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By F. E. Smith, David R. Mitchell, B. M. Bird

DENSE-MEDIA processes utilize the familiar laboratory float-and- sink procedure on a commercial scale. Just as wood chips float on water and sand sinks, ,so coal floats and refuse sinks when placed in a medium intermediate in specific gravity between the coal and refuse. Liquids intermediate in specific gravity between coal and refuse used in commercial plants are of four types: (1) Organic liquids of high specific gravity-halogenated hydrocarbons; (2) dissolved, salts in water; (3) pseudo liquids obtained by suspending solids, such as sand, in water, and (4) fluidizing a mass of sand or other solids by air currents. Those most widely used for cleaning coal are solutions of calcium chloride in water and a suspended-sand pseudo liquid. Laboratory float-and-sink testing is an intermittent operation during which every opportunity is given for particles lighter than the medium to float and particles heavier to sink. Commercial processes are continuous, vertical and horizontal currents of the separating medium occur as either part of the process or unavoidably produced by the introduction of feed and withdrawal of products, so that the exact separation of the laboratory technique is not duplicated by commercial processes. However, separations close to the theoretical are obtained in commercial machines by careful technical control of the process. Most machines in commercial installations are crowded to get as much out of the equipment as possible, so that careful technical control is necessary to get the recoveries and grade of product desired. Sizes usually cleaned are plus 3/16-in. or plus 1/8-in. in the United States and plus 1/16-in. in Great Britain: Coal as small as 1 mm. has been cleaned in some experimental installations. The separation of coal from refuse in sizes finer than about in. is made difficult by viscosity' effects and hence at the present time cleaning is confined to the coarser sizes. Technical advances in the art of cleaning coal by dense-media

Jan 1, 1943

By George Mieyr, H. M. Ziesemer

Prior to 1909 that mountain of porphyry known as Sacramento Hill had hardly been touched though it had always been thought to contain ore. During that year, exploratory work was started by underground methods; drifting and raising continued until 1913. It was proved that a mineralized zone existed, the limits of which had not been determined ; so, because of the lower costs of exploratory work and the greater desirability of vertical sections, it was decided to prove the extent of the ore zone by churn drills. Drilling continued until 1917, when it seemed almost certain that the horizontal limits of the orebodies had been determined. Ore continued in depth in one direction beyond a point where it was economical to explore by churn drilling; this extension is still being developed by underground methods. The irregularities of the boundaries of the ore zones, together with the variable grades of ore encountered, made it necessary to drill on the corners of 100-ft. squares. Two ore zones were proved, known as the East and West Orebodies. The Sacramento Hill porphyry stock intruded into the Dividend fault. The fault ran roughly east and west with a dip to the south, having pre-Cambrian schists on the north against Paleozoic limestone on the south. This intrusion was accompanied by a silica breccia on the south periphery, along the limestone contact side. The ore lay in the silica breccia and in the porphyry, some distance from the breccia. NO ore was found in the heart of the porphyry mass on the north side, along the schist contact. The West Orebody is elliptic in shape, having a major axis of 1200 ft. (366 m.) and a minor axis of 800 ft. (244 m.); these diminish with depth until, at 300 ft., the axes are 500 ft. and 300 ft., respectively. The ore consists of chalcocite, some bornite, chalcopyrite, and considerable pyrite in a siliceous gangue. About 30 per cent. of the copper is caused by

Jan 1, 1923

By James F. Magee

There is nothing new about dragline dredging for placer gold. The use of the separate unit for excavating preceded the large barge with excavator mounted upon it, which has reached a high state of perfection through use in every part of the world. But at present there is a vogue for a small, inexpensive plant combining a dragline excavator on caterpillar mounting and a gravel-washing plant on a floating barge. The most efficient ones use a bucket of 1 to 2 yd. capacity with boom from 40 to 70 ft. long. The barge varies from 20 by 30 ft. to 36 by 48, and carries the trommel screen, pump, riffle sluices and power engine. Plants in Oboville District In the Oroville district eight such plants have been built since 1933, and have been operated with varying success. The most successful of these is the plant of the Wyandotte Gold Dredging Co. This organization of six active partners constructed its first plant on Wyandotte Creek in the autumn of 1933. To September of 1935 about one million cubic yards of gravel was dredged for an output of about $225,000 in gold. The operation has been successful from the beginning, because of wise management, which was based upon good plant design and proper principles of operation. All the partners have taken a more or less active part in the operation. Usually there is one at work on each shift, and they have conducted their own prospecting and building also. They elected H. F. England as manager, with wide power of control, and he carries out this responsibility energetically and successfully. One of the other plants, started shortly before the Wyandotte, finally abandoned its operation and sold its ground to the latter company, which successfully worked it for a profit. The failure of the other plant was due principally to poor excavating equipment. Another organization that built a plant some months later than the Wyandotte company had considerable difficulty in management and was unable to keep ahead of expenses. Finally, late last summer, it entered into an agreement with the Wyandotte company to have the latter supply

Jan 1, 1937

By William Johnson

IT is now recognized that several important types of reactions in metallic systems proceed by the formation of nuclei and the growth of these nuclei. The process of freezing is a simple example of this, as Tammann pointed out years ago.1 Tammann held that ' the rate, of freezing is determined by a rate of nucleation, expressed as the number of nuclei formed per unit volume of unfrozen liquid per second, and a rate of growth of these nuclei, expressed as the linear rate of radial growth in units of length per second. For isothermal freezing the conception is simple; for ordinary freezing, extending over a range of temperature, it is not as simple, for the values of the two constants must change with change in temperature. There is ample evidence that the postulated mechanism is correct even though a quantitative derivation of the rate of isothermal or of ordinary freezing in terms of the two constants has been lacking. In recent years other reactions have been found to proceed in a similar fashion. It has been well established, particularly by Bain,2-8 that. the formation of pearlite from the eutectoid decomposition of the solid solu-tion austenite proceeds in such a way, and Polanyi and Schmid, Tammann and Crone, Karnop and Sachs, and others9-11 have shown that the process of recrystallization proceeds in a similar way. Isothermal reaction rates have been determined for eutectoid decom-position by a number of investigators. Bain's2-8 work on the formation of pearlite from austenite is especially valuable in this respect-the type of isothermal reaction curve obtained, as illustrated in Fig. 13, showed an initial slow rate, accelerating to an intermediate maximum rate which then decelerated to the completion of the reaction; similar curves have been obtained by Wever and his collaborators.12 Other eutectoid decompositions show similar behavior: for example, the decomposition of the beta eutectoid in the copper-aluminum system, studied by Smith

Jan 1, 1939

By H. M. Davis, T. S. Jones

A methodfor accelerating the reduction of a metal oxide by carbon monoxide is to incorporate in the reduction system a nonreducible oxide which has a strong affinity for carbon dioxide and will remove it from the product gases. The effectiveness of this method was investigated by veduction experiments on specially prepared powder mixtures of SrO-ZnO ("active'.) and SrCO3-ZnO (reference). Measurements at 750o and 677°C showed that the rate of reduction of ZnO by CO was as much as an order of magnitude greater in the presence of SrO. Under the experimental conditions at least as much CO2 as generated by veduction was absorbed when SrO was present. Enlzancernent of the veduction rate by SvO resulted from modification of' gaseous djfitsion processes. THE specific question posed in this investigation was whether the reduction reaction CO + ZnO - Zn(g) + COa [1] could be accelerated by incorporating strontium oxide into the oxide charge undergoing reduction. Provided the strontium oxide was active enough, it could remove carbon dioxide from the product gases of ( 11 and form strontium carbonate, thus modifying Reaction [ 1] to CO + ZnO + SrO = Zn(g) + SrCO3 [ 2] This study of the comparative rates of Reactions [ I] and [2] can be considered as a particular case of a general scheme for increasing the rates of reduction of metal oxides by carbon monoxide. The limits of applicability of this scheme are indicated in the simple thermodynamic analysis presented in the appendix. This analysis primarily dictated the choice of the system, CO-ZnO-SrO, employed in this investigation. In addition, it was thought that a study of this scheme by use of the CO-ZnO-SrO reaction system would be of special interest in view of indications in the literature1-3 that the gaseous reduction of zinc oxide is prone to rate control by diffusion in the gas phase. The distinction should be pointed out between this and other efforts to increase the rates of reduction reactions through the use of addition agents. Additions of a wide range of chemicals have been tried with de- grees of apparent success varying from slightly negative to highly positive. The reasons for making additions have included the use of salts to produce effects akin to catalysis,4, 5 the alteration of the microstruc-tural details of the reduction process (including solid-state diffusion),6-8 and the conversion of an en-dothermic reaction into one that is exothermic or autogenous.9-12 The means used to attempt alteration of the enthalpy change has commonly been to incorporate lime into the charge, so that heat is generated by reaction with either of the reaction products, carbon dioxide or water. The use of lime in this way makes endeavors such as that of Edstrom and Wiberg similar to the present one. Furthermore, the basic principle behind the present work has previously been set forth.13 However, a detailed investigation of the type of reaction described in this work does not appear to have been conducted. EXPERIMENTAL PROCEDURE From both conceptual and physical standpoints, Reaction [2] is to be considered as the sum of two reactions:

Jan 1, 1968

By N. F. Schulz, H. A. Lex, J. D. Zetterstrom

A green ball of iron ore faces many perils from the time it is formed until it finally emerges from the pelletizing furnace as a hardened pellet. For instance, if the rate of heat transfer into a ball is sufficient to produce vapor from either the free or combined water more rapidly than it can escape at a tolerable pressure, the ball may split, spall, or even explode, a failure commonly known as decrepitation. To avoid such failures, one must either limit the rate of heat transfer during the drying and preheating stages, at the expense of production rates, or improve the decrepitation resistance of the green balls. The latter remedy may often be accomplished through changes in ore preparation, balling procedures, or the judicious use of binders or other additives. INTRODUCTION Pelletization has become established as an especially desirable method for the agglomeration of fine taconite concentrates and it promises to be equally satisfactory for improving the physical structures of certain natural ores. A high-quality pelletized iron ore consists of uniformly sized spheres, usually about 1/2-in. diam, which are strong enough to resist abrasion and breakage during handling and which reduce well without disintegration in the blast furnace. The unfired agglomerates, "green balls", are subject to several destructive effects that must be avoided or minimized if a high-quality product is to be obtained by pelletization. Among these are abrasion and impact deformation or breakage during handling of the wet green balls, deformation and breakage by compressive forces in the bed of ore in the pel-letizing furnace, decrepitation during drying and preheating, wind erosion, and radial cracking at firing temperatures. Moisture condensation from the warm saturated gases downstream from the drying zone on wet, cool balls may cause bed collapse if it becomes excessive. Decrepitation is defined as the sudden disintegration of green balls, usually with an audible pop, that occurs when they are heated too rapidly during the drying or preheating stages of the pelletization process. The extent of ball disintegration may vary from merely splitting off a small fragment to almost total disintegration into the original ore particles making up the ball. Such ball destruction results in a decreased yield of pellets, and the fragments, which also tend to interfere by obstructing the gas flow through the bed, must eventually be screened from the fired product and recycled. The closely related type of ball failure that sometimes occurs during the high temperature firing stage, resulting in radial cracks without fragmentation, was not considered to be decrepitation for the purpose of this investigation. Failure by decrepitation is not usually a serious problem in the pelletization of taconite concentrates. The problem is significant, however, in the pelletization of some natural ores, especially those containing hydrous iron oxides. In some instances, economicd production rates cannot be maintained if the drying and preheating rates are slowed down enough to avoid decrepitation. OBJECTIVES This investigation was undertaken to: (1) Develop a practical laboratory means for quantitatively measuring the tendency for green balls to decrepitate in iron ore pelletizing furnaces, and (2) Investigate the causes and cures of ball decrepitation. MATERIALS Two iron ores were used in the work reported here: a taconite concentrate at 90% minus 325 mesh, containing 65.0% Fe, 8.4% SiO2, and no loss-on-ignition; and a crude oxidized ore at 54% minus 325 mesh, containing 59.1% Fe, 3.6% SiO2, 1.1% A12O3, and 9.5% loss-on-ignition. For a special test of effect of particle size distribution on decrepitation, two other

Jan 1, 1967

By George Comstock

THESE notes should be considered as a further discussion of Mr. S. W. Miller's paper on "Some Structures in Steel Fusion Welds."1 In that paper and the resulting discussion; several conflicting opinions were expressed as to the identity of the needles or small crystals present in oxyacetylene and electric welds. An interesting specimen of an electric weld examined by the writer seems to afford new evidence regarding the needles, that may be worth presenting at this time. The specimen consisted of a piece of 3/8 -in. (9.5-mm.) steel plate, about 2 ¼ by 1 ¾ in. (5.7 by 4.5 cm.) in size, on which some iron had been deposited by arc-welding to a depth of about 3/16 in. (4.7 mm.). The weld appeared to be a very good one, with no noticeable break or boundary between the plate and the deposited iron. Sections for microscopic examination were cut in three planes at right angles to each other through the deposited metal, two of these sections also extending through the steel base. After polishing in the usual way, the microscope showed that the deposited metal was full of very small, round, gray, oxide spots, while the steel plate contained quite a number of alumina inclusions and a little slag. The sections were etched with nitric acid in ordinary alcohol, and structures similar to those described by Mr. Miller were then displayed. Fig. 1 shows the typical appearance of the deposited metal, which was quite uniform in all three of the planes examined. The round dark-gray spots are oxides, and the pale angular crystals are evidently what, Mr. Miller called cementite and Mr. Jeffries martensite, while Dr. Ruder and Prof. Boylston suggested that they might be nitride. The boundary between this structure and the steel base was sharply defined under the microscope. Fig. 2 shows the structure of the plate just under the weld; this is almost martensitic and resembles a coarse-grained casting. This coarse cast structure soon became finer as the distance from the weld increased, finally, becoming very fine, with numerous small particles of sorbite. This very fine structure, shown in Fig. 3, became coarser in turn and finally merged into the original normal structure of the steel plate, shown

Jan 1, 1919

By H. S. McKnight

One phase of Canada's rapid development in mining and metallurgy during the past few years has been the creation of Canadian Copper Refiners Ltd., and the establishment of its modern electrolytic copper refinery at Montreal East, Quebec. Canadian Copper Refiners Ltd. is made up of three well-known metal firms whose combined activities cover the entire industry from the mine to the market. They are Noranda Mines Ltd., Toronto, Nichols Copper Co., New York, and British Metal Corporation, Ltd., London. Noranda Mines is the principal owner and provides the greater part of the raw material received by the refinery for treatment. Nichols Copper Co. designed and built the plant and is operating it under contract. British Metal Corporation acts as sales agent and markets the refinery's products. Montreal East was chosen as the site of the new refinery only after a careful survey had been made of the entire eastern part of Canada. The location chosen offers many advantages, chief of which arc the relatively low costs of power, labor, fuel and bupplies, and the fact that it is situated on Montreal harbor, the nearest seaport to the points of origin of the ram materials. All incoming material is received by rail. A majority of the plant's product is exported through the port of Montreal to European markets, being handled to the docks in railroad cars. A large proportion of the product is delivered by means of an industrial railway to the adjacent rolling mill of the Canada Wire & Cable Co., Limited. The refinery was designed to treat primarily the copper produced by Noranda Mines, Ltd. and Hudson Bay Mining &. Smelting Co., Ltd., and its rated capacity is 75,000 short tons per year. A general layout of the plant is shown in Fig. 1. Its capacity can be readily doubled, as shown by the dotted lines. Figs. 2 and 3 are sections taken through the furnace department and the tank house respectively. Except for the main office and laboratory and an auxiliary building containing the stores, warehouse, change rooms, compressor room and machine shop, the entire plant is under one roof. The type of building construction consists of reinforced concrete foundations supported on concrete piles, a steel structure covered with Robertson Protected Metal siding and a 3-in.

Jan 1, 1934

By L. F. Mondolfo

An aluminum-copper 4 pct Cu alloy aged at room temperature for times increasing up to 78,000 hr was annealed at 170°C and the hardness and electrolytic potential determined during retrogression and subsequent aging. It was found that there is a change of behavior with increasing time of aging at room temperature which indicates that, given sufficient time, retrogression disappears and the room-temperature aging tends to progress directly into the high-temperature aging. WHEN an age-hardenable alloy is aged at low temperature after proper quench, changes of properties and structure take place. If this material is then heated to a temperature higher than the previous one, but still well below the solution-treatment temperature, the properties and structure changes produced by the low-temperature aging disappear and the material apparently reverts to the as-quenched condition, ready to undergo aging from the start. This phenomenon is termed reversion or retrogression. First discovered by Cayler3l it has been extensively investigated, as shown by the number of publications listed in the bibliography. From all the information available the following facts emerge: 1) All aeg hardenable alloys can be retrogressed.9 13, 19) 24, 33, 41, 42, 44, 47, 53, 54, 61, 63, 64, 66, 73, 78 2) All the properties changes that take place during aging at low temperature can be retrogressed to a smaller or larger extent.4,5,7,12,19,32,49,50,57,58,60,67,75,76 67, 75, 76 3) Retrogression requires that the temperature be well above the preliminary aging temperature. If the difference between the two temperatures is small, Little or no retrogression takes place.7,20,32,33,41,49 57. 65 4) The larger the difference between the preliminary aging and the retrogression temperature, the faster and more complete is the retrogression.20, 33, 41, 48, 65, 67 5) Retrogression can be produced several times in the same alloy.23, 35,41,57,59 6) The amount of retrogression that can be obtained depends on the aging temperature. Alloys aged at the lower temperatures can be retrogressed the most. The higher the preliminary aging temperature the less retrogression can be produced.20,25,33,37,44,49,54,58 7) Appreciable retrogression after aging at elevated temperatures is possible only if the preliminary aging has lasted a short time. After a certain time of aging at high temerature retrogression does not take place any more,:5,6,9,10,11,21,40,58 8) During retrogression the Guinier-Preston zones redissolve and disappear. The other precipitate

Jan 1, 1960

By C. N. J. Wagner, E. N. Aqua

Dilute Fe-Si alloys (0 to 5 wt pet Si) were cold-worked by making filings at room temperatuve. The analysis of the broadening of the X-vay powdev pattern peaks yields anisotropic particle sizes normal to the (110), (100), and (112) planes which are a consequence of deformation faults (probability a) and twin faults (probability p). The combined fault probability (1.5a +ß) increases from 0.01 in pure iron to 0.02 in Fe-5 pct Si. The root mean square stvains vary with crystallographic ovientation due to elastic anisotropy of the alloys, and increase from about 0.0035 in pure iron to 0.005 in Fe-5 pct Si measured in the [100] direction. Assuming that deformation and twin faults occur with equal probability, the X-ray data would imply that the stacking-fault energy does not change upon alloying. THE crystallographic aspects of the plastic deformation of dilute Fe-Si alloys has been studied many times since the observation of glide band structures by Barrett et a1.l These glide bands were much straighter than the wavy bands observed by Gough2 in unalloyed iron nearly 40 years ago. This difference in the morphology of the slip band structure has been verified many times, most recently by replication electron microscopy3 and dislocation etch-pitting methods.4,5 These observed differences in deformation behavior have been considered to result from the degree of cross slip that occurs in pure iron and in the Si-Fe alloys. The lowered tendency for cross slip would result from a lowering of the stacking-fault energy of iron by the silicon alloying addition. Experimental evidence for this lowered stacking-fault energy in the Si-Fe alloys, obtained with transmission electron microscopy, is the observation of dissociated dislocations in Fe-6 pct si6 and Fe-3 pct Si alloys,7 and the observation of sharply defined cellular substructures in Fe-3 pct si6,7 compared to the more diffuse substructure in zone-refined iron.' The activation energy for recovery of cold work is greater in the Si-Fe alloys than it is in pure iron, indicating that cross slip has become a more difficult process.9 The purpose of this investigation is to determine the change in stacking-fault probability from the broadening of powder pattern peaks in dilute silicon-in-iron solid solutions, when cold-worked at room temperature. The knowledge of the stacking-fault probability and the dislocation density, both of which can be deduced from line-broadening analysis of two orders of reflections from (110), (200), and (112) planes, will permit us to calculate the change in stacking-fault energy upon alloying silicon into iron. Previous X-ray investigation of cold-rolled Fe-5 wt pct Si (100)[001 ] single crystals did not reveal any line broadening, whereas cold-rolled Fe-3.1 wt pct Si (001) [110] and (001)[100] single crystals10 showed line bro2dening as a consequence of small particle sizes (-200A) and root mean square strains (-0.25 pct), which are comparable to those found in cold-worked iron filings.11 EXPERIMENTAL PROCEDURE A series of five Fe-Si alloys containing nominally 1 to 5 wt pct Si and pure iron were cold-worked by making filings at room temperature. The actual silicon content deviated at the most by +0.1 pct which is of no significance in the present study. The carbon contents of these materials were less than 0.02 pct. The X-ray diffraction patterns were measured with molybdenum, cobalt, and iron radiation using a GE and a Philips diffractometer. The (110)-(220), (200)-(400), and (112)-(224) pairs of reflections were

Jan 1, 1968

By D. M. Schuster, E. Scala

The elastic effects occurring in the matrix of a composite reinforced by discontinuous fibers were studied by means of photoelastic techniques. A hirefringent plastic was employed as the matrix material with high-strength a Al2O3 whiskers as the reinforcing fibers. It was found that for whiskers aligned parallel to the tensile load direction: (I) Matrix reinforcement occurred along the length of the whisker to within about 5 diameters of the whisker tip for a length to diameter ratio, L/D, of 40. (2) Significant stress concentrations were created in regions immediately surrounding the tips; the fine as-formed tapered ends exhibited the minimum stress concentration whereas the square-ended whisker produced relatively high values, K r 2.5 for L/D = 40. (3) The axial and radial stress distributions could he determined quantitatively; the stress distribution at the whisker-matrix interface was in general agreement with theoretical calculations. (4) The highest source of stress concentration occurred at points of fracture in whiskers which had ruptured after incorporation into the composite. Whiskers aligned perpendicular to the load direction neither reinforced nor caused appreciahle stress concentrations in the matrix. ThE properties of composites have generally been formulated empirically on the basis of macroscopic tests. There are still many questions concerning the mechanical and chemical interactions occurring at the interface between the reinforcing fiber and its matrix. Continuously reinforced plastics and dispersion-hardened metals represent the two extremes of composite reinforcement. Whether artificially produced or formed in situ, the whisker composite falls between these two extremes and is an example of discontinuous fiber reinforcement. The effect of fiber shape, size, surface condition, and end configuration on the stress distribution in the matrix is important since the presence of stress concentrations, especially in any high-strength, thin-wall structure, could become the cause of catastrophic failure. DOW,' in his theoretical discussion of discontinuous fiber reinforcement, has pointed out that appreciable stress concentrations occur at the tips or ends of the reinforcing fibers. It is the purpose of this study to examine directly, by means of the photoelastic technique, the stresses which occur in the vicinity of a discontinuity or whisker tip and to measure qualitatively and quantitatively the effects of whisker geometry when embedded in a birefringent matrix material. The use of sapphire (a A1,O3) whiskers was decided upon as the reinforcing agent because of their high elastic modulus (E- 60 X 106 psi) and in some cases strengths in excess of one and a half million psi. Sapphire whiskers are of further practical interest since they retain large fractions of their strength up to temperatures approaching the melting point (3720oF).2 The whiskers were grown, by the vapor-phase reaction commonly employed,3 as part of this study to insure a physically uniform supply. Tensile and bend tests were performed to verify that the whiskers were of the expected ultra-high strength. The high-strength whiskers can be identified and selected from the combustion boats by surface perfection, shape, and size; otherwise, strength values can vary by a factor of ten or more. Macroscopic defects are quite common on the surface of large bladed whiskers and the principal experiments were conducted with hexagonal whiskers of about 0.002 in. diameter and lengths ranging from 0.1 to 0.4 in. Upon completion of these two phases of the experiment, several birefringent resins were evaluated. A plastic, developed by Zandman,4 which is supplied by the Budd Co., was found most suitable and was used as the matrix material for the whisker composite throughout the study. It has a sensitivity of 60.5 lb per in. order, calibrated in tension and cures without introducing residual stresses. Young's modulus for this matrix material is 430,000 psi in the fully cured condition. Since good wetting and bonding between the sapphire and the matrix material is essential to the interpretation of the results, a wettability test was performed. The contact angle was measured to be 168 deg where perfect wetting is defined as 180 deg; therefore, the Budd Plastic wets the sapphire

Jan 1, 1964

By D. D. Pollock, D. I. Finch

PREVIOUS work' on a four-component system (Cu-Mn-Ni-Fe) resulted in the development of consistent relationships between the chemical composition and the electrical properties of these manganin-type alloys. The present study was undertaken to develop alloys with temperature coefficients of resistivity and thermoelectric properties more desirable than those of the manganin type, and to determine whether the relationships which had been found for the Cu-Mn-Ni-Fe alloys could be extended to five-and six-component alloy systems. PREPARATION OF ALLOYS The five- and six-component alloys were made from OFHC copper rod, ARMCO iron, electrolytic nickel, manganese cathode chip, and special high-purity aluminum and indium. A Cu-Mg master was used for deoxidation. The compositions of these materials are given in Table I. The alloys were melted and cast as indicated previously,' except that no cover was used and the melts were teemed. EXPERIMENTAL PROCEDURE The finished wire size of 0.0808 in. diam was again selected for the reason that the test specimens would be self-supporting, thus eliminating any extraneous effects which might have been introduced by winding smaller diameter wire on spools or forms. The following tests were performed on the finished wires: A) Chemical Analyses—All of the components of these alloys were determined by premium gravimetric methods. The principle residual impurity contained in these alloys is 0.008 pct Mg (by weight), maximum. Tables II and 111 present the mean analyses computed from at least four determinations of each constituent. B) Electrical Characteristics—The test procedures forthe determination of the thermal emf vs copper, resistivity, and the resistance-temperature relationship are given in detail in Ref. 1. It was also shown that the resistance-temperature relationship is of the form Pt = P,n + At -B/2, [1] where P, is the resistance at t C expressed in percent of a given standard resistance, P, is this per- 0 centage at 0°C, and A and B are constants for a given, properly treated, composition. The results of the electrical tests are also given in Tables II and 111. INTERPRETATION OF DATA The modified Linde2 formula, known to be valid for dilute binary solid solutions, was applied to the complex Cu-Mn-Ni-Fe type alloys. This relationship is of the form where Ap is the increase in resistivity. Zb the valence of the solute, Zn the valence of the solvent, and K and K are designations assigned by Robinson and Dorn3 to the constants for the periodic group to which solute element belongs. The units of K, are -cm per valence difference squared per at. pct; those of K2 are pa-cm per at. pct. For the sake of brevity, these units are not repeated in the following discussion. Calculations were made to determine if this formula was accurate for five-component systems. No experimental studies were made of the Cu-In and Cu-A1 binary systems. The effects of indium additions upon the resistivity of copper are given by Linde. These data, along with those of the effects of Mn and Fe, permitted the calculation of the effects of Al.

Jan 1, 1959

By C. Wert, G. Mah

A relaxation peak thought to be due to the presence of C-C pairs in cobalt has been observed. It exists both above 420"C, where cobalt has the fcc structure, and below 420"C, where cobalt has the hcp structure at equilibrium. The effect is thought, however, to be caused by motion of C-C pairs in the fcc phase in both instances; enough retained fcc phase was deduced to be present at temperatures below 420°C to make the phenomenon possible. Measurements of the aniso-tropy of the effect in single crystals of various orientations of fcc phase showed the effect to have a maximum value in longitudinal strain for a [loo] crystal and a minimum value for a [Ill] crystal. This observation seems to rule out the possibility of (110) nn pairs being responsible for the effect. From measurements of the strength of the relaxation in the alloys, we reach the conclusion that both the binding energy of the pairs and the specific relaxation per pair are smaller than corresponding quantities for interstitial pairs in bcc metals. DETERMINATION of the details of atom placement of small atoms such as carbon, nitrogen, oxygen, and hydrogen in metals has been a difficult problem. In certain alloys such as martensite extensive departure from random placement of the interstitials can be deduced from X-ray diffraction off the atoms of the host metal, but such diffraction techniques are of small help for small departures from randomness. A technique which does offer promise in the latter instance is the anelasticity of these interstitial alloys. Most previous investigations using this property have utilized alloys in which the solvent is one of the bcc metals, alloys such as These studies have been interpreted to show that an interaction exists between interstitials which causes them to form clusters in more than random numbers; the binding energy of interstitials in such clusters has been deduced to be about 0.1 ev per atom (for small clusters of size two to four atoms). Similar investigations have been carried out on close-packed solvent metals, Ni-C by and Diamond and Ag-O by Papazian.8- In both of these svstems. no relaxation of the singly dissolved interstitial is expected, so an-elastic behavior of the interstitials must be caused by their association in some cluster or complex of non-cubic symmetry. Since relaxations in these alloys were observed to have a strength which varied about as the square of the interstitial concentration, the effect was deduced to be caused predominately by motion of i-i pairs in the crystal. A striking difference is observed in relaxation strength of interstitial alloys between the bcc and fcc systems. The specific effect per interstitial atom is much larger for the alloys in the bcc crystals than for those in fcc crystals. Comparing clusters of size two in the Nb-O system4 and the Ni-C system,7 one finds the magnitude of the anelastic effect per interstitial atom in the former to be some 100 times greater than that in the latter. Such a difference in relaxation strength might be caused by a difference in concentration of the pairs (this means a higher binding energy in the bcc crystals). It might also be caused by a large difference in shape factor of the elastic strain field about the pairs between the two cases (a much more noncubic shape factor would be required for the bcc crystals). This investigation was undertaken to examine the possibility of C-C pair formation in alloys of cobalt and carbon using anelastic effects. Since cobalt has both fcc and hep phases, it seemed to offer the chance that measurements over a range of frequency might permit comparison of properties of pairs in the two crystal types. Although this goal was not reached, several significant facts were deduced from the observations. 1) An anelastic phenomenon believed to be associated with the presence of C-C pairs in cobalt exists. It has many features in common with that observed in nickel. 2) The effect is thought to be caused by pair motion in the fcc phase. 3) Calculations of the relaxation strength A, which includes as a parameter the product of the pair concentration, C, and the square of the shape factor ', show that this parameter is much smaller in the CO-C alloy system than in the interstitial alloys in the bcc systems. 4) From this finding, we reach the conclusion that both the binding energy of C-C pairs in cobalt and the specific relaxation strength per pair are small compared to corresponding values for such pairs in the bcc systems. 5) The crystalline anisotropy of the effect permits the identification of reasonable geometrical models of close C-C pairs. I) EXPERIMENTAL PROCEDURE A) Method of Measurement. The anelastic measurements-—all of which were constant frequency measurements of internal friction—were designed to study the expected phenomenon in both the hcp and fcc structures in cobalt. Knowledge of similar measurements in Ni-C alloys led us to believe that the damping peak should occur below the transformation temperature for frequencies near 1 cps and above for frequencies near 100 kcps. This surmise was correct. The low-frequency measurements were made on wire specimens using a vacuum torsion pendulum; the damping peak was found at about 2'70°C at a frequency of 1 cps. Because of large superimposed damping of magnetic origin at this temperature, a longitudinal magnetic field of about 1500 oe was applied to the

Jan 1, 1969

By F. Keller, R. H. Brown

BECAUSE of the extensive use of Alclad 24s alloy sheet in aircraft construction, there is much interest in the metallurgical changes caused by heat-treatment of this product.1,2 One of these changes is the result of the diffusion of soluble elements from the core into the coating during treatment. This paper deals with the thermal treatments that may influence diffusion and with the practical effects of diffusion on the serviceability of the product. As is well known, Alclad 24s-T sheet has a core of high-strength alloy combined with surface layers of relatively pure aluminum. The microstructure of a cross section of this product is shown by Fig. I. hot only does the relatively high-purity coating have a high resistance to corrosion, and hence serves as a mechanical barrier between the core metal and the corroding environment, but in addition this coating I exerts electrochemical protection over areas where the core may be exposed, such as cut edges. In addition, the coating affords electrochemical protection to projecting heads of *417S-T, 17S-T and 24S-T rivets, or attached members made from these alloys. Under some conditions of heat-treatment, however, diffusion of copper into the coating will alter the electrochemical relationship between the coating and the core to the extent that only partial protection will be obtained under some corrosive conditions. The reason for the electrochemical protection lies in the fact that the coating layers of pure aluminum are anodic to the alloy core. The addition of copper to aluminum produces alloys in which the potential is lower than that of the pure metal. Moreover, as the amount of copper in solid solution in z4S alloy is increased, the potential of the alloy becomes more cathodic. When heat-treated at 920°F. and quenched in cold water, 24s-T is about 0.16 volt cathodic to pure aluminum. However, copper will diffuse from the core into the coating, and if it reaches the surface the potential will be altered in a cathodic direction. Thus the potential dif-erence between the core and coating may be less than 0.16 volt, depending upon the thickness of the coating, and the time and temperature of heat-treatment. Of the methods available for determining the extent of diffusion of copper from the core into the coating of Alclad 24S-T, two are generally used; namely, the metallographic and the solution potential method.3 METALLOGRAPHIC METHODS Metallographic methods will reveal the progress of diffusion of copper into the coating. For instance, the diffusion zone in the coating intermediate between the coating surface and the core is shown in Fig. I. This photomicrograph is of a polished and etched cross section of 0.040-in. Alclad 24S-T sheet. Diffusion proceeds into the coating more rapidly along the grain boundaries than through the body of the grains. consequently, the diffusion zone is not of uniform width

Jan 1, 1944

By Oliver Bowles

Dimension stone is a term applied to stone sold in blocks or slabs of specified shapes and usually of specified sizes, contrasted with crushed, broken and pulverized stone covered in another chapter. Dimension stone includes cut stone, rough building stone, ashlar,* rubble, monumental stone, paving blocks, curbing, flagging, and many types of ornaments and novelties carved from stone. Riprap-large, irregular blocks used for shore protection-is classed with crushed and broken stone. Composition, Varieties, and Properties Dimension stones are of many kinds. The principal varieties are granites, trap rock (diabase, basalt, and gabbro), sandstone, limestone, and marble. Slate is covered in a separate chapter. Granite is a visibly granular crystalline rock consisting essentially of feldspar, quartz, and mica or hornblende. The basaltic rocks are darker in color than the granites. They contain little or no quartz and consist largely of plagioclase feldspar, augite, pyroxene, and hornblende. They are classed commercially as black granites. Limestone consists essentially of calcium carbonate. Dolomites and magnesian limestones used as dimension stone are classed with the high-calcium limestones. Marble is a crystalline form of limestone, but in the trade, any carbonate rock which will take a polish is called a marble. Many limestones which are fossiliferous but which will take a polish are sold as a decorative stone for lobbies of hotels and office buildings. Sandstone consists essentially of silica in the form of sand grains cemented into a coherent mass. Although rock occurrences are numerous and widespread, the exacting requirements of use condemn all but a small fraction of them for commercial use as dimension stone. No deposit that has closely spaced joints or planes of weakness can be used because sound blocks of moderate to large size are demanded. Uniform texture and grain size, constant and attractive colors or color pattern, and freedom from impurities that may cause stains or deterioration usually are demanded. Hardness is a variable property. Granites and diabases are as hard as or harder than steel, while limestones and marbles may be scratched with a knife. The hardness of sandstone depends upon the degree of cohesion of the grains. Workability depends to a considerable extent on hardness, but the degree of hardness has little influence on use except where stones are subjected to abrasion as on steps or floors. "Texture" as applied to stone relates to the arrangement, uniformity, and size of the constituent grains. Stones are of many colors and thus can satisfy a variety of tastes. For monumental stone, a marked contrast between polished and tooled surfaces is preferred in order that inscriptions may be read easily. Strength requirements usually may be disregarded because any sound structural stone suitable in other respects is almost invariably many times as strong as would be required for any ordinary use. The pressure on the base course of the Washington Monument, Washington, D. C., is less than 700 psi, and highgrade granites, limestones, sandstones, and marbles will sustain a crushing load of 10,000 to 25,000 psi. A structure made of stone with a crushing strength of 15,000 psi would have to be nearly 21h miles high before crushing of the lower courses would occur. However, stone disintegrates more readily under severe

Jan 1, 1960

By A. M. Gow

The trend in ball milling has been toward mills of larger diameter, but without fundamental laws as a guide. The speeds at which mills are run have been a matter of cut-and-try. This paper deals with both diameter and speed and proposes to show the laws which apply to some laboratory ball mills, ranging in diameter from 18 to 42 in., run at various speeds. The correlation of power, speed and grinding rate of the respective mills will be shown by curves of markedly significant similarity. Before presenting the results some consideration will be given to the mechanics of ball milling. Mechanics and Theory of Ball Milling As early as 1904, Herman Fischerl reported observations on specially constructed ball mills which allowed the paths of balls to be studied. The following conclusions were drawn: 1. Balls do not grind the ore, but crush it by impact. 2. At slow speeds the balls roll down the inclined heap, but at higher speeds the balls close to the wall adhere to it until they reach a certain height, whence they are thrown through an arc to the bottom. 3. The falling balls do not come down in clusters, but in series, the balls of each row keeping to their own line of flight according to their distances from the wall while ascending. 4. A further increase in speed results in the balls adhering during the whole of the circuit to the side of the drum. (This centrifuging speed may be called the "critical" speed and may be taken as a reference basis, since it is a constant function of the diameter.)2

Jan 1, 1930

By F. W. Warnaars

The Los Bronces copper deposit is located on the west side of the Andes Mountains in central Chile about 54 km (34 miles) northeast of Santiago. The deposit consists of a hydrothermal breccia complex that was emplaced in the western part of an earlier porphyry copper mineral system. This system exhibits propylitic, sericitic, silicic to potassic hydrothermal alteration with disseminated and stockwork copper-molybdenum sulfide mineralization over an area of about 12 km2 (5 sq. miles). The Rio Blanco Mine, about 800 m (0.5 miles) east of Los Bronces, is an underground block caving mine located in the central part of this system. The mineralization at Rio Blanco is characterized by one of the highest primary copper grades known for porphyry copper systems. Present mining at Los Bronces is from an open pit located in the northern part of a hydrothermal complex that is composed of at least seven different copper-bearing tourmaline breccia pipes. Together these pipe form one large contiguous body about 2 km (1.2 miles) long and 0.7 km (0.4 miles) wide at the surface. This body crops out at elevations of between 3.5 and 4.1 km (2 and 2.5 miles) above sea level. Each breccia pipe has a characteristic shape, matrix, type and degree of mineralization and alteration. Quartz, tourmaline, specularite, anhydrite, pyrite, chalcopyrite, sericite, chlorite, and rock flour are present in significant quantities in most breccia matrices. The clasts consist mainly of quartz monzonite, andesite, and minor amounts of quartz latite porphyry. The seven different breccia pipes are identified, from oldest to youngest, as Ghost, Central, Western, Infiernillo, Fine Gray, Anhydrite, and Donoso. The breccias coalesce, interfinger, or display gradational contacts. In places they form sharp contacts with each other and with the surrounding intrusive or volcanic host rocks. Early breccias are disrupted or cut by subsequent breccia events. Explosive emplacement was followed by collapse after the release of hydrothermal pressures. The Los Bronces breccia complex has sharp contacts with the surrounding intrusive stock and andesites. These contacts dip inward on the north, west, and south margins. The eastern contact is nearly vertical and/or dips slightly outward and suggests a westward tilting of the body of about 15° after emplacement. The breccia complex is not fully explored at depth, but is known to extend at least below the 3 km (2 mile) elevation in its central eastern part, about 1 km (0.6 miles) below the highest breccia outcrop. Primary copper sulfide minerals are most abundant in the Donoso and Infiernillo breccias where the matrix consists mostly of tourmaline, quartz, sulfides, specularite, and/or chlorite with minor amounts of rock flour, sericite, and clay. The volume of the matrix material is mostly smaller than in the other breccias. Secondary enrichment enhanced the primary copper grade in the southern two-thirds of the Los Bronces breccia complex and in much of the surrounding porphyry system. Primary grades of 0.3% to 0.5% copper have been enriched to approximately 0.9%. This enrichment may extend from surface outcrops to a depth of more than 500 m (1, 640 ft) in more permeable parts of the breccia complex. A leached and oxidized capping of variable thickness covers a large part of the enriched layer and exceeds 300 m (984 ft) at one location. The shape and depth of the enrichment blanket and the capping suggest that the enrichment process is still active.

Jan 1, 1983

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954'and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,' and Bond,' respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961

By J. A. Elias, A. J. Heckler

A simplified method is described for the prepauatior~ of comnposite samples for determination of one quadrant of an X-ray pole figure of a sheet material by the Schulz reflection method. Other special conzposite sampling methods were used to investigate specific areas of the pole figures. Plotting nets for these sampling plans were drawn by a computer. Step-scanning techniques were used to obtain detailed information about specific regions of a pole figure. Satisfactory pole figures were obtained for large-grained (0.5 to 1 in. diam) sheet materials. COMPOSITE sampling techniques for preparing one quadrant of an X-ray pole figure have been reported by a number of authors.'-5 All of these methods are similar in that they use a composite sample prepared by stacking and holding together coupons cut from a sheet material. The schulze reflection technique is applicable to the composite sample so that only minor corrections are needed for defocusing and absorption effects. Also, a relatively large area of a sheet is sampled through the use of multiple cross sectional pieces. In general, sampling methods necessary to obtain a composite-type specimen have been formidable enough to discourage their use in routine pole figure determinations. This paper presents a versatile sampling technique which is simpler than those previously described along with an accurate method for obtaining stereographic plotting nets for any orientation of a composite specimen surface. A step-scanning technique is used to obtain more quantitative determinations of specific regions in pole figures, and the composite technique is satisfactorily applied to determine pole figures of very large grained sheet materials. REVIEW OF PREVIOUS TECHNIQUES Mueller and ~nott' first proposed a technique for obtaining one complete quadrant of an X-ray pole figure by using a sheet sample and six different composite samples in which the individual coupons were aligned and held together by two types of jigs. Data from the seven different samples were overlapped to obtain a single quadrant. ~eieran~ and Lopata and ~ula~ obtained a complete quadrant of a pole figure from a single sample prepared by forming a cube from coupons cut from a sheet. These coupons were bonded together using an epoxy cement, and a cut was made at 54.7 deg to the normal, transverse, and rolling directions of the sheet, Fig. I. The normal direction of the cut face projects into one quadrant of a stereographic projection at equal angles to the three principal orthogonal reference directions mentioned above. X-ray reflection data obtained along a spiral path in physical space could then be plotted on a stereographic net offset 54.7 deg from the normal, as shown in Fig. 2. A rotation about an axis representing the surface normal is designated as a, and a rotation about an axis lying in the plane of the surface is 4. From Fig. 2 it is apparent that a tilting angle of no more than 55 deg @ is necessary to obtain the complete quadrant. ~eber~ devised an improved sampling technique by cutting coupons 45 deg to the rolling direction of a sheet, stacking and bonding these with an epoxy cement at an angle of 54.7 deg to a reference plane, and finally grinding and lapping a flat specimen surface parallel to this plane. An important consideration of this technique and that of Lopata and ~ula~ is variation in the diffracting power of the specimen surface due to the bonding medium. While any composite-type sample will have some such variation due to boundaries between coupons, the problem can be minimized by elimination of the bonding medium and by avoiding prolonged etching times which could lead to significant inter lame llar attack of the coupon faces. EXPERIMENTAL TECHNIQUE We were working concurrently though independently on a technique similar to ~eber's,' but which does not

Jan 1, 1968

By C. M. Wayman, R. Bullough

The selection rules fir twinning in fcc, bcc, and hcp lattices as established in Part I are used to predict the positions, relative to the matrix (untwinned) reciprocal lattice, of reflections due to double diffraction from the twins. These doubly diffracted reciprocal lattice points, which often coincide with ordinary matrix reciprocal lattice points, are deduced from kinematical considerations. 1. INTRODUCTION. A Bragg diffracted beam under certain conditions may be rediffracted to produce a third beam i .e., the incident beam, the first diffracted beam, and the rediffracted beam). In such a case an initial incident beam is diffracted by a set of planes; the diffracted beam may then be rediffracted by a second set of crystallographically different planes. The initially diffracted beam acts as an incident beam for the second set of planes, thus resulting in a twice-diffracted beam. This twice-diffracted beam may be regarded as a singly diffracted beam from a set of lattice planes whose structure factor is zero. In order to find the reciprocal lattice point corresponding to the doubly diffracted beam, it is customary1,2 to combine vectorially the component reciprocal lattice vectors which head to the extra reflections. For example, hcp metals may exhibit the forbidden (0001) reflections.* As Fig. 1 shows, the (0001) reciprocal lattice point results from: (1010) + (1011) = (0001) Similarly, combination of the beams (1011) and (1010) gives rise to: (1011)- (1010) = (0001) As Pashley and stowell2 have pointed out, even if in fact the double diffraction points lie on the Ewald sphere, they may not actually represent observed doubly diffracted beams because the initially diffracted primary beam, i.e., the source, must also correspond to a reciprocal lattice point which lies on the sphere of reflection; however, the reciprocal lattice point corresponding to the planes causing the rediffraction need not lie on the sphere. A little consideration of the Ewald construction in Fig. 2 makes this argument clear. In Fig. 2 the incident beam is represented by the wave vector ko. This beam is initially diffracted by the lattice planes (hkl) which are represented by the reciprocal lattice vector r(hk1) The reciprocal lattice point (hkl) of course lies on the Ewald sphere in order that the Bragg condition be satisfied. The initially diffracted beam is represented by the wave vector kl. If now kl is rediffracted by a second set of planes (h'k'l') resulting in k2 the lattice point (h"k"l") must lie on the Ewald sphere if the double diffracted beam k2 is to be observed. It is clear that (h"k"l") is the vector sum of (hkl) and (h'k'l'), and that (h'k'l') need not in fact lie on the Ewald sphere. In the usual1,2 analysis the origin (000) of the reciprocal lattice is shifted to the point (hkl). However the translation (000)— (hkl) automatically shifts the point (h'k'l') to the Ewald sphere, i.e., (h'k'l')— (h"k"1"). It is to be seen that (hkl), the source reflection, must lie on the Ewald sphere; if it does not the translation (000) — (hkl) places the "new" origin off the sphere, not satisfying the Ewald construction and hence the Bragg condition. The point (h"k"1") of course must lie on the sphere if it corresponds to an observed doubly diffracted beam. It is to be noted that crystals having the hcp structure, as just discussed, are intrinsically capable (i.e., without lattice defects such as twins) of double diffraction, as contrasted to fcc and bcc crystals which are extrinsically capable (requiring lattice defects or reoriented lattice regions). The "allowed" bcc reciprocal lattice points (which comprise an fcc lattice) are (110), (2001, (211), (220), (310), (2221, (321), (4001, and so forth. The combination

Jan 1, 1967