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By Carl A. Holley

Agglomeration is very closely identified with the mining industry. Ores must be crushed finer and finer to separate minerals from gauge and the fine ore concentrates must be agglomerated so they can be handled for further processing. This paper reviews each type of agglomeration device and summarizes the areas of usage for each type of agglomerator.

Jan 1, 1980

By E. O. Wagner, V. F. Parry

This paper summarizes investigations during 1949 on three pilot plants for drying low-rank fine coal by entrainment in hot gases. Detailed operating results on processing seven coals having moisture ranging from 24 to 62 pct, formulas and data for calculating performance of large units, and general conclusions on the problem of drying fine coal are presented.

Jan 9, 1950

By R. C. Wilmoth, R. D. Hill, R. B. Scott

A cost breakdown is given for reclamation and mine drainage abatement conducted by the Federal Water Quality Administration's demonstration project near Elkins, W. Va. Costs for construction of control measures have been developed and include backfilling strip mines, sealing subsidence areas, reconstructing stream channels, and installing mine seals to prevent the entrance of water and air.

Jan 1, 1973

By Booker Morey, Ashok Gupta

Amid controversy, the resource recovery industry is rapidly approaching its first commercial operations. Some of the problems are reviewed along with some of the important systems that are being developed for resource recovery. Market specifications for the inorganic fraction recovered from municipal solid waste are reviewed along with the details of the unit operations that have been tested.

Jan 1, 1976

By S. D. Dahlgren

ORDERED G.P. zones having the cesium chloride structure were found to exist in the bcc iron-rich grains of an Fe-Au-Cu alloy that had been supersaturated with approximately equal atomic percentages of gold and copper, and aged at 400° and 350°C. Streaks and superlattice spots in electron diffraction patterns revealed the presence of the ordered zones in the aged material. The ordered Ll2 structure is commonly found for precipitates in fcc metals (e.g., Ni3A1 in nickelL7') but it is uncommon to find precipitates in bcc metals having the cesium chloride structure. The formation of the G.P. zones caused age hardening of the grains. Samples containing 3.8 at. pct each of gold and copper (with the remainder being iron) were annealed at 95@ or 1125°C in quartz capsules and were quenched by breaking the capsules under water. X-ray diffraction patterns revealed two solid solutions in the quenched samples. One solid solution was bcc and the other was fcc. The microstructure consisted of iron-rich grains of 0.3 mm diam surrounded by a yellow gold-copper-rich grain boundary network. The Au-Cu phase diagram %hows continuous solid solubility of gold and copper with ordered phases forming below 410°C. None of the ordered Au-Cu phases have the cesium chloride structure. Both Fe-Au and Fe-Cu phase diagrams3 show extended miscibility gaps and only terminal solid-solution phases. Consequently, it is reasonably certain the iron-rich grains consisted of an a-phase terminal solid solution, and the grain boundary network consisted of a gold-copper-rich terminal solid solution. Lattice parameters of the quenched solid solutions were consistent with the suggestion that the quenched phases were terminal solutions. The lattice parameter of the bcc phase (2.879A) obtained upon quenching from 950°C was higher than that (2.866A) for pure iron. The fcc phase in this sample had a lower lattice parameter than that for a 50 at. pct Au and 50 at. pci Cu solid solution, i.e., 3.866 compared to 3.877A. The lattice parameter for the 50 pct Au and 50 pct Cu solid solution was interpolated from data for Cu-Au solid solutions.4 More gold and copper were soluble in iron at 1125°C than at 950°C as indicated by a 0.012A increase in the bcc lattice parameter for a sample quenched from 1125°C. After the alloy had been quenched from 950° and 1125°C, the bcc lattice parameters were 2.879 and 2.891A1 respectively G.P. zones having the cesium chloride structure-which formed during low-temperature aging—were detected by electron diffraction and observed with electron transmission microscopy. In Fig. 1, the asymmetrical streaks parallel to ( 100) directions indicate that platelike G.P. zones had formed parallel to (100) planes of the matrix. The direction of streak asymmetry shows that the bcc unit cell of the G.P. zones was larger than the bcc cell of the matrix. The ordered cesium chloride structure is indicated by low-intensity superlattice spots at 010 positions which are nonallowed for bcc structures. The superlattice spots are streaked; therefore they are from the G.P. zones and are not caused by rel-rod effects of a thin matrix phase. The appearance and size of the zones observed in electron transmission microscopy and the appearance of the asymmetrical streaks in the electron diffraction patterns for the Fe-Au-Cu alloy were the same as those observed for a similarly treated Fe-Au alloy.' Ordered G.P. zones were detected also for an Fe-Au-Cu sample aged only at 400°C. The production of the ordered cesium chloride structure zones by low-temperature aging of super-

Jan 1, 1968

By C. E. Birchenall, G. Derge

IN studying the kinetics of slag-metal reactions, it has become increasingly apparent that a complete knowledge of all aspects of interface phenomena will be required to clarify these processes adequately. A part of the data required for all oxidizing slags used in the refining of impure iron to steel is the rate of exchange of iron between the slag and metal phases. The simplest equilibrium of this type is that between liquid iron and iron silicate slag when both phases are equilibrated with the silica crucible containing them. In this study, the exchange of iron between the two liquid phases has been measured by using radioactive Fe as tracer. The observed high exchange rate indicates the ease with which such interfaces may be crossed in refining processes. The experiments required for this study involved relatively minor and normal modifications of well established techniques. Melting was accomplished by induction heating in heavy walled, fused silica, rotating crucibles." Rotation was used to minimize dilution of the slag by crucible erosion. The melting stock was ingot iron. Slags were prefused in iron crucibles using chemically pure grade oxide reagents. The special conditions applying to the active iron additions will be described for individual experiments. Suitable precautions were observed with regard to protection against radiation hazards.' Identification of Activity This particular study was initiated several years ago, but held in abeyance because the radioactive iron available at that time contained a foreign activity which concentrated in the slag so as to mask the iron activity and render the results unin-terpretable. With the benefit of experiences from other studies, radioiron of suitable purity can now be prepared. As received from the Isotope Div. of A.E.C., the unit appears to contain Fe + Fe50 and a high activity cobalt. The cobalt and iron are separated by repeated ether extractions, and the purified iron stored for sufficient time for the Fe'7 44 day half-life) to decay to negligible activity, leaving only Fe as the active isotope. This was confirmed by the absorption curves for slag and metal samples from heat No. 1. In Fig. 1 the experimentally measured points for the absorption curves of slag and metal are fitted by the calculated slope of 5.8 mg per sq cm in aluminum, which corresponds to the Mn K doublet emission resulting from the capture of an orbital electron of Fe" by the nucleus. This shows that the radioactive species are the same in both slag and metal and identifies it as Fe55 Description of Individual Heats For the first heat, the radioactive iron was contained in the prefused slag. The active Fe55 had been precipitated with carrier and was added as Fe2O3 during fusion in the iron crucible. The charge of 500 grams of ingot iron was melted, the protective iron sleeve added, rotation started, and a prefused, inactive slag was added to allow the system to approach equilibrium. After about 5 min at temperature, the wash slag was skimmed and the active slag added. Initial slag and metal samples were taken as soon as the slag was molten. Additional samples were taken at indicated intervals thereafter. Slag samples were dipped with a small iron spoon and metal samples were sucked into 1/4 in. ID silica tubes. The slag and metal samples were pulverized and mounted for radioactive counting. The slag samples were analyzed chemically for FeO. Temperature was read after the last slag sample by immersion of a Pt-Pt-Rh thermocouple protected by a fused silica sheath. Since no significant variation of rate with temperature was observed

Jan 1, 1954

By O. J. C. Runnals

The intermetallic compounds NpAl2, NpAl3, and NpAl have been prepared, and examined by X-ray diffraction methods. The compounds are isostructural with the corresponding U-Al compounds. NpAl3 is face-centered cubic with a = 7.785A and has the MgCu2 structure. NpAl is simple cubic with a = 4.2624 and has the AuCU3 structure. NpAl4 is body-centered orthorhombic with a = 4.428, b = 6.268, and c = 13.71A. The published description for the atomic positions in UAl, applies also to NpAl4 THE U-Al system has been examined by Gordon and Kaufmann.1 They identified the following intermetallic compounds: UAI2, UAl3, and a third, tentatively identified as UAl5. A structure analysis of the latter compound by Borie2 proved that the formula UAl4 was more consistent with the X-ray data. The crystal structures of UAl2 and UA have been reported by Rundle and Wilson.3 UAl2 was found to be isostructural with MgCu. The atomic positions in the simple cubic UA1, cell were found similar to those in the AuCu3 structure. Three analogous compounds exist in the binary system Np-Al. X-ray data for the compounds NpAl2, NpAl3, and NpAl4 are reported below. The neptunium used in the investigation was supplied through the courtesy of the Argonne National Laboratory as neptunium (V) nitrate. It was stated to have a radioactive content of 99.25 pct Np237. The impurity limits had been established by a spectrographic analysis given in Table I. Any titanium, boron, or bismuth impurity should be effectively removed during the fluorination of NpO2 to NpF4, and sodium, lithium, magnesium or strontium during the alloying procedure. The oxalate ignition technique, described by Westrum for the preparation of finely-divided reactive PuO2, was used.The neptunium (V) nitrate solution, containing 100 mg Np, was evaporated to dryness on oxalic acid crystals. The resulting oxalate was calcined to NpO, by heating in platinum at 650°C for 2 hr. An equimolar mixture of anhydrous hydrogen fluoride and purified hydrogen was passed over the NpO2 for 2 hr at 500°C. According to Fried and Davidson" the above fluorination conditions should produce the purple-black fluoride, NpF3 However, the light-green product showed only NpF4 lines on an X-ray diffraction pattern and contained only an estimated 5 pct of finely dispersed black NpF3 particles on microscopic examination. NpAl3: An intimate mixture of 50 mg of neptunium fluoride and aluminum powder (99.99 pct pure, —28 to $60 mesh) was heated to 900°C in a BeO crucible in vacuum by a tungsten coil for 2 hr, to allow the following reaction to proceed: NPF4 + 7Al + NpAl, + 4AlF. [1] The formation and sublimation of aluminum mono-fluoride in this system was verified from an X-ray diffraction analysis of the sublimate. The diffraction pattern was similar to one obtained in the aluminum reduction of UF4 to UF3,6 showing both Al and AlF3 lines. The resulting alloy was sintered at 1100°C for 1 hr. A powdered specimen of the crystalline product was sealed in a thin-walled quartz capillary for X-ray examination. The photograph was taken on a 14.32 cm General Electric powder diffraction camera, using filtered copper radiation. The films were calibrated in terms of a NaCl standard pattern. The wavelengths used in the calculations were 1.5418A for Cu K and 1.5405A for Cu K The powder diffraction pattern showed that NpAl is simple cubic with a = 4.262 % 0.005A, and is isostructural with UA13 where a = 4.27A1 or a =

Jan 1, 1954

By W. D. Haentjens, A. P. Pipilen, M. Weintraub, A. A. Orning

W. D. Haentjens (Barrett, Haentjens and Co., Hazleton, Pa.) — The authors are to be complimented on undertaking a project which has little available experimental data. There are so many variables in the hydraulic transport of solid materials that it is difficult to correlate the experimental information from one series of tests into usable data involving other materials or even similar materials but of different size consists. The friction data is of particular interest to those involved in pipeline design. Most such pipelines, however, involve portions which are not level and the effect of sloping or vertical lines might also be considered in extensions of this test work. Pump manufacturers are concerned about criticism resulting from the stated amount of degradation occurring in a pump. The amount of degradation is affected somewhat by pump design and this should be taken into consideration. The pump which was loaned for this work was a modification of a standard medium duty slurry pump. This modification was for maximum particle size, however if minimum degradation is the object, then other design changes would be indicated. Although there is a tendency to be less concerned with degradation in industrial applications, it is nevertheless an important factor in many uses and further studies should be made. In particular, the amount of degradation could possibly be segregated into more classifications, rather than charge some losses to the pump which apparently are occurring in other handling. It seems difficult to evaluate the degradation which occurs in handling the coal into the pump sump and in removing it from the line into the tank. Each handling, of course, contributes some degradation, as does the screening operation itself. These are all charged to the pump, or to the pipe line and pump together; and, although they may be small, they could possibly be evaluated. It is interesting to note the verification of the old rule of thumb of maximum particle size equal to approximately one-third of the pipe size. Our experience has shown size distribution to have an effect on the flow characteristics and if this data is available for the tests which were run, it would be interesting supplementary information. A. P. Pipilen, M. Weintraub and A. A. Orning (Authors' Reply) — In this paper the authors have attempted to outline some of the major factors affecting a rational design for a solids-liquid transport system. They are grateful to Mr. Haentjens for pointing out several other equally important considerations. Pump manufacturers, in general, should be complimented on the strides that have been made in decreasing particle degradation within the pump. Considerable research and a great deal of mathematical analysis is required before pump design in this field can become a science rather than an art, for each system requires a different set of compromises. As Mr. Haentjens indicates, maximum-particle-size handling capability may be inconsistent with minimum degradation; even more important, the rotor profile for the most efficient transfer of energy to the fluid may have to be compromised to reduce particle breakage, for, whenever particle density differs from fluid density, the two phases will have different trajectories. Some evidence of this geometric factor is provided by a cursoy analysis in the Bureau of Mines Report of Investigations now in preparation, where it is indicated that, for the pump used, degradation decreased when the tangential velocity was decreased and when the radial velocity was increased. This relation, itself, is probably a function of particle size and concentration. Some data on particle size distribution, as requested by Mr. Haentjens, will be provided in the Report of Investigations referred to above in addition to that already presented in Table II of the original paper. However, in the limited number of tests it is difficult to distinguish between cause and effect, for not only did the particle size distribution alter the flow characteristics, but, through the medium of degradation, the operating conditions rapidly altered the particle size distribution.

Jan 1, 1965

By M. J. Hordon

Measurements of the 103 yield stress of ordered and disordered poly crystalline Cu ,Au were related to the ordered antiphase domain size determined by resistivity measurements. For undeformed material, a yield stress maximum wa obtained at a critical domain diameter of about 40A. Plastic deformation resulted in a marked increase in the yield stress and electrical resistivity of the ordered alloy compared to the disordered, the strain hardening rate increasing regularly with initial antiphase domain size. Order hardening was accompanied by a sharp reduction in size of the initially large domains. It has been observed that the yield stress of ordered and partially ordered Cu3Au alloy varies sensitively with antiphase domain size aid degree of order.ly2 In addition, ordering of the lattice leads to a marked increase in the strain hardening rate (order hardening) as compared to the rate for the disordered alloy. In the present investigation, changes in the electrical resistivity and yield stress of ordered polycrystalline Cudu with varying initial domain diameters were measured after tensile plastic deformation in order to examine the effect of cold work on the antiphase domain size. EXPERIMENTAL PROCEDURE Au-Cu alloy of 99.99 pct purity analyzing 50.85 wt pct Au-balance copper was obtained from the Handy-Harmon Co., N. Y., in the form of 0.061 in. diam drawn wire. Wire specimens 3 in. in length were given the following annealing treatment in nitrogen: 500" for 72 hr, 820" for 15 hr, and 450" for 5 hr, followed by a water quench. The annealing sequence resulted in a completely disordered structure with a grain size of about 0.2 mm. The disordered specimens were then reannealed at 360' in nitrogen for periods varying from 10 min to 150 hr followed by quenching to produce ordered structures with varying domain sizes. The degree of ordering and variation of domain size was followed by electrical resistivity measurements made at room temperature using a low resistance precision Kelvin double bridge apparatus. The specimen resistance was determined over a length of 4.0 cm between two brass knife-edge contacts while the specimen was immersed in an oil bath to minimize temperature variations. In addition, the current flow in the circuit was minimized by a current pulse technique in balancing the bridge in order to avoid heating the specimen. Using a sensitive galvanometer to detect the bridge null, the accuracy of the resistance measurement Wire specimens were plastically strained in tension with an Instron tensile unit at strain rates in the range 5 x 10"5 sec-' to 2 x 10"4 sec-'. Stress and extension data were fed into the Instron chart drive amplifier to obtain the actual stress-elongation curve from which the yield stress at 10"3 strain was determined. The maximum resolution of the apparatus was approximately 50 psi stress and 3 x 104 strain. At various plastic strain levels, deformation was interrupted and the electrical resistivity determined after removing the stress. RESULTS AND DISCUSSION 1) Yield Strength of Ordered Cudu. In order to determine the effect of the ordered antiphase domains on the initial yield stress, specimens were prepared with varying domain sizes ranging from zero for 5 completely disordered structure to about lo5A for a completely ordered structure by suitable annealing treatment. Domain sizes were estimated by comparing room temperature electrical resistivity data with the original data of Jones and sykes3 as modified by rdle.' In agreement with previous work, the resistivity varied sensitively with domain diameter and degree of order, decreasing from approximately 11.6 x l0- ohm-cm for the disordered structure to about 5.9 x l0- ohm-cm for ordered domains above 10"3 cm in diameter. Fig. 1 shows the change of the 103 yield stress with ordered domain size. It is evident that the maximum

Jan 1, 1963

By Dennis Peterson

INTRODUCTION The business arena has dramatically changed for most producers and consumers of commodities. International debt, currency shortages, political upheavals, etc., require corporations today to be sophisticated and flexible enough to change their purchasing and sales techniques in order to maximize returns. Many external factors, such as interest rates, trading partners, currency changes, and government edicts, can have an adverse effect on a company's bottom line. Totally out of a company's ability to control or predict, these. factors force the commodities based corporation to constantly re-evaluate its operating scope and domain. The principle of back-yard only operations and the laissez-faire with blinders style of management is no longer a viable way to run a business. The industrial world has been operating for the past 10 to 15 years as though there were no commodity nor raw material crisis. For developed countries the primary products sector has become marginal, whereas it was central in the first half of the century. A radical change in the method of doing business is necessary to offset a depression in the industrial economy. The risk of collapse may be heightened by a banking crisis caused by massive defaults on the part of commodity producing debtors, whether in the third world or in our own farm producing sector. The raw materials economy has become divergent with the industrial economy. This is a major change in the world economy with tremendous implications in both developed and developing countries for economic and social policies and economic theories. Basic competition issues, such as low labor costs, are likely to become less of an advantage in international trade. In developed countries these costs are going to account for a smaller portion of total costs. The total costs of automated processes are lower than those of traditional plants with low labor costs. Automation in the commodities sector eliminates the hidden but high cost of not processing at capacity created by poor quality, rejects and maintenance for product change-overs. The cost of capital will become increasingly important in international competition. Over the last ten years the U.S. has become the highest cost country in this area. Reversing the U.S. policy of high interest rates and costly equity capital should be a priority for management decision makers. In the rapid industrialization of this century, Japan developed by exporting raw materials, (principally, silk and tea), at steadily increasing prices. Germany developed by leap frogging into the high-tech industries, mainly in electricity, chemicals and optics. The United States did both. Both avenues are blocked for today's rapidly industrializing countries because (a) the deterioration of the terms of trade for primary products, and (b) it requires an infrastructure of knowledge and education far beyond the scope of a poor country. Many explanations exist for the explosion of international money flows. The shift from fixed to floating exchange rates in 1971 may have given initial impetus by inviting currency speculation. The surge in liquid funds flowing to petroleum producers after the oil shocks of 1973 and 1979 was definitely a major cause. There can be little doubt that the U.S. government deficit also played a big role. The American budget deficit has become a massive void, sucking in liquid funds from all over the world and making the U.S. the world's major debtor country. In reality, a trade and payments deficit is actually a loan from the seller of goods and services to the buyer, that is, to the U.S. From now on, the global ramifications of business will have to be treated in economic theory and business policy alike. Economic theory teaches that the comparative advantage factors of a real economy determines operative and financial policy. These comparisons -- labor costs, productivity, raw materials cost, energy costs,

Jan 1, 1990

By F. F. Poland

The purpose of this paper is to describe the recent applications and improvements made in the process and equipment for the recovery of metallic zinc from secondary metals by means of high temperature electric resistor furnace distillation. The process and high temperature furnace, as developed by Revere Copper and Brass Incorporated, Research and Development Department, was described in a previous paper. † Since the publication of that paper the process and equipment have been licensed to others. Consequently its field of application has been expanded, particularly for the treatment of scrap brass, galvanizers dross and scrap zinc. Other applications are being considered, particularly the melting of metallic titanium and special alloys requiring a controlled atmosphere. Consideration is also being given to modification in design that would allow the melting of copper cathodes for the production of oxygen-free and electrolytic tough pitch copper shapes without the necessity of blowing and poling. In the design of a furnace for melting copper cathodes it is intended that the fundamental principle of charging the solid material into a large pool of molten metal through a double door charging vestibule as shown in Fig 3 of the previous paper, † would be adhered to and, in addition, either dehydrated and desulphurized producer gas or commercial nitrogen, that is, approximately 96 pct nitrogen, 2 pct hydrogen 2 pct CO, also dehydrated, would be used to provide a protective atmosphere for the resistors and to flush out more soluble gases from the molten copper. The operation of a small unit producing approximately 1000 lb of copper per hr has shown that the commercial nitrogen will allow the production of tough pitch electrolytic copper when the metal is transferred from the meltdown unit contemplated to a special type induction unit where the oxygen absorption and temperature can be controlled. Standard practice in treating low grade scrap brass has been to oxidize the zinc by blowing air through the molten metal. This operation results in the recovery of approximately two-thirds or less of the zinc content of the brass in the form of an impure zinc oxide having only a fraction of the value of the zinc in metallic form. The balance of the zinc is lost to slag, fume and drosses. Fig 1 shows the revised flow sheet of the process for the treatment of scrap brass. For this application and as shown on the flow sheet a low frequency induction furnace has been substituted for the Wilkins-Poland type as a melting unit. This type of furnace has been found the most suitable for the purpose as will be shown by the following discussion. Serap Brass The melting of refinery scrap brass preparatory to distillation presents a melting problem quite different from the usual melting of brass mill scrap for recasting because refinery scrap is a heterogeneous mixture of alloys each having different melting and boiling points, and coated with a variety of corrosion products and foreign materials. In addition, brass and copper plated pieces of sheet iron, stainless steel, ceramic materials, and others are present that do not melt except at temperatures above the boiling point of the liquid bath. In the previous paper it is noted that difficulty was encountered in the melting of refinery grade scrap brass without excessive loss of zinc by volatilization and that 5 to 10 pct razorite flux was used to alleviate this condition. While this flux was successful in preventing the excessive loss of zinc by volatilization it interposed a low heat conductivity layer between the source of heat and liquid charge and resulted in lowering the melting rate of the furnace. This same problem presents itself in all types of furnaces in which the metal is heated by radiation and conduction from above the charge. It has been found in melting this type material that the melting rate per hour or per square foot of hearth area

Jan 1, 1950

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By P. M. Kelly, E. P. Butler

The stability of a 70/30 Mn-Cu alloy aged to peak damping has been investigated using electron microscopy, X-ray diffraction, and torsional pendulum measurements. Storage at room temperature or at 100" C causes a reduction in damping capacity. This is shown to be due to the formation of subdomains which "lock" the main domain structure and so hinder their movement. After storage the damping capacity can be restored by a retransformation treatment, which generates structures identical to those found in newly aged specimens. Plastic deformation by rolling also causes a decrease in damping capacity. In this case the damping capacity can only be restored by retransformation if the amount of deformation is less than about 5 pct. THE general metallography and structure of these high damping capacity alloys has been discussed in Part I of this work.1 Part II deals with some of the variables that affect the damping capacity. In particular, the stability of the damping capacity of a 70/30 alloy aged for 2 hr at 425° C and quenched has been investigated. The temperature sensitivity of the damping capacity of a 70/30 alloy aged for 2 hr at 450° C has been reported by Birchon.2 The damping capacity begins to decrease with increasing temperature, and is very low above the M, temperature of 125°C. The cubic — tetragonal transformation is completely reversible and there is no apparent thermal hysteresis associated with the change in damping capacity. Another important effect was first reported by Dean and his coworkers.3 They noticed a decrease in the damping capacity with time for specimens of a quenched tetragonal alloy. More recently workers at the Admiralty Materials Laboratory 4 have studied the stability of an aged 70/30 alloy. They found that the damping capacity decreased to half its original value after about 1000 hr at room temperature. EXPERIMENTAL The techniques used for electron microscopy and X-ray diffraction have been described in Part I. The damping capacity was measured by means of a torsional pendulum, using rectangular specimens, 3 by 0.3 mm with a 6 cm gage length. The specific damping capacity, S.D.C., was calculated as a percent amplitude decay in free vibrations over 10 cycles, starting at an amplitude which corresponded to a 700 psi surface shear stress. Because of the stress dependence of the damping,&apos; the values obtained were about a third those reported for a 5000 psi surface shear stress.&apos; RESULTS a) Effect of Aging Temperature. The effect of aging temperature on the damping capacity is shown in Fig. 1. The damping capacity reaches a peak of 12 pct after aging at 400° to 425°C) then begins to decrease as the volume fraction of a Mn increases. At higher aging temperatures the structure becomes cubic again with a low damping capacity. b) Stability of the Aged Structure. The damping capacity of the aged alloy decreases with time at room temperature. This process could be accelerated by storing at 100°C, when about 100 hr were required for the damping to fall to half its original value. The results of room temperature and 100°C storage, for times up to 1000 hr, are shown in Fig. 2. The damping capacity starts to decrease after about 24 hr at 18° C and 1 to 2 hr at 100°C. It was found, however, that the damping could be almost completely restored by retransformation. The specimens were held at a temperature above the M, for a short time, 250° C for 5 min, and then quenched. The values of damping capacity for specimens that were aged, stored, and then retransformed are shown by the full points in Fig. 2. X-ray measurements of the c/a ratio and hardness readings on the specimens did

Jan 1, 1969

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970

INTRODUCTION The meaning of cash flow has already been defined as after-tax earnings available for use by the corporation or business. It is therefore apparent that a significant part of mineral economic evaluation is concerned with correct and accurate computation of taxable income under existing tax laws, and the proper treatment of tax allowances and deductions. The various methods of depreciation, depletion, and amortization are all means whereby the investor can earn back or recover, before taxes are imposed, the investments made for purposes of doing business or for the production of income. Each of these three types of tax deduction are applied to different investment items such as property, equipment, buildings, research, etc. The cost of buildings, equipment, machinery, and transportation equipment are representative of capitalized business costs that must be recovered by depreciation over the life of the asset. The property investment costs of acquiring natural resources such as minerals, oil and gas, and standing timber are examples of investment costs that may be recovered by depletion. Several other capitalized business costs, such as research expenses and trademark expenses, may be recovered by amortization. The term "capitalized" means that the in- vestment cost is not deducted as an operating expense in the year that it is incurred, but is spread out over a period of years through depreciation, depletion, or amortization deductions according to lawful schedules. Of course, any capitalized cost can only be deducted once. The other costs of doing business which are not capitalized, such as labor and operating costs, are said to be "expensed," i.e., they are written off for tax purposes in the year they occur. DEPRECIATION Depreciation, according to US tax law, is a deduction from taxable income permitted as a "reasonable allowance for the exhaustion, wear and tear of property out of its use or employment in a business." The original cost of the property is the usual basis for determining depreciation. Since depreciation write-off is applied over the useful life of the asset, the first step is to determine the estimated useful life or its allowable depreciable life. These two lives may or may not be the same. No average life is applicable to all types of depreciable assets under different conditions or in different types of business. It is the taxpayer&apos;s responsibility to determine the useful life of the asset according to his own operating conditions and experience, within the guidelines set by the US Internal Revenue Service (IRS). The Class Life Depreciation Range (ADR) System permits the taxpayer to choose from a range of depreciable lives at 20% below or above the present guideline life. The second step required in calculating depreciation is to determine an estimated salvage value for the asset. The salvage value is an estimate, made at the time of acquisition, of the amount of money which can be realized by the sale of the asset at the end of its useful life. The four depreciation methods most widely used in the US are: (1) the straight-line method, (2) the declining balance method (double declining balance), (3) sum of the years - digits method, and (4) units of production method. Straight-Line Depreciation Method The straight-line depreciation method is the simplest for calculating depreciation. The depreciation for each year is determined by subtracting the estimated salvage value from the first cost of the asset and dividing the result by the years of life. The method gives equal annual deduction over the depreciable life. Salvage value equal to or less than 10% of the first cost may be ignored. [first cost - salvage Straight line = years of life ] Declining Balance Depreciation Method Declining balance depreciation, or double declining balance (DDB) as most frequently applied, is used for accelerating depreciation in the early years of the asset and is the fastest depreciation method allowed by the US Internal Revenue Service. The declining balance

Jan 1, 1980

By G. K. Manning, W. E. Few

T has been known for some time that both&apos;inter-granular carbide and intergranular oxide phases cause brittleness in molybdenum. Parke and Ham&apos; indicated that 0.0025 pct 0 present in molybdenum after solidification from the melt was sufficient to induce intergranular brittleness during forging. However, material containing 0.06 pct C could still be forged. However, adding this amount of carbon to insure deoxidation causes the formation of carbides on freezing. These carbides are precipitated at grain boundaries, and Rengstorff and Fischer&apos; have shown they have an unfavorable effect on the room-temperature ductility of molybdenum. Take? in 1928 proposed that the solubility of carbon was a constant value of 0.30 pct from room temperature up to 1800°C. In 1935, Sykes, Van Horn, and Tucker&apos; obtained X-ray data suggesting that the solid solubility of carbon in molybdenum was between 0.07 and 0.09 pct at temperatures from 1500" to 2100°C. The a-solubility line for carbon was included in the Mo-C diagram given in the Metals Handbook as a tentative line based on the data of Sykes, Van Horn, and Tucker. In order to determine the partial phase diagrams for these systems, it was necessary to construct a high-temperature furnace suitable for heat treating molybdenum at temperatures up to 4000°F. A molybdenum resistance furnace was built for this purpose in which samples could be heat treated in a purified atmosphere and quenched from any desired temperature.&apos; Experimental Work Solubility of Carbon: Arc-cast molybdenum supplied by the Climax Molybdenum Co. and 18-gage molybdenum wire samples produced by powder metallurgy at the Fansteel Metallurgical Co. were used in determining the a-solubility line for the MO-C system. The cast molybdenum contained 0.032 pct C initially. Two lots of 18-gage wire were used, one containing 0.011 pct C and the other 0.005 pct C initially. All material contained a carbide phase as received. Fig. 1 illustrates the carbides found in the untreated material. Heat treatment in a purified hydrogen atmosphere was found to reduce the carbon content in the as-cast molybdenum. Purified argonT also decarburized molybdenum samples at temperatures above 3500°F; however, the carbon content remained constant during heat treatment in purified argon at lower tem- peratures. The argon was purified by passing it over titanium at 750 °C and then through a magnesium perchlorate drying tower. The hydrogen was purified by passing it through a commercial hydrogen deoxidizer, followed by a drying tower. Specimens having different initial carbon contents were heat treated in argon at 3500°F for periods ranging from 5 min to 5 hr and were analyzed for carbon. Samples of the same final carbon content had the same microstructures regardless of time at temperature. Furthermore, a gradient between center and surface in the amount of undissolved carbide particles present was never observed. It was concluded that at these low carbon levels, and at the high temperatures involved, diffusion proceeds so rapidly that the specimen is always substantially homogeneous in carbon content, in spite of the gradual loss in carbon. Based on the above findings, the following procedure was used to determine the carbon-solubility limit at 3000°, 3500°, and 4000°F. At each of these temperatures, a number of samples were heat treated, as shown in Table I, and rapidly cooled to room temperature. Since the samples lost carbon in proportion to the length of time heated, a series of samples were obtained of varying carbon contents. By use of a rapid cooling rate, the phases present at the high temperature were retained at room temperature. All samples were examined microscopically. Those found to contain either no excess carbide phase or only a very small amount were then analyzed for carbon. The samples actually analyzed for carbon

Jan 1, 1953

By P. E. Arnold, G. S. Ansell

RELAXATION in metals has been studied in detail by many workers in recent years.1-5 These studies have shown that there is an energy-loss peak observed in a metal placed in mechanical resonance at low frequencies which may be correlated with various metallurgical processes. These experiments have been largely used to study single-phase materials. In order to study the effect of a finely dispersed second phase in a metal matrix upon this phenomenon, the relaxation behavior of an aluminum-aluminum oxide SAP-Type alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions was investigated by the use of internal-friction measurements. The alloys studied, designated MD 2100, consist of a matrix of commercial-purity aluminum containing a finely dispersed second phase of aluminum oxide. The aluminum oxide is present in this alloy in the form of fine platelets approximately 130A units thick and several microns on edge. The mean free path betwen dispersed platelets is approximately 0.5 p. The grain size of this alloy is extremely stable at temperatures as high as the melting temperature of the aluminum matrix. In the as-extruded condition the grain diameter is several microns, while in the recrystallized condition it is several millimeters in diameter. The damping characteristics of the alloy samples were determined using a torsional-pendulum device. The internal-friction constant was determined for this alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions over the temperature range from 343" to 923°K at frequencies of 0.9, 1.3, and 1.8 cycles per sec. An internal-friction peak was observed in testing the fine-grained alloys which was not observed for the coarse-grained alloys. This peak, which might be associated with a type of grain-boundary relaxation, was observed at each of the three different test frequencies for the fine-grained sample. The temperature at which the relaxation peak occurred for each of the three different frequencies is shown in Table I. From these data an activation energy of relaxation for each pair of frequencies was determined by comparing the temperature shift of the relaxation peak with frequency between each of the test frequencies, assuming that an Arrhenius-type rate equation is applicable. The activation energy of relaxation determined from these data is also shown in Table I. The mean value of the activation energy was about 6 kcal per mole. The activation energy for the relaxation process determined in this investigation indicates that the relaxation associated with the grain boundaries in this aluminum-aluminum oxide SAP-Type alloy is quite a different process than grain boundary relaxation in single-phase aluminum alloys. In these latter alloys, the activation energy for relaxation has been found to be the activation energy for self-diffusion, approximately 36 kcal per mole1,2 Where the activation energy is the same as the activation energy for self diffusion, it has been proposed that the relaxation phenomena is dependent upon vacancy formation and motion. It is apparent therefore, that, in this aluminum-aluminum oxide SAP-Type alloy, the relaxation must be due to another type of atom transport. It has been shown previously in studies of the high-temperature, low-stress, steady-state creep behavior of as-extruded aluminum SAP-Type alloys, that the activation energy for steady-state creep is one that may be characterized by the nucleation of dislocations from the grain boundaries. It is proposed that the relaxation behavior observed here is due to a similar effect. In this case, the internal-friction peak is a resonance behavior due to the time-dependent nucleation of dislocations from grain boundaries in the sample. A process of this type would have an activation energy which is undoubtedly stress-dependent and of the form Q = Q, + (dQ/du)u

Jan 1, 1962

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG&apos;s ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid&apos; have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey&apos; presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,

By W. Mckewan, W. M. Fassell

The oxidation rates of copper have been determined at temperatures from 600" to 900°C in oxygen from 14.7 to 400 psi total oxygen pressure. The oxidation rate of copper is unchanged by oxygen pressures within the range studied. The observed data extend Feit-knecht&apos;s conclusion concerning the pressure independence of copper from atmospheric pressure to 400 psi. All samples studied in the above-mentioned temperature and pressure range have both Cu2O and CuO present in the oxide film. NUMEROUS papers have been published on the oxidation of copper, some of which have noted the effect of oxygen pressure on the oxidation rate of copper. It must be noted, however, that no data on the oxidation rates of copper at pressure in excess of 1 atm have been reported in the literature. (Le Chatelier¹ reported that a black oxide of silver was formed at 300°C and 15 atm pressure.) This is likewise true for the other metals. This investigation was initiated to obtain experimental oxidation rate constants for pure metals at elevated temperatures and high oxygen pressure. Copper was selected as the first metal since probably more reliable data are available on its oxidation rates and related physical and chemical properties than for any other metal or alloy. As a general summary, the following conclusions appear well established for the oxidation of copper: 1—The oxide coating consists of Cu2O with a superficial coating of CuO providing the ambient oxygen pressure exceeds the equilibrium pressure for the coexistence of Cu2O and CuO.² The following sequence of phases is then Cu/Cu2O/CuO/O2 (gas). The Cu2O consists of large crystals that have no relation to the orientation of the metal crystals, except for a very thin layer adjacent to the metal." The CuO consists of very fine crystals randomly oriented. If the oxygen pressure is below the equilibrium pressure for the coexistence of Cu2O and CuO, the coating consists of Cu,O only. 2—The rate-determining factor in the parabolic oxidation of copper is the diffusion of Cu+ ions through the Cu,O layer.4,6,7 The Cu+ ions are accompanied by electrons to maintain electrical neutrality. The mechanism of the reaction at the Cu2O/CuO interface and the method of growth of the CuO is in some doubt. 3—On copper, there are three reported pressure effects: (a) At pressures below 0.3 mm Hg oxygen pressure, the oxidation rate increases directly with pressure.&apos;, &apos; .Vxygen starvation at the surface may account for this effect. (b) At oxygen pressures from 0.3 to 63 mm, the oxidation rate increases as the 7th root of the oxygen pressure providing the temperature is such that only Cu2O is present in the film. (c) At pressures from above the equilibrium pressure for the coexistence of Cu2O and CuO (varies with temperature) to atmospheric pressure, the oxidation rate is independent of the oxygen pressure.&apos; Equipment In order to determine the oxidation rates of metals in an oxidizing atmosphere at pressures up to 400 psi, the equipment is somewhat different than for low pressure work as is shown in Figs. 1 and 2. A Leeds and Northrup Micromax recording controller (A) is used to control the temperature of the Ni-chrome furnace winding in conjunction with a Micromax electric drive unit. The drive unit adjusts a 20 amp Variac (variable transformer) to control the power input into the Nichrome furnace winding. Due to the "self heating" of the sample by oxidation, frequently encountered in oxidation rate studies, it is essential that the sample temperature be measured independently. This is done by means of a series of six chromel-alumel calibrated thermocouples located spirally around the oxidizing metal sample. Each thermocouple is partially shielded from the direct radiation of the furnace wall by

Jan 1, 1954

By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969