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By L. Adler

A relatively simple and effective technique is proposed to deal with the failure of geologic masses containing weakness planes. This technique, termed irextended" rupture envelope, provides a means to clearly distinguish rock and soil from fractured rock and, on a theoretical level, considers a matrix-inclusion system. It may also constitute the link between Mohr's and Griffith's failure theories. Included in the article are five sample problems concerning site location, structural design, strengthening the plane of weakness, changing the magnitudes of major and minor principal stresses and changing the orientations of major and minor principal stresses. Engineers trying to solve design problems in rock and soil mechanics have often assumed an iso-tropic and homogeneous medium. For naturally occurring geologic masses this assumption has always been viewed with regret. The following analysis which deals with the effects of plane anisotropy on failure presents a solution to this. The planes of weakness are joints, faults, bedding planes, fracture and cleavage (natural and induced), foliation and schistosity. The physical properties of these weakness planes include an undulating surface, frictional resistance, discontinuous extent, filling material, tightness and presence of water to cause a hydrostatic pore pressure. All of these properties relating to failure can be summarized in Mohr's rupture envelope for the plane of weakness. This, along with the geometrical orientation, strike and dip, of the plane of weakness produces what is termed an irextended" rupture envelope. MOHR'S STRESS CIRCLE AND RUPTURE ENVELOPE The significant features of these concepts are listed below.' 1) A point on the u - r coordinate plane represents the normal and tangential stress components on a reference area in the material. This area can have any orientation. (Fig. la)

Jan 1, 1963

By E. H. Denny

In the past few years many men, including technically trained engineers, have been asphyxiated in metal mines, coal mines, tunnels and surface wells where a few relatively simple precautions with regard to ventilation and air testing would have saved them. Death from mine gases is analogous in some respects to death from poison and from drowning. The respiratory passages of a victim who has breathed oxides of nitrogen from burning explosives are badly irritated and a few hours or even a day after exposure he may develop a quick and fatal pneumonia; if, however, he enters without respiratory protective apparatus an atmosphere deficient in oxygen (a condition that may occur in unventilated or poorly ventilated parts of all underground mines) he collapses and if not rescued dies more quickly and surely than a lone nonswimmer who falls suddenly into deep water. An example of an atmosphere virtually without oxygen was demonstrated by an air sample taken by a Bureau of Mines engineer wearing oxygen breathing apparatus in a Cripple Creek shaft some years ago, during the recovery of the bodies of two victims of asphyxiation; analysis of the sample by the Pittsburgh laboratory of the Bureau showed the presence of 18.40 per cent of carbon dioxide, 0.27 per cent of oxygen, and 81.33 per cent of nitrogen, although the atmosphere apparently was clear and normal. In a mine one can pass from good, breathable air to an atmosphere that will kill as quickly as one can dive from a board to deep water below. Some Instances of Asphyxiation by Gases in Metal Mines The following typical examples of comparatively recent instances of asphyxiation in metal mines were taken chiefly from reports of various kinds of the U. S. Bureau of Mines.

Jan 1, 1940

By E. H. Denny

In the past few years many men, including technically trained engineers, have been asphyxiated in metal mines, coal mines, tunnels and surface wells where a few relatively simple precautions with regard to ventilation and air testing would have saved them. Death from mine gases is analogous in some respects to death from poison and from drowning. The respiratory passages of a victim who has breathed oxides of nitrogen from burning explosives are badly irritated and a few hours or even a day after exposure he may develop a quick and fatal pneumonia; if, however, he enters without respiratory protective apparatus an atmosphere deficient in oxygen (a condition that may occur in unventilated or poorly ventilated parts of all underground mines) he collapses and if not rescued dies more quickly and surely than a lone nonswimmer who falls suddenly into deep water. An example of an atmosphere virtually without oxygen was demonstrated by an air sample taken by a Bureau of Mines engineer wearing oxygen breathing apparatus in a Cripple Creek shaft some years ago, during the recovery of the bodies of two victims of asphyxiation; analysis of the sample by the Pittsburgh laboratory of the Bureau showed the presence of 18.40 per cent of carbon dioxide, 0.27 per cent of oxygen, and 81.33 per cent of nitrogen, although the atmosphere apparently was clear and normal. In a mine one can pass from good, breathable air to an atmosphere that will kill as quickly as one can dive from a board to deep water below. Some Instances of Asphyxiation by Gases in Metal Mines The following typical examples of comparatively recent instances of asphyxiation in metal mines were taken chiefly from reports of various kinds of the U. S. Bureau of Mines.

Jan 1, 1940

By C. G. Dunn

According to a recently suggested effect of silicon on the re recrystallization textures of high-purity Fe-Si alloys with (111)[112] type rolling textures, the recrystallization texture for a rolled (110)[001] oriented iron crystal probably should be entirely different from that of a (110)[001] oriented 3 pct Si-Fe crystal. Comparative studies of iron and 3 pct Si-Fe crystals, however, show that both have (110)[Ool] recrystallization textures when the rolling textures are the (111)[112] type after reductions in thickness of about 70 pct. Qualitatively the results from the iron crystal are like those of polycrystalline high-purity 3 pct Si-Fe and not like polycrys-talline high-purity iron. The large effect previously noted probably involves unknown impurities or processing variables rather than silicon itself. Some problems on experimental and analytical procedure for a spherical X-ray specimen, which was machined from a laminated composite of sheet specimens, are treated in the Appendix. A possible strong effect of silicon on the textures produced in cold-rolled high-purity Fe-Si (HPFe-Si) alloys during primary recrystallization and normal grain growth was suggested in a recent paper.' All the textures were far from the random-orientation type, but that of iron, or of Fe-Si alloys of low silicon composition, was entirely different from the texture of 3 pct Si-Fe. The same effect was noted for the textures obtained prior to normal grain growth, i.e., for primary recrystallization.2 It is the main purpose of the present paper to provide some clarification of this silicon effect. All the HPFe-Si alloys from zero to 3 pct Si, which were rolled by two or more stages separated by anneals, developed (111)[112] type rolling textures.2 Thus, there was no effect of silicon on the rolling textures. Earlier, Gensamer and Mehl3 also found no effect of silicon on the rolling textures of Fe-Si alloys; they obtained the Kurdjum.ow and Sachs (K-S) rolling texture for iron,4 which is characterized as the three ideal components: (100)[011], (112)[li0], and (111)[112]. There is a difference between the HPFe-Si multiple-stage rolling texture and the K-S single-stage rolling texture, but this is a variable processing effect. Of interest here is the fact that the recrystallization textures from (111) [llZ] type rolling textures were different depending on the amount of silicon in the alloy. There was a relatively strong (110) [001] component in the recrystallization texture of HP 3 pct Si-Fe5,8,2 but no such component in HP 0.6 pct Si-Fe, for example; the recrystallization texture for the latter was two (111) [110] type components and a (111) fiber component 1,2 Several publications have shown that a strong (110) [001] recrystallization texture is derivable from a (111) [112] type rolling texture for 3 pct Si-Fe crystals reduced in thickness by about 70 pct.7-10 Furthermore it appears that the strongest of these (110) [001] recrystallization textures occurred when the orientation of the crystal prior to rolling was (110) [001].7 Barrett and evensoon11 found that the rolling texture of a (110)[001] oriented iron crystal was (111) [llj]. Accordingly, it seemed desirable to determine whether a (110) [001] oriented iron crystal, upon rolling and annealing, would behave like the 3 pct Si-Fe crystal (or the polycrystalline HP 3 pct Si-Fe) and thus produce a (110) [001] recrystallization texture contrary to the suggested silicon effect, or would behave like the polycry stalline HP iron or HP 0.6 pct Si-Fe and thus produce (lll) [110] type components in agreement with a silicon effect. Briefly, the idea here involves the use of more precisely defined textures to obtain if possible better control of important variables that affect the recrystallization process. PROCEDURE A (110) oriented crystal of Ferrovac "E" iron (99.9 pct pure) was prepared in sheet form 0.080 in. thick with the [001] direction parallel to the long dimension of the specimen.'' This crystal was etched to 0.073 in. thickness (to remove some small included grains) and then was cold rolled in a 6-in.-diam mill to a final thickness of 0.022 in. The rolling was unidirectional except for an inadvertent reversal at 0.061 in. thickness. At this thickness, and also at 0.040 in., the rolling was interrupted for transmission Laue photographs. Molybdenum Ka-radiation filtered with zirconium was used in a transmission method1' to obtain the cold-rolled (110) pole figure. The sample was a 0.002-in.-thick section taken from the central region of the 0.022-in.-thick cold-rolled crystal. For the primary recrystallization study, cold-rolled samples were etched from 0.022 to 0.021 in. thick and annealed in hydrogen at 850°C. Primary recrystallization to a fine-grained structure, Fig. 1, was obtained in a 5-min anneal. Eleven sheets after

Jan 1, 1963

By C. H. Mathewson

ABOUT fifty pages of Henry M. Howe's profound treatise, "The Metallography of Steel and Cast Iron," are devoted to twinning with special reference to the origin, nature and general significance of the Neumann bands in ferrite. Howe believed with Osmond and Cartaud1 that the Neumanns are mechanical twins and his careful observations leave no doubt that these straight-sided narrow bands habitually occur parallel to trapezohedral planes of form {211}. Attempt's to develop the structure of the bands by various methods so that their identity could be established beyond question have not been conspicuously successful. Howe thought that they deflected slip bands. Some of the etching figures which have been developed within and adjacent to Neumann bands support the contention that they are twins. A good example of this effect in ferrite containing 0.6 per cent. of nickel and 1.3 per cent. of phosphorus, originally due to Harnecker and Rassow,2 was reproduced in. the 1928 lecture before the Institute of Metals Division on twinning in metals.3 In this case, the sides of the figures might represent the traces of cubic planes laid bare by etching a properly oriented grain of ferrite, twinned along a plane of form {211}. Our own observations in this direction may be represented by Fig. 1 which shows in a deeply etched cavity in the boundary region between a Neumann band and the original crystal two small crystal surfaces which resemble the faces meeting at a reentrant angle in the simple cube twinned along a bisecting plane of form {211} as sketched in Fig. 2.

Jan 1, 1928

By Arthur Coffinberry

EVE have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, com-bined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was, undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atones, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such informa-tion is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By J. N. Hobstetter, J. J. Becker

Deformed copper single crystals exhibited, upon annealing, a recrystallized twinned grain with a twin plane parallel to an active deformation plane, rotated approximately 22" about its pole, or else did not recrystallize at all. If extraneous deformation was not carefully removed, no simple orientation relationship was found. RECRYSTALLIZATION textures have been a subject of practical interest for many years, but any real understanding of their formation will have to start with a study of the recrystallization of carefully deformed single crystals. Some efforts have been made in this direction,'-' but much more experimental information is needed before a satisfactory picture of the crystallography of recrystallization can be formed. This paper reports a few results in copper single crystals. The crystals studied in this investigation were grown by the Bridgman method," and their orientations determined by the back-reflection Laue technique." Some specimens were simply deformed in compression, others were sheared, and still others tested in a rotating-grip device, in attempts to remove end constraints. The details of their deformation behavior are described elsewhere.' The deformed specimens were annealed and the orientations of the recrystallized grains were determined optically, as described by Barrett and Levenson.8 Compressed Specimens Specimen 17-A, whose orientation is given in Fig. 1, was compressed to a total of 19 pct. As observed before,' increasing deformation took place by increasing density of slip lines in initially formed clusters, with little if any formation of new slip clusters in unslipped areas. The specimen was then etched in nitric acid until its length had been reduced from 0.766 to 0.735 in. It was annealed at 1000°C, in increments of a few minutes. After 63 min, two small grains had appeared in the center, Fig. 2. They were found to be twinned with respect to each other (AB, Fig. 4). After 30 min more, the specimen was completely recrystallized. A typical view of it is given in Fig. 3. A summary of all orientations found is given in Fig. 4, in which the prominent grain G is in (001) standard projection, and the poles of the active slip planes after deformation are indicated by SP (primary slip plane), CrSP (cross-slip plane), and CnSP (conjugate slip plane). All the orientations found were related through seven orders of twinning. A "family tree" of these twins is given in Fig. 5. Furthermore, the BG twin composition plane lies close to the cross-slip plane

Jan 1, 1954

By S. Stopek, E. D. Hinkley, R. H. Rediker

Epitaxial heterojunctions have been prepared by melting the lower -melting-point semiconductor of the interface between two dijferent semiconductors. when the temperature is reduced, the melted material recrystallizes, having alloyed into the higher -melting-point semiconditctor. The electrical and elcctro-optical properties of such single-crystal heterojunctions between GaAs and Gash and between p-type InAs and n-type Gash are the subject of this paper. The forward current varies as exp (AV), where A is substantially independent of temperatuve. For Gds-Gash heterojunctions at temperatures above, 370°K, if the current-voltage relationship were to he expressed as exp (qV/nkT), then n would he less than unity. The injection luminescence associated with forward current is, for the most part, characteristic. of the lower bandgap semicondutctor. These results can he explained by carrier injection into the lower bandgap semiconductor by tunneling through a barrier at the interface. The photovoltaic effect measured for incident photons having energies in the range between the bandgaps of the two semiconductors is much smaller than that produced by higher-energy photon The smallness of this between -the-gap photovoltaic response can he explained by the low probability for penetration of the barrier by the carriers produced in the smaller -bandgap semiconductor. THE technique of interface alloying has been used to produce single-crystal junctions between dissimilar semiconductors.' Oriented wafers are placed on a carbon heater strip, Fig. 1. so that semiconductor S1, which has the lower melting point, is supported by semiconductor S2. Electrical current passed through the heater strip produces a temperature gradient such that S2 is at a higher temperature than S1. As the temperature is raised the lower face of S1 begins to melt. Before the entire wafer can melt, however, the heater-strip current is turned off and, as illustrated in Fig. l. the melted portion recrystallizes, having alloyed into S2. Junctions have been fabricated by the above procedure between GaAs and germanium, between GaAs and GaSb, and between InAs and GaSb. Mroczkowski, Lavine. and Gatos have described the metallurgical and chemical aspects of the GaAs-Ge junction.2 The transition from GaAs to germanium is not monotonic and a portion of the recrystallized region consists of the GaAs-Ge eutectic. Since gallium is an acceptor and arsenic is a donor in germanium, since germanium dopes GaAs, and since the electrical properties of the GaAs-Ge eutectic have not been investigated, any interpretation of the electrical characteristics in terms of simple heterojunction theory would be incorrect. That the rectification of GaAs-Ge heterojunctions is not a property of the impurity doping of the GaAs or the germanium, but is most probably due to the impurity distribution in the recrystallized region, is clear from the fact that forward conduction occurred for all the GaAs-Ge interface-alloy junctions (whether they be n-n,n-p. p-n. or p-p) when the germanium was biased positively. The electrical characteristics of these GaAs-Ge heterojunctions will not be discussed further in this paper. Electron-beam microprobe analysis of GaAs-GaSb heterojunctions showed that the transition from arsenic to antimony atoms was without structure. and that the transition occurred within a 2 to 3 region.' In this paper we will describe the electrical properties of the GaAs-GaSb heterojunctions as well as electrical and electro-optical properties of the InAs-GaSb heterojunctions. A band model for the junction will be proposed which can explain these properties. ELECTRICAL PROPERTIES OF GaAs-GaSb HETEROJUNCTIONS After interface alloying. in preparation for the electrical and electro-optical experiments, ohmic contacts were made by conventional means. For example. Kovar tabs clad with tin were alloyed to n-GaAs or similar tabs clad with Au-Zn were alloyed to p-GaAs. The units were mounted and then etched. All four combinations of conductivity types

Jan 1, 1965

By K. G. Black, B. P. Faulkner

Laboratory batch flotation rests are used for comparison of the floatability of ores and for comparison of the effect of various treatments on ore floatability. Although it is difficult to predict exact recoveries for continuous flotation on the basis of batch tests, considerable quantitative information can be obtained through their use. A simple method is presented which provides a convenient means of quantitatively evaluating results from laboratory batch tests. The information obtained is in the form of a discrete flotation rate distribution, which, if desired, can be used directly in a simulation of continuous flotation. Equation of Batch Flotation The validity for batch flotation of the first-order kinetic equation is accepted: [ ] where k is flotation rate of a class of articles and W (t) is weight of particles of the class in cell at time t. Thus, at time t, the fraction of the original amount of the class of particles still remaining in the cell is [ ] where W (0) is weight of class of particles in cell at time zero. If there are several classes of particles in the cell, each with its own flotation rate, k4, the fraction of the particles remaining is [ ] where W (t) is now the total weight of n classes, a, being the original fraction of W (0) belonging to the ith class. Accordingly, [ ] [Fig. 1] shows the result of a typical batch test. Such result can be characterized by a set of particle classes, each set described by a flotation rate, [ki,] and a corresponding fractional magnitude, [ai.] [ ] Multiple Regression Equation Eqs. 3 and 4 may be combined to give

Jan 1, 1973

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

By Arthur C. Spencer

In extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,' it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity, applied to an elastic brittle mass offering strung resistance to deformation, produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45' to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45. This general conclusion, resting upon analytical mechanics, is completely supported by the results obtained by DaubrBe2 in experiments upon the deformation of wax and resin prisms under compression. Let us then first consider one of Daubree's diagrams. In the case illustrated in Fig. 1, four sets of fractures in two approximately right-angled pairs (that is to say, in conjugate sets) were produced by endwise compression of a square cross-sectioned prism. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45o. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism, and place it between two fixed and

Jan 1, 1906

By C. H. Li, J. Washburn, E. R. Parker

Yield stress in single crystals of zinc was shown to be dependent on prior annealing temperature and rate of cooling after annealing. Rate of strain hardening beyond the yield was not sensitive to annealing procedure. A tentative mechanism for the effect was discussed. COMPARATIVE mechanical tests of metal single crystals generally show a large scatter of results. Many factors may contribute to this variation. The present investigation was undertaken to evaluate the influence of two factors not ordinarily considered of major importance—annealing temperature and cooling rate after annealing. Since plastic properties of crystals are thought to depend on the presence of lattice imperfections, it follows that a variation in properties should result from differences in the distribution and density of these imperfections. Furthermore, in the light of current theories of interaction between edge dislocations and lattice vacancies,' it seems possible that annealing temperature and subsequent rate of cooling might play a part in this distribution. Analysis of the effect of these variables on plastic properties may lead to a better understanding of the annealed state. Single crystals of zinc which have been strained in simple shear undergo complete recovery of mechanical properties upon subsequent annealing. This behavior is useful because a single specimen can be used repeatedly, thus eliminating the uncontrollable variables introduced by the use of many crystals. The test section of the crystals used for these experiments was a cylinder 1/8 in. thick with a cross-sectional area of about 1/3 sq in. The specimens were acid-machined from spherical single crystals 1 in. in diameter in such a way that the slip plane (0001) was at right angles to the axis of the cylinder. In testing, a shear stress was applied along one of the slip directions, [2110] in the (0001) plane.' All crystals, unless otherwise noted, were grown in a helium atmosphere from molten 99.99 pct pure Horse Head Special Zinc. Fig. 1 is a family of curves obtained from one crystal. Each curve was obtained by deforming the crystal to 10 pct strain at a rate of 3 pct per min, following an anneal of 1 hr at 260°C. The strain direction was reversed every other time so that no progressive change in shape of the specimen took place during the series of tests. Since the stress-strain curve was reproducible within a fairly narrow range under the same conditions of annealing, it was then possible to determine the effect of changes in annealing conditions. A crystal was tested repeatedly as previously described but the annealing temperature and rate of cooling preceding each test were varied (Fig. 2). Two cooling rates were used, approximately 30°C per min and 3°C per min. Annealing was conducted at three temperatures, 200°, 300°, and 400°C. For a given annealing time and rate of cooling the room temperature flow stress was higher the higher the annealing temperature. The increase in flow stress was small as the annealing temperature was increased from 200° to 300°C but rose rapidly when the annealing temperature was raised from 300" to 400°C. Faster cooling from the high temperature produced an even greater strengthening of the crystal. The curves were obtained in the order indicated by the numbers. The stress level associated with a certain annealing treatment was, within the limits of scatter, always the same regardless of the

Jan 1, 1954

By M. Gensamer

IT has been suggested by a number of people that it would be worth while for some one to attempt to summarize or condense the proceedings of this symposium. This task has fallen to me as organizer and co-chairman. Its difficulty will be appreciated by anyone who attempts to read the whole proceedings. It is therefore with trepidation that I offer the following digest. In recent years there has been a renewal of interest in America on this subject of the cohesive strength of materials, and a growing appreciation of the need for a better theory of cohesion failure. The theories of elastic action and plastic action are well developed, particularly the former. The theory of plastic action is still in the course of development, but it is well along. Plastic action is terminated by cohesion failure and what is needed is a theory that will tell us when to expect the cohesion failure. In the past it has generally been assumed that cohesion failure will occur when a critical value of the maximum tensile stress has been reached. Many experiments have shown that this is not strictly true, and this symposium concerns itself with the failures of this simple hypothesis, and with the efforts that have been made to devise a more satisfactory theory. The most active contributor in recent years to knowledge in this field is Dr. McAdam, and he was asked to open the symposium with a summary or condensation of his papers and views. Undoubtedly it is presumptuous to attempt a still greater condensation, but perhaps it will be useful, because even his contribution to this symposium contains no summary, no concise statement of just what his contribution has bees. Dr. McAdam makes two main points. The first is that the cohesive strength is not a single valued quantity, but that it is a function of all three principal stresses and hence must be represented diagrammatically by a surface in a three-dimensional figure. Dr. McAdam has attempted so to delineate the cohesion limit, basing his

Jan 1, 1944

By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The microhardness of single crystals of tungsten disilicide has been investigated by the Knoop method. The average random room-temperature hardness of the WSi, matrix was 1350 kg per sq mm. Hardness crnisotropy was noted with respect to plane and indenter orientation as determined by single-crq.stal X-rny studies. Annealing at 1600" and 1800°C decreased the average hardness to 1310 and 1230 kg per sq tnm, respectively, and produced a second phase identified by X-ray diffraction and electron-microprobe analysis to be wSio.7. Ball-impact experiwzents produced rosettes at 850°C. Optical and electron microscopy showed evidence of slip and cross slip and twinning produced by microhardness indentations. Prismatic (100), [001] slip was found and cor~elated with hardness data. THE present study was undertaken to investigate the hardness anisotropy of as-grown and annealed single crystals of tungsten disilicide. The existence of the silicide WSiz in the W-Si system has been well-established and its structure thoroughly investigated zachariasen2 found WSi, to have a tetragonal C type of structure, similar to that of MoSi, with lattice parameters a = 3.212A, Kieffer et al. studied the W-Si system and measured the density and microhardness (at a 100-g load) of both polycrystalline WSi, and WSi,.,. The values found were 9.25 g per cu cm and 1090 kg per sq mm for WSi,, and 12.21 per cu cm and 770 kg per sq mm for WSi0.7, respectively. According to Samsonov et a1.5 the microhardness of polycrystalline WSi2 is 1430 kg per sq mm (at a 120-g load). EXPERIMENTAL The WSi, single-crystal boules investigated in this paper were grown by a Verneuil-type process using an electric arc by the Linde Division of the Union Carbide Corp.6 The largest specimens were 8 mm in diameter by 16 mm long. The crystals had an average density of 9.01 g per cu cm with a tungsten • silicon content of 99.9 wt pct. The major impurities were: 87 ppm O, 41 ppm N. 54 pprn C, 500 ppm Zr, 50 ppm Na, and 50 ppm Mn. The crystals were silicon-poor, the average silicon content being 22.20 pct (stoichiometric value is 23.40 pct), and tungsten-rich, the average tungsten content being 77.70 pct (stoichiometric value is 76.60 pct). As-received single crystals were ground and analyzed by powder X-ray diffraction technique using Cu Ka radiation. Laue and layer line rotation patterns were obtained on cleaved sections of WSi, single crystals. Electron-microprobe traverses of representative crystals were done using a Phillips-AMR electron microanalyzer. Carbon replicas were used to prepare electron micrographs. This work was done with a JEM-6A electron microscope. Prior to the metallographic examination, the specimens were mounted in Lucite and then polished for short times on polishing wheels using 9-, 3-, and 1-p diamond-grade pastes. Finally they were fine-polished with Linde A powder for 24 hr on a Syntron vibratory polisher. The samples were etched with 4H 2 O:1HF:2HNO3, which is a medium fast-acting etchant. The combination 1HF:2HNO3:5 lactic acid is also a satisfactory etchant. Annealing runs for selected specimens were made at 1600" and 1800°C for 3 hr at 1.0 to 3.0 x 10-5 mm Hg. A Brew tantalum resistance furnace with WSi2 powder for setters was used. The WSi2 powder was the same as that used for the crystal growth. Temperatures were measured with a calibrated W, W-26 pct Re thermocouple and a microoptical pyrometer. Powder X-ray diffraction, emission spectrographic, and electron-microprobe analyses were done after the annealing runs. For microhardness measurements a Tukon Microhardness Tester Type FB with a Knoop indenter was used. Although measurements were taken at loads ranging from 25 to 1000 g, the 100-g load was chosen as the standard load. All measurements were taken at room temperature. Only indentations of cracking classes 1 and 2 were considered.' DISCUSSION OF RESULTS Powder X-ray diffraction analysis showed the as-received crystals to be single-phase WSi2. Laue and layer line rotation patterns obtained on cleaved sections of WSi2 single crystals proved them to be tetragonal WS 2 2 The results also indicated that the c axis of the crystal was oriented parallel to the boule or growth axis. Electron-microprobe traverses across the matrix of the as-grown crystals showed them to be homogeneous WSi,. Optical and electron microscopy of etched crystals, however, revealed that they contained minute amounts of the "golden" and the "blue" second phases as opposed to the "white" or WSi2 phase. These two second phases were concentrated in inclusion and etch-pit

Jan 1, 1965

By Stephen H. Stow

A relationship exists between the color and the chemical composition of the pebbles from the Bone Valley Phosphate Formation. Darker-colored pebbles are relatively high in iron oxide and relatively low in calcium phosphate when compared to lighter-colored samples; the brown color of the phosphate pebbles can be correlated with their iron content and the black and gray colors with their organic carbon content.1,3 It was anticipated that the darkness of a phosphate sample might be quantitatively measured by a simple reflectivity test and that the amount of reflected light could be correlated with the chemical composition of the rock, especially with the elements which cause the color and darkness of the Florida phosphates. Twenty-one samples of production grade phosphate rock from Hillsboro County, Fla., were studied. All samples were ground to -200 mesh for reflectivity tests and analyses. All analyses are accurate to well within ±2% of the reported value, except for aluminum and organic carbon, which are accurate to only ±15% of the reported amount. Reflectivity measurements were taken with a model 610 Photovoltmeter for tri-stimulus amber, blue and green, and white lights. Experimental procedures and data are available upon request. Results Table 1 contains linear correlation coefficients (LCC) for the element-reflectance relationships for the samples. The top portion of the table refers to the LCC between the percent of light reflected off the samples and the percent of a given element (or its oxide) as analyzed. In the lower portion of the table the LCC refers to the relationship between the same reflectance data and the chemical analyses which have been corrected on the basis of 0% acid insoluble material (chiefly quartz) in the phosphate rock. Each LCC presented in Table I is computed for the 14 coarser samples exclusive of the seven concentrates since the concentrate samples appear to have anomalous reflectivities upon comparison with the coarser grades. Only the most significant LCC for each element is presented in graphical form. Discussion of Data Iron: [Fig. 1] is a graph of the relationship between iron and reflectivity (LCC = - 0.98). A good correlation with Fe2O3, is expected due to the relationship between the tan (or brown) color and the abundance of iron oxide, the principal mode of occurrence of iron in Florida phosphates.8 Note the location of the seven triangles which repre-

Jan 1, 1972

By Otto W. Nuttli

THE magnetic method of prospecting is well suited to determination of faulting in the basement rock. In addition to establishing the horizontal position of the fault, it often furnishes valuable information concerning the depth and amount of faulting. Consider a simple case of a vertical fault, represented in cross-section in Fig. 1. Let A A' represent the plane of observation (ordinarily the surface of the earth), and BB'B"B"' the upper surface of the basement. Assume that the sedimentary rocks are nonmagnetic, so that the magnetic susceptibility of the material above the basement is zero. Let k indicate the susceptibility of the basement rock, c the density contrast between it and the neighboring sedimentary rocks, and the amount of vertical displacement. Fig. 1 shows the material, indicated by cross- hatching, which gives rise to the magnetic anomaly. In most cases it can be assumed that is small compared to the thickness of the sedimentary rocks. The semi-infinite, rectangular slab of rock of susceptibility k, density contrast , and thickness t may then be replaced by a semi-infinite sheet CC' of mass t per unit area at depth 2 (the mean depth of the slab). Nettleton 1 states that this approximation results in an error of less than 2 pct for the computed gravitational field intensity when t is as great as 2/2 and decreases rapidly for smaller values of t. By a theorem of Poisson, the magnetic field intensity can be determined readily from the gravitational field. The theorem states that W = (I/) • (U/i) i1 [1] where W is the magnetic potential associated with the structure, I is the intensity of magnetization which is assumed to have the direction of the inducing field, ? is the constant of gravitation, the density contrast, U the gravitational potential associated with the structure, i the direction of the inducing magnetic field, and i1 a unit vector in that direction. The multiplication indicated in Eq. 1 is

Jan 1, 1956

By D. Mizer, J. B. Clark

In a recent investigation of the entire magnesium-yttrium phase diagram, Gibson and Carlsonl report the maximum solid solubility of yttrium in magnesium as 8.0 wt pct Y at 1050°F (565°C). However, independent studies of the precipitation in magnesium-yttrium alloys, 2 conducted prior to the publication of the above phase diagram, indicated a greater solid solubility of yttrium in magnesium. Accordingly, the magnesium-rich region of the diagram was re-investigated to determine more accurately the liqui-dus, solidus, and solvus of the magnesium solid solution in this system. Metallography and thermal analysis were chosen as the best corroboratory methods for accurately determining this region of the diagram. A magnesium-yttrium master alloy was prepared from yttrium of 99.9 pct purity and singly sublimed magnesium of 99.9 pct purity. Subsequently, the twelve magnesium-yttrium alloys shown in Fig. 1 were prepared using standard alloying procedures for magnesium. Metallographic samples of the alloys were heat treated under an SO, atmosphere in an electric furnace capable of control within ±3oF of the desired temperature. Alloy samples for the metallographic determination of the solvus, and for the precipitation studies were solution treated at 1000° F for 16 hr. Subsequent aging times for the solvus determination varied from a minimum of 6 hr for the higher temperatures up to 816 hr for lower temperatures. Periods of 30 min at temperature were used to generate liquation for the metallographic placement of the solidus and eutectic horizontal. The liquidus and the eutectic horizontal were determined by thermal analysis. Simple time-temper- ature heating and cooling curves were obtained from 10-g alloy samples heated and cooled in a well-insulated electric furnace. An Iron-Constantan thermocouple was placed in direct contact with the sample. The thermocouple did not contaminate the alloy sample since metallographic examination showed that the alloy melt did not wet or attack the thermocouple. The heating and cooling rates were approximately 5 to 8OF per min. The standard metallographic procedures for magnesium were used in polishing and etching the magnesium-yttrium alloys studied. Glycol etchant* was etchant was used to reveal precipitate in the solvus determination. The redetermined magnesium-rich region of the magnesium-yttrium diagram is shown in Fig. 1. The

Jan 1, 1962

By J. J. Bikerman

In a recent study' of the martensitic transformation of Cu-Zn ß-phase alloys, it was noted that the MS temperature at the surface was raised due to the loss of zinc by volatilization. It seems likely, therefore, that the MS temperature may serve as a guide for the measurement of composition. From a knowledge of the dependence of the transformation temperature on composition, 2 it should be possible to detect variations in zinc content which are less than 0.1 at. pct by measuring the MS temperature throughout the sample. It is unlikely that an electron microprobe analysis could detect accurately such small zinc losses because the presently accepted limits of accuracy of the micro-probe analysis in simple ternary systems are of the order of 2 to 5 pct of the amount present.3 In the present study, a composition gradient was produced by precipitating the a primary solid solution, and reheating for a very short time within the 0-phase field. The nominal composition, in atomic percent, of the ternary ß-phase alloy used, 64.2 Cu, 34 Zn, 1.8 Si, was selected because it had an MS temperature of +4°C, thereby simplifying the experi-

Jan 1, 1968

By William E. Ford, Edward Salisbury Dana

1. Simple Hydrocarbons. Chiefly members of the Paraffin Series C,H2,+2. SCHEERERITE. In whitish monoclinic crystals. Perhaps a polymer of marsh-gas (CHI). Found in brown coal at Uznach, Switzerland. HATCHEITITE. Mountain Tallow. In thin plates, or massive. Like soft wax. Color yellowish. Indices, 1.47-1.50. Ratio of C to H = nearly 1 : 1. From the Coal-measures near Merthyr-Tydvil in Glamorganshire, England; from Galicia. PARAFE-IN. A native crystallized paraffin has been described as occurring in cavities in basaltic lava near Paterno, Sicily. Indices, 1.49-1.52. OZOCERITE. Mineral wax in part. Like wax or spermaceti in appearance and consistency. Colorless to white when pure; often leelr-green, yellowish, brownish yellow, brown. Indices, 1.51-1'54. Essentially a paraffin, and consisting chiefly of one of the higher members of the series. Occurs in beds of coal, or associated bituminous deposits, as at Slanik, Moldavia; Roumania; Boryslaw in the Carpathians. Also occurs in southern Utah on a large scale.

Jan 1, 1922

By P. A. Laxen, H. R. Spedden

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.'*' Study of the adsorption of sodium from an aqueous solution oftheon quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained."." Three main factors which appeared likely to affect the adsorption of sodium are: l—concentration of sodium in the solution, 2—concentration of onotherof cations in the solution, and 3—anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in thesethe amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxyl-ion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory' except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying." To minimize the laborious preparation of quartz, experiments were made to determine .whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na" activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot 11) and 2000 (lot 111) as determined by the Bloecher method." Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.' It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß+ radiation and a 1.30 mev r radiation. The decay scheme is illustrated in the following equation: ß+ NaR-------'8'77NeZ2 3 years The /3 radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang.R The original active material was 1 ml of solution containing 1 millicurie of Na" as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen." In brief, it included the following steps: 1—Ascertainment of linearity between concentration of Na" and activity measured. 2—Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3—Taking precautions to avoid evaporation of water during centrifuging

Jan 1, 1953