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By E. E. Gardner, P. A. Schumann

A description of a new four-point probe configuration which permits measurement of epitaxial layer resistivity is given. An analytic solution to the potential distribution due to a point current source on a multilayered structure is briefly described. Typical solutions for this probe configuration are presented. Probe spacing, layer thickness, substrate resistivity, and substrate thickness enter into the calculation. Correction factors for typical cases are given. A brief description of the construction of a probe which can achieve a small spacing of 15 is presented. The prohe is constructed so that all points are adjustable by micrometers and the probe spacing and configuration can be easily altered. Measurements of layer resistivity with the four-point probe are compared with those taken with the three-Point probe and diode-capacitance techniques. TWO techniques of obtaining profiles of N/N+ epitaxial structures are given. The reproducihility of the probe spacing and resistivity measurement is discussed. The effects upon the resistivity measurement of errors in the measurement of the lager thickness, substrate resistil)itv, and substrate thickness are presented. SINCE its introduction by valdes' in 1954, the four-point probe has been the most widely used tool for determining semiconductor resistivity. Its usefulness ranges from the evaluation of bulk semiconductor ingots to the characterization of impurity profiles in diffused structures. In general the four points, two current probes and two potential probes, are placed on one surface of the material being tested either in an in-line array or in a square array. Numerous correction factors1 8 have been worked out for these configurations which are dictated by the finite geometry of the sample being tested. One method of evaluating thin wafers has been proposed which has two probesg on each side of the wafer. Further modifications have added a fifth'' and a sixth" probe. One paper1' has discussed the accuracy of the four-point probe and the precautions necessary in its use. With the exception of the method where two points are placed on opposite sides of the wafer, the four-point probe is restricted to evaluation of wafers with a homogeneous resistivity or to the case where an isolating junction exists between the substrate and the layer (epitaxial or diffused) being evaluated. Due to the relative resistivities and thickness, the resistance of the epitaxial layer is much greater than that of the substrate, and consequently a majority of the current flows through the substrate. The potential distribution at relatively large distances from the current sources is determined by the substrate resistance, and hence the AV/I value is a measure of the substrate resistivity and not that of the epitaxial-layer resistivity. In the immediate vicinity of a current source the potential distribution is determined by the layer resistivity among other factors. Consequently, if the potential probe is placed very close to the current source, then with appropriate correction factors it is possible to determine the layer resistivity. This was the theoretical basis for using two closely spaced probes on opposite sides of an epitaxial wafer. However, due to mechanical problems, it is desirable to place the four probes on the same side of the wafer. This paper discusses the potential distribution in

Jan 1, 1965

By H. Conrad, E. Stofel

The fracture behavior of 60-deg-oriented sapphire crystals was investigated for both tension and compression. Plastic flow on the basal plane was found to be a factor in reducing the tensile stress required to produce fracture in the temperature RECENT experiments1-' have shown that single crystals of a alumina (sapphire) can deform plastically, particularly at temperatures greater than 1000°C. The effect of this plastic flow on the fracture behavior of sapphire was not established, but range 1100º to 1500ºC. Mechanical twins, both (0001) and (0111) types, were produced by compression in the temperature range 1100" to 1300°C. Cracks propagated more readily along the twin boundaries than in the nontwinned crystal. experiments with other ceramic crystals4'5 have shown that plastic flow can initiate cracks that lead to catastrophic failure. This suggests by analogy that plastic flow might also be an important factor in the fracture of sapphire crystals. A recent experimental investigationS undertaken to determine the mechanism of plastic flow in sapphire provided an opportunity to study the type of fracture produced after various amounts of plastic shear strain. The results of this study of fracture are reported in the present paper. During the course of

Jan 1, 1963

By R. W. Hertzberg, R. W. Kraft

A study of the fracture behavior of unidirectwn-ally solidified Cu-Cr eutectic alloy was performed. Fractured whiskers, grain boundaries, and the interface between proeutectic Cr dendrites and the Cu matrix were the predominant failure initiation sites where grain size was larger. Strain induced void formation was restricted at lower solidification rates. This was attributed to a lack of adequate plastic constraint and a probable preferred orientation. A modification of the Crussard et al. model is presented to explain the appearance of "elongated dimples" on the shear fracture surface. A Cu-Cr alloy containing about 1.8 at. pct Cr solidifies by a eutectic reaction forming filamentary crystals of chromium within a continuous copper solid solution matrix.' Webb and Forgeng2 have shown by bend tests that the extracted chromium filaments, which are ordinarily curved and branched (due to random solidification), have the high strengths associated with whiskers. If an ingot of the eutectic alloy is unidirectionally solidified and appropriate control exercised over the thermal gradient, growth rate, and impurity level, the chromium fibers can be forced to solidify as fibers which are substantially parallel to the growth direction, Fig. 1. Uniaxial tensile tests on these straight chromium fibers extracted from controlled ingots3 have confirmed the earlier bend test results on curved fibers. Combining the facts that the strength and modulus of the chromium filaments are higher than the more ductile copper matrix and assuming that a "good bond" exists between the two phases, the Cu-Cr controlled eutectic system fulfills the requirements for effective fiber reinforcement of ductile matrices as established by studies on fiber glass reinforced plastics and other two-phase systems.4 Therefore, it was decided to study the fracture characteristics of morphologically simple specimens of chromium fiber reinforced copper (i.e., specimens of the controlled eutectic with substantially parallel reinforcing fibers) with the objective of establishing the dominant aspects of fracture. PREVIOUS WORK Comparatively little work has been done to understand the manner in which ductile alloys fail be- cause of the limited demand for this kind of information. Ordinarily ductility is specified for safety or similar reasons and when a part deforms plastically its useful life is terminated. In recent years, however, a number of investigators have begun to

Jan 1, 1963

By Frank E. Hauser, Philip R. Landon, John E. Dorn

The flow and fracture strengths of polycrystalline aggregates of high purity magnesium and a solid solution of aluminum in magnesium were determined as functions of temperature and grain size. Magnesium was found to obey two distinct fracture laws. Over the high temperature range, the fracture stress decreased with increasing test temperatures in a manner that closely paralleled the flow stress-temperature relationship. However, over the low temperature range, the fracture stress was independent of the test temperature though highly dependent on grain size, following the trend that is typical for the low temperature brittle fracturing of polycrystalline aggregates of body-centered-cubic and close-packed-hexagonal metals. Even at 78°K, however, plastic strains of 1 to 7 pet were obtained preceding onset of brittle fracturing. Over the brittle fracture range of temperatures, the fracture stress increased linearly with the reciprocal of the square root of the mean grain diameter, while over the entire range of temperatures investigated, the flow strength was observed to increase linearly with the reciprocal of the square root of the mean grain diameter. PREVIOUS investigations', 'have shown that deformation of coarse grained aggregates of high purity magnesium is interrupted by fracturing at very small strains. Such tendency toward brittle fracturing increased with increasing grain size and decreasing test temperature. In several respects, however, low temperature fracturing of magnesium appeared to differ from the truly brittle type exhibited by zinc, molybdenum, tungsten, and iron, so often characterized as a cleavage mode of fracturing. The absence of a well-defined cleavage mechanism for fracturing and the fact that some plastic deformation precedes fracturing might suggest that magnesium does not exhibit the same kind of brittle fracturing that is common to body-centered-cubic metals and to other close-packed-hexagonal metals. But, as will be shown, the low temperature fracture laws for magnesium are analogous to those that apply to iron, molybdenum, tungsten, and zinc in spite of differences in mechanisms and in plastic strains to fracture. In view of these observations. the low temperature fracturing of magnesium will also be called brittle fracturing. This, of course, does not imply that the brittle fracturing of metals is synonymous with the brittle fracturing of glass or other nonmetallics. Whereas the brittle fracturing of glass probably obeys Griffith's law, the low temperature brittle fracturing of metals arises from stresses induced by a series of dislocations piled up at an opaque grain boundary. Experimental Results All tests were made on tensile bars having gage sections that were 2 in. long and 0.375 or 0.25 in. wide. In order to develop a series of grain sizes, the

Jan 1, 1957

By Robert T. Ault

The nature of fracture in unnotched tensile and notched tensile sheet and round specimens and V -notched and precracked Charpy-type sheet specimens of both wrought stress -relieved and re-crystallized molybdenum was investigated over the temperature range of -78° to 300°C. The sharp rise in fracture stress, for unnotched tensile samples, as the temperature is increased above the brittleness transition temperature (Tb), is found to be a result of an increase in flow stress due to plastic constraint and an increased strain rate which results from the onset of necking at Tb . Quasi-brittle fracture in notched tensile samples is found to occur when the tensile stress at the elastic-plastic interface, beneath the root of the notch, reaches a maximum critical value, which is independent of test temperature over the range from —78° to 25°C, but dependent on microstructure. In the temperature range between 150° and 300°C, unnotched tensile and notched tensile samples alike are found to fracture by a ductile fibrous tearing process which is discontinuous in nature, as a result of the competition between the processes of tearing, through continued plastic flow, and local work hardening. Results from the V-notched and fatigue-cracked Charpy-type impact tests demonstrate that crack initiation is the governing factor in the low-temperature (-78° to 25°C) fracture process for molybdenum. In recent years, there has been considerable interest, and a commensurate number of investigations, concerning the duc tile-to-brittle transition in refractory metals. There has not developed, however, a satisfactory explanation for the uniaxial tensile fracture-stress transition which accompanies the well-known ductility transition. This matter therefore warranted investigation. In a similar manner, the increased importance of notched tensile strength values in evaluating materials and in design criteria requires a better understanding of the factors which control the fracture behavior of notched tensile samples. In a previous investigation1 of the nature of initial yielding and fracture in notched sheet molybdenum at room temperature, it was suggested that plastic constraint was the controlling factor in governing the fracture behavior of notched samples. The final portion of this investigation was concerned with the fracture toughness of molybdenum. Of particular interest was the comparison of effective surface energies for fracture in V-notched samples with fatigue-cracked, Charpy-type samples in order to ascertain the relative importance of the initiation and propagation phases of the fracture process. MATERIALS AND TEST PROCEDURE Sheet tensile, notched tensile, and V-notched Charpy specimens were prepared from 50-mil, stress-relieved molybdenum sheet.* Half of these specimens were vacuum-annealed for 1 hr at 1200°C and 7.5 x l0-5 Torr and furnace-cooled to produce a relatively uniform grain size of 0.30 mm diameter. Round notched and unnotched tensile specimens were prepared from warm-rolled and swaged 5/8-in.-diam bar.* These specimens were vacuum-annealed for 1 hr at 1350°C and 5 x lom5 Torr and furnace-cooled to produce a grain diameter of 0.11 mm. Material analyses in ppm were: C N O H Sheet 290 10 4 1 Bar 50 30 30 2 The unnotched tensile sheet specimens had a 1/4-in. gage width and a 1-in. gage length. The unnotched tensile round specimens had a 9/32-in. gage diameter and a 1-1/4-in. gage length. The sheet and round notch tensile specimens are shown in Fig. 1. All of the notched tensile specimens tested were tandem-notched in order to study the location and mode of fracture initiation. The tandem-notched specimens were carefully machined so that the largest variation in notch depth on a single specimen was 0.001 in. Thus, when fracture occurs, the extent of plastic deformation that exists in the un-fractured notch section is that which exists just prior to fracture. All of the tandem-notched sheet specimens were electrolytic ally polished and chemically etched prior to testing. The V-notched Charpy-type specimens machined from the 50-mil sheet material had the standard dimensions of 2.125 in. long, 0.394 in. deep, and a 0.010-in. root radius. The unnotched tensile and notched tensile tests were conducted over the temperature range of -78° to 300°C, in a 10,000-lb Instron Universal Testing Machine, at a constant crosshead speed of 0.020 in. per min. The V-notched Charpy-type

Jan 1, 1964

By C. J. Beevers

Tlze influence of zirconium hydride precipitate mprphology on the fructure of Zr-H alloys tested at strain rates of 10- sec at 20° and - 196°C and at strain rates of -500 sec.-1 at 20°C has been inves-tigated. The critical stage in the embrittlement of these alloys was the fracture of the zirconium hyhide precipitates to form large interval cracks at a stress of 25,000 10 137,000 psi. In specimens con-temping up to 100 ppm H the preciptates existed as isolafed platelets in the zirconium matrix and their fracture as enhanced by low temperature (—196°C) and high strain rate (-500 set-f) loading. These resl~lts lead to the conclusion that the rate of strain hardening of the zirconium metal controls the frac-tzrm of the hydride platelets. Increased hydrogen contents of 500 to 2000 ppm resulted in an increase in the 1)volume fraction and size of precipitates and crlso led to crack propogation in the hydride at both 20 and —196C at the low strain rates (10'* sec-'). Quenching led to refinerment of hydride precipitate size and reduced the degree of embrittlement at — 196°C; this effect is attributed to the absence of fracture of the fine precipitates. The formation of zirconium hydride precipitates has been shown to be the cause of hydrogen embrittlement of zirconium.' Several investigators'-" have studied the problem in broad outline, demonstrating that impact-loading conditions, testing temperatures below room temperature, and increasing hydrogen content produce increased brittleness. For example, Muehlenkamp and schwope2 showed that the transition temperature for notched impact tests was raised from 150" to 350°C on increasing the hydrogen content from 45 to 490 ppm. The degree of embrittlement is also controlled by the morphology of the zirconium hydride precipitates. The solubility of hydrogen in zirconium decreases from 600 ppm at 550°C to 10 ppm at 20"C,~ so that the form of the zirconium hydride precipitates (ZrH2) can be modified by varying the cooling rate through the Zr-aZr + ZrH2 phase boundary.= Forscher showed that quenching a specimen containing 35 ppm H from above 315°C resulted in a reduction in area of 70 pct at -196"C, whereas slowly cooling from above 315°C resulted in a ductility of half this value. The role of the hydride precipitate in the fracture process has been examined by Young and schwartz6 and more recently by westlake.' From metallo-graphic observations on slowly cooled Zr-H alloys they have suggested that cracks are nucleated in the hydride precipitates by the interactions of twins in the zirconium metal with the hydride. The experiments reported in this paper show that crack propagation in the zirconium hydride precipitates is the critical stage in the embrittlement of Zr-H alloys. The factors influencing fracture of the hydride precipitates and crack propagation in the zirconium metal will be related to the problem of embrittlement. EXPERIMENTAL TECHNIQUES The zirconium used in these experiments was produced from an ingot of vacuum arc-melted iodide zirconium forged down to 1 in. diameter at 800' to 850°C. The 1-in.-diameter bar was surface-machined and cold-swaged to 0.375 in. diameter. After a vacuum anneal at 800°C for 1 hr the hardness was 60 to 70 Vdh. The total impurity content was approxi-

Jan 1, 1965

By G. C. Gould

The nature of freckle segregation is determined by chemical analyses, microradiograplzy, and electron microprobe. In addition, the influence of chemistry variation on freckle formation is studied in laboratory experiments. It is demonstrated that controlled laboratory solidification can produce freckle segregation. "FRECKLE" segregation is a discontinuous, rod-like segregation observed in vacuum consumable -electrode ingots. Figs. 1 and 2 show this segregation as pencil-like, dark etching areas of segregation found in longitudinally and transversely sectioned consumable-electrode ingots. In most cases the segregation is perpendicular with respect to gravity and parallel to the longitudinal axis of the ingot. The segregation is most often encountered at or around midradius in large vacuum consumable-electrode ingots. The austenitic alloys, A-286* and 718, † have shown particular susceptibility to this mode of segregation. The origin of these rodlike pockets of segregation is not well-understood. It has been suggested that the segregation is a result of a portion of the electrode dropping off and passing through the arc un-melted. On the other hand, smeltzer1 has demonstrated the freckle segregation in A-286 to be comprised of low-melting constituents relative to the matrix melting point. The discontinuous nature of the segregation is the most perplexing facet of the freckle-segregation problem. It was to gain some insight into this part of the problem that this work was undertaken. I) PROCEDURE At the outset of the work identification of the phases present and the elements concentrated in the freckle areas was undertaken. The electron micro-probe was used to determine general enrichment as well as -specific phase chemistry. Microradiography using cobalt and chromium radiation was also used on the freckle areas again to determine the elements involved in the segregation. X-ray diffraction patterns were made from portions of these same foil specimens. Optical microscopy and Knoop hardness measurements were also used

Jan 1, 1965

By J. H. Smith, H. W. Paxton

ALTHOUGH many structural and kinetic investigations have been made for alloys of iron and nickel, only meager data exist from thermodynamic investigations. The purpose of this note is to estimate the free energy of the Fe-Ni solid solutions from thermodynamic data available for ternary alloys containing iron and nickel. The lack of a description of the thermodynamic behavior for the Fe-Ni system has required the structural and kinetic analyses of the system to assume some form of solution behavior, usually regular, e.g., the mar-tensite transformation analysis of Kaufman and Cohen, 1 consistent with the limited thermodynamic data. Indications that this system could exhibit ideal solution departures might have been suggested by the large deviations from additivity rules observed in the density and lattice-parameter measurements of Jette and Foote2 who interpreted this in terms of possible solute-solvent interactions. Later Turkdogan et al. 3 and more recently Ward and wright 4 found a minimum in the graphite solubility in liquid Fe-Ni solutions near the concentration of FeNi3 with deviations from linearity persisting at all concentrations. This was interpreted by Ward and wright4 to indicate negative heats of solution and was suggestive of short-range ordering. The infinitely dilute activity coefficient of carbon (?oC) was also observed by smith5 to pass through a maximum near the FeNi3 concentration in Fe-Ni solid solutions. Recent investigations of the liquid solutions over the entire concentration range by Zellars et a1.' and Speiser et a1.," using vapor-pressure determinations, revealed both negative departures from Raoult's law and a nonregular solution behavior. The solid alloys have been studied by Oriani 8 and Kubaschew-ski and von Goldbeck6 employing gaseous H2/H2O equilibria with Fe and FeO. Both investigations were in substantial agreement, indicating very small departures from ideality. However, Oriani observed the formation of Fe3O4 (instead of FeO) at XFe= 0.441 which severed the equilibrium and precluded experimental investigation of the nickel-rich alloys. Heat-capacity and heat-content measurements have been evaluated by Montgomery10 and found generally unsatisfactory for gleaning thermodynamic information. This is due to the unknown final states of the alloys caused by the interference of the martensite transformation on cooling iron-rich concentrations and superlattice formation, magnetic transformation, and the varied heat treatments used by investigators of nickel-rich concentrations. As an alternative to the experimental difficulties, indirect estimates of the solid-solution behavior have been made by Fleischer and Elliott11 and Smith et a1.12 From their measurements of the solubility of Fe-Ni alloys in liquid lead, Fleischer and Elliott calculated the nickel activity (aNi) (and integrated for aFe) by assuming: 1) liquid lead has no solubility in solid Fe-Ni alloys, 2) Henry's law is obeyed throughout the liquid lead-rich phase (0— 12 at. pct Nil, and 3) Henry's law constant is independent of relative iron and nickel concentrations. The estimate of Smith et a1.12 was obtained

Jan 1, 1964

By R. W. Gurry, L. S. Darken

The solubility of cementite in austenite is computed by thermodynamic methods from the observed solubility of graphite. It is found that the solubility of cementite is greater than that of graphite in the entire austenite temperature range. Thus the prior discrepancy between this portion of the phase diagram and the observed metastability of cementite is partially resolved. FOR several years it has been apparent that a serious discrepancy exists in certain observations pertaining to the Fe-C system. Direct experimental data indicate: 1-That the curve representing the solubility of graphite in austenite'" crosses that for cementite4 at about 945°C as shown in Fig. 1. 2— That graphite and austenite saturated therewith are stable1 relative to cementite at all temperatures between the eutectoid, about 723°C, and the eutectic, about 1153°C. These observations are mutually incompatible in view of a well-known consequence of the second law of thermodynamics, namely, that the stable phase (presumably graphite at all temperatures) has a lower solubility than the metastable phase (presumably cementite). Hence either 1 or 2 above must be in error; either the measured solubility of graphite or of cementite, or the observation as to the stability of graphite, is in error. Our present purposes are: 1—To collate the available data on cementite and prepare a table of HO — HO° and of (Fa— HO°)/T. This tabular method seems the best and most convenient way to represent the heat and free energy of formation. 2—To determine whether the measured solubilities of cementite and graphite in austenite are in accord with the above table and the measured thermodynamic properties of austenite, in order to resolve, if possible, the existing paradox of these two solubilities. Enthalpy of Cementite The enthalpy of cementite at 273 °K, H279 — HOcem, was computed by integration of the low temperature heat capacity as measured by Seltz, McDonald, and Wells" 68" to 298 °K) and as given by the Debye functions recommended by them (0" to 68°K); the result is included in Table I. At higher temperature HCem — H,,"" is given by Kelley who used the data of Naeser7 (298" to 1037°K) and of Umino8,9 (273° to 1923°K). We have recalculated Hcem — H273 cem from the data of UminoO in the following way. In the equilibrated alloy at temperature the weight fraction of cementite Pct c -Pct cr is PctC -PctCr designated f(C), and the

Jan 1, 1952

By C. Law McCabe, R. G. Hudson

The Knudsen cell has been employed to determine the free energy of formation of Mn7Cs in the temperature range 800" to 950°C. A value of 66,440 cal was found for hH°o for a-manganese. Measurements of the pressure of manganese over a mixed carbide, (Fe,Mn),C, points to a power relationship between aun7cs and N.4,. RECENTLY Kuo and Perssonl have reported that the carbide of manganese which is in equilibrium with graphite at temperatures up to 1100° C is Mn7Ca. There are no published data on the thermo-dynamic properties of this compound. In order to determine the stability of Mn7Ca, it appeared that, by obtaining the pressure of manganese above 8-manganese and also above Mn,C, in equilibrium with graphite, the free energy of formation of Mn7Ca from 8-manganese and graphite could be obtained. In addition, the vapor pressure of manganese, reported by Kelley From data of Bauer and Brunner,' is subject to some uncertainty and further determinations of the vapor pressure of manganese seemed warranted. In this investigation of the pressure of manganese vapor above pure manganese and also above the carbide of manganese in equilibrium with graphite the apparatus used is the Knudsen orifice cell. The same apparatus, experimental procedure, and method of calculating the pressure was used in this investigation as in one previously reported.~ Care was taken to insure that the cells were at constant weight before using them in a run. The manganese charged in the cell was CP grade powder, carbon free, obtained from the Fisher Scientific Co. A spectroscopic analysis of the manganese after appreciable amounts of it had vaporized from the Knudsen cell showed that no element was present in sufficient quantities to contribute to a weighable weight loss or to decrease the vapor pressure of manganese to any appreciable extent. The spectro-graphic analysis was 0.002 pct Cu, 0.05 pct Fe, 0.002 pct Pb, and 0.002 pct Ni. 8-manganesea is the allo-tropic form of manganese which was present in the cell at temperatures used in this investigation. The manganese carbide, Mn,Ca, was made in the following way: In a closed graphite cell manganese powder was added to graphite powder, which was made from graphite rods for spectrographic use. The manganese powder was the same as that described previously; 5 pct excess graphite was added over that required for the formation of Mn7C,. The mixture was heated in a closed graphite cell for approximately 20 hr at 1350°K under vacuum. X-ray analysis revealed that there was no manganese present after this treatment, but that the lines due to Mn,C, were present. In order to prove that there was no volatile carbide of manganese which was effusing out of the cell, the following experiment was performed: A graphite effusion cell containing graphite power, in excess of that to form Mn,C, of a desired amount, was brought to constant weight on heating at 1228°K. The required amount of manganese was accurately weighed and then added to the graphite effusion cell. The cell was placed in a vacuum at 1228°K for one week, which was the time calculated for the manganese to have effused completely, assuming instantaneous formation of Mn,C8. The cell was then weighed again. This experiment was carried out on two different occasions and both times the weight loss of the cell came within 1 pct of the weight of manganese originally charged minus the weight of manganese left in the cell, as determined by chemical analysis. These data are summarized in Table I. This agreement is considered to be within experimental error and is taken as proof that no carbide of manganese is volatile in this temperature range. It was established, by X-ray analysis, that Mn,C, formed before appreciable amounts of manganese vaporized from the metal powder which was charged. The identification of the carbide of manganese which was present in the Knudsen cell in equilibrium with graphite and manganese vapor was carried out by Kehsin Kuo at the University of Uppsala. He established that the authors' sample, which was submitted to him for analysis, contained the phase

Jan 1, 1958

By Robert A. Rapp

The standard molar free energy of formation of MOO,was determined between 750o to 1050o C in galvanic cell measurements involving the solid electrolyte Zr0.85 Ca0.15 O1.85. Use of the reference electrodes Fe + FexO and Ni + NiO Provided two independent determinations of FoMoo2. The data may be represented by the equation FMoO2 = -137,500 +40.0T(°K) which is in good agreement with previous CO/CO, gas equilibrium measurements of Gleiser and Chipman. The standard molar free energy of formation of molybdenum dioxide has recently been reported over a large range of high temperatures from the calorimetric experiments of King, Weller, and christensen.' Gleiser and chipman2 have also recently determined ?FmoO2 from 926o to 1068oC in CO/CO2 gas equilibrium measurements. Earlier gas equilibrium studies have been made and reviewed by Gokcen.' Over the temperature range studied by Gleiser and Chipman their values for ?FoMoO2 differed from the calorimetric data by about 700 cal. This investigation was undertaken to resolve this difference and thereby establish the two phase mixture of Mo + MOO, as an electrode of well-known oxygen potential for galvanic cell applications at very high temperatures. The galvanic cell technique involving the Zr,.,, Ca,0.15 01.85 solid electrolyte was introduced for the

Jan 1, 1963

By G. Horvay, J. G. Henzel

Nomograms and charts are provided which permit rapid determination of the mold-casting interFace temperature and the speed of solidification when a semiinfinite ingot is cast into a semiinfinite mold. The physical properties of the mold, the frozen metal, and the liquid metal are not assumed to be equal, but they are assumed to be temperature independent. The results are correlated with charts prepared by Paschkis and Hlinka—using Columbia University's Analog Computer—for the freezing of finite ingot slabs when a constant surface temperature is impressed, and with experimental cooling curves obtained by Pellini in sand and iron molds for 7 in.-sq steel castings. x = coordinate directed to right of zero (freezing direction) y = coordinate directed to left of zero (melting direction) e = position of freezing front (in x direction) ? = position of melting front (in y direction) $ = temperature (function of position and time) ? = fixed temperature 2L = width of finite slab Y = a fixed position in the semiinfinite mold, or the width of a finite mold (see Section 7) Properties y = density, lb per cu ft c = specific heat, Btu per lb deg F k = conductivity, Btu per ft hr deg F X = heat of fusion, Btu per lb k = k/Yc = temperature diffusivity, sq ft per hr* b - = = - heat diffusivity, Btu per sq ft deg F Vhr Subscripts 2 = pertaining to the still-liquid metal (case of freezing), or the medium which furnishes the heat (case of melting) 1 = pertaining to solidified metal (case of freezing), or to molten metal (case of melting)* 0 = pertaining to mold (case of freezing), or to the still-solid metal (case of melting) f = pertaining to fusion condition (eg.,?f - fusion temperature) i = pertaining to the location x = 0 (the mold-ingot "interface")

Jan 1, 1960

By R. H. Tien

Temperature distribution as well as position of the solidified front is solved by means of "heat balance integral", for the case of freezing a slab with time-dependent surface temperature. Numerical solutions for the cases of linear variation and exponential decay for surface temperature are given. Application also includes solidification of casting. An increased interest in the heat-transfer problem involving a change of phase has been developed in recent years. Practical problems include solidification of a casting, freezing and thawing of soil, ice formation, and others. Despite the importance of the topic, a literature search reveals relatively few solutions which may be extended to practical problems. Due to mathematical complexity, which comes from the nonlinearity of governing differential equations, exact analytical solutions which have been published are limited to a few cases with simple boundary conditions. Although numerical solutions of these problems have become available after highspeed digital computers were introduced, lack of simple and general methods of programming for computation makes this approach impractical. The case of the semi-infinite slab with constant surface temperature was solved in the 19th century. In honor of Neumann, who first found an analytical solution, this kind of problem is generally referred to as the Neumann solution. As has been shown in Fig. 1, the problem to be analyzed is the freezing of a semi-infinite region (x > 0) which is initially liquid at the melting temperature with the surface (x = 0) maintained at time-dependent temperature. This analysis can be applied to the study of many casting processes where most of the heat removal is essentially unidirectional. "Heat balance integral" which has been used by Goodman1 is employed in this analysis. The concept of "heat balance integral" is to define a quantity, d(t), called the thermal layer. Beyond this thermal layer, for all practical purposes, there is no heat transfer, and the region is at the equilibrium temperature. "Heat balance integral" is obtained by integrating the conduction equation with respect to the space variable over this thermal layer d(t). Choosing some plausible temperature distribution, usually a polynomial or a finite trigonometric series in the space variable, this integral equation becomes an ordinary differential equation, with time as the independent variable, which can be solved by classical methods. The thermal layer and "heat balance integral" are equivalent, respectively, to the boundary-layer thickness and the momentum integral in hydrodynamics. A modern account of Prandtl's concept of the boundary layer and von Karman's momentum integral may be found in Ref. 2. Although the problem considered here has been limited initially to uniform melting temperature, the present method is equally applicable to the case with arbitrary temperature distribution in the liquid. STATEMENT OF THE PROBLEM The physical situation and coordinate system used in the problem to be analyzed are shown in Fig. 1. Notations used are listed in the table of nomenclature. Let us assume a semi-infinite region extending over positive x, initially at the uniform melting temperature. At the surface x = 0, a time-dependent temperature, which has a numerical value

Jan 1, 1965

By J. W. Freeman, D. N. Frey

Fundamental reasons for the improvement in creep resistance of an austenitic alloy by cold working were investigated mainly by X-ray diffraction. The creep resistance was found to be improved by the internal stresses in the lattice of the alloy induced by the cold work. THIS investigation was concerned with the fundamental reasons for improvement in creep resistance of an austenitic alloy as a result of cold working. Also, the investigation was carried out to elucidate the conditions under which cold working could be expected to improve the creep resistance. To achieve these ends, creep resistance and internal structure were correlated for a variety of cold-worked conditions. Since the aim of the investigation was not to obtain specific and extensive information on any one alloy, creep testing was done with a single stress at 1200°F. Structural studies were carried out primarily with X-ray diffraction characteristics. The alloy used, low carbon N-155, was selected on the basis of being representative of at least some of the alloys used in gas turbines. Low carbon N-155 alloy in the form of %-in. sq bar stock was used in this investigation. The chemical composition, in percent, was: C, 0.13; Mn, 1.43; Si, 0.34; Cr, 20.73; Ni, 18.92; Co, 19.65; Mo, 3.05; W, 1.98; Cb, 0.98; N, 0.14; and Fe, balance. The bar stock was produced from a 13-in. sq billet, finished to 7/s in. round cornered square between 2060" and 1910°F. Prior to use in this particular investigation, the bar stock was solution-treated 1 hr at 2200°F and water quenched. This procedure was used in order to put the stock in a condition where effects of prior processing were minimized. Experimental Procedure The specific approach to the problem was twofold. First, the influence of cold working, under various conditions, on the creep rate under a single stress at 1200°F and on the internal structure was in part determined. Second, the effect of annealing at various times and temperatures on the creep rate and internal structure of the cold-worked samples was in part evaluated. The first step was basic to the investigation—creep resistance and structure were to be correlated. The second step was taken to see if the annealed samples showed some internal changes which could also be correlated with changes in creep resistance. This it was felt would facilitate solution of the basic problem. The creep and structural studies were carried out on samples reduced approximately 5, 15, and 40 pct at room temperature and 15 pct at temperatures up to 2200 °F. Annealing of various of the samples was done at 1200°, 1400°, 1600°, and 1800°F for time periods up to 1000 hr. Studies of the annealed samples were concentrated on materials rolled approximately 5, 15, and 40 pct at room temperature and 15 pct at 1400°F. The creep tests were carried out at 1200°F under 40,000 psi, the latter being approximately the 1000 hr rupture stress of the material

Jan 1, 1952

By I. J. Bear, H. W. Paxton

Studies have been made of the method of propagation of yield in iron single crystals in the range of 205' to 295OK by microscopic and X-ray techniques. 'The results show yielding in two stages, of which the second corresponds closely to the Lüders extension in polycrystalline iron. IRREGULAR macroscopic markings On the polished surface of a polycrystalline mild steel test piece during the lower yield extension were first observed by Liiders.' The lower yield stress was not very constant. Sylvestrowicz and Hall2 showed that it was possible to obtain a constant lower yield stress by using a specimen in the form of a moderately flexible thin strip; the macroscopic markings in this case then appeared as a band of deformation (Lüders' band) which propagated steadily from one or occasionally

Jan 1, 1956

By P. A. Fisher, J. B. Wilson, D. J. Whitehead, C. J. P. Ball, A. C. Jessup

The properties of a new magnesium alloy ZT1 containing 3.0 pct Th, 2.5 pct Zn, 0.7 pct Zr are described. The alloy possesses good creep and fatigue resistance up to 650°F, is free from microporosity, and is readily sand-cast. ZT1 is shown to be superior to zinc-free Mg-Th-Zr alloys. THE advent of the jet engine created a demand for a light sand-casting alloy capable of being cast into large complex shapes and capable of resisting creep at temperatures up to 500°F. This demand has been largely met by alloys of the magnesium-cerium mischmetal-zirconium types, containing about 3 pct Ce mischmetal and 0.7 pct Zr, typified by Elektron magnesium alloys MCZ and ZREI, the latter alloy also having a zinc addition of 2.5 pct. These alloys utilize the valuable properties at elevated temperatures conferred by the addition of rare earth metals to magnesium, a fact which has been known for many years and discussed by several investigators.1-1 Murphy and Payne8 showed that the addition of the powerful grain-refining element zirconium to Mg-Ce mischmetal alloys produced alloys with attractive room temperature properties combined with good creep properties and castability. With the increasing power of modern jet engines the temperatures to which some of the magnesium parts are subject are likely to exceed the safe working range of the cerium-mischmetal-containing alloys, and at the beginning of the research considerable interest had been shown by aeroplane engine designers in a magnesium sand-casting alloy suitable for service at higher temperatures, e.g., 600°F and above. At an early stage in the development of this type of alloy a check on the fatigue properties at elevated temperatures indicated that, since the fatigue limit even at 108 eversals was appreciably higher than any permissible creep stress, the main emphasis of the research could be concentrated on creep behavior. The primary aim in developing the new alloy has therefore been to attain maximum creep resistance; but due consideration has also been given to other important properties such as castability, tensile strength, and cost. It is by now well established that it is not possible to correlate creep strength with other short time mechanical properties such as are obtained in tensile

Jan 1, 1954

By H. Herman, C. Chiou, M. E. Fine

From variation in Young's modulus and Vicker's hardness during GPl zone formation in A1-2 at. pct Cu the following was observed: 1) the presence of grain boundaries does not have any perceptible? effect on the aging reaction; 2) the modulus charge is orientation dependent; 3) the activation energy for zone growth is confirmed to be 11 * 1 kcal per mole; 4) reaging after reversion is preceded by an incubation time that varies with temperature. An analysis is applied to the present data and to data of other workers and kinetic laws dependent on the quenching rate are determined. In Al-base Cu alloys the decomposition product of a supersaturated solid solution at low temperatures (for example 25°C) and the first product at moderate temperatures (for example 150oC) are Guinier-Preston zones of the first kind (GPI).' These zones are nonideal and are thought Jo 'Onsist roughly of sheets of Cu atoms up to 150A in diam and one or two atoms thick.' The kinetics of the reaction, ass — a2

Jan 1, 1961

By Chester T. Sims, Robert I. Jaffee

The thermoelectric behavior of the Pt—Pt-Re thermocouple and the resistance of rhenium to attack by certain molten metals is discussed. In addition, data are presented on the stress-rupture behavior of drawn wire, the tensile characteristics of rolled sheet, the variation of Young's modulus with temperature, and the effect of specimen size and fabrication method on the work harden ability. Mechanical properties of thoriated rhenium are discussed. This includes data on the effect of thoria in rhenium on tensile properties, ductility, work hardening, and recrystallization. RECENT work by the authors', has described methods of fabrication and some of the physical and mechanical properties of rhenium. Rhenium was established as a high melting, dense, refractory-type metal with favorable mechanical properties. In addition, Todd and co-workers' and others" have studied such properties of rhenium as the work function, specific heat, and the resistance of rhenium to the water cycle. Revelation of these and other properties has led to serious consideration for application as electrical contacts, high temperature thermocouples, and wear resistant materials. chanical properties reported previously,' several additional examinations have been conducted. The stress-rupture behavior and the Young's modulus of rhenium have been investigated at elevated temperatures. Tensile data have been obtained for rolled sheet, and a study of the relative work hardening characteristics of rod, wire, and sheet has been conducted. Variation of Modulus of Elasticity With Temperature—The Young's modulus of a % in. diam annealed rhenium rod was determined from room temperature to 880"C (1620OF). The rod, approximately 6 in. in length, was activated in a transverse vibration apparatus suspended in a furnace. The resonance frequencies of the rod were measured and used to calculate the moduli values. The driven frequency was 569 cycles per sec, and a protective helium atmosphere was used. The data, plotted in Fig. 1, show that the modulus decreases in an approximately linear manner with temperature over the range tested.

Jan 1, 1957

By G. K. Manning, A. R. Elsea, C. R. Simcoe

It was found that a critical boron content exists which yields the maximum boron-hardenability effect in hypoeutectoid steels, as was predicted from the mechanism proposed in a previous paper. The hardenability of boron steels with boron contents between 0.00005 and 0.0017 pct was dependent on the boron content, austenitizing temperature, quenching temperature, and austenite grain size. The effects of these variables on hardenability can be explained by the mechanism previously proposed for the boron effect. A MECHANISM has been proposed to explain the effect of boron on the hardenability of steel.' The proposed mechanism assumes that transformation particles nucleate at concentrations of lattice imperfections where the energy level is high, and

Jan 1, 1957

By R. L. Smith, I. G. Greenfield

The binary system Ga-Sb has been investigated by thermal, X-ray, and metallo-graphic methods. 'The intermetallic compound GaSb melts at 705.9OC and forms a eutectic with antimony at 11.8 atomic pct Ga. This eutectic melts at 589.8OC. A eutectic appears to be formed at 29.8°C but is too close to the composition of pure gallium to be detected. IN the course of an investigation of the semiconducting properties of the intermetallic compound, GaSb, the phase equilibrium between gallium and antimony has been investigated. Recently, the phase diagram of similar systems, such as In-Sb,' In-AS,' and Bi-As3 have been determined. These diagrams have the same general appearance in that an intermetallic compound is formed at 50 atomic pct and a eutectic is formed on both sides of the intermetallic compound. Jenny,& who has been investigating the semiconducting properties of intermetallic compounds, has concluded from thermal data of several alloys that the phase diagram of the Ga-Sb system resembles those mentioned previously. This paper represents a more detailed study of the Ga-Sb equilibrium. Experimental Procedure The gallium that was used to prepare the alloys was obtained from A. D. Mackay Inc. and the Aluminum Co. of America; the latter reported the purity as 99.95 pct. The antimony was obtained from Bradley Mining Corp. who specified a purity of 99.997 pct. Since the intermetallic compound of GaSb was prepared primarily to be used for further studies of the semiconducting properties, additional purification by a standard zone-melting technique under an atmosphere of hydrogen was performed. Hall-effect measurements on this material indicated an impurity content of less than 3 ppm.5 The antimony also was purified by zone melting and used in conjunction with the compound GaSb to make the necessary alloys for the determinations of the antimony-rich side of the phase diagram. The antimony-rich alloys were chill cast in Vycor tubes which were evacuated to a pressure of less than one micron. Since these alloys expand on freezing, precautions were taken to prevent oxidation of the ingot in the event the tube fractured. To insure homogeneity, the brittle alloys were ground and then placed in the furnace for the thermal-arrest determinations. Since the cost of gallium is high, the experimental procedure was complicated somewhat because of the necessarily limited sizes of the melts. In order to economize, the gallium-rich side of the diagram was determined by using a 35 g ingot of pure gallium initially and adding increasing amounts of antimony in order to obtain additional alloys. The furnace used in the determination of the cooling curves is illustrated in Fig. 1. A 2¼ in. quartz tube, sealed at one end, was fitted with a brass flange which was attached with DeKhotinsky cement. The brass collar was water cooled to prevent the cement from softening. An "0" ring was used to provide a seal between the brass collar and the furnace cover. Nichrome ribbon was wound around a 2 ½ in. asbestos-covered copper core which was used to reduce the thermal gradient in the furnace. The insulation consisted of alternate layers of asbestos and aluminum foil surrounded by sil-o-cel refractory and

Jan 1, 1956