Search Documents

By U. N. Bhrany, N. Arbiter

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and

Jan 1, 1961

By Paul M. Tyler

THE winning of metals from Nature has been advanced to a degree of efficiency that commands admiration even in this Machine Age. Economy of human effort underground, in surface plants, and in treatment works, and better means of performing all manner of operations have cut costs and im¬proved products to an extent that seems far beyond the wildest imagin¬ings of those that labored in the days of hand mining and muscular metallurgy. Principles and methods borrowed from other professions and sciences - mechanical engineering, chemistry, and physics-all have con¬tributed to the rapid development of ore production and treatment, but no small part of the achievements must be credited to the free exchange of ideas within the industry itself and mass attack upon problems of mutual concern. The esprit de corps or class consciousness that has contributed so effectively to the progress of the metal industries has been less apparent among nonmetallic mineral producers. As a class they have been handicapped by inadequate contact with the metal-mining fraternity as well as among themselves.

Jan 1, 1935

By William D. Southard, Joseph W. Schlitt, Bruce P. Ream, Lawrence J. Haug

The operation of Kennecott 's Bingham Canyon copper precipitation plant, one of the world's largest, is described. This description includes a brief historical review of precipitation at Bingham and the general layout and operation of the present cone cementation facility. Current practices are based on results of studies undertaken to define improvements needed in each unit operation. These improvements were required to meet changing plant conditions and were implemented primarily within the constraints of the existing facilities. Specific unit operations included were the cone precipitators, the cone discharge thickener, the cone effluent settling basins, and the plate and frame filter presses. As a result of these improvements, loss of precipitated copper decreased and the degree of precipitation increased, raising copper recovery by 9 t/d. At the same time, iron consumption was reduced by 22.5 t/d. Problems in drying the cement copper were also overcome so that a product containing 12-15% moisture could be consistently delivered for smelting.

Jan 1, 1980

By Walter E. Hopper

(Wilkes-Barre Meeting, June, 1911.) I. LOCATION AND EXTENT. THE Caddo oil-field, shown in Fig. 1, is located in Caddo parish, northwestern Louisiana. The known producing territory of oil is covered by townships 19 N, 20 N, 21 N, 22 N, and ranges 15 and 16 W., shown in Fig. 2. The center of the field may be taken as Oil City, 24 miles north of Shreveport, on the Kansas City Southern railway. Shreveport is the second largest city in the State, and is the connecting point of five rail-road-lines. Drilling at the present time, however, is going on all over northern Louisiana, especially in Caddo and the neighboring parishes. II. HISTORY AND DEVELOPMENT. Natural gas escaping at the surface is found at numerous places in northwestern Louisiana. At Shreveport, the plant of the Shreveport Ice & Refrigerating Co. has been lighted by natural gas for 20 years. The well was drilled for water, but was abandoned on account of the gas. A test well, put down in 1905 near the western limits of Shreveport, was driven to 1,650 ft., and encountered indications of gas and oil at various depths, but did not succeed in finding enough to be profitable. Attention was first attracted to the Caddo field in 1895 by indications in water-wells from 40 to 60 ft. deep, in which the pressure of natural gas was noticeable. This indication of gas in a shallow well led to the drilling of the first well in the Caddo field, the old Savage Brothers & Morricell, or the Caddo Lake Oil and Pipe Line No. 1. The rig for this well was erected in May, 1904, and drilling began in June, 1904. The well was bailed Mar. 23, 1905, with a small amount of oil. It was deepened July, 1905, and converted into a "gasser " Jan. 3, 1906. It was abandoned January, 1907. In consequence of the finding of oil in the Savage well, drilling-operations were pushed with energy; and in April, 1905, four wells were drilling. Great trouble was experienced with

Apr 1, 1911

Willet G. Miller, Toronto, Canada (communication to the Secretary): In his interesting paper Mr. Lindgren says: " As to ultimate results, it would seem as if we should be justified in concluding, with Prof. Suess, that the gold-supply of the world will gradually decrease if no further important improvements are made in the processes for the extraction of this metal; but regarding events so far distant no predictions may safely be made." It seems to the writer that no very important improvements require to be made in order at least to keep up the present production for many years to come. In many parts of the world there are large deposits of auriferous material which can be worked if present conditions are slightly changed. In the territory occupied by the Archean protaxis of the Province of

Jan 1, 1903

By E. J. KENNEDY

FEBRUARY 15-18 will be the outstanding dates of the month for members of the A. I. M. E., for then the 141st Meeting of the Institute is to be held in the Engineering Societies Building, at New York. What with 41 technical sessions, the Annual Business Meeting at 4 o'clock Tuesday afternoon,, two sessions of the Section and Division delegates, minor committee meetings, and the many luncheons and dinners, the Dinner-Smoker, Informal Dance, President's Reception and the Dinner-Dance, the opportunity will be limited to do- more-than cast sheep's eyes at New York's other multitudinous attrac¬tions until the meeting is over. The technical program is diverse but well organized. The sessions are almost equally divided among the four days, with ten on Monday, Tuesday, and Wednesday, and 11 on Thursday. The meeting opens Monday morning with registration. Be sure to attend to this detail. Failure to do so may have its repercussions at the meeting and throughout the year.

Jan 1, 1932

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963

By M. D. Curran

AS applied to coal, the term processing is subject to many interpretations. To some it means preparation of coal for the market by mechanical means such as crushing, sizing, washing, or treating with oil or chemicals to eliminate dust or improve combustion quality. To others it means conversion of the coal to other commodities as in carbonization to produce coke and by- products, or to liquids by application of the hydrogenation process. I prefer to classify the various forms of mechanical treatment under the heading of beneficiation and apply the term processing to those methods of treatment that destroy the coal sub- stance through distillation or hydrogenation.

Jan 1, 1939

Secretary's Note.—M. Beutter's introductory remarks, being simply a resume of Prof. Hone's paper, with a disclaimer of the intention to criticise it, have been omitted, and the remainder of this contribution lias been somewhat condensed, without omitting any essential statements. M. Beutter, St. Etienne, France* (communication to the Secretary†):—Professor Home observes in $ 47 of his paper that the fluid-compression of steel diminishes piping by forcing the liquid and viscous metal, while the pipe is forming, or after it has formed, into the space so produced, and proceeds to study the different systems of compression, alluding to the four principal ones: Whitworth, Illingmorth, Williams, and Harmet. Having now for many years had in use the last-named process, that of M. Henri Harmet, I shall attempt to explain the difference between it and the three other processes named. The Harmet process does not diminish or close the pipe after it has formed, but prevents it from forming; and I may add that it is the only one of the four which produces this result. It is true that the Whitworth process diminishes the interior hollow by localizing it around the central axis of the ingot, which is afterwards removed by trepanning the hollow forg-ings for which this process has been, I believe, always exclusively used. The Illingworth and Williams processes, which, in my opinion, are applicable only to small ingots, of necessity allow the pipe to form, or (to use the expression of Professor Howe) they allow the surface of the lake of liquid steel to sink into the interior of the ingot, since they involve waiting a certain time before compression, so that (in the case of the Williams process) the ingot-mold can be opened without danger, or (in the case of the Illingworth process) so as to avoid the risk that the steel may enter the grooves produced by the removal of the distance-bars. During the time required for

Jan 1, 1908

By John W. Buch

IN my review a year ago I pointed out that a small coal-mining companies as well as large had decided that the so called ?central shop? was a benefit. These central shops replaced in a large measure the commercial shops operated by those who have no direct connection with production of cod. Central shops in this time of salvage and major repairs have proved their worth. In addition, many of the larger companies had in their central shops equipment available for the production of many thousands of parts for our vast war machine and, as subcontractors, are doing this type of work. This is a real contribution to the war endeavor. Lack of new supplies has resulted in exhaustion of those stocks formerly stored or hidden in underground shanties. This means that the small stock of repair parts likely LO be available to any mine

Jan 1, 1943

By A. D. Schwope, L. R. Jackson, K. F. Smith

Burghoff and Blank1 have pointed out that the creep properties of hard-drawn coppers are closely associated with their individual softening characteristics and have further shown that the creep resistance of various types of copper is improved, under certain circumstances, by cold stretching. In the design of certain types of electrical machinery, it is important to have the creep resistance as high as possible; furthermore, short-time creep strength is important since in many cases stresses are large only during warming-up and cooling-down periods. In this paper, data are presented showing the effect of cold work on the short time creep strengths of various types of commercial copper under several conditions. It is shown that trends from short-time creep tests are evident at longer times. Materials Used in the Investigation The coppers used in this investigation were commercial grade and of two basic types, oxygen free high conductivity (OFHC) and tough pitch. Additions of silver in amounts of 15 and 25 oz per ton were added to each of the two coppers. The analyses of these six coppers are given in Table 1. Originally, they started as wire bars 4 X 4 X 54 in. A. square rod was made by hot rolling the wire bars to 9/16-in. rod in 8 passes. This rod was then cold drawn to 0.445-in.-diam rod and annealed for 3 1/2 hr at 1000°F. It was then cold drawn to 0.325-in. rod and again annealed at 1000°F for 3 1/2 hr. Hard square rods were then made by cold rolling to 0.257 X 0.257-in. rod. Soft wire was made from the hard- drawn material by annealing at 650°F for 3 hr. The final rolling was performed using a set of 9-in. grooved rolls revolving at 30 rpm, which produced square wires. Reductions of approximately 5, 20, 30, and 40 pct were obtained using several passes in the same direction for the large reductions. The 5 pct reduction by drawing was accomplished using a steel die having 2 parallel bearing surfaces. The die angle was 7 1/2 degrees and the wires were lubricated with a paste of ceresin wax dissolved in carbon tetrachloride. The speed of drawing was 13 fpm. Since work was done on only two sides of the wire simultaneously, it was necessary to rotate it 90 degrees each pass to insure uniform deformation. The room-temperature tensile properties of the various tempers are given in Table 2. The grain size of the an- nealed 0.257-in. wires was uniform and averaged about 0.035-0.045 mm. Experimental Procedures for Short-time Creep Tests Standard creep-test frames (Fig 1) were used for the testing. Special fixtures were designed to apply axial compressive and tensile loads to the copper wires. The compression specimens were 1 in. long and the ends were ground flat and parallel. The creep in compression was indicated by the movement of reference marks s-ratched on intersliding platinum strips attached to the moving heads of the fixture. The movement was measured with an optical micrometer fitted with a filar eyepiece on which the smallest division was 0.00005 in. The tensile creep specirriens were 4 in. long which provided ample gripping surface for the jaw-type grips. The platinum strips were attached to a one-inch gauge length of the wire and the creep measured as previously described. The single-specimen furnaces were connected to individual power and control sources. The controlling equipment consisted of Foxboro controllers

Jan 1, 1950

By Arthur Notman

THE raw material men in all industries, and copper is no exception, are accustomed to think of them- selves as the whole show, and not without justice, for if there were no copper mines the world would have no copper. Nevertheless, many different things costing money and resulting in profits must be done to their product before it is ready for the world's use. In other words, they are making the frequent mistake of Chinking in terms of partial costs. Nobody really uses electrolytic copper. Possibly that is why nobody seems willing to pay anything for it. The manufacturers, being canny, do not buy any more electrolytic than they feel that they can work up and sell profitably, although they like to make the raw material men Chink that they will take all that can be produced. This is a state of affairs that has aroused my sympathy and curiosity, and has induced me to study the financial history of the copper wire and brass industry of the country or such portion of it as publishes any records readily available to the curious minded. About 60 per cent of the electrolytic copper used in this country is drawn into wire and consumed by the electrical industries. The remaining 40 per cent is

Jan 1, 1926

By James H. Bechtold

The yield strength of annealed tungsten was found to have a strain rate exponent 12 times as great as that of low carbon steel. The effects of temperature and strain rate could be correlated through the Zener-Hollomon parameter with a heat of activation associated with yielding of 32,000 cal per g-atom. This heat of activation is independent of strain although both the temperature and strain rate dependence of the yield strength vary with strain. MOST metals have mechanical properties that are relatively insensitive to strain rate, especially at temperatures below that at which creep is important. In iron and molybdenum," however, relatively large strain rate effects are observed in the temperature range where the rapid increase in yield strength occurs which leads to the ductile to brittle transition. In this temperature range Zener and Hollomon' have suggested that the effects of strain rate and temperature T on the yield strength could be correlated through a single parameter, P, in the following manner where Q is a heat of activation characteristic of the metal and associated with some unspecified relaxation process. They also observed that if the temperature is restricted to a relatively narrow range— below room temperature for steel—that the logarithm of the yield strength could be expressed as a linear function of the logarithm of P. From this relation the logarithm of stress should be a linear function of the logarithm of the strain rate at constant temperature: where r will be referred to herein as the strain rate exponent. At a constant strain rate the logarithm of stress should be a linear function of l/T, ay(e = C) ~ eT [4] where q = Qr [5] and is referred to herein as the temperature exponent. These equations have been found to relate the effects of temperature and strain rate on the yield strength of molybdenum in the temperature range wherein the ductile to brittle transition occurs, —75° to +150°C.2 Bechtold and Shewmon3 have shown recently that the ductile to brittle transition in annealed tungsten occurs in the temperature range +150° to +350°C. In this temperature range the yield strength in-

Jan 1, 1957

Sailing westward from the Society Islands in the fall of 1774, England's noted explorer Captain James Cook discovered New Caledonia-that long, linear island that has played such an important and varied role in the history of nickel. Upon his return to England the following year, Cook's announcement of this uncharted island generated governmental interest, but its distance from the Island Empire, the troubles in the colonies, and the difficulties with France combined to keep English interest indirect and in the background of the then-current events.

Jan 10, 1968

By THEODORE DWIGHT

Members of the Institute have already received a special pamphlet descriptive of the United Engineering Society building, and wilt doubtless be interested in the progress that has been made up to date-February 24th-in erecting this home for the engineering profession. The old buildings on lots Nos. 25 to 33 W. 39th St., New York, were,' removed many months ago, but final contracts for the new, building were not let until the summer of 1905. The size of the building is 115 ft. on 39th Street, and 88 ft. in, depth; the height from, the sidewalk to the top of the parapet is 220 feet. The cubic contents of the building from the. bottom of the basement floor, to the top of the roof, including the pent houses, is 2,290,000 cubic feet. The number of light's, in the building will be between 4,000 and 4,500. The air supply for Auditorium and Lecture. Halls will amount to nearly 10.0,000 cu. ft, per minute, and the exhaust. to 90,000 cu. ft. per minute. In excavating for cellar and foundations, the average depth where good rock was. found was 37 ft.-it varied, however,: from 27 to 65 ft., due to an old water-course having run through the center of the lot; this condition, and the presence of soft rock, which rapidly disintegrated when exposed to air and water, made the foundation-work very difficult. As two of the column-footings of the building have to sustain a weight of 3,000,000 11) each, the most substantial foundations are necessary; 13,000 cu. yd. of earth were excavated for the foundation and basement; and 1,600 cu. yd. of concrete were necessary, to build up the footings. In the completed building there will be about 3,500,000 bricks. Owing to the number of auditoriums, and their location, and the placing of the library on the top floor; where allowance will have to be made for the enormous weight of 300,000 books, the structural steel work has been unusually complicated in this building. For instance, over the auditorium there are two 60-ton plate-girders, made up

Mar 1, 1906

By W. G. Davenport, M. Paneni

Experiments in sheets of mercury and water have confirmed that the dynamics of bubble rise are simi-lur in Liquid metal and aqueous systems. RECOGNITION that bubble/metal interactions are important in pyrometallurgical refining processes (e.g., steelmaking, vacuum degassing, deoxidation of copper) has led to a number of investigations into the dynamic behavior of bubbles rising in liquid metals. Terminal velocities of bubbles rising in mercury (20°C)' and silver (1000" to 1050"c)1,2 have been measured. Good agreement between aqueous and liquid metal systems has been obtained. Shapes of air bubbles rising in mercury have been determined experimentally by Davenport, Bradshaw, and Richardsonl who used a system of electric probes to measure maximum horizontal and vertical dimensions, Fig. 5. In the present work the motion and shape of nitrogen bubbles rising in a thin sheet of mercury (i.e., a "two-dimensional" environment) have been studied with the view of confirming dynamic similarity between aqueous and metallic systems. The use of thin sheets of liquid permitted direct visual and photographic comparisons of bubble behavior in clear liquids and in mercury. EXPERIMENTAL METHOD The thin sheets of mercury or water were held in a clear acrylic plastic container, Fig. 1. The sheets of liquid were 80 cm high by 30 cm wide and 0.47 cm thick. Single bubbles were formed by injecting the desired volume of nitrogen into an inverted semicircular cup (stainless steel). The cup was then rotated into the upright position using an external handle thus releasing a single bubble of measured volume. Nitrogen was injected into the cup from a nitrogen cylinder through the external handle and a hollow rotating axle. The volume of a bubble (volume range 0.01 to 10 cu cm) at any instant was obtained by connecting a soap film meter to a small gas space above the liquid. By this technique any change in the volume of a gas bubble in the liquid (i.e., during cup filling or during rise) produces an equivalent displacement from gas space A into the buret B. This displacement is determined by measuring the movement of a horizontal soap film in the buret. Bubble shapes were determined using single-frame photography. Rising velocities were determined by cinephotography with a 1/100-sec stopwatch in the field of view. In both cases dimensions were referenced to a rule attached to the container surface, also in the field of view. Linear dimensions were measured on projections of the single-frame negatives. Rising velocities were calculated from measured heights of rise (10 to 20 cm) and times of rise. The effects of disturbances caused by cup rotation and by bubble release were minimized by photographing bubbles at a point not less than 25 cm above the cup. MATERIALS Mercury: Technical-grade purified: minimum 99 pct Hg; Johnson Matthey and Mallory Limited, Toronto. Nitrogen: Technical-grade purified nitrogen: 99.99 pct Nz, 0.01 pct 02, trace argon; Air Liquide Canada Limitee, Montreal.

Jan 1, 1970

By Fun-Den, Wang

An open pit rock structure usually contains geological planes of weakness. They are formed by joints, faults, bedding planes, fractures, and cleavages. Rock slope failures often occur in the form of sliding of rock blocks along a plane or several planes. Such a rock block has three- dimensional geometry, and consequently a vector method of analysis has been found useful in evaluating its stability. Rock blocks of a tetrahedral shape with one free surface have been analyzed by Londe. Rock blocks formed by sets of parallel joints have been analyzed by Wittke. The present chapter presents the analysis of rock blocks formed by planes of weakness of arbitrary orientation, and of three-dimensional geometry.

Jan 1, 1972

The program of 'the Chicago meeting, which is to be held Sept. 22-26, is as follows: Monday. Morning-Registration. Afternoon-Technical Session. Evening Smoker. Tuesday. Morning and Afternoon-Excursion by boat to Gary and trip, through United States Steel Co's. plant. Evening-Technical Session. Wednesday. Morning- Technical Session. Afternoon-Technical Session. Evening-Banquet, Congress Hotel. Thursday. Morning and Afternoon-Special train to La Salle and De Pue, Ill., Inspection of Zinc Smelters, Cement Works, and Coal Mines. Trip to Starved Rock and points of historical interest. Evening-Return by train to Chicago. Friday. Morning-Optional trips. 1. East Chicago Metallurgical Plants and Oil Refineries at Whiting, Ind. 2. North Chicago and Milwaukee. 3. Local Chicago Plants. 4. Coal trip to Franklin and McCoupin Counties.

Jan 6, 1919

By Dilip K. Das, Douglas T. Pitman

ONE of the major uses of barium in metallic form is as a getter material in vacuum tubes. Because of the high chemical reactivity of the metal, Ba-Al alloys are extensively used. Numerous methods for the preparation of Ba-Al alloys have been published, a few of which1-4 are cited here. Most of these methods were found to be quite elaborate, involving the reduction of BaO, and not too well adapted for the close control of the final composition of small amounts of alloys prepared for laboratory use. A simple laboratory method for the preparation of Ba-A1 alloys in small batches starting from pure metals was devised, so that it was possible to control the desired compositions to within 1 pct. The pertinent features of the alloy system Ba-Al5 are 1) an intermediate compound BaAl, with the melting point of 1050°C, and 2) a eutectic between aluminum and BaAl4 at 98 pct Al. The accompanying sketch shows the experimental arrangement for the preparation of the alloys. Weighed amounts of aluminum and barium were placed in an alumina and a stainless steel crucible, respectively. According to the supplier's specification, the purity of the metals used in the alloys is as follows: a) aluminum rods—99.9 pct Al, and b) barium rods—99.5 pct Ba. The stainless steel crucible, tapered at the bottom and having a 1/16 in. diam hole, rested on top of the alumina crucible. The assembly was placed inside a graphite sleeve which rested on a refractory platform. The platform moved the assembly up and down through the field of a radio frequency coil. A glass bell jar was placed between the crucible assembly and the radio frequency coil to maintain a steady flow of helium around the melt. A small window was cut out on the wall of the alumina crucible to observe the progress of the re- action and to record the temperature with an optical pyrometer. The platform was first raised high enough to move the barium out of the radio frequency coil field in order to allow only the aluminum to melt. The assembly was then lowered so that the barium began to melt and flow out through the small orifice into the molten aluminum. In order to keep the violence of the exothermic reaction under control, the rate of flow of barium was carefully regulated by raising or lowering the crucible assembly. All the samples prepared by this technique were examined by a Norelco X-ray diffractometer using CuKa radiation, The diffraction specimens were prepared by placing the finely powdered samples in flat specimen holders. The Ba-Al alloys prepared with a high barium content were found to consist mainly of BaAl4. The structure of BaAl4 has previously been reported by Alberti and Andress.8 They found that BaAl4 was body-centered-tetragonal with an a0 = b0 = 4.530Å and c0 = 11.14Å. An alloy whose composition was found by chemical analysis to be almost 100 pct BaA1, was used to determine the relative intensities. The d-spacings were obtained from the same alloy to which a small amount of tungsten had been added as a calibrating material. Accurate values for a, and c, were calculated according to the method proposed by Taylor and Floyd.' The calculated values are: a, = b, = 4.566Å and c0 = 11.250Å. The measured d-values for BaAl4 are shown in Table I along with relative peak intensities above background and hkl indices. Acknowledgment The authors are grateful to L. J. Cronin, the head of the Techniques Dept., for suggesting the problem and for his constant interest. References 1Froges and Camargue: German Patent No. 809107, 1951. French Patent No. 935324, 1949. 2E. Bonnier: Annales de physique, 1953, vol. 8, pp. 259-312. 3M. Orman and E. Zemhela: Prac Institute of Metals; 1952, vol. 4, pp. 437-445. 4E. Fujita and H. Yokomizo: Reports Gov. Chemical Industrial Research Institute, Tokyo, 1952, vol. 47, pp. 291-297. 5E. Alberti: Ztsch. fur Metallkunde, 1934, vol. 26, p. 6. 6E Alberti and K. R. Andress: Ztsch. fur Metallkunde, 1935, vol. 27, p. 126. 7 A. Tnslor and R. W. Floyd: Acta Crystallographica, 1950, vol. 3, p. 285.

Jan 1, 1958

By C. G. Dunn

IDENTIFICATION Of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereographic projection with one pole per orientation.1 However, accurate data based on calculations of the positions of all {100} planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. METHOD OF COMPUTING ORIENTATION OF A TWIN It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given it terms of two angle variables, two sets of which appear in the following equations: [Polar NetWalff Net x=rsinOocos4pyx=rcos0. y=rsinB,sin4,ny-rsin0.cos¢,, z=rcos0,,z=rsin0.sin4,,] The three numbers x, y and z determine a length r as well as a direction [(0, 0)] in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 +12)1/3, where h, k and 1 are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {100} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3 4 Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A1 being one of the four {112} or {III}

Jan 1, 1945