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By C. L. Shapiro, R. Schempp

DuRing the past few years, general interest in the steel-producing and steel-consuming industries has been centered on the so-called "inherent characteristics" of steels. While often vaguely described, these characteristics are known to influence the response to heat-treatment and the hardening characteristics of the material. Although most of the recent papers and discussions have associated the "inherent characteristics" with the austenitic grain size and emphasized the importance of it, comparatively little is known of the variables that may affect the size of the austenite grain. The work to be described in this paper was carried out during the course of a study on the inherent characteristics of tool steel containing one per cent carbon. The discrepancies encountered in the determination and classification of the austenitic grain size led to an investigation of some of the variants influencing the austenitic grain size as determined by standard methods. Methods of Determining Austenitic Grain Size The present methods used for the determination of the austenitic grain size may briefly be classified in two groups: 1. Etching at room temperature to reveal the austenite grain size prior to cooling. 2. Etching at elevated temperatures, cooling to room temperature, and observing the structural conditions that existed at the temperature from which cooling occurred. The outstanding methods of the first group are: (1) the McQuaid-Ehn test, (2) optimum rate of cooling, (3) quenching and etching. McQuaid-Ehn Test.—This established and accepted test does not need much elaboration. It consists of pack carburizing at a definite temperature for a standard period of time and slowly cooling in the furnace. The temperature is 1700" F. (925' C.) and the time is 8 hr. The interpretation and evaluation of this test are fairly well defined in the A.S.T.M.

Jan 1, 1937

By Frederick Becket

DOCTOR Albert Sauveur, distinguished scientist and Honorary Mem-ber of this Institute, predicted in the first Howe Memorial Lecture that the privilege of delivering this annual address would be considered a highly significant honor. The intervening years have well borne out Sauveur's prophecy. I wish to assure the American Institute of Mining and Metallurgical Engineers that I also deeply appreciate this honor, recognizing at the same time the present and even more the future respon-sibilities with which it is accompanied. Several of the previous lecturers had the good fortune to attend the classes of Professor Howe and to work in his laboratories. I was similarly favored, although in my instance and to my great regret the period was all too short. However, Howe's book, published in 1903, "Iron, Steel and Other Alloys," afforded me abundant opportunity to continue these studies. How well I remember the inspiration I derived from this famous book by Howe, the metallurgical master, pioneer, and educator! Remembering that Professor Howe contributed numerous papers to The Metallographist, a magazine supported from a technical point of view by the world's pioneers in metallography, I was curious a few days ago to learn the nature of Howe's early contributions to this magazine. The first paper by Howe in the first year of The Metallographist (1898) dealt with the allotropic theory; the second also treated of allotropy, and I quote the first sentence. of that paper: The allotropic theory of the hardening of steel may, like so many other important theories, have to be accepted or rejected not on direct proof or disproof, but on the accumulation of circumstantial evidence for or against it.

Jan 1, 1938

By W. B. Agocs

IN August 1954 a low altitude test geophysical survey was made in the Green Pond area of Morris County, New Jersey, with a Gulf Research and Development Co. Model II total magnetic field variation magnetometer mounted in a Sikorsky S-55 helicopter. The test was made in this area to compare the results of a high precision, very low altitude magnetometer survey with an existing ground magnetic survey in this area having known magnetite concentrations, so that the method could be used in areas of difficult access for the detailing of airborne magnetometer anomalies of interest in place of ground surveys. The load capacity of the Sikorsky S-55 permitted installation of a recording scintillation counter so that a radioactivity survey would be made simultaneously with the magnetometer survey. The area surveyed is located at approximately 41°00'N and 74o28'W, just south and east of the town of Green Pond, N. J. The outstanding topographic feature of the region is Copperas Mountain, a well defined ridge, maximum elevation 1222 ft, which runs the entire length of the survey. The lowest point in the survey, 810 ft, is in the extreme eastern corner. Topography of the area is shown in Fig. 1. The three major rock units outcropping in the area are all metamorphic: the Pochuck gneiss, which has been divided into two metamorphic facies; the Byram gneiss; and the Green Pond conglomerate. The relative ages of the Pochuck and Byram formations, both pre-Cambrian, are in doubt, but it is believed that the Pochuck is the older of the two.' The Green Pond conglomerate is Silurian.' Distribution of the outcrops and mine locations is shown in Fig. 1. Two facies of the Pochuck gneiss can be distinguished locally—the Copperas Mountain and Kitchell members. The Copperas Mountain member is a hornblende gneiss, and all the mines and prospects in the area are in this unit. The Kitchell is a quartz-plagioclase feldspar gneiss. The Byram gneiss is a relatively nonresistant valley formation which is high in the potash feldspar. The Green Pond conglomerate is a well indurated quartzite-conglomerate which forms the Copperas Mountain and the Green Pond Mountain's ridge to the north. It overlies the gneisses with a strong angular discordance that may be a fault. The geologic structure of the Green Pond area is relatively uncomplicated. The foliation planes of the gneisses dip steeply to the southeast, and the Green Pond conglomerate dips steeply to the northwest. Additional faulting in the area is indicated at the contact between the Kitchell member of the Pochuck and the Byram along the base of the topographic spur extending to the southeast from Copperas Mountain. The magnetite mines of Pardee, Winter, Davenport, Green Pond, Copperas, and the Bancroft shaft are described by Bayleyl and Stampe2.' The ore is in the Copperas Mountain member of the Pochuck gneiss. The magnetite veins are 10 to 50 ft wide and up to 300 ft long, dipping to the southeast at angles ranging from 40" to 75". The locations of these mines are shown in Fig. 1. Dip Needle Survey: The dip needle survey shown in Fig. 2 was taken from a U. S. Bureau of Mines Report of Investigations." The figure numbers below the local, individual map area outlines refer to the figures in the aforementioned reports which were not contoured. The area of the dip needle survey was confined almost exclusively to the outcrops of the Pochuck gneiss. The separation between survey profiles was 100 ft and the distance between stations on the profiles was 25 ft in highly anomalous zones to 100 ft in magnetically flat areas. A total of 16 1/2 miles of traverse was surveyed over an area of approximately 1/2 sq mile with 2050 stations. The magnitude of the magnetic anomalies is difficult to determine due to the lack of information concerning the type of dip needle used and the procedure followed in making the dip needle survey. This latter would include the method of "zeroing" the dip needle and the procedure of reading at the stations, whether on the swing or statically. Calibrations made of the Gurley dip needle, Lake Superior type, show a static sensitivity of 385 gamma per degree in the range from —25" to +35o, corresponding to a variation in the total field of —9600 gamma to +13500 gamma in a total field of 57000 gamma, inclination 72". The sensitivity increases to 16 gamma per degree from a deflection of 60" to 76", and from 76" to 172" the sensitivity decreases continuously to a low of 260 gamma per degree. From the above it may be seen that it is difficult to assign an arbitrary sensitivity for the dip needle used on this survey. However, an estimated value of 100 gamma per degree may be assigned. On this basis, the majority of the magnetic anomalies, whose deviation is +20°, would be 2000 gamma. Locally, west and northwest of the Pardee mine the magnetic anomaly is +50°, or 5000 gamma; in the Green Pond mine area deviations of +75" are observed that would correspond to anomalies of 7500 gamma. The areal extent and width of the dip needle magnetic anomalies is comparable to profile and station spacing. Hence it is concluded that part of the detail may be due to control, and the probable cause of the magnetic anomalies is at or near surface exposures of magnetite concentrations in the form of veinlets and disseminations whose locations correspond to the local magnetic anomalies. On the basis of the magnetics, none of the magnetite concentra-

Jan 1, 1956

On the following pages are abstracts of papers published by the Institute during the year 1932 as Technical Publications, Preprints, in bound volumes and in Mining and Metallurgy. For abstracts of papers that appear in bound volumes in 1932 but that were published as Technical Publications in 1930 or 1931, see the Transactions for those years. Papers that appear in this volume are not abstracted here. Many of the Technical Publications have been reprinted in bound volumes. Information regarding this disposition, and number of pages in each paper, may be found in the list beginning on page 309. Volume numbers are given as listed on page 3 and in the paragraph at the beginning of the index, page 315. The abstracts are grouped as follows: Page Page Metal Mining.................... 265 ferrous Alloys)................. 279 Milling and Concentration......... 268 Coal Division.................... 287 Iron and Steel Division............ 270 Petroleum Division............... 292 Nonferrous Metallurgy (Reduction Nonmetallic Minerals............. 299 of Ores)....................... 277 Mining Geology.................. 301 Rare Minerals and Metals......... 279 Mining Administration (Accounting, Institute of Metals Division (Found- Taxation, Industrial Relations). . 304 ing and Metallography of Non- Geophysical Prospecting........... 304 Metal Mining The Mineral Industry. By Scott Turner. (Min. & Met., June, 265. 3500 words.) Abstract of an address delivered before the Royal Canadian Institute, Toronto, April 16, briefly outlining the importance of mining in the United States, in Canada, and in the world. Comparison is made of the mineral production for 1886, 1900, 1910, 1920 and 1929, showing that in the 43 years from 1886 to 1929 that of the world increased nearly tenfold, of the United States over twelvefold and of Canada thirtyfold, but that Canada's output was equivalent to only 2 per cent of the world total and to 5 per cent of that of the United States in 1929. Statistical tables and graphs show value of production, percentage of world production contributed by Canada and the United States, etc. The mining situation in Canada is briefly reviewed: only those American engineers who have had occasion to examine the figures appreciate the rapidity of growth of Canadian mineral production. The treatment of minerals involves vast complex industries. When we are producing, say, 6 billion annually, the employment of 2 million workers provides indirect support to perhaps 10 million people. Exploiting mineral deposits is peculiar in certain ways, for the deposits are exhaustible, are of rare occurrence when measured in terms of outcrop area compared to total earth area, and may suddenly be handicapped or superseded by new discoveries; moreover, the economic position of the contained metals is 'affected by the use of scrap metal and the existence of invisible stocks. The largest and most valuable of the mineral deposits are not the metals, but rather the fuels. The record of the coal industry in recent years is one of brilliant technical achievement; its economic position is far from satisfactory. A so-called world fuel

Jan 1, 1932

By E. T. Turkdogan, L. S. Darken

Calcium ferrite melts were equilibrated with sulfur and oxygen-bearing gases at temperatures within the range 1290°C to 1620°C. The results show that at oxygen partial pressures below 10-4 atm the sulfide-reaction occurs and at higher oxygen pressures the sulfur dissolves in the melt principally as sulfate ion. It is also observed that when the product increases, sulfate ions are converted to pyrosulfate ions and the results permit the evaluation of the pyrosulfate/sulfate ratio. It is shown that the ratio y CaSO,/rCaO increases with decreasing concentration of calcium oxide in calcium ferrite, silicate and aluminate melts. Indications are that oxy-acids, e.g. silica, alumina and ferric oxide, increase yCaS0,. A few experiments were carried out within the sul-tide range and the results are in accord with those obtained by other investigators on aluminate and silicate melts. BECAUSE of the industrial importance and theoretical interest, many investigators have studied the reactions between molten oxides, silicates or alumi-nates, and gases containing oxygen and sulfur. The early work reviewed by Schenckl and studies made by Bardenheuer and Geller2 indicates that solution of gaseous sulfur in an oxide melt resulted in the replacement of the oxide ions by the sulfide ions. Measurements made by Grant and Chipman3 on the equilibrium partition of sulfur between molten iron and complex silicate melts also demonstrated that, for a given temperature and silicate composition, the distribution of sulfur between slag and metal increased with decreasing oxygen content of the metal. Fincham and Richardson4 studied the effects of temperature and partial pressures of sulfur and oxygen on the solubility of sulfur in simple silicate and alumino-silicate melts. They observed that at oxygen partial pressures below about 10-5 atm sulfur in the gas dissolved in the melt as sulfide ions, replacing an equal number of oxide ions of the melt. At oxygen partial pressures higher than 10-3 atm, sulfur entered the melt as sulfate ions. Similar studies were made by St. Pierre and Chipman5 using calcium ferrite and calcium silico-ferrite melts. The experimental data presented in this paper were obtained in this Laboratory about 10 years ago; this is the first formal presentation although a preliminary report was given previously.6 In each of these experiments, a pure synthetic CaO-Fe2O3 melt in a platinum crucible was equilibrated with a gas mixture (SO2-O2, SO,-air, SO2-CO, or SO2-CO2-CO) at a temperature ranging from 1296°to 1620°C. The experimental technique was essentially the same as that reported by Darken and Gurry,7 the main difference being that the atmosphere in the reaction chamber contained sulfur dioxide together with oxygen, or carbon dioxide-carbon monoxide

Jan 1, 1962

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for spectroscopically pure silver, and for o series of solid solutions of silver with cadmium, indium, and tin, using a Ke-type torsion pendulum apparatus. Some experiments have also been made to investigate the effect of nonmetallic impurity on grain boundary relaxation in silver. The effect of the alloying elements is to increase the grain boundary viscosity, and to raise the activation energy for grain boundary relaxation from 22,000 cal per mol for pure silver to 43,000 cal per mol for the solid solutions; the same value being obtained, within the limits of experimental error, for all the alloying elements and solute concentrations investigated. Results of the experiments show exactly the same trend as those obtained previously for a similar series of copper solid solutions. They are in agreement with the general theory of grain boundary relaxation developed by Zener and Ke, but do not seem to be in agreement with either of the mechanisms so far put forward to explain grain boundary slip. EXPERIMENTS described in this paper were made as part of an investigation into the effect of alloying elements in substitutional solid solution on grain boundary viscosity, measured by the internal friction method developed by Ke.&apos; The apparatus and experimental procedure have already been described.&apos; Preliminary work was done with spectro-scopically pure silver. Experimental Work Materials Used—All the materials were supplied in the form of % mm diam wire by Messrs. Johnson Matthey and Co. Ltd. The silver and all the alloying elements used were spectroscopically pure. Composition of the alloys is given in Table I. They were all melted and chill cast under the same conditions as the copper alloys. The ingots were rolled to 1/4 in. sq rod with intermediate annealing at 600°C in an atmosphere of cracked ammonia when necessary. These rods were then drawn to wire by standard procedure with intermediate bright anneals at suitable steps in the drawing operations. Specimens from the annealed wires were sectioned longitudinally. mechanically polished, and examined under the microscope. They were then etched and reexamined. Grain sizes were reasonably uniform for all wires, and no traces of a second constituent were observed. The wires were weighed before and after testing so as to measure any loss of the alloying element due to evaporation. The loss was less than the accuracy of measurement—< 0.1 pct of the total weight— for the Ag-In and Ag-Sn alloys, but appreciable loss of weight occurred in the case of the Ag-Cd alloys. The percentage loss is given in Table 11. X-ray diffraction photographs were taken of all thc wires after test to determine whether there was any marked preferred orientation. Results of the examination are given in Table 111. Experiments on Spectroscopically Pure Silver-— Experiments were made on specimens in which the grain diameter was small relative to that of the wire, and on one specimen in which the grains were grown by the usual strain-anneal method to extend across the full diameter of the wire. These large grained specimens will be referred to as single crystal specimens. The wires were annealed for 11/2 hr at 700°C, and experiments were made at two frequencies of vibration, 1.5 and 0.4 vibrations per sec. The variation of internal friction with temperature is shown in Fig. 1. Experiments on a second small grain specimen gave approximately the same results as for the first wire. It will be seen from Fig. 1 that the peak in the curve for the small grained wire, which is presum-

Jan 1, 1957

By Alexandre Mitinsky

The theory of elasticity, the science of the strength of materials, and all our calculations regarding engineering structures are based on Hooke&apos;s law, that in loaded bodies the deformations are proportional to the load producing them. Without this law it would be impossible to design intelligently engineering structures such as bridges, frames, axles, etc. This being the case, the proportional limit,l that is, the point at which deformation ceases to be proportional to load, is the most important factor in engineering design. Further, the working fiber stress should be fixed in reference to the proportional limit instead of, as is usual, in reference to the ultimate strength. The incorrect use of the ultimate strength instead of the proportional limit in setting the working fiber stress is probably due to two reasons: (1) it is a more delicate operation to measure the proportional limit; (2) it is usually assumed, though incorrectly, that the proportional limit is determined by the ultimate strength. In Germany the poin&apos;t at which permanent set first appears is often taken instead of the proportional limit. The two points will coincide if Gerstner&apos;s law, that elastic deformations are proportional to the loads producing them both before and after permanent set, is true; and the limit of proportionality and the elastic limit or point of permanent set will both be represented on a stress-strain diagram, by the point at which the line ceases to be a straight line and becomes curved or changes its inclination. It is to be further noted that the difference in definition between proportional limit and elastic limit introduces a difference in methods of determination in the testing laboratory. The German method of determining the elastic limit by alternately loading and unloading the test specimen is a lengthy process and time has in itself a very considerable influence on the results of physical tests.

Jan 1, 1916

By J. E. Flinn, S. A. Duran

The steady-state creep behavior of poly crystalline cad mi inn was studied over a temperature range of (1.56 to 0.94 Tm. Two distinct mechanisms were found to occur over this temperature range. They were described by: where and represerqt the minimum strain rates corresponding to the low- and high-temperature regions, respectirely. The two regions of constant acti11ation energy were connected by a transition region where the strain rate was controlled by both mechanisms acting in parallel. At temperatures below a transition temperature of about 0.7 Tm the agreement between the activation energy value for creep and that for self-diffiision suggests a rate-controlling mechanism of dislocation climb. For cadwzium, steady-state creep at temperatures above 0. 7 Tm appears to be controlled by another mechanism, perhaps involving the behavior of dislocation jogs. FRENKEL et al.1 studied the high-temperature creep of polycrystalline cadmium and reported an activation energy of 21 kcal per mole for the 0.5 Tm < T < 0.8 Tm range. Based on observations of creep rate at only two temperatures, a value of 22.1 kcal per mole was determined by Medbury. These two investigations were for the purpose of showing agreement between the activation energy for creep and that for self-diffusion, reported3 as 18.2 and 19.1 kcal per mole, respectively, for diffusion parallel and perpendicular to the hexagonal axis. Gilman4 investigated prismatic glide in single crystals of cadmium over a higher-temperature range of 0.72 to 0.93 Tm, and found an activation energy of 29 kcal per mole. He also reported5 an activation energy higher than that of self-diffusion for prismatic glide in zinc single crystals deformed at temperatures near the melting point. This value was in good agreement with those found for an equivalent temperature range by Flinn and Munson6 and by Tegart and sherby7 for polycrystalline zinc. These two independent studies also disclosed at lower temperatures another value of activation energy near that for self-diffusion. It would be expected from the creep results on zinc and single-crystal cadmium that creep studies on polycrystalline cadmium, extended to temperatures near the melting point, might yield an activation-energy value higher than the 22 kcal per mole value found in earlier studies. The purpose of this paper is to report the steady-creep behavior of polycrystalline cadmium over a temperature range of approximately 0.5 to 0.9 Tm EXPERIMENTAL METHOD The cadmium used in this study was obtained in the form of as-cast rods, 0.5 in. diam, through the courtesy of the Bunker Hill Mining Co. The material was of 99.995 pct purity, as determined by spectro-chemical analysis. The creep specimens, which were 0.250 in. diam by 0.400 in. long and annealed at 300°C for 45 min to produce a stable average grain diameter 0.25 mm, were tested in compression using an apparatus similar to that described by Sherby.8 The specimen temperature was controlled to within ±0.5°C with the help of appropriate constant-temperature baths. The applied stress was maintained within 1.0 pct of the desired value by the additions of lead shot at fixed strain increments. No barreling was observed over the strains encountered during testing. Isothermal creep tests9 were used in the study with only a few differential temperature tests10 run for comparison purposes. Steady-state creep data were obtained over a temperature range of 60 to 287°C (0.56 to 0.94 Tm) at five stress levels ranging from 28.1 to 140.6 kg per sq cm. RESULTS The minimum or steady-state creep rate may be described by an equation of the following form:" where i is the minimum strain rate, S is the structure factor, F is a stress function, Qc is the energy of activation, T is the absolute temperature, and R is the gas constant. The minimum strain rates obtained in this study for cadmium were recorded on a semilogarithm plot as a function of the reciprocal absolute temperatures for the various stress levels, as shown in Fig. 1. This figure shows a characteristic transitional behavior" with a parallel interaction of two mechanisms. It is obvious that the activation energies corresponding to the individual processes are insensitive to stress because the curves are parallel. The discrete activation-energies values for the low- and high-temperature regions for the various stress levels are reported in Table I, and were determined by the least-mean-square method. For the low-temperature region, an activation energy of 20.7 ± 0.6 kcal per mole was obtained, and for the

Jan 1, 1967

By F. W. Luerssen, J. F. Elliott

F LUSHING the early slag from a stationary open Fhearth having a high percentage of hot metal in its charge is necessary in order to remove silica from the system. The flush slag is strongly oxidizing and is somewhat acidic. It has, however, considerable capacity to extract phosphorus from the bath and it also removes considerable manganese. It seems probable that factors which control the distribution of phosphorus and manganese between slag and metal in the refining period also should be dominant in the flush and postflush periods. Several studies, as summarized elsewhere,1,2 support the viewpoint that conditions closely approaching equilibrium for these elements are rather readily established during the refining period. Over the years these studies have repeatedly demonstrated that 1—high slag v01ume, 2—low bath and slag temperature, 3—basic slag, and 4—strongly oxidizing slag favor rapid elimination of phosphorus from the bath to the slag. They also show that the following conditions favor retention of manganese in the bath: 1—low slag volume, 2—high bath and slag temperature, 3— basic slag, and 4—minimum oxidizing power of slag. When it is considered that the flush slag often carries as high as 75 pct of the manganese charged and only 25 to 60 pct of the phosphorus charged, it is evident that in removing silica much manganese is sacrificed but phosphorus removal is far from conplete. Because of overriding circumstances, this is accepted in most operations and actually it is considered to be inevitable. This may account for the fact that little attention has been paid to conditions affecting the elimination of phosphorus and manganese in the flush slag. A recent study of the behavior of various charge oxides has developed considerable information on the flush and postflush periods. Because the data are felt to be of general interest, they have been brought together and Presented in this paper. The object is to show the various factors in the flush and postflush periods which influence elimination of phosphorus and manganese. Physical Conditions During and After Flushing Physical conditions existing during the flush vary from plant to plant, from shop to shop, from furnace to furnace, and even from heat to heat. They are strongly influenced by the physical and chemical character of the charge oxide which is ordinarily necessary to provide sufficient oxidizing power early in the heat. Invariably the period is characterized by a vigorous reaction between the principal re-actants: the hot metal being added and the charge oxide. During the flush, it is probable that the slag acts to some extent as an oxidizer; but, because of the critical influence of the behavior of the charge oxid&apos;e on flushing action, it seems apparent that the oxide itself is the dominant oxidizer. Fig. 1 shows the course of two heats which were selected as being typical of the group studied. Heat A was charged with 55 pet hot metal, based on the total metallics charged, and heat B had 57 pct hot metal. As indicated in Table I and Fig. 1, the melt-down slag, which is not usually voluminous and which is principally FeO, expands greatly in volume and will show rather high levels of SiO2, MnO, and P2O5 very soon after the beginning of the hot metal addition. Simultaneously, large volumes of CO are liberated which cause violent mixing of slag and metal. It is of interest to note that the time required to bring carbon down to a low level is very much longer than that required for the removal of silicon, manganese, or phosphorus. At the end of flush, carbon in the bath is still approximately 2 pct. When strongly reducing hot metal is brought into contact with strongly oxidizing conditions within the furnace! it is probable that the rate of mass transfer to the slag (and atmosphere) of silicon, manganese, phosphorus, and carbon initially depends principally on the rates at which the two participating phases are brought into contact That is, it depends on the nature of the various reactions. Later in the flush period, when the scrap is virtually all dissolved and the action of the bath has settled down to a steady and somewhat gentle boil, it is likely that other factors, such as the transfer of oxygen across the slag-metal interface, become dominant. The temperature of the slag-metal system is far from uniform. Heat is being driven by the flame down through the slag. Bubbling and surging of the metal also frequently brings portions of the bath in contact with the flame. At areas of contact between the ore and liquid metal, or slag and liquid metal, the oxidizing reactions generate much heat. On the other hand, scrap is being melted which tends to absorb large quantities of heat. Because the liquid bath is high in carbon, the steel scrap is brought into solution rapidly. This can proceed at a rather low temperature; and until much of the scrap has been taken into solution, the bath temperature would not be expected to increase appreciably. Consideration of these factors leads to the conclusion that during the flush period the slag should be rather hot and the bath relatively cold. Both observation and temperature measurements bear this out. Experimental Data The extended program of charge oxide evaluation permitted study of the widely varying conditions existing during the flushing period. Slag and metal analyses and bath temperatures reported herein (Tables I and 11) were obtained toward the latter portion of the work. Four different types of charge oxide, sinter, two types of hydraulic cement-bonded soft ores, and a pyrobonded agglomerate were used in the study. Although the heats reported were from only one 205 ton furnace, they show variations in flush slag analyses all the way from 25 pct FeO, which is typical with the use of a hard natural charge ore, to 45 pct FeO which resulted when a very poorly agglomerated fine ore was used. The physical behavior of the flushes showed a correspondingly wide variation from well controlled reactions to violent surges following periods of inac-

Jan 1, 1956

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"&apos; and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By Carl A. Zapffe, George A. Moore

IN a previous publication from this laboratory1 the conclusion was drawn that the embrittling effect of occluded hydrogen on iron and steel must result from the precipitation of the gas within small openings through the crystal structure. A review of the literature then published indicated the real existence of crystal sub- structures of the mosaic type and gave presumptive evidence that the "rift openings" associated with hydrogen occlusion are the same as the "disjunctions" of the mosaic theory. Inasmuch as no clear conception of the actual nature of the crystal fragments and openings inherent in these theories has been established, it was considered desirable to obtain direct micrographic evidence of their true configuration. In this direction the standard methods of metallographic attack have proved useless. Recourse was had, therefore, to the direct examination of the surfaces upon which failure by cleavage had resulted from the presence of hydrogen. It was expected that such a surface, un- affected by chemical attack and undistorted by polishing, would reveal the fine openings penetrated by the gas and thus indicate the real nature of the substructures. MATERIALS STUDIED In commercial steels, defects caused by hydrogen take various external forms ac- cording to such factors as structure and purity, and to the extent to which hydrogen either occludes or produces chemical changes. The present work relates only to the well-known transcrystalline hydrogen embrittlement-"pickling brittleness"-in which elemental hydrogen occluded within the grain develops cleavage characteristics. For example, hydrogen embrittlement resulting from hydrogen reaction products is excluded from detailed study. It was also desirable, as far as possible, to have the study uncomplicated by other elements which themselves cause brittleness. Three types of iron were used. These included ingot iron, decarburized free- machining steel, and a specially prepared, aluminum-killed, electrolytic iron. This , choice allowed a comprehensive selection of unavoidable minor impurities and inclusions, which could subsequently be shown to have no specific effects on the structures within the grains. Carbon, and any other impurities free to react with hydrogen, were first removed by a preliminary annealing treatment in hydrogen. Subsequent treatment in vacuo extracted much of this hydrogen and its gaseous reaction products. The resultant ductile iron was then embrittled either by a second anneal in hydrogen, followed by rapid cooling, or by cathodic electrolysis. Group I: Prepared from Armco Ingot Iron As shown in Table I, the principal impurity in this iron was oxygen, which survived the purifying treatment to a large extent. Two series were prepared. The first (Nos. SIO-24) was purified only one day in hydrogen and dehydrogenized one day in nitrogen. Containing both hydrogen and its

Jan 1, 1943

By Milton E. Wadsworth, W. Martin Fassell, William H. Dresher

A study of the rate of dissolution of molybdenite (MoS2) in alkaline solution was carried out under carefully controlled conditions. Effects of temperature, oxygen over-pressure, and KOH concentration were evaluated. Studies were made in the temperature range 100°C to 175°C and in the pressure range 0 to 700 psia of oxygen. Under these conditions molybdenite was found to leach according to a linear mechanism. Both oxygen over-pressure and KOH concentration were found to control the rate of leaching. The mechanism has been explained in terms of adsorption of oxygen at the molybdenite surface followed by configurational rearrangement of the adsorbed molecules. The hydroxyl ion dependency is believed to be diffusion-controlled. Laboratory batch studies have shown that molybdenite can be readily dissolved in alkaline solutions under moderate conditions of temperature and pressure. Commercial application of this process to the production of ferro-molybdenum and molybdenum chemicals is promising in view of the ease of dissolution of molybdenite and the relatively noncorrosive conditions involved in the process. HIGH temperature-high pressure techniques have long been used to great advantage in the organic chemical industry, the petroleum industry, and the paper industry. Only recently, however, have these methods been used to extract metals from their ores on a commercial scale. The Chemical Construction Corp., together with interested producers of nickel and cobalt, has done much to develop methods of producing nickel and cobalt powders by the use of high temperature-high pressure techniques.&apos; The Howe Sound Co. is currently operating a plant near Salt Lake City in which the new Chemical Construction Corp. technique is applied to cobalt-arsenic sulfide concentrates. In this method the concentrates are leached in a dilute solution of sulfuric acid under air pressure at a high temperature. Near Edmonton, in Alberta, Canada, the Sherritt Gordon Co. is also using the new method in conjunction with its ammoniacal leach process.&apos; National Lead Co., at Fredricktown, Mo., is operating a process similar to that of Howe Sound. In spite of the rapid growth of high temperature-high pressure hydrometallurgical processes, there has been very little work done on fundamental principles involved in this type of process. Conse- quently the literature lacks any significant data in this field. Oxidation of pyrite,3 phalerite,4 galena,5 and recently molybdenite" in alkaline solutions has been reported to some extent. This investigation was initiated, therefore, to broaden the application of high temperature-high pressure hydrometallurgy and also to contribute some insight into the basic mechanisms of oxidation in an aqueous medium under these conditions. In addition to the immediate consequences of these processes much valuable information remains to be learned about fundamental reactions when they are carried out at temperatures and pressures slightly higher than those normally encountered. Leaching of molybdenite by alkaline solutions under oxygen pressure has recently been reported in the Russian literature by E. S. Usataya,8 who found that leaching rate increased with an increase in the pH of the solution—the strongest effects being observed at a pH of 10—and also with an increase in temperature. Usataya also has reported the formation of a protective film on the surface of the molybdenite when the leaching solution was weakly alkaline, neutral, or acidic. He believes that this oxidation process explains the migration of Mo+ + in the oxidation zones of molybdenite ore deposits and the subsequent impoverishment of the ores. Equipment: The high temperature-high pressure reaction unit used in this work was especially designed for kinetic studies of this nature, emphasis being placed on accuracy of measurement and precision of control. As details of the unit&apos;s construction and operation have been discussed elsewhere,7 Only basic features and principles of operation will be discussed at this point.

Jan 1, 1957

By J. J. Taber

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton&apos;s equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?&apos; lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.&apos; It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By H. Rumfelt

The author demonstrates an approach for analyzing overcasting requirements for a stripping project. This approach to the problem employs indicated trends in the relationship of the weight of the machine (only electropowered draglines are considered) to its ability to do stripping work. Strip mining in the domestic coal industry is contributing a greater proportion of overall production than at any time in the past. U.S. Bureau of Mines statistics show that the percentage of total production mined in 1958 by stripping methods increased to more than 30 pct, up from 22 pct in 1951. The tendency to favor strip and open pit mining exists in other mining activities, but such trends are not as clearly outlined as in the coal industry. Significantly, the depth of overburden in coal properties considered suitable for stripping is also increasing. A depth of 50 to 60 ft of overburden was once considered to be about the maximum amount that could be handled economically. Today, a depth of 80 to 100 ft is frequently taken into consideration for simple overcasting operations (i.e., excavating overburden and dumping it in the spoil position where it remains indefinitely). Accompanying these changes, there have been continuing studies searching for procedures to appraise deeper stripping problems. Although the only known practicable way to accurately evaluate a proposed stripping venture is to make studies (including cost estimates) step by step, it is nevertheless desirable to have a quick method for making preliminary evaluations of potential strip mining operations. A recently devised digital computer method of providing a preliminary simple overcasting analysis for a stripping prospect relates the indicated trends in the relationship of the weight of the machine to its ability to do stripping work. In addition, this approach employs situations where the geometry of each cut-and-spoil section is assumed to take certain defined relationships for varying overburden depths. Slopes are necessarily considered to be stable, which means such practical factors as the mechanics of soils are neglected for the sake of convenience. Definition of Terms: Photographs A and B show a shovel-type and a dragline-type of simple overcast operation, plus terms used to denote certain parts of a pit. Pits that follow a straight line when projected on a horizontal plane are referred to as straightaway. It has been assumed that all section drawings accompanying this article pertain to straightaway cuts which, in turn, means that areas can be compared by relative volume. The volume of overburden is measured in virgin cubic yards. Material displaced from its virgin state to a spoil area normally occupies a larger volume than when in situ; the difference is termed swell, and it is expressed as a percentage of the original volume. For example, if the original cut volume is denoted V cu yd, and the spoil volume is 1.2 V cu yd, the swell is a positive 20 pct. MAXIMUM USEFULNESS FACTOR (MUF) CONCEPT Men experienced in overburden removal give emphasis to the weight of the machine in relation to its value as an excavator. From the writer&apos;s understanding, value has been only loosely defined and discussed generally and vaguely. The concept is considered important, however, since it is based upon the observations of many men. It provides a clue for the approach taken to solve deep stripping problems. In the procedure described below, value has been arbitrarily established as the product of the nominal dipper size of the shovel (or dragline) times a functional dumping reach. MUFs—Shovel: A shovel&apos;s capability to handle thick overburden is usually limited by its ability to dispose of the spoil. Thus the dumping reach, as well as its dumping height, is significant. The angle of repose of spoil material must also be considered. Although such slope angles vary among different mines, jobs, and materials, a slope of 1.25 to 1, frequently found in both planning and practice, is used by this author in the illustration of this analytical method. The relationship of the shovel&apos;s geometry to a stripping operation is shown in Fig. 1. To gain maximum advantage in constructing spoil piles, the shovel is placed so that its tracks adjacent to the spoil are as close as possible to the rib of the coal deposit. A vertical plane passing through the line

Jan 1, 1961

By J. E. Lamar, J. S. Machin

INSULATING materials include a wide variety of nonmetallic mineral products such as exfoliated vermiculite, expanded gypsum, 85 pct magnesia, diatomite, asbestos, perlite, cellular glass, pumice, silica aerogel, expanded aggregates and mineral wool. Except mineral wool, most of these products, or the materials from which they are manufactured, are described in other chapters of this book. PROPERTIES OF INSULATING MATERIALS The insulating properties of the materials considered in this chapter result in general from entrapping extremely small pockets of air in such a manner that heat is not transferred by convection. The minimum heat conductivities of such insulating materials are slightly greater therefore than the conductivity of still air. In addition, conductivity varies with the overall density of the material, the temperature range in which the measurements are made, and the form into which the material is fabricated. However, the numerical value of heat conductivity should not be the sole criterion of an insulating material; for a particular application it may be advantageous to use a material of somewhat higher conductivity in order to secure other desirable engineering properties. This is especially true with certain materials that are used because of their refractoriness. Comparative insulating values of some commonly used insulating materials are shown in Table 1. In comparing the values presented in this table it should be borne in mind that heat conductivity varies with the mean temperature, with the overall density, and with the amount of moisture present. With fibrous or granular materials it varies with fiber or grain size and with the amount and kind of binder, if any is used. Under some circumstances it may vary with the arrangement of

Jan 1, 1949

By R. A. Salathiel, A. D. Kaiser, P. H. Monaghan, B. E. Morgan

The productivities of many hydrocarbon-bearing for-rnntions appear to be reduced during drilling, completing and repairing operations. The reason for these othcarwise unexplainable low productivities may be a drastic reduction of formation permeability immediately surrounding the borehole. A possible cause of the reduced permeability is swelling and dispersion of clays present in porous media when contacted by fresh water or mud filtrates. Hence, the invasion of fresh water or mud filtrate into hydrocarbon-bearing formations that contain clays may cause low productivities as a result of formation damage. Present laboratory investigations have yielded results which supplement existing literature on formation damage. An expanded-type clay, montmorillonite, way found in hydrocarbon-bearing formations not previously analyzed. When sand columns and formation cores containing montmorillonite were contacted by fresh water, their oil permeabilities were reduced. This reduction in oil permeability way restored partially but not completely by a repair procedure, i.e., flooding with kerosene containing organic agents or flooding with water containing electrolytes. Hence, where montmorillonite is present in formations, prevention of formation danzage was indicated to be the only complete solution to the problem. To prevernt formation damage, results suggested use of an approximately 1 per cent solution of calcium chloride or stronger solutions of sodium or potassium chloride. In conventional rotary drilling operations the wall of the hole is exposed to drilling mud for days, weeks, and in some instances for as long as several months. During this time, drilling mud filtrate seeps slowly into formations surrounding the hole. The permeability and stability of many formations, especially those containing clayey materials, are impaired by the mud filtrate. Often interaction between the mud filtrate and the formation causes drilling and production difficulties. Serious reduction in productivity of oil and gas formations during drilling, completing and repairing wells has been noted often in recent years. Cases are known of development wells which produced only small volumes of fluid upon completion. However, after a period had elapsed, they began to produce oil or gas in commercial quantities. In other cases, results of drill-stem tests taken during the drilling of deep wells have indicated good production should be obtained from shallow formations. Later difficulty has been experienced in obtaining production from these shallow formations which had remained in contact with drilling muds for an extended time. In yet other cases wells have failed to attain the productivities expected from previous performance after the use of drilling mud as a circulating fluid during workover operations. It is evident from the field behavior cited that the productivities of certain oil- and gas-bearing formations have been damaged by exposure to drilling muds. This reduction in well productivity, called "formation damage", causes serious consequences. In development wells, expensive remedial operations are incurred. In wildcat wells, good formations may appear to be marginal or even non-productive. The importance of formation damage has been recognized by a number of investigators1-s who have considered the effects of fresh water, saline solutions and aqueous mud filtrates on the permeabilities of formations. A general conclusion from such studies is that interaction between water and formation clays reduces permeability of reservoir rock and that the permeability decreases as salinity of the water decreases. Data in these references, however, concern the permeability change with only a single fluid present. A more pertinent and direct consideration in the production of oil and gas from wells is the permeability change when two fluids, oil and water, are present. Recognizing this, Nowak and Kreuger2 and Bertness1" considered several ways in which mud filtrates and saline solutions caused reductions in the oil permeability of formation cores. Investigations discussed here were designed to supplement information in the literature on changes in oil

By Lester Blackner

THE PROPERTY AND LOCATION THE Ray Consolidated Copper Co.&apos;s mining property is located on Mineral Creek 6 miles north of Kelvin, at Ray, Pinal County, Ariz. (Fig.. 1) . The mining claims now owned by the company consist of 126 lode claims, comprising 2,144.9 acres, containing at the beginning of operations 82,904,368 tons of 2.19 per cent. copper ore. GENERAL CHARACTERISTICS OF THE OREBODY The main orebody is a disseminated deposit in schist and porphyry formed by secondary enrichment. Its existence was proved by churn drilling, and it is at present one of the largest proved copper deposits in the world. The orebody itself covers .205 acres with an average thickness of 121 ft., and occupies a definite belt which has a northwest direction. Its length is approximately 5,000 ft. The width varies, being about 2,000 ft. at the west end and 2,500 ft. at the east, narrowing down irregularly front both ends to a few feet in the center. The thickness of the body varies greatly along the line of lode, ranging from a few feet up to 470 ft. thick. The ore horizon is not constant, but varies, following in a broad sense the topography The body in general dips slightly to the northeast, and is broken up by numerous small faults and fractures. The ore-bearing formations, consisting of mineralized schist and mineralized granite porphyry, stand fairly well and offer no difficulty in mining operations.

Jan 6, 1915

By J. C. Bradbury

The year of the Centennial is upon us. Not only is AIME marking its 100th birthday, but the cement industry is also celebrating 100 years of activity (see article by Roy Grancher, page 48). Fort Dodge, Iowa, and gypsum also tried to get into the act but missed by one year. Frank Apple-yard&apos;s gypsum article (page 53) informs us that the Fort Dodge area has been producing gypsum continuously for 99 years. That would seem to make AIME and the industrial minerals doddering oldsters. Not so-our Institute shows more energy than ever, and the word for industrial minerals is growth. These are the mineral resources of the future, the raw materials for the abundant life to come

Jan 1, 1971

By H. A. Wriedt

Zinc-vapor pressures in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C were measured by an isopiestic method. Thermody-na?nic properties of zinc in these solutions were derived directly and those of iron with a Gibbs-Duhem integration. Zirzc and iron exhibit large, positive, and moderately temperature-sensitive deviations from ideality. Excess enthalpies and Gibbs energies are positive in the ranges studied. It has been establzshed in relating published phase equilibria to the Gibbs energies of forming solid solutions that positive departures from ideality also exist in the fcc solutions. Tlze stability, as defined by Darken, of the bcc solutions is small but positive at 703.5"C. Its decrease with decreasing temperature indicates that a miscibility gap may exist in the stable or metastable bcc solutions at lower temperatures. The changes of thertnodynanlic properties relatable to changes in magnetic state are minor compared to other changes due to alloying. The accuracy with which the relation between lattice parameter and composition of the bcc solutions is known has been improved. Zinc increases the lattice parameter of a iron by O.ZOZA per unit atom action zinc to at least NZn = 0.25. TO our knowledge, only Ciganl has previously investigated thermodynamic properties of the bcc solutions of the Fe-Zn system. He measured zinc-vapor pressures in the temperature range from about 320" to 360°C by an effusion technique. We have measured the vapor pressures of zinc in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C by an isopiestic technique. This investigation and the pursuant thermodynamic computations are part of a program for studying several properties of these solid solutions. In the appendix we report a remeasurement of the relation at room temperature between the lattice parameter and zinc content. Related work not reported herein embraces measuring the diffusivity2 of zinc in ferrite at 700" to 900°C and the Curie point temperature3 as functions of composition. EXPERIMENTAL METHOD AND APPARATUS Purified iron at a series of constant temperatures was saturated with zinc at a series of constant zinc-vapor pressures, the range of conditions being so limited that the equilibrated solid solutions were ferri-tic. The equilibration was conducted in long capsules, Fig. 1, that had been evacuated, gettered with titanium, and sealed. The purified iron, part of a vacuum-melted ingot of electrolytic-iron stock (Glidden Co. 1044-grade), had the impurity contents listed in Table I. It was used in the form of millings about 0.001 in. thick. A zinc of 99.999 pct purity (United Mineral and Chemical Corp.) and later one of 99.9999 pct purity (Cominco Products, Inc.) were used, with no observed difference in results. Sufficient zinc was placed in the capsule (separate from the iron and kept at a different temperature) to supply the vapor phase and the iron alloy, while leaving a pool of pure liquid zinc throughout the run. The imposed temperature of the residual zinc pool fixed the vapor pressure of zinc throughout the capsule; condensation was avoided at other locations by making this the lowest temperature in the capsule. Two common complications of nonisothermal systems were, we believe, effectively absent from ours: first, molecular species other than monatomic have no appreciable concentration in zinc vapor at 700" to 900~~: second, the development of zinc-pressure differentials in the capsules was suppressed by use of relatively large-diameter tubing and the absence of diluents in the zinc vapor other than desorbed impurities. The specimens and zinc pool were located at two isothermal zones (each ranging within 1°C over several inches) of a wire-wound, 37-in.-long vertical-tube furnace. The required temperature distribution was achieved by external adjustment of the currents in three electrically isolated windings. The temperatures of the isothermal zones were controlled independently by ther-

Jan 1, 1968

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman&apos;s arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman&apos;s paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman&apos;s work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"&apos;. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963