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By J. H. Jackson, P. D. Frost, C. H. Lorig, L. W. Eastwood, A. C. Loonam

It is well known that for equal weights of material, thin sections of the lighter structural alloys are more resistant to buckling under a compressive stress than thin sections of more dense material. Therefore, structural parts having the same resistance to buckling stresses are generally lightest when they are made of magnesium alloys. Consequently, there is considerable interest in the development of strong alloys having densities equal to or lower than that of magnesium and strength-weight ratios equivalent to those of the strongest aluminum alloys. The development of commercial magnesium-base alloys has been very successful, and their importance among materials in the structural field has been amply demonstrated. However, an even wider structural application of magnesium alloys might be effected if improvements could be made in the cold rollability and cold-forming characteristics. Such improvements, along with production of less directionality in properties. could be effected if the hexagonal close-packed lattice of present alloys could be replaced with a cubic lattice. In 1942, a project, having as its objective the improvement of some of the characteristics of commercial magnesium-base alloys, was initiated at Battelle Memorial Institute under the sponsorship of the Mathieson Chemical Corporation. At that time, one of the authors,* then Chief Metallurgist for the Mathieson Chemical Corporation, postulated that the addition of lithium to magnesium in sufficient quantities to change the crystal structure of the resultant alloy from a hexagonal to a body-centered cubic lattice should produce a magnesium-rich alloy which would have the desired improvements in cold-working characteristics with less directionality in properties. To test this view, a series of alloys was made and was found to have many of the attributes that were predicted. The view that magnesium-lithium alloys were of structural interest was also held by others. In 1943 and 1945, Dean and Andersonl,² obtained patents on magnesium-base alloys containing from about 1 to 10 pct lithium, from about 2 to about 10 pct manganese, and the balance substantially all magnesium; and on magnesium-base alloys containing from about 1 pct to about 10 pct lithium, from about 2 to about 10 pct manganese, from about 0.5 to 2 pct silver, and the balance substantially all magnesium. They noted that an alloy containing 83 pct magnesium, 10 pct manganese, 5 pct lithium, and 2 pct silver could be cold rolled by any of the usual methods and that this alloy was considerably harder and stronger than most other magnesium-base alloys heretofore available. In 1945, Hume-Rothery, et al.,3 predicted that magnesium-lithium base alloys should be soft and ductile and that such compositions, to which was added a third element for the purpose of producing a precipitation-hardening type of alloy, should be ductile, strong, and lighter than magnesium itself. Hume-Rothery investigated the binary magnesium-lithium and ternary magnesium-lithium-silver equilibrium relations and criticized the existing equilibrium diagrams. The binary magnesium-lithium equilibrium diagram has also been investigated by Grube, Von Zeppelin, and Bumm, Henry and Cordiano, Sal'dau and Shamrai, Hof-mann,' and Shamrai.8 The work of most investigators agreed with that of Grube, whose constitution diagram is shown in Fig 1. From the standpoint of development of structural alloys, the room-temperature equilibrium relations are of great interest. An examination of Fig 1 reveals that, from 0 to 5.7 pct lithium, the existing phase is alpha, which is a solution of lithium in hexagonal magnesium. The boundary between the alpha, and alpha plus beta regions, occurs at a Mg/Li of 16.5, corresponding to 5.7 pct lithium by weight. Between 5.7 pct and 10.3 pct lithium, there exists a mixture of the alpha phase (lithium dissolved in hexagonal magnesium) and the beta phase (magnesium dissolved in body-centered-cubic lithium). The boundary of the alpha plus beta and beta regions occurs at a Mg/Li of 8.7, corresponding to a lithium composition of 10.3 pct. Much of the work described here was directed toward obtaining an alloy made up of a large proportion, or entirely, of the body-centered-cubic beta structure. In his early work, Loonam found that specimens of lithium-bearing alloys were very malleable. Ingots of alloys prepared at that time were extruded to 3/8-in. diam bars, and the mechanical properties and the effects of heat treatment were then determined. These data are given in Table 1. The outstanding ductility of the alloys, combined with their moderately high strength, evoked considerable interest.

Jan 1, 1950

By C. E. Armantrout, J. A. Rowland, D. F. Walsh

THE close-packed-hexagonal structure of mag-J- nesium is converted to a ductile and malleable body-centered-cubic lattice by the addition of lithium in excess of 10 pct. Further, the density of magnesium or magnesium-base alloys is decreased by additions of lithium. The practical possibilities of such alloys as a basis for uniquely light, malleable, and ductile structural materials were pointed out by Dean in 1944' and by Hume-Rothery in 1945.2 It was apparent to these investigators, however, that more complex compositions would be required if strengths sufficient for structural applications were to be developed in these alloys. In a search for strengthening additions, various investigators w have examined a number of the ternary and more complex alloys containing magnesium and lithium. An investigation of the fundamental characteristics of these alloys was undertaken by the Bureau of Mines. The investigation was initiated with a study of the magnesium-rich corner of the equilibrium diagram for the ternary system, Mg-Li-Al. The following data from published investigations of Mg-Li-A1 alloys were available: 1—a description of isothermal sections at 20" and 400°C through the Mg-Li-A1 constitution diagram by F. I. Shamrai;' 2—a diagram by P. D. Frost et al." showing approximate phase relationships at 700°F for a number of the Mg-Li-A1 alloys; and 3—diagrams showing the constitution at 500" and 700°F for the Mg-Li-A1 alloy system published by A. Jones et al.' Where compositions and temperatures permit comparison, these diagrams show disagreement. The 700°F isotherms of Frost and Jones differ only in the placement of the phase boundaries. But Sham-rai's 400°C (752°F) isotherm shows a variation in phases as well as in phase boundaries. Although rigid comparison of these different isothermal sections might not be justifiable, it seems impossible to reconcile Shamrai's construction with the isotherms of Frost or Jones. The isothermal sections presented in this paper were prepared to determine compositions which might be suitable for age hardening and to develop the general slope and placement of the various phase boundaries in the magnesium-rich corner of the diagram. Sections at 375", 200°, and 100°C were selected for investigation. In constructing these sections, the solubility of aluminum in magnesium, as reported by W. L. Fink and L. A. Willey Vn 1948, was used at the binary Mg-A1 boundary and the solubility of lithium in magnesium was obtained from the equilibrium diagram for that system as reported by G. F. Sager and B. J. Nelson" in the same year. The solubility of magnesium in lithium was determined experimentally and conforms in general to data reported by P. Saldau and F. Shamrai." Parameters for AlLi and MgI7A1, were taken from American Society for Testing Materials X-ray diffraction data cards. Experimental Procedures Although the isothermal sections presented in this paper are not unusually complex, the experimental techniques involved in their construction are made extremely difficult by the relatively high vapor pressure of lithium and the great chemical activity of both magnesium and lithium. Because of these characteristics, which make precise control of the composition of equilibrium-treated filings practically impossible, the disappearing phase method was used in preference to the parametric method in conjunction with metallographic studies. The alloys used in this investigation were melted and cast in an atmosphere of helium using a tilting-type furnace which enclosed a steel crucible and mold in a single unit. Each portion of the charge (500 to 600 g) was cleaned carefully just before placing it in the crucible; and the charge, crucible, and entire melting apparatus were evacuated and then washed with grade A helium while preheating to approximately 100°C. The alloys were melted and chill cast in an atmosphere of helium. Alloys prepared in this way were relatively free from inclusions and a fluxing treatment was considered unnecessary. The cylindrical ingots obtained were scalped and then reduced 96 pct in area by direct extrusion, yielding % in. diam rod. Sections of the rod, approximately 3 in. long, were given equilibrium heat treatments and then sampled for metallographic examination, X-ray diffraction study, and chemical analysis. The surface of each equilibrium-treated rod was machined to a depth sufficient to insure removal of contaminated material before samples for chemical analysis or X-ray diffraction study were obtained, and all decisions on microstructure were based on the examination of the central portion of the metallographic specimen. All specimens homogenized at 375°C were analyzed after this equilibrium heat treatment. When the composition of an alloy placed it in a critical area of the 200" or 100°C isothermal section, a check chemical analysis was made on a sample taken from the alloy specimen as-heat-treated at the particular temperature. Standard chemical procedures of gravimetric analysis were used in the determination of magnesium and aluminum; lithium, potassium, and sodium were determined by flame photometer methods

Jan 1, 1956

By J. P. Martin, A. H. Geisler, J. H. Crede, E. Both

The investigation of a 50 pct Co alloy was undertaken to determine whether there was any direct correlation between the structure and properties of Co-Fe alloys which were given various magnetic heat treatments. The magnetic anisotropy and texture of the 0.002-in. cold-reduced 98 pct material tend to decrease and change in nature with increasing temperature of the recrystallization anneal. Annealing samples in a magnetic field had little effect on either the magnetic properties or texture. However, cooling them in a magnetic field greatly improved their magnetic properties. THE beneficial influence of a magnetic field applied during the heat treatment of certain soft magnetic materials has been known for a long time. Early work showed that the presence of a magnetic field of a few oersteds during the heat treatment of Fe-Ni alloys will cause a large increase in maximum permeability. A pronounced increase in the residual induction which is produced by the magnetic anneal causes the hysteresis loop to approach the shape of a rectangle. Such results are beneficial since the desired properties are high permeability, high induction at maximum permeability, high residual induction, and low coercive force. More recently Libsch and coworkers1 studied the effect of magnetic annealing on the hysteresis properties of a series of Co-Fe alloys prepared from powders. They observed good response for the 35 and 50 pct Co alloys but little response for the 42 pct Co alloy. They pointed out that this was somewhat surprising since the 42 pct alloy has a high linear magnetostriction and zero crystal anisotropy and similar conditions in Fe-Ni alloys give excellent response to magnetic annealing. They found optimum properties to be at the 50 pct composition with residual induction, Br = 19,000 gauss and coercive force, Hc = 0.68 oersteds after the magnetic anneal. Before the magnetic anneal these values were B, = 12,600 gauss and Hc = 1.15 oersteds. The optimum treatment consisted of cooling from above the y-a transformation temperature to 900°C in a field of 20 oersteds, holding 11/2 hr at 900°C, then cooling at a rate of 20° to 25°C per min in the field to below 230°C. Cooling rate mainly affected coercive force with the value decreasing from 1.09 to 0.88 oersteds as the rate was increased from 3° to 48°C per min. Cooling from 1020" to 900°C in a field followed by further cooling to 230°C without the field gave properties decidedly inferior to those for samples annealed with the field applied throughout the cooling. They concluded that to get the best properties the samples must be cooled in a field to a threshold temperature above which the alloy is plastic enough to be affected by magnetostriction. In this respect the holding temperature must be high enough so that the alloy exhibits good plasticity to permit the optimum orienting of magnetic domains by relaxation of magnetostriction. In contrast, the holding time was of less significance for there was little improvement when the time exceeded 1/2 hr. The improvement in properties effected by magnetic annealing has usually been attributed to the establishment of a domain texture caused by the "freezing in" of magnetic strains. On the other hand, Smoluchowski and Turner2,3 apparently found that a magnetic field applied during recrystallization could alter the crystal texture. If this effect is real, improved properties would also be expected when

Jan 1, 1954

By T. Saburi, C. M. Wayman

The massive and martensitic transformations in ß Cu-Ga alloys were studied by optical microscopy and by transmission electron microscopy and diffraction. These types of transformation are distinct and do not merge into one another. An internal fine structure due to stacking faults was found in both the massive phase (m) and the martensite, but the origin of the faults is believed to be different in each case. The faults in the martensite are due to the lattice invariant or "second" shear of the phenom-enological theory, while those in the are probably growth faults and deformation faults arising from the transformation volume change. Evidence is presented for ordering in the ß phase prior to transformation into martensite, and the crystal structures of and ß' and ßi martensites are discussed. THE results from some previous investigations1,2 have led to the suggestion that martensitic and massive transformations have certain common characteristics. It presently seems established that massive transformations like martensitic transformations are essentially diffusionless,1,2 but unlike martensitic transformations, when a new phase forms massively there is no shape change or surface relief.= If the massive-type transformation is crystallographically similar to martensitic transformations, one would expect a fine structure as a result of the lattice invariant shear4 which is a part of the transformation mechanism. The existence of such a fine structure (i.e., slip, twinning, or faulting), if any, can be verified by transmission electron microscopy, and thus the present investigation was undertaken to compare the internal structure of massively and martensitically formed phases in Cu-Ga alloys which were derived from a parent of the same composition. The transformation characteristics of ß Cu-Ga alloys were also studied. The bcc ß phase in the Cu-Ga system, Fig. 1, is stable above 616oc.' Depending upon the cooling rate, ß Cu-Ga alloys can undergo three different types of phase transformations. The ß phase of eutectoid composition (23.7 at. pct Ga) decomposes into the ? phase (hcp) and the phase (complex cubic) by means of a eutectoid reaction. When the cooling rate is increased so that the decomposition of 0 into [ and ? is suppressed, the ß phase transforms into a nonequilibrium hcp phase, herein denoted ?m by a process of very rapid growth called a "massive" transformation. At even faster quenching rates the massive transformation can be suppressed and the ß transforms martensitically. Massive transformations, apparently similar to those in the Cu-Ga system, have also been studied in the Cu-Zn2,6-8 and Ag-Cd systems.9 Definitive characteristics if the Massive Transformations in 0 Cu-Ga Alloys1 1) The most remarkable feature of the massive transformation in Cu-Ga is that there is no bulk composition change on transformation. According to Massalski,1 the resulting [, phase is a supersaturated extension of the equilibrium [ phase. The lattice parameters continue the trend exhibited

Jan 1, 1965

By I. A. Lesk

The various materials utilized in the construction of integrated circuits, and the resultant materials interfaces, are discussed with emphasis on a materials system that is compatible with all types of integrated circuits and minimizes the number of different interfaces. Problems with interfaces may originate in the silicon, on its surface, and between other materials within the integrated-circuit package independent of the silicon. ThE difference between integrated-circuit theory and practice may generally be spelled out in terms of the difficulties in fabricating a desired structure. There are, of course, problems in forming the requisite materials, of the necessary composition and geometry, where needed. A distinct class of problem, however, is associated with interfaces— generally between different materials, but occasionally between regions of the same material. We require that each interfacial system perform its proper electrical, mechanical, and thermal function, and do so in an unchanging manner with time under the most severe operating conditions. In a practical sense, we deal in nonideal systems, such that it is generally not possible to form an interface exactly the way it was intended, even if we allow for a knowledge of the practical limitations of the fabrication system. Another way of looking at this situation is to realize that, when we form a group of interfaces under apparently the same experimental conditions, there are often differences of important consequence between them. Very high-magnification pictures, such as are obtained by an electron microscope, reveal fine structure that often differs over the area of a given sample, as well as from sample to sample. Low-magnification pictures look better, but don't eliminate the problem. The trend towards integrated circuits, and away from circuits fabricated utilizing separate components, is very strong in many areas of electronics. A typical silicon monolithic integrated circuit, still in place in the wafer on which it was fabricated, is shown in Fig. 1. The increased reliability which is being experienced through the use of integrated circuits can, to a large extent, be credited to the reduced complexity of the interface system that is present in the electronic system. A glance at Fig. 1, however, with all of its epitaxial and diffused p-n junctions, and interconnect system, shows that interfaces have been far from eliminated. Fig. 2, depicting a schematic cross-sectional view of a (partial) typical integrated circuit, illustrates in detail the numerous interfaces that occur in this type of structure. Besides the individual circuit elements, there are interfaces for isolation, and, Fig. 3, even a crossover requires a series of interfaces. What has been accomplished, however, irrespective of whether or not the total number of interfaces in the circuit is increased or decreased, is that the variety of interfaces is very much reduced. This is because there are fewer materials involved. Since the expense incurred in an R & D program to improve reliability is pretty much directly proportional to the variety of interfaces involved, it is economically advisable to work with integrated circuits for highest reliability. That is not to say that circuits built using standard components could not be made as reliable as integrated circuits, but that the expense involved because of the more complex over-all interface system would be much greater. Although electronic performance utilizing integrated circuits with all silicon elements (i.e., transistors, diodes, resistors, capacitors) is adequate for many applications, there are numerous instances where thin-film passive elements must

Jan 1, 1965

By C. B. Smith, A. G. Guy

The power and convenience of tensor analysis are employed in deriving the equations that describe three-dimensional diffusion in an n-component system plus vacancies. A "Kirkendall coordinate system, '' defined in principle by Kirkendall markers, is used in defining the intrinsic diffusion coefficients that are of primary interest. The defining equations are then transformed to local cartesian coordinates and to fixed cartesian coordinates, the latter being convenient for experimental measurements. Finally, it is shown how the intrinsic diffusion coefficients can be calculated from the experimentally determined quantities. It is generally recognized that any treatment of the essential diffusion phenomena in metallic systems—the jumping of atoms from one lattice position to another—must be based on movement of the atoms past Kirkendall interfaces.' A logical extension of this idea is the proposal that, fundamentally, diffusion must be described mathematically in terms of "Kirkendall coordinates." The basic equations thus obtained may then be transformed into other coordinate systems, when such transformation leads to simplification of either the experimental or mathematical treatment of diffusion data. Tensor analysis is clearly the appropriate mathematical tool for this purpose, since it provides methods both for determining general equations that are valid for all coordinate systems and for conveniently transforming the equations from one coordinate system to another system related to the first in some known fashion. For the present purpose three coordinate systems are used, and it is convenient to begin with a description of the relations among these three systems. FICK LAW FOR KIRKENDALL COORDINATES The reference coordinate system, and the one that is useful for most experimental measurements, is a cartesian coordinate system, xi (i = 1, 2, 3), fixed with respect to some point in the specimen, such as an end of the alloy bar undergoing diffusion. A second set of coordinates, the Kirkendall coordinate system, is one that in principle can be described by the location of inert markers (Kirkendall interfaces). A convenient mathematical relation between Kirkendall coordinates, x'i, and the reference cartesian coordinates, ii, is obtained by specifying that the Kirkendall coordinate system coincide with the cartesian system at time, t = 0. After diffusion has occurred for some time, t = t, the Kirkendall coordinate system will differ from the reference system in the manner shown schematically for the one-dimensional case in Fig. 1. The third coordinate system is Darken's1 local cartesian-coordinate system, xi, which is identical with ii in orientation and units, but which moves with the point under consideration in the Kirkendall coordinate system. Even though most diffusion problems are essentially one-dimensional, there is an advantage in first carrying out the analysis of the three-dimensional problem to gain a clearer insight into the assumptions that are made in the usual one-dimen-

Jan 1, 1962

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

By Charles A. Stickels, Edward E. Hucke

The dihedral angle, formed by the intersection of three interfaces, is often determined by measuring a sample of apparent angles of intersection seen on a random plane of polish, then comparing the exerimental distribution of angles to the distribution calculated by Harker and Parker. Statistical tests show that the latter distribution does not satisfactorily describe the population from which samples are drawn. It is concluded that the major reason for this discrepancy is the presence of a range of dihedral angles in all specimens. When reasonable care is used experimentally, random measuring error is unimportant. It is shown that measurements made on dispersed second-phase inclusions are subject to a systematic error depending on inclusion size, which can be minimized by using adequate magnification. A dihedral angle, calculated from a sample of observed angles as though a unique dihedral angle were present, is termed an "effective dihedral angle". Experience has shown that "effective dihedral angles'' are reproducible quantities, useful for characterizing samples. Methods of determining an "effective dihedral angle", establishing its reliability, and making comparisons between samples are discussed. THE authors have recently reported measurements of the dihedral angle formed by liquid-lead inclusions lying in nickel grain boundaries.' Di- hedral angles were measured by the statistical method first employed by Harker and parker2 and used subsequently by many other workers.3"8 Since a relatively high degree of accuracy was necessary in the authors' experiments, the reliability of this method of dihedral-angle measurement was examined. Briefly, this method of measuring dihedral angles is usually performed as follows. A multiphase alloy is prepared, equilibrated under conditions which allow sufficient interface mobility to establish equilibrium, quenched to room temperature, then prepared for metallographic examination. A large number of observed angles, formed by the traces of grain boundaries and/or interphase boundaries on the plane of polish, are measured at high magnification. If all orientations of interfaces in the specimen are equally probable, Harker and parker2 showed that the population of observed angles is described by a distribution function containing a single parameter, the dihedral angle, 8. certain properties of the population, e.g., the mode or median, have been calculated from this distribution function in terms of the dihedral angle.3, 9 Thus, if the mode or median of a sample is identified with the corresponding property of the population, a unique value for the dihedral angle is determined. One defect in this procedure lies in identifying the properties of a sample of observed angles with the properties of the population from which they are drawn. If one were to proceed in a more rigorous fashion, it would be necessary to find a function of sample properties which is an estimator of the dihedral angle. Then by determining the distribution function for the estimator one could set limits on the value of the dihedral angle. The most apparent obstacle to this straightforward approach is the complexity of the distribution function assumed to describe the population. In analytical form, the distribution function may be written:2, 10

Jan 1, 1964

By R. W. Cahn, C. D. Graham

The rate of growth of a single grain growing into a strained aluminum single crystal, measured by the conventional heat-cool-etch technique, is shown to decrease with time at temperature. The growth rate measured by means of X-rays, with the sample continuously at temperature, is found to be linear. Evidence is presented to show that the decreasing growth rate obtained by the conventional technique is due to abnormal recovery in the strained grain, and that the recovery in turn results from the heating and cooling cycles, rather than from the effects of etching. The experimental apparatus is described in an appendix. FREQUENTLY, the rate of grain boundary motion during recrystallization is determined by heating a sample to a known temperature for a given time, cooling to room temperature, and etching to reveal the boundary position. The cycle of operations is repeated as many times as necessary to establish the rate of boundary motion. Although this heat-cool-etch technique has been used by a number of workers over a period of many years,'-!' other investigators have encountered difficulty with the method."'. " They have attributed the erratic results to the effects of repeated heating and cooling, or of etching, or both, and have adopted an alternative experimental procedure in which a number of identical samples are employed, each sample being cooled and etched only once. This alternative method ove1.comes some difficulties, but introduces others. In particular, the incubation periods of the observed grains are unknown: any effect of crystal orientation on growth rate cannot be determined easily. A preferable method would be to measure the motion of a recrystallizing grain boundary with the sample at temperature without etching," but such measurements have in the past been restricted to nonmetals. This paper describes the construction and operation of a device, the goniometer furnace, with which the position of a moving grain boundary between a recrystallizing grain and the strained single crystal into which it grows can be measured by means of X-rays, with the sample maintained continuously at temperature. Goniometer Furnace The operating principle of the goniometer furnace is shown in Fig. 1. The sample, in the form of a bicrystal strip, is surrounded by a furnace, not shown in the sketch, and can be rotated about the two axes A and B which intersect at the point where the X-ray beam strikes the strip. The strip is oriented so that one of the two grains gives a strong Bragg reflection, which is detected by a suitably placed Geiger-Miiller counter coupled to a counting-rate meter When the strip is moved parallel to its own length in the furnace, arrow C, so that the X-ray beam strikes the second grain, there is in general no strong reflection. By noting the position of the strip at which the drop in Geiger counter reading occurs, it is possible to determine the position of the boundary. Measuring the change in boundary position with time at temperature gives the rate of growth of the recrystallizing grain. Details of the construction and operation of the goniometer furnace are given in the Appendix. Measurements showed that the temperature in the furnace was uniform within ±10°C over its working length of about 28 cm. The temperature at the measuring position, i.e., at the point where the X-ray beam struck the sample, was estimated to be constant within ±2oC. Using the goniometer furnace, the position of a stationary boundary could be measured with a reproducibility of ±0.3 mm. At elevated temperatures, 500" to 625"C, with the boundary in motion and the X-ray reflection less sharp, the estimated accuracy of each measured boundary position dropped to about ±1 mm. Experimental Results The test pieces were single crystals of 99.6 pet A1 —principal impurities 0.19 pet Fe and 0.12 pet Si— 1 mm by 1 cm in cross section and 6 to 10 cm in length, grown by the strain-anneal method. This relatively low purity material was used because of the difficulty encountered in producing strain-anneal single crystals of very high purity—99.996 pet—

Jan 1, 1957

By M. C. Flemings, A. A. Tzavaras

Analytical and experimental procedures are descrihed for quantitative determination of volume-fraction microporosity in metals by mimorarlio-graphg. The analysis assumes spherical pores but allows for the observed fact that pores or portions of pores smaller than a given thickness do not project an image on the film. Volume-fraction microporosity was measuured in cast low-alloy steel and shown to vary from 0.6 x 10-4 to 10 x 10 depending on mode of solidification and on whether the material was air- or vacuum-cast. The aim of work described herein was to develop a method of quantitative measurement of the volume fraction of microporosity in cast metals. Microporosity, present in nearly all castings and ingots, is always interdendritic in nature and may be large enough to be seen on a polished surface with the naked eye. More generally, it is smaller in size, and its detection more difficult. Three techniques might be considered for measurement of microporosity: 1) lineal analysis of a polished metallographic surface, 2) density measurement, or 3) quantitative microradiography. As will be shown later, volume fractions of porosity in directionally solidified castings may be the order of 10-4 to 10-3; such small amounts of porosity are difficult to identify and measure on a polished surface. Density measurement is also not a suitable technique (for alloys) when the volume fraction of porosity is low. This is because the density of the base metal is often not known within the necessary accuracy, due to microsegregation or partial phase transformations. In general, it is not possible to completely eliminate microsegregation without also altering the porosity. Because of the limitations of the foregoing techniques, quantitative microradiography was employed to determine amount of porosity. In recent work, microradiography has been found to be useful for qualitative measurement of porosity, including determination of size and shape of individual pores;&apos;)&apos; however, quantitative determination of amount of porosity has not been attempted. I) CALCULATION OF VOLUME-FRACTION POROSITY The following analysis employs procedures similar to those of Cahn and Nutting3 and Hilliard.4 Major simplifications are that pores are assumed to be spherical and to be present in sufficiently small quantities that no overlapping occurs. A basic difference from the previous treatments is that the limited "sensitivity" of microradiography is considered. Assume first 1) cavities are spherical and of uniform diameter, 2) cavities are randomly distributed, 3) volume-fraction porosity and specimen thickness to pore radius ratio are sufficiently small that overlapping of the projected images of cavities is negligible, 4) sensitivity is limited (i.e., holes or portions of holes of less than a given thickness do not project an image on the film). The sensitivity, is defined as: where 5 = minimum thickness of void from which an image will be projected on the film and t = specimen thickness. Now, from Fig. 1, it is possible to distinguish between two different types of holes. These are 1) holes whose centers lie within the region t/2 > X > 6/2, where X is distance from one surface of the specimen (positive into the specimen), and 2) holes whose centers lie within the region (6 — r) < X < 6/2, Holes whose centers lie outside X = (6 -r) project no image on the film. These two types of pores are considered separately below. Type 1 Pores. When 6 is greater than 0, the image of a spherical cavity of radius r appears on the film as a circle of radius a which is smaller than r. From geometry, Fig. 1: a2=r2-52/4 [2] where a = radius of image of pore on film and r = radius of pore. Since the pores are randomly distributed and spherical V =4/3pr2Nv [3] where V = volume fraction of voids and Nv = number of pores per unit volume and the number of images of Type 1 pores per unit area of film, N&apos;A, is

Jan 1, 1965

By R. L. Fullman

IN the investigation of metallurgical transformations and the relationships between microstructure and properties of metals, it frequently is desirable to obtain a measurement of the relative amounts of the various phases present and of the mean size of particles into which each phase is dispersed. The relative amounts of the phases can be measured by the classical methods of area, lineal, and point analysis,1-5 in accordance with the principle that the volume fraction of a phase, the fraction of a polished cross section occupied by the phase, the fraction of a random line occupied by the phase, and the fraction of randomly arrayed points occupied by the phase are all equal. The validity of this relationship depends only on the attainment of a truly random sample of area, length, or points, and not on the size, shape, or distribution of the particles constituting the phase. Smith and Guttman8 have derived a relationship between the interface area per unit volume S, and the measurable quantities L., the interface length per unit area on a cross section, and NL, the number of interfaces per unit length intersected by a random line. Their equation, Sv = — L8 = 2NL is also valid regardless of the distribution of particle sizes and shapes. In contrast to the situation concerning measurement of relative fractions of phases and of interface area, the measurement of particle sizes in opaque samples has not been subjected to a complete analysis. It has been common to measure some lineal or area dimension of particles on a polished cross section and to use the mean value as a qualitative measure of particle size. In the present paper, quantitative relationships are established among the various mean dimensions on a polished cross section and the actual dimensions of the particles present. Particles of Uniform Size Spheres: If a metal sample contains particles of a phase a dispersed in the form of spheres of uniform size, a polished cross section through the sample will reveal circular areas of phase a with radii from 0 to ?, the radius of the spheres. Consider a cube of unit dimensions to be cut from the sample. If a cross section parallel to one of the cube faces is examined, the average number of particles per unit area (N,) equals the number of particles per unit volume (Nv) times the probability p1 that the plane would intersect a single sphere positioned at random within the unit cube. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length 2r would lead to the plane intersecting the sphere, the probability of intersecting a single sphere is just 2r. N8= Nvp1 = Nd-2r [1] Applying the equality of area and volume fractions, the relationship is found between sphere size and average area s of uniform spheres intersected by a random cross section, 4 - f = NV V = Nr . — pra = N s = Nd . 2rs S = —pr2 [2] A similar analysis reveals the average traverse length across spheres of uniform size when random lines are passed through the sample. If a randomly oriented unit cube is cut from the sample and a randomly positioned line is passed through the cube parallel to a cube edge, the number of spheres intersected by the line (Nl) equals the number of spheres per unit volume times the probability p1 of the line hitting a single randomly placed sphere in the cube. Since possible positions of the line occupy unit area, and possible positions for which it will pass through the sphere occupy an area of pr2, the probability of the line hitting a randomly placed single sphere is pr2. NL = Nv p1 = Nvpr2 [3] Combining this relationship with the equality of volume and lineal fraction, the desired relationship is obtained between radius and mean lineal traverse length -i, for spheres of uniform size. 4 - - 3 l=4/3r [4] Circular Plates: Consider a sample containing particles of a phase a in the form of circular plates of uniform radius r and thickness t, where r >> t. If the plates are randomly oriented, as in a sufficiently large sample of a fine grained polycrystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the plates are not randomly oriented, it is necessary to randomize the orientation of the cross-sectional planes and traverse directions. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of plates cut by the cross-sectional plane per unit area is equal to the number of plates per unit volume times the probability of a plate intersecting a single randomly positioned and randomly oriented plate in the cube. If J is the component of the plate diameter in the direction normal to the cross-sectional planes, the probability of a plane cutting a single randomly oriented plate is equal to J, the mean value of J for all possible orientations of the plate. Let 4 be the dihedral angle between a plate and the cross-sectional plane, and let p?, d? be the probability that a plate makes an angle between 4 and ? + d? with the cross-sectional plane. Then for ran-

Jan 1, 1954

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent papers on interface energies in metals¹,² the concept of an equilibrium of forces has been used in the measurement of interfacial tensions. Mathematically the equilibrium of three forces is given by the relations: where the 2&apos;s are the interfacial tensions (interface energies per unit area of interface) of three phases or grains meeting at angles 21 22 and 23 (212 relates to the 1-2 boundary formed by grains 1 and 2;223 to the 2-3 boundary, etc.). If these relationships are valid, one can calculate relative values of the interface energies from measured boundary angles on specimens which have been brought to equilibrium. Since Eq 1 may be derived through a mathematical process of minimizing the grain boundary energy under the restriction that the ?&apos;s be independent of boundary orientation: the concepts of surface tensions and equilibrium of forces are not particularly essential. To deal with the general case involving dependence of boundary energy on boundary orientation, it becomes desirable to drop certain concepts formerly held (namely that energy per unit area is identical with force per unit length or surface tension) and to use the energy concept alone. It is appropriate, therefore, to use E in place of ? in deriving and using the more general equations that express the anisotropic nature of the grain boundary energy. Herring3# &apos; recently has derived the required general equations using the principle of minimization of energy. Specifying the boundary orientations in terms of angles (4) measured with reference to crystal axes within the grains, Herring&apos;s equations take the form E23 + E21 cos?8 + E12 cos?2 — sin ?12 + sin?2-?E12/?12 =O [2] where the partial derivatives are measured in the direction of counterclockwise rotation of the boundaries. Eq 2 implies that an infinitesimal displacement of the triple point along the 2-3 boundary produces no change in the boundary energy. Similar equations apply for infinitesimal displacements along each of the other two boundaries. From such equations Herring obtains the following general relationship (1 + E1 E2) sin?8 + (E2 — E1) cos?3 ________ E38______________ = (1+ E2 E8) sin ?1+ (E3— E2) cos ?1 __________^5____________[3] (1 + E sin ?2, + (E1 — E8,) COS ?2 1 E28 where E1 = 1/E23- E25 and PC and c8 have similar expressions. It is apparent that Eq 3 reduces to Eq 1 when the c&apos;s vanish. Eq 3 also reduces to Eq 1 when the E&apos;S are all equal. Shockley and Read&apos; have pointed out one limitation to these equations. When E plotted versus 4 appears as an energy cusp, as their theory requires, for example, for the energy near a twin boundary position, then Eq 3 (and therefore Eq 1 also) no longer applies if one boundary is in the minimum energy position. One of the equations of form Eq 2, however, applies if the infinitesimal displacement is along the boundary associated with the energy cusp. From the foregoing treatment it will be apparent that equilibrium angles alone are not sufficient in general for calculating relative interface energies.

Jan 1, 1951

By C. G. Dunn, F. W. Daniels, M. J. Bolton

J. P. Nielsen—The data that Dr. Dunn and his associates have been obtaining are welcome checks on the theoretical aspects of grain boundary energies. With reference to the comments on the validity of the inter-facial tension concept, I should like to say that I have been having considerable difficulty myself in untangling the confusion between "interfacial tension" and "interfacial energy." The confusion however resolved itself for me when I learned that "interfacial tension" for solids, or at least crystals, is used with two distinct meanings. One meaning12. &apos; "hat is implied for "interfacial tension" is the work necessary to produce or increase the surface of the solid in question by a unit area, temperature and pressure held constant. This comes from the somewhat surprising but simple fact that surface tension and surface energy in the case of liquids are identical quantities. This synonymity has carried over to crystals, where it should be kept in mind that the tension connotation has meaning only by analogy with liquids and that no real stresses are being referred to. The only reason that there is apparently a set of stresses acting at a grain boundary junction is the optical illusion that liquid interfaces are being observed for the grain boundaries. The other meaning3,14,15 for the term has to do with actual states of stress in the surface of a material as would be measured by a system of forces applied to the surface to equate the surface stress state with that in the body of the crystal. J. B. Hess—Since the authors have proposed that the surface tension concept should be discarded in order to deal with the general case of interface energies in solids, their attention should be called to a recent paper by Gurney." The latter has shown, from a thermodynamic argument, that surface tension is a valid concept in solids. In fact, Gurney has rejected the idea that surface tensions are merely mathematical fiction and, instead, has given an interpretation of their physical reality. Finally, he has concluded that, as long as appreciable atomic migration takes place, specific surface energies and surface tensions must be equivalent in solids as well as in liquids. Accordingly, the authors&apos; eqs 2 and 3 can be written with equal accuracy in terms of interface tensions, simply by replacing each E,! with its numerically and dimension-ally equivalent Interfacial tension ?,,. If the interfacial tensions (or specific energies) are independent of interfacial orientation, as is true in liquids, then the general equations that define the geometry at equilibrium of the common junction of three interfaces reduce to eq 1. However, neglect of the effect of boundary orientation is never completely justified theoretically&apos; in dealing with crystalline solids; hence, use of eq 1 in such cases must always be considered as an approximation, though clearly a reasonable one for many purposes.1,2 At the same time, one should not be surprised that the assumption that interface tensions in solids are free from orientation

Jan 1, 1951

By R. T. DeHoff, L. J. Buteau, J. Kronsbein

Network topology is introduced and used to describe sinter bodies at various stages of the sintering process. The matrices of incidence, loop-branch. tree-branch, and cut-branch are constructed and their relationship to the three-dimensional void space and the common two-dimensional bounding surface is established. The sintering body is assunzed to remain connected but this is not so with the void space. The topological invariants known as Betti numbers are related to this observed fact and provide parameters which measure the progress of the sintering process. They are extracted from the matrices by means of known algebraic operations. Experimental procedures are given which permit actual construction of the various matrices and determination of the Betti numbers by serial sectioning of the sinter bodies. A sinter body is produced by exposing a large number of metallic particles (0.00001 to 0.3 in. diam) to a temperature that is near but below their melting point. When these particles are maintained at such a temperature for a sufficient length of time, it is found that the interparticle contacts become welded. As time increases, these welds, often referred to as necks, grow. All of the space between the particles constitutes a single connected void; an ultimate consequence of sintering is the breaking up of the void into separated parts. A mathematical apparatus for describing the geometric characteristics of a sinter body at each stage of the process was first proposed by F. N. Rhinesl when he introduced the application of topology to this problem. He described the sinter body in terms of one of its topological invariants, the genus. The most important advantage of a topological description is invariance with respect to continuous deformations. This means that particle sizes and shapes need not be considered, resulting in considerable simplification and generalization of the geometric description. In the case of a sinter body, wherein the internal geometry is particularly complex, the simplification provided by topological concepts is absolutely essential. The important parameters in the Rhines model are the number of particles and the interparticle contacts. The invariant considered called genus is given by Euler&apos;s formula for the connectivity of two-dimensional surface of the sinter body. This surface includes the pore-solid interface. The Euler formula is G = C - P + 1 [1] where C = number of interparticle contacts, P = number of particles, and G = genus of the surface bounding the sinter body. In topology the term genus may be used to mean the number of self re-entrant cuts that can be made on a closed surface without dissecting it into more than one connected surface. Its use is restricted to the surface and does not apply to the three-dimensional volume enclosed or excluded by it. In the case of sintering, the volume enclosed by the surface is defined as the sinter body; the volume excluded will be referred to as the void space. There is an intrinsic reason for using genus as a characteristic number associated with a sinter body. The genus is related to the Gaussian curvature by the integral of the product of the principal curvatures taken over the entire surface of the sinter body, as given by

Jan 1, 1965

By J. J. Pye, J. B. Drew

Mzasurements of the surface diffusion coefficients of metals have been made. Diffusion profiles for the Ag-Ag system were obtained by means of a radioactive point source and a precision auto-radiographic technique. The activation energy for silver self diffusion (=8.1 kcal per mole) is lower than that previously reported (-10 kcal per mole) on poly crystalline wire by Nickerson and Parker. The bresent data indicate an effect due to parasitic volume diffusion at temperatures above 500°C. RELATIVELY few measurements have been made of the surface self-diffusion coefficients of metals. Nickerson and arker&apos; measured the diffusion of silver over the surface of poly crystalline wires and estimated that the activation energy was 10.3 kcal per mole. Winegard and chalmers2 carried out measurements on both polycrystalline and single crystal surfaces but did not report a value of the activation energy. They found, however, that at temperatures between 250" and 400°C the diffusion coefficients were on the order of lo-&apos; sq cm per sec and that there was an acceleration of the migration of silver on the polycrystalline sample when a change of surface shape occurred. Winegard and Chalmers used an autoradiographic technique, hereafter designated ARG, and Nickerson and Parker used a surface scanning geiger counter in order to determine the diffusion profiles. More recently, Hackerman and simpson3 measured the surface self-diffusion coefficient of copper at a single temperature (750°C), and the value of the diffusivity (- 10-5 sq cm per sec) is in agreement with that given by jostein from his thermal grooving measurements. This paper reports the results of an investigation of the surface self-diffusion coefficients of silver over a large temperature range and describes the adaptation of autoradiographic (ARG) techniques for the determination of diffusion profiles obtained from a radioactive point source. EXPERIMENTAL PROCEDURE The experimental procedure is a modification of the method employed by Hackerman and simpson3 in their measurements on copper. A brief description of their technique is as follows: A radioactive needle which sinters to the surface during the diffusion an- neal serves as the source of diffusing atoms. After the diffusion run the needle is removed and the surface is scanned with a shielded counting arrangement. The diffusion profiles reported in this paper were obtained by a modification of the above procedure which employs a precision ARG technique. Previous investigations in this laboratory and elsewhere51B have shown that under carefully controlled developing conditions and by the use of calibration sources a linear relation exists between the concentration of the isotope and the photographic density for values below unity. The use of ARG under these conditions has advantages over the counter scanning method in that cumbersome shielding and requirements for great mechanical precision of the scanner are eliminated. Also the ARG gives a complete picture of the surface which is advantageous in studies of anisotropic diffusion. A recording microdensitometer having a 0.1 p wide slit was employed. At low temperatures the disturbing effects of subsurface radiations are negligible. The diffusion anneals are carried out in the cell shown in Fig. 1. The needle is formed by grinding down a 1.0 mm rod of high-purity silver until a tip of 0.2 mm radius or smaller is formed. This tip is plated withA"&apos; which becomes the source of the diffusing atoms that are detected by ARG. The needle carrier and the crystal holder, Fig. 1 are constructed of quartz and ports are provided in the holder pedestal which allow free vapor circulation ((2.0 oz) and the carrier apron fits snugly over the crystal holder cap, insuring that the needle does not move and scratch the surface. Temperatures are provided by a stabilized tubular furnace which can be quickly positioned around the cell, thus bringing the crystal up to temperature in a time that is short compared to the diffusing times. The diffusion anneals range from 2 hr for the high-temperature samples to about 25 hr for those at the lowest temperature. The possibility of vapor transport of the radioactive metal as a contributing factor in the diffusion profile was investigated in two ways. One method was to suspend the needle directly over a dummy sample, raise the temperature, for periods of time equal to the diffusion times, and then take an auto-radiograph of the surface. Negligible radioactivity appeared. In the second method a thin slot in the crystal face on one side of the source provided a "cong path" for surface diffusion. If evaporation was the primary source of surface atoms the region of radioactivity around the source would be symmetrical. This was not the case. The profile dipped abruptly at the edge of the slot but on the other side of the source the usual diffusion profile appeared.

Jan 1, 1963

By Lawrence A. Shepard, Richard H. Krock

A series of ductile, two phase W-Ni-Fe composites, sintered in the presence of a liquid phase, were tested in tension. Identical room temperature stress-strain curves were obtained for specimens containing from 80 to 92 wt pct W (58 to 75 vol pct W particles). The composites exhibited a maximum elongation of 29pct at room temperature, and 10.7 pct at 77 °K. The tungsten particles in the composite elongated by the same amount at these temperatures. Single-phase alloy specimens matching the composition of the composite matrix showed about one half the flow stress of the composites. The test results demonstrated that the mechanical properties of W-Ni-Fe composites are determined by the tungsten particles alone and are independent of matrix volume fraction or mean free path over the composition range studied. A general prediction of the plastic behavior of two-phase alloys or composites from a knowledge of the properties, size, shape, and dispersion of the individual components is not, at present, possible. The excellent theoretical and experimental exposition of the dispersion-strengthening problem applies only to cases where the stronger phase is present as fine particles and in volume fractions of a few percent. Materials in which the stronger phase constitutes a significant fraction of the volume, although of broad engineering interest, have received comparatively little analytical attention. This important group of materials is the concern of the present study. The degree of deformation of each phase during the plastic working of a ductile two-phase alloy has been established by Boas and Honeycombe,1 Clare-brough,2 and Clarebrough and berger.3 These workers empirically correlated the recrystallization temperature of the individual phases with the degree of cold work sustained by each. It was shown that the deformations of both phases are equal and therefore the same as that sustained by the composite whole when the volume fraction of the stronger phase exceeds 35 pct. At yielding, however, deformation begins in the weaker phase. A direct correlation of composite strength, as a function of deformation, with the strength of the individual components cannot be made. In the presence of stronger phase particles, the flow stress of the weaker matrix phase is enhanced by an additional hydrostatic component. The development and potential magnitude of matrix strength promotion upon straining has not even been experimentally established. Quantitative work in this field has been confined to ceramic-metal composites. These materials fracture at strains considerably below 1 pct by cracking of the ceramic particles.4-6 An indication of the potential constrained matrix strength capacity is given by the observation by Nishimatsu and Gur-land4 that the maximum tensile strength of a WC-Co composite is almost double the bulk strength of the cobalt matrix. The relationship between composite strength and geometry is ordinarily expressed in terms of the mean-free matrix path (referred to subsequently as MFP) between the stronger particles.* This factor takes into account both the volume fraction of matrix phase and the average size of the particles. unke17 concluded that composite strength varied directly with the decreasing log MFP, following the Gen-samer8 relationship. However, Gurland and ~radzil~ reported a strength maximum at an MFP of the order of 1 p in WC-Co composites. A ductile two phase metallic composite was chosen for the present investigation of composite mechanical properties with the view of avoiding the difficulties and ambiguities noted above. The W-Ni-Fe heavy alloy of Green, Jones, and pitkin9 contains 80 to 94 wt pct W, and nickel and iron in a weight ratio

Jan 1, 1963

By N. S. Stoloff, R. G. Davis

It is concluded from an X-ray stztdy that the formation of the hcp Mg3Cd superlattice is a nuclea-tion and growth reaction. A two-phase, ordered-plus-disordered, region is observed between 153" nnd 141"C. A maximum in the flow stress is observed both at temperature and in quenched specimens within the two-phase region. The peak arises fro112 the extra energy required to create antiphase boundary upon cutting the ordered regions. Hardening during isothermal annealing in Mg3Cd has been shown to be similar to the domain hardening in Cu3Au-type alloys in that up to the maximum the structure is ordered domains growing into a short range ordered matrix. The hardening is due to a combination of short range order strengthening and the strengthening produced when antiphase boundary has to be created. In a recent study1 of the effect of long-range order upon the mechanical properties and deformation modes of hcp Mg3Cd a comparison was made be- tween quenched (disordered) and slow-cooled (fully ordered) specimens. The most striking observations were that the disordered alloy yields at a much higher stress than the ordered alloy, and that there is a change in slip mode from primarily (_0001) ba_sal slip in the disordered state to (0001), {1010}, {1122}, and {l011} slip in the ordered state. The main purpose of the present work is to extend these observations to determine whether MgsCd exhibits a peak in flow stress at an intermediate degree of order, or at a critical domain size, as do other orderedstems. However, disagreement exists about the Mg3Cd order transformation with respect to: 1) the location of the critical temperature for order, 165°C or 153"~,&apos; and 2) how the degree of order varies with temperature. Welber et a1.5 concluded from specific heat measurements that the formation of Mg3Cd is a second-order reaction with the degree of order a continuous function of temperature, while Moore and Raynor concluded that it is neither a first-order reaction, with the degree of order a discontinuous function of temperature, nor a second-order reaction. Consequently it was considered necessary to undertake an X-ray investigation into the change in degree of order and structure in the

Jan 1, 1964

By R. I. Jaffee, F. C. Holden, H. R. Ogden

The effects of grain size and shape on alloys of titanium with nitrogen and aluminum have been determined. Increasing a grain size decreases strength and hardness and increases impact resistance. Quenching from the ß field produces subgrain markings delineating a plates in Ti-N alloys but not in Ti-AI alloys. This suggests a precipitation from the high nitrogen alloys. ALPHA titanium alloys are single-phase alloys with the hexagonal-close-packed structure of a titanium. If these alloys are worked and annealed within the a field, equiaxed structures result in which strength is derived from the solid solution of the alloying elements present. Strain hardening can be used to increase further the strength of a titanium alloys. This is the only other mode of strengthening the a type of alloy. Quenching from the ß field has been noted by many investigators to have little effect on the strength of iodide titanium and on commercial titanium. Ti-A1 alloys were found to be little different in hardness, whether annealed in the a field or quenched from the ß field.&apos; These facts illustrate a characteristic of a titanium alloys: they are insensitive to heat treatments from the ß field. Underlying this heat-treatment insensitivity are the facts that the a-ß field is generally narrow in a titanium alloys, the transformation-temperature range increases with a-stabilizing content, and the a solubilities of the alloying elements are greater than the ß solubilities. When quenching is done from the ß field, there is no supersaturation of the alloying elements in the acicular transformation structure produced. Welds in a titanium alloys generally are ductile, because no transformation hardening occurs during cooling.1,2 Other desirable features of a alloys are: no thermal-stability problem, excellent toughness, and retention of strength at elevated temperatures better than a-ß or ß alloys of comparable room-temperature strength. The prime factors governing the properties of a titanium alloys are the amount and kind of solute present. This can change the a phase from a soft, tough material into a hard, brittle material with no apparent change in microstructure. Moreover, brit-tleness can exist over a wider alloy-content range, without change of phase, than in most other metals. The solutes for a titanium may be divided into interstitial and substitutional types. Oxygen and nitrogen dissolve interstitially in rather large amounts, extending well through the brittle range, and the transformation-temverature ranges are raised in the process.:&apos; , carbon has a maximum interstitial solubility of about 0.5 pct at the peritectoid temperature, while at lower temperatures the solubility decreases to about 0.2 pct.3,5 Substitutional a solutes include aluminum and tin. Aluminum has a high a solubility of 25 pct Al, and increases the transformation-temperature range markedly.6,7 Tin has a high a solubility of about 20 pct, but has a relatively innocuous effect on the transformation-temperature range.&apos; The choice between interstitial and substitutional solutes generally has been conceded to the substitutional solutes because of a belief that they do not have as adverse an effect on ductility and notch toughness. However, a recent investigation8 on the effect of hydrogen on titanium has shown that this element, which is not under compositional control, has a powerful detrimental effect on notch toughness. Hydrogen was shown to form a hydride which is practically insoluble (about 0.002 pct) in a titanium at room temperature, although the solubility at the eutectoid temperature of about 300°C is relatively high, about 0.16 pct. Limited data were presented on the effect of hydrogen on a alloys, where the same impairment of toughness as in unalloyed titanium is found. The work reported here describes the effects of interstitial and substitutional solutes on 1—the mechanical properties of high purity titanium free of titanium hydride and 2—the influence of structural variables on these properties. Nitrogen was selected as an example of an interstitial solute with high solubility and aluminum as a substitutional solute with high solubility. All compositions were well within the ductile range, since it was not intended to study the brittleness problem here, but to study only the factors influencing optimum mechanical properties. Procedures The alloys were prepared from iodide titanium as 1/2 Ib ingots double melted to insure homogeneity.

Jan 1, 1955

By George A. Roberts, Arthur H. Grobe

Tensile, hardness and density properties are presented for a new 18-8 stainless steel powder for the —50, —100, and —140 mesh cuts and also for a prepared blend containing 62 pct —325 mesh powder. The data were obtained for sintering temperatures of 2100° to 2350°F and for compacting pressures of 30 to 50 tons per sq in. A NEED has existed for a stainless steel powder of uniform composition from particle to particle, which could be readily molded and sintered, and which would yield moderate to high strength and ductility when processed into parts by standard powder metallurgy techniques. The literature reveals that previously available powders have been lacking in one or several of these desirable characteristics. Originally attempts to produce stainless steel powder by blending and diffusing elemental metal powders were unsuccessfu1.l A truly alloyed stainless steel powder reported by Dale in 1947 yielded reasonable mechanical properties but required an exceptionally high sintering temperature of 2400°F in pure dry hydrogen.&apos; A later development reported in 1950 by Stern provided a stainless type powder of excellent molding properties&apos; but this powder likewise required sintering at temperatures over 2350 °F and did not yield properties as high as those previously reported. The powder was not truly alloyed prior to sintering. A prealloyed stainless steel powder has been developed that is readily moldable at 30 to 50 tons per sq in., can be sintered at low temperatures (2100" to 2300°F), and which yields compacts with both high strength and ductility. The powder is prepared by the liquid disintegration method," direct from molten metal. Early attempts to make 18 pct Cr, 8 pct Ni stainless steel powder by this method did not produce a usable powder for pressing and sintering because of a preponderance of spherical particles with relatively high, surface oxide content. It was learned that silicon additions to iron alloys, powdered by this process, gave bright powder of low-oxide content and such additions were made to 18-8 stainless with similar results. An attendant change in particle shape occurred reducing the number of spheroids materially. The optimum composition which has been studied and is reported here contains approximately 2.5 pct Si. Silicon additions to stainless steel of the 18-8 type improve the resistance to high-temperature oxidation and promote the formation of ferrite. Corrosion resistance is, however, controlled by chromium content and even though ferrite may exist the corrosion resistance is not generally impaired.4 Experimental Procedure A detailed study of the 18-8, 2.5 pct Si powder has been made in accordance with the following outline: 1. Four blends a. — 50 mesh b. —100 mesh

Jan 1, 1952

By George A. Roberts, Arthur H. Grobe

H. H. Hausner (Sylvania Electric Products Inc., Bayside, N. Y.)—I tested the 18-8 stainless steel powder described by Grobe and Roberts and the results were excellent. The powder was compacted and sintered in purified hydrogen to a very low density (approximately 20 pct and more porosity). Where the other powders show very little ductility when sintered to such a low density, the described stainless steel was surprisingly high in ductility. I would appreciate it if the authors could give us some data on a similar powder but without silicon and also data on 430 stainless steel powder. H. S. Kalish (Sylvania Electric Products lnc., Bay-side, N. Y.)—I should like to verify the excellent results obtained by Grobe and Roberts with their pre-alloyed stainless steel powder. It seems to me, however, that their data are conservative and that even better densities and higher tensile strength can be obtained with these powders by the selection of proper particle size fractions. The accompanying data were obtained by sintering compacts pressed from the powder made by Vanadium-Alloys Steel Co. to 0.8 in. in diam about % in. high in a cylindrical double action die without the use of lubricant. The compacts were sintered for 1 hr at 2370°F in hydrogen purified by passing it through a Deoxo unit (palladium catalyst) and a Lectrodryer. Even the density obtained using the as-received (—100 mesh) compacted at 40 tsi was quite high as was the hardness. This indicates that by increasing the sintering temperature slightly above 2350°F the coining and subsequent secondary sintering operation can be avoided. With the — 325 mesh fraction, however, very much higher density can be obtained and a high hardness. I have no tensile data to present, but I feel that it is not too optimistic to expect. that unusually high tensile strengths and good ductility can be obtained in this sintered material on the basis of the density and hardness data. The sintered stainless steel made by the above-described methods came out of the furnace very bright and clean. The purified hydrogen atmosphere is important in sintering stainless steel to reduce the oxide present in the powder. The result of such a sintering is good densification and good ductility of the sintered product. G. A. Roberts (authors&apos; reply)—We are greatly indebted to Messrs. Hausner and Kalish for their discussions of our paper. Their encouraging remarks are greatly appreciated and their confirmatory data will do much to add to the value of the paper. At the present time it is impossible to provide complete data on a similar stainless steel powder without silicon, but we do know that, in general, the properties are slightly inferior. Data on such a powder and on other stainless steel types are to be published in the near future.

Jan 1, 1952