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WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 5 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and file this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. II. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the undersigned are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1923

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1939

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1943

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1936

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1934

CERTIFICATE OF INCORPORATION [AMENDED Nov 22, 1912, AND JUNE 27, 1919 ] WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 5 of Article I of said law, the existing unincoiporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and file this Certificate for that purpose, and do Certify as follows I That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained II That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council, that the undersigned are all members of said Council as the same was constituted on the 29th day of December, 1904

Jan 1, 1923

WE the undersigned, being all persons of full age and citizens of the United States and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 5 of Article I. of said law, the existing unincorporated association known as American Institute of Mining and Metallurgical Engi¬neers, Incorporated, do hereby make, acknowledge and file this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. II. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the undersigned are all members of said Council as the same was constituted on the 29th day of December. 1904.

Jan 1, 1938

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1941

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1944

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 5 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and file this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. II. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under-signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1934

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

S. Tandanand, Twin Cities Mining Research Center, U. S. Bureau of Mines As an addition to the fine reviews on drilling presented in the foregoing papers, we feel it would be appropriate to mention briefly some work in this area by the U. S. Bureau of Mines. The Bureau has had under way for several years at its Twin Cities Mining Research Center studies directed toward a better understanding of basic drilling mechanisms. The work includes drillability investigations with diamond rotary, and with percussive drilling systems, as well as fundamental studies of rock behavior under drill bit types of loading. Results of our work to date have contributed the following to the state of the art. MECHANISM OF ROCK FAILURE-Rock fragmentation through use of mechanical energy systems, including drilling systems, consists of two major components-machine and rock. The two components are related to each other by their functional behavior and their resultant motion which the components mutually influence. Forces in the systems are transmitted directly to the bit which in turn induces stresses in the rock. When the induced stresses exceed the strength of the rock, the rock fails resulting in penetration. Rock strength is a function of the forces applied to the rock. Stresses under a drill bit, regardless of bit configurations, are essentially compressive, resulting in a condition where the rock has the highest resistance to failure. The ratio of principal stresses induced under drill bits is an indication of the mode of failure in the rocks. Initially, compressive stresses under the drill bit cause rock to undergo inelastic deformation. The impression observed at the first stage of crater formation under the drill bit shows that rock is no longer elastic. Associated subsurface failure at this stage precedes total rupture which subsequently appears at the rock surface. Thus, explanation of crater formation, by applying theory of elasticity alone, is likely to be over-simplified. ENERGY VERSUS VOLUME OF ROCK REMOVED-Experimental results show that energy per unit volume of rock removed is constant for a particular rock and bit type. Rock offers a definite resistance to penetration, depending on the method of the energy application; this may be defined as the drilling strength of a rock. Energy consumption in a drilling system may be divided into two components: 1) Energy required to move the machine parts; and 2) energy consumption in breaking rock. Component 1 is dependent on the type of the machine. Component 2 is dependent on the strength properties of rock and the efficiency of the bit in rock cutting. The sum of the energy required in both components determines the total energy required in breaking rock. Our work in this area has included consideration of both diamond and percussive drilling systems. PENETRATION RATE-For a drilling rate expression to be useful in predicting field performance, it should include the operating characteristics of the drilling machine. Eq. 37, for example, is simply a statement of the fact that the drilling rate is determined by the power output of the machine (2pNT) and the power requirements to break the rock in the hole (AER). In order to predict the performance of a particular drill and the effect, for example, of the rotary speed, on the drilling rate, R, Eq. 37 must be modified to include the

Jan 1, 1967

By Herman Blumenthal, Ronald Silverman

lnfiltrability of a porous Tic compact, produced by powder metallurgy technique, depends on the capillarity of the compact and the surface condition and nature of the individual particles. Capillary forces raise the liquid metal infiltrant into the interconnected pores of the compact and the complete filling of these pores is a function of their geometry as well as the wettability of the Tic particles. The paper deals especially with the improvement of this wettability through surface conditioning of the Tic particles. INFILTRATION, a technique for preparing dense powder metallurgy parts by filling the void spaces of a porous body with a liquid metal, has been used for the manufacture of titanium carbide-base cermets. Although the infiltration process was

Jan 1, 1957

By E. B. Fitch

The operating behavior of liquid-solid cyclones is outlined, together with the nature and range of the process results obtainable, to serve as a background for engineers wishing to consider application of this new process tool.

Jan 3, 1953

R. W. NEWCOMB,* New York, N. Y. (written discussiont).-On page 1638 mention is made of a new -instrument with an exceptionally high resistance that has been developed by Charles Engelhard. All friction and wear of moving parts of the moving system has been elimi-nated by replacing the hardened steel pivots and jeweled bearings, commonly used on other instruments, by a double metallic filament, one at the top and One at the bottom, under slight tension. Any pos-sible distortion of the moving coil, because of tension, has been eliminated by introducing a solid spindle as the axis of the coil between the points on the coil where the metallic filament is attached. The filaments serve not only as a support for the moving coil; but also to lead in the current from the binding posts to the moving coil, and as a source of counter-torque; instruments so constructed, do not require leveling, and are mechanically very robust. The clock of the recorder serves only to drive the chart at its specified rate and -to operate a small contact-making device; i.e., there is no other mechanical load on the clockworks. The contact-making de-vice is so constructed that there is a quick-make, a quick-break, and a wiping effect while the contact is being made. Contact surfaces on this switch are of platinum platinum-iridium. The operation of this contact, which occurs once each minute, sends a current, from a 6-volt supply; through a solenoid magnet, which operates the depressor bar mechanism in the case of the single-record instrument; in the case of the multiple-record instrument, it operates the automatic switch and color-changing features, as well as the depressor bar.

Jan 12, 1919

By Gilbert Thiessen

THE use of a pneumatic process for removing fine material (usually less than 48-mesh) is increasing in, the preparation of stoker-size coal. The fine material, produced as a byproduct, is known as dedusting-plant dust. Since fusain is the most friable ingredient in bituminous coal (it may readily be rubbed to an impalpable powder with the fingers), it tends to accumulate in this byproduct. While studying the properties of cokes produced by blending Illinois coals with other materials, considerable quantities of fusain were required. Dedusting-plant dust suggested itself as a-convenient supply. It became necessary, therefore, to determine how much fusain was contained in a measured sample of dust, how the fusain was distributed with respect to size and specific gravity in the sample, and whether or not it would be feasible or desirable further to concentrate or to recover the fusain from, the dust before using it in the blends to be coked. The results obtained indicate the possibilities of production of a high-fusain material.

Jan 1, 1936

By H. l. Burghoff, J. S. Porter

This paper presents the results of an investigation of the effect of cold-working and annealing treatments upon the occurrence of preferred orientation in annealed brass wire. The subject has received less consideration than has the same phenomenon in annealed brass sheet or strip, and perhaps very properly so in view of the obvious and undesired results obtained in the forming or drawing of strip having preferred orientation, which results are in contrast with the lack of any spectacular visual evidence in wire. The factors of cold-working and annealing that control preferredness in strip are naturally expected to function similarly in wire. Indeed, one might expect the condition to be commoner in annealed wire, because the severity of the cold-working between anneals in commercial Practice is usually much greater for wire than for strip. For example, a wire that is to be finished in the annealed condition on a diameter of 0.040 in. is commonly subjected to a final reduction of 90 per cent between the last two anneals, the large reduction being accomplished in the successive drafts of a multiple-die machine. Wire for rivets, for instance, on 0.125-in. diameter, although given a slight reduction of about Io per cent after the final anneal, may have been given a prior reduction of 75 to 80 per cent. Barrettl states the fiber axis of annealed 70-30 brass wire to be [111], with some indication of [IOO] as a secondary fiber axis. Croft and Sachs2 have reported briefly on some differences in brass wire with random and with preferred orientations. They showed statistical plots of the twin-band angles with respect to the wire axis or direction of drawing as observed on an axial plane. They also pointed out that the resistance of the wire to corrosion-cracking when externally stressed and exposed to a mercurous nitrate solution decreased as the degree of the preferred orientation increased. Material and PRocedure All the wire for the investigation was processed from one portion as cut for extrusion from a cast billet of the following analysis: 70.13 per cent copper; 0.01 lead; 0.01 iron; 0.02, nickel; 29.83 zinc (by difference). The billet section, 8 in, in diameter, was extruded hot to 3/4-in. diameter, after which it was processed by alternate cold-drawing and annealing treatments as indicated in Fig. I. The earliest anneals in process were at about 1100°F. and the next to the last reductions by drawing were 58 per cent. The diameter of the finally annealed wire was 0.132 in. Semifinal anneals were at 800°F., 950°F. and 1100°F. and reductions of 47.5, 74, 83.5 and 89.5 per cent were employed in drawing to 0.132 in. The final anneals were at 87s°F., 1050°F. and 1250°F. and were

Jan 1, 1944

By H. l. Burghoff, J. S. Porter

This paper presents the results of an investigation of the effect of cold-working and annealing treatments upon the occurrence of preferred orientation in annealed brass wire. The subject has received less consideration than has the same phenomenon in annealed brass sheet or strip, and perhaps very properly so in view of the obvious and undesired results obtained in the forming or drawing of strip having preferred orientation, which results are in contrast with the lack of any spectacular visual evidence in wire. The factors of cold-working and annealing that control preferredness in strip are naturally expected to function similarly in wire. Indeed, one might expect the condition to be commoner in annealed wire, because the severity of the cold-working between anneals in commercial Practice is usually much greater for wire than for strip. For example, a wire that is to be finished in the annealed condition on a diameter of 0.040 in. is commonly subjected to a final reduction of 90 per cent between the last two anneals, the large reduction being accomplished in the successive drafts of a multiple-die machine. Wire for rivets, for instance, on 0.125-in. diameter, although given a slight reduction of about Io per cent after the final anneal, may have been given a prior reduction of 75 to 80 per cent. Barrettl states the fiber axis of annealed 70-30 brass wire to be [111], with some indication of [IOO] as a secondary fiber axis. Croft and Sachs2 have reported briefly on some differences in brass wire with random and with preferred orientations. They showed statistical plots of the twin-band angles with respect to the wire axis or direction of drawing as observed on an axial plane. They also pointed out that the resistance of the wire to corrosion-cracking when externally stressed and exposed to a mercurous nitrate solution decreased as the degree of the preferred orientation increased. Material and PRocedure All the wire for the investigation was processed from one portion as cut for extrusion from a cast billet of the following analysis: 70.13 per cent copper; 0.01 lead; 0.01 iron; 0.02, nickel; 29.83 zinc (by difference). The billet section, 8 in, in diameter, was extruded hot to 3/4-in. diameter, after which it was processed by alternate cold-drawing and annealing treatments as indicated in Fig. I. The earliest anneals in process were at about 1100°F. and the next to the last reductions by drawing were 58 per cent. The diameter of the finally annealed wire was 0.132 in. Semifinal anneals were at 800°F., 950°F. and 1100°F. and reductions of 47.5, 74, 83.5 and 89.5 per cent were employed in drawing to 0.132 in. The final anneals were at 87s°F., 1050°F. and 1250°F. and were

Jan 1, 1944

By M. C. Fuerstenau, R. B. Bhappu

The response of beryl to sulfonate flotation was examined. The dependence of flotation recovery on sulfonate concentration, pH, and the absence or presence of various ions is also demonstrated. The response of quartz and feldspar to sulfonate flotation at various values of pH is given to. show the conditions necessary for selective separation. Finally, beryl was successfully concentrated from a natural ore using a technique devised from experimental observations on systems of pure minerals. With the possible exception of quartz, the flotation characteristics of silicate minerals are rather poorly understood. This is due in part to the com- plexity of the mineral systems themselves and in part to an insufficient amount of flotation data. The complexity of the systems arises from the wide range of chemical composition that the silicate minerals can assume. This is reflected in the variability of such physical properties as hardness and cleavage. Although the chemical composition of silicate minerals can vary considerably, a general grouping can be accomplished conveniently on the basis of the assemblage of SiO4 tetrahedra in all the silicates. That is, it has been shown that six basic groups can be obtained, depending on the arrangement of oxygen sharing between adjacent silicon atoms (or substituted aluminum). When all four oxygen atoms are shared, a framework structure such as quartz or feldspar is obtained. When three oxygens are shared, infinite sheets are obtained as in the micas and clays. When two oxygen atoms of the tetrahedra are shared, infinite chains are obtained, such as those in

Jan 1, 1963

By C. G. Dunn, M. Sharp

IN twinned crystals of the face-centered cubic metals the lattice of one twin is a mirror image of the other in a common twin boundary. When several twins appear within large grain in a sheet specimen, the twin one boundaries form a set of lines at the surface of the specimen which coincide with (111) planes of the large grain. Furthermore, for twins of the same orientation, these lines are parallel. Generally, the presence of identically oriented regions with straight parallel boundaries coinciding with a (111) plane of the surrounding crystal is strong evidence for identifying the island regions as twins of the parent crystal. However, Fig. 1, which shows the macrostructure of a large grain of copper with island regions that satisfy these conditions. is not an illustration of (111) twins. Since the reverse side of the specimen has much the same appearance, it was thought at first that these regions, which appear dark in the macrograph, actually were twins. According to X-ray data, however, these regions are second-order twins of the large crystal. With regard to their formation, these second-order twins formed by secondary recrystallization in a cube texture matrix. Growth occurred in the direction of the arrow (see Fig. 1) as the specimen moved slowly into a gradient temperature furnace as described previously.' Nucleation of the second-order twins occurred, therefore, on the ends facing opposite the arrow. If the origin of the second-order twins were due to repeated twinning, some first-order twin structure should be visible on these ends. This proved to be the case, as very small twins were readily found with the aid of a microscope, and probably could have been seen, in some instances, under ideal lighting conditions without aid of a microscope. Fig. 2 shows a cross-section view taken perpendicular to both the surface and the (111) trace of the parent crystal (visible as a straight boundary in Fig. 1) at the beginning point of growth of a second-order twin and where one first-order twin was relatively thick. In the micrograph, A is the large parent grain; B is the first-order twin of A; and C, which is a first-order twin of B; is a second-order twin of A. Between A and B and between B and C the major straight portions are traces of common (111) twin boundaries. The straight portion of boundary between A and C, however, is not a common crystallographic plane to the two lattices; it is a (111) plane of A and a (115) plane of C. Without considering the mechanism of twinning itself, the origin of the second-order twins may be accounted for in terms of repeated twinning and special growth characteristics. After each nucleation, a selective growth process can be thought of as favoring growth of the first-order twin in local spots only and favoring growth of the second-order twin to an extent comparable with that of the parent grain over relatively large areas in a way similar to that described for twinning in aluminum.' It has already been pointed out that the boundary between the large grain (A) and the second-order twin (C), which is responsible for the straight boundary portions in Fig. 1, involves a (111) plane of A and a (115) plane of C. The same combination of planes is not only possible in first-order twins, but actually appears quite frequently.3 Their prevalence in first-order twins and their presence here in second-order twins, together with the necessary occurrence of a large number of common lattice sites at the boundary, is an indication that this combination produces an "energy cusp"' boundary. (Energy cusp boundaries have been described by Shockley and Read.") The configuration of atoms near a {Ill), (115) boundary in first-order twins is of course different from the configuration near the same type of boundary in second-order twins. References 1 M. Sharp and C. G. Dunn: Secondary Recrystallization Texture in Copper. Journal of Metals (January 1952) Trans. AIME, p. 42. 2W. G. Burgers and W. May: Stimulated Crystals and Twinning in Recrystallized Aluminum. Recueil des travaux chimiques des Pays-Bas (1945) 64, p. 5. aD. Whitwham, M. Mouflard, and P. Lacombe: Discussion of W. C. Ellis and R. G. Treuting, "Atomic Relationships in the Cubic Twinned State." Trans. AIME (1951) 191, p. 1070; Journal of Metals (October 1951). 4 W. Shockley and W. T. Read: Dislocation Models of Crystal Grain Boundaries. Physical Review (1950) 78, p. 275.

Jan 1, 1953