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By S. Vela, R. M. McKinley, L. A. Carlton

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.' The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measzcrement of the re.rulting pressure changes at an adjacent well with a very sensitive differential pressure gauge. This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusivity, trans-missibility and storage. The primary objective in presenting these data is to demonstrate the potential of the methcid for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (I) pulse-test data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data: (2) pulse-test values for permeability are comparable with core va1ue.s; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should. The pulse-testing technique by Johnson et al.' is an ideal source of data for purposes of reservoir description, for it provides a measurement of formation storage S = +ch, hydraulic diffusivity 91 = k/+cp and transmissibility T — This paper describes an application of this method in a producing oil field. Results were analyzed to give numerical values for the parameters 7, T and S. These values were compared with oil-water production data (for the effect of fluid saturation), with core data and with data from an interference test. The reservoir in which the pulse-test survey was run is the result of a structural trap formed by a fault along the east side of a north-south trending anticline. A down-structure aquifer providcs a natural flank water drive for the pool. The producing formation is a dolomitic lime- stone having mainly vugular permeability; the formation oil has a gravity of 29" API with negligible dissolved gas. The field contains 19 wells, all on pump, arranged on 40-acre spacing along the top of the anticline. Fig. 1 shows the location of all these wells except two at the south end of the field. The dashed line on the right-hand side of the figure represents the approximate location of the fault with respect to well positions. Pulse-Test Survey and Analysis of Data A pulse-test requires a pulsing well and a responding well. In the field, changes were made in the rate of flow at the pulsing well by stopping and starting the pump periodically and measuring the corresponding pressure

Jan 1, 1969

By Milton T. Pana

Computer techniques now have been applied to the solution of a wide variety of scientific and engineering problems in the mining industry, but generally not in great depth in any one area. In mining, the area covered in greatest depth and with the greatest success has probably been mine planning and to a lesser degree production scheduling. A rather comprehensive review of the literature related to mine planning and production scheduling indicates that contributions in these areas have been geographically, as well as organizationally, widespread. Of twenty-six papers reviewed, eleven were from industry, eight from educational institutions, four from computer vendors, two from the Bureau of Mines, and one from a private consultant. The conclusions that can be derived from the literature are: First, the-state-of-the art has advanced to the point that computing ore reserves and developing mining plans with the aid of the computer is now a routine practice; second, the application of the computer to mine planning problems has markedly improved our ability to estimate ore reserves, more accurately define pit limits, and determine an optimum mining sequence. MINE PLANNING The papers in this section deal essentially with the problem of determining the final pit limits of an orebody and the ore reserves associated with a given pit limit. The problem is probably best described by Soderberg25 and more recently by Reibell. 23. There are two techniques currently being applied to this problem by several mining companies: 1) the multiple-cone technique and 2) the Lerch-Grossman algorithm. The multiple-cone technique is the older of the two techniques and has the advantage of being more flexible, allowing an engineer to easily vary pit slopes in different sectors of the design. The technique can also be used to define intermediate pit contours. The Lerch-Grossman algorithm is appealing in that the final solution is given in the form of a true mathematical optimum. The technique is limited, however, in that the size of the blocks in the orebody model are a function of the desired

Jan 1, 1969

By D. McLean

For many pu@oses uniform strength is desired over a long temperature range, coupled to a band of softness at the hot end for easy shaping. Various types of material fulfill such a requirement to different degrees, depending on the regularity of their atomic structure. In long-chain polymers and vitreous glasses the irregular structure leads to a steep temperature dependence of deformation resistance and the temperature band between the hard and brittle condition and the soft condition is only about 100 C. In crystals and especially metals the atomically regular structure leads to a much smaller sensitivity over a wide temperature band, thus approaching the ideal behavim. The reason for this insensitivity is that the regular crystalline structure deforms by the movement of dislocations and the elastic interactions of dislocations in- PLASTICS, GLASSES, AND CRYSTALS The ease or otherwise of deformation varies with temperature much more in some substances than in others. This is an important matter when service over a wide temperature range is needed, especially volve energies of several hundred electron volts compared with which the energy of thermal agitation is insignificant. However, temperature affects a metal's defmmation resistance through its influence on the annealing, m coarsening, of the three-dimensional dislocation network. This coarsening is a phenomenon very similar to grain growth and ideas about grain growth can be applied to it. Taking into account also the temperature dependence of the glide resistance from alloying additions, a reasonable account can be given of the overall effect of temperature on deformation strength and of stress and grain size on deformation rake. Special structures me described. some arising from these ideas and as yet untried, which may benefit metals and polymers but not ni-treous glasses. when in addition a degree of softness suitable for shaping is required at some stage. It would be nice if one could write on this subject in as much detail about plastics, glasses, and so forth, as about metals, but there has been far more study of this matter in metals than in other substances, which is one reason why most of this paper concerns metals. However, in Fig. 1 there are shown the deformation strengths of several nonmetallic substances as a function of temperature. In many tests the attempt at deformation caused breakage and the graph lines are then drawn dashed. Long-chain plastics, a glass, and a crystalline substance are included in Fig. 1. The notable feature of all of them is the sensitivity of the

Jan 1, 1969

By H. M. Manasevit, R. L. Nolder, L. A. Moudy

The observation that silicon-on-sapphire crystallo-graphic relationships exist which are unrelated to one another implies that there are regions of sapphire orientations containing these relationships which are separated by boundaries. The presence of these boundaries is demonstrated, initially on rounded cylindrical surfaces md more definitively on flat sapphire substrates with orientations along primary crystallograPhic zones. By means of reflection electron and X-ray diffraction techniques the crystallographic relationships have been studied. Two new relationships have been found, viz., (111) Si (1014) sapphire and (001)Si (1012) sapphire. Also found were multicrystalline relationships. The approximated boundaries between the crystallographic regions for each relationship are shown by means of a stereo-graphic projection. These studies also clarify discrepancies in the literature concerning the silicon-sapphire relationships on the (1120) sapphire substrate. SINCE the first report of the deposition of single-crystal silicon on sapphire in 1963' this epitaxial system has been the object of study by many semiconductor laboratories. In particular, there has been strong interest in the crystallographic relationships between the two materials. In 19652,3 we demonstrated that at least four distinct modes of orientation relationships can occur, namely, (100)Si (0112) sapphire, (111)Si 11 (1124) sapphire, (111)Si (1120) sapphire, and (111)Si (0001) sapphire. Each relationship could be obtained when the substrate plane was at the particular orientation indicated. Other workers as well as our laboratory concurred in general with the initial results. However, two discrepancies were observed. First it was observed by Joyce et a1.4 that on a (1120) substrate a (110) silicon deposit could be obtained. This was actually consistent with the (111)Si (1124) sapphire mode. Second, two other laboratories,5,6 as well as our own,7 have found a deposition on the basal plane which is different than our initial findings. Even though a (111)Si deposit was obtained, the crystallographic relationships were not identical to those previously found. Subsequent work in our laboratories has confirmed that the form found in these later investigations of the basal plane is by far the more predominant, and the original finding was an anomaly. The relationships which have been previously estab1.ished are summarized in Table I. It is seen that at present a rather small number of possible substrate orientations has been investigated. Therefore, it seemed appropriate that a systematic investigation of silicon epitaxy on various sapphire substrate orientations would be of value. It was expected that the answers to three questions could be obtained from such an investigation. These are as follows: 1) Since we know of at least four distinct modes of orientation relationships, over what range of substrate orientation do these modes occur and what is the form of the boundary expected between the different regions in which each mode occurs? 2) Are there other modes which occur on substrate orientations not previously investigated? 3) What is the explanation for the discrepancy between our laboratory's findings and those results reported by Joyce et al.4 concerning the relationships occurring on (1120) substrates? APPROACHES AND EXPERIMENTAL METHODS Two different approaches were used. Initially, depositions were carried out on rounded cylindrical surfaces which lay perpendicular to the (0112) plane.* By this means the presence of boundaries and their approximate positions could be determined. Finally and more definitively, depositions on flat sapphire substrates with a variety of orientations, mostly along primary crystallographic zones and about the (1120) plane, were studied by means of reflection electron diffraction and X-ray diffraction (using back-reflection Laue patterns and full circle goniometer techniques) in order to determine crystallographic relationships. The sapphire orientations investigated by these means

Jan 1, 1969

By R. R. Beebe

Marcona Corporation produces about 3.5 million long tons of iron ore pellets annually on its two travelling grate pelletizing machines at San Nicolas, Peru. During 1969, these pellets will be shipped to customers in four marketing areas--Japan, the United States, Europe, and South America. All of these sales are on the open market, and product quality is a major concern. Typical chemical, structural, and quality test results for Marcona pellets are given in Table 1. [ ]

Jan 1, 1969

By E. S. Machlin

The wzodel of Blandin and Diplunt;, generalized to include a phase factor, is applied to the carbon-carbon interaction in iron. Darken&apos;s "energetic" model is generalized to include not only first neighbor interactions but further neighbor interactions as well. On the bases of these generalized models relations are derived for the activity of carbon in both austenite and ferrite in terms of the carbon-carbon Pair interaction energies. A single function then yields the pair interaction energies consistent with the experimental activities of carbon in both ferrite and austenite. Thus, a simple explanation is given for the observation that the nearest-neighbor interaction between carbon is repulsive in austenite and attractive in ferrite. Certain consequences of this approach are explored. OnE object of the present paper is to attempt to take into account the consequences of electrostatic contributions to the carbon-carbon pair interaction energy for carbon as a solute in iron. Friedel&apos; has shown that oscillations in electrostatic potential are to be expected about a solute atom in a metallic solution. Blandin and 6lant6&apos; have shown that such oscillations yield an interaction energy between pairs of solute atoms that obeys the relation: W{ = A cos(2ftFri + 4>)/(kFri)3 [l] where kF = Fermi wave vector, ri = distance between solute atoms comprising the pair7 <p = phase factor dependent only on electronic nature of solute and solvent, A = coefficient dependent only on electronic nature of solute and solvent. Machlin3 found that Eq. [I] accurately described the pair interaction energy derived from short-range order measurements based on field ion microscope observations of dilute alloys of platinum. He also found that the value of the phase factor $ derived from residual resistivity measurements agreed well with that obtained from the analysis of the short-range order data. Harrison and paskin4 were able to predict the long-range ordering energy of 0 brass using Relation [I] and residual resistivity values to predict the value of the phase factor $. Machlin5 has repeated their analysis and applied it to the prediction of the long-range ordering energy in AgZn and AgCd with excellent agreement between prediction and experiment. Both A and $ are independent of the crystal structure. The Fermi wave vector depends uniquely upon the conduction electron concentration per unit volume in the spherical approximation of the Fermi surface. Thus, Eq. [I] is expected to apply to both fer- rite and austenite with only one set of values of A and $. Mossbauer studies6 yield the result that iron has one 4s electron. We shall make an assumption found to hold previously for platinum3&apos;7 and nikel, which is that only the s electrons are involved in shielding the perturbing potential of carbon. With this assumption, kF = 1.35 A-l. Although A and $ may be obtained from certain mdels&apos;&apos;&apos; we shall take A and $ to be empirical constants in the spirit of Kohn and osko.&apos; Thus, Eq. [I] involves two adjustible parameters. Consequently, two independent relations in A and $I are required in order to evaluate them for carbon as a solute in iron. We may use a recent analysis of Aaronson, Domain, and poundg who showed that Darken&apos;s energetic model,1° as well as others, can be used to describe the activity-temperature data for carbon in iron in both the aus-tenitic and ferritic phases. Darken&apos;s model takes into account only first neighbor pair interactions. For our needs, all neighbor pairs need to be taken into account. It is convenient to generalize Darken&apos;s model. The result for the partition function for austenite is: over the temperature range 800" to 1200°C and where the uncertainty corresponds to one standard deviation. Eq. [4] effectively yields only one relation. Another relation is required to obtain unique values for A and $. One property of Eq. [4] is that it is independent of crystal structure. Hence, data for a iron can be used to obtain another relation. To arrive at this relation we must generalize Eqs. [2] and [3] so that they may be applied to the bcc a iron. The result is that:

Jan 1, 1969

By V. Koump, T. F. Perzak, R. H. Tien

A series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts Mere measured during essentially one-dimensional freezing of Al-Cu alloys. The dimensions of the ingots were 3 by 5 by 6 in. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experitments. For each alloy the rate of heat removal was varied to give a total jreezing time in the range 3 to 30 min. The results of these measurements cowlpared favorably with the theoretical model of freezing of binary alloys with time-dependent surface temperature. IN engineering analysis of solidification of commercia1 steels and nonferrous alloys it is a common practice to assume that an alloy freezes by propagation of an isothermal solidification front, i.e., essentially as a pure metal. In two recent theoretical investigations&apos;j2 the present authors explored the possibility of a more realistic approach to the problem of solidification of alloys. In the proposed model the freezing of an alloy is assumed to take place by propagation of two isothermal fronts, i.e., the liquidus front and the solidus (or eutectic) front. The region between the two fronts contains both liquid and solid and is referred to as the solid-liquid region. The width and the solid content of the solid-liquid region vary with alloy type, solute concentration, and cooling rate. For a given alloy system, initial concentration of solute, and the mode of heat removal, the proposed model yields the temperature distribution within the solid skin, temperature, solid fraction, and concentration distributions with the solid-liquid region, and the rates of propagation of the liquidus and the solidus fronts. This model is obviously of considerable practical importance in engineering analysis of solidification processes, since it gives a more realistic estimate of skin strength during solidification and a better estimate of the total freezing time. Before the new model can be used with confidence, however, it is necessary to test this model experimentally. The experimental testing of the proposed model is a relatively simple matter since the effects to be measured are large and a relatively simple experiment will suffice. The theoretical model predicts, for example, that during freezing of an alloy containing substitutional type solute (negligible diffusion in the solid during freezing) the solid-liquid region occupies an appreciable portion of the ingot, even at low concentration of solute.&apos; Another prediction of the theo- V. KOUMP, formerly with U. S. Steel Corp., is now with Research and Development Center, Systems and Process Division, Westinghouse Electric Corp., Pittsburgh, Pa. R. H. TlEN is Senior Scientist, Fundamental Research Laboratory, U. S. Steel Corp., Research Center, Monroe ville, Pa. T. F. PERZAK, formerly with U.S. Steel Corp., is now with Fiber Industries, Greenville, S. C. Manuscript submitted March 6, 1968. IMD retical model, easily verifiable by experiment, is that the rate of propagation of the solidus (or eutectic) front increases as the solidus front approaches the center of the slab. This prediction is contrary to well-known behavior of the solidification front during freezing of pure metals, where the rate of propagation of the solidification front decreases with time and freezing is completed at the lowest rate. A rather severe test of the proposed model is provided by comparison of theoretical predictions and experimental measurements of the effects of cooling rate and composition on the rates of propagation of the liquidus and the eutectic fronts. In order to test the soundness of the formulation and the method of solution of the problem of solidification of alloys a series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts were measured during essentially one-dimensional solidification of A1-Cu alloys. The A1-Cu system was chosen strictly as a matter of convenience. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experiments. For each alloy the rate of heat removal was varied to give the total freezing time in the range 3 to 30 min. The results of these measurements are compared with the predictions of the theoretical model of solidification of binary alloys, with time-dependent surface temperature.&apos; Before the experiments described in this paper were undertaken, a serious attempt was made to utilize the measurements of previous investigators to test the theoretical model. In the course of this preliminary study a careful review was made of experiments of Pellini and coworkers3 and Doherty and Melf~rd.~ The measurements in Pellini&apos;s work were carried out using a steel containing at least four major components. Evaluation of the solid fraction-temperature relation for this steel (required in the theoretical model) is difficult and uncertain. Doherty and Melford, on the other hand, measured the solid fraction-temperature relation experimentally, but did not give sufficient data to explore the effects of composition and the cooling rates on solidification. Hence it was not possible to utilize these measurements to test our theoretical model. EXPERIMENTAL METHOD The experimental technique used in this investigation differs somewhat from the more conventional techniques employed in solidification studies. This technique was developed primarily to eliminate con-vective mixing in the molten metal caused by pouring of molten metal into the mold. In our experiments A1-Cu alloys were melted directly in the mold. The mold assembly used in solidification experiments is shown in Fig. 1. The mold was fabricated from *-in. stainless-steel sheet. The dimensions of

Jan 1, 1969

By James A. Berberick

Research methods to develop an economic model for the determination of regional mineral advantage are discussed. An industrial complex conceptual framework is used to study potential mineral resource outputs of Kansas. A procedure for making a comparative cost analysis of potential outputs for a Kansas-based industrial complex is outlined and illustrated. Methods for estimating aggregate demand and for developing an input-output matrix for a hypothetical limestone complex are explained. The input-output matrix is expressed in physical units. A computer algorithm for converting physical production data and input cost data into total cost per unit of output information is briefly explained and flowcharted. Limitations and usefulness of this procedure in determining regional advantages are surveyed.

Jan 1, 1969

By D. E. Coates, G. R. Purdy, S. V. Subramanian

The morphological stability of the planar solid-liquid interface in dilute ternary alloys, undergoing steady-state unidirectional solidification, is analyzed in terms of both the constitutional supercooling principle and the perturbation methods recently developed by Mullins and Sekerka. First, various steady-state solutions for the two solute distributions ahead of a planar interface are examined. The nature of the solutions depends on the size and concentration dependence of the off-diagonal diffusion coefficients. W~thin the framework of the constitutional supercooling principle, a cumulative contribution to instability frorn the two solutes is found to exist in the absence of diffusional interaction. It is shown that the latter can produce a further enhancement of instability or can have a stabilizing influence, depending on the form of the liquidus surface and on the sign of the solute-solute interaction. A perturbation analysis, which ignores diffusional interaction, verifies the cumulative influence of lhe solute fields and demonstrates that the Mullins-Sekerka stability criterion for binary systems (with capillarity accounted for) can be readily extended for application to ternary systems. SOME time ago, Tiller et al.&apos; calculated the solute concentration distribution ahead of the planar solid-liquid interface of binary alloys undergoing steady-state unidirectional solidification. An earlier qualitative proposal that the transition from planar to nonplanar growth morphologies is associated solely with the onset of constitutional supercooling in the liquid layer ahead of the moving interface2 was used in conjunction with this calculation to put the now well-known constitutional supercooling (C-S) stability criterion into quantitative terms. Mullins and Sekerka,3 in a recent and very elegant analysis, established a more complete criterion (hereafter referred to as the M-S criterion). Interfacial stability was investigated by determining the time derivative of the amplitude of a sinusoidal perturbation of infinitesimal amplitude which had been introduced into the originally planar shape of the moving interface. Of particular importance is the fact that capillarity was included in the boundary conditions of their calculation. The purpose of the present paper is to extend all of this earlier work on dilute binary systems for application to dilute ternary alloy solidification. The analysis is divided into three sections. In the first the two solute distributions ahead of a moving planar interface are considered. Mathematical solutions are de- termined for situations in which: a) diffusional interaction is negligible, 6) diffusional interaction must be considered but circumstances permit use of constant diffusion coefficients, and c) the concentration dependence of off-diagonal diffusion coefficients can be described by first-order dilute solution approximations. In the next section, a stability criterion analogous to the C-S criterion is developed and the influence of diffusional interaction on interface stability is analyzed. Finally, the perturbation formalism of Mullins and Sekerka, with capillarity included in the boundary conditions, is extended for analysis of ternary systems in which diffusional interaction is negligible. The study of interface stability in binary systems usually commences with the assumption that the equilibrium distribution coefficient and the slope of the liquidus line are constant at values corresponding to infinite dilution. Similar assumptions have not been introduced into the present treatment; that is, we do not assume planar solidus and liquidus surfaces joined by tie lines which yield constant distribution coefficients. The latter involves the assumption of no ther-modynamic interaction between solute species in both the solid and liquid. We consider a ternary phase diagram for which the solidus and liquidus surfaces are, in general, nonplanar and of course pass through the corresponding binary solidus and liquidus lines. These lines are not assumed to have constant slope. In the dilute regions we are concerned with, the following assumptions are made: i) The solidus and liquidus surfaces are of a form such that both the solidus and liquidus temperatures are monotonically varying functions of each solute concentration. ii) The tie lines are such that the equilibrium distribution coefficient of a given solute is greater than unity for every point on the solidus (or liquidus) surface or it is less than unity for every point. STEADY-STATE SOLUTE DISTRIBUTIONS IN THE LIQUID As will be demonstrated in the next section, a knowledge of the steady-state solute profiles is not a necessary prerequisite for the formulation of a ternary C-S stability criterion. However, in that details, such as the complete description of the equilibrium liquidus temperature profile, require an evaluation of the solute distributions, the overall treatment is enhanced if these distributions are determined. Consider a ternary system (solvent plus solutes 1 and 2) for which a planar solid-liquid interface is in unidirectional motion at constant velocity V. At this stage it is unnecessary to limit ourselves to dilute solutions. For a stationary frame of reference the generalized forms of Fick&apos;s equations are:

Jan 1, 1969

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher&apos; estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,&apos; however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,&apos; in his test of Cottrell&apos;s theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell&apos;s theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley&apos;s assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12&apos;13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a&apos;, an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

By Werner Engelmaier

Constant-strain rotating-bending fatigue tests were conducted on 2024-T3 aluminum alloy constant-strain McAdams-type specimens in ultrahigh vacuum, 10-lo Torr, and in atmospheric air. In the elastic strain range the ratio of vacuum-to-air fatigue life varied from about 10 at a maximum bending stress of 37 ksi to near unity at the endurance limit. After 10 pct of the fatigue life, intergvanular microcracks appeared on the surface which did not appreciably propagate further until the last 5 pct of the fatigue life, where trans-granular cracks propagating first in slip-plane cracking and then in the stress-dominated mode led to failure. No reduction in residual tensile strength resulted from the fatigue of the specimens short of fracture. The mechanism governing the fatigue life operates between the occurrence of the intergranular microcracks and the initiation of the trans granular cracks. MORE than forty years ago, Mc Adam&apos; and Haigh2 published the first systematic studies showing that the fatigue properties of metals were greatly affected by environments. Gough and sopwith3 found in a later study that the fatigue life of metals subject to corrosion can be substantially increased by reducing the atmospheric pressure. This and their later work4&apos;5 was, however, done in a vacuum of only 10~3 Torr. Subsequent studies6-&apos; at a vacuum of 10- Torr showed that water vapor is the primary agent affecting the fatigue properties of aluminum alloys. Only recently was ultrahigh vacuum used for fatigue studied.l Various theories have been put forward to explain this phenomenon. Wadsworth and Hutchings12 postulated that cracks form very early in the test and that the chemical attack by the corrosive components of the atmosphere at the root of the cracks enhances the speed of the crack propagation. They also noted that chemisorbed layers of gas on the fresh crack surfaces prevent cold welding of the crack and make the separation irreversible. Ham and Reichenbach, on the other hand, reported that their specimens showed no cracks after a run in vacuum, even though the runs were long enough to have caused the specimen to fracture in atmospheric air. They also reported that in argon at 0.14 Torr the fatigue life was about 5 times longer than at 7 X lo-&apos; Torr. Jacisinll reported that fatigue tests in dry nitrogen showed results close to those obtained in ultrahigh vacuum. The present experiment was designed to determine the extent to which cumulative fatigue damage, i.e., the accumulation of length of fatigue cracks, reduces the residual static tensile strength of an aluminum alloy in both ultrahigh vacuum and atmospheric air and to obtain fatigue-life data for this aluminum alloy at various strains. It was also hoped that information ex- tracted from these data might support one of the previously mentioned theories. 1) EXPERIMENT Test Specimens. The material tested was commer-cial 2024-T3 aluminum alloy. In addition to aluminum, this alloy contains approximately 4.4 pct Cu, 0.5 pct Fe, 0.5 pct Si, 0.6 pct Mn, 1.5 pct Mg, plus smaller amounts of other elements.13 Some typical mechanical properties of this aluminum alloy are listed in Table I.&apos;~ The material was used in the as-received condition, i.e., solution-treated and cold-worked. Mc Adam-type1&apos; constant-stress specimens and notched fatigue specimens were machined from 4 -in. -diam rods, Fig. 1. The critical section of the McAdam-type samples was polished with a 45-deg spiral motion to a No. 8 microfinish. The notch in the notched specimens was machined on a lathe with a forming

Jan 1, 1969

Jan 1, 1969

By Nestor Torres-Acuña, Fathi Habashi

Metallic copper of purity equal to commercial electrolytic copper is deposited during the anodic dissolution of technically available white metal, Cu2S, in m acidic solution of&apos; copper(II) sulfate as electrolyte and copper sheets as cathodes. The process may be applied on commercial scale since it has the advantage of by passing the converting and poling steps, decreasing pollution problems due to SO, and recovering the sulfur of the white metal in the elemental form. The anodic dissolution is believed to take place in three steps: The working conditions that lead to 98 pct cathodic current efficiency are: 30 gpl Cu2+ and 100 gpl H2SO4 in electrolyte, current density 1.0 amp per sq dm, and tetnperature of bath 40°C&apos;. DURING the smelting of copper, nickel, lead, and zinc sulfide ores, large amounts of sulfur dioxide are produced. Because the release of this gas in the atmosphere causes pollution problems, many attempts were made in the past for its recovery either in liquified form or processed to sulfuric acid. Although these two forms of sulfur are the usual forms that are consumed by the chemical and metallurgical industries, their storage and transport usually raise economic problems. It was realized, long ago, that a process by which sulfur can be recovered directly in the elemental form would be most attractive. Elemental sulfur is easily stored and transported, and is readily converted to SO2, H2S, or H2SO4 when needed. Processes aimed to recover the metals from their sulfide ores, and at the same time by-product sulfur in the elemental form, were recently reviewed.&apos; As early as 1882, Marchese2 patented a process in which a matte having the composition: Cu 15, Pb 14, Fe 41, and S 25 pct was electrolyzed. According to cohen3 the process was applied on a pilot scale by the Aktiengesellschaft fur Bergbau-, Blei-, und Zinkhiitten-betriebe at Stolberg, Rheinland, Germany. The process was unsuccessful, however, owing to the contamination of the electrolyte during electrolysis. Studies in this field were reported by Bernfeld4 and Egli.5 Borchers et a1.6-8 developed the process further by using white metal (Cu 78.2 pct, S 19.6 pct) instead of the matte, and a pilot plant was operated by the Mansfeldschen Kupferschiefer Co. at Eisleben, German~.~ It appears, however, that the process never went into commercial operation. Further studies in this direction were carried out by Russian workers.10-23 The International Nickel Co. of Canada erected a pilot plant at Port Colborne in 1951 to apply the process to nickel matte which is essentially pure nickel sulfide."&apos;- 26 Full-scale plant went into operation at the Thompson Refinery in Manitoba in 1964.27 In this method nickel sulfide matte is melted and cast into anodes analyzing 76 pct Ni and 20 pct S with small amounts of copper, cobalt, and iron. These anodes are then electrolyzed in an aqueous solution of NiS04 at pH 4. Further work on this method was reported in the literature.28-31 In this paper, experiments on the anodic dissolution of white metal in aqueous copper sulfate solution are reported. EXPERIMENTAL White metal, Table I, obtained from The Anaconda Co., was cast in form of anodes 10 by 7.5 by 1 cm, Fig. 1. The anodes are mechanically strong and do not break easily; when polished they gave a shiny gray metallic appearance. From the chemical composition shown in Table I, it can be seen that the atomic ratio Cu:S corresponds approximately to the formula CU2.06S. The copper in excess to the formula Cu2S is most probably present as a separate phase since metallic copper could be seen under the microscope, Fig. 2. Fig. 3 shows the X-ray diffraction pattern of white metal which matches fairly well with that of reagent-grade Cu2S.

Jan 1, 1969

By M. Yokoi, K. Yoshida, T. Ishihara

The solubility of aluminum in cryolite melts has been determined by measuring the weight loss of aluminum submerged in melts contained in closed silicon nitride crucibles. The solubility in pure cryolite has also been checked with radioactive isotopes. The solubility decreases with increasing A1203 concentration, decreasing temperature, and decreasing cryolite ratio. The change of aluminum solubility in pure cryolite with the activity controlled by using Al-Ag and A2-Cu alloys supported the assumption that aluminum would dissolve in the form of monovalent ions according to the reaction 2AI + A1&apos; —3 A1&apos;. DURING the electrolytic production of aluminum, the electrodeposited metal redissolves in the bath in some form and is subsequently oxidized back to the former ionic state. This dissolution is believed to cause a decrease in current efficiency. Reported data on the solubility of aluminum in cryolite melts are scattered. The mechanism of the dissolution has not yet been determined, although certain tentative interpretations have been proposed. Many previous studies were performed under different test conditions. Studies were performed in open Systems and closed systems,&apos;o and some were apparently not given sufficient time to Saturate." The solubility can be determined either analytically or gravimetrically. The analytical determination involves measurement of hydrogen gas evolved when frozen cryolite bath saturated with aluminum is treated with sodium hydroxide or hydrochloric acid. The gravimetric determination, adopted by many investigators,&apos;-37&apos;3>14 involves measurement of weight loss of the metal after equilibration with a known amount of salt. It appears that the former technique yields much smaller values of solubility than the latter technique. This large difference in results strongly suggests that the dissolved metal in the cryolite melt is no longer in the metallic state. In the present study, the solubility was determined by the gravimetric technique at various activities of aluminum using A1-Ag and Al-Cu alloys. An attempt was also made to determine the ionic (or atomic) state of the dissolved metal from the solubility data. 1) EXPERIMENTAL Apparatus. Preliminary tests demonstrated that silicon nitride was suitable as a container material since it is compatible to both the fluoride melts and molten aluminum. Crucibles were made from silicon powder nitrided with Nz gas at 1600°C. The good compatibility between crucible and melts is due to the near perfect nitrogenation of silicon. Only small amounts of silicon were found in the aluminum metal after the experiments. The crucible dimensions were 90 mm inside height, 38 mm ID, 105 mm outside height, and 50 mm OD. Close-fitting lids made of silicon nitride were also prepared. The crucible was placed in a close-fitting graphite crucible heated by a vertical Kanthal furnace, Fig. l. The lid and crucible are fastened tightly together by the condensation of vaporized bath in the narrow gap between them. The temperature was measured in the wall of the graphite crucible and controlled within * 5°C. The temperature difference between the measuring point and the interior of the melts was initially determined. Materials. The materials used were: Greenland cryolite (impurities CaF,, 0.5 pct; AlzO3, 0.2 pct; high-purity aluminum metal (purity 99.99 pct); A1203 and AlF, (provided by Nippon Light Metal Co., Ltd); reagent-grade NaF and CaF2; and 99.9+ pct Ag and Cu. Powdered reagents were carefully dried before use. A1-Ag and A1-Cu alloys were prepared before the experiments; their composition was checked by analysis

Jan 1, 1969

By P. Marier, T. R. lngraham

The kinetics of the sulfation of MnO,, MnzO3, and Mn3O4 in SO,, SO3, and O, mixtures was examined and the descending order of sulfation rates at temperatures near 400°C was found to be Mn,O3 > MnO, > Mn3O4. The respective activation energies for the thermal decomposition of MnO, and Mn,O, are 39 and 47 kcal. At 900°C, the thernzal decomposition of MnSO, to MnzO3 is slower than that to Mn3O4. The respective activation energies are 62 and 51 kcal, respectitely. MANGANESE is used to improve the hot workability of steel in the proportions of approximately 13.5 Ib of ferromanganese per ton of steel produced. This requirement accounts for about 95 pct of its large industrial market in North America. The remaining 5 pct is used in the battery and chemical industries. In most North American ores, the percentage of manganese and the manganese-to-iron ratio are not suitable for the direct production of ferromanganese. Hence, most of the North American requirements for manganese are satisfied by importing ore. Typically, many of the studies done on native low-grade manganese resources have been directed toward the production of ore substittes" and the recovery of manganese from open-hearth slags.3 Of the wide variety of processes which have been proposed, the most popular involve compounds in the Mn-S-O system. The thermodynamic properties of manganese and its compounds were reviewed by ah&apos; in 1960 and, more recently, lngrahams discussed the thermodynamics of some of the reactions involved in the Mn-S-O system at normal roasting temperatures. The conditions for producing manganese sulfide during the reduction roasting of manganese sulfate are discussed by Fuller and Edlund.9 A novel scheme was proposed recently by zimmerley7 for utilizing waste sulfur dioxide from stack gases to recover the manganese from ocean-mined manganese nodules. Very little of the work published on manganese compounds has been related to reaction rates. Singleton et 1.&apos; studied the rates of reaction on the MnO-C and Mn7C3-3MnO systems and observed linear and parabolic kinetics respectively in the systems. Tatievskaya et a1.&apos; studied the low-temperature reduction of Mn&, MnO,, and Mn& in HZ and CO, and reported activation energies in the range 1628 kcal. In this paper, the rates of some of the decomposition and formation reactions involving MnSO4, MnOz, MnzO3, and Mn3O4 will be examined after the conditions for the thermodynamic stability of the individual compounds have been designated. CONDITIONS FOR STABILITY OF MnSO4, MnOz, MnZO3, AND Mn3O4 The areas of stability for h&apos;hSO4, MnOz, MnzO3, and h3O4 were established from the data of Mah4 and Ingrahams and are shown in the predominance area diagram,10 logpq- logpsq, in Fig. 1. The diagram is drawn for two temperatures, 700°K, solid lines, and 1100°K, dotted lines. The sketch for the lower temperature includes the conditions likely to prevail in the Zimmerley patent7 when manganese nodules react with sulfur dioxide and that for the higher temperature indicates the conditions for recovering MnzO3 or Mn3O4 from MnSO4 during a roasting reaction. From the fact that the boundary between the areas of stability of MnOz and hSO4 at 700°K is parallel to the abscissa, it is evident that MnOz and SO2 should react together to produce MnSO4, irrespective of the oxygen pressure in the system. If the source of sulfur for sulfation were from waste flue gases, it is likely that the oxygen content of the gas stream would be more than sufficient to oxidize any MnsO4 to MnzO3, 107 atm of O2 required, or even to convert any Mnz03 to MnOz, 0.02 atm OZ required, prior to sulfation. At 1100°K, the diagram indicates that MnSO4 may be converted directly to either MnzO3 of Mn3O4, depending upon the prevailing partial pressure of oxygen. When the gas stream contains more than 1 pct Oz, logpq = -2, only MnzO3 would be recovered from an experiment done under equilibrium conditions. At oxygen partial pressures of less than 1 pct, one would expect to bring about a reversible exchange between MnSO4 and Mn3O4 by appropriate adjustment of the partial pressure of SOZ. These various reactions will be described in the subsequent kinetic experiments.

Jan 1, 1969

By T. E. Hill

The Bureau of Mines investigated the possibility of physically separating Missouri and Minnesota granites into commercially usable fractions of feldspar, quartz, and mica by mineral dressing techniques. The probability of r covering a feldspar fraction from raw granite suitable for commercial uses was developed through correlation of the iron oxide content by extensive petrographic studies. This probability evaluation also included Wisconsin granites and a high-feldspar iron ore concentration tailing from Missouri. Laboratory recoveries of feldspar and quartz were on the order of 80 percent. Mineral content of each fraction was generally over 95 percent, indicating excellent response to separatory techniques, Acid leaching of feldspar and quartz concentrates to remove iron oxide improved the grades chemically; however, occluded iron oxide particles in the leached products prevented attaining top grades of feldspar. Mica was removed as scrap grade at low recoveries. Each concentrate conformed to some category of commercial feldspar, quartz, or mica.

Jan 1, 1969

By O. R. Morris, G. L. Hawkes

A galvanic cell, using as electrolyte a fused salt solution of calcium carbide and as electrodes carbon and a Fe-C alloy of known composition, has been set up to study the thermodynamics of Fe-C alloys in the temperature rmzge 800" to 1000°C. Time independence and reproducibility of the cell electromotive force were taken as evidence of the reversible behavior of the cell. Carbon was believed to be present in the electrolyte as the so-called acetylide ion, C;-. The plots of the cell electromotive force us temperature for a specific alloy composition were straight lines within the limits of experimental error. The average Partial molar enthalpy of carbon in iron relative to pure carbon was found to be +10,610 i 93 cal per g-atom C. Thermodynamic analysis of the data has led to the following equation for the carbon activity, ac, based upon pure carbon as the standard state: In ac = In Zc + 10,560/RT + (10.02 + 77O/T)ZC - 2.350 where ZC is the lattice ratio [nC/(nF, - nc )] and T is the absolute temperature. This equalion gives carbon activity values generally slightly lower than those from gas equilibration studies reported in the literature. METAL LOGRAPHIC examination of a polished cross section of the steel anode used in the electrolysis studies of fused salt solutions of calcium carbide by Morris and Harry revealed extensive carburization of the steel by the electrodeposited carbon. This carburization was reflected in the variability, with time, of the applied potential to the electrolysis cell, necessary to maintain a constant current density at the electrodes. This observation suggested the setting up of a galvanic cell of the "alloy concentration" type to study the thermodynamics of some metal-carbon alloys. Cells of this general type have been widely used for the study of alloy systems.2 In view of the availability of published data in respect of the austenite phase of the Fe-C system, it was decided to carry out measurements upon these alloys before proceeding to studies of less well documented systems. The galvanic cell may be written: where [C] is carbon dissolved in iron. The electrolyte was a fused salt solution of calcium carbide, containing some 5 to 10 mol pct of carbide. The cell reaction is believed to be: C(s)-[CI [I1 Carbon forms an interstitial solid solution in iron, with the atoms located in the octahedral interstices. In the fcc crystal structure of austenite there is one octahedral interstice per iron atom. Thus, the lattice ratio, ZC, shown by Gurney3 to be the fundamental concentration parameter in the context of interstitial solutions, is given by: where nc and nFe are the number of carbon and iron atoms, respectively. chipman4 has recently shown empirically the advantages of using this concentration parameter instead of the more usual atom ratio or atom fraction. The cell electromotive force, E, assuming reversible behavior, is related to the carbon potential or the partial molar free energy of carbon in the solid solution relative to pure carbon at the same temperature and pressure, GP at the composition ZC, by the equation: where z is the carbide ion valency and F is the Faraday constant. An activity of carbon, ac, in the solution relative to the value of unity assigned to pure carbon, and an activity coefficient, qC , are defined such that: where R is the gas constant and T the absolute temperature. GF is further related to the relative partial molar enthalpy Hm, and the temperature coefficient of the cell electromotive force, (aE/aT)Zc, by the equations: Measurement of the cell electromotive force thus enables calculation of the relative partial molar thermodynamic properties of carbon in iron, if z is known. At E = 0, the solid solution is in equilibrium with pure carbon. More convenient for many purposes is the standard state based upon the infinitely dilute solution, Henry&apos;s law. The relationship between the activity coefficient of carbon based upon this standard state, and that based upon the pure carbon standard state, qC , may be obtained by considering the free energy of transfer of carbon from the latter standard state to the former. The relationship is: where +:H is the activity coefficient of carbon in the hypothetical standard state based on a reference of

Jan 1, 1969

By Amitava Gangulee, Michael B. Bever

The order-disorder transition in Ag-Mg alloys in the range 17 to 26 at. pct Mg was investigated and some thermodynamic, electrical and mechanical properties of ordered Ag-Mg alloys were measured. A modification of the phase diagram is proposed on the basis of measured transition temperatures. The stability of the ordered structure is analyzed in terms of the quasichemical theory. Kinetic aspects of the order-disorder transition were also investigated. The energies of ordering at 273°K of Ag-Mg alloys were measured by liquid metal solution calorimetry. The electrical resistivities and the tensile Properties of the ordered alloys were measured. The exothermic energy of ordering increased with magnesium concentration up to the composition Ag3Mg; it is discussed in terms of the quasichemical theory. Pronounced order hardening was observed and can be explained by several strengthening mechanisms, which are particularly effective because of a change in crystal structure associated with the ordering transition. IN silver-rich solid solutions containing approximately 17 to 26 at. pct Mg, long- range ordering may occur during appropriate therma1 treatments. Clare-brough and Nicholas1 first detected such long-range order in the solid solution of composition Ag3Mg and suggested that the unit cell of the superlattice contained 256 atoms. x-ray2 and electron diffraction3 investigations confirmed the occurrence of long-range order, but indicated a shifted Ll2-type structure. On the basis of recent X-ray measurements the crystal structure of ordered Ag3Mg has been confirmed as type D023.4 The present paper is concerned with the order-disorder transition in silver-rich Ag-Mg solid solutions and some thermodynamic, electrical, and mechanical properties of the ordered alloys. The effects of short-range order on the properties of silver-rich solid solutions containing up to 26 at. pct Mg are discussed in a concurrent paper.5 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Specimens. Specimens of Ag-Mg alloys containing from 18 to 26 at. pct Mg were prepared in the form of 1.0-mm-diam wires as described in Section 1.1 of Ref. 5. Disordered specimens were prepared by annealing at 773°K for 1 hr and quenching into iced brine. Ordered specimens were prepared by annealing at 773°K for 1 hr and slowly cooling to room temperature over a period of 15 days. The specimens were stored at 78°K. 1.2) Resistivity Measurements. Electrical resistivi- ties were measured by a potentiometric method.&apos; Equilibrium values were obtained at several temperatures. The kinetics of ordering were investigated by following the time-dependent changes of the resistivity of initially disordered specimens during annealing. The specimens were enclosed in copper capsules and immersed in salt pots; the heating up was accelerated by injecting preheated helium into the capsules. 1.3) Calorimetry. The energies of ordering of the alloys were measured in a tin solution calorimeter as the difference between the heat effects of additions of completely ordered and disordered specimens of the same composition. The procedure and the method of calculation have been described.6 Magnesium was used for thermal compensation in most calorimetric runs in order to improve the accuracy.677 1.4) Mechanical Tests. Tensile tests were carried out with wire specimens at room temperature as described in Section 1.5 of Ref. 5. Microhardness measurements were also made.? 2) RESULTS AND DISCUSSION The characteristics of the order-disorder transition of silver-rich Ag-Mg solid solutions will be discussed first. Some thermodynamic, electrical, and mechanical properties of the ordered alloys will then be considered and compared with the corresponding properties of dis-disordered alloys. 2.1) The Order-Disorder Transition. 2.1.1) Thermodynamic and Structural Aspects. The transition temperatures Tt were determined from discontinuities in the slope of the equilibrium resistivity vs temperature curves. Normalized curves for three compositions are shown in Fig. 1. The transition temperature increases with the magnesium concentration and reaches a maximum at the stoichiometric composition Ag3Mg. The transition temperature of the alloy Ag3Mg was measured as 665° ± 2°K and compares with published values of 660°,1 663°,8 and 66°k.3 In the slopes of the resistivity vs temperature curves of alloys containing 22.2 and 22.5 at. pct Mg, discontinuities were observed at two temperatures. Such upper and lower discontinuities indicate a two-phase field. A modified form of the published phase diagram9 is shown in Fig. 2. A two-phase field was found only on the low-magnesium side of the composition Ag3Mg. On the high-magnesium side, the existence of a two-phase field could not be established because of insufficient resolution, but such a field must be present. This part of the phase diagram can be made complete by a eutec-toid-type reaction a = (a&apos; + ß). The existence of a boundary between the two-phase fields (a + ß) and (a&apos; + ß) is also in accord with published lattice parameters.3 The crystal structure of ordered Ag3Mg (type Do23)

Jan 1, 1969

By J. F. Smith, J. E. Davison

A value for the enthalpy of formation of z2 of -3.14 i 0.21 kcal per g-atom has been measured by the technique of acid solution calorimetry. This result is in quite good agreement with two earlier determinations by tin solution calorimetry and by direct reaction caloriinetry, and averaging of values determined from the three independent calorimetric techniques gives enhanced precision and accuracy with AHh8 (CaMgZ) = - 3.15 i 0.05 kcal per g-atom. For comparison with experimental data, values for the enthalpies of formation of CaMgz, SrMgz, and BaMgz of -9.8, -7.9, and -2.8 kcal per g-atom were estimated from a calculation based on the LVigizer-Seitz approximation as modified by Raimes for polyvalent elements. While complete quantitative accord between these calculated talues and available experimental data is lacking, nonetheless numerical accord is better than might be expected and, more importantly, parallel numerical trends are observed between experimental and calculated vnlues. WITHIN the past decade the enthalpy of formation of CaMg, has been determined a) from measurement of magnesium vapor pressures over binary Ca-Mg alloys,&apos; b) by solution calorimetry with liquid tin as the solvent,&apos; c) from measurement of hydrogen vapor pressures over ternary alloys of calcium, magnesium, and hydrogen,3 and d) by direct reaction alorimetr. The value from tin solution calorimetry is the most precise and is probably the most reliable, and this value is within the quoted uncertainties of the other three experimental results. The overall agreement among the four independent investigations is quite good, particularly so when the diversity of techniques is noted. On the basis of this agreement, CaMgz was chosen as a test material to evaluate the operation of a newly constructed apparatus for the determination of enthalpies of formation of intermetallic phases by acid solution calorimetry. This was believed to be a severe test because of the high chemical reactivity of both calcium and magnesium which reactivity presumably accounts for the fact that an early determination5 of the enthalpies of formation of Ca-Mg alloys by acid solution calorimetry yielded values significantly more negative than the four recent determinations. EXPERIMENTAL APPARATUS AND MATERIALS Experimental Apparatus. The enthalpy of formation of CaMg, was determined by measuring the difference between the heat evolved when dissolving the metallic compound and the heat evolved when dissolving equivalent amounts of unreacted metallic elements in hydro- chloric acid. This was done differentially with an apparatus consisting of twin calorimeters which were constructed to be as nearly identical as possible. The advantage of differential calorimetry is that systematic errors arising from the individual calorimeter design tend to cancel. A schematic representation of the apparatus is shown in Fig. 1. A dead air space around both calorimeters was provided by a large, thermally insulated jacket. Each calorimeter consisted of a 2-liter Dewar flask which was completely enclosed in a copper container. Each Dewar contained 1600 g of 2.5hr HCl to act as the solvent, and thermal effects resulting from solvent evaporation were minimized by covering the acid with 50 g of mineral oil. There was no detectable reaction between the acid and the mineral oil. Equivalent amounts of mechanical energy were added to the calorimeters through twin stirring rods which were driven at the same rpm by a single motor with the intent of the stirring being to maintain thermal equilibrium throughout the solvent. To calibrate the heat capacities of the calorimeters, known amounts of electrical energy could be added by passing measured voltages and currents for known times through submerged heaters, approximately 20 ohms, which were wound noninductively from Manganin wire. A 6-v storage battery was used as a power source, and a dummy heater was used as an exercise circuit to allow the battery to stabilize at a constant electromotive force before energizing one or the other of the calorimetric heaters. A type K-2 potentiometer was used to measure the potential drop across an energized heater while the current was determined from the potential drop across an external standard resistor. Times of energization were measured with an electric timer, and the electrical energy supplied to a heater

Jan 1, 1969

By Thomas R. Bur

Symmetry theory, based on ground work established in the study of single crystals and experimental procedures utilizing ultrasonic pulse velocities of spherical specimens plotted on equal area polar projections, enables the direct identification of a material&apos;s elastic symmetry system and the determination of its orientation, as well as the position of the elastic coordinate axes. The method is especially useful for elasticity studies of polycrystalline and amorphous materials for which this knowledge of symmetry is a prerequisite in determining the independent elastic constants. Projections based on theoretically derived velocities are given for a single crystal from each of the major crystallographic symmetry systems except the triclinic. Projections based on experimentally derived velocities are given for one brass and several rock spheres.

Jan 1, 1969