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By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e'i; ei being parallel to the Burgers vector b, and e'3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?'1,?'2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?'2s'11b'1—?'1s'12b'1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s'12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x'i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x'i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b'1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b'1s033 sin a- rn2b's33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

By John Fulton

The Menominee range is one of the four great mining belts that flank the western prongs of Lake Superior. It has received its name from its location along the north side of the Menominee river, which at this place flows between the States of Michigan and Wisconsin. The term "range" is derived from the elevated ridge, extending in a westward direction, and along the southern flank of which the iron-ore mines are located. This range is some 200 to 300 feet high above the general level of the adjacent country, and is made prominent by its surroundings of low, swampy lands. Its whole length is about 27 miles, and it is intersected, at intervals along its course, by gaps which are threaded by streams. The geology of the Menominee range is peculiarly interesting. It is composed of three distinct groups of Hurouian rocks. The supporting group consists of light-colored limestone beds of a crystalline, siliceous character, called the "Norway limestone belt." The map, Fig. 1, and the section, Fig. 2, will give a general notion of the position and structure of the range. The properties shaded in the map are those of the Penn Iron Mining Company, which is the Michigan representative of the Cambria Iron Company of Johnstown, Pennsylvania. This belt is at least 1200 feet thick. It outcrops boldly at many localities along the range, especially north of the Norway, Quinnesec and Chapin mines. At Quinnesec it can be studied readily. The next, or Banking group, which is estimated at a thickness of 1000 feet, is called the Quinnesec ore-formation. It consists, in the portion next to the limestone, of siliceons or jasper slates, largely impregnated with iron oxide. These are succeeded by argillaceous hydro-mica black and flesh-colored slates. This formation embraces the deposits of the iron-ores. The third group consists of a series of dark gray, slaty or schistose beds, with occasional quartzose bands, having a thickness of 2000 feet. It is called the Lake Hanbury slate group.

Jan 1, 1888

Since this paper was written, some changes have taken place, materially reducing the cost of iron-making as estimated in the text. These are chiefly reductions in the prices of ore and fuel. The charcoal used is now made in bee-hive ovens, and the price is con-

Jan 1, 1895

By Ralph E. Grim

THE technology of clay minerals is defined, for the purpose of this review, as- the application of fundamental data regarding clay minerals, and techniques of handling them, to the various industries, arts, and professions concerned with clay materials. The aim of the paper is to narrate recent developments in clay mineral technology. This review does not claim to be complete, and perhaps gives undue emphasis to matters that have been worked on in the author's laboratory or with which he has some other connection. In the United States in recent years, particularly since the end of World War 11, interest in clay mineralogy has increased greatly. Many laboratories in many different fields have embarked on studies of clay minerals but unfortunately much of this work has not been published. CERAMICS In the field of ceramics, in recent years, a great deal of interest has developed in clay mineralogy. Papers too numerous to be reviewed here have been published portraying the clay mineral composition of substantially all the important types of ceramic clays in all countries. There has been a growing tendency to attempt to solve processing problems on the basis of clay mineral data rather than chemical analytical data. Likewise, there is an in- creasing tendency to control the characteristics of raw materials on the basis of clay mineral composition rather than chemical composition. In the United States in the last few years something like 50 differential thermal analyzers have been set up, and many are for the sole purpose of controlling raw material and processing. The ceramic industry is currently increasing its attention to the influence of exchangeable ions and soluble salts on physical properties. Ion concentration in clay suspensions has long been a matter of interest, but now it is also of interest in clays in the plastic state because of its recognized importance in the plastic, shrinkage, and bonding properties of clays. Students of clay have long recognized that an understanding of the plastic properties of clays is based on an understanding of the character of the water in clay-water systems, the nature of the binding force between individual clay mineral particles, and the factors that control the character of the water and the nature of the bonding force. In the last few years, some extremely important contributions have greatly increased the understanding of the nature of water adsorbed on the clay mineral surfaces. In this connection the work

Jan 1, 1952

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By Strathmore R. B. Cooke, Thomas E. Ban

MUCH experimental work has been performed on the mechanism of agglomeration and pelletizing of moist ore and concentrates and on the process of firing agglomerates, but except for the work of Tigerschiöld and Ilmoni1 much of the published information is empirical, and the literature contains no information concerning the structure of fired pellets. Results of a preliminary study of the microstructures occurring in pellets produced both in the laboratory and on a pilot-plant scale are presented in this paper. Most of the results were obtained from pellets prepared from Mesabi magnetic taconite, but through the courtesy of the staffs of the Minnesota Mines Experiment Station and the Bethlehem Steel Co., fired pellets produced from limonite and hematite ores and from Lebanon magnetite have also been examined. The work has been restricted almost entirely to pellets produced without additives, the exceptions being those in which coal was. added to the filter cake before rolling. Schwartz has described the microstructures occurring in ore sinters produced under reducing conditions.2 Many of the structures and constituents he describes are common to fired pellets, but the constituents normally occur in markedly different proportions. His statement that "in all satisfactory sinter the amount of hematite is small, perhaps not over 2 or 3 per cent" is inapplicable to pellets produced by pilot plant operation or by any process in which air is not deliberately excluded. Pilot plant pellets contain over 90 pct by weight of hematite, and those produced in the smaller furnaces of the Minnesota Mines Experiment Station contain more than 80 pct of that constituent. Preparation of Specimens It is difficult to examine unfired pellets microscopically because of their insufficient coherency to withstand sectioning and polishing. Fired pellets sometimes lack coherency and frequently contain holes which are troublesome during polishing. Impregnation of both air-dried and fired pellets is readily accomplished by the use of methyl methacrylate monomer.3 The dry pellets are covered in a test tube with excess monomer, to which a small amount of accelerator has been added. When the test tube is placed in a cooling bath and evacuated with an aspirator, most of the entrapped air is removed, and disruption of weak pellets by boiling of the monomer is reduced to a minimum. Polymerization is then effected by immersion of the test tube in a water-bath at about 45°C, this temperature being held for 4 or 5 days. The test tube may then be broken away from the solidified mass and the pellets sectioned by a carborundum wheel or a diamond saw. Where time is important, impregnation is carried out at a higher temperature by Meyer's method.4 Air-dried pellets must be impregnated with especial care; otherwise swelling occurs and the solids are displaced. It is more important to be certain that the monomer forms a reasonably complete network throughout the specimen than that all entrained air is removed, and for this reason the vacuum technique may be omitted. Impregnated agglomerated products and pellets are extremely coherent, section well, and may be polished either by hand or by machine. Hand polishing is not satisfactory for the examination of conditions existing at the boundaries of grains, and for this machine polishing must be used. The Graton-Vanderwilt machine gives excellent results, provided that pressure on the specimen is considerably in excess of that recommended by the manufacturer. Mineralogy of Fired Pellets Only two opaque iron minerals, magnetite and hematite, have been recognized in pellets. The complete identity of these artificial minerals with their corresponding natural counterparts is shown by their mineralographic characteristics and their X-ray structures. Wüstite has not been found. Slag is the most common transparent constituent of fired pellets. Occasionally conditions have been appropriate for the crystallization of fayalite from the slag, and at other times another crystalline sil-

Jan 1, 1952

By R. E. Reed-Hill, W. H. Hartt

High-purity magnesium single crystals, oriented with basal plane parallel to stress axis, were deformed in tension at room temperature so as to form second-order (1011)- (1012) twins. Investigation by optical and replica electron microscopy revealed that these twins can support very large internal strains approaching 1000 pct and that fracture follows as a direct consequence of these strains. At low strains the basal plane within (10i1)- (10i2) twins rotates with increasing deformation until it becomes approximately parallel to the twin boundaries. This rotation is not consistent with deformation by basal slip in the double twin, but may be rationalized in terms of nonbasal slip. Observations also indicate that basal slip in the primary (1011) twin, prior to second-order twinning, may contribute to this rotation. Deformation markings that are difficult to interpret in terms of slip on previously observed systems were noted in the twin bands. A possible means of rationalizing these markings is to relate them to grain boundary shear. The fracture associated with these twins is thought to initiate by formation of voids at the twin boundaries. These grow into microcracks, with ultimate fracture occurring by tearing of the interconnecting regions. THE significance of deformation and fracture along second-order (10i1)-(10i2) twins in polycrystalline magnesium1-' and many magnesium alloys4 was discussed in a previous paper.5 It was noted that this double twinning mode effectively controls the room-temperature deformation and fracture of magnesium single crystals, oriented with the basal plane parallel to the tensile axis. Reed-Hill and Robertson6 observed that, although these crystals may fracture at a macroscopic strain of less than 1 pct, shear strains up to 1000 pct could occur within (1011)- (10i2) twin bands. They concluded that the fracture was "ductile" and resulted from concentrating the deformation into a very small volume. The present research was undertaken to obtain a better understanding of the deformation and fracture associated with these twins. EXPERIMENTAL TECHNIQUES The experimental procedure involved straining high-purity magnesium single crystals in tension at room temperature. Specimens were oriented so that the applied stress direction was within 2 deg of the [1010] crystal axis. The specimen cross section was rectangular with faces closely parallel to (1210) and (0002). The specimen preparation and testing procedures have been described in detail elsewhere.5 Second-order (1011)- (1072) twins nucleated during straining were studied using optical and replica electron microscopy techniques. For the latter, cellulose acetate-carbon double replicas were employed. Observations were made on the (1210) crystal surface, which is the plane of shear for twins of this type. In addition to the single crystals, some investigations were carried out on longitudinal polycrystalline specimens. These were obtained from high-purity magnesium plate with a texture in which the basal planes of the grains tended to be nearly parallel to the specimen axis. All. polycrystalline specimens were annealed prior to testing in order to produce a coarse grain structure, permitting Laue back-reflection X-ray photographs to be obtained from grains of interest. EXPERIMENTAL RESULTS a) Deformation Within ( 101 l )-( 1072) Twins. Fig. 1 is an optical micrograph demonstrating the extent of the plastic deformation that can occur in (1011)-(10i2) twin bands. Notice at the lower left corner of the photograph the large displacement of the dark band (a polishing step) where it crosses the twins. The shear strain in the twin band at this position was computed to be 700 pct, using the ratio of step width to twin thickness. It was previously shown5 that (1011)- (1012) twin bands are often composed of small, separate twins aligned close to the macroscopic habit plane. Fig. 2 is an electron micrograph from near the upper end of the twin band in Fig. 1. This illustrates that the twin habit often does not coincide exactly with the macroscopic band habit, but may be inclined at a slightly smaller angle to the matrix basal plane. Figs. 3 through 6 are electron micrographs of the twin band in Fig. 2 illustrating successive steps in the development of deformation inside the band. A twin band such

Jan 1, 1969

By D. K. Sarin

The sub-level caving mining method has been applied in base metal mines in Canada under a wide range of ore body and wall rock conditions. This method has been used for primary, as well as secondary mining of both small and large ore bodies of varying ore values. Early experiences of almost all operations were somewhat disappointing. This paper details the initial problems encountered, the design changes made and solutions evolved. Additional experience and the development of operating skills, have helped the method gain acceptance as a viable method for the mining conditions to which it has been adopted.

Jan 1, 1981

By S. Ramachandran, L. A. Vazquez, N. L. Grauerholz

A novel process is described for the selective flotation of scheelite from low-grade (- 0.5% W03) tungsten ores having appreciable quantities of calcareous and siliceous gangue minerals. Specifically developed for the Tempiute, Nevada facility of Union Carbide, the process yields tungsten concentrates exceeding 15 percent W03 with at least 85 percent recovery. This condition was not achieved through conventional processes. This process consists of conditioning the ore pulp with judicious amounts of lime, followed by soda ash and sodium silicate as modifiers. The scheelite is then floated using a mixture of oleic and naphthenic acids as collector. Contrary to the common observation as to the deleterious effects of calcium in fatty acid flotation systems, lime addition is found to be beneficial in achieving satisfactory results. The process has also shown excellent results on a Brazilian scheelite ore.

Jan 1, 1976

By D. L. Albright, R. W. Kraft, J. A. Ford

HE unidirectional solidification of A1-CuAl, eutec-tic specimens to produce an essentially parallel lamellar structure has been described previously.' Ingots solidified in this manner ordinarily exhibit three macroscopic zones. In Zone I, at the head end of the ingot, a large number of slightly elongated grains occur in which the lamellae are highly distorted and twisted. After a few centimeters of growth, this distribution gradually changes to a small number of coarse grains elongated in the growth direction and in which the lamellae are quite regular, Zone 11. Zone 111, at the tail end of the ingot,

Jan 1, 1963

By L. S. Darken

IT has long been recognized that the driving force in an isothermal diffusion process may be regarded as the negative gradient of the chemical potential (partial molal free energy) of the diffusing substance. This equivalence is exactly analogous to the fact that a mechanical force is the negative gradient of the potential energy. Nernst1 in 1888 expressed these driving forces in terms of osmotic pressure, which is directly related to the chemical potential and free energy. The relationship between the diffusivity, mobility and activity coefficient of electrolytes in aqueous solution has been developed in great detail by Onsager and Fuoss2 with results which have recently been confirmed experimentally by Harped and Nuttall.3 This interpretation of the driving force in isothermal diffusion has been discussed earlier by the author 4.6 who pointed out4 that "for a system of more than two components it is no longer necessarily true that a given element tends to diffuse toward a region of lower concentration even within a single phase region"; departure from the behavior of an ideal solution may be so great that the concentration gradient and the chemical potential gradient, or activity gradient, may be of different sign, thus giving rise to "up hill" diffusion. Since, in the discussion of that paper,4 some skepticism as to the validity of this conclusion was expressed, it seemed desirable to adduce experimental evidence to support it. Evidence of such diffusion in nonmetallic systems has already been reported. For example, it was observed by Hartley11 in a series of experiments in which sodium chloride diffused from a saturated solution in about 5 pct acetone in water into a solution virtually free of salt but with essentially the same acetone concentration. Specifically, a wine glass containing crystalline salt and saturated solution was totally immersed in a large glass cylinder containing the acetone-water solution without salt; the difference in specific gravity was such as to prevent convection. Diffusion of salt was accompanied by a marked depletion 0f acetone in the wine glass; after 3 days the acetone concentration decreased from 5.37 pct at the top of the glass, where the salt concentration was low (0.93 pct), to 1.84 pct at the bottom where the salt concentration was high (21.64 pct). This "uphill" diffusion was found to be such that the partial pressure (activity) of acetone was essentially equalized throughout the system when a steady state gradient of sodium chloride was maintained. In order to demonstrate the existence of such diffusion in metals, a series of four weld-diffusion experiments was made. In these measurements pairs of steel of virtually the same carbon content, but differing markedly in alloy content, were welded at the end and held at 1050°C for about two weeks. Subsequent analysis showed that carbon had diffused so as to produce an inequality

Jan 1, 1948

By Donald W. Gentry, John F. Abel

This paper presents some of the results of a rock mechanics instrumentation program designed for, and implemented at, longwall panel 4N at the York Canyon Mine near Raton, New Mexico. The objective of this particular instrumentation program was to determine the response of the rock mass to longwall mining of a thick coal seam utilizing shield-type supports. Measurements were made in the rock along the ground surface, above the coal seam, in the coal seam, and immediately below the coal seam. Longwall test panel 4N had a total developed length of 762 m (2500 ft) and a face width of 168 m (550 ft), Fig. 1. The seam mining height in the panel area was approximately 3 m (10 ft). The average depth of overburden above the panel is 107 m (350 ft) although it ranges from 73-134 m (240-440 ft). Roof support at the face was provided by 116 Hemscheidt 320 HSL shields. These shield-type supports weigh 11.4 metric tons each.

Jan 3, 1978

By B. T. Brady, Wilson Blake

One of the more widespread experimental procedures currently used in experimental rock and soil mechanics work involves the use of a short circular cylinder loaded axially between nonrigid end plates1-5 (Fig. 1a and b). It is widely recognized 6 that a number of undesirable features are connected with this test procedure ; the most noteworthy of these is the development of a nonuniform stress distribution throughout the specimen resulting from an elastic mismatch between the specimen and the end plates. In general, the end plates and specimen possess different elastic properties. As a result of this elastic mismatch, the uniform distribution of stress and strain applied to the end plates is altered at the interface, the degree of which is dependent not only on the magnitude of the elastic mismatch but also on whether there is any relative movement between the specimen and the end plate. A convenient measure of the elastic mismatch is the ratio (vp/Ep) / (v8/E3), where v and E are Poisson's ratio and Young's modulus and the subscripts s and p refer to the specimen and end plate, respectively. For most tests that use steel end plates, (v8/E8) is greater than (vp/Ep) ; i.e., the specimen tends to expand or contract laterally more than the end plates. Because of the frictional restraint offered by the end plates, shearing stresses are developed at the interface that, for compression testing, act inward producing a "clamping" effect (Fig. lc). The effect of this "clamping" is to produce a state of triaxial stress throughout the specimen. Fig. Id illustrates the coordinate system and stress nomenclature used. In a homogeneous, elastic two-dimensional plate loaded uniaxially at the edge, a uniform stress distribution is obtained at a distance from the

Jan 1, 1972

By G. W. Healy

Activities of oxides in the ternary FeO-MnO-SiO system are calculated from data on the binaries, using the Gibbs -Schuhmann method. These activity data are used, together with thermodynamic relations, to calculate the contents of oxygen, silicon, and manganese in liquid iron, and the composition of the corresponding oxide phases in equilibrium with it. Excellent agreement was found between calculated and experimental metal compositions, indicating that thermodynamic methods, such as those presented, can supply useful data on slag-metal equilibria, and are therefore capable of wider application. When molten steel containing oxygen is treated with a deoxidizer, the product of the reaction is composed of the oxides of the deoxidizing elements together with more or less iron oxide. This assemblage of oxides is presumably very close to equilibrium with the melt since it is formed directly from elements dissolved in it. Therefore, it is likely that metal analyses corresponding to a given oxide phase composition are calculable with considerable precision where sufficient information is available on activities in both phases. The present study was made to test this hypothesis in the case of deoxidation by silicon and manganese. Here experimental data on the relationship among oxygen, silicon, and manganese in the metal phase are available, as are activity data for the MnO-SiO2, FeO-SiO2, and FeO-MnO binary systems. A further objective was to demonstrate in a specific example how gaps in the data may be filled by judicious interpolation, and how the Gibbs-Schuhmann method is applied to obtain activities in ternary systems. The rigorous derivation of the latter, requiring considerable facility in handling partial differential equations, tends to mask the real simplicity of the method, and repel the very engineers and experimenters who would benefit the most from its use. I) GENERAL PROCEDURE Deoxidation of steel with silicon and manganese results in the formation of two phases, metal and oxide. The number of components is four—Fe, Mn, Si, and 0. The phase rule then gives the number of degrees of freedom: If temperature and pressure are fixed, 2 deg of freedom remain. Consequently, it suffices to fix the concentration of two of the components of the system for all the concentrations to be determined and, at least in principle, calculable. The practical problem is then to discover a straightforward method of calculation with a minimum of trial and error solutions. The type of reactions to be dealt with are like the following: Si (in steel) + 2 O(in steel) = SiO2(in oxide phase) The standard free energy of this reaction is readily obtained from the literature, so that the equilibrium constant can be calculated by the expression: Since the metallurgist is concerned with percentages rather than activities, a real solution requires information that will permit activities to be converted to concentrations. This information is fairly adequate for the elements dissolved in molten steel, but is not available for the FeO-MnO-SiO2 oxide system. Therefore, the first step in this study was to find the relation between activity and concentration for the three oxides making up the system. The next step was the calculation of slag and metal compositions that are in equilibrium with one another. As shown by the phase rule, it is sufficient to assume the values of two composition variables in order to calculate the rest. But which two are picked makes a vast difference in how difficult the calculation turns out to be, so that it is necessary to make preliminary trial of several routes to find the easiest one. A convenient method is to begin with the slag, and to pick FeO concentration and that of one of the other oxides. Starting with the relation between oxygen dissolved in the liquid steel and FeO in the slag permits a good first estimate to be made of the oxygen content of the steel in equilibrium with FeO, because the iron content being fairly close to 100 pct, Fe has an activity close to unity. Using this first estimate of oxygen activity, approximate values of the manganese and silicon contents of the melt are readily calculated from the appropriate equilibrium constants. A minor correction for the depar-

Jan 1, 1963

By Herbert Dumont

Since 1947 Preussag AG Metal1 has used a process for fuming zinc- and lead-containing dump slags and residues from vertical retorts in a half-shaft furnace at their Hüttenwerk Harz at Oker. Contrary to the classic shaft furnace, only one side of the half-shaft furnace is fitted with tuyeres. The opposite side is a bricked slope. The upper shaft section is piped. There zinc vapor and combustion gases are burned by sucked-in air. Gases and fume enter a boiler located on the rear length of the furnace via a piped fire bridge. The gases are then cooled in an air preheater prior to dedusting in a bag filter. The furnace is charged with briquettes of metal-bearing materials, coal and pitch. The leaded zinc oxide fume is comparatively rich in both lead and zinc. The copper in the feed is recovered in low-copper matte. The slag can be discarded. The Oker plant comprises 13 furnaces of 2.9 to 4.9 m length in the tuyere area. Two other plants in Italy and Spain are processing zinc leach residues by this technique. Fuming of zinc-lead-oxide ores as well as partially roasted sulfide- zinc-lead-copper bulk concentrates will be possible.

Jan 1, 1970

By T. Leser, A. W. Jenike

The problems of caving and underground subsidence can be considered as the failure of a highly compacted rock and its subsequent flow in the form of broken rock. The problem is complex because the propagation of failure and flow have to be considered simultaneously; the yield strength of the virgin rock and the broken rock are different; and, while under certain conditions it is sufficient to consider the virgin rock as homogeneous, the density and the yield function of broken rock are both pressure and time dependent. A study of the failure and flow of solids with a pressure dependent yield function has been published recently by Jenike.' In this paper the density of the broken rock is assumed to be only time dependent and the consequences are examined in the case of one-dimensional vertical subsidence into an initial cavity. The following describes an attempt to develop a tool which, in combination with other tools, may lead to mathematical solutions of real problems of caving and subsidence. STATEMENT OF THE PROBLEM An underground cavity of horizontal cross section 4 = 1 and height 6 is assumed to exist at some depth below the surface. At the time t = 0 rock above the cavity fails and completely fills out the cavity with expanded broken material. With passing time the broken rock consolidates and subsidence proceeds continuously upuard in a vertical shaft. The phenomenon is one-dimensional (see Fig. 1). The problem consists of finding the displacement and the velocity with which the frlmt of the subsidence (wave front) moves upward as a function of the time and of the rock properties. DIFFERENTIAL EQUATIONS CONTROLLING THE PHENOMENON With the assumptions that the broken rock is a continuum and that the subsidence occurs continuously, we can apply the one-dimensional differential equation of contitiuity (conservation of mass) and the equation of preservation of momentum The latter equation is replaced by an assumed relation based on experience, which takes care of the

Jan 1, 1962

By R. A. Thomas, R. L. Solbod

The importance of transverse diffusion on the finger development in a miscible-phase displacement at an adverse mobility ratio of tbree was studied in a porous plate 1/4-in. thick, 3-in. wide and 18-in. long. Fast displacement rates (29 ft/D) and slow rates (1.6 ft/D) were used to determine the effect of residence time on the geometry of the fingers. The shape of the fingers was observed directly by use of the X-ray technique. At fast rates numerous narrow fingers were observed, but at slow rates a single somewhat bulging finger was produced. The amount of material moved transversely by diffusion across the plate was sufficient to modify the finger geometry in the slow-rate run because of the long residence time. These results are in contradiction to some of the postulates in the literature. The composition of the effluent stream, however, was not affected by the flow rate. This result is not inconsistent with the observed change in the shape of the finger in a short model, but it seems likely that a short model does not offer adequate and proper scaling of the reservoir. The model used was probably a valid one for studying the effect of transverse diffusion on the finger geometry, but a longer model would be needed for proper scaling of the effect of the change in the finger shape on the efficiency of displacement as measured by the composition of the effluent stream. INTRODUCTION Fingering can be defined as the uneven advance of the injected phase as it moves into a porous medium displacing the resident phase from the pore spaces of the rock. The use of this term is usually restticted to the situation in which the displacing phase is less viscous or more mobile than the fluid being displaced. Under these conditions, not only are fingers formed, but the length and width of the fingers grow with distance traveled in the porous medium. This subject has become one of great interest to the oil industry because of the present trend toward the use of various forms of miscible-phase displacement to increase oil recovery. Since in nearly all of the known modifications of the miscible-phase displacements an unfavorable mobility ratio exists (the displacing phase has a lower viscosity than that of the crude oil), the conditions are proper for fingering to develop. An appreciable amount of fingering appears to be a severe handicap to these processes for it increases the volume of agent required for the process to be a success, and such an increase puts a severe strain on the economics of the proposed processes. In some cases, such as for a mobility ratio of 200 unfavorable, it has already been demonstrated that the proposed process would not be economic if the fingering in the field were to be of the same magnitude as that observed in the laboratory. A number of aspects of fingering have been studied and reported in the literature. While the phenomenon of fingering cannot be regarded as a completely understood subject, considerable information exists on the effect of the path length and the mobility ratio on the growth of fingers. Less-complete data are available on the effect of the diameter of the flow path on the character and amount of the fingering, and even less agreement in results exists on the effect of rate of flow on the nature of fingering. This paper deals with one aspect of this latter subject. OBJECTIVE The objective of this study was narrowed down to one rather specific feature of the behavior of fingers in miscible-phase displacement in porous media. The variable studied was the effect of rate of flow on the nature and the development of fingers. It should be made clear at this point that, while rate was the apparent variable, the real variable was residence time; that is, at low rates the fluids are present at a given spot in the porous medium for a longer time interval than at fast rates. The purpose of the study, therefore, was to determine the changes which occur in the fingering and the possible benefits which might accrue from a longer residence time during that period when fingers are

By J. Philibert, A. G. Guy

Diffusion in the presence of deformation was studied by the method of vacuum dezincification of copper-rich and silver-rich solid solutions containing 7 to 30 pct Zn. The specimens were designed to permit the study of diffusion in separate portions of a given specimen characterized by strain rates ranging from essentially zero to approximately 10 sec-. No effect of deformation on diffusion was observed. BEGINNING with the work of Buffington and Cohen: interest in the question of the effect of stress or strain on diffusion has largely been concentrated on the enhancement of diffusion in specimens subjected to Continuous plastic deformation. The present research is a contribution to this limited area. However, as a preliminary to focusing attention on this special topic, it will be desirable to make a broad survey of the larger question, especially since there has been considerable foreign work in areas outside those of current interest in the United States. Since most of the topics referred to in the following section are both complex and imperfectly understood at present, it has been expedient in most instances to offer only a guide to the general nature of the work rather than a critical evaluation. PREVIOUS WORK The effect of elastic stress on diffusion has received considerable attention, especially with regard to the thermodynamic driving force for diffusion. The thermodynamic treatments have been based on the work of Gibb, Voigt, Planck, and Leontovich.' Konobeevskii and Selisski6 made a first attempt at treating the problem in 1933, and Gorskii7 a few years later gave a solution applicable to single crystals as well as to polycrystalline specimens. In 1943 Konobeevski8 published treatments that have been the basis of much Russian work up to the present. For example, Aleksandrov and Lyubov used his work in explaining the velocity of lateral growth of pearlite. Early work in the United States was that of Mooradian and Norton, which showed that lattice distortion tends to be relieved before it can significantly affect the diffusion process. Druyvesteyn and Berghoutl1 observed a slight effect of elastic strain on self-diffusion in copper, while de Kazinczy12 found that both elastic and plastic deformation increased the rate of diffusion of hydrogen in steel. On the other hand, Grimes58 observed no effect of either elastic or plastic straining on the diffusion of hydrogen in nickel. High-frequency alternating stresses have been reported by various investigator s13-l5 to increase the rate of diffusion. A special form of elastic stressing is the imposition of hydrostatic pressure, a condition that is amenable to Conventional thermodvnamic analysis. Most of the experimental results in this area are consistent in showing a slight decrease in diffusion rates at high pressures.16-l8 Although Geguzinl reported a pronounced effect of relatively small pressures, Barnes and Mazey20 failed to Corroborate this finding, while Guy and Spinelli21 advanced an explanation of the phenomenon observed by Geguzin. It has been recognized that the thermodynamic treatment of diffusion phenomena in an arbitrarily stressed body is complicated by the fact that the desired state of quasi-equilibrium of the shear stresses cannot be maintained during a general diffusion process. However, attempts have been made by Meix-ner22-24 and Fasto to treat certain restricted cases, such as relaxation. FastovZ7 has also incorporated the general stress tensor into the thermodynamics of irreversible processes. The lattice strain that accompanies the formation of a solid solution has been the subject of much study,28-s0 and indirectly it has entered into many recent theories of diffusion. However, some Russian investigators31'32 have taken other views of this matter and have predicted large effects on diffusion rates because of concentration stresses.o In completing this brief resume of previous work involving elastic strains and before proceeding to a consideration of the effect of continuous plastic deformation, it should be pointed out that deformation of various additional types may also influence diffusion. The effect of cold-working on subsequent diffusion has been studied directly by AndreevaS and by Schumann and Erdmann-Jesnitzer, while indirect evidence has been obtained by Miller and Guarnieri and by Vitman.38 Thermal stresses may also influence diffusion, contributions to this subject having been made by Fastovs7 and by Aleksandrov and Lyubv. The work of Johnson and Martin,o Dienes and Damask,3Band DamaskS considered the question of radiation-enhanced diffusion. In considering previous work on the subject of plastic deformation and diffusion, attention will be directed to those studies concerned primarily with diffusion rather than with its relation to Creep, e.g., the work of Dorn, or to the acceleration of diffusion -controlled reactions. Observations of the effect of

Jan 1, 1962

By Clarence O. Babcock

Model pillars of limestone, marble, sandstone, and granite, with length-to-diameter (LID) ratios of 3, 2, 1, 0.5, and 0.25 (0.286 for granite), were broken in axial compression to determine to what extent an increase in end constraint increased compressive strength. Radial end constraints of 13 to 23% of the average axial stress in the pillar, produced by solid steel rings bonded with epoxy to the ends of dogbone-shaped specimens, increased compressive strength somewhat above that of cylindrical pillars without ring constraint. However, when the results were compared with those obtained by other investigators for straight specimens of several rock types taken collectively, with LID ratios greater than 0.5, the resulting strengths were not significantly different. Thus, the amount of end constraint produced by the solid steel rings was about the same as that produced by the friction from the steel end plates. In other tests, a radial prestress of 3000 or 5000 psi was applied prior to axial loading by adjustable hardened steel rings to increase the constraint above that obtained for the solid rings. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 3000 psi prestress, was 54.3% for limestone, 40.3% for marble, 44.7% for sandstone, and 23.4% for granite. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 5000 psi prestress, was 74.2% for limestone, 51.2% for marble, 61.6% for sandstone, and 29.7% for granite. These constraints increased the compressive strength significantly above the strength of straight specimens and solid-ring constrained specimens. These results suggest that large horizontal stresses in orebodies mined by the room-and-pillar method should increase the strength of the pillars and allow an increase in ore recovery by a reduction of pillar size when major structural defects are absent. One important objective of the U.S. Bureau of Mines (USBM) mining research program is the rational design of mining systems. In the design of room-and-pillar mining operations, pillar strength is a fundamental variable. It is customary to estimate this strength from uniaxial compression tests of rock samples and to correct this value for the length-to-diameter (LID) ratio of the in-situ pillar. This method of estimating pillar strength corrects for pillar shape but does not consider the effect of a large horizontal in-situ stress field that sometimes exists in underground formations. The purpose of the work covered in this report was to determine to what extent the compressive strengths of model pillars of relatively brittle rock loaded in axial compression were affected by lateral end constraint. In previous work, Obert l used solid steel rings bonded to the ends of dogbone-shaped specimens to study the creep behavior of three quasi-plastic rocks -salt, trona, and potash ore - during a test period of 1000 hr. These rings provided radial constraint during the loading cycle of 20 to 50% of the axial stress for specimens with LID ratios of 2, 0.5, and 0.25. He concluded that (1) "for a quasi-plastic material the end constraint strongly affects the specimen strength, and (2) as D/L increases (length-to-diameter decreases), the specimens lose their brittle characteristics and tend to flow rather than fracture." He also concluded that model pillars constrained by rings were better for use in predicting the strength of mine pillars than either cylindrical or prismatic specimens. This conclusion appears to be valid where mine pillars, roof, and floor are a single structural element. In the present study, 460 specimens of four relatively brittle rocks — limestone, marble, sandstone, and granite - were tested to failure. The study consisted of two parts: (1) the effect on the compressive strength of end constraint produced during the axial loading cycle by solid steel rings bonded with epoxy to the ends of the specimens, and (2) the effect on the compressive strength of increased end constraint produced in part by a prestress applied prior to axial loading and in part by lateral expansion of the specimen during the loading cycle. The first part of this study was reported in some detail earlier.2 EXPERIMENTAL PROCEDURE AND EQUIPMENT Model rock pillars of the sizes and shapes shown in Fig. 1 were broken in axial compression when the ends were constrained as shown in Fig. 2. he straight specimens were broken without ring constraint. The specimens of dogbone shape were broken with (1) solid

Jan 1, 1970

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"' and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7'8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965