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By R. P. Carreker

GERMANIUM is a member of that group of ele-nents—carbon, silicon, germanium, and tin-— that are currently of particular interest because of their interesting electrical properties. Near room temperature these materials of diamond cubic crystal structure are characteristically brittle. However, there have been several recent reports that germanium is not brittle at elevated temperatures These observations may be summarized as follows: 1—Germanium single crystals were observed to creep in bending under a maximum fiber stress of 6 kg per mm&apos; (8500 psi) at 500°C and above.&apos; The creep curves were sigmoidal, with an induction period that decreased with increasing temperature. 2—Germanium crystal bars have been bent 90" about radii ten times the bar thickness at 550°C.&apos; 3—-Audible clicks were heard when l/4 in. thick crystals were bent drastically at 450" to 500°C. No microstructural evidence of mechanical twinning was observed 4—Slip lines have been observed in tensile specimens deformed at 600°C, and are coincident with (111) planes, the close-packed planes of the diamond cubic structure.] The slip direction has not been established. 5—A germanium crystal has been compressed approximately 20 pct along a <110> axis at 700°C." The results reported subsequently were obtained in exploratory experiments intended to indicate some aspects of the behavior of germanium single crystals when tested in simple tension. Specimen Preparation A single crystal bar of n-type germanium was used. It was of purity corresponding to a resistance range of 2 to 20 ohm-cm. Tensile specimens were prepared by cutting small rectangular bars

Jan 1, 1957

Established as a Division February 22, 1928 J J Golden, Chairman M Tenenbaum, Past Chairman Gerhard Derge, Chairman-Elect R W Shearman, Secretary-Treasurer AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1960

BUFFALO C E Moyer, Chairman (Buffalo, N Y ) R M Jordan, Vice-Chairman H A Morlock, Secretary CHICAGO M E Nickel, Chairman (Chicago, Ill) A M Kroner, Vice-Chairman W R McLain, Secretary-Treasurer

Jan 1, 1960

By T. P. Meloy

Economic constraints require that the optimum mineral processing circuit be chosen for a given ore and then the circuit be optimized. Meloy (1983) developed a general methodology for finding the best circuit for a given ore. This analysis, however, did not specify a way to optimize the best circuit once it has been found. To optimize a given circuit, it is necessary to find the optimum set points for each unit operation in the circuit. Developed in this paper is a simple, general equation which, when applied, defines the optimum separation set point for the maximum mineral grade. This general equation, Equation (4), applies not only to simple ores, but also to complex ores containing variable and locked particles. Currently, the optimum set point can be calculated only for heavy media and cyclone circuits, because they are the only unit operations for which the necessary data has been measured.

Jan 1, 1984

By Harry C. Gatos, Frank J. Bachner, Mario D. Banus

The portion of the Nb-Sn phase diagram between 75 and 79 at. pct Nb at temperatures near the liquidus has been investigated by melting alloys of known composition and examining the microstmc-tzlres resulting when these melts were quenched. The Nb-Sn samples were contained in magnesia sleeves, and were mounted in a high-pressure apparatus. It was shown that Nb3Sn me1ts by a peri-tectic decomposition and that the composition of the compound Nb3Sn at the peritectic horizontal lies between 77 and 78 at. pct Nb. Analysis of the phases present in the samples was accomplished by anodic staining techniques and an electron-microbeam analyzer. DURING the past several years a great deal of work has been devoted to the Nb-Sn system, and the bulk of this work has been primarily concerned with the intermetallic phase Nb3Sn. However, the melting characteristics of Nb3Sn have not been investigated because of the difficulty in maintaining known compositions due to tin losses by vaporization, and the added difficulty of containing Nb-Sn alloys without sample-container reaction at the high temperatures involved. This paper reports on the development of a technique for containing Nb-Sn alloys under pressure high enough to prevent tin losses at temperatures in excess of the liquidus. Using this technique, melts of known composition were made and a phase diagram near the liquidus is proposed based on the microstructures resulting when these melts were quenched. EXPERIMENTAL The Nb-Sn alloys weighing 0.7 g each were prepared in the form of cylinders. Niobium powder, -200, +325 mesh, and tin shavings with a minute amount of tin powder for a binder were mixed in the desired proportions and cold-pressed at 50,000 psi in a 0.150-in. die. This cylinder was then enclosed as shown in Fig. 1, and the entire arrangement mounted in a 2.6-in. pyrophyllite tetrahedron.&apos; The desired temperatures (-2500°C) presented several problems in high-pressure container materials. Boron nitride, the usual sample holder, was found to react with niobium to form the nitride. However, MgO cans and plugs machined from refractory rods did not melt nor react with the sample. Thick tantalum contact disks were used to carry the large currents (~450 amps) to the graphite heater, since tantalum did not melt and had enough strength to prevent extrusion of the sample. It was further observed that the graphite heater and tantalum disks could not be in direct contact with the pyrophyllite because it melts and decomposes at these temperatures to kyanite and coesite (SiO2),2 the former reacting with graphite and the latter with tantalum to form the silicide. The use of a MgO outer sleeve

Jan 1, 1965

By J. F. Haseman, J. E. Davenport

IN the brown rock phosphate fields of Tennessee there are large deposits of phosphate matrix in which quartz is a major constituent of the gangue, and which cannot be beneficiated by the conventional washing process to yield a concentrate of suitable grade for use in the electric furnace. A huge tonnage of high-grade phosphate concentrate is produced in the Florida pebble district from low-grade siliceous feed. However, the characteristics of the low-grade siliceous Tennessee ore are such that flotation under the conditions employed in treating the Florida ore1-2 results in inadequate beneficiation. INVESTIGATION OF FLOTATION METHODS Flotation has been used in Tennessee primarily to produce a concentrate of premium grade by moderate enrichment of a marketable grade of phosphate.3,4 A secondary use was to increase the recovery of phosphate from the fines (down to approximately 200 mesh) from medium-grade ores with a concomitant moderate increase in over-all grade.3,5 It was considered desirable to investigate methods of improving the grade of washed products from low-grade siliceous Tennessee ore when these products were substantially below the requirements for use in the electric furnace. The present paper describes the results of a laboratory-scale study of factors that affect the beneficiation of such siliceous phosphate ore by flotation. The primary objective of the investigation was to ascertain the conditions under which the ore could be made to yield a concentrate suitable for reduction in the electric furnace. It was assumed that a phosphate concentrate for electrothermal reduction should contain at least 26 pct P205 and should have a weight ratio of silica to lime of not more than 0.80. Since a concentrate of moderate grade can be used in the electric furnace, and since, as Grissom4 has shown in detail, the ore will not bear the cost of expensive treatment, the study of collectors was limited to the relatively inexpensive fatty acids. A secondary objective was to determine whether a portion of the phosphate could be recovered in a grade suitable for treatment with phosphoric acid to produce 45 pct superphosphate. The ore consisted of variably cemented sand interlayered with clay. The sand layers were composed of grains of quartz, phosphate, and clay embedded in a matrix of clay and phosphate. Some clay was finely disseminated in the phosphate grains. Little massive high-grade phosphate was present. The material used in the flotation tests was a washed sand that had been separated from the ore in a bowl classifier at the TVA phosphate-washing plant. The percentage composition of the sand was as follows: P205, 20; Si02, 40; CaO, 29; Fe203, 2; A1203, 3; F, 2.3. The particle-

Jan 1, 1947

By Frank G. Miller, Ralph A. Seban

Problems relating to thermal methods of oil recovery have been given increasing attention during the past year. The nature of the physical and chemical processes underlying thermal recovery are not yet well understood. The need for pertinent basic information is recognized generally. One of the processes involved is the transfer of heat by conduction in oil reservoir rocks containing moving reservoir fluids. This technical note deals with heat conduction in a laboratory sand column filled with a moving hydrocarbon and therefore should be contributory to the presently inadequate fund of knowledge on thc over-all subject. In an analysis of the flow of vaporiziny propane through a horizontal column of sand, one of the present author9 demonstrated correspondence between thc measured values of pressure along the length of the column and those predicted by a theory which postulated that the enthalpy of the propane was invariable along the length of the column. This postulate way implied as a deduction from the principle of conservation of energy but the details of the deduction were not given. The specific purpose of this technical note is the presentation of these details both as an adjunct to the earlier analysis and to supply some additional details on the processes involved in this type of flow. Results disclose that rates of heat transfer by conduction, in the direction of fluid motion, generally would be small for systems of the type studied. FUNDARIENrAI. ENERGY EiQUAI-[ON The principle of conservation of energy may be applied to a section of the porous material on the basis that heat transfer, like fluid flow, is possible in the x direction only. Transfer of heat in the y and z di&apos;rections is prevented by suitable insulation or by taking the medium as infinite in directions perpendicular to the x axis. For steady state heat conduction and conditions of steady fluid flow the principle of conservation of energy specifies that any reduction in the enthalpy rate increases the flow of heat in the same proportion. Stated mathematically, dH KA 87 —- = - — - — U) * dx W dx........ Lvhere is the flow of heat in the positive x W dx direction. TEMPERATURE DISTRIBUTION IN DIRECTION OF FLOW The column of sand used in the previoi~sly described research is divisible into three different flow regimes. each of which may be analyzed independently. In the entrance region the liquid approaches the saturation state. A transition region is postulated following the transverse section at which the saturation state of the liquid is attained. In this transition region gas and liquid phases are both envisioned as present, with no vaporization occurring and with fluid movement restricted to the liquid. The upstream end of the exit region is at the transverse section of the column where the fraction of the pore space occupied by gas first becomes great enough for gas flow and where vaporization of the liquid begins. Fig. 1 indicates schematicaHy the thermodynamic processes undergone hv the fluid in the three flow regimes.

Jan 1, 1956

NORTH AMERICA ALASKA Anchorage.-Strandberg, H. College.-Barber, R. J. Burns, W. T. Henricksen, R. Henton, H. M. Joesting. H. R. Comet.-Albertson, F. E. Douglas.-Cahill, W. E. Carlson, L. Fairbanks.-Andregg. J. N. Coats. R. R.

Jan 1, 1938

By D. T. Peters, S. Floreen

The age hardening behavior of an Fe-8Ni-13Mo alloy was studied after the matrix had been varied to produce either ferrite, cold u~orked ferrite, or nzassive nzartensite. The aging behavior of the cold worked ferrite and murtensite structures were very similar. The martensite aging kinetics were much different from those observed in earlier studies of aging of maraging steels, even though the martensite wzatri.r had the same dislocation structure as those found in maraging steels. The results suggest that the previously observed precipitation kinetics of maraging steels ?nay have been controlled by the nucleation be-haviov, which in turn were dictated by the alloy compositions and the resultant identities of the precipitating phases. IT is well known that the rate of precipitation from solid solution depends not only on the degree of super-saturation, but also on the density and distribution of dislocations in the matrix structure. These imperfections often act as nucleation sites, and may also enhance atomic mobility. &apos;Thus, the presence of dislocations is important since the type and distribution of precipitates may be determined by them. The precipitate density and morphology in turn affects the mechanical properties of the alloy. A number of studies have been devoted to the precipitation characteristics in various types of maraging steels.&apos;-" These are iron-base alloys containing 10 to 25 pct Ni along with other substitutional elements such as Mo, Ti, Al, and so forth, that are used to produce age hardening. The carbon contents of these steels are quite low, and carbide precipitation is not believed to play any significant role in the aging reactions. After solution annealing and cooling these alloys generally transfclrm to a bcc lath or massive martensite structure characterized by elongated martensite platelets that are separated from each other by low angle boundaries, and that contain a very high dislocation den~it~.~~~~~~~~-~~ Age hardening is then conducted at temperatures on the order of 800" to 1000°F to produce substitutional element precipitation within the massive martensite matrix. Most of the aging studies to date have revealed several common traits in these alloys, regardless of the particular identity of the precipitation elements. Generally hardening has been found to be extremely rapid, with incubation times that approach zero. The agng kinetics, at least up to the time when reversion of the martensite matrix to austenite begins to predominate, frequently follow a AX/~~ = ktn type law, where x is hardness or electrical resistivity, t is the time, and k and n are constants. The values of n are frequently on the order of 0.2 to 0.5, which are well below the idealized values of n based on diffusion controlled precipitate growth models. Finally, the observed activation energy values are typically on the order of 30 kcal per mole, and thus are well below the nominal value of about 60 kcal per mole found for substitutional element diffusion in ferrite. The common explanation of these observations is that the precipitation kinetics are controlled by the massive martensite matrix structure. Thus, the absence of any noticeable incubation time has been attributed, after ~ahn," to the fact that the precipitate nucleation on dislocations may occur without a finite activation energy barrier. The low values of the activation energy are generally assumed to be due to enhanced diffusivity in the highly faulted structure. If this explanation that the precipitation kinetics are dominated by the matrix structure is correct then one should observe a distinct difference in lunetics between aging in a martensitic matrix and aging the same alloy when it has a ferritic matrix. Such a comparison cannot be made with conventional maraging compositions, but could be made with the alloy used in the present study. In addition, the ferritic structure of the present alloy could be cold worked to produce a high dislocation density so that one could determine whether ferrite in this condition would age similarly to martensite. EXPERIMENTAL PROCEDURE The composition of the alloy used in this study was 8.1 pct Ni, 13.0 pct Mo, 0.10 pct Al, 0.13 pct Ti, 0.012 pct C, bal Fe. The alloy was prepared as a 40 lb vacuum induction melt. The heat was homogenized and hot forged at 2100°F to 2 by 2 in. bar, and then hot rolled at 1900°F to $ in. bar stock. The aging lunetics were followed by Rockwell C hardness and electrical resistivity measurements. Samples for hardness testing were prepared as small strips approximately 2 by $ by 4 in. thick. Electrical resistivity was studied on cylindrical samples approximately 2 in. long by 0.1 in. diam. The method for making the alloy either martensitic or ferritic was based on the fact that the alloy showed a closed y loop type of phase diagram. At high temperatures, above approximately 24003F, the alloy was entirely ferritic. Small samples on the order of the dimensions described above remained entirely ferritic after iced-brine quenching from this temperature. In practice, a heat treatment of 1 hr in an inert atmosphere at 2500°F followed by water quenching was used to produce the ferritic microstructure. These samples were quite coarse grained and usually en-

Jan 1, 1970

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe&apos; using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"&apos; pure silwer and Ag-0.5 at. pct ~n;&apos; and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l&apos; Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele&apos;~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,&apos;~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,&apos; Gallaher,&apos; and Gallagher and Wash-burn.&apos; Ives and Ruff&apos; found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By Samuel H. Dolbear

NOT WITHSTANDING the extremely low ebb of business activity, the nonmetallic industries have fared somewhat better than some other branches of mining. The average price level in nonmetallics, although far from satisfactory, has resisted any cataclysmic fall such as has been suffered by copper and other metals. Stocks, also, though too abundant, represent no corresponding overhang of the market, which should result, in some branches, in a more rapid recovery. Research work has continued in some industries with interesting developments.

Jan 1, 1933

By Lawrence P. Bonicatto

The steel industry&apos;s increased demand for higher grade pellets has caused the pellet producers to investigate methods of upgrading their product and the Hanna Mining Co.&apos;s Groveland plant on the Upper Peninsula of Michigan is no exception. The low grade iron deposit is a complex mixture of magnetite and hematite with chert, quartz, jasper and various iron silicates.1 Beneficiation is by Humphrey spirals and anionic flotation of the iron minerals.2 Flotation of the spiral tailings makes up about 75% of the concentrate, while a minor amount of concentrate (less than 3%) is produced in magnetic circuits. The concentrate is pelletized at the rate of 1.6 million tpy. The initial concentrating facilities were constructed in 1958 and the concentrate was marketed as sinter feed until a pelletizing plant was added early in 1963. Grade improvement soon became a high priority research project, and several methods of concentration were investigated.

Jan 3, 1968

ALBERT J. PHILLIPS, Chairman E. H. Dix, JR., Past-chairman R. H. LEACH, Vice-chairman R. F. MEHL, Vice-chairman W. M. COME, Treasurer LOUIS JORDAN, Secretary 29 West 39th St., New York, N. Y.

Jan 1, 1937

[PRESIDENT GEORGE OTIS SMITH, District 4 WASHINGTON, D. C. PAST PRESIDENTS SAMUEL A. TAYLOR, District 3 PITTSBURGH, PA. E. DEGOLYER, District 0 NEW YORK, N. Y. FIRST VICE-PRESIDENT W. H. BASSETT, District 1 WATERBURY, CONN.]

Jan 1, 1928

BUFFALO C E Moyer, Chairman (Buffalo, N Y I R M Jordan, Vice-Chairman H A Morlock, Secretary CHICAGO M E Nickel, Chairman (Chicago, Ill ) A M Kroner, Vice-Chairman W R McLain, Secretary-Treasurer

Jan 1, 1959

By S. R. Dunbas, D. C. Jillson, E. A. Anderson

THE present work was undertaken to furnish information, lacking in the literature, on the deformation mechanisms active in pure titanium at room temperature. Since it was started, Rosi, Dube, and Alexander&apos; have indicated that slip can occur in coarse-grained (2 to 6 mm diameter) titanium on the {1010} and {1011} planes and twinning can take place on the {1072}, (1122) and (1151) planes. Liu and Steinberg,&apos; working with titanium flakes produced by fused salt electrolysis, found evidence of twinning on the {1032$, {1121), {1122}, (1123}, and (1154) planes. The crystals used in the present work were substantially longer (up to nearly 2 in. in length) and possibly purer. Production of Large Crystals It was the purpose of this part of the work to provide single crystal or large grain specimens for use in the deformation studies rather than to study the mechanism of crystal growth. Accordingly, all further exploratory studies on methods were abandoned when it was found that cold-rolled bars sealed in vacuo in individual Vycor tubes and given three or more cycles of 4 hr at 1200°C and three to five days at 850°C, gave large grains. Eighteen specimens about 0.2 in. square x 2 in. long yielded 33 useful grains, ranging from Va in. to nearly 2 in. in length, with an agreeably wide range of orientations, Fig. l. The 0.25 in. thick strip from which the starting specimens were cut had been reduced 67 pct on 18 in. diameter rolls from a scalped, hot-forged (959" to 1000°C), arc-melted, iodide titanium ingot. Thc bar was at room temperature, but the rolls were at 200°C. Reductions of about 0.03 in. per pass were used. The bar was cut into four segments, each of which was rolled in a somewhat different manner. No effect on the growth of large grains was noted. The composition of the titanium, determined on turnings from the ingot scalping operations, is given in Table I. The Rockwell A hardness of the ingot was 26. The standard starting specimens, about 1/4x1/4x2 in., were milled on all four sides, hand polished on 280 and 400 mesh emery papers, etched for 3 min in a 50 HF-50 glycerine solution, rinsed, and dried in alcohol and ether just before sealing them in Vycor tubes. The average specimen weight was 7.5 g, and the tube volume was 6.5 cc. A vacuum of less than 1 micron pressure was applied. The specimen tubes were placed in an evacuated Inconel muffle to minimize the danger of collapse of the glass tubes at temperature. In practice the specimens were first heated to 1200 °C for 4 hr and then transferred fairly quickly to an 850°C furnace where they were held for three to five days. This cycle was repeated at least three times before the specimens were cooled, removed from the tubes, lightly polished and etched on one surface for examinstion. Those in which large grains had not developed were resealed in Vycor and returned to the cycling. Satisfactory specimens (about one out of every four cycled) were polished with emery paper on all four side;, then metallographically polished using ctchinz between wheels to remove distorted metal and, finally, given a very light etch to reveal the grain boundaries. This was necessary because the surface was roughened by the sublimation of titanium under high temperature vacuum conditions. Specimens were identified by TiXl numbers using supplementary letters to designate specific grains.

Jan 1, 1954

By R. D. Rubright, Owen J. Hart

In the Bingham district over a span of more than 90 years, 43,947,104 tons of "non-porphyry" copper, lead, zinc, gold, and silver ore have been mined from a folded and faulted alternating series of Pennsylvanian and Permian limestones and sandstones and from some Tertiary intrusives. This ore came from six major mine areas located east, south, and west of the Bingham stock, site of Kennecott's porphyry copper deposit. The sediments were affected by varying degrees and types of metamorphism within 2000 feet or more of the Bingham stock. The intrusives consisting of the mineralized Bingham and the unmineralized Last Chance stocks and numerous dikes and sills of granite and monzonite were intruded into the asymmetrical northwest-trending and plunging Bingham syncline. Extrusives, although present, contain no ore. The bulk of the non-porphyry ore in the district was found above the Midas thrust. The primary ores are found in three major types of deposits: concordant bedding fissures, crosscutting fissures, and replacement deposits. These deposits consist of both copper and lead-zinc ore bodies that contain various amounts of gold and silver. These are in places roughly zoned both laterally and vertically and have been mined for up to 10,000 feet outward from the center of the Bingham stock and up to 5000 feet vertically below the surface. Secondary ore was of minor importance and was found in and under the oxidized zone at shallow depths. Genetically the Bingham stock, the ores, and related phenomena have had a common source.

Jan 1, 1968

W. N. Triplett (Geology of the Silver-Lead-Zinc Deposits of the Avalos-Providencia District of Mexico, P. 583) was born in Tecumseh, Mich., and attended the University of Michigan and Massachusetts Institute of Technology. From 1912 to 1917 he worked for Moctezuma Copper Co., a Phelps Dodge subsidiary at Nacozari, Sonora, Mex. He served in Army as Second Lieutenant Field Artillery from 1917 to 1918 and from 1919 to 1922 returned to Moctezuma Copper Co. From 1922 to 1952 he has been with Compania Minera de Penoles, S. A., a subsidiary of American Metal Co., Monterrey, N. L., Mexico in Unit Dept. as chief geologist and at present is consulting geologist. Mining geology and operation is of particular interest to Mr. Triplett. He presented a previous paper before with M. W. Hayward entitled, "Occurrence of Lead-Zinc Ores in Dolomitic Limestones in Northern Mexico." Besides being an AIME member, he holds membership in Society of Economic Geologists. Fishing, hunting and photography are his favorite hobbies.

Jan 1, 1952

Executive Committee, Board of Directors C E Reistle, Jr, Chairman, H DeWitt Smith, Vice-Chairman, T B Counselman, Grover Holt, A W Thornton Finance Committee, Board of Directors Andrew Fletcher, Chairman, R B Caples, C R Dodson Investments Erle V Daveler, &apos;57, Chairman, Henry Krumb, &apos;59, John E Warren, &apos;57, G F Moulton, ex officio as Treasurer, Andrew Fletcher, ex officio as Chairman, Fi¬nance Committee Endowment W W Mein, Jr, Chairman, N G Alford, E V Daveler, W J Coulter, J V N Dorr, R B Gilmore, J B Haffner, 0 H Johnson, Henry Krumb, D H McLaughlin, J R McMillan, J B Morrow, L F Reinartz, Wilfred Sykes, C E Weed Honorary Memberships Andrew Fletcher, Chairman, L F Reinartz and H DeWitt Smith, ex officio as Past Presidents, C E Reistle, Jr , ex officio as President, M L Rai¬der, &apos;60, Henry Krumb, &apos;58, D H McLaughlin, &apos;57, P D Merica, &apos;59

Jan 1, 1956

By R. T. Hukki

This paper presents a preliminary analysis of the fundamental relationship between the net energy used and the respective product size throughout the entire range of sizes covered by crushing and grinding, and an attempt to find a sensible correlation between the existing theories. Walker, Lewis, McAdams, and Gilliland&apos; have given the following differential equation of a general form for comminution: dE = -C§ [1] where E is the net energy required per unit weight in a certain process of comminution; x is the factor indicating the fineness of the product; n is the exponent indicating the order of the process, and C is a constant related with the material, units chosen, etc. H exponent n in the above equation is replaced by numerical figures 2, 1, and 1 1/2, the integrated form of the general equation leads to the well known fundamental theories represented by the law of von Rittinger,&apos; law of Kick, and the third theory of comminution by Bond, respectively. The total net energies (E) from infinite feed size to a product of size x are as follows: The net energy required in a certain process of comminution is proportional to the new surface developed according to the law of von Rittinger, to the weight or size of the bodies treated according to the law of Kick, and to the length of the new cracks formed which initiate breakage according to the theory and explanation by Bond. On a logarithmic paper, where particle size is presented on the abscissa and energy consumption on the ordinate (see Fig. 21, all three relationships are represented by straight lines. The slope m of the line according to the law of von Rittinger is equal to -1.0; of Kick, 0; and of Bond, -0.5. Experimental evidence in favor of the law of Rittinger has been presented, e.g., by Gross and zimmerley5 on quartz crushed in a drop weight crusher and evaluated for surface by the method of dissolution, by Dean on magnetite crushed by a similar method and evaluated for surface by the determination of coersive force, by piret7 and co-workers on a group of minerals crushed again by a similar method as well as by compression and evaluated for surface by permeability and gas adsorption methods, and by schellinger8 on a group of minerals ground in a calorimetric ball mill and evaluated for surface by gas adsorption. Experimental evidence in favor of the law of Kick seems to be scant in the field of comminution. On the other hand, in the field of mechanical engineering Kick&apos;s law seems to be of fundamental nature in processes such as cutting, pressing, shaping, and rolling of metallic substances. Experimental evidence in favor of the third theory has been provided by Bond." To a large extent, data are based on the vast amount of grindability tests performed in the laboratories of Allis-Chalmers Manufacturing Co. In addition to the devoted proponents of one or the other of the basic theories listed above, certain investigators have indicated that one of the theories might be applied for a certain range of sizes, while another theory might be used for other sizes. In a discussion of a paper by Bond," Dobie" presented a statement at the International Mineral Dressing Congress in London (1952) indicating that 1) for large particles, the law of Kick was approximately correct; 2) for finer particles, von Rittinger&apos;s suggestion was nearer to the truth; and 3) Bond&apos;s new

Jan 1, 1961