxygen activity coefficient and the concentration of the added element. The same type of discrepancy exists for system Fe-Si-0.' In the earlier paper an attempt was made to fit both sets of data by a single curved line (Fig. 6 of ref. l), the form of which is contrary to the theoretical requirement of a finite slope at infinite dilution. In the light of experience on the Fe-A1-0 system the discrepancy must be recognized as one which can be resolved only by more refined measurements. Accordingly Figs. 6 and 10 are retracted. It is pointed out also that until the discrepancy is resolved Figs. 7, 8, and 11 are subject to some uncertainty. Qualitatively the following conclusions still appear valid: 1—The activity coefficient of oxygen is reduced by addition of silicon. 2—In dilute solutions the activity coefficient of silicon increases with its concentration. 3—With respect to equilibrium in reaction 1, the above effects are approximately compensating. The discussion of K'1 in the previous paper requires no revision. It was pointed out that the constancy of the product [% Si] [% 0]² ndicated a compensating effect of the activity coefficients of silicon and oxygen. Therefore, as a very good approximation, K1 = K'1 and the following average values are suggested both for K, and K', at the temperatures 1550°, 1600°, and 1650", respectively, 1.0x10-", 2.8~10-" and 5.5 ~lo-'. Revision of the thermodynamic treatment is necessitated by the recent appearance of new data, based on a combination of combustion and solution calorimetry,' which yields for the heat of formation of low-cristobalite from the elements, the value —209,330 ±250 cal per mol at 25°C. This is about 4000 cal larger than the value previously accepted. The new value for cristobalite is used, together with Kelley's tables of high-temperature heat contents" and entropies and with Korber and Oelsen's' heat of fusion of silicon to obtain the following equation for the standard free energy of cristobalite in the temperature range 1700" to 2000°K: Si (1) + 02 (g) = Si02 (crist.); ?F° = -217,700 + 47.OT [4] The free energy of solution of 0, in liquid iron is:8 O2 (g) = 20 (in Fe); AF° = -55,860 - 1.14T [5] and these two equations are combined to give: Si (1) + 20 = SiO, (crist.); AF° = -161,840 + 48.14T [6] ?F°1873 = -71,700 cal. From the experimental value of K, = 2.8x10-5, Si + 20 = SiO2 (crist.); ?F°1873 = -39,000 cal. [7] The combination of Eqs. 6 and 7 yields the free energy change when liquid silicon dissolves in iron to form the dilute solution of unit activity (1 pct). Si (1) = Si; ?F°1873 = -32,700 cal. [8] The heat effect in this process according to Korber and Oelsen' is an evolution of 28,500 cal per gram

Jan 1, 1954

By Howard I. Smith

THE mineral trona was discovered on Government land in 1938, about 18 miles west of the town of Green River, Wyo., in the core of the John Hay, Jr., well, a test well drilled for oil by the Mountain Fuel Supply Co. in sec. 2, T. 18 N., R. 110 W., sixth principal meridian. Although no oil or gas was reported, the drilling led to a discovery of great potential economic importance and exceptional scientific interest. Trona is a relatively rare mineral found at various places in playa deposits but not previously found at any great depth. It is composed of hydrous sodium carbonate and sodium bicarbonate (Na2CO3.NaHCO3.2H20). Pure trona contains the equivalent of 70.35 per cent of sodium carbonate. Total sodium computed to carbonate times 1.42 equals the percentage of trona in the absence of other sodium carbonate minerals in the sample. ANALYSES Two short pieces of core sent to the author a few days after the completion of the Hay well were analyzed by R. C. Wells[t] and found to be exceptionally pure trona. A brief article on this discovery has already been published.1 Arrangements were then made through W. T. Nightengale[$] for the author to inspect and sample the core. The company log of the well included notations of sodium salt crystals from a depth of 1190 to 1820 ft. Not being able to identify all the minerals present, the author selected several specimens of the core for petrographic examinations and sampled the sections of trona for analysis. J. J. Fahey, of the Geological Survey, examined the specimens and reported most of the crystals to be a new anhydrous sodium carbonate and calcium carbonate mineral (Na2CO3.2CaCO3), which he named shortite,2 after Maxwell N. Short.* He analyzed the samples of trona, with the results shown in Table I. [ ] In addition to the 10 ft. I in. of trona in the first section, it is reasonable to assume that the 9 ft. 8 in. for which no core was available for sampling is either mostly trona or some other soluble salt, but it should not be included in calculating reserves. In the part of the core between 1590 ft. 3 in. and I600 ft. 4 in. the material insoluble in cold water, amounting to about 5 per cent, was estimated petrographically to contain 70 per cent clay, 25 per cent shortite, and 5 per cent pyrite. ACCOMPANYING MINERALS Fahey later secured about 600 ft. of the core for a detailed examination and study

Jan 1, 1942

By H. D. Outmans

The author applies the theory of hydrodynamic stability to fluid flow in porous media and concludes that the displacement of miscible liquids is stable if the stability coefficient, as defined by Eq. 19.2 or Eq. 27.0, is positive. The conclusion is invalid, however, since it is based on a faulty argument. To demonstrate this, the reader is referred to Eqs. 4.1 through 4.5 of the paper which describe, in differential form, the first-order disturbances c, u, v, w and p. In these same equations, cx, cz, gl, g3 and are functions of the stable concentration c. This concentration c is known and depends on x, z and t (the author assumes cy = 0). It follows that cx, cz, gl, g3 and µ are also functions of x, z and t. With this in mind, we turn to Eqs. 8.1 through 8.5 which were derived from Eqs. 4.1 through 4.5 by substituting Eq. 6.0. The significance of this substitution is that the author thereby limits the solutions of Eqs. 4.1 through 4.5 to equations of the form of Eq. 6.0. Eqs. 8.1 through 8.5 represent an infinite linear system with five unknowns: c, u, v, w and p. The coefficients cx, cz, gl, g3 and µ in this system are known at each point and at each instant; the coefficients containing derivatives of f are unknown. If this infinite linear system in c, u, v, w and p is to have a nontrivial solution, then it is indeed necessary (as the author states) that the determinant of the coefficient matrix of Eqs. 8.1 through 8.5, i.e., ( A 1, be equal to zero. This condition, however, is not sufficient. A non-trivial solution exists if, and only if, the rank of the coefficient matrix of the entire infinite system is smaller than five. In other words. all minors of order five must vanish and only if all the coefficients in Eqs. 8.1 through 8.5 are constant is this equivalent to the condition |A| =0. Constant coefficients means that gl, g3 and µ, for instance, are constant; and, since they depend on c it follows that c must be constant. We conclude that the condition I A I = 0, on which the author bases his calculations, is necessary and sufficient for a nontrivial solution only if the concentration c is constant. In other words, the author does not investigate the stability of a miscible displacement but, rather, only the stability of the flow of a homogeneous liquid. Using the initial condition and the fact that the coefficients are constant, we find

T. L. Joseph (University of Minnesota, Minneapolis, Minn.)—Mr. Killian is to be commended for his inquiry as to why a decrease of 15.3 pct in coke consumption was accompanied by a decrease of only 1.9 pct in the CO/CO, ratio of the top gas. Although I encouraged him in his efforts to find a more significant and meaningful carbon-gas ratio, the method, calculations, and conclusions originated entirely with the author. Whether we agree entirely with the assumptions underlying his corrected ratio, I think we can all agree that a better ratio is needed, and that he deserves credit for recognizing the need and for doing something about it. To be most useful, the CO/CO, ratio for the top gas should reflect the way in which the carbon is gasified in the furnace, particularly the degree of oxidation and the extent of heat release. The effect of CO, from the decomposition of the limestone and the effect of the reaction of CO and water vapor in the upper part of the furnace on the quality of top gas should be isolated from the effect of more basic reactions such as ore reduction and solution loss. The reduction of sufficient iron oxide to produce a ton of pig iron and the accompanying changes in the proportions of the carbon gases can be expressed on a mol basis as follows: 16.5FeA + 16.5CO - 33FeO + 16.5CO, [1] 33FeO + 33.0CO = 33Fe + 33CO. [2] The CO, from eq 1 normally escapes from the furnace because it does not react with coke at the temperature of its release. However, as much as 50 pct of the CO, from eq 2 may react with coke because it is released at temperatures above 1000°C: 16.5CO. + 16.5CO2 = 33CO [3] Thus we see that the gasification of 16.5 mols or about 200 lb of C in solution loss will regenerate as much CO as is required for the last stage of reduction. The pronounced effect of reaction 3 on the final proportions of CO and CO, in the gas stream is obvious. It also follows that reaction 3 materially alters the heat release but it cannot be entirely eliminated in Lake ore practice. A previous study indicates that 100 lb of solution loss may be necessary to maintain the reducing power of the gas. A reduction of 100 lb from the normal level of 200 lb would mean that over 1,-000,000 additional Btu are released in the process. The 100 lb of additional carbon which will be burned at the tuyeres will release 437,000 Btu and the absorption of 583,000 Btu by eq 3 would be prevented. One of the chief objectives of sized ore burdens and more uniform distribution of the gas stream is to minimize solution loss by completing reduction higher in the furnace and in turn to release the maximum amount of heat from the carbon charged. It was odd, indeed, to find that the use of sized ore and sinter in the careful tests reported by Dobscha had changed the CO/CO2 ratio very little. The author has stressed the close correlation between his corrected CO/CO, ratio and production. A correlation of fuel consumption and the CO/CO, might be more logical. Fuel consumption on the prepared ore burden decreased 15.3 pct whereas the corrected CO/CO2 ratio decreased 19.0 pct. Although this agreement between the reduction in fuel and the reduction in corrected CO/CO2 ratio is not as close as the correlation with tonnage, it indicates the corrected ratio is superior to the normal ratio which decreased less than 4 pct. Some adjustment should be made for the reaction: CO + H2O = CO2 + H2 —700Btu [41 because there is evidence to indicate that about one half of the hydrogen is formed in the upper 21 ft of

Jan 1, 1953

Some Things We Don't Know about the Creep of Metals. By H. W. Gillett (T.P. 1087) Reduction of Iron Ores under Pressure by Hydrogen. By Michael Tenenbaum and T. L. Joseph (T.P. loll, with discussion) Induction Furnaces for Rotating Liquid Crucibles. By E. P. Barrett, W. F. Hol- bRook and C. E. Wood (T.P. 986, with discussion) Mechanism of Solidification and Segregation in a Low-carbon Rimming-steel Ingot,. By Anson Hayes and John Chipman (T.P. 988, with discussion) Solidification of Rimming-steel Ingots. By A. HultGRen and G. PhRagmen. (Contribution 112) Dendritic Structure of Some Alloy Steels. By Daniel .I. Martin and James L. Martin (T.P. 1066, with discussion) Occlusion and Evolution of Hydrogen by Pure Iron. By George A. Moore and Donald P. Smith (T.P. 1065, with discussion) Structure of Iron after Con~pression. Hy Charles S. Barrett (T.P. 977, with discussion) Structure of Iron after Drawing, Swaging, and Elongating in Tension. Ry Charles S. Barrett and L. H. LevensoN (T.P. 1038, with discussion) Magnetic Torque Studies of the Texture of Cold-rolled and of Recrystallized Iron-silicon Alloys. By Leo P. TaraSovJ(T.P. 1012, with discussion) Influence of Atmosphere and Pressure on Structure of Iron-carbon-silicon Alloys. By Alfred Boyles (T.P. 1046) Kinetics of the Decomposition of Austenite at Constant Temperature. By J. H. Austin and R. L. Rickett (T.P. 964, with discussion) Reaction Kinctics in Processes of Nucleation and Growth. By William A. Johnson and Robert F. Mehl (T.P. 1089, with discussion) Phase Changes in 3.5 Per Cent Nickel Steel in the Acl Region. By I. N. Bavarine (T.P. 1031, with discussion) Chromium in Structural Steel. By Walter Crafts (T.P. 1055) Surface Allotropic Transformation in Stainless Steel Induced by Polishing. By J. T. BuHwell and J. WUlff (T.P. 1032, with discussion) Nature of :Passivity in Stainless Steels and Other Alloys, I and 11. Ry H. H. Uhlig and John WUlff (T.P. 1050, with discussion) Thermal Expansion of Nickel-iron Alloys (Nickel from 30 to 70 Per Cent). Ry J. M. Lohr and Charles H. Hopkins (T.P. 987, with discussion) Low-temperature Transformation in Iron-nickel-cobalt Alloys. By L. L. Wy~Ian (T.P. 1013, with discussion) Fracture of Steels at Elevated Temperatures after Prolonged Loading. By R. H. Thielemann and E. R. Parker (T.P. 1034, with discussion)

Jan 1, 1939