Search Documents

By J. Waldman, M. B. Bever, A. K. Jena

The heats of formation at 273°K of 6 silver-rich Ag-Cd solid solutions and the heat of formation at 78°K of one solid solution have been measured by tin solution calorimetry. The heats of formation are analyzed in terms of the quasichemical theory. If the enthalpy diffel-ence between a hypothetical fcc form and the hcp form of cadmium is taken into account, this analysis does not lead to the conclusion put forth in the literature that electronic effects make significant contributions to the heats of formation of silver-rich Ag-Cd solid solutions. The temperature dependence of the heats of formation is appreciable and negative near 78ºK, but decreases gradually to nearly zero abore 400°K. The relative partial enthalpies per grarn -atom of silver at 541°K and cadmium at 532" and 541°K in tin have also been determined. THE composition range of the silver-rich Ag-Cd solid solutions stable at room temperature extends to about 40 at. pct Cd. Heats of formation of these solid solutions at 308" and 723°K have been measured by solution calorimetry.1,2 Heats of formation for an average temperature of 800°K have also been calculated from vapor pressures.2,3 The heats of formation deviate from the values predicted by the quasichemical theory above about 30 at. pct Cd. This deviation has been attributed to electronic effects at the Brillouin zone boundaries.2 The heats of formation of Ag-Cd alloys are essentially the same at 308", 723", and 800°K; consequently the temperature dependence of the heat of formation d?H/dT = ?Cp is vanishingly small, although from the exothermic heats of formation a negative value would have been expected. In the investigation reported here the heats of formation at 273°K of 6 silver-rich Ag-Cd solid solutions and the heat of formation at 78°K of 1 solid solution have been measured by tin solution calorimetry. The results are analyzed in terms of the quasichemical theory and the dependence of the heats of formation on temperature is discussed. The relative partial enthalpies per gram-atom of silver in tin at 541" and cadmium in tin at 532" and 541°K were obtained in the course of this investigation. The values of the temperature dependence of the relative partial enthalpies per gram-atom of silver in tin derived from the data reported by various investigators2,4-9 are contradictory. The literature contains only a value for 517°K of the relative partial enthalpy per gram-atom of solid cadmium in tin.2 EXPERIMENTAL PROCEDURES Samples of Ag-Cd solid solutions were prepared by melting weighed amounts of silver (99.99 pct pure) and cadmium (99.95 pct pure) in graphite crucibles under a flux of molten potassium chloride.10 The solidified ingots were sealed in evacuated Vycor tubes and annealed at 775°K for 10 days. The ingots were swaged and drawn into wires. The wires, sealed in evacuated Pyrex tubes, were held at 725°K for 5 hr and cooled to 365°K at an average rate of 2.5ºK per hr, followed by furnace cooling to room temperature. Chemical analysis of samples taken from different parts of each ingot gave no indication of segregation. Metallographic examination showed the samples to be homogeneous. Samples of the solid solutions or of the component elements were added to tin-rich baths in a calorimeter." At the start of a run the bath consisted of pure tin. Silver was used in the form of wire of 0.01-in. diam as supplied and cadmium in the form of lumps. Gold (99.999 pct pure) was added with the samples in order to reduce the endothermic heat effect of additions of Ag-Cd solid solutions. Samples of only one composition were added in a run and the ratio of the weight of alloy to that of gold was the same in all additions of a given run. In each run several calibrating additions of tin were made from 273°K. The heat contents of tin were calculated from the following equation, which is based on published data:12 (HTºK- H279º) = 6.70 T - 72,300/T + 20 cal/gram-atom; 505°K < T < 650°K The heat effect of each addition was plotted against the average of the sum of the atom fractions of solutes in the solution before and after that addition. The total concentration of solutes at the end of a run was less than 2 at. pct. In this range the heat effect was a linear function of the atom fraction of the solutes. The heat effect at infinite dilution and the composition dependence of the heat effect were obtained from the plots. RESULTS AND DISCUSSION Evaluation of Data. The linear dependence on composition of the heat effects of additions suggests that in the dilute range the enthalpy interaction coefficients other than the first-order coefficients of silver, cadmium, and gold are negligible, as shown in a concurrent publication.13 The heat effects at infinite dilution and the values of the composition dependence of the heat effects are listed in Table I.

Jan 1, 1970

By J. E. Dutrizac, R. J. C. MacDonald, T. R. lngraham

When sintered disks of synthetic chalcopyrite (CuFeS2) were leached in acidified aqueous solutions of ferric sulfate, the following reaction stoichiometry was obtained: CuFeS2 + 2Fe2(SO4)3 = CuSO4 + 5FeSO4 + 2S Over the temperature range from 50º to 94ºC, the reaction displayed parabolic kinetics. The parabolic rate constant for the dissolution of copper is given by the equation: log.k(mg2/cm4-hr)= 11.850 - 3780/T The activation energy for the dissolution process is 17 ± 3 kcal per mole. The parabolic kinetics have been attributed to the progressive thickening of a sulfur film on the surface of the chalcopyrite. When the leaching solutions contain less than 0.01 molar Fe+3 , the Fe concentration influences the rate of leaching, probably through a mechanism involving the diffusion of ferric sulfate through the sulfur layer. At higher Fe+3 concentrations, the rate control in the leaching. reaction has been attributed to the diffusion of ferrous sulfate through the sulfur. The rate of reaction is insensitive to changes in acid concentration and in disk rotation speed. ThE reaction of acidic ferric sulfate solutions with various sulfide minerals is of practical interest for both bacterial and heap leaching. This leaching medium is generally used with low-grade ores that cannot be treated profitably by conventional means. In both bacterial leaching1-3 and heap leaching, the active agent for sulfide dissolution is ferric sulfate. Although the reactions of ferric sulfate with chalcocite, covellite, and bornite have been investigated,4*7 the kinetics of leaching chalcopyrite with ferric sulfate have not been thoroughly studied. This paper reports a study of that reaction. EXPERIMENTAL Reagent-grade sulfur was purified by the method of Bacon and FanelliB and then it was vacuum-distilled to remove any soluble magnesium salts that had been introduced during the purification procedure.9 From stoichiometric quantities of the purified sulfur and hydrogen-reduced electrolytic copper sheet (99.90 pct Cu), CuS was synthesized at 450°C in a vacuum-sealed, pyrex vessel. About 24 hr was required for the completion of the reaction. A similar procedure involving hydrogen-reduced iron wire (99.90 pct Fe) was used to synthesize FeS1.002. A 2-furnace arrangement was required. The iron was heated to 800°C while the sulfur was maintained at about 400°C. Although the reaction to consume the sulfur was rapid, the material required additional heating (1 week) in a sealed silica ampoule at 800°C before it was homogenized. X-ray powder diffraction analysis confirmed that the copper sulfide was covellite and that the iron sulfide was troilite. The composition of the iron mineral was confirmed by wet chemical analysis. The two sulfides were ground to minus 100 mesh, weighed in equimolar amounts, mixed thoroughly, and pressed into pellets at 80,000 psi. The pellets were vacuum-sealed in pyrex ampoules and then sintered for 3 days at 550°C after an initial heating at 450°C for a few hours. The pellets were then cooled, polished with 3/0 emery paper, rinsed in acetone, and stored. The material had the characteristic brassy color of chalcopyrite and was shown by X-ray diffraction to be CuFeS2. Microscopic examination of the polished surfaces revealed small inclusions of pyrite (approximately 0.5 vol pct) as the only impurity. The presence of small amounts of a second iron compound will not alter the amount of dissolved copper but might increase the amount of ferrous ion slightly. It was calculated that dissolution of all of the pyrite and 100 mg of Cu (a typical value) would change the expected ferrous concentration by only 4 pct. Microscopic examination of a pellet after leaching revealed that the pyrite was not preferentially solubilized; only those pyrite grains at the surface were attacked. Hence, the pyrite is unlikely to alter the rate of copper dissolution. The chalcopyrite disks were about 1.7 mm thick and 27 mm in diam. They were about 80 pct of theoretical density, and for this reason their true reaction area was somewhat larger than the 5.8 sq cm area presented by the polished face. The disks were cemented to lucite cylinders in such a way that only the polished face was exposed. The disks were then leached by methods previously described.6,7 RESULTS AND DISCUSSION Stoichiometry and Kinetics. The initial experiments were directed to the problem of resolving the stoichiometry of the leaching reaction. Disks of CuFeS2 were leached at 80°C for various periods of time in acidified ferric sulfate solutions that were protected from oxidation by a cover of flowing nitrogen. When the disks had been partly leached, they were removed, their soluble salts were washed out, and then they were treated with CS2 in a Soxhlet extraction apparatus. The ratio of elemental sulfur to dissolved copper thus obtained was approximately 2 to 1. After the extraction of elemental sulfur from the pellet, the residue consisted of unreacted chalcopyrite only. For runs in which an appreciable amount of copper was dissolved, the ratio of ferrous ion to cupric ion in the solution was

Jan 1, 1970

By T. Toda, R. Maddin

A study has been made of the microstructure and mechanical properties of splat-cooled aluminum-base gold alloys with gold concentration from 0.25 to 5.0 wt pct. These alloys have been quenched from the liquid state by a torsion-catapult technique, which has made it possible to pepare specimens suitable for mechanical property measwements. From the electron micrographs it has been shown that the solid solubility of gold in aluminum can be extended to 2.5 wt pct (0.35 at. pct) by splat-cooling, while the maximum equilibrium solubility is known to be less than 0.3 wt pct (0.04 at. pct). The very fine grain size (several tenths of a micron), the extended solid solubility, and the fine dispersion of a second phase (AuAl2) contribute concurrently to a substantial strengthening effect. In Al-5 wt pct Au splat-cooled specimens of less than 50 thickness, the yield strength is 17 kg per sq mm or 6 times as large as the strength of bulk specimens. For the Al-1.0 to 2.5 wt pct Au solid solution obtained by splat-cooling, the yield strength reaches 7.5 kg per sq mm after an aging treatment (for 10 hr at 200°C), while it is 3.7 kg per sq mm for the corresponding bulk specimens. A great deal of research has been done in recent years on the structure and the properties of metals and alloys rapidly quenched from the liquid state.&apos; The term "splat-cool" has been used with the meaning of a rapid quenching from the liquid state., The splat-cooling techniques have produced large numbers of new structures, which are expressed in terms of metastable phases,3 concentrated solid solutions,4 amorphous phases,5&apos;6 new phases,7 and so forth. Nearly all previous studies have concentrated on the physical properties; i.e., crystallography, structure, electrical resistivity, magnetism, and so forth, of the splat-cooled metals and alloys. The mechanical strength of splat-cooled metals and alloys has hardly been investigated except for some recent work by MOSS&apos; on A1-V alloys. The principle common to all experimental techniques developed to obtain very rapid quenching rates is based on the heat transfer by conduction. Liquid must be in good thermal contact with a substrate of high heat conductivity. Both of the published devices known as the "gun" and the "piston and anvil" techniques suffer from certain shortcomings. For example, the specimen obtained by the gun technique is very small and flaky, and hence inadequate for mechanical properties measurements. On the other hand if the material is forced to yield a continuous speci- men by the piston and anvil technique, it is probable that some plastic deformation occurs during the quench. A novel method for rapid quenching of a liquid metal or alloy, the "torsion-catapult", has been devised by Roberge and Herman9 at the University of Pennsylvania. In the apparatus the melt is thrown out of a curved furnace by a catapult and impinges on a copper substrate. The apparatus has the advantage of producing a continuous foil which is relatively large in size and of a quality suitable for the measurements of mechanical properties. The quenching rate is estimated to be of the order of l05 to l06 ºC per sec, (comparable to rates achieved by the piston and anvil technique). In selecting an alloy to be studied we were made aware of the fact that gold was believed to be "insoluble" in in and consequently age hardening in the A1-Au system appeared to be interesting. Quite recently Heirnendahl13-15 revealed that the solid solubility, as determined by transmission electron microscopy, was 0.3 wt pct Au at 640°C and 0.25 wt pct Au at 600°C, decreasing with decreasing temperature. In an A1-0.2 pct Au alloy after quenching from a solution treating temperature of 600°C the yield stress was 2 kg per sq mm, and it increased up to 6 kg per sq mm after aging for 1 to 10 hr at 200°C. The precipitation occurred in the form of platelike particles mainly on (100) matrix planes. The intermediate phase n&apos;, the equilibrium phase n (AuAl2), and lattice relationships between both precipitates and the matrix were also investigated by electron microscopy. One of the purposes of the present research is to determine whether or not the solid solubility in this system, in which gold has a very small solubility in

Jan 1, 1970

By J. C. Swartz

New measurements of graphite and cementite solubilities in ferrite have been obtained to resolve disagreements among previous data. To measure graphite solubility, specimens of iron were equilibrated with rarious carburizing atmospheres at temperatures be-twee~z 480" and 1435°C. The carbon activity of each atmosphere relative to graphite was taken from published data. After quenching from each equilibration treatment the concentration of carbon (typically 10 pprn by wt) was determined from the height of the Snoek peak in the internal friction spectrum. A few inclividual analyses by combustion support the reszdts of Smith on the solubility of graphite near the eutectoid temperature. Combination of these combustion and internal friction analyses determines In a, (at 0.01 wt pct) = 24,000/RT - 12.72, where a, is the activtity relative to graphite in ferrite at fixed cornposition. The same specimens were used to determine the solubility of self-stressed cementite precipitates. The results indicate solubilities of 6.3, 23.2, and 68 pprn carbon by wt at respectively 400°, 500". and 600°C. The once large discrepancy between the cementite solubility determined by internal frictiori and that calculated from flee energy data has been almost completely resolved. A recent study1 (hereafter designated I) on the solubility of cementite in a iron did not fully resolve the disagreement among previous data. The remaining disagreement is illustrated by the phase diagram in Fig. L The data of I are represented by the line labeled "stress-free" cementite. They determine a heat of solution of cementite of (14.8 * 0.2) kcal per mole which contrasts with the (20 * 1) kcal per mole derived from Smith&apos;s graphite solubility2 and the formation energy of cementite.3 Toward resolving this disagreement we have obtained new data on the solubilities of graphite and cementite. METHODS As in I the Snoek peak in the internal friction spectrum was used to measure the concentration of carbon dissolved in ferrite. This method relies on the relation C=kQ-1 [1] in which C is the concentration of dissolved carbon, Q-I is the Snoek peak height, and k is a proportionality factor which is a function of the peak temperature, polycrystalline texture, and other parameters characteristic of the ferrite lattice. To determine true heats of solution via Eq. [1], it is necessary to establish that k is independent of the temperature from which the specimen is quenched. Some evidence on this point is contained in a separate report.* Additional evidence is shown by the data points in Fig. 1. These represent the Snoek peaks of two specimens carburized to about 10 ppm C, copper plated, and quenched first from 888º then from 588°C. The copper plate was removed before each Snoek peak measurement. These data show that there is no detectable dependence of k on quenching temperature. The solubility of graphite was determined by repeatedly carburizing various specimens of iron wire with gas mixtures of known carbon activity relative to graphite. To cover a wide temperature range within the a phase boundaries it is desirable to use as low a carbon concentration as is compatible with reasonable precision. With the present internal friction apparatus the best compromise of these desires is a concentration near 10 wt ppm. The dashed line in Fig. 1 was used to approximate the activity of carbon* for

Jan 1, 1970

By Peter Soo

Pvestrained Ferrovac E iron has been neutron-irradiated at approximately 90°C to an integrated flux of 1020 nut (E > 0.82 mev]. The irradiation was found to produce an incveased temperature dependence of the flow stress in addition to a greatly increased athemal stress. Measurements of the flow stress and stress relaxation, from which the activation volume and activation energy for slip were deduced, show that neutron irradiation changes the rate -controlling slip process to one based on dislocation interactions with tetragonal distortions which are Produced around submicroscopic interstitial loops in the lattice. The study indicates that without prestraining prior to irradiation the chances of detecting a change in the rate -controlling slip process are greatly reduced because in the initial stages of slip a substantial fraction of the radiation defects are swept out of the slip plane by gliding dislocations. Thus, activation parameters which are subsequently measured are representative of a greatly reduced defect density and would not differ appreciably from those for unirradi-ated material. The large increase in the athermal component of the flow stress is probably connected with the presence of depleted zones in the lattice which are introduced by irradiation. ALTHOUGH fast neutron-irradiation has not been observed to markedly alter the activation parameters for slip in bcc metals,&apos; small but significant changes do occur. Most experimenters agree that irradiation predominantly increases the athermal component of the yield stress.&apos;-= In addition to this, Laidler and smidt7 have shown that in iron irradiated to 5 X 10" nvt and molybdenum irradiated to 10" nvt, changes occur in the activation volumes for slip. A similar conclusion has been reached by Milasin and Malkin8 for irradiated iron. Work by Ohr et a1.5 shows that for Ferrovac E iron, irradiated to 1.2 X 1016 nvt, small increases in the activation energy for slip also occur. So far these changes in the activation parameters have not been explained on a firm theoretical basis. One important factor which would minimize the chances of detecting a change in the slip mechanism upon irradiation is the presence of "channeling" which has been observed in molybdenum,9 niobium,10 and iron.11These channels are formed by gliding dislocations which sweep irradiation defects out of the active slip planes and thereby create zones in which continued dislocation motion is encouraged. The activation parameters for the dislocations gliding in the defect-free channels would, therefore, be similar to those for unirradiated iron and a change in the rate-controlling slip process would be difficult to detect. In the present work, an attempt has been made to reduce the effect of uneven deformation on the measured activation parameters for slip in neutron-irradiated Ferrovac E iron polycrystals, so that a more realistic assessment of the effects of neutron-irradiation could be made. Primarily, the experiments involve the irradiation of specimens which had been prestrained to 9 pct elongation at room temperature prior to insertion into the reactor. It was hoped that the introduction of a large number of evenly distributed dislocations would substantially decrease any channeling effect which might otherwise occur. MATERIAL AND EXPERIMENTAL PROCEDURE The starting material was vacuum-melted Ferrovac E iron, an analysis of which is given in Table I. The standard tensile specimen had a gage length of 1.125 in., a cross-sectional diameter of 0.120 in., and a re-crystallized grain size of 1.2 x 10-3 in. All tensile tests were conducted on a floor model "Instron" tensile machine at a strain rate of 3 x 10-4 per sec. The irradiation of the prestrained specimens was performed in the Brookhaven High Flux Beam Reactor to an integrated flux of 1020 nvt (E > 0.82 mev) at a temperature of about 90°C. All specimens were excap-sulated in high-purity aluminum sheaths which were lightly swaged around the samples to ensure good thermal contact. Subsequent measurements on the irradiated specimens showed that within experimental accuracy the swaging had not deformed them. EXPERIMENTAL RESULTS Fig. 1 shows the flow stresses for a series of unirradiated control samples. In order to produce a comparable dislocation substructure throughout the test sm range, all specimens were prestrained

Jan 1, 1970

By Barry D. Lichter, Pierre Sommelet

High-temperature heat contents of InAs and GaAs were measured over the temperature range 400°K to temperatures above the melting points using a di-phenyl ether drop calorimeter. Smoothed values of the thermal properties have been derived and tabulated at even temperature interuals . The heats of fusion of InAs and GaAs were determined as, respectively, 8790 ± 200 and 12,590 ± 300 cal per g-atom at the respective melting points of 1210º ± and 1513º ± 1°K, yielding entropies of fusion of 7.26 * 0.16 and 8.32 ± 0.20 cal perºK per g-atom, respectively. A general discussion of the thermal properties of III-V com-pounds is given. THE low-temperature heat capacities of InAs and GaAs have been determined by Piesbergen.1Using a dynamic temperature modulation technique, Miller2 has determined the heat capacities of the compounds as well as GaSb and Ge between room temperature and 650°K; however, it has been observed that values determined by drop calorimetry for GaSb3 and for germanium4 are consistently about 5 pct lower than Miller&apos;s results. Cox and Pool10 report values for the heat content of InAs and GaAs and the heat of fusion of InAs. No value for the heat of fusion of GaAs appears to have been previously reported. This paper reports results of high-temperature heat content investigations of InAs and GaAs measured in the range 400" to above 1500°K employing a diphenyl ether drop calorimeter. These results, together with our previous results on III-Sb compounds3 as well as heat-content measurements5 of solid InP and Gap, are used in a general discussion of these compounds. EXPERIMENTAL PROCEDURES High-purity samples of the compounds, stoichio-metric to ±0.1 at. pct, were supplied in the form of crushed crystal fragments by Dr. Carl Thurmond of the Bell Telephone Laboratories. The sample preparation, description of the calorimeter, and details of the heat content measurement have been previously described.3 Samples were sealed in evacuated silica capsules and suspended by a Pt-Rh wire in a Pt-wound vertical tube furnace, heated to temperature

Jan 1, 1970

By S. S. Shen, M. J. Pool, P. J. Spencer

Heats of solution of gold and copper in dilute Au-Cu-Sn alloys have been determined using a liquid metal solution calorimeter. The self-interaction coefficient, Au - has been calculated at constant copper concentrations and n cu has likewise been determined at constant gold contents. Good experimental agreement is obtained between the interaction coefficients and nAu Cc thus demonsbating the reliability of the measured heat values. The measured data are compared with the Predictions of certain solution models. In previous publications,1,2 the results of calori-metric investigations of dilute Ag-Au-Sn and Ag-Cu-Sn alloys have been presented. The present work on the Au-Cu-Sn system concludes a program of studies of enthalpy interaction coefficients in dilute alloys of the Group IB metals with tin. Since the definition and derivation of an enthalpy interaction coefficient has been discussed previously,1,2 no restatement of this theory will be presented here. From the determination of the partial heat of solution of gold and copper in ternary alloys of various copper and gold contents, values of the interaction coefficients can be calculated. These coefficients give an insight into the various solute interactions that occur in the liquid solutions since changes in their magnitude and sign reflect bonding changes that are taking place in alloys of varying solute contents. EXPERIMENTAL Details of the design and operation of the liquid metal solution calorimeter used in this work may be found in a paper by Poo1.3 For the present studies copper of 99.999 pct purity was supplied by American Smelting and Refining Co., gold of 99.999 pct purity by A. D. Mackay, Inc., and tin of 99.99 pct purity by Baker Chemical Co. At the commencement of each series of experimental drops, a tin solvent bath consisting of between 70 and 90 g of the pure metal was inserted in the calorimeter. The weight of the bath was accurately determined and to it were added appropriate amounts of gold or copper to give alloys of the desired composition. For determinations of approximately 0.0015 g-atom samples of Cu were used and for measurements of ?HAu approximately 0.0025 g-atom additions of Au. The heat capacity of the bath was determined at regular intervals during a series of drops using tin calibration samples. Measurements were made of the heat of solution of copper in alloys containing a constant 0.01, 0.02, 0.03, and 0.04 mole fraction of Au, respectively, in order to determine ?HCu in each alloy, and the same mole fractions of copper were used to determine equivalent values for nAu at constant copper concentrations. The composition of the bath was maintained at the desired constant gold or copper content by making calculated additions of the appropriate solute throughout the experiments. The limiting values ?HAu in alloys of constant copper content and of %c, in alloys of constant gold content were studied as a function of the mole fraction of copper or gold respectively in order to determine and nCu. Heat content and heat capacity data used in calculating values of ?ºHAu and ?HCu at the experimental temperature of 720°K were obtained from Hultgren et a1.4 &apos; RESULTS AND DISCUSSION Determinations of ?HAu. The partial heat of solution of gold in pure tin as a function of gold concentration was determined in the previous study of dilute Ag-Au-Sn alloys1 and can be represented by the least-squares expression: ?HAu(l) =-8075 + 2413xAu [l] which is valid between XAu= 0.00 and xAu = 0.05. The standard error in the constant term, which represents the partial heat of solution of gold at infinite dilution in tin,?HºAu(l)is 35 cal per g-atom, while the standard deviation of the slope, which represents n Au is ± 619 cal per- agtom. Corresponding expressions for ?HAu(l) in alloys containing constant mole fractions of 0.01, 0.02, 0.03, and 0.04 copper were obtained from the data listed in Table I and are themselves given in Table II. Fig. 1 illustrates the partial heat of solution of gold as a function of its concentration in each of the alloys. For the four alloys of constant copper concentration, the values obtained for ?HºAU(l) (in order of increasing copper content) are -8141 i 36 cal per g-atom, -8210 ± 42 cal per g-atom, -8202 ± 46 cal per g-atom and -8268 ± 51 cal per g-atom. The corresponding values of the self-interaction coefficient, n Au, for these alloys are 3103 * 644 cal per g-atom, 2425 ± 676 cal per g-atom, 2574 * 717 cal per g-atom and 2523 ± 899 cal per g-atom. In Fig. 2 these values of n Au are plotted as a function of the copper content of the alloys and are seen to remain approximately constant within the experimental limits. The addition of increasing, small amounts of copper to dilute binary Au-Sn alloys thus has no apparent effect on Au-Au interactions in these dilute liquid solutions, although more exothermic values of ?HºAu(l) do result from an increase in the copper content of the alloys. Analogous behavior was observed with additions of silver to dilute Au-Sn alloys.&apos; By

Jan 1, 1970

By E. T. Turkdogan, L. S. Darken, R. J. Fruehan

Further consideration is given to the application of the quadratic formalism to evaluate the thermodynamics of binary metallic solutions from experimental data. The use of the thermodynamic relation, in(r1/r2) dN2= 0, in the evaluation of activity data is discussed. The empirical correlations derived previously for enthalpies and entropies of solutions in Part II are shown to be predicted theoretically for a special case. The applicability of the quadratic formalism to the activity coefficients for binary organic solutions is demonstrated. DARKEN&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. In a subsequent paper (Part II) Turkdogan and Darkeen2 extended this formalism to the enthalpy and excess entropy of binary metallic solutions, and showed that the available data for the activity coefficients and heats of mixing of many solid and liquid binary metallic solutions confirm reasonable applicability of the quadratic formalism. Much variation was noted, however, in the extent of the terminal regions from one system to another, commonly from about 10 to 70 at. pct. For the present purpose, equations derived previously need be given only for one of the terminal regions, e.g. region (I), 0 < N2 < N&apos;2: where subscripts 1 and 2 indicate quantities for components 1 and 2 and superscript ° the values at infinite dilution; other terms are: N = atom fraction, y = activity coefficient, = partial molar enthalpy of solution, ?HM = molar heat of solution, ?Sx = excess partial molar entropy, ?Sx = excess molar entropy. The heat and entropy like terms (constants) el, and S12 are defined in the following expression for the temperature dependence of a12, thus a12 £12 — s12 rnl 2.303RT 2.303 R l J Using this formalism, the thermodynamics of binary systems in the terminal regions may be described over a temperature range of experisental interest in terms of eight quantities: Lº1—Lº2, ?Sx1,?Sxº2 , £12 ,£21,fiai, S12, and S21. In the previous paper, these quantities were evaluated for many solid and liquid binary solutions, and two significant correlations were observed between these thermodynamic quantities pertaining to the terminal regions, thus [10] and [11] Combining Eqs. [9], [l0], and [ll] and rearranging gives a12 -a21 = 1.382R log rº2- 0.08(?S2xº- ?S1xº) [12] Since the second term involving entropies is small and Eqs. 1101 and [ll] are empirical relations, the above equation may be simplified to a12 = 2.74 log rº2 [13] Using the values of a&apos;s and y°&apos;s compiled in Parts I and 11, a12 - a21 is plotted against log(rº2/rº1) in Fig. 1; the line drawn has a slope of 2.74. For Hg-K at 300°C, log(yº2 /yº1)= —5.10, not shown in Fig. 1, and from correlation [13], a12 - a21 = -13.97; this is to be compared with -10.76 derived from the activity data (Part II).

Jan 1, 1970

By Hans-Jürgen Schaller, Horst A. Brodowsky

Activity coefficients of boron in palladium were determined at concentrations up to PdB0.23 by reducing B2O3 between 870" and 1050°C in a controlled H2-H2stream and measuring the resulting weight gain. The deviations from ideal behavior closely resemble those of the system Pd-H and are interpreted in terms of three principles: 1) The solute atoms occupy octahedral interstitial positions. 2) They donate their valence electrons to the 4 d and 5s bands of palladium, raising its Fermi energy. 3) The lattice strain energy is lower for two nearesl -neighbor interstitial particles than for two farther separate ones. SOLID solutions of hydrogen in palladium are a useful subject for studying thermodynamic aspects of the formation of alloys and of nonstoichiometric systems.1-3 The activity of hydrogen is readily measurable to a high degree of accuracy,4&apos;5 even at low temperatures where the deviations from ideal behavior are more pronounced, and its simple structure facilitates an interpretation of these deviations in terms of a detailed model. Two effects are discussed to account for the non-ideal properties:3 An "electronic" effect, connected with the rise of the Fermi energy, as electrons of the interstitial hydrogen atoms enter the electron gas of the metal, and an "elastic" effect, due to an interaction of the regions of strain around each interstitial atom. The electronic effect is based on the idea that the lowest energy levels of the dissolved hydrogen atoms are higher than the Fermi energy, so that the electron will not occupy a localized state but enter into the electron band of the metal.6 The elastic effect is based on the observation that dissolved hydrogen distorts and expands the palladium lattice. The hypothesis is put forward that the elastic strain energy is lower for two adjacent dilatational centers than for two separate ones; i.e., they attract each other. The resulting pair interaction can be used to calculate an elastic contribution to the thermodynamic excess functions by means of one of the statistical methods. This model permitted a detailed description of the solution properties of hydrogen in palladium3 and in palladium alloys.798 An extension of the approach to describe the excess functions of substitutional palladium alloys is possible.9 In order to further test and refine the model, an investigation of other interstitial alloys was started. Palladium dissolves considerable amounts of boron in homogeneous solid solution.10 The palladium lattice expands linearly up to nB = 0.23 (nB = B/Pd atomic ratio), the highest concentration studied." The expan- sion, extrapolated for 1 mole of interstitial per mole of palladium, is 17 pct of the lattice constant of pure palladium vs 5.7 pct in the case of hydrogen.12 The fact that the lattice expands rather than contracts is a strong indication that interstitial positions are occupied. According to neutron diffraction experiments, hydrogen occupies the octahedral sites of the fcc lattice.13 Unfortunately, this direct evidence is not available for the Pb-B system, mainly because of the high-reaction cross section of boron with thermal neutrons. However, by way of analogy and on the grounds of the rather close similarities between the two systems to be reported here, it seems safe to attribute octahedral positions to the dissolved boron, too. At higher boron contents, compounds of stoichiomet-ric compositions are reported such as Pd3B, which has the structure of cementite,14 so that a close structural relationship seems to exist with the system r Fe-C. In their study of hydrogen absorption in Pb-B alloys, Sieverts and Briining noted that alloys with an atomic ratio of about nB = 0.16 are no longer homogeneous15 This observation was confirmed in an extensive X-ray investigation.11,16 The phase boundaries of two miscibility gaps were established. One two-phase region was stable below a transition temperature of about 315°C and extended from nB = 0.015 to 0.178. The other one extended from nB = 0.021 to 0.114 slightly above the transition temperature and had an apex at nB = 0.065 and 410°C. All phases involved have the fcc structure of pure palladium with lattice expansions proportional to their boron contents. The occurrence of miscibility gaps, i.e., the coexistence of dilute and concentrated phases, points to an energy of attraction between the dissolved particles, in the Pb-B system as well as in the Pd-H system. The filling up of the electron bands seems to be analogous, too, in the two systems, as indicated by the hydrogen absorption capacit15,17,18 and by the suscepti bility of Pd-B alloys.l8 In both types of experiments, boron acts as an electron donor. A chemical method was used to measure the activity of boron in palladium. Boron trioxide was reduced in a moist hydrogen stream: B2O3 + 3H2 = 2B + 3H3O [l] At known activities or partial pressures of boron trioxide, hydrogen, and water, the activity of boron could be calculated from the law of mass action. The equilibrium concentration of boron corresponding to this activity was determined as the weight gain of the sample. EXPERIMENTAL The samples consisted of small pieces of foil of 0.1 mm thickness and about 100 mg weight. The palladium was supplied by DEGUSSA, Germany, and stated to be

Jan 1, 1970

By M. J. Mullikin, J. B. Conway

for use in describing combined first- and second-stage creep data. In the above ?o represents the instantaneous strain on loading, ?t the limit of transient creep, ?S the steady-state creep rate, t the time, and ? a constant leading to the exhaustion rate of transient creep. It was noted that this equation was similar in form to that proposed originally2 by McVetty. This type of equation was also suggested by Andrade and Aboav3 in studies of the shear strain of cadmium. Calculation of the constants ?o, ?t, ?, and ?s, in Eq. [ l] is somewhat involved due to the slight complexity of this relationship. In the paper by Garofalo a computer approach based on a least-squares analysis was recommended. Such an approach involves a trial and error solution but when a computer facility is available the difficulties in this calculation are of little consequence. It does mean however that the evaluation of this type of equation would become quite tedious if computer facilities were not available. Some recent studies have identified a fairly straightforward method for calculating the constants in the Garofalo equation. While not leading to a least-squares evaluation the approach is accurate and is recom-

Jan 1, 1967

By R. A. Pasternak, B. Evans

A dynamic technique for the determination of solubilities of gases in metals has been explored, using the N-Nb system as a test case. An initially clean sample, maintained at constant high temperature, is exposed to the gas at low pressure: the rate of sorp-tion and the corresponding change in sample resistance are measured continuously. A pronounced decrease in the slope of the resistance concentration curve is observed at the terminal solubility. The rate of gas uptake by the sample was determined in an ultrahigh-vacuum flow system equipped with a servo-control which maintains constant pressure in the sample chamber; the system and the technique have been described in detail elsewhere. 1,2 The sample was held at constant temperature during sorption by maintaining approximately constant power input into it; this results in constant temperature, since the emissivity of a metal is independent of moderate concentrations of dissolved gas. The simple electrical circuit used both for heating and for resistance measurement is shown in Fig. 1. The power input into the filament is where R is the filament resistance, RL is an adjustable resistance in series with the filament, and VT is the constant dc potential of the power source. If RL is set equal to R at the beginning of an absorption run, the power input becomes insensitive to subsequent resistance changes; for example, an increase of 20 pct in sample resistance is accompanied by a decrease in power input of less than 0.8 pct; i.e., the

Jan 1, 1967

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.&apos;- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin&apos; has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled&apos; that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By K. A. Jackson, J. D. Hunt

A new classification of eutectics is proposed, based on tlze entvopies of wzelting of the tuio eutectic phases. The clnssification was used to predict suitable tvansparent analogs of the metallic systems. Experimental confir?nation loas obtained for the theovetical shape of the lamellar solid-liquid interface, fov the fault mechanisms of lanzellar spacing changes, and for the development of low-energy solid-solid boundaries between the lamellae. An explanation is presented to account jov the irvegular and coinplex regular structures zrhich are found in some eritectic systems. FrOM experimental observations, single-phase materials can be divided into two groups according to their solidification characteristics, those that grow as faceted crystals and those that do not. acksonl&apos; showed from thermodynamic reasoning that the type of growth depended on a factor a which was almost thg entropy of melting. Most nonmetals have high entropies of melting (a greater than 2) and grow with crystalline facets. Most metals have low entropies of melting (CY less than 2) and grow almost isotropically with no facets. The authors propose that eutectics may be classified in a similar manner. There are three groups of eutectics, those in which both phases have low entropies of melting, those in which one phase has a high and the other phase has a low entropy of melting, and those in which both phases have high entropies of melting. Lamellar or rodlike structures are formed in systems in which both phases have low entropies of melting. In these alloys dendrites of either phase may be formed, when the alloy is rich in the relevant component. Examples are Pb-Sn, Sn-Cd, Pb-Cd, Sn-Zn, Al-Zn. Irregular, Fig. 14((), or complex regular, Fig. 14(b), structures are formed in alloys in which one phase has a high entropy of melting and the other has a low entropy of melting. Examples are A1-Si, Zn-MgzZnll, Pb-Bi, Sn-Bi. When the alloys are rich in the low entropy of melting phase, dendrites are formed; when the alloys are rich in the high entropy of melting phase, faceted primary crystals are produced. These crystals are sometimes called hoppers or pseudodendrites. In this work the term dendrite will only be used to describe nonfaceted primary crystals. Dendrites are not formed during solidification in high entropy of melting single-phase materials. The third group of eutectics includes alloys in which both phases have high entropies of melting. Each phase grows with a faceted solid-liquid interface. Since most metals do not have high entropies of melting, metallic examples in this eutectic group are rare. However they may occur between some intermetallics and semiconductors or semimetals such as silicon, germanium, and bismuth. Attempts have been made to study eutectic solidification visually by watching the growth process.374 Since metals are not transparent, the observations had to be made on external surfaces. This difficulty can be overcome by using transparent analogs of the metallic systems. As was mentioned earlier, most single-phase compounds have entropies of melting greater than 2 and so grow as faceted crystals. Recently organic materials with entropies of melting less than 2 were investigated.&apos; These materials grow in exactly the same way as the low entropy of melting metals. When the materials are pure, they grow with a solid-liquid interface parallel to an isotherm; when they are impure, cells or dendrites are formed. Since these materials are transparent, have low melting points, and even have cubic structures, they should be ideal for making up transparent analogs of the metallic eutectics. The purpose of the present work was to investigate these organic eutectics and to see whether this quite different series of eutectics could be classified in the same way as the metallic systems. The observations made on the organic alloys are also discussed with reference to the current theories of lamellar growth. Explanations are proposed to account for the structures formed in the other eutectic groups. EXPERIMENTAL Thin cells containing the organic alloys were uni-direction ally solidified on a specially constructed microscope stage.&apos; Uniform growth rates were obtained by moving the cells, with a motor drive, through a fixed temperature gradient, so that the solid-liquid interface remained stationary with respect to the microscope objective lens. The cells were made by fusing two microscope cover slides 7/8 by 7/8 by 1/100 in. together on three sides, leaving a gap of 1 to 3 mils between the slides, and these were filled by surface tension. A preliminary investigation of the phase diagram between two components could be made very rapidly. One side of the cell was filled with component A and the other side with component B. Since only a small amount of mixing could occur every composition from pure A to pure B was present in the cell. When the cell was placed in the temperature gradient a pictorial representation of the phase diagram was obtained. Eutectics, peritectics, "interorganics", and solid -solid transformations could be readily detected. Fig. 1 shows part of a eutectic phase diagram. The Sample was first grown slowly then stopped. The two

Jan 1, 1967

By A. J. Opinsky

ThE superior performance of nonsag tungsten wire in lamps has been ascribed to the large-grained micro-structure that can be developed in it. The orientations of these large grains have been studied several times; most published data1-&apos; appear to be similar to those plotted in Fig. 1. These new data were obtained by X-ray back-reflection Laue technique from all of the large grains occurring in thirteen different wires that had been heated at the lowest possible temperature for the formation of large grains. Here the wire axis is plotted in terms of the principal directions of the cube. Rosi decided that the preferred orientation of the large crystals could be described by a single ideal orientation, (531), being parallel to the wire axis.&apos; Rieck2,3 and Mannerkoski&apos; have essentially confirmed this finding. Opinsky, Orehotsky, and Seigle argued that the data suggest that (211) is parallel to the wire axis instead of a single ideal orientation.5 This {211} contains the (531) ideal orientation and would appear to be a more general case. Ahlborn and Wassermann report that their orientation data stretch from ( 110) through (531) to (311) 8 This is part of the locus of (211). All these investigators have determined the orientations of the large grains by back-reflection Laue techniques. They have all obtained essentially similar results. On the other hand, Swalin and Geisler, who obtained their data by neutron diffraction, indicated that the preferred orientation of the large grains in doped wire is (110) .7 These findings cannot presently be reconciled with the pole density data described in the previous paragraph. Rosi1 and Rieck2 have advanced arguments about how their orientations could occur. Nevertheless, the crystallographic link between the (110) (cold-worked) fiber texture and the preferred orientation of the large grains has remained missing. This link can be provided through the concept of coincidence-type boundaries. Such boundaries separate two grains that have a certain number of common lattice sites. Coincidence relationships that result from rotations about low index directions are given by Brandon et a1 .&apos; What is desired is a calculation of those orientations that bear a coincidence relationship with the (110) fibers of the cold-worked matrix. This situation arises in the following fashion. Heating the tungsten wire for a combination of time and temperature falling short of the formation of the nonsag structure yields a structure that is still fibrous in nature and the preferred orientation remains (110). During grain growth, the growing grain is in contact with these fibers. It is hence possible that the entire process may begin by the passage of a coincidence boundary into a (110) fiber. The calculations were carried out analytically and checked graphically. Following Brandon et a1.,8 coincidence relationships from 1 in 5 to 1 in 19 have been considered. The results of the calculations are given in Fig. 2. Of the coincidences examined, some of those occurring upon rotation about ( 110) come closest to the experimental points in Fig. 1. Nineteen of the twenty-three data points in Fig. 1 can be attributed to the ideal orientations A, B, C, and D in Fig. 2. As determined analytically, three crystals lie within 4 deg of point A, four lie within 21/2 deg of point B, eleven lie within 5 deg of point C, and one lies within 1 deg of point D-a total of nineteen. The off-lying points are near the |110| point of the triangle.

Jan 1, 1968

By A. Gittens

In two recent papers stevens13,14 has compared the methods used by various investigators to calculate the contribution of grain boundary sliding to the total creep strain. In previous work Gittins15 has shown that the strain due to grain boundary sliding Egb may be estimated from the lateral, d, and vertical, v, displacements of a longitudinal marker line as it crosses a grain boundary. He obtained the formula, where nL is the number of grains per unit length measured on the specimens before creep, and \p and ?2 are, respectively, the angle between the grain boundary and the stress axis in the plane of the surface and normal to the surface (see Ref. 13, Fig. 1). The subscript L indicates that observations are made in a longitudinal direction parallel to the stress axis. It was generally found more convenient to measure the grain size of a specimen before creep; this was necessary to characterize the specimen. Stevens13,14 however prefers to define Egb in terms of NL, the number of grains per unit length after creep. Since nL - NL(l + €1) where cr is the total strain, Eq. 1 11 becomes The quantities d and ?, can be determined directly from the marker lines, while v and ?2 are found by sectioning normal to the surface. In the interior when symmetry considerations suggest that v = d and ?1 - ?2 the strain due to grain boundary sliding may be estimated from a suitable internal longitudinal marker line by the equation To determine cgb at the surface using either Eqs. |1| or [2] requires a large number of observations, particularly if many estimates of cgb are required, and also it is impossible to determine the variation of cgh with creep strain on the same specimen because the specimen must be sectioned to determine ?2. Gittins15 found that for a number of materials the sliding vectors d and v were related to each other so that provided one was measured the other could be estimated. Also during creep, grain boundaries tend to migrate to meet the surface at angles close to 90 deg,16 so that the term nL(v/tan?2)L was comparatively small when 4,- 90 deg. By determining the frequency distributions of ?2 on control specimens this term can be estimated without sectioning the creep specimen. In this way an empirical equation based on Eqs. |1| and |2| enables cgb to be determined with reasonable accuracy with fewer observations of the angles and sliding components. For B brass, the relationship between the sliding vectors indicated that ceb = 0.85nLVL . In Table I of Stevens paper this equation is stated to be incorrectly derived. However it should be pointed out that this is an empirical equation derived from Eq. |1|, based on a knowledge of the relationship between d and v and on the frequency distributions of ?1 and ?2 for a particular material under given experimental conditions. It was used only when these relationships were known, to reduce the number of observations required to estimate cb. Therefore the comment "derivation incorrect does not apply. Gittins did in fact make use of Eqs. |1| and 131. Author&apos;s Reply I must apologize to Dr. Gittins for the inadvertent misrepresentation of his work. Other slight errors in Table I have been pointed out to me. Langdon (No. 12 Table I), Gifkins (No. 7, Table I), and possibly other workers did not measure the number of boundaries per unit length after creep (A&apos;) but the corresponding quantity bejove creep (n). As Dr. Gittins points out, a completely analogous set of equations to those given in the paper can be derived by the same method: using the number of boundaries per unit length before instead of after creep. The basic equations corresponding to Eqs. [2] and 171 of the paper, from which all the others can be derived, are

Jan 1, 1968

By J. C. Scully

In June, 1965, Sanderson and scully5 reported at the Conference on Environment Sensitive Mechanical Properties of Materials at the Research Institute for Advanced Studies at Baltimore that thin foils of titanium could be prepared by chemical polishing in a mixture of 44 pct HF and 73 pct HNO3 in the volumetric ratio 2:3. The technique is simpler than that since reported by Rice and Orava. As-received annealed titanium (containing 0.8 pct Fe and 30 ppm H) in the form of sheet 0.05 cm thick is placed in the solution and moved up and down. The reaction is violent but suitable foils are obtained very easily and consistently. A typical micrograph is shown in Fig. 3. The small precipitates were not identified. Yamane and ueda6 observed many spotlike features which they referred to as small dislocation loops. While their spots may be due to the reaction of the warm foil with the air as suggested by Rice and Orava, the precipitates in Fig. 3 are also found when foils of titanium are prepared by electro-polishing at low temperatures and subsequently examined in the electron microscope without any inter- mediate warming. Furthermore, they are not a surface effect. It is necessary to add that alloys of titanium cannot be so easily thinned by the chemical polishing solution described above since it contaminates the a, phase with hydrogen and produces y hydride. These matters are described at length in a paper7 and their relevance to stress corrosion is considered elsewhere.&apos;-* Author&apos;s Reply The authors are grateful to Dr. Scully for bringing to our attention his hitherto unpublished technique for thinning unalloyed titanium, and deeply regret the unintended apparent duplication. The chemical thinning solution (7 parts HNO3 and 3 parts HF, by volume) reported by us is the same as that with which, for some period in the past, we had experienced success in the preparation of foils from single and polycrystalline niobium. Its subsequent effective application to titanium was a logical step, which, clearly independently of Scully, was conceived by Mr. Rice, to whom full credit is due. A few comments are warranted concerning some of the details of the preceding Discussion. It is evident to the discerning reader that the two thinning techniques under consideration are chemically almost identical, and in that sense are equally "simple". The chemical aspect is, of course, the one of primary importance in both communications. Thereafter, the relative simplicity is dictated by the mechanics of the actual thinning operation selected by the individual investigator. Our standard dimpling, or dishing, procedure was chosen with a view toward providing, for the electron transparent areas of the sample, the maximum protection from extraneous deformation during handling. That the long, straight dislocations visible in Scully&apos;s electron micrograph of a seemingly recovered structure closely resemble handling dislocations would tend to indicate the merit of our adopted technique. Features similar to those which Scully has attributed to precipitates, without any apparent diffraction contrast confirmation, were not observed in any of our clean foils taken from annealed or deformed specimens. This was admittedly somewhat surprising since the 3700 ppm (nominal) Fe in the A-70 commercial-grade titanium examined should have given rise to TiFe precipitates. Presumably these existed but were un-resolvable. Curiously, Scully&apos;s "precipitate1&apos; density is fairly high although the iron content quoted was less than one-fourth of that in our material. One is forced to conclude from the evidence that prior thermal and mechanical treatments are responsible for the two different types of structure observed.

Jan 1, 1968

By Paul Cherin

ThE angle of intersection, 0, between h2k2l2 planes and the (loo), (110), (101), and (111) planes was calculated on an IBM 7040 using the well-known relationship

Jan 1, 1968

By W. C. Winegard, C. J. Beinjessner

PREVIOUS investigations 1,2 of Fe3P described by pearson3 and schubert4 show that Fe3P has a bct unit cell having four Fe3P tetrahedra centered around each lattice point. The space group is 14, No. 82, and all atoms occupy general positions 8(g). The cell dimensions3 are: a = 9.090, c = 4.446 kX, with an axial ratio of c/o = 0.4891. We have measured the lattice parameters of Fe3P, using a Fe as an internal temperature standard, at 23°, 414°, and 678°C and computed the thermal expansion over this temperature range. The Fe,P was prepared by melting under vacuum (after flushing with argon) a commercially pure iron and "ferrophosphor" in a high-frequency induction furnace. Part of the ingot was crushed for X-ray examination and for chemical analysis. X-ray diffraction and light microscopy indicated iron phosphide (Fe3P) present as the major constituent and a small amount (about 5 pct) of a Fe. Chemical analysis showed 0.05 wt pct Si, 0.008 wt pct N, 0.018 wt pet C, and less than 0.02 wt pct each of other metallic elements. X-ray diffraction powder patterns were obtained from a mixture of iron and Fe3P sealed in an evacuated quartz capsule using a Unicam high-temperature

Jan 1, 1968

By H. Biloni

PORE formation during solidification has recently been studied theoretically by Piwonka and Flemings.1 For the ordinary conditions of cellular solidification, these authors state that there is a difficulty in explaining the formation of pores. The difficulty arises because the conditions necessary for pore formation are not those obtained during cellular growth. Therefore Piwonka and Flemings1 had to examine various unusual possibilities in order to explain the apparent presence of pores in a cellular substructure of aluminum, taken from Doherty.2 For aluminum, Doherty and Davis3 have developed a pitting technique to reveal substructure, which depends upon the condensation of vacancies from supersaturated solution after quenching. This technique as further developed4 was used to study solidification substructures. In the case of striations, delineation of the substructure is produced by the absence of surface pitting after quenching: in the vicinity of the striations the dislocations which constitute this substructure are sinks for vacancies. In the case of the cellular substructure the experimentally observed effect is the same. However, in this latter case Doherty and Davis4 suggested that micropores associated with the cellular substructure were the agent responsible for providing sinks for vacancies. This interpretation seemed necessary for the cellular substructure because no misorientation arising from a dislocation array could be observed. It is noted especially that Fig. 1 presented by Piwonka and Flemings1 and Fig. 5 by Doherty and Davis,4 as

Jan 1, 1968

By R. Kossowsky

USING etch-pit techniques, Johnston and Gilman&apos; have shown that the stress dependence of dislocation velocity can be represented by the expression where r, is the dislocation velocity, a is the applied stress, and oa, is the stress to produce a unit velocity. Noble and Hul12 showed that the exponent m is strain-dependent and increases rapidly in the work-hardening region. This was explained by arguing that in the work-hardened material the applied stress required for any given velocity will be greater than in the annealed material by an amount equal to a back stress due to work hardening. schadler3 has stressed the importance of substructure as a possible source of error in dislocation velocity measurements, and took care to make velocity measurements in which dislocations moved such short distances that interactions with boundaries were avoided. schadler3 also pointed out that, if standard testing equipment is used, measurements of m from flow stress data could be seriously in error in materials with a high initial work-hardening rate. Noble and Hu112 have further argued that, due to the strain dependence of m , the extrapolation to zero strain4 to obtain the true value of m can be justified only in the preyield region. Microstrain experiments in high-purity iron5,6 have led to the conclusion that aiA (Ref. 5) (defined as the stress to first produce a permanent set of 10-6 in. per in.) and oflow are not controlled by the same deformation mechanism. It has been proposed5,6 that aA is governed by the lattice resistance to the motion of screw dislocations in a given slip plane and that oflow is controlled by the lattice resistance to a full-scale cross slip. The purpose of this note is to extend Noble and Hull&apos;s argument further and to show that measurements of m from flow stress data can be in error due to the rapid increase in stress in the microstrain region6 when stress is increased beyond aA. Double z-one-refined single crystals of molybdenum (with the (101)[ 111] slip system operating and a Schmidt factor of 0.475) were used in an experimen-

Jan 1, 1968