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By W. A. STERLING

IN the opencut iron mines of the Mesabi Range in Minnesota, the trend in mining is in the development of mining equipment and mining methods which will move surface overburden and ore-bearing materials with less labor and at a cheaper cost. This is a must for most of the independent operators. Their reserves of direct-shipping ore are extremely small and their operations are being conducted in small, or intermediate pits, with a high stripping ratio in the outer fringes, or shore lines of older pits. and in ore bodies passing from direct shipping to the washing and the intermediate, or retreat ore state. The trend is toward deeper stripping, longer and steeper hauls, and the necessity of moving a total of from three to five or six tons of overburden and ore material for each ton of shipping-grade ore produced. This naturally calls for greater production, with larger shovels, or draglines. cheaper drilling and blasting costs through the drilling of larger-diameter blastholes, and cheaper haulage through the use of trucks of larger capacity and more extensive use of belt-conveyor systems. This trend is notable both in stripping and mining.

Jan 1, 1948

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7

Jan 1, 1923

By AIME AIME

IF the observation of our British friends is true that Americans put new records in bigness above everything else then the 150th meeting of the Institute was not the grand success it seemed to be. Just why the attendance slumped a little this year is anyone's guess, but the favourite explanation seemed to be that half the country is planning to come to the New York World's Fair this summer and that two trips from the hinterland to the me- tropolis, with another to San Francisco of course, can hardly be justified with the present condition of the stock market and the prices of the products of our mines. Certainly, some were pre- vented from coming too by the epidemic of respiratory afflictions that was rampant in February. Unfortunately. several succumbed after they had reached New York.

Jan 1, 1939

By T. Lane Carter

BEFORE describing the experience with the Chinese on the Rand and the work they have accomplished, it will be necessary, sary, first, to give a brief account of labor-conditions in the Transvaal since the war, and then to show how the necessity of importation of labor arose. As is well known, the Transvaal mines are run on the dual system of labor-that is, the rough work is done by colored laborers under the superintendence of white men. From the start of mining operations in South Africa there has been the cry of shortness of native labor, due in great measure to the failure of Kaffirs to work continuously in the mines. While he works, the Kaffir is a satisfactory laborer, but his period of service is short, averaging about nine months. People unacquainted with the Kaffir have maintained that, by offering a higher wage and better accommodation, better results would be obtained from the native workers, but an increased wage simply aggravates the trouble. The Kaffir's wants are few. While at work he spends little of his money, and before long has sufficient capital with which to buy wives and become a gentleman of leisure. Doubling the wage of the Kaffir means that he acquires a competency in half the time, so that his period of service is correspondingly reduced. In 1899, before the war, there was always a cry about the scarcity of Kaffir labor. The highest number of natives at work was in July and August, 1899, when nearly 100,000 were employed. At the outbreak of hostilities the Kaffirs were scattered far and near, many doing well during the war by working for the military authorities. On the, resumption of mining operations on the Rand a serious mistake was made. Based on past experience, it was argued that if the whole industry decided to start anew with

Sep 1, 1908

By J. M. Roberts, D. M. Barnett

The activation energy required to break a pinned dislocation line away from its condensed atmosphere of impurity atoms is calculated as a .function of applied stress, without neglecting line tension. Reasows are presented for not assuming the effect of line tension to be negligible when considering the problem of freeing a small segment of dislocation from an impurity atmosphere. The dislocation is considered to he pinned at each atomic size along its length and the pinning points are assumzed immobile. The development is a refinement of the origznal cottrell-bilby1 theory. The solution is compared to recent approximations developed by cottrell3 and Haasen5 in which line tension con- IN 1949 Cottrell and bilby1 considered the problem of determining the force required to pull a dislocation away from its condensed atmosphere of impurity atoms. They also examined the effect of thermal fluctuations on this force. The dislocation line was pictured as bowing out in a triangular loop under the action of an applied stress, and the activation energy necessary to free the dislocation from its atmosphere was calculated as a function of stress, line energy, and dislocation-solute atom interaction. siderations were neglected. A qualitative explanation of the yielding process in terms of the activation of Frank-Read sources is presented, but the lack of a realistic solution to the dynamic dislocation problem involved prevents an extension of the model at present. A self-consistent correlation between the present calculations and experimental data for delay time associated with yielding and the temperature dependence of the upper yield stress was made. Favorable agreement was noted. It is concluded that extension of the original Cottrell-~ilby' theory which includes line tension effects can just as well describe the yielding process as other approximations3,5 which neglect line tension. Cottrell and Bilby found the form of the activation energy vs stress curves to be almost independent of the line energy and the interaction energy (i.e., these parameters only affected the activation energy U by a scale factor). A check of the theory was accomplished by comparison with the experimental data of McAdam and Mebs2 for the lower yield stress as a function of temperature. cottrell,3 in 1957, attempted to obtain a simple closed-form solution for the activation energy as a function of stress by linearizing the quartic equation relating displacement of the dislocation line and applied stress. It was argued that since the contribution to the line energy/atomic plane of a dislocation is made by the long-range stress field of the dislocation through a term of the type (Gb3/2p)ln A/ro, where

Jan 1, 1963

By J. E. Johnson

(Cleveland Meeting, October, 11,1912.) THE subject of blast-furnace slag is one which has had much consideration, particularly from the scientific standpoint, and several years ago technical literature contained many learned discussions on the oxygen-ratio of the acids and the bases, all on the assumption that acids and bases must be present in a ratio depending on molecular weight and chemical valency. Much work has also been done, sometimes in conjunction with the former, on the total heat and the temperature of initial fusion or softening of various slags. A wider knowledge of the blast-furnace now enables us to say that for practical purposes this work has been of almost no value. It is now generally admitted that on the physical side the important point of a given slag is neither its total heat of fusion nor its softening-point, but its free-running temperature, since this is the critical temperature of the furnace. This temperature bears no definite relation to the softening-temperature, as determined by Seger cones, for instance, because some slags melt relatively like ice, with a very short viscous-range, while others melt relatively like tar, with a very long viscous-range. In one the difference between the softening- and the free-running temperature may be very small, as little as 100° F., while in another this difference may easily be 200° or 300°. The importance of this difference is so great in practice as to destroy completely the value of exhaustive investigations, even such as those of 0. Boudouard, published a few years ago.1 * Presented also at the Joint Meeting of the Institute with Section IIIa, Metallurgy and Mining, of the Eighth International Congress of Applied Chemistry, New York, September, 1912. 1 It may not be amiss at this point to call attention to the excellent suggestion of Woolsey McA. Johnson, made several years ago, for determining the temperature at which different slags have the same practical fusibility. This suggestion

Oct 1, 1912

By Saluja, Sunder S.

Man had to learn to break rocks as early as the Stone Age, when they formed his main source of raw material. He started with chipping and over the years has reached a stage where he can employ atomic blasts and break, with one blast, millions of tons of rock. In between these two extremes there have been several stages of development including fire setting, use of the expansion of water on freezing in chipped cracks in cold climates, the use of low or deflagrating explosive black powder in about the 17th century, the use of high explosives with the discovery of nitroglycerine in 1846 by Sobrero, followed by the monumental discoveries of the great Swedish scientist Alfred Nobel in the latter half of the nineteenth century.

Jan 1, 1968

By J. R. Linney

A HISTORY of the ore-mining and iron-smelting industry of the Adirondacks comprises a century and a half of pioneering by rugged individualists, both men and women. By geographical location, the climate is most severe-long, cold winters with heavy snowfall, and short seasons of vegetation growth; this, together with its remote location from large centers of population, adds considerably to the difficulties of conducting mining operations in this area.

Jan 1, 1943

By Serge L. Delinois

President Kennedy said that before 1970 this country will send a man to the Moon and get him back on Earth safely. Today, no one doubts that his promise will become reality. He who asks "What, then, is next for us in space?" is no longer considered a dreamer. And one of the very first things he discovers in trying to answer this question is that in whatever does come next, geologists and mining engineers will play a prominent role. This will be true not only in the conquest of the Moon, but also in that of the whole solar system. After 1970, it is very likely that a permanent lunar camp will be established. This beachhead, supplied entirely from Earth, in the beginning, will gradually develop into a research complex where virtually all scientific disciplines are investigated.

Jan 1, 1966

DISCUSSION, G. Derge and D. J. Girardi presiding N. A. Gokcen (Michigan College of Mining and Technology, Houghton, Mich.)—While the authors present very interesting results on the effect of sulphur upon the solubility of oxygen, they have not established convincingly the lines of two-fold saturation (the valleys in Fig. 2) and the ternary eutectic point. Their contention that sample S-7, upon melting at

Jan 1, 1954

By A. Boltax

H. Herman and M. E. Fine (Northzcesteriz University)—The author is to be complimented on the quality and completeness of his work. Of special interest to us was the exponent of time in the exponential rate equation, n = 0.28 ± 0.03, since it is consistent with results for the early stage of quench-aging in A1-2 at. pct Cu, n = 1/3, first determined in this laboratory."' In that work we attributed the early kinetics to attraction of vacancy - solute atom complexes to the plate-shaped zone due to the strain field about the zone and the lowering in free energy. To our knowledge, Hirano et 1.' were the first to

Jan 1, 1962

By J. B. STEWART

T HE position of each hole of any series of holes was carefully located by the surveyor, plotted in plan and elevation, and numbers assigned to them. The second series was staggered halfway between the first and so on for each succeeding series. Two and a, half to three months was frequently required to grout a series of holes calculated to insure safety for sinking a distance of 10 meters or say 33 ft. Naturally the initial operation called for drilling and grouting two series of holes but thereafter each sinking campaign required only one series of holes as shown in Fig. 8. The pump handling about 75 gal. per minute corresponds to 46 tons of grout or 6 tons cement delivered as a fair over-all average for the 24 hours. Thus 600 to 800 tons of cement was used for a single section of 33 ft. depth of shaft. One campaign used nearly 1100 tons of cement. Some holes were effectually sealed with as low as 30 tons, while many required 60, and some 80 to 90 tons.

Jan 1, 1926

By Jay R. Burns

TWO magnesium sand-casting alloys are commonly favored in the United States. These are referred to as H and C alloys (Dow Chemical Co.) or 4Mz65 and AM260 alloys (American Magnesium Corporation). Both are of an aluminum-zinc-manganese type. H alloy contains 6 per cent aluminum and 3 per cent zinc and is characterized by relatively good toughness. C alloy contains 9 per cent aluminum and 2 per cent zinc and is employed where high yield strength and pressure tightness are required. Examination of magnesium castings poured in Europe and England,'J however, demonstrates that H and C alloys are replaced by .%8 and AZ~I, respectively. That is, A8 reprcsents a magnesiurn alloy having superior toughness while A291 is suitable for high yield strength and pressure-tight applications. The basic difference between the .Ameri-can and European alloys is that the foreign alloys employ a somewhat higher aluminum content and less zinc than is found in H and C alloys. The mechanical properties of the alloys, when divided into high and low-aluminum groups, are quite similar, as determined from separately cast foundry-control type test bars ,In this paper the decrease of mechanical properties caused by any given amount of microporosity is measured for H, C, A8, and AZ~I alloys. The relative susceptibility of each of the four alloys to microporosity is also determined. Typical mechanical properties and nominal chemical analyses are reported in Table I. The apparent similarities between the two alloys in each group have led to considerable discussion as to the relative merits of each of the compositions.2 Popular points for comparison between the alloys have been the relative susceptibility of each of the four alloys to microporosity6 and the effect of this microporosity on their mechanical properties. It is primarily intended, in this paper, to show the

Jan 1, 1946

By Jay R. Burns

TWO magnesium sand-casting alloys are commonly favored in the United States. These are referred to as H and C alloys (Dow Chemical Co.) or 4Mz65 and AM260 alloys (American Magnesium Corporation). Both are of an aluminum-zinc-manganese type. H alloy contains 6 per cent aluminum and 3 per cent zinc and is characterized by relatively good toughness. C alloy contains 9 per cent aluminum and 2 per cent zinc and is employed where high yield strength and pressure tightness are required. Examination of magnesium castings poured in Europe and England,'J however, demonstrates that H and C alloys are replaced by .%8 and AZ~I, respectively. That is, A8 reprcsents a magnesiurn alloy having superior toughness while A291 is suitable for high yield strength and pressure-tight applications. The basic difference between the .Ameri-can and European alloys is that the foreign alloys employ a somewhat higher aluminum content and less zinc than is found in H and C alloys. The mechanical properties of the alloys, when divided into high and low-aluminum groups, are quite similar, as determined from separately cast foundry-control type test bars ,In this paper the decrease of mechanical properties caused by any given amount of microporosity is measured for H, C, A8, and AZ~I alloys. The relative susceptibility of each of the four alloys to microporosity is also determined. Typical mechanical properties and nominal chemical analyses are reported in Table I. The apparent similarities between the two alloys in each group have led to considerable discussion as to the relative merits of each of the compositions.2 Popular points for comparison between the alloys have been the relative susceptibility of each of the four alloys to microporosity6 and the effect of this microporosity on their mechanical properties. It is primarily intended, in this paper, to show the

Jan 1, 1946

By W. H. Adams

One of the most attractive subjects for technical writers is the gigantic industry of the manufacture of sulphuric acid. This is no doubt, natural when we take into account that it has grown in this country during the past twenty years, from a production of 60,000 tons in the year 1867, to that of nearly 450,000 tons in 1887. We may well excuse much of the literature which but repeats the same old story, as it serves to bring to the public notice, at proper intervals, the hidden resources of our land; and this constant application of essential truths will sooner or later be the means of freeing us from dependence upon the Old World for necessary chemical products. The present increase in manufacture of this acid in the United States is almost wholly from pyrites ores, which we have in unlimited quantities close at hand. The largest consumption of such acid is for treatment of other native products, petroleum, rock-phosphates, etc.; and, considering the knowledge we have gained during the past twenty years, it is safe to say that the industry is but fairly established, and the causes which have operated to place us in our present proud position are but natural incentives for a further growth and an increased consumption of the many other undiscovered or undeveloped resources of our American soi1. In one of his earlier editions Muspratt says: " It would seem that the manufacture of sulphuric acid, though as extensively carried on as any other business, yet seems to be the least understood; and the ignorance of some manufacturers appears to be only equalled by that of writers, who, in their description of the production of this acid, give figures of apparatus, and vaunt as improvements, things which have been exploded for years. It is possible to find in the works of eminent men drawings of apparatus, for the production of sulphuric acid, which never could possibly have worked one day—some, in fact, could never have worked at all."

Jan 1, 1888

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers'-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded' that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-' and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By R. W. Smith, R. W. Lai

Very recently there has been a quickening of research effort in the field of silicate mineral flotation, particularly as regards the flotation of beryl.' These studies have already contributed much to the understanding of both anionic and cat-ionic flotation of silicates. Of particular interest concerning anionic flotation has been the work done on heavy metal activation of silicates by M. C. Fuerstenau and co-workers.4,7 In addition. in the paper by Fuerstenau, Rice, Somasundaran and Fuerstenau7 attention was paid to low pH anionic flotation of beryl in the absence of activators. This subject was also covered in the papers by Avotins,3

Jan 1, 1967

By Donald E. Grimes

In conjunction with Inland Steel&apos;s development of lead-bearing steels possessing improved machin-ability because of tellurium and/or selenium additions, it was decided to determine liquidus and solidus temperatures in the Pb-PbTe-PbSe sub-ternary system. With the exception of alloys in the PbTe-PbSe system, it is believed that no previous study of this subternary has been performed. Thermal analysis was employed in a general survey of the subternary. In addition to PbTe, PbSe, and pure lead, ten ternary compositions were selected at intervals of ten at. pct. Sixty-gram alloys were prepared by sealing an appropriate mixture of the elements in quartz crucibles with a central thermocouple-well under a vacuum of less than 10 p. All three elements were 99.999+ pct pure with only trace impurities detected by spectroscopic examination. After the alloys had been heated at least 20°C above the liquidus in a Kanthal furnace, cooling and heating curves were obtained. Two or more cooling curves were employed both for the determination of each alloy liquidus and for the solidus of those al- loys containing greater than 50 at. pct Pb. Cooling rates were 0.5° to 3.5°C per min during the 5 min immediately prior to the start or end of solidification. For those ternary alloys containing 50 at. pct Pb, the solidus was determined from heating curves. Temperatures were measured with a Pt/Pt-10 pct Rh thermocouple which was calibrated in the same apparatus against the freezing points of zinc (A. D. MacKay—99.999 pct), antimony (A. D. MacKay-99.999 pct), and copper (ASARCO—99.999+ pct) both before and after the experimentation. The only interruptions in the continuous strip-chart recording of the temperature occurred for brief periods at significant points of interest when direct readings were made with a Rubicon Type B potentiometer sensitive to * 1 µv. The average liquidus and solidus temperatures obtained in this investigation are listed in Table I together with probable errors based on the accuracy of the thermocouple calibration and the reproduci-bility of the data. No chemical analyses of the alloys were performed because the synthetic or as-charged compositions were felt to be reliable. The melting points obtained for PbTe (924.7° ± 0.7°C) and PbSe (1084.0° ± 0.6°C) compare favorably with recent findings of other investigators.&apos;-&apos; As indicated in Table I, both the liquidus and solidus temperatures increase as selenium replaces tellurium for a constant atomic percent lead. As a result, the ternary liquidus and solidus temperatures for a given percent lead lie between the corresponding binary temperatures published in the literature. It should be noted that those ternary alloys containing 50 at. pct Pb exhibit a relatively narrow liquid-plus-solid region (<80°C) when compared with alloys containing greater than 50 at. pct Pb. Alloys with 60, 70, or 80 at. pct Pb not only have a much wider liquid-plus-solid region (>500°C) but also exhibit considerably lower and approximately constant solidus temperatures which thus form a virtually isothermal solidus "plane" slightly below the melting point of pure lead (327.3°C). For these alloys

Jan 1, 1965

By R. W. Mancantelli, J. R. Woodward

IN 1947 a large low grade deposit of uranium was located in the northwest corner of Saskatchewan, in the Beaverlodge property of Eldorado Mining & Refining Ltd. Most of the values occur as thin seams and as coatings on other minerals, and the ore, which is light and friable, is not amenable to the usual gravity methods of concentration. The acid leaching process developed to retreat the company&apos;s Port Radium tailings was also impractical, as the percentage of carbonates is high and the percentage of sulphides relatively low. Construction of the mill building and installation of equipment, both scheduled for 1952, awaited selection of a satisfactory ore dressing process on or before Oct. 1, 1951. An extensive research program on dressing of ores from the Ace mine therefore was undertaken by the Mines Branch in Ottawa, a research team at the University of British Columbia, and an ore dressing group at the company&apos;s Port Hope refinery. Pilot plant operations were conducted at the Ottawa plant of Sherritt Gordon Mines Ltd. under the general direction of C. S. Parsons, consultant on metallurgy and ore dressing for Eldorado. In mid-September, having compared results of the several research programs, Dr. Parsons recommended a process employing a carbonate or basic leach. He reported that, while the chemistry of the process had been proved, engineering of the flowsheet was incomplete, and he suggested that under normal conditions further pilot plant work at the Ace mine might be profitable. However, since this would involve a delay of 12 to 18 months in bringing the property into operation, he recommended that design of the concentrator proceed immediately. Concentrator capacity was determined by two considerations: 1) the amount of ore then available and 2) the expectation that continued improvements would be made in the ore dressing process as a result of the intensive research being carried out by the Mines Branch of the Department of Mines and Technical Surveys. As these improvements could affect both the chemistry and the en-

Jan 1, 1956

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&apos;k&apos;l&apos;) 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&apos;k&apos;l&apos;), and that (h&apos;k&apos;l&apos;) 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&apos;k&apos;l&apos;) to the Ewald sphere, i.e., (h&apos;k&apos;l&apos;)— (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