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

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

Jan 1, 1969

By Carl Altstetter, Roy Adams

Measurements of enthalpy changes and transformation temperatures me reported for the fcc -hcp marten-sitic transformation in pure cobalt single and multi-variant crystals andpolycrystalline specimens. From these measurements the free-energy difference between the two phases was calculated for both heating and cooling and for repeated cycles through the transformation. For heating of single crystals the average value of enthalpy change was 113 cal per mole but on cooling it was 84 cal per mole. This difference is interpreted in terms of lattice imperfections which are introduced during transformation. A calorimeter suitable for measurement of enthalpy changes of athertnal transformations is described. COBALT exhibits an allotropic phase transformation at around 417°C' where an hcp phase (a = 2.507, c = 4.0686, c/a = 1.6228)~ stable at low temperatures transforms to an fcc phase stable up to 1495°C. The transformation has a hysteresis of about 30°C— the exact magnitude of the hysteresis depending on the number of transformation cycles, grain size, impurity content, and prior treatment.'-6 The athermal character of the transformation and surface relief due to transformation shear indicate that the transformation is martensitic. Pole mechanisms for the transformation have been discussed by Sebilleau and Bibrin, Bilby, Seeger,' and Basinski and Christian. These authors have proposed that the cooling transformation is effected by rotation of a Shockley partial dislocation around a pole dislocation with a screw component of 2a/3(111). Such a rotation would change the stacking of close-packed planes from the abcabc fcc stacking to the ababab hcp stacking sequence. This mechanism would predict a lattice correspondence of {111}fcc~~(0002~cp, have been observed. One would expect the heating transformation to occur similarly, involving dislocation movements on the (0002)hcp. However, a high density of pole dislocations and high dislocation ve- locity are required to account for microscopic observations. Furthermore, the high back stress developed on the Shockley partial dislocation as it rotates toward the sessile dislocation associated with it makes it doubtful that this is in fact the transformation mechanism. A mechanism for spontaneous nucleation of partial dislocations1*l2 seems more reasonable. If a single crystal of cobalt is cycled through the transformation but never heated above 600°C, it will remain single."13 However, if the specimen is heated through the transformation and held for a short time at or above 1000°C before cooling, the cooling transformation usually involves all four {lll}fcc habits, resulting in neighboring orientations of hcp differing by 70.5 deg. This condition is termed multivariance and has been observed by Bibring and sebilleau5 and Nelson and ~ltstetter.' The latter authors used single crystals of cobalt grown in an electron beam zone refiner. They proposed that the strongly directional cooling caused the initial cooling transformation to occur on the {lll)fcc most nearly perpendicular to the temperature gradient. Transformation shear on one set of {lll}fcc planes immobilized dislocations on the other {lll}fcc planes involved in the initial transformation. Since there is only one (0002)hcp plane orientation, the product of subsequent heating transformations could have no more than two variants—the original fcc orientation or its twin. If, however, the specimen was annealed at a high temperature, such as 1000°C, there would be relaxation of dislocations into low-energy configurations, and in the absence of a sharp temperature gradient transformation on all four (111 Ifcc planes could occur. If a dislocation mechanism is responsible for the transformation, the perfection of the lattice should affect the reversibility of the transformation. Mutual constraints of neighboring grains in polycrystalline material would inhibit dislocation movement resulting in increasingly sluggish transformation. Indeed, Nelson and Altstetter found the M, to decrease and the A, to increase in going from single crystals to multi-variant specimens to polycrystals. The effect is enhanced by decreasing the grain size of a solid specimen or a powder.6'14 Data on the free-energy difference necessary to initiate the transformation gives information about the driving force of the transformation. This is an important consideration in the understanding of the transformation mechanism. The free-energy change associated with the transformation of the hcp phase to the fcc phase at some temperature T different from the equi-

Jan 1, 1969

By Strathmore R. B. Cooke, Paul B. Queneau

The kinetics of the dissolution of scheelite in basic solutions of carbonate and fluoride were investigated. Work was also done with solutions of alkali metal chloride, hydroxide, phosphate, and mixtures of phosphate and fluoride. The study was conducted at 90 psig and at temperatures ranging from 100" to 155"C, and both natural and synthetic scheelite single crystals were used. The interaction of scheelite with carbonate solutions generally followed a parabolic rate law, and resulted in the formation of calcite crystals on the attached surface. The transport of the CO3 through the calcite to the scheelite surface was probably rate -controlling between 115" and 135°C. Positive deviations from Parabolic behavior were observed at 100" and 155?C, presumably due to the calcite grain growth, and to the formation of a noncoherent calcite layer, respectively. The leaching of scheelite with alkaline fluoride solution produced a calcium fluoride reaction-product which covered the surface as a sheet-like layer. Below 110°C the dissolution rate was parabolic; at 115" and 135°C it was linear. In the linear region, the periphery of the calcium fluoride layer lifted from the sample. Only the lower layers, braced by the scheelite substratum, remained unbroken. This bound layer, approximately constant in thickness, limited the rate at which the fluoride could attack the scheelite. The phosphate and phosphate-fluoride leaches dissolved scheelite at a linear rate; solid reaction products were respectively hydroxyapatite and fluorapatite. Sodium hydroxide and chloride were not effective leachants, and did not produce observable solid reaction products. THE feasibility of pressure leaching of scheelite pulps with basic solutions containing either carbonate or fluoride ions, as indicated by the following equations, has been established by previous investigators:1-3 200°C CaWO4s + CO37q - CaCO3s+WO4aq [1] 200°C CaWO4s + 2Faq ^ CaF2s+WO4aq [2] It is to be noted that a commercial process employing reaction [I] is in use at Union Carbide's operation near Bishop, Calif. In the earlier work referred to, it was apparent that the precipitation of the solid reaction-product on the scheelite particles sharply reduced contact of the leachant with the scheelite. We have extended this work by studying the kinetics of dissolution employing single crystals of scheelite of known exposed surface area. In addition, the effectiveness of solutions of phosphate, of phosphate with fluoride, and of chloride and hydroxide as leachants for scheelite have been investigated. EXPERIMENTAL Apparatus. The low-pressure autoclave used in this wo (100 psig maximum) is essentially that of J. Halpern4 as modified by F. A. Forward.5 Constructed entirely of 316 stainless steel, its maximum capacity is 4000 ml. The temperature in the autoclave was regulated to *0.5?C by a Wheelco thermocouple controller. A 4-in. diam, three-bladed impeller, circulated solution upward against the sample, and a strobo-scope permitted holding the stirring rate to *15 rpm. A check valve and a "pop" type safety valve were installed, a sample holder was fixed to an externally adjustable rod, and a water-cooled condenser was placed in series with the sampling valve. The stainless steel sample holder, Fig. 1, held the epoxy-mounted sample (f) five mm above the impeller. Tightening the tapered sleeve (d) positioned the epoxy-resin specimen-mount by forcing it back against the spacer (c). The mount (e) was 1 in. diam. Sample Description and Preparation. Both synthetic and natural scheelite crystals were leached. The former were single crystals of 99.95 pct purity which were leached approximately perpendicular to the "c" axis; they were supplied by the Gallard-Schlesinger Chemical Manufacturing Corp. The natural crystals, supplied by Minerals Unlimited, were transparent, analyzed 99.8 pct CaWO4, and in ultraviolet illumination exhibited the characteristic blue glow of substantially molybdenum-free scheelite. To permit exposure of an essentially constant surface area of scheelite to the leachant, the samples were mounted in Scotchcast Brand Resin No. 250 (Minnesota Mining and Manufacturing Co.). The mount-

Jan 1, 1970

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 V. T. Stringfield, H. H. Cooper

ONE of the earliest investigations of ground water in Florida was made in 1513 when Ponce de Leon arrived at St. Augustine in search of the Fountain of Youth. The history of the development of the water resources of the State shows that the large artesian reservoir that underlies Florida was discovered in the latter part of the last century. Part of that history is given by L. C. Johnson' who states that the first successful artesian well in Florida was drilled at St. Augustine between 1880 and 1882. After the City of Jacksonville failed to obtain a flow of artesian water at a depth of nearly 400 ft and abandoned the drilling, R. N. Ellis, City Engineer, and L. C. Johnson, using Johnson's knowledge of the geologic structure of the artesian reservoir, estimated correctly that artesian water could be obtained at a depth of about 500 ft. Thus began the development of the large artesian system in the northeastern part of the State. In 1908, the Florida Geological Survey issued its first report on the ground water of central Florida. More recent reports give the results of investigations that have been in progress in cooperation between the Florida Geological Survey and the U. S. Geological Survey since 1930. As a result, the ground-water geology and hydrology of Florida are now so well known that ground-water problems such as confronted early investigators no longer exist. However, new problems arise and new discoveries are made as the demand for more ground water increases with the development of the State. Water-Bearing Formations Descriptions of the geologic formations and a map showing their distribution at the surface are given in a recent report by Cooke.' The geologic formations that yield the ground-water supplies in Florida represent only a small part (about 1000 ft) of the total thickness of the sedimentary rocks (more than 15,000 ft) that underlie Florida. The water-bearing rocks that yield fresh water include more than two dozen formations that range in age from Eocene to recent. The Eocene formations, which consist chiefly of limestone, are the oldest and the deepest of the formations in Florida that yield fresh water to wells. In 1944, on the basis of a study of the foraminifera, the Applins -ivided the limestone of Eocene age into six formations, which are as follows, from top to bottom: Age or group Formation Jackson Ocala limestone icAvon Park limestone Claiborne -j Tallahassee limestone aLake City limestone Wilcox Salt Mountain limestone xOldsmar limestone The Ocala limestone and the underlying formations of Claiborne age, along with some of the overlying limestone of Oligocene and Miocene age, constitute the principal source of water in Florida and southeastern Georgia and generally may be regarded as forming one artesian aquifer or water-bearing unit. This aquifer is referred to in this paper as the Floridan aquifer, a name proposed by Parker.' In part of Seminole County alone more than 1000 flowing wells yield water from the Floridan aquifer. A yield of 6500 gpm, or about 9.5 million gal per day, by natural flow from a well penetrating the aquifer at Jacksonville, Florida, was observed in 1942. A yield of about 7000 gpm by natural flow was reported for a well 1390 ft deep at St. Augustine in 1887. The largest yield reported from a pumped well penetrating the aquifer is 7500 gpm, or about 10.5 million gal per day. The aquifer is also the source of some of the large springs, such as Silver Springs, whose discharge, according to measurements made by the U. S. Geological Survey, has ranged from 526 to 1350 sec-ft, or from 340 to 872 million gal per day. The top of the Ocala limestone, as represented by contours in Fig. 1, indicates in a general way the geologic structure of the formations that comprise the Floridan aquifer. The Ocala is at or near the surface in the areas represented by shading in the northwestern part of the peninsula and also in an area in western Florida adjacent to Alabama and

Jan 1, 1952

By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e'i; ei being parallel to the Burgers vector b, and e'3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?'1,?'2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?'2s'11b'1—?'1s'12b'1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s'12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x'i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x'i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b'1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b'1s033 sin a- rn2b's33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

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 R. G. Wheeler, J. W. Goffard

The Larson-Miller parameter was used to correlate time, temperature, and indentation creep of magnesium, aluminum, and some of their alloys. In the temperature range 300" to 450°C, the short-time Meyer hardness of pure magnesium was less than that of the magnesium alloys tested, but for long times the pure magnesium has greater indentation creep resistance. Aluminum (1100 alloy) had 1.5 to 2.5 times more indentation creep resistance than magnesium at 300" and 450oC, respectively. Hardening of aluminum with a dispersion of Al2O3 was effective in the time and temperature ranges studied. New technologies have required the development of new materials and the utilization of the more familiar materials for new and unusual applications. The use of magnesium and aluminum and some of their alloys, because of their desirable nuclear characteristics, light weight, low cost, and ready availability, has been extended to the 300" to 450°C temperature range. In this temperature range the basic consideration of these materials must be their rate of plastic flow rather than offset yield strengths. The indentation testing reported here arose from a need for design data for the load-holding ability of supports made of these materials. Test Procedure—Hardness indents were made with a 0.275-in.-diam quartz indentor and a 10.65-lb load. The indentor was made by fire-polishing a spherical surface on the end of a fused quartz rod. The samples were held at temperature in a graphite crucible controlled to ±2°C. A thermocouple was attached to the sample and test temperatures were recorded. The diameter of the spherical indentation was measured at the end of a test period and the compression stress (Meyer Hardness) was determined by: H___________load__________ m = projected area of indent Samples were 1 in. in diam and at least 1/4 in. thick. It was observed that at the higher temperatures and longer times, the quartz indentor would stick to the magnesium sample. The quartz indentor was, therefore, frequently inspected and fire-polishing repeated when necessary. The area of sticking was always a small fraction of the area of indent and was therefore considered to have an insignificant effect on results. Correlation of Hot-Indentation Test Data with Time-Temperature Parameter—Sherby and Dorn' have correlated creep or tensile data of a' solid solutions of aluminum with a temperature and strain-rate parameter suggested by Zener and Holloman. underwood2 used this parameter to correlate creep properties of some steels with hot hardness, and upon the basis of this correlation a means of obtaining creep properties from short-time (and inexpensive) hot hardness tests has been demonstrated. Since the validity of the correlation of creep properties with a time-temperature parameter and the correlation of creep properties with hot hardness have been shown, it follows that hot hardness may correlate with the time-temperature parameter. The hot-indentation data obtained was expressed as Meyer hardness, and was shown to be time and temperature dependent. Correlation of Meyer hardness, time, and temperature with the parameter was made using the relationship: Hm = Meyer hardness t = time, hours T = absolute temperature, OK K = constant A value for the constant K was calculated by equating In l/t + K/T at different temperatures and times but at the same hardness. The correlation was tested by plotting Hm vs the parameter, In 1/t +K/T. Since materials are being sought which have high hardness at low indentation creep, i.e., a high Meyer hardness for long time at high temperatures, low values of the parameter are ofthe most interest. TEST RESULTS Magnesium—Pure magnesium (99.98 pct) cut from extruded rod was indentation tested perpendicular to the rod axis at temperatures of 300°, 350°, 400°, and 450°C for times ranging from 6 sec to 112 hr. Fig. 1 shows the time dependency of Meyer hardness at the four constant temperatures. Fig. 2 shows the correlation of the Meyer hardness of pure magnesium with the time-temperature parameter using a K of 22,720 in Eq. [I]. At the bottom of Fig. 2, the effect of doubling the time of indentation t2 = 2(t1), on the abscissa for any time is shown graphically. This effect is of constant magnitude. Also shown graphically are the magnitudes of the effects on the

Jan 1, 1960

By V. C. Williams

Some of the physical, chemical, and electrical processes for conversion of saline water to potable or industrial water are economically surveyed from an engineering viewpoint. Since all these processes require energy for drive and equipment for containment, the correlative economic factors are developed which indicate directive influences in the choice of particular regional processes. The supply of natural waters and its distance also affect decision. Any one process will probably not prove dominant in the field because auxiliary considerations such as the saline water source; types and continuing availability of fuel; electric power use or recovery; area economic status and advancement; and the political pressures of population, group demands, and land use tend equivocally to obscure capital and operation cost decisions. Basic engineering considerations, data, and economic factors are presented to assist in the direction of these decisions. An exploding world population, increasing industrialization, advancing standards of living, and the desire of less-privileged nations for betterment focus attention sharply on a major problem: water. *19 Up to now, in retrospect, people have had it relatively easy in the handling of this problem. All the better dams in the most advantageous sites, the better aquifers, the shortest aqueducts have been built. In another phase of the problem, concern is evident that wastes cannot indefinitely be disposed of merely by keeping them dilute and discharging them promiscuously. 7-9 And, perhaps, as past civilizations have done,l5 water, watersheds, streams, and irrigation may have been mismanaged or, at the least, not adequately studied.3,5,36,37 In this last is perhaps the core of the problem. As Gross states, "Ignorance and too often, indifference are contributing factors. Archaeology and theology both furnish ample testimony to the existence of rich lands where deserts now stand; it was man who ravaged his land. Unless education is a companion to water development, development might as well be forgotten. But without water, there is no beginning."13 The U.S. is showing increasing concern about its water for predictions are that by 1980 the daily withdrawals will be 494 billion gal, a figure nearly equal to the dependable supply.Is This is based on a conservative projected population of 230 million. The major categories of withdrawals are: To make available this per capita average of 2150 gal per day will require an expenditure of $219 billion over the next 20 years. The U.S. is not alone in this concern. The United Nations shows as arid zones of the world: all of Africa north of the equator and south of the 20's parallel; all of the Arabian peninsula; all of the middle east and Iran, Iraq, Pakistan, Afghanistan, northern and central India; a great band about 1000 miles wide along the 40'~ parallel from the Caspian Sea east across Russia through China to the Pacific Ocean; all of Australia except the coastal plain; the Caribbean Islands; the western nations of South America; and the western third of the United States and of Mexico. With one quarter of the earth's 57,500,000 sq miles of land thus suffering from lack of good water, increasing attention goes to the treatment of brackish and sea waters. The U.S. has been a leader in this field4,12, 16123,24 through its Office of Saline Water in the Dept. of Interior because even now some of its cities and regions are short of potable water. 11j'7,M Industrial water is also of vital concern as a result of ever higher industrialization1,14122 Other nations, among them JaPan, Israel,13188 Germany, Union of South Africa, Australia, Netherlands, France, Yugoslavia, Russia, and groups such as the Organization for European Economic Cooperation (OEEC)' are also diligent. The objective is low cost water, which means that both technology and economics have prominent roles in saline water conversion processes. TECHNOLOGY: SALINE WATER CONVERSION A number of reviews of methods have been made, principally by staff members of the Office of Saline Water (U.S. Dept. of Interior). Jenkins,31'32 Gillam,34p

Jan 1, 1962

By M. M. Rao, P. G. Winchell

The growth rates of bainitic plates were measured at 400°C in Fe-Ni-C alloys containing 0.10 atom-fract~on nickel and 0.0012 to 0.0075 atonz-fraction carbon. The growth rates are adequately represented by where xc is nearly the atom fraction carbon of the bulk austenite and PXCy is nearly the carbon atom fractlon in the ferrlte of radiids p In equilibrium with austetzite. The form of the equation is that predicted by a model in which carbon diffusion in austernite controls the gvowth, but the numerical constatnt is two orders of magnitude below that suggested by the model. THE growth of bainitic plates in steel is often assumed to be controlled by the diffusion of carbon away from the advancing plate tip. This hypothesis predicts that the growth rate will increase as the carbon content of the austenite, xCz, is reduced toward the carbon content of the saturated ferrite comprising the plate tip, PxCY The growth rate should vary approximately as (xCg- pxCy)-1. Experimental observation of the growth behavior at low carbon levels should provide a significant test of this model. An alloying element in addition to carbon is required so that low-carbon austenite can be experimentally observed while undergoing bainitic transformation. Nickel was selected. The presence of nickel complicates the interpretation of the data in two ways: First, diffusion of nickel during the transformation would make analysis very difficult. Nickel is assumed immobile during the transformation. Second, nickel affects the solubility of carbon in ferrite and austenite in equilibrium. This effect has been evaluated.' At the completion of our experimental work Goode-now et al.2 published data in essential agreement with the observations to be reported here. Since their discussion is abbreviated and their data are scanty in the region of interest, we believe the present work is of significance. I) THE MODEL OF BAINITIC PLATE GROWTH The rate of lengthening of a plate is assumed to be controlled by the diffusion of carbon from the advancing ferrite-austenite interface into the surrounding austenite. The precipitation of carbides is assumed to be a secondary process. For ease of analysis the carbon-atom ratio,* pxCy, of austenite in equilibrium with ferrite which is convex with minimum curvature radius p, and the carbon-atom ratio, PxCY, of that ferrite in equilibrium with austenite are assumed independent of location on the ferrite-austenite interface. Since these carbon contents vary with the radius of curvature of the ferrite, p, their assumed positional independence must be held as an approximation. The consequences of these assumptions have been developed approximately by zener3 and Hillert,4 and the resulting equation for a platelet has been applied to bainite by Speich and cohen5 and Kaufman, Radcliffe, and Cohen.8 The Zener-Hillert equation* for plates is: The analysis of Hillert is supported by that of Hor-vay and cahn7 which involves no mathematical approximations but does include the assumption that the a/y interface coincides with an isoconcentration line. The solutions of Horvay and Cahn for elliptic paraboloids are replotted in Fig. 1. The shape of the paraboloid is expressed in terms of the ratio of the principal radii of curvature at its tip, A =p1/p2, which is also the ratio of the minor to the major axis of the elliptic cross section. The Zener-Hillert equation for plates is also plotted. The agreement is within a factor of two for (pxyaCr - xyC )/(xyC - PxCaY) between 0.5 and 100. This is the range of interest here and in most other work on bainite. The original form of the Zener-Hillert equation was the form given above with the right-hand side replaced by (pxCya -xCy)/(PxCya). This replacement is not appropriate here. 11) THE EXPERIMENTAL PROCEDURE Alloys were prepared and three kinds of experiments carried out. Continuous-cooling-transformation experiments were carried out on wires by measuring temperature and resistance during continuous cooling. Isothermal-transformation experiments were carried out on wires by measuring electrical resistance as a

Jan 1, 1968

By Robert E. Green, Robert A. Swanson

Ultrasonic attenuation and stress were measured simultaneously as a function of strain for aluminum single crystals tested in compression. The propagation mode and polarization of the ultrasonic waves were chosen with reference to the theoretical analysis presented in Part I. Good experimental agreement was found with this theory and with earlier experimental work in tensile tests. Support is given to the contention that ultrasonic -attenuation measurements are much more sensitive to the early stages of plastic deformation than are conventional stress -strain measurements. Dislocation meclzanisms are suggested which are compatible with both the present and the earlier experimental observations. A brief historical introduction of previous work concerned with the study of dislocation motion by ultrasonic-attenuation measurements has been given in Part I. The purpose of the present experimental investigation was to make use of the theoretical considerations from Part I in order to gain further knowledge concerning dislocation motions during plastic deformation. Emphasis was placed on the choice of propagation modes and polarization of the waves, such that interactions between these waves and dislocation movement on a specific slip system could be investigated. EXPERIMENTAL PROCEDURE Since the primary concern of this investigation was dislocation damping, other sources of damping were eliminated as much as possible. The test specimens were 0.5-in.-diam single crystals of 99.99+ pct pure aluminum grown from the melt by a modified Bridgman technique. Ultrasonic-attenuation measurements were made at a frequency of 10 megacycles per sec using a Style 56A001 Ultrasonic Attenuation Comparator manufactured by Sperry Products Inc. after a design by Chick, An- derson, and Truell.1 At this frequency the particle vibrations are essentially adiabatic and thermo-elastic damping should be absent. This frequency was selected since it was one of the frequencies used by Hikata et al.2 n conjunction with tensile tests on aluminum crystals, thus allowing direct comparison with this work. The use of quartz-crystal transducers insures that the amplitude of vibration is not sufficient to cause the break away of the dislocation loops from weak pinning points. The quartz-crystal transducers used all possessed a resonance frequency of 10 megacycles per sec and were thin circular discs 0.375 in. in diameter. X-cut crystals were used to generate the longitudinal waves and AC-cut crystals to generate the transverse waves. Aluminum was chosen as the basic material because it is a typical fcc metal whose deformation behavior is well-known and because the most recent work at the time the present research was initiated was that by Hikata et al. who used aluminum. The present tests were run in compression to see if such tests could be satisfactorily run in compression without being severely masked by grip effects.. A second reason was to compare the results in compression with those of the tension experiments of Hikata et at. Finally, shorter specimens could be run in compression with less over-all damping than in tension. All of the aluminum-crystal test specimens used were oriented for plastic deformation by single slip; i.e., they possessed the orientation having a maximum Schmid factor of 0.5. Because of the well-known time dependence 3 of plastic strain at constant stress, the test specimens were subjected to a quasi-static loading. Previous investigations4-' have indicated that attenuation after plastic deformation is also time-dependent, so any continuous loading of the specimen would show that changes in attenuation were also a function of strain rate. By loading the specimen to a given stress level and holding it constant until the recovery process was essentially complete, the time dependence was eliminated. The quartz transducer was permanently bonded to the aluminum crystal using Eastman 910 cement. Excess cement was removed from around the quartz with DMF (dimethyl formamide). Eastman 910 was found to be far superior for bonding, especially with regard to the shear-wave transducer, since it formed a solid bond which readily supports shear-wave propagation. The solid bond formed by the Eastman 910 cement also insured that the quartz

Jan 1, 1964

By J. W. Goss, M. J. Coolbaugh

Most grouting has been done to stop water flaw in mines and for stabilizing foundations of various man-made structures, a survey of the U.S. literature reveals. Apparently Sun Manuel is one of the first mines in this country to use grout extensively underground for strengthening and stabilizing ground in drifts, shafts, and stations. A comparison with other procedures as well as details of the Sun Manuel program are covered. The employment of pressure grouting as a ground stabilizer at the San Manuel Copper Corp. mine reduces delays in both development and production, lowers costs, and makes possible safer working conditions. It specifically reduces delays in haulage operations and permits the maintenance of normal ventilation. In development work this grouting allows faster excavation by cementing together highly fractured or broken ground that otherwise would require extensive cribbing or spiling. In drift repair, it consolidates the loose or fractured rock over the timber or steel drift supports, thus decreasing the frequency of repair, lessening the hazards from falling rock, and curtailing delays due to blockage of drifts by muckpiles and repair operations. Pressure grouting is the process of pumping an accurately controlled mixture of cement and water into loose, fractured, or porous rock. The ratio of water to cement varies according to the nature of the rock encountered, from the thinnest mixture of 30 gal of water per sack of cement, used to fill very fine fissures, to very thick grout of 5 gal of water per sack of cement, used to fill large fissures or extensive areas of loose, broken rock. The pumping pressures at San Manuel vary from about 100 to 1000 psi, depending upon the compactness of the rock, while at other mines the pressures sometimes go as high as 5000 psi. In order to grout an area in which ground water is encountered, the pumping pressure of the grout must be increased by an amount equal to the pressure of the ground water. GROUTING IN DEVELOPMENT WORK The areas under development at San Manuel include many sections of loose, highly fractured rock. Prior to the advent of the grouting program, drifts, shafts, and stations in these areas could not be excavated without utilizing extensive support such as cribbing, spiling, and breast boarding. This slowed down the development work and increased the costs considerably over that required for excavating in more competent ground. Now, when a particularly bad area is contacted, the mining is temporarily stopped while the bad portion of drift or shaft is grouted. After the grouting is completed, the excavating is resumed with an approximate decrease of 50 pct in lost time and costs. Grouting in Drifts and Turnouts: The grouting procedures and patterns used in drifts and turnouts are very similar. The standard procedure for grouting such a turnout is shown in Fig. 1. After the ground is supported as well as possible with cribbing or lagging, the gaps between the back lagging and side lagging are plugged with empty cement sacks or additional timber, if necessary. The ground surrounding the proposed turnout is then grouted in two stages. In the first stage, the broken and caved rock is drilled and grouted to a depth of 5 to 10 ft, depending on the depth of the broken rock. This stage forms a grouted seal that allows higher pressures to be used at depths beyond 10 ft without developing excessive leaks at the face. After a grout hole is drilled, a 10-ft long pipe is wedged tightly into it with empty cement sacks. Grout is then pumped into the hole until the pressure reaches 200 to 300 psi, and the pipe is subsequently removed if it hasn't become cemented in. No more than one hole at a time is drilled and grouted because the grout has a tendency to go from one hole into another, plugging up the latter. Five or six holes are usually adequate for the first 10 ft of grouting. Experience has shown bentonite to be a useful admixture to the grout, particularly when it is indicated that the grout is being lost into large fissures or voids. Bentonite increases the plasticity of the grout enabling it to remain in place more easily until it has begun to set. In the second stage, the longer holes are drilled through the previously grouted rock, after which the

Jan 1, 1961

By Ben-Zion Weiss, Melvin R. Meyerson

Chromium diffusion coatings on commercial Armco iron lead to carbide precipitation at the grain boundaries in and below the coatings. High compressive stresses are introduced into the coating and, as a result, tensile stresses are introduced into the base material below the coating. In coated samples, fatigue cracks form at the grain boundaries below the coating after only a limited portion of the total lifetime (5 to 10 pct). Residual tensile stresses and a stress concentration caused by precipitated carbides seems to be responsible for early crack nucleation. Stage I of Propagation may be divided into two substages: I-a in which the crack Propagates along grain boundaries, and I-b in which the crack propagates along slip boundaries according to a shear mode. In uncoated samples, the cracks form at slip bands after 40 to 50 pct of the total lifetime. In coated samples the Propagation process takes longer than in uncoated samples because of the moderate rate of crack extension until the crack breaks through the coating. The chromium-diffusion coating causes little if any increase in fatigue life. CHROMIUM diffusion is one of the most popular processes used to apply coatings to iron alloys. This popularity stems from the fact that the diffusion treatment is comparatively easy to carry out, and it improves certain surface properties such as corrosion and wear resistance as well as some other properties. Very little effort has been devoted to the investigation of the effect of chromium-diffusion coatings on mechanical properties and particularly on fatigue properties. Since the chromium coating usually represents a small fraction of the total volume of the base material it is generally assumed that the macro properties are dependent principally on the base material rather than the coating. Insofar as fatigue is concerned, there are indications that the fatigue life of the chromium coating is not less than that of the basic material and the fatigue properties are generally not reduced by it.' But chromium diffusion causes drastic structural and chemical changes in the region of the material surface2-4 which introduce additional residual stresses. Such changes must affect fatigue crack nucleation and may sometimes affect the initial stages of propagation. Furthermore, it is conceivable that the secondary stages of the crack propagation could be influenced by some irreversible structural changes in the core of the material, which stem from the long-time heat treatment at high temperatures required to apply the coating. This paper analyses the structural and compositional changes produced in commercial Armco iron by a chromium-diffusion coating and the effect of the coating on fatigue crack initiation and propagation. EXPERIMENTAL PROCEDURES The investigations were carried out with commercial Armco iron. The chemical composition of the iron, the number of specimens tested, the grain size produced during chromizing and heat treating, and the thickness and microhardness of the chromized layers are shown in Table I. Samples were chromized by a gas diffusion process. The temperature and time of the diffusion coating process were chosen according to a previous grain growth study. It had been found that at a temperature of 970°C and a holding time of between 3 and 9 hr there are practically no changes in grain size. To describe the grain size more accurately the ASTM method5 was supplemented by a statistical analysis of the mean volume diameter as outlined by Fullman6 and The The mean volume diameter was deter- mined from D = p/2m where D is the mean volume diameter, and m is the mean reciprocal value of grain diameters as seen on the micrograph. The shape and the size of the asymmetrical sample, see Fig. 1, were chosen so as to facilitate the study of fatigue crack initiation. Before coating, the samples were machined and the surface of the groove was polished. After chromizing, the two side surfaces were machined and polished so as to retain the coating only on the top surface of the groove. Residual stress in the chromized layer was measured on the top of the grooved section of the specimen after the diffusion process. The inclined incident X-ray beam procedure was used.9'10 The computations were performed with the initial assumption of a zero surface normal stress component. An electron microprobe analyzer was used to obtain the relative amounts of chromium and iron con-

Jan 1, 1970

By J. E. Drury, W. M. Byers, E. J. Lynch

Measurements made with starch ~~~~s indicate that the Presence of starch serves to depress the streaming potential of a clay mud system. Measurements with pure starch slurries show that the addition of NaCl or CaO reduces the streaming potential significantly. The addition of NaOH, however, causes only a minor reduction in potential even when there are large changes in mud resistivity. INTRODUCTION In their excellent study of the streaming potential, Hill and Anderson' proposed that the presence of conductive solids within the filter medium will reduce the generated potential. This theory was demonstrated with measurements on shaly sandstone cores having various "b" factors; the cores with the higher negative b factors showed markedly lower potentials. (The factor b was originally defined by Hill and Milburn2 in an expression relating the resistivity of a shaly sandstone to the resistivity of the interstitial water: log F, = log F,, + b (log 100R,)'. 'he factor b, therefore, is a measure of the contribution of the conductive solids to the total conductivity of the sample. It has been found experimentally to be directly related to the amount of chemically exchangeable ion per unit pore volume.) In the logical extension of this hypothesis to the streaming potential created by filtration through mud cakes, they suggested that the presence of nonconductive starch in a drilling mud would have the opposite effect; i.e., it would cause the streaming POtential to be increased. The high streaming potentials that they observed with lime muds were attributed to this cause. A cross-plot of some of their results which are relevant to this discussion is given in Fig. 1. The lime-mud curves and untreated-mud curve are taken from curves given in their paper. The gyp-mud line was estimated from their statement that the measured streaming potential for gyp muds in the range of 1.5 to 2.0 ohm-m was approximately 18 mv/1,000 psi. These gyp-mud potentials were the lowest that they reported for any of the bentonitic-clay muds, and were the only ones which were less than the untreated-mud potentials. This very low streaming potential of gyp muds has also been observed in field studies.' By way of comparison, a U. of Texas publication4 gives the approxi-ate compositions for lime and gyp muds shown in Table 1. These materials are added to a bentonitic-clay mud base. It can be seen that both of these muds contain significant amounts of calcium salts and that the gyp mud has the higher concentration of starch. It would appear from this and from the data shown in Fig. 1 that starch may well be the cause of a streaming-potential reduction, rather than a potential increase. EXPERIMENTAL A series of streaming-potential experiments has been performed using a cell of a design similar to that reported by Wyllie.5 Calomel electrodes were used in both the mud slurry and the filtrate. Pressure in the cell was generated with high-pressure nitrogen. The primary objective of the investigation was to determine the effect of starch on the potential. Five different slurries were made which ranged in composition from untreated ben-tonitic mud (Baroid Aquagel) to a pure starch suspension (Baroid Im-permex). The intermediate slurries were prepared by mixing together a 9-lb/bbl clay mud with a 12-lb/bbl starch suspension in the ratios 1:3, 1:1 and 3:1. When starch was used alone, it was necessary to use an 18-Ib/bbl mixture, since leaner mixtures would not form a suitable filter cake. The clay mud used in the experiments was aged for three months before use. In addition to this series of measurements on the starch-clay mud mixtures, other experiments were performed to determine the effect on the potential of the absolute starch and Aquagel concentration, and the effect of adding various chemicals. RESULTS The effect of starch on the streaming potential is shown clcarly in Fig 2. Increasing percentages of starch resulted in n continually decreasing

By Ian MacGregor

INTRODUCTION I retired in 1977 and have been enjoying myself ever since doing odd jobs for various people - on occasions, politicians. I commend it to you as post retirement - get involved in situations that nobody else will take on. It produces all sorts of excitement, it is a lot of fun and, courtesy of the media, you provide great raw material for their current Punch and Judy shows. The example of the adventures in the Escondida financing made me think about the history of the minerals industry in the United States. In order to see more clearly what is going to happen in the future, we have to look at the past and what we have learned, and try to extrapolate from that a scenario for the future. This paper is about global material cycles and the financial needs of the extractive industries. Since about 2,000 years B.C. we have been living in the Iron Age. Since about 4,000 B.C. we have been living in the Copper Age. These have been the two foundations of modern industrial society. Understanding the use of metals and materials helps us understand the civilization in which we live today. Let me focus more closely on the United States, particularly in this century. In the first two-thirds of this century the United States was growing and expanding and developing. It was providing for its inhabitants a society which was enjoying the benefits of a rising standard of living, improved opportunities and the ability to support a population growing at quite a dramatic rate. It is still growing. In the Department of Commerce, there is a clock that shows how many people there are in the United States. It turns all the time; the numbers are going up. On January 21,1980, when Ronald Reagan was sworn in as President, the number on that clock was a little over 220 million, and in the last week before he left, it was travelling towards 245 million. During his period in Washington, we have added , the equivalent of one total state such as California. That gives the dimensions of the U.S. appetite for raw material inputs. The inputs are of critical importance. COMPARATIVE ADVANTAGE During the first two-thirds of this century, the minerals sector enjoyed comparative advantages. There was a clear understanding of the importance of minerals enshrined in the tax legislation of the country from the early decades of this century - the depletion allowance. No other country identified as clearly that the supplies of minerals were finite. As they are used up, just as with a wearing-out machine, one must get capital back to replace the resource when the time comes. Within the last decade, that idea has been questioned and criticised. It is now seen as giving money away to a preferred part of the economy, instead of recognizing what depletion is all about. In previous times it insured that the U.S. always was able to regenerate the capital in its minerals industry, so that it could remain competitive. The U.S. had plenty of everything, including energy. We had a growing population. Equally important, we had an agriculture that led the world in productivity, even as far back as the turn of the century. It continues to do so. We still retain that comparative advantage, an ability to produce our foodstuffs in quantity and quality at excellent cost. Look at another ingredient of our comparative advantage, the energy position. We ran through the first two-thirds of the century with ever- decreasing energy costs. In the 1940s and 1950s the coal industry went into a decline. Why? Because the $3.00 - $5.00 a ton cost of mining coal in the U.S. represented relatively expensive energy. A ton of good grade bituminous coal contains 25 million BTU's. $0.20 a million BTU's represents $5.00 a ton at the pithead. That price was undermined by the increasing ability to find petroleum at even lower costs. At the apex of the growth of development of the American dominated

Jan 1, 1990

By M. E. Wadswort, A. S. Peck

Infrared data disclose that phenacite reacts with oleic acid to form a chemisorbed oleate monolayer on the mineral surface. The absorption band characteristic of the antisymmetrical C = 0 oleate structure appears at a spectral wavelength of 1623 cm-'. Chemisorption also results in the displacement of OH- and silicate from the mineral surface. Infrared absorbance at 1623 cm-1 is correlated with float-ability at different pH for -60-mesh phenacite particles. Phenacite, Be2SiO4, is an ore mineral often associated with quartz, microcline, and chrysoberyl in pegmatites and mica schist. Experimental phenacite beneficiating processes have been confined principally to the flotation of low grade ores occur-ing in several mountain ranges of Utah and Nevada. The U.S. Bureau of Mines ' has recently reported on the separation of phenacite from ore deposits of Mount Wheeler, Nev. Infrared techniques were previously applied by the authors to characterize the role of sodium oleate and oleic acid in the flotation of several non-sulfide minerals.23 A parallel study was projected to the flotation of the orthosilicate mineral phenacite with oleic acid. Infrared spectra provided a 'molecular fingerprint' of the mineral surface and permitted identification of the reaction mechanisms. Infrared data were complemented with flotation and chemical tests. EXPERIMENTAL PROCEDURES The experimental procedures used in this investigation, for which data are presented in graphical or spectral form, are described in chronological test order. Phenacite crystals from Mt. Antero, Colo., were obtained from Ward's Co., Monterey, Calif. The crystals were fragmented in a porcelain mortar to -60 mesh and then pretreated with 0.5 molar HC1 for 15 min to remove iron. Then, the mineral particles were washed free of acid with distilled water and dried. Part of the dried material was ground to a fine powder with a Fisher Grinder using an agate mortar and pestle. Next, the powder was placed in a graduated cylinder and mixed with 500 ml of distilled water. The mineral in suspension was decanted from the settled fraction after 5 min, and the colloidal suspension was used for adsorption tests in which a high specific mineral surface area was required for adsorption and infrared analysis. Conditioning was performed in 50 ml glass centrifuge tubes for both infrared and flotation test determinations. Twenty ml of colloidal suspension was used for the infrared adsorption tests. One and a half g of deslimed -60-mesh HCl pretreated phenacite was added to 20 ml of distilled water for flotation conditioning tests. Six mg of oleic acid was used for each infrared adsorption test, and 0.2 mg of oleic acid was used for the flotation conditioning tests. HCl and NaOH were used for pH modification. The pulps were stirred at a speed of about 1500 rpm for 3 min. Then, the solids were separated out and either dried at 50°C or immediately transferred to a float cell. The pH of the residual liquid was determined with a Beckman Zeromatic pH meter. The flotation procedure is described as follows: 1) A 325-1111 glass micro-float cell was filled with distilled water. 2) Conditioned mineral was placed in the cell and the pulp was aerated through the glass fritted bottom at 7 psi pressure. 3) Floated mineral was skimmed from the cell with a glass slide until flotation ceased. (The end point was reached in all tests in less than 2 min.) 4) The flotation products were dried, weighed, and the recovery was calculated. Samples for infrared analysis were made into mulls using either oleic acid or series 13-21 Halocarbon oil obtained from Halocarbon Products Corp., Hacken-sack, N.J. The mulls were placed between two sodium chloride windows. A characteristic phenacite infrared band at 1868 cm-' was used as an internal standard for quantitative determinations in which absorbance at this position was quantified by the baseline-tangent method4 and related to absorbance at 1623 cm-'. The ratio obtained by dividing absorbance at 1623 cm-' by absorbance at 1868 cm-' was defined as an absorbance quotient for use in graphical presentation.

Jan 1, 1968

By J. C. Wilhoit, J. B. Cheatham

Although an oil well is a long cylindrical hole with an irregular bottom, it appears likely that the nature of the stress concentration at the bottom of the hole can be ascertained from an analysis of the stresses around a short cylindrical cavity with rounded comers and smooth bottom. Such a cavity is studied primarily because it leads more readily to a solution to the problem by the use of stress functions. In this paper the stress distribution around a short cylindrical cavity subjected to bit loading, overburden and drilling-fluid pressures is determined by means of an analytical solution which approximately satisfies the boundary conditions of the problem. From this solution the stresses at the corner of the hole are calculated to be about 35 per cent lower than comparable results obtained by photoelastic and relaxation analyses. This difference is apparently due to the large radius of curvature at the corner of the cavity in the present analysis. Since good agreement is obtained between the results of this analysis and the stresses calculated for a similar loading on a semi-infinite elastic solid, it is concluded that the bit action in the region near the center of the hole is not appreciably affected by the presence of the sides of the hole. INTRODUCTION Much has been written concerning drilling "under down-hole conditions" and pertaining to the stress distribution in the rock at the bottom of an oil well.1-5 For example, it is known that identical rocks can be drilled more rapidly at the surface than under subsurface conditions of pressure and stress.6 Information on the behavior of rocks under loading can be obtained from triaxial test data.7-9 From such tests it is found that rocks exhibit brittle failure when the confining pressure and pore pressure are equal, but the mode of failure may change to ductile as the difference between the confining pressure and the pore pressure is increased. Brittle failure implies that there is very little permanent deformation before fracture, whereas ductile failure indicates that permanent deformation takes place before fracture. Some rocks are ductile at differential pressures of 5,000 psi , but other rocks are brittle even at differential pressures of more than 50,000 psi. Cuttings embedded in mud at the bottom of the hole may act as a plastic mass which the bit teeth must penetrate in order to attack the virgin rock below. 10 During drilling, the mud pressure acts as the confing pressure, and in many cases the difference between the mud pressure and the formation pore pressure IS sufficiently low so that the rock most likely falls in a brittle manner. Very little penetratiori by the bit teeth may be required for brittle failure of the rock. For these brittle materials, the elastic stress distribution is of practical interest in determicing the possible effects of a given loading on failure. The penetration of bit teeth into ductile or plastic rock has been analyzed previously ll,12 and will not be considered further in the present work. During actual drilling, many teeth act at various points ovel an irregular hole bottom. In the present analysis a solution is obtained for an idealized problem of determining the elastic stress distribution caused by only one tooth acting alone at the center of a smooth hole bottom. It obviously is not proposed that any driller should put a special one-tooth bit on bottom, but it is hoped that extensions of the simpler problems can eventually lead to a better understanding of more complex actual drilling phenomena. To obtain a solution by the use of stress functions, a short cylindrical cavity with rounded corners and smooth bottom is studied. The solution to this problem should give an insight into the nature of the stress concentration at the bottom of an oil well which is in reality a long cylindrical hole with an irregularr bottom. After selection of the proper curvilinear co-ordinate system, the stress functions are expressed as series of Legendre polynomials. The coefficient of each term in the series is then determined to satisfy the boundary conditions at a finite number of discrete points on the boundary of the cavity with least square error. Results are compared with bottom-hole stresses obtained by photoelastic and relaxation analyses.

By H. L. Marcus, C. D. Turk

Titanium was physically vapor-deposited by electron beam high rate evaporation. Rates of 50,000 and 85,000Å per min at deposition temperatures of 480°, 535°, and 595°C were used. Deposited thickness ranged front 0.004 to 0.010 in. The evaporated titanium had a high degree of basal Plane texture. The specimens were tested in tension at temperatures ranging from 78° to 520°K. From the data, the yield stress, thermal component of the yield stress, and work hardening characteristics were found as a function of temperature, deposition rate, and deposition temperature. It was found that Taylor's equation, best fit the work hardening data with m = 1/2. MANY investigations have been made on the tensile deformation characteristics of commercial- and high-purity titanium.1"7 The data obtained from these experiments emphasize the fact that the mechanical properties are generally related to the method of production. The correlation of mechanical properties to production history arises from the dependence of impurity concentration on the extraction and melting technique used. Additional effects are derived from crystallographic texturing which can result from fabrication history. Lee and Backofen8 and other investigators9 have shown that crystallographic texturing in titanium sheet has a significant effect on the deformation characteristics. Bunshah and Juntz10 prepared high-purity titanium by high rate physical evaporation techniques. These authors found the deposited material to have a columnar structure with grain sizes ranging from 12 to 104 µ, depending upon the substrate temperature. The room-temperature strengths of the coarse-grained distillate were similar to arc-melted, rolled. and annealed crystal bar titanium. Commercial-purity titanium was also produced experimentally in our laboratory using high rate physical vapor deposition techniques. The commercially pure material has a finer structure than the high-purity distillate,10 and is highly textured. Since the method of preparation and degree of texturing affect the mechanical properties, a research program was initiated to determine the temperature dependence of the yield stress and work hardening characteristics as a function of high rate deposition parameters. This paper relates the results of the investigation. EXPERIMENTAL A) Material Preparation. The titanium was received in the form of commercial-grade 0.096-in.-diam wire which has a composition of 0.016 pct C, 0.0037 pct N, 0.110 pct 0, 0.011 pct H, 0.05 pct Mn, 0.051 pct Fe. balance Ti. The wire was continuously fed into a vacuum evaporation unit as shown schematically in Fig. 1. The deposition chamber was evacuated, purged with argon, and reevacuated to a pressure of 10-5 Torr which was maintained during deposition. A focused electron beam was used to evaporate the titanium from a water-cooled copper crucible. The titanium vapor was condensed onto a preheated titanium substrate. The temperature of the substrate was controlled within ±5°C for the deposition temperatures of 480°, 535°, and 595°C. Control of the input power enabled the use of two deposition rates. 50,000 and 85,000Å per min. The evaporated titanium had a final analysis similar to that of the input titanium, within experimental limits. B) Testing. The evaporated titanium was physically stripped from the titanium substrate and machined into tensile specimens with 1-in. gage lengths. In addition, tensile specimens of as received annealed 35-A titanium sheet with a 20 µ grain size and 45 pct cold-rolled 35-A were also prepared. All specimens were tested in tension in an Instron at a strain rate of 3.3 x 10"4 in. per in. per sec. Proportional limit has been used as a measure of yield strength. Tests were conducted at 78°, 220°, 300°, and 520°K. Metallography, X-ray diffraction, and electron microscopy were used to correlate structure with the deposition parameters and mechanical properties. Room-temperature X-ray measurements were made to determine the phases present. Pole figures and a scans were made to determine deposition texture. Because the vapor deposition was symmetrical about the normal to the substrate, there was no preferred di-

Jan 1, 1969

By D. Turnbull, J. H. Hollomon

THERE is a large body of evidence'" indicating that solidification during the liquid-solid transition is usually induced by heterogeneities present in the liquid. By dispersing liquid metals into small droplets, the impurities responsible for catalyzing solidification are isolated within a small number of these droplets. The effect of the foreign body therefore is restricted to a single drop by this technique. Thus upon cooling below the melting temperature, solidification is initiated by homogeneous nucleation in the majority of the droplets that do not contain impurities. In the case of solidification of liquid metals, the activation energy for nucleation is so great that its rate changes by orders of magnitude for a change in temperature of only several degrees centigrade.' Effectively homogeneous nucleation occurs at a critical temperature upon continuous cooling. Thus by microscopic observation of single particles during cooling, a temperature at which the rate of homogeneous nucleation becomes sensible can be determined.3 since at the temperatures at which nucleation occurs in the absence of impurities the rate of crystal growth is extremely rapid, the temperature at which the entire particle solidifies is very nearly the temperature at which the nucleation of the solidification occurs. Thus for liquids that freeze at high temperatures the onset of nucleation can be established by simply observing the temperature at which the marked heat evolution and increase in brightness of the particle occur. For liquids that freeze at lower temperatures the onset of nucleation can be determined by a rumpling and change in shape of the particle resulting from its solidification. The microscopic technique for observing the solidification of small particles has already been described." In earlier papers the nucleation of solidification of pure metals 5,6 and of alloy systems7 showing complete liquid and solid solubility have been described. In the present paper, the observations are extended to a simple eutectic system (Pb-Sn) where the possibility of the formation of two solid phases exists. Metals for the investigation were obtained from the American Smelting and Refining Co. in the form of pure lead and pure tin, 99.8 and 99.9 pct purity, respectively. An ingot of each of the pure metals was made into shot by heating the metals at a temperature about 50 °C in excess of the melting point and pouring the liquid slowly into a container of water at 15°C. Samples of the shotted pure metals were weighed out to make alloys containing 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, and 90 atomic pct Pb. Samples of each alloy were then melted in separate beakers. Each melt was poured through a pyrex funnel into a cylindrical mold (% in. ID). The casting solidified in 10 to 20 sec. The inside of the mold as well as the funnel through which the metal was poured were coated with graphite to eliminate adherence of the metal. Analyses were performed on some of the compositions and are given in Table I. The compositions also were checked for these samples and for those that were not analyzed by determining the spread between the liquidus and the solidus upon melting the small metal particles. These measurements agreed as well with the nominal compositions as the analyses listed above. Results The results of the supercooling experiments for the several alloys are summarized in Table II and plotted on the constitution diagram in Fig. 1. Data for the pure lead and pure tin were taken from earlier investigations. The values for the maximum supercooling of the several alloys are the average of several determinations on a number of drops of each alloy. The maximum value in any determination was within about 2 pct of the average. For the alloys containing from 20 to 60 atomic pct Sn, inclusive, two marked changes of the surface structure were observed upon cooling. At the higher temperature, after the first appearance of the solid phase it continued to grow slowly at a constant temperature and then stopped. At the lower temperature the alteration of surface structure was abrupt. For the alloys containing from 70 to 95 atomic pct Sn, inclusive, an abrupt change in surface structure was observed at a single critical temperature.

Jan 1, 1952

By P. R. Celmer, Leonard R. Weisberg

THE principle of fractional crystallization has been successfully used to prepare high-purity (99.999 pct) Ga. Hoffman and Scribnerl removed single crystals of gallium solidifying in a gallium melt, while Zimmerman2 grew single crystals from the melt by the Kyropolous technique. In contrast, attempts at purifying gallium by zone refining have been less successful. ichards, reported that despite the passage of 40 zones through a gallium ingot, there still remained 5 to 70 ppm each of Cu, Fe, Ca, Mg, Si, Al, and Ag. Previously, Detwiler and Fox4 detected only one impurity, Pb, segregating in zone-refined ingots. These surprising results prompted an investigation of the factors controlling impurity segregation in gallium. Possible reasons for this were insufficient diffusion of impurities in the melt; recontamination of the melt by its oxide film which is not affected by the passage of the zone; reaction of gallium with the boat; sudden freezing of gallium following supercooling, especially since gallium easily supercools to and trapping of impurities at grain boundaries. Impurity segregation tests were carried out by directionally freezing gallium using the Bridgman rnethd, modified in that the molten gallium is lowered out of a furnace into a slush of dry ice and trichloroethylene, thus minimizing supercooling. Since the gallium is contained vertically, the oxide film is in contact only with the tail end of the melt. It was found that Teflon makes an excellent crucible for gallium since it is quite pure, non-reactive, translucent, flexible, machinable, and is not wet by gallium. The gallium crystals could be grown at various speeds, and the melt could be vigorously stirred by a Teflon rod moving through the gallium in a vertical reciprocating fashion. Single crystals could be grown by placing a solid Teflon plug at the bottom of the melt drilled out in such a way to cause the solidifying gallium to follow a winding path. Thus, even if many crystals are originally nucleated, only one grain will predominate. The grain structure of the gallium crystals was revealed by an etchant composed of equal volumes of HC1, HNO3 and HF, diluted with water to half strength. Emission spectrographic analyses were carried out on samples removed from the front and tail ends of the resulting gallium ingots. Typical results of this study are summarized in Table I. The rate of freezing in all three cases was about 1 in. per hr. It can be seen that even though stirring of the melt does help, it is even more important to grow a single crystal of Ga in order to obtain good segregation of impurities. The effect of crys-tallinity on the segregation of impurities was previously observed6 in the directional freezing of germanium; however, in this case, the effect was much less pronounced. This dependence of impurity segregation on the crystalline perfection of Ga may be related to its thermal conductivity which is the most anisotropic of all metals.7 The anisotropic thermal conductivity can cause the solid-liquid interface to be nonuniform, thus leading to trapping of impurities during freeing, and therefore reduced segregation. In conclusion, it is indicated that zone refining of gallium would be more successful if seeding and similar precautions are taken to insure single crystal growth. The authors are indebted to Mr. H. H. Whitaker for the spectrographic analyses and to Drs. B. Abeles and F. D. Rosi for helpful advice and encouragement throughout the course of this work. This research was supported by the Electronics Research Directorate, Air Research and Development Command, under Contract No. AF33(616)-5029. REFERENCES 'J. 1. IToffmon and B. T. Scribrer: I. Research h'atl. Bur. Standards, 1935, "01. 15, p. 205. 'W. Zirnmerman: Science, 1954, vol. 119, p. 41. %J. L. Richards: Nature, 1956, vol. 117, p. 182. 'D. P. Detwiler and W. M. Fox: I. Metals, 1955, "01. 7, p. 205. 5P. W. Bridgman, Proc. Am. ilcod. Sci., 1925, vul. 60, pp. 305,385,423. "S. L1. Christian: private c ommuni cation. 'K. W. Powell: roy. Sac., 1951, vol. 209, p. 525. 'W. G. Pfann: Zone Re fining, p. 20. John Wiley and Sons, Inc., New York, L058.

Jan 1, 1962