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By H. J. Ramey

As fluids move through a wellbore, there is transfer of heat between fluids and the earth due to the diflerence between fluid and geothermal temperatures. This type of heat transmission is involved in drilling and in all producing operations. In certain cases, quantitative knowledge of wellbore heat transmission is very important. This paper presents an approximate solution to the wellbore heat-transmission problem involved in injection of hot or cold fluids. The solution permits estimation of the temperature of fluids, tubing and casing as a function of depth and time. The result is expressed in simple algebraic form suitable for slide-rule calculation. The solution assumes that heat transfer in the wellbore is steady-state, while heat transfer to the earth will be unsteady radial conduction. Allowance is made for heat resistances in the wellbore. The method used may be applied to derivation of other heat problems such as flow through multiple strings in a wellbore. Comparisons of computed and field results are presented to establish the usefulness of the solution. INTRODUCTION During the past few years, considerable interest has been generated in hot-fluid-injection oil-recovery methods. These methods depend upon application of heat to a reservoir by means of a heat-transfer medium heated at the surface. Clearly, heat losses between the surface and the injection interval could be extremely important to this process. Not quite so obvious is the fact that every injection and production operation is accompanied by transmission of heal between wellbore fluids and the earth. Previously, the interpretation of temperature logs',' has been the main purpose of wellbore heat studies. The only papers dealing specifically with long-time injection operations are those of Moss and White3 and Lesem, et al.' The purpose of the present study is to investigate wellbore heat transmission to provide engineering methods useful in both production and injection operations, and basic techniques useful in all wellbore heat-transmission problems. The approach is similar to that of Moss and White:' DEVELOPMENT The transient heat-transmission problem under consideration is as follows. Let us consider the injection of a fluid down the tubing in a well which is cased to the top of the injection interval. Assuming fluid is injected at known rates and surface temperatures, determine the temperature of the injected fluid as a function of depth anti time. Consideration of the heat transferred from the injected fluid to the formation leads to the following equations. For liquid, Eqs. 1, 1A and 2 are developed in the Appendix. These equations were developed under the assumption that physical and thermal properties of the earth and wellbore fluids do not vary with temperature, that heat will transfer radially in the earth and that heat transmission in the wellbore is rapid compared to heat flow in the formation and. thus, can be represented by steady-state solutions. Special cases of this development have been presented by Nowakl and Moss and White.3 Both references are recommended for excellent background material. Nowak' presents very useful information concerning the effect of a shut-in period on subsequent temperatures. Since one purpose of this paper is to present methods which may be used to derive approximate solutions for heat-transmission problems associated to those specifically considered here, a brief discussion of associated heat problems is also presented in the Appendix. Analysis of the derivation presented in the Appendix will indicate that many terms can be re-defined to modify the solution for application to other problems. Before Eqs. 1, 1A and 2 can be used, it is necessary to consider the significance of the over-all heat-transfer coefficient U and the time function f(t). Thorough discussions of the concept of the over-all heat-transfer coefficient may be found in many references on heat transmission. See McAdams5 or Jakob," for example. Briefly, the over-all coefficient U considers the net- resistance to heat flow offered by fluid inside the tubing, the tubing wall, fluids or solids in the annulus, and the casing wall. The effect of radiant heat transfer from the tubing to the casing and resistance to heat flow caused by scale or wax on the tubing or casing may also be included in the over-all coefficient. According to McAdams, on page 136 of Ref. 5>

By S. R. Balajee, I. Iwasaki

The adsorption mechanism of corn starch and its derivatives at mineral-solution interfaces was investigated by the adsorption of cationic starch, unmodified corn starch, British Gum 9084, and anionic starch on quartz and hematite. The adsorption of these starches, which decreases in the order mentioned, is dependent on the balance between the magnitude of the electrostatic interaction and the magnitude of the hydrogen bonding. There exists a critical starch concentration for both optimum flotation and flocculation conditions of iron ores, which corresponds to a point where the starch adsorption reaches a saturation coverage. Flocculation occurs due to the adsorption of starch via electrostatic and hydrogen-bonding forces and by interparticle bridging as a result of the conformation of starch molecules at the interface. The depressant property of starches and starch derivatives in flotation' and their flocculation char: acteristics in clarification and filtration2.3 have long been recognized on a wide variety of ores. The effectiveness of a starch as a depressant for iron minerals has been the subject of much investigation in recent years both in the amine flotation of siliceous gangue and in the anionic flotation of activated silica from iron ores. It has been reported that the depressant activity of starches and dextrins in the cationic flotation of quartz from hematite increases with molecular weight, branching, and number of hydroxyl groups, 1 and that the selectivity is affected by changing the configuration of starch molecules and the composition of its polar groups.4 ,5 The manner in which starches are solubilized was shown to exert a significant influence as a depressant in the anionic silica flotation, and a series of articles covering the practical aspects of flotation and flocculation have already been reported.618 Chemical modification of the starch structure, the pulp pH, the calcium ion, and the residual starch concentration were identified as some of the more important variables affecting the flotation behavior. In the flocculation of iron ores, it was noted that most starches flocculated suspensions of hematite in water but did not flocculate similar suspensions of quartz,9 and that an excessive use of starch restabilized the suspensions due presumably to protective action. 6 An admirable application of such an observation to practice may be cited in the selective flocculation and desliming in the anionic silica flotation of iron ores, which resulted in superior metallurgy and lower reagent cost. 10 From detailed adsorption measurements, Schulz'and Cooke4 established that the adsorption of starches and their derivatives depended on the types of minerals and of starches, pH, and electrolytes present. Their adsorption data and the foregoing flotation and flocculation observations suggested that an electrical interaction between starches and charged mineral surfaces might be playing a role in their adsorption process. Adsorption of organic polymers, particularly of synthetic origin, at solid-liquid interfaces has been extensively studied in recent years,' and it is realized that their adsorption mechanism is considerably more complex than that of simple ions or molecules. A polymer molecule possesses a number of functional groups, and the adsorption at a point may restrict the adsorbability of adjacent groups. The mechanism may be further complicated by the conformation of the polymer molecules which may exist as coiled spheres, helices, or extended chains as a result of intramolecular interactions among functional groups as well as intermolecular interactions with solvent molecules. The object of the present investigation was to examine the effect of the chemical modification on the adsorption characteristics of starches and starch products on quartz and hematite at several pH values, so that by correlating this information with flocculation and flotation results, adsorption mechanism of starches on mineral-solution interface may be elucidated. EXPERIMENTAL MATERIALS Quartz: St. Peter sand was screened at 35 mesh and the undersize was scrubbed and deslimed at a Fagergren cell. The deslimed sand was cleaned with 0.1 N hot hydrochloric acid and washed repeatedly with distilled water, For anuscript, measurementsl the -200-mesh fraction of the sand was ground dry in a porcelain mill for 3 hr. The specific surface of the finely ground quartz was

Jan 1, 1970

By M. J. Marcinkowski, E. N. Hopkins

An investigation has been made of the ß(fcc) — a(hexagonal) transformation which occurs in lanthanum using both electrical resistivity and transmission electron microscopy techniques. It has been shown that the ß phase can be retained below the transformation temperature by rapid quenching but that the sample immediately begins to transform to the a phase. The transformation is observed to nucleate in the vicinity of inclusions. Based on the above observations, a detailed model of the transformation has been advanced which involves the nucleation of an extrinsic stacking fault bounded by a pair of Shockley partial dislocations in the vicinity of some heterogeneity, i.e., an inclusion. The stress field of the resultant dislocation pair acts to nucleate extrinsic faults in adjacent planes and leads quite naturally to the B-a conversion with a minimum of strain energy induced in the crystal. LANTHANUM possesses an fcc structure ß) (8) upon cooling transforms to a hexagonal modification (a) in much the same way as cobalt. The one exception, however, is that the stacking sequence of the closest packed planes in a La is ABAC ABAC, and so forth,1 whereas in cobalt it is ABAB, and so forth, i.e., hep. Mainly on the basis of transmission electron microscopy techniques, there seems to be little doubt that the 0 — a transformation in cobalt involves a dislocation mechanism2 although its exact nature still remains obscure. Although the ß - a transformation in lanthanum is somewhat more complex than that occurring in cobalt, it was thought that its very uniqueness would be helpful in understanding fcc — hexagonal transformations in general. Such a general understanding of these transformations is important since they represent what are perhaps the simplest of the martensitic class of transformations. The experimental techniques used were those of electrical resistivity and transmission electron microscopy. EXPERIMENTAL PROCEDURE The lanthanum used in this investigation was prepared by the calcium reduction of lanthanum fluoride in a tantalum crucible under an argon atmosphere as described by Spedding et al. The residual calcium was removed by vacuum remelting in a tantalum container. Portions of the metal were then analyzed by emission spectroscopy as well as vacuum fusion. The amounts of the various impurities that were found are listed in Table I. A portion of the lanthanum ingot was swaged at room temperature into 0.030-in.-diam rod for the resistivity samples while the remainder was rolled into 0.010-in.-thick sheet for the transmission electron microscopy phase of this investigation. In order to eliminate the plastic deformation induced in the samples during fabrication, they were sealed in evacuated tantalum lined quartz capsules and annealed for 1 hr at 700° C. Specimen resistances were measured using the conventional "four-wire" technique described by MacDonald, 4 employing a type K-3 Universal Potentiometer and a standard 0.001-ohm resistor, both manufactured by Leeds and Northrup Co. By taking into account all of the possible errors in the apparatus, it was felt that the absolute resistivities of the approximately 0.87-in.-long specimens measured are reliable to 3 pct. Resistances from room temperature to 700°C were measured using a vacuum furnace. In order to avoid sample contamination by the thermocouple, chromel-alumel leads were spot-welded into a tantalum shield which in turn was welded to the lanthanum specimen. Resistances below room temperature were obtained by transferring the sample to a helium gas-filled quench tube and slowly dripping liquid nitrogen into a surrounding dewar flask. A steady reduction of temperature to about —190°C was completed in about 23 hr, and the resistances were measured at various temperature intervals. As will be shown shortly, rapid quenching from above about 350°C was sufficient to suppress the B -a transformation initially but subsequent annealing at lower temperatures leads to a partial ß --a conversion. To investigate this aspect of the transformation, the samples were suspended in the hot zone of a helium-filled furnace from which they could be rapidly dropped into the quench tube mentioned previously which was now

Jan 1, 1969

By Peter Soo

Pvestrained Ferrovac E iron has been neutron-irradiated at approximately 90°C to an integrated flux of 1020 nut (E > 0.82 mev]. The irradiation was found to produce an incveased temperature dependence of the flow stress in addition to a greatly increased athemal stress. Measurements of the flow stress and stress relaxation, from which the activation volume and activation energy for slip were deduced, show that neutron irradiation changes the rate -controlling slip process to one based on dislocation interactions with tetragonal distortions which are Produced around submicroscopic interstitial loops in the lattice. The study indicates that without prestraining prior to irradiation the chances of detecting a change in the rate -controlling slip process are greatly reduced because in the initial stages of slip a substantial fraction of the radiation defects are swept out of the slip plane by gliding dislocations. Thus, activation parameters which are subsequently measured are representative of a greatly reduced defect density and would not differ appreciably from those for unirradi-ated material. The large increase in the athermal component of the flow stress is probably connected with the presence of depleted zones in the lattice which are introduced by irradiation. ALTHOUGH fast neutron-irradiation has not been observed to markedly alter the activation parameters for slip in bcc metals,' small but significant changes do occur. Most experimenters agree that irradiation predominantly increases the athermal component of the yield stress.'-= In addition to this, Laidler and smidt7 have shown that in iron irradiated to 5 X 10" nvt and molybdenum irradiated to 10" nvt, changes occur in the activation volumes for slip. A similar conclusion has been reached by Milasin and Malkin8 for irradiated iron. Work by Ohr et a1.5 shows that for Ferrovac E iron, irradiated to 1.2 X 1016 nvt, small increases in the activation energy for slip also occur. So far these changes in the activation parameters have not been explained on a firm theoretical basis. One important factor which would minimize the chances of detecting a change in the slip mechanism upon irradiation is the presence of "channeling" which has been observed in molybdenum,9 niobium,10 and iron.11These channels are formed by gliding dislocations which sweep irradiation defects out of the active slip planes and thereby create zones in which continued dislocation motion is encouraged. The activation parameters for the dislocations gliding in the defect-free channels would, therefore, be similar to those for unirradiated iron and a change in the rate-controlling slip process would be difficult to detect. In the present work, an attempt has been made to reduce the effect of uneven deformation on the measured activation parameters for slip in neutron-irradiated Ferrovac E iron polycrystals, so that a more realistic assessment of the effects of neutron-irradiation could be made. Primarily, the experiments involve the irradiation of specimens which had been prestrained to 9 pct elongation at room temperature prior to insertion into the reactor. It was hoped that the introduction of a large number of evenly distributed dislocations would substantially decrease any channeling effect which might otherwise occur. MATERIAL AND EXPERIMENTAL PROCEDURE The starting material was vacuum-melted Ferrovac E iron, an analysis of which is given in Table I. The standard tensile specimen had a gage length of 1.125 in., a cross-sectional diameter of 0.120 in., and a re-crystallized grain size of 1.2 x 10-3 in. All tensile tests were conducted on a floor model "Instron" tensile machine at a strain rate of 3 x 10-4 per sec. The irradiation of the prestrained specimens was performed in the Brookhaven High Flux Beam Reactor to an integrated flux of 1020 nvt (E > 0.82 mev) at a temperature of about 90°C. All specimens were excap-sulated in high-purity aluminum sheaths which were lightly swaged around the samples to ensure good thermal contact. Subsequent measurements on the irradiated specimens showed that within experimental accuracy the swaging had not deformed them. EXPERIMENTAL RESULTS Fig. 1 shows the flow stresses for a series of unirradiated control samples. In order to produce a comparable dislocation substructure throughout the test sm range, all specimens were prestrained

Jan 1, 1970

By Didyk M. Marko, Vásquez Ñ. Gregorio

INTRODUCTION The Salvador Division of Codelco Chile is an important copper molybdenum production center, located 1,200 km north of Santiago and 124 km east of the Pacific Ocean, in the foothills of the Andes Range. El Salvador Mine produces by block caving 8,600,000 t of ore with a content of 1 .l0% Cu and 0.02% Mo, from a copper porphyry ore body. The geology of the ore body shows a great heterogeneity as to rocks, grade distribution, ore height and undercutting levels. This has resulted in a variety of designs for the productive units (blocks) and in the mineral handling systems. Up to now, 4 systems have been employed: grizzly and intermediate haulage; slusher drifts with intermediate ore pass and haulage; slusher drifts with scraper loading directly into trains; and, LHD. On the other hand there is a marked dispersion in the final results from each block mined out. We report here the conclusions reached after analyzing the data gathered on the mining of 163 depleted blocks, representing a total production of 102,000,000 t, with an undercut area of 340,000 sq m. The final results of each block, characterized in terms of tonnage and fine cop- per recovery, were studied as a function of a number of design, geological, and operational parameters. BASIC CONCEPTS Indices of Efficiency In order to evaluate the final result of each block, or group of blocks, the following indices of efficiency were defined : Tonnage Recovery (TR) . It is the ratio between the ore tonnage extracted and the in situ tonnage estimate for each block or group of blocks. Grade efficiency (E) . It is the ratio between the Cu mill feed grade and the in situ Cu grade estimate for each block or group of blocks. Grade efficiency is numerically equal to the ratio between fine copper recovery (FR) and tonnage recovery (TR) . Figure 1 shows the final results for 163 mined out blocks, in terms of tonnage and fine copper recovery. Different grade efficiencies are also indicated. The marked dispersion in the final results of mined out blocks must be stressed since it greatly incides in mine planning. It must be kept in mind that an eventual concentration of low overall efficiency in the blocks during a given period (e.g., one year) will make it necessary to bring into production new blocks over the standard development schedule. It is worth noting that the final results in the 163 mined out blocks corresponding to a production of 102,000,000 t of ore with a mill feed grade of 1.445% were obtained from an ore estimate of 93,000,000 t and a grade of 1.671% Cu, which represents 110% tonnage recovery and 86% grade efficiency. Parameters Studied The following parameters are considered in this study: Geological Parameters. These parameters depend exclusively on the geological and geotechnical features of the ore body. IN SITU GRADE: The initial estimate of the block grade. Four copper grade categories were considered : (a) lower than 1.3% ; (b) 1.3 to 1.6%; (c) 1.6 to 2.0%; (d) higher than 2.0%. The overall initial in situ estimate of the ore body was 1.6% Cu. IN SITU TONNAGE: Initial tonnage estimate of the block. Four categories are considered: (a) below 500,000 t; (b) 500,000 to 1,000,000 t (c) 1,000,000 to 1,500,000 t; (d) over 1,500,000 t. CONTACTS SLOPE: Since up to 4 rock types can be found in a block, resulting in a corresponding number of contacts, a horizontal con- tact was defined as that which forms an angle of less than 45" with the horizontal and a vertical contact that which forms an angle of more than 45" with the horizontal. GRADE DISTRIBUTION: As in rock types, horizontal and vertical grades were defined. ORE HEIGHT: The distance measured between the undercut level and the top of ore. Four categories are considered: (a) less than 60 m; (b) 60 to 100 m; (c) 100 to 150 m; (d)over 150 m

Jan 1, 1981

By Walter A. Backofen, Donald H. Avery

Intense primary and cross-slip traces were observed in easy glide on Cu: 6 pct-A1 single crystals deformed in tension. A mechanism of cooperative source operation is developed which recognizes that both the applied stress and that resolved from dislocation arrays contribute to the stress on a source. By considering the stress from arrays, the activation of secondary systems in easy glide and the difference in appearance of slip markings on pure and solid-solution crystals are explained. Furthermore the cross-slip system is predicted to be second favored during easy glide for a large range of orientations. FROM many studies of easy glide in fcc metal crystals, a pattern of observations has developed which still requires full explanation. In pure copper, aluminum, and silver, the easy-glide, slip traces are fine and uniform with steps 50 to 100A on the primary* system.1-4 Yet it has not been at all clear why slip in the pure materials should occur in this way. On the contrary, one might expect, with simple slip and a low hardening rate, that the weakest sources on the primary system would operate extensively to produce strong slip traces. In a brass, however, intense slip steps up to 0.5 are found on both primary and cross-slip system4,6-9 seeger10 has pointed out that in a material of low stacking-fault energy such as a brass, extensive easy-glide cross-slip could not be thermally activated, but rather must originate on the cross-slip plane. In further explanation, the wilsdorfs4 and seeger10 noted that only the cross-slip system would not harden differently than the primary, whatever the latent hardening tendencies of other systems; therefore, in brass, which exhibits high latent hardening, the cross-slip is the only secondary system which could be expected to operate extensively, once it became active. The explanation of how the cross-slip system, on which the applied stress is low, becomes activated has been related, in a nonspecific way, to pileups by Hirsch11 and Honeycombe.l2 In the work to be described, deformation traces on solid-solution Cu: 6 pct A1 single crvstals were studied with conventional light microscopy and a mechanism proposed to explain both the observed activation of secondary systems in easy glide and the difference in appearance of slip markings on pure and solid-solution crystals. EXPERIMENTAL In preparing the Cu-A1 single crystals, rectangular bars approximately 0.4 in. by 0.4 in. by 6 in. were first machined from ingots made by vacuum melting copper of 99.999 pct and aluminum of 99.99 pct purity. They were then packed in powdered graphite and the crystals grown in a modified Bridgman apparatus at a rate of 5 mm per hr under an atmosphere of purified nitrogen. Crystal perfection as indicated by Laue back-reflection spots was good except for the last inch to freeze, which was discarded. Orientations so determined are shown in Fig. 1. Tensile specimens with a reduced gage section were obtained by masking the ends with electrical tape and chemically polishing in a solution of 20 pct HNO3, 24 pct HAc, 52 pct H3PO4, 2 pct Hcl, and 2 pct H20 at room temperature.13 Finally, the specimens were electropolished in a 30 pct ortho-phosphoric acid bath at 12 v. Tensile deformation was performed in an Instron testing machine at a strain rate of approximately 1 pct per min. During easy glide, extensive cross-slip was observed with all crystals, in spite of the low Schmid factor on this system, and in no case was any other secondary trace encountered. A certain sequence of slip-line development was associated with the extension. At yielding, intense primary traces passing completely through the crystal developed at some point on the gage section, generally near the grips; weak cross-slip traces also appeared, extending from the primary traces into the adjacent undeformed crystal, Fig. 2. Further extension led to primary traces adjacent to the first-formed and connecting with those of the cross-

Jan 1, 1963

By Michael Hoch, Walter C. Wyder

The isothermul section of the Nb-Ti-Zr-O system at 1500°C was investigated using X-ray dzffraction and metallographic techniques. UP to 66.7 at. pct 0, the system contains nine four-phase regions. Tsopleths at 10, 20, 30, 40, 50, and 55 at. pct 0 weye constructed. The purpose of this investigation was to determine the general shape of the quaternary equilibrium phase diagram of niobium, titanium, zirconium, and oxygen at 1500°C. The system was truncated at 66.7 at. pct. O., PREVIOUS INVESTIGATIONS The Ti-Zr-O system was investigated in this laboratory.' The binary systems of interest have been compiled and discussed by anssen2 and Levin, McMurdie, and Ha11. Elliott4 has determined the Nb-O system by metallographic and X-ray diffraction techniques. He shows the existence of three oxides, namely NbO, NbO2, and Nb2O5. At 1500°C the solubility of oxygen in niobium is about 4 at. pct. No solid solubility region is shown for either NbO or NbO2. EQUIPMENT The same equipment as that for the study of the Ti-Zr-O system was used. The X-ray diffraction patterns were analyzed with the help of the ASTM card set5 and NBS circulars.6 MATERIALS The niobium powder (99 pct pure), the titanium powder (99.6 pct pure), the niobium pentoxide, and the zirconium dioxide used in this study were purchased from the Fairmount Chemical Co., Newark, N.J. The zirconium powder (99.4 pct pure) was obtained from the Charles Hardy Co., Inc., N.Y. Reagent-grade titanium dioxide was purchased from the Matheson Co., Inc., Norwood, Ohio. The oxides were dried in air at 700°C for 24 hr before use. Though the materials used were not "hyper-pure," the impurities present do not affect the results (lattice parameters, phase boundaries), within the experimental accuracy. PROCEDURE Samples of the desired compositions were made up, in mole pct, from the materials listed above. In some cases the intermediate binary compounds, such as NbO and TiZrO4 were prepared beforehand and used in the preparation of the samples. This technique enabled equilibrium to be reached from two sides. The components of each sample were mechanically mixed in a mortar and pestle and pressed into 3/16-in. diam pellets. The pressures used in compacting were of the order of 50 to 100 x 103 psi. Sintering was accomplished by heating the samples in a tungsten crucible (3/4-in. high, %-in. diam, 1/8-in. wall, lid with XB-in. hole). The pellets were separated from each other and from the crucible by means of small spiral coils of tungsten wire placed between the stacked pellets and on the bottom of the crucible. The sintering time was from 4 to 12 hr at 1500°C under a vacuum of 6 x 101-5 to 1 x 10-6 mm of Hg. All samples were reground after the first or second heating repressed, and reheated. In most cases: equilibrium was obtained after the first heating, as the X-ray diffraction pictures after each heating remained unchanged. Quenching of the samples from 1500°C was at first only possible by allowing the crucible and its contents to lose heat by radiation. The temperature dropped from 1500° to 900°c in approximately 1 1/2 min, which was considered adequate when compared to the times used by other investigators to reach equilibrium in the temperature range of 1000°c and lower. Later, a new technique for faster quenching of the samples was cleveloped. This technique involved the removal of the samples from the crucible, whereupon they were quenched by coming in contact with the water-cooled copper base of the furnace. This manipulation was performed without breaking the vacuum. The sample pellets were placed on a tungsten wire rack inside the crucible. The wire rack passed through the hole in the crucible lid, where it was connected to a small nonmagnetic chain. The chain was fed to the side of the furnace by means of a brass rack which fitted between the body and lid of the furnace. Suspended at the end of the chain, near the furnace wall, were three magnetic washers. With the use of a strong

Jan 1, 1962

By R. Stickler, A. Vinckier

An optical and electron microscope study was made on a commercial 302 stainless steel heat treated for massive carbide precipitation. Convincirg evidence was obtained that the grain boundary precipitate does not grow away from the grain boundary into the matrix, but grows as a network of large thin dendrites in between the grains. IN austenitic stainless steels the carbon in supersaturated solution precipitates when the steel is heated in the temperature range 450" to 1000°C. During such heat treatments the chromium-rich carbide occurs primarily at the grain boundaries and has adverse effects on the corrosion resistance and low-temperature ductility of the material. It has been shown that the morphology of the precipitated particles differs widely depending on the time and temperature of the heat treatment, the nature of the boundary, the misfit between the grains, and so forth.1"5 It was assumed by Mahla et al.,' Streicher,' and Mc Nutt' that the carbide particles which nucleate in the grain boundary grow in various geometric or dendritic forms away from the boundary into the matrix. However, Kinzel,' Hatwell et a, and Plateau et aL4 found that the particles nucleate in the grain boundary and grow as a network of thin dendrites in the grain boundary interface. We have made a comprehensive studyg of the precipitation occurring in a commercial 302 austenitic stainless steel heat treated for times ranging from 0.15 to 1500 hr at various temperatures from 480" to 1065"~. This study was made to elucidate the influence of heat treatments on both the mechanical and the corrosion properties of this steel. Part of this investigation which is pertinent to the morphology of the grain boundary carbides referred to above is separately reported here. We found that the particles which nucleated in the boundaries grew in the interface of these boundaries, thus supporting the viewpoints of Kinzel,' Hatwell et al.,3 and Plateau et al.4 Furthermore, when carbide particles nucleated in the matrix very close to the boundaries, they possessed a morphology distinctively different from the particles growing in the grain boundaries. MATERIAL A study of metallographic samples and of fracture surfaces of a 302 stainless steel is reported in this paper. The composition and heat treatments are listed in Table I. Polished and etched samples were examined und813r the optical microscope, and carbon extraction replicas of etched micrographic samples and various fracture surfaces3'8'9 were examined under the electron microscope. RESULTS AND DISCUSSION A representative optical micrograph of the 302 steel, condition A, is shown in Fig. l(a). Particles can be seen on the grain boundaries but no traces can be found of particles which grow from the grain boundaries into the matrix. A carbon extraction replica of this sample shows numerous large thin dendrites, Fig. l(b). The lateral dimension of such carbide particles vary up to 100 p, and their thickness estimated from the amoun! of electron penetration i:; between 500 and 1000A. Such large dendrites are extracted from almost all grain boundaries and, if they had grown into the grains, they would definitely be revealed by etching traces in the matrix, Fig. l(a). The reason why these large dendrites on the extraction replica appear to be grown into the grain is due to the mechanism of the extraction replica process. Thus, these dendrites are supported by the carbon replica film only at the edges originally along the grain boundary trace A-A, Fig. l(b), in the polished metal section and have subsequently fallen over onto the carbon replica film during handling. Although such dendrites generally fall only to one particular side of the grain boundary trace, one finds occasionally that parts of a dendrite have fallen to both sides, as shown in Fig. l(b). Further evidence for the growth of carbide in the grain boundary can be obtained from the appearance of fracture surfaces. A small impact specimen of the 302 steel, condition A, was broken at liquid nitrogen temperature. The fracture path follows the

Jan 1, 1962

By N. E. Brown, F. L. Versnyder

THE apparent dependency of the electrical characteristics of hexagonal crystalline selenium on microstructure has aroused much interest in microscopical studies of selenium. Microscopic observations on the crystallization of selenium have been made by Escoffery and Halperin,' P. H. Keck,' and other investigators. It is the purpose of this paper to discuss the microstructural changes observed on polished cross-sections of single layers of selenium after various heat treatments. Observations were also made on crystallization of the free-surface layer of these deposits. In general, all of the transformations studied were either transformations of the vitreous selenium to hexagonal selenium or micro-structural transformation of the hexagonal selenium itself. Procedure The selenium used in this work was obtained from the American Smelting and Refining Co. and was approximately 99.96 pct pure. An intentional impurity of 1 part per 2,000 of bromine was added to the material prior to evaporation. A thickness of approximately 0.002 in. of this selenium was vapor deposited on an aluminum base plate. The maximum plate temperature during the vacuum vapor deposition was 140°C. Mounting of the cross-sectional specimens for metallographic study could not be done in plastic mounting media, as is customary, since temperatures in excess of 50°C would cause unwanted transformations. Consequently, a simple clamp-type device was used to mount the specimens for preparation. All grinding operations were then done carefully by hand in order that the specimen not become heated during this operation. Wet polishing was done on the conventional metallographic polishing laps, using successively finer grinding powders. An extremely careful polish is necessary, since observation and micrography of the specimens are done in the unetched condition under polarized light. The two observations of crystallization made on the free surface of vitreous selenium deposits (Figs. 4 and 5) were made on surfaces which were perpendicular to the cross-sections studied. These free-surface layers were examined directly, i.e., no pre- vious metallographic preparation, as obtained from the vacuum vapor deposition. Microscopic Observations A study was made of polished cross-sections of the vitreous selenium as-deposited. It was noted that in all cases there was columnar crystallization adjacent to the base plate, which appeared to occur during the vacuum deposition process. This observation has also been made by Keck? It also was observed that vagrant spherulitic crystallization occurred in the vitreous selenium. The term "vagrant" is used, since these spherulitic grains appear to crystallize at random throughout the vitreous selenium during the vacuum deposition process. Columnar crystallization at the A1-Se interface and a typical spherulite observed in a polished cross-section of "as-deposited" vitreous selenium may be seen in Fig. 1. Cross-sectional samples of vitreous selenium studied after heat treating individual samples for 20 min in 10" steps from 80" to 220°C revealed that crystallization—in this case, columnar crystal growth —proceeds from the aluminum base plate to the surface of the specimen (Fig. 2). Crystallization was microscopically observed to be complete after the 130°C heat treatment. Visual examination of the free surface of the specimen after the 130 °C heat treatment revealed the readily recognizable grey appearance of the completely crystallized selenium, in corroboration of the microstructural observations. No microstructural transformations then appeared to take place between 130" and 190°C. At 190°C the beginning of recrystallization appeared and proceeded until the columnar grain structure had been completely transformed to equiaxed grains between 210" and 220°C (Fig. 3). Naturally, the grain size of the recrystallized grains at the lower temperatures (190" to 210°C) was smaller than is illustrated in Fig. 3. In addition, polished cross-sections of deposits heat treated at 140°C for 10 min to cause complete crystallization and, subsequently, heat treated in 10" steps from 80" to 220°C for 20 min were studied. As expected, no microstructural transformations took place until the beginning of recrystallization was observed at 190°C. A comparison with the previously studied specimens revealed that recrystallization proceeded almost identically in the two experiments although in the first case the deposits were vitreous prior to the series of heat treatments and in the second case they had been crystallized by a previous heat treatment. By heat treating for longer times (180 min) at lower temperatures, the

Jan 1, 1956

By E. J. Dulis, R. M. Fisher, K. G. Carroll

IT is well known that ferritic steels containing more than 15 pct Cr when subjected to temperatures in the range of 700" to 1000°F exhibit increasing hardness and decreasing ductility. The phenomenon has been widely termed the "885 °F embrittlement," after the temperature of most marked effect.'.' In view of the excellent review articles available in the literature3-6 only a brief account of experimentally established facts need be given here. The extent of changes in physical characteristics during embrittlement depends on chromium concentration and time at temperature, higher alloy content and longer time both promoting more rapid and extensive changes. In a 27 pct Cr steel, changes in impact strength and in angle of fracture in bending can be detected after only a 1 hr exposure at 885°F; after 50 hr this steel becomes quite brittle. Hardness increases slowly with time during thousands of hours exposure and may attain a maximum hardness number twice as large as that of the unexposed steel. Microstructural changes accompanying embrittlement have been described as an initial widening of grain boundaries followed by eventual darkening of ferrite grains. Embrittled steels etch more readily, e.g., the weight loss of a 27 pct Cr steel in acid solution may occur at a rate one hundred fold greater following exposure at 885 OF. Marked changes which accompany embrittlement have been observed in electrical resistivity, specific gravity, and magnetic coercive force. Changes in physical properties may be readily removed by heating at temperatures above the embrittling range, such as a treatment at 1100°F for 1 hr. It has frequently been noted that the 885 °F embrittlement suggests precipitation on a submicro-scopic scale of a chromium-rich constituent, the nature of which has not been revealed by X-ray diffraction. Progressive broadening of the body-centered cubic diffraction lines during embrittlement has been observed," and recent observations by Lena and Hawkes' upon single crystals have shown early asterism in X-ray photographs, disappearing within an hour at 900 °F. Many workers have ascribed8-13 the phenomenon to a precipitation of a phase (FeCr), which is known to cause embrittling effects at temperatures much higher than 885°F. Two general observations, however. suggest that a precipitation cannot be responsible for the 885°F phenomenon: 1—prior cold work greatly enhances a formation, whereas it scarcely affects the 885 °F embrittlement, and 2—the presence of an alloying element such as nickel or manganese may have an effect on the 885 °F embrittlement which is opposed to its effect upon a formation. The slight enhancement of a formation and 885°F embrittlement observed in the presence of elements with strong carbide and nitride forming tendencies' is probably a consequence of lessened chromium depletion of the matrix. The bar graph in Fig. 1 shows a typical example, taken from two 27 pct Cr steels used in this work, of the hardness after exposure for 10,000 hr at 900°, 1050°, and 1200°F. Steel A (0.03 pct C, 3.13 pct Mn) showed marked hardening at 900" and 1200°F, whereas steel B (0.12 pct C, 0.63 pct Mn) exhibited only the 900°F hardening. The cr phase was found in steel A at the higher temperatures but not in steel B. Presumably a formation is enhanced by the low-carbon and high-manganese concentrations in A," Thus there are two distinctly different hardening phenomena present which cannot both be ascribed to v precipitation without invoking a transition phase possessing remarkable properties. Materials A number of chromium steels exposed for long periods (5000 to 34,000 hr) at 900°F, as well as unexposed samples of one of the steels, were available for this investigation. Table I gives the chemical compositions and aging treatments of these steels. In addition to these steels exposed in the elevated temperature test furnaces of the National Tube Division, a number of high-chromium steels were heated for short periods in small laboratory air furnaces and lead baths. Supplementing these commercial steels, a sample of high-purity (0.018 pct C, 0.002 pct N) 28 pct Cr iron, exposed 1000 hr at 887°F. was furnished by the Union Carbide and Carbon Corp. In addition, an alloy of iron and chromium of high purity containing 46 pct Cr was used. This

Jan 1, 1954

By J. Szekely, Robert G. Lee

Calculations are presented for the prediction of the combined radiative-convective heat loss from molten steel held in a ladle, covered by initially molten slag. A mathematical formulation is given and numerical solutions are presented of the resultant partial differential equation. It is shown that a slag layer of about 2 to 3 in. thick would prevent any significant heat loss from the top metal surface for Periods of up to 1 hr. For thinner slag layers (or in the absence of the protective slag) appreciable heat losses would occur; plots given in the paper allow the quantitative evaluation of the fall in the metal temperature due to this heat loss. The ironmaking-steel processing operation involves several intermediate steps where the molten metal is held or transfered in ladles. The quantitative assessment of the heat losses occurring under these conditions is of considerable importance in process design considerations since the temperature of the metal may have to meet rigid specifications in any given part of the processing sequence. While the metal is held in a ladle, heat is lost by two mechanisms: i) by conduction into the ladle walls; ii) by radiation and convection from the top surface. Calculations relating to the conductive heat loss, are readily made and information may be found in the literature both on data pertaining to metallurgical situations and on the techniques that are available for performing additional computations.'-3 The evaluation of the combined convective-radiative heat loss is less straightforward, especially when there exists a protective slag layer covering the metal. In this latter case, as the top slag surface loses heat partial solidification may occur and the latent heat thus given up by the slag may represent an effective barrier to the heat loss from the metal. A semiquantitative assessment of the role played by the slag in preventing heat loss from the metal has been made in a previous paper,4 where it was shown that a slag layer 6 in. thick would act as a near-perfect insulator for periods of up to 2 hr. However, this first paper reported on an essentially preliminary investigation that considered only one slag layer thickness; furthermore, the boundary conditions used for the calculations were somewhat restrictive since no allowance was made for changes in the metal temperature. The purpose of this second paper is to extend the scope of the preliminary investigation previously reported by: i) considering several slag layer thicknesses; ii) allowing for variations in the metal temperature; and finally iii) by performing calculations on the net loss from the metal rather than from the slag surface. FORMULATION Consider a slag phase extending from y = 0 to y = L1, covering a metal phase that occupies the region extending from y = Ll to y = L, as illustrated in Fig. 1. Denote the slag and metal temperatures by TS and Tm and assume that initially both slag and metal are molten, having a uniform temperature Ti. At time = zero the surface represented by the y = 0 plane (top slag surface) is brought into contact with cold air, the temperature of which is given as T Thus for time > zero, heat will be transfered from the slag to the air by natural convection and thermal radiation; as a result of this heat loss the slag temperature will fall and after some time a solid phase is formed and a solidification boundary (more realistically described as a zone) will move progressively from y = 0 toward y = L1. Once the region of temperature gradients, moving ahead of the solidification zone, reach the slag-metal interface (y = L1) there will be a net transfer of heat from the metal through the slag to the cold air, across the y = 0 plane. In the formulation of moving boundary problems, involving phase changes that require computer solution, it is convenient to represent both phases by a single equation, making allowance for the latent heat of solidification by assigning an appropriate temperature dependence to the specific heat content. Thus the energy equation for the whole of the slag may be written as follows:

Jan 1, 1969

By P. G. Winchell, A. J. Heckler

An experimentally simple method for determining the effect of alloying elements on the activity of carbon is validated in Fe-Ni-C austenite. The technique consists of the equilibration of carbon between specimens of different nickel contents within a sealed silica capsule. The attainment of carbon equilibrium within each capsule is evidenced by: 1) in each capsule specimens of the same nickel content attained the same final carbon content regardless of their initial carbon contents, 2) in every capsule the final carbon content was reached for most nickel contents by carburizing and by decarburizing. The activity of carbon attained within each capsule was calculated from the carbon content of a binary Fe-C alloy placed within the capsule, and from the activity coefficient of carbon in the Fe-C system as found by Smith for CO/CO2/C equilibrium. The activity of carbon in Fe-Ni-C austenite determined by this method at 1000°C agrees with prior work by Smith, who used mother method. The measurements are extended to 800°and 1200°C. The activity coefficient of carbon 7c, in Fe-Ni-C austenite is given by: where xC is the ratio of carbon to metal atoms and XNi is the ratio of nickel to metal atoms and where the standard state is chosen such that yC = 1 as xc approaches zero in Fe-C alloys. This equation appears to be valid for xni < 0.3, and 1073° < T<1473°K. ThE activity of carbon in Fe-C austenite has been measured by smithL at 800°, 1000°, and 1200°C. Smith has also studied the effect of nickel on the activity A. J, HECKLER and P. G. WINCHELL are Graduate Student and Associate Professor of Metallurgical Engineering, respectively, School of Metallurgical Engineering, Purdue University, Lafayette, Ind. This paper is based on a thesis submitted ty,to Purdue University, in partial fulfillment of the requirements for the degree of M.S. in Metallurgical Engineering which A. J. HECKLER received from Purdue in January 1962. Manuscript submitted August 13, 1962. IMD of carbon in austenite at 1000°C. In both these studies the activity of carbon was fixed by a flowing CO-C02* *Gas mixtures of hydrogen and methane were also used in Ref. 1 but these results are not incorporated in Ref. 2 or in the present study. gas mixture. In the present work, Smith&apos;s results for Fe-Ni-C austenite are confirmed and extended to 800" and 1200°C by a different experimental technique. EXPERIMENTAL PROCEDURE In essence the experimental technique consisted of enclosing specimens of various nickel contents in an initially evacuated silica capsule and annealing the capsule until carbon equilibrium was attained among the enclosed specimens. The carbon activity obtained within the capsule was determined from the final carbon content of the binary Fe-C alloy included in each capsule and the results of smith.&apos; In order to evaluate this method the absence of nickel transfer between specimens must be established and the attainment of carbon equilibrium between samples must be assured. The absence of nickel transfer was demonstrated in the case of an originally pure iron sample which was annealed at 1200°C in a capsule with a 27.3 at. pct Ni alloy. The final nickel content of the iron specimen was less than 0.1 at. pct, a change which has a negligible effect on carbon activity. The attainment of carbon equilibrium was demonstrated within every capsule and in over half the results by achieving the same final carbon content in a sample which carburized during equilibration and in a sample of the same nickel content which decarburized during equilibration. The base Fe-Ni alloys were vacuum melted from Ferrovac E or electrolytic iron and Mond or electrolytic nickel. The samples were rolled and/or swaged and their carbon content adjusted to the desired pre-equilibration level either by methane-hydrogen carburization or by direct carbon transfer from a graphite source in a sealed silica capsule. As mentioned previously, high-carbon and low-carbon samples were prepared for most nickel levels in each capsule. The specimens were cleaned and

Jan 1, 1963

By H. Habenicht, J. J. Scott

An experimental method is described to compare strain data for rock and rock bolts when exposed to shock waves released by blastings. Static and dynamic strains were measured. Bolt gage response indicated a static decay of the bolt anchorage coupled with a reaction due to blasting vibrations. A distinct loss of bolt tension was indicated during vibrations and this was accompanied by a smaller but steady loss of tension due to static loading. The strain losses were found to relate to the shock source distance and the vibrational amplitude in the rock and bolts. Millions of roof bolts are used each year to stabilize mine openings and prevent their failure. Frequently, bolts become loose and lose their effectiveness as reinforcement to the mine structure. Many attempts have been made to determine the cause of loosening, including observation of the bolt tension or bolt torque through the use of torque wrenches, compression pads, and load cells. Pull tests have been used extensively to determine anchorage characteristics.102 These investigations have shown that even when bolts are loaded below the nominal anchorage capacity of the rock under &apos;static&apos; conditions they exhibit a decay of load through adjustments and slippage at the bolt anchor. Since bolts are quite often found with the plate hanging loose from the rock surface, this condition suggests that some additional mechanism may have played a part in loosening the anchorage. Vibration from blasting or shock loading have been suggested as one cause in this type of anchorage deterioration. This paper gives the results of an investigation carried on at the University of Missouri at Rolla to determine the influence of shock waves on rock-bolt anchorage stability. ROCK BOLT ANCHORAGE UNDER DYNAMIC LOADING CONDITIONS In this report dynamic loading conditions are defined as conditions under which rock and bolts are exposed to vibrations occurring as a consequence of blasting, machine vibrations, earthquakes, rock bursts, etc. Whatever the location of the shock source, the waves created suffer extensive alterations along their travel paths, depending upon the vibrational properties and geometric parameters of the transmitting media. Together with reflection, refraction and diffraction at material boundaries, waves suffer changes in their nature to form tensile, compressive and shear waves. They become polarized, retracted, accelerated, dispersed, so that the waves incident at a point in the material can be the result of either one or a combination of this wide range of processes. A certain fraction of the wave energy will be lost due to friction, deformation, and material failure at the anchor-rock contact. Thus, the physical nature of wave propagation is such that it inhibits an exact analytical solution. For this reason this investigation should be considered qualitative rather than quantitative even though numerical data have been used as a base. CONCEPT OF THE INVESTIGATION Experiments were designed to find, from a series of rock bolts installed in natural mine rock, whether or not, and to what extent, bolt tensions would be influenced when bolts were exposed repeatedly to shock waves such as those produced by blasting. Electronic instrumentation available in the rock mechanics laboratory of the University of Missouri at Rolla was used to observe wave development in the rock and vibrational reactions in the bolts. EXPERIMENTAL PROCEDURE Fig. 1 illustrates schematically the experimental equipment. Electric resistance wire strain gages were used as sensors for the strain response of the rock and the bolts. Bolts were 5 ft long and 5/8 in. in diam, equipped with two-leaf type expansion shells for 1 3/8 in. boreholes. The bolt gages were mounted by use of Du Pont Household Cement, covered with an epoxy insulation and then enclosed in a copper foil for electronic shielding. For details of placement and the wiring diagram see Fig. 2 and 3. The output of both the rock gages and the bolt gages was fed into cathode ray oscilloscopes from which the vibrational traces could be photographed. A static strain indicator was also used to read the output of all gages.

Jan 1, 1968

By Appendix by A. S. Goldoni, R. E. Tate, E. M. Cramer

The diffision coefficient for self-diffision of plutonium in the temperature range 350" to 440°C has been measured by using puZ3 as the tracer isotope. Autoradiopaphic techniques were used to inzlestigate the possibility of grain boundary diffusion, hut only evidence for volume diffusion was found. The least-squares fit of the data gives the .following equation for the diffision coefficient: The computer least-squares technique for fitting the nonlinear equations is outlined. DETERMINATION of the self-diffusion coefficient of the fcc 6 phase of plutonium is in principle a straightforward experimental task. However, the chemical reactivity, the intense @ activity, and the toxicity of plutonium put limitations on the experimental techniques. The technique selected included roll bonding for preparation of the diffusion couples and pulse-height analysis of the @-particle activity to determine the distribution of the PU tracer in the diffusion couples. EXPERIMENTAL PROCEDURE Couple Preparation. Cylinders about 0.5 in. in diam were cast from two special stocks of plutonium, one of which had been enriched in puZ3&apos;, as shown in the isotopic analyses listed in Table I. For each roll-bonded composite sheet, a cylinder 0.437 in. in diam and 0.190 in. thick was turned from each kind of plutonium on a lathe in a 98 pct He atmosphere. The two freshly machined cylinders were positioned face to face in a tube of commercially pure aluminum which had been sealed at one end by welding and the assembly was evacuated on a vacuum manifold overnight. The elapsed time between machining the faces of the plutonium cylinders and evacuating the loaded tube was about 15 min. After overnight evacuation of the assembly the indicated vacuum was 1 X 10"5 torr or better. The aluminum tube was then warmed and pinched off with a cold-welding tool. The pinched-off weld was also fusion-welded as an additional precaution against leakage of air into the evacuated assembly. The assembly was immediately heated for 30 min in a 250°C furnace and reduced in thickness by being passed through a rolling mill with rolls heated to 200°C. The rolling schedule (four passes of 100 mils each with a 10-min reheat after two passes) reduced the thickness of the assembly to 100 mils. The rolled assembly was allowed to cool normally in air. The rolled assembly was sheared at the edges and the aluminum peeled from the composite plutonium sheet. The elliptical sheet was about 0.060 in. thick and usually three 0.383-in.-diam disks could be punched from its central portion. The sheet was heated on a hot plate to the ductile low 0 range (140°C as measured by temperature-indicating pellets) before each disk was quickly punched. The quality of the bond in the disks was evaluated by metallographic examination of the scrap sheet adjoining the hole left by the punch. Only well-bonded specimens without oxide in the interface (as indicated by metallography) were considered satisfactory for further use. More than half of the specimens so examined contained sufficient oxide in the interface to be rejected. Diffusion Anneal. Each disk to be diffusion-annealed was wrapped in 1-mil-thick tantalum foil and sealed within a Pyrex capsule evacuated to 1 x 10~5 torr or better. This capsule was then sealed within another Pyrex capsule at a similar pressure. The diffusion anneals were carried out at temperatures between 350" and 440°C in Marshall furnaces adjusted to have a temperature gradient of not more than *1/2"C over a 5-in. length. This gradient was then further smoothed by using a nickel tube as a liner in the furnace. The liner was divided into three longitudinal cavities by a septum of nickel sheet to which two calibrated Chromel-Alumel thermocouples were attached. One thermocouple was used for controlling the furnace temperature by means of a Brown Pyrovane controller equipped with a Capaciline anticipation circuit; the second thermocouple was monitored twice daily with a Leeds and Northrup K-2 precision potentiometer.

Jan 1, 1964

By R. W. Armstrong, P. C. Jindal

The hardness dependence on grain size for polycrys-talline cartridge brass and a leaded brass has been measured by Brine11 and Rockwell B testing. In each case, the hardness, H, depends on the average grain diameter, 1, according to: H =Ho + kHl-1/2 where Ho and kH are experimental constants. Diamond pyramid hardness values have also been measured as a function of the indentation size and grain size to give additional information on the nature of the hardness test and the dependence of hardness on micro-structure. The hardness of polycrystalline brass depends on its grain size. Bassett and Davis&apos; demonstrated this as early as 1919 by making Brinell hardness measurements on cartridge brass. Since then, the hardness of this type of material has been measured as a function of grain size by making Rockwell,2&apos;3 Vickers,4 and Brinell5 tests. he hardness dependence on grain size has also been measured for other materials. Angus and summers6 investigated the grain size dependence of the Brinell hardness of polycrystalline copper and a Cu-4.5 pct Sn bronze. In other studies, nickel,? Armco iron,Big an Fe-0.07 pct C alloy,I0 and an 0.39 pct C-12.45 pct Cr stainless steel" have been investigated. In some of the preceding cases, the hardness results have been analyzed to show that the hardness varies with the average grain diameter, 1, according to an l-l\4, l-1/4 or I-2 dependence,11-13 The studies of the influence of grain size on hardness have not been based on any theoretical model. This may be because the hardness of a material is itself a complicated property. However, attempts have been made to correlate, experimentally and theoretically, the hardness of a material with its unidirectional stress-strain behavior.14-l6 On this basis, Hall" proposed that the polycrystal hardness dependence on grain size might follow directly from the Hall-Petch18,19 relation for the grain size dependence of the yield stress. Thus, the hardness-grain size relation was given as: H = Ho + kHl-1/2 [1] where Ho and kH were taken as experimental constants. The relation was applied to the measurements on brass,&apos; copper,6 bronze,= and Armco iron.&apos; More recently, this relation was shown by Armstrong and jindal20 to adequately describe the measurements on cartridge brass made by Bassett and Davis&apos; and Babyak and Rhines.5 In this case, the relationship was taken a step further by independently relating the values of Ho and kH to the values of oyand ky, previously reported by Armstrong, Codd, Douthwaite, and petch21 from measurements of the yield stress dependence on grain size for this type of material. In the present investigation, new Brinell and Rockwell B hardness measurements have been made as a function of grain size for a cartridge brass and a leaded brass. In addition, diamond pyramid hardness values were measured as a function of the indentation size. All these results are applied to a further analysis of the hardness dependence on grain size. MATERIALS AND EXPERIMENTAL METHODS Cartridge brass and a leaded brass were selected for this investigation for two main reasons: it was anticipated 1) that these materials could be cold-worked and recrystallized to a wide range in grain size and 2) that the results to be obtained on these typical industrial materials could be usefully compared with previous investigations. The chemical analyses of the actual materials which were employed are given in Table I. The as-received 1/2- and 3/4-in.-thick plates were given various reductions in thickness by cold rolling. The rolled material was heat-treated at various temperatures between 330" and 850°C for differing time periods from 5 min to 9 hr to achieve a variation in the average grain diameter between 0.0339 and 0.000543 cm.22 During heat treatment, the brass was protected from zinc loss by packing it in chips or foils of the same composition material. Reasonably equi-axed grain structures were obtained in each case. The metallurgical grain sizes of the specimens were determined from measurements of the average linear intercept on a random line. Annealing twin interfaces were not counted along with grain boundaries. The

Jan 1, 1970

By G. M. Schwartz, G. A. Thiel

THE first record of the quarrying of dimension stone in Minnesota dates back to 1820 when limestone was quarried locally for part of old Fort Snelling. Limestone quarries were operated at Stillwater, Mankato, and Winona as early as 1854. Granite was quarried first at St. Cloud in 1868, and within a few years thousands of tons were shipped to widespread points. Rough dimension stone for large buildings furnished the first important market, but beginning in 1886 paving blocks were in demand. The largest shipment was in 1888, when 1925 cars were shipped from the St. Cloud area. Quartzite was quarried first at New Ulm in 1859 and somewhat later at Pipestone and elsewhere in southwestern Minnesota: The productive dolomite quarries at Kasota were opened first in 1868 and have continued as large producers of a variety of stone to the present time. At present, the industry is controlled by relatively few operators, and for that reason detailed figures on dimension stone are not released for publication. A general idea may be obtained from the data in the Minerals Yearbook for 1948. The figures for total stone produced in Minnesota are 1,804,000 tons valued at $5,090,652. Probably the largest item in the latter figure is received from dimension stone. A better idea of the situation, in relation to the country as a whole may be gained by using the data for 1930 when more companies were operating in Minnesota, and complete figures were published. In that year Minnesota produced granite valued at $2,668,119 and ranked third among the states in value. Minnesota&apos;s production of granite was almost exclusively for dimension stone. In the same year Minnesota produced 300,000 tons of limestone (dolomite) valued at $840,860, and this likewise was mainly dimension stone. In finished limestone Minnesota ranked second among the states in 1930. Sandstone and minor amounts of quartzite are the only other dimension stones that have been produced in Minnesota, but the quarries are now inactive. The commercial stones of Minnesota have been described in two reports by Bowled and by Thiel and Dutton.2 The early history of quarrying in Minnesota and extensive notes on the various rocks are given by N. H. Winchell.3 Small limestone and dolomite quarries were numerous throughout the area of Paleozoic rocks in southeastern Minnesota. Early production was largely dimension stone. With the increased use of Portland cement, most of these ceased production, and today only those at Kasota and Winona remain in operation. In recent years many quarries have reopened and new ones started, but these are devoted to the production of crushed rock and agricultural lime. As the application of modern quarrying and finishing methods increased, small companies in the granite business have dropped out, and the remaining companies have modernized their plants, purchased old quarries, and opened up new ones, thus furnishing a wide variety of granites suitable for most of the customary uses. It is the purpose of this review to present notes on&apos; the geology and operations of each of the quarries now operating within the state. Granites and Related Igneous Rocks The term granite as used in this report includes granites, gneisses, diorites, gabbros, and other igneous rocks. The granites of greatest economic importance are found in three widely separated regions, see Fig. 1. 1-Central Minnesota in the region of the city of St. Cloud, 2-the upper Minnesota River valley region, 3-the northeastern portion of the state, commonly referred to as the Arrowhead region. The St. Cloud Region: The rocks of the St. Cloud region are mainly granites and related rock types such as monzonites and quartz diorites. The stones may be grouped into three major types, namely, pink granite, red granite and gray granite. Most of the pink granite occurs in the area to the southwest of St. Cloud. The rock is best described as stone with large pink crystals set in a finer grained black and white background. The minerals of the matrix occur in remarkably uniform sizes, and the pink crystals are sufficiently uniform in. their dis-

Jan 1, 1952

By J. L. Taylor, Pol Duwez

THE present knowledge of the Ti-Al system is limited to the portion of the diagram extending from pure aluminum to the intermetallic compound TiAl3&apos; A preliminary investigation of the titanium-rich Ti-A1 alloys revealed that the solubility of aluminum in titanium is quite extensive and that the transformation temperature of titanium is raised by alloying with aluminum. From an X-ray diffraction study of alloys containing up to 75 atomic pct Al (TiAl3), the phase boundaries at 750°C were located as follows: the a titanium solid solution extends from 0 to about 36 atomic pct Al, a two-phase region exists from 36 to 46 atomic pct Al, and an intermediate phase of varying concentration extends from 46 to 62 atomic pct Al. The purpose of the present paper is to describe the crystal structure of this new phase. The alloys were prepared by melting in a helium arc furnace on a water-cooled copper plate, using a furnace essentially the same as that described in ref. 2. The titanium metal was of the iodide type furnished by the New Jersey Zinc Co., and a piece of pure aluminum (99.99 pct) was obtained through the courtesy of the Aluminum Co. of America. After melting, the samples, weighing approximately 5 g, were sealed in evacuated fused silica tubes and homogenized for 4 hr at 1000°C. The specimens were then held for 10 days at 750°C and rapidly cooled to room temperature. Filings were then taken from each sample, sealed in evacuated vials, annealed at 750°C for 4 hr, and rapidly cooled to room temperature by quenching the vials in water. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using K copper radiation filtered through a nickel foil. Structure Determination The X-ray diffraction patterns of the alloys containing 46, 50, 55. 60, and 62 atomic pct Al were identical, except for a slight shift in the positions of the reflections. The alloy containing 55 atomic pct Al was chosen far structure determination. The powder pattern contained 37 reflections and the a, doublets were well resolved in the back-reflection range. The relatively small number of reflections and the sharpness of the pattern were considered as an indication of a simple atomic arrangement in a relatively small unit cell of high symmetry, and an attempt was therefore made to solve the structure without single crystal work. A satisfactory fit was found on a large scale Hull-Davey tetragonal chart for an axial ratio of approximately 1.45. All the reflections were readily indexed and the tentative unit cell dimensions were computed to be a - 2.81 kX, c - 4.07 kX, and c/a = 1.448. The indices (hkl) and the values of d and sin2 A are given in Table I. The agreement between observed and computed sin2 is quite satisfactory. Once the unit cell was known, the details of the structure were readily found. First, it is obvious that the number of atoms per unit cell cannot exceed two, since more than two atoms would lead to a density greater than that of pure titanium. The next logical step is to assume that the two atoms occupy the corner and center of the cell. If this assumption is correct, the structure may be described as follows: space group D1, - P 4/mmm; one titanium atom in a: 000; one aluminum atom in d: 1/2 1/2 1/2: and no extinctions. Assuming this structure to be the correct one. intensities were computed by means of the usual equation: sin2 0 cos 0 where F is the structure factor; 8, the Bragg angle. and p, the multiplicity factor. The calculated values of intensities are compared in Table I with the visually estimated intensities. The agreement is quite satisfactory and the structure is therefore confirmed. The crystal structure of TiAl just described is the same as that of AuCu ordered. The AuCu ordered

Jan 1, 1953

By R. Bakish, C. S. Barnett

IN experiments on tantalum strained in tension, Bechtold did not observe deformation-twinning even at a temperature as low as that of liquid air.&apos; This is an unexpected behavior for a metal of body-centered-cubic structure. Therefore, it is desirable to determine whether the lack of twinning is an inherent characteristic of this particular metal, or whether the reluctance to twin can be overcome under suitable conditions. The following experiments were performed under conditions favorable to twinning and cleavage in their competition with slip, namely, with impact loading on large-grained sheet at low temperatures. The crystallography of cleavage in tantalum sheet was also investigated carefully because of the remarkable ductility of tantalum at low temperatures and because recent tests on oxygen-embrittled tantalum had disclosed unusual cleavage behavior for a metal of this structure: cleavage primarily on (110) planes and only occasionally on {100}.2 The tantalum, supplied by Fansteel, was of 99.9 pet purity, with the chief impurities being iron (0.03 pet) and carbon (0.03 pet). Coarse grains were produced by the strain-anneal method, the anneal being 4 hr at 2000°C in a vacuum of 10-3 mm Hg, followed by furnace cooling. Impact deformation was applied in various ways: a) by hammer blows on an anvil, the specimen and anvil being immersed in liquid nitrogen ( —196°C), b) by driving a precooled center-punch into the sheet, and c) by bending around a crystallographically determined axis with a hammer blow. The impact-deformation produced bands and slip lines on the surface, Fig. 1. The bands have every appearance of being deformation twins, a) They are tilted with respect to the untwinned surface. b) They have the appearance of Neumann bands in iron, thin lens shape, some having serrated edges. c) The orientation in each is different from that of the surrounding matrix and uniform within a given band, see slip lines within them in Fig. 1. d) Upon repolishing and etching, the difference in orientation and the resemblance to Neumann bands is again evident, Fig. 2. (In this micrograph the slight bend in the bands as they cross grain boundaries was noted frequently and results from the high degree of preferred orientation in the sheet.) e) The bands persist after annealing treatments that would have removed them had they been a low-temperature martensitic phase, e.g., after an anneal of 1/2 hr at 900°C. When back-reflection Laue data were plotted for single-surface analysis of several grains, every trace of the bands in each grain could be explained by (112) planes. In addition, two of the bands were located in space by traces on two surfaces, and these also were found to lie on (112) planes within the error of the stereographic plot. Since (1 12) is the anticipated composition plane for deformation twins in body-centered-cubic metals it is felt that the observations listed above are conclusive evidence for the identification of the bands as twins. Similar tests with impact at —77° and at 25°C produced no twinning. It is concluded that the critical shear stress for slip at the rates of straining used was always low enough to prevent the applied stress from reaching the value required for twinning at these temperatures. It was noted that the serrations along the edges of the twin bands exhibited parallel crystal facets. Several similarly oriented notches are visible in Fig. 1, and a remarkable set is shown in Fig. 3. It appears from Fig. 1 and similar areas that notches are frequently associated with the intersection of a slip line with a twin, although not all such intersections are at notches. In some instances a slip line appears to enter the twin, cross it, reflect from the opposite side and recross it, producing a pattern resembling a notch but without producing the notch itself, see Fig. 1. It is suggested that the stress concentration at the end of a slip line is responsible for these details. The strain energy associated with the pile-up of dislocations at a twin boundary may be lessened by untwin-ning or failing to twin a portion of the twin band, or

Jan 1, 1959

By D. T. Camp, J. A. Clum

WITH experience, the indexing of back-reflection Laue patterns for cubic crystals is usually a straightforward matter. However, for noncubic systems where in general tables of interplanar angles are not available or when inexperienced personnel are involved, properly indexing a crystal is normally a tedious, time-consuming affair. The authors have written a digital-computer program which calculates and prints out a table of interplanar angles for an arbitrary crystal structure and then systematically searches through this table attempting to obtain a consistent fit to back-reflection Laue data supplied by the user. Of course it is possible simply to calculate a desired set of interplanar angles should this be the only requirement. The program was originally written in ALGOL for use on a Control Data G-21 computer and a preliminary version is described elsewhere.&apos; A version in FORTRAN TV which has been run on an IBM 7040 and one in FORTRAN II run on an IBM 1620 are also available. While it is not the purpose of this communication to describe the program in detail, an indication of how the program operates may help one to decide whether the program would be useful under particular circumstances. The hypothetical example chosen involves the indexing of the zinc crystal which has a hexagonal structure and a c/a ratio of 1.856. Input data for this example consists of only nine cards: The first card controls the list of families of planes to be considered. If the Miller indices of a prospective family are (h k 1), the first digit places a limit, in this case 3, on the absolute values of any individual index. The second digit limits the sum (h +k + l + 1), in this case to 5. Therefore the families (013) and (112) are considered but the family (122) is not. All systems, including the hexagonal, are treated using three-digit Miller indices. The second card contains the crystallographic parameters required to define the system. The first digit is 0 if the system is rectangular, that is all angles are 90 deg. If the system is nonrectangular, as in this example, the digit 1 so indicates. The next three values are the lengths of the sides of the reference cell, a, b, c. The final three entries on the card are the angles, a, 8, y between the sides. The digit 0 on the third card indicates that more data follows, the digit 6 shows that a set of six planes is to be indexed, and the value 2.0 indicates that agreement between a tabulated angle and an input angle is considered adequate if their absolute difference is less than 2 deg. The fourth card lists the measured input angles. a12 = 38 deg, a13 = 24 deg, and so forth. More input angles are listed on cards five to eight with the latter giving the input angle 058 = 40 deg. The final card in this series indicates by the digit 1 that no more data is to be processed. The program operates in the following manner: 1) The input data from cards 1 and 2 is read, thereby indicating the crystal system to be examined and the crystallographic parameters of the particular crystal to be indexed. 2) A table of interplanar angles is generated. 3) The input angles contained on cards 4 to 8 are read. 4) The measured input data is systematically compared with the generated table of standard angles. All combinations of poles whose interplanar angles compare with the requisite, specified accuracy are printed out. If no adequate fit is found an indication of this is printed. A typical line from the generated table of interplanar angles is: (001) - (111) 74.92 64.99 It can be shown that in the Miller-Bravais system the first value corresponds to the angles between (0001)-(1121) and the second to that between (0001)-(1011). This particular set of data gave the following result for the planes 1 to 6: (011) (110) (121) (111) (112) (010) The ALGOL version also has the option of simply providing the Greninger-chart coordinates ? and 6

Jan 1, 1967

By J. C. Fisher

Martensite transformations in steels and other alloys are characterized in part by the absence of composition changes during the growth of a new phase. Transformation occurs rapidly, and there is insufficient time for long range diffusion or partition of alloying elements to take place; martensite reactions in alloys thus are similar to phase transformations in single component systems. A fundamental understanding of martensite transformations in steels is impossible without knowledge of the free energy change upon transforming austenite (face centered cubic iron containing alloying elements) to ferrite (body centered cubic iron containing alloying elements) of the same chemical composition. The present paper assembles the best information available concerning the influence of temperature and composition on this free energy change. Most of the material has been taken from the work of Johansson,&apos; Mehl and Wells,2 Zener3,4 and Smith;5 and indirectly, through these authors, from the work of Austin.6 In agreement with the generally accepted viewpoint, martensite is assumed to be an ordered solution of carbon in ferrite of the same composition as the parent austenite; only at high temperatures and low carbon concentrations is the carbon in ferrite distributed at random. The properties of the disordered solution are estimated by extrapolating the known properties of iron-carbon solid solutions into the range of supersaturation, and the free energy change associated with ordering is estimated from the theory developed by Zener. By incorporating Smith&apos;s recent thermodynamic measurements and Zener&apos;s theory of ordering, the present analysis modifies previous estimates of the free energy change associ- ated with martensite transformations. Consider a two component system consisting of a solvent A and a solute B. Let Na and Nb represent mol fractions of A and B respectively, let aa = raNa and ab = YbNb represent activities, and let superscripts 1 and 2 refer to phases 1 and 2. The partial molal free energies of A and B in phases 1 and 2 can be summarized as follows: free energy standard state Fa&apos; - Fao1 = RT In an1 pure A&apos; Fa2 - Fa2 = RT In aa2 pure A2 Fb1 - Fbo = RT In ab1 pure B Fs2 - FB2 = RT In aB2 pure B. The free energy of a gram atom of phase 1 is* AF1 = Na&apos;Fa1 + Nb&apos;Fb1 and that of phase 2 is AF2 = NA2FA2 + NB2Fb2. A martensite transformation from phase 1 to phase 2 requires Na1 = Na2 = Na and NB1 = NB2 = Nb, and the free energy change per gram atom accompanying transformation is AFi-2 = NA(Fa2 - Fa1) + Nb(Fb2 - Fb1) = NA[RT In (aA2/aA1) + AFa1?2] + Nb RT In (aB2/aB1) = Na[RT In (ra2/ra1) + AFa1?2] + Nb RT In (TaVTB1). [1] where yn2, yn1, yB2, yB1 are activity coefficients, and where Ma&apos;+* is the free energy change upon transforming a gram atom of pure A from phase 1 to phase 2 at the temperature in question. For martensite transformations in plain carbon steels, A = iron (Fe), B = carbon (C), 1 = austenite (7). 2 = ferrite (a), and Eq 1 is AFr ?a= NFe[RT In (rf.a/rfer) + AFF.r?a] + TVc RT In (eca/rc1)- L2] Nothing is known concerning the values of yFea and yca for carbon concen- , trations in excess of 0.025 pct. However, the approximation rf.7 = 7f." = 1 cannot be appreciably in error for small carbon concentrations, and Eq 2 reduces to Afr-a = NfeFfer?a1 + NC RT In (rca/rcr)- [3] Johanssonl and Zenera have calculated MFfr?a from the specific heat measurements compiled by Austin.6* Their calculated values agree closely, and are summarized in Table 1. The activity coefficients relative to graphite for carbon dissolved in iron vary with temperature according to the relationships d In rcr/d(1/T) = AHcr-R dlnyca/d(l/T) = AHCa/R where AHc? and AHca are the heats of solution of graphite in y and a iron. Assuming the values of AH to be independent of carbon concentration and temperature, In rCr = AHcr/RT + I1 In rca = AHCa/RT + 12

Jan 1, 1950