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By W. R. Hibbard, J. D. Nisbet

The high temperature properties of Fe-Cr-Co-Ni base alloys and the effects of hardening element additions on these properties are rationalized on the basis of general principles of alloying. DURING the past few years the base elements in high temperature austenitic alloys have gradually been changed from iron-rich materials to nickel-rich, then to cobalt-rich and more recently to various iron, cobalt, and nickel combinations, all with an approximately constant chromium content of 20 pct. Concurrently, the hardening additions of the incongruous* elements, have been shifted from small amounts of a single element to various ratios of molybdenum, tungsten, columbium, carbon, titanium, and aluminum with the percentages of these constituents continually increasing. It has been known that the typical soft high temperature alloy (such as Inconel) consisted of face-centered cubic austenite, but the effect of varying the composition of the base elements, iron, chromium, nickel, and cobalt, has not been broadly analyzed. Therefore, it was reasoned that the first major problem in the understanding of the properties or the further development of high temperature alloys was to study systematically the effect of composition upon the mechanical properties of face-centered cubic Fe-Ni-Co-Cr austenitic solid solutions. The matrix of the strong high temperature alloys (such as Inconel X) is usually also a face-centered cubic solid solution of iron, nickel, chromium, and cobalt but with additional phases which can be generally classified as intermetallic compounds and carbides. It is usually observed that combinations of the hardening elements, tungsten, molybdenum, columbium, tantalum, titanium, aluminum, carbon, and others have been used in these strong high temperature alloys. Thus, it was reasoned that a second major problem in studying these alloys was to understand the effect on mechanical properties of adding

Jan 1, 1954

By Paul Gordon

It is shown that equations for grain-boundary migrntion given by Gordon and Vandermeer, based on a theory first advanced quantitatively by Lucke and Detert, satisfactorily explain recent data on both GRAIN boundary migration in recrystallization and in postrecrystallization grain growth has been the subject of extensive studies for many years. Only solute-independent and solute-dependent boundary migration during recrystallization in zone-refined, poly crystalline aluminum, and during grain growth in zone-refined tin. with the advent of zone-refining, however, has it been possible to carry out such studies on high-purity metals, and thus to delineate quantitatively the major effect On the migration rates of very small percentages of dissolved imPurities. Earlier exPerimental work almost invariably gave migration rate parameters which disagreed with theoretical predictions

Jan 1, 1963

By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.' A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.' After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By J. H. Brophy, A. L. Prill, H. W. Hayden

An error lzas been found in the conventional way of determining the time exponent of linear shrinkage for the solution-precipitation stage of liquid-phase sintering. Large amounts of shrinkage due to initial rearrangenzent result in erroneously low exponents and tni si dentification of the rate-controlling process. Two alternative, mathematically correct, methods of calculation are applied to existing data on Fe-Cu, WC-Co, and Tic-Ni-Mo. This results in reidentifi-cation of the rate-controlling process and somewhat better agreement with related data. In each case the solution-precipitation process is solution-controlled and not diffusion-controlled. THE liquid-phase sintering process has been the object of a considerable amount of research for many years. Linear shrinkage vs time data at various sintering temperatures have been used recently in an attempt to identify the prevailing mass-transport processes in a number of metallic and nonmetallic systems. There is an analytical error inherent in the methods previously used for handling data during the "solution-precipitation" stage of shrinkage which must be recognized before the correct rate-controlling processes can be determined. It is the purpose of this paper to show how the error has affected previous conclusions and to suggest corrections. A number of mechanisms have been proposed to explain experimental observations during sintering in the presence of a liquid phase. The earliest of these is due to Price, Smithells, and williamsl who attributed the observed growth of the solid phase to the simultaneous solution of smaller particles and growth of larger particles. From the work of Lenel et al.2,3 and Gurland and Norton4 has come the suggestion that the liquid-phase sintering process may be divided for analysis into three steps: 1) rearrangement upon formation of the liquid phase; 2) solution and reprecipitation of the solid phase in the liquid; and 3) "coalescence" or a final stage of sintering, characteristically slower than the solution-precipitation process. The sequence of steps is shown schematically in Fig. 1. Kingery5 presented a thermodynamic and kinetic analysis of the first two "stages" of the liquid-phase sintering process in which the functional dependence of lineal shrink- age on time at temperature was used to identify the rate-controlling mass-transport process. Table I summarizes the time dependences and processes considered by Kingery.5 This method of data presentation has been employed by Kingery and coworkers for Fe-CU,6 WC-Co, and a number of nonmetallic systems," and bv Whalen and Humenik for Tic-Ni-Mo and Fe-cu.8 In each of these studies, the rate-controlling step during the "solution-precipitation" stage was identified from the slope of the curve in that stage on a logarithmic plot such as Fig. 1. However, in all of the previous studies, at a certain composition, relatively large amounts of shrinkage due to rearrangement preceded the solution-precipitation stage. Under these conditions, the larger the amount of rearrangement shrinkage the

Jan 1, 1965

By C. E. Birchenall, J. R. Stubbles

ThE equilibrium between lead, lead sulfide (PbS), and atmospheres of H2 and H2S has been determined previously by Jellinek and Deubel,' and SudO.' Blbem and Kroger3,4 used Jellinek's data to calculate the sulfur dissociation pressures of PbS crystals (of

Jan 1, 1960

By Stanley L. Lopata, Eric B. Kula

SEVERAL methods are available for determining pole figures by X-ray means.' The earlier film methods have been replaced by techniques in which the intensities are measured by Geiger counters on an X-ray diffractometerZm7. These methods utilize either flat transmission or reflection samples,214°8 cylindrical specimens,3 or spherical specimens.7 A single transmission or reflection sample will not yield information over the complete pole figure. The cylindrical specimens suggested by Nortod and the spherical specimen of Jetter and Borie7 have the advantage of allowing the whole pole figure to be obtained without any corrections to the intensity for absorption, There is a lower limit to the size of sheet which can be conveniently studied, however, and sample preparation can be rather tedious. Probably the most common method today for determining the complete pole figure is that developed by Schulz. A flat reflection sample is used for determining the pole figure from the center out to about 70". Because of the geometry of the system used, little or no correction for absorption or irradiated volume is necessary.4'6 A separate transmission sample is used for the region near the edge of the pole figure. This procedure requires two separate samples, one of which must be a thin carefully-prepared transmission sample. Furthermore, since the reflection and transmission data are in different arbitrary intensity units, a region of overlap must be obtained, and the intensity data from one set of measurements converted to units of the other. These are serious disadvantages of this method, and they point out the need for a simplified procedure. Since the reflection technique can be used for planes whose normals lie up to about 70° from the sample surface normal, it is apparent that a complete pole figure can be obtained by reflection alone if sample surfaces are cut at oblique angles to the rolling plane Specifically, if a rolled sample is cut so that the normal to the surface formed lies equidistant (54" 44') from the rolling plane normal, rolling direction, and transverse direction, then complete information for one quadrant of the pole figure can be obtained by reflection from the surface. Fig. 1 shows this oblique surface, as well as the position of the pole of this surface in the pole figure. When a surface has been cut oblique to the rolling plane, the standard polar stereographic net is inconvenient to use, and it would be more desirable to have the center of the net coincide with the pole of the oblique plane. Fig. 2 shows such a net, where the center has been offset 54' 44' to correspond to a specimen cut as in Fig. 1. This net was in effect obtained by rotating a standard polar stereographic net 54" 44' with the help of a Wulff net. With the experimental setup used. a sample can be cut from plate of 1/2-in. thickness or br Gen- erally thinner sheet is under investigation, and a composite specimen must be used. A convenient procedure has been to bond together, using epoxy resin, sufficient sheets to form a cube. These are clamped in a vise, and when dry, the whole vise is rotated and a flat surface ground at the required angle. The sample is then mounted inside a larger steel ring using Koldmount, the backside ground flat and parallel to the approximate desired thickness. The sample is then polished and etched to remove any effects of cold working during grinding. With this method only one quadrant of the pole figure is obtained. Often pole figures show symmetry around the rolling and transverse directions, and any slight asymmetry is due to scatter. Should the pole figure not be symmetrical, four oblique surfaces, corresponding to the four quadrants of the pole figure, would have to be examined. In most cases there is symmetry at least around the rolling direction, which reduces to two the number of quadrants to be investigated. For many purposes all that is required is an average polefigure for the four quadrants. This canreadilybe obtained with composite specimens of sheet material, where sheets Corresponding to each of the four quadrants can be intermixed. The four quadrants can be obtained by considering sheet in the normal position, and by rotatiolls of 180" around the sheet normal, the rolling direction, and the transverse direction. If desired, the whole thickness of the sheet can be used, yielding an average of the surface and interior textures; or the surface material can be removed from each sheet, resulting in a pole figure for the center alone. Eugene S. Meieran of the Massachusetts Institute of Technology has independently developed the same method. His results, adapted to a pole figure goniometer with a specimen spiraler, will be described in another publication.

Jan 1, 1962

By Paul A. Farrar, Harold Margolin

The system Ti-Cr has been re investigated From 40 to 100 pct Cr. The high-temperature modification of TiCr, was found to exist in the temperature range from 1365 where it terminates in the eutectoid reaction TiCr,(TI)* — HE chromium-rich region of the Ti-Cr system was investigated by Vogel and Wenderott,' Mc Quillan,' Van Thyne et dl.,' and Cuff Duwez and Taylor determined the crystal structure of the low-temeperature modification of TiCr, to be fcc a = 6.943A and Levinger' discovered the existence of a second (high-temperature) modification of TiCr, and determited its crystal structure to be hexagonal a = 4.932A, c/a = 1.617i. No information was obtained as to the temperature range over which each modification of TiCr? existed; therefore the present investigation was initiated. I) Experimental Techniques Alloys employed for the delination of this system were prepared from iodide titanium and high-purity chromium. The purity of these materials is as follows: Iodide titanium: purity 99.99 pct; major impurities—carbon 0.0001 pct; oxygen 0 to 0.002 pct; nitrogen 0 to 0.002 pct; silicon 0 to 0.005 pct; manganese 0.001 pct; copper 0.001 pct (Foote Mineral Co., Lot 609-29). Chromium #1: metallic purity 99.997 min.; interstitial content—oxygen 0.27 to 0.46 pct; hydrogen 0.028 to 0.038 pct; nitrogen 0.0002 pct (Ave-quipo Inc.). Chromium #2: purity 99.9 pct; major impurities—carbon 0.01 pct; oxygen 0.013 pct; nitrogen 0.02 pct; silicon 0.01 pct; sulfur 0.03 pct; iron 0.01 pct (Fulmer Research Institute Ltd.). A total of sixteen alloys of thirteen different compositions was prepared in the range from 40 to 95' *All percentages are given in weight percent. pct Cr. The compositions of the alloys prepared were as follows: Ti-40, 45, 50, 60, 62, 64, 66, 68, 70, 80, 85, 90, and 95 pct Cr. Two buttons were prepared of the 66, 90, and 95 pct Cr alloys. The 40 pct Cr and one of the 66 pct Cr alloys were prepared from the chromium # 2. All the other alloys were prepared from chromium #1. The alloys were arc-melted as 25-g buttons in a copper-hearth glass-walled furnace7 under an inert atmosphere of high-purity helium. The alloys were sintered at 250 amp and melted twice at 350 amp for 30 sec with the buttons being turned over between melts. Weight losses during melting were determined and in the range 45 to 68 pct Cr they were found, in all cases, to be less than 1.25 pct of the total alloy weight. A number of the high-chromium alloys shattered during cooling from either the first or second melt, which made the weight loss considerably larger than usual. The 70 and 80 pct alloys lost approximately 5.7 pct of their total weight, the 85 pct alloys 1.5 pct, the 90 pct alloy 2 pct, and the 95 pct alloy 3 pct. However, it is felt that the actual composition of the alloys in this region is probably within approximately 1 pct of the intended composition, as a large portion of the material lost was that due to shattering after melting. Nominal compositions were therefore used in plotting data and referring to the alloys. The alloys were cut into specimens, wrapped in molybdenum sheet, and encapsuled in argon-filled quartz or Vycor tubes for heat treatment. The heat-treatment times and temperatures are given in Table I. The specimens were quenched in iced brine (I.B.Q.) following heat treatment. The standard techniques of grinding, polishing., and etching were used in preparing the specimens for metallo-graphic examination. For alloys below 68 pct Cr

Jan 1, 1963

By Paul A. Farrar, Felix Ermains, Harold Margolin

The systems Ti-Crand Ti-Vhave been reinvesti-gated in the region up to 40 wt pct alloying addition using both conventional and rapid quenching techniques. The Ti-Cr eutectoid temperature was determined to be at 667° & 10° C and 14.5 wt pct Cr. The solubility of the Cr in a Ti was found to be less than 1 pctat 700"C. The P transus of the Ti-V system was found to be depressed to 510°C at 40 wt pct V and the solubility of V in a Ti was found to be less than 2 wt pct at 700°C. Investigation by a. d. McQuillan1-3and m. k. McQuillan4 on the systems Ti-Co, Ti-Cr, Ti-Cu, Ti-Fe, Ti-Mn, Ti-Ni, and Ti-V has cast doubt as to the position of the ß/a + ß boundaries in many of these systems. Their investigations were carried out using hydrogen pressure and/or rapid quenching experiments, as opposed to the conventional quartz capsule techniques employed by most other investigator.'" By these methods, the ß/a + ß boundary was found to be lower than that obtained by conventional techniques in all except the Ti-Fe system. In the latter, the ß/a + ß boundary was essentially the same as the boundary obtained by conventional technique.7' On the basis of rapid quenching results in the Ti-Cr system, M. K. McQuillan4 placed the eutectoid temperature below 550°C whereas other investigations using conventional techniques had placed the eutectoid variously as between 650' and 700°C,5 between 675' and 700°C,6 between 650" and 675°C,7 at 670°C,8 and above 625"C.la9l3 In order to check these results, a reinvestigation of four of the systems was undertaken using both conventional and rapid-quenching techniques. The Ti-Fe and Ti-Mn systems will be dealt with in anoth er paper, with only the Ti-Cr and Ti-V systems being discussed here. EXPERIMENTAL TECHNIQUES Alloys employed for the delineation of the systems under investigation were prepared from iodide titanium sheet capsules containing the alloying materials,

Jan 1, 1962

By Roger N. Dokken

It is well-known1-4 that Fe-Si alloys from approximately 9 to 27 at. pct Si show an ordered structure of the Fe3Si type at room temperature. Recently Meinhardt and Krisement,' through an investigation of Fe-Si alloys at room temperature by neutron diffraction, discovered that at 10.8 at. pct Si ordering of the FeSi type occurs while above this composition the normal Fe3Si-type superstructure appears. This FeSi type of ordering was also found by Davies8 as indicated by X-ray diffraction measurements on an Fe-8.7 at. pct Si alloy. Meinhardt and Krisement7 extended their neutron-diffraction work and determined the phase-boundary temperatures for both FeSi- and Fe3Si-type ordering. Ordering phenomena can also be studied by resistance measurements.4,8-11 Krivoglas and Maty-sina" carried out a theoretical development of the

Jan 1, 1965

By E. C. van Reuth

FIFTY-three alloys have been examined in the Fe-W and Co-W alloy systems in an attempt to verify the finding of o phases in these systems as reported by Goldschmidt.' The alloys were examined metallographically and by X-ray diffraction. The 10-g specimens were made by powder metallurgy techniques. Very fine, high-purity powders were compressed in a double-acting die at 120,000 psi after hydrogen reduction. All compacts were then sintered for 200 hr at 950°C in a helium atmosphere. Metallographic investigation and X-ray diffraction proved this time to be sufficient to allow complete homogenization before the subsequent high-temperature anneal. Each specimen was then sealed into an evacuated silica capsule and annealed at 1400"or 1500 C (except two) for 25 hr. (The 60 pct Fe and 55 pct Co alloys taken to 1610"and 1680°C respectively were held at these temperatures for 1hr. However, since these structures were at equilibrium before the anneal, and in view of their resultant structures, it is assumed that they reached equilib-

Jan 1, 1960

By Wilhelm in der Schmitten

A necessary condition for a uniaxial stress distribution in compression testing is that the specimen end surfaces make full contact with the apparatus compression plates. In addition all compression surfaces must be machined perpendicularly to the loading axis. In general this condition is not sufficiently fulfilled in a simple apparatus. Therefore on application of the load the compression plate may first touch the specimen at one point only. This may cause crumbling of the specimen if the material under investigation is brittle (e.g., ionic crystals). It also precludes a precise study of the beginning of deformation as the effective cross sectional area is unknown. In addition a complex stress state is set up which renders quantitative work impossible, e.g., on dislocation density and arrangement as a function of stress. To overcome these difficulties a "self-adjusting" upper compression plate is required. A simple and reliable method of achieving this is shown in Fig. 1: A steel hemisphere is placed on the specimen. As soon as the compression plate (which no longer needs precise machining) makes contact with this hemisphere the load is uniformly distributed over the whole specimen surface, and a homogeneous uniaxial state of stress results. An advantage of the method is that the loading is always central, even when the specimen surface is not parallel to the compression plate (Fig. 1, dashed line). Therefore to a first approximation a uniaxial state of stress is maintained if the misorientation of the specimen end surface is small. Two typical stress strain curves of identically prepared sodium chloride crystals are shown in Fig. 2; curve 1 was taken without and curve II with the hemisphere under otherwise identical conditions. The improvement in the accuracy of defining the beginning of elastic and plastic deformation is clearly indicated. The writer wishes to thank the Deutsche Forschungsgemeinschaft for financial support, and Professor P. Haasen for providing facilities for this work.

Jan 1, 1962

By J. E. Hilliard, H. E. Cook

It is shown that for systems having a miscibility gap the spinodal composition (c,) in the vicinity of the critical temperature (Tc) is related to the equilibrium composition (c,) by where cc is the critical composition. This expression is exart for the limit T — Tc and is a good approximation down to (T/Tc) - 0.9. If the miscibility gap meets the composition of the pure components THE recent theoretical treatment by cahn1,2 on spinodal decomposition of solid solutions has revived interest in methods of estimating the chemical spinodal, * i.e., the locus on a binary phase By use of the appropriate expression, the spinodal can be drawn on the Phase diagram almost by inspection with an accuracy comparable to that of lengthy calculations in which a free-energy function is fitted to the phase diagram. Satisfactory agveemenf is also obtained with spinodals comPuted from experimental free-energy curves. where G is the Gibbs free energy of the homogeneous solution and c the atomic fraction of component 2, the derivative being evaluated at constant temperature (T) and pressure (P). (These subscripts will hereafter be omitted from the partial derivatives.) If experimental measurements of G as a function of c and T are available in a single-phase region above the spinodal, then these can be extrapolated to obtain a series of metastable free-energy isotherms in the two-phase region, and from these isotherms a series of spinodal compositions can be calculated. Because the value of is very sensitive to experimental errors, an elaborate analytic procedure is required for

Jan 1, 1965

By P. M. Kelly

TWO analytical methods for calculating the positions of matrix and twin reflections on electron-diffraction patterns of a twinned cubic crystal have recently been published.1,2 Meieran and Richman1 considered the case of twinning on (1 12) in a bcc structure, while a more general treatment, capable of analyzing twinning on any plane in a cubic crystal, was developed by Johari and Thomas.2 The latter authors applied their general rotation matrix to both (111) twinning in face-centered crystals and {112} twinning in body-centered crystals and they derived separate expressions for these two cases. This separate treatment masks the fact that in a holosymmetric cubic crystal a (111) twin is crys-tallographically equivalent to a {112} twin.3 This is analogous to the crystallographic equivalence of rotation and reflection twins in centrosymmetric crys tals. A particularly simple example of this equivalence occurs when the two twin planes are perpendicular to each other—for example (111) and (112). Then, if twinning on (111) moves a point P to a new position P1, and twinning on (112) moves P to P2, P1 and P2 will be related to each other by a 180-deg rotation about [110]— the direction normal to both (111) and (112). Since there are diad axis axis along (110) direction in a holosymmetric cubic crys tal the two positions P1 and P2 must be crystallo-graphically equivalent. In other words if a particular pole (hk l) is in a position P1 after twinning on (Ill), then after twinning on (112) a pole of the type {hkl}—but not the particular pole (hk1)—will also be in the position P1. As a result, when only the general (as opposed to the particular) indices of poles after twinning are required, twinning on (111) gives the same results as twinning on (112). To convert the results for a (111) twin to those applicable to a (112) twin, when the particular (as opposed to the general) indices of poles after twinning are required, all that is necessary is to multiply the indices of the twin poles by the matrix for 180-deg rotation about [lie], i.e., The analytical methods suffer the disadvantage that a new set of calculations must be performed for each different diffraction pattern or, as is done in the Meieran and Richman treatment,1 a lengthy list of the location of the twin spots in reciprocal space must be prepared. All the tedious computation involved in these analytical approaches can be avoided by simply plotting, on tracing paper, a stereographic projection of a crystal twinned on say (112). By superimposing this twin stereogram on a standard (001) projection (preferably with the points and indices in a different color from those on the twin stereogram) the relative positions of both matrix and twin reflections can be determined by inspection. Alternatively, a composite projection can be

Jan 1, 1965

By W. E. Newell

The basic principles and assumptions involved in D. L. White's solution5 for ultrasonic wave amplification in piezoelectric semiconductors are summarized. If the gain per unit length is maximized at each frequency without regard to the drift-field power density, the gain increases linearly with frequency. Therefore it would seem that very high gain is possible for frequencies in the hundreds of megacycles. However, with present materials the resulting drift-field power density is so large that cooling would be a major problem. For this reason it is more realistic to judge the capabilities of an ultrasonic amplifier in terms of the gain that is possible with a specified power density. In this case the gain at high frequencies does not increase but decreases more rapidly than l/f. The calculation of the gain us frequency at a fixed power level involves the repeated solution of a cubic equation and is therefore tedious. For the purpose of comparing different materials, sufficient accuracy can be obtained from an approximate solution which may easily be plotted as three straight lines on logarithmic graph paper. This method is used to compare the Performances of CdS, CdSe, ZnO, and GaAs. At a power density of 10 watts per cu cm, the first three give maximum gains of 60 to 80 db per cm in the vicinity of 60 megacycles. At the same power density, GaAs has a maximum gain of about 7 db per cm near 150 megacycles. Although an increase in mobility usually increases the gain for a specified power density, it is shown that there is an optimum mobility above which the gain decreases. An approximate expression for the optimum mobility is established. It is well-known that the interaction between charged particles and an electromagnetic wave can be used to amplify the electromagnetic wave. In the conventional traveling-wave tube, electrons in a vacuum are caused to move at a velocity slightly greater than the wave velocity, thereby coupling energy into the wave.' In principle, the same effect would be evident in a solid except that repeated collisions prevent the electrons from attaining a velocity greater than that of an electromagnetic wave. However, the drift velocity of electrons can be made to exceed the velocity of an acoustic wave in a solid. In 1956, weinreich2 noted that the deformation potential provided one means of coupling energy from drifting electrons into an acoustic wave, but the effect was too small to be of any practical importance. It was not until 1961 that White and Hutson demonstrated that the piezoelectric effect provided a strong enough coupling to give appreciable amplification of an ultrasonic wave and awakened wide interest in electron-phonon interactions. Qualitatively the effect may be described as follows. An acoustic wave propagating through a piezoelectric material is accompanied by an electric-field wave. If the vibrations are properly oriented with respect to the crystal axes of a piezoelectric semiconductor, the local electric fields are axially directed and cause bunching of the charged carriers. If the drift velocity of these carriers is less than the velocity of sound, they tend to be dragged along by the acoustic wave. This electroacoustic effect results in a net potential appearing across the material and in attenuation of the acoustic wave. On the other hand, if the drift velocity exceeds the velocity of sound, energy is coupled from the carriers to the acoustic wave and amplification results. Related effects which are being investigated include ultrasonic amplification in semimetals6-' and semi-conductor, and current saturation in piezoelectric semiconductors.'4-17 There are various problems which hinder the immediate application of ultrasonic amplification in a practical device. First, there are the traditional problems encountered in the design of acoustic delay lines: attenuation in the electromechanical transducers, reflected waves (which can lead to self-oscillation in an amplifying device), mechanical tolerances necessary to maintain phase coherence, and so forth. Second, there is the problem of selecting the best material from among the various piezoelectric semiconductors as they become available in single-crystal form with a wide choice of characteristics. This paper deals with the second problem and shows that the most realistic way of comparing materials is in terms of the gain which can be obtained without exceeding a

Jan 1, 1964

By P. Schwarzkopf, J. H. Brophy

A modification of the Mendenhall wedge blackbody1 has been used to determine solidus temperatures and to anneal alloys in the tantalum-rhenium binary system. The technique has proven to be simple and accurate with modest power requirements. For temperatures up to 2800° C a piece of 10-mil tantalum sheet was folded double and formed as shown in Fig. 1. The middle of the resulting ribbon filament was a cylindrical-shaped crucible with less than a 1/8-in. opening. After inserting a specimen in the cavity, the filament was clamped between molybdenum electrodes in a high vacuum chamber. A representative filament 2 in. long and % in. deep was heated to 2800°C with a current of 700 amp at 4 v. The specimen temperature was determined by sighting into the cavity with a Leeds and Northrup optical pyrometer. The twisted filament shape was necessary to avoid serious geometric changes during thermal expansion. For temperatures between 2800" and 3000°C a 4-mil tungsten filament was employed. To facilitate fabrication it was warm-folded, and a twisted segment of 10-mil tantalum was used to support one end to absorb thermal expansion. This element assembly required about 700 amp at 10 v to reach 3000°C. Two geometric modifications of the filament were helpful for solidus temperature determinations. A shallow chamber, with depth to opening ratio of 3 to 1, permitted direct observation of the specimen through the optical pyrometer. The fact that the specimen was visible permitted the melting point to be determined when sharp features on the specimen surface became rounded; it also indicated that blackbody conditions did not prevail. By standardizing against the melting point of molybdenum, the observed melting temperature was corrected by the following form of Wien's Law: in which T is the true temperature, To is the observed temperature, and K is a constant characteristic of the filament geometry and determined experimentally for the molybdenum standard. The resulting corrected melting point for each alloy served as a reference temperature for the second more precise filament geometry. With a 6 to 1 depth to opening ratio, the specimen was indistinguishable from the filament interior, indicating good blackbody conditions. Using this technique, a series of specimens was isothermally treated at temperatures above and below the corrected direct reading. Incipient melting was detected by visual or micrographic examination of the specimen after cooling. This procedure was checked with specimens of pure chromium, molybdenum, and tantalum. Table I represents the values obtained, together with the solidus temperatures in the tantalum-rhenium binary system determined by the same technique. The alloy specimens were approximately 1/8 in. in diam. They were pieces of 10-g buttons melted four times in a nonconsumable tungsten electrode arc furnace on a water cooled copper hearth in 2/3 atmos of titanium gettered helium. Several sources of error are possible in such temperature measurements. Within the accuracy of the pyrometer no gradients were detectable near the specimen, and element distortion was virtually eliminated by twisting the tantalum. Compensation was made for the 1/8-in. sight glass by inserting several identical thicknesses and extrapolating to zero thickness. As a result an additional 10°C correction was added to all observations in the temperature range of 2500" to 3000°C. The principal source of error was then in the operation of the

Jan 1, 1961

By L. F. Mondolfo

An investigation of the relationship between properties of the elements and type of binary diagram formed was conducted. It was found that, for each type of equilibrium diagram, the factors for the size, valence, electronegativity, period, melting point, entropies of fusion, and sublimation calculated for each pair of elements cover a range of values. However, these factors show sufficient relationship to the equilibrium diagram so that the correlation of several of them can be used to predict the type of diagram formed, or at least limit the choice to only a few types. ThE goal of the metallurgist concerned with alloy development has always been to find a method that predicts the properties that can be obtained when a certain metal is added to another one. In most cases a qualitative predictiton of properties can be made if the equilibrium diagram is known. However, this means that for new metals the alloy development has to start with the experimental determination of the equilibrium diagrams. Because this determination is at least as complicated and time-consuming as the determination of the properties themselves, most alloy development has taken place by trial and error, and the study of the equilibrium diagrams has followed rather than preceded the creation of new alloys. Alloy structures and properties depend on the interaction between electrons and a complete knowledge of these interactions would permit prediction of structure and properties of alloys. Unfortunately direct measurement of these interactions is extremely difficult and somewhat doubtful and only properties that depend on them can be measured easily and with certainty. Study of the relationship between properties of the elements and equilibrium diagrams is not new. Besides the well known Hume-Rothery rule of the necessity of an atomic diameter fit within 15 pct for extensive miscibility in the solid, and the wide knowledge of the effect of such factors as size, electronegativity, electron-atom ratio on solid state features,"' work relating to liquid state and liquid-solid reactions can be found in the literature. Of particular interest is the work by Axon,3 who investigated the effect of size and melting point on a selected number of eutectic and monotectic dia-

Jan 1, 1962

By James F. Watson, Jack L. Christian

The austenite to martensite solid state phase transformation in the 300 series austenitic stainless steels was studied over the temperature range of 788° to -423°F. The primary variables controlling this transformation are temperature, plastic strain, and chernical composition. Consequently, temperature effects were studied by measurements at 78", -100°, -320°, ad -423°F; plastic strain was controlled by cold-rolling the alloys varying amounts between 40 and 80 pet; and chemical compositions were varied by using 301, 302, 304 ELC, and 310 stainless steel alloys which exhibit varying degrees of austenite stability. The martensite contents of various alloys were correlated with several mechanical properties including yield and ultimate tensile strength, elongation, and notched tensile strength (Kt = 6.3). The yield and tensite strengths generally increased with increasing martensite content, but ) no correlation was observed between elongation and martensite content. The notched/un-notched ratio (Kt = 6.3) at -423°F exhibited a maximun at about 65 pct martensite. Attempts to correlate austenite stability (as measured by the Ms temperature) with both martensite content, and incremental increases in martensite content resulting from tensile testing were generally unsuccessful because the variable of cold Work could not be separated. As a result, only a general correlation of these variables was obtained. A (111) pole figure of austenite in a cold-rolled 301 stainless steel mas prepared an attempt to further investigate directionality as exhibited by mechan- ical properties. Yield strength was correlated with this pole figure, but ultimate and notched tensile strengths were not. 1 HE literature contains a wide variety of references pertaining to the austenite to martensite solid state phase transformation in austenitic stainless steel, see references 1 through 18. Discussions of the crystallography and kinetics of this transformation are given in references 2, 7, 8, 'and 11, while further discussions of austenite stability and hardening mechanisms are given in references 1, 3, and 10. Two important processing variables involved in this reaction are the degree of cold work and the temperature at which cold work is performed, and the nature of these effects are outlined in references 4 and 12, and 15 and 16 respectively. The latter two references deal primarily with cold rolling conducted at subzero temperatures. The effect of chemical composition on the austenite to martensite reaction was treated in detail by Eichelman and Hull, and they determined an equation for the M, temperature of this type of steel which included the effects of nickel, chromium, carbon, nitrogen, silicon, and manganese.5 Previous studies have shown that austenitic stainless steels of AISI types 301, 302, 304ELC, 310, and 301-N exhibit mechanical properties between 78" and -423"~ that are microstructure dependent, and the dependence of this microstructure on chemistry, temperature, tensile stress, and prior deformation is in general accord with previous investigations which have measured the effects of each of these variables on structure, or more specifically, the austenite-to-martensite transformation.lg The behavior of fully stable alloys, such as ATST type 310, at cryogenic temperatures is

Jan 1, 1962

By R. E. Reed-Hill, J. L. Martin

Kinking is an important deformation phenomenon in poly crystalline a zirconium. The crjlstallo-gvaphic features of the most important form of kinking have been determined with the aid of twins formed at 77°K in grains previously kinked at high temperatures. It has been .found that the kink-band boundaries correspond to walls of edge dislocations with (1150) Burgers vectors and dislocation lines parallel to (1070). The present observations imply that basal slip is an important secondary-slip mode in polycrystalline zirconium. Previous single-crystal studies13 did not veveal this mode Other evidelzc.e for (0002)(1120) slip is also presented. ThE first studies of kinking in hexagonal metals were made by orowan,1 using single-crystal cadmium wires. He suggested that this was a new de- formation mode in metals, different from ordinary glide or twinning. Next, Hess and Barrett2 studied zinc-crystal rods in compression, and were able to offer an explanation of the phenomenon described by Orowan. They concluded that kinks required no new deformation mechanism and were a special form of deformation band that developed gradually and solely from basal glide. Similar kink bands were then observed by Washburn and parker3 on zinc crystals deformed in tension at low stresses and high temperatures. In titaniun,4 kink bands associated with {1010}<1120> prism slip have been observed in coarse-grained specimens. Magnesium5 and rhenium6 have also been observed to kink in conjunction with their basal- and {1010} prism-slip systems, respectively. Yttrium has (1010) as a predominant slip plane, but no observations of kink bands were reported.7 Since no previous investigations of kink bands in zirconium have apparently been made, this study was proposed. Its aim was to determine the crys-tallographic features of a type of kink band frequently observed in polycrystalline zirconium. EXPERIMENTAL APPARATUS All tests were performed on a type TTC Instron machine. The cross-head speed usually chosen in tension or compression was 0.02 in. per min. Ten-

Jan 1, 1964

By David A. Thomas, John F. Peck

Sam Leber (General Electric Refractory Metals Laboratory)—I think that the authors should differentiate between the curved grains obtained by swaging and the crumpled grains produced by drawing. This can be seen most easily in the transverse sections of Fig. 2d, and is also apparent in Fig. 2c. This difference in structure indicates that the mode of deformation shou1d affect the texture, since the cylindrical texture should be maintained or even increased by the curved grains developed by swaging. Drawing, on the other hand, crumples the grains. This should convert the cylindrical texture into a normal fiber texture. This has been substantiated by a comparison of tungsten wires fabricated by similar drawing and swaging schedules. Although cylindrical textures have been detected in drawn iron wires, they were weak in comparison to tungsten wires which included swaging as part of the fabrication process. It should also be noted that large curved surfaces developed by swaging are concentric with the surface. The postulated (100) surface of these crystals would be confirmed by a (100) cylindrical texture, as was observed in tungsten. The preservalion of the (100) cylindrical texture by swaging would maintain the <100> direction in the radial position required for easy flow. This might provide a partial explanation for the decreased rate of work hardening observed in the swaged wire. J. F. Peck and D. A. Thomas (authors&apos; reply) — The authors appreciate Dr. Leber&apos;s comments on the differences in textures, microstructures, and properties of swaged and drawn wires. The evidence of the prominence and persistence of the cylindrical texture in swaged bee wires seems quite consistent with our microstructural observations and interpretations. We are presently engaged in further work to correlate the development of texture and micro-structure in drawn bee metals.

Jan 1, 1962

By N. A. Tiner

A study was made of the effects of temperature, type of loading, and electric polarization on the fracturing behavior of copper and zinc coated with mercury. Copper showed an em-brittlement only in cyclic loading, whereas zinc showed an em-brittlenzent in both static and cyclic loading. The embrittle-ment of zinc in static loading was prevented by sub-zero cooling to a temperatzcre of about -70°F. The emhrittlement of both metals was sliglztly reduced by cathodic polarization of mercury. The basic processes involved in fracturing were discussed in the light of these observations. When a solid metal is in contact with certain liquid metals possessing high wetting characteristics, a weakening effect is produced, and the solid metal fractures in brittle manner at a relatively low stress. This lowering of the fracture stress generally is considered different from the stress cracking caused by a corrosive liquid environment and is attributed to the lowering of the solid-liquid interface tension at the grain boundaries.1-4 The purpose of this paper is to describe a number of observations on the special features of fracturing of copper and zinc coated with a liquid mercury film, and to analyze the basic processes involved in fracturing in the light of these observations. EXPERIMENTAL OBSERVATIONS I) Effect of Type of Loading—The evidence appears to indicate that in static loading, metals usually fracture by the initiation of microcracks in the interior preferentially at the grain boundaries or at the intersection of slip bands.&apos; In cyclic loading, cracks develop on the surface within the active slip zones, and gradually propagate with increasing num- ber of cycles.6&apos;7 Because of this difference in the manner of initiation of cracks, a series of bare and mercury coated copper and zinc specimens was subjected to static and cyclic loading, and their fracturing behavior was examined. The specimens were machined to 0.25 in. in diam and 1 in. in length from a high-purity commercial bar stock, and annealed at an appropriate temperature. Mercury was applied to the surface of the specimens by rubbing with cotton wool soaked in a saturated solution of HgCl2 or by etching with a dilute solution of HC1 and rubbing with purified mercury and by washing in water. The static tension load-extension curves were obtained by means of a Riele Screw Power Universal Testing Machine. The room-temperature load-extension curves for copper and zinc are shown in Fig. 1. The deformation behavior of copper, as judged from the general configuration of the load-extension curve, was not affected by mercury coating. The maximum load to fracture and the elongation at the maximum load were practically the same for both specimens. The mercury coated copper, however, showed somewhat less localized necking and had smaller reduction of area than the uncoated metal. The behavior of mercury coated zinc was radically different from the behavior of uncoated metal. The load-extension curves were the same at the

Jan 1, 1962