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By John W. Wagner, Robert K. Willardson

Single crystals of Pbl-xSnxTe have been grown from nonstoichiometric, cation-rich melts with the objective of producing as-grown, bulk material containing carrier concentrations ranging from 1016 per cu cm to 1018 per cu cm. Three specific crystal composi-tions were investigated in detail; x = 0.00, 0.10, and 0.17. Pull rates of from I to 3 mm per hr were used. Single crystals were successfully pulled from melts containing as little as 30 at. pct Te. Hall coefficients, resistivities, and carrier mobilities of these materials were determined. The relationship between the composition of the melt and the carrier concentration in the as-grown crystal has been studied for the three crystal compositions of interest. BULK single crystals of Pb,-,Sn,Te have previously been grown from stoichiometric melts.1,2 Such crystals are p-type and have relatively high carrier concentrations ranging from -9 x 1018 per cu cm for PbTe to -8 x l020 per cu cm for SnTe at 77°K. These carrier concentrations result from deviations from stoichiometry (lead vacancies) in the as-grown crystals. Since lower carrier concentrations are desirable for electrooptic device applications, these crystals are usually subjected to long-term, isothermal anneals.' This paper reports on the growth of Pbl-xSnxTe single crystals from nonstoichiometric melts with the primary objective of producing as-grown material containing relatively low (1016 to 1018 per cu cm) carrier concentrations and also reports on the general characteristics of these crystals. The phase relationships in the Pbl-xSnxTe systems are such that materials solidifying from nonstoichiometric, cation-rich melts will have smaller deviations from stoichiometry than materials grown from stoichiometric melts. Fig. 1 is the T-x phase diagram for PbTe in the vicinity of the stoichiometric composition.3 A crystal grown from a stoichiometric melt will solidify at a melting point maximum at which the solid will contain -0.5002 atom fraction of tellurium. PbTe single crystals grown in our laboratories from stoichiometric melts have carrier concentrations of 9 x 10" per cu cm, indicating that the excess tellurium in the crystals is as expected from this phase diagram. However, growth of PbTe from a lead-rich melt will result in material having a more nearly stoichiometric composition. Although the addition of Sn to the melt shifts the solidus curve further toward the tellurium-rich side,4 the general discussion given for PbTe applies to the Pbl-xSnxTe systems as well. EXPERIMENTAL Single crystals of Pb1-xSnxTe have been grown in our laboratories from nonstoichiometric, cation-rich melts using the Czochralski technique and boric oxide liquid encapsulation. The details of the growth apparatus and growth technique have been reported in a previous paper on growth of these alloys from stoichiometric melts.2 In the present study, three specific crystal compositions were investigated in detail; x = 0.00, 0.10, and 0.17. Growth of alloy crystals from nonstoichiometric melts requires considerable care, and good quality single crystals were obtained in this study only by optimizing the mechanical and thermal stability of the growth system and by using pull rates of from 1 to 3 mm per hr (Pbl-xSnxTe crystals are easily pulled from stoichiometric melts at rates of from 5 to 10 mm per hr). The liquid encapsulation technique was found to yield near-ideal conditions, since the B2O3 layer increased the thermal stability at the growth interface, permitted easy attainment of near-ideal thermal gradients, and dampened vibrations at the melt surface. The hygroscopic character of the B2O3 was a slight problem and vacuum heat treating was necessary to completely remove the water from the boric oxide. During initial growth, the seed diameter was reduced and a narrow neck (1 to 2 mm diam) of several millimeters length was grown. The latter steps were found to be necessary for the growth of single crystals, i.e., if either of these two requirements were

Jan 1, 1970

By Pradeep K. Rohatgi, David N. French, Surendar M. Jain, Clyde M. Adams

The effect of solute concentration and diffussivity on dendritic solidification of dilute binary aqueous solutions has been investigated; chlorides of sodium, potassium, lithiurn, and hydrogen were used as solutes. Dendrite spacings were measured in spherical droplets and in unidirectionally solidified specimens. In the droplets, the freezing rate is uniform over the entire specimen and remains constant from the beginning to the end of solidification. In the unidirec-tionally frozen specimens the freezing rate varies within a given volume of liquid during the solidification cycle; in addition, it varies with location uithin the specimen. Mass transport analysis has been used to calculate the supersaturation, AC, supercooling, AT, and transcerse growth velocity, V , of ice dendrites during solidijication from the dendrite spacings measured in the droplels. The ice dendrite spacing in a given solute increases lineary with the solule concentralion at a fixed freezing rate. The ualues of AC, AT, and V increase with an increase in solule concentration. The value of AT in the aqueous solution is of the same order of magnitude as in Al-Cu alloys of the same concentration; the dendrite spacings in Al-Cu alloys also increase with an increase in solute concentralion. For the jamily of aqueozrs solulions incestigaled, the dendrite spacing increases linearly with solute diffusivity at fixed values of concertralion and freezing ,rate. The values of ?C and ?T decrease, whereas the value of V increases with an increase in solule diffusicity. The measured dendrite spacings , L, can be expressed by the relatiun: L = K;(dfa/db) 4 K2C +K3D - K4 where dfs/d? is-change in fraction solid with time (freezing rate), C is solute concentration, D is solute diffusivit K1 = (14 * 4)pmin1'2, K2 = (70 ± 10) pl (moles)- K3 = (24 r 3) . l05 psec (cm)-~. K. = -132 ± 10) 1. FREEZING of solutions is almost always an ehunmix-ing" process because the composition of crystallizing solid generally differs from that of the parent liquid. " Solute concentration and transport are therefore in]portant considerations in solidification of solutions. The influence of these factors on the dendritic solutions produced from metallic solutions is of practical significance since the properties of the solid aggre-gate are often strongly influenced by dendrite spacing.''' Alexander and Fthines3 found that dendrite spac- ings generally increase with solute concentration in several metallic systems. Michael and Bever1 have observed an increase in a aluminum dendrite spacings in dilute A1-Cu alloys. Rohatgi and AdamsJ have reported a linear increase in a aluminum dendrite spacings with increasing copper contents up to 28 pct in A1-Cu alloys. Bolling and Tiller"' have theoretically examined the effects of solute concentration and diffusivity on the growth of cells and dendrites. Their analysis of dendritic growth assumes a steady-state growth and the maximum possible velocity for dendrite propagation. In addition, the quantitative analysis is restricted to dendrites of rotational symmetry and is therefore not directly applicable to the plate-shaped dendrites of ice obtained in the present study. There are practically no experimental observations of the effect of solute diffusivity on dendrite spacings in metallic systems. The reason appears to be the lack of experimental data on solute diffusion coefficients in liquid metallic solutions. The present work is concerned with the effect of solute concentration and diffusivity on dendritic solidification of dilute aqueous solutions: the solutes examined are potassium chloride. sodium chloride, lithium chloride. and hydrogen chloride. There were several reasons for selecting these solutes. The variation of dendrite spacing with freezing rate in these solutiolls is similar to that observed in A1-Cu alloys.8 These aqueous solutions have almost identical phase diagrams at dilute concentrations. Fig. 1. and the diffusion coefficients show very little variation with solute Concentration.9,10 Dendrite spacings were measured as a function of freezing rate. solute concentration. and solute diffusivity. Dendrite spacings were measured in two different types of freezing systems. droplet and unidirectional, respectively. In the droplet freezing system

Jan 1, 1970

By K. M. Rolls, J. Wulff, D. A. Colling

Solid-solution alloys of the Ta- Ti system containing up to 70 at. pct Ti were melted and fabricated into wire. Steady magnetic-field measurements of cold-worked wires at 4.2°K indicate that the resistive critical field increases smoothly with increasing titanium, reaching a maximum of 93 kG (J = 1 amp per sq cm) for a composition of about 50 at. pct Ti. The composition dependence of the resistive critical field indicates it is largely paramagnetically limited for alloys containing more than 35 at. pct Ti. For cold-worked wires the value of the critical current density, Jc , was found to be insensitive to composition changes for compositions in excess of 20 at. pct Ti. It was observed that Jc could be increased by final-size heat treatment at 400°C without altering the value of- the resistive critical field. Experimental data are used to calculate the electronic specific-heat coefficient and the "upper critical field" for the alloys studied. THE effect and importance of metallurgical structure on superconducting properties have been summarized by Livingston and Schadler.1 Specific work on solid-solution alloys such as Nb-zr2-7 and Nb-Ti5-7 have shown that critical current density (Jc) and superconducting transition temperature are structure-sensitive. Berlincourt et al.6,8,9 in their studies of transition-metal alloys find that Ta-Ti alloys remain superconducting at fields comparable to Nb-Ti alloys. 6,8 Transverse critical current tests of a Ta-10 at. pct Ti alloy10 and longitudinal critical current tests of a Ta-25 at. pct Ti alloy1' indicate that such alloys are capable of carrying high currents at intermediate fields (-40 kG). The work reported in the present paper was undertaken to explore the superconducting properties of further compositions in the Ta-Ti alloy system as well as the structure sensitivity of the superconducting properties. I) EXPERIMENTAL PROCEDURE Alloys were prepared by melting tantalum (Fansteel Metallurgical Corp., 99.96 pct purity) and iodide, crystal bar titanium (Foote Mineral Co., 99.92 pct purity) mixtures in an arc furnace on a water-cooled copper hearth using a tungsten electrode. Melting was accomplished in a purified, gettered argon atmosphere at pressures from 250 to 400 Torr. Each alloy was turned and remelted fourteen times to assure complete mixing of tantalum and titanium. Ex- cessive coring in the cast samples was, nevertheless, observed. This was somewhat reduced by annealing in vacuo at 1000°C for 13 hr. The ingots were then machined to 0.250 in. diam, jacketed in Type 304 stainless-steel tubing, and swaged to 0.140 in. diam. They were then drawn to 0.010-in.-diam wire. Alloys containing up to 70 at. pct Ti were readily cold-drawn to wire in this manner. Later experiments showed that oxygen additions up to -3000 ppm could also be cold-worked into wire. Test samples for superconductivity measurements in the 2-in, air-core Bitter solenoids of the M.I.T. National Magnet Laboratory were prepared from 10-in. lengths of 0.010-in.-diam wire, cleaned of residual wire-drawing lubricant. Current contacts were made by clamping clean copper tubing over both No. 18 current lead wire and the ultrasonically indium-tinned ends of the specimen wire.12 Potential leads of No. 32 copper wire were connected to the specimen by ultrasonic soldering in an indium bath. The potential lead separation was about 4 cm, corresponding to the circumference of the Bakelite rod to which the wire was affixed with half-mil Teflon tape. The final specimen configuration is shown in Fig. 1. Specimens were lowered into a liquid helium bath (4.2oK) in a double solenoid dewar and positioned so that the maximum magnetic field was oriented transverse to the wire axis of the gage section. Measurements were made by passing a current through the specimen at a preset solenoidal magnetic field. The current was increased until a 1-pv potential difference appeared across the gage section (1/4 µv per cm). At low magnetic fields, however, it was not possible to use this criterion because power-dissipation difficul-

Jan 1, 1967

By C. Gatlin, N. E. Garner, A. Podio

Experimental data from single chisel blows on Leuders limestone are presented. A pressure chamber, similar in design to well known microbit drilling chambers, was utilized to impose variorcs stress states on the sample. Confining pressure of zero to 10,000 psi and borehole pressures from zero to 5,000 psi have been used in the studies. Pore pressure was zero and the rock samples dry in all instances. Force-displacement records and visual examination of the craters indicate that the mode of failure depends on both confining and borehole pressure in certain ranges, ranging from brittle, through a transition, to near plastic. The mode of failure is reflected in the observed blow force and energy data, as well as the shape of force-penetration curves. INTRODUCTION A previous paper' presented initial data from the project on which this paper is the second report. While the first paper dealt with impact studies on synthetic rocks, the literature cited there is also pertinent to this paper, but will not be listed again in order to avoid needless repetition. This paper presents experimental data from single chisel impacts on limestone at certain simulated wellbore stress states. Specific variables investigated were combinations of borehole and confining pressure, crater geometry, a narrow range of impact velocity and the forces required to drive the chisel into the specimens under the varying conditions. EXPERIMENTAL PROCEDURE The same basic apparatus described in our earlier paper, except for the pressure vessel, was used in this study. Fig. 1 shows the complete experimental system. Fig. 2 shows details of the pressure cell, which is quite similar to the well known microbit drilling chamber. The confining (overburden) pressure system provides independent pressure control over the sample except for two, 21/4 in. diameter areas located on the sample ends. These two areas provide a pore pressure entrance on the bottom and a striking surface on the top where borehole pressure can be controlled. The ends are isolated from the confining pressure by O-ring seals. The borehole and pore pressures are related through the striking surface; they will be the same unless a seal is deposited on the borehole surface, either a mud cake or some other impermeable membrane. In these studies pore pressure control was not used, as the rocks were dry and unsaturated in all cases. Rock samples were prepared from 4-in. cubes as illustrated by Fig. 3. The circular disks of adhesive vinyl plastic protected the impact surface from the resin coating (Scotchcast No. 2) and were removed just prior to each test. This procedure insured a fresh uncontaminated surface for the impact. Fig. 4 shows the dimensions and loading of the sample, including the concentrations around the "borehole" periphery (O-ring seal). The rock used in this study was Leuders limestone, of Permian age (Leonard), quarried near Leuders, Tex. Geologically, Leuders limestone is a light gray, fossili-ferous limestone (oolitic foraminifera1 biosporite). Its fossil content is 80 to 90 per cent and consists primarily of calcitornellid, ostracods, pelecypods and oolites with the remaining part intraclasts. There are hematite or limo-nite rims on some of the intraclasts. The porosity is approximately 20 per cent, but the permeability is less than 1 md. There is no apparent orientation in the structure. Triaxial tests have been conducted to determine the variation of the physical properties of Leuders limestone in three orthogonal directions', and it is known to be unusually isotropic and uniform. Physical parameters for this rock are: uniaxial compressive strength = 9,700 psi; F = 32 and C = 2,700 psi; where + and C are Coulomb equation values (t = C+u tan +). Impact tests were run under the combinations of confining and borehole pressures shown in Table 1. Samples were dry with atmospheric pore pressure in all cases. Tests, in which elevated borehole pressures were applied, used a single layer of household Saran-Wrap to prevent horehole fluid invasion into the sample. This proved to be simple and reliable. The blunt wedge used in all the tests was 0.75 in. long and had an included angle of 60" with a 0.05-in. flat. In addition, a sharp 60" wedge was used for all confining pressures at zero borehole pressure. The chipper speed

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc at temperatures below 200°C has been studied using both single crystal and polycrystal samples. Anomalous results were obtained for single crystal samples, the data indicating that in some cases grain boundary diffusion predominated. These anomalous results are presumed to be due to low angle lineage boundaries in the single crystals. When volume diffusion occurred in either single or polycrystal samples, the values for the diffusion coefficient were as much as several orders of magnitude larger than would be expected from high temperature data. ONSIDERABLE work has been done on self-^-*diffusion at temperatures in the neighborhood of two thirds of the melting temperature (in OK) and higher, but very little has been done at lower temperatures. This is particularly true of self-diffusion in single crystals. This paper reports work on self-diffusion in zinc at temperatures below 200 °C where both polycrystalline and single crystal samples have been used. The measurements were made using both the sectioning and absorption techniques. The experiments on diffusion at low temperatures were initiated primarily for three reasons: to obtain data from single crystal diffusion covering a wide range of temperatures, to obtain values of the activation energy for grain boundary diffusion, and to obtain, if possible, a lower limit to the temperatures at which the absorption technique may be used. It is possible to determine whether volume or grain boundary diffusion predominates at low temperatures by analyzing the manner in which the concentration of the diffusing atoms varies with the depth of penetration. The analysis is possible only for the sectioning technique. For volume diffusion and for the boundary conditions of the present experiment, the curve of the logarithm of the concentration, C, vs the square of the penetration depth, x, is a straight line with the slope proportional to — 1/D. If grain boundary diffusion predominates, Fisher' has shown that a curve of In C vs the first power of the penetration depth should be a straight line. This linear dependence of concentration on depth has been observed experimentally by several investigators. (See, for example, refs. 3 and 4.) Following Fisher's analysis, the grain boundary diffusion coefficient can be written as where 8 is the grain boundary width, D, is the volume diffusion coefficient at the temperature involved, t is the time of diffusion, C is the concentration of diffusing material, and x is the depth of penetration. A more general analysis employing the same model as Fisher's but with fewer assumptions has been given by Whipple.' In contrast to Fisher's analysis the more general analysis of Whipple does not always yield a straight line relation between In C and x. Recently Turnbull and Hoffman have discussed both analyses and have applied the Fisher-Whipple model to a more refined dislocation model of the grain boundary. They have also discussed the possibility of a large effect of grain boundary direction on diffusion. In the case of the absorption technique, for which results are also given, one simply gets a value for the diffusion coefficient with no indication of the predominating mechanism. Experimental Techniques Single crystals of 99.99+ pct Zn were grown using a modified Bridgman method. Polycrystal samples were prepared in three grain sizes (small, about 4 mm2; medium, about 9 mm'; and large, about 25 mmz) by quenching, air cooling, and furnace cooling. The grains of the polycrystalline samples tended to be columnar, with some preferred texture such that the c-axis was inclined at about 20" to 25" from the normal to the diffusion face, particularly in the medium and large grain size samples. The samples were cut from the rod, polished, and heavily etched, and faces cut accurately parallel using a jeweler's lathe. They were again etched to remove the lathe smear and annealed for 3 hr at 250" to 300°C. After annealing, they were etched, examined, and the orientation determined by Laue back reflection photographs. They were then electroplated with Zn. The plated surfaces were examined for uniformity; nonuniform coatings were removed by etching and the samples replated without additional preparation. For the diffusion anneals, the samples were placed in pairs, with active faces together, in evacuated Pyrex tubes. Constant temperature baths were used, and the variation in temperature did not exceed ±l°C, Diffusion runs were made at l00°,

Jan 1, 1957

By J. D. Verhoeven

The effectiue distriblltion coefficient has been Measured in a series of vertical, normal freezing experirtzents with large current densities passing through the solid-liquid interface. The results indicate that the effect of the current on solute redistribution is due to electvotransport in the liquid. The high currents produced extensive mixing in the liquid which was considerably reduced by solidifying in small lubing. Analysis of the convection indicates that it probably vesulls from a horizontal temperature gradient produced by the Joule heating- of the electvic crirver~t. Due to the strong dependence of this convection upon the specimen radius, it is conclnded that only for specit~ens with radii of less than somewhere between 1 and 2 mm wilt electric field freezing be getlerally effec-tire at enhancing the purification of zone-melting experittierats in loe-melting alloys. Experiments on 0.8-mm lubes illustrate some interesting potential applications of this techniqne as a means of solute control on smcrll specimens. In a number of papers published within the last few years'-4 it has been found that passage of large dc currents through the solid-liquid interface of a freezing alloy produces a change in the solute redistribution accompanying the solidification. It had been predicted theoretically by Hucke et al.s and by Pfann and Wagner that such an effect would occur as the result of electrotransport within the liquid boundary layer at the solid-liquid interface. These authors independently derived the following relation between the effective distribution coefficient and the variables of the process: Where k0 is the equilibrium distribution coefficient, V is the mobility of the solute relative to the solvent, E is the electric field intensity, D is the solute diffusion coefficient, R is the rate of interface motion, and 6 is the boundary layer thickness. Both groups of authors show that this equation predicts the possibility of extending the purification ability of zone-melting experiments by the addition of an electric current. However, there are other effects in addition to electro-transport which could be produced by the high dc current and might, perhaps, invalidate the applicability of Eq. [I]. For example, high electric current might affect the interface reaction or perhaps the equilibrium distribution which was assumed to exist at the interface. It was the purpose of this work to determine the applicability of Eq. [I] by systematically investigating a simple system for which all of the necessary parameters were known. It was of particular interest for speculating on the potential usefulness of this technique to determine the maximum practical field intensities obtainable, and the effect of these high fields upon convective mixing in the liquid. The initial work in this study was published in a previous paper3 which will be referred to as I. In that work, a current density of 2000 amps per sq cm was used with specimen diameters of 5 mm. The results gave a qualitative confirmation of Eq. [I.], and also showed that a large amount of convective mixing was produced in the liquid by the current. The present study is an extension of that work to smaller specimen diameters and higher current densities. Two points were overlooked in I and will be emphasized here: a) the value of ko has not been well-established in the Sn-Bi system and b) the observed convection could be due to thermal convection produced from the Joule heating. EVALUATION OF k0 To evaluate Eq. [ I.] it is necessary to know the value of the equilibrium distribution coefficient, k,. Tn I the value of k, was taken as 0.3 from a published phase diagram.7 According to ansen' the best data on the phase boundaries of the Sn-Bi system are those of Davidson.5 The data of Davidson give a k, value ranging from 0.21 to 0.25 for the compositions studied in this work, or an average value of around 0.23. In a recent publication, Rigaud and Tougas'10 determined ko by means of a solidification technique. For an alloy of approximately the same composition as that used in this work they obtained a ko value of 0.39. Hence, there is considerable uncertainty in the value of ko and, consequently, a series of experiments were made to determine k, more accurately.

Jan 1, 1968

T.B.King (Depaytment of Metallurgy, Massachusetts Institute of Technology)— A valuable contribution of the authors is in the factual information which they have been able to gather; this type of information is quite difficult to obtain. In many respects, however, it would have been better if they had not subsequently embarked on a discussion of the chemistry of the converter process. It seems inconceivable that the authors do not refer to the papers of Schuhmann and his associates14 which have set the thermodynamic foundation for the whole copper smelting operation. In addition, a very useful review on the physical chemistry of copper smelting by Ruddle 5 appeared as long ago as 1953. An examination of this literature would have convinced the authors that there is no cause to be surprised at a correlation between the magnetic content and the silica content of converter slags, though they rightly point out that one should distinguish between the total magnetite content of the slag and the amount of magnetite which may be considered to be in solution. It is not true that the lowest melting converter slag is that corresponding to the eutectic between ferrous oxide and silica. The simplest slag system which can be considered is a three-component system, since both ferric and ferrous iron are present. As Schuhmann, Powell, and Michal have shown, there are lower melting compositions than this eutectic in the ternary system. The most unfortunate impression given by this paper is that the driving force for chemical reaction is determined by the heat of reaction: of course the entropy change must be taken into account. It would have been more correct to list, in Table VI, values for free energies of formation. Nor can it be said that the data in Table VI represent the "best available data." They do not corregtond with any of the recent, acknowledged sources. F. E. Lathe and L. Hodnett(author's reply)— We are pleased that Dr. King finds the factual information in our uawer of some interest. Dr. King suggests that it would have been better if our analysis and discussion of the data had been omitted, largely because our list of references is so. incomplete. If he will carefully read our introduction, he will see that the questionnaire was sent out in the hope of obtaining data which would throw light on certain questions relating to the use of converter refractories. We did not attempt (nor would the AIME have published!) a complete review of the literature on copper converting, as Dr. King has apparently assumed, nor indeed a complete analysis of the data submitted, but tried only to find a sound basis for the choice of refractories, taking into consideration common variations in converter practice. We hope our paper indicates that, by raising the silica content of the converter slag and operating at a higher temperature, the normal circulating load of magnetite can be greatly reduced, and the whole reverberatory-converter operation improved to a major degree, with resultant important savings. Under such operating conditions, chrome-magnesite brick may be expected to stand up better than those of straight magnesite. Regardless of the choice as between these brick types, however, we find the cost of converter refractories to be so low in comparison with other converter costs as to justify operation under the more severe conditions suggested. Valuable as are the papers by Schuhmann and associates and the book by Ruddle, we make no apology for omitting reference to them, nor for using heats of reaction without mention of entropy changes or free energies of formation. Our primary object was to interest the practicing copper metallurgist, with whose language we may claim to be fairly familiar; we think it would have been unwise to include the highly theoretical phases of the subject which Dr. King suggests. The interest shown in our preliminary paper presented at the New York meeting in 1956, and the trends in practice whtat we have observed since that time, suggest that we did not wholly miss the target. In conclusion, we sincerely hope that Professors King and Schuhmann will independently review the data obtained in our questionnaire and submit a paper giving their own recommendations as to the choice of refractories and the particular converter operating conditions which will result in the lowest overall cost of copper smelting and converting.

Jan 1, 1960

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's, and Pilling and Bedworth'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' 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.'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'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'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 H. J. Ramey

As fluids move through a wellbore, there is transfer of heat between fluids and the earth due to the diflerence between fluid and geothermal temperatures. This type of heat transmission is involved in drilling and in all producing operations. In certain cases, quantitative knowledge of wellbore heat transmission is very important. This paper presents an approximate solution to the wellbore heat-transmission problem involved in injection of hot or cold fluids. The solution permits estimation of the temperature of fluids, tubing and casing as a function of depth and time. The result is expressed in simple algebraic form suitable for slide-rule calculation. The solution assumes that heat transfer in the wellbore is steady-state, while heat transfer to the earth will be unsteady radial conduction. Allowance is made for heat resistances in the wellbore. The method used may be applied to derivation of other heat problems such as flow through multiple strings in a wellbore. Comparisons of computed and field results are presented to establish the usefulness of the solution. INTRODUCTION During the past few years, considerable interest has been generated in hot-fluid-injection oil-recovery methods. These methods depend upon application of heat to a reservoir by means of a heat-transfer medium heated at the surface. Clearly, heat losses between the surface and the injection interval could be extremely important to this process. Not quite so obvious is the fact that every injection and production operation is accompanied by transmission of heal between wellbore fluids and the earth. Previously, the interpretation of temperature logs',' has been the main purpose of wellbore heat studies. The only papers dealing specifically with long-time injection operations are those of Moss and White3 and Lesem, et al.' The purpose of the present study is to investigate wellbore heat transmission to provide engineering methods useful in both production and injection operations, and basic techniques useful in all wellbore heat-transmission problems. The approach is similar to that of Moss and White:' DEVELOPMENT The transient heat-transmission problem under consideration is as follows. Let us consider the injection of a fluid down the tubing in a well which is cased to the top of the injection interval. Assuming fluid is injected at known rates and surface temperatures, determine the temperature of the injected fluid as a function of depth anti time. Consideration of the heat transferred from the injected fluid to the formation leads to the following equations. For liquid, Eqs. 1, 1A and 2 are developed in the Appendix. These equations were developed under the assumption that physical and thermal properties of the earth and wellbore fluids do not vary with temperature, that heat will transfer radially in the earth and that heat transmission in the wellbore is rapid compared to heat flow in the formation and. thus, can be represented by steady-state solutions. Special cases of this development have been presented by Nowakl and Moss and White.3 Both references are recommended for excellent background material. Nowak' presents very useful information concerning the effect of a shut-in period on subsequent temperatures. Since one purpose of this paper is to present methods which may be used to derive approximate solutions for heat-transmission problems associated to those specifically considered here, a brief discussion of associated heat problems is also presented in the Appendix. Analysis of the derivation presented in the Appendix will indicate that many terms can be re-defined to modify the solution for application to other problems. Before Eqs. 1, 1A and 2 can be used, it is necessary to consider the significance of the over-all heat-transfer coefficient U and the time function f(t). Thorough discussions of the concept of the over-all heat-transfer coefficient may be found in many references on heat transmission. See McAdams5 or Jakob," for example. Briefly, the over-all coefficient U considers the net- resistance to heat flow offered by fluid inside the tubing, the tubing wall, fluids or solids in the annulus, and the casing wall. The effect of radiant heat transfer from the tubing to the casing and resistance to heat flow caused by scale or wax on the tubing or casing may also be included in the over-all coefficient. According to McAdams, on page 136 of Ref. 5>

By Claude P. Heiner

W-hile the litle of this paper embraces the entire West Coast, the author, in the interest of simplification, has confined the discussion to California—particularly the central section. California's population has risen 45 pct since 1940. Its electric requirements have also increased, not only because of the growth in industry and population but also because of the widespread tendency of all types of electric consumers to use more electricity than ever before. The growth of California's electric utilities is shown by published data covering operations of three of its large systems and is given in Table 1. New Capacity Steam Driven In meeting these additional electric loads there has been a substantial increase in generation from fuel burning plants as shown by the published energy statistics given in Table 2. Increased Fuel Oil Consumption A study of construction plans of the three electric utility systems named in Table 2 clearly shows that expected new electric loads are to be met, to a large extent, by new steam generating capacity as shown by Table 3. D. D. Smalley, Vice President of the Pacific Gas and Electric Co., in an address before the Pacific Coast Electrical Association in June 1948, stated that California utilities plan to meet new electric loads through greater use of steal11 plank and that in 1951 approximately 45 pct of the area's electric production would be by steam as compared to 33.6 pct in 1946. He stated that if load growth develops as expected and if the year 1952 is dry, thereby requiring high load factor steam operation, the Pacific Gas and Electric Co. would need the equivalent of nearly 25 million barrels of fuel oil. Federal Power Commission reports show that the energy input to the Pacific Gas and Electric Co. system was approximately one billion kilowatt-hours greater in 1947 than in 1946. They also show that the steam plant operating capacity factor in 1946 was approximately 35 pct; in 1947 it, was 72 pct due, probably, to the extreme drought. able 3 shows that Pacific Gas and Electric Co. now has under construction 327,000 kw of hydro capacity which, by 1950, will bring its total hydro generating capacity to 1,313,899 kw. In addition to hydro capacity under construction that company also has 975,000 kw of steam generating capacity under construction, which by 1951 will bring its total steam capacity to 1,560,834 kw. If it is assumed that this total steam electric capacity is operated at a capacity factor of 45 pct, in 1951, over 6 billion kilowatt-hours would be generated. If the load growth on the Pacific Gas and Electric system continues at the current rate of approximately one billion kilowatt-hours per year and if it is assumed that 70 pct of this increase would be generated by steam (30 pct assumed to be generated by hydro facilities with average water conditions), the steam electric production in 1960 would amount to 12 billion kilowatt-hours, which would require fuel the equivalent of 24 million barrels of oil or 6 million tons of coal. Government Projects Inadequate Much has been written with respecl to the plans of the Department of Interior in regard to the installation of hydroelectric plants as a part of multipurpose dams relating to reclamation. flood control, and power generation. An examination of the effect of such plans on the power supply for central and northern California is of interest. The Depart,ment of Interior now has five 73,000 kw units at its Shasta hydro plant on the Sacramento River. It now appears that its three 25,000 kw unit Keswick hydro plant on the same river will be available during the winter of 1949 to 1950. Its estimates show that in a dry year there is sufficient water for operation of Shasta units at an average load factor of 36 pct and Keswick units at a load factor of 41 pct. It is also giving consideration to the development of the Pine Flat and Haas hydroelectric plants on Kings River for generating capacities of 45,000 kw each. The total installation of Government, units in Central Valley and Kings River in California is relat.ively small when compared with t.he

Jan 1, 1950

By J. W. Freeman, E. E. Reynolds, A. E. White

Fram a study of 63 systematic alloy modifications it was found that molybdenum, tungsten, and columbium, added individually or simultaneously, and increases in chromium cause major improvements in 1200°F rupture strengths of Cr-Ni-Co-Fe base alloys. Rupture strengths were a function of the effect of composition modifications on both the inherent creep resistance and the amount of deformation the alloy would tolerate before fracture. THIS paper describes the results of an investigation of a series of alloys with systematic variations of the chemical composition of the following basic alloy: C, 0.15: Mn, 1.7; Si, 0.5; Cr, 20.0; NI, 20.0: Co, 20.0: Mo, 3.0; W, 2.0; Cb, 1.0; N, 0.12; Fe, 32.0 pct. The 62 modifications of this alloy were produced under conditions which minimized all factors influencing properties at high temperatures except composition. Melting, fabrication, and heat treatment were carefully maintained constant. Stress-rupture properties at 1200°F were used as the primary criteria of evaluation of the alloy. The objective of the study was to obtain data for determining the fundamental role of the influence of alloying elements on properties of heat-resistant alloys at high temperatures. In addition the results should be useful in determining optimum chemical compositions, the sensitivity of properties to variations in composition, and the degree to which alloy content could be reduced while retaining worthwhile properties. It is difficult or impossible to develop correlations between properties at high temperatures and systematic variations in chemical composition from published data for wrought heat-resistant alloys developed for gas turbines.' ' The main reason for this is the extreme dependence of the properties on conditions of treatment of the alloys." In most cases variation in final treatments between alloys so influences the properties that the influence of chemical composition is obscured. In addition it is recognized Table I. Basic Alloy and Some Modifications Used Basic AllOy, Variations in Element Pct Composition, Pct C 0.15 0.08. 0.40. 0.60 Mn 1.1 0.03,0.25.0.50,1.0,2.5 S1 0.50 1.2, 1.6 Cr 20.0 10, 30 Ni 20.0 0, 10,30 Co 20.0 0. 10, 30 MO 3.0 0. 1.2.3, 5, 7 W 2.0 0, 1, 5, 1 Cb 1.0 0.2,4,6 N 0.12 0.004, 0.08, 0.18 Fe 32.0 that variations exist between heats of the same alloy which are related to melting practice and that there is a strong possibility that conditions of hot working influence response to final treatments. The development of heat-resistant alloys has been based on the gradual accumulation of data roughly related to composition from extensive testing programs. There is every reason to believe that in most cases the optimum compositions have been achieved by this procedure in the alloys commercially available. There are, however, very little data showing the influence of systematic variations of composition free from the influence of other factors, particularly for alloys of the type investigated. Several investigators of cast alloys have demonstrated compositional effects, notably Grant,1-6 Epremian,t Guy,8 and Harder and Gow.9 Sykes10 eviewed the work on the wrought alloy Rex 78 and the systematic variations of carbon, copper, molybdenum, and cobalt leading to the development of the stronger Rex 337A alloy. From the papers by Wilson11 and Henry12 it is possible to deduce the beneficial effect of substituting cobalt for iron in 0.45 pct C-20 pct Cr-20 pct Ni-4 pct Mo-4 pct W- 4 pct Cb alloys. Wilson mentioned but did not present the extensive compositional studies involved in developing these alloys. Binder" showed optimum properties for 3, 2, and I pct, respectively, for molybdenum, tungsten, and columbium in 20 pct Cr-20 pct Ni-20 pct Co-30 pct Fe alloys for limited systematic variations of these

Jan 1, 1953

By J. W. Leomrd, B. A. Donahue

Results of research are presented examining the extent to which the analytical characteristics of the relatively distinct coal bands from a variety of coal seams can be related to each other. This paper dis-cusses an approach for developing a practical coal petrographic quality control program based on conventional analyses, most of which is part of the standard A.S.T.M. procedure. The work is a final follow-up to Part I of this series which was prepared by the authors as an approach to applying conventional coal petrography to single coal seams. Recent published work by the authors entitled Petrography for Coal Mining and Coal Prepration: Part I dealt with interrelating various chemical and physical properties of coal1 measured using conventional analyses made on distinct petrographic bands taken from single coal seams. Since most coal production facilities process coal from a single coal seam or from very closely related coal seams in the same area,2 emphasis on interrelating the properties within a single seam appeared appropriate. The distinct petrographic bands were analyzed on the assumption that such differentiated data would be more representative of a heterogeneous coal seam than the single analytical value commonly used to characterize each property of an entire seam.34 Effort was directed at demonstrating the extent to which the interrelated chemical and physical properties 5,6 could be developed into nomographs or petrographic standardization graphs. Thus, one analysis, determined on a series of petrographic fractions separated from a single sample, was used to estimate numerous other properties in each fraction by referring to the previously established petrographic standardization graphs. This conventional approach to coal petrography was undertaken as a suggested feasible means by which a few coal analyses could be employed to develope a more penetrating knowledge of the properties of coal from any given seam in order to monitor more extensively its performance at the point of utilization. Such procedures can support development of the type of in- formation commonly sought through automated testing and through the use of computers.7 The broad knowledge which can be developed through these procedures is intended for application in the generation of an analytical profile or broad characterization of coal. These estimates were not intended as replacements for individual coal analytical tests. In this expanded second part of the research program, distinct petrographic bands from nine coal seams in the Central Appalachian Region were physically and chemically analyzed to elucidate the extent to which this concept of conventional petrography could be broadened for application to numerous coal seams. In presenting this second phase of work, the relationships developed are presented individually and not in a connecting series of nomographs or petrographic standardization graphs as in the previous work, thus leaving open the combinations of possibilities to individual interpretation and application. MATERIAL AND EXPERIMENTAL WORK Nine coal seams, representing a wide range of rank, from the Central Appalachian coal fields were used in this study. The distinct petrographic bands from the Kittanning, Pond Creek, Jawbone, Tiller, Poca-hontas No. 3, No. 2 Gas, Eagle, Winifrede, and Pittsburgh coal seams were separated by carefully removing a portion of each band at the face of the seam. The following were determined: ash, sulfur, free swelling index, heating value, bulk specific gravity, volatile matter, Hardgrove Grindability Index, and Gieseler Plastometer measurements. Determinations, where procedures were available, were carried out using ASTM standard procedures.8 Bulk specific gravity was determined using a kerosene volume displacement procedure modified from a method applied by Headlee and McClelland of the West Virginia Geological survey,9 Those bands with a bulk specific gravity greater than 1.60, which is generally above the practical specific gravity cleaning range of bituminous coals, were excluded and no analyses were performed. Much of the initial organization of this second phase of work was developed through the extensive use of a computerized statistical monitoring program (see Ref. 4). However, in order to achieve the closest possible interpretation of results, the final organization of data proceeded mainly from exhaustive trial

Jan 1, 1968

By J. J. Gilman, T. A. Read

S URFACE effects in the cleavage of brittle crystals have been known for some oftime,1, 2 but our knowledge of surface effects in the plastic deformation of crystals is of relatively recent origin. In 1936, Roscoe9 eported his observations comparing oxidized and clean cadmium crystals. He found that cadmium crystals 1/2 mm in diam when covered by an oxide film less than 1200 atoms thick had critical shear stresses about twice those for clean crystals. This effect is anomalous in that it cannot be caused by the inherent shear strength of a normal oxide film. Either an interaction between the film and the crystal causes the large increase in strength, or the oxide film has an abnormal mechanical strength. Several authors since Roscoe have studied surface effects in crystal plasticity. A complete review of the literature will not be presented, but most of the results may be summarized as follows: 1—The critical shear stress for slip is increased markedly by very thin oxide films on zinc4 and cadmium crystals;" ' also, the entire stress-strain curve is raised by an oxide coating;3,4 both effects increase with decreasing specimen radius. 2—Surface active substances such as oleic acid destroy the hardening effect of oxide films.4, 6-8 The time required for the reduction of the hardening effect to begin increases with the viscosity of the solvent4~ 3—There has been dispute in recent years about the effects of surface active substances themselves on plastic deformation. Rehbinder, Lichtmann, and Maslenikov9 state that surface active substances reduce the strength of metal monocrystals markedly and increase the number of slip lines per unit length at a given strain. The effect varies with orientation for tin crystals being smallest for x, = 0, largest for x, = 45", and intermediate as x, + 90°.10 Several workers claim to have disproved the results of Rehbinder')"." but Rehbinder and Lichtmann9 have defended themselves and Masing with his collaborators" has confirmed some of Rehbinder's results. 4—Immersion of metal specimens in electrolytes such as sodium chloride reduces their strength12,13' and subsequent cathodic polarization increases the strength reduction. For noble metals, the strength reduction occurs for both anodic and cathodic polarization," increasing with increasing polarizing voltage. 5—Electroplated copper coatings effect the creep rates of zinc monocrystals. Poly crystals are not affected." 6—Immersion in dilute acid destroys the hardening effect of an hydroxide film. When an acid solution is applied to a steadily creeping crystal, the creep rate jumps to a very high value and then drops gradually to a steady value which is higher than the initial steady rate.*' " If the hydroxide film to be removed is very thin (about 100A thick), the creep rate does not change measurably, but a small rapid strain-increment is observed when dilute acid is applied." 7—Crystal plasticity depends on specimen dimensions. This was observed by Lichtmann and Ven-stroml" for monocrystalline tin and by Andrade and Kennedy" for polycrystalline lead. 8—Immerson of copper crystals in mercury has no effect on their stress-strain curves.'" 9—Bombardment of creeping cadmium crystals with a particles which penetrate the surface to only 0.005 mm may increase their creep rates as much as five times.''' The experiments which will be described in this paper pertain to: (a) the effect of a crystal's shape on its plastic deformation, and (b) the effect of metallic surface films on plastic deformation. For the work pertaining to (a), crystals of zinc, tin, and lead were grown which had various shapes. These were tested in simple tension. Macroscopic rotations about the tension axis which are unpredicted by the classical theory of slip were observed, and serrated edges were observed in tin crystals. For the work pertaining to (b), the effects of evaporated and electrodeposited films of copper, nickel, gold, and zinc on the mechanical properties of zinc, tin, and lead crystals were determined. The films influenced both slip and twinning of the crystals in creep and tensile tests. Experimental Details Chemically pure zinc, tin, and lead were used in this investigation. The zinc was 99.999t pct pure;

Jan 1, 1953

By D. T. Peters, J. C. Bisseliches, J. W. Spretnak

The pain boundary relaxation phenomenon in high-purity copper, 0FHC copper, and a precipitation-hardenable alloy o-fCu-2 uit pct Co has been studied by internal ,friction and elastic aftereffect techniques. The data were analyzed by assuming the broad distribution of relaxation times observed obeys a lognormal distribution law which enables calculation of the relaxation strength. Grain size had no effect on relaxation strength, although the peak width increased with increasing grain size and decreasing temperature. A double grain boundary peak was produced in high-purity copper by annealing to produce secondary recrystallization. The activation energy measured for 99.999 pct Cu is 37.5 * 3 kcal per mol and 46.5 kcal per mole for OFHC copper. A small peak in the Cu-Co alloy at about 220°C at 1 cps was deduced to be the grain boundary peak. Its height increased and its activation energy decreased with increasing aging time. Except for erratic peak positions the observations were consistent with the theory of pain boundary sliding. BEFORE the mechanism of the grain boundary internal friction peak in metals can be satisfactorily explained, the detailed characteristics of the relaxation process must be documented. Of interest are the effect of grain size on relaxation strength, the high-temperature background, and peak width and position. The effect on the grain boundary peak of a precipitate at grain boundaries and of the change in distribution of the particles with aging time must also be explained by any existing or forthcoming theory. The model which has received the most attention was proposed by KG' and zener2 and proposes that the anelastic strain results from sliding of adjacent crystals at grain boundaries. The sliding is limited by the interlocking of grain corners. It follows, according to this model, that the relaxation strength is independent of and the relaxation time is proportional to the grain size. The proportionality between grain size, D, and relaxation time, t, has been confirmed by K&' and Bisseliches . In this case, the internal-friction peaks of various specimens can be superimposed by plotting Q-' as a function of the parameter vD exp H/RT where v is the frequency and H the activation energy. However, the data of Starr et 01.' and Leak6 fit better to a parameter containing D to an exponent near two. A meaningful relationship is not always deducible from the shift of peak temperature with grain size. KG7 demonstrated that a twofold variation in grain size obtained by varying the amount of cold work followed by identical recrystallization anneals will cause a peak shift that is too large to be accounted for even by an exponent of two. Since the decreased grain boundary area existing with a larger grain size is exactly compensated for by an increased sliding distance, the relaxation strength should not decrease with increasing grain size. The height of the internal-friction peak has generally been observed to be rather insensitive to grain size as long as the average grain diameter does not approach the specimen diameter. Exceptions have been reported by Koster, Bangert, and Lang8 for copper, and by Leak6 for iron. The observations for copper could well have been confused by the presence df 0.3 pct0. The possibility that the peaks may simply be increasing in width with increasing grain size and that the relaxation strength, which is proportional to the area under the peak, may remain constant was not examined. his point has been checked in this investigation using high-purity copper. Atomic mechanisms to account for damping by sliding at grain boundaries have been proposed by KG7 and Mott. KG predicts the activation energy to be identical to that for self-diffusion. Mott's "island" model suggests the activation energy is nL where n is the number of atoms in an island and L is the latent heat of fusion per atom. Other authors have felt that a value equal to the activa-

Jan 1, 1964

By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By E. J. Ripling

A NY mechanism proposed to explain hydrogen embrittlement in titanium and its alloys must, of course, be consistent with the experimental data that characterize this embrittlement. Unfortunately, however, the mechanical behavior of hydrogen-bearing titanium, at least a-ß titanium, has not been unequivocally defined. Lenning, Craighead, and Jaffee have clearly shown that hydrogen cmbrittles a-titanium by elevating its transition temperature, probably as the result of the formation of titanium hydrides. Therefore, in these alloys, hydrogen acts like at least one other interstitial contaminant, namely, nitrogen.&apos; On the other hand, ß-titanium has been shown by these same investigators to tolerate very large amounts of hydrogen without suffering severe mechanical damage.2 Mixing these two phases, however, to form the most important class of commercial alloys, the a-ß alloys, again results in severe hydrogen embrittlement, although the mechanism by which the embrittlement is produced is not of the same type as that which causes brittleness in a alloys. Ductility damage due to hydrogen increases as the strain rate is reduced in a-ß alloys, while embrittlement in a alloys increases as the strain rate is increased, since the latter is a transition temperature behavior. Steel, like the a-ß alloys, becomes more hydrogen sensitive at slow strain rates, suggesting that the mechanism producing the embrittlement in these two metals is similar. Brown and Baldwin&apos; described the hydrogen-produced ductility depression in steel as a function of testing temperature and strain rate by defining the slope of the two surfaces that produced the depression in a three dimensional chart, Fig. 1. One of these surfaces was given by the equations (de/de)4 > 0 (de/dT) < 0 [1] while the other was defined by the pair of equations Surfaces of the type given by Eq. 1 are suggested in two ways. One is an embrittlement mechanism wherein the diffusion rate of hydrogen is competitive with the rate at which the material is being deformed, as suggested by the planar pressure theory of Zapffe and his co-workers.&apos; The other is the diffusion controlled extension of Orowan&apos;s theory on delayed fracture in glass by Petch and Stables.&apos;&apos; Surfaces of the type given by Eq. 2 are also compatible with a mechanism of pressure build up in voids, according to de Kazinczy,&apos; since the solubility of hydrogen in the metal increases with testing temperature so that as the temperature is raised, the pressure in the voids is reduced. Kotfila and Erbin recently presented some data on the dependence of ductility on testing temperature and strain rate for the a-ß 3 pet Mn complex alloy at four different hydrogen levels.H Although data were presented for only three testing temperatures at three different strain rates, their results indicated that surfaces of the types defined in Eqs. 1 and 2 are produced in the alloy when the hydrogen level is sufficiently high—200 and 300 ppm—Fig. 2. Jaffee and his co-workers presented data on a number of different a-ß alloys which indicated the existence of surfaces of the type described by Eq. 2, but the ductility recovery at low temperatures as given by Eq. 1 was not found." In an attempt to aid in crystallizing this description of the ductility dependence of hydrogen-bearing a-ß alloys, tests were conducted by the author on a-ß titanium 140A with three different hydrogen contents. The tensile properties of two as-received rods and one vacuum annealed rod* were obtained over a range of testing temperatures and strain rates as shown in Figs. 3 and 4. Hydrogen analyses were made by the Battelle Memorial Institute on four pieces of the rod whose properties are shown as solid circles in Fig. 4. The hydrogen content of these pieces, taken at widely spaced intervals within the rod, were 280, 270, 289, and 270 ppm, indicating that the hydrogen content within a single as-received rod was quite uniform. One of the broken test pieces whose properties are shown in Fig. 3 as solid circles was also analyzed, and found to have a hydrogen content of 310 ppm. The analyses obtained on two of the vacuum annealed specimens were 92 and 170 ppm.

Jan 1, 1957

By James Boyd

Scientists and engineers must concern themselves not only with technical problems, but with the socio-economic difficulties of our scciety. The author states that raw materials are basic to the economic process and that mineral raw materials occur naturally in nearly limitless quantities. He feels that the economic pocess will provide sufficient raw materials for man&apos;s needs, and discusses in some detail the world economic environment. As our society grows in complexity, it becomes more urgently incumbent upon scientists and engineers to bring their experiences to bear on the solution, not only of technical problems, but also on socio-economic difficulties. It is to this field that I have directed a large part of my energies. RAW MATERIALS BASIC TO THE ECONOMIC PROCESS There are certain premises, frequently overlooked, which bear emphasis. As economics concerns the production, distribution, and consumption of goods, so our whole society is based on raw materials. Without the basic extractive industries of agriculture and mining, there would be no economic problems with which to deal. This principle has been expressed as "All productivity is based on three factors: 1) natural resources, whose form, place, and condition are changed by the expenditure of 2) human energy (both muscular and mental), with the aid of 3) tools.77* It seems strange that such an obvious statement needs to be made. It is forgotten by all of us, however, at one time or another when we get involved in the complicated theories of economics dealing with the financial and fiscal policies of the various governments, in the financing of enterprises, in marketing, and in labor relations. Unless decisions in all of these fields are made with this, and the rest of the "Ten Pillars of Economic Wisdom," consciously in mind, the resultant policies are doomed to eventual failure, whether these are policies of individuals, companies, or governments. The economic process is basic to society. But economics and the social aspects of humanity are inevitably intertwined. If human needs are not provided for within the basic economic structure, conflicts arise to disrupt the most carefully laid social plans. Similarly, it is the failure of society to cope with basic economic prerequisites that leads to discord within the body politic and thus to eventual economic disaster. We who are engaged in the various aspects of the mineral industry, therefore, have a large part to play in society&apos;s future development. MINERAL RAW MATERIALS OCCUR NATURALLY IN NEARLY LIMITLESS QUANTITIES Throughout my career in and out of government, I have formed my decisions on two principles: 1) Fundamentally, all mineral raw materials exist within the earth&apos;s crust in quantities greatly exceeding man&apos;s needs; 2) Any problems of supply of these materials are primarily economic in nature. With respect to my first assumption, analyses by geochemists enable them to estimate the quantities in which each of the known elements exist in the earth&apos;s crust. One of the most cautious and famous suggests that the average copper content of the lithosphere to a depth of ten miles is about 55 ppm. If this is valid, then the lithosphere contains about 1.4 quadrillion (1.4 x 10 ") tons of copper metal — an unimaginable quantity. This is 8,500,000-fold that which has been consumed by man in his existence. To illustrate further, consider that the deepest copper mine in history went to about 9000 ft below the surface; the present copper mines of the world now average less than 1500 ft in depth. We can assume that in most continental land areas of the world it is technically feasible to mine to a depth of at least one mile. The land areas of the world to an average depth of one mile, then, contain 343 billion tons (343 x 10&apos;) of copper metal, or 2000 times that which has been extracted to date. I don&apos;t believe man will ever expend his energies to extract copper from rocks which contain only a few parts per million, but he knows that each element

Jan 1, 1968

By H. W. Schull

The Alligator Ridge gold deposits are located in northwest White Pine County at the southwest end of Alligator Ridge. Alligator Ridge is on the west side of Long Valley in the range of hills that separates Long and Newark valleys. The nearest population center is Ely, about 113 km (70 miles) to the southeast. Access to the Alligator Ridge gold mine from Ely is via US Highway 50 and the Long Valley Ruby Marsh Road. The latitude and longitude is approximately 39° 45&apos; north and 116° 30&apos; west. The Alligator Ridge gold deposits occur in the lower 61 m (200 ft) of the Mississippian-Devonian Pilot Shale formation, a laminated calcareous carbonaceous siltstone. The gold deposits contain carbonaceous, oxide, and jasperoid type gold ore. For more details on the geologic features of the deposits, see Schull, Sutherland, and Ilchik (in press). The discovery story of Alligator Ridge began in the spring of 1976 when the areas mapped as jasperoid on the 1:250,000 scale geologic map of White Pine County (Hose and Blake, 1976) were examined and sampled. Seventeen samples, about 23 kg (50 lb), were collected from an area about 0.65 km2 (0.25 sq mile). Of these 17 samples 10 reported atomic absorption values of less than 0. 1 ppm Au and 7 reported values in the 0.1 to 1.0 ppm Au range. In June of 1976 20 lode claims were staked to claim the area of the rock chip sampling. The claims&apos; end and side center lines were used as a grid for soil sampling. Sample stations were 91 m (300 ft) apart and sample lines were 229 m (750 ft) apart. The samples were sieved to - 180 µm (- 80 mesh). Out of 99 soil samples, seven samples reported Au values in the 0.1 to 1.0 ppm range. Of the seven auriferous samples, five were located over the jasperoid outcrops previously sampled; one over unmineralized Pilot Shale a few hundred m (ft) downslope from some Au-bearing jasperoid; and one from a 15 x 15 m (50 x 50 ft) talus outcrop area of hitherto unnoticed mineralized Pilot Shale. Subsequent sampling, mapping and drilling would show that this 15 X 15 m (50 x 50 ft) outcrop area was the top of the Vantage 1 ore body, about 1.27 Mt (1,400,000 st) of over 3 g/0.9 t (0.11 oz/st) Au. Late in the summer of 1976 about 30 more 1.4 to 2.2 kg (3 to 5 lb) rock chip samples were collected in the course of preliminary geologic mapping. This mapping and sampling showed that the gold-bearing jasperoids occurred at the contact between the Pilot Shale and the underlying Devils Gate Limestone. Rock chip samples of 0.1 ppm Au or greater were restricted to the jasperoids and the mineralized outcrop area of Pilot Shale located by the soil sample survey. Rock chip samples from the area of mineralized Pilot Shale were in the 3 to 5 ppm Au range. Activity resumed in the summer of 1977 with a more detailed soil geochemical survey. The jasperoid areas were defined as large geochemical gold anomalies of values greater than 0.1 ppm and locally greater than 0.2 ppm Au. Soil samples from the area of mineralized Pilot Shale outlined a greater than 0.1 ppm gold anomaly 61 x 152 m (200 x 500 ft) in size. Further geologic mapping showed that elsewhere, even where bleached and silicified, the Pilot Shale areas were geochemically very low in gold (less than 0.1 ppm Au). In November, 1977 twelve rotary percussion drill holes were drilled to test the gold-bearing jasperoid areas and the mineralized Pilot Shale area. Drilling of the jasperoid areas showed that the jasperoids gave way at shallow depths [less than 24 m (80 ft)] to unmineralized unaltered Devils Gate Limestone. A five hole cross pattern was drilled to test the area of mineralized Pilot Shale. Four of the five holes re-

Jan 1, 1985

By H. E. Cline, E. F. Koch, J. L. Walter

It has been postulated and, in a few instances shown, that some kind of dislocation structure will be present at semicoherent interfaces to accommodate small lattice mismatches. In the present study of the NiAl-Cr eutectic, regular arrays of interface dislocations are observed at the boundary between the chromium-rich rods and the NiAl-rich matrix. The networks were examined by transmission electron microscopy and selected area diffraction. The rods and the matrix have a crystallographic relationship in which all directions and planes of the two phases are parallel. The dislocation networks are cmposed of a<100> dislocations lying on the intersections of the cylinders with (100) planes. Dislocations forming hexagonal rather than square arrays are also observed at certain areas of the network. The morphology of the network is consistent with the interpretation of mismatch being accommodated by interface dislocations in the cylindrical geometry. The measured spacing between dislocations was used to calculate an apparent lattice mismatch between the phases (˜0.35 PCt)interface network energy (-140 ergs per sq cm), and network strengthening (-10,000 psi). It has been proposed by Frank and Van der Merwe1 that dislocations should be present at the boundary between two semicoherent crystallographically related phases. The role of the interface dislocations would be to reduce the internal stresses, caused by the mismatch in atomic spacing across the interface. Such dislocations have been observed at the interface between expitaxially grown films and Substrates.2-4 Interfacial dislocations have also been observed at precipitate-matrix interfaces.&apos;-&apos; Directionally solidified eutectics have been shown to have semicoherent phases1&apos; and would, therefore, be expected to have interfacial dislocations as found by Weatherly at a lamellar fault in A1-A12Cu.11 The NiAl-Cr eutectic appeared to be a promising system to examine because both phases are cubic, the lattice mismatch is small, and the phases are crys-tallographically related. Furthermore, the eutectic is easily thinned for transmission microscopy. Indeed, interfacial dislocations were observed and this report describes the nature of the dislocation networks in the boundary between the NiAl-rich ma-trix-phase and the fine chromium-rich rods.21 I) EXPERIMENTAL PROCEDURE Ingots, 3/4 in. in diam and 6 in. long were made by melting in vacuum and casting under argon using 99.9 pct pure material. The composition, in at. pct, was 33 pct Ni, 33 pct Al, and 34 pct Cr. The ingots were then placed in A1203 crucibles on a water-cooled base, melted by means of induction, and withdrawn from the hot zone at the rate of 1 in per hr under argon.* * T his material was first directionally solidified in this laboratory by E. R. Stover Slices were taken perpendicular to the growth direction of the directionally solidified ingot for metallography and for transmission electron microscopy. The electron transmission samples were thinned mechanically, then thinned electrolytically in A-2 electrolyte* *A-2 electrolyte: 62 ml perchloric acid, 700 ml ethanol, 100 ml butylcellosolve, 137 ml distilled H20. until a hole appeared in the foil. 11) EXPERIMENTAL RESULTS A) Optical Microscopy. The microstructure, viewed on a plane perpendicular to the growth direction, is shown in Fig. 1. The structure consists of cells or colonies of parallel chromium-rich rods in the NiAl matrix. The cells occur when there are impurities present12 or, in a ternary eutectic, if the composition is slightly off the eutectic composition. The axis of the chromium-rich rods is parallel to the growth direction except near the cell boundaries. Here the rods may assume angles to the growth direction; however, examination shows that the crystallographic relationship between the rod and the matrix remains the same. Fig. 1 includes cell boundaries where the rods formed at a large angle to the growth direction. The variation of rod position across the cells made it possible to Fig. 1-Structure on plane perpendicular to growth direction. Rods near cell walls are at large angle to growth direction. Magnification 315 times.

Jan 1, 1970

By R. H. Edsal, G. Horvay

The transient one-dimensional heat-conduction equation is solved for two semi-infinite media, at different initial temperatures, brought into (poor) thermal contact. It is shown that the two interface temperatures gradually approach the well-known, instantaneously assumed, common interface temperature of the case of zero contact resistance. The present analysis, with slight modifications, may be used in fair approximation also for the class of problems involving a change of phase. One particular application of the boundary value problem solved in this paper concerns the determination of the temerature distribution in metal castings and molds.P This problem has been treated extensively by analytical methods (see e.g., the literature listed in Refs. 1 to 4) by electrical analogs (see e.g., Refs. 11 to 14) and also by experimental methods (see the literature listed in Refs. 4, 5), but prior to the work of Pellini and Ruddle the experimental results were rather unreliable. Immediate motivation for the work described in this paper was to better understand the results of Pellini,&apos; which are typified by the curves of Fig. 1. Pellini cast 20-in. high, 7-in. sq steel ingots into cast-iron molds of various thicknesses. He measured the temperatures at mid-height, at a number of stations in the casting and the mold, and obtained the cooling curves shown in Fig. 1. The most conspicuous thing about Fig. 1 is the large temperature discontinuity at the interface between casting and mold, due presumably to the shrinking away of the casting from the wall and the attendant creation of an airgap, as the casting cools. Such a contact resistance slows down the anticipated freezing rate; an analytical prediction of this is of much interest in foundry practice. The determination of the effect of contact resistance in the presence of a change of phase will be dealt with, by an approximate method, in a separate paper.&apos; In the present paper the much simpler problem is considered in which there is contact resistance but no change of phase. This problem frequently arises in the analysis of aircraft structures.+ It can initial temperature, and may be regarded as semi-infinite. We suppose the thermal properties in the two media to be time, temperature, and space independent; there are no sources or sinks within the media. In Fig. 2(a) we illustrate, schematically, the case of no contact resistance. The semi-infinite media "0" and "2:&apos; initially at temperatures 8 (- m) and 8(+ -), respectively, are brought into contact at time t =0. A common interface temperature 8,i = is instantaneously established, and thereafter remains constant. Temperature curves are drawn for three instants of time. When there is contact resistance between the two media, the temperature equalization occurs as sketched in Fig. 2(b). Fig. 2(c) illustrates a temperature curve, using the dimension-less notation Barber-Weiner-Boley6 have stated the equations [23a, b] given below, which govern the heat transfer in the two media, and solved them for a rather complicated special case. In their example both media "O" and "2" are finite, are insulated at their far ends, and there is steady heat input into medium 2. In Eq. [27] we give the general solution of the most important special case, where the two media are semi-infinite and there are no sources or sinks. In this case the results may be stated in simple closed form. In Fig. 3, to be discussed in the next section, we illustrate the variation of the interface temperature when steel at 2760" is brought into contact with iron at 100". This example, if we disregard the effect of the heat of fusion, is comparable to Pellini&apos;s experimental results, Fig. 1. (Unfortunately, however, experimental determination of the interface temperatures was difficult to carry out, and hence Fig. 1 is not very accurate near the interface.) In Figs. 4 and 5 of the following section, we similarly compare Pellini&apos;s sandcasting tests with analytical results for the case where steel at 2760" is brought into contact with sand at 100". It will be pointed out that, insofar as the interface temperatures are concerned, heat of fusion has a minor effect, and so the present approximation, with small modifications, may be

Jan 1, 1961