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By J. E. Berry

AII evaluation is made of the acoustic velocity log for measurement of formation porosity. Plots of field-observer1 velocities vs core-measured porosities of sandstones and limestotnes with inter intergranular porosity show that the velocity log gives a useful measure of porotity, in agreement with published data. A new method of plotting electrical and velocity log data makes it easier to recognize hydrocarbon-water coritnct~ from log darn and to make serni-quantitative estinlates of hydrocarbon saturation. Two examples of this interpretation technique are given. This paper also discusses the various factors that affect acoustic velocity and shows how corrections can be made for some of these factors. INTRODUCTION Although the continuous velocity log was developed primarily as an aid to seismic interpretation, it is finding widespread use for measurement of porosity. The purpose of this paper is to evaluate this use of the log. Results are presented for the velocity-porosity relationship in many sandstones and one limestone. Practical applications of porosity values derived from the velocity log to improve interpretation of electrical surveys are presented. Various parameters which affect velocity in porous media are considered. Porosity, composition, cementa-tion, pressure difference (overburden pressure minus fluid pressure), fluid saturation, and wellability are discussed. Some of the ideas are opinions based on general considerations of well logging problems while others are supported by published data and our own observations. Major conclusions from these studies arc given in the body of the paper and detailed discussions of some of the various factors affecting porosity are given in the Appendix. POROSITY Sandstones The primary factor affecting the velocity of sound in porous media is porosity. Wyllie, et al,1 have reported a time average equation for the relationship between velocity and porosity.* This has found considerable acceptance in the industry. Other relationships between velocity and porosity have been proposed, none of which are entirely satisfactory. It is doubtful that any one relationship will completely describe all situations. We have tried an empirical relationship based on correlating log velocities with core-measured porosities. Measured porosities were averaged over a depth interval equal to the spacing used in recording the velocity logs. The depth range for the information used was from 2,000 to 12,000 ft. Velocity measurements were normalized for the effects of depth and overburden pressure. A detailed discussion of the basis for this normalization is given in the Appendix. The change is usually insignificant and when working with individual formations it can be neglected. All velocity measurements were normalized to a depth of 10,000 ft. The velocity-porosity data for sandstones in Fig. 1 came from 20 wells scattered throughout the Mid-Continent and Gulf Coast areas. The scatter of the data points is attributed to three causes: 1. There is no theoretical basis for expecting an exact velocity vs porosity relationship and it is not possible to correct precisely for the effects of such factors as impurities, grain shape, manner of cementation, etc. Some of these factors are discussed in the Appendix. 2. Porosities measured by core analysis are not necessarily representative of what the velocity log "sees". 3. Inaccuracies appear in the velocity log reading. This is particularly true of velocities from one-receiver logging tools.*" A linear-time curve (time-average equation) is plotted in Fig. 1 along with the best straight line through the points. Velocities used for the linear-time curves were 19,500 ft/sec for the matrix velocity (zero porosity) and 5,500 ft/sec for fluid velocity. For clean sandstones with velocities greater than 10,000 ft/sec, there is little difference between the velocity-porosity and the time-porosity curves. Both curves are well within the scatter of data points. The data points in Fig. 1 were restricted primarily to clean sandstones, using the SP and/or gamma-ray logs as clues to the lithology. Where a lithologic de-

By Garth M. Crosby

Hugh E. McKinstry (Professor of Geology, Laboratory of Mining Geology, Harvard University, Cambridge, Mass.) Pre-Cambrian age for the Coeur d'Alene mineralization, as indicated by isotope studies and recently discussed by Silverman, Long, and Kulp' would explain some features of the mineralogy of the district that have long been a puzzle. In the Silver Belt, especially in the Sunshine mine, lead-zinc min erali zation passes downward into tetrahedrite ore. Although commercially speaking this is a rich silver zone, the silver is, quantitatively, a mere impurity amounting to a small fraction of 1 pct. In effect the zonal change is from lead-zinc down into copper mineralization—-the usual zonal change that occurs in many districts. In the Burke-Mullan portion of the district, on the other hand, lead-zinc ore does not pass downward into copper mineralization of the Sunshine type. Instead, pyrrhotite appears in depth while the tenor in lead and zinc declines. The change occurs at increasingly greater depth away from the Gem stocks, deepening irregularly by some 3000 ft within two to four miles. As noted by Crosby, biotite, grunerite, and garnet appear in the deep zone. The marked difference between this apparent zonal change and the more nomal change to a copper zone is quite explainable if already existing pre-Cambrian veins have been locally metamorphosed by a Tertiary intrusive. The chief obstacle to this explanation is the evidence that mineralization cuts Laramide intrusives, but evidence on this point is conflicting as indicated by Crosby's observations and summary. This is not the first instance of a problem in determining the time-relationship of mineralization to a spatially associated intrusive. At the Noranda mine veins of chalcopyrite extend into a diabase dike which apparently cuts the ore, although Price2 concludes that the ore is later. However, at the Normetal mine diabase of a similar dike is thought3 to intrude the orebody but is cut by stringers of chalcopyrite. In the Sullivan Mine, B. C.,4 galena follows a fracture in a larnprophyre dike which, itself, cuts the main orebody. In the Sudbury district dikes of olivine diabase are clearly younger than the nickel ore, yet where they cut the Creighton orebody they contain stringers of chalcopyrite. In the laboratory, Hawley5 has developed veinlets of sulfide (chalcopyrite) it] silicate gangue by heating specimens of ore in a stream of H2S at 410 °C. From this and other evidernce. it seems clear that sulfides can be transferred from one site to another — at least through short distances — at temperatures well below their melting points. It would seem then that even if sulfide Mineralization in the Gem stocks can be shown unequ ivocably to be later than the intrusive the possibility of "remobiliza tion" need not be more than local. Thus the zonal relationships are quite in accord with a pre-Cambrian age for original deposition of the lead, zinc, copper, silver, and uranium in the Coeur d'Alene district. REFERENCES 1. A. Silverman, A. Long, and J. L. Kulp: Discussion of: The Gem Stocks and Adjacent Orebodies, Coeur d'Alene District, Idaho. Mining Engineering, May 1960, pp. 470-471; AME Trans., 1960, vol. 217, p. 117. 2. Peter Price: Geol. & O. D. at the Home Mine, Noranda, Quebec. Can. Inst. M & M Bull 263, 1934, p. 108; also,Trans. CIMM 1939, pp. 108-140. 3. w. L. Brown Nometal Mine in structural Geology of Canadian Ore Deposits, Montreal, 1948, p. 690. 4. C. O. Swanson and H. C. Gunning: Geology of the Sullivan Mine. Can. Inst. Mining & Met. Trans. vol. 48, 1945, p. 653. 5. J. E. Hawley: Heat Effects on Sulphides and Possible Applications. Univ. Toronto Studies, Geol. Ser. No. 46, 1941, p. 34.

Jan 1, 1961

By H. L. Shergold, O. Mellgren

Concentration of fine quartz particles at the iso-octane/water interface has been investigated under different conditions of pH and dodecylamine concentration. The results obtained from the related studies on the effect of amine concentration and pH on the interfacial tension, adsorption density, electrokinetic potential, contact angle, and concentration of the various amine species in the system are presented. A good correlation was obtained between these different variables. It is well-known that very fine mineral particles are difficult to float in conventional flotation machines. Flotation rate studies have revealed that the rate of flotation of fine mineral particles is much smaller than that of coarser size fractions. The theories accounting for this behavior have been discussed by Arbiter and Harris1 and also Meloy.2 Theoretically, a hydrophobic fine particle might never make contact with a bubble because of the presence of an energy barrier in the vicinity of the air/water interface.' This energy barrier will have electrostatic, hydrodynamic, and Van der Waals force components. It was thought that by using an oil phase instead of air the energy barrier would be decreased so that fine particles could be concentrated at the oil/water interface more readily than at the air/water interface. The technique used involves dispersing the fine particles in water, containing the appropriate chemical reagents, and injecting a fine dispersion of iso-octane oil droplets into the pulp. After vigorous conditioning, the pulp is passed into a separating column where the oil droplets coated with a layer of mineral particles rise to the surface to form a separate layer. Air is introduced into the base of the separating column to ensure that heavy agglomerates of oil and particles report with the organic layer. This technique has been described previously4 and adopted by Lai and Fuerstenau5 who studied the alumina-dodecyl sulfonate system. The interfacial phenomena in the system composed of hematite, water, and iso-octane in the presence of sodium dodecyl sulfate have been studied and the results reported" earlier. This paper describes the results obtained from investigations into the interfacial phenomena in the quartz/water/iso-octane system in the presence of dodecylamine. The technique used in measuring the interfacial tension, electrokinetic potential, contact angle, and adsorption density were similar to those described previously? Materials Selected pieces of a high purity natural quartz, from the Isle of Man, were crushed in a laboratory jaw crusher and pulverizer. The — 52+72 mesh size fraction was retained and leached with successive washes of hot concentrated hydrochloric acid to remove iron impurities. When no iron was detected in the solution by ammonium thiocyanate, the quartz was washed thoroughly with distilled water until the conductivity of the wash water assumed that of the distilled water. Samples of 25 g of the —52+72 mesh quartz were ground for 5.25 min in an agate vibratory mill. The ground product was 100% —44 m and 57% —10 am, as determined by the Andreasen pipette. The specific surface area of the sample used for the adsorption and flotation tests was 0.94 sq m g-l. This corresponds to a mean particle diameter of 2.4 am. The —44 am quartz sample was stored under vacuum in the presence of silica gel crystals. For the contact angle determination between the three phases, quartz, iso-octane, and water, a piece of the natural quartz was ground into a block about 15 mm long, 15 mm wide, and 5 mm thick. One surface of the block was then polished by successively finer grades of silicon carbide "paper." The final polishing was conducted with alumina on a "hyprocel" paper. The polished quartz specimen was cleaned using nitric acid and ethyl alcohol followed by a wash with distilled water and then stored under distilled water. This pro-

Jan 1, 1971

By W. L. Penberthy, H. J. Ramey

Experimental work on the combustion oil recovery process has consisted of both laboratory and field studies. Although field experiments are the ultimate test of any oil recovery process, they are costly, time consuming and difficult to analyze quantitatively. Laboratory combustion tube experiments can be opertzted far more rapidly and cheaply, but are subject to scaling and interpretation problems. This paper points out some important design problems, operational criteria and considerations in2portunt to interpretation of results. An analytical hcut model of movement of a burning front axiully along a cylinder with heat loss through an annular insulation was developed. The result was used to identify steady-state temperatrrre distributions both ahead of and behind the burning front, with and without heat loss. Results indicate potential operating limitations on the minimum burning front rielocity (or air flux) which may be used for any given combustion tube. Results also enable estimating the effective thermal diffusivity and over-all heat loss from experimental data and thickness of the brnning zone. Resu lts of operation of a combustion tube constructed recently verify this preliminary theory in the region immediately ahead of and behind the burning front surprisinRly well. INTRODUCTION Many field and laboratory studies of the forward combustion oil recovery process have been conducted since the early publications of Kuhn and Kochl and Grant and Szasz2 in 1953 and 1954. In view of the complex and costly nature of this type of investigation, it is not surprising that no complete theory of the nature of the forward combustion Drocess is yet available. However, gross effects are understood well enough that reasonable design procedures are available for planning field operations. Nelson and McNeil 3,4 have published two comprehensive papers concerning design procedures. One major consideration in planning field operations is the fuel concentration at the burning front. Fuel concentration controls air requirements — an important cost factor in forward combustion. Although fuel concentration can be estimated from field test results by various methods, results are subject to great uncertainty in view of natural limitations on experimental observations. Nelson and hlcNeil4 recommend that fuel concentration be determined from laboratory combustion tube studies. Fuel concentration is only one of many important factors which can be studied by combustion tube experimentation. An obvious goal of imporrance must be development of a comprehensive theory of the forward combustion process. If a theory of this process can be established which matches controlled laboratory experimentation, it should be possible to apply this theory to field operating conditions with some confidence. Laboratory combustion tube studies have already yielded important information concerning the combustion process. However, details concerning the design, construction and operation of combustion tubes are rare. Combustion tubes used by various investigators vary in size, length and mode of operation. Therefore, one purpose of this paper is to present considerations important to design, construction and operation of a combustion tube. In regard to previous combustion tube studies, attention is called to Refs. 1 through 9. These references describe a wide variety of equipment types and present a great deal of pertinent experimental data. In general, combustion tubes usually consist of thin-walled stainless steel tubes containing an oil sand pack mounted within a pressure jacket. Provisions have often been made to heat the tube ex tern a lly by separately controlled heaters to reduce heat losses. This step usually permits operation at low air fluxes (air rate per square foot burning front surface) similar to those encountered in field operations. Burning is usually conducted from the air inlet end of the tube to the outflow end. The tube orientation used has been vertical or horizontal. For vertical tubes, burning has been conducted vertically downwards. As a result of laboratory studies, many of the

Jan 1, 1967

By Hans Lundberg

Jan 1, 1927

By E. DeGolyer

PROSPECTING for new deposits is a part of the ordinary routine business of the petroleum industry to an extent that is not true for any other mineral industry. The health of the industry depends upon whether we are successful or unsuccessful. How many know what it costs to find oil today and what it has cost in the past? Very few, I will wager. The industry is not well informed upon this extremely important point. We cannot deal in averages for lack of information. Does it cost more or less than previously? Prospect wells are increasingly deeper and, since the introduction of the core drill, prospecting techniques have required increasingly expensive field oper-

Jan 1, 1939

By Fred H. Lippold, Wm. H. Wolf

Methods of fair payment for excavating, supporting, and concrete lining tunnels have been sought by various owners for years. Tunneling techniques have changed with the development of equipment-from the hand-mucking operation to the machine mucker and, most recently, to machine-boring; from tunnel supports using timber sets to steel sets to rock bolts and, most recently, to shotcrete support; and from hand-placing the concrete lining using wooden forms to pumping or pneumatic placing using steel forms. As tunnel construction techniques advanced, so did methods for payment for the work performed. The recent development of tunnel-boring machines, or "moles," is precipitating another change. These changes have led to some difficulty in providing proper payment for the various items of work for different types of tunnels. As a major construction agency engaged in water-resources development in the western states, the U.S. Bureau of Reclamation has long been aware of the need for clarification of payment provisions in tunnel construction. The Bureau has some 150 miles of tunnels completed on its projects and about 50 miles of tunnels under construction. In this construction, the Bureau has benefited by the advance made by contractors in improving the techniques of tunnel excavation. To assure that the Bureau has an up-to-date approach to payment provisions, the Chief Engineer recently established a "standard" method of payment for all types of tunnels. It is believed that this new method of payment will be equitable for all contractors bidding on various types of tunnels using the diversity of methods of excavation now available to them. These payment provisions provide for different quantities for excavated tunnels using the blasting technique or using machine-boring techniques. In this way, the contractors have a choice in excavation methods and an equal opportunity to be low in their bids. We believe this will be an incentive to all contractors to be as progressive as the development of new equipment economically allows.

Jan 1, 1970

By W. R. Webb, M. O. Peterson

WHEN men drive haulage equipment ranging up to 22 tons in an open pit operation, they must live with the realization that their safety is dependent upon the machines they drive and how well they operate them. The hazards inherent in their jobs must be recognized, met, and defeated. It comprises a never ending struggle toward perfection-an almost un- obtainable goal. The Jones & Laughlin Benson Mines, at Adirondack State Park in New York, created a safety program which resulted in only one three day lost time accident from April 1948 to April 1952. At the very start of the program, management of the open-pit operation recognized the hazards existing at Benson. The program was designed to meet each danger. With a knowledge of the problem faced, the process of minimizing each facet was planned along lines of maintenance of equipment and training of personnel. Its success is evident. In the ever-present struggle, care and maintenance of machines and application of experience to new equipment design are mainstays. Truck Haulage Benson produced 2.9 million tons of crude iron ore and 1.6 million tons of waste in 1951. To do the job, truck mileage reached 500,000 miles. The tremendous mileage emphasized to safety planners, the fact that the more work done, the greater the possibility of risk in haulage operations. Instrumenting the aim of the safest equipment possible is a methodical servicing program. Like other segments of the drive, the servicing program is based on greater production with fewer accidents. Every truck is serviced at least once per eight-hr shift. Examination includes inspecting and tightening wheel studs, checking tires, steering apparatus, lights, brakes, wipers, heaters, fire extinguishers, and refueling. A running history of the equipment's operating life is kept in the form of service and maintenance records. Machine operators are constantly on the alert for malfunctioning of units. At the first sign of trouble the truck is returned to the garage for exchange. No truck functioning incorrectly is kept on the line, regardless of its shift check schedule. The program resulted in a reduction of the number of costly overhauls and cut down the number of haulage accidents. Miscellaneous Mobile Equipment Auxiliary units, operating within the pit, have presented definite safety problems. The highest accident rate in the pit occurred on trucks carrying water and bits to the churn mills. The weight and awkwardness of bits and drill stems, combined with remote delivery points were direct causes of numerous accidents. Here, the problem has been one of equipment handling, rather than haulage. All air compressors for secondary drilling are truck mounted, facilitating mobility. In addition to making it easier to move the equipment, truck mounting has eliminated many of the hazards connected with relocating machinery. By making air compressors independent of other units, drilling operations have been speeded up considerably. Unseen rocks in the path of moving vehicles are a constant source of tire damage. At Benson the problem has been met by supplying each loading crew with a bulldozer for cleanup operations. The pitman directs the dozer operation, and when truck drivers back into loading areas, he serves as an extra set of eyes. Modern Truck Garage Provides Drive-Through Service Simplicity is the essence of any preventative maintenance program. At Benson, a modern garage, with a drive-through service bay simplifies servicing. Shift inspection of the 22-ton haulage units is accomplished with minimum delay and maximum thoroughness. Major repair work and periodic overhauls are done in the repair section of the truck garage. Crane facilities for handling heavy assemblies ease the job and add to the safety factor. Other mobile machinery,

Jan 1, 1952

INTRODUCTION Mineral explorationists range throughout the world looking for mineral deposits which can subsequently be made into mines. Mines are not found! Mines are made, usually at great cost and not often without significant risk. The process of making a mineral deposit into a mine involves a great deal more than a complete appraisal of the deposit. The making of a mine demands detailed feasibility studies of many factors, any one of which, if shown to be negative, could prevent the deposit from becoming a successful mine. Total feasibility analysis involves at least three major fields of study: (1) economic analysis, (2) financial analysis, and (3) political and environmental analysis. Economic analysis is essential for proper decision making at many stages in the evaluation of a mineral deposit. It is the yardstick by which the proposed mining project and alter- native investment opportunities are measured. Economic analysis is concerned with costs and potential profits and can be applied at various stages in the evaluation of a mineral deposit to determine if the project merits the additional funds necessary to bring about each succeeding stage. The nearer any deposit approaches to becoming a mine, the more carefully the economic analysis should be made. Financial analysis has reference to how, where, and at what cost the investment funds can be obtained to finance the proposed mine project. Political and environmental analysis has reference to the many intangible factors that can affect the making of a successful mine. These factors loom larger today than ever before, due to the profusion of government regulations and various environmental constraints now imposed upon the mineral industry both by law and by the weight of public opinion. Ultimately, many of these intangible factors can be resolved back into the economic analysis as an added cost to mine development, but more and more often they have become insurmountable obstacles to any development of certain deposits. The role of financial analysis and the analysis of intangible factors must never be underestimated when making a feasibility study upon which to base investment decisions; however, the emphasis of this text will be upon economic factors. THE PARAMETERS OF MINERAL ECONOMIC ANALYSIS The two major elements of economic analysis are: 1) The potential earnings or annual generated cash flow of the project. 2) The investment costs necessary to realize such earnings. If the difference between the two elements is large enough, i.e., if the return on investment from the cash flow is high enough to attract investors, the project can be said to be financially feasible. The mineral economic analysis must take into consideration many parameters, some of which are known or knowable within certain limits, and others of which are unknown or unpredictable within certain limits and for which estimates must be made. Because both known and estimated parameters enter into the same analytical computations, it is important for the analyst to realize the nature of each when considering the results of an analysis. Some parameters such as the grade of mining block, although estimated, are said to be known within mathematically defined limits. Other parameters, such as the future price for minerals produced, etc., can only be estimated or "guestimated" within reasonable limits for which no precision can be assigned. Known or Knowable Mineral Economic Parameters Known or knowable parameters are: 1) Tonnage and grade of valuable minerals for the total mineral body and for individual mining blocks. 2) Metallurgical recovery of valuable mineral. 3) Minimum operating life of mineral de- posit at any specified production rate. 4) Royalty schedule, property payments, etc. 5) Sales-purchasing agreements, smelter schedules, marketing contracts, etc.

Jan 1, 1980

By J. H. Hamilton, J. R. Lewis, J. H. Dismant, W. M. Fassell

RECENTLY this laboratory undertook the task of preparing some low carbon metallic cobalt by the carbon reduction of precipitated cobalt oxides. The oxides came in two lots and had the compositions given in Table I. Industrially, cobalt rondels' are made by the carbon reduction of cobalt oxide in small reverberatory furnaces at temperatures near but not above 1050 °C. This is a slow and tedious small batch process but does give cobalt metal which is low in carbon (1 pct C). Inasmuch as these cobalt oxides were relatively low in copper and iron it was decided to reduce them with petroleum carbon in a small three-phase electric arc furnace of about 3 to 5 Ib of metal capacity. It was hoped such a procedure would save considerable time and perhaps also indicate an improved commercially feasible process. The furnace was preheated by using small pieces of carbon electrodes to maintain the arc until a temperature of 1500°C was reached. The broken pieces of electrodes were then removed and 500 g of the cobalt oxides and 60 to 100 g of petroleum coke added. At the end of the reduction reaction, a high lime flux was added to the furnace to facilitate the removal of sulphur. Due to the fineness of the cobalt oxide powder used and also to the presence of chlorides there was considerable dust lost in charging the furnace. This was overcome by preparing briquettes composed of the cobalt oxides, charcoal, and a little bentonite to serve as a binder. The results obtained are summarized in Table 11, which shows that the cobalt metal produced in the arc furnace was high in carbon varying from 2.5 to 3.5 pct. This, of course, is much too high. For certain uses, such as in the preparation of permanent magnets, the carbon content of cobalt must be low. It was necessary therefore to find an effective method of reducing the carbon content of the cobalt that had been prepared in the arc furnace. Van Arkel3 recommends the use of Co2O3 as a means of removing carbon from cobalt. Experiments by the authors indicate that carbon is removed with difficulty by this method. Other methods used, including lancing of the molten high carbon cobalt with a jet of oxygen, proved to be ineffective. The method finally used makes use of the fact that cobalt metal is decarburized by carbon dioxide at the temperature of the molten metal. Two methods were used: 1—carbon dioxide was bubbled up through the molten cobalt, and 2— molten cobalt was maintained in a carbon dioxide atmosphere. In the first method the gas was introduced below the surface of the molten metal by means of a quartz tube. A high frequency induction furnace was used to keep the cobalt molten in both of these experiments. This kept the metal somewhat agitated and no doubt was an important factor in hastening the decarburization 'process by the second method. Both methods gave satisfactory results as shown in Table 111. An interesting observation in connection with this 'work was that a small sample of carburized cobalt metal could be decarburized by heating it with an acetylene torch adjusted to give an oxidizing flame. This may have been due to the presence of carbon dioxide in the products of combustion. Samples of molten high carbon steel were decarburized by the same method and it is suggested that nickel and perhaps manganese can be decarburized in a similar manner. Additional work, including rate studies and other theoretical aspects of this problem, is in progress in this laboratory.

Jan 1, 1953

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1'2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By Norman F. Schulz, Emert W. Lindroos, Strathmore R. B. Cooke

DURING the course of an investigation of the effects of various starch products on hematite and quartz in regard to their separation by flotation, it was found that whereas most starches flocculated suspensions of hematite in water, they did not flocculate similar suspensions of quartz. However, a derivative of whole corn starch containing approximately one tenth aminoethyl group (-—CH,CH2NH2) per glucose unit proved to be an exception. This aminoethyl starch was a very good flocculant for both hematite and quartz, and also possessed the property of depressing both minerals in cationic flotation tests. In view of the widespread use of starch as a flocculating agent of solids in tailing water, pulps, and for coal slimes, ore and various other purposes in sulphide and nonsulphide flotation, attention is called to the effective surface activity of aminoethyl starch in flocculating suspensions of the two minerals investigated. Test Materials The starch products employed included Globe Pearl starch No. 144 and fresh aminoethyl starch, both supplied by the Corn Products Refining Co. Dr. A. L. Elder" has kindly furnished a description The minerals used in the various tests are listed in Table I. Their specific surfaces were determined by the air permeability method, which gave results reproducible to within plus or minus 3 pct. Surface areas obtained by krypton adsorption were greater than the air permeability values by a factor of 2.0 for quartz and 62.4 for hematite. Starch Adsorption on Mineral Surfaces Starch adsorption data were obtained by agitating for 1 hr measured volumes of neutral starch solutions of known concentrations with weighed quantities of finely divided mineral of measured specific surface. The mineral then was separated from the pulp liquor by centrifugation and the residual starch content determined by chemical analysis. The analytical procedure consisted of oxidizing the starch with an excess of dichromate in acid medium at elevated temperature and titrating the excess dichromate by the ferrous ammonium sulphate—potassium permanganate method. Analytical results were reproducible to within less than 1 pct. Adsorption data obtained in unbuffered solutions near the neutral point are plotted in Fig. 1. The adsorption on either mineral was far greater for the aminoethyl starch than for the Pearl starch. Flocculation The degree of flocculation was determined for a given pulp by measuring the time required for the supernatant liquid to reach a certain degree of clarity. This was accomplished by passing a standard light beam through the pulp, contained in a glass settling tube, and measuring the time required after agitation ceased for the intensity of the transmitted beam to reach a predetermined value. Starch reagent was added to each pulp in small uniform increments, and the settling time was determined after each such addition. Increase in pulp liquor volume due to the added starch reagent was ignored in these tests. Pulps were maintained at or near neutrality. of the preparation of the aminoethyl starch: "Three hundred and sixty grams of powdered unmodified corn starch was slurried in 3 liters of water and stirred during gelatinization. Eighty-six grams of ethylenimine was added slowly during reflux which was continued for 4 hr. The yellow solution set to a gel upon cooling. This was broken up and neutralized with HC1. The thick paste was dried on hot rolls. Adsorbed polyethylenimine and salts were removed from the yellowish products by washing first with acidified aqueous '60 per cent' alcohol. The white product contained nitrogen corresponding to about one aminoethoxy group per ten glucose residues." Only laboratory samples of this starch derivative have been prepared. The starch reagents for use in flocculation, flotation, and adsorption tests were made up by dispersing the appropriate quantities of air-dry starch in cold water, adding boiling water, and heating for 30 min at 120°C under pressure. When used ip adsorption tests, the starch solutions first were cleared of insoluble matter by centrifugation.

Jan 1, 1953

By J. B. Macelwane

Historically whenever application of scientific results to a new problem required the special experimental background, the economic outlook and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering based on the professional requirement grew up in the engineering colleges. This is precisely what is happening now in geophysical engineering. THE Mineral Industry Education Division of AIME has long been interested in geophysical education. Organized in 1938, a Committee on Geophysical Education presented a number of reports in succeeding years. The AIME is an engineering society; hence it might be expected that the interest of the Mineral Industry Education Division would have centered about the relation of courses in geophysics to engineering education. However, this was not the case. The burden of the discussion held under the auspices of the Committee on Geophysical Education bore on geophysics in general and particularly on its relation to geology. In the decade that has passed since those meetings much water has flowed under the bridge. Not only have the geophysical sciences developed at an extraordinarily rapid rate but the practical importance and the range of their applications have spread in ever widening circles and have even assumed a very prominent place in research programs of the military, the Army, the Navy and, particularly, the Geophysical Research Directorate of the Air Force at Cambridge, Mass. So enormously have the geophysical sciences as such grown in scope and in degree of specialization that no one man in a lifetime of study can hope to master the theoretical and experimental complexities or even to follow intelligently in the published literature all the varied accomplishments of basic research in these fields. As in the other sciences, most of the results of geophysical research have potential economic value and are being applied to a wider and wider range of human needs. Here we see a parallel with the older sciences and their relation to engineering. Whenever the applications of scientific results required the special experimental background, the economic outlook, and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering grew up in the colleges and universities. In the words of the "Report of the Committee on Adequacy and Standards of Engineering Education" in the January 1952 number of the Journal of Engineering Education: "Engineering education in America was not developed after a preconceived plan. It evolved in parallel with the needs of a growing country, a country engaged in the development of a vast industrialization. From the first it filled a practical need, and its design emanated largely from an evaluation of the professional requirement." The advent of the railroad created a need for scientifically trained engineers and the response was the curriculum in civil engineering. The development of steam power created the demand for a curriculum in mechanical engineering. Neither of these types of engineers was trained to cope with the requirements of electrical power, and so there came to be a curriculum in electrical engineering. The advent of radio communication and of electronics during the first World War and in the years that followed resulted in the establishment of electronics engineering, sometimes within the curriculum in electrical engineering and sometimes independent of it. The complexities of industrial management have created an ever increasing demand for industrial engineers and the consequent building up of a curriculum in industrial engineering. The wide industrial application of chemical processes required a type of engineer whose background was training in chemistry but who was able to design processes and plants on an industrial scale; hence we have the curriculum in chemical engineering. The advent of the airplane created an entirely new set of problems which were solved by the training of aeronautical engineers. Many of these have called for more and more science and mathematics. Such was the history of the older engineer-

Jan 1, 1953

By J. B. Macelwane

Historically whenever application of scientific results to a new problem required the special experimental background, the economic outlook and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering based on the professional requirement grew up in the engineering colleges. This is precisely what is happening now in geophysical engineering. THE Mineral Industry Education Division of AIME has long been interested in geophysical education. Organized in 1938, a Committee on Geophysical Education presented a number of reports in succeeding years. The AIME is an engineering society; hence it might be expected that the interest of the Mineral Industry Education Division would have centered about the relation of courses in geophysics to engineering education. However, this was not the case. The burden of the discussion held under the auspices of the Committee on Geophysical Education bore on geophysics in general and particularly on its relation to geology. In the decade that has passed since those meetings much water has flowed under the bridge. Not only have the geophysical sciences developed at an extraordinarily rapid rate but the practical importance and the range of their applications have spread in ever widening circles and have even assumed a very prominent place in research programs of the military, the Army, the Navy and, particularly, the Geophysical Research Directorate of the Air Force at Cambridge, Mass. So enormously have the geophysical sciences as such grown in scope and in degree of specialization that no one man in a lifetime of study can hope to master the theoretical and experimental complexities or even to follow intelligently in the published literature all the varied accomplishments of basic research in these fields. As in the other sciences, most of the results of geophysical research have potential economic value and are being applied to a wider and wider range of human needs. Here we see a parallel with the older sciences and their relation to engineering. Whenever the applications of scientific results required the special experimental background, the economic outlook, and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering grew up in the colleges and universities. In the words of the "Report of the Committee on Adequacy and Standards of Engineering Education" in the January 1952 number of the Journal of Engineering Education: "Engineering education in America was not developed after a preconceived plan. It evolved in parallel with the needs of a growing country, a country engaged in the development of a vast industrialization. From the first it filled a practical need, and its design emanated largely from an evaluation of the professional requirement." The advent of the railroad created a need for scientifically trained engineers and the response was the curriculum in civil engineering. The development of steam power created the demand for a curriculum in mechanical engineering. Neither of these types of engineers was trained to cope with the requirements of electrical power, and so there came to be a curriculum in electrical engineering. The advent of radio communication and of electronics during the first World War and in the years that followed resulted in the establishment of electronics engineering, sometimes within the curriculum in electrical engineering and sometimes independent of it. The complexities of industrial management have created an ever increasing demand for industrial engineers and the consequent building up of a curriculum in industrial engineering. The wide industrial application of chemical processes required a type of engineer whose background was training in chemistry but who was able to design processes and plants on an industrial scale; hence we have the curriculum in chemical engineering. The advent of the airplane created an entirely new set of problems which were solved by the training of aeronautical engineers. Many of these have called for more and more science and mathematics. Such was the history of the older engineer-

Jan 1, 1953

By Norman L. Newbern, Robert E. Green

An investigation of the effect of size on the deformation properties of metal single crystals made it desirable to grow from the melt cylindrical aluminum single crystals possessing exactly the same crystallographic orientation but varying in diameter. Methods for the growth of rather large (up to 3 in. diam) aluminum single crystals in molds of the desired shape are well known. However, when one applies the same techniques to the growth of smaller (less than 1/8-in. diam) specimens many additional problems arise. Two of the major problems are the construction of the molds to be used and the removal of the thin specimens from these molds without deformation after growth has been completed. Also the problem of the constraint forces exerted by the mold on the specimen is much more pronounced for the smaller specimens. The technique described herein is a zone-melting method in which no mold is used since the surface tension of the molten metal and its oxide is sufficient to retain the melt. The specimen is suspended vertically in a manner similar to that of Keck and Golay.2 However, while Keck and Golay supported the specimen from both ends, the method used here supports the specimen only at the upper end. The surface tension of the molten aluminum and aluminum oxide contains the melt and suspends a length of newly grown crystal that has already passed through the molten zone until the weight of the newly grown crystal is equal to the component of surface tension holding the specimen together in the molten region. When the weight of the newly grown crystal is equal to the component of surface tension holding the specimen together the specimen pulls in two in the molten zone. The length of crystal which can be grown before this separation occurs varies with the diameter of the specimen and the size of the molten zone. In order to prevent the specimen from pulling in two a tube of glycerine is placed beneath the furnace in such a manner that the newly grown crystal passes into the glycerine which provides sufficient buoyancy to allow aluminum single crystals in wire form to be grown to lengths determined only by the length of the tube containing the glycerine. A schematic diagram of the experimental arrangement is shown in Fig. 1. The furnace used is constructed as follows. High-resistance nichrome wire is coiled on a 3/8-in. diam fused quartz tube. The distance between the windings is much less over a length of about 3/8 in. at the center so as to develop a hot spot. This core is located in the center of a 4-in. diam steel cylinder 5 in. in height and insulated from it by Kayolite. The temperature of the furnace is controlled by means of a thermocouple located near the central hot spot and a Minneapolis-Honeywell temperature controller. Temperature ins,ide the furnace is measured with a thermocouple and a standard potentiometer in the usual manner. By the above method it is possible to grow high-purity (99.99 pct Al) aluminum single-crystal wires over a range of sizes. Crystals varying from 1/8 to 1/64-in. diam were grown by the authors. Since the tube containing the glycerine cannot contain a crystal longer than approximately 3 ft, the growth of crystals longer than this presents another problem. It was found that one could cut the newly grown crystal without deformation in the region between furnace and glycerine tube try means of a cutting torch and then by moving the glycerine tube slightly aside continue

Jan 1, 1962

By M. S. Hunter, D. L. Robinson

An extremely fine subgrain structure found in aluminum and aluminum alloys is shown and a method for revealing this structure is described. The appearance and some of the characteristics of this structure are described and the possible significance of subgrain structure in terms of chemical, electrochemical, and metallurgical processes is considered. GRAINS and grain boundaries, which constitute the principal manifestations of the crystalline aggregates known as metals, play such an important part in determining the characteristics and properties of metals and alloys that their nature and behavior have long been of much concern to the met-allographer. Many investigators have speculated on the possible existence of a finer structure within the usual grain structure and, through X-ray diffraction and metallographic techniques, have revealed evidence that such finer structures exist. Among these structures are the mosaic blocks and domains described by Burgers1 and others in their contributions on crystalline structure and the dislocation theory, the small units associated with polygoniza-tion described by Cahn,2 and the intragranular blocks revealed more recently by Lacombe and Beaujard.3 his paper describes some novel methods for clearly revealing a very fine granular substructure within the usual grains of pure aluminum and aluminum alloys. It also compares the characteristics and behavior of this subgrain structure with those of the ordinary grain structure and gives some examples of the manner in which this substructure may influence the characteristics of aluminum alloys. Metallographic investigations of aluminum and its alloys have dealt extensively with the functions and behavior of grains and grain boundaries and have evolved a definite concept of the relation between grain structure, orientation and physical, mechanical, chemical, and electrochemical behavior. During the examination of etched samples, a roughening or mottling of the body of certain grains has occasionally been observed. Such roughening obviously represented differential attack by the etching solution, but its true significance was not at first realized. It is now known that this roughening probably rep- resented a subgrain structure, although the particular etching treatments used were not capable of revealing this subgrain structure clearly. Also, in practically all cases, the subgrains were apparently far too small to be resolved by the light microscope. Recently, a method has been developed for revealing clearly the subgrain structure of most aluminum alloys. This method is somewhat unique in that it eliminates much of the usual tedious mechanical polishing and the attendant danger of a surface layer of flowed metal and at the same time is simple, rapid, and effective. It involves the use of the Alcoa R5 Bright Dip, a patented chemical polishing treatment licensed by Aluminum Co. of America. This treatment produces a bright, highly polished surface at least the equal of any mechanical polish and also etches the subgrain boundaries as well as the ordinary grain boundaries to reveal both the grain and subgrain structure simultaneously. Metallographic specimens to be examined are taken through the customary grinding and polishing operations used for aluminum alloys.' The usual care required in the final polishing operation to prevent a flowed surface layer and to obtain a high polish is not necessary, however, because any flowed layer is eliminated and a high polish is produced by the final immersion in the Alcoa R5 Bright Dip. Depending on alloy type, this dip takes from a few seconds to about 3 min, after which the sample is rinsed well, blown dry, and is ready for examination. The substructure can be revealed by some of the usual metallographic methods such as electropolish-ing or mechanical polishing and etching but no method has been found which is the equal of the new chemical polishing treatment. Mechanical polishing followed by the usual metallographic etching is not entirely satisfactory for revealing this substructure, probably because of the flowed surface layer resulting from the mechanical polish. If the usual etching methods are prolonged sufficiently to remove this layer, the specimen surface becomes quite rough and the substructure is not defined clearly.

Jan 1, 1954

By Patricia J. Rand, Kailish Narayan

Atlantic Richfield Co. began operating a commercial uranium solution mining project in April 1975, in Live Oak County, Tex., 10 miles southwest of the town of George West. The operation is designed to produce 250,00 lb of U308 per year and is jointly owned by Atlantic Richfield Co., Dalco, and U.S. Steel. The proprietary process employed in this operation consists of injecting an alkaline leaching solution into the ore-bearing formation through a pattern of injection wells. The uranium-bearing solution is then removed through producing wells using submersible pumps in central production wells. The produced solution is pumped through a pipeline to the plant area where the uranium is extracted. The barren solution is refurbished and returned to the pattern area for reinjection. The injection field and plant site are located in the drainage of Spring Creek, a small intermittent stream tributary to the Nueces River. Land use in the area is primarily agricultural cattle ranching and farming---but several producing gas fields are present in the areas as well. A nine month enviromental baseline study was conducted on the property beginning in Feb. 1975. Plants and animals of the Clay West area were identified and representative terrestrial and aquatic communities were analyzed. Physical and chemical parameters of the soils were described and analyzed. The surface and underground waters were analyzed chemically; radionuclides, heavy metals, nutrients, and pesticide concentrations were measured in the creek sediments; bacteriological measurements were made in creek water and sediments; radionuclide and chemical levels in plants and animals, both terrestial and aquatic, were measured. These studies, though not required by existing, state or federal laws, were considered necessary to assess the existing conditions before operations began on site. The in-place leaching technique for uranium mining eliminates the enviromental disturbances associated with open pit or underground mining. No grinding and crushing of ore is needed, nor are large tonnages of waste tailings produced. Surface subsidence is not expected since less than 5 lb of uranium is present per ton of rock and even complete removal of such small amounts should not cause subsidence. Solution mining has fewer environmental problems than conventional mining. Members of the Texas Water Quality Board recognized the differences which exist and have recently formulated new environmental control procedures which apply specifically to solution mining. Some of the solution mining activities which are of particular concern are discussed in the following pages. Process Description The produced uranium-bearing solution is pumped through a pipeline from the pattern area to the plant area. The first pattern area consists of a nest of 125 fluid injection, production, and monitor wells [(Fig. 1)]. Injection wells have 4-in. casings and are spaced 50 ft apart on a square grid. Production wells have a 6-in. casing and are located in the center of each square. A block flow sheet of the plant is given in [Fig. 2]. The produced solution goes through parallel trains, each consisting of a carbon column and an ion exchange column in series. The carbon column removes any sand present in the produced solution and the ion exchange column extracts the uranium. The depleted solution is treated with chemicals and returned to the field for reinjection. The uranium retained in the ion exchange column is removed periodically with a sodium chloride solution. Uranium-bearing solution from the ion exchange column is passed through a charcoal column for removal of impurities and then to a precipitation tank where the uranium is precipitated as yellowcake slurry. The yellowcake slurry is clarified, filtered and dried to produce a granular yellowcake product. Environmental Considerations Sources of waste solutions to storage reservoirs, the backwash reservoir and atmospheric discharges are shown in the block flow sheet [(Fig. 2)]. These waste solutions pose a relatively small problem and are adequately controlled by conventional means. There is one area, however,

Jan 1, 1978

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By H. Margolin, A. Coucoulas

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKcll radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuAl2, and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band.1,4 Europium in EuAl2 appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref. 1. One of the other phases was identified as Co5Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acia Cryst., 1959, vol. 12, p. '162. A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently hiher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1 week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961