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By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By G. R. Speich

The distribution of carbon and the type of substructure in iron-carbon martensites containing 0.02 to 0.57pct C has been studied in the as-quenched condition and after tempering at 25" to 700°C by using electrical resistivity, internal friction, hardness, and light and electron microscope techniques. in marten-sites containing less than 0.2 pct C, almost 90 pct of the carbon segregates to dislocations and to lath boundaries during quenching; in martensites containing greater than 0.20 pct C, appreciable amounts of carbon enter normal interstitial positions located far from defects. Tempering martensites with carbon contents below 0.20 pct at temperatures below 150°C results in additional carbon segregation to dislocations and to lath boundaries but no carbide precipitation whereas -carbide precipitation occurs in martensites with carbon contents exceeding 0.2 pct. Above 150°C, a rod-shaped carbide (either Fe3C or Hagg) is precipitated in all cases. At 400°C, spheroidal Fe3C precipitates at lath boundaries and at former aus-tenite grain boundaries. At 400" to 600"C, recovery of the martensite defect structure occurs. At 600" to 700°C, recrystallization of the martensite and Ost-waW ripening of the Fe3C occur. The effects of the carbon segregation that occurs during quenching and the subsequent substructural changes that occur during tempering on martensite tetragonality, hardness, and precipitation behavior are discussed. A mathematical analysis of carbon segregation during quenching is presented. RECENT studies of the strength of low-carbon martensitel-4 emphasize the importance of carbon segregation to the martensite lath boundaries and to the dislocations contained between them during quenching. Unfortunately, very few studies of the tempering of low-carbon martensites have been conducted, so the exact nature of this segregation is poorly understood. In fact, most early tempering studies5,6 were restricted to carbon contents greater than 0.20 pct. Moreover, these studies did not determine the amount of carbon segregated to the martensite substructure during quenching so that the initial state of the martensite was not established. Aborn7 studied the precipitation of carbide in low-carbon martensite during quenching but did not establish whether carbon segregation occurs prior to carbide precipitation, nor did he study the subsequent tempering sequence in detail. In the present work we have used electrical resistance and internal friction measurements, supplemented by electron transmission microscopy to establish the carbon distribution in as-quenched specimens. Specimens thin enough to avoid carbide precipitation (but not carbon segregation) were employed. The redistribution of carbon on subsequent tempering below 250°C was followed by measurements of elec- trical resistance. Additional studies were made on specimens tempered at 250" to 700°C to elucidate the overall tempering behavior of low-carbon martensites, including the formation of cementite and recrystalli-zation of the martensite. EXPERIMENTAL PROCEDURE Eight iron-carbon alloys with 0.026, 0.057, 0.097, 0.18, 0.20, 0.29, 0.39, and 0.57 wt pct C were prepared as 8-lb ingots by vacuum melting. Typical impurities in wt ppm were 40 Si, 20 Mn, 30 S, 10 P, and 10 N. These alloys were hot rolled to 3 in. plate at 1095°C) (2000°F). The hot-rolled plates were surface ground to remove scale and the decarburized layer, then cold rolled to 0.010 in. sheet. Specimens cut from the sheet were austenitized for 30 min at 1000°C (1830°F) in a vacuum tube furnace in which the pressure did not exceed 2 x 10-3 torr. Chemical analysis of specimens after austenitization indicated no decarburization at this pressure. Immediately before quenching, the furnace was filled with prepurified helium. The specimen was then pushed rapidly through an aluminum foil gasket, which sealed the bottom of the furnace, into an iced-brine bath (10 pct NaC1, 2 pct NaOH). The quenching rate at the M, temperature is about 104'c per sec for 0.010 in thick specimens, as calculated from Newton's law of heat flow2 using a heat transfer coefficient of 25 ft-'. This quenching rate is sufficiently high so that all the alloys transformed completely to martensite throughout the entire 0.010 in thickness and no carbide precipitation occurred in the martensite. All specimens were immediately transferred to liquid nitrogen after quenching and stored there until needed. Tempering below 250°C (480°F) was done in silicone oil baths thermostatically controlled to *;"C. Tempering above 250°C was done in circulating air furnaces or lead pots with the specimens contained in evacuated silica capsules. Electrical resistance was determined by measurement of the potential drop across both a standard resistance and the specimen, connected in series. All resistance measurements were made in liquid nitrogen (77K, -196°C) to minimize thermal scattering of electrons and thus maximize the contribution of impurity scattering to the resistance. Specimen dimensions were 5.10 by 0.19 by 0.025 cm. Although the precision in the electrical resistance measurements was +0.1 pct, the electrical resistivities could only be measured with an accuracy of +5 pct because of uncertainty in the specimen dimensions. Internal friction measurements were performed in an inverted pendulum apparatus at vibration frequencies of either 1.9 or 66 Hz. The specimen dimensions were 5.10 by 0.375 by 0.025 cm. Hardness measurements were made with a Leitz-Wetzlar microhardness machine with loads of 100 g. Specimens were examined by light microscopy after etching in 2 pct Nital and by electron transmission microscopy after preparation of thin sections by electrolytic thinning in a chromic-acetic acid solution.

Jan 1, 1970

By M. Gell, G. R. Leveran

The high- and low-cycle fatigue properties of the nickel-base superalloy, Mar-MBOO, in columnar-grained and single-crystal forms were determined at room temperature. It was found that the fatigue lives of these materials were greatly affected by the size of preexisting cracks in MC-type carbides contained in the micro structure. Most of the data falls on two curves given by: (zN)'/A€= K, where Nf is the number of cycles to failure, Af is the total strain range, and K is a function of carbide size. No difference was observed in the fatigue behavior of the columnar-grained and single-crystal materials for the same MC carbide size. Matrix slip and crack initiation occurred at precracked MC carbides and, to a lesser extent, at micropores. Fatigue crack propagation was mainly in the Stage I mode, i.e., on cry stallo graPhic slip planes. The Stage I fracture in these materials was unusual in that distinct features were observed on the fracture surfaces. In high-cycle fatigue, these features resembled those commonly observed on the cleavage fracture surfaces of bcc and hcp materials. Yet, in this study, the cracks propagated slowly in a cyclic manner. In low-cycle fatigue, the Stage I facets contained equiaxed dimples, similar to those observed on the tensile fracture surfaces of ductile materials. These observations indicate that both local normal and shear stresses are involved in these Stage I fractures. A model is proposed to explain these results based on the weakening of the cohesive energy of the active slip planes by reversed shear deformation and the fracture of the bonds across the weakened planes by the local normal stress. RECENT developments in casting technology have produced cast nickel-base superalloys in columnar -grained and single-crystal forms.1'2 The tensile and creep properties of the nickel-base superalloy, Mar-M200, cast in these forms have been shown to be superior to the corresponding properties of the conventionally cast polycrystalline material.lp2 This improvement in properties results, in part, from the elimination of grain boundaries in the single crystals and the alignment of the grain boundaries parallel to the stress axis in the columnar-grained castings. As part of a program to evaluate the fatigue properties of nickel-base superalloys cast in single-crystal and columnar-grained forms, a study has been made of the cyclic deformation and fracture of Mar-M2OO at room temperature. M. fiFl I .hininr Mpmher AIMF ic ^pninr Rocoarrh Accn^iata anH I) EXPERIMENTAL PROCEDURE The composition range of Mar-Ma00 in weight percent is: 8 to 10 Cr, 9 to 11 Co, 11.5 to 13.5 W, 0.75 to 1.25 Cb, 1.75 to 2.25 Ti, 4.75 to 5.25 Al, 0.01 to 0.02 B, 0.03 to 0.08 Zr, 0.07 to 0.12 C, bal. Ni. All of the castings met the above specifications. The castings were solutionized for 1 to 4 hr at 2250°F followed by aging at 1600°F for 32 hr which resulted in a 0.2 pct offset yield stress of 150,000 psi at room temperature. The microstructure of the material consisted of cuboidal, coherent particles of ordered, fcc Ni3(A1,Ti) (commonly designated y'), approximately 0.3 p on edge, distributed in an fcc y solid-solution matrix. MC carbides together with shrinkage and gas micropores were also distributed throughout the materials. The MC carbides and micropores were located preferentially in the interdendritic interstices, as well as in the grain boundaries in the columnar-grained castings. The (100) direction of all the single crystals and the common (100) axis of the grains in the columnar materials were aligned within about 5 deg of the specimen axis. Fatigue testing was carried out in the high-cycle (HCF) and low-cycle (LCF) fatigue regions, with the major difference being gross yielding of the specimen occurred during the first cycle in the LCF region. This division also corresponded with the more usual one in which the life of a specimen in LCF is less than lo4 cycles and that in HCF is greater than lo4 cycles. The designs of the high-cycle fatigue and low-cycle fatigue specimens are shown in Figs. l(a) and (c), respectively. The gage sections of both HCF and LCF specimens were electropolished prior to testing. The HCF specimens were tested in an MTS, closed-loop, hydraulic fatigue machine at 10 cps in air. The specimens were cycled between a tensile stress of 5000 psi and a maximum tensile stress which ranged from 35,000 to 125,000 psi, Fig. l(b). The LCF specimens were cycled under strain control from zero to a maximum tensile strain, Fig. l(d), in a Wiedemann-Baldwin testing machine. The experimental procedure has been described elsewhere.3'4 Both HCF and LCF tests were interrupted periodically in order to replicate the development of slip and cracking at the specimen surface. This was accomplished by placing plastic replicating tape around the gage section of the specimen while the specimen was in the mahine. The size of the MC carbides for all specimens was measured on a polished longitudinal section through the gage section after fatigue testing. The method of measurement consisted of carefully scanning the entire polished section in order to locate the largest MC carbides. Photographs were then taken of the six longest carbides oriented approximately normal to the

Jan 1, 1969

By E. Miller, J. M. Eldridge, K. L. Komarek

The liquidus curve of the Mg-Pb system was accurately redetermined. The compound Mg2Pb decomposes peritectically at 538.2° ± 0.3°C to liquid and to a compound p' which melts congruently at 35.0 at. pct Pb and 549.0° ± 0.3°C. The solidus curve of ß' was determined. X-ray diffraction studies indicate that 4' has an orthorhombic structure. Activity values of magnesium calculated from the phase diagram agree with those published in the literature. EXPERIMENTAL thermodynamic properties of binary metallic systems have to be consistent with values calculated from the phase diagram. In systems forming intermetallic compounds the shape of the liquidus curve near a compound is determined by the thermodynamic properties of the coexisting solid and liquid phases. Hauffe and Wagner' neglected the temperature dependence of the chemical potentials and obtained the potential differences of the components of the liquid alloys, relative to stoichiometric liquid. Their calculations were based on the liquidus curve and on the heat of fusion of the compound, and were only valid near the congruent melting point. Steiner, Miller, and Komarek2 developed equations which account for the temperature dependence and obtained the chemical potentials of liquid Mg-Sn alloys over the entire phase diagram from the liquidus and solidus curves and from enthalpy values with the pure components as the standard states. The Mg-Pb phase diagram has been studied by several investigators whose results have been compiled and critically evaluated by Hansen.3 Although the liquidus curve was poorly defined, the general features of the diagram, i.e., one congruent melting compound, Mg2Pb, of essentially stoichiometric composition, two eutectics, and limited terminal solid solubilities, seemed to be suitable for a similar thermodynamic analysis. A careful redeter-mination of the liquidus by thermal analysis revealed, however, the existence of another compound. The liquidus curve between the two eutectics was precisely delineated and the structure and solidus curve of the new compound were investigated. The revised phase diagram was thermodynamic ally analyzed to evaluate the activity of magnesium in the liquid alloys. EXPERIMENTAL PROCEDURE The magnesium metal (Dominion Magnesium Ltd., Toronto, Canada) had a purity of 99.99+ pct; lead (American Smelting and Refining Co.) contained 99.999 pct Pb. Most experiments were carried out in graphite crucibles. Several experiments were made in high-purity alumina (Triangle R.R., Mor-ganite, Inc.) and in Armco iron crucibles to test the inertness of the graphite crucibles. Chemical analysis of magnesium and detailed description of the procedure for thermal analysis have been given previously. For the determination of the solidus curve of the compounds, specimens of initial composition Mg2Pb were equilibrated in a closed isothermal system with magnesium vapor. The source of the magnesium vapor was an alloy which had a gross composition lying in the 0' + L field at the temperature of equilibration. As equilibrium was approached, the specimens lost magnesium to the two-phase reservoir thereby lowering the activity of magnesium in the specimens until activity and composition equaled that of the ß'/ß' + L boundary. Crucibles (1.9 cm ID by 2.2 cm OD by 4.1 cm high) and tightly fitting lids were machined from a molybdenum rod; small, shallow trays were fashioned from thin (0.005 in.) molybdenum sheet, and all the molybdenum components were degreased in hot carbon tetrachloride and then dried. The pieces were then degassed in vacuum at 950°C for about 6 hr. The two-phase alloy was placed at the bottom of the crucible and small specimens of the Mg2Pb compound, weighed on an analytical balance, were placed in two molybdenum trays above the two-phase alloy. The crucible was closed by forcing its lid on and then inserted in a titanium crucible. This crucible was evacuated, flushed twice with argon, and welded under argon. The specimens were equilibrated for about 1 week in a resistance furnace regulated by a Celectray controller, and the runs were terminated by water quenching. The specimens were again weighed and the equilibrium compositions were calculated on the basis that the weight losses were solely due to a loss of magnesium to the two-phase alloy. The structure of the B' phase was investigated by the Debye-Scherrer X-ray diffraction technique. Selected ingots from thermal-analysis experiments containing about 35 at. pct Pb were re-melted, slowly cooled, and crushed in an argon-filled glovebox until the entire ingot passed through a 50-mesh sieve. The powder was thoroughly

Jan 1, 1965

By W. A. Backofen, D. H. Avery, G. A. Miller

An evaluation has been made of the relative importance of yield strength (?) and stacking-fault energy (y) to the rate of fatigue-crack growth in materials of fcc structure. Pure copper and its solid-solution al-loys with aluminum and nickel were chosen for the study because they provided sufficient range in both quantities of interest that either could be varied independently of the other. Experiments involved alternating tension and compression of flat specimens which were prepared with sharpened internal notches so that most, if not all, of the crack-nucleation interval could be eliminated. Growth rate (dC/dN) was concluded to be proportional to the square of the plastic-strain amplitude (€,,) over a strain range of approximately 6x 10-4 to 6 x 10-3. The factor, k, linking dC/dN and ep in dC/dN = kEp2 increased and decreased with corresponding variations in y, but it did not respond syste?>/atically to change in ay, indicating that y is the significant variable in crack growth at constant plastic-strain amplitude. In polycrystalline material, k varied by a factor of 5 over the available range of y. In a few single-crystal experiments on Cu-A1 alloys the growth rate responded less strongly to change in y. It has been suggested that single crystals behave somewhat differently than poly crystalline material because there is more extetnsive substructure near the grain boundaries in the latter, and this facilitates crack advance by separation along subgrain boundaries. A point of some controversy in current work on fatigue relates to the effects of strength and stacking-fault energy on crack growth. In recent experiments a separation was made between the cycling intervals for crack nucleation and the subsequent growth that eventually ends a specimen's fatigue life.' The study was carried out on Cu-A1 alloys primarily, fatigued in alternating four-point bending to constant deflection. A nucleation interval of about 10' cycles (at a total strain amplitude = 0.2 pct) was found to be insensitive to aluminum content in the range 0 to 7.5 wt pct, while the growth period was increased approximately forty fold over the same compositional range. The increase was not in any sense linear, however. Rather, most of the change occurred below 4 pct A1 or a stacking-fault energy, ?, of about 15 ergs per sq cm. It was argued that the plastic-strain amplitude was approximately constant, and therefore the effect of composition must have grown out of the reduction in stacking-fault energy. Several studies have shown that, with high ?, cross slip is encouraged, subgrain structure is introduced during fatigue, and cracking is aided through propagation along subgrain boundaries.1-5 Therefore, lowering ? sufficiently to interfere with substructure formation would be expected to retard growth rate. On the other hand, it is a general rule that resistance to fatigue cracking increases as strength is raised. Accordingly, there might still have been some doubt that Y was the controlling variable, since strength would be increased as y was lowered by the aluminum additions. To help in dispelling that doubt, an experiment was made on a polycrystalline Cu-Ni alloy similar in strength to the Cu-A1 alloys but of higher ?; the crack-growth interval was found to be essentially that of pure copper.' Further support for this position on stacking-fault energy as it relates to crack growth is derived from work by Boettner and McEvily,6 in which the actual crack-growth rate was measured on samples previously notched so as to minimize the nucleation period. Unfortunately, it was necessary in isolating strength level to compare different alloy systems and grain sizes. Recognizing the complication, it was still concluded that growth may be retarded by a reduction in y, per se. A related study has also been made by Roberson and Grosskreutz.7 The zinc content of a brass was systematically changed to alter strength and stack-ing-fault energy, although not below the 15 ergs per sq cm at which pronounced change in growth interval was found in the earlier work. The results were limited to more or less conventional S-N diagrams so that nucleation and growth events could not be separated. No definite conclusions were drawn, but

Jan 1, 1967

By J. L. Walter

Extra-low carbon iron sheet, when deformed and annealed, undergoes exaggerated or abnormal grain growth in the critically deformed regions of the sheet. This exaggerated pmth occurs, for low strains (3 to 6 pct), only in sheet which has a fine dispersion of precipitates in the subsurface region of the sheet and fewer and coarser precipitates in the sheet interior. These particles have been identified as manganese sulfides. Wing the anneal, grains near the surface are gvowth-inhibited by the fine particles but the grains in the interior are free to grow normally. With the additional driving force provided by the strain energy, the interior grains first grow into the small subsurface pains. Eventually, these growing grains grow completely through the sheet. Calculations of limiting grain sizes at various values of strain indicate that a volume fraction of precipitates in excess of 10-' would be required to eliminate exaggerated growth in material strained to 10 pct. OPEN-COIL annealing has made decarburization of sheet steel both efficient and economically practical. Use of such material for porcelain-enameling stock is one of many possible applications of low-carbon iron since carbon in steel is deleterious to porcelain-enameling properties.' However, the extra-low carbon iron presently available presents another problem, that of exaggerated grain growth in regions where the sheet has been deformed as by bending or stretching. In exaggerated grain growth a few grains start to absorb their neighbors and these may become very much larger than the average grains of the sheet. Other names for exaggerated grain growth are coarsening, critical grain growth, secondary recrystallization, abnormal grain growth, or discontinuous grain growth. While this grain growth does not affect the enameling qualities of the low-carbon iron sheet, their presence results in a marked reduction of tensile-yield strength in the region of the sheet containing the large grains. The loss of tensile yield strength may render the material unsuitable for many applications . This report describes the results of a study undertaken to determine the cause of the exaggerated grab growth in extra-1ow carbon iron and, if possi- ble, to prescribe practical procedures for its prevention. GENERAL THEORY The driving force for exaggerated grain growth is the grain boundary free energy. This driving force is proportional to (l/rl + l/r2) where rl and r2 are the mutually perpendicular radii of curvature of the boundary between the growing grain and the grain being consumed. Thus, the greater the difference in size between the growing grain and the matrix grains, the higher the driving force for grain growth. If, however, the matrix grains are free to grow simultaneously, the driving force for exaggerated growth will be diminished. Stability toward growth of the matrix grains may be caused by a) a strong single orientation texture (texture inhibition),' b) a dispersed second phase,3"5 c) the thickness effect,' or d) intergranular segregation.7"9 As exaggerated growth occurs when growth of the matrix grains has been slowed by the stabilizing processes mentioned above, there must be an additional factor acting to promote growth of a few of the grains to the point where they are enough larger than the matrix grains that boundary energy driving forces are sufficient to cause continued growth. For instance, at the annealing temperature, growth-inhibiting inclusions may slowly dissolve and coalesce. Eventually, a grain boundary becomes unlocked and migration occurs at the expense of neighboring grains. Or, an additional driving force may be supplied to some of the grains if the material is strained. Then, since some grains will be strained less than others, the difference in strain energy between adjacent grains may be sufficient to overcome boundary locking and allow growth of the grains with lower strain energies. In the present study, therefore, such factors as the presence or absence of dispersed phases, the nature of the exaggerated growth, and the effect of strain have been considered. EXPERIMENTAL PROCEDURE I) Material and Processing. Three types of low-carbon iron were used in this study; types A and B were commercial grades, each from a different supplier.* The precise details of the processing of

Jan 1, 1963

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

By R. W. Carpenter, J. C. Ogle

It is possible, by using pack-rolling instead of conventional rolling, to reduce a number of metals to thicknesses of 2µm or less. Such thinfoils are generally made at room temperature without intermediate annealing. In addition, pack-rolled foils fail by developing pinholes at thicknesses near 2µm instead of developing the shear cracks usually observed in cold-rolled ductile metals. This paper presents the results of a general investigation of the deformation substructure and texture developed in copper and iron pack -rolled from 130 to about 2µm thickness. Electron microscopy showed that in both metals a fine (0.2 to 0.5?µ m) deformation subgrain structure formed during pack-rolling; in neither case was this substructure grossly different from substructures formed during conventional rolling. The deformation texture formed in pack-rolled iron was quite similar to usual bcc textures; however, in the case of copper, the cube texture was stable during pack-rolling and the normal copper deformation texture was unstable. It is shown analytically that the constraining pack induced a large hydrostatic pressure in the foils during pack-rolling. The pinhole failure mechanism is attributed to the presence of the large hydrostatic pressure during pack-rolling; this strongly suppressed the growth of shear cracks. The stability of the cube texture in copper is also probably due to the unusuul stress distribution developed during pack-rolling. EXPERIMENTS at several laboratories have shown that very thin foils of the common structural metals and many of the rare earths can be made by "pack-rolling". 1-3 The technique was originally developed to make specimens for nuclear scattering experiments and foils for X-ray filters. It is also useful for making experimental laminar metallic composite bodies and foils thin enough for direct examination by ultra-high voltage electron microscopy without the need for special thinning techniques. Pack-rolling in the present context means a three-layer pack, with the material to be rolled into foil comprising the center layer. The outer two layers, which constrain the foil during reduction, are ordinarily austenitic stainless steel. Typically, a 130 µm (0.005 in.) metal strip can be reduced to a final thickness of 2 µm or less by this process. This is accomplished at room temperature, without intermediate annealing. It has been observed that foils produced by this process do not exhibit at any stage of their reduction the severe work-hardening found in strip rolled by conventional cold-rolling methods. Neither is the failure characteristic the same."&apos; Conventionally cold-rolled ductile metal strip fails by developing shear cracks on planes whose normals nearly bisect the angle between the rolling direction and normal to the rolling plane; these are planes of maximum shear stress. In pack-rolling this mechanism has not been observed; failure occurs by the formation of pinholes on the foil surface (penetrating the foil). If pack-rolling is continued the hole density increases. These differences in behavior imply the existence of appreciably different substructure in pack-rolled foils compared to substructure in conventionally rolled material, or perhaps that the geometry of pack-rolling has an effect on the foil behavior. This paper describes an investigation of deformation substructure and texture in some specimens of pack-rolled copper and iron, and some considerations of the stress distribution in the foils during rolling that result from the geometry of pack-rolling. EXPERIMENTAL DETAILS Three different materials were used for pack-rolling in the present work: soft copper sheet (99.8 pct Cu, 0.03 pct 0, electrolytic tough pitch) and two types of iron, Ferrovac E* and Armco iron. Each was "Crucible Stccl Co. initially in the form of 130 µm annealed strip with grain size ranges of approximately 10 to 40 µm. The initial texture of the copper (determined as noted below) was the normally observed cube type (001)[100]; there was evidence of a small amount of material in the cube-twin orientation reported by Beck and Hu.4 The initial texture of the Ferrovac E was similar to that reported for recrystallized iron by Kurdjumov and sachs,5 who list the principal orientations as {111}<112>, {001}<110> 15degfrom RD and a weak component {112}(110) 15 deg from RD. The starting texture of the Armco iron was not determined. Pack-Rolling Procedure. A four-high mill was used for all specimens. The work roll and backing roll diameters were 1.625 and 5.25 in., respectively. The peripheral roll speed of the work rolls was about 2.5 in. per sec. All foils were initially reduced from 130 to 100 µm by conventional straight rolling and then inserted into a pack, without any intermediate annealing, for further reduction. The pack consisted of an 0.033 in. (838 µm) thick 3 by 6 in. polished sheet of austenitic stainless steel, folded to make a 3 by 3 in. jacket. After folding, the jacket was given a small reduction to close the fold tightly before insertion of the foil. During pack-rolling a constant change in roll spacing was made every third pass. The roll-spacing change corresponded to a 5 pct reduction in thickness for a new pack. This approached a 10 pct reduction when the pack had decreased to about half its original thickness. At this point the deformed pack was discarded and a new one

Jan 1, 1970

By Milton E. Wadsworth, R. Ted Wimber

Cobalt sulfate solutions containing ammonium acetate and chloroplatinic acid were reduced by hydrogen in a pyrex-glass lined autoclave in the temperature range of 170o to 232°C and hydrogen partial pressure range of 115 to 830 psia. The reduction rate was directly proportional to the hydrogen partial pressure and surface area of the pyrex glass and was independent of the quantity of chloroplatinic acid added initially. Experiments involving the variation of the relative concentration of ammonium acetate indicated that the reducible cobalt complex was probably the diacetate complex of cobalt, Co(AC)4H20, or a new mononcetate complex Co Ac, which was in solubility equilibrium with a pink precipitate of CO(AC)-4HzO. THE reaction in which a metal is dissolved by an acid to produce gaseous hydrogen and a salt solution was discovered early in the history of chemistry. In 1859 Beketoff found experimentally that this reaction could be reversed; i.e., a salt solution could be reduced by gaseous hydrogen to produce a metal and an acid. A review of work done on this phenomenon since that time may be found elsewhere., The hydrogen reduction of a cobalt salt solution is facilitated by complexing the cobalt ion. An ammonia complex of cobalt has been reduced commercially in the recovery of cobalt metal. A new reducible complex of cobalt was discovered5 when it was found that a co-baltous sulfate solution containing ammonium acetate could be reduced by hydrogen at temperatures in the region of 200°C. When a cobalt sulfate-ammonium acetate solution was heated to a temperature below its normal boiling point, a violet color became apparent, indicating complex formation. The nature of this complex was investigated5 by the addition of NH4Ac to a CoSO4 solution maintained at 85o. During the first additions of NH, Ac, the pH of the solution remained fairly constant at about 5.85. However, as the ratio of NH,Ac to CoSO, approached two, the pH rose and then leveled off at about 6.05. The absorption spectra of a Co(Ac), solution and a CoSO,, NH Ac solution were obtained at 85°C and were compared and found to be the same. These findings suggested that the diacetate complex of cobalt, Co(Ac),.4H20, was formed at 85°C. When a cobalt sulfate-ammonium acetate solution was heated to a temperature above about 165o, a finely divided pink precipitate appeared. The X-ray diffraction pattern of this precipitate indicated that it was Co(Ac), - 4H,O. In addition, it was discovered that when chloroplatinic acid, H,PtCl;, was added initially to the cobalt sulfate-ammonium acetate solution, a faster reduction was obtained. The roles of the solution complex, pink precipitate and chloroplatinic acid in the reduction process were then investigated. APPARATUS The experimental work was carried out in a two-liter stainless-steel autoclave. Adetailed description of the autoclave and the auxiliary equipment used in maintaining constant temperature and pressure may be found elsewhere.= Because the stainless steel was corroded, and also because it acted as a hydrogena-tion catalyst, an all-glass liner was fabricated such that the solution came only into contact with flame-polished pyrex glass. EXPERIMENTAL PROCEDURE The solutions used in the experimental work were prepared by dissolving reagent grade chemicals in distilled water. Although variation of the brand of ammonium acetate appeared to have no effect on the experimental results, CoSO, 7H O from the J. T. Baker Chemical Co. of Phillipsburg, N. J.,was found to give faster reductions than that prepared by Allied Chemical and Dye Corp., N. Y. The former was used throughout the course of the experimental work and was weighed up at the outset of each experiment. The ammonium acetate was dissolved to form a 6M stock solution, which was stored under refrigeration. A 10 pct solution of chloroplatinic acid (J. T. Baker Chemical Co.) was diluted to a 1.15 x 1Q2 M stock solution, which was standardized by precipitation of K,PtCl, as outlined by Scott. The appropriate volume of the chloroplatinic acid, H,PtCl,, solution was pipetted into the clean, dry glass liner. The cobalt sulfate-ammonium acetate solution, which had previously been saturated with

Jan 1, 1962

By W. J. Slatosky

As a means of effecting better control of endpoint temperatirres at the Jones & Laughlin basic oxygen furnace plant, a set of mathematical equations has been developed. The eqlutions are the product of a themlochemical anaysis of the process and aye designed to calculate the required scrap, lime, and hot metal additions in terms of a number of independent variables. Results of test heats have warranted adoption of this technique by the Prodrrction Department. BECAUSE of the autogeneous nature of the basic oxygen steel-making process, bath temperature can be controlled without an external fuel supply by charging the furnace with additions that are thermally balanced. The thermal requirements of the charge materials are such that, during the refining process, they throttle the heat generated by the metallurgical reactions in a manner designed to result in a speci-fied temperature at the completion of the heat. In the past, operating personnel at the basic oxygen furnace plant of Jones & Laughlin&apos;s Aliquippa Works relied on their experience and technical knowledge of the process to determine the quantities of charge additions needed to result in a finishing temperature in the range 2880"to 2920" F. (The charge consists primarily of 93 tons of scrap and hot metal plus an amount of lime sufficient to maintain a basicity ratio of 2.8 to 3.2). Estimates of these materials are based on a consideration of the effects on finishing temperature of 1) iron silicon content, having a variation of 0.8 to 1.8 pct; 2) iron temperature, ranging from 2250°to 2600°F; and 3)any excessive cooling of the furnace due to a production delay. The end temperature of the preceding heat also serves as a guide in that, if a heat was within the specified temperature range, the succeeding heat could be charged with materials of nearly the same proportions, provided the hot metal used in each of the two charges was of approximately the same temperature and composition. On the other hand, if a heat was outside the specified tapping range, or if the hot metal used in that heat was of different analysis and temperature from that of the iron to be charged, an adjustment in the proportion of additions is in order for the following heat. Due to the complex thermochemical behavior of the process and to the inexact and subjective nature of the described method of determining charge additions, consistently accurate temperature control was not to be expected. Therefore, those heats out- side the specified tapping range necessitated subsequent adjustments by either reblowing the cold heats for a suitable length of time so as to elevate the bath temperature to the desired level, or cooling hot heats with a proper amount of scrap. Because extra time is required to make these adjustments, production is delayed. In an attempt to devise a method for improving temperature control, an analysis of the thermochemistry of the process was undertaken. This, in turn, led to the development of a set of mathematical equations which enable the calculation of the quantities of scrap, lime, and hot metal needed to result in any specified tapping temperature range. The analysis was not intended to be a repetition of work done by others such as McMulkinl or ~hilbrook.&apos; It was meant to be an extension of their work so that charge additions could be calculated not in terms of silicon alone but, rather, as a function of all independent variables. This paper presents the derivation of these relationships, their effectiveness in controlling bath temperatures, and a method of utilizing them on an operational basis. The Heat Balance—The first step undertaken in the analysis of the problem was the enumeration of the pertinent variables. A list is presented in Table I where it is noticed that these quantities have been separated into the following three categories: important variables, variables considered as constants, and variables to be neglected. The breakdown was an arbitrary one designed to facilitate the analysis; otherwise, the mathematical treatment would have been exceedingly cumbersome and complex. Fortunately, experience has shown that these simplifying assumptions do not seriously impair the accuracy of the calculations. These variables along with the limiting assumptions listed in Table n were then used to write a heat balance of the process by applying the equation of continuity, Rate of Rate of Rate of Increase = Income - Outgo PI ] of Heat of Heat of Heat.

Jan 1, 1962

By A. Gatti, R. L. Fullman

A very fine dispersion of aluminum oxide is produced by internal oxidation of solid-solution alloy of 0.14 pet A1 in Ag. The particle size of the aluminum oxide is approximntely 50 to 100A in radius. The yield strength of the alloy is increased markedly by internal oxidation. A further increase in strength is produced by cold working the internally oxidized alloy. Recrystallization is retarded by the finely dispessed aluminum oxide particles, so that the strength increase resulting from cold work is retained on annealing at temperatures 14 to about 700°C. MANY workers&apos;-3 in the past have studied various aspects of the internal oxidation of aluminum-silver alloys. This paper is an extension of these studies with emphasis placed on the effect of time and temperature of annealing on the strength of these alloys after oxidation and subsequent cold working. Two general conditions are necessary to internally oxidize an alloy. First, oxygen must diffuse through the base material more rapidly than does the addition; otherwise oxidation will take place as a surface layer. Secondly, the affinity of oxygen for the addition must be greater than for the base material. After internal oxidation of certain alloys takes place, a marked increase in hardness accompanied by higher yield stress and improved creep properties is noted, presumably as a result of the highly dispersed oxide within the base material. Meijering and Druyvesteyn1 also noted that the internally oxidized portion of a partly oxidized alloy failed to recrys-tallize under annealing conditions that led to coinplete recrystallization of the unoxidized part. EXPERIMENTAL-METHODS AND PROCEDURES Few alloys can be made to contain a second phase that is extremely stable at high temperatures. Silver plus aluminum in solid solution was chosen for these internal oxidation studies because of the high rate of oxygen diffusion through silver and the very stable nature of aluminum oxide. Two alloys were vacuum cast. The nominal compositions were: Alloy A—1 pct Al, balance Ag; Alloy B—0.1 pct Al, balance Ag. Chemical analysis, which does not distinguish between aluminum and aluminum oxide, showed the conlposition to be: Alloy A—1.6 pct Al, and Alloy B—0.14 pct Al. The ingots were machined for surface cleaning, swaged and drawn to 0.020-in. diam wire. A sample 20 ft long of the 0.020-in. dianl wire of each composition was annealed 24 hr at 800°C in pure dry hydrogen. Each wire was then cut into two equal pieces. Photomicrographs of the 0.14 pct A1 alloy are shown in Fig. 1, the annealed 0.020-in. wire at the left and the oxidized wire to the right. The oxidation treatment for the first set of data was 1000 hr at 800°C in air. After this treatment the 1 pct A1 proved to be brittle. It is assumed that high alunlinum oxide concentration at the grain boundaries was responsible. The 0.14 pct Al wire remained ductile and all further data were derived using this alloy. One-half of this wire, about 5 ft, plus 5 ft of as-homogenized wire, was then drawn cold to 0.005 in. diam. All tensile tests were conducted with an Instron Engineering Corp. tensile-testing machine, Model TT-B. Unless otherwise indicated, the tests were made at room temperature with a strain rate of 0.1 per min. All metallographic samples were etched with an aqueous solution of 2 pct each of CrO3 and H2SO4 . EXPERIMENTAL RESULTS AND DISCUSSION PARTICLE SIZE DETERMINATION A study was made of the particle size of the aluminum oxide produced in the samples of Ag + 0.14 pct Al, oxidized 1000 hr at 800°C. A cross section of the as-oxidized wire was mounted in bakelite, polished, and etched with an aqueous solution of 2 pct each of CrO3 and H2SO4. The specimen was then thoroughly cleaned by stripping successive coatings made by applying 10 pct nitrocellulose in amyl acetate. The final replica of the cross section was made by applying 2 pct nitrocellulose in amyl acetate. The replica was stripped, transferred to a copper screen, shadow cast with chromium at 10 deg and photographs taken using a Phillips Metallix electron microscope at an accelerating potential of 100 kv. A photograph of an etched sample of the as-oxidized material is shown in Fig. 2. We believe the pits in the photograph are places were A12O3 inclusions were sitting in the matrix. By inspection, it appears that the volume fraction ob-

Jan 1, 1960

By F. S. Pettit

The oxidation of Ni-3 to 25 wt pd Al alloys has been studied in 0. 1 atm of oxygen at temperatures between 900° and 1300°C. These alloys have been found to oxidize by three different mechanisms which depend on the temperature of- oxidation and the alloy composition. Two of the three mechanisms do not permit a continuous layer of Al,0, to be formed on the alloy surface and the oxidation rates are greater than that for pure nickel. The third mechanism results in the formation of an external A1203 scale and lke oxidation rates are about three orders of magnitude smaller than those for pure nickel. The minimum amount of aluminum required for the formation of external scales of A L,0, has been determined. NICKEL-base alloys are currently the main source of materials for use at elevated temperatures in gas turbine engines. These alloys are usually coated to obtain oxidation resistance. Coatings on nickel-base alloys are frequently formed by reaction of the alloy with aluminum whereby alloyed nickel aluminides are formed. The alloyed nickel aluminides provide protection to the nickel base alloy because external scales of A1203 (alumina) are formed during oxidation and mass transport through A120, is slow in comparison to mass transport through most other oxides. In view of the protective properties of A1203, it is important to know how much aluminum is required in these alloys in order to form external scales of AlzO,. The present paper is concerned with the oxidation kinetics and the oxidation mechanisms of Ni-A1 alloys and the minimum amount of aluminum required in these alloys for the formation of external scales of Alz03. THEORETICAL CONSIDERATIONS When a Ni-A1 alloy is heated in oxygen at elevated temperatures, the following reactions can take place on the surface of the alloy where the oxide phases are assumed to be virtually pure: These oxide phases are in the form of nuclei scattered over the surface of the alloy and, in view of their rapid formation, they need not be in equilibrium with the alloy. As the oxidation process continues, equilibrium between the alloy surface and the oxide phases is approached and the stability of the oxide nuclei is determined by the composition of the alloy at the alloy/oxide interface because of the following reactions: 3NiA1204 + 2A1 (alloy) = 4AlzO3 + 3Ni (alloy) [41 4Ni0 + 2Al (alloy) = NiA120, + 3Ni (alloy) [ 5 1 Application of the mass-action law to Eqs. [4J and [5J yields the following equilibrium conditions for these reactions: where aA1 and aNi are the activities of aluminum and nickel, are the standard free energies of formation of NiO, A1203, and NA1204, respectively, R is the gas constant, and T is the absolute temperature. If the composition of the alloy at the alloy/oxide interface is such that (akl/ahi) is greater than the equilibrium values defined by Eqs. [6] and [7], then Reactions (41 and [5] will go to the right as written. Conversely, if the alloy composition is such that the activity ratio (aLl,/aki) at the alloy/oxide interface is less than the equilibrium values, then Reactions [4] and [5] will proceed to the left. The equilibrium activity ratios in Eqs. [6] and 171 can be calculated since values for the standard free energies of formation of the oxide phases are available. Standard free energies of formation for NiO and A1203 have been tabulated by Elliott and ~leiser.&apos; The standard free energy of formation for NiA1204 can be obtained from the data of Tretjakow and Schmalzried.&apos; The results of these calculations are tabulated in Table I. Table I shows that the following inequality is valid over the temperature interval 900" to 1300°C: (Reaction [5]) (Reaction [4]) « 1and therefore the aluminum activity for these compositions can be taken as equal to the square root of the activity ratios (i.e., aNi = 1). If equilibrium is estab-

Jan 1, 1968

By George W. King

The yield strength of a dispersion-hardened W-3.8 vol pct Tho,alloy, in both the recovered and recrys-tallized condition, was investigated and cornpared with that ofrecrystallized pure tungsten over the temperature range of 325" to 2400°C. It is deduced that the Orowan mechanism is obeyed in the recrystallized alloy. In the recovered alloy, a further enhancement of the yield strength results from the retained substructure which is stable up to temperatures in excess of 2700°C. Temperature and strain rate cycling tests were also performed, and the apparent activation energy for the deformation process was derived. This activation energy, - 3 ev, for the recovered and also the recrystallized alloy was about the same as that for re crystallized pure tungsten. However, the activation volume of the recovered alloy, -10-2 cu cm, was about an order of magnitude lower than that of the recrystallized alloy or pure tungsten. This fact accounts for an enhancement oj- the temperature dependence of the yield stress of the recovered alloy. A dislocation velocity exponent of about 4 to 13 was deduced frorn the strain rate cycling tests , which is in good agreement with values reported for tungsten single crystals. VARIOUS theories have been developed to explain the enhanced yield strength of a metal containing a dispersed second phase of small hard particles. These theories are thoroughly reviewed by Kelly and Nicholson.&apos; The theoretical models can be separated into two types. The first type assumes direct interactions between moving dislocations and dispersoids. One of the most widely investigated models for this mechanism is the bowing out of dislocations between the dis-persoids and their subsequent pinching off in order to bypass the obstacles. This is the well-known Orowan mechanism.&apos; The second type is an indirect effect of the dispersion because of its ability to stabilize to high temperatures the substructure introduced by cold working. In this instance, the increment in the yield strength is expected to be inversely proportional to the square root of the subgrain diameter. In the present work, a quantitative study was made of the strengthening effect caused by a thoria dispersion in a recrystallized W-3.8 vol pct Thoz alloy over the temperature range 325" to 2400°C. The results are compared with the increment predicted for the Orowan mechanism based on the calculations by ~shb~.~ In addition, the alloy was tested in the recovered state so that any additional strengthening resulting from the substructure produced during fabrication could be measured. The respective contributions can be separated in this manner, provided that the particle size distribution of the dispersion remains the same in both the work-hardened and the recrystallized state. Particle size distribution measurements showed that this condition was met in the present work. I) EXPERIMENTAL PROCEDURES A) Material Production and Fabrication. The alloy investigated is essentially the same as that reported much earlier by ~effries,~ who also found the strength of tungsten to be improved by the thoria dispersion. The procedure for producing the alloy consisted of mechanically blending a thorium nitrate solution in proper concentration with tungsten oxide (WO3) powder, followed by hydrogen reduction to metal powder. After reduction, the dispersed second phase is present as thoria (Thoz). The pure tungsten powder used for comparison was produced in the same manner except that the thoria doping step was omitted. The powders were consolidated by cold pressing and self-resistance sintering in hydrogen. The resulting ingot had a cross section about 0.6 sq in. and a density about 93 pct of theoretical. The ingot was swaged to 0.174-in.-diam rod at temperatures varying from 1650°C initially to -1200°C near final rod sizes. Two intermediate recrystallization anneals were employed during fabrication. Analysis of the swaged rods is reported in Table I. B) Electron Microscopy Techniques. Carbon extraction rrPxcas prepared by a technique reported by ~00&apos; were used to quantitatively evaluate the thoria particle size and distribution. Electron nlicrographs of extraction replicas were taken at 20,000 times but were then enlarged two to three times in printing. The areas photographed were randomly selected. A Zeiss Particle Size Analyzer (Model TGZ3) was used to count and measure the sizes of all particles present on the print. About three thousand particles were counted in determining a distribution curve. Electron transmission microscopy was used to determine the effect of annealing on the substructures of the materials. Thin foils were produced by a two-stage thinning process. The rods were first ground on emery paper to ribbons about 10 mils thick and then a jet of 5 pct KOH was used to electrolytically reduce a portion of the cross section of the ribbon. Final perforation was achieved by immersing the specimen in a 5 pct KOH solution and electrolytically polishing at a current density of about 0.3 amp cm-&apos;. The foils were examined with a Hitachi HU-11A electron microscope. C) Tensile Testing. Tensile testing was performed in an Instron Testing Machine equipped with a radiation-type vacuum furnace which operates at about 1O"S torr at temperatures as high as 2400 °C. The same furnace was used for annealing the tensile specimens.

Jan 1, 1970

By Claude P. Heiner

mountain region to M tht Coast points for domestic consumption and for export are shown in Table 11. There is considerable disparity in rates from both Rock Springs, Wyo., and Castle Gate, Utah, to the four coast cities where the slack coal is to be used for purposes other than export. The rate on coal to be exported is the same from either starting point to any of the four coast cities even though there is a difference of as much as 341 miles in the shipping distance. It is interesting to note that the freight rate between Sunnyside, Utah, and Fontana, Calif., on coking coal is $5.05 per ton and that coal up to 8 in. can be moved on this rate if it is suitable for coking. This rate was published late in 1942 on a contemplated annual movement of more than 500,000 tons. There have been decreases in freight rates since 1923 on movements of slack coal from Utah into Seattle and Portland due to pressure on the railroads and to greater. quantity of coal shipped. It is the author,&apos;, opinion that a movement of slack coal in excess of 3 million tons of coal per year from Utah to any point in central California would justify a freight rate equal to that puhlished for Fontana, Calif.. or $5.05 per ton. The movement of 3 1/2 million tons of coal per year on the basis of 240 mine working days per year would require that 14,600 tons be handled each mine working day. If it is assumed that shipments could be arranged for a 6-day week, the average railway movement would he 11,200 tons, or approximately 3 trains containing fifty-five 70-ton coal cars per day. Such movements of coal would require railroad equipment represented by the investment amounts stated in Table 12 and entail the services of 250 men. Table 12 ... Railroad Equipment and Investment Required To Move 11,200 Tons of Coal a Day from Utah to California Railroad Equipment Cost 2800. 70-ton coal cara at $6.000 each $16,800.000 32 locomotives at $310.000 each. 9.920.000 Miscellaneous eauiument:.......... .5;000:000 Total........................ $31,720,000 It therefore appears that, under presently known mining methods, the lowest price at which coal could be sold f.0.b. the mine in amounts of 3 1/2 million tons per year for generation of power in central California would be $4.60. It also appears that the lowest freight rate that could be expecled between intermountain points and the central California area would be $5.05 per ton, making a total cost of coal delivered at a plant site of $9.65 per ton. Conelusions The following are the author&apos;s conclusions: 1. Coal mines in Utah and in the Kemmerer and Rock Springs districts of Wyoming could increase annual production by 6 1/2 million tons per year. 2. Under present conditions coal could probably be delivered to any steam electric plant in central California at a price not to exceed $9.65 per ton. 3. The use of coal at such a price, while higher than the equivalent present price of fuel oil, is entirely feasible. 4. There are adequate railroad facilities for movements of large quantities of coal from the intermountain region to the Rest Coast. 5. In a national emergency it probably would be extremely difficult, if not impossible, to obtain sufficient oil to meet requirements of the greatly expanded West Coast steam electric generatsing capacity. 6. The intermountain region contains ample coal reserves to supply all conceivable demands for West Coast power generation for a number of generations. 7. Increasing demands of labor threaten to lessen, if not eliminate, savings in cost of coal production through the use of new mining machinery. 8. Continuation of experiments in socialism by the Federal Government through construction of hydroelectric generating plants, particularly those unrelated to land-use reclamation, defies justification. Rates under this concept of a governmental function are subsidized through greater taxation of its people. Private capital is available to construct steam plants, or hydro plants where feasible, and should be permitted to continue in order to preserve the principles of our free enterprise system. DISCUSSION (L. C. McCabe and Robert P. Koenig, presiding) C. C;. BALl*—I was asked to lead off the discussion, but it is not with the thought that I might be able to add anything to the paper. The thoroughness with which it was prepared rather forestalls the asking of many questions. Your treatment, Mr. Heiner, is a very valuable contribution. I do want to suggest—that although you have limited your study to this specific question, with certain geographic limitations, many of the things in your paper apply just as well to the eastern coals. I want to agree 100 pct with your final conclusion concerning government-subsidized construction. Id. C. McCabe*—It is certainly worthwhile to take stock occasionally to see where we are going in problems of this nature. I agree with Mr. Heiner that ultimately the only reliable source of fuel that the West Coast has is coal hut the time factor is the difficult element to evaluate. Just before I came here I discussed this subject with N. B. Hinson, Vice President and Executixe Engineer of the Southern California Edison Company, and Chairman of the West Coast Inter-Power Exchange Committee. He has given much thought to utilities&apos; fuel supply and it was very helpful to me in preparing a discussion of the paper to talk with him beforehand. Stock taking and forecasting of future development are essential to the continuing success of any enterprise. Mr. Heiner has called attention to the unprecedented growth of central and southern California and to the increased demands for fuel and power which have accompanied it. He discusses the increased fuel oil and natural gas requirements and the probable limits on the future use of these fuels and of hydroelectric power. In contrast to the calculable limits of these sources of electric energy, the author points to the availability of enormous reserves of coal in the Rocky Mountain States adjacent to the Pacific Coast which can be utilized for power generation. That there will be increased use of coal for power generation in the area under discussion is generally accepted hut it is in the timetable of such development that there is not complete agreement. In a recent report, Mr. Hinson reviewed the future power outlook for the Pacific southwest area. He pointed out that the use of steam plants in connection with water power plants in this region has made the maximum use of hydroelectric energy possible, and that the correct balance between hydro and steam generating plants produces the most economical overall system. Steam plants in the area which had been installed to protect against deficiency in hydro energy in dry years were used to carry war loads. Fortunately, no dry

Jan 1, 1950

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1&apos;2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:&apos; Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal&apos;3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.&apos; Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By Andrew Cosgarea, William R. Upthegrove, Morteza Mirshamsi

The capillary-reservoir technique was used with lead-210 and cadmium-115m to determine the self-diffiLsion coefficients of both cadmium and lead in the liquid binary Cd-Pb system. The self-diffusion coefficients of pure cadmium and pure lead were obtained and were compared with the theoretical predictions. Good to excellent agrement between the experimental and predicted values was obtained. The self-diffusion coefficients of cadmium were tneasuved in alloys containing 2.50, 9.13, 17.40, 31.00, 45.00, 69.00, and 97.00 lot pct Cd by determining- the amount of cadniiutn-115m which diffused out of a small-bore capillavy into an infinite reservoir during- a given time peviod. Sinzila7-measurements were made with lead-210 to determine the self-diffusion coefficients of lead in these identical alloys. Diffusivities were determined from measurenzents performed in the temperature interval of 290" to 480°C. The results were correlated with the Ar-vhenius equation, and the maximum variation of the equation parameters (Q and Do) was also inrestigated . THE theory of diffusion in liquids, particularly liquid metals, is relatively undeveloped in contrast to that for the gaseous and solid states. Although the practical application of liquid metals as heat-transfer media has become increasingly important, few liquid-metals systems have been investigated. Experimental data of fundamental significance in this field are not readily obtained, which may explain but not justify the present lack of knowledge. What work has been completed is primarily restricted to liquid diffusion of pure metals; little work has been done in liquid-metal diffusion of binary mixtures. A review of liquid-metal diffusion theory and research is available elsewhere.1-4 In an effort to add to the knowledge of liquid-metal systems and to increase the basic understanding of the diffusion process in liquids, a study of diffusion in the binary-liquid system, Cd-Pb, was undertaken. The capillary-reservoir technique5 was employed to measure the self-diffusion coefficients of cadmium and lead in molten binary alloys. Measurements were made with seven selected compositions and over a temperature range from 290° to 480°C. The experimental apparatus consisted essentially of the following items: constant-temperature bath, diffusion cells, capillaries, capillary-filling device, and a radioactive tracer counting system. EXPERIMENTAL APPARATUS Constant-Temperature Bath. A cylindrical steel vessel, 8 in. in diam and 15 in. deep, surrounded by an insulated heating coil was used with a sodium-potassium nitrate salt mixture heating medium. The bath was maintained slightly below the desired control temperature by the furnace-heating element; and a 250-w heater, actuated by a Bayley proportional temperature controller, was utilized for the final control of the temperature. A constant-speed mixer stirred the salt to insure a uniform temperature within the bath. Four calibrated Chromel-Alumel thermocouples were placed at various positions in the salt bath to verify the absence of temperature gradients. The observed temperature variation during any diffusion run was less than 0.l°C. The entire furnace assembly was mounted on four shock absorbers to exclude building vibrations and the stirrer propeller blades were adjusted so not to induce vibrations within the reservoir. A schematic diagram of the furnace and the constant-temperature bath is shown in Fig. 1. Diffusion Cell. The diffusion cells and associated parts were the same, except for slight modification, as the one used by walls1 in this laboratory, and are shown in detail elsewhere.&apos; A graphite crucible, 4 in. long and 40 mm (1-1/2 in.) ID, enclosed in a 60-mm (2-1/4 in.) Pyrex tube cell about 18 in. long, was used as a container for the melt. The reservoir (molten alloy in the graphite crucible) was usually about 2 to 2-1/2 in. deep. Graphite was used because of its satisfactory nature as a refractory material and the low solubility of carbon in molten Cd-Pb alloy.677 The Pyrex cell was closed at the bottom and fitted at the top (open end) with a 2-in. Dresser coupling. A brass flange was welded to the top of the coupling. The upper part of the diffusion assembly was bolted to this flange with an O-ring seal. The lower part of the diffusion cell was supported in a 3-in. brass cylinder which was open to allow for circulation of salt around the cell. The top assembly consisted of two synchronous motors, a drive shaft, a thermocouple well, and controlled-atmosphere inlets and outlets. One motor was used for rotation of the capillaries at a rate of 1/2 rpm in the reservoir during the diffusion run. The other motor was used for the vertical positioning of the capillaries and the capillary holder by means of a simple screw drive. The capillary holder and drive assembly were lowered into the reservoir for the run and raised after the desired diffusion time at a rate of approximately 0.4 in. per min. Capillary holders were made of graphite. These

Jan 1, 1967

By O. D. Gonzalez

Existing measurements for the steady-state permeation of hydrogen in a iron above 100°C have been examined for contribution of determinate errors. The analysis leads to a recommended equation for the permeability of hydrogen in a iron: o= (2.9 ±0.5) x 10-3 exp - (8400 ± 400)/RT cu cm (ntp H2) cm-1 sec-1 atm-1/2 THE permeability of a iron to hydrogen has been the subject of numerous investigations over the past 40 years, and at present there are thirteen sets of published results for the rate of steady-state permeation of hydrogen in a iron above 100°C. The numerical values in each set of results are entirely self-consis-tent, but the spread among the sets is too large to be attributed solely to experimental error, i.e., to error other than in the specimen itself. Several reasons have been advanced to explain the disparities, but to date the relative importance of experimental inaccuracy to the spread remains uncertain. The purpose of this report is to examine in detail the sources of determinate errors inherent in the experiments and to assess as far as possible the contribution of the errors to the results. The ultimate goal is the selection of values for the permeability and heat of permeation most nearly representative of hydrogen in a iron. The analysis is limited to those experiments in which the permeation rate was observed at steady state—a condition in which traps for hydrogen within the metal are filled to a fixed level15 so that the trapping mechanism is not reflected in the rate of passage of the gas. Furthermore only data are examined in which surface processes are judged to have little or no influence on the flow. It is hoped with these restrictions to obtain values of the permeability and the heat of permeation which will be as closely related as possible to the mechanism of lattice diffusion. I) DEFINITION OF TERMS; UNITS In this report the data for permeation are given in terms of a coefficient oj permeability, ?, which is defined by the equation: jt=?A/?x{p1/2-po1/2) [1] where jt is the total flow of gas normal to the surface of a membrane of planar geometry, e.g., a disc, of area A and thickness ?x; pi and po are the pressures in the input and output sides, respectively. For flow radial to the walls of a membrane of cylindrical geometry, e.g., a tube, the corresponding equation is: where 1 is the length of the cylinder, and ri and ro are the inner and outer radii, respectively. The flux normal to the surface is given by Fick&apos;s law: j= -D(dc/dx) [3] At steady state the concentration gradient will be constant, and integration of Eq. [3] gives for the total flow through a disc of area A and thickness Ax: h =-DA(co - ci) [4] where c, and ci are the concentrations of solute at the output and input surfaces, respectively. When surface control is absent, co and ci are given by Sievert&apos;s law c = Kp1/2, and substitution therewith into Eq. [4] gives directly Eq. [I] where ? = DK. Integration of Fick&apos;s Eq. [3] in cylindrical coordinates will give Eq. [2] where again ? = DK and is thus shown to be independent of geometry (provided that surface control is negligible). The coefficient of permeability, or simply the permeability,* must be expressed in proper units. In *The term permeability will refer in this report always to the coefficient defined above; permeation will be used to specify the general phenomenon of gas passage through a membrane. this report ? will be expressed in the units of cu cm (ntp H2) cm-1 sec-1 atm-1/2. The variations of D and K with temperature are given by D = Do exp(-Ea/RT) and K = KO exp(-?Hs/RT) where E, is the activation energy for diffusion and AH, the heat of solution, each usually expressed in calories per mole of solute. The variation of permeability with temperature will thus be given (for conditions where surface control is negligible) by ? = ?o exp(-?Hp/RT) where ?0 = DoKo and ?Hp = Ea + ?Hs. The units of ?0 are the same as those of 6, and??Hp will be expressed in calories per mole H. 11) SUMMARY OF PERMEABILITY RESULTS Table I gives the values reported to date for the permeability of H2 in a iron in terms of ?o and ?Hp. Except where noted the parameters listed were taken directly from the numbers reported by the various investigators with only a change in units. The temperature limits within which the listed ?o and ?Hp hold are given in column 7; the limits marked in parentheses in this column indicate the entire temperature range covered in each investigation. The listed values of ?o and ?Hp are those giving a linear plot of ln? against T-1 at the higher temperatures in each set of measurements, and thus presumably represent the case for which surface control was negligible. Column 6 gives values of 9 at a representative tem-

Jan 1, 1970

By K. T. Koone, R. J. Blackwell

One of the more important problems to be solved in designing a miscible flood is related to the size of the solvent bank used. Size of the bank may be critical to economic success. Too large a bank loses money; too small a bank may deteriorate and fail to maintain the miscibility needed for high recovery. An important factor in deterioration of a small bank is permeability channeling. In a highly stratified reservoir, solvent speeds ahead in the more permeable zones and mixes laterally with fluids bypassed in adjacent, low-permeability strata. Numerical solutions have been obtained .for the differential equations that describe the movement of a slug through a two-layer system in which mixing occurs both in the direction of flow and transversely. The solvent slug is assumed to have the same density and viscosity as the resident fluid and the pushing fluid. These solutions have been verified by comparing them with similar concentration profiles obtained in the laboratory in a 36-ft stratified model packed with glass beads. The theoretical study revealed that when the dominant mechanism causing a bank to fail is lateral mixing the bank size needed for a given recovery may increase with length rather than decreasing as the square root of reservoir length, as suggested by one-dimensional mixing theory. From a comprehensive examination of the variables, a generalized correlation is developed that relates strata thicknesses, bank size, fluid velocity, mixing coefficients, system length and simple solvent-resident fluid phase behavior to the area miscibly swept. INTRODUCTION Miscible displacement, or solvent flooding, continues to receive widespread attention as a method for increasing oil recovery over that possible in conventional gas-drive or waterdrive projects. A basic economic requirement in the application of such processes is the use of as little solvent as possible. A basic physical requirement is that enough solvent be used to maintain miscibility. Economics places an upper limit on the size of a solvent slug, and physical considerations establish a lower limit. Consequently, the practicality of any given miscible process requires that the economic limit be greater than the lower limit imposed by physical requirements. Procedures exist for determining the economic limit; however, procedures for determining realistic minimum bank sizes exist for only special reservoir situations. In the past, bank size has usually been selected on the assumption of a piston-like displacement for which only longitudinal mixing is important. This assumption leads to the favorable conclusion that bank size, expressed as per cent of pore volume, is inversely proportional to the square root of length. Collins considered the problem of transverse mixing of solvent with fluids in bypassed zones with the assumptions that no forward mixing occurs and that the concentration is uniform in the permeable stratum of interest. 1 Lauwerier considered a mathematically similar problem in thermal recovery operations.2 Their work suggests the much less favorable conclusion that bank size could be directly proportional to the length or even higher powers of the length. This paper considers the physical behavior of a small solvent bank as it moves through a real reservoir, without imposing many of the restrictive assumptions of past treatments. To facilitate mathematical description, an idealized, two-layer model that permits mixing both laterally and in the direction of flow will be considered. A calculation procedure for solving the descriptive equations will be developed for a displacement involving fluids of equal density and viscosity. In addition, laboratory experiments designed to check the computational results will be described, and the coincidence of calculated and observed results will be discussed. The use of many solutions for a variety of bank sizes, strata thicknesses and characteristic system lengths to develop a usable correlation between

Jan 1, 1966

By K. Tanaka, J. D. Mote, J. E. Dorn

It) an attempt to ulLcoce.lP the operative strain-rate-contl-olliy: dislocation nieclzanistns, specially oviented sizgle clystals of the intel-nzediate 1zexagonal phase containing Ag plus 33 at. pct A1 were tested in tension over a wide range of temperatures. Slip was observed to take place by the {0001} <1120> {l100} mechani fracture took place across the(i100) plane and winning occurred by the (i01Z) ?lechanisn. Basal slip exhibited a strong yield point over the -alzge from 77 to 450°K, the upper ,esolved shear st]-ess having the exceptionally high value of 10,500 psi over this entire ?-a?zge of tenzpei,atuves. The critical 9-esolved shear stress for prismatic slip decreased f7-om 48,000 psi at 4.3"K to 23,000 psi at 170°K (Region 1) follozcirg zt:lzich it decl>eased sloz&ly to 21,500 psi at 475°K (Res&apos;on II); from 475" to 575°K (Regioz III), the c7-itical esolced shear stress dec&apos;-eased precipitously to 2000 psi; and from 575" to 750°K (Region IV) it decreased less afi&apos;dly to a low value of about 500 psi. Pvistintic slip in Region I was pobably controlled by the tliel-nally activated riecharzisui of nucleation and g,-ozcth of kinks in dislocations lying in Peierls potential troughs. In Region II for prismatic slip the critical 1-esolved shear stress was slzocn to be deteemined by sh0l.t-range 01-dering, Overall the forgiorz fo basal slip, 7.c.lre1-e a Strong yield-point phenorlienu ia7as observed, the critical vesolved slzea?-stress was shoztn to be determined by n conibirzation 0-f Szizuki locking and short-range-order Izavderzizg, The precipitous decrease in the critical resolved shear stress with increase in ter,/pe7-atrir-e over Region HI was tentatively ascribed to a decrease in the degree of slort-)ange 07-del;iqq (0)- clusteing) and also the effect of fluctuations the degree of o?der, It is at pgreser2t zrtzce)taitz as to 1t1hethe1- these or other possi1)le effects are also ,esponsible. fo- the data obsel-ved 172 Region IV. 1NTEREST in inter metallic compounds stems not only from their role in dispersion hardening of polyphase alloy ystems but equally from their potentialities for high strength, hardness, and stability not only at atmospheric temperatures but especially at elevated temperatures. As summarized in a re- cent symposium of the Electrochemical Society on "Mechanical Properties of Inter metallic Compound", most of the experimental evidence regarding the mechanical behavior of intermetallic compounds centers about the effect of temperature on the hardness and ductility of polycrystalline specimens. The available data reveal that the plastic behavior of intermetallic compounds might be rationalized in terms of the usual dislocation mechanisms appropriate to a solid solutions providing the additional complexities arising from crystal structure, long-range ordering, short-range ordering, and defect lattices are taken into consideration. It is apparent, however, in terms of the history on a solid solutions, that a complete detailed mechanistic rationalization of dislocation processes may not be possible until the deformation processes are studied in single crystals of intermetallic compounds. The present paper contains a preliminary report on the plastic behavior of single crystals of the hexagonal Ag-A1 intermetallic phase over a wide range of temperatures. The results confirm the thesis that single crystal data provide a most effective method of identifying operative dislocation mechanisms in intermetallic compounds. EXPERIMENTAL TECHNIQUES Several factors prompted the selection of the hexagonal Ag-A1 intermetallic phase for this preliminar investigation on the plastic properties of single crystals of intermetallic compounds: 1) This phase has a wide solubility range5 which would permit future investigations on the effect of composition and axial ratios on slip mechanisms. 2) Although it undoubtedly exhibits short-range ordering (or clustering) this intermetallic phase is free from complexities arising from long-range ordering.6 3) Since the atomic radii of aluminum and silver are practically identical, the possible complications due to Cottrell locking are minimized. 4)Whereas the dislocations on the basal planes are expected to dissociate into Shockley partials and are thus susceptible to Suzuki locking, those on the prismatic planes probably remain complete. 5) The axial ratio, being 1.61, is almost ideal, suggesting that short-range ordering may be almost spherically symmetrical. The present investigation was conducted exclusively with the hexagonal Ag-A1 alloy containing 33 at. pct Al. Preliminary investigations revealed that this alloy undergoes basal slip by the (0001)

Jan 1, 1962

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.&apos; It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins&apos; solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion&apos; is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965