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By Herbert Herman, M. E. Fine

THE first decomposition product of a supersaturated aluminum-rich A1-Ag alloy at low tempera- tures is Guinier-Preston zones.'-, The zones are ideal and each consists of a spherical shaped silver-rich cluster about 16 A in diam syrounded by a silver-poor shell approximately 72A in diam.' The composition of the two regions is not known with certainty., After quenching from the solution anneal, these zones form rapidly on aging at temperatures as low as -30°C.5 The rate of zone formation increases with aging temperature; the activation

Jan 1, 1961

By Colman Goldberg

IT is customary to plot crystallographic planes or axes on a Wulff stereographic net which is ruled with parallels of latitude and meridians of longitude. If a single crystal is placed at the center of a sphere, the coordinates of a crystallographic plane or axis are the coordinates of the point where the axis intersects the sphere. The standard (HKL) projection is the projection for which the sphere is rotated so that the (HKL) pole is at the center of the projection. Schiebold and Sachs' and many others have published standard projections for the more important planes of a cubic crystal. With Tables I and 11, it is possible to plot any plane (HKL) of a cubic crystal on a standard (001) projection if the absolute values of the individual H, K, and L are nine or less, which is almost always the case. Using the methods outlined by Barrett,' the standard (001) projection can be rotated so that any arbitrary plane is at the center of the projection. The tables are believed to be important for two reasons: 1—The heretofore published standard projections usually are not of the proper size to fit the stereographic nets available. With these tables a standard projection can be made which will be of exactly the proper size for the available stereographic net. 2—With the tables, planes that do not appear on the previously published standard projections can be easily plotted. For these reasons, the tables are especially useful in the study of optical reflections from etched surfaces and can also be used to make a standard projection for the axis which is normal to the macroscopic surface. (This axis can be found by X-ray or optical methods.) Then if the crystal is etched, the effect of the etchant can readily be determined by comparing the latitude and longitude of the reflecting planes (as determined with an optical goniometer) with the standard projection that has been prepared. Use of the Tables Fig. 1 shows the meridians and parallel which have been designated as zero longitude and latitude. The tables themselves are self-explanatory. The

Jan 1, 1953

By R. W. Heckel

The conzpaction of metal powders is analyzed through density-pressure curves as a three-stage process — die filling, individual particle motion, gross compact deformatim. The densification occurring during each of these stages is evaluated quantitatively. The amount of densification in the first and second stages is primarily a function of particle geometry. The densification taking place in the third stage is dependent mainly upon the material. AT the present time the densification of powders during compaction is usually described by terms such as "compactibility," "compressibility," and "compression ratio." Schwarzkopfl has proposedthat compactibility be defined as the minimum pressure needed to produce a given green strength, while compressibility be used to indicate the extent towhichthe density of a powder is increased by a given pressure. Compression ratio is generally defined as the ratio of the compact density obtained at a given pressure to the apparent density of the loose powder. 13alshina found that the pressure imposed on a compact affects the relative volume of the compact according to the following relation: hP= - LV + C [ll where: P is the applied pressure, V is the relative volume of the compact, Ratio of the specific volume of the compact to that of the material without porosity. Lisa constant described as the modulus of pressing and is determined by the slope of a plot of h P vs V, and C is a constant which is determined by the intercept of a plot of InP vs V. Several drawbacks of the Balshin analysis may be noted from Fig. 1, which is a plot of pressure (loga-

Jan 1, 1962

By M. H. Richman, E. S. Meieran

An analytical method is presented which enables the electron diffraction patterns from a twinned region to be indexed. The method has only been applied to (112) twins in bcc lattices, but can easily be adapted to other types of twinned lattices. Calculations of all twin spots, including those superimposed on matrix spots, is made possible by this method. SINCE the advent of transmission electron microscopy, the analysis of selected-area electron diffraction patterns has become very important in the interpretation of electron micrographs. Frequently, as in the case of some martensites, twinned areas are observed and give rise to complex diffraction patterns, which so far can be analyzed only for the simplest orientations of the thin foil specimen with respect to the electron beam. In order to simplify the analysis of twin patterns of more complex orientations, an analytical method was devised which is capable of predicting the positions of all reflections from both matrix and twin regions for all possible foil orientations. Although the method has only been applied to the case of bcc metals twinned about a (112) plane, it is equally applicable to other Bravais lattices. This method has been successfully applied to selected-area electron diffraction patterns of Fe-Ni and Fe-Ni-C martensites and drawn tungsten wire. PROCEDURE Imagine the reciprocal lattice corresponding to a bcc material, with each point hkl representing the crystallographic plane (hkl). Since the extinction conditions require that for this lattice, only reflections where h + k + 1 = even integer are allowed, the three dimensional reciprocal lattice is actually fcc. Since in real space twinned regions and matrix regions are mirrored across a (112) plane, the twinned reciprocal lattice is derived from the matrix reciprocal lattice by a rotation of 180 deg about a (112) direction. While it is possible to calculate how a point hkl will shift under a twinning transformation to a new point htktlt using only the reciprocal lattice based on the orthonormal vectors [100], [010], and [001], the calculations are greatly simplified if a new orthonormal coordinate system containing the twin axis is introduced. The twinning operation then becomes a simple rotation of 180 deg about a principal coordinate axis (in this case the twinning axis), and a retransformation back to the original reciprocal space will give the position htktIt of the twinned reflection.

Jan 1, 1963

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By G. F. Bolling

HE high mobility of grain boundaries in zone-refined metals has been particularly demonstrated for lead above 150°C in grain growth studies1 and in the extensive work by Aust and Rutter.1 In these investigations, no elaborate precautions were taken to eliminate oxygen from the zone-refined lead; however the alteration of creep characteristics by oxygen concentrations of less than 5 x 10 -5 wt pet

Jan 1, 1962

By A. S. Keh, H. A. Wriedt

The Precipitation of nitrides in quenched Fe-N alloys, aged between 25° and 200°C, was studied by transmission electron microscopy. Different dislocation substructures were introduced into the materials by recrystallization, cold working, and by Phase transformation prior to the introduction of nitrogen. It was found that the precipitated nitrides, tentatively identified as Fe16N2, have (100) habit planes. Nucleation takes place Preferentially at dislocations and at subboundaries. It sometimes occurs in the matrix, probably on vacancy clusters, but rarely on high-angle boundaries. The process of nucleation on dislocations and subboundaries is very temperature dependent. At room temperature there is no particular orientation relationship between the dislocations involved and the (100) planes on which the nitride Particles formed. With increasing temperature, the nucleation sites tend to become restricted to those dislocation segments lying in (100) planes. The change of yield stress of the 0.022 and 0.043 pet N alloys during quench aging can be correlated semiquantitatively with the change in particle distribution. Strain aging in quenched alloys can be separated into two stages. The early stage is attributed to nitrogen segregation to dislocations and the later stage is associated with precipitation. When previously quench-aged specimens were strained and aged, no additional Precipitates could be seen, although a considerable amount of strain aging occurred. DURING the past two decades, the precipitation of nitrides from a iron has been extensively studied by various techniques. It has been established that two types of nitride exist. The stable nitride, Fe4N, forms at temperatures above 250oC and Fe16N2, the

Jan 1, 1962

By Hsun Hu

The microstructural changes during rolling and at various stages of recrystallization in (111)[112] oriented single crystals of Si-Fe have been studied by transmission electron microscopy. At very low deformation, the dislocation structure consists of jogged dislocation lines, edge dislocation dipoles, and numerous dislocation loops, which may be interpreted by the jog-formation mechanism in moving screw dislocations. Up to 70 pct rolling reduction, no sharply defined cells are formed. Subgrain forma- tion takes place somewhat earlier in the annealing process than in a similarly processed (110)[001] crystal. This may be partly responsible for the reported difference in the rate of recrystallization between (111)[112] and (110)[001] crystals. Evidence indicates that the formation of recrystallization nuclei occurs largely by the coalescence of sub -grains. This is consistent with previous observations on other Si-Fe crystals. AVAILABLE data in the literature indicate that the main features of rolling and annealing textures in (111)[112] and (110)[001] crystals are essentially similar. A (111)[112] or (111)[112] crystal can be rolled 70 pct without changing its initial orienta-

Jan 1, 1964

By F. Garofalo

It has been shown by various investigators that during constant stress creep the dependence of minimum creep rate, 6,, on stress, o, is given by em = A onat low stress levels, md by 6, = A&apos; exp [ß s] at high stress levels. In these relations A, n, A&apos;, and ß are constant at constant temperature. A single relation has been found which satisfies conditions for both high and low stresses and agrees well with experimental results. This relation is 2, = AN (sinh a s)n, where A" is a constant at constunt temperature and a = p/n. This relation also satisfies the linear relation, 6, = k s, found at temperatures near the melting point at low stresses. EXPERIMENTAL creep results have led to a number of empirical relationships between minimum creep rate, 6,, and the applied stress, s. Under conditions of constant stress it is generally found that at low-stress levels,&apos;-&apos; the dependence of minimum creep rate is given by 6, = Asn. At high-stress levels&apos;74 the experimental results fit the relation, 6, = A&apos; exp [po l. In these relations A, n, A&apos; and ß are constant at constant temperature. A model based on climb-of-edge dislocations from a pile-up array leads to a relation similar to that found experimentally at low stresses.&apos; On the other hand. theories based on chemical-reaction rate,5 nonconservatively moving dislocation jogs, and jog migration and climb-of-edge dislocations4 lead to a relation similar to that found experimentally at high stresses. No difference in mechanism between low and high stress levels has been clearly defined; it is questionable whether such a difference really exists. In any event, the major argument usually given in substantiation of a change in mechanism from low to high stresses is that no single relation exists for defining the stress dependence of the creep rate over wide ranges in stress. However, such a relation has been found and is of the form, dm = A" (sinh a s)n, where A" is a constant at con- stant temperature and a = ß/n. This relation agrees well with experimental results over wide ranges in stress and temperature for copper, aluminum, an A1-3.1 pct Mg alloy, and an austenitic stainless steel. STRESS DEPENDENCE OF MINIMUM CREEP RATE At low stress levels the minimum creep rate, gm, depends on the stress, 0, under conditions of constant stress creep through the relation em=Aon [1] The quantities A and n have been defined previously. In the range in which this relation applies, a linear dependence is found in a log em,-log o plot. Above the stress range of application of relation [I], the minimum creep rate increases much mar; rapidly than predicted by relation [I]. This behavior is shown in Fig. 1 for a series of creep tests on copper4 at various temperatures ranging from 673 o to 973°K. Relation [I] is satisfied at the lower stresses, although the results at 973°K are quite limited. In all cases the transition beyond the applicable range of relation [I] is a gradual one indicating no abrupt change in mechanism. For all test temperatures, values of n have been determined from the results in Fig. 1. These are reported in Table I under Alog tm/hlog o. At high stress levels the stress dependence of minimum creep rate under conditions of constant stress is given by im = A&apos; exp [ß a] 2] All factors have been defined previously. In a log em-0 plot, relation [2] predicts a linear function. Experimentally, a pronounced deviation from the prediction of relation [2] is found at lower stresses. As the stress is lowered, the minimum creep rate decreases more rapidly than predicted by relation [2]. This shown for copper in Fig. 2. Again it is found that the transition from high to low stresses is gradual and no really sharp change is found. Values of p determined from the high stress results are given in Table I. The dependence of minimum creep rate on stress at constant temperature for all ranges in stress

Jan 1, 1963

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10&apos; per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute&apos;.&apos; for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.&apos; Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By R. E. Carter, F. D. Richardson

Self-diffusion coefficients have been measured for iron in wustite (700° to 1000°C) and for cobalt in cobaltous oxide (800&apos; to 1350°C) by means of radio-isotopes. Both sectioning and decrease of surface-activity methods have been used and a particular shortcoming of the latter method has been disclosed for wustite. The effects of oxygen pressure on the composition of cobaltous oxide and on the diffusion coefficient of cobalt in the oxide have been established. The effect of the preparation conditions of the cobalt-oxide specimens on the diffusion measurements has been determined. It has been concluded that diffusion of cobalt occurs via vacant cation sites and that a cobaltous-oxide disk reaches equilibrium with its environment in a time which is very short compared with that needed for diffusion of the radio-isotope. THE availability of radioactive isotopes in recent years has permitted the measurement of many self-diffusion coefficients which were hitherto impossible to determine. With the advent of radioactivity, the method of measuring diffusion coefficients has also changed. The earlier sectioning method by which the concentration profile of the diffusing species was determined in the diffusion specimen has often been rejected in favor of the decrease of surface-activity method first developed by Von Hevesy,&apos; and extended by Steigman, Shockley, and Nix,&apos; and Raynor, Thomassen, and Rouse." With the experimental arrangement where an infinitely thin deposit of tracer is diffused into a semi-infinite cylinder, the decrease in activity of the active face due to diffusion of the tracer into the specimen is measured by counting the active face before and after diffusion. Under these conditions, the appropriate solution of the diffusion equation is R = e*(l-<K/Z) [1] where R is the ratio of the counting rates after-to-before diffusion, $& is the Gaussian error integral of \/Z, and Z is defined as Z = p2Dt, p being the linear-absorption coefficient of the detected radiation in the diffusion specimen, D the self-diffusion coefficient, and t the diffusion time. In the older sectioning method the concentration distribution of the tracer is found after diffusion by analysing thin parallel sections cut from the active face of the diffusion specimen. As seen from the solution of Fick&apos;s second law for the distribution of an infinitely thin source after diffusion into a semi-infinite cylinder the log of the concentration plotted against x&apos; will be a straight line of slope log e/4 Dt. The diffusion coefficient thus can be calculated directly. The units of the tracer concentration are completely arbitrary, since any change in units does not change the slope of the log c vs x2 lot. Although both of the above methods have been widely used, a thorough experimental comparison does not appear to have been made. Birchenall and Mehl,&apos; during an investigation of the self-diffusion rate of a and r iron by the surface method using Fe" tracer, diffused and sectioned one welded couple. The diffusion coefficient from this run agreed with those by the surface method. Buffington, Bakalar, and Cohen," during an investigation on a and y iron

Jan 1, 1955

By L. G. Schulz, P. Spiegler

The electrical resistivity and the temperature coefficient of resistivity were measured with a potentiometric method using pure mercury as a reference material. Measurements were made nea,v roorn temperature. A detailed study was made of Hg,TI, near its melting temperature. THE work to be described was originally undertaken to provide the necessary data for interpreting the results of some optical experiments,&apos; but because of the growing importance of liquid metals,273 it appeared that the results of the resistivity measurements should be published separately. For convenience the alloys selected were those which are liquid at room temperature. Special consideration was given to the Hg-T1 alloy closely corresponding to Hg,Tl, because recent X-ray diffraction results of Smallman and Frost seemed to show that the solid structure may persist to some extent into the 1iquid. EXPERIMENTAL PROCEDURE A potentiometric method was employed in which the resistivity of mercury was used as a reference. The essential features of the samples are shown in Fig. 1. A capillary tube CT with a bore of approximately 1.5 mm was fitted into two end cups, T, which were made of Teflon. A pair of current electrodes CE were immersed into the excess liquid metal which partly filled the end cups. The potential electrodes PE were inserted into CT through short pieces N of a no. 18 hypodermic needle held in place with Saureisen cement SC. As shown, the lower ends of the PE7s were reduced in diameter to 0.25 mm to minimize the distortion of the liquid metal cross section. Several methods were used to insert an alloy into the sample, but the usual one with mercury alloys was to fill the sample container with a weighed quantity of pure mercury* and then add weighed the sample tube in a vacuum. Because of rapid corrosion, samples containing gallium were of necessity prepared in a vacuum. To obtain the specific resistivity of an alloy the resistance of the sample containing the alloy was measured and compared with the resistance when the container was filled with mercury. Resistances were measured in the temperature range of 20" to 60°C to obtain the temperature coefficient of resistance. The electrical measurements were made by connecting the sample in series with the standard one-ohm resistance, and the potential drop measured alternately over the sample and the standard resistance. To correct for stray thermoelectric effects provision was made for reversing the direction of the current, and the true potential drop was taken to be the average of that obtained for the two directions of current flow. Various materials were used for the electrodes, the most uniform results being obtained with nickel. EXPERIMENTAL RESULTS The numerical results are presented graphically in Figs. 2 and 3 and in tabular form in Tables I and 11. Following are remarks on results of individual alloys. 1) Hg-In—This was the first alloy studied, and

Jan 1, 1960

By D. C. Jillson

WORK in recent years1-&apos; has indicated a complexity of the processes of deformation of metal crystals not previously appreciated and not fully accounted for by any hypothesis so far advanced. Furthermore, the nature and mechanism of formation of nuclei of recrystallization have not been determined precisely. The deformation of single crystals of zinc has been studied frequently, but the purity of the zinc and the perfection of the specimens sometimes have been given little consideration. Methods have been developed recently that readily yield zinc single-crystal specimens of high quality.5 In the present work, such specimens were deformed in various ways under various conditions, and deformed specimens were annealed to obtain information regarding recovery, recrystallization, and grain growth. The paper attempts to correlate and evaluate previous data, as well as to present new data, in order to determine areas in which more detailed work might be done most profitably. Tests at temperatures from the freezing point (419.46°C) to room temperature revealed glide only on basal planes in a close-packed direction (100)*, as reported by Mark, Polanyi, and Schmid6 and others. Markings probably similar to those observed by Kolesnikov7 and Boas and Schmid8 were noted in specimens stretched at elevated temperatures, but it seemed clear that these were not caused by prismatic or pyramidal slip (see second paragraph of section on Phenomena Involving Bending of the Basal Plane). Twinning Twinning on the octahedral plane of a face-centered cubic metal has been pictured as a process of simple homogeneous shearing along that plane in a [112] direction. It was recognized by Mathewson and Phillipsv and others""" that the (102) twinning of zinc required a somewhat more complex mechanism and might be considered as a homogeneous shearing of (102) planes in a [211] direction plus slight adjustments of atoms to positions of greater stability or lower energy, or as a single movement of each of the atoms in the same sense into the final positions. Gough and Cox" modified Mathewson&apos;s mechanism to obtain a more stable lattice configuration, but it is not clear that they succeeded, and their mechanism requires movement of some of the atoms in a sense opposite to that of the overall twinning movement. They also suggested that twinning may occur as a result of previous basal slip. This conclusion was based on the observation that twinning caused by alternating torsion was clearest and most profuse at positions for maximum basal slip rather than for maximum stress on (102) planes in the close-packed direction (not the twinning direction), and no mechanism was described. It might be wondered whether resolution of stresses on the twinning plane in the twinning direction would have afforded a simpler explanation. If twinning is essentially a simple homogeneous shearing along the twinning plane, it would seem that twins should grow by a smooth, continuous mechanism, and, indeed, that a simple reversal of stresses should reverse the shearing and de-twin the crystal. Cylindrical tablets 1/8 to 1/4 in. thick were cleaved from singlle-crystal specimens and were squeezed, perpendicular to a second-order prism plane, to give a tensile stress perpendicular to a first-order prism plane. A "click" was heard and a thin, needle-like twin appeared on the basal cleavage face. If squeezing was continued smoothly, the twin, viewed at magnifications up to X500, grew smoothly and quietly (fig. 1). X-ray examination verified that the twinning was of the (102) type. Rotating the compression axis 90" to reverse the stress then caused a smooth, continuous shrinkage and ultimate disappearance of the twin (fig. 2). The squeezing also caused a rumpling of the basal

Jan 1, 1951

By A. Gatti

A dispersion of AI2O3 was produced within chromium by the hydrogen reduction of a solid solution of Cr2U3-A1203. The yesulting powder. was compacted, extruded, and the material tested in tension at various temperatures and in creep at 1800°F. The material is ductile above 1200°F and is at least twice as strong as electrolytic chvomium at all temperatures. Its creep resistance, rupture strength, and ductility at 1800°F warrant further work to improve its Low -temperatutre properties. BECAUSE of its high melting point and excellent corrosion resistance, chromium has long been considered as a base for high-temperature alloys. Most chromium base alloys, however, are extremely brittle at low temperatures. Elements such as nickel and iron lower the melting point of chromium and thereby limit its high-temperature usefulness. Chromium-alumina materials made by othersl, 2 have shown good high-temperature creep resistance but poor ductility and thermal shock resistance. Pure ductile chromium3 is weak at high temperatures and reverts to a brittle state if exposed to nitrogenous atmospheres. In sintered aluminum powder (SAP)4 and internally oxidized alloys of silver, copper, and nickel, fine dispersions of oxide phases can control hardness, recrystallization, and yield stress. The possibility of formation of a ductile, high-strength material by precipitating dispersions of alumina in a chromium matrix appears worthy of investigation. MATERIAL Powder Production—Chromium oxide and alumina in amounts to produce a final alloy of Cr + 16 pct AI2O3 by weight were colloid milled, filtered, dried and high fired for 16 hr at 1600°C in air. The resulting solid solution of oxides was ball-milled to a fine powder and the chromium oxide reduced to chromium by heating in pure dry hydrogen for 64 hr at 1400°C. Final Materials Produced by Powder Metallurgy Techniques—-Chromium powder, containing a disper-sion of alumina, was pressed into 1 1/8-in. diam slugs at 25 tons per sq in. and sintered 16 hr at 1400° C in pure dry hydrogen. The sintered slugs were encased in a stainless steel can, 2 in. in diam, and extruded at 1200° C through a 1/2-in. die. The 16 to 1 extrusion ratio produced a final chromium-alumina rod 1/4 in. in diam about 30 in. long. Samples of the rod were plunge-ground to small rupture bars of 0.82-in. gage length with a 0.01-sq-in. cross section. RESULTS Microstructure Studies—Fig. 1 is the microstruc-ture of the material in the as-sintered condition while Fig. 2 is the microstructure of the material as-extruded. Comparison of the as-sintered and as-extruded micrographs show the redistribution and realignment of the alumina inclusions by the extrusion

Jan 1, 1961

By P. G. Winchell, J. K. Jackson

The strtcture of body-centered Fe-Ni-C alloys (0 to 16.5 wt pct Ni) containing less than 0.015 wt pct C was investigated by measuring the carbon-diffusion peak at low frequencies with a torsion pendulurrr. By determining the Snoek damping in ferrite and in quenched alloys of identical composition, the effects of nickel content and heat treatment were separated, and the existence of a structure in which Snoek damping is greatly reduced was revealed in the quenched ternary alloys. The relative amount of this structure increases with increased nickel content and cooling rate. It is proposed that this structure may be highly imperfect or tetragonal. In Fe-Ni-C alloys containing only ferrite the addition of nickel (0 to 5.1 wt pet) decreases tke area of the carbon-diffusion peak and shifts its position to lower temperatures but broadens the peak only slightljl. The decrease in peak area with increasing nickel implies that short-range interactions with the nickel atoms prevent some of the carbon atoms from participating in the relaxation process. The shift in the peak position indicates a long-range effect of nickel on the movement of carbon atoms so that at 300°K the diffisivity of carbon in -ferrite is increased by about 35 pct by the addition of 5.1 tut pct Ni. The results are presented as distributions of relaxation strength 072 the activation energy under the assumption that the frequency factor is invariant. BODY-CENTERED iron-base solid solutions dissolve carbon interstitially in the octahedral sites. The occupation of an octahedral site produces a tetragonal distortion of the surrounding lattice. These sites fall into three sets according to the orientation of the tegragonal distortion associated with each and may be identified by their lattice coordinates as: type 1/2 0 0, type 0 1/2 0, type 0 0 1/2. At low carbon levels in cubic ferrite the carbon atoms are distributed at random1 among these sites. In high-carbon body-centered iron-base solid solutions, which are unstable with respect to several two-phase mixtures, a tetragonal structure occurs as the product of the diffusionless transformation of austenite. This transformation is commonly accompanied by appreciable microstrain and its product is called martensite. The tetragonality of martensite, a supersaturated solution of carbon in a iron, is maintained prior to decomposition even though local diffusion of carbon occurs as evidenced by carbide precipitation. The tetragonality is taken as evidence that one set of octahedral sites is preferentially occupied by carbon. (This preferential occupation is called ordering below.) Support for this view is presented by the absence of strain-induced carbon-atom diffusion in high-carbon solid solutions (martensite). Such diffusion occurs in ferrite and produces the 40°C internal-friction peak observed at 1 cps frequencies.&apos; Thus, there appears to be qualitative evidence favoring the view that at sufficiently high carbon levels tetragonality arises spontaneously as a result of the ordering of the carbon atoms; however, no experimental evidence exists concerning an equilibrium between cubic and tetragonal body-centered solid solutions. Moreover, attempts to estimate the energy of ordering7-&apos; predict a value too low to maintain the tetragonality observed at medium carbon levels, 0.3 to 0.6 wt pct C. In the present work an attempt using internal-friction measurements is made to establish the presence or absence of tetragonality in low-carbon body-centered solid solutions formed by quenching austenite. Fe-Ni alloys containing about 0.01 wt pct and 0 to 15 wt pct Ni were selected for the study. While the work was in progress Gilbert and Owen10 reported that the transformation which occurs in these alloys during quenching at rates up to 5000°C per sec is not martensitic but is more properly categorized as massive. Thus, the solid solution

Jan 1, 1964

By A. L. Titchener, M. B. Bever

The stored energy of cold work was investigated in drawn gold-silver wires by tin-solution calorimetry as a function of strain, strain rate, initial grain size, and temperature of defornation. The energy expended in the deformation process was measured. Hardness was also measured and was correlated with the stored energy as a function of strain and strain rate. Mechanisms of energy storage are discussed. THE variables which determine the amount of energy stored in a metal during cold work are of two kinds: those involving the metal and its condition and those involving the process of deformation. For example, the stored energy differs between one metal and another and between different degrees of purity of a single metal. It also depends on the nature of the deformation process and particularly the extent, rate, and temperature of deformation. Most investigators have reported the stored energy as a function of strain (or some similar geometric parameter) or of the energy expended during deformation. In general the stored energy increases with strain, rapidly at first, but more slowly at large strains until a saturation level is reached. Information about the effects of other variables, however, is limited. Some data are available on the dependence of the stored energy on the purity of a metal1 and on the composition of

Jan 1, 1960

By G. P. Bowman, D. F. Howard, R. K. Saxer, J. R. Myers

This study was undertaken to redetermine the phase diagram of the lead molybdate-bismuth molyb-date salt system. A portion of this diagram was originally determined by Zambonini in 1920, and more recently by Beale. Thermal analysis and X-ray methods were used to define this system. The diagram was found to be a simple eutectic type with an eutectic at 11 mol pet lead molybdate and 634OC. A maximum solid solubility of 6 mol pet was found at the lead molybdate end of the diagram. Solid solubility at the bismuth molybdate end of&apos; the diagram appeared to be quite limited and possibly nonexistent. These results generally agree with those of Beale, but differ significantly from those of Zambonini. MOLTEN salt systems have been vigorously investigated since World War 11. Much of this work has been performed as pure research; however, consideration has recently been given to their possible use as coolants in nuclear reactors. Because of this application and other potential applications, it was decided to reinvestigate the lead molybdate-bismuth molybdate phase diagram. This diagram was originally determined by Professor F. Zambonini of the University of Turin in 1920.&apos; In 1961, a portion of this diagram was redetermined by Beale.2 With the quality equipment and high-purity materials available today, it was expected that discrepancies between the results of this present investigation and Zambonini&apos;s work would be obtained. This investigation was conducted in two parts. First, the general shape of the phase diagram was determined by cooling-curve analysis. Next, the primary solid-solution phase at the lead molybdate end of the diagram was investigated by means of X-ray diffraction techniques. EXPERIMENTAL PROCEDURE High-purity lead molybdate, assaying 99.993 pet, and high-purity bismuth molybdate, assaying 99.989 pet, were employed during this investigation.* The results of a spectrographic analysis of the two salts are presented in Table I. Twenty-two experimental compositions were prepared for cooling-curve analysis. Compositions selected are presented in Table 11. Several randomly selected samples were analyzed chemically to check that the compositions of the prepared specimens were within the limit of

Jan 1, 1964