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By W. P. Sykes

IN an earlier paper1 the composition-temperature limits of the gamma iron phase in the iron-tungsten system were reported as approximated Fig. I.-DIAGRAM OF ALPHA-GAMMA LOOP AS DETERMINED BY MICROSTRUCTURE AND THERMAL ANALYSIS. by thermal analyses. At that time no attempt was made to develop metallographic evidence of the coexistence of two phases in the iron-rich solid solution at temperatures between 900° C. and 1400° C.

Jan 1, 1931

Executive SIDNEY J. JENNINGS, Chairman. GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C. STONE2 J. H. JANEWAY4 BRADLEY STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 6, 1918

By Lawrence Adler

The authors are to be complimented on using a novel and potentially helpful technique to analyze the effects of mine roof trusses. However, some criticisms of their application and analysis seem appropriate to further its acceptance. This discussion will deal with the normal structural analysis format covering: 1) material, 2) load, 3) structure, and 4) analysis. It will then briefly review the testing procedures and finally cover miscellaneous items.

Jan 12, 1978

Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C. STONE2 J. H. JANEWAY4 BRADLEY STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 11, 1918

By John Harmon

THIS paper was written-with two objects in view: (1) To describe in detail what has been done toward the ventilation of the main unit of the Portovelo mines and the results; (2) to give information that may be useful to anyone who may have to make a preliminary mine ventilation survey, with recommendations for the improvement of the existing system and finally the maintenance of the improved system.

Jan 1, 1931

[Indexes to Vols. 1-35, 36-55, 56-72, 73-117 (set of 4 Indexes). DIVISIONAL TRANSACTIONS AND SPECIAL EDITIONS Coal Division Volume, 1930, 1931, 1932, 1934, 1936, 1938, 1940, 1942, 1944, 1946. Institute of Metals Division Volume, one each year 1927-1946. Iron and Steel Division Volume, one each year 1928-1946. Metal Mining, Nonmetallic Minerals and Mining Geology Volumes, 1934, 1935 (Out of print), 1937, 1940,* 1941, 1943.ø]

Jan 1, 1946

WILLIAM L SAUNDERS, President GEORGE H PEGRAM, 1st Vice-president ALFRED D FLINN, Secretary J V W REYNDERS, 2d Vice-president JACOBS LANGTHORN, Treasurer HENRY A LARDNER Assistant treasurer Finance Committee House Committee GEORGE H PEGRAM, Chairman ; ALFRED D FLINN. Chairman J VIPOND DAVIES FREDERICK F SHARPLESS BANCROFT GHERARDI JOHN H DUNLAP WILLIAM L SAUNDERS CALVIN W RICE W F M GOSS, ex-officio F L HUTCHINSON

Jan 1, 1923

By G. C. Stone

IN common with many members of the Institute, I was much interested in Mr. Kent's paper on " Manganese Determinations in Steel," * read at the Virginia meeting. Having recently had an opportunity to collect a similar series of results for spiegel, I venture to offer them to the Institute, hoping that they may also prove of interest. Sample No. 1 was taken at our works, where the spiegel was made,

Jan 1, 1883

Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL EILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C.' STONE2 J. H. JANEWAY4 BRADLEY, STOUGHTON Papers and Publications BRADLEY STOUGHTON, Chairman

Jan 7, 1918

By John Fulton

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

Jan 1, 1888

By B. C. Burgess

AFTER many years of close and friendly association with talc and soap-stone, this orthographically distinguished mineral steps forth in this edition, for the first time in a chapter of its own. Pyr, the Greek for fire, and phyllite, a rock or stone, form its name and at the same time refer to the first recorded use of pyrophyllite as firestones or hearthstones. Another derivation of "phyllite" is from the Greek phyllites, "of leaves," alluding to the beautiful white radial crystal aggregates that form when pyrophyllite is heated. Pyrophyllite used by the Chinese for carving is called agalmatolite, from the Greek agolma, meaning an image. COMPOSITION AND PROPERTIES Pyrophyllite has previously been grouped with talc because of the close similarity of the minerals in physical and optical properties. They have the same space group; and chemically they are closely related, pyrophyllite being the aluminum silicate A12Si4010(OH)2 and talc the magnesium silicate Mg3Si4010 (OH) 2. Another arrangement of the pyrophyllite formula is generally given as A12034Si02H20 because it expresses the chemical composition as usually determined (alumina 28.3 pct, silica 66.7 pct, water 5.0 pct). Vanderbilt gives pH values of pyrophyllite 5.6 to 8.4.29 Pyrophyllite usually is white, pale green, cream or pale yellow, buff or light gray. It is found in darker shades and other colors principally due to oxidation of contained iron minerals. It is translucent in thin sections. In hardness it is 1 to 2 in the Mohs scale. Its specific gravity is 2.8 to 2.9. In bulk specific gravity, the powdered mineral ranges from 0.4 to 0.7. Its luster is pearly to dull; it is infusible in the Bunsen burner flame, slightly affected by aqueous solutions of sodium carbonate and hydrochloric acid. It is decomposed by sulphuric acid, with separation of gelatinous silica. It is characterized chiefly by its micaceous structure and cleavage, its softness and greasy feel. Two other varieties occur

Jan 1, 1949

By R. R. Wilson

THE Cassidy Colliery operated by the Granby Consolidated Mining, Smelting & Power Co., Ltd., is situated about 9 miles in a southerly direction from the city of Nanaimo on Vancouver Island. The coal seam worked, which is called the Douglas bed, outcrops in the western part of the property, clipping easteyrl, and is opened by a slope 7 by 14 ft. in the clear, and is timbered by 12 to 14-in. framed sets of timber, 4 ft. center to center. A separate manway provides for a traveling road and at the same time forms an intake airway. The general average of the dip of the seam at Cassidy is 18°, and varies in thickness from 1 to 25 ft., averaging about 8 ft. The main slopes follow straight down the dip a distance of 4545 ft. At the bottom of the main slope two rock tunnels were driven a distance of 1500 ft. to the south, cutting through a fault, and opening up an area in the same seam which is known as No. 7 South Section. The coal is found in this section at a vertical depth of 1560 ft., and is very soft and friable. The immediate roof is a strong, sandy shale overlain by massive sandstone while the floor is a light-colored shale, hard when freshly exposed. It does not soften materially oil exposure. In the folding of the coal measures a great thrust caused a movement along the coal seam as indicated by the slickensided nature of the coal. The floor has buckled and this has rolled and squeezed the coal-so that with rare exceptions it shows no normal bedding but curved slip planes, which frequently start at right angles to the floor, curving upward and then in the direction of the dip. As such planes are slickensided it is probable that there is a coating of clay which is more or less impervious to gas.

Jan 1, 1927

By F. H. Willcox

IN Bessemer-steel practice, air is blow, through a bath of iron, or projected strongly upon its surface to burn out silicon, manganese, and carbon. Toward the end of the blow, when the iron is not protected. from oxidation by these elements and the excess of air becomes great, there is oxidation of the iron. In open-hearth practice, the same difficulty is experienced with dissolved gas and oxides in the product, though not to as great or severe a degree as in the Bessemer process because the oxidizing conditions grow less severe as the end of the heat is approached, and if the bath is allowed to boil for a time it undoubtedly frees itself from a large part of the gas and oxides which have been absorbed in the earlier part of the process. Basic open-hearth steel is usually assumed to contain a larger proportion of oxides than acid open-hearth steel, but it may be said that all steel, Bessemer and open-hearth, contains more or less oxide of iron dissolved in the fluid metal at the end of the "blow" or "heat." That certain metals are solvents for their respective oxides has been shown, in the case of copper, by Heyn, and, in the case of iron, by Law. It is indicated that the solubility of iron oxide in iron increases with the purity and temperature of the metal. This confirms what is observed and known by operating men, and these observations may be summarized as follows: 1. Cast irons is rarely subject to oxidation, as is logical from its composition. 2. Normal steel, unless deoxidizers are added, contains blow holes. 3. Steel known to be oxidized is full of blow holes. 4. The addition of deoxidizers prevents, to a greater or less degree, the formation of blow holes in normal steel. With these observations in mind, it is logical to deduce that the cause of blowholes lies in part in the presence of dissolved oxide of. iron in the

Jan 2, 1917

By Michael P. Robinson

It has been suggested that streaming potentials are not nomlally logged because the streaming potentials known to be generated across mud filter cakes are substantially cancelled by streaming potentials generated in contiguous shale beds. Laboratory measuments of streaming poterztials acrons hand specirnens of shale have been adduced as evidence to support the suggestion. The experiments show that streanzing potential depends on the resistivity of the equilibrating solution and on pressure drop. Meizsurenlents were made perpendicular to the bedding planes of the shales. The mechanism of streaming potential generation in shale which the suggested cancellation theory iniplies has been critically examined. Conclusions reached are tested by comparing self potentials logged before and immediately after changing the resistil~ity (but not the weight) of mud in a borehole. The resultant SP change is found to equal the theoretical electrochetnical potential change, i.e., cancellation of .strearning potential is independent of mud resistivity. Since streaming po/entials generateal across mud filter cakes depend critically upon mud reistivity, shale .strearlling potential in situ must he equally sensitive. Using plausible values for the pemleahility, porosiy arzd compressibility of shale, the van Ererdingerl-Hurst approach shows that the pressure drop between horehole pressure and formation pressure in a radially honzogeneous shale is unlikely to coincide with the zone of filtrate invasion. If, perchance. this coincidence occurs with one mud a chatzge 10 a second must result in non-coincidence, i.e., a .YP logged in the second mud should show a streaming potenlial. The dilernrna may he overcome by postrrlating: (I) perrneabilities of shale7 parallel to their beddine planes greatly exceed their cross-bedding permeabilities; (2) a resistivity-sensitive mud cake of low permeability forms either on the face of, or probnhly in the lanlinations of, many shales. These postulates are examined with reference to the pres.sure and SP histories of the McClosky and Aux Vases zones in the Illinois Basin and some srcpport for them found. It is concluded that a definitive solultion to the streaming potential problem does not exist. INTRODUCTION Recently Gondouin and Scala' published a contribution to the streaming potential problem which is notable particularly for the elegance of its experimental techniques. The conclusions drawn by Gondouin and Scala from their studies amplified those previously suggested by Schehck'. In essence they suggested that the streaming potentials known to develop across mud filter cakes" are not normally observed on SP logs because they are largely cancelled by streaming potentials generated in adjacent shales. This suggestion appears so reasonable that many workers in the logging field will be prone to accept it. We incline strongly to the view that the suggestion is basically correct. Nevertheless, it is important to realize that the cancellation hypothesis in the form put forward by Gondouin and Scala does not appear to meet all the known experimental facts. It is the principal intention of this note to call attention to what appears to be a flaw in the relevancy of the experimental evidence adduced by Gondouin and Scala and to suggest an alternative hypothesis to remove it. The consequences of the new hypothesis are compared with field data which, we believe, are unique. A second but not less important purpose of this note is to emphasize that even the new hypothesis does not fully explain all field observations. Hence we conclude that further study of the streaming potential problem is required before it can be said that a definitive solution to it has been attained. The bare experimental bones of laboratory data on streaming potentials appear to be as follows. 1. A streaming potential is developed across a mud filter cake. This streaming potential is virtually independent of cake thickness but depends on the mud resistivity. The relationship is of the form, 2. A streaming potential is developed across a shale. This potential is independent of shale thickness but depends on the resistivity of the permeating solution if the shale has been first equilibrated in this solution. The relationship is of the form, The relationship in (1) was determined first by Wyllie3, confirmed by Gondouin and Scala and qualita-

By R. H. Hiltz, N. J. Grant

Solid-solution titanium-cerium alloys, cold-rolled to 0.010 in. thickness, and annealed, were internally oxidized to produce a fine dispersion of CeO2 in the titanium matrix. The oxidized alloys were cut into sheet stress-rupture specimens and tested for rupture life at 426°C, 538°C, and 648°C. There was noted an improvement in strength over that of pure titanium, the internally-oxidized alloys showing curves with a much flatter slope on the log stress—log rupture life plot, characteristic of the stable metal-metal oxide class of alloy. DURING the past 3 to 4-year period, considerable interest has been aroused by the potential offered by alloys based on the ultra fine dispersion of a hard insoluble phase in pure metals or solid-solution alloys for use at high temperatures. The impetus to the development and study of such alloys was provided by Irmann.1,2 through the success of the SAP alloy (pure aluminum containing about 12-14 volume pct of A12O3). Subsequent studies have thrown light on the true potential of this class of alloys in the remarkable stability of the structure after long-time exposure at high stresses and high temperatures.a-5 While success has been demonstrated in the special case of the A1-Al2O3 alloys, and more recently

Jan 1, 1959

By N. G. W. Cook

The conventional cyclic system of deep-level mining by drilling and blasting gives rise to an inadequate degree of stope sorting when mining thin reefs. This results in poor utilization of the capital facilities of a mine in the form of shafts, haulages, airways, and associated equipment. Continuous and controlled removal of the thin gold-bearing portion of the reefs would permit better stope sorting and hence greater utilization of capital facilities. Results of experiments to develop hard-rock cutting machines for mining are reported and the benefits which could be derived from their use are discussed. Mining, from exploration through refining, is essentially a process of sorting in which the payable mineral, or metal, is progressively separated from the other constituents of the earth's crust with which it was originally associated. This takes place more distinctly at each step of the operation. What is it that determines the degree to which sorting should be carried out at each of the several steps comprising a whole mining operation? The formal answer is that degree of sorting at each step which results in the lowest overall cost for the complete separation. In practice, individual steps are chosen from those available in current technology, each of which effects a degree of sorting such that the quantity of material which must be sorted in the succeeding step is economically acceptable. It follows that any new technological development has repercussions throughout the whole mining operation and, more important, that the solution to excessive costs in any one step of the operation may lie not in improving the costly operation itself so much as in increasing the degree of sorting preceeding that operation. This concept, particularly in relation to deep-level mining of thin, tabular gold-bearing reefs in South Africa, is discussed here, and the most recent results achieved in the development of hard-rock cutting machines for stoping more selectively than is possible with explosives are presented. Deep-Level Mining Deep-level mining involves operations which are either not encountered, or are of only trivial importance, in near-surface mining. Near-surface, the major operations are those of rock breaking, transport, and milling. In deep-level mining, hoisting, environmental control, and strata control assume major importance. Some idea of the relative magnitude of these operations may be gained by comparing the separate amounts of energy which are required, or which must be controlled, to effect the various operations when, say, mining a tabular deposit 40 in. thick at 8000 ft below surface, Table 1. It is true that the costs of handling a given quantity of energy are not the same for each operation. Nevertheless, Table 1 does emphasize the fact that the operations of hoisting, strata control, and environmental control are of unique and major significance in deep-level mining. In particular, hoisting and environmental control place a heavy load on the reticulation system of the mine—the shafts, haulages, and airways. Typically, a new, deep gold mine with an annual revenue of about $35 million requires a total capital expenditure of about $140 million of which some $100 million is invested in developing and equipping this reticulation system. The ratio between annual turnover and capital invested of about one-quarter is exceptionally low, and it typifies the poor utilization of capital by the current technology of mining hard rock at depth. The average thickness of the reefs in the new South African goldfields varies from 10 to 30 in.,l and even in the thicker reefs the gold is often confined within a small fraction of the nominal thickness. Nevertheless, it is universal practice to mine these reefs at a stope width of about 40 in. or more, so that the quantity of rock broken in the stopes and hoisted out of the mine is between two and ten times the quantity of rock actually carrying a significant amount of gold. The reason for the adoption of such excessive stope widths is to be found in the method of rock breaking by drilling and blasting. The only free surface to which a blast hole can break is the stope face. It follows2 that each hole cannot have a burden in excess of the height of the free face if it is to break satisfactorily. To

Jan 1, 1971

By Fritz Wald, Richard W. Stormont

lHE general constitution of a number of metal-lead telluride and metal-tin telluride systems has recently been studied in an effort designed to furnish background information for the study of degradation mechanisms on junctions between thermoelectric power generation materials and metals.1"4 This paper reports further results of that effort. It was found that cobalt-lead telluride constitutes a stable pseudobinary section through the ternary Co-Pb-Te system. Materials used in the study were lead and tellurium of semiconductor-grade purity (American Smelting and Refining Corp., 99.999+ pet). Cobalt (Johnson Matthey & Co., 99.999 pet purity) was used in the form of slices cut from rods of 5 mm diam. Twenty- gram charges of the alloys were melted in evacuated quartz ampoules. Thermal analysis, as described previously,2'3 and metallographic and X-ray diffraction methods (Debye-Scherrer photographs) were used as investigative tools. Substantial difficulties were encountered in polishing, as reported previously for the lead telluride-iron system.3 A number of different etches were used, including dilute aqua regia, Murakami solution, an etch containing copper nitrate,3 and HC1-HNO3-acetic acid-water mixtures. None of these etches gave consistent results over the complete range of cobalt concentrations. On the alloys containing bulk cobalt in the form of primary

Jan 1, 1969

By E. F. Steeb, P. C. Rosenthal

BlANKS 8 in. long were cut from the as-received bar stock and austenitized at 1560° F for 1 hr, oil quenched, tempered at 1140°F for 1 hr, and water quenched. The heat-treated blanks were machined into tensile specimens which were subsequently used for the straining operation. Some of the tensile specimens were temper embrittled at 900°F for 24 hr and air cooled prior to or following the straining operation. The specimens were strained in tension up to 5 pct total strain (elastic plus plastic) either at room temperature or at 900°F. The reduced sec- tion of the tensile specimen employed was 5 in. long and 0.600 in. in diam. This size specimen was sufficiently large to permit two standard Charpy impact bars to be machined from it. One group of specimens was temper embrittled at 900°F for 24 hr under stress of about 20,000 psi applied with a hydraulic tensile testing machine. Approximately 0.34 pct plastic strain occurred during this treatment. A comparison of series "A" and "B" data in Table I at 0 pct strain, reveals that the steel was rather highly susceptible to temper embrittlement, the embrittling treatment causing the transition temperature to rise 165°F. The 28 ft-lb level, which was near the center of the sharp-rising portion of the transition curve, was selected as the

Jan 1, 1959

By C. M. Tucker, Kent R. Van Horn, W. P. Sykes

RECENT investigations of the molybdenum-carbon alloys have been reported by Becker and Ebert1‡, Westgren and Phragmén2, T. Takei3, and H. Tutiya4. Takei3 studied the Mo-C system by employing metallographic and X-ray methods, and the other publications described the determination of the crystal structure of the molybdenum carbides. In exploring this system by a technique previously applied to the tungsten-carbon series5, the results of Takei were confirmed with two definite exceptions; i.e., first the composition of the eutectic, and second the nature of the carbon-fish intermediate phase. Consequently, a more thorough examination of the molybdenum-carbon constitution was initiated in an effort to correlate the data supplied by the microstructures, diffraction patterns and chemical analyses. METALLOGRAPHIC INVESTIGATION A briquette of molybdenum powder when heated in a carburizing atmosphere at 1500° to 1600° C. for several hours develops the carbon-rich layer shown in Fig. 1. The carburization was accomplished by placing the briquette in a carbon tube, which was heated in the hydrogen atmosphere of an alundum muffle wound with tungsten resistor. While the macrostructure indicates two distinct shells, and suggests the possibility of two carbon-rich phases, no evidence of this condition could be detected by the microscope, which revealed but one high-carbon constituent. This carbide forms next to the molybdenum as a relatively

Jan 1, 1935

By R. E. Reed-Hill

A simple accurate graphical method for orienting fcc crystals using (111) slip traces on a single surface is described. Solutions placing the pole of the surface in a unit stereographic triangle are obtained using a Wulffnet, a (111) standard projection showing the four (111) planes, and a (111) standard projection ruled into unit stereogmphic triangles. The multiplicity of solutions is described in relation to this method. AN accurate, rapid single-surface technique for orienting fcc crystals, using (111) slip or twin traces, has been a matter of continuing interest, as evidenced by the periodic appearance of papers on this subject.'-4 This note presents a new method possessing some advantages over those previously reported. It is an analog to the technique for hcp metals5 where the solution is based upon a stereographic rotation of the specimen surface on a (0002) standard projection that contains the planes of the possible features that might account for the observed traces. In the hexagonal solution, the axis of rotation is the basal-plane trace in the surface. In the fcc case, the axis of rotation is one of the observed ( 111) slip or twin traces. It has been observed that the solution is greatly facilitated if the indicated movements of the (111) traces during the rotation of the surface are plotted directly on a paper copy of a Wulff net as shown schematically in Fig. 1. The trace selected to represent the axis of rotation is assumed to fall at the north-south poles of the Wulff net. The directions of the other traces are then plotted as points at the proper angles around one-half of the basic circle of the net. The loci of points corresponding to the movements of these traces (directions) during a 90-deg rotation of the surface, about the polar axis of the net, are then easily and accurately drawn by following the appropriate small circles on the Wulff net. The solutions to the problem are obtained with the aid of a (111) standard projection of the (111) planes, see Fig. 2. This is normally a Xerox copy of a carefully drawn master made on high-quality tracing paper. The (111) standard projection is superimposed over the Wulff net and rotated about its center until the points of intersection of the loci of surface traces, drawn on the Wulff net, and the great circles representing the (111) traces, all lie along a common meridian of the Wulff net as demonstrated in Fig. 3. This latter great circle represents a possible position of the surface. The pole of this plane is then plotted on the (111) standard projection. Its location in a unit stereographic triangle may be readily obtained by superimposing (over the standard projection) another tracing paper (111) standard projection subdivided into unit stereographic triangles. The result of this last operation is shown in Fig. 4. MULTIPLICITY OF THE SOLUTIONS The maximum possible number of (111) traces on a single grain surface is four. Any one may be selected as the axis about which the surface is rotated. Corresponding to each such choice are three possible surface-pole orientations, related to each other by a simple 120-deg rotation about the pole of the (111) basic circle. This is a direct result of the threefold symmetry of the (111) standard projection. Since each of the four rotations will normally give a different set of three-pole positions, there are, accordingly, twelve possible solutions. Each of these twelve solutions places the surface pole in the same relative position in a stereographic triangle so that all are crystallo-graphically equivalent. Accordingly, only a single solution is required to obtain a basic orientation of the crystal. It should be noted, however, that the orientations obtained by reflecting* any of these twelve orien- *The reflected orientations may be obtained by a 90-deg rotation of the opposite sense to that shown in Fig. 1. This rotation places the correspond-ing trace loci in the lower hemisphere of the Wulff net rather than in the upper hemisphere. tations through the surface are also possible orientations that could account for the surface traces. Thus, a given set of four traces always corresponds to a pair of basic orientations related by reflection through the specimen surface. This ambiguity can only be re-

Jan 1, 1967