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By Richard M. Foose

Five miles southwest of Mt. Holly Springs, Cumberland County, Pennsylvania, the Philadelphia Clay Co. has been mining and milling a white clay since 1896; for use in white cement, as a filler in rubber, pigment and paper, in the manufacture of insecticides, and for other minor purposes. Until late in 1942, when the mine was abandoned because of labor shortage, combined underground mining and surface stripping produced approximately 30,000 tons of clay a year, of which 10,000 tons were refined in the mill. Geology Lower Cambrian Antietam quartzite and the Rilontalto quartzite, stratigraphi-cally older, trend N.55°E. and make a sharp 1600-ft. anticlinal ridge of the South Mountains. The Tomstown dolomite overlies the Antietam quartzite on the southeast flank of the anticline, which is displaced near its crest by a steeply dipping oblique fault. Erosion of the less resistant Tomstown formation has resulted in a narrow valley at an elevation of 700 ft. Directly on top of the Antietam quartzite and at the base of the Tomstown formation is a zone of sandy white clay, lenticular along the strike of the formations, ranging in thickness from 10 to 300 ft. within a mile. All of the formations dip steeply to the southeast, from 65" to vertical. The clay crops out at an elevation of about 1000 feet. Origin and Character The uppermost part of the Antietam formation is sericitic and schistose at many places, and at all these places weathering is in an advanced stage. The clay is the residual product of weathering of this sericitic quartzite or sandy schist. The crude clay has the physical aspect of a sandy kaolin, but there Are large areas in the clay formation that are low in free silica, and commonly the 30 ft. adjacent to the Antietam quartzite is notably free of silica. The overlying Tomstown dolomite has been weathered almost completely to a mixed yellow and brown clay, which carries a zone of nodular and chunky limonite and manganese ore, 4 to 12 ft. thick, about loo ft. from the contact with the white clay. In mining, this zone is an important "marker," indicating where the white clay may be expected in an advancing tunnel. The contact of the white clay formation with the yellow and brown clay of the Tomstown formation is relatively sharp, although the line of contact is irregular and therefore responsible for the lenticular character of the white clay formation. Following is an analysis of the refined clay containing less than one per cent of moisture when dried at 212°F.: SiO2, 67.05 per cent; Al2O3, 22.27; Fe2O3, 0.40; CaO, 0.00; TiO2, 1.05; MgO, 0.52; Na20, 0.04; K2O, 0.88; ignition loss, 7.65; total, 99.86.

Jan 1, 1948

By H. Brandhorst, C. G. Dunn

THE main purpose of the present note is to provide further information on the effect of orientation on strain-induced grain boundary migration in sheet material. A secondary purpose is to draw attention to the presence of a possible (hkl) dependent surface energy driving force, when the two grains of a bicrystal specimen have different (hk2) planes at the gas-metal interface, and to suggest means of eliminating this effect from the strain effect. If two grains A and B of a bicrystal have specific surface energies ? A and ? B respectively, there exists a driving force for grain boundary migration equal to 2(? B - ? A)/t, where t is the thickness of the specimen.' When t is quite small and the residual strain energy densities €A and €B of grains A and B, respectively, adjacent to the boundary are nearly equal, it is possible that the surface effect may be larger than the strain effect. he difference € B - € A gives a driving force per unit area of grain boundary due to an applied strain.)2 However, with increasing t the surface effect decreases while the strain effect presumably remains constant. Therefore, at some sufficiently large value of t, it is possible to ignore surface energy driving forces.* On the other hand, the surface effect is eliminated for all value of t when both grains have the same (hkl) orientation or have identical values of surface energy. Although the previous study provided information on the effect of orientation on strain-induced erain boundary migration,' no orientations with the (100) plane in the plane of the sheet were included. The present paper provides information of this kind. A seed crystal reorientation technique4 was used to prepare a large bicrystal of silicon iron (3 1/4 pct Si) consisting of two (100) grains in the (100) [001] and (100) [Oil] orientations. After a cold rolling strain (7 pct reduction to 3/4 mm final thickness), small specimens were prepared as before2 and then annealed in hydrogen. The boundary migration was such that the grain in the (100) [011] orientation always grew. After overnight anneals at 1100° or 1000°C, none of the initial (100) [001] grain remained. An anneal of 30 min at 950°c, however, provided information on the start of boundary migration. Fig. 1 shows both the initial position (lower line) and the final position (upper curved line) of part of the boundary, as revealed by thermal grooves. In a different area, part of the final boundary was not revealed by thermal grooves; the rate of boundary migration presumably was too high for the growth front to be defined by the time dependent thermal grooving process. In another area there was a vacated intermediate position connected to the initial position of the grain boundary. This indicates that only part of the boundary

Jan 1, 1962

By Richard M. Foose

Five miles southwest of Mt. Holly Springs, Cumberland County, Pennsylvania, the Philadelphia Clay Co. has been mining and milling a white clay since 1896; for use in white cement, as a filler in rubber, pigment and paper, in the manufacture of insecticides, and for other minor purposes. Until late in 1942, when the mine was abandoned because of labor shortage, combined underground mining and surface stripping produced approximately 30,000 tons of clay a year, of which 10,000 tons were refined in the mill. Geology Lower Cambrian Antietam quartzite and the Rilontalto quartzite, stratigraphi-cally older, trend N.55°E. and make a sharp 1600-ft. anticlinal ridge of the South Mountains. The Tomstown dolomite overlies the Antietam quartzite on the southeast flank of the anticline, which is displaced near its crest by a steeply dipping oblique fault. Erosion of the less resistant Tomstown formation has resulted in a narrow valley at an elevation of 700 ft. Directly on top of the Antietam quartzite and at the base of the Tomstown formation is a zone of sandy white clay, lenticular along the strike of the formations, ranging in thickness from 10 to 300 ft. within a mile. All of the formations dip steeply to the southeast, from 65" to vertical. The clay crops out at an elevation of about 1000 feet. Origin and Character The uppermost part of the Antietam formation is sericitic and schistose at many places, and at all these places weathering is in an advanced stage. The clay is the residual product of weathering of this sericitic quartzite or sandy schist. The crude clay has the physical aspect of a sandy kaolin, but there Are large areas in the clay formation that are low in free silica, and commonly the 30 ft. adjacent to the Antietam quartzite is notably free of silica. The overlying Tomstown dolomite has been weathered almost completely to a mixed yellow and brown clay, which carries a zone of nodular and chunky limonite and manganese ore, 4 to 12 ft. thick, about loo ft. from the contact with the white clay. In mining, this zone is an important "marker," indicating where the white clay may be expected in an advancing tunnel. The contact of the white clay formation with the yellow and brown clay of the Tomstown formation is relatively sharp, although the line of contact is irregular and therefore responsible for the lenticular character of the white clay formation. Following is an analysis of the refined clay containing less than one per cent of moisture when dried at 212°F.: SiO2, 67.05 per cent; Al2O3, 22.27; Fe2O3, 0.40; CaO, 0.00; TiO2, 1.05; MgO, 0.52; Na20, 0.04; K2O, 0.88; ignition loss, 7.65; total, 99.86.

Jan 1, 1948

By J. Philip Neal, Carroll P. Rogers

Feldspars, the most abundant minerals of the igneous rocks, occur in numerous forms and mixtures. The feldspars of commercial significance are found in widely distributed pegmatites as large crystals usually free of iron- bearing impurities and thus suitable for hand-cobbing, and also in larger bodies where the ore contains various types of feldspar inter- mingled with quartz and relatively free of iron- bearing impurities, or at least readily unlocked from impurities present at relatively coarse mesh. The latter type of ore includes some pegmatites, and the ''alaskite" bodies so common in the Spruce Pine district of North Carolina. On the west coast of the U.S. and in Oklahoma there is-r has been--commercial recovery of natural feldspathic sand as a source of alumina in glass and ceramics. "Aplite" in commercial terminology is a light-colored igneous rock with a granitic composition and a fine sugary texture, often banded with readily removable iron impurities. Two areas in Virginia produce aplite for the glass industry: one located in the vicinity of Piney River, Amherst County, and the other near Montpelier in Hanover County. According to Deer et al. (1966) the word feldspar derives from the Swedish feldt or falt (field) and "spath:" chunks of rock appearing in tilled ground overlying granite. Castle and Gillson (1960) indicate a Germanic origin, citing "spat," which is said to refer to any transparent or translucent material which is readily cleavable. The term "spar" has in the past been applied to minerals other than feld- spar, such as barite, calcite, and fluorite. It is correct to call the latter "fluorspar." There is a true barium feldspar, but it is rare and of no present economic importance. What is recognized as feldspar or "spar" by present producers and consumers consists of three silicate minerals which, if pure, would have the formu- las KAISi,O, (microcline or orthoclase), NaAlSi,O, (albite), and CaAl,Si,O, (anorthite). These are almost never found in pure form in nature, but occur together in great abundance in a three-component system. A considerable number of different combined ratios of these three exists, with the exception that isomorphism between potassium spar and calcium spar is very limited. User specifications for feldspar products are largely built around the prevalent naturally occurring ratios. Pas- sages following will refer to "K-spar," "Na- spar," or "Ca-spar." Nomenclature and Descriptive Terms Relating to both the mineralogy and the economics of feldspar are certain terms whose coverage it is useful to specify. Commercially, aplite is a feldspathic rock mined and beneficiated in two locations in Virginia, in which both titanium and feldspar minerals are present-the latter now being the major, if not the only, economic product. Technically, the term aplite when applied to this rock is of questionable accuracy. But, in light of accepted commercial usage, the term will be here used to designate it. Regarding the Virginia rock, Ross (1941) is cited.

Jan 1, 1975

By Howard R. Keil

Prior to World War 11, approximately 500 tons per day, or one-third of the ore being shipped to the Golden Cycle Mill at Colorado Springs, Colo., from the Cripple Creek district, was being treated in the flotation plant. The remaining 1000 tons, along with the flotation concentrates, received the usual roasting and cyanide treatment. Since it was not possible to make a disposable tailing on the general run of Cripple Creek ores by flotation alone, it was necessary to treat the flotation tailings by cyanidation, along with the roasted ore. By this treatment, an overall economical tailing could be made. The gold ores from the cripple creek district are the highly siliceous sulphotel-lurides with approximately 3 pet total sulphides. In the lower grade ores most of the values are found in very finely disseminated pyrite. In some of the higher grade ores the tellurides, calaverite and sylvanite, can be recognized. After several years of floating cripple Creek gold ores, having a very low mineral content, it was concluded that this type of ore required a type of flotation machine that would give a rather violent aeration and agitation. This action produced a fairly deep froth column which contained not only the free mineral, principally pyrite, but also most of the middling product; this was most essential in producing a low grade tailing by flotation alone that could be discarded to waste. After investigating most of the current types of flotation machines, it was decided to convert to the Fagergren type. During World War 11, the flotation plant was modified to handle lead and zinc ores. The treatment of these ores was carried on until April 1946. At this time the flotation plant was again reconverted to handle the Cripple Creek ores. Selecting Ores for Flotation During the period of reconversion a considerable amount of experimental work was carried on in the laboratory to determine if a disposable tailing could be made by flotation alone, on certain selected Ores from the Cripple Creek district. It was found that most of the dump Ores and a few of the low grade mine ores could be treated by this method with very satisfactory results. After the preliminary test work in the laboratory, it was decided to carry on further work On a plant-size scale to see if similar results could be obtained. On April 15, 1946, a part of the plant was put into operation as a pilot plant. The various ores that had been found suitable for treatment by this method in the laboratory, were run through the pilot plant at the rate of 200 tons per day for a period of several months. Results were so encouraging that it was decided to put the plant in full-scale operation. Since that time plant capacity has been the from 500 to 1000 tons per day. This has been done not by the installation of more machinery but by (I) crush-

Jan 1, 1949

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts'1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By J. E. Drury, W. M. Byers, E. J. Lynch

Measurements made with starch ~~~~s indicate that the Presence of starch serves to depress the streaming potential of a clay mud system. Measurements with pure starch slurries show that the addition of NaCl or CaO reduces the streaming potential significantly. The addition of NaOH, however, causes only a minor reduction in potential even when there are large changes in mud resistivity. INTRODUCTION In their excellent study of the streaming potential, Hill and Anderson' proposed that the presence of conductive solids within the filter medium will reduce the generated potential. This theory was demonstrated with measurements on shaly sandstone cores having various "b" factors; the cores with the higher negative b factors showed markedly lower potentials. (The factor b was originally defined by Hill and Milburn2 in an expression relating the resistivity of a shaly sandstone to the resistivity of the interstitial water: log F, = log F,, + b (log 100R,)'. 'he factor b, therefore, is a measure of the contribution of the conductive solids to the total conductivity of the sample. It has been found experimentally to be directly related to the amount of chemically exchangeable ion per unit pore volume.) In the logical extension of this hypothesis to the streaming potential created by filtration through mud cakes, they suggested that the presence of nonconductive starch in a drilling mud would have the opposite effect; i.e., it would cause the streaming POtential to be increased. The high streaming potentials that they observed with lime muds were attributed to this cause. A cross-plot of some of their results which are relevant to this discussion is given in Fig. 1. The lime-mud curves and untreated-mud curve are taken from curves given in their paper. The gyp-mud line was estimated from their statement that the measured streaming potential for gyp muds in the range of 1.5 to 2.0 ohm-m was approximately 18 mv/1,000 psi. These gyp-mud potentials were the lowest that they reported for any of the bentonitic-clay muds, and were the only ones which were less than the untreated-mud potentials. This very low streaming potential of gyp muds has also been observed in field studies.' By way of comparison, a U. of Texas publication4 gives the approxi-ate compositions for lime and gyp muds shown in Table 1. These materials are added to a bentonitic-clay mud base. It can be seen that both of these muds contain significant amounts of calcium salts and that the gyp mud has the higher concentration of starch. It would appear from this and from the data shown in Fig. 1 that starch may well be the cause of a streaming-potential reduction, rather than a potential increase. EXPERIMENTAL A series of streaming-potential experiments has been performed using a cell of a design similar to that reported by Wyllie.5 Calomel electrodes were used in both the mud slurry and the filtrate. Pressure in the cell was generated with high-pressure nitrogen. The primary objective of the investigation was to determine the effect of starch on the potential. Five different slurries were made which ranged in composition from untreated ben-tonitic mud (Baroid Aquagel) to a pure starch suspension (Baroid Im-permex). The intermediate slurries were prepared by mixing together a 9-lb/bbl clay mud with a 12-lb/bbl starch suspension in the ratios 1:3, 1:1 and 3:1. When starch was used alone, it was necessary to use an 18-Ib/bbl mixture, since leaner mixtures would not form a suitable filter cake. The clay mud used in the experiments was aged for three months before use. In addition to this series of measurements on the starch-clay mud mixtures, other experiments were performed to determine the effect on the potential of the absolute starch and Aquagel concentration, and the effect of adding various chemicals. RESULTS The effect of starch on the streaming potential is shown clcarly in Fig 2. Increasing percentages of starch resulted in n continually decreasing

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By T. R. A. Gokcen

THE possibilities of separating and purifying metals by high vacuum distillation were examined by Kroll.1 He suggested vacuum treatment for the removal of zinc from the lead produced after Parkes desilverizing. The St. Joseph Lead Co. developed the first commercial vacuum dezincing process at their Herculaneum refinery, as described by Isbell.² The Broken Hill Associated Smelters at Port Pirie, Australia, has, after several years of pilot plant operations and fundamental investigations, developed a continuous process, which will be described briefly in a forthcoming publication." As the full-scale continuous vacuum dezincing plant at Port Pirie is still experimental, publication of full practical details of the plant will be deferred until the unit is operating as a normal part of the continuous refinery. This paper deals only with theoretical aspects of vacuum distillation processes, with particular reference to vacuum dezincing. The method of mathematical analysis is of general interest as it may be applicable to other metallurgical separations which have been investigated recently.4-6 Evaporation Processes At about atmospheric pressure, or higher, most liquids possess a boiling point—a temperature at which any heat put into the liquid is absorbed only as latent heat, not as specific heat. If a steady heat input is supplied, the liquid's temperature rises to this value, then remains constant while bubbles of vapor form beneath the surface. The rate of evaporation is determined solely by the rate of heat transfer to the liquid; the temperature of boiling is determined by the partial pressures of the volatile constituents in the liquid, and the total pressure above the surface. If the rate of heat transfer to the liquid is increased, the temperature remains constant, and the rate of boiling increases. When evaporating metals under vacuum, however, the partial pressures concerned are generally so small that boiling does not occur, because at even a fraction of a millimeter below the surface the hydrostatic pressure is usually too great to permit the formation of a pocket of vapor. In addition, the high thermal conductivity of metals tends to prevent the local superheating which is necessary for bubble formation.' Although this effect is doubtless also exerted when boiling metals at higher pressures, the magnitude will be less because the degree of superheat required to form bubbles is very much less at the higher temperatures involved. Under vacuum, therefore, evaporation of volatile constituents takes place only from the exposed surface, and the rate of evaporation depends upon the surface area, the surface concentration of volatile constituents, the surface temperature, and the partial pressures of volatile constituents immediately above the surface. If the heat input is raised above a certain level, the effect is not to increase the evaporation rate at constant temperature, but to raise the temperature of the liquid until at some higher level an increased rate of evaporation (and thus of latent heat absorption) again balances the heat input rate.? Many substances (including metals) have a very large intrinsic evaporation rate at quite low temperatures—far below their normal boiling points. However, at atmospheric pressure, the large numbers of atoms evaporated are almost completely deflected back into the liquid (or solid) surface by air molecules. Thus the back condensation rate is practically equal to the gross evaporation rate, and the net evaporation rate is practically zero. It can therefore be seen that an overall distillation rate depends not only upon the intrinsic evaporation rate, but also upon the ability of the volatile atoms to move away from the evaporating surface. This movement is facilitated by the provision of a condensing surface close by. Vacuum Distillation: The function of the vacuum above the evaporating surface is to remove foreign molecules, so that the chances of deflection of an evaporated atom back into its source are reduced. When the residual gas pressure is reduced so far that the evaporated atoms have a high probability of reaching a nearby condensing surface without suffering collision with a foreign molecule, the state of affairs is termed "molecular distillation." This process is practiced commercially today for the purification of numerous organic chemical products of high unit value, but not, to the writer's knowledge, for any metallurgical separation. When the degree of vacuum produced in a still is not sufficient to promote molecular distillation, then the evaporated molecules must diffuse through the

Jan 1, 1954

By John C. Shyne, Eric R. Morgan

BORON as a hardenability agent of commercial importance has been the subject of extensive study in recent years. It has been suggested in the past that boron increases hardenability by combining with nitrogen, thus rendering it innocuous.&apos; More recently it has been proposed that boron increases hardenability by reducing the free energy of sites of ferrite and pearlite nucleation.&apos; The segregation of boron to grain boundaries, the primary site of nucleation, would account for the large hardenability effect of minute additions of boron in steel. This grain boundary theory has found general acceptance while the concept of boron as a nitrogen scavenger has been disregarded. However, the interaction of boron and nitrogen in steel is considered to be important to hardenability because boron may be made ineffective by combination with nitrogen.". * The present work was undertaken to examine some of the effects of boron and nitrogen arid their interaction in steel. A base composition of moderate hardenability was chosen. This was a 0.35 pct C steel containing 2.50 pct Ni and 0.30 Mo. This composition was used because it contained no strong carbide, nitride, or Table I. Composition of Steels by Analysis, Wt Pct Steel C Ni Mo 0&apos; B N* Base 0.35 2.50 0.30 0.0012 nil <0.0001 Boron 0.35 2.50 0.32 0.0012 0.0022 <0.0001 Nitrogen 0.33 2.60 0.35 0.0015 nll 0.0052 Boron plus nitrogen 0.35 2.48 0.30 0.0006 0.0020 0.0040 * Obtained by vacuum fusion technique. boride-forming elements. The other alloys examined were modifications of the base composition and contained nitrogen, boron, or nitrogen plus boron. The compositions of the four alloys used are listed in Table I. The alloys were vacuum melted from electrolytic iron, electrolytic nickel, ferromolybdenum, and fer-roboron. When required, nitrogen was added by admitting a partial pressure of nitrogen over the melt after vacuum melting. The alloys were cast into 21h-in. diam ingots and hot rolled to %-in. sq bars. No ingot pattern was discernible on the polished and etched cross sections of the hot-rolled bars. The alloys were normalized at 1650°F, then machined into standard %-in. diam end-quench hardenability test bars. Four different austenitizing treatments were used: 60 rnin at 1550°F, 45 rnin at 1800°F, 30 rnin at 2000°F, and 20 rnin at 2000°F followed immediately by 30 rnin at 1550°F. The 1550" and 2000°F treatments were carried out in duplicate for each of the four steels. In order to prevent surface oxidation the bars were austenitized while buried under charcoal in an atmosphere of argon. After quenching the bars in a conventional end-quench fixture, the hardness surveys were made in the usual fashion on parallel flats ground along opposite sides of each bar. These were ground 0.050 in. deep rather than the conventional 0.015 in., to avoid decarburized or deboronized regions.5 The austenite grain sizes which resulted from each heat treatment were observed metallographically using Vilella&apos;s etch for martensite. The criterion used as a measure of hardenability was the distance from the quenched ends of the bars at which a hardness of RC 35 was observed. This hardness represented the inflection point on the hardness vs distance plot. Fig. 1 shows the hardenability of each steel after the several heat treatments. The duplicate tests demonstrated excellent reproducibility; the distance to Rc 35 was reproduced within 1/16 in. for duplicate test bars. All four alloys had the same grain-coarsening characteristics. Neither boron nor nitrogen had any observable effect on grain size. The grain sizes resulting from the various austenitizing treatments were ASTM 7 at 1550°F, ASTM 4 at 1800°F, and ASTM 2 at 2000°F. The small amount of boron in the boron steel greatly enhanced hardenability when the samples were austenitized at 1550°F. The low hardenability of the boron plus nitrogen steel showed that nitrogen eliminated the boron contribution to hardenability. Both steels containing nitrogen, with and without boron, exhibited lower hardenability than the base composition when quenched from 1550°F.

Jan 1, 1958

By N. E. Rogen, N. J. Grant

WHILE direct measurements of the growth of precipitate particles during aging is of fundamental value, few such measurements have been made. Direct measurements by means of optical or electron-microscopy and X-ray techniques are preferred, however, many of the aging studies have been based on indirect methods such as electrical resistivity and hardness. Because of the minute size of most precipitate particles (less than 1000A) the light microscope is of limited use while electron microscopy is subject to slowness, etching problems and consequent resolution problems. It is fortunate that alloys of the Nimonic type, based on Ni-Cr-Ti-Al, lend themselves to accurate and relatively easy particle size measurements. With proper balance of titanium and aluminum, the only aging precipitate is the gamma prime (r&apos;) Ni3,(Al, Ti)2 phase and this phase is the basis of the high-temperature strength of these allos.3-6 The Ni3(Al, Ti) phase is a face-centered-cubic, ordered structure with nickel atoms occupying the cube faces. Titanium atoms can replace three out of every five aluminum atoms and when substituting do so preferentially.2 Electron microscopy has shown that during aging of most of the commercial alloys of this type, precipitate particles are unusually uniform in size and distribution, and that the volume of (r&apos;) phase is large (20 pct).4,7 The aim of this investigation was to measure the growth of (y&apos;) phase during aging. In so doing, it was hoped that a clearer understanding of the aging process would be attained. X-ray line broadening was used as the measure of precipitate particle size. This technique was selected because it can measure and average the diameter of thousands of particles in one operation. The variations in hardness and matrix lattice parameter with aging were also studied and related to the particle size. EXPERIMENTAL PROCEDURE An alloy of the following composition was studied: Cr Ti A1 C Ni Wt pct 20.71 2.98 1.43 0.04 bal. At. pct 22.06 3.47 2.95 0.18 bal. The alloy, a 15- lb vacuum melt, was forged to 1/2-in. diam at a temperature of 1900" to 2200°F; was solution heat treated for 4 hr at 2000°F and water quenched; and was then aged in various ways. The ASTM grain size was 4 to 5. No (7&apos;) phase could be detected by X-ray analysis after solution treatment and electrolytic extraction. Aging was performed on 2-in. long specimens at 1400°, 1500°, and 1600°F for increasing times. One-half inch sections were removed after each time increment and were then electropolished in a solution of H3P04 saturated with chromium trioxide at a potential of 30 v and rectified with a tantalum electrode. Rockwell hardness measurements were taken using one side of the polished specimen. Matrix lattice parameter determinations were made on the other side using filtered chromium radiation references with the position of the (220) line of a silicon standard. To enable the precipitate particles of the (y&apos;) phase to be measured using X-ray line broadening techniques, it is first necessary to separate and concentrate this phase by electrolytic extraction. Extraction is necessary because the difference between matrix and precipitate lattice parameters is only approximately 0.5 pct and intensities of.the (y&apos;) phase lines are very weak relative to those of the matrix. The extraction techniques employed have been described before and found to produce a reasonably quantitative separation.398 A water solution of 15 pct H3Po4 is used at a current density of 0.5 amp per sq in. at 6 v. The precipitate particles are separated from the liquor by centrifuging and decanting and are then washed, dried and repowdered. A plot of the X-ray intensity vs diffraction angle for the (111) line of the precipitate particles was used as a measure of particle size. The intensity curve approximated the shape of Gaussian distribution function and its breadth was measured at the half height. The (220) line of a silicon standard was used to correct the measured line breadth for instrumental and other broadening errors. The Scherrer formula was used to calculate particle

Jan 1, 1961

By T. H. Alden

A correlation has been found in rock-salt structure single crystals between the latent hardening, measured by the direct stress activation of oblique slip systems, and the stress-strain behavior in simple compression. Materials with high latent hardening, like LiF, strain-harden at a low rate (Stage I) even when severely constrained. KCl, in contrast, shows low latent hardening and a tendency to strain-harden at a high rate (Stage 11). This correlation suggests that oblique slip is essential for Stage II hardening of these materials. THE role of secondary slip in the strain hardening of metal single crystals is a topic of lively controversy. On the one hand are theories in which secondary dislocations participate directly in Stage II hardening in the fcc metals, for example through the production of sessile dislocations,1 forest intersections, or jog formation. Much of the experimental evidence on which these theories are based has been reviewed by Clarebrough and Hargreaves.~ On the other hand, a recent theory5 denies that secondary slip has an essential role in Stage II hardening or in the transition from Stage I to Stage 11. In the latter view, Stage I is not terminated by an increase in the activity of secondary systems but by the exhaustion of undeformed material.6 The experiments reported in this paper will not resolve this controversy since the materials being studied are cubic ionic crystals rather than metals. However, the results do show in an unusual way a direct connection between "secondary" (nonortho-gonal or oblique) slip and strain hardening in these materials. Specifically, a correlation has been found between two independently measured properties, first the latent hardening of oblique (110)(1i0) slip systems as measured by direct stress activation of these systems, and second the stress-strain behavior at small strains. From prior work, it was known that in most cubi-cally oriented rock-salt structure crystals, two orthogonal slip systems operate and exclude the other equally stressed pair, oblique to the first pair.7&apos;8 This observation apparently indicates that a significant interference exists between slip on oblique (110) planes and a relatively small interference between orthogonal (110) planes. The present experiments were begun with the intent of obtaining a quantitative measure of this difference by means of a study of latent hardening in these crystals. I) EXPERIMENTAL METHODS The experiments were basically of two types, first the determination of stress-strain curves by compression along a single (100) axis, and second the measurement of latent hardening by compressive prestrain along one cube axis followed by the determination of the yield stress in a second (latent) cube direction. All tests were done at room temperature in an Instron machine by compression between lapped, parallel steel faces. Three specimen shapes were used. For long crystals (nominal dimensions, 1/8 in. square by 1/2 in. long) the ends were lubricated with an oil-graphite mixture. Superior results with short crystals (about 1/8 in. cube) were obtained using 0.003-in. teflon film.&apos; Thin crystals (1/4 in. square by 3/32 in.) were used for latent-hardening measurements and similar results were obtained with either lubricant. Test specimens were cleaved from Harshaw single crystals which had been irradiated to a dose of lo8 roentgen using a cobalt-60 source. The irradiation raises the yield stress and tends to prevent plastic deformation during sample preparation.10 Prior to testing, the irradiation hardening was removed by an anneal at 400°C. Ideal compression specimens have flat, parallel faces. In short specimens particularly, satisfactory results demand a close approximation to this ideal. In the present work, cleaved surfaces were often used directly as compression faces. The degree of success using this method depends on two factors: 1) the smoothness of cleavage faces, and 2) the extent to which the crystal is deformed or crushed by the chisel during the cutting of a long crystal into short pieces. Unfortunately, only one material of those studied, LiF, was completely satisfactory. NaF, NaC1, KC1, and KBr behaved less well so that

Jan 1, 1964

By H. C. Fiedler

The development of cube-on-edge secondary re crystallization texture in Si-Fe strip depends upon the ability of inclusions, such as manganese sulfide, to restrain nomal grain gvowth. The ability of inclusions to perform this function is shown to depend upon their size and distribution. The desired uniform dispersion of many small inclusions is obtained by controlling the cooling rate from above the solution tempmature of the inclusions or, alternatively, by drastic &apos;quenching from above the solution temperature followed by heat treating at a lower temperature. The development of the cube-on-edge secondary recrystallization texture in Si-Fe strip depends upon both establishing the proper primary recrystallization texture and having inclusions to restrain normal grain growth. It has been suggested that the first requirement is met with a texture which, though weak, is near (110)[001]. A mechanism for secondary recrystallization originally proposed by ielsen&apos; is consistent with the presence of this primary texture. It is visualized that a secondary grain appears where two adjacent grains happen to be sufficiently similar in orientation to be capable of behaving as a single large grain. This pair of grains will grow at the expense of its smaller neighbors as a consequence of its having lower grain boundary free energy. Other explanations of the origin of the secondary recrystallization texture have been offered,&apos; and it can be concluded that the mechanism is not fully understood. Nevertheless, it is apparent that operationally the necessary primary recrystallization texture is obtained simply by interposing an anneal during the cold reduction to final gage. The role of inclusions in the development of the secondary recrystallization texture has been demonstrated by May and Turnbull4 in a comparison of a high-purity heat and a heat containing manganese sulfide. They showed that the driving force for secondary recrystallization is inversely proportional to the diameter of the matrix grains and that the function of the inclusions is to maintain a small matrix grain size. Other inclusions, such as various sul- fides,&apos;)&apos; silicon nitride,8 and vanadium nitride,&apos; titanium carbide,&apos;&apos; and vanadium carbide," have been shown to be effective in promoting secondary recrystallization to the cube-on-edge texture. There is also evidence that silica inclusions in Si-Fe strip made by powder-metallurgy techniques perform this function.&apos; This report is concerned with the second of the two requirements for secondary recrystallization, namely the importance of the metallurgical control of the size and therefore number of inclusions. While the concepts involved are simple, they are fundamental to the making of this material. EXPERIMENTAL PROCEDURE A heat containing 3.27 pct Si, 0.026 pct S, 0.06 pct Mn, and 0.004 pct C was made in an air induction furnace from electrolytic iron, 98 pct ferro-silicon, electrolytic manganese, and iron sulfide. The heat was divided between graphite and baked-sand molds with a cavity 2-5/8 by 5 in. and with walls 2-3/4 in. thick. Slabs, 1 in. thick and 2-5/8 by 5 in., were cut from the ingots and hot-rolled either in the as-cast condition or after one of the heat treatments described later. After pickling, the 80- to 100-mil-thick hot-rolled band was, unless otherwise noted, heat-treated for 5 min at 900°C before being cold-rolled to 25 mils. After a heat treatment of 1 to 3 min at 860°C, the strip was cold-rolled to 12 mils, the final thickness. The percent cube-on-edge texture was determined by dividing the maximum torque as averaged from four samples by the maximum torque of a 3-1/4 pct Si-Fe single crystal having the (110) plane in the plane of the sample. The torque measurements were made in a field of 1000 oe on 1-in.-diam disks. RESULTS AND DISCUSSION The importance of the thermal history of the ingot is evident in Fig. 1 from the appearance of strips heat-treated in a temperature gradient. The sample

Jan 1, 1964

By A. E. Dwight, Paul A. Beck

Known CsCl-type phases in transition metal alloys are shown to be formed preferentially at an electron concentration of approximately 6; a tetragonally distorted version of the CsCl structure is stable at -e/a = 6.5. The relationship of the distortion to electron concentration is verified by experimental data for the quasibinary systems Time ,Os) , Ti(Re,Ir), and Ti(Re,Pt) and the ternary system Ti-Ru-Rh. It was noted some years ago1j2 that the occurrence of CsC1-type ordered structures in equiatomic binary alloys, AB, of transition metals correlates with the location of the component elements in the periodic table. One of the components, A, must be to the left and the other component. B, must be to the right of the chromium group. It was pointed out2 that the CsCl structure does not occur in CrFe. is metastable in VFe,3 and is stable in TiFe up to high temperatures, and that this progressively increasing stability may correspond to an increase in electron transfer between the two components and to a correlated decrease of the magnetic moment associated with the iron atoms. Such a decrease was in fact later demonstrated by Nevitt. 4 The binary CsC1-type phases that are formed by a transition metal with either another transition metal or a lanthanide are listed in Table I. Thirty-three of these phases occur at an average electron concentration (average number of electrons outside of closed shells) of e/a = 6. The five phases that are formed at an electron concentration of e/a = 5.5 appear to be borderline cases. This is suggested for instance by the fact that TiRe is bcc. without any long-range order, while TiTc (at the same electron concentration) has a CsCl ordered structure. Six of the undistorted CsCl phases formed by transition metals with one another have an average electron concentration of e/a = 6. 5. Table I. With the exception of Zr4,Rhs4 and Hf48Rh52. the B component in these phases is a first long-period transition metal, i.e.. iron or cobalt. TiNi. with an electron concentration of e/n = 7, appears to undergo transformation at around room temperature to a more complex ordered struct~re.~ The five other CsCl structures known to occur at e/a = 6.5 have either scandium or a lanthanide metal as the A component; the difference in the elec-tronegativity and in the e/a ratio between the component elements is in these phases very large, A(e/a) - 7, and they may be expected to have a rather strong ionic bond component. Presumably the ionic bond stabilizes the CsCl-type structure at the equiatomic composition and it overrides the electron concentration requirement. When the B element is not from the first long period and the A component is not a rare earth metal. equiatomic (AB) alloys of transition metals with an average electron concentration of e/a = 6.5 in most cases have a crystal structure closely related to the CsC1-type, but slightly distorted tetragonally, Table I. This was first found6 for VRu, NbRu. and TaRu. It was noted6 that the undistorted CsCl structure is also stable in the three systems. but at a lower electron concentration, near e/a = 6. In these systems this requires a deviation from equiatomic stoichiometry. which is otherwise ideally suited for the CsC1-type structure. A similar situation was later found in the Ti-Rh7 and the Ti-Ir systems. 8 The Ti-Rh alloys undergo a second distortion and become orthorhombic when the rhodium content becomes somewhat larger than 50 pct. As mentioned previously. TiRe does not have the CsC1-type ordered structure. In order to investigate how close TiRe is to the borderline of stability of the

Jan 1, 1970

By R. A. Graham, R. W. Rohde

The effect of hydrostatic pressure upon the austenite start temperature of a commercial Fe-28.4 at. pct Ni-0.5 at. pct C alloy has been determined. For pressures to 20 kbar, the austenite start temperature decreased from its atmospheric pressure value of 380°C at the rate of about 4°C per kbar. These data are analyzed by two different thermodynamic approaches; first, considering the transformation as an isothermal process, and second, considering the transformation as an isentropic process. It was found that both these approaches fit the experimental data equally well. The effect of hydrostatic pressure upon the austenite start temperature is best described by considering the mechanical work done during the transformation as that work obtained by multiplying the applied pressure with the gross volume change of the transformation. It is widely recognized1 that strain has an important effect on the initiation of martensitic transformations.* For example, the martensite start tempera- *In this paper, use of the term martensitic transformation implies the reversal of martensite to austenite as wen as the formation of martensite from austenite. ture, M,, may be increased by plastic deformation. Similarly, plastic deformation is observed to lower the austenite start temperature, A,. The effect of uniaxial stress on the M, of iron-nickel alloys has been studied by Kulin, Cohen, and Averbach.2 They found that the martensite start temperature was significantly changed by stresses well within the elastic region. Moreover, the effect of tensile and compres-sive stresses differed. These effects were explained in terms of the interaction of the applied stress with both the dilational and shear components of the transformation strain. The magnitudes of the influence of uniaxial tension, compression and hydrostatic pressure on Ms were measured in 30 pct Ni 70 pct Fe by Pate1 and Cohen.3 Their thermodynamic calculations and similar calculations by Fisher and Turnbull4 predicted the experimental results when the transformation was assumed to occur isothermally at some fixed driving force. This driving force was assumed to be supplied by a combination of the chemical free energy difference between the austenitic and martensitic phases and the work performed during transformation by the applied stress. More recently, Russell and winchel15 reported the effect of rapidly applied shear stress on the reversal of martensite to austenite in iron-nickel-carbon alloys. They performed a thermodynamic analysis of this transformation based upon the assumption that the re- versal occurred adiabatically. They concluded that the applied shear stress did not significantly interact with the transformation strain and thus did not assist in inducing the reversal. Rather they concluded that the reversal was effected by localized strain heating which resulted from the gross local shear deformation of the experiment. In either the adiabatic or isothermal analysis it is necessary to compute the work performed by the interaction of the applied stress and the transformation strains. In the case of hydrostatic pressure this interaction has been treated by two different methods. In either case the applied pressure is assumed to remain constant during the transformation. In one treatment the applied pressure is assumed to interact directly with the dilatational strain associated with the formation of an individual martensite plate.3&apos;4 This local strain has been measured at atmospheric pressure in iron-nickel alloys by Machlin and Cohen.6 In the above treatment this local strain is assumed invariant with temperature and pressure changes. In the other treatment the applied pressure is assumed to interact with the gross volume change of the transformation.7,8 The usefulness of this latter treatment has been demonstrated by Kaufman, Leyenaar, and Harvey7 who calculated the effects of pressure upon the martensite and austenite start temperatures of Fe-10 at. pct Ni and Fe-25 at. pct Ni alloys. Excellent agreement was obtained between their calculations and their experimental data on an Fe-9.5 at. pct Ni alloy. However, this treatment suffers from the fact that the data required to calculate the volume change of the transformation (i.e., the initial specific volumes, the thermal expansion and compressibility data for both the austenitic and martensitic phases) is, in general, not available for any material except pure iron. Thus the calculations of Kaufman et al.7 were necessarily performed by assuming that the volume change of the martensitic transformation in the iron-nickel alloys was that same volume change occurring during the a-? transformation in pure iron. While this approximation may suffice for very dilute alloys it is likely to be inaccurate in high nickel alloys. We have performed measurements of the effect of hydrostatic pressure to 20 kbar on the A, temperature of an Fe-28.4 at. pct Ni-0.5 at. pct C alloy. The composition is similar to the alloy used by Pate1 and Cohen3 to determine the effect of pressure upon the M, temperature. The present measurements permit calculation of the interaction between the applied pressure and the transformation strain. Additionally, measurements have been made which allow precise determination of the gross volume change of the transformation. The data allow direct comparison between the alternate hypotheses of the interaction between the applied pressure and a dilatational transformation strain characterized by either the formation

Jan 1, 1970

By David L. Holt, Walter A. Backofen, Anwar-uI Karim

Specimens of a hydrided Mg-0.5 Zr alloy were strained in tension at 500°C and constant rates of 2 x10-3 5 x 10-3, and 2 X 10" min-1. Hydride-denuded zones formed at grain boundaries normal to the tensile-stress direction as a result of magnesium transport during difusional flow. The width of the zones could be measured and the measurement used for calculating the diffusional component of the imposed tensile strain. The strain from diffusional flow was found to increase with imposed strain at a diminishing rate, tending to saturate at approximately 12 pct. Strain rate sensitivity of flow stress was low. The apparent non Newtonian character of the diffusional flow is attributed to a non Newtonian process acting in parallel with it which could be boundary shear. Fracture grows out of voids that form in the denuded zones. DEFORMATION of a grain by diffusion of atoms from boundaries stressed in compression to boundaries stressed in tension is Newtonian viscous,1-3 and evidence has accumulated in recent years that such a process may be responsible for the high strain-rate sensitivity of the flow stress of super-plastic alloys.4"7 One piece of evidence is that experimental stress: strain-rate relationships can be quantitatively explained.5-7 There is also metallo-graphic evidence of diffusional flow in superplas-ticity, but in a limited amount. The formation of striated bands on the surface of superplastically deformed specimens has been attributed to diffusional flow.5"7 The basis of that attribution came from experiments on a coarse-grained, nonsuperplastic and hydrided Mg-½ wt pct Zr alloy which formed hydride-denuded, light etching zones at tension-stressed boundaries when strained in tension at 270?C.6 The origin of these zones had already been traced to the diffusional flow of magnesium atoms to the boundaries.&apos; The particular observations in the more recent work were of striated-band formation on the surface and denuded-zone formation internally, with both the bands and zones having the same width and appearing at tension-stressed boundaries. It was argued that the bands were a surface manifestation of the zones and hence of diffusional flow. Of course in superplastic alloys which do not contain internal metallographic "markers", the surface bands can be the only metallographic indication. In the present work, denuded-zone formation was utilized, as it has been by others,9-11 to extend the observations of diffusional flow and to measure the strain, ed, resulting from it. Grain size had to be large to measure ed with accuracy. The grain size chosen for this study was -30 , and with that a strain of 10 pct from diffusional flow produces a denuded zone only 3 µ in width. The large grain size naturally precludes superplasticity. The observations of diffusional flow were complemented by determining the strain from the other operative deformation modes: slip, e,, and grain boundary shear, egb. An incremental specimen extension is the sum of increments from slip, and grain boundary shear as well as diffusional flow. Division by a common length is required to convert to strain. If this length is taken as the initial specimen length, then imposed engineering strain, e, is given in terms of the component engineering strains by e = ed + es + egb [1] Stress:strain-rate relationships are determined by the way in which this "strain balance" is made up. EXPERIMENTAL Material. Zirconium hydride markers were introduced into the Mg-0.5Zr alloy by annealing in hydrogen at 450°C for 30 min. The hydride concentration was particularly high at zirconium rich stringers, which was fortunate in that the transverse boundaries at which denuded zones form lie perpendicular to the stringers. Grain size after annealing was 30 µ. Photomicrographs of unstrained and strained material are shown in Fig. 1. Procedure. Specimens were strained in tension with an Instron machine at crosshead velocities of either 2 x 10"3, 5 x X or 1 x 10-2 in. min-&apos;. Specimen length and diameter were 1.0 and 0.2 in., respectively, so that initial strain rates in tests at constant crosshead speed were 2 x 10"3, 5 x X and 1 X l0-2 min-1. Tests were made at 500°C which is a compromise temperature at which diffusional flow is still measurable but grain growth is not active enough to interfere with metallographic measurements. The tests were made in a hydrogen atmosphere. Strain Balance. An equation additional to [I] is eg = ed + es [2] where eg is strain measured from grain elongation. Measurement was made of ed, eg, and, of course, e, which enabled all the strains in Eq. [I] to be determined. For this purpose, strained specimens were sectioned longitudinally, polished, and etched. The strain from diffusional flow, ed, was computed by measuring on photomicrographs the width in the tensile direction of denuded zones at either end of a grain XI, X2, adding them, and dividing by twice the initial longitudinal grain dimension L0, Fig. 2. Reported values are the results of measurements on seventy randomly selected grains; 95 pct confidence limits on ed were +1.5 pct strain. To measure eg, the maximum length, L, and the maximum width, W,

Jan 1, 1970

By R. L. Fullman

IN the investigation of metallurgical transformations and the relationships between microstructure and properties of metals, it frequently is desirable to obtain a measurement of the relative amounts of the various phases present and of the mean size of particles into which each phase is dispersed. The relative amounts of the phases can be measured by the classical methods of area, lineal, and point analysis,1-5 in accordance with the principle that the volume fraction of a phase, the fraction of a polished cross section occupied by the phase, the fraction of a random line occupied by the phase, and the fraction of randomly arrayed points occupied by the phase are all equal. The validity of this relationship depends only on the attainment of a truly random sample of area, length, or points, and not on the size, shape, or distribution of the particles constituting the phase. Smith and Guttman8 have derived a relationship between the interface area per unit volume S, and the measurable quantities L., the interface length per unit area on a cross section, and NL, the number of interfaces per unit length intersected by a random line. Their equation, Sv = — L8 = 2NL is also valid regardless of the distribution of particle sizes and shapes. In contrast to the situation concerning measurement of relative fractions of phases and of interface area, the measurement of particle sizes in opaque samples has not been subjected to a complete analysis. It has been common to measure some lineal or area dimension of particles on a polished cross section and to use the mean value as a qualitative measure of particle size. In the present paper, quantitative relationships are established among the various mean dimensions on a polished cross section and the actual dimensions of the particles present. Particles of Uniform Size Spheres: If a metal sample contains particles of a phase a dispersed in the form of spheres of uniform size, a polished cross section through the sample will reveal circular areas of phase a with radii from 0 to ?, the radius of the spheres. Consider a cube of unit dimensions to be cut from the sample. If a cross section parallel to one of the cube faces is examined, the average number of particles per unit area (N,) equals the number of particles per unit volume (Nv) times the probability p1 that the plane would intersect a single sphere positioned at random within the unit cube. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length 2r would lead to the plane intersecting the sphere, the probability of intersecting a single sphere is just 2r. N8= Nvp1 = Nd-2r [1] Applying the equality of area and volume fractions, the relationship is found between sphere size and average area s of uniform spheres intersected by a random cross section, 4 - f = NV V = Nr . — pra = N s = Nd . 2rs S = —pr2 [2] A similar analysis reveals the average traverse length across spheres of uniform size when random lines are passed through the sample. If a randomly oriented unit cube is cut from the sample and a randomly positioned line is passed through the cube parallel to a cube edge, the number of spheres intersected by the line (Nl) equals the number of spheres per unit volume times the probability p1 of the line hitting a single randomly placed sphere in the cube. Since possible positions of the line occupy unit area, and possible positions for which it will pass through the sphere occupy an area of pr2, the probability of the line hitting a randomly placed single sphere is pr2. NL = Nv p1 = Nvpr2 [3] Combining this relationship with the equality of volume and lineal fraction, the desired relationship is obtained between radius and mean lineal traverse length -i, for spheres of uniform size. 4 - - 3 l=4/3r [4] Circular Plates: Consider a sample containing particles of a phase a in the form of circular plates of uniform radius r and thickness t, where r >> t. If the plates are randomly oriented, as in a sufficiently large sample of a fine grained polycrystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the plates are not randomly oriented, it is necessary to randomize the orientation of the cross-sectional planes and traverse directions. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of plates cut by the cross-sectional plane per unit area is equal to the number of plates per unit volume times the probability of a plate intersecting a single randomly positioned and randomly oriented plate in the cube. If J is the component of the plate diameter in the direction normal to the cross-sectional planes, the probability of a plane cutting a single randomly oriented plate is equal to J, the mean value of J for all possible orientations of the plate. Let 4 be the dihedral angle between a plate and the cross-sectional plane, and let p?, d? be the probability that a plate makes an angle between 4 and ? + d? with the cross-sectional plane. Then for ran-

Jan 1, 1954

By AIME AIME

THIS year&apos;s Chairman of the Institute of Metals Division is a relatively rare phenomenon in the metallurgical profession; he is an expert historian of metallurgy, he is a confirmed collector and student of old works on alchemy, chemistry, and metallurgy-vide: the famous Biringuccio and he is a profound student (with a somewhat idealistic slant) of recent trends in world affairs and in what some incurable optimists call civilization; and at the same time he is still possessed of a sense of humor. Incidentally he is also one of the bestknown nonferrous metallurgists in this country and abroad, and for fifteen years has been a willing worker in A.I.M.E and the Institute of Metals Division.

Jan 1, 1943

By Carl Scholz

FROM the engineer&apos;s standpoint, labor organizations are of interest in so far as they &apos;affect efficiency, maximum production and unit cost, and in this respect the earlier labor organizations&apos; which existed in the age of the Guilds were ideal, inasmuch as they stood &apos; for competency of the apprentice and close cooperation &apos; between employers and employees. In later years the tendencies of the labor organizations have gone in the opposite direction and, instead of cooperating &apos;with the engineer, they usually oppose him on the mistaken theory, that labor-saving devices reduce forces, and costs; in this respect, the united Mine Workers of America have been particularly active and, to a very great extent, successful.

Jan 1, 1921

Dr. James Douglas, who is memorialized on another page of this Bulletin, who held a place in the affections and regard of Institute members second to that of no other living roan, left in his will the sum of $100,000 for the maintenance of the Library of the American Institute of Mining Engineers. This is in addition to the $100,000 which Dr. Douglas gave during his lifetime. We believe that it is Dr. Douglas&apos; wish that the library, the great means by which the benefits of Institute membership may be extended to those distant from headquarters, should be maintained by the Institute at the highest possible level of efficiency and serviceability.

Jan 9, 1918