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By H. Conrad, V. Damiano, J. Hanafee, N. Inoue

The effects of hydrostatic pressure up to 400 ksi at 25" to 300°C on the mechanical properties of three forms of commercial beryllium (hot-pressed block, extruded rod and cross-rolled sheet) were investigated. Three effects of pressure were studied: mechanical beharior under pressure, the effect of pressure-cycling, and the effect of tensile prestraining under hydrostatic pressure on the subsequent tensile properties at atmospheric pressure. For all three materials the ductility increased with pressure whereas the flow stress did not appear to be significantly influenced by pressure. An increase in the subsequent atmospheric pressure yield strength generally occurred as a result of pressure-cycling or prestraining under pressure, whereas either no change or a decrease in ductility occurred. The only exception to this was sheet material, which exhibited some improvement in ductility following a pressure-cycle treatment of 304 ksi pressure. The effects of pressure-cycling and prestraining were relatively independent of the temperature at which they were conducted. Stabilized cracks of the (0001) type were found in hot-pressed specimens and {1120) type in extruded and sheet specimens following straining under pressure. Also, pyramidal slip with a vector out of the basal plane, presumably c + a, was identified by electron transmission microscopy for extruded rod and for sheet strained under pressure. Small loops similar to those previously reported were found after straining at pressures of the order of 300 ksi. THE use of beryllium in structures is limited because of its poor ductility under certain conditions. Therefore, one objective of the present research was to determine if the ductility of beryllium at atmospheric pressure could be improved by prior pressure-cycling or prestraining under hydrostatic pressure. Another objective was to study the mechanisms associated with the plastic flow and fracture of the polycrystalline form of this metal with pressure as an additional variable. Since the early work of Bridgman,1 it has been recognized that many materials which are brittle at atmospheric pressure exhibit appreciable ductility when strained under high hydrostatic pressure. This effect has been reported for beryllium by Stack and Bob-rowsky2 and by Carpentier et al.3 and has been attributed to the operation of pyramidal slip systems with slip vectors inclined to the basal plane while cleavage or fracture is suppressed.4 That such slip may occur simply by the application of pressure alone without external straining (pressure-cycling) is suggested by the results on polycrystalline zinc5 and polycrystalline beryllium,6 where nonbasal dislocations with a vector (1123) were reported. A significant improvement in the ductility of the bee metal chromium by pressure-cycling has been reported.7 On the other hand, limited studies on the pressure-cycling of the hcp metals zinc67819 and beryllium6 indicated no improvement in ductility; there only occurred an increase in the yield and ultimate strengths. The study on beryllium was limited to hot-pressed material. Consequently, additional studies on the effects of pressure-cycling on other forms of beryllium seemed desirable, especially since for chromium some authors10 have been unable to detect any improvement in ductility while others find a large improvement.7 That the ductility of polycrystalline beryllium at atmospheric pressure might be improved by prior straining under hydrostatic pressure was suggested by the known beneficial effects of cold work on the ductile-to-brittle transition temperature in the bee metals. It was reasoned that, by straining under hydrostatic pressure, fracture would be suppressed, and during the propagation of slip from one grain to its neighbor dislocations with a vector inclined to the basal plane"-'4 would operate. Upon subsequent straining at atmospheric pressure, these dislocations with a nonbasal vector would continue to operate and thereby reduce the tendency for fracture to occur, by assisting in the propagation of slip across grain boundaries and by interacting with any cracks that may develop. It was recognized that maximum improvement in ductility would probably occur at some optimum amount of prestrain under hydrostatic pressure. If the pre-strain was too small, an insufficient number of dislocations with a nonbasal vector would be activated; if it was too large, internal stresses (work hardening) might increase the flow stress more than the fracture stress, or incipient cracks or other damage could develop. EXPERIMENTAL PROCEDURE 1) Materials and Specimen Preparation. The materials employed in this investigation consisted of hot-pressed block (General Astrometals, CR grade), extruded rod (General Astrometals, GB-2 grade with a reduction ratio of 8:1), and cross-rolled sheet (Brush S200, 0.065 in. thick). The analyses of these materials and mechanical properties at room temperature and atmospheric pressure are given in Table I. The grain size of the hot-pressed block was 15 to 16 µ, that of the extruded rod 10 to 11 µ, and that of the sheet 7 to 10 µ in the rolling plane and 5 to 6 µ in the thickness, all determined by the linear intercept method. Al-

Jan 1, 1969

By John C. Bilello

The brittle fracture behavior of cold-worked sintered tungsten was studied over the temperature range 4.2° to 298°K using a high-sensitivity strain measuring system and electronfractography. Similar observations were made on a swaged electron beam zone-refined monocrystal. In sintered tungsten irreversible plastic deformation was observed during cyclic load-unload tests at stress levels well below the fracture stress for all temperatures, but general microyielding could be detected only down to 202°K. For the zone-refined samples macroyielding occurred at all test temperatures with evidence for twinning below -202°K. The fracture stress of the sintered tmgsten was virtually independent of temperature, while the zone-refined crystal showed a 2.3 times increase over the same temperature range. Electronfractography confirmed the presence of numerous rod-shaped and spherical submicroscopic voids which ranged in diameter from 1400 to 4300A in the sintered tungsten; no voids could be found in the zone-refined tungsten. Contrast effects observed on the replicas in the vicinity of certain voids indicated that plastic deformation could be induced by the local stress concentration. It has been suggested that the presence of these voids may be responsible for the low-temperature brittle failure of sintered tungsten. Based m this suggestim und on the evidence obtained here, a dislocatim model is presented to account for the brittle behavior of sintered tungsten. In this model slip, which is induced by the local high stress concentration in the region at the edge of a favorably oriented void, could cause the void to grow to a microcrack of critical size. STUDIES of brittle fracture in bcc metals have led to the well-known experimental relationships between grain size, yield stress, fracture stress, and temperature which have formed the basis for the various dislocation pile-up1-3 or interaction4'= models for slip-induced microcrack nucleation. While microcracks can be nucleated by deformation twins,6,7 there has been no direct evidence furnished by transmission electron microscopy to support conclusively either the Zener pile-up or Cottrell dislocation reaction models for producing micro-cracks in all "brittle" materials. In addition to the "inverse" grain size relationship for yield and fracture stresses the cottrel14 theory predicts that the fracture stress below the transition temperature should behave in a fashion similar to that of the yield stress above this temperature. Such behavior has been verified for several bcc metals.8-10 With reference to both grain size effects and the tem- perature dependence of the fracture stress below the transition temperature, the behavior of sintered tungsten appears anomalous. Early work by Bechtold and Shewrnon 11 showed no apparent temperature dependence of the fracture stress below the ductile-brittle transition temperature (DBTT). They attributed this result to the intergranular nature of the fractures observed. More recent work by Wronski and Four-deux12'13 on considerably purer material did not show any systematic relationship between the fracture stress and temperature below DBTT. The dependence of flow and fracture stresses on grain size is also not clearly established for sintered tungsten. Koo, for example, has shown that the DBTT for sintered tungsten depended chiefly on the annealing temperature and was relatively insensitive to the actual grain size achieved. Using electrofractography and transmission electron microscopy, Wronski and Fourdeuxl3 showed that numerous spherical and rod-shaped submicroscopic voids could be found in sintered tungsten but not in melted tungsten of nominally the same purity. They suggested that these voids could be responsible for the temperature insensitivity of the fracture stress below the DBTT. In the present work the temperature dependence of the fracture stress for high-purity commercially sintered tungsten has been determined. The presence of submicroscopic voids in sintered materials was confirmed, and these were studied in detail to examine the role they could play in nucleating brittle fracture. A dislocation model is suggested which could cause an inherent spherical void to lengthen into a Griffith crack of critical size. EXPERIMENTAL PROCEDURE Commercially sintered tungsten rod was obtained in the as-swaged condition from Sylvania. A zone-refined crystal was obtained from the same source. This crystal was grown by giving three zone passes (at 25.4 cm per hr) to a sintered rod of high-purity tungsten. The rod axis prior to cold working was -15 deg from the [110] direction. Originally the zone-refined rod was -6 mm in diam; it was reduced to -3 mm by eight swaging passes, at high temperatures, with each step having about the same reduction of area. The final swaging step gave a 7.5 pct reduction of area at 1050°C. All swaging operations were performed in a hydrogen atmosphere. For the sintered rod a similar working schedule was employed. Metal-lographic examination of the sintered material revealed that the cold-worked structure had an apparent grain diameter of -25 u transverse to the swaging direction (obtained by the intercept method). In the longitudinal direction cold-worked grains were approximately 1.5 to 2 times their diameter. No distinct fiber structure could be observed optically for the zone-refined rod. The cold-worked structure in the

Jan 1, 1969

By Murray F. Hawkins, W. J. Ainsworth

In all types of subsurface pressure gauges the extension which occurs in the pressure-sensitive element is a function of the difference between the external (well or calibration) pressure and the internal pressure within the gauge, rather than a function of the external pressure only. The internal pressure is near atmospheric and depends upon (a) the quantity of air sealed within the gauge at the time of calibration or measurement, (b) the quantity of moisture (liquid water), if any, sealed within the gauge, and (c) the temperature at which the calibration or well measurement is made. Part of this correction for the change of internal pressure with temperature is taken care of by the customary temperature coefficient of the gauge. However, part of it is not, and while this portion may be only a few psi, it is nevertheless predictable or preventable, and should be considered in precision measurements. ERROR NO. 1 If air is sealed in the gauge at the same temperature and pressure for both the calibration and the well measurements, the usual temperature correction will take care of any difference between calibration and well measurement temperatures. However, if air is sealed within the gauge at temperature T1 and pressure P1 at calibration but at temperature T2 and pressure P2 for a well measurement, because different amounts of air are sealed within the gauge in each case, the internal pressure at. or corrected to, calibration temperature Tr will he different by where all temperatures and pressures are absolute. The calibration temperature is used, and not the well measurement temperature, because the usual temperature correction reduces the well measurements to calibration temperature. The correction term as calculated by the above equation is separate from. and in addition to, the usual temperature correction. Example: T, = 540°R, sealing temperature at calibration P, = 14.7 psia, sealing pressure at calibration T2 = 460°R, sealing temperature at well P2 = 14.7 psia, sealing pressure at well Tr = 660°R, calibration temperature AP = 660 [14.7/460 — 14.7/540] = 3.1 psi While this error is small even under these somewhat maximal conditions, it nevertheless represents a practical situation which did occur, and which as a matter of fact gave rise to this note. Where AP is positive, as above, the correction is added to the measured pressure; where negative, subtracted from the measured pressure. This correction should also be considered in successive calibration runs where the gauge, for example, may be warm from a previous calibration at an elevated temperature. ERROR NO. 2 Where a small quantity of moisture (liquid water) is sealed within the gauge at atmospheric conditions, the increased vapor pressure of the water at higher well or calibration temperatures will cause an increase in internal pressure. This moisture will come presumably from condensation within the gauge following temperature changes, from moisture on the operator's hands, and from atmospheric moisture (rain, mist, fog, etc.). Calculation shows that approximately 0.2 cc of water (three to four drops) is sufficient to saturate the air within an Amerada RPG-3 Gauge at 160°F, at which temperature the vapor pressure of water is about 5 psia. As the vaporization occurs in a sealed volume, the increase in internal pressure will be in excess of this 5 psi. At higher temperatures the pressures will be higher; however more water will be required to saturate the air within the gauge. Some experimental work was carried out with an Amerada RPG-3 Gauge at 200°F fitted with a 1,000 psi element, both with a dry recording chamber and with a small amount of water added. The results directly proved the existence of the error due to the presence of moisture, and, it is felt, indirectly, due to the differences in sealing temperatures and pressures, as both effects may be ascribed simply to an increase in the moles of gas within the recording chamber. SUMMARY In precision measurements the error introduced by sealing the gauge during a well test at a different temperature and pressure from that of calibration may be corrected for by using the equation presented, or it may be prevented by taking care always to seal the gauge at near calibration conditions. The error introduced by sealing moisture in the gauge may be prevented by taking care to keep moisture out of the gauge, or by removing the moisture by either warming or evacuating the gauge. Both of these errors are independent of the range of pressure measurement and the type of gauge, and are in addition to the usual temperature correction. ACKNOWLEDGMENT Appreciation is expressed to W. B. Kendall, Geophysical Research Corp., Tulsa, Okla., who pointed out the error from differences in sealing temperatures during some winter work in Canada. ***

Jan 1, 1956

By Benny J. Nelson

AS a part of the fundamental research program of Aluminum Research Laboratories, some data were obtained on the ternary system Mg-Al-Mn. As very little information on the magnesium corner of this diagram has heretofore been published, it seems desirable to make available the values found for the liquidus and solidus surfaces of this system. Procedure The settling procedure was used for the determination of the liquidus compositions. Metallo-graphic examination of quenched samples, and stress-rupture upon incipient melting, were used for the solidus determinations. The settling procedure has been described in a previous paper.' Briefly, this method involved saturating the alloy with manganese at a temperature substantially above that at which the sohbility was to be determined, then cooling the melt to the latter temperature, and holding it at that temperature for a substantial period of time. Samples for analysis .were carefully ladled from the upper portion of the melt at hourly intervals during the holding period. After the ladling of each sample, the melt was stirred to redistribute some of the manganese that had already settled, because it appeared that when the latter particles of manganese again settled, they aided in carrying down more of the manganese and thus hastened the attainment of equilibrium. The melts were prepared and held in a No. 8 Tercod crucible holding approximately 4 lb of metal. The manganese was added either in the form of a prealloyed ingot (Dow M) containing about 1.5 pct Mn or by the use of a flux (Dow 250) containing manganese chloride. In calculating the flux additions, it was assumed that the manganese introduced would be equal to 22 pct of the total weight of the flux. Temperatures were measured with an iron-constantan thermocouple enclosed in a seamless steel tube, the lower end of which was welded shut. This protection tube also served as a stirring rod. The samples ladled from the upper portions of the melts at the various intervals were analyzed for aluminum, manganese, and iron. When making the alloys which were to be used for the determination of the solidus, 2½ in. diam tilt mold ingots were cast, scalped to 2.0 in. in diam, and extruded into ? in. diam wire. The principal impurities in the melts for this investigation were iron and silicon; their total not exceeding 0.03 pct. Portions of the wire, approximately 2 in. in length, were enclosed in stainless steel capsules for protection from the atmosphere. Bundles of these capsules, with a dummy capsule containing an iron-constantan thermocouple, were heated inside a large steel block (acting as a heat reservoir) in a closed circulating-air type electric furnace. At ap- propriate times, the capsules were removed and quenched in water. The wires were examined metallographically to determine the temperature of initial melting. Short times at temperature were used at the beginning for wire specimens of all alloys to obtain quickly the approximate temperatures at which melting could be first observed. When approximate solidus temperatures had thus been determined, equilibrium heating was attempted. This equilibrium heating consisted of an 8 or 16 hr period at a temperature, about 50 °F below the lowest temperature at which melting occurred when short heating cycles were used, followed by further heating for 1 hr periods at consecutive 10" higher temperatures. The theory for the method of stress-rupture at incipient melting has been well covereda and its limitations are recognized. Thus, if the interfacial tensions are such that the first minute quantity of liquid is "bunched up" at the grain boundary junctions instead of spreading out along the grain boundaries,³ temperatures higher than the solidus are required before melting will be manifested by rupture of the specimen. This point will be elaborated later. Specimens of the wires with a reduced section (approximately 1/16 in. diam) were suspended vertically in a tubular furnace. The setup used is shown in Fig. 1. The clamp holding the specimen was made from alumel thermocouple wire and the thermocouple was thus completed across the specimen by attaching a chrome1 wire to its lower end. Temperatures were read from a Speedomax recorder used in conjunction with a calibrated thermocouple. The small weight attached to the specimen and a vibrator attached to the furnace tube, to aid in distributing the molten constituent along the grain boundaries, were used to bring about rupture at a temperature closely approximating the solidus. The specimens were heated at a rate of about 5°C per min. The rupture of the specimens was indicated both by sound and by the action of the recorder. An argon atmosphere containing a small amount of SO² was used for protection of the specimen. The assembly was taken out of the furnace immediately following rupture and the specimen removed. Some of the broken specimens were examined metallographically and will be referred to later. Results and Discussion Fig. 2 shows a set of typical time-composition curves for liquid samples of the Mg-Al-Mn alloys used for the settling tests. The data as presented

Jan 1, 1952

By C. D. Hall, F. E. Dollarhide

Conventional static tests of fluid-loss agents do not realistically simulate conditions in a fracturing treatment. The dynamic tests reported here show that fluid-loss volume is better represented as proportional to time, rather than as the square root of time. This leads to a different equation for fracture area. The leak-off rate increases with increasing shear rate at the fracture wall, but appears to approach a limiting value. Pressure effects are minor. Spurt loss ordinarily is not affected by the flow velocity in the fracture and is inversely proportional to concentration of agent. The filter cake, once it is well established, is resistant to damage by the flow of plain fracturing liquid (without fluid-loss agent). The latter two findings indicate that a treatment employing a high-concentration spearhead followed by plain fluid can offer a more economical treatment under suitable conditions. INTRODUCTION The successful design of hydraulic fracturing treatments depends on accurate knowledge of the fluid-loss properties of the fracturing fluid. Howard and Fast,' in giving the basic equation relating fracture area to fluid and treating parameters, described three mechanisms which might control the rate of fluid leak-off from the fracture. One mechanism usually is dominant in a given well treatment. For each mechanism, the leak-off velocity is inversely proportional to the square root of time, and the proportionality constant is designated as the fracturing-fluid coefficient. For the wall-building type of fluid-loss agent, the coefficient is determined by a filtration test in a pressure cell, usually with a rock wafer or core as the filter medium. In these static tests, the cumulative volume generally is proportional to the square root of time, after an initial spurt volume. The static-fluid-loss test is not representative of the con,-&tions under which a fluid-loss agent performs in a fratturing treatment. The marked difference between the dynamic- and static-fluid-loss behavior of drilling fluids reported in the literature2,3 implies that dynamic testing is also needed with fracturing fluids. We have therefore undertaken a study of the dynamic-fluid-loss behavior of fracturing fluids. The testing apparatus has also afforded opportunity to evaluate the resistance of the filter cake to removal or damage by flowing fluid containing no fluid-loss agent, with and without sand. The results of these studies offer a means for more accurate evaluation of fluid-loss agent performance, and point the way to a "spearhead" fracturing technique which may offer more economical treatment for some wells. EXPERIMENTAL METHODS The dynamic-fluid-loss testing method is applicable to any type of wall-building fracturing fluid. The present study aimed first at finding what phenomena are involved, and therefore has been limited in the number of materials tested. All of the results specifically reported herein are for kerosene containing a commercial solid fluid-loss agent, which is commonly used at 50 lb/1,000 gal of oil. Another agent in liquid form, used usually at 20 ga1/1,000 gal oil, has shown all the same phenomena in dynamic tests, and generally the same level of fluid-loss control as the solid agent. The dynamic-fluid-loss core cell used in all tests is shown in Fig. 1. The fracture was simulated by the an-nulus between a 2.03 in. OD sandstone core and the surrounding pipe. Annulus widths of 0.234 and 0.117 in. were used, and the core was 3.5 in. long. The annular geometry provides a uniform fluid velocity and a well-defined shear rate over the entire filtering surface, and permits a large filter area (144 sq cm) in a reasonably compact cell. The leak-off fluid passed into a 0.5 in. diameter axial hole in the core. A hollow steel rod through this hole was threaded into a rounded "streamliner" upstream of the core, and into a mounting stud downstream. The streamliner and the stud had the same outside diameter as the core. In all tests except those where sand was circulated, the mounting stud had protruding rings which constricted the annulus, to minimize any tendency for channeling of the fluid to the side exit port. The ends of the core were sealed by Neoprene, steel and Teflon washers. The leak-off fluid was conducted from the hollow rod to an exit tube, through a metering valve (a fine-pitched needle valve) and a quick-opening toggle valve in series, and into graduated cylinders for volume measurement; Two separate circulating systems were used in the experimental program. The extensive initial testing was done at 50 to 150 Psi. The fluid was circulated by a variable speed Moyno pump, and the flow rate was read by a rota-meter flow meter. The filtration Pressure was supplied by holding a back-pressure with a throttling valve. The discharge streamcould be diverted into any of four sections

Jan 1, 1965

By T. L. MacKay

Oxidation rates of single-crystal and poly crystalline zirconium in oxygen at temperatures from 307° to 815°C obey the parabolic rate law for short ex-posure time, 4 to 6 hr. The activation energy for the oxidation of single-crystal zirconium between 420° and 790°C is 42.6 ± 0.7 kcal per mole, and in the temperature range 307" to 600°C the activation energy for oxidation of poly crystalline zirconium is approximately the same. The high-activation energy is indicative that diffusion through the bulk oxide film is the primary mode of mass transport for both types of metal. The higher oxidation rates for poly -crystalline zirconium in this temperature range were attributed to differences in the orientation of the grains in the metal with respect to the oxidizing surfaces. Above 600°C, vain growth was observed in polycrystalline zirconium, and the oxidation rates approached those of single-crystal zirconium. ThE kinetic data of previous oxidation studies1-' of zirconium in oxygen have been interpreted by both parabolic and cubic rate laws. There is some evidence that there is a transition from the parabolic to the cubic rate law at prolonged exposures, but the question is still controversial. For the parabolic rate law activation energies are reported in the range 18.6 to 35 kcal per mole, and for the cubic rate law in the range 38 to 47 kcal per mole. So far as the mechanism of zirconium oxidation is concerned, inert marker studies10,11 have indicated that the oxidation proceeds by oxygen (anion) diffusion through the oxide film toward the metal-metal oxide interface. Pemslerl2 observed that the orientation of the grains in the zirconium metal substrate affected the rate of formation of the oxide film on the surfaces of the grains and that the orientation dependence of the corrosion rate persisted beyond the initial stages of reaction. The rate of oxidation was a minimum when the c axis of the grain was parallel to the surface of the sample, and rose to a maximum when the c axis was inclined at about 20 deg to the plane of sample surface, and decreased again at higher inclinations. cox13 observed that in 300°C steam a thin oxide film was formed initially on zirconium and that this oxide film, which exhibited interference colors, became dark first along the grain boundaries and then over the whole surface in an inhomogeneous manner as the film thickened. Cox proposed a mechanism in which oxygen diffused along preferred paths created by grain boundaries in the metal and formed a much thicker film at or near the grain boundary than on the central zone of the grain. In the present study, the oxidation rates of single crystals of zirconium were measured in oxygen and compared with the oxidation rates of polycrystalline zirconium of the same bar stock. It was felt that such a comparison would elucidate the role of grain boundaries in the metal substrate. SAMPLE PREPARATION Single crystals of zirconium were prepared by following the procedure of I3apperport,14 starting with 1/4-in. rod purchased as crystal-bar zirconium. Zirconium rods 2 in. long were wrapped in tungsten foil and sealed in quartz tubes at pressures of less than 10-6 mm of mercury. Large single crystals were grown by thermal cycling above and below the a-/3 transformation temperature, 862°C. Several specimens were simultaneously subjected to the same cycling procedure, heating to 1200°C, holding for 4 hr, then cooling in the furnace and holding at a temperature of 840°C for 5 to 10 days. This cycle was repeated five or six times for each set of specimens. The grain size of the crystal-bar zirconium before thermal cycling was between 10 and 30 p. Fig. 1 shows the microstructure of an end section of as-received crystal-bar zirconium. A longitudinal section of each zirconium rod after thermal cycling was polished and examined under polarized light, see Fig. 2, and the largest single crystals were selected for this study. Zirconium rods 1/8 in. in diameter and 1/2 in. long with spherical ends were machined from the single crystals and from the as-received bar stock. An X-ray examination showed that the c axis of the single crystals made either a 34-deg or an 89-deg angle with the rod axis. The specimens were chemically etched for 2 min in solution consisting of 15 parts hydrofluoric acid (48 pct), 80 parts nitric acid, and 80 parts water. The chemical polish removed 1 to 2 mils from the surface. EXPERIMENTAL The Sartorius vacuum microbalance used in this study has a sensitivity of 0.5 pg and a capacity of

Jan 1, 1963

By David J. Mack

THE structures and properties of the copper-aluminum alloys have been the subject of much study since the classic investigation of Carpenter and Edwards1 focused attention on the engineering utility of these alloys. It was recognized at an early date that the metallographic structures developed in the aluminum bronzes were similar to those developed in steels, both in the annealed and the rapidly cooled state. Most investigators have been concerned with the acicular, martensitic-like structure formed from the ß solid solution upon rapid quenching; the transformation of the ß under equilibrium cooling to a lamellar eutectoid having been relatively neglected. With the introduction in 1930 by Davenport and Bain2 of the isothermal transformation technique for studying eutectoidal decompositions, a new field was opened. Although an enormous amount of work has since been done on the isothermal transformation of steel, study of structurally analogous systems has been almost totally overlooked. The outstanding exception was the prize-winning paper† of Smith and Lindlief3 who investigated the decomposition of the ß phase in copper-aluminum alloys by isothermal methods. This was followed in 1934 by Wasserman's reviews of available information on analogous transformations in eutectoid alloys. Since that time no comprehensive study of isothermally transformed eutectoids analogous to steel has appeared, although many valuable contributions have been made to an understanding of the structures developed in such systems. Important papers have been published by Kurdjumow, Gridnew and co-workers, 5-17 Obinata,18,19 Greninger,20,21 and others .22.28 The work to be described in this paper was an out-growth of preliminary studies on the isothermal transformation of a eutectoid aluminum bronze, after it became apparent that the alloy under study was reacting somewhat differently than the similar alloy used by Smith and Lindlief. PRELIMINARY EXPERIMENTS The material used in this study was a high purity aluminum bronze especially prepared by Ampco Metal, Inc. It analyzed: Copper-88.o7 pct, Aluminum-11.89 Oct, Iron-0.02 pct, Manganese-0.01 pct, Others-Balance. Although some disagreement exists on the exact composition of the eutectoid, this alloy was believed to be of essentially eutectoid composition even though some pro-eutectoid* delta particles existed in the microstructure of furnace cooled specimens. Specimens transformed isothermally at temperatures slightly below the eutectoid showed relatively large amounts of pre-eutectoid delta, but as will be shown later, this results

Jan 1, 1947

By K. J. Rosengren

INTRODUCTION Mount Isa Mines Limited operates a major mining complex at Mount Isa in northwest Queensland, Australia. The location is arid and remote, some 600 miles distant from the nearest port of Townsville on the eastern coast (Fig. I). Current mine production is 6 million long tons per annum comprising 3.8 million tons of copper ore and 2.2 million tons of silver-lead-zinc ore. Copper ore production is scheduled to increase to 5.8 million long tons per annum by 1973 and a new silver-lead-zinc mine is being developed at Hilton, 13 miles north of Mount Isa. The Mount Isa and Hilton orebodies occur in a single stratigraphic member, termed the Urquhart Shale. This shale is conformable with several other sedimentary formations striking north-south and dipping approximately 65º west. The silver-lead-zinc orebodies occur in bands conformable with the shale bedding and tend to be of tabular shape, varying in width from a few feet to nearly 200 ft. The copper orebodies occur in breccia bodies, locally known as "silica-dolomite", within the Urquhart Shale and tend to be more irregular and massive with widths up to several hundred feet. The detailed geology is described by Bennett (1 2). At present, production comes almost entirely from underground operations with only about 25,000 tons per year of carbonate ore from open pit operations. The mining method used in the copper orebodies is sublevel open stoping with pillar recovery by pillar blast before stope filling or by sublevel caving after stope filling. A large primary sublevel caving operation was also carried out until recently in one of the orebodies. The wider lead orebodies are mined by sublevel open stoping, with or without pillar recovery, while cut and fill stoping is used in the narrower orebodies. Details of the mining methods are given by Davies (3). The company's interest in open pit mining stems from a large open pit which was mined out in 1965 and a further large open pit planned for future production. In addition, the company is currently evaluating several large ore deposits in Australia and New Guinea. All of these orebodies would be mined by open pit methods and rock mechanics studies of slope stability are now a standard feature of all open pit evaluations.

Jan 1, 1972

By R. F. Mehl, J. K. Stanley

THE recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are employed.1 Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystallization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress .4,5† The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed .27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert measurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now

Jan 1, 1942

By F. J. Martin, W. G. Hubler

The Beattie mine is at about the center of Duparquet township in the Province of Quebec, Canada. It is 22 miles northwest of the town of Noranda. The elevation is approximately 1200 ft. above sea level. This locality, long considered a favorable one from the geological point of view, has been prospected for over 20 years, but no discoveries of economic importance were made until the present orebody was found by John Beattie in 1930. The specific gravity of the ore is 2.77. The gold occurs in intimate association with the sulfides, pyrite and arsenopyrite, which in turn are very finely disseminated in a silicified porphyry. The bulk of the gold is associated with the pyrite, only a small proportion being with the arsenopyrite. There are small amounts of magnetite, ilmenite and chalcopyrite present in the ore. There is also some hematite in the ore that is mined from near the surface in the open pit. Metallurgical Problems and Methods or Attack 1. The ore is extremely hard and resistant to grinding. 2. The sulfide minerals are finely disseminated in the gangue. 3. The gold, in turn, is so intimately associated with the sulfides that grinding to even 5 microns will not release all of the values for cyanidation. 4. It is necessary to make a high ratio of concentration in order to obtain a product sufficiently high in gold to meet high shipping and treatment charges. Hardness of the Ore.—Owing to the extreme resistance of the ore to grinding, it was recognized that grinding costs would be high. Microscopic tests showed that grinding to 95 per cent minus 325 mesh would be necessary to liberate a sufficient amount of the values in order to obtain a tailing assaying 0.02 oz. gold per ton, which is considered to have the economical minimum gold content that can be obtained. It is not feasible to grind this hard low-grade ore (0.18 to 0.20 oz.) to 95 per cent minus 325 mesh, so it was necessary to overcome the problem in another way. The following method was decided upon: (1) Fine crushing to minus 1/4 in.; (2) relatively coarse primary grinding; flotation of low-grade concentrates in the primary and rougher circuits and discarding the

Jan 1, 1935

By John H. G. Monypenny

The range of chromium content of stainless steel is, in most cases, included in the limits 11 to 14 per cent., or the middle part of the range, 9 to 16 per cent., specified by the discoverer. For some time after the steel was produced commercially, the carbon content was about 0.3 to 0.4 per cent. and occasionally higher; only rarely was material with 0.25 per cent. carbon or less produced. The reason for this is obvious from the nature of the alloys of chromium available for making such steels; as the lowest carbon content generally available was about 1 per cent., and this in conjunction with a chromium content of about 60 per cent., the production of a 12-per cent. chromium steel with less than 0.25 to 0.30 per cent. carbon was impossible. The advent, on a reasonable commercial scale, of carbonless ferrochromium has modified this condition, however, so that for the last three years stainless material containing 0.1 per cent. or less carbon and the normal amount of chromium has been on the market. As far as the author is aware, the material was first made on a commercial scale by the firm with which he is associated in June, 1920, when a 5- or 6-ton cast of material containing 0.07 per cent. carbon and 11.7 per cent. chromium was made and cast into 12-in. ingots. The necessity for using a totally different raw material, carbonless ferrochromium, instead of the ordinary low-carbon ferro (0.6 to 1.0 per cent. carbon) has led to the idea that stainless iron is a quite distinct product and quite different from stainless steel. While this may be true from a commercial aspect, it is wrong metallurgically. The name stainless iron is unfortunate as the material is a very mild stainless steel and forms the lowest carbon member of a series of steels of continuously varying content which are, in many respccts, the counterpart of the series of ordinary carbon steels ranging from "dead soft" to tool steels. In an article on stainless steel in the Journal of the Society of Chemical Industry, November, 1920, the author said "Just as in the far-off days 'steel' was regarded as a hard product of iron, and little or no attempt was made to grade it into harder or softer varieties, so at present stainless

Jan 1, 1924

By John H. G. Monypenny

The range of chromium content of stainless steel is, in most cases, included in the limits 11 to 14 per cent., or the middle part of the range, 9 to 16 per cent., specified by the discoverer. For some time after the steel was produced commercially, the carbon content was about 0.3 to 0.4 per cent. and occasionally higher; only rarely was material with 0.25 per cent. carbon or less produced. The reason for this is obvious from the nature of the alloys of chromium available for making such steels; as the lowest carbon content generally available was about 1 per cent., and this in conjunction with a chromium content of about 60 per cent., the production of a 12-per cent. chromium steel with less than 0.25 to 0.30 per cent. carbon was impossible. The advent, on a reasonable commercial scale, of carbonless ferrochromium has modified this condition, however, so that for the last three years stainless material containing 0.1 per cent. or less carbon and the normal amount of chromium has been on the market. As far as the author is aware, the material was first made on a commercial scale by the firm with which he is associated in June, 1920, when a 5- or 6-ton cast of material containing 0.07 per cent. carbon and 11.7 per cent. chromium was made and cast into 12-in. ingots. The necessity for using a totally different raw material, carbonless ferrochromium, instead of the ordinary low-carbon ferro (0.6 to 1.0 per cent. carbon) has led to the idea that stainless iron is a quite distinct product and quite different from stainless steel. While this may be true from a commercial aspect, it is wrong metallurgically. The name stainless iron is unfortunate as the material is a very mild stainless steel and forms the lowest carbon member of a series of steels of continuously varying content which are, in many respccts, the counterpart of the series of ordinary carbon steels ranging from "dead soft" to tool steels. In an article on stainless steel in the Journal of the Society of Chemical Industry, November, 1920, the author said "Just as in the far-off days 'steel' was regarded as a hard product of iron, and little or no attempt was made to grade it into harder or softer varieties, so at present stainless

Jan 1, 1924

By Oscar A. Glaeser

THE mine and plant of the United Verde Copper Co., located in Yav-api County, at Jerome, Arizona, have been described in various technical publications and, therefore, a brief outline of its essential features will suffice. The orebodies are of the schist replacement type, the main sulfide mass being a large lens-shaped body approximately 7 acres in cross-sectional area. In general, the mineralization is found along the iron-schist contact, with the orebodies extending about 1000 ft. along this contact and varying from a few feet to 250 ft. in width. The mine is located on a mountain slope and has openings into it on three horizons, as follows: 1. Raises and ore passes open vertically into the shovel pit. These extend down to the 1000-ft. level, where they terminate as loading bins in the Hopewell adit. The main fan intake air shaft, which also extends vertically down to the 1000-ft. level, has its surface opening on the hillside at the extreme north end of the shovel pit, and the main mine air return exhausts through a raise at the extreme south end of the shovel pit. 2. The 500-ft. level adit. 3. The Hopewell adit on the 1000-ft. level. The mine has a vertical downward extent of 2000 ft. below the 1000-ft. level. Underground operations are carried on through two main shafts, both of which are wholly underground. Shaft 5 is the ore-hoisting shaft. It has three compartments and extends from the 800 to the 3150-ft. level. Shaft 6 is the service shaft, and is used for lowering and hoisting men and material. It has a large cage compartment and three smaller compartments for counterweights, ladderway, and pipe and power lines. This shaft extends from the 500 to the 2550-ft. level, and is now being extended to the 3000-ft. level. An air shaft for the downward movement of fresh air from the fan has been provided, and extends to the 2550-ft. level at this time. Work has been started to extend this air shaft to the 3000-ft. level. A return airway for vitiated mine air, in the form of raises and short connecting drifts, extends downward to the 2100-ft. level. The underground mining operations extend from the 300 to the 3000-ft. level. There are about 45 stopes in active operation on the 17 levels

Jan 1, 1929

By Charles H. Fulton

Experimental work on the process was begun on a laboratory scale at Cleveland, Ohio, in 1914, and transferred to East St. Louis, Ill. in 1916, where a commercial sized furnace was in technical operation until January, 1918. The essential steps of the process are as follows: Oxidized zinc ore or roasted zinc concentrate is mixed with crushed coke and coal-tar pitch and formed into briquets 9.25 in. (23.5 cm.) in diameter and 21 in. (53 cm.) long in a manner similar to that used in the manufacture of graphite or carbon electrodes, except that much less care and time are required. The composition varies with the nature of the ore; in one case, the composition was 100 parts ore, 70 parts coke, and 18 to 20 parts pitch. These briquets maintain their form and volume during and after the distillation of the zinc. This object is gained by using coke as the matrix and coal-tar pitch as the binder; this pitch becomes coke on heating and unites the ore particle and the original coke particle into a continuous mass. The briquet is an electrical conductor but only to such a degree that it can be used as a resistor. The size of the ore, as in the present practice of zinc metallurgy, ranges from fine material, such as flotation concentrate, to coarse table and fine jig concentrate. The process is not restricted to any particular kind of ore, but is applicable to pure high-grade ores, ores high in iron, and complex zinc-lead ores, since the residue from the distillation IS held immovably in place within the briquet. In the case of complex zinc-lead ores, the distillation is conducted with a carefully regulated temperature so that a high percentage of lead is retained in the distilled briquet, which may then be smelted for its lead content. In present zinc smelting practice, the reduction fuel is from 40 to 50 per cent. of the weight of the ore. In the briquet, it is from 60 to 85 per cent. of the ore; but unless the ore is exceptionally high in residue, the distilled briquet may be used over again as coke, or as a high ash coke for fuel purposes in power production. Baked briquets are hard and tough and may be handled roughly

Jan 1, 1921

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contarnination could be reduced about 80 pct. The water company's supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters. and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West Penn Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs supplying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical'" Coal Measures"' rocks, the principal source being pyrite (and marcasite) in Pittsburgh and Rooster coals. Springs and seeps on hillsides issue from sandstone and limestone formations intersecting shale or clay land surfaces, or from perched water tables. The two reservoirs create an artificial permanent water table. Soap-hardness tests on three seepage samples taken in a dry summer ranged from 150 to 500 ppm. Water sampled came from aquifers above Pittsburgh and Rooster coals, obviating the possibility of contact with pyrite-containing coal. Since acid contamination of mine waters is the result of chemical reactions of oxygen and water with pyrite, it will be reduced by the exclusion of either air or water. The Sunnyhill Coal Co. has applied this principle in its "contouring" method of strip mining by burying contaminated coal-waste material under a compact, smoothed-up surface of top-soil, gravel, clay, and sand at a cost

Jan 1, 1950

By T. E. Leontis, F. N. Rhines

THE oxide scale that forms upon magnesium at elevated temperatures is nonprotective in the sense that the rate of oxidation is constant and thus does not decrease with the growth of the scale as it does with other common metals. This generality was first stated by Pilling and Bedworth1 and has been verified by Suzuki2 and by Scheil.3 Pilling and Bedworth argued that the nonprotective characteristic could be predicted from the fact that magnesium oxide occupies less space than does the metal from which it springs, wherefore the scale is not expected to cover the metal so completely as to exclude all direct access to the atmosphere. Linear oxidation is thought by Scheil to be common to all cases where the reaction occurs at the oxide-metal interface. According to Suzuki,2 the product of high-temperature oxidation in the air is MgO contaminated with no more than traces of a nitride. When the metal is allowed to burn freely a fume composed of cubic crystals of Mg04 is given off. Delavault5 observed that excrescences form upon liquid magnesium and alloys in the course of oxidation. Beyond this it is known that the use of atmospheres containing small quantities of sulphur dioxide6 or carbon dioxide serve to retard the oxidation of solid magnesium and that beryllium7and calcium8 minimize the oxidation of molten magnesium exposed to the air. Many studies have been devoted to the nature and rates of "protective" oxidation, as exemplified by the cases of copper and iron, wherein the rate is characteristically parabolic. The theory of parabolic oxidation is well developed.9 Linear oxidation, on the other hand, has received but little attention and the theories proposed by Pilling and Bedworth and by Scheil have yet to withstand careful examination. There exists no comprehensive survey of the high-temperature oxidation of magnesium (or of any other metal that exhibits linear oxidation) over a broad range of temperature, under a variety of atmospheric conditions and covering a large group of alloys. It has been the purpose of the present investigation to provide such a survey, with the object of gaining a fuller understanding of linear oxidation, especially as applied to magnesium. EXPERIMENTAL PROCEDURE AND RESULTS The experimental studies undertaken were of two kinds: (I) measurement of the rate of oxidation as influenced by the

Jan 1, 1946

By Kenneth A. Gutschick, Robert S. Boynton

Lime has become a very general loosely used term that includes virtually all finely divided types of limestone as well as burned forms of lime. However, actually (and according to Webster) lime is only calcined limestone (known as quicklime, calcium oxide, or calcia). It also embraces the secondary product of quicklime-namely hydrated lime or slaked lime (calcium hydroxide). Fundamentally there are two basic types of limestone-high calcium and high magnesium (dolomitic). The dolomitic quicklimes and hydrated limes correspond to their "high calcium" counterparts in terminology. The only difference is that the dolomitic types are a combination of the elements, calcium and magnesium, whereas high calcium limes contain only 0.5 to 2 pct of magnesium. Both types, which are made through calcination at high temperatures, are shown chemically as follows: [ ] In the above reactions either type of limestone is burned (calcined) in furnaces known as lime kilns so that the carbon dioxide content of the stone is expelled as a gas. With high calcium limestone 44 pct of the weight of the stone is lost; with dolomitic limestone the loss is 48 pct. Also, both reactions are chemically reversible since quicklime absorbs carbon dioxide readily and in so doing transforms itself back to the original carbonate form. Most quicklimes correspond in size to the original rock, which varies from one to eight inches, depending upon the type of kiln employed. Slight shrinkage occurs during calcination. A few limestones when calcined will decrepitate (break down) into a fine powdery form; however, chemically it is the same as the pebble or lump-sized material. For some uses the lumps of quicklime are pulverized and packaged. Since quicklime has great affinity for moisture and carbon dioxide, it is perishable. When it absorbs moisture and CO2 slowly from the atmosphere, the resulting product is "airslaked." Consequently, it must be stored in dry, moisture-proof areas that are free from CO2. Because of its fugitive nature, it is usually consumed within a few weeks after manufacture. A more stable form of lime is hydrated lime-commercially made by adding water to the quicklime until the lumps break down into a fine, white powder. This product, which is usually packaged, can be stored more safely; and many of its uses are interchangeable with quicklime. The irreversible chemical reactions of hydrated lime for both high calcium and dolomitic types are: [ ]

Jan 1, 1960

By L. E. Young

THE progress of mineral industry education will be limited to the period prior to World War II and will be considered as primarily a division of engineering education. Its relation to progress in the mineral industry and to the activities of the American Institute of Mining and Metallurgical Engineers will be emphasized. The history of mineral industry education has been recorded most completely and authoritatively by Dr. T. T. Read in his recent volume in the Seeley W. Mudd Series of American Institute of Mining and Metallurgical Engineers publications, entitled, The Development of Mineral Industry Education in the United States. Therefore, most of the historical details will be omitted from the discussion and an effort will be made to point out significant developments and to analyze trends. INTRODUCTORY STATEMENT AND SIGNIFICANT POINTS IN PROGRESS Among the significant points in the development of mineral industry education in the United States since 1871, the following deserve particular mention: I. The number of institutions offering undergraduate instruction has increased, particularly during the years 1890 to 1925; the number of students enrolled in undergraduate study has increased greatly, largely on account of the development of courses in petroleum engineering and increasing interest in metallurgy. 2. The selection of students to be admitted to undergraduate courses has been improved through the advisement, counseling, and guidance programs sponsored by the Engineers' Council for Professional Development. 3. Improved instruction methods and the training of the teaching staff have been promoted by the educational institutions themselves, but with the most effective stimulus and guidance of the American Society for Engineering Education and the Engineers' Council for Professional Development. 4. The accrediting of undergraduate curricula through the Engineers' Council for Professional Development, considering both qualitative and quantitative criteria, has done much to improve standards of instruction in engineering education for the mineral industry. 5. Undergraduate curricula and courses are revised currently to meet the needs of the American mineral industry. New curricula are developed currently to permit specialization in technical fields, particularly in the fourth year of undergraduate work. 6. There has been a strengthening of the fundamental courses in mathematics, physics, mechanics, and chemistry, and at the same time these courses are being adapted to the most recent developments in the industry, including metallurgy, geophysics, petroleum engineering, petroleum technology, ceramics and so forth. 7. There has been continuing improvement in plant and laboratory facilities of the educational institutions.

Jan 1, 1947

By J. K. Stanley, R. F. Meel

The recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are emp1oyed.l Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystal- lization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress. 4,5 The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed.27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert mcasurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now available for the case of three-dimensional recrystallization (recrystallization of

Jan 1, 1942

By R. F. Meel, J. K. Stanley

The recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are emp1oyed.l Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystal- lization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress. 4,5 The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed.27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert mcasurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now available for the case of three-dimensional recrystallization (recrystallization of

Jan 1, 1942