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By M. E. Wadsworth, J. S. Cho

The kinetics of silicate adsorption from aqueous colloidal (SO2 . nH2O) silicate sols on thoria (ThO 2) surfaces were determined at 100, 150 and 200°C in an autoclave system. The amount of chemisorbed silica on the thoria surface was determined by means of infrared spectroscopy. First order kinetics were observed in all cases with the anomalous result that the first order rate constant was found to vary with the initial amount of silica added to the system. These results have been correlated quantitatively by means of a strain model of adsorption involving two types of surface silicate bonding, both of which may be readily observed in the infrared spectrum. Initial adsorption occurs rapidly to produce one type of surface silicate followed by a slow transition to a second type of surface bonding, the latter transition representing the slow step in the adsorption process. Initial interest in silicate adsorption on thoria arose from the dispersive effect silica has on finely divided thoria in aqueous suspensions. Spaepen et al studied the equilibrium adsorption of silica on thoria and noted increased adsorption up to approximately 215°C with a notable decrease in adsorption at temperatures above 215°C. Similar results were observed by Cho and Wadsworth2 who identified two types of surface silica by infrared spectroscopy. At temperatures of 100°C and above, rapid initial adsorption occurred producing a surface species with maximum infrared absorbance at 9.4 After extended periods of time, the 9.4 species converted to a more strongly bonded surface silicate with maximum infrared absorbance at 10.3. The latter was very strongly bonded and difficult to remove by desorption in hot distilled water, while the 9.4 species could be removed more readily by similar treatment. The 9.4 and 10.3-p species were distinguishable from free unadsorbed silica which had maximum infrared absorbance at 9.1 The kinetics of the formation of the strongly chemisorbed silica (10.3) on thoria as determined by infrared examination are presented in this study. EXPERIMENTAL PROCEDURE As a source of silicate, Ludox SM (16.36% SiO2) or Ludox HS (30.25% SO2), DU Pont colloidal silica in aqueous suspensions, was added directly to a thoria slurry made up of one liter of distilled water and one gram of thoria. The thoria used was designated D-16-650 and was received from the Chemical Technology Div. of Union Carbide Nuclear Co. It was prepared by firing thorium oxalate at 650°C. The D-16 thoria had a surface area of 32.4 ± 0.6 sq m per g as determined by nitrogen adsorption.* This thoria 'Determined by Unlon Carbide Nuclear Co., ORNL. had a total adsorption capacity for silicate of approximately 19.4 mg of silica per gram of thoria.1 This amounts to approximately one SiO2 molecule for every surface thoria site. In all cases in this study.

Jan 1, 1963

By William H. Shockley

Though China has been widely explored by mining engineers during the past dozen years, comparatively little has been published concerning its mineral resources. The few moilographs scattered through the transactions of various societies contain far less information than the private reports made to the numerous syndicates which have sent out engineers. The best general account of the geolopy and mineral resources of China is to be found in the works of von Richthofen,' a remarkably gifted observer. The observations recorded here in this paper were made in the service of the Pekin Syndicate (which has kindly given me permission to publish them), during the first months of 1898, among the coal- and iron-fields of southeastern Shansi. This is one of the largest anthracite-regions known, the area being

Jan 1, 1904

By J. A. Bowers

THIS investigation of the effect of bottom shape and life on slag volume was carried out in two Lectromelt top-charge furnaces whose rated capacity is 1000 lb per hour. Unfortunately, just as the work [ ] was started, our steel tonnage was reduced approximately one half, therefore we did not accumulate enough data from which to draw any definite conclusions. Furthermore, the life of the linings in these furnaces was greatly decreased by intermittent operation, which was a further handicap in making a study of this kind. The weight of the heats from which the data were taken varied 1200 lb but all the information was corrected to the standard weight charge for these furnaces of 4500 lb. Almost all the heats were plain carbon; a few contained a small percentage of added copper.

Jan 1, 1947

By A. T. Robinson, J. E. Dorn

The electrical resistivities of aluminum alloys containing CU, Ge, Zn, Ag, Cd, and Mg were found to increase linearly with the atomic percentage of the solute atoms. Application of Linde's rule to these data suggests that each aluminum atom contributes 2.5 electrons to the metallic bond. ALTHOUGH aluminum invariably exhibits a Jt\. valence of three in ionic solids, it does not follow necessarily that its valence in the metallic state is also three. As a matter of record, many properties suggest that the number of bonding electrons in metallic aluminum is less than three. For example, as shown in Fig. 1, the atomic radii1 of the metallic elements in the solid state decrease with increasing atomic number at the beginning of any one period. The atomic radius of aluminum, however, is greater than that which would result from a regular decrease in atomic radius with increasing atomic number, suggesting that the number of bonding electrons in aluminum is somewhat less than three. Correlated with the anomalously large atomic radius of aluminum is its abnormally low melting temperature. As the atomic numbers increase in any one period, the melting temperatures of the metallic elements increase.' As shown in Fig. 2, however, the melting temperature of aluminum (13) is only slightly greater than that of magnesium (12). Again the number of bonding electrons in metallic aluminum appears to be nearer two than the expected value of three. In addition Ageev and Ageeva3 alculated the electron density distribution in the aluminum lattice. A comparison of such electron density curves for various assumed valence states of aluminum with experimentally determined curves suggests that the actual number of bonding electrons in metallic aluminum is between two and three. Hume-Rothery and Raynor', " have suggested that the above-mentioned abnormalities are associated with the overlapping of the Brillouin zones of metallic aluminum when it is in the usual face-centered cubic structure. The importance of the number of bonding electrons in metals has been extended recently into the field of mechanical properties. While formerly it was thought that the plastic properties of alpha solid solutions were primarily dependent upon the lattice strain induced in the solvent by the solute, it is now known that the difference in the number of bonding electrons of the solute and solvent also has its influence on the plastic properties."1' In order to achieve a satisfactory correlation of the effect of alloying elements on the plastic properties of aluminum alloys,"'T however, it was necessary to assume that the number of bonding electrons contributed by aluminum was about two rather than the expected value of three. It appeared to be desirable, therefore, to seek other criteria for evaluating the number of bonding electrons contributed by aluminum to its alpha solid solutions, especially in view of the practical as well as the theoretical importance of the effect of valency on the plastic properties. Norbury' was perhaps the first to illustrate that the increase in resistance of alpha solid solutions is associated with the differences in valence of the solute and solvent metals. In a series of illuminating investigations Linden-'' has shown that the electrical

Jan 1, 1952

By Edward E. Hicke, Charles A. Stickels

The dihedral angle of liquid-lead inclusions in solid nickel has been measured as a function of temperature from 371 to 816 C at zero pressure. and as a function of pressure up to 50,000 psi at 317 and 593 C. Thermodynamic expressions are derived for the temperature and pressure coefficients of interfacial tensions in this system. A method is presented for obtaining relative tempmature and pressure coefficients from dihedral-angle data, and the resulting values are used in conjunction with the thermodynamic relations to calculate excess properties of the solid-liquid interface. Defining the position of the solid-liquid interface by the condition that the excess concentration of lead is zero, the excess concentration of nickel and the excess entropy at the solid-liquid interface are: where y(593) is the interfacial tension of the nickel grain boundary saturated with lead at 593C and zero pressure. These values are considered reliable to within a factor of two. While similar calculations are not possible for the nickel grain boundary, it is shown that the expwimental results imply that the excess concentration of nickel at the boundary and the excess entropy of the boundary are negative. THE temperature and composition dependencies of interfacial tensions in metal systems have been reported by several authors in the last 15 years.'-' No measurements of the effect of pressure on inter- facial tensions in metals have been reported, although measurements made on nonmetallic gas/liquid and liquid/liquid systems suggest that a measurable effect should exist.6-l2 The purpose of these experiments was to determine the influence of temperature and hydrostatic pressure on dihedral angles in the Pb-Ni system. The equilibrium dihedral angle is expressed as a ratio of interfacial tensions by2: where 8 is the dihedral angle, yGB is the Ni-Ni grain boundary tension, and SL is the solid Ni-liquid Pb interfacial tension. Three sets of ex- periments were run to determine: a) the effect of temperature from 371" to 816°C on the dihedral angle at zero pressure; b) the effect of pressure up to 50,000 psi on the dihedral angle at 371° and 593°C. THERMODYNAMICS The properties of interfaces of most direct concern are the interfacial tension, excess concentrations of various components at the interface and the excess entropy of the interface, S°. These quantities are defined following Gibbs. Consider an interface separating phases a and 0. Construct two surfaces C, and C such that all properties of phase a remain uniform up to C, and all properties of phase 0 remain uniform up to C. The region between C, and Cp is the interfacial region. Let a "dividing surface", D, be constructed in the interfacial region such that it passes through all points "similarly situated with respect to the condition of the adjacent matter."l3 Surface D divides the interfacial region into a portion a' adjacent to phase adjacent to phase . Let a closed curve, C, enclose an area A in D. Erect normal lines to D along C; these lines and the surfaces C,, Cp, and D then enclose volumes V and V' in the two halves of the portion of the

Jan 1, 1964

This issue presents the first of several articles making up the Bump Symposium, which was held at the 1958 Annual Meeting of AIME. Other Symposium papers will appear in the September issue of Mining Engineering. THE term mountain bump describes the sudden rupture of one or more coal pillars under excessive stress. These bursts occur with varying degrees of violence and sometimes include adjacent strata, especially the bottom rock. Many failures do not develop enough violence to be dangerous and are regarded as an aid to coal production, but severe occurrences are accompanied by tons of flying coal, dense clouds of dust, and excessive gas emission. Such bursts sometimes throw heavy machinery several feet. Major factors to be considered in the problem are the nature of the strata above and below the seam and the depth of cover. Bumps are classified as to their nature, extent of damage, and point of occurrence, e. g., face bump, coal bump, high side bump, low side pavement bump, and district bump. The problem is extremely complex, and it cannot be over-emphasized that preventive measures, if they are to be successful, must be based on a thorough study of conditions in the individual mine. In western Canada, for example, the McGillivray mine, operating in a 9-ft seam at 2000 ft, has experienced severe bumps, but there have been no occurrences in the International mine, which operates in the same coal seam at 2400 ft, where the coal averages 17 ft thick. Differences in conditions governing the operation of these two mines are described in one of the following articles (see page 883). Again, most bumps in coal mines take place along pillar extraction lines, but at the Sunnyside mine in Utah they also occur a long way from active workings and sometimes in virgin territory. It is usual, too, for such failures to occur under fairly deep cover. But at Sunnyside, to cite only one instance, there have been disturbances along the main fault zone under less than 500 ft of cover. All too often conditions favorable to bumps are revealed only by actual mining—at Springhill No. 2 mine, drilling in roof and pavement strata disclosed a 60-ft sandstone bed after operations had started— and where extraction has advanced too far for preventive measures to be incorporated in the mining plan, districts have had to be abandoned. But in an era when premium ores are being rapidly depleted in the face of rising demands, abandonment is not easily justified. There must be systematic planning to eliminate coal mine bumps, insofar as this is possible. As in the Gary district of West Virginia (see page 888) much has been accomplished by planned operations based on known factors in bump control. But even this is not enough. Precise instrumentation is needed to indicate where bumps are likely to occur, and in both the U. S. and Canada stress analysis studies are being carried out with this object in view. These pages reveal the progress being made.

Jan 1, 1959

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.' Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:' Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.' Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965

By H. J. Beach, W. C. Goins

The laboratory development and field use of oil well cement compositions* with high resistance to drilling mud contamination are described. Resistance is obtained by adding a I-lb mixture composed of three parts paraformaldehyde to two parts sodium chromate tetra-hydrate for each sack of cement. This mixture neutralizes the cement-retarding properties of quebracho and other tannins, starch, sodium carboxymethylcellu-lose, Ignite, and monovalent salts of lignosulfonic acid. The retarding properties of calcium lignosulfonate are unaffected. The decontaminating mixture may be used in common cement (designated Type I by ASTM specifica-tions,' Class A by API Std. 10A2) or in a slow set slurry prepared from common cement by addition of calcium lignosulfonate. No changes in slurry viscosities or thickening times are caused by the protecting reagents. The method has been used in 185 field jobs where an improved success ratio has been obtained in plug setting. INTRODUCTION Field experience and laboratory investigations have established contamination by drilling mud as a major factor in oil well cement failures. During 1955, 12 attempts were required to set six open-hole cement plugs in the Timbalier Bay field, La. Eighteen to 30 hours elapsed between placing and testing the plugs in preparation for sidetracking operations. Considerations of rig time expense required immediate resetting where soft cement was drilled after a reasonable waiting period. Sea water drilling mud was used in each well and daily additions of thinners, usually lignites, had been required. Sodium carboxymethylcellulose had been added regularly to control fluid loss. The 50 per cent plug failures were attributed primarily to contamination by the mud. Similar experiences can be found in other fields along the Texas and Louisiana coasts where drilling muds normally contain large quantities of organic treating materials. Cement contamination was the subject of a survey by the Mid-Continent District Study Committee on Cementing Practices and Testing of Oil-Well Cements of the API.3 Data collected from member laboratories and released in Sept., 1951, reported the effects of a number of drilling mud treating chemicals on cement. The study revealed that many of the additives, notably the organic materials in relatively small quantities, had marked effects on the properties of cements tested. Severe losses in strength and erratic thickening time resulted from small additions of mud treating chemicals such as quebracho, starch, sodium carboxymethylcellulose, and lignite. The report included no recommendations of methods for overcoming the problem. One investigation of the contamination problem reported the successful use of activated charcoal in setting cement plugs after conventional slurries had failed.4,5 The investigation indicated that an optimum concentration of 5 per cent activated charcoal was effective in combating contamination from 16.7 volume per cent of treated mud. Laboratory and field muds were included in tests and contained varied quantities of ode or more of the following: quebracho, caustic, starch, lime, and calcium lignosulfonate. The function of the charcoal appears to be physical, removing the organic materials by adsorption. The method may be employed in API Class A or Class D (unretarded slow set) cements. The chemical approach presented here is based on

Jan 1, 1958

By B. M. Larsen, T. E. Brower

For some years we have been carrying on a rather comprehensive investigation of the occurrence of oxygen in liquid open-hearth steel. This investigation was interrupted by the war emergency and is therefore incomplete, with many questions still answered only partially, if at all; yet it seemed worth while to present a report of progress on this difficult field of research, if for no other reason than to promote discussion and further investigation of this important problem. The significance of such studies depends in large measure upon the accuracy of measurements of oxygen content in liquid steel while it is still in the furnace or as it flows into the ladle, or thence into the mold and there is, as we shall show, good reason for believing that the main source of uncertainty is in the sampling, not in the analytical method as such. The difficulty arises from the fact that any method of sampling is of itself apt to alter the amount of oxygen in solution in the liquid steel, because this oxygen is in a readily reactive condition. On the one hand, being usually present at a concentration appreciably in excess of that corresponding to equilibrium with the carbon then present, it may decrease rapidly in percentage by reaction with carbon and evolution of CO, especially if the liquid metal is in any way shaken or brought in contact with a cooler solid surface. On the other hand, it may increase rapidly by ab- sorption of oxygen from a slag, a furnace atmosphere, or from air. These circumstances, which are inherent in the problem, as well as our conclusion that, despite the considerable amount of careful work already done, there is still no method of sampling liquid steel acceptable as an unquestioned standard, ed us to undertake systematic comparisons of oxygen content of large numbers of samples taken: (I) by a single method at different positions and levels in the bath; (2) at the same place by different sampling methods; and (3) from bath, tapping stream and pouring stream. The different sampling methods yield somewhat different values and there is as yet no way to tell with certainty which is the most accurate. But the general reproducibility and consistency of the results give us some confidence in certain inferences we draw from them: namely, that the "spoon" method of sampling, properly carried out, gives somewhat more consistent results than the "bomb" method, as it has usually been practiced; that, in the bomb method, an aluminum cap is preferable to a steel cap; that the oxygen content of liquid steel in a finished heat is substantially the same all over the bath at the same level, and tends to decrease at lower levels further from the slag interface; also that it tends to decrease, and to decrease erratically, from furnace bath to tapping stream entering the ladle. Accordingly it seemed desirable to report these observations in detail as a first step, so that the reader may judge their significance as a contribution towards solution of the main problem, which is to find a means of pre-2

Jan 1, 1945

[ ]

Jan 1, 1940

By Guy R. Johnson

In working brown iron-ore mines on the system employed at Longdale, namely, stoping from the top down, the usual procedure is to drive a succession of upraises from the lowest adit to the highest, or to the top of the deposit, as the case may be. These up-raises are usually driven 120 feet apart., along the strike of the vein,. As the work goes on, they are connected by levels, 10 feet spa* (vertically), and then serve as chutes. A transit is useless in surveying these chutes, and the writer has for several years made use of a hanging compass. The method of using this instrument, described in a former paper (Trans., xx.,.105), embracing as it does the use of a cord and several strips. of wood,

Jan 1, 1894

By Ronald J. Roman, Craig Olsen

Alterations were performed on a previously developed heap leaching model representing sulfuric acid solution leaching of a malachite sandstone ore. The alterations were made in order to approach a more realistic solution to the leaching equations used in the model and to provide a means of obtaining a constant acid con- centration in the model' s simulated heap effluent solutions. This constant acid concentration is desired if the effluent solutions are to be treated in a solvent extraction-electrowinning plant. An economic study was made showing a use of the leaching model for an imaginary heap leach operation. The example illustrates a method of selecting heap leaching parameters if data are available on mining costs, dump costs, capital cost, etc. This was achieved using an incremental investment technique.

Jan 1, 1974

By Carlos Kovacs-Figueroa

Complying with air pollution regulations created the need to dispose of increased sulfuric acid production by the Morenci smelter. As a result, a two-module leaching plant was constructed to leach Morenci flotation tailings. The leaching plant was equipped to perform the following operations: leach feed pumping, agitated leaching, two-stage countercurrent decantation, neutralization of leached tailings, and copper precipitation. Ancillary facilities were provided for neutralizer and flocculant preparation as well as precipitant handling and recovery of precipitates. Plant control is automatic from a central control panel supervised on a shift schedule by one operator and two helpers. Construction of the first module was initiated in April 1973 and leaching of tailings commenced in November 1974. Construction of the second module began in January 1975 and was completed in November 1975.

Jan 1, 1977

By A. S. Appleton

The diffusion of carbon in Fe-Co-C austenites was studied as a function of cobalt concentration up to 12 at. pet, using an autoradiographic technique. The diffusion coefficient was found to initially decrease and then increase with increasing cobalt concentration, the trends being more marked the higher the temperature of diffusion. These effects were paralleled by variations in the activation energy and the constant for diffusion which, however, were found to be dependent also on the carbon content. The results are compared with the previously available data and their significance is discussed in terms of the kinetics of solid-state reactions in this systern. THE influence of cobalt on the diffusivity of carbon in austenite was first studied by Smoluchowski,' his data being that most commonly cited in works

Jan 1, 1964

By Graham P. Crutchfield

The W. I. Cook pool in Shackelford County, Texas, has been the subject of a number of papers and articles. Its unique position both as to operation and development has made it an ideal location for unit repressuring. The major portion of the pool is located on the W. I. Cook ranch and most of the oil leases are owned by Roeser & Pendleton, Inc. and the Continental Oil Co. and operated by Roeser & Pendleton, Inc. The Humble Oil & Refining Co. and Tom James operate producing leases which have a vital bearing on the unity of the pool. Both have cooperated in the repressuring project. Practically the entire royalty is owned by Mrs. W. I. Cook and she has given the operators her entire cooperation in all phases of unit repressuring.

Jan 1, 1931

By L. Massé, Th. Koulomzine

NOTE ON HAALCK'S FORMULA QUANTITATIVE interpretation of magnetic anomalies is admittedly a difficult process. Few authors have attempted a general approach to this problem. A [ ] number of publications can be found widely scattered through scientific periodicals, which present particular solutions obtained by the introduction of simplifying assumptions, such as the reduction to an equivalent magnet or pole, or the hypothesis of a very thin vein. The practical applications of these solutions are necessarily very restricted though they have given satisfactory results in isolated cases. Probably the most widely known equation of this type was given by Haalck.l His classic work contains curves calculated for typical conditions, and has now become a standard reference. However, a close scrutiny of Haalck's derivation reveals that, aside from the hypothesis of a thin vein, it rests on the

Jan 1, 1947

By L. Massé, Th. Koulomzine

Note on Haalck's Formula Quantitative interpretation of magnetic anomalies is admittedly a difficult process. Few authors have attempted a general approach to this problem. A number of publications can be found widely scattered through scientific periodicals, which present particular solutions obtained by the introduction of simplifying assumptions, such as the reduction to an equivalent magnet or pole, or the hypothesis of a very thin vein. The practical applications of these solutions are necessarily very restricted though they have given satisfactory results in isolated cases. Probably the most widely known equation of this type was given by Haalck.' His classic work contains curves calculated for typical conditions, and has now become a standard reference. However, a close scrutiny of Haalck's derivation reveals that, aside from the hypothesis of a thin vein, it rests on the

Jan 1, 1949

By A. E. Hunt, G. P. Clapp

This paper constitutes in substance a part of a more elaborate chapter, accompanied with extended tables of analyses, prepared for the book of Mr. Fred. H. Whipple on " Water-Supply." In advanee of that use of the material, however, it seemed appropriate to lay a portion of it before the Institute; and this opinion of the authors, the Council, by accepting the paper, has ratified. It may seem at first glance, nevertheless, that a paper dealing chiefly with this subject in its sanitary aspects, and only treating in a subordinate way of the one subject (boiler-scale) usually deemed to concern our professions, is somewhat out of place in our Transactions. But reflection will, we trust, correct this impression. In recent periods, and in continually increasing degree, the managers

Jan 1, 1889

By D. A. Rice, M. C. Fuerstenau

Flotation data indicate that sulfonate and amine adsorb physically on manganese oxide; oleate also adsorbs physically if the zero point of charge is sufficiently high. Chemisorption of oleate occurs on pyrolusite between pH 8 and 9, and possible mechan- isms of collector adsorption involving metal ion hydrolysis are discussed. The flotation characteristics of most metal oxides1-15 have been examined with standard collectors such as fatty acids and sulfonates. From these studies it would appear as though electrical phenomena are important when shorte r-chained collectors are involved. For example, Iwasaki, Cooke, and Choi9 have shown that dodecyl amine and dodecyl sulfate float iron oxide above and below the zero point of charge, respectively. In another system, D.W. Fuerstenau and Modi10 have shown that dodecyl sulfate, dodecyl

Jan 1, 1969

By H. B. Aaron

DIFFRACTION micrography provides a useful tool for studying complex strain fields. Newkirk1 observed an X-ray diffraction effect due to strain interactions at the intersection of slip lines in LiF and attributed this effect to a reduction of primary extinction due to strain-gradients. It is the object of the current study to correlate the observations and rationalize the appearance of the strain fields around intersecting slip planes in x-ray extinction contrast studies by a semiempirical method. Fig. 1 shows typical strain patterns observed by Newkirk on (200) reflections in LiF using chromium radiation and a variation of the Berg-Barrett (B-B) technique. In other reflections (e.g., {220}) the strain patterns are absent. If one defines a vector 3 along the striations from the more to the less dense portion, and a vector v in the direction of the X-ray beam parallel to the reflecting plane, such that both 3 and v lie in the reflecting plane of the crystal, Fig. 1, then the positions of the striations on (200) reflections appear to be confined such that where is the angle between v and 3, Fig. 1. It will be seen later that 3 is the projection of Sb on the reflecting planes. In some instances the strain effects are observed only above the slip plane, Fig. l(C), in others only below, Fig. l(D). Where the strains appear to be both above and below the slip line, Fig. l(E), one sees that there are actually two slip lines present, Fig. 1(F) and (G). Furthermore, the strain patterns are observed in the vicinity of the intersection of emergent edge dislocations (diagonal lines on the micrograph) with emergent screw dislocations (horizontal lines on the micrograph), e.g., Fig. l(HJ) and (MN), but not in the vicinity of the intersection of two emergent edge dislocation arrays, Fig. l(HJ) and (KL). However, in the latter case the contrast of the dislocation array itself is reduced along (KL) and increased along (HJ). Line (AB) in Fig. 1 is the edge of the crystal, and the material to the left of (AB) is the side of the sample. Any empirical correlation will have to include most, if not all of the aforementioned observations. Lang2 and Newkirk1 determined that the condition for contrast is given by g-b#0 [2] where b is the Burgers' vector and g the diffraction vector (normal to the reflecting planes). If one assumes that the direction of the observed strain fields is given by the vector sum of the slip vectors (Sb1) of the intersecting slip planes, then Eq. [2] may be generalized to g-S#0 [3]

Jan 1, 1963