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A statistical investigation of folding at Mount Isa disclosed similar patterns in both the shales and the "silica dolomite" zones. Analysis of these patterns yields 3 groups of folds fully developed north plunging folds, fully developed south plunging folds, and flexuresrepresenting stages of development of folds. Interpretation of results indicates that a regional force from a southerly direction was responsible for the folding.The general pattern of shearing is allied to that of folding, with the exception of bedding-plane shearing. Many shears resulted from continued application of force on folds which ruptured after overthrusting. Other shears resulted from rupture of the more incompetent shale members, without associated folding. The shear pattern is consistent with the theory of a regional force from a southerly direction.INTRODUCTIONThe notes on folding and shearing presented in this paper are part of a current study of the structural geology of Mount Isa.FOLDING 1Measurement of FoldsInvestigation of folding underground involved the measurement of plunge, strike and dip of the axial plane, and the order of magnitude of each fold, together with its location and the rock type. The total number of folds measured was 701, of which 411 occurred in shale areas and 290 within the "silica dolomite" zones. All folds measured are located on main levels, from 7 level to 13 level inclusive. The sections of the mine involved are the Black Star, Black Rock and Racecourse. Detailed investigation of folds on the upper levels (4, 5 and 6) has not yet been done, but observations there suggest...

Jan 1, 1961

By R. Greenwood

The advent of the space age and its promise of interplanetary flight has prompted new ideas for propulsion systems that will allow maximum energy with minimum fuel weight. The use of cesium as the source of energy for such rocket flights has been found desirable. Theoretical efficiency of a rocket fuel is measured in terms of specific impulse, defined as the number of pounds of thrust per pound of propellant consumed per second. Specific impulse is usually expressed in seconds (the number of seconds for which one pound of fuel would produce one pound of thrust) although it is really a measure of total energy, not of power. The most sophisticated chemical fuels have a specific impulse of 300 to 400 sec; liquid hydrogen heated by nuclear reactor has a specific impulse of 1000 to 1200 sec. Specific impulses as high as 20,000 sec, however, are theoretically attainable with the ion rocket, in which free cesium ions are accelerated across a voltage drop and ejected at high velocity.' Characteristics of the system have been sketched by Boden.2 The desirable properties of an ion propellant are: 1) low ionization potential, 2) low boiling point, and 3) high atomic weight. Alkali metals best fulfill these requirements, and Table I indicates the superiority of cesium. The use of heavy complex ions such as UCl3 is ruled out by their instability and other disadvantages.' Despite its enormous superiority in specific impulse, the ion rocket is inherently low-powered, capable of very small acceleration. Application of ion propulsion will be limited to large rockets and spaceships on missions requiring powered flight for weeks or months and employing a separate chemical propulsion system for escape from the earth's atmosphere where power requirements are large but of brief duration. For example, Kraemer and Larson3 considered the case of an unmanned 25,000-lb pay-load placed in a 300-mile orbit by chemical rockets, proceeding thence by ion propulsion to the vicinity of Mars, where it would go into orbit once again. Calculations provide for 8500 lb of cesium for such a voyage. The question of whether such quantities of cesium will be readily available to the space program does not appear to have been considered by geologists and mining engineers. Present Production and Uses Literature on industrial applications of cesium is scanty. The metal is used in scintillation counters, photocells, infra-red detection devices, and as a "getter" in low-voltage vacuum tubes. Production is sporadic and total figures are not published, but the annual consumption is measured in pounds rather than in tons. The few pollucite deposits known, small as they are, can easily supply the present limited demand for gram or pound lots of cesium. Until recently the price of cesium was $2 to $4 per gram, but according to Chemical Engineering, cesium salts are now available at $13 to $27.50 per lb. Geochemical Distribution As a large alkali ion, the cesium ion accompanies potassium in geological processes and tends to be concentrated in the latest crystallizing fractions of potassium minerals in much the same manner as rubidium. Most of the cesium in igneous rocks, therefore, is in the micas and potash feldspars of granites, and especially in granitic pegmatites. The cesium content rises markedly in the micas of the late by-drothermal replacement stage in complex pegmatite~.' Typically, cesium is only 0.5 to 0.01 times as abundant as rubidium in potassium minerals. Rb', with a radius of 1.47 A, is close enough in size to K' (1.33 A) so that rubidium forms no minerals of its own. Cs+ is so large (1.67 A) that only small concentrations can be taken up in potassium minerals; when cesium is present in solution in larger concentration it forms the mineral pollucite, Cs3-Na2A17Si17O48.3H2O, which is known only in pegmatites. In the weathering of igneous rocks, cesium is dissolved, carried to the ocean, and apparently in-

Jan 1, 1961

By R. W. Heckel, H. W. Paxton

The growth of grain boundary films and Widmanstiitten plates of proeutectoid cementite in hypereutectoid steels ulas considered quantitatively in three plain carbon steels and one "pure" iron-carbon alloy. Growth was found to take place at a slower rate than would be predicted on the basis of a model invoking rate control by long range diffusion of carbon. The films in the pure alloy grew faster than those in the plain carbon steels. A possible explanation is suggested. In 1904, Nernsst' and Brunner2 postulated that ionic crystals growing in supersaturated aqueous solutions grew at rates determined by diffusion through the solution to the growing crystal interface. The gradient down which the diffusion took place was assumed to be fixed by the supersaturated bulk solution concentration, the concentration dt the crystal surface and some arbitrary distance. The flux of material to the crystal was described as Flux where D is the diffusion coefficient, A the crystal surface area, Ci the bulk solution concentration, Co the saturated solution concentration, and 6 the thickness of the diffusion zone. It is obvious that the expression is an adaptation of F+ick's3 first law of diffusion (steady state). This was the initial formulation of what will be defined here as "diffusion controlled growth," i.e., growth limited by the long range diffusion of a component either to or from the advancing interface assuming both phases at the interface to be in equilibrium. This idea of equilibrium interface concentration implies an infinite reaction rate at the interface. Volmer, Zener,' and 11schner6 have derived expressions for the diffusion controlled growth of spherical precipitates in metallic systems. These analyses agree that the growth in a given direction should be parabolic with time. Brown and Hawkes7 observed that graphite, formed both from the decomposition of cementite and from the decomposition of eutectoid austenite in cast irons, grew according to a parabolic relationship and, therefore, concluded that the laws of diffusion controlled growth, as defined above, were obeyed. They, among others, failed to consider, however, that parabolic growth is a necessary, but not sufficient, condition for diffusion controlled growth. Mehl and Dube"' have pointed out that equilibrium may not be realized because the concentration at the interface cannot change instantaneously from that of the bulk to the saturation value. Furthermore, they propose that an equilibrium solute concentration in the parent phase adjacent to the precipitate would remove the thermodynamic activity gradient across the interface and, thus, stop the growth process. Frisch" has also emphasized the importance of interface concentrations that vary throughout the growth of a new phase. The variation in activity across an interface, as discussed by Onol' and Cahn and Hilliard,12 is of fundamental importance to this question. Ham13 considered the data of Turnbull14 on the growth of barium sulfate in aqueous solutions. He concluded that the data could be analyzed in terms of a radiation-type boundary condition. Flux across interface = K (c, - C,) [21 where C, is the concentration in the solution at the interface, Co the saturated solution concentration, and K the proportionality constant. The edgewise growth of Widmanstlitten plates, frequently referred to as the rate of lengthening, was first considered by Zener.'' Basing a mathematical analysis on steady-state (constant velocity) growth he concluded that where G is the growth rate, D the solute diffusivity, Ci the concentration in the bulk, Co the equilibrium interface concentration, C, the concentration in the precipitate, a a constant, Y the radius of curvature of the edge of the plate, and rC the critical radius, i.e., the radius which would increase the activity of solute at the interface at equilibrium under the influence of capillarity to that of the bulk. Zener1'

Jan 1, 1961

[NORTH AMERICA UNITED STATES ALABAMA AUBURN Sturm & O'Brien, Consult. Engrs. °Sturm, Rolland G. BESSEMER Granger, W. C. BIRMINGHAM Air Reduction Sales Crockett, John M. Amer. Cast Iron Pipe Co. Carter, Sam F., Jr. Donoho, C. K. Anderson Elec. Corp. Davis, Moss V. J. B. Clow & Sons Neptune, Maurice D. Connors Steel Div. °Sandelin, Robert W. Hayes Aircraft Corp. Ricketts, W. E., Jr. Willhelm, A. Clyde, Jr. McWaine Cast Iron King, O. H. Worthington, B. W. Shook & Fletcher Sup. Co. Gearhart, Thomas A. Southern Res. Inst. Dismukes, Edward B., Wheelahan, Edmund J. Thomas Foys Miller, Ralph M. Union Carbide Metals, Co. Brandler, Edgar A. U. S. Pipe & Fdry. Co. Clay, Donald H. Unaffiliated Berg, H. A. Caldwell, H. A. Gilmer, H. U. Harris, Thomas H. Templeton, J. B.]

Jan 1, 1961

By A. D. Hahn

This report describes reconnaissance by the Federal Bureau of Mines of titanium-bearing sandstone in Kemper County, Miss. The purpose was to determine the ilmenite, rutile, and associated heavy-mineral content of black-sand-bearing Eocene deltaic formations" The investigation was part of a survey of titanium resources of the United States. Ilmenite (FeTi03), an iron-titanium oxide, is the major titanium-bearing mineral consumed in the titanium pigment industry. Rutile (Ti02), titanium oxide, is used mainly in producing welding-rod coatings and titanium metal. The fieldwork was conducted during the first half of November 1959. Seven holes, totaling 304 feet of bore, from which 64 samples of cuttings were taken, were drilled in the north-central part of the county; and two holes, totaling 172 feet of bore, from which 34 samples of cuttings were taken, were drilled in the southeastern part.

Jan 1, 1961

By A. Gene Collins

Rapid, sensitive, and precise methods of determing major, minor and trace constituents of oilfield brines are needed. Several methods have been developed or adapted by the Federal Bureau of Mines at the Petroleum Research Center, Bartlesville, Okla. The following methods are described in this report: Spectrophotometric and volumetric for iodides and bromides; potentiometric for pH, alkalinity, acidity, borate boron, total boron, and organic boron; gravimetric for potassium; disodium ethylenediaminetetraacetate (EDTA) volumetric for total hardness, calcium, and magnesium; spectrophotometric for fluorides; and color comparison .for arsenic. Adequate sensitivity, precision, and accuracy were obtained for each method. The Bureau of Mines pioneered in research on the analysis of oilfield waters (2, 46, 47).6 However, several of these early procedures were quite time consuming. Also, they did not include methods for determining trace and minor constituents of brines.

Jan 1, 1961

By K. E. Tame

A resume of the history and state of the art of physical beneficiation of uranium ores is presented along with a detailed description of research on concentration of uranium ores by attrition grinding. The information on flotation, gravity concentration, electronic sorting, and selective grinding was gathered to complement the study of attrition grinding methods. Both dry and wet grinding procedures were investigated as potential methods of upgrading a variety of ore types, ranging in grade from 0.02 to 0.42 percent U308. A Mardun4 disintegrator that employs high-speed rotating paddles in a cylindrical shell lined with interrupter bars was used in most of the dry grinding studies. Attrition scrubbing devices, which impart a violent mixing or attritioning action to ore pulps, and cylindrical mills, employing rods or punchings as grinding media, were used in the wet grinding tests.

Jan 1, 1961

By R. W. Heckel, J. H. Smith, H. W. Paxton

The habit plane of proeutectoid cementute precipitated from austenite was studied using a two-trace surface (analysis coupled with a direct X-ray back-reflection determination of the orientatzon of the parent Matrix. The results were the same as those obtained by earlier workers1 - 2 who used Indirect methods to determine the orientation of the matrix. The data indicate that a range or habit planes in the parent phase is operative which is not in agreement with accepted existing theories. In 1933, Mehl, Barrett. and smith1 obtained a non-unique result in a study of the Widmanstätten habit plane of proeutectoid cementite. Their data are shown in Fig. 1. These results were verified by Greninger and Troiano,2 although they did not pre-sent any data. Both of these investigations relied upon indirect methods of determination of the matrix lattice orientation. Theoretical considerations of Widmanstatten precipitates have usually proved or assumed an orientation relationship between matrix and precipitate; the habit plane expressed relative to the matrix is generally unique, although it may be irrational.3 Opinion is divided as to the factors influencing the choice of habit plane. Mehl4 felt that a nucleus which was plate shaped to minimize strain energy and surface energy during its formation could maintain this shape by the point effect of diffusion; the

Jan 1, 1961

By R. F. Hewlett

All ore reserve estimates are based on some system for assigning an area of influence to each drill hole. Commonly used methods of calculation are the polygonal, triangular, statistical analysis, and cross-sectional. Each of these methods is based on different volumetric considerations and the weighting of grade with tonnage varies with each method. Because the characteristics of each mineral deposit are different, a preliminary survey of these characteristics should be made for each individual deposit to determine which method or methods should be used. In this project the several methods were not only compared with one another, but also against actual production records. Basic data was derived from a mined out portion of the Silver Bell pit near Tucson, Ariz. All calculation was carried out on a digital computer, and the first step was development of computer programs which would yield the desired information. The second step was the coding of input data into punched card form. Cost and speed of computer operation were measured, and these results are given with the computer program summaries on page 38.

Jan 1, 1961

By Dorothy M. Richardson

The Bureau of Mines has participated in the American Petroleum Institute Research Project 48A (API-RP48A) program on the Separation and Identification of Sulfur Compounds in Crude Petroleum. The lack of reference compounds or infrared spectral data has made difficult the identification of individual sulfur compounds boiling above 140° C. The recent acquisition of 24 alkylthiophnnes has made possible a limited study of this important class of sulfur compounds. The infrared spectra of 2-monoalkylthiophenes and 2,5-dialkylthiophenes for the 2 to 15p range are reported. Correlations for determining the 2-alkyl and 2,5-dialkyl substituted thiophenes are derived from this information. The 2-alkylthiophenes show a unique pattern in the 5.50 to 6.54 region, while the 2,5-dialkylthiophenes show a distinctive pattern in the 5.6µ to 6.7µ region. A skeletal vibration occurs in the 9.5 to 10.0µ region for all of the thiophenes investigated. These data will aid the infrared spectroscopist in the identification of compounds of the type reported.

Jan 1, 1961

By J. J. Demeter

Experiments were conducted in 2- and 4-inch-diameter standpipes to evaluate the effectiveness of standpipes as pressure seals. During the experiments, these standpipes conveyed Alan-Wood magnetite (60 to 230 U.S. standard sieve mesh) by gravity flow from one vessel to another of relatively higher pressure. The information obtained has been helpful in a Federal Bureau of Mines investigation of how to make either synthesis gas or hydrogen by a modified steam-iron process employing a continuous recycling stream of granular iron-iron oxide at temperatures of 600° to 900° C. In this process the mixture of granular material flows by gravity from a reduction vessel at low pressures to an oxidation vessel at higher pressures. Data from the 2- and 4-inch-diameter standpipes indicate that it would be practical to use a standpipe as a pressure seal between the reductor and oxidizer. Investigators found that, by gravity flow, the standpipe could convey the Alan-Wood magnetite against pressure gradients up to 1.07 pounds per square inch per foot of column height.

Jan 1, 1961

The first session of the Rocky Mountain Coal Mining Institute was called to order by John T. Maulsby, Superintendent of Maintenance and Planning, Columbia-Geneva Steel Division, U. S. Steel Corporation, Dragerton, Utah, representing the past-president. W. K. Dennison, Jr., Superintendent. Koehler line. Kaiser Steel Corporation. Raton, New Mexico, who was unable to attend. Mr. Maulsby welcomed the members and guests, and introduced the President, A. Z. Dimitroff, Mining Electrical Engineer, Health and Safety, District 1-L, U. S. Bureau of Mines. Denver. Colorado. The text of President Dimitroff's address of welcome is as follows: The President's Remarks Guests and Members of the Rocky Mountain Coal Mining Institute: The distinct honor and privilege of officially welcoming you to this, the fifty-seventh regular meeting of the Institute, is indeed a pleasure. Your officers and committees have tried to provide a varied program which I am sure should have something of interest to all of us. The theme of this meeting, "Where Do We Go From here'?", appeared rather fitting for the In¬stitute this year because, as most of you know, until only two weeks ago we thought that this is the last time we will be able to meet at the Colorado Hotel, which has been the favorite spot of most members. Your officers and many of you were literally asking just that question.

Jan 1, 1961

By John E. Shelton

Flotation tests were conducted on two samples of copper-nickel-bearing ore from the Harriman area near Rockport, Maine. The samples were taken by Roland F. Beers, Inc., for tests in cooperation with the Federal Bureau of Mines. One sample, analyzing 0.38 percent copper and 0.71 percent nickel, was essentially a disseminated pyrrhotite in hypersthene. Pentlandite, chalcopyrite, pyrite, and millerite were intimately associated with the pyrrhotite. Locked series flotation tests on this sample showed that 87.4 and 73.4 percent of the copper and nickel, respectively, could be recovered in a bulk concentrate that analyzed 3.47 percent copper and 5.34 percent nickel. The copper-and nickel-bearing minerals were collected with sulfhydric collectors in an alkaline circuit. Cleaning the concentrate three times with the addition of pH regulators was sufficient to attain the previously stated grades. The second sample had analyses of 0.31 percent copper and 0.85 percent nickel; talc and hypersthene were the main gangue minerals. Bulk sulfide flotation, made while depressing the talc, resulted in a concentrate that analyzed 2.33 percent copper and 4.70 percent nickel at recoveries of 70.0 and 54.4 percent, respectively. Flotation of the talc followed by bulk sulfide flotation resulted in a nickel content greater than 5 percent. A locked-series test showed that 60.7 percent of the copper and 73.7 percent of the nickel could be recovered at grades of 1.29 and 4.85 percent, respectively.

Jan 1, 1961

By W. Gibson Jaworek

Of increasing importance to the student of fuels economics has been the extent to which different primary energy sources can substitute for each other in the various energy markets of the nation. Knowledge of the nature and extent of fuel interchangeability can aid the fuels economist in projecting trends of energy utilization, as well as giving him a better understanding of the past and present conditions of fuel markets. It is also important to the consumer to know just how much flexibility he can maintain in his energy consuming operations. And, finally, various governmental bodies show keen interest in the degree of energy substitutability in determining public policies concerning the fuels industries. The presence of excess fuel production capacity in the United States during the early 1960's indicates that fuel interchangeability should become more prevalent in the increasingly competitive energy markets of the nation. Discussion of fuel intercompetition is almost always restricted to qualitative terms-because of the lack of comparable statistical data, between the different energy sources in geographic or "type-of-use" fuel, markets. There are exceptions, of course, such as, the excellent fuel consumption data which are available on steam electric generating plants throughout the nation. In other sectors, statistics are at best incomplete.' Inmost instances, indirect fuel consumption indicators, such as sales of fuel burning equipment, are extensively used to measure market shares of a particular fuel; however, these indicators are hard to evaluate precisely without prior knowledge of the total competitive market.

Jan 1, 1961

By N. E. Hanna

An important goal in the development of coal mining explosives has been to improve their safety characteristics through suitable formulation. In the United States no systematic effort to establish factors influencing the incendivity to firedamp and to coal dust of explosives through research was made until the last decade. In consequence, American permissible explosives underwent only very slight modifications and many remained substantially the same as in the early years. As part of a long range program for increasing the safety of permissible explosives, the Bureau of Mines undertook to determine how the amounts and particle sizes of the principal constituents of these explosives affect their incendivity. It was found that an increase in the relative amount of sodium chloride and a decrease in its particle size significantly decreased the incendivity of our permissible explosives to firedamp (7-9).6 This is in agreement with findings reported by Dolan (4) for compositions of nitroglycerin and salt. One important result of the work at the Bruceton station has been the recent introduction of salt-formulated permissibles by several explosives manufacturers. This paper describes a statistically designed experiment for studying the effects of the particle size of ammonium nitrate and the type of carbonaceous materials used on the incendivity of permissible explosives. Interest in these particular effects goes back as far as the first formulations of coal mine explosives, around 1910 in the United States and even earlier in Great Britain and other countries. Although it is well established that fine

Jan 1, 1961

By Nick Derick

The continued growth of steel production in the Western States is contingent upon the development of new iron ore sources. Recent development of economical techniques for concentrating and agglomerating taconites has focused attention on the low-grade magnetite deposits near Atlantic City, Wyo., as potentially important sources of iron ore for blast furnace smelting. Therefore, the Federal Bureau of Mines has made comparative evaluations of blast furnace burdens that incorporate pellets produced from Atlantic City concentrates. The Bureau also has evaluated the relative effect of Utah coke on blast furnace performance, using a high-quality Eastern coke as a basis for comparison. This work was done in the Bureau's experimental blast furnace at Bruceton, Pa. Tests determined the maximum wind rate that could be used while a continuous stock movement was maintained in the furnace. The furnace was operated at wind rates ranging from 800 to 1,400 std. c.f.m., them maximum limit of the blowers for the 1.75 in.-diameter tuyeres used. Using a normal Utah ore burden and Utah coke, the furnace went into a tight hanging condition with a wind rate above 950 std, c.f.m. Using the experimental pellet burden again with Utah coke, the wind rate could be increased to 1,000 std, c.f.m. and probably to 1,050 std. c.f.m, before tight hanging occurs. This represents an increase of 5 to 10 pct. in the wind rate. The experimental results indicate an accompanying increase of iron production, as much as 8 pct.

Jan 1, 1961

By Northcutt Ely

Jan 1, 1961

By W. W. Fowkes

The Federal Bureau of Mines examined a low-temperature tar obtained from a small-scale commercial unit for carbonizing North Dakota lignite for products that might be important to the economic processing of the tar. Tie tar may be divided into three distinct parts: (1) Tar acids, 45 volume-percent; (2) tar bases, 1 volume percent; and (3) neutral compounds, 54 volume-percent. It has a boiling range of approximately 150° to 380° C. (the decomposition temperature) and yields 18 weight-percent as hard pitch. The tar distillate up to 365° C. may be separated as: (1) Tar acids, 48 volume-percent; (2) tar bases, 1 volume-percent; and (3) hydrocarbons, 51 volume-percent. The tar-acid distillate, boiling to approximately 265° C., was characterized in some detail; the neutral fractions and the tar bases were less thoroughly examined. In general, as might be expected of a primary low-temperature tar, the lower boiling fractions are less in quantity compared with the usual high-temperature tar. The homologous series of each major class appears to be rather complete, although some components are present in very small amounts. The tar is quite unstable thermally, and might be more conveniently processed by extraction methods rather than by distillation procedures. The neutral fraction of the tar is highly aromatic, and might be considered as base stock for the production of liquid fuels.

Jan 1, 1961

By Orville D. Mussey

During, 1956 the water used in mining iron ore in the United States amounted to about 2 billion gallons and the water used in producing iron concentrates-amounted to about 166 billion gallons. By 1980 an increase of about 65 percent is anticipated in the amount of water used for mining and beneficiating iron ore. Except for boiler-feed makeup water the quality requirements for water, for mining and beneficiating iron ores are not stringent. Adequate supplies. of water for development should be available at reasonable cost with the possible exception of some in arid regions.

Jan 1, 1961

By J. L. Meijering

Oxidation hardening of cylindrical and spherical specimens first decreases with depth below the surface, but then increases again as the center is approached. This is in agreement with the view that this change in hardness is mainly determined by the change in velocity of the oxidation boundary, which affects the dispersion of the oxide. WHEN a thick slab of silver containing 0.3 pct Mg by weight is internally oxidized, the hardness measured on a cross section is found to decrease considerably with distance from the surface.&apos; This phenomenon has been attributed to the diminution of the velocity of the oxidation boundary. The smaller this velocity is, the more slowly the free-oxygen concentration rises towards the concentration in equilibrium with the oxygen gas. And a small 0 concentration favors dissociation and thus conglomeration of the oxide. For instance, the hardness decreases more rapidly during long annealings in nitrogen than in air.&apos; Measurements by Gregory and Smith3 on sections through internally oxidized Al-silver wire showed a smaller variation in hardness, probably because the wire diameter was only 0.9 mm. Wood4 found a drop in hardness with depth in internally oxidized Al-copper strip, and also—by electron microscopy—the concomitant increase in Al2O3 particle size. Under certain circumstances internal oxidation leads to formation of rather irregular inner oxide films in the midst of dispersed oxide. This special sort of conglomeration—discussed in Ref. 5—is also favored by greater depth below the surface.3,5 In this paper hardness measurements in large diameter cylindrical and spherical specimens are described. Here the oxidation velocity* goes through ness initially decreases with depth but increases again towards the center. Normally, the diffusion coefficient D1 of oxygen is very large compared to D2, that of the dissolved metal. If, furthermore, the atomic fraction c2 of the latter is much larger than the O-solubility cl- but c2D2 << c1D1- the velocities in question are easily calculated2 to be: for the cylinder and for the sphere. Here p is the radial coordinate of the oxidation boundary and R the specimen radius, which in dilute silver alloys is constant, as no external oxidation occurs. These equations have been derived for a divalent solute; for nondivalent solutes c2 has to be multiplied by half the valency. The equations are not valid near the center. For which can be considered as a standard case,2 the Eqs [I] and [2] begin to yield U-values which are appreciably too high for p/R = 0.05 and 0.15, respectively. But at the v-minima they are still very good approximations. These minima lie at p = emlR= 0.37R in the cylinder and p = 1/2 R in the sphere. Other factors besides the velocity v will also influence the hardness. The oxide concentration cox is constant in a flat strip, apart from a narrow region in the middle,2 but in cylindrical and spherical specimens cox decreases steadily with depth. When C1 << c2 and c1D1 >> c2D2 one can calculate

Jan 1, 1961