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By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969

By Carl H. Samans

In their recent complete review of the subject of age-hardening,' R. F. Mehl and L. K. Jetter classify the main types of precipitation-hardening alloys under two headings, depending upon the nature of the precipitate and the character of the precipitation. In the alloys falling under the first heading, which display "continuous precipitation" and are typified by the aluminum-copper alloys, "precipitation seems to occur without much regard to grain boundaries and apparently at much the same rate at every point," although an acceleration in regions plastically deformed has definitely been established.2 In the second type of alloys the precipitation is "discontinuous," as in the copper-silver system for example, and "seems to start in restricted regions, primarily those contiguous with the grain boundaries, and to spread inward in an advancing wave." The reasons for the occurrence of these two greatly different types of precipitation are unknown, as are those for many other reactions that take place in the solid state. In the present paper only the first or "continuous" type of precipitation will be dealt with, for which a complete crystallographic mechanism has been worked out for the process of precipitation from a supersaturated solid solution of copper in aluminum. Based upon this mechanism, an explanation of the various property changes found experimentally will be developed in the second paper of this series. In later papers ('discontinuous precipitation" in copper-silver alloys will be explained, and an effort will be made to rationalize the two processes and types of precipitation. Crystallography of the Precipitation Process Through the extensive investigation by R. F. Mehl, C. S. Barrett and F. N. Rhines3 on the Widmanstätten structure in aluminum-rich copper

Jan 1, 1940

By Carl H. Samans

In their recent complete review of the subject of age-hardening,' R. F. Mehl and L. K. Jetter classify the main types of precipitation-hardening alloys under two headings, depending upon the nature of the precipitate and the character of the precipitation. In the alloys falling under the first heading, which display "continuous precipitation" and are typified by the aluminum-copper alloys, "precipitation seems to occur without much regard to grain boundaries and apparently at much the same rate at every point," although an acceleration in regions plastically deformed has definitely been established.2 In the second type of alloys the precipitation is "discontinuous," as in the copper-silver system for example, and "seems to start in restricted regions, primarily those contiguous with the grain boundaries, and to spread inward in an advancing wave." The reasons for the occurrence of these two greatly different types of precipitation are unknown, as are those for many other reactions that take place in the solid state. In the present paper only the first or "continuous" type of precipitation will be dealt with, for which a complete crystallographic mechanism has been worked out for the process of precipitation from a supersaturated solid solution of copper in aluminum. Based upon this mechanism, an explanation of the various property changes found experimentally will be developed in the second paper of this series. In later papers ('discontinuous precipitation" in copper-silver alloys will be explained, and an effort will be made to rationalize the two processes and types of precipitation. Crystallography of the Precipitation Process Through the extensive investigation by R. F. Mehl, C. S. Barrett and F. N. Rhines3 on the Widmanstätten structure in aluminum-rich copper

Jan 1, 1940

By G. A. Yuko, J. W. Barton, J. G. Parr

ALTHOUGH previous work1 has shown the compo- sition range of the complex face-centered cubic phase,2 Ti2Ni, to be narrow, no precise limits were established. The purpose of this investigation was to prepare homogeneous alloys on either side of the stoichio-

Jan 1, 1959

By Eckley B. Coxe

Having been appointed, on February 19th, 1890, a member of the Commission created by the Legislature of Pennsylvania for the purpose of investigating the " Waste of Coal Mining, with the View to the Utilizing of the Waste" (waste in this case referring specially to the small sizes of anthracite heretofore thrown away), my attention was naturally directed to the mash economical method of burning these small sizes.* Although I had been Familiar with the burning of anthracite for • many years, I found when I came to study the matter carefully that I was far from thoroughly understanding it, particularly with reference to the hurning of the smaller sizes, and that the literature of the subject, which was not very extensive, had more of a tendency to confuse than to enlighten me. I began therefore to investigate the subject so as to arrive if possible at some definite principles applicable to the question. With the aid of my assistant, Mr. John R. Wagner, I began at Drifton a series of experiments upon the burning of small anthracites. We first erected a small furnace with a grate 3 feet long and 2 feet wide, with which we experimented about two months. From the information thus acquired, we designed and built another furnace of about the same size, which gave us facilities for extending our investigations still further. After experimenting several months with the second furnace, we built a third one, which was much larger, having a grate area of about 68 square feet, which was exactly the size of the grate used in the boiler-plants of' Coxe Bros. &

Jan 1, 1894

By M. R. Klepper, H. Landsberg

Many of the sedimentary rocks contain small amounts of radioactive constituents. These vary in quantity in different layers. Some recent deposits show rather high activity as; for example, the deep sea oozes and some lake deposits.lv2 Measurements made in boreholes have also shown considerable changes in activity from horizon to horizon. The first to publish data on this fact was Ambronn,3 and recently Russian geophysicists have shown remarkable variations of activity from one layer to the next in various wells. Spak4 felt even that he was able to line up horizons from data measured in two neighboring wells.‡ The measuring of radioactive radiation is fairly difficult. Large errors are possible by the circulation of gaseous emanations in the well and porous strata. It is, therefore, never certain whether the activity of the layer where the instrumental device or collector is located will be measured, or that of some adjacent layer. For this reason it seemed to be advantageous to take samples of rocks into the laboratory and test them there for their contents of radioactive material. Such a method has been followed in the past to distinguish radioactive ore from other rocks. Radioactivity of rocks, especially of the igneous type, was also determined in the laboratory by numerous authors for absolute age investigations.= Corresponding data from studies of sedimentary formations are scarce. Specimens taken from a core of the Bradford oil sandstone were tested by Landsberg and Ingham,7 with the results illustrated in Fig. 1, which shows that within relatively small vertical distances the differences of relative activity were considerable. If one assumes that the distribution of radioactive material is fairly uniform throughout a layer, measurements of radioactive radiation in various horizons would offer additional information for stratigraphic

Jan 1, 1940

By M. R. Klepper, H. Landsberg

Many of the sedimentary rocks contain small amounts of radioactive constituents. These vary in quantity in different layers. Some recent deposits show rather high activity as; for example, the deep sea oozes and some lake deposits.lv2 Measurements made in boreholes have also shown considerable changes in activity from horizon to horizon. The first to publish data on this fact was Ambronn,3 and recently Russian geophysicists have shown remarkable variations of activity from one layer to the next in various wells. Spak4 felt even that he was able to line up horizons from data measured in two neighboring wells.‡ The measuring of radioactive radiation is fairly difficult. Large errors are possible by the circulation of gaseous emanations in the well and porous strata. It is, therefore, never certain whether the activity of the layer where the instrumental device or collector is located will be measured, or that of some adjacent layer. For this reason it seemed to be advantageous to take samples of rocks into the laboratory and test them there for their contents of radioactive material. Such a method has been followed in the past to distinguish radioactive ore from other rocks. Radioactivity of rocks, especially of the igneous type, was also determined in the laboratory by numerous authors for absolute age investigations.= Corresponding data from studies of sedimentary formations are scarce. Specimens taken from a core of the Bradford oil sandstone were tested by Landsberg and Ingham,7 with the results illustrated in Fig. 1, which shows that within relatively small vertical distances the differences of relative activity were considerable. If one assumes that the distribution of radioactive material is fairly uniform throughout a layer, measurements of radioactive radiation in various horizons would offer additional information for stratigraphic

Jan 1, 1940

By H. T. Clark, H. K. Work

The instrument for the rapid determination of carbon in steel, described in this paper, was developed originally to facilitate the operation of the pilot-sized open-hearth furnace in the Jones & Laughlin Research and Eevelopment Laboratory. In this small furnace, with its shallow bath, the drop in carbon is accelerated, and a rapid, reliable test for carbon content is indispensable. This problem becomes rather acute when it is desired to finish heats at a carbon content higher than can be estimated with any degree of accuracy by the fracture test. Several independent methods for determining carbon were investigated, therefore, and it was found that a relatively simple magnetic device could be made to give reproducible results. A laboratory instrument was designed and set up for the use of the furnace operators. It was tested exhaustively in the laboratory and was used with considerable success for following the carbon content in the furnace bath. As soon as sufficient data had been compiled to indicate that the instrument might have a wider application, a more rugged model was constructed and placed in the mill to be tested on commercial heats. Finally, about a year ago, instruments were furnished to the plant open-hearth shops, and these have been in use since that time. As a matter of convenience, the instrument has been named the "Carbanalyzer," and will be referred to by this designation in the following pages. $ Eaklier Investigations While by far the greatest number of magnetic investigations in which the carbon content of ferromagnetic materials was considered have had to do with the evaluation of the magnetic properties of steels of known

Jan 1, 1940

By H. K. Work, H. T. Clark

The instrument for the rapid determination of carbon in steel, described in this paper, was developed originally to facilitate the operation of the pilot-sized open-hearth furnace in the Jones & Laughlin Research and Eevelopment Laboratory. In this small furnace, with its shallow bath, the drop in carbon is accelerated, and a rapid, reliable test for carbon content is indispensable. This problem becomes rather acute when it is desired to finish heats at a carbon content higher than can be estimated with any degree of accuracy by the fracture test. Several independent methods for determining carbon were investigated, therefore, and it was found that a relatively simple magnetic device could be made to give reproducible results. A laboratory instrument was designed and set up for the use of the furnace operators. It was tested exhaustively in the laboratory and was used with considerable success for following the carbon content in the furnace bath. As soon as sufficient data had been compiled to indicate that the instrument might have a wider application, a more rugged model was constructed and placed in the mill to be tested on commercial heats. Finally, about a year ago, instruments were furnished to the plant open-hearth shops, and these have been in use since that time. As a matter of convenience, the instrument has been named the "Carbanalyzer," and will be referred to by this designation in the following pages. $ Eaklier Investigations While by far the greatest number of magnetic investigations in which the carbon content of ferromagnetic materials was considered have had to do with the evaluation of the magnetic properties of steels of known

Jan 1, 1940

By W. S. Gatley, F. C. Appl

This paper presents a combined analytical and experimental study of chisel penetration vs time during chisel impact on rock, a problem of fundamental importance in improving the performance of roller-cone bits or percussion drilling toots. For a given force-time relationship between chisel and rock, the problem of determining the penetration (displacement) vs time of the chisel is formidable. This is so because the rock is a nonlinear system with distributed mass and distributed damping (friction, dissipation of energy due to rupture, etc.). Since the literature does not contain adaptable solutions, the rock behavior to impact was simulated approximately by an "equivalent" lumped system, that is, an "equivalent" mass, spring, dashpot system. With this assumption, an analytical solution was found for chisel penetration vs time due to a sinusoidal load between chisel and rock. From this solution were found curves, in terms of dimension-less variables, for the maximum depth of penetration vs the frequency of the sinusoidal loading and for the energy transfer vs frequency. The results of this analysis were used to predict the penetration rate of rotary rock bits us rotary speed. The curve indicated that an optimum speed exists. To verify this analysis, an experimental apparatus was constructed and used to apply a sinusoidal pulse to a chisel penetrating a rock specimen under atmospheric conditions. Strain gauges were mounted on the chisel shank and a velocity transducer was mounted between the chisel and the rock surface. The velocity was integrated electrically and picked up simultaneously with the strain gauge signal on an oscilloscope. Permanent records were made photographically to provide simultaneous records of force us time and penetration us time. In comparing the experimental results for limestone and dolomite with the theoretical results, good agreement was found in the frequency range of the experiments. Unfortunately, the inertia effect (peak penetration) indicated by the theory occurs at a frequency much higher than could be obtained experimentally with the apparatus constructed. A "rate-of-loading" effect is indicated theoretically, but has not yet been verified experimentally. INTRODUCTION The process of drilling with percussion tools or rotary rock bits is basically related to the transient response of rock to surface impact. Each time a bit tooth contacts the rock, high stresses are developed which result in penetration and rock removal. As the tooth moves on, stresses are relieved and a new cycle begins as the next tooth contacts the rock. Thus the drilling process, which consists of an endless succession of these cycles, can be studied in terms of a single cycle. It is apparent, therefore, that the study of single-chisel impact on rock is fundamentally important in improving the performance of roller-cone and percussive-type drills. Previous studies in this area have been conducted by Simon1 and Hartman2 by means of drop tests. In these tests a chisel was attached to a weight and allowed to fall, due to the force of gravity, so that the chisel was driven into a rock specimen upon impact. Strain gauges were attached to the chisel shank and the resulting force-vs-time curves were recorded photographically from an oscilloscope screen. The depth of penetration and crater dimensions were also measured. These tests have provided much valuable information but, as mentioned by the investigators, have not provided complete information on the effect of "rate of loading'! This is partly due to the fact that the chisel motion during drop tests is not a controlled motion which can be varied in form and frequency. Therefore, it seemed that additional information could be obtained by studying chisel impact under conditions where both the motion and the frequency of loading could be controlled. This paper presents a combined analytical and exper-

By E. A. Gulbransen, K. F. Andrew

Weight loss measurements were made using a sensitive microbalance operating in a high vacuum system. The Langmuir equation was used to Calculate the vapor pressures of the several metals and alloys. Aluminum lowered the vapor pressure of i9,on in a 5.4 Al-94.6 Fe alloy, and of iron and chromium in a 4.8 Al-21.5 Cr-73.7 Fe alloy. The influence of oxide films formed on the alloys on the effective vapor pressures of the alloys was also studied. These studies were used to aid in the inte9,pretation of the high temperature oxidation of alloys based on iron, chromium, and aluminum. RECENT studies on the oxidation of chromium1 and the heat resistant alloy 5 Al-22 Cr-73 Fe showed transitions in the rate of oxidation at 900o and 1050oC respectively. The transition for chromium occurred at a temperature where the rate of evaporation of chromium from oxide-free surfaces equalled the rate of chromium atoms reacting with oxygen. This paper presents new vapor pressure studies on iron, chromium, and the specially prepared alloys 5.4 Al-94.6 Fe, 21.9 Cr-78.1 Fe, and 4.8 Al-21.5 Cr-73.7 Fe. The ternary alloy is similar in basic composition to the patented heat-resistant commercial alloy known as Kanthal. The binary alloys were studied to show the individual effects of aluminum on the vapor pressure of iron and of iron on the vapor pressure of chromium. The purpose of the proposed studies was to test the influence of metal volatility on the oxidation behavior of heat-resistant alloys based on iron, chromium, and aluminum. Since oxide films formed on the metal may limit metal transfer to the surface, the influence of oxide films on metal volatility was also studied. LITERATURE A) Vapor Pressure. The vapor pressure of iron has been studied by Jones, Langmuir, and Mackay,' Dornte and Nrton. Edwards. Johnston. and Ditmar. and McCabe, Hudson, and Paton. Stull and SinkeT have calculated a heat of sublimation at 298° K of 99.83 kcalper g atom. The vapor pressure of chromium has been reported by Bauer and Brunner,' Speiser, Johnston, and Blakburn, Gulbransen and Andrew,'' Vintaikin,o McCabe, Hudson, and Paton, and Kubaschewski and Heymer.12 Good agreement was obtained except for the early work of Bauer and Brunner.' Stull and Sinke7 calculate a heat of sublimation at 298°K of 95.0 kcal per g atom. Vapor pressure measurements on aluminum have been made by Brewer and Searcy,13 Bauer and Brunner,aand Farkas.I4 Stull and Sinke,7 giving Brewer and Seary's' data the most weight, derive a heat of sublimation of 77.5 kcal per g atom at 298 oK. B) Method. Two methods15 are used for measuring the vapor pressure of metals: 1) The Langhuir free evaporation method, and 2) the Knudsen effusion method, In the Langmuir method, used in the present work, the vapor pressure of the metal P is given by the equation: Here M is the molecular weight of the vapor species. T is the absolute temperature. (dw/dt) is the rate of sublimation in g per sq cm per sec and a is the condensation coefficient. a is a measure of the efficiency of condensation of molecules striking the metal surface from the vapor. If condensation results from each collision a is unity. This coefficient has been found to be unity,a, le for metals. These results establish the general validity of the Langmuir free evaporation method as applied to metals. EXPERIMENTAL A) Vacuum Microbalance Method. A modification of the Langmuir free evaporation method was used. Strip specimens were suspended from a sensitive microbalance operating inside of a high vacuum system. For alloys, microbalance methods17 must be used on large area samples at relatively low temperatures to minimize composition changes. The

Jan 1, 1962

By W. B. Nelligam, J. Tittman

Refinements in radiation logging techniques during recent years have involved increasing usage of scintillation ditectors. These detectors produce voltage pulses whose heights are related to the energies of the gamma rays which initiate them. Analysis of the gamma-ray spectrum, as indicated by the pulse heights, yields information about the chemical elements composing the formations surveyed. Refined scintillation counter techniques can furnish chemical information concerning earth formations in situ, from a study of the gamma-ray spectra emitted by the formation either naturally or as a result of neutron bombardment."' Accompanying the rising interest in gamma-ray scintillation spectroscopy, there has been increased activity in the development of accelerator-type neutron sources (in contrast to encapsulated chemical-mixture sources). Such neutron generators are attractive for several reasons: (1) they greatly reduce radiation hazards to personnel; (2) there is a great reduction in contamination danger if they are lost in the hole; (3) they can produce larger neutron intensities than can conveniently available encapsulated sources; and (4) they are capable of being pulsed, thus permitting new techniques in logging. In the past, both accelerator and encapsulated neutron sources have been used by others in conjunction with scintillation-detector pulse-height analysis. The results have not been too encouraging, due to the interference among different gamma-ray spectral lines and to the fact that the gamma-ray peaks were not too clearly distinguishable above the large and ill-defined background "noise".'.' This paper is a status report on laboratory studies of a technique using a borehole accelerator as a neutron source, which gives an improved scintillation spectrum, thus permitting more accurate chemical analyses of the formations penetrated. The Schlumberger-accelerator neutron source' is presented; the origins of inelastic and of thermal-neutron, capture gamma rays are dis- cussed, and results are given for some laboratory measurements performed in borehole geometry. THE NEUTRON GENERATOR-TUBE ACCELERATOR In the attempt to develop an accelerator neutron source which would have the desirable properties outlined in the "Introduction" and which would operate satisfactorily under borehole logging conditions, a small-diameter, cylindrical, neutron generator tube has been developed. This tube utilizes the principle of accelerating deuterons (heavy hydrogen nuclei) by a high voltage so that they bombard a tritium (heavy, heavy hydrogen) target. The resulting reactions produce large numbers of neutrons of 14 Mev energy. Furthermore, the tube is permanently sealed and, thus, the use of pumping techniques in the sonde is avoided. The tube consists of a pressure control, an ion source in which the deuterons are stripped of their electrons, an accelerating gap down which the deuterons are sped by the high voltage, a secondary electron suppressor and a tritium-loaded target. Obviously, the tube requires auxiliary circuitry in a sonde for the control of the ion source, tube pressure, high voltage and other operating variables. Neutron yields, both continuous and pulsed, have been produced under simulated field conditions in the range between 1 and 10 times those conventionally used in neutron logging applications. For the experiments discussed in this paper, neutron-pulse repetition rates in the range between 500 and 5,000 pulses/sec are adequate. Furthermore, by making suitable adjustments in operating conditions, one can vary the pulse width from a minimum of several microseconds up to dc. As will be seen later, the present application to well logging does not require that one have available pulses of neutrons which are appreciably shorter than the time it takes for fast neutrons to slow down to thermal energy in water. As a consequence, much of our interest has been directed towards the operating characteristics of the tube with pulses longer than about 10 microseconds in duration. Our experience to date shows that tubes can be operated in this manner with reasonably constant, average neutron outputs.

By E. Buehler, H. J. Levinstein

The temperature ranges in which the three inter-metallic phases in the Nb-Sn system form have been determined and the composition and structure of two of the three phases has been established. The kinetics of the formation of Nb3Sn in cored wire samples has been studied in the temperature range of 800° to 1050°C. From 800°to 950°C the rate of formation increases by four orders of magnitude. The rate-controlling step for the formation process in this temperature range appears to be the diffilsion of tin through NbSn. At higher temperatu~es a change occurs in the mechanism of the formation process such that up to a temperature of 1050°C the rate of formation of Nb3Sn does not increase above the rate observed at 950°C. For temperatures helow 950°C the current-carrying capacity of the wire increases with increased percent reaction reaching a maximum value when the formation process is 90 to 95 pct complete. The maximum current-carrying capacity obtainable in this temperature range is independent of the temperature. Above 950°C tlze current-carrying capacity obtainable in the wire decreases with increasing temperature of formation. A model is proposed which accounts for the ohserved behavior. RECENTLY, Buehler et a1.l reported the results of an investigation of the process variables which influence the superconducting properties of Nb3Sn-cored wire. These results indicated that at least four variables affect the properties of the manufactured wire. These include composition, particle size of the starting powder mix, temperature of heat treatment, and time of heat treatment. In order to understand completely the role of these variables, it is necessary to have an accurate knowledge of the phase equilibria in the Nb-Sn system. At the present time, phase-equilibrium diagrams for the Nb-Sn system have been published by a number of investigators.2-5 The diagrams differ as to the number of phases present, the composition of the phases, and the temperature range of stability of the phases. The present investigation was undertaken in order to resolve these differences. Since the investigation of Buehler et al. demon- strated that the length of time at the temperature of heat treatment affected the superconducting properties of Nb3Sn, it is apparent that it is necessary to understand the kinetics of the formation process as well as the equilibrium conditions before a complete understanding of the system is possible. As a result, the kinetics of formation of the various phases in the system were also studied in this investigation. EXPEFUMENTAL PROCEDURE Diffusion couples and sintered powdered compacts were employed in the phase-diagram investigation. The diffusion couples were made by filling 1/8-in.-ID monel-sheathed niobium tubes with tin. The monel sheath was employed to facilitate drawing.' The tubes were then drawn to a tin-core diameter of 32 mils. Samples approximately 3 in. long were then cut from the drawn composite. The tin was drilled out of the ends to a depth of 1/4 in. and niobium-wire plugs were inserted into the ends and peened over. The monel was removed by etching in concentrated nitric acid, after which the samples were sealed in evacuated quartz bulbs and heat-treated in a resistance-wound tube furnace. The samples were quenched into ice water upon removal from the furnace. The diffusion couple samples were examined metallographically employing a chemical etching solution consisting of 10 ml of saturated chromic acid per g of NaF. In addition, two anodizing solutions were used for phase-identification purposes. The first was the picklesimer7 solution; the second consisted of equal parts by volume of 30 pct H2O2 and concentrated NH4OH to which 1 g of NaF was added per 25 ml of solution. The anodizing conditions for the second solution were 2 v and 100 ma with a tin cathode. The powdered compacts were made by pressing previously mixed powders of 99.9 pct pure Sn and 99.6 pct pure Nb supplied by the United Mineral Co. into cylinders 3/8 in. in diameter by 1/2 in. long. The cylinders were then sealed in quartz tubes and heat-treated in the same manner as the diffusion couples. The samples were examined metallographically and by X-ray diffraction techniques. Since it was desirable to be able to correlate the kinetic data with current-carrying capacity, the type of specimen chosen for this part of the investigation had to be a compromise between the optimum system for studying kinetics and one which was suitable for making current-carrying capacity

Jan 1, 1964

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.&apos; The U. S. Bureau of Mines2-&apos; described and later improved the apparatus for a now widely used method generally known as the "Boyle&apos;s law" method. In the present form of the Washburn-Bunting method,&apos; the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle&apos;s law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle&apos;s law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle&apos;s law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

By H. D. Keiser

Minor industrial minerals included in this chapter are: the alum minerals, bromine, calcium chloride, epsomite and other natural magnesium salts, iodine, meerschaum, quartz, industrial crystals other than quartz, and nonfuel gases (air, helium, carbon dioxide). Alum Minerals The natural alums comprise a group of hydrated double sulfates, the most important of which are potash alum, KAI(S04)2.12H20, the "alum" of popular usage; ammonium alum, (NH4)AI(SO4)2, known mineralogically as tschermigite; and soda alum, NaAI(SO4)2.12H20. Kalinite, KAI(SO4)2.11H20, and mendozite, NaAl(SO4)2, 11H20, are fibrous monoclinic alums, distinct from the isometric species potash alum and soda alum.4 Alunite, KAI3(S04)2(OH)6, also known as alumstone or alum rock, has been used as a raw material in the manufacture of alum since early times. All the natural alums are highly soluble and occur as surface evaporation products in arid regions or in sheltered places. Potash alum, together with the other natural alums, commonly occurs as an efflorescence or crevice filling in argillaceous rocks and brown coals that contain disseminated pyrite or marcasite. The mineral is derived by the action of sulfuric acid, formed during the weathering of the sulfide, upon alkali-rich aluminum silicates. Ammonia alum is found chiefly in lignite or broad-coal beds and bituminous shales. Alunite is most commonly associated with acid volcanic rocks, where the rock has been largely altered and alunite formed owing to the presence of sulfuric acid solutions or vapors. Aluminum sulfate, which for most uses is the essential ingredient of alum, may be found in saline residues resulting from the evaporation of natural water and may be formed by the action of acid waters upon aluminous rocks. A deposit of natural potash alum occurs in an irregular network of veins associated with sulfur in rhyolite in Esmeralda County, Nevada, about 35 miles west of Tonopah and 10 miles north of Silver Peak. Alum was recovered at a plant operated on the property between 1920 and 1923 by crushing the ore to ¾ in., grinding to minus 80-mesh, and counter-current leaching; the resulting alum solution was then filtered and crystallized. Alunite was of much interest during World War I as a source of potash and during World War II as a source of alumina. The wellknown deposits at Tolfa, Italy, are veins in trachyte and have been the basis of alum manufacture there since the middle of the fifteenth century. Pure alunite is insoluble in water and in common acids, but if it is heated to 500°C it loses its water of hydration, and the residue consists largely of anhydrous potash alum, part of which is readily soluble in water or acids. If the heat is increased beyond 500°C, most of the sulfur combined with the alumina is released as oxides and the residue consists of potassium sulfate and alumina. Thus, either potash alum (and aluminum sulfate) or potassium sulfate and alumina may be made. In the

Jan 1, 1960

By D. H. Polonis, M. B. Kasen

AN unusual thermal etching phenomenon has been observed on the surface of a Cu-Si alloy. The observations were made during studies of vacancy condensation pit formation which were reported in previous papers.1,2 Figs. 1 and 2 are photomicrographs of the surface of a Cu-4.8 pct Si alloy after heating in vacuo (3 x X mm Hg) to 525°C and subsequently holding at that temperature for 16 hr in an impure (air-contaminated) argon atmosphere. Under these conditions preferential removal of silicon from the matrix by oxidation results in a surface which is entirely a phase overlying an a plus y structure. The light areas of Fig. 1 are regions in which very little thermal etching has occurred, while the majority of the surface has experienced severe etching. Similar regions in Fig. 2 are seen as plateaus above contours produced by net transfer of material from the specimen surface. Twin boundaries are also visible in Fig. 2. The difference in matrix mi-crostructure between Figs. l and 2 reflects the par- ticular orientation of low-index planes with respect to the surface of observation. Thermal etching contours of this type have been studied in detail by Hondros and Moore Both of the photomicrographs show that one or more dark spots are located approximately at the center of every protected area; where two spots are in close proximity, the protected areas have merged. The microstructures indicate that the anomalous resistance to thermal etching is related to the presence of these spots. Williams and Hayfield have shown that local regions of unusually high oxidation resistance can be caused by a surface monolayer of atoms with a work function higher than that of the base material. The result is an inhibition of the rate of electron removal from the base material and a decrease in the oxidation rate. The source of the protected layer may be either surface diffusion from contaminants on the specimen surface or pipe diffusion of solute atoms followed by migration across the surface. In the latter case the driving force is a difference in chemical potential resulting in a Gibbs adsorption phenomenon. In the present case, chemical polishing of the specimen surface precluded contaminants of a strictly surface nature. Consequently, diffusion of impurity atoms from within the lattice appears to be the most tenable explanation of the observed phenomena. The authors propose that the structures of Figs. 1 and 2 reflect the diffusion of impurity atoms along extended dislocations within the individual a phase grains prior to surface oxidation. The central spots within the protected regions are seen as sites of dislocation emergence which have become locally decorated with oxide in the manner discussed in Ref. 1. Williams and Hayfield observed protected regions adjacent to the grain boundaries of iron-contaminated copper which they attributed to the segregation of iron to the grain boundaries coupled with high dif-fusivity along the complex dislocation array at such boundaries. No evidence of such grain boundary protection was observed in the Cu-Si alloy; this

Jan 1, 1964

By C. E. Berry

Natural stone or manufactured porcelain pebbles are used as the grinding elements in pebble mills and the mills are lined with stone or porcelain blocks. Steel balls usually form the grinding medium in ball mills, and the mills may be lined with steel. Pebble mills are used to avoid contamination by metal of the material being ground, to avoid rapid wear due to corrosion, and for other specialized reasons. Belgian silex (silica) blocks formerly were used widely for lining pebble mills, because of their good resistance to wear, light color, and low cost, but the importation of these blocks was suspended early in the war. The stocks of Belgian silex diminished so rapidly that it was found desirable to compare the properties of a number of domestic substitutes for use in critical operations. Accordingly, a study was made to determine the best substitutes for fine grinding of white pigment and for certain heavy-chemical process work such as the disintegration of phosphate rock in weak phosphoric acid solution. A comprehensive survey of substitute lining materials was not contemplated. It was stipulated at the beginning of the investigation that only materials on the market, available in large quantities, would be tested and that these should be reasonable substitutes from a wear-resistance viewpoint as determined from known physical characteristics. Marble and limestone, for example, could be eliminated immediately. Quartzite, granite and porcelain were selected as likely substitutes for Belgian silex and were subjected to quality tests. Materials Tested 1. Belgian Si1ex.—Sample blocks of a standard grade were taken from crates in which they had been imported. The stone was light gray in color and contained inclusions of small clusters of quartz crystals as well as light colored portions that might be calcite. This was a siliceous rock which appeared to be of igneous origin. 2. Quartzite.—Samples of quartzite were obtained from a quarry in Minnesota. The blocks exhibited a crystalline fracture. The stone was pink in color and composed of fine quartz crystals bound together with a siliceous cement. 3. Granite A was a fine-grained granite quarried in South Carolina. 4. Granite B was coarse-grained granite quarried in South Carolina. 5. Granite C was a coarse-grained granite quarried in North Carolina. 6. Porcelain A.—Sample blocks of the pebble-mill lining material were obtained direct from the manufacturer. It was white in color and of lower specific gravity than the natural materials. It did not have a crystalline structure. 7. Porcelain B.—Sample pebble-mill lining blocks of the porcelain were received direct from the manufacturer. It was white

Jan 1, 1947

By C. E. Berry

Natural stone or manufactured porcelain pebbles are used as the grinding elements in pebble mills and the mills are lined with stone or porcelain blocks. Steel balls usually form the grinding medium in ball mills, and the mills may be lined with steel. Pebble mills are used to avoid contamination by metal of the material being ground, to avoid rapid wear due to corrosion, and for other specialized reasons. Belgian silex (silica) blocks formerly were used widely for lining pebble mills, because of their good resistance to wear, light color, and low cost, but the importation of these blocks was suspended early in the war. The stocks of Belgian silex diminished so rapidly that it was found desirable to compare the properties of a number of domestic substitutes for use in critical operations. Accordingly, a study was made to determine the best substitutes for fine grinding of white pigment and for certain heavy-chemical process work such as the disintegration of phosphate rock in weak phosphoric acid solution. A comprehensive survey of substitute lining materials was not contemplated. It was stipulated at the beginning of the investigation that only materials on the market, available in large quantities, would be tested and that these should be reasonable substitutes from a wear-resistance viewpoint as determined from known physical characteristics. Marble and limestone, for example, could be eliminated immediately. Quartzite, granite and porcelain were selected as likely substitutes for Belgian silex and were subjected to quality tests. Materials Tested 1. Belgian Si1ex.—Sample blocks of a standard grade were taken from crates in which they had been imported. The stone was light gray in color and contained inclusions of small clusters of quartz crystals as well as light colored portions that might be calcite. This was a siliceous rock which appeared to be of igneous origin. 2. Quartzite.—Samples of quartzite were obtained from a quarry in Minnesota. The blocks exhibited a crystalline fracture. The stone was pink in color and composed of fine quartz crystals bound together with a siliceous cement. 3. Granite A was a fine-grained granite quarried in South Carolina. 4. Granite B was coarse-grained granite quarried in South Carolina. 5. Granite C was a coarse-grained granite quarried in North Carolina. 6. Porcelain A.—Sample blocks of the pebble-mill lining material were obtained direct from the manufacturer. It was white in color and of lower specific gravity than the natural materials. It did not have a crystalline structure. 7. Porcelain B.—Sample pebble-mill lining blocks of the porcelain were received direct from the manufacturer. It was white

Jan 1, 1947

By Edwin R. Walker

The old adage, " Necessity is the mother of invention," is fully borne out in the case of the device described in this paper. About four years ago the firm of the writer received instructions from Sir John Hawkshaw, C. E., and I. Wolf Barry, Esq., C. E., to construct and erect three large Guibal fans for ventilating a portion of the Metropolitan and District Underground Railway, of London. On account of the cost of coal and the very limited space for boilers, it was arranged that the fans should be driven by gas-engines. Those who have had experience with Guibal fans will be aware that as each blade or vane passes the lower edge of the shutter a pulsatory action takes place. When the fans above mentioned were set to work, the pulsation or vibration of the immense volumes of air discharged was so great that it caused a corresponding vibration of the window-sashes, doors, etc., of the surrounding buildings; and this was so unpleasant that the shopkeepers and others near obtained an injunction against the railroad company, compelling it to stop one of the fans. The work was by this time out of our hands, and we only casually heard what had taken place, learning also that, in addition to this injunction, another was threatened in the case of the second fan, and that the railroad company had thus far escaped the enforcement of this threat by agreeing to run the second fan at a few short stated intervals only during each day. In considering the case, it occurred to us to incline the lower edge of the shutter, instead of making it parallel with the axis of the fan,. by which means we thought that the waves of air might be broken

Jan 1, 1891