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By G. D. Cody, D. S. Beers, B. Abeles

The thermal diffusivity (thermal conductivity divided by specific heat) of Armco iron has been measured over the temperature range 30º to 1025ºC. The results are in good agreement with the thermal diffusivity computed from published values of thermal conductivity and specific heat, except near the Curie point and at the a to y phase transition, where the measured diffusivity undergoes rabid variations. The differences observed are ascribed to a rapid variation in the electronic thermal conductivity near the Curie point, and a decrease in the lattice thermal conductivity, at the a to ? phase transition. A major difficulty in measuring the thermal conductivity of materials at high temperatures is the determination and elimination of radiation losses. It has been shown, however, that in measuring thermal diffusivity D (thermal conductivity/specific heat) radiation losses can be taken into account exactly.' In order to test the performance of a newly designed apparatus for measuring thermal diffusivity of solids,' we measured Armco iron to an accuracy of 2 pct in the temperature range 30" to 1025°C. This material was selected since both the thermal conductivity,3'4 k, and specific heat,5 C, are known accurately in this temperature range and thus the measured values of D could be compared with D computed from the pub-

Jan 1, 1962

By R. M. Treco

THE thermal expansion of pure beryllium was first investigated by Hidnert and Sweeneyl in 1925 on a single cast specimen stated to be of 98.9 pct purity. A study of the coefficients of expansion by X-ray methods has recently been made by P. Gordon' on powder obtained from the Brush Beryllium Co. assaying 97 wt pct beryllium with about 2 wt pct oxygen as an impurity. The present work pertains to about the highest purity metal obtainable from the Brush Beryllium Co. This metal was in the form of lumps which were remelted and cast in a high-vacuum induction furnace. Expansion data in this paper deal with beryllium extruded into bars of rectangular cross-section 4x1/2 in. and the anisotropic expansivity of a large cast single crystal. Analysis of the cast metal after extrusion indicated a beryllium assay of 99.28 pct. Impurities were 0.170 pct Fe, 0.140 pct Al, 0.014 pct Mg, 0.086 pct Si, 0.020 pct Cu, 0.020 pct Mn, 0.007 pct Ni, 0.007 pct Ca, 0.080 pct C, 0.179 pct 0, (as BeO). Part I—Extruded Metal Thermal expansion measurements were obtained with a fused quartz-tube differential type dilatom-eter3 on specimens cut from the extruded sections in longitudinal and transverse directions. Specimens were machined to a diameter of 0.250 in. and a length of 3.000 in. One sample from each direction was vacuum annealed for 1 hr at 800°C. The dilatometer tube was placed in a vertical tube furnace having a uniform temperature zone which was twice the length of the sample. Average time for a complete thermal cycle to 500°C was 18 hr. Temperatures were observed with two chromel-alumel thermocouples attached to the sample about 1 M in. apart. The accuracy of temperature measure-ment was ± 0.25°C. An argon gas atmosphere sur-rounded the specimen to prevent oxidation of the beryllium. Samples were identified as shown in table I. Results - The original plan included measuring expansion up to 1000°C, but the first two runs on sample No. 5 showed that a permanent contraction occurred from

Jan 1, 1951

By D. E. Furman

The thermal coefficients of linear expansion for several stainless steels have been determined over the temperature range from —300° to 1000°F. The steels studied include types 301, 304, 316, 347, 310 and 330. This wide selection of compositions allows an insight into the effects of austenite stability and alloy content on the expansion characteristics. THE recent increased use of materials in low temperature applications has created a field for which the properties of austenitic iron, chromium, nickel alloys are particularly suited. Tensile and impact values of stainless steels at subzero temperatures have been made available in the technical literature but, as yet, little information has been published with respect to expansion characteristics. In order to supply this need, a study was made of several of the more common compositions. Those selected were types 301, 304, 316, 347, 310 and 330 stainless steel. Both the mean and instantaneous coefficients of linear expansion were determined over the temperature range from —300°F to 1000°F. Procedure The materials used were commercial grades with the exception of type 301 which was made in a 10# high frequency furnace. The compositions are listed in table I. All steels were given an anneal at 1950°F for 30 min and water quenched prior to machining the expansion specimens. Expansion readings were taken on specimens 0.250 in. in diam by 4.000 in. long with a fused quartz tube expansion apparatus similar to that described by Hidnert and Souder.1 Temperature measurements were made with a chromel-alurnel thermocouple calibrated for use at subzero temperatures. A bath of propane was used for temperatures from —300° to —100°F and one of alcohol from —100°F to room temperature. These baths were contained in large mouthed Dewar flasks and cooled to the desired temperature levels by passing liquid nitrogen through glass cooling coils placed in the flasks. The baths were stirred constantly for temperature equalization and were heated by immersing metal rods which were replaced frequently enough to give a heating rate of approximately 150°F per hr. A resistance wound furnace was used for heating from room temperature to 1000°F and throughout this range rates of about 450°F per hr were maintained. The furnace was designed so that the temperature gradient over the specimen was within 5°F. In most instances, the expansion readings were taken during heating from —300° to +300°F at

Jan 1, 1951

By Alan T. Gorton, T. L. Joseph, Gust Bitsianes

High-temperature X-ray diffraction techniques were used to determine thermal expansion coefficients of iron and its oxides. Lattice parameters of a and iron, wiistite, magnetite, hematite, and goethite were determined and plotted as a function of temperature. From these results, the true and mean linear thermal expansion coefficients were calculated. In the case of noncubic crystals, the expansion coefficients were determined along each of the crystallographic axes. The effect of the magnetic transformation on lattice parameter was measured for a iron and magnetite at their respective curie temperatures. COEFFICIENTS of expansion for iron and its oxides were determined from the temperature dependence of their lattice parameters. From these data, the true linear coefficients were derived by means of the formula: at =[(l/ao )(dao/dt)] [1] where at is the true linear coefficient of expansion, a, is the lattice parameter in angstrom units, and all variables are referred to the temperature, t, in OC. Thus the true expansion coefficient represents the instantaneous change in lattice parameter on a unit basis and at a particular temperature. A second expansion coefficient is also often used. It is termed the mean linear coefficient and is defined in the following way: am = [ao(t) - ao(O)]/ao(0) l [21 This coefficient represents the average change in lattice parameter on a unit basis but at a specified parameter length, ao at O°C, and over a specified temperature range,1 to 0°C. Generally the true co-

Jan 1, 1965

By D. N. Williams

THE present study was undertaken with two specific objectives: measurement of the thermal-expansion coefficient of ß titanium and examination of the effect of solid-solution alloying on the thermal expansion coefficient. Four titanium alloy niaterials were available in the form of annealed 5/8-in. diam rod. Three of these, Ti-8V, Ti-20V, and Ti-6A1-4V, were prepared in the laboratory from 140 Bhn sponge. The

Jan 1, 1962

By B. A. Kulp, R. R. Reeber

Lattice parameters for the wurtzite form of' CdS mere measured by powder X-ray diffraction techniques over the temperature range 26° to 1000 K'. A negative thermal -expansion coefficient was determined parallel and perpendicular to the c axis below 13.5°K. Near 808°K, the curves of the a, parameter, the differential thermal expansion, and the resistivitv vs absolute temperature exhibited a reversible discontinuity. j\. direct determination of the lattice parameters of CdS over an extended temperature range is of particular use in interpretation of the effects of high pressure on the band structure of semiconductor materials. For example, Langer' has studied the effects of pressure on the absorption edge of CdS from 77°K to room temperature. In order to properly interpret his results it is necessary to know the change in lattice constants as a function of temperature for the wurtzite, zincblende, and rocksalt2 modifications of this material. Thermal-expansion measurements for CdS, wurtzite phase, have previously been determined over a limited temperature range.s74'5 The zincblende phases, of other compounds with similar bonding, have been investigated by Novikova et a! .'' Previous thermal-expansion measurements for metals with hexagonal symmetry have for the most part used bulk sample techniques for low-temperature result. Most X-ray measurements at low temperature have been on materials with cubic symmetry.'jQ The use of X-ray powder-diffraction techniques offers a convenient and accurate method of measurement over a wide temperature range. The X-ray method, besides measuring unit cell size, also provides information about change in structure type and the nature of some of the stacking defects present. I) EXPERIMENTAL PROCEDURE The thermal expansion was measured by X-ray powder-diffraction techniques. Lattice parameters for the range 300" to 1000°K were determined in a 19-cm Unicam camera. From 26" to 300°K a 34-cm back-reflection camera with the Van Arkel" film arrangement was used. The sample was bonded to a copper cold finger below a helium, hydrogen, nitrogen, oxygen, dry ice, or ice brine bath in a metal cryistat. che inner bath was surrounded by another one for radiation shielding. Nitrogen was used in this outer bath for the very low-temperature runs while dry ice and acetone was used for the 195°K point. CuKa X-rays, filtered with a nickel foil, entered the cryostat through a 0.001-in.-thick aluminum window. During a typical 9-hr exposure the sample was continuously rotated through a 30-deg arc. Heat losses from the sample holder limited the minimum temperature attained to 26°K with helium in the inner dewar. Temperature calibration between 25" and 125°K was determined with an Allen Bradley 300-ohm carbon resistor. The resistor was attached to the back of the copper finger with a thin layer of silicone grease. Liquid He, HZ, N2, and O2 baths were used to calibrate the resistor. Temperature variation is estimated to be *2"K with a slightly higher uncertainty at room temperature and 264°K. The thermal expansion of high-purity germanium from 373" to 900°K was measured as a calibration for the Unicam camera. This value was compared with the known value1' for the thermal expansion. A discontinuity in the thermal-expansion coefficient of the CdS a, parameter was observed. Similar discontinuities in the resistivity and differential thermal analysis at the same absolute temperature indicate that the temperature error is *5°K in the temperature range above 500°K. Temperature errors in the Unicam camera below 500°K are appreciably higher due to large gradients in the resistance furnace. II) SAMPLE PREPARATION The CdS was Eagle Picher ultrapure grade. The crystallite size range of the as-received powder

Jan 1, 1965

By R. J. Wasilewski

Axial expansion has been determined by X-ray diffraction up to 600° to 760°C in a titanium and four high-oxygen alloys. Expansion data cannot be fitted to the usual quadratic expression and anomalies observed are believed indicative of the changes in the bonding configuration of the valence electrons. Furthermore, there is significant disagreement between data obtained on poly crystalline and single crystal powder specimens. The major disagreement occurs within the temperature range (-470°C) where both mechanical and electrical properties also show markedly anomalous behavior. X. HIS work forms part of an investigation of physical properties of pure titanium and its osolid solutiono alloys with oxygen and nitrogen. In view of the anomalies observed in both the electrical resistivity' and the susceptibility behavior it was decided accurately to determine the thermal expansion behavior of the pure and alloyed a titanium. PREVIOUS WORK The axial expansion coefficients reported for pure titanium are listed below. As can be seen, there is a marked discrepancy between the axial expansion and the experimentally determined coefficients on poly crystal line material. Thus, if we take the most recently reported axial expansivities3,4 we obtain perature interval of 25o to 700°C. The experimental value reported for polycrystalline metal is, however, of the order of 9.7 x 10o6 per OC. EXPERIMENTAL I) Pure Titanium. High purity titanium powder of -325 mesh was used throughout most of this work. The only significant impurities present were the interstitials, oxygen and nitrogen, which analyzed respectively 650 and 80 ppm. The purity of the ma-

Jan 1, 1962

By Nicholas J. Grant, Noboru Komatsu

Metallographic and X-ray studies were made of oxide dispersion strengthened Cu-12 vol pet SiO2 and Cu-3.5 vol pet Al2O3 alloys following time exposures at temperatures approaching the melting. point of the matrix metal. Changes in hardness, oxide particle size and crystal structure were studied to determine the time-temperature stability of these alloys. An interpretation of the mechanism of oxide agglomeration is proposed. One of the most striking features of dispersion strengthened metal-metal oxide alloys is their stability at elevated temperatures, both with respect to recrystallization and maintenance of mechanical properties after exposure at high temperatures. A small amount of work has been done on the re-crystallization phenomenon in dispersion hardened metal-metal oxide alloys'l and several theoretical treatments have been advanced regarding the stability of these alloys by Lenel and Ansell,8 and by Grant and his co-workers.9, 10 This paper reports on metallographic and X-ray studies following various heat treatments of Cu-AI2D3 and Cu-SiO2 alloys at elevated temperatures and the effect of subsequent cold work on the recrystallizalion temperature. An interpretation of the recrystallization behavior of this type of alloy, based on the decomposition and agglomeration of oxides, is proposed. EXPERIMENTAL PROCEDURE Cast ingot bars of copper-1.59 pet Si and Cu-0.77 pet Al, 7/8 in in diam, were annealed in argon for 80 hr at 1000CC for homogenization. The homogenized rods were machined into fine chips and ball milled. Milled particles in the range minus 20 to plus 60 mesh were separated for internal oxidation. The internal oxidation was accomplished by the same method used by Preston and Grant,9 except that the oxidalion temperature for the Cu-Si alloy was 750°C, and for the Cu-A1 alloy was 800°C. These powders were then hydrogen-reduced at 450°C, compacted in a copper container, evacuated at room temperature to 0.04 µ, and sealed for extrusion. They were extruded at 1400°F (760°C) with a ram speed of 55 in. per min for an extrusion ratio of 15.6 to 1 to give a rod 0.38 in. diam by about 3 ft long.

Jan 1, 1962

By Y. H. Liu, R. Kiessling

The chromium, iron, and tungsten borides have been treated with ammonia at different temperatures. They are attacked, forming metal nitride and boron nitride, and the results are summarized in the tables. In the tungsten-nitrogen system a new phase has been observed, closely related to the known ß phase. THE present investigations were begun to determine whether any ternary phases exist in the transition metal-boron-nitrogen systems for the metals chromium, iron, and tungsten. Attempts to prepare such phases were made by using the borides of the metals as starting materials and ammonia as the nitriding agent. Although no new ternary phases have been found to exist, the results may be of some interest with regard to the technical use of the borides. General Procedure A steady stream of dry ammonia was passed through a silica reaction tube, the central part of which was kept at the reaction temperature while its ends were water-cooled. Weighed amounts of the borides were placed in a silica or porcelain boat and heated at different temperatures for a period of 10 to 24 hr. The boat was then rapidly removed from the reaction zone to the quenching zone, the water-cooled end of the tube, by means of a simple magnetic device. The nitrogen content of the products was determined by the increase in weight of the specimens, and the phase analysis was carried out by X-ray methods. For this analysis a Guinier-type camera, constructed at this Institute, was used with a bent, ground quartz crystal monochromator. The general reaction, which occurred in all the experiments, may be summarized as: metal boride + nitrogen -* boron nitride + metal nitride For the higher temperatures pure metal was formed instead of metal nitride. It is sometimes difficult to Discussi detect boron nitride among the reaction products by X-ray methods. Prolonged exposures of some specimens showed, however, that the strongest reflections of boron nitride were present. Additional evidence for its presence was given by the increase in weight of the specimens after nitriding. This increase was always greater than that corresponding to nitride formation only and was often in close agreement with the formula given above. Finally, a white powder, which was shown by X-ray methods to be boron nitride, was left if the reaction products after nitriding Fe,B at 448°C and FeB at 768°C were dissolved in diluted sulphuric acid. Ch rom iu m - Boron - N itrogen Five phases have been found to exist in the Cr-B system,' , and all were used as starting materials. Investigations on the Cr-N system have shown the existence of two nitrides with ideal composition Cr,N and CrN.".' * The results are summarized in Table I. All the borides are attacked and decomposed into chromium nitride and boron nitride, and the kind of nitride formed depends only on the temperature and not on the boride used as starting material. The lowest reaction temperature, however, is different for the different borides. Thus the 6 phase begins to react at about 735 "C, the r phase at about 800°, the S phase at about 900°, the 7, phase

Jan 1, 1952

By W. C. Ellis, M. E. Fine

WHEN certain binary Fe-Ni alloys are worked cold and then stabilized by a stress-relief anneal, their Young's moduli are nearly invariant over a substantial temperature range determined by composition and work-anneal history.' In the present investigation addition of molybdenum to such alloys (besides increasing the yield strength) was found to diminish the sensitivity of the thermal coefficient of Young's modulus to composition changes. Such alloys are of interest for applications requiring 1 a metal with controlled, low temperature coefficient of Young's modulus and substantial magnetic permeability.' Young's modulus ordinarily decreases with rising temperature. In ferromagnetic alloys a change in modulus on heating due to loss of ferromagnetism modifies the .temperature dependence. Far below the Curie temperature ferromagnetism alters the modulus in two ways: a—Addition of the energy of magnetization, a function of interatomic distance, changes the relation between interatomic energy and distance.' This lowers the modulus in the Fe-Ni and Fe-Ni-Mo alloys of this investigation. b—An applied stress changes the ferromagnetic domain arrangement so that linear magnetostriction contributes to the strain and further lowers the modulUs.~ Since in the alloys of this investigation both effects lower the modulus, loss of ferromagnetism on heating changes the slope of the modulus-temperature curve in a positive direction. With increasing temperature the slope of the modulus-temperature curve, due to progressive loss of ferromagnetism, becomes less negative, goes through zero (the modulus is minimum), becomes positive, and resumes its normal negative value above the Curie temperature.' The increase in modulus and decrease in curvature in the modulus-temperature curve occurring on work hardening have been attributed to a reduction in effect (b).'. Vn the absence of ferromagnetism work hardening through introduction of residual strains would be expected to decrease the modulus.' Alloy Preparation—Test Methods Four series of alloys having nominal molybdenum contents of 5, 7, 9, and 10 pct and containing 47 to 58 pct Fe (the analyzed compositions are given in Table I) were melted in air and cast as bars weighing from 2 to 6 lb. The charge consisted of electrolytic nickel, Armco iron, molybdenum (99+ pct) or ferromolybdenum (62 pct Mo), manganese, and aluminum as a deoxidizer. The bars were swaged cold to the desired diameters with intermediate anneals. Alloys in this composition range are reported" to be face-centered cubic and ferromagnetic at room temperature. The Curie temperatures" decrease with molybdenum. For example, keeping the Ni/Fe ratio at unity and increasing the molybdenum from 0 to 17 pct decreases the Curie tempera- ture from approximately 500°C to room temperature. (The 17 pct Mo alloy requires quenching to retain a single phase.~) Young's modulus at a series of temperatures from —50" to 100°C was determined by a dynamic method previously described.', " In this method Young's modulus is calculated from the resonant frequency (in this case approximately 50,000 cycles per second) of a rod sample (approximately 2 in. long) vibrating longitudinally in the first mode. The densities of the samples at room temperature, Table I, were determined by the standard method of weighing in air and reweighing in redistilled bromobenzene. The linear coefficients of expansion, Table I, needed to calculate the sample length and density at the temperature of measurement, were obtained by observing the change in length (22" to 100°C) of an 8 in. gage distance with a two microscope cathetometer. The values of density and coefficient of expansion in the few samples checked are independent of treatment to the accuracy reported. This was assumed to be general for all the samples. The modulus values are accurate to &0.05x101' dynes per sq cm. However, values of thermal change in modulus are accurate to 20.005~ 10" dynes per sq cm. Young's Modulus Values at 25°C: The modulus values of O', 5, and 10 pct Mo alloys at 25 °C are plotted in Fig. 1 as functions of nickel. After working cold, the samples were either recrystallized at 950" to 1000°C or given a low temperature stabilizing anneal at 400° C. The 400°C anneal does not reduce the hardness nor cause recrystallization. Annealing at 400 °C does

Jan 1, 1952

By S. J. Hruska, G. M. Pound

The critical supersaturations for appreciable nucleation rate of cadmium crystals on copper and glass substrates at 186°Kwere measured as a junction of thermal-beam energy over a range of source temperatures between 616" and 839OK. There was no effect of source temperature on critical super saturation. This implies that the adsmbate prior to nucleation is in thermal equilibrium with the substrate. THE deposition of metallic vapors on solid substrates has been found to exhibit a critical behavior in that the rate of formation of deposit increases markedly when the intensity of the vapor source is increased slightly.* Evidence of the ability of sub- where Je is the flux which would arrive if the substrate were equilibrated with bulk condensate at the adsorbate temperature. The following work was undertaken to test this hypothesis. A) Energy Exchange Between Metallic Vapor and Substrates. When a freely translating atom collides with a stationary solid body its energy and momentum undergo changes which determine whether the atom is reflected or adsorbed. An atom is considered to be reflected if it returns to a freely translating state after remaining under the influence of the body for only a time comparable to the period of oscillation of atoms on the surface. An atom which remains for a longer time is said to be in an adsorbed state. The parameter which describes the energy transfer occurring at the interface is the thermal-accommodation coefficient which may be defined in terms of energy as Ei = average energy of impingent atoms, Eeq = average energy of an emergent atom which has equilibrated with the substrate, and Eem = average energy of an emergent atom. If a temperature is assigned to each of these energies, we have at as defined by Knudsen.2 Since this allows no distinction between reflected and evaporated atoms, a more specific definition is introduced for the present purposes, namely 71 = probability that an impingent atom is transferred to an adsorbed state, aj = thermal-accommodation coefficient for reflected atoms, and aTc = thermal-accommodation coefficient for adsorbed atoms. During a time t,, the mean stay time, prior to evaporation the adsorbed atom (adatom) will interact with the substrate and this will have the net effect of transferring the adatom towards a state of

Jan 1, 1964

By J. F. Butler, H. W. Paxton

The vapor pressures of manganese in equilibrium with several alloys in the iron-manganese-carbon system between 1200° and 1275°K have been measured using the Knudsen effusion technique in conjunction with a vacuum microbalance. The effect of orifice area of the effusion cell upon the measured pressure has been determined. The binary iron-manganese system shows small negative departures from ideality, and the system of mixed carbides, (Fe, Mn)7C3, in equilibrium with graphite behaves ideally. THIS work is a continuation of the investigations in which the Knudsen effusion method has been used to determine thermodynamic activities in systems and at temperatures of interest to metallurgists. In a previous publication,' the free energy of formation of Mn7C3 was determined and some preliminary work on the solution behavior of this carbide with the hypothetical "Fe7C3" was reported. The present work deals with this latter topic and also includes data on the binary ir-on-manganese system. EXPERIMENTAL METHOD The Knudsen effusion method was used to measure the vapor pressure of manganese in both the alloy and carbide sections of this investigation. This dynamic method of vapor pressure measurement presents a problem when studying solid alloy systems in which one of the components has a much larger vapor pressure than the others. Over-all depletion of the alloy in the most volatile component will occur during evaporation so that the pressure of that component will decrease. Even more serious than the over-all concentration change is the surface depletion of volatile component in the alloy brought about by the slow rate of diffusion of this component from the interior to the surface of the solid particle. Since knowledge of this surface composition is necessary in order to relate it to the activity determined through the measurements, changes in surface composition from the analyzed bulk composition are to be avoided in dynamic vapor pressure studies of solid alloys. The system under investigation in this study presents the problem of surface depletion of manganese since its pressure at 1230°K is 105greater than iron and 1020 greater than carbon. Since the existence of a volatile manganese carbide had been ruled out previously,' the high manganese pressure relative to iron and carbon insured that the only species leaving the effusion cell was manganese. Therefore, the effusing species required no analysis so that the manganese pressure was determined directly from the weight loss of the effusion cell. In order to detect small weight losses near the beginning of effusion, a vacuum microbalance was used to weigh the cell continually. These initial weight loss data allowed the rate of manganese effusion to be determined before the surface of the alloy became depleted in manganese. The apparatus used in this investigation is shown in Fig. 1. Temperature was measured using chro-

Jan 1, 1962

By A. Steiner, K. L. Komarek

Activities of aluminum in solid Ni-A1 alloys have been determined between 20 and 60 at. pet Al and 1200" and 1400°K by an isopiestic method in which nickel specimens, heated in a temperature gradient, are equilibrated with aluminum vabor in a closed all-alumina system. The activity of aluminum shows a strong negative deviation from Raoult's law at low concentrations but increases by three orders of magnitude within the ß(NiAl) phase. The partial molar enthalpy and entropy of mixing are negative. Using Wagner and Schottky's theory of ordered compounds, a degree of disorder of 4 x 10 -4 for NiAl and 1.25 X 10-2 for FeAl has been calculated THE Ni-A1 system has been studied by a great number of investigators, and the results, as far as the phase diagram is concerned, have been compiled by Hansen.1 The phase boundaries from 0 to 50 at. pet Ni are well-established. At higher nickel contents the boundaries are still in dispute and an additional phase, A12Ni3, has been reported.' The phase diagram is dominated by a very stable high-melting compound, NiA1, with a relatively wide range of homogeneity. Heats of formation of solid alloys have been determined calorimetrically by Oelsen and Middel3 from 20 to 95 at. pet Ni and by Kubaschewski4 from 25 to 80 at. pet Ni. According to the most recent compilation5 no other thermodynamic investigations have been reported for the Ni-A1 system. Due to the corrosive nature and the low vapor pressure of aluminum, a method has been employed for determining activities of aluminum which was previously developed for the Fe-A1 system.= Nickel specimens, heated in a closed evacuated alumina system in a temperature gradient, were equilibrated with aluminum vapor from a source within the system kept at constant temperature. After complete equilibration the specimens were analyzed and activities calculated from the known vapor pressure of aluminum. APPARATUS AND EXPERIMENTAL PROCEDURE Materials. The nickel specimens were made from wafers of electrolytic nickel (International Nickel Corp.) of 99.99 pet purity which were rolled to a 0.001-in.-thick foil by Driver-Harris Co. and to a 0.005-in.-thick sheet in our laboratory. The aluminum (Aluminum Corp. of America) had a purity of 99.99+ pct. The alumina tubes and crucibles were made of impervious recrystallized alumina with an alumina content of 99.7 pet (Triangle RR, Mor-ganite Inc.). Experimental Procedure. Annular specimens were punched from the sheet, the punching burrs removed, and the specimens degreased in carbon tetrachloride and acetone and weighed on a micro-balance to within an accuracy of ±0.01 mg. The specimens were positioned with alumina spacers along an alumina tube, and the positions measured. Aluminum metal was machined into cylindrical shape, and placed into an alumina crucible. The tube with the specimens was then inserted into a hole drilled into the aluminum metal. An alumina tube with its closed end at the top was slipped over the specimens so that its lower end fitted snugly into the alumina crucible. The assembled reaction tube was inserted into a mullite tube with a water-cooled brass head which had an opening for a quartz thermocouple protection tube and a metal-to-glass connection to a conventional vacuum system. A Pt-Pt 10 pet Rh thermocouple could be raised and lowered in the quartz tube which was placed along the outside of the alumina reaction tube. The mullite tube was heated by two separately controlled resistance-tube furnaces so that in the experimental temperature range an over-all temperature gradient of approximately 150o to 250°C could be imposed on the reaction tube. The position of the mullite tube was adjusted so that the surface of the aluminum metal was always at the temperature minimum. The reaction tube was thoroughly evacuated before and during slowly heating the assembly up to the melting point of aluminum. A pressure of less than 2 µ (Hg) was maintained during an experiment. Once the aluminum had melted, it isolated the contents of the alumina tube from the surroundings. Several times during an experiment the temperature gradient was carefully measured. An experiment lasted from 3 to 6 weeks and it was terminated by air cooling the evacuated mullite tube. For further details of the experimental procedure the paper on the Fe-A1 system6 should be consulted.

Jan 1, 1964

By P. A. Farrar, M. D. Silver, K. L. Komarek

Thermodynamic properties of Hf-0 alloys have been determined from 0 to 25 at. pct 0 between 1000" and 1200°K by equilibrating specimens with alkaline metal oxide-metal vapor combinations. Partial molar-free energies, enthalpies, and entropies of oxygen have been obtained and are conzpared with similar results for the Ti-0 and ZY-0 In continuation of a thermodynamic investigation of the Ti-O and Zr-O systems1 activities of oxygen and lattice parameters of Hf-0 alloys have been deter- system. The positional entropy in all three systems corresponds to an ideal random interstitial solution with one interstitial site per one metal atom. The lattice parameters of hafnium and Hf-O solid solutions have been determined in the range 0 to 20 at. pct O from measurements of Debye powder patterns. mined. All three metals dissolve large quantities of oxygen to form interstitial solid solutions. The phase diagram of the Hf-O system is shown in Fig. 1.' The maximum solubility of oxygen in the cph a phase is considerable (up to 25 at. pct O). The solubility in the high-temperature phase is much smaller. The only stable compound in the solid state is HfO2 which may exist with a certain oxygen deficiency. The low partial pressure of oxygen of Hf-0 alloys required the application of an indirect method. As the most suitable procedure a method, first applied by Kubaschewski to the V-O system,3 was combined with a principle developed by Herasymenko for the

Jan 1, 1963

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult's law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult's law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.' One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys' revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult's law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.' Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By J. Eldridge, K. L. Komarek

Activities of aluminum in solid Fe-Al alloys have been determined between 0 and 75 at, pct Al and 1100" and 1400°K by an isopiestic method in which iron specimens, heated in a temperature gradient, are equilibrated in a closed all-ceramic system with aluminum vapor. The activity of aluminum in these alloys shows a strong negative deviation from Raoult's law at low concentrations but increases rapidly above 40 at. pct Al. The enthalpy and entropy of mixing me both negative. For an alloy with equiatomic composition the values are: HM = -7300 cal and SM = -0.85 eu. Sodium chloride has been added at lower temperatures to accelerate the evaporation of aluminum. Equations have been derived to calculate activities of aluminum from experimental data. THE Fe-Al system has been the object of a great number of investigations.' Most of these studies have been concerned with the phase diagram and specifically with the order-disorder reactions in the range of solid solutions of aluminum in iron. The results have been compiled by Hansen2 and presented as a complete phase diagram, Fig. 1. More recently, Taylor and ones' have found that both ordered and disordered alloys can exist in the a field up to the solidus curve separated by a line starting at 18.75 at. pct Al at room temperature up to 37 at. pct Al at 1375°C. Chipman and coworkers4-7 have studied repeatedly the activity of aluminum in liquid dilute Fe-Al alloys. They have measured the distribution equilibrium of aluminum between liquid iron and

Jan 1, 1964

By B. L. Averbach, Morris Cohen, L. L. Seigle

Free energies, enthalpies, and entropies of mixing of Ni-Au solid solutions containing 5 to 95 atomic pct Ni have been determined by the electromotive force method at 700° to 900°C. The thermodynamic activities exhibit large positive deviations from Raoult's law, and the entropies of mixing are almost twice those of ideal solutions. The enthalpies of mixing are positive (heat is absorbed) and are attributable to the lattice distortional energy resulting from the size difference between the nickel and gold atoms. This factor appears to be responsible for the miscibility gap at lower temperatures. IN the thermodynamic study of metallic solid solutions, most interest has been directed toward systems with negative deviation from Raoult's law, namely, those exhibiting superlattice or compound formation. The results of previous investigations are summarized in recent publications.'-' Relatively little experimental work has been carried out on solid solutions which manifest a positive deviation, possibly because the range of solubility in such cases is usually quite limited. Nevertheless, the relationship of the thermodynamic properties of these solutions to diffusion, nucleation, and precipitation in the solid state are of considerable importance. The binary Ni-Au alloys are particularly suited to an investigation of these relationships. Despite the presence of a miscibility gap at lower temperatures, Fig. 1, indicating a large positive deviation from Raoult's law, complete solid solubility is found above 840°C. Moreover, the difference in the atomic scattering powers of nickel and gold is sufficiently great to permit X-ray diffraction studies of atomic arrangements and pre-precipitation phenomena. Radioisotopes of both nickel and gold are available for diffusion work, and finally, a large difference in nobility between the two elements facilitates measurement of the thermodynamic properties. The present paper describes the experimental determination of the free energies, enthalpies, and entropies of mixing of solid Ni-Au alloys. Table I gives a list of the symbols used in the paper. Experimental Method The stability of nickel chloride relative to gold chloride" indicated that the galvanic cell method could be used for determining the thermodynamic properties of Ni-Au alloys. An electrolytic cell (Fig. 2) was constructed, similar to that of Weibke and Matthes,7 in which the electrodes were solid nickel and Ni-Au alloys, and the electrolyte was a fused mixture of alkali chlorides containing NiCl,. The cell electrodes were made from fine gold granules and carbonyl nickel shot melted together under argon, chill cast, swaged to 1/16 in. diam rod, and annealed for one week at 850°C. Commercial reagent and chemically pure grade salts, purified by dehydration, were used for the electrolyte. The cell, operating in an atmosphere of purified argon, was heated in a resistance-wound cylindrical furnace whose temperature was controlled to within ±0.5ºC. The potential developed between the pure nickel and the alloy electrodes, which is related to the thermodynamic properties of the alloys by standard equations to be presented later, was measured with a potentiometer and a mirror galvanometer sensitive to 10-7 v. Dehydration of the electrolyte was carried out in the assembled cell by evacuating at 100°C for about

Jan 1, 1953

By A. T. Aldred, K. M. Myles

The vapor pressure of chromium over solid V-Cr alloys has been measured by the torsion-effusion method in the temperature range 1450" to 1650°K. The chemical activities as well as the free energies, entropies, and enthalpies of formation of the alloys have hem computed from the vapor-pressure data. The activities of both chromium and vanadium exhibit fairly small negative deviations from Raoult's law over the entire composition range. The values of the excess entropies and the enthalpies of formation found at 1550°K are considered in terms of the changes in the clzaracteristic properties of vanadium and chromium that occur upon alloying. RECENT interest in the theory and properties of transition-metal alloys has shown the need for relevant thermodynamic data. The present investigation of the V-Cr system was undertaken as part of a more general study of thermodynamic properties of transition-metal alloys. The system was chosen because of the reported complete solid solubility of the components at all temperatures1 and because the difference in magnitude of the vapor pressures of vanadium and chromium allowed a simple effusion technique to be used. The torsion-effusion method was employed to minimize compositional changes in the alloys during the experiments. EXPERIMENTAL Equipment. The torsion-effusion apparatus, shown diagrammatic ally in Fig. 1, consists of a torsion system suspended inside a vertical vacuum chamber whose lower end is surrounded by a high-temperature vacuum furnace. An auxiliary optical lever and screen are used to determine the angle of rotation of the effusion cell. The torsion fiber is an annealed, high-purity, tungsten wire usually between 0.003 and 0.007 cm in diameter and about 43 cm long. The wire supports a concave mirror and a rigid tantalum connector tube. The effusion cell is fastened to the lower end of the connector tube by a dovetailed yoke and har- ness arrangement. The cells, which are 1.27 cm in diameter and 4.4 cm long, were made by electron-beam welding tantalum endcaps onto a 0.025-cm-wall tantalum tube. The two orifices, formed by drilling, have similar areas ranging from 0.011 to 0.031 sq cm. The noninductive sheath-type furnace consists of a single-phase tantalum heating element 6.35 cm in diameter, 15 cm high, and 0.013 cm thick; the element is completely surrounded by radiation shields in an evacuated chamber. The power system includes a 17-kva self-saturating saturable core reactor with an integral magnetic amplifier and a water-cooled, 15-kva, step-down power transformer with a multitap secondary. Temperatures are controlled to within ±1/2o at 1600°K by means of a unit that includes a reference voltage source, a dc electronic null detector, a current-adjusting proportional band relay, and the self - saturating reactor. At 1650°K the temperature variation within the cell, vertically and horizontally, is 3/4oK. Unwanted motions of the torsion system are damped by the movement of an aluminum vane, which is mounted on the connector tube, between the poles of an electromagnet. When not in use the magnet is withdrawn and rotated 90 deg to prevent its interaction with the rotation of the system. Measurements. The vapor pressure, p, is re-

Jan 1, 1964

By John P. Huger

me phase diagram for the system Ag-Si has been established by thermal analysis. The diagram is a simple eutectic type with a eutectic at 3.0 pct Si and 840°C. From the liquidus curve and with the aid of regular solution theory, the thermodynamic properties of the liquid Ag-Si system at 1420 °C have been determined. Silicon exhibits positive deviations from Raoultain behavior at all compositions, while silver exhibits both positive and negative deviations. MEASUREMENTS of silicon activities in liquid iron alloys by means of distribution studies between the immiscible liquids silver and iron have been reported by Chipman, Fulton, Gokcen, and caskey.' The applicability of this technique is dependent, however, on the accuracy of the silicon activity values in the Ag-Si alloys, particularly in the dilute silicon region. Darken and Gurry2 have shown that log ?si/(1-xSi)2 is approximately linear with composition, but uncertainty exists in the extrapolation to dilute solutions. Their calculations are based on the old Ag-Si phase diagram of Arrivaut3 and any variation in the position of the liquidus curves will strongly influence the extrapolation. The purpose of this study is to redetermine the Ag-Si phase diagram and calculate the associated thermodynamic properties. EXPERIMENTAL The Ag-Si phase diagram was determined by thermal analysis of liquid alloys. The alloys were contained in a 35 mm alumina crucible under a protective stream of purified argon. The crucible was placed inside a 64 mm alumina tube fitted with a gas-tight, water-cooled, copper head. The tube and assembly were heated in a manually controlled globar furnace. The temperature was measured with a Pt, Pt + 10 pct Rh thermocouple in a high-temperature porcelain protection tube. The thermocouple calibration4 was checked against the melting point of pure silver at the start and during the course of the experiments, and against both gold and silver at the completion of the experiments. The alloys were prepared from granular silver analyzing 99.95 pct Ag and powdered silicon analyzing 99.88 pct Si and 0.026 pct Fe. Approximately 150 g of alloy were used for each run. The composition of the alloy was determined by withdrawing samples of the liquid alloy with a vycor tube-aspirator bulb device. Analysis of solidified samples agreed, for alloys containing less than 23 pct Si, within ±0.3 pct Si of the calculated composition. Duplicate samples showed a variance within 50.05 pct Si of the mean analysis. The alloy was heated to 100' to 20pC above the estimated liquidus temperature and then the furnace was adjusted to give an average cooling rate of 2" to 7°C per min. A cooling curve was obtained by taking potentiometer readings at 15-sec intervals. Several analyses were made by recording the thermocouple output on a high-speed, Stip-chart recorder, with the exception of run NO. 11, a minimum of two thermal analyses were made for each alloy and the cooling curves then obtained duplicated the liquidus and eutectic temperatures to about 1°C. RESULTS The results of the thermal analysis are given in Table 1, and are represented as the Ag-Si phase dlagram, Fig. 1. The eutectic composition was found

Jan 1, 1963

By M. T. Hepworth, R. Schuhmann

Hydrogen solubility measurements were made on a series of Ti-O alloys, and a portion of the 800°C isotherm for the Ti-O-H system was determined. Activities of oxygen and titanium were calculated from the experimentally measured activities of hydrogen, using ternary Gibbs-Duhem integrations. The data were extrapolated to obtain thermo-dynamic properties of binary Ti-O solutions. The thermodynamic properties of a Ti-0 solid solutions thus determined were compared with properties predicted from interstitial models. The Gibbs-Duhem equation, long used to calculate activities in binary systems, has been extended. recently to ternary systems.1"3 When the activity of one component in a ternary system is known as a function of composition, the activities of the other two components can be calculated from that of the first by an integration procedure, provided certain restrictions are observed on the path of integration. Often the activity of one component in a ternary system can be measured readily, while the activities of the other two components are difficult to measure. Gibbs-Duhem calculations are especially applicable to such systems. The further possibility arises of developing a new and indirect approach to activity measurement in binary systems. The proposed new method for binary systems consists of adding varying amounts of a third component whose thermodynamic behavior is easily measured. The activity of this added component is determined experimentally as a function of composition. Then the activities of the two components of the original binary system are calculated by Gibbs-Duhem integrations and extrapolations. For the work to be described in this paper, the Ti-0-H system was selected as a promising system for evaluating this approach. Investigations of the Ti-H system have shown that the activity of hydrogen can be measured precisely with little difficulty. Pure titanium transforms from a low-temperature a form (hcp) to a higher-temperature /3 firm (bcc) at 882.5"~ The phase transformation occurs in a temperature range where hydrogen pressures are easily measured. Also, the diffusivity of hydrogen at temperatures above 600" or 700"~ is large enough that equilibrium can be reached within a reasonable time.

Jan 1, 1962