Search Documents

By Vard H. Johnson

IN 1943 the U. S. Bureau of Mines undertook drilling in an effort to develop new reserves of coking coal in an area near Paonia, Colo., as a part of an attempt to alleviate the shortage of known coking coal of good quality in the western United States. Geologic mapping of the area was undertaken by the U. S. Geological Survey with the purpose of first furnishing guidance in location of drillholes and later aiding in interpreting the results of the drilling. The drilling program was under the general supervision of A. L. Toenges of the U. S. Bureau of Mines. J. J. Dowd and R. G. Travis were in charge of-the work in the field. Geologic mapping was started by D. A. Andrews of the Geological Survey in the summer of 1943 and was continued from the spring of 1944 to 1949 by the writer. The first few holes drilled failed to locate coking coal, but in the summer of 1944 coking coal was discovered by drilling 6 miles east of Somerset, Colo., the site of present mining. In the succeeding years, 1945 to 1948, 100 to 150 million tons of coal suitable for coking were blocked out by drilling. The ensuing discussion of the geologic controls on the distribution of coking coal in the area is based on the geologic mapping as well as the drilling done in the Paonia area, more complete descriptions of which have appeared or are in process of publication.1-5 In order that the possible geologic controls affecting the present distribution of coking coal may be considered, it is necessary to discuss briefly the indicators. of coking quality coals. Coking Coal Coal that cokes has the property of softening to form a pastelike mass at high temperatures under reducing conditions in the coke oven. This softening is accompanied by the release of the volatile constituents as bubbles of gas. After release of the contained gases and upon cooling, a hard gray coherent but spongelike mass remains that is referred to as coke. This substance varies greatly in physical properties and, to be suitable for industrial use, must be sufficiently dense and strong to withstand the crushing pressure of heavy furnace loads. Western coals have a generally high volatile content and therefore form a satisfactory coke only when they attain a rather high fluidity during the process of heating and distillation in-the coke oven. When this high degree of fluidity is developed, the volatile constituents escape and leave a finely porous coke. On the other hand, when the degree of fluidity is low the product is an excessively porous and therefore physically weak mass that is called char.6 Small quantities of oxygen present in coal are believed to decrease the fluidity of the material during the coking process and to favor the development of char rather than coke. In consequence, coal chemists have for some time considered the possibility of developing an index to coking. qualities by inspection of chemical analyses of coals.7 A formula has now been developed that does permit a rough preliminary estimate of the cokability of coal on the basis of the analysis on an ash and moisture-free basis. Coals may be eliminated as possible coking fuels if the oxygen content is greater than 11 pct. Similarly the ratio of hydrogen to oxygen must be greater than 0.5 and the ratio of fixed carbon to volatile constituents must be greater than 1.3. If the coal, on the basis of these limiting factors, appears to have possible coking qualities, the following formula permits determination of the coking index: Coking index =[ a+b+c+d 5] a equals 22/oxygen content on ash and moisture- free basis, . b equals two times the hydrogen content divided by oxygen content on moisture and ash-free basis, c equals fixed carbon/1.3 x volatile matter, and d equals the heating value on moist, ash-free basis/13,600. Coking indices higher than 1.0 suggest that the coal will coke, and indices above 1.1 indicate good coking tendencies. Although generally usable, this formula is not completely satisfactory because the percentage of oxygen shown in ultimate analyses is derived only by difference; i.e., by subtracting the sum of the percentages of the constituents determined analytically from 100 pct.8,9 Although the coking index indicates the coking tendencies of coal, it is necessary to make physical tests of coke before its industrial value can be determined. The U. S. Bureau of Mines has developed a standard procedure for determining the approximate strength of coke that would be formed from a given coal. In this test one part of ground coal, mixed with 15 parts of carborundum, is baked to form a standard briquette. The weight, in kilograms, necessary to crush the briquette is termed the agglutinating index. This test determines the relative fluidity attained in the coking process by measuring the cementing strength of the coal in the briquette. A

Jan 1, 1952

By Raymond C. Boettner

The present work had for its purpose: 1) the identification of crack nucleation sites in AISI 4340, quenched to martensite and tempered over a range of 'temperatures; and 2) the comparison of fatigue processes in AISI 4340 with processes observed previously in pure metals From constant def1ection-bending fatigue tests, martensite boundaries were identified as the favored crack nucleation sites in quenched and tempered AISI 4340. It, also, was concluded that the fatigue processes operating- in this lous-alloy steel were similar to Processes observed in pure tnetals. ALTHOUGH much engineering data has been accumulated on the fatigue properties of quenched and tempered martensitic steels,' fatigue as a process is not as well understood in martensite as it is in pure metals.' Important features of the fatigue process, such as the identity of the nucleation sites, have not been determined in the commercially important high-strength low-alloy structural steels. The present work had for its purpose: 1) the identification of crack nucleation sites in a low-alloy steel, i.e., AISI 4340, which had been quenched to martensite and tempered over a range of temperatures; and 2) the comparison of fatigue processes in the AISI 4340 with processes observed previously in pure metals. This comparison of the fatigue processes in the different tempers was restricted to the high-strain low-cycle part of the S-N curve. Under these test conditions, previous work on a number of metals has shown that a large number of cracks are nucleated in less than 30 pct of the fatigue life.3 Furthermore, crack nucleation sites are not restricted to inclusions but are also associated with intrinsic structural characteristics of the metal. MATERIAL A 20-lb ingot of vacuum-melted AISI 4340 (for composition see Table I) was hot-rolled to 1-in.-diam rod and then cold-rolled to a 1-in.-wide strip, 0.08 in. thick. Fatigue specimens, see insert of Fig. 1, were machined from the strip with the long dimension parallel to the rolling direction. m this orientation, the stringers of 1 to 2 p inclusions present in the sheet lay parallel to the stress axis in the specimens. The specimens were austenitited at 2050°F in order to obtain a large prior austenite grain size, i.e., 2 mm, which facilitated the subsequent identification of the prior austenite boundaries. A helium atmosphere was used to minimize decarburization. After austenitiza-tion at 2050°F, the specimens were transferred to a 1450°F furnace so that specimen distortion was held to a minimum in the subsequent oil quench. Previous work4 indicated that refrigeration in liquid nitrogen prior to tempering reduced the percentage of retained austenite in the quenched specimens to less than 5 pct. Tempering was carried out in air over the temperature interval of 200°to 800°F to produce a range of mechanical properties, Table I. The preparation of the fatigue specimen was completed by grinding about 0.005 in. from each surface and electropolishing in a chrome trioxide-acetic acid solution for 30 min. Examination of etched cross sections of specimens prepared in this fashion showed the foregoing specimen preparation to be adequate for the removal of the decarburized layer present after the heat treatment. Transmission electron microscopy showed that the as-quenched microstructure of this alloy consisted of a mixture of martensite plates containing either a high density of dislocations or microtwins. Previous work5'6 indicated that in the course of oil quenching autotem-pering resulted in the formation of E carbide on the martensite and microtwin boundaries. Tempering for 2 hr at temperatures up to about 400°F resulted in further precipitation of the E carbide. Finally, at about 400°F, cementite began to replace the E carbide on the martensite and microtwin boundaries in addition to forming a Widmanstatten structure within the plate matrix. EXPERIMENTAL S-N curves were obtained using electropolished specimens cycled at 1800 cpm as cantilever beams in fully reversed bending at selected constant deflections. The deflections were translated into surface strains by means of a calibration curve obtained through the use of strain gages. An argon atmosphere was used to minimize environmental effects. To investigate the development of fatigue slip bands, the specimens of the different tempers were unidirec-tionally bent to a surface strain of 0.005 to 0.007, photographed to record the location and appearance of slip bands so introduced, and then cycled to failure

Jan 1, 1968

By W. G. Pfann

A simple method of obtaining multistage batch separations by crystallization was described recently. Known as zone-refining, it comprises passing short molten zones through a long solid charge. This technique can now be used on a continuous basis by means of the zone-void method described in this paper. Feed enters, at an intermediate point, a column down which molten zones travel, and waste and product leave at the ends. Materials move in the column through the agency of voids, which are introduced at the ends and travel toward the feed inlet. The voids and molten zones are moved by external heaters in a simple manner, and the principle of reflux is utilized. ANEW method of obtaining multistage separations by crystallization was described recently.' Named zone-refinina.,-, the method comwrises slowly passing a series of molten zones through a long solid charge. Solute becomes concentrated at one or the other end of the charge, depending on whether it raises or lowers the freezing point of the solvent. The separation increases with the number, P, of zone-passes, approaching a limit as P approaches infinity. Zone-refining has been highly effective in purifying germanium and other substances.2,3 and new applications are steadily increasing. Zone-refining is a batch method and as such it has certain limitations inherent in batch operation. If it could be made continuous, its scope and utility would be greatly broadened. This end has been achieved by the zone-void method described in this paper. In the zone-void method feed is introduced continuously at an intermediate point in a column down which molten zones travel, while impure waste and purified product leave at the ends. Both the flows of feed, waste and product, and also the travels of the zones, are actuated by external moving heaters in a simple manner; and the system utilizes the principle of reflux. The method provides, in the field of crystallization, the counterpart of the continuous fractiona-tion column in the field of distillation. The following will be discussed: apparatus and mode of operation, fundamental nature of the separation, design theory, and practical considerations. The method will be described in terms of a binary solute-solvent system in which the solute is an impurity to be removed and the solvent is the desired product. The distribution coefficient, k, defined as the ratio of solute concentration in the solid freezing out of a molten zone to that in the liquid in the zone, is assumed to be constant and less than one. The process is equally effective for k's greater than one and for ternary or higher order systems. Method and Apparatus The essential features of a continuous zone-refining process are represented in highly generalized form in Fig. 1. A series of molten zones, produced by moving heaters, travels slowly down the column or charge (to the left in Fig. 1). If there were no flows of feed, waste, or product, the process would simply be batch zone-refining, the action of the molten zones being to sweep solute down the column, solvent up the column. For the process to be con- tinuous, with stripping and enriching sections in the column, feed must enter, and waste and product must leave, as indicated. The zone-void process accomplishes both objectives, namely, the indicated movements of zones and the indicated flows of material. Zones are moved by moving heaters, just as in batch zone-refining. Materials are made to flow by creating voids at the waste and product exits and causing these voids to move to the feed inlet. Since there must be a net flow of material from the feed inlet to each of the outlets, the indicated movements of voids are in the desired directions, because movement of a void in a given direction corresponds to flow of material in an opposite direction. In order to produce the desired movements of voids, the column is folded into two vertical sections having the feed inlet in common at their upper ends. Voids are displaced upward by the liquids in the molten zones and their travel is actuated by the motions of the zones. Voids travel with the zones in the enriching section and move continuously. Voids travel opposite to the zones in the stripping section and move intermittently. Creation and travel of voids will now be examined in detail. The enriching section of a column in operation, with its void generator, is shown in Fig. 2. The column section is a vertical tube around which a series of closely fitting, regularly spaced heaters travel slowly upward. Each heater produces a molten region, the temperatures of the heaters and the cooling between heaters being controlled so as to maintain the molten zones approximately constant in size. A void is normally present atop the molten zone in each heater. As the heater rises, it continuously melts solid above it, which drips through the void into the molten zone and continuously freezes out solid below it, of concentration k times that of the liquid in the zone. When a molten zone and void reach the feed inlet, which is kept molten, the void is displaced by an equal volume of feed liquid. Generation of voids of controlled size in the enriching section is shown in Fig. 3. The void generator is a tube of small cross-section, provided with lateral heat-conducting fins which sense the position of the heater. Liquid can escape only when the entire outlet tube is within the heater. If any part of the outlet tube is outside the heater, liquid cannot escape,

Jan 1, 1956

By Charles White Merrill

Mankind's progress is measured in minerals. Man's emergence from prehistory is marked by passage through a Stone Age and a Bronze Age and into the present era, sometimes called the Iron Age or the Age of Metals. With the evolution of civilization and the development of a modem industrial economy, minerals become more and more important. Structures, roads, and machines are built largely of minerals; the energy to heat the structures and to drive the machines is mostly mineral; agricultural fertility is maintained by mineral fertilizers and water; and military strength is provided by fortresses, armaments, and munitions, largely of mineral origin. Thus in the material world, in the productivity of the economy, access to minerals has paramount importance. Every evidence indicates increasing dependence on minerals in the modem economy, particularly on the mineral fuels as energy sources to provide the power base for advancing industrialization. Both the total and the per capita consumption of almost every mineral is increasing in the industrialized nations. Moreover, nations with predominantly agrarian economies call themselves underdeveloped and universally strive to industrialize. Most mineral consumption trends in the more advanced economies have been greatly exceeding population growth-which itself has been advancing at an accelerating rate-and sometimes have surpassed the growth in real income. Some minerals have only recently been adopted or grown to importance in use. Titanium metal did not appear as a commercial product until 1948, and even coal seriously displaced wood as a source of heat less than two centuries ago. On the other hand, minerals have always played an important role in construction. The prehistoric megaliths that form the dolmens of Salisbury Plain are stone; the pyramids are andesite faced with limestone; and many other ancient structures are built of mineral materials. In modem times the whole course of architecture has been redirected by new building materials, mostly mineral. Most conspicuous is the sky-

Jan 1, 1964

By I. R. Kramer

The apparent activation energy, U, JOY plastic deformation of aluminium, copper, and gold single crystals and polycrystalline aluminum was found to he dependent upon surface condition. At low strains, the value for U for aluminum single crystals was 4200 cal per mole ; however, this value decreased to 920 cal per mole when the specimens were polished during the test at a rate of 50 X 10-5 win-1 The activated volume also was found to increase with the rate of metal removal. That the surface plays an important role in plastic-deformation processes has been adequately demonstrated.1-4 Of particular interest at this time are the observations4 that the creep rate of single crystals of fee metals is increased markedly when specimens are polished during the deformation process. These observations were interpreted in terms of a dislocation debris layer at the surface regions of the crystal. This layer, which appears to be a region containing a high concentration of dislocations or segments of dislocations, not only will impede the egress of dislocations on the primary slip system, but will also provide a barrier against which dislocations may pile up. By this means, a stress which opposes the motion of dislocations will be generated. It is considered that this stress must be taken into account in any theory which describes the plastic-deformation process. Although a detailed dislocation model cannot be given at this time, it may be stated that the stresses opposing the motion of dislocations arise from the dislocations in the debris layer, Ts, and ti due to the resistance to motion imposed by internal obstacles such as Lomer-Cottrell barriers, subgrain and grain boundaries, forest dislocations, and so forth, as well as the resistance due to the presence of jogs on dislocations and the interaction of the stress fields of dislocations, and so forth. In essence, we have added an additional term, ts, to the usual form of the equation T = Ta- Tb, where Tb is the back stress due to the various types of obstacles which impede the motion of dislocation. Accordingly, the net stress, t, acting on a dislocation may be written as where Ta is the applied shear stress. For deformation which occurs by a thermally activated process5,8 ?=Ae-u/kT = A e(u,-VT)/kT [2] and U = Uo- Vt PI where U = activation energy for plastic flow, y = shear strain rate, Uo = activated energy for plastic deformation in the absence of stress and depends upon the particular deformation process, V = activated volume, k = Boltzmann constant, T = temperature, OK, and A = frequency factor. From Eqs. [I] and [3], U = Uo- V(Ta - Ti - TS) [4] and it is seen that if Ts decreases, the activation energy, U, must decrease if V remains constant. However, as will be shown, V is a function of the surface conditions. In their work on aluminum, Lytton and coworkers7 reported that at low strains the activation energy was 3400 cal per mole and at high strains it was 28,000 cal per mole. The lower value was interpreted in terms of the energy necessary to overcome the Peierls force, while the higher value was associated with the energy necessary for dislocations to move by a cross-slip process. It will be shown that the lower activation energy is associated with the surface debris layer rather than with the Peierls force. EXPERIMENTAL PROCEDURE Single crystals having a nominal cross section of 1/8 in. and a 3-in. gage length were prepared by a modified Bridgman technique using a multiple-cavity graphite mold. The initial purity of the metals was 99.997, 99.999, and 99.999 pet for aluminum, copper, and gold, respectively. The orientation of the specimens is given in Fig. 1. The measurement of the activation energy as a

Jan 1, 1964

By G. L. Kulcinski, R. D. Leggett

Irradiated uranium containing 635 ppm of carbon, mostly in the form of UC precipitates, was annealed at temperatures from 650" to 900°C under hydrostatic pressures of 0 to 1000 bars. Postirradiation examination revealed that the carbide particles are not stable in the r phase of irradiated material but are stable in unirradiated material annealed under identical conditions. The degree of carbide dissolution appears to be connected with the fission product concentration and independent of annealing pressure. THIS paper describes the change in appearance of carbide particles in irradiated uranium after the uranium has been postirradiation-annealed. It has been proposed by several investigators&apos;-5 that fission gas-induced swelling in irradiated uranium may be reduced by incorporating a fine dispersion of second-phase particles into the metal. Because of the low solubility of carbon in uranium6 and the apparent stability of UC precipitates at high temperatures,6-8 this system has received some attention. The stability of UC particles to low-temperature irradiation has been demonstrated many times, as well as their stability during postirradiation anneals in the high a or B phases.9 Unirradiated uranium containing UC particles has been annealed high in the r phase, and the solubility of carbon was found to be only -115 ppm at 1050ºC.6 Vacuum annealing of irradiated uranium to the same temperature produces a spongelike sample, due to the formation and growth of fission gas bubbles."14 This highly disrupted lattice has made any determination of the stability of UC at these temperatures impossible. Nevertheless, it has always been tacitly assumed that the UC particles were still present. Recently, postirradiation, high pressure-high temperature tests have been performed on irradiated uranium containing a secondary phase of UC. 14 Examination of these samples after 100-hr, 900°C tests revealed that the carbides are not stable, and the results of these tests are presented here. 1) EXPERIMENTAL PROCEDURE The samples, high-pressure equipment, and subsequent analytical techniques are the same as those described elsewhere.14,15 Briefly, cylindrical samples of commercial-purity uranium that had been irradiated at <350°C to 0.37 at. pct B.U. were subjected to 90O°C, 100-hr anneals in NaK at pressures ranging

Jan 1, 1970

By D. E. Light, J. Y. Somnay

The use of alkyl acid phosphates and their alkali salts as collectors for the uranium minerals brannerite and uranothorite was investigated. In particular a detailed flotation study was carried out using isooctyl acid phosphate as a promoter. Tests were conducted on an Elliot Lake ore analyzing 0.11% U 3 O 8, chiefly as brannerite, and approximately 9% pyrite. Pyrite was floated with conventional reagents; the flotation of brannerite from the sulfide tails was studied to determine the optimum pH and pulp density to employ with isooctyl phosphate. 4 uranium recovery of over 90% was possible with a selectivity index of 8.95 when these tails were floated at 17% solids and a pH of 1.7. The effect of various modifying agents was also investigated. Aluminum sulfate, lactic acid and sodium silicate improved the selectivity of collection yielding selectivity indices of 9.5 to 11.5. Ferric chloride was found to be a depressant for brannerite. A Bancroft ore which analyzed 0.13% U308, and contained uranothorite was also amenable to flotation using isooctyl acid phosphate. The composite uranium concentrate obtained assayed 0.41% U308 at a recovery of 95.3% and a ratio of concentration of 3.24. Previous investigations1,2 on the flotation of brannerite, pitchblende, uraninite and/or uranothorite from various Canadian ores showed that fatty acids, including oleic acid and tall oils, petroleum sulfo-nates and alkyl acid phosphates, were suitable collectors for these uranium minerals. Additional work carried out by the Mines Branch in Ottawa on brannerite ores from the Elliot Lake area3 used the tall oil Acintol FA-1, or FA-2, as a collector. A recovery of 92% of the uranium in a concentrate which contained about 55% of the weight and assayed 0.2% U3O8 was obtained from a feed of 0.1% U308 in this latter instance. Eigeles et a1.4 carried out flotation on pitchblende ores and found that the most promising results were obtained with alkyl acid phosphates and their alkali salts as collectors. Within the homologous series of alkyl phosphates, the best flotation characteristics were displayed by isooctyl phosphates. Further, isooctyl phosphate derivatives were much less sensitive to hardness forming salts than oleic acid, enabling all flotation tests to be made with tap water. This paper describes tests employing alkyl acid phosphates for the flotation of ores containing brannerite and uranothorite. The flotation work described herein was conducted in conjunction with the development of a leaching process for Elliot Lake, Ontario, brannerite ores. In this process pyrite in the ore was concentrated by flotation and roasted, providing sulfur dioxide which was used to produce sulfuric acid in situ in a liquid-solid extraction process. A 40% conversion to sulfuric acid was indicated at a leaching temperature of 80°C; this resulted in the extraction of 93% of the total uranium after a contact period of 6 hr. A rotary kiln was used as a leaching vessel. Preconcentration by flotation was studied in conjunction with the above process to reduce the bulk of solids for leaching and, consequently, capital expenditure. The materials and methods used in this study will be described initially. Then the results will be presented in two sections, the first dealing with the brannerite ore, and the second with the uranothorite. Finally an economic analysis of the results on the brannerite material will be made. MATERIALS AND METHODS The two ore samples examined were from uranium-producing mines. One was a brannerite ore, a uraniferous quartz pebble conglomerate from the Elliot Lake area, which contained 0.11% U3O8, 4.3% S and 4.5% total Fe. Mineralogical studies of similar samples indicated the presence of quartz, microcline, sericite, pyrite and minor quantities of rutile, pyrrho-tite and zircon. The other ore was from a biotite-rich pegmatite in the Bancroft area; feldspar, quartz and biotite formed the major gangue components. Uranothorite was the principal uranium mineral; the head assay was 0.13% U 3 O 8. Preparation of Feed: The ores were crushed to —10

Jan 1, 1963

By N. J. Grant, Per Knudsen, J. T. Blucher

The fatigue behavior of three SAP alloys was studied in ternzs of strain rate and temperature, at high strains. The k values in the modified Manson-Coffin equation, Nk4 = C, were less than 0.5 under all test conditions, and change with strain amplitude for the lower-oxide alloys at about 2 pct strain. Lowest k values were near 0.25. Strain rate had no effect on life at 80 F, but had an increasingly greater effect with increasing temperature above 500". Life decreased with decreasing strain rate, above 500"F, and with increasing temperature. Ductility at fracture in a tension test was indicated to be an important factor in determining 1ife in these big+-strain tests with the SAP alloys. INEVITABLY, in the course of mechanical tests at elevated temperatures, particularly if significant time at temperature is involved, there are large changes in structure; these changes make it difficult to relate behavior patterns over ranges of temperature or strain rates at high temperatures. Such changes are to be expetted in low cycle fatigue at low strain rates and high temperatures. Accordingly, it was of great interest to examine the low cycle fatigue behavior of SAP / an aluminum oxide dispersion-strengthened aluminum, a type of alloy which had shown unusual structure stability to temperatures as high as 1000" to 1150°F and resisted recrys-tallization essentially to the melting temperature.&apos;j3 Since the matrix is pure aluminum, there are no complications of averaging, agglomeration, or phase solution. It was also desirable to check the Manson-Coffin equation4?&apos; for the SAP alloys, namely N~E~ = , where ep is the total plastic strain amplitude, k and C are constants, and N is the number of cycles to failure. Here, too, was an opportunity to check the roles of temperature and strain rate with a very stable material. Tavernelli and coffin6 had concluded that k had a value of about 0.5 for many alloys and C was equal to ~/2, where E is the fracture ductility determined from a static tension test. The results were obtained from low-temperature tests where creep and diffusion processes are unimportant. Manson7 found k = 0.6 fitted his data reasonably well; however, in later analyses of a large amount of low cycle fatigue data generated at room temperat~re@"~ he found k to vary from 0.6 for short lives to 0.21 for long-life fatigue tests. In the latter studies,89g Manson separated the total strain range into elastic and plastic components when he found that k was influenced by the nature of the strain. The use of EL (total strain) instead of EP (total plastic strain)4&apos;5 makes a difference in the resultant k value. The ratio of changes with temperature, strain rate, and strain; further, there are the problems in the determination of the elastic strain. Based on these considerations, and the improved fit of points in a plot of by Wells and Sullivan,&apos; is also utilized in these studies. Anderson and wahl,14 using commercial 1100 aluminum, and Blucher and Grant,15 using 99.99 pct pure aluminum, found an increase in life with increasing test temperature. Anderson and Wahl were the first to report low cycle fatigue results from SAP materials. With increasing temperature, the role of strain rate becomes more important. In this regard, care must be exercised to differentiate between frequency (wherein strain rate may vary from zero to a maximum in each cycle, sinusoidally, for example), and constant strain rate, as used in the present study, in a saw-tooth type cycle; in the latter case, the frequency is not specified but can easily be calculated from the strain and strain rate data. It has generally been found that life in low cycle fatigue tests decreases with decreasing frequency16 or with decreasing strain rate at elevated temperatures.15 Coffin,17 reviewing Eckel&apos;s work,16 also reported that k increased with decreasing frequency for acid lead, yielding values from 4.0 at a frequency fo 6.6 cycles Per day to 1-46 at a frequency of 7440 cycles per day; the value of k decreased to 0.58 at a frequency of 2.38 x lo6 cycles per day. EXPERIMENTAL PROCEDURE Three SAP alloys, of two nominal compositions, were tested. Alcoa supplied XAP 005 as 2-in.-diam extruded bar, of nominal composition A1-7 wt pct A1203. The Danish Atomic Energy Commission supplied SAP 930 (A1-7 wt ~ct Ala3) and SAP 865 (A1-13 wt pct Al&) manufactured by Swiss Aluminium Ltd., in the form Of $-in.-diam extruded rod. Metallographic comparison of the structures of XAP 005 and SAP 930 showed the former to have a more uniform oxide distribution. Button-head specimens were machined in the longitudinal direction of the bar with 0.4 in. gage length by 0.2 in. diameter, with a fillet radius of j-B in. After machining, the specimens were electropolished in a 1 to 4 mixture of perchloric acid to methanol to remove all machining marks. All test bars were in the as-extruded condition. The fatigue tests were performed on a hydraulically activated, axial strain machine, with complete reversal of strain.15 Test conditions were:

Jan 1, 1969

By Atmaram H. Soni

A statistical study of machinability led the writer to examine existing data in regard to a thermal conductivity-mechanical properties relationship. Various functional relationships were proposed and the multiple correlation determined by statistical methods discussed in detail in the 1iterature.4 The relationship having the greatest engineering and statistical significance is discussed below. The data for cast and wrought aluminum alloys&apos;&apos;2 have been compiled and analyzed separately. The results of these analyses are presented in Table I. The empirical equations for estimating the thermal conductivity (cal sec-&apos; cm-I °C) are: for cast aluminum alloys K = 0.584 -0.00984/ -0.00263 Hb [1] and for wrought aluminum alloys K = 0.604 -0.00424l- 0.00170 Hb [2] where 1 and Hb are the percentage elongation and Brinell hardness number. Results of a similar analysis pertaining to stainless steel3 are also given in Table I. This empirical equation for estimating thermal conductivity (Btu per sq ft per hr per °F per in.) is K = 216.19- 1.716l - 0.0997 Hb [3] The relationship between electrical resistivity and mechanical properties was also examined for aluminum alloys using the same statistical method. These results are listed in Table II. While the situation of exact multiple correlation

Jan 1, 1965

By W. Bonfield

The temperature dependence of the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-6 in. per in.) and the stress-plastic strain curve of polycrystalline Cu 1.9 wt pct Be have been measured for the solution treated condition, an intermediate condition containing G.P. zones and ?&apos; precipitate and the overaged ? precipitate condition, in the range from -58° to 200° C. A transition in micro -yield behavior and a large temperature dependence were noted for the intermediate condition, which are interpreted in terms of the interaction of glide dislocations with two differently sized zones. In comparison the microscopic yield stresses of the solution treated and overaged conditions were less sensitive to temperature variations and are satisfied by the Mott-Nabarro and dislocation bowing theories, respectively. A determination of the temperature dependence of the yield stress of a precipitation hardening alloy has provided a powerful tool for evaluation of the operative deformation mechanism. There is a marked contrast between the effect of temperature on the yield behavior of a metal containing coherent zones or intermediate precipitates, which can be "cut through" by mobile dislocations, and a metal containing a dispersion of noncoherent particles, through which dislocation "bowing out" is the dominant role of deformation.&apos; These studies have in general been confined to single crystals, as it was considered that similar experiments on polycrystalline material did not produce good data because of the lack of sensitivity with which the yield stress could be determined. However, this objection has been removed by the introduction of mi-crostrain techniques, with which the yield stress in polycrystalline materials can be measured to a strain sensitivity of 10-6. Such measurements have not only shown that the deformation of polycrystalline precipitation hardening alloys can be examined with the same detail as single crystals, but also that some unexpected results are obtained.&apos; In this paper the results obtained from a study of the temperature dependence of the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-6 in. per in.) and the stress-plastic strain curve of a polycrystalline Cu 1.9 wt pct Be precipitation hardening alloy (Berylco 25) are discussed. The temperature dependence of the alloy was measured for three different conditions: 1) The solution treated condition (a supersaturated solid solution of a containing ~12 at. pct Be3) which is obtained by water quenching the alloy from 800° C. 2) The condition of y&apos; intermediate precipitate, to- gether with some G.P. zones,&apos; which is produced after an aging treatment of 2 hr at 315°C from the solution treated condition. (The alloy was cold rolled to 40 pct reduction prior to aging to minimize grain boundary precipitation effects.)4 3) The condition with equilibrium ? precipitate structure2 which is developed after an aging treatment of 24 hr at 425° C. EXPERIMENTAL PROCEDURE Tensile specimens of gage length 1 in. and with rectangular cross section of 0.18 by 0.06 in. were prepared from the solution treated, cold rolled alloy and were either resolution treated for 1 hr at 800°C, followed by water quenching, or aged for 2 hr at 315°C and 24 hr at 425° C to produce the desired precipitate structures. The microstrain characteristics of the aged specimens were determined at temperatures from —58" to 200° C and those of the solution treated specimens from -58° to 30° C. Each temperature was controlled to ± 0.2°C, which was a level of stability sufficient to eliminate thermal expansion effects from the measurements (~1.2°C temperature increase produced an extension of 2 x 10-6 in.). The microplastic behavior of the specimens in the temperature range below 82" C was measured with a standard Tuckerman strain gage,5 while at temperatures above 82°C a modified Tuckerman gage with a reduced strain sensitivity (4 x10-6 in. per- in.) was used. A load-unload technique was used to establish values of the microscopic yield stress. The specimen was strained at a constant cross head speed of 2 x 10-2 in. per min to a given stress level, at which the total strain was measured. Then the specimen was immediately unloaded at the same rate and any residual plastic strain determined. This procedure was repeated for an increasing series of stress levels until the microscopic yield stress was established by a direct measure of the stress to produce a residual plastic strain of 2 x 10-6 in. per in. (It should be noted that, as reversible dislocation motion occurs at stresses less than the microscopic yield stress,2 the plastic strain rate at this level was not constant.) In an ideal test, the microscopic yield stress would be determined from a continuous stress-strain measurement, rather than from a load-unload sequence, in order to eliminate mechanical recovery effects.6 However, it was found experimentally that mechanical recovery was negligible in Cu 1.9 wt pct Be at small plastic strains for all the temperatures investigated, as the microscopic yield stress was independent of the number of load-unload cycles employed (i.e., the values measured for specimens subjected to different numbers of cycles was within the experimental scatter determined for specimens tested in an identical manner). Therefore, it is reasonable to consider the microscopic yield stress determined in the load-unload

Jan 1, 1969

"Butte originated as a placer mining camp. The first gold discovery was made in the year 1864, near what is now Main Street. Placer mining was vigorously prosecuted along Silver Bow Creek and in Missoula, Buffalo, Town and Parrot gulches for a period of five years, at the end of which time, in 1870, the camp was practically deserted. In the meantime, the quartz veins so prominently traceable over the hillsides were located, the first location being made by W. L. Farlin and called the Black Chief claim, and later restaked as the Travona. Reasoning from the presence of the gold placers, free-milling gold ores were eagerly looked for by the early prospectors. Claims covering the great Rainbow and other silver lodes were located in the sixties. The presence of valuable silver ores in these veins caused the staking out of many claims, believed to be valuable only for silver, but which later proved to be enormous copper producers.Treatment of these early discovered rich ores was first attempted in arrastres. Later, stamp mills were built. The Centennial dropping 10 stamps, was the first, and in 1875 Mr. Farlin built the Dexter 10-stamp mill, intro¬ducing chloridizing-roasting. More successful processes were soon introduced and several large mills built, among which were the Alice, Lexington, Silver Bow, Moulton and Bluebird, in all representing a total of 290 stamps. The silver mining industry reached its zenith in 1887 and declined rapidly in the early nineties, following the sudden drop in the price of silver in 1892.During this period of silver mining activity the business of copper mining was making rapid strides. Development of the veins, located as silver veins, had uncovered copper ore in many instances. There was great activity in ""claim staking'' in the years from 1871 to 1879, during which period most of the claims covering the present productive copper area were located."

Jan 1, 1913

By AIME AIME

IN a recent technical paper of the Central Committee of the French Coal Mines (Note technique No. 198, by L. Lahoussay) the author points out that continuous in¬crease in depth of mine shafts makes it more and more necessary to look for appropriate means to reduce the weights and dimensions of the hoisting ropes. Increasing depth demands a larger section and weight for the cable if the useful load is not to be cut down at the same time. This naturally leads to increased cost per ton, and at the same time creates serious mechanical difficulties. The dimensions of the hoisting engine must be increased, acceleration at the start must be decreased so as to avoid periods of excessive peak power loads, and a longer time be allowed to slow down the speed of the hoist when applying brakes. The hoisting rope, upon which depend the dimensions and hence the mass of the hoisting engine, presents the greatest obstacle to the development of hoisting from greater depths. Evidently, for a given depth, the total weight of the rope can be notably reduced by utilizing a wire rope of decreasing section, approaching the theoretical logarithmic form. This is a solution frequently adopted for great depths. Of course, the weight of the rope could be easily&apos; diminished by reducing the useful load, but it is certain that with increasing depth of mining, more effort must be made to confine the hoisting to a small number of shafts, and increase the load hoisted per trip.

Jan 1, 1933

By D. E. Mikkola, G. E. Poquette

X-ray diffraction was used to study the growth of antiphase domains in quenched (or "disordered&apos;? Cu3Au annealed in the range 300" to 385°C. Measurements of the long-range order parameter indicate that a high degree of order is established rapidly at these annealing temperatures. Average domain sizes obtained by Fourier analysis of the superlattice peak profiles show that antiphase domain growth is analogous to classical metallurgical grain growth (i.e.,fol-lows a D2 US kt relation). The activation energy for the growth process, 44 kcal per mole, indicates diffusion control. The anisotropy in the observed effective domain sizes from seven different superlattice peaks can be best accounted for by a configuration involving antiphase domain boundaries on {100 } and (111 ) planes, where the (100) boundary is the low-energy type, {lOO} Type I. The disappearance of the (111) antiphase domain boundary during domain growth is dif-fusion-controlled with an activation energy of 48.5 kcal per mole. On the other hand, the behavior of the parameter representing the amount of (100) Type I boundary indicates that there may be a conversion of the higher-energy boundary types to (100) Type I boundary during the growth process. THE order-disorder transformation in the alloy Cu3Au has been the subject of numerous experimental investigations over the past 40 years, most of which have involved measurements of convenient physical properties such as resistivity and hardness as a function of heat treatment. The interpretation of these data is difficult because measurements of this type have the disadvantage that they yield total changes resulting from several different atomic processes which may be occurring simultaneously. The present study was undertaken to establish by means of X-ray diffraction the kinetic behavior of one of these atomic processes, namely antiphase domain growth. In the completely ordered state Cu3Au has an L12 structure which can be described as an fcc type arrangement of atoms in which the gold atoms occupy the corner sites and copper atoms the face-centered sites. Three other equivalent unit cells can be formed by allowing two gold atoms to occupy opposite face-centered sites and copper atoms to occupy the remaining corner and face-centered sites. These four different unit cells are crystallographically related by a shift of 1/2<110>. Quenching from above the critical temperature (392°C) to room temperature retains the "disordered" structure-a "random" arrangement of copper and gold atoms having the fcc structure. Annealing the disordered alloy below the critical temperature causes ordering to occur through the nucleation and growth of ordered regions at different points throughout the crystal. These small ordered regions, each based on one of the four types of unit cell, grow by consuming the disordered material until they impinge to form a domain structure in which the domains are antiphase by a shift of 4(110). The boundaries between domains are called antiphase domain boundaries (APDB) and they have been found to lie primarily on &apos; {100} planes in highly ordered Cu3Au. Two types of APDB can occur on ( 100) planes. An example of an (001)1/2[110] shear type APDB is shown in Fig. I. Because of the layer of copper atoms separating the domains in this case, there are no near-neighbor violations across the boundary and it has a low surface ener This type of APDB will be referred to as {lOO} Type I. Fig. 2 shows an (001): [011] climb type APDB, (100) Type 11. This type of APDB can be described as resulting from removal of a (200) plane followed by a shift of 1/2<110> to bring the separated regions together. Near-neighbor violations across (100) Type I1 APDB make it a high-energy boundary. There are numerous other possible APDB configurations; however, it is only worth noting that shear type APDB can be produced on the (111) plane by motion of a normal fcc dislocation with Burgers vector 1/2<110> through the ordered structure. A (111); [110] shear type APDB is shown in Fig. 3. Again, because of the near-neighbor violations this type of APDB has a higher energy than the (100) Type I APDB.

Jan 1, 1970

By George B. Langford

The McIntyre mine is in the Pearl Lake section of the Porcupine gold area. The rocks are Keewatin lavas intruded by quartz porphyries and albitite dies of Algoman age. Gold-bearing quartz veins are found in the Keewatin rocks near the porphyry stocks. The whole area has been highly compressed by forces acting along a N. 20°W. line. These forces folded the Keewatin rocks before the intrusion of the Algoman rocks, and later schisted both the Keewatin and Algoman rocks. Vein fractures were developed after the folding but before the development of the schist by the compres-sive forces being locally broken up into couples. These couples were set up by the differential resistance to deformation of porphyries and basalts, and also by the competency of the dacites and incompetency of the tuffs and fragmental rocks. During the important period of vein formation, two zones were developed—an inner productive zone in which the quartz veins are ankerite-bearing and an outer barren zone in which the quartz veins are calcite-bearing. The vein solutions originated in the same magrna that supplied the albitite dikes. Introduction The McIntyre mine, in the Porcupine gold area of northern Ontario, has passed its twenty-sixth birthday and has been producing gold since early in 1912. During this time approximately ten million tons of ore has been mined and over three and a half million ounces of gold recovered. This amount of ore would be sufficient to fill 2300 standard railway freight trains, each of 100 cars, and the gold produced, although only equivalent to a cube 51/2 ft. to the side, would weigh approximately 100 tons, a load for three freight cars. Silver has been produced in the ratio of 1 oz. of silver to every 4.4 oz. of gold, so that the total silver recovery is in the neighborhood of 700,000 ounces. The early history of the mine, like that of many others, shows that for several years it fought an uphill struggle for existence. One of the important features in winning this fight was the early recognition of some of the geological conditions responsible for the ore deposits, and the application of this knowledge in the search for ore and in the acquiring of adjoining properties. As early as 1913—only two years after the mine was opened—a geological department was organiaed. It has functioned almost continuously since that date and has demonstrated the importance

Jan 1, 1941

By George B. Langford

The McIntyre mine is in the Pearl Lake section of the Porcupine gold area. The rocks are Keewatin lavas intruded by quartz porphyries and albitite dies of Algoman age. Gold-bearing quartz veins are found in the Keewatin rocks near the porphyry stocks. The whole area has been highly compressed by forces acting along a N. 20°W. line. These forces folded the Keewatin rocks before the intrusion of the Algoman rocks, and later schisted both the Keewatin and Algoman rocks. Vein fractures were developed after the folding but before the development of the schist by the compres-sive forces being locally broken up into couples. These couples were set up by the differential resistance to deformation of porphyries and basalts, and also by the competency of the dacites and incompetency of the tuffs and fragmental rocks. During the important period of vein formation, two zones were developed—an inner productive zone in which the quartz veins are ankerite-bearing and an outer barren zone in which the quartz veins are calcite-bearing. The vein solutions originated in the same magrna that supplied the albitite dikes. Introduction The McIntyre mine, in the Porcupine gold area of northern Ontario, has passed its twenty-sixth birthday and has been producing gold since early in 1912. During this time approximately ten million tons of ore has been mined and over three and a half million ounces of gold recovered. This amount of ore would be sufficient to fill 2300 standard railway freight trains, each of 100 cars, and the gold produced, although only equivalent to a cube 51/2 ft. to the side, would weigh approximately 100 tons, a load for three freight cars. Silver has been produced in the ratio of 1 oz. of silver to every 4.4 oz. of gold, so that the total silver recovery is in the neighborhood of 700,000 ounces. The early history of the mine, like that of many others, shows that for several years it fought an uphill struggle for existence. One of the important features in winning this fight was the early recognition of some of the geological conditions responsible for the ore deposits, and the application of this knowledge in the search for ore and in the acquiring of adjoining properties. As early as 1913—only two years after the mine was opened—a geological department was organiaed. It has functioned almost continuously since that date and has demonstrated the importance

Jan 1, 1941

By H. C. Weed

THE Inspiration Consolidated Copper Co., located in the Globe-Miami district at Inspiration, Ariz., became a producer of copper in 1915. From 1915 until 1948, 116,278,000 tons of ore were produced from underground workings by the block-caving system of mining. In April 1948, open-pit ore production from portions of the ore body was started and earlier plans for block-caving in these areas were abandoned. The change was due to economic conditions.

Jan 8, 1950

By T. P. Chen, F. W. Bowdish

Studies made with a captive bubble apparatus on the sulfidization and collection by amyl xanthate of true chrysocolla specimens have defined the ranges of pH value and sulfide concentration which permit contact between the bubble and the mineral surface. Titanium compounds were the most effective of the materials found to activate the sulfidization of chrysocolla. With titanium activation, the contact angles and the ranges of pH value and sulfide wncentration giving bubble contact were all increased. Chrysocolla ores were concentrated by flotation. Chrysocolla ores occur at many localities in grade and quantity sufficient to make mining and millin feasible, but no satisfactory method of concentratio has been found. Although chrysocolla may be leached with acid, only those ores without acid-consuming gangue may be leached economically. Because of its potential importance, a study of the conditions nece sary for flotation of chrysocolla has been carried ou The literature contains a few references to flotation of chrysocolla. Two methods were developed by the U. S. Bureau of Mines.1,2 The first consisted of a fatty acid soap and a high xanthate as collectors of chrysocolla from a synthetic ore, while the second involved the use of hydrogen sulfide and xanthate. Ludt and DeWitt3 demonstrated the difference in adsorptive powers of chrysocolla and quartz for bas triphenyl methane dyes and suggested the use of butyl, hexyl or octyl-substituted malachite green as collector. Jackel4 emphasized the effects of combin tions of reagents such as Aerofloat 31, pine oil, and Reagents 404 and 425 with sodium sulfide and zinc hydrosulfite as conditioning agents. Although he reported recoveries of 89% from a synthetic ore and 98% from a natural ore containing azurite, malachite, chalcopyrite and chrysocolla, careful application of Jackel&apos;s method to chrysocolla from Tyrone, N.M., failed to give a high recovery. MATERIALS AND TECHNIQUE Samples from Inspiration, Ariz., and Tyrone and Magdalena, N. M., were used for experimentation and verified as true chrysocolla by leaching tests, specific gravity tests and X-ray diffraction. Chrysocolla does not dissolve at pH 4, although malachite and azurite do. Chrysocolla is about half as dense as the copper carbonates. X-ray diffraction analyses by the powder camera method confirmed the samples as true chrysocolla. A captive bubble apparatus, which cast an enlarged image of the air bubble and the mineral surface upon a screen, was used to check on the character of the surfaces. The specimens were prepared by grinding a flat surface on a glass plate using fine abrasive; then they were washed and kept in distilled water until they were to be treated with reagents. Before each reagent treatment, the specimen was carefully checked for cleanliness in the captive bubble apparatus. It was assumed that the surface was clean if, after fine grinding and washing of the specimen, the bubble would not stick. Specimens were handled with glass forceps, and precautions were taken to avoid contamination of the mineral surfaces. Contact angle measurements were carefully made several times on each treated specimen to obtain reliable average values. EFFECT OF pH VALUE AND SODIUM SULFIDE CONCENTRATION In each experiment, a specimen with a freshly ground surface was immersed for 10 min in a solution of sodium sulfide, washed and immersed for 15 min in a solution containing 30 mg per 1 of potassium amyl xanthate. The specimen was then washed again in distilled water and tested for contact angle in the captive bubble apparatus while submerged in distilled water. In this series of experiments, the pH of the sulfidizing solution was varied from 3 to 7, and the concentration of sodium sulfide, containing 60% Na2S, was varied from 50 to 650 mg per 1. Many combinations of pH value and sulfide concentration resulted in no contact between the bubble and the surface, but over a limited range of conditions, contact angles varying from 24ºto 52ºwere obtained. The data in Fig. 1 show sulfidization conditions that lead to bubble contact and those that do not. The region of contact is surprisingly small, which may indicate why flotation of chrysocolla involving sulfidization has proven so difficult in practice. Several features of the system are illustrated in Fig. 1. In the region between pH values of 4 and 6 with sodium sulfide concentrations below about 350

Jan 1, 1963

By C. O. Dale, W. J. Rundle

THE upper Mississippi Valley zinc-lead area was the first major lead producing section in the United States. The lead ore, found near the surface in crevices, was relatively pure galena that could be smelted directly into lead, at first in log hearth furnaces and later in more efficient blast type furnaces. French Canadian fur traders encouraged the Indians to mine the lead ore and showed them how to smelt it into lead that had a high value for bullets.1 Nicholas Perrot found lead ore on the Mississippi River bluffs near the junction of Wisconsin and Illinois and in 1690 established a trading post on the Wisconsin side of the river opposite the present site of Dubuque, Iowa.2 Shortly after 1720 discovery of Mine La Mott in Missouri diverted considerable attention from the Upper Mississippi area. Mining continued on a desultory basis with operations concentrated in the Galena, Illinois-Dubuque, area. In 1740 at least 20 miners were at work in the Fever River area around Galena and are reported to have shipped 2500 70-lb pigs of lead to Kaskaskia in 1741.3 Julien Dubuque established a mining and smelting operation in 1790 near the city that bears his name &apos;and was granted sole right to exploit the mining operations on the lands of the Sauk and the Fox Indians. He is reported to have produced 30,000 70-lb pigs of lead in 1805. Following the death of Dubuque in 1810 the Indians refused to let the white miners enter their lands, and little was done on the Iowa side of the river until the Indians were removed by treaty with the United States government in 1832.4 Early mining was entirely for lead but as the crevices were followed down, increasing percentages of zinc sulphide and zinc carbonate were encountered and at first discarded. Later a market became available for the zinc ores, and hand jigging devices were made to separate the lead," the zinc, and the rock or waste materials. The first record of zinc production from -the area is for 1860. Production of zinc passed that of lead before 1900, reached a peak of 64,000 short tons&apos; in 1917, fell off rapidly and continually to about 2000 short tons in 1938, and since 1940 has ranged from 11,000 to 19,000 short tons. Lead has been of considerably less importance since 1900, and at present only about 10 pct as much lead as zinc is produced. Practically all of the zinc ore has come from orebodies that are rather flat and wide with, considerable length as compared to width. Most of the early lead came from the crevice type deposit, but present production is from the predominately flat zinc orebodies. The Graham-Snyder orebody, scene of Eagle Picher operations, is practically all zinc with little or no lead being recovered. Marcasite, present in varying amounts, makes production of finished concentrates by gravity separation impractical. Satisfactory lead and zinc concentrates have been produced since flotation was introduced in the area in 1927. An acid recovery plant was operated for about 20 years after World War I, but it has been dismantled, and no recovery of the iron sulphides in the ores of the district is being made at the present time. In June 1950 there were three companies operating mines and mills, Tri-State Zinc Co., Calumet & Hecla Consolidated Copper Co., and Eagle Picher Mining and Smelting Co. The Vinegar Hill Zinc Co. had completed a shaft at a new orebody and had started to develop the mine which will supply the Cuba City mill. The Cuba Mining Co. was holding the Andrews Mine inactive. The Dodgeville Mining Co. was not operating but was exploring for additional reserves. Several small mines were selling ore to the Eagle Picher mill. A general area map is given in Fig. 1. The Eagle Picher Mining and Smelting Co. entered the area in 1946 with an active exploration campaign. Leases on a block basis were secured for the area south from the Wisconsin-Illinois line near

Jan 1, 1952

By William A. Longacre

IN a previous paper1 the author discussed the problem described by the title of this paper, outlining and reviewing the Gish-Rooney method, with comparison and brief analysis of the interpretation techniques of Roman2 and Tagg.3 Some aspects of the simple type of two-layer system were reviewed from various sources.4,5,6 THE TWO-LAYER PROBLEM For the configuration shown in Fig. I, and for any electrode separation A, the apparent resistivity is a function of the relative depth [HA], the overburden resistivity pi, and a factor K defined by the equation [ ] where p2 is the resistivity of the lower bed, Thus, by the known theory of electrical images, [ ] THE MULTILAYER PROBLEM As the number of isotropic, homogeneous, horizontal layers increases, the difficulties of interpretation multiply. The theory becomes much more involved, and in view of the state of our knowledge, the general problem is virtually impossible of exact solution. However, certain types of [ ] multilayer problems can be worked out in terms of two-layer theory. Hummel,7 Pirson,8 Tagg,3 Watson,9 and others have pointed out the possibility of building up approximations of multilayer resistivity curves with suitable combinations of two-layer curves. Many three-layer curves can be constructed in this way to a good degree of accuracy, and special types of four-layer curves can be approximated. It is very likely that as the number of layers increases, the method of combination will not give good approximations except in very special cases, In the analysis of actual field data, the author has found that many obviously multilayer curves can be solved partially with a good degree of accuracy, using the theory that thin adjacent beds may be considered as one layer or zone, and applying two-layer theory to the extremities of the field curve. MODIFIED TAGG METHOD OF INTERPRETATION Tagg&apos;s second method, though superior to his first, necessitates a large number

Jan 1, 1941

By Irving Cadoff, Jack Medoff

THE linear thermal expansions of oriented single crystals of zinc were measured in the range from 20" to 416°C using a Leitz HTV optical lever differential dilatometer. The single crystals, supplied by Dr. J. J. Gilman, General Electric Research Laboratory, Schenectady, N.Y., were prepared from 99.999 pct-purity zinc, and were in the form of rods approximately 2 in. long by 0.15 in. in diameter having the following orientations: x = 1.5, 12, 20, 30, 37.5, 49, 60, 73, and 82 deg where x is the angle between the specimen axis and the (0001) plane of the crystal. From the family of expansion vs temperature curves, the instantaneous expansion coefficients were calculated at 100°C intervals, and Fig. 1 shows a plot of these derived coefficients for each orientation. Coefficients were obtained from the raw data using the chord-slope method. The curves in Fig. 1 indicate a positive temperature coefficient for low x, a negative temperature coefficient for high X, and an expansion coefficient invariant with temperature, amounting to about 43 x 106, for a crystal orientation of approximately 52 deg. From the available data, it is possible to arrive at the values for the axial thermal-expansion coef- ficients a, and a, by extrapolating the curve of the expansion coefficient vs orientation to zero and 90 deg orientations. More precise values for a, and a, are obtained if the instantaneous coefficients are plotted against the square of the cosine of the orientation angle, as shown in Fig. 2. The extrapolated terminal points of the best straight line through the data points of such a plot define the axial coefficients at that temperature. The theoretical justification for the linearity of this curve comes from inspection of a rearranged form of the general anisotropic equation for expansion: ax=a, + (a, -a,)cosZx [1I in which a, is the expansion coefficient in the "c" or [0001] direction and a, the expansion coefficient in the "a" or [ll50] direction. From Fig. 2, the axial coefficients at 100°C, for example, were found to be a, = 13.9 x 10&apos;6 and a, = 62.4 x 10"6 per "C. In the same way, the coefficients were determined for 20", 200°, 300°, and 400°C. This data is summarized in Fig. 3. It is of interest to observe the common intersection of the curves in Fig. 3, which seems to bear out the earlier observation, from Fig. 1, of a

Jan 1, 1964