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By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen's method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen's method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen's5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen's method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen's method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen's method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By Richard A. Queeney, Lance G. Peterson

ESTIMATES of the stacking fault free energy of copper reported in the literature show an extensive divergence of results. Based on measurements of dislocation node radii, Thornton et al.7 find the lower limit of stacking fault energy to be 60 ergs per sq cm: Jossang and coworkers4 estimate the same value should be less than 40 ergs per sq cm. Assuming stacking fault free energy to be twice the coherent twin boundary free energy, Valenzuela8 reports 72 ergs per cm, while Inman and Khan2 cite a value of 24 ergs per sq cm. which can no doubt be accounted for by almost complete absence of interstitials in solution. However, the minute concentration was sufficient to permit observable recovery of dislocation damping. Assuming a dislocation density of 1010 CM -2 and an average loop length of 0.5 , a concentration of interstitials as low as 0.01 at. ppm is sufficient to reduce dislocation damping by more than a factor of ten. The concentration of interstitial solute atoms in Ferrovac E-0.15 pct Ti was thus estimated at 0.01 at. ppm < (C + N) < 2 at. ppm. The absence at elevated temperature of strengthening due to interstitials, Fig. 1, was therefore anticipated in the titanium alloy. The temperature dependence of the flow stress below 300°K was unaffected by addition of either titanium&apos; or zirconium.&apos; Observed, however, was an initial difference in the absolute value of the flow stress below 320oK, Fig. 1. Grain size may account for the difference; the grain diameter of Ferrovac E was 30 to 45 µ and that of Ferrovac E-0.15 pct Ti 65 to 90 µ. Although second phase particles in the form of titanium carbides and nitrides precipitated in the Ferrovac E-0.15 pct Ti alloy, the spacing was too large to produce any strengthening effect. The mechanical properties measured, therefore, were inherent to the bcc lattice. 1W. C. Leslie and R. J. Sober: Trans. ASm, 1967, vol. 60, pp. 99-111. 2 H. Conrad: Journal of Metals, 1964, vol. 16, pp. 582-88. 3 A. S. Keh and W. C. Leslie: Materials Science Research. H. H. Stadelmaier and W.W.Austin, eds., vol. 1.pp. 208.50, Plenum Press, New York, 1963. 4A. S. Keh, Y. Nakada, and W. C. Leslie: Dislocation Dymmics, Rosenfield, Hahn, Bement, Jr., and Jaffe, eds., pp. 381-406, McCraw-Hill Book Co., New York, 1968. &apos;W. J. Bratina, J. T. McCrath, and H. E. Rosinger: Can. Met. Quart., in press. 6 W. J. Bratina, J. T. McGrath, and D. Mills: Suppl. Trans. Japan Inst. Metals. 1968, vol. 9, pp. 436-43. &apos;H. E. Rosinger and C. B. Craig: Can. Met. Quart., In press. %. Mills. J. T. McGrath. and W. J. Bratina: ScriptaMet,, 1968, vol. 2, pp. 311-13. The purpose of this note is to present the results of a direct measurement of the stacking fault free energy in copper. The present method avoids both the question of interaction forces of nodal dislocations and the assumption that the coherent twin boundary free energy is one-half that of a stacking fault. Fig. 1 shows a transmission electron micrograph of a stacking fault intersecting a high angle grain boundary in copper: Fig. 2 is a schematic representation of the intersecting interfaces. To produce the specimen, pure copper was rolled to 0.002 in. thickness and annealed for several hours at 875°C. These foils were strained in tension to l04 µ in. per in., and rean-nealed to 8 min. Recrystallization and/or grain growth were not observed during the second anneal, indicating that intersections such as Fig. 1 are equilibrium configurations. Many such stacking faults were observed, but few were noted as intersecting grain boundaries in well-illuminated areas. The intersection of Fig. 1 was well away from the specimen edge. Since similar defects have not been observed in fully recrystal-lized and annealed copper, it is felt that this defect is due to the tensile straining. Electron transmission

Jan 1, 1970

By D. T. Camp, J. A. Clum

WITH experience, the indexing of back-reflection Laue patterns for cubic crystals is usually a straightforward matter. However, for noncubic systems where in general tables of interplanar angles are not available or when inexperienced personnel are involved, properly indexing a crystal is normally a tedious, time-consuming affair. The authors have written a digital-computer program which calculates and prints out a table of interplanar angles for an arbitrary crystal structure and then systematically searches through this table attempting to obtain a consistent fit to back-reflection Laue data supplied by the user. Of course it is possible simply to calculate a desired set of interplanar angles should this be the only requirement. The program was originally written in ALGOL for use on a Control Data G-21 computer and a preliminary version is described elsewhere.&apos; A version in FORTRAN TV which has been run on an IBM 7040 and one in FORTRAN II run on an IBM 1620 are also available. While it is not the purpose of this communication to describe the program in detail, an indication of how the program operates may help one to decide whether the program would be useful under particular circumstances. The hypothetical example chosen involves the indexing of the zinc crystal which has a hexagonal structure and a c/a ratio of 1.856. Input data for this example consists of only nine cards: The first card controls the list of families of planes to be considered. If the Miller indices of a prospective family are (h k 1), the first digit places a limit, in this case 3, on the absolute values of any individual index. The second digit limits the sum (h +k + l + 1), in this case to 5. Therefore the families (013) and (112) are considered but the family (122) is not. All systems, including the hexagonal, are treated using three-digit Miller indices. The second card contains the crystallographic parameters required to define the system. The first digit is 0 if the system is rectangular, that is all angles are 90 deg. If the system is nonrectangular, as in this example, the digit 1 so indicates. The next three values are the lengths of the sides of the reference cell, a, b, c. The final three entries on the card are the angles, a, 8, y between the sides. The digit 0 on the third card indicates that more data follows, the digit 6 shows that a set of six planes is to be indexed, and the value 2.0 indicates that agreement between a tabulated angle and an input angle is considered adequate if their absolute difference is less than 2 deg. The fourth card lists the measured input angles. a12 = 38 deg, a13 = 24 deg, and so forth. More input angles are listed on cards five to eight with the latter giving the input angle 058 = 40 deg. The final card in this series indicates by the digit 1 that no more data is to be processed. The program operates in the following manner: 1) The input data from cards 1 and 2 is read, thereby indicating the crystal system to be examined and the crystallographic parameters of the particular crystal to be indexed. 2) A table of interplanar angles is generated. 3) The input angles contained on cards 4 to 8 are read. 4) The measured input data is systematically compared with the generated table of standard angles. All combinations of poles whose interplanar angles compare with the requisite, specified accuracy are printed out. If no adequate fit is found an indication of this is printed. A typical line from the generated table of interplanar angles is: (001) - (111) 74.92 64.99 It can be shown that in the Miller-Bravais system the first value corresponds to the angles between (0001)-(1121) and the second to that between (0001)-(1011). This particular set of data gave the following result for the planes 1 to 6: (011) (110) (121) (111) (112) (010) The ALGOL version also has the option of simply providing the Greninger-chart coordinates ? and 6

Jan 1, 1967

By Elmer Weber, W. M. Baldwin

Solid lead obeys a single parabolic weight increase vs. time law. In contrast, liquid lead undergoes three successive parabolic weight increases vs. time laws, the first of which has a low constant relative to the latter two. The conversion times for the change from one parabola to the next decrease with increasing temperature. IN recent reports on the subject,1,2 it was noted that zirconium and titanium scale in air by a complex mechanism. The scale first forming on the metal is protective to the extent that it gives a low constant, K, for Tammann&apos;s, and Pilling and Bedworth&apos;s parabolic equation: w² = Kt [1] relating weight increase, w, due to chemical reaction of the metal with the air, and time, t. After hundreds of hours of apparent stability in some cases the first scale yields to another that offers little protection to the metal. This transition from one scale to another, from a slow parabolic oxidation reaction to a fast one, was not due to impurities in the atmosphere or incidental effects (changing environment, etc.) but was a specific behavior of the metal itself, the transition occurring at definite times (dependent on temperature) and showing other reproducible traits. In view of this behavior how can long-time service behavior be predicted from short-time laboratory tests, not only in the case of these metals, but in any case? Certainly a systematic study of the type of scaling behavior described above—wherever it is found—would help to answer this question. The present paper is a report on the behavior as it is found in lead—the only metal to the authors&apos; knowledge for which the behavior has been described at all, if inadequately, for our present purpose.* At least four oxides of lead are known, of which one occurs in two allotropic forms. They are ß (red) tetragonal PbO stable up to 486°C;8 a (yellow) orthorhombic PbO stable from 486°C up to its dissociation temperature in air at about 2300°C;9 minium or Pb3O4 which from the dissociation pressure data given in Fig. 1 decomposes to PbO at 540°C in air; lead sesquioxide or Pb2O3,; and lead dioxide or PbO2 which, according to Fig. 1, decomposes in air at 400°C to minium. In view of the high dissociation temperature of PbO, lead will scale up to at least its boiling point. Further, it is known that oxygen is almost insoluble in liquid lead.&apos;V his implies a fair probability that an oxide scale would not dissolve in the molten metal and would afford the same protection to lead in the liquid state as in the solid. All of the oxides of lead for which specific gravity data are available are more voluminous than an equivalent weight of metal or a lower oxide from which they might form, hence the scales will be in compression. Lead oxides are known to be ductile, so it would be anticipated that they would form coherent nonporous scales. It is not surprising to learn, then, that both solid and liquid lead scale according to the Tammann, and Pilling and Bed-worth law.14,15 (Gruhl states that at 600°C and above lead oxidizes linearly with time because of "spitting" of the scale.) The parabolic constants K reported by various investigators3,14-16 are badly scattered, however, as shown in Fig. 2. The oxides formed on solid lead were described as being reddish-brown but were not chemically identified by Pilling and Bedworth.15 Gruhl&apos;s descripdin³ of the appearance of the scales On his liquid samples indicates that a (yellow orthorhombic) PbO is formed initially on the specimens but gives Way eventually—at least at temperatures below 486 °C— to .ß (red tetraunal) PbO, and that below 540°C minium—Pb3O4 :is firmed at an even later time as an overlay on either the red or yellow PbO. Fig. 3 is a graphical interpretation of Gruhl&apos;s description. Gruhl does not indicate any change in the parabolic scaling rate as yellow PbO converts to red. He does indicate that minium reduces the scaling rate, al-

Jan 1, 1953

By W. D. Forgeng, P. F. Wieser

MnSi alloys containing from 2 to 24 at. pct Si have been investigated by metallographic and X-ray methods. Contrary to published data, the temperature of the ß-manganese to a-manganese transformation is lowered by the addition of silicon. The existence of two additional intermediate phases E and ( is demonstrated. E, ranging in composition from 12 to 15.5 at. pct Si, forms by a peritectoid reaction between ß manganese and the second new phase, (. The latter phase is homogeneous at silicon contents from 16.2 to 18 at. pct and forms peritectically from the 0 phase and liquid. The eutectic reaction occurs between the ( phase and MnsSi rather than the ß phase and Mn3Si. As a result of this investigation, a modification of the manganese-rich section of the MnSi equilihrium diagram is proposed. The binary diagram of Mn-Si, according to Hansen,&apos; Fig. 1, exhibits in the low-silicon region (below 24 at. pct Si) a peritectic transformation at 900°C of 0 manganese + Mn3Si to a manganese as determined by R. Vogel and H. Bedarff2 as well as a thermal effect at 980°C between 16.2 and 22.6 at. pct Si reported by the same authors. The nature of the latter transformation was unknown. K. Amark, B. Boren, and A. westgren3 reported indications that possibly four more phases existed in the range of 10 to 27 at. pct Si. The present investigation deals with the phase relations in the range of 2.1 to 17.7 at. pct Si. A few spot checks were conducted up to 23.84 at. pct Si. EXPERIMENTAL PROCEDURE Small experimental heats were prepared by induction melting in a vacuum furnace using argon as a protective atmosphere. The crucible was of commercial-quality magnesia. The furnace charge consisted of silicon metal and dehydrogenated electrolytic manganese. The typical analysis for these materials is shown in Table I. The molten alloy was tapped into 2-in.-square, 7-in.-long ingots. After visual inspection, a small quantity of alloy in the middle portion of the ingot was separated for use in this investigation.MnSi alloys containing from 2 to 24 at. pct Si have been investigated by metallographic and X-ray methods. Contrary to published data, the temperature of the ß-manganese to a-manganese transformation is lowered by the addition of silicon. The existence of two additional intermediate phases E and ( is demonstrated. E, ranging in composition from 12 to 15.5 at. pct Si, forms by a peritectoid reaction between ß manganese and the second new phase, (. The latter phase is homogeneous at silicon contents from 16.2 to 18 at. pct and forms peritectically from the 0 phase and liquid. The eutectic reaction occurs between the ( phase and MnsSi rather than the ß phase and Mn3Si. As a result of this investigation, a modification of the manganese-rich section of the MnSi equilihrium diagram is proposed. The binary diagram of Mn-Si, according to Hansen,&apos; Fig. 1, exhibits in the low-silicon region (below 24 at. pct Si) a peritectic transformation at 900°C of 0 manganese + Mn3Si to a manganese as determined by R. Vogel and H. Bedarff2 as well as a thermal effect at 980°C between 16.2 and 22.6 at. pct Si reported by the same authors. The nature of the latter transformation was unknown. K. Amark, B. Boren, and A. westgren3 reported indications that possibly four more phases existed in the range of 10 to 27 at. pct Si. The present investigation deals with the phase relations in the range of 2.1 to 17.7 at. pct Si. A few spot checks were conducted up to 23.84 at. pct Si. EXPERIMENTAL PROCEDURE Small experimental heats were prepared by induction melting in a vacuum furnace using argon as a protective atmosphere. The crucible was of commercial-quality magnesia. The furnace charge consisted of silicon metal and dehydrogenated electrolytic manganese. The typical analysis for these materials is shown in Table I. The molten alloy was tapped into 2-in.-square, 7-in.-long ingots. After visual inspection, a small quantity of alloy in the middle portion of the ingot was separated for use in this investigation.

Jan 1, 1964

By J. D. Testerman

A statistical technique to identify and describe naturally occurring zones in a reservoir and to correlate these zones from well to well is described. The technique is particularly useful in describing a reservoir where cross flow between adjacent strata is important in determining reservoir behavior. Although it has been used primarily for permeability zonation, the technique is general and can be used to correlate any reservoir property or related data, such as the information contained in well logs. INTRODUCTION One of the first problems encountered by the reservoir engineer in predicting or interpreting fluid displacement behavior during secondary recovery processes is that of organizing and using the large amount of data available from core analysis. Permeabilities pose particular problems in organization because they usually vary by more than an order of magnitude between different strata. Due to the sheer volume, it is almost always necessary to group data and to use an average value to represent a number of measurements. Perhaps the most common method now used to group permeability data is the capacity-fraction technique, which ranks permeabilities in order of magnitude, regardless of the physical location of the permeabilities within the reservoir. The cumulative per cent capacity is plotted against cumulative per cent thickness. This plot is divided into an arbitrary number of zones, generally of equal thickness. Five zones (or averaged groups of data) usually are obtained, each of which is treated as homogeneous in subsequent calculations. The division so obtained has no physical meaning; strata in the same zone, calculation-wise, are usually not adjacent in the reservoir. Reservoir engineering techniques being developed will handle crossflow that occurs between adjacent communicating reservoir strata because of imbibition and gravity segregation. Since crossflow occurs between physically adjacent layers within the reservoir, a new zonation technique recognizing the actual location of strata within the reservoir is necessary. Similarly, the recognition of natural zones is important for predictions of oil recovery by processes involving diffusion. One such process is miscible displacement, where predictions of lateral diffusion within the reservoir must recognize the actual location of the invaded zones in relation to the rest of the formation. Natural zones must also be adequately recognized to account for heat transfer within the reservoir during thermal exploitation. Because of the complexity of the problem, statistics appear to offer the only practical hope of dividing a reservoir into physically-meaningful natural zones. This paper presents a statistical technique for identifying these natural zones and for ascertaining which ones are likely to be continuous between adjacent wells. The zones defined have minimum variation of permeability internally and a maximum variation between zones. The technique is general and can thus be applied to reservoir properties other than permeability. The method will guide the reservoir engineer in estimating which zones are likely to be continuous between wells. However, a statistical correlation based on permeabilities in two different wells is no guarantee that the zones so defined are, in fact, continuous. Rather, the assumption of continuity must be consistent with geological data concerning the depositional environment, as well as justified on the basis of engineering judgment in combination with statistics, just as judgment is required with conventional zonation methods. CALCULATION PROCEDURE The reservoir zonation technique is a two-step operation. The steps are individually described, and a sample calculation is presented in the Appendix. ZONATION OF INDIVIDUAL WELLS First, the set of permeability data at a single well is zone, into Zones. These zones are selected so that variation is minimized within the zones and maximized between the zones. The equations4,6 used to zone the data are where B = the variance between zones, , = the number of zones, i = the summation index for the number of zones, j = the Sumation index for the number of data within the zone, mi = the number of data in the ith zone, k,. = the mean of the permeability data in the ith zone, k . = the over-all mean of the data in the well, W = the pooled variance within zones, N = the total number of

By Shozo Saito, P. A. Beck

Mettrllographic and X-ray diffraction study of Cb-Co alloys in the Composition range of 7 to 33 nt. pct Cb, after annealing at 1175 °&apos;, showed that near 25 al. pct Cb on MgNi,-lype hexagonal Laves Phaseexists in a narrow composition range, and that an MgCl- type cubic Laves Phase occurs between approximately 27 and 32.6 ut. pd Cb. Lattice parameter and density measures indicated that, in both phases. the deviations from proper Loves sloichimetry result from the substitution of cobalt atoms for some 0f the columbium atoms. Tlle same phases occurant 1000&apos;C, together with an additional phase of unknown structure, which appears between the hexagonal Laves phase and the cobalt-bose terminal solid solutions KOSTER and Schmid&apos; identified a phase corresponding to the composition VCo,, and more recently the crystal structure of this phase has been determined.&apos; In the Ta-Co system Korchynsky and Fountain recently found two intermediate phases at the composition Taco,, one of them metastable. In contrast to the V-Co and the Ta-Co systems, in the Cb-Co system no intermediate phase has been found4 at the composition CbCo,. The present investigation was undertaken in order to reexamine the question of the existence of such a phase. EXPERIMENTAL PROCEDURE Twelve alloys were prepared by arc-melting in a water-cooled copper crucible under helium atmosphere. Electrolytic cobalt and 99.9 pct pure colum-bium powder have been used as starting materials. It was found that melting losses can be reduced by compressing the colunlbium powder in the form of thin pellets before melting. For the alloys used the melting losses were not higher than 1 pct. The intended compositions of all alloys and the chemical analyses of three of them are given in Table I. Specimens from all alloys were annealed in evac- uated fused silica tubes at 1175°C for 3 days and quenched in cold water. A second set of specimens of most alloys was annealed at 1000°C for 7 days and then quenched in cold water. The annealed and quenched specimens were examined metallographically, using the following etchant: 60 pct glycerine +20 pct H,NO, + 10 pct HF + 10 pct water. Powder specimens for X-ray diffraction were prepared by crushing annealed solid specimens in a mortar. Alloys containing 27.3, 28, 29.7, and 32.6 at. pct Cb annealed at either 1175" or 1000°C were very brittle and it was found unnecessary to reanneal the powders. However, alloys containing 24.8 at. pct Cb, or less, especially those annealed at 1000°C, were much less brittle and re-annealing was required to remove the strains present in the crushed powders. In each case reannealing was done at the same temperature at which the corresponding solid specimens were annealed and it, too, was followed by quenching in cold water. In many instances X-ray diffraction patterns were also taken of the polished and etched solid specimens and compared with the corresponding X-ray diffraction patterns obtained with powders. The X-ray diffraction patterns were taken with an asymmetrical focusing camera, using CrK radiation. For precision lattice parameter measurements some X-ray diffraction patterns were taken with a symmetrical focusing camera, again using CrK radiation. EXPERIMENTAL RESULTS A microscopic examination of the alloys annealed at 1175°C revealed that the alloy containing 25.5 at. pct Cb was composed of a single phase, but that the 24.8 at. pct Cb alloy did contain a small amount of a second phase, identified by means of X-ray diffraction as having a fcc structure, undoubtedly the terminal solid solution based on cobalt. Apart from the few very weak lines corresponding to this minor phase, the X-ray diffraction patterns of these alloys could be well interpreted in terms of a MgNi,-type hexagonal Laves phase structure. The indexing of the X-ray diffraction pattern, Table 11, yas based on the lattice parameter values a, = 4.740A and c,

Jan 1, 1961

By John D. Verhoeven

A technique has been developed for carrying out normal freezing experiments with a current density of 2000 amp per sq cut passing through the solid-liquid interface. The equation relating the effective distribution coefficient to the equilibrium distribution coefficient in electric field-aided solidification, originally developed by Huckc et al.,1 has been modified for the case of concentrated solutions. Preliminary experiments on the Sn-Bi system give qualitative agreement with the equation. The data are analyzed by a slightly novel use of the normal freeze equation which allows one to determine the effective distribution coefficient more easily. Very extensive mixing in the liquid was found at these high current densities and it is postulated that the mixing results from a vertical component of the magnetic Lorentz force generated by the electric current. In the search for techniques of obtaining ultrahigh-purity metals the inefficient but very effective technique of electrotransport has received little attention. Electrotransport is most effective in the liquid state and a natural application, therefore, is to apply an electric field across the liquid zone of a zone-melting experiment. The present investigation was undertaken to study the effect of an electric field upon solidification of metals, so that the usefulness of electrotransport in such solidification experiments as zone melting could be determined. In zone-melting and normal-freezing experiments it is difficult to achieve complete mixing in the liquid in the immediate vicinity of the solidifying interface. Consequently a solute build-up will occur at the interface in the portion of the liquid where complete mixing does not occur (an equilibrium distribution coefficient, ko, less than one, and unidirectional atom motion will be implied throughout). This local solute build-up produces a corresponding rise in the solute concentration in the solid so that the ratio of the solute concentration between the solid and the bulk liquid is larger than the equilibrium distribution coefficient. This ratio is defined as the effective distribution coefficient, k,. The differential equation describing the solidification process may be derived by applying the continuity equation to an expression for the net solute flux at the interface. The solution to this differential equation then allows one to determine the solute distribution in the liquid and the relationship between k0 and ke. One of the most useful solutions to this equation was first derived by Burton, Prim, and Slichter,&apos; in which they assumed that a) the equilibrium distribution of solute was maintained on the plane of the interface, 11) the solute build-up ahead of the interface in the liquid disappeared at a distance 6 from the interface, and c) the solute distribution in the liquid was invariant with time. The following well-known relation between ko and ke was then obtained, where R is the rate of solidification and D the diffusion coefficient of the solute in the liquid. This equation appears to correlate the data from a number of different types of solidification experiments very well. Application of an electric field across the solid-liquid interface can produce an additional flow of solute atoms as a result of the electrotransport. When the polarity of the field is such as to direct the electrotransport flux away from the interface the solute build-up may be diminished, even to the point of producing a solute depletion and a consequent ke smaller than ko. The quantitative description of this process and the resulting form of Eq. [I] was first given by Hucke et al.1* and then inde- where E is the electric-field intensity and U is the differential mobility, i.e., the velocity of the solute atoms with respect to the solvent atoms per unit electric field. Both authors follow the method of Burton, Prim, and Slichter in their derivation, the only difference being the additional electrotransport term in the flux equation. It has been pointed out1,3 that Eq. [2] predicts the possibility of a noticeable increase in the purification of materials by solidification in an electric field. The validity of Eq. 121 has not been checked experimentally and it is possible that other factors&apos; arising from the presence of an electric field across

Jan 1, 1965

By J. O. Edstrom, G. Bitsianes

Parabolic rate constants were determined for the formation of wiistite by the solid state reaction between magnetite and iron. The reaction was diffusion controlled and inert marker studies indicated that the mass transport through the wiistite layer was accomplished by means of iron migration. Relationships between rate constants and self-diffusivities are discussed. The transport capacity for iron through dense wustite layers was found to be sufficient to carry on reduction, even in gaseous reduction processes. REDUCTION of iron oxides has been the subject of many investigations. Most of the work, however, has been done on rather crude material and there have been difficulties in correlating the data on a quantitative basis. The reverse process of the oxidation of iron has been studied more thoroughly and usually by starting from the pure metal. As a result, the mechanisms of oxidation are now fairly well known.It has generally been found that the oxidation of metals follows the so-called parabolic 1aw;Q hat is, when the oxides are formed as dense layers, their thicknesses are proportional to the square root of the reaction time. This parabolic law follows directly from Fick&apos;s first law of diffusion The flux, J, is defined as the quantity of diffusing substance passing per unit time through unit area of a plane at right angles to the direction of diffusion. This flux is proportional to the concentration gradient of the diffusing substance, and the factor D, known as the diffusion coefficient, is introduced as the proportionality factor with dimensions of (length)&apos;/time. If the flux is measured as the increase of thickness of the oxide layer (Ax) per unit time (t) and the assumption is made that the concentrations of the reactants at the phase boundaries of the layer are independent of time, Eq. 1 reduces to Integration of this expression yields the parabolic function ax = k . t. [31 The product of the diffusion coefficient and the concentration difference across the oxide layer is included in the constant k. When iron is exposed to a highly oxidizing atmosphere, the oxide phases are formed normally in a topochemical fashion, i.e., the interfaces between the phases maintain parallel positions to the original surface of the specimen. Above 570°C, the phases are orientated usually in the order of iron, wiistite, magnetite, and hematite, a condition in conformance with the requirements of the Fe-0 system. Below 570°C, the wiistite phase is unstable and has not been found as a normal constituent in the oxidation products of iron. There is a strong probability that continuous layers of the solid oxides are formed as the specific volumes of the phases increase in direct order from iron to hematite.&apos; , &apos; Regarding mass transport through dense solid oxide layers, Wagner&apos; has postulated that diffusion in oxides generally may be interpreted as migration processes of ions and electrons. There must be normally a concentration gradient across the growing oxide layer for diffusion to occur. This condition requires that there be deviations from the ideal stoi-chiometric composition of the oxide and accordingly deviations from the strict order of an ideal lattice. Such "lattice defects" include interstitial ions, cation and anion vacancies, quasi-free electrons, and electron holes and are decisive for all migration processes.&apos; Cations, anions, and electrons all may have some mobility in the oxides but the movement of one of the particles generally far exceeds that of the others. Previous work&apos;, 1,2,7 has shown that during the oxidation of iron the migration through the wiistite layer, and probably also the magnetite layer, is confined to the movement of iron ions. Migration through hematite, however, has been found to take place by oxide ion movement. These behaviors are in direct agreement with the type of vacancies present in the respective oxides. Reduction of Iron Oxides The gaseous reduction of iron oxides, like the oxidation of iron, takes place in a topochemical fashion at distinct interfaces between the appearing phases."-&apos;" Porosities might be expected in these reaction products, since their specific volumes are less than that of the starting material. Frank and van Der Merwe" have shown, however, that it is theoretically possible for nonporous layers to form if the degree of misfit in specific volume is less than about 15 pct. These aspects on porosity formation

Jan 1, 1956

By Howard Martens, Pol Duwez

IN two papers published in 1949, alloys of chromium with the refractory metals tungsten, molybdenum, tantalum, and columbium were investigated in view of their possible use as high temperature resisting materials. For the Cr-Ta system, a partial phase diagram was presented and the only intermediate phase was identified at Ta2Cr3. A phase of the same composition was also observed in the Cb-Cr system. The X-ray diffraction data presented in these papers, however, were insufficient for crystal structure determination. It is shown in the present study that the only intermediate phase in both the Ta-Cr and the Cb-Cr systems corresponds to the ideal stoichiometric ratio TaCr2, or CbCr2. Both structures are cubic, MgCu, type. At high temperature, however, TaCr2 has a hexagonal MgZn, type structure, which can be retained at room temperature by fast cooling. The alloys were prepared by melting in a helium arc furnace on a water-cooled plate. The design of the furnace was essentially the same as that described in ref. 3. Some alloys were also obtained by sintering compacts made of the mixed powders pressed at 80,000 psi. The sintering was carried on for 4 hr at 1375°C. The tantalum and columbium powders were supplied by Fansteel Metallurgical Corp., North Chicago, 111. The tantalum powder was the reagent grade, with a particle size smaller than 400 mesh and a total impurity content less than 0.1 pct. The columbium powder was smaller than 325 mesh and contained approximately 0.1 pct C and traces of Fe, Ti, and Zr. The electrolytic chromium powder from Charles Hardy, Inc., New York, was smaller than 300 mesh and contained about 0.1 pct Na, 0.05 pct Ca, and traces of Cu, Al, Mg, Si, and Co. Powder diffraction patterns were obtained with a 14.32 cm camera, using copper Ka radiation filtered through nickel foil. The powder pattern of the TaCr2 alloy obtained by sintering at 1375&apos;C was different from that obtained on the same alloy rapidly cooled from the melt. Contrary to this result, the powder pattern of CbCr2 was the same, whether the alloy was made by sintering at 1375°C or by melting, and was similar to that of the TaCr, sintered. It was also found that the structure of the TaCr2 specimen obtained by melting was retained after heating for 4 hr at 1590°C, but transformed into the structure found in the sintered specimen after heating for 4 hr at 1375°C. Hence, the structural change of TaCr2, appears to be a reversible polymorphic transformation. CbCr2 and ToCr2 Structure, Low Temperature Form By using large scale Hull-Davey charts, the powder pattern of CbCr, and of the low temperature form of TaCr2 were readily interpreted on the basis of a face-centered cubic lattice with a parameter of approximately 6.95 kX. The indices of the reflections together with the values of sin&apos; 0 are given in Tables I and 11. From this list of observed reflections, it appears that the (200), (600), (024), (046), and (028) reflections are missing. The lack of (h00) reflections for h 4n indicates a four-fold screw axis. The missing (Okl) spectra for k + 1 An indicate the existence of a diamond glide d. The combination of these symmetry elements can be found in the O— Fd3m space group, which is therefore the most probable one. After having determined the approximate density of TaCr, by the immersion method, the number of molecules per unit cell was calculated and found to be nearly eight. This information, added to the fact that the most probable space group is O leads to the consideration of a structure of the MgCu2 type, in which the atoms have the following positions: 8 magnesium in a and 16 copper in d. On the basis of this structure, intensities were computed by means of the usual formula: 1 cos&apos;20 I a sin2 cos where F is the structure factor; 8, the Bragg angle: and p, the multiplicity factor. As shown in Tables I

Jan 1, 1953

By T. H. Alden

BaCKOFEN, Avery, and Turner have shown"2 that the large tensile elongation in superplastic metals is correlated with a high strain-rate sensitivity of the flow stress. At present, the reported superplastic materials are complex eutectic or eutectoid systems with a large solubility range in at least one of the terminal phases. This note describes the behavior of a solid-solution alloy (at 22°C)5,= Sn-1 wt pct Bi, which has been processed in order to produce a fine grain size.2,3,6 The chill-cast, 1/2-in.-diam ingot was homogenized for 1 week at 130°C, extruded at O°C to 0.083 in. diam, quenched within 15 sec, and stored at -196°C. Samples were warmed to room temperature 16 hr prior to mechanical testing or metallography. During tension testing at room temperature, it was found that the flow stress reached a steady-state value which depended on the imposed elongation rate and was independent of strain to an error of about ±5 pct. In Fig. 1 is plotted log a vs log e where a is the measured steady-state flow stress and i the imposed strain rate. These quantities were calculated using "instantaneous" area and length to an accuracy in the sample diameter of ±5 x 10-4 in. The log a-log 1 curve is sigmoidal. The strain-rate sensitivity, which may be given by d log old log 6,&apos; has a maximum value of about 0.48 between i = 5 x 10-4 and 5 x 10-3 per min. The value is well above frequently measured values for metals at creep temperatures (0.1 to 0.3) and comparable to the rate sensitivity for Pb-Sn solder: which has been shown to be superplastic.2,3 Note, however, that below or above the strain rate of 10-3 per min the rate sensitivity of Sn-1 pct Bi decreases and at high rates is more nearly like that of conventional metals. The grain size of this material is relatively uniform, Fig. 2, and may be specified by an average linear intercept i.&apos; Grain growth occurs at room temperature but after 16 hr, L = 5. Tensile elongation was measured on finer-grain-size specimens, which had been at room temperature 15 min prior to testing. After 15 min, the samples are fully recrystallized. Three strain rates, 5 x 10-3, 10-2, and 2.5 x 10-2 per min, were employed for which the measured elongations varied from 425 to 500 pct. These results would seem to justify the term superplastic, applied to this alloy, although the ductility is inferior to that of the Sn-Bi eutectic.3 The Sn-1 pct Bi alloy, which is a single-phase material with equiaxed, fine grains, is an excellent one on which to make an estimate of the Nabarro-Herring9 creep rate. According to the model of Avery and Backofen2 a substantial part of the deformation must be accomplished by N-H creep in the strain rate-temperature regime in which d log a/d log 1 = 0.5. The maximum N-H creep rate is given by9 L2kT where v is the atomic volume and D the self-diffusion coefficient. For this test v = 3.O x 10-23 cu cm, D = 1.4 e-23,300/RT = 2.5 x 10-l7 sq cm per sec,7 L = 5x 10+4 cm, T = 295°K, and a = 2000 lb per sq in. = 1.38 x 10&apos; dyne per sq cm. The calculated creep rate is E= 4 x 10-11 per sec which may be compared with the measured creep rate at this stress, Fig. 1, of 6.7 x 10-5 per sec. The N-H creep rate is seen to be negligible. Earlier consideration2 of this question was in error because incorrect diffusion coefficients were used. The assistance of R. R. Russell in metallography is acknowledged gratefully.

Jan 1, 1967

By N. O. Taylor

THE failure, by swelling, of several cast aluminum-zinc, spiral, pump rods, used to circulate water in a constant-temperature bath, brought up the question as to whether the presence of tin in varying quantities would have any appreciable influence in controlling this action. Previous workers had found the same difficulty with aluminum-zinc alloys, due to their swelling in water or solutions of electrolyte^.^ It was known that pure aluminum was practically insoluble in concentrated sulfuric and nitric acids, presumably due to the formation of an oxidized film on the surface. Concentrated sulfuric acid had little or no effect on pure zinc and tin and concentrated hydrochloric acid would attack all three metals. These facts aroused curiosity as to the probable reaction of the ternary alloys of these metals, and tests were made to determine their resistivity to the action of common laboratory reagents. Samples, covering the entire range of the ternary series of aluminum, zinc and tin alloys, were made up from good grades of the commercial metals.2 The materials were melted, at as low temperatures as possible, in graphite crucibles in a gas-fired crucible furnace. Graphite crucibles were used in preference to clay, to prevent the absorption of silicon by the aluminum, as found by previous workers. The melted materials were stirred thoroughly with pine sticks in order to ensure complete mixing and the greatest possible freedom from oxidation, and were cast in sectional, iron molds giving bars % in. in diameter and 5 in. long.

Jan 1, 1927

By John A. Emery

The Pea Ridge iron ore deposit near Sullivan, Missouri, is a dike-like mass of magnetite enclosed in Precambrian porphyries. The ore body tops at the Precambrian surface at a depth of 1300 feet below the present surface and extends to an unknown depth. It dips nearly vertically, intersecting the dip and strike of the enclosing porphyries at an extremely sharp angle. Faulting, both pre- and post-ore, appears to be of minor consequence, and present knowledge indicates that no preferred structural conditions existed prior to emplacement. The ore body is composed of magnetite with specular hematite, quartz, apatite, and pyrite occurring as accessory primary minerals. Specular hematite in appreciable quantities occurs on parts of the cap and the footwall of the ore body. Fresh porphyry breccia is enclosed in the magnetite along the hanging wall and in the western portion of the ore body. Hanging-wall quartz-amphibole and footwall quartz-hematite occur as replacements of certain porphyries. Further alteration has caused sericitization of parts of these zones. The ore deposit is interpreted as having been formed essentially by a single injection of a magmatic differentiate with hydrothermal end phases forming the quartz-amphibole and quartz-hematite portions of the deposit.

Jan 1, 1968

By W. A. STERLING

IN the opencut iron mines of the Mesabi Range in Minnesota, the trend in mining is in the development of mining equipment and mining methods which will move surface overburden and ore-bearing materials with less labor and at a cheaper cost. This is a must for most of the independent operators. Their reserves of direct-shipping ore are extremely small and their operations are being conducted in small, or intermediate pits, with a high stripping ratio in the outer fringes, or shore lines of older pits. and in ore bodies passing from direct shipping to the washing and the intermediate, or retreat ore state. The trend is toward deeper stripping, longer and steeper hauls, and the necessity of moving a total of from three to five or six tons of overburden and ore material for each ton of shipping-grade ore produced. This naturally calls for greater production, with larger shovels, or draglines. cheaper drilling and blasting costs through the drilling of larger-diameter blastholes, and cheaper haulage through the use of trucks of larger capacity and more extensive use of belt-conveyor systems. This trend is notable both in stripping and mining.

Jan 1, 1948

By J. J. Fritts, J. L. Patrick, T. L. Wright, C. O. Ensign, W. S. White, J. W. Trammell, J. C. Wright, D. J. Hathaway, R. J. Leone

The copper deposit at White Pine, Michigan, from which a little more than 5 per cent of United States primary copper currently is produced, is a large stratiform orebody, 4 to 25 feet thick and several miles across. The present ore column, containing about 1.2 per cent copper as chalcocite and native copper, is confined to the basal beds of the Nonesuch Shale. This upper Keweenawan (Upper Precambrian) formation is a distinctive gray siltstone unit, about 600 feet thick, overlying and overlain by thick red-bed sequences. All these rocks contain abundant volcanic debris, but the latest known igneous activity within 50 miles antedated the Nonesuch Shale. The rocks are unmetamorphosed and only moderately deformed, mainly by tilting and faults. Pyrite, presumably syngenetic, is the only prominent sulfide throughout most of the Nonesuch Shale. The basal beds of the formation, however, contain disseminated copper minerals instead of pyrite and constitute the cupriferous zone. On a regional scale, the top of the cupriferous zone cuts across bedding, and ranges from an inch or so above the base of the formation in some areas to more than 50 feet in others. However, within the cupriferous zone the distribution of copper shows remarkable stratigraphic control. Certain beds are copper-rich compared to the beds that lie between them and the differences persist throughout the White Pine region. Several darkgray thinly laminated beds in the lower 10 to 25 feet of the Nonesuch Shale are rich enough and sufficiently close enough together to constitute a mineable thickness where they lie within the cupriferous zone. Pyrite is the characteristic sulfide of the Nonesuch Shale as a whole. The principal sulfide mineral of the cupriferous zone at the base of the formation is chalcocite. The succession of minerals outward and upward from the center of the cupriferous zone is native copper-chalcocite-bornite-chalcopyrite- pyrite. The bornite and chalcopyrite are confined to a narrow fringe at the margin of the cupriferous zone. This pattern of mineral zones is believed to represent reaction between syngenetic pyrite and introduced copper. The main copper mineralization is independent of structure and apparently antedates deformation. Details of the geometry of the cupriferous zone indicate the possibility that copper was introduced from the underlying sandstone prior to lithification. The source of the mineralizing solutions and their copper is not known.

Jan 1, 1968

By John T. Eastlick

The Banner mining district is about 70 miles northeast of Tucson in the southern part of Gila County, Arizona. Production from the district, valued at about $26 million, is chiefly from copper-silver-lead zinc ores. The stratigraphic section consists of Precambrian conglomerates, quartzites, dolomites, and limestones, Cambrian quartzites; Devonian limestones; dolomites, and shales; Mississippian limestones; Pennsylvanian limestones and shales; and Cretaceous volcanic and sedimentary rocks. Deformation of these rocks presumably started near the end of the Cretaceous, and extended into the late Tertiary. The sedimentary rocks were folded, faulted, and intruded by fine grained diorite, quartz mica diorite, and dacite porphyry. At least four distinct stages of mineralization are recognized. In the first stage of contact metamorphism and the second stage of hydrothermal alteration, favorable zones were prepared for ore deposition. Metallization occurred in three of the mineralizing stages. Magnetite, pyrite, and hematite were deposited near the end of the second stage of hydrothermal alteration. The third stage included the main deposition of sphalerite, chalcopyrite, bornite, and galena. In the fourth and final stage, minor amounts of sulfide minerals were deposited with a late anhydrite and quartz gangue. The ore deposits in the form of veins and veinlets, pipes, irregular massive replacements, and bedded replacements are localized by the extent and distribution of metamorphic and hydrothermal alteration, by the proximity to the intrusive contacts, and by the effects of structural development. Oxidized ores of copper, lead, and zinc constituted the principal production of the district prior to 1940, but, for the most part, supergene enrichment was of minor economic importance. The ore bodies of the district are in the mesothermal class of deposits, occurring as normal metasomatic replacement and vein types.

Jan 1, 1968

By Hal T. Morris

The main Tintic mining district in central Utah has produced approximately 13,500,000 tons of ore, containing silver, lead, gold, copper, zinc, and other metals, valued at more than $315,000,000. More than 90 per cent of this ore has come from large, irregular ore bodies that have replaced folded and faulted limestone and dolomite strata. Of lesser importance are replacement veins that chiefly cut contact-pyrometasomatized carbonate rocks and fissure veins that cut altered intrμsive bodies and volcanic rocks. The district is in the west-central part of the East Tintic Mountains, a north-trending fault-block range near the eastern margin of the Great Basin. The consolidated sedimentary rocks exposed at the surface and in mine workings are miogeosynclinal deposits more than 10,000 feet thick that range in age from late Precambrian to Late Mississippian. They are folded and strongly faulted and are partly overlain by volcanic tuffs and agglomerates and by extensive flows of porphyritic and vitrophyric quartz latite, latite, and trachyandesite of Eocene age. All of these rocks are locally concealed beneath thick alluvial deposits of Pliocene and Quaternary age. The Eocene and older rocks are cut by dikes, sills, and small stocks of porphyritic quartz monzonite, monzonite, and latite, which are genetically related to the ore deposits. The district is inactive except for the production of halloysite clay and for minor leasing activity and exploration ventures. Several exploration targets remain untested.

Jan 1, 1968

By H. A. Wheeler

IT may surprise some of our members to learn, among the industries based on the mineral resources of the United States that of clay now ranks third, being exceeded in value of product only by pig-iron and coal. The present annual value of clay-products exceeds the value of the outputs of gold and silver, and also exceeds the combined values of copper, lead, zinc, aluminum, mercury, antimony and nickel. These facts are shown in Table I. which gives the statistics for the year 1902

Jan 1, 1905

By David W. Brunton

(San Francisco Meeting, October, 1911.) MINE-DRAINAGE and the ever-increasing demand for water on the plains have within the past few years necessitated the driving of a great number of adits and tunnels, including many of considerable size and great length. In most instances, ex isting conditions have called for extreme rapidity of execution; and this necessity, coupled with the high altitudes at which most of the work has been carried on, excessive freight-rates, and difficulty -of access, has involved many complex and interesting problems. One of the most rapidly executed undertakings of this class is the Laramie tunnel, recently completed for the Laramie-Poudre Reservoirs & Irrigation Co. This tunnel is driven through Green ridge, a spur of the Continental Divide, which separates the Laramie river from the Cache-la-Poudre in Laramie county, Colo. Green ridge is extremely persistent, and further northward in Wyoming is known as Sherman hill, the highest point on the Union Pacific railway. At the point where the tunnel is driven, two opposing bends bring these streams within 2.5 miles of each other, with a difference in elevation of 500 ft. The rock exposed on the banks of the two rivers does not differ materially in hardness; and, without a geological study of the conditions involved, it would appear that the difference in the depth of erosion of the two streams is due principally to the greater volume of water at this point in the Cache-la-Poudre, which has a drainage-area above the tunnel-portal of 110 sq. miles, as against 30 sq. miles of natural drainage for the Laramie. To increase the water-supply at the tunnel, however, this latter amount has been augmented by two side collection-canals, which bring the available drainage-area up to 84 square miles. The nearest railroad shipping-point to the eastern portal is

Apr 1, 1912

By R. C. Philp, Allan Gibb

INTRODUCTION. THE term matte is applied to smelting-products so extremely diverse in composition and physical properties that it appears impossible to devise any generic formula to represent, chemically, the manner in which the varied proportions of the almost unlimited possible constituents combine with each other. Mattes produced in copper-smelting, in distinction from those produced in smelting-operations in which the recovery of copper is secondary to that of other metals, cover a narrower range in composition. The copper-content of such mattes vary from 20 to 80 per cent., and even this range is much smaller in general practice since it is found advantageous, when possible, to produce mattes with about. 50 per cent. of copper in the first operation. Further, it is unusual that arsenic or antimony occurs in copper-ores in sufficient proportions to form arsenides or antimonides in such quantities that they will separate out from the furnace-products, as is common in lead-smelting. Generally, the mattes produced in copper-smelting are composed mainly of copper (usually greater than 35 per cent.), iron and sulphur, the remaining elements being usually in proportions sufficiently small to allow of their treatment as impurities, rather than as essential constituents of the mattes. In modern practice of smelting copper-ores in blast-furnaces the tendency is to approach pyritic smelting as nearly as pos¬sible, the furnaces being low and the air supplied being largely in excess of that required for complete combustion of the carbonaceous fuel. Hence the atmosphere of the blast-furnace thus used is usually oxidizing or Dearly neutral? and, as a consequence, the reduction of metallic iron that was a necessary evil of former practice is of unusual occurrence in operations where the main object is the recovery of copper. Hearth-accre-

Nov 1, 1905