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Diffusion in Solid Metals. BY ROBERT F MEHL (Institute of Metals Division Lecture Tech Pub 726 in Metals Tech, Aug , also Trans, vol 122 22,500 words ) Diffusion in solid metals constitutes one of the important fundamental phenomena in metallurgical behavior Apart from its obvious importance in processes such as chromizing, carburizing, nitriding and calorizing, it plays an important part in the processes of homogenization, age-hardening, and transformations in steel, its scientific importance is no less great Diffusion may occur within a grain, along a grain boundary, or upon a surface, though the exact and even the relative values of these separate processes are known for only a very few cases The requirement of solid solution formation presents the possibility of identifying solid solution phases by a study of diffusion layers Some distortion accompanies diffusion, leading to little¬ understood grain-size changes Distortion assists diffusion though usually it dis¬appears before diffusion has become extensive In a binary system the rate of diffusion is the more rapid in the lower melting metal Many of the published data are too qualitative to permit sound scientific conclusions Age-hardening data may be treated as diffusion data and rates of reaction in steel could profitably be studied from this point of view Studies on diffusion are of great importance to the develop-

Jan 1, 1937

Terminology Relating to Nonmetallic Elements in Metals. See IRON AND STEEL Ferromagnetism in Metallic Crystals. BY L W MCKEEHAN (Tech. Pub 554, Metals Tech , August; also Trans, vol 111. 20,500 words ) The directions for easiest magnetization of ferromagnetic single crystals are those of simple crystal- lographic forms and the extra energy needed for magnetization in other than these preferred directions depends upon the material selected for test The history of magnetic tests upon metallic single crystals, reviewed in detail, shows that crystals of one metal agree rather well as to the magnitude of such energy differences. This makes ~t probable that these differences are really charactenstic of the ferromagnetic

Jan 1, 1935

By P. E. Price, N. J. Grant

DURING the course of creep studies in iron-chromium-nickel alloys, it became necessary to establish the limits of the two-phase ferrite-austenite field at 1300°C. The shape of this region, predicted from the iron-chromium and chromium-nickel binary

Jan 1, 1960

By A. J. Lena, M. F. Hawkes

Changes in hardness, tensile properties, microstructure, electrical resistance, and X-ray diffraction effects indicate that lattice strains are necessary for the embrittlement of ferritic stainless steels when heated for relatively short times at 475°C (885°F). It is suggested that 475°C (885°F) embrittlement is due to the accelerated formation of an intermediate stage in the formation of s under the influence of these strains. FERRITIC stainless steels (low carbon alloys of iron with more than 15 pct Cr) are subject to two forms of embrittlement when heated in the temperature range of 375° to 750°C. The embrittlement which occurs after long time heating between 565" and 750°C is well understood; it is caused by the precipitation of the hard, brittle s phase. Sigma is an intermetallic compound of approximate equi-atomic composition with an extended range of formation in Fe-Cr alloys. The maximum temperature at which this form of embrittlement can occur is dependent upon chromium content; and is approximately 620°C for a 17 pct Cr steel and 730°C for a 27 pct Cr steel. The other form of embrittlement occurs after relatively short heating periods in the range of 375" to 565°C; in the higher chromium steels, hours may be sufficient as compared to months for s embrittlement. This phenomenon is not at all well understood and several controversial theories have been proposed. The rate and intensity of embrittlement increase with increasing chromium content but the maximum rate occurs at 475°C re-gardless of chromium content. As a result of this, the phenomenon has been termed 475°C (885°F) embrittlement. The effect of 475°C embrittlement on the properties of ferritic stainless steels has been thoroughly reviewed by Heger.1 The embrittlement causes a pronounced decrease in room temperature impact strength and ductility, a large increase in hardness and tensile strength, and a decrease in electrical resistivity and corrosion resistance. Microstructural changes accompanying embrittlement are minor and difficult to interpret with a general grain darkening, appearance of a lamellar precipitate, grain boundary widening, and precipitation along ferrite veins having been reported at various times. With the exception of reported line broadening, X-ray diffraction studies by conventional Debye analysis of solid samples have been of little value. BY making use of electron diffraction methods, Fisher, Dulis, and Car-roll' have recently shown the existence of a chromi-um-rich, body-centered cubic phase in 27 pct Cr steels which had been aged at 482°C (900°F) for as long as four years. Two types of theories have been advanced to account for the embrittlement. The first of these requires the precipitation of a phase not inherent in the Fe-Cr system with various investigators suggesting a carbide,3 nitride,3 phosphide,4 or oxide." Theories of this type have difficulty accounting for the influence of alloying elements on the embrittlement and for the facts that a minimum chromium content is necessary for embrittlement and the intensity of embrittlement increases with increasing chromium content. The second type of theory that has been proposed relates 475°C embrittlement to s phase formation which is inherent in the Fe-Cr system. An assumption of this kind can adequately explain the influence of alloying elements, for they exert an effect on 475°C embrittlement similar to that on s phase for-mation as can be seen in Table I. The minimum chromium content is essentially the same for both phenomena and it has been shown12,13 that s is a stable phase in the embrittling temperature range. In addition, it has been reported14,15 that pure alloys embrittle to the same extent as commercial type alloys. There are, however, several factors which have prevented complete acceptance of a s phase theory. Foremost of these is that the embrittlement can be removed by reheating for short time periods above 600°C, which in the higher chromium steels is within the stable s region. No s has ever been observed after one of these curing treatments, nor has any s been found as a result of embrittlement at 475°C. In addition, the simple precipitation of s cannot explain the time-temperature relationships for reactions between 350°and 750°C. This behavior is shown schematically in Fig. 1. Newell 16 and Ried-rich and Loib4 have shown that 475°C embrittlement follows a C-type curve as illustrated, while Short-

Jan 1, 1955

By W. L. Chu

It was observed that chromized coatings on low carbon steel could be embrittled by cooling slowly through the 475°C range. A higher chromium coating was more susceptible to embrittlement than a lower chromium coating. Coating structure and composition could be correlated with the chromizing process and prior carbon content of the steel. IT was recently observed that during the fabrication of rectangular tubings made with chromized thin gage 1010 steel, a high percentage of these parts were fractured readily in a brittle manner under the light impact-forming load employed. Ensuing investigation indicated the cause for such brittle failures to be the so-called 475°C embrittlement of the chromized coatings. The experimental work and results are briefly reported. Rectangular tube sections of normalized AISI C1010 steel, which had a cross-section of 0.5x1.5 in. and a wall thickness of 0.030 in., were chromized to yield coatings having several ranges of thickness, varying from 0.0005 to 0.002 in. Essentially, the chromizing process is similar to that described by Samuel and Lockington,' which consists of heating the parts in a sealed container at about 955°C for 4 hr in intimate contact with a chromizing mixture* samples in a hydraulic press, and the other employed a simple beam bending test of the flat sides of the tubing walls. Neither, however, was able to differentiate the relative brittleness of samples known to include both the brittle and tough types, since the impact-brittle samples were found to deform readily in a manner similar to the tough ones. Both the tough and brittle samples were studied by reflection microscopy. Observation showed that the microstructures of the steel cores were similar in content and distribution of inclusions as well as in the ferritic grain size. Results of Filar micrometer measurements showed that coating thicknesses+ of the brittle samples averaged 0.0007 in., whereas those of the tough samples averaged 0.0016 in. The micrographs of Fig. 2 illustrate the structural differences between coatings of both types of samples. By dissolving the steel cores in nitric acid, coatings of both the brittle and tough samples were isolated. Simple bending tests showed that coatings of the brittle samples cracked readily at about 90" bend, whereas those of the tough samples could be bent nearly 180° without cracking. The coatings as well as the steel cores were analyzed for carbon and

Jan 1, 1956

THE transformation, in a sample of levitation melted iodide titanium, has been studied with a Leitz hot-stage microscope. The specimen was etched in HF:HNO3: glycerine, (1:1:2) giving a structure shown in Fig. 1, and was then heated at approximately 5OC per min. At 870°C (±5OC) the etching product disappeared, the a-grain boundaries showed in relief, and some new grain boundaries (presumably of ß) appeared (Fig. 2, see arrow). Some evidence of ß-grain growth is indicated by the apparent longitudinal movement of a ß-grain boundary shown in Figs. 2 and 3 (see arrows). The specimen was later heated to 1000°C and then cooled at 2°C per min. At 845°C rumpling of the surface was first noticed, Fig. 4, and continued at constant temperature. The photomicrograph reproduced in Fig. 5 was taken 6 sec after Fig. 4, at 845°C. Fig. 6 shows the structure after cooling to room temperature. The room-temperature structure, showing a rumpled surface has been observed by previous investigators.' These structures presumably indicate a sheer transformation ß - a, athermally nucleated, but capable of isothermal progression.

Jan 1, 1960

By J. S. Ll. Leach, L. R. Rubin, M. B. Bever

The energies of formation of ordered and disordered solid solutions of composition CusAu and the energy of ordering in this alloy were determined by tin solution calorimetry. The degree of order was measured by X-ray diffraction and electrical resistance and microhardness measurements were made on ordered and disordered specimens. AMONG the phenomena associated with the order-disorder transformation of a solid solution, the change in internal energy is of special interest because of the part it plays in the various theories of ordering. Published values for the decrease in internal energy accompanying the formation of a superlattice from a disordered solid solution of composition CuAu range from —370 to —2260 cal per gram-atom. Some of these values represent calculations based on theory and others are the results of experimental measurements. The distinction between the change in internal energy, AE, and the change in enthalpy, AH, can here be neglected, because they are approximately equal for solid-state reactions at normal pressure. An analysis of ordering by Bragg and Williams' predicts an energy change of —605 cal per gram-atom for the formation of a superlattice in the alloy Cuau from a completely random solution. Peierls" application to Cuau of Bethe'sb earest-neighbor theory yields —560 cal per gram-atom for the formation of a superlattice from a matrix which initially contains short-range order. Cowley' extended the nearest-neighbor approach to include as many as five shells of neighbors; on this basis a change in energy of —500 cal per gram-atom is expected. Eguchi," using a quantum-mechanical treatment, calculated a value of —2260 cal per gram-atom for the difference in the energy of completely disordered and completely ordered Cu,Au. Sykes and Jones- eated a completely ordered alloy and measured its heat capacity as a function of temperature. This measured heat capacity agrees closely with the corresponding value found by the Kopp-Neumann (or mixture) rule up to about 250°C and above this temperature exceeds it, especially near the critical temperature for ordering. The difference between the integrals with respect to temperature of the observed and the Kopp-Neumann heat capacities was considered to be the energy of ordering. By this method Sykes and Jones found a value of —530 cal per gram-atom. This value is not adjusted for the short-range order remaining above the critical temperature. The pres- ence of such short-range order is suggested by the difference between the measured heat capacity and the extrapolated Kopp-Neumann heat capacity immediately above the critical temperature. Values reported by Weibke and von Quadt' and by Hirabayashi, Nagasaki, and Maniwaa were obtained in the course of investigations primarily aimed at other objectives. Weibke and von Quadt measured the temperature coefficient of the electromotive force of a Cu-CuAu cell. They obtained a value of —1010 cal per gram-atom for the heat of formation of the alloy at 500°C, at which temperature there is no long-range order. They also obtained —1380 cal per gram-atom as the heat of formation of the ordered alloy at 370°C. Considering the heat of formation of the disordered alloy to be independent of temperature, they estimated the energy of ordering at 370°C as —370 cal per gram-atom. At this temperature long-range order is incomplete and the degree of order changes rapidly with temperature. Hirabayashi, Nagasaki, and Maniwa," using an annealing calorimeter, investigated an alloy containing 23.4 rather than 25.0 atomic pct Au and thus could not obtain complete order. Thelr value of the energy of ordering was —490 cal per gram-atom. Orianis has recently investigated the Au-Cu system by the galvanic emf technique. He reports values for the heats of formation of Cu-Au alloys, from which the heat of formation at 427 OC of an alloy of composition CuAu may be found by interpolation. This value is —1080 cal per gram-atom. In the work here reported, disordered and ordered alloys of composition CuAu and corresponding mixtures of gold and copper were dissolved in liquid tin and the heat effects measured. These heat effects are small, since the dissolution of gold in tin is exothermic and the dissolution of copper is endothermic. The method, therefore, yields fairly precise values of the heats of formation of disordered and ordered alloys and of the energy of ordering. Experimental Procedure The calorimeter consisted of a long-necked Dewar flask immersed in a constant temperature salt bath and has been described by Ticknor and Bever." The chief changes in this equipment were an improvement in vacuum and the replacement of the mercury thermoregulator by a resistance thermometer control circuit. The solvent, which was maintained at a constant temperature near 350°C, consisted of 500 grams of 99.99 pct pure tin. The solute samples were mixtures of gold and copper in the proportion corresponding to the composition Cu,Au or solid solutions

Jan 1, 1956

By H. J. Levinstein, W. H. Robinson

A method of chemically polishing silver for metal-lographic examination has been developed. The samples are prepared by polishing on 0, 2/0, and 3/0 paper. They are then polished on 600 micro-cut paper, followed by a final mechanical polish on a cloth containing 5µ diamond paste. The samples are then chemically polished in a solution of 100 cc of saturated chromic acid and 5 cc of a 5 pct HC1 solution. The chemical polishing is performed by swabbing with a cotton ball saturated with the solution. During the chemical polishing, the sample is rinsed frequently in running water. Polishing in this manner for 5 min is sufficient to remove the strained material from the previous polishing operations. The amount of material removed is approximately 4µ/min. The surface obtained is flat and free of pits. Fig. 1 is an interference micrograph of a silver surface polished by this technique. If the solution employed is of improper HC1 content, an interference color film will form on the sample. This film can be removed either by swabbing with a cotton ball saturated with ortho-

Jan 1, 1962

By P. Shahinian, M. R. Achter

In a comparison of the creep -rupture properties of nickel in air arid in vacuum there is a reversal in relative strengths with variations in stress. At low stresses the properties are better in air while at high stresses they are better in vacuum. In the early stages of creep in a high stress test the specimen in air nzay have the lower creep rate but the one in vacuum is creeping at a lower rate in the later stages. A mechanism, involving two competing processes in terms of oxidation strengthening and weakening by surface-energy reduction, is proposed to explain these reversals. It had generally been assumed that, relative to their properties in air, the high-temperature strengths of metals would be increased in an inert atmosphere as a result of the elimination of the deteriorating effects of oxidation. However, several recent investigations have shown that the creep strength may be greater in air than in nonoxidizing gases. Pickus and Parker1 found that the creep rate of nickel was lower in air than in hydrogen or nitrogen. Internal oxidation was mentioned by Shepard and Schalliol as a possible cause for the longer creep life of Hastelloy C in air than in vacuum or helium. Sweetland and Parker, who observed lower creep rates for aluminum and copper in air than in helium, discuss the possible applicability of the dislocation-barrier mechanism to explain their results. Surface oxide layers may interfere with the escape of dislocations through the surface or with their generation there. In addition to showing the strengthening in air of low-alloy and stainless steel, and nickel and cobalt-base alloys, shahinian4 presented notch-effect data which indicate the role of stress concentrations; alloys of relatively low ductility were more sensitive to atmosphere strengthening when notched specimens were used. Although Bleakney's copper wires had a lower reduction of area in air than in vacuum, it is difficult to interpret his results in terms of strength changes since the stresses employed were not measured. In contrast to these data showing the strengthening in air, a number of investigations, most at relatively low temperatures, have demonstrated that the environment may cause a decrease in strength. These results are generally explained in terms of the effect of environment on surface energy. In a review of the subject, Benedicks and Harden use the concept of atomic bonding to explain how the adsorption of impurities would decrease the energy of a clean surface. A decrease in surface energy would facilitate the propagation of cracks or extension of the surface. Use of this mechanism is made by sato7 to explain the weakening of steel specimens bent in various liquids, by Potek and Shcheglakovs for the reduction of fracture strength of steel in molten metal, and by Benedicks and Harden for the reduction of strength of a variety of materials in a number of liquids. A similar explanation might be used for the results of Forestier and Clauss. The fracture stress of fine wires pulled in a variety of gases, including air, is lower than in vacuum. They attributed their results to the "tendency" for the gases to condense on the metal surface. That the strength of metals is affected by the type of gas in which the test is conducted has been demonstrated convincingly; the mechanism of the effect, however, is still uncertain. This investigation represents one in a series to explore the influence of variations in alloy composition and test conditions on the atmosphere effect in the expectation that the results would afford an insight into the processes taking place. To determine the effect of specimen composition, the present investigation was conducted

Jan 1, 1960

By J. R. Cahoon, W. V. Youdelis

In a previous communication by one of us,1 a theory of inverse segregation was presented by which the maximum segregation and segregation distribution throughout a unidirectionally solidified, binary-alloy ingot could be calculated. The theory, which is based on the mechanism of volume contraction and interdendritic flow, quantitatively accounts for the observed maximum segregation in the A1 (rich)-CU' and Al-Zn2 alloy systems, and for the segregation distribution along the ingot lengths for the A1-Cu system.''4 One of the drawbacks to a more extensive use of the segregation equations is their complexity, particularly for the calculation of the segregation distribution throughout the length of the ingot, involving long tedious numerical calculations to obtain the segregation. Computer pro- grams, written in Fortran II for use on an IBM 1620 computer, have been developed by the authors (and are available from them), providing quick and accurate methods for the determination of the theoretical maximum segregation in any binary-alloy system, and also for the segregation distribution in any unidirectionally solidified binary-alloy ingot. The segregation distribution is controlled by the lengths of the various solidification zones'74 which are in turn controlled by the cooling rate, and are determined from temperature-distribution curves obtained during solidification. The theoretical segregation distributions shown in Fig. 1 illustrate the effect of the zone lengths on the distribution Curve 1, indicative of a slowly cooled ingot, represents an ingot having long solidification zones, while Curve 2, indicative of a rapidly cooled ingot, represents an ingot having relatively short zones. Although these distributions are calculated for an A1-10 pct Cu ingot, the shape of the distribution would be similar for any binary-alloy ingot. These curves show clearly why early workers obtained results which indicated that the maximum (chill-face) segregation approached zero at very fast cooling rates.3 Actually, the maximum segregation is independent of cooling rate,' but even at short distances from the chill face the amount of segregation drops considerably, particularly in a rapidly cooled ingot, making it very difficult to establish the amount of segregation occurring at the chill-face. The authors would like to thank Dr. J. A. Goldak for his assistance in the preparation of the programs. The financial assistance of the Steel Co. of Canada and of the National Research Council of Canada in the form of Scholarships to one of us (J. R. Cahoon) is gratefully acknowledged.

Jan 1, 1964

By J. H. Brophy, S. J. Michalik

A constitution diagram for the system Mo-Ir has been determined. The maximum solubility of iridium in molybdenum is 16 at. pct at 2110ºC and decreases to less than 5 at. pct at 1500°C. The solubility of molybdenum in iridium is 22 at. pct. Three intermediate phases appear in the system: 8 MoJr, having the p-tungsten structure; a phase, a cornplex tetragonal structure; and the hcp ? phase. Metallography, melting point determinations, X-ray diffraction and fluorescence, and electron micro-probe unalyses were employed in establishing the diagram. PREVIOUS to the present investigation, the intermediate phases in the Mo-Ir system were identified, but no detailed account of the phase diagram has been reported in the literature. Raub1 investigated alloys of Mo-Ir over an extensive range of composition between the temperatures of 800º and 1600°C. The in-termetallic compound MosIr was found to exist with nearly pure molybdenum, as the solubility of iridium in molybdenum was not detectable parametrically in this temperature range. MO3Ir was found to be iso-morphic with a ß-tungsten type structure, having a parameter of 4.959Å. An intermediate hcp phase, designated as the ? phase, ranged in composition from 52 to 78.5 at. pct at 800ºC, and from 41 to 78.5 at. pct Ir at 1200°C. Parameters noted for the ? phase were as follows: at 42.7 at. pct Ir, a = 2.771i0, c = 4.4366, c/a = 1.601; at 78.5 at. pct Ir, a = 2.736A, c = 4.378A, c/a = 1.600. Molybdenum was found to be soluble in iridium up to 16.5 at. pct Mo (83.5 at. pct Irj, with the parameter of iridium increasing to 3.845A at the solubility limit. Knapton,2 who investigated alloys between 15 and 85 at. pct Ir, essentially agreed with Raub's data, but, in addition, found a a phase in as-melted alloys near 25 at. pcto Ir. The oaphase lattice parameters were a = 9.64Å, c = 4.96Å, c/a = 0.515. The a phase was replaced by the 8 -tungsten phase on annealing at 1600°C. Knapton concluded that the a was stable only at elevated temperatures, and placed the composition of the a phase at approximately 30 at. pct Ir. The intermetallic compound Mo3Ir, with a lattice parameter of 4.965A, was included among the 8-tungsten structures reported by ~eller.' Matthias and Corenzwit,4 and Bucke15 studied the superconducting nature of MosIr, and reported a superconducting transition temperature of 8.$K. The present investigation describes the phase relationships in the Mo-Ir alloy system determined by melting point measurements, X-ray diffraction and fluorescence, and metallography. EXPERIMENTAL PROCEDURES Alloys for the determination of the phase diagram were prepared from powders. Commercial 99.9 pct Mo from Fansteel Metallurgical Corp. and 99.9 pct Ir powder from J. Bishop and Co. Platinum Works were used. The powders were weighed to nominal compositions, mixed, and then pressed, without binder, into compacts weighing 4 to 6 g. These were presintered in uacuo between 1200' and 1400°C for 1 hr, to reduce the degree of spattering during subsequent arc-melting. The compacts were arc-melted in a nonconsumable tungsten electrode furnace six times on alternate sides on a water-cooled copper hearth in an atmosphere of zirconium-getter ed argon at 500 mm of mercury pressure. In almost all cases, this procedure yielded buttons of satisfactory homogeneity. The composition of all melted buttons were confirmed by X-ray fluorescent analysis using the experimentally determined ratio of the iridium La1 line intensity to that of the molybdenum Ka1 line as a function of composition. In this determination four alloys analyzed by wet chemical methods were used as standards. An uncertainty range of ±1 at. pct has been attributed to all indicated compositions. All heat treatments and solidus measurements were carried out in tantalum resistance heating elements in vacuum conditions of 10-4 to 10-5 mm of mercury. A detailed account of this procedure has been reported by Schwarzkopf and Brophy.8 In the heat treatment and solidus measurements of iridium-rich alloys (50 at. pct Ir or greater), a tungsten lining was inserted into the tantalum resistance heating element because of a eutectic reaction which occurs between iridium and tantalum at 1948ºc.7 Heat treatments and solidus measurements carried out at compositions less than 40 at. pct Ir both with and without tungsten linings within the resistance

Jan 1, 1963

By N. Pessall, A. D. McQuillan

The phase relalionsllips in an isothernzal section of the Ti-Zr-H system at 750°Chave been investigated by measurement of hydrogen equilibrium pressures. The resulting diagram indicates that the hydride phase has an anomalously wide range of homogencity extending from 66.6 to 30 at. pct H in alloys containing about 15 al. pet Zr. Measurement of the heat of solution of hydrogen as a function of alloy composition in ß-phase alloys indicates no anomalous behavior in the region of 15 at. pet Zr, and suggests that the extensive range of homogeneity in the hydride phase at about this composition must he attributed to an enhanced stability of the, hydride phase. THE manner in which titanium and zirconium react with hydrogen and the constitutional diagrams of the two metal-hydrogen systems are qualitatively very similar,'-6 as can be seen from Fig. 1 which shows the constitutional diagrams of the two systems. Quantitatively, however, there are some differences. For example, the exothermic heat of solution of hydrogen in ß titanium is smaller than that in ß zirconium, and consequently the equilibrium hydrogen pressure of a Ti-H alloy is higher than a Zr-H alloy at the same temperature and hydrogen concentration. Other differences manifest themselves in the hydride phases which exist at high hydrogen concentrations. In the Ti-H system, above room temperature, there exists only a single hydride phase in which the metal atoms are arranged on a fee lattice, but in the zirconium system there are two hydrides, and whereas the hydride of lower hydrogen concentration has a fee structure, the higher hydride has a face-centered tetragonal structure. The tetragonal hydride retains its stability up to temperatures in excess of 450oC.7 From the foregoing, it would be expected that the constitutional diagram of the ternary Ti-Zr-H system would have a very simple form, especially as titanium and zirconium are completely miscible in both the a and ß forms.8 The present work, which consists of a study of an isothermal section of the ternary system, was carried out in order to check the assumption frequently made that the electronic structure of the two metals and the mechanism by which hydrogen is held in solution in the metals is the same for each. Although this proved largely to be true, certain inter esting and unexpected features of the ternary system emerged which must be explained before we can really say that the reactions of titanium and zirconium with hydrogen are fully understood. EXPERIMENTAL PROCEDURE The most convenient method of studying hydrogen-metal systems is by the measurement of the hydrogen pressure in equilibrium with the hydrogen dissolved in the metal as a function of hydrogen concentration and temperature. In binary systems, the results are easily interpreted in terms of alloy constitution, since two-phase regions can be recognized by the fact that the hydrogen pressure at constant temperature does not vary with the hydrogen concentration in the alloy when it is in the two-phase condition. This criterion does not apply in ternary systems, but there is usually a marked change of slope in the isothermal pressure-composition curves when a phase boundary is crossed, and with care, and a knowledge of the limiting binary systems, the phase structure of the alloys can usually be deduced. In the

Jan 1, 1962

By Horace Pops, L. L. Isaacs

SOLID-STATE transformations at low temperatures are frequently studied by optical metallography. Greninger and ooradian' and Hull and Gar-wood2 have examined the martensitic-type transformations in 0-phase Cu-Zn alloys during continuous cooling below room temperature. The lowest range of temperatures in the apparatus described by these investigators is limited to approximately 110°K. Present studies of reversible first-order phase transitions near liquid-helium temperatures have necessitated the design of a new cold-stage cryo-stat for optical metallography. The features of interest of this instrument are as follows: a) temperatures down to 4.Z°K are obtainable; b) the specimen is always under vacuum, thereby avoiding the condensation of moisture; c) specimens can be rapidly cooled or heated at varying rates, thus permitting studies of transformation hysteresis. Fig. 1 shows the details of the cryostat. All major parts are made of type 304 stainless steel. Both helium and nitrogen cans are Heliarc-welded to the helium filling tube, permitting the use of a common shielding can. Hence, the over-all weight and the area of the evacuated surface are mini- mized. The copper sample holder is screwed into the bottom of the helium can. To assure good thermal contact between the sample holder and the refrigerant, an indium ribbon is placed on the threads

Jan 1, 1964

By P. Pietrokowsky

lntermediate phases in the binary metal alloy systems Ti-Zn, Ti-Hg, Zr-Zn, Zr-Cd, and Zr-Hg have been investigated by X-ray powder diffraction methods. Gamma-TiBHg and Zr3Hg have a beta tungsten structure; TiHg and ZrHg are analogous to ordered AuCu (L l0 type); delta-TixHg and ZrHg, are isomorphous with ordered AuCu,, (L l2 type); ZrZnz is face-centered cubic (C 15 type); TiZna crystallizes in a C 14 type structure; and Zrll-, occurs in cubic and tetragonal modifications in which a random distribution of atoms exists. Additional information for the intermediate phase TiZn, is presented. THE physical metallurgy of titanium and zir-conium when alloyed with elements in subgroup 11-B of the periodic table has received comparatively little attention in the literature. Laves and Wallbaum' reported the existence of several intermediate phases in the system Ti-Zn. They identified TiZn as a CsCl (B 2) structure and described TiZn, as an ordered Cu,Au (L 1, type) crystal structure. Gebhardt' investigated very limited zinc-rich regions in the systems Ti-Zn and Zr-Zn. Phase relationships in these partial constitution diagrams were deduced from the results of thermal analysis and metallography, X-ray results being inconclusive. The first zinc-rich intermediate phase in either system was not identified. More recently, Anderson, Boyle, and Ramsey" have had occasion to refer to a partial Ti-Zn phase diagram (unpublished data) covering the region 0 to 10 atomic pct Ti, wherein two intermediate phases corresponding approximately to TiZn,, and TiZn,, were indicated. The metals used in this investigation and typical analyses as determined by the suppliers are given in Table I. The iodide-process zirconium which was used was not hafnium free. Experimental Methods Alloy Preparation: The relative ease with which titanium and zirconium combine with other elements places extensive restrictions on the methods by which alloying can be achieved. The direct current electric arc melting procedure was found to be unsatisfactory for preparing these binary alloys and for this reason solid state diffusion methods were utilized. The iodide process titanium and zirconium rods were filed by hand. Fines were subjected to a magnetic separation and classified as to size as either finer than 200 mesh or coarser than 200 but finer than 80 mesh. Powder mixtures of various binary combinations of titanium and zirconium with zinc and cadmium were compacted in a 12 mm diameter die and then placed in Vycor or quartz vials which were evacuated and sealed. The mercury alloys were prepared in a similar manner; the proper weight of liquid mercury being placed in a vial with minus 200 mesh titanium or zirconium. These ampoules were then heat treated at various temperatures and times depending on the characteristics of the particular alloy system. Upon completion of the heat treatment the ampoules were cooled rapidly and the specimens weighed. The loss in weight varied from 1 to 3 pct (except as noted in the text) and for this reason the calculated compositions were accepted as a fair measure of the actual alloy compositions. X-Ray Dif raction Techniques: Powder diffraction experiments were conducted at room temperature with a 143.2 mm Debye-Scherrer X-ray camera in which the film was placed in the Straumanis arrangement. When copper radiation was used, a nickel filter was employed, and for the cobalt target a filter of iron oxide was used. In both cases, the /i? filter was placed between the X-ray target and the powder specimen which was mounted on a glass fiber. The lack of information based on optical metallography placed reliance on the results obtained from the X-ray experiments for determination of

Jan 1, 1955

By P. Duwez, H. Martens

Dimensional changes generally occur during the sintering of metal powder compacts. These changes may have several causes and their magnitude depends upon the numerous variables involved in the process, such as the nature of the powder, size and shape of the grains, compacting pressure, rate of heating, maximum temperature, length of time at temperature, and furnace atmosphere. Among all the variables, time, temperature, and compacting pressure are probably the most important ones, and the effect of each one of the other variables can be studied separately once the effect of these is well understood. The most precise method of studying the phenomenon of dimensional changes in a compact consists of heat treating the compacts at various temperatures for different lengths of time. In this method, only very small specimens can be used, in order to achieve rapid rates of heating and cooling. The technique involved in these measurements is very simple, but is time consuming. Another experimental approach to the problem consists of measuring the change in length of a compact as it is being heated at a constant rate. Although the two variables, time and temperature, are combined into a single one (rate of heating), the results obtained by this technique may be of great interest from both practical and theoretical points of view. The purpose of this paper is to describe a systematic investigation of the change in length during sintering of compacts made of one or several metal powders. Experimental Procedure The change in lenght of compacts during sintering was measured with an automatic recording dilatometer. In this instrument the change in length and the temperature are recorded as functions of time on two separate charts and the rates of heating and cooling may be varied from 1 to 20°F per min. The temperature may be kept constant at any value up to 2200°F during any predetermined length of time and the change in length recorded as a function of time. Provision is made for atmosphere control inside the fused silica tube containing the specimen. Three different magnifications are provided, so that 1 in. on the chart corresponds to 0.002, 0.005, or 0.010 in. change in length. The mechanism following the change

Jan 1, 1950

By J. M. Roberts, D. M. Barnett

The activation energy required to break a pinned dislocation line away from its condensed atmosphere of impurity atoms is calculated as a .function of applied stress, without neglecting line tension. Reasows are presented for not assuming the effect of line tension to be negligible when considering the problem of freeing a small segment of dislocation from an impurity atmosphere. The dislocation is considered to he pinned at each atomic size along its length and the pinning points are assumzed immobile. The development is a refinement of the origznal cottrell-bilby1 theory. The solution is compared to recent approximations developed by cottrell3 and Haasen5 in which line tension con- IN 1949 Cottrell and bilby1 considered the problem of determining the force required to pull a dislocation away from its condensed atmosphere of impurity atoms. They also examined the effect of thermal fluctuations on this force. The dislocation line was pictured as bowing out in a triangular loop under the action of an applied stress, and the activation energy necessary to free the dislocation from its atmosphere was calculated as a function of stress, line energy, and dislocation-solute atom interaction. siderations were neglected. A qualitative explanation of the yielding process in terms of the activation of Frank-Read sources is presented, but the lack of a realistic solution to the dynamic dislocation problem involved prevents an extension of the model at present. A self-consistent correlation between the present calculations and experimental data for delay time associated with yielding and the temperature dependence of the upper yield stress was made. Favorable agreement was noted. It is concluded that extension of the original Cottrell-~ilby' theory which includes line tension effects can just as well describe the yielding process as other approximations3,5 which neglect line tension. Cottrell and Bilby found the form of the activation energy vs stress curves to be almost independent of the line energy and the interaction energy (i.e., these parameters only affected the activation energy U by a scale factor). A check of the theory was accomplished by comparison with the experimental data of McAdam and Mebs2 for the lower yield stress as a function of temperature. cottrell,3 in 1957, attempted to obtain a simple closed-form solution for the activation energy as a function of stress by linearizing the quartic equation relating displacement of the dislocation line and applied stress. It was argued that since the contribution to the line energy/atomic plane of a dislocation is made by the long-range stress field of the dislocation through a term of the type (Gb3/2p)ln A/ro, where

Jan 1, 1963

By J. W. Downey, M. V. Nevitt

MUELLER and Knott' have reported that Ti2Cu has the Si2Mo-type (Cllb) structure. The lattice parameters of Ti2Cu and the positions of the titanium and copper atoms are given by them as follows: ao = 2.944A; co = 10.786A 6 atoms per unit cell: 2 Cu (a) 000; 1/2: 1/2, 1/2 4 Ti (e) 002; 1/2, 1/2, 1/2 + z 00 -2 ; 1/2. 1/2. 1/2- z where z = 0.341 We have found eight other binary compounds which appear to be isostructural with Ti2Cu. All of them involve the combination of a titanium group element with a copper group element or a titanium group element with palladium. The compounds and their lattice parameters are given in Table I. The alloy samples were prepared by arc melting metals having a purity of 99.9 pct or better. They were homogenized for 72 hr at 900°C in evacuated capsules and quenched in tap water. Filings were prepared, and these were reannealed for 4 hr at 700°C, also in evacuated tubes. The lattice parameters were determined by a least squares Bnalysis of the back reflection lines of patterns made with cobalt radiation. It was not possible to make a precise determination of the lattice parameters of Zr2Au because the filings underwent rapid oxidation at room temperature. The evidence supporting the large tetragonal cell containing 6 atoms involves the presence of the reflections 002, 101, 004, 112, 114, 202, and other reflections with higher indices for which I = 3n. Three or more reflections corresponding to these indices, which cannot be indexed on the basis of a small body-centered tetragonal cell containing 2 atoms, are observed in the patterns of all of the compounds listed in Table I. They are strongest and most numerous when the components have large differences in their atomic scattering factors, as is the case in Ti2Pd, Zr2Cu, and Hf2Cu. The values of the z parameter should be regarded as approximate They were selected on the basis of the best agreement between the observed intensities of two pairs of closely spaced powder pattern lines (004): (112) and (114): (202) and the corresponding intensities calculated for several values of z. An ordering scheme was assumed in which titanium, zirconium, or hafnium atoms occupy the titanium positions of Ti2Cu, and copper, silver, palladium, or gold atoms occupy the copper positions. Calculated and observed intensities of the aforementioned lines and the other lines of the patterns are in satisfactory agreement, but a refinement of the z parameters and a final confirmation of the ordering arrangement must await a more detailed study. It is interesting to note that in transition metal systems at A2B stoichiometry the Si2Mo-type structure competes for stability with two other fre-

Jan 1, 1962

By J. W. Downey, R. A. Morris, M. V. Nevitt

An experimental survey has determined the occurrence of Ti2 Ni-type phases in binary and ternary alloys of Ti, Zr, or Hf with first, second, or third long-period transition metals and also in ternary systems in which 0 is the third component. The existence of eleven previously unreported isomorphs is cited and some approximate phase boundaries are given. Lattice parameters are reported for the new phases. The periodic table relationships involved in the occurrence of the phase are discussed. A previous paper' reported the occurrence of a group of Ti2Ni-type phases (structure-type E93) containing Zr in combination with Rh, Ir, and Pt, and Hf in combination with Rh, Pd, Ir, and Pt, and cited evidence to show that all of the Zr phases and the Hf-Pd phase are not binary phases but occur only when 0 is present. More recently one of the present authors found that in the ternary systems of Ti and 0 with Cr, Mn, Fe, Co, and Ni the occurrence of the Ti2Ni-type phase could be correlated qualitatively with valency electron concentration, and that the role of 0 appeared to be that of an electron acceptor.' This paper describes the results of a broader investigation of the occurrence of Ti2Ni-type phases in binary and ternary systems containing Ti, Zr, or Hf. EXPERIMENTAL PROCEDURE Alloys were prepared by arc melting. The purity of the metals Zr, Rh, Hf, Ir, Pd, and Pt was given in the previous paper.' The additional materials used for this work were metals with a minimum purity of 99.9 pct and reagent grade ZrO2, TiO2, Cr2O3, and NiO. Chemical analysis of several alloys in each system indicated good agreement between intended compositions and cast-button compositions. For the heat treatment precautions were taken to avoid oxygen contamination. The specimens were wrapped in Mo foil and sealed in fused quartz tubes at a room temperature pressure of 1 x mm of Hg. These capsules were then annealed in a vacuum furnace at an external pressure of 5 X mm of Hg. Since the major constituent in most of the alloys studied was the brittle Ti2Ni-type phase, Debye-Scherrer patterns with sharp lines could be obtained with powder crushed from the annealed solid samples without being reannealed. Metallographic, X-ray diffraction, and density determination techniques previously described1, 2 were used. RESULTS AND DISCUSSION Zr-Rh-O, Zr-Ir-Oand Zr-Pt-O Systems-Figs. 1 through 3 show the approximate boundaries of the Ti2Ni-type phase fields at the temperatures indicated in the ternary systems Zr-Rh-O, Zr-Ir-O and Zr-Pt-0. In each isothermal section the Ti2Ni-type phase field is labeled E and the unidentified binary phase found in the previous work' is labeled ?. The dotted lines, which are not phase boundaries, correspond to the composition (Zr2 B)1-xOx. In each system the Ti2Ni-type phase field is displaced to the high-Zr side of this composition line. However, the departures from Zr2B stoichiometry for the metal components are not as high as Zr3B, as was inferred from the previous work. Lattice parameters of the Ti2Ni-type phases in the alloys shown as triangular data points in Figs. 1 through 3 are given in Table IA. The probable compositions of the Ti2Ni-type phases have been estimated from the isothermal sections. Although there are a few exceptions that probably result from uncertainties in phase boundary location and from the effect of variation of oxygen content, the generalization can be

Jan 1, 1961

By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade' in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965