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By Brian F. Dyson

The surface tensions at 1550°C of some Fe-S alloys (in the range 0.008 to 0.052 wt pct S), Fe-Sn alloys (0.31 to 48.4 wt pct Sn), Fe-P alloys (0.038 to 2.38 wt pct P), Fe-Cu alloys (2.15 to 22.8 wt pct Cu), and Fe-1 pct C-S alloys (0.005 to 0.076 wt pct S) along with the surface tension of the base iron have been measured by the sessile-drop method. A mean value of 1754 dynes per cm was found for the surface tension of the base iron. Sulfur was found to be highly surface-active, the surface-tension results being in quantitative agreement with existing data. Tin and copper were found to be less surface-active than sulfur while phosphoms was completely nonsurface-active. The surface tensions of Fe-1 pct C-S alloys were found to be lower than those of the Fe-S alloys containing the same sulfur content. This was shown to be a mmzifestation of the increase in the thermodynamic activity of suZfur by carbon. It is only in recent years that attempts have been made to measure the surface tension of liquid iron of known high purity.1-3 Earlier measurements4-7 were made on liquid iron containing variable amounts of what are now known to be surface -active solutes. The exact value of the surface tension of liquid iron is still, however, open to some doubt. Halden and Kingery' reported a value of 1720k 34 dynes per cm at 1570°C, Kozakevitch and Urbain8 gave 1790k 25 dynes per cm at 1550°C, while Van-Tszin-Tan et al. obtained a value of 1865k 37 dynes per cm at 1550°C. The first systematic investigation into the effect of controlled solute additions on the surface tension of iron was made by Halden and Kingery.' They showed that sulfur and oxygen were highly surface-active, whereas nitrogen was only slightly active, and carbon inactive. A subsequent investigation by Kingery indicated that two other group-6B elements, selenium and tellurium, were also surface-active. This highly surface-active nature of sulfur and oxygen has recently been substantiated by Kozakevitch and Urbainla and Van-Tszin-Tan et al. l1 Kozakevitch and Urbainl2 have also conducted an experimental survey of the effects of a number of metals on the surface tension of liquid iron. Their surface-active nature was, in all cases, less than that of the group 6B elements. The present investigation was undertaken to study in more detail the surface tensions of dilute Fe-S alloys and to measure the surface tensions of binary alloys of iron containing phosphorus, copper, and tin. The effect of sulfur additions on the surface tension of Fe-1 pct C alloys was also determined. EXPERIMENTAL PROCEDURE The sessile-drop method was employed in the present investigation. An apparatus was built similar in principle to that described by Humenik and Kingery.lS It consisted of a horizontal silica tube, which could be evacuated to pressures less than 10-5 torr, with its central portion surrounded by a water jacket within which was a high-frequency coil. This generated heat in a tantalum susceptor placed inside the silica tube, which in turn radiated heat to the specimen mounted on a recrystallized alumina plaque. Temperatures were measured by an optical pyrometer and photographs of the molten drop were taken on a fixed-focus plate camera giving a magnification of X2. Surface-tension values were determined from the resultant drop using the method described by Baes and Kellogg.l4 The high vapor pressure of molten iron made it necessary to conduct all the experiments under a 1/4 atm of argon (greater than 99.995 pct purity). The analysis of the base iron used in the investigation is given in Table I. Each sample was approximately 3 g in weight and had a hemispherical base to ensure a uniform advancing contact angle on melting. The iron alloys were prepared individually in the sessile-drop apparatus by drilling a hole in the top of each sample and adding the required amount of solute, the drops being analyzed after the experiment. This method of preparation had the advantage of ensuring a consistent minimal contamination by oxygen due to refractory attack and also allowed surface tension to be measured at the same time. Every precaution was taken to ensure that the specimen was not contaminated by grease when it was introduced into the apparatus, the samples being cleaned in acid, dried in alcohol, and rinsed in petroleum ether. All handling was done with tweezers. Once the specimen had been placed inside the susceptor, the furnace was evacuated and the Sample leveled. The furnace was then degassed at approximately 1000"C before the argon was introduced. In every case the surface tension was determined at 1550" C.

Jan 1, 1963

By P. Wynblatt, J. E. Dorn

The effect of strain rate, temperature, and interstitial impurity concentration on the flow stress was investigated in a poly crystalline Fe-2 pct Mn alloy. The temperature dependence of the flow stress was found to be independent of the interstitial impurity concentration, removal of interstitials merely decreasing the atherma1 stress level. Below 160%, the large temperature dependence of the flow stress was interpreted in terms of the Dorn-Rajnak theory of the Peierls mechanism of plastic deformation. Above 160"K, some other thermally activated intrinsic meckanisln seems to be operating. The strong temperature dependence of the flow stress of bcc iron at low temperatures has been studied by numerous investigators and interpreted in terms of several different thermally activated dislocation mechanisms. The following mechanisms have been proposed: a) interaction of dislocations with interstitial impurity atoms1 or with solute atoms in general; b) interaction of dislocations with clusters of impurity atoms;3 c) resistance to the motion of dislocations due to jogs on screw dislocations;* d) resistance to the motion of dislocations due to the Snoeck effect;' and e) interaction of dislocations with the intrinsic resistance of the bcc lattice or Peierls "hills". In previous work: it was found that the plastic behavior of polycrystalline iron containing 2 wt pct Mn (and 100 ppm C + N) is in good agreement with predictions based on the Peierls mechanismlo from 77" to 160°K whereas from 160" to about 370°K another as yet unidentified thermally activated mechanism is operative. The purpose of the present investigation was to determine the effect of interstitial impurities on the temperature dependence of the flow stress, by purifying the previously investigated alloy with respect to interstitial impurities. The investigation revealed that removal of the interstitial impurities to a level that eliminated Cottrell locking and the Portevin-LeChatelier effect (i.e., serrations in the stress-strain curve due to dynamic strain aging) affects neither the strong temperature dependence of the flow stress at low temperatures nor the general characteristics of the higher-temperature behavior. Such purification, however, lowered the athermal yield stress. I) EXPERIMENTAL PROCEDURE AND RESULTS The material used in this investigation consisted of an Fe-2 wt pct Mn alloy having the following additional elements present: 0.004 pct C, 0.006 pct N, 0.05 pct 0, 0.004 pct S, 0.003 pct P, and 0.001 pct Si. This was the same material as that studied in the previous investigation and will henceforth be referred to as the "impure material". The as received -jr by 2 in. hot-rolled bars were cold-rolled to 0.08-in. thickness, recrys-tallized under argon for 30 min at 80O0C, and further cold-rolled to 0.053-in. thickness. Flat tensile specimens 3 in. wide having a 1.625-in.-long gage section were machined from the sheet and then purified. The first stage of purification consisted of holding the specimens at 850°C for 24 hr in a stream of hydrogen saturated with water vapor at room temperature. Material prepared in this fashion will subsequently be referred to as "wet hydrogen purified material". It has been estimated that this type of treatment reduces the carbon content of iron to less than 5 ppm.' The second stage of purification consisted of holding the specimens in a closed system through which hydrogen was circulated past the heated specimens as well as a zirconium hydride getter. The specimens were held at 850°C and the getter at 800°C. The process was continued for 212 hr. The starting material for this process was wet hydrogen purified material. Material prepared in this manner will be referred to as "ZrHz purified material". The technique used was substantially the same as that described by Stein et al.' who have shown that the carbon level at the end of the process is reduced to about 5 parts per billion. The mean grain size of the three materials was found to be -60 C( for the impure material and -160p for the wet hydrogen and ZrHz purified materials. All tensile testing was carried out on an Instron Testing Machine either in controlled-temperature baths or at fixed-point baths such as boiling liquid nitrogen, and so forth. When fixed points were used the temperature was kept constant to better than *1°C whereas in all other tests the temperature variation was less than *2°C. Test of Purity. It was not possible to determine the purity achieved at each stage of the purification because the resulting level of interstitial impurities was near or below the limit of sensitivity of standard analytical techniques. It was possible, however, to obtain a qualitative measure of the extent of purification from the appearance of the stress-strain curves for the three materials. Fig. 1 shows the stress-strain curves for the three different materials tested at 300°K. It can be seen that the effect of wet hydrogen

Jan 1, 1967

By P. G. Shewmon, H. E. Collins

A study has been made to determine the sites at which sulfur adsorption occurs on copper surfaces. measurements were made of the relative torques, Ys, at the intersection of twin boundaries with surfaces near the three low-index orientations, i.e., (100), @lo), and 011), over a range of H2S/H2 ratios. HZS concerztvations j'ro~n 3 to 1500pp)n between 830" and 1050°C were used. It is concluded that sulfur adsorption occurved preferentially though not exclusively at edge sites near the (100) and (110) surfaces in the HzS range — 700 Ppm giving rise to negative torques near these orientations. Beyond this HzS range, adsorption occurred at all sites. Near the (111) surface, 7/y little with HzS concentration up to approxiwzately 75pptn. Above this range, the results indicate adsorption is occurring OH both terrace and edge sites. SCIENTIFIC interest in surfaces and their interactions with a gaseous environment dates back to the beginning of the 19th century. The scientific luminaries of that period—Faraday, Maxwell, Rayleigh, Dewar, and Gibbs—were already concerned about such processes. However, it has only been within the past several decades that adsorption on metal surfaces has been actively studied. This increased interest in adsorption has been brought about by the advent of new and improved experimental techniques and apparatus, e.g., ultrahigh vacuum, and field-emission and ion microscopes. However, most of the work done using these techniques has been carried out at low temperatures. When adsorption studies have been made at either low or high temperatures, they usually gave no indication of the particular surface orientations or type of sites on which adsorption was occurring. In the last few years, there have been a series of studies in which the surface tension, y,, and/or its derivative with respect to orientation, 7, have been studied as a function of orientation and atmosphere.'-7 Nearly all of the work on the relative torque,* ~/y, silver annealed in hydrogen and air.6 Recently Winterbottom and Gjostein" have used a modified and more accurate Mykurian method to determine the y plot of gold in hydrogen The only work in which T/~, has been measured over a range of chemical potentials for a given solute, p2, is that of Robertson and shewmon7 on the Cu-0 system. They measured T/Y, vs Po, (10"" to 10- l3 atm) at 1000°C in various mixtures of Hz0 and HZ. From this work they estimated the value of p2 at which one half of the surface sites are occupied with oxygen, pg, as being in the range 10- l6 to 10- l5 atm of oxygen. They also found that increasing Pa increased the magnitude of ~/y, near the (111) and (100) orientations. This indicates that oxygen is not adsorbed preferentially at step edges, but uniformly over all surface sites. In addition, they did one experiment on sulfur adsorption on copper surfaces, which indicated that sulfur adsorption decreases ~/y, near the (100) orientation, while not affecting ~/y, near the (111). This could be interpreted as indicating that sulfur adsorbs preferentially at step edges near the (100). In this paper the primary objective of the work has been to carry out a study of sulfur adsorption on copper surfaces over a range of temperatures and p,. In conjunction with this work, thermal grooving at grain boundaries has been examined as a method of determining the effect of sulfur adsorption on y,. METHODS Ideally, one would like to have information on the quantity of solute adsorbed on a surface and the types of sites at which it is absorbed as a function of p2. The total quantity adsorbed or the surface excess is given by the thermodynamic equation Thus data on the variation of y, with pz indicates the value of p2 at which adsorption becomes appreciable and the quantity adsorbed. The type of adsorption site is more difficult to deduce but information on this can be obtained from the variation of rz with 8, the angular deviation of the surface orientation. This is obtained from the thermodynamic equationlg Data on t and ys as functions of p2 have been obtained by the following methods. 1) Twin Boundary Grooving—By determining the effect of adsorption on the torque, 7, where T is the variation of surface energy, y,, with orientation, it is possible to obtain some indication as to the preferred sites of adsorption. Experimentally, the torque value measured is the relative torque, 7/ys The twin boundary grooving technique suggested by Mykura'' was used in this study to determine near the three low-index orientations— (loo), (110), and (111). Mykura's equation relates 7 /yS to measurements of the di-

Jan 1, 1967

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.'- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin' has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled' that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By Klaus Schwerdtfeger

The equilibria in the Cr-N system have been investigated in the temperature range 1100° to 1310°C by reacting chromium powder with Nz-Hz gas mixtures. The solubility of nitrogen in chromium in equilibrium with chromium subsitvide ("Cr,N") is given by Chromium subnitride is nonstoichiotnetric; its nitrogen content is always less than that corresponding to the formula CrzN. The lattice paranzeters of quenched samples have been measured; c, and a. parameters are found to increase with increasing nitrogen content. The growth rate of the subnitride layer on chromium plates was measured by a thermogravimetric technique, using a silica spring balance. The self-diffu-sivity obtained from the theoretical analysis of the parabolic rate constant is found to decrease with increasing nitrogen content, i.e., with decreasing vacancy concentration in the nitrogen sublattice. The intrinsic nitrogen diffuivity is derived from another series of rate measurements using "CrzN" plates; the intrinsic diffusivity, DN = 3.2 X 10-a cmZ sec-' at 1200 C, is found to be essentially independent of- the subnitride composition. The concentration gradient was measured in a chromium subnitride layer by the X-ray method and found to be consistent with the derived diffusivity value. TWO chromium nitrides are known to exist:' the nonstoichiometric subnitride "CrzN" and the nitride CrN. In the present work the kinetics of the formation of chromium subnitride from chromium and nitrogen have been investigated at 1100" and 1200°C. In additional experiments the relevant equilibria have been measured. The data are used to evaluate the diffusivity of nitrogen in chromium subnitride. Since chromium nitrides are often found in chromium-containing steels, the results are expected to be helpful in the interpretation of the chemical reactions between chromium steels and nitrogen. Equilibria in the Cr-N system have been determined by several investigators.2"3 The rate of nitriding of chromium was measured by Arkharov et a1 .' in ammonia in the temperature range 800" to 1200°C. The parabolic rate law was observed. Due to the undefined nitrogen activity of the ammonia atmosphere, it is dif- ficult to interpret these rate data theoretically. An additional difficulty arises from the fact that the two-layer scale consisting of CrN and "Cr2N" was formed at the temperatures below 1030°C. The rate of nitriding of technical chromium (95 pct) was measured by Zaks in nitrogen at -1 atm in the temperature range 800" to 1300°C. EXPERIMENTAL METHODS The chromium samples were reacted with Nz-HZ gas mixtures in a vertical tube furnace, wound with Pt-10 pct Rh resistance wire. The gas-tight reaction tube was of high-purity recrystallized alumina. In nitrogen solubility measurements the nitrogen content of chromium was determined by the Kjeldahl method, on samples quenched in the cold part of the furnace. The nonstoichiometry of the subnitride and the nitriding rates were measured thermogravimetrically using a sensitive (+0.1 mg) silica spring balance. For the equilibrium measurements samples of 1 g of chromium powder contained in high-purity alumina crucibles were used. In order to remove most of the oxygen and nitrogen impurities from the chromium, the samples were initially annealed in purified hydrogen until a constant weight was obtained. The chromium plates (approximate dimensions 2 by 1 by 0.08 cm) used for the rate measurements were machined from ingots obtained by arc-melting of iodine-processed chromium. According to manufacturers' specifications the purity of the chromium powder was 99.9 pct Cr and that of the iodine-processed chromium 99.99 pct Cr. Our own spectroscopic analysis of the chromium powder yielded 0.02 pct Fe, 0.05 pct Mn, 0.05 pct Si, and 0.02 pct Ti as major impurities with all the other detectable elements below 0.005 pct. The nitrogen partial pressure of the gas phase was controlled by mixing prepurified hydrogen and nitrogen with constant pressure head capillary flowmeters. Oxygen and water vapor were removed from the mixed gas by passing it through columns of platinized asbestos (450°C) and anhydrone. The gas flowed upward in the furnace with flow rates of 300 to 500 cu cm per min (25"~). Gas tightness of the furnace system was ensured by pressure checks at regular intervals. The furnace temperature was controlled electronically in the usual manner. The reported temperatures were measured with a Pt/Pt-10 pct Rh thermocouple and are estimated to be accurate within ±$C The X-ray measurements were made with a Debye-Scherrer camera and a diffractometer using chromium radiation {\Ka = 2.29092A). EQUILIBRIUM MEASUREMENTS The experimental results of the equilibrium measurements are contained in Tables I to In. Fig. 1 shows the solubility of nitrogen in solid chromium in the temperature range 1100" to 1310°C. In Figs.

Jan 1, 1968

By E. Amott

A test is described in which the wellubility of porous rock is measured as a function of the displacement properties of the rock-water-oil system. Four displacemet operations are carried out: (I) sponlaneous displaceti?ent of water by oil, (2) forced displacement of water by oil oil in the same system using a centrifuging procetllrre, (3) spontaneous displacement of oil by water. and (4) forced displacment of oil by water. Ratios of the spontaneous displacement volumes to the total displucenlent volumes are used as wettability indicates. Cores having clean mineral surfaces (strongly preferentially water-wet) show displacement-by-waler ratios approaching 1.00 and displacement-by-oil ratios of zero. Cores which ([re. strongly preferentinlly oil-wet give the reverse resu1ts. Neutral wellability cores show zero values for both ratios Fresh cores from different oil reservoirs have shown wettabiltties in tlris te.st covering rrlti~ost 111e conlplrtt, range of thr: te.st. Notvever, nlo.s/ of tlle fresh California cores tested were slightly prcfere111icrlly wclter-\vet. The chrrnge.~ in coro u ('liabilities, as indicated hy this te.st, r~.sril/ing from various CO~P hanrlling procedures tt,ere oh.served. In sonie ca.sc,s /Ire ~,cttahilitio.c. of fresh cores were changell by drxi:~g or 11y e.x/rclct ing with iolcreiii~ or. dioxunc~; in o/h~r cases they were 1101 changed. Co~ltrrc/ of cort,.s ~.ith filtrc~t~c. from water-base rlrilling rilrrrls crlrc.sed littlc change in we/ /ahility ivhile contnct with filtrates frorii oil-hus~ ri1rlcl.s tlecrrascrl the prefcrerlcc, of the, cores for )I.NI Usitig thi,s test to ri.crl~lute n~r~ttubili~y, N .vt~ldy was iilarle of /lie correlmtio~i of wettability with wa/erfloocl nil recovery for orttcrop Ohio sand.stone and for Al~ln-tlunl. Resul/.v indicate thml no single correlatioti between these factors applies to different porous rock syste~n. It is thought that diflerences in pore gen~netry resrrlt in diflrrerrce.~ in this correlurio~z. INTRODUCTTON Most investigators who have reported on the wettahility of porous rock have described such rock as prcferentially water-wet or preferentially oil-wet. In some cases a third classification, neutral wettability. has been used. The efficiency of water floods in each of these wettability groups has been described in numerous publications. Several methods for characterizing porous rock wet tability more precisely have been reported,' " but it appears that because of one weakness or another. none of these has been generally accepted. Early in our studies in this field, it was found that the displacement efficiency of oil by water in a particular porous rock having a strong preference for water was quite different from that in a similar rock having only a moderate preference for water. Thus, there appeared to be a need for a practical, reasonably precise wet tability test. one which could classify porous rocks into 10 to 20 different groups rather than the two or three broad groups listed above. The test developed to meet this need is described in this paper. Also, changes in wettability, as indicated hy this test, resulting from various core handling procedures are discussed. Finally, data showing the corrclation of wettability with waterflood oil recovery for two different types of cores are presented and discussed. Some confusion has resulted from the failure of certain writers to define clearly some of the wettability terms they have used. Accordingly, the following commcnts concerning definitions are offered. The wc t ta-hility of a solid surface is the relative preference of that surface to be covered by one of the fluids under consideration. It is felt that this is the generally accepted definition. The fluids being considered must bc specified (or understood) before the term wettability has any significance. In the work reported here these fluids are water (3 per cent brine) and oil (kerosene). The term preferential wettability is sometimes used, but we think that the word preferential is redundant here and should not be used. Tn line with the definitions of Jennings', a preferentially oil-wet solid surface is regarded as a surface which will show an oil advancing contact angle less than 90" (measured through the oil) in the water-oil-solid system. Oil will spontaneously displace water, if both are at the same pressure, from such a surface. A preferentially water-wet surface is analogous. This is consistent with the wettability definition above. As Jennings has said, frequently the term oil-wet is used to mean the same thing as preferentially oil-wet. However, oil-wet also has been used occasionally referring to an oil-covered surface when the availability of water was limited. To avoid confusion from this source, we do not use the terms oil-wet and water-wet. DESCRIPTION OF WETTABTLITY TEST The following points were considered desirable in a wettability test for our purpose. 1. The test should be a displacement test resembling

By J. G. Patchett, R. W. Rausch

Fresh waters and the presence of clay in many Rocky Mountain and West Coast sands require special methods of log analysis. Archie's saturation equation requires addition of a shale correction term, and the SP equation must also be modified to account for clays. Suitable equations were developed several years ago, but have not been widely used due to the algebraic complexity. A computer-oriented method has now been developed to overcome this problem. The basic shaly sand equations are rearranged in four different ways to permit solution for various sets of available input data. Essential to application of the method is the correction of observed SP values to those that would be observed if the resistivity of the formation waters were exactly interchangeable with the activity. A graphic method for doing this is given. Where conditions require consideration of the effect of clay in the sands, the method presented has been found to improve the accuracy of water-saturation determinations. INTRODUCTION Log interpretation in many Rocky Mountain and West Coast basins is complicated by rapid vertical and lateral changes in water resistivity. Calculation of formation water resistivity from the SP curve becomes difficult in zones that contain clay, since changes in SP deflection may be due to changes in either clay content or water salinity. In hydrocarbon-producing reservoirs, the problem is further complicated because hydrocarbon saturation also reduces the SP.1 A log interpretation system using computers has been developed to provide a solution to this problem, based on equations proposed by de Witte.2 Four different simultaneous solutions of de Witte's equations have been made. Each solution method uses a different set of input data as independent variables. Thus, a choice of solution method is possible, depending upon the logs run and the availability of other data. Two of the solutions do not require a knowledge of water resistivity. This system is intended to be used primarily in multiple sandstone-shale sequences of low and moderate resistivities where the principal contaminant in the sandstones is clay. However, where sufficient regional data are available, interpretation in single-zone sandstone reservoirs can also be improved by using the method. THEORY AND HISTORY OF SHALY SAND ANALYSIS The log interpretation formula originally proposed by Archie3 in 1941 is applicable only to rock-fluid systems wherein the rock has negligible electrical conductivity. In 1949, Patnode and Wyllie4 showed that if the rock itself can be considered conductive due to the presence of clay, a different calculation approach is necessary. During the following years, this problem was investigated at great length, as was the related problem of the effect of rock conductivity on the SP.5-11 These investigations established functional relationships between SP, resistivity, water saturation and water resistivity for such a formation. Refs. 2 and 12 provide summaries of these studies. Unfortunately, practical use of these relationships required that water resistivity be known independently from the SP. Although log interpretation methods for rock systems containing clay were proposed at that time,' they were not generally accepted for routine use. There are three principal reasons for this. First, in many field situations involving high-salinity water, rock conductivity may be neglected (even if present) without introducing appreciable error. This may be seen by considering the following expression for waier-saturated rock.' 1/R2=1/R1+1/FRn....(1) where 1/R, is conductivity due to clay. As Rw becomes small, I/FRw becomes much greater than 1/R, which may be neglected. Where 1/R, may be neglected, the sandstone is called clean. If the term may not be neglected, the sandstone is termed dirty or shaly. For resistivity purposes, the classification between clean and shaly sands then depends not only upon the conductivity due to shale in the sand, but also upon the resistivity of the associated water (shale is used here to mean surface condition due to disseminated clay). A sand of given conductivity might safely be treated as clean in association with high-salinity water, but would require shaly sand methods if associated with fresher waters. Shaly sand methods are not required in many areas having saline waters; but in Rocky Mountain and West Coast sands having relatively fresh waters (often more than 0.3 ohm-m resistivity at formation conditions), the shaly sand methods are needed. Errors Rw calculations from the SP due to the presence of shale are likewise related to water salinity. In saline water formations drilled with fresh mud, the ratio of mud filtrate resistivity to water resistivity is high, the SP is large and the presence of shale can introduce large errors in water resistivity calculated by the conventional method. When the resistivity ratio is low, the errors are smaller. At zero SP, no error would result from shale. Thus, from the SP viewpoint, a given rock could be shaly if associated with a saline water, and clean in association with a fresh water, which is the opposite of the resistivity-oriented definition above.

By M. I. Jacobson, A. S. Yue, A. E. Vidoz, F. W. Crossman

An equation governing the concept of constitutional supercooling under the combined effect of concentration and temperature gradients was used to produce platelike Al-CuAl2 eutectic composites for mechanical properties studies. Compression specimens were prepared from a single-colony Al-CuA12 eutectic composite ingot, 2 in. in diam and 12 in. long. The specirrzens were cut such that the platelets were oriented parallel, 45 deg, and perpendicular to the compression direction. Since the ingot was of eutectic composition, The aluminum-rich matrix could dissolve 5. 7 wt pct Cu in solid solution, and therefore could be strengthened by precipitation hardening. Specimens were tested at room temperature and elevated temperatures in the unidirectionally solidified, solution-treated, and solution-treated plus aged conditions. The results were compared with those for the conventionally cast and extruded specimens. For the controlled material, the highest strengths were obtained with platelets oriented parallel to the compression axis. In the unidirectionally solidified condition, 0.2 pct offset yield strength was 32,000 psi; however, this was increased to 59,000 psi by solution treatment, and further increased to 90,500 psi by solution treatment and aging. The attainment of high compressive strengths in the Al-CuAl2 eutectic composites was interpreted in terms of the buckling of elastic CuAl2 platelets in the plastically deformed a aluminum matrix. SINCE the discovery of high-strength whiskers,' scientists and engineers have made significant progress toward incorporating these whiskers into metallic matrices, forming composites for basic studies and structural application. The general procedure is to produce the whiskers first and then to bind them together with a ductile matrix. The production of whisker-reinforced composites requires tedious handling techniques,, particularly when it is desired to align the whiskers unidirectionally. Furthermore, the interfacial bond between the whisker and the matrix is frequently poor3 so that the resulting composite has strengths lower than expected. These disadvantages are generally true for any metallic composite produced by physically mixing the components. It is possible to eliminate these shortcomings by growing whiskers directly in the matrix material by eutectic solidification.4-8 In eutectic solidification, the matrix phase and a whisker phase are grown approximately simultaneously from a liquid of the same overall composition at the eutectic temperature. If the solidification process is controlled by varying the freezing rate, the temperature gradient, and the impurity content, platelike or filamentlike whiskers are produced parallel to the growth direction. The morphology of the grown-in reinforcement, i.e.. plates or rods, generally depends on the volume fraction9 of the dispersed phase present in the eutectic mixture. Since the unidirectional eutectic solidification is a one-step process, i.e., the liquid-solid transformation process, an excellent interfacial bond between the matrix and whisker is obtained. An additional advantage is that no special handling technique for whiskers is needed. In recent years, many investigators10-13 have studied the effects of growth variables on the micromorpholo-gies of binary eutectic alloys produced by controlled solidification. The study of their mechanical properties was initiated by Kraft and coworkers14-16 who found that the strength of cast A1-CuA12 eutectic alloy can be increased threefold by unidirectional solidification. In the A1-AL3Ni system, a strength of 50,000 lb per sq in, was reported for the unidirectionally solidified eutectic alloy, a value five times higher than for conventionally cast material. Thus, the unidirectionally solidified eutectics can be used as fiber-reinforced composite materials. In this paper, we shall first use an equation17 as a guide for the production of eutectic composites in general and the Al-33 wt pct Cu eutectic in particular. Experimental data supporting the theoretical prediction are given. Second, the compressive properties of the grown A1-33 wt pct Cu eutectic were thoroughly investigated in terms of platelet orientations, thermo-mechanical treatment, and temperature. The experimental data are interpreted in terms of a buckling model of fibers in elastic fiber-plastic matrix metallic composites. EXPERIMENTAL PROCEDURE Crystal Growth. The following experimental procedure was adopted for the production of controlled microstructures in the A1-33 wt pct Cu eutectic alloy. The controlled solidification was accomplished with a movable resistance-wound radiation furnace. Fig. 1 is a schematic drawing of the solidification apparatus. A water-cooled chiller was placed into a degassed high-purity graphite crucible containing the charge. Rubber stoppers wrapped with aluminum foil were used to seal both ends of the quartz tube through which a dried argon atmosphere was passed under a slight positive pressure. At both ends of the quartz tube, radiation shields were used to minimize heat loss. The quartz tube was held in place by two steel clamps and the furnace was drawn vertically by means of a steel cable against the steel truss which permits the furnace to move without touching the tube. The drive mechanism consisted of two pulleys, a counter weight.

Jan 1, 1969

By R. B. Burt, James A. Barr, I. S. Tillotson

THE pumping of solids in water suspension is an important part of many metallurgical and mining operations. In most cases, it is still in the rule of thumb category for which no universal formula has been developed, and much research is needed. Because of the limited and incomplete data available, this article may be classed as an experience paper, which is presented with the hope that some contribution will be made toward the development of the so-called universal formula. This formula, if and when developed, may be evolved from several factors, many of which are not now available for general application. The designing engineer is interested in obtaining accurate forecasts on: 1-the minimum velocities needed to prevent choke-ups in the pipeline, which in turn dictates pipe sizes, 2-power required for pumping, 3-pump selection. The basic factors for a given problem will include: 1-weight per unit of time of solids to be handled, 2-specific gravity of solids, for calculation of volume, friction and power, 3-screen analysis of solids with the colloidal acting, i.e., the slime fraction, a very important factor, 4-shape of particle or some means of determining a friction constant, 5-effects of percentage of solids, 6-development of a viscosity factor to be used in the overall calculations, 7-calculation of the lower limits of pipeline velocities permissible, 8-calculation of total head, pump horsepower, and 9-setting up of pump specifications. In certain limited cases horsepower and total heads and minimum velocities may be computed and a suitable pump selected from basic data, but in many cases, as in mining of Florida pebble, phosphate, experience rather than a hydraulic formula still should be used as a basis of selection. Pumping Florida Pebble Matrix Pumping at the Noralyn mine of International Minerals and Chemical Corp. will be used as an example. Other areas will vary as to the characteristics of the matrix, especially the slime content. A typical screen analysis of this matrix is: +14 mesh, pebble size,* 2.1 pct; -14 +35 mesh, 11.4 pct; -35 +150 mesh, 60.5 pct; -150 mesh, 25.0; total, 100 pct; moisture in bank, 20.0 pct; weight per cu ft in bank, 120 lb. The -150 mesh fraction may increase to as much as 35 pct in adjacent areas. When thoroughly elutriated, the matrix has a relatively slow settling rate, which is an important factor in permitting lower pipeline velocities without choke-ups. Exact data is not available to evaluate settling rates. For a factor of 100 a suspension of clean building sand in water is suggested. When pumping long distances, a quick settling matrix allows the coarser solids to settle out along the bottom of the pipeline, causing drag, turbulence, and increased friction. With a slow settling matrix as at Noralyn, turbulence acts to keep the solids in suspension at a lower friction head, regardless of the pumping distance. When the pebble, content of the matrix, i.e., the +14 mesh fraction, is in excess of 10 pct of the total solids, trouble may be expected from settling out even in normal pumping distances. To prevent choke-ups and maintain tonnage, an additional pump must be added in the long runs, where one pump would otherwise be satisfactory. A typical pulp handled is: total volume, 7800 gpm; water, 4500; solids pumped per hr, 4200 lb; sp gr pulp, 1.4; percent solids in pulp, 46.; pipe size, 16-in. ID; pulp velocity, 12.85 fps; probable critical velocity, 10 fps, as below this minimum -velocity choke-ups would be numerous. In calculating friction heads the Armco handbook is used where a roughness factor based on 15-year-old pipe is set up. Because the pipe used in pumping matrix is, smooth and- polished because of the scouring, action of the phosphate and its silica content, the head losses in the Armco table for water are practically the same as in pumping the Noralyn matrix through smooth pipe, plus the fact that conditions vary widely over short periods, making accurate determinations difficult to obtain. New pumps and pump, changes are being tested continuously and a wealth of data built up. This has resulted in a substantial improvement and lower relative costs in pumping matrix. The Florida phosphate industry is constantly seeking to offset higher wage and material costs with improved technique. Until a few years ago a 12-in. discharge pump was commonly used, with heads as low as 80 ft. Sizes have gradually increased and heads more than doubled. For example, the following pump was placed under test at the Noralyn mine: make, Georgia Iron Works; size, suction 16 in., discharge 14 in.; impeller, 39-in. diam; motor, 600 hp, slip ring; full load speed, 514 rpm. The results were increased head, higher capacity than the older design, with fewer pumps in the line from mine to washer.

Jan 1, 1952

By R. H. Jamison

A relatively new haulage system is described. Employed by the Delmant Fuel Co.. the "Full Dimension" system provides an uninterrupted flow of coal from a loader or continuous miner at the face to the main line transportation system. This system is said to provide a higher percentage of recovery as well as additional safety and production. Delmont Fuel Co. is employing a comparatively new system of transportation known as a Full Dimension system. Cne of these systems has been in operation for a year at the company's 10-B Mine as a part of a conventional section. A second was installed at the No. 10 mine in late 1960 to handle the production of a Colmol in a pillar section. SYSTEM COMPONENTS A Full Dimension system is a haulage system that provides an uninterrupted flow of coal from a loader or continuous miner at the face to the main line transportation system. The equipment required for this system consists of a series of interconnected chain conveyors that are mobile and articulated. They will retract or extend a sufficient distance for the development of a five-entry system; or, in the Colmol pillar section, it provides reach of 210 ft in all directions from the section belt. The components of this system are: l)One 160-ft chain line placed in tandem with the belt conveyor. It has a self-propelled drive, is 20 in. wide and 9 in. deep. Moving this conveyor requires the assistance of a loading machine or cutting machine. 2) One 40-ft piggyback that discharges along the entire length of the 160 ft chain conveyor. 3) A mobile bridge carrier, which is a self-propelled conveyor with four wheel steer and four wheel drive, twenty-eight feet long, it delivers coal to the receiving end of the piggyback. Axles steer individually making possible almost lateral movement. 4) Another 40-ft piggyback, duplicate of item 2 that delivers coal along the entire length of item 3 (mobile bridge carrier). 5) A second mobile bridge carrier, similar to the first, which deliver coal to the piggyback (item 4). 6) A third 40-ft piggyback, duplicate of items 2 and 4. This pig is attached to the loading machine and delivers its coal along the length of the second mobile bridge conveyor. Since the original preparation of this paper, the Delmot Fuel Co. has been able to eliminate the 160-ft chain conveyor. This was accomplished by connecting the outby piggyback directly to a loading machine with an extended boom. The loading machine loads directly onto the belt. This change has resulted in a substantial reduction in moving time and greatly increased flexability. A single trailing cable powers the entire string of equipment. It is attached to the side of the equipment in such a way as to keep it off the ground and afford maximum protection. The tramming rate of this equipment is 90 fpm. The conveyor capacity in a conventional section at Delmont's mines is 7.5 tpm and in the Colmol section is 5.5 tpm. This regulation is a simple function of conveyor speed. To visualize operation of this equipment, it would be well for me to touch briefly on local conditions in the Upper Freeport seam in which we mine. (Also, see the photographs of some of the equipment in use.) DELMONT'S TOPOGRAPHY The Delmont Fuel Co. operates two mines in this seam in Westmoreland County, Pa. The No. 10 mine, which was opened in about 1912, is now almost worked out. Depending on economics in the industry, it has a life of two to four years on a declining production basis. A year ago a new drift mine was opened which is called No. 10-B. It is about two miles from the cleaning plant and is connected thereto by an overland belt conveyor. The new mine is being developed at a rate calculated to take up the slack as the old mine plays out. The Upper Freeport seam averages 4.2 ft in thickness in the area of the Delmont mines. It carries 4 in. of boney coal at the top of the seam and a middle man of from 2 to 4 in. We mine just above a 1-in. slate parting which has 4 to 6 in. of highly laminated coal beneath it. This material normally makes a very firm bottom. The roof varies from dark shale to sand rock and 36-in. bolts are placed on 4-ft centers for roof support. All working places are driven 20 ft wide on development and 25 ft wide on retreat. Selection of mobile chain conveyor equipment when it became available, was a very natural move for Delmont Fuel to make, because chain conveyors and piggybacks had been in use at the company's mines for about 12 years. Grades in the new mine

Jan 1, 1961

By Hsun Hu, R. S. Cline

The annealing behavior and the mechanism of re-orientation during recrystallization of iodide titanium cold-rolled 94 pct have been studied in detail. Results indicate that recrystallization occurs by the nucleation and growth of new grains, as in other common metals. Recrystallization nuclei form by the coalescence of subgraim, and the change in texture as a result of recrystallization is largely due to selective growth among the nuclei formed. The annealing of titanium is characterized by a wide range of overlap of the various stages of the annealing process, which may be responsible for a range of activation energies observed, and for the apparently gradual change in the annealing texture as a function of time or temperature. The deformation and recrystallization characteristics of titanium and zirconium are very similar. In cold-rolled strip, the deformation texture consists of two symmetrically oriented components, each having the basal plane laterally tilted at about 30 deg from the rolling plane and the [1010] direction parallel to the rolling direction. Upon annealing for recrystallization, the change in texture can be described, for simplicity,* as rotations around [0001].2'6'8 According to McGeary and Lustman,' recrystallization occurs in zirconium through normal growth of the subgrains, which they called "domains", without the nucleation of new grains; and the magnitude of rotation around the [0001] axis increases gradually during the progress of recrystallization. If these conclusions were true, the mechanism of recrystallization in zirconium would be basically different from that in most metals, since it is commonly known that recrystallization with reori-entation always involves the migration of high-angle boundaries. In an attempt to clarify the situation, the mechanism of reorientation during recrystallization in iodide titanium cold-rolled 94 pct was studied in detail. The structural and textural changes upon annealing at various temperatures were examined by optical and transmission-electron microscopy, X-ray pole figures, pole density distribution measurements, and micro-beam techniques. EXPERIMENTAL PROCEDURE Material and Specimen Preparation. An iodide titanium crystal bar was are-melted and solidified in a cold-hearth crucible under a purified argon atmosphere. The solidified ingot had dimensions of approximately 3 by 1/2 by 3 in. One face of the ingot was somewhat uneven, but was as clean and shiny as the remaining parts of the ingot. Large grains with a Widmanstatten internal structure were clearly shown on the shiny surfaces, indicating the occurrence of P — a transformation upon rapid cooling from the melt. Analysis of the are-melted ingot indicated C 0.033, N 0.010, H 0.013, 0 0.002 in weight percent, and traces of iron, copper, and silicon as detectable impurities. The ingot was cold-rolled -40 pct to 0.300 in. thick with a reduction of 0.005 in. per pass. The defects on the uneven side of the ingot were then removed by machining. This reduced the thickness to 0.285 in. The piece was then recrystallized by annealing at 800°C for 1 hr in a fused silica boat charged into a fused silica tube furnace under a vacuum of 10~5 mm Hg. To refine the grain size, the recrystallized metal was again cold-rolled 40 pct to 0.170 in., then annealed at 700°C for 1 hr. These treatments yielded a strip with a uniform equiaxed grain structure, having a penultimate average grain diameter of 0.04 mm and a hardness of approximately 90 Dph. Final rolling reduced the thickness from 0.170 to 0.010 in., corresponding to a reduction of 94 pct. The strip was rolled in both directions by reversing end for end between passes. Surface lubrication was provided by oil-soaked pads attached to both rolls. Specimens of 1 in. length (for X-ray examinations) and +in. length (for hardness and microstructure examinations) were cut from the rolled strip, and a width of & in. was cut from the edges of each specimen by a jeweler's saw. These specimens were then etched in a solution of 10 cu cm HN03, 5 cu cm HF, and 50 cu cm H,O to 0.008 in. thick to remove the surface metal, as well as the distorted metal at the saw cuts, prior to annealing or measurements. To minimize any surface reaction with the atmosphere, all specimens were kept in an evacuated desiccator. Isothermal Anneals. All annealing treatments were conducted in vacuum in a fused silica tube furnace as described earlier. The temperature of the furnace was controlled to within *2"C. The specimen was placed in a fused silica boat, then pushed into the hot zone of the furnace. It took about 5 to 6 min for the specimen to reach the furnace temperature. After the specimen was held at temperature for a desired length of time the boat was pulled to the cold zone of the furnace; the heating-up period was excluded from the isothermal annealing time. Thus, the uncertainty in annealing time is higher for very short anneals, but negligible for long anneals.

Jan 1, 1969

By Nicholas J. Grant, Ulf Kalling, John Chipman

THE operation of a blast furnace is dependent to an important extent upon the sulphur content of materials charged and the desired limit of sulphur in the product. It has long been known that the blast furnace is the most efficient tool for desulphurization in common use and that this efficiency is associated with the strongly reducing conditions of the hearth and is enhanced by increased basicity and fluidity of the slag. The chemical reactions of desulphurization may be studied from the viewpoint of the ratio of the process or of the final equilibrium conditions. Both kinds of studies contribute to an understanding of the process and both are included here. A simple measure of the desulphurization power of a slag is given by the ratio: Pct sulphur in slag (Pet S) Pct sulphur in metal [Pct S] This ratio was used by Holbrook and Joseph',' to measure relative desulphurizing powers under controlled laboratory conditions. It was also used by Hatch and Chipman3 as a measure of the equilibrium distribution. For the latter purpose it would be preferable to employ thermodynamic activities rather than percentages, but until very recently this has been impossible for lack of data. Now, thanks to the work of Morris and Williams and Morris and Buehl," the effects of carbon and silicon upon the activity of sulphur in the metal are known. The confirmation of this work and its extension to include the effects of other elements by Sherman and Chipman and by Rosenqvist and Cox' make it possible to calculate the activity of sulphur in pig iron of any composition. Hence it is now possible to use data on the equilibrium distribution of sulphur to find its activity in the liquid slag and to approach an ultimate solution of the thermodynamic aspects of the problem. The rate of transfer of sulphur from metal to slag is the problem of major industrial importance and indeed the principal need for equilibrium data has been as a necessary adjunct to the kinetic studies. The rate of approach to equilibrium under laboratory conditions seems slow compared to the requirements of industrial practice, and it is clear that further laboratory studies of rates are needed. In the research reported below, the items which were investigated were the following: I—The role of mechanical stirring on the approach to equilibrium. 2—The role of MgO in desulphurization as compared to CaO. 3—The role of MnO in desulphurization. 4— The limiting reactions which constitute the slow steps in desulphurization. Experimental Procedure The experimental set-up and procedure previously described by Hatch and Chipman" were essentially followed with several small modifications. The graphite crucible containing the slag and metal charge was altered to provide considerably more active stirring and mixing of the slag and metal in the carbon monoxide atmosphere. For this purpose the crucible was machined to provide two deep cylindrical wells which were interconnected at top and bottom as shown in Fig. 1. A graphite screw with a flat thread and of shallow pitch (4 threads per in.) spinning at 600 to 800 rpm was used to lift the slag and metal over the partition between the two wells and throw them over into the second well, where the metal settled through the slag into the reservoir at the bottom. It was possible to see actual particles of slag and metal being thrown over the partition. In this respect, the stirring was more vigorous than used in the work of Hatch and Chipman. A charge of 400 g of wash metal was first melted, and 20 g of FeS was then added to yield a bath containing 1.65 pct S. Immediately 400 g of slag (as pure mixed oxides) was added and fused. The slag was generally fused in 1 hr * 10 min. Within 30 to 45 min after melting, the temperature was adjusted to 1525"C, and the first slag and metal samples were taken. The slag was picked up on the end of a cold Armco iron rod, whereas the metal was sucked into a silica tube. The wash metal composition was (in percent): 4.29 C; 0.022 S; 0.021 P; 0.38 Si. The slags used were of four fixed starting compositions covering a wide range of acid-base ratios shown in Table I. Deliberate variations in MgO were made in these slags to check the role of MgO in blast-furnace desulphurization. Changes due to additions and reactions were followed by analysis of samples. Additions of Mn and MnO were made to most of the heats to note the role of Mn and MnO on desulphurization. Three heats (62 through 64) were made in an open pot induction crucible (graphite) using a

Jan 1, 1952

By K. G. Wikle, W. W. Beaver

The factors which control the rate of dissolution of pure gold in cyanide solution were studied both directly and through measurement of solution the current-potential curves for the anodic and cathodic portions of the reaction. The mechanism of dissolution is probably electrochemical the reaction in nature, and the rate is determined by the rate of diffusion of dissolved oxygen or cyanide to the gold surface, depending on their relative concentrations. The significance of the results and the effects of impurities are considered. ALTHOUGH the dissolution of gold in aerated cyanide solutions has been used as an industrial process for treatment of gold ores since the late nineteenth century, the factors which determine the rate of the reaction have never been identified unambiguously. Studies of the rate of dissolution by Maclaurin,1 White,2 Christy,3 Beyers,4 Thompson,6 and others are contradictory in their conclusions; some claiming that diffusion of the reactants to the gold. surface controls the rate, and others that the chemical reaction is inherently slow and related to high activation energy for the reaction. Christy3 and 'Thompson" both suggest that the reaction is electrochemical in nature and that the dissolution of gold proceeds at local anodic regions while the oxygen is reduced at cathodic regions on the gold surface. Although their studies are ingenious and do indicate an electrochemical reaction under the conditions of study, their experiments were of limited nature and failed to identify the rate-controlling process in the system. The importance from an industrial viewpoint of a knowledge of the mechanism and rate-controlling factors in gold dissolution can be illustrated as follows: If the rate is controlled by a slow chemical reaction rather than by diffusion of the reactants, then an increased temperature should have a marked accelerating effect; agitation of the slurry should have no effect on rate: and increased concentration of reactants should cause acceleration of the rate. If the rate is controlled by the diffusion of one or the other of the reactants to the gold surface, then increased agitation should increase the rate; increased temperature will increase the rate, but not as much as for the case of a slow chemical reaction; increased concentration of the reactant which is diffusion limited will increase the rate; and the concentration of other reactants should be without effect on the rate. It may be concluded that for design of a commercial process for gold leaching, the rate-controlling factors of the reaction should be understood so that an intelligent choice of the conditions of agitation, temperature, and reactant concentration may be made. The experiments described here lead to the unambiguous conclusion that in a system of pure gold and a pure aerated cyanide solution the rate of dissolution is controlled either by the rate of diffusion of dissolved oxygen or cyanide to the gold surface, depending on the relative concentrations of each. There is also ample, but not conclusive, evidence that the mechanism of the reaction is identical to that of electrochemical corrosion. The practical significance of these conclusions will be discussed later in the paper. Experimental The experimental method used in this work was to employ an electrolytic cell which performed the overall gold-dissolution reaction, and to study the anodic and cathodic reactions of this cell as to their nature and the rate-controlling factors. Simple experiments on the rate of dissolution and the potential of the dissolving specimen also were performed under conditions of agitation, temperature, and concentration identical to those used in the electrode studies. Analysis of the electrode studies by well established theories of electrochemical corrosion were made, and the results were found to bear a one-to-one relation with actual rate and potential measurements. Electrode Studies: The Anodic Reaction: The gold specimen used for all of the electrode studies and the rate determination consisted of a sheet of 99.99 + pct Au wrapped around a lucite rod and sealed at the edges with plastic cement, thus forming a cylinder of gold of known and constant area (8.0 sq cm). The lucite rod was threaded into a brass spindle which could be rotated at speeds of 100, 300, and 500 rpm. For the electrode studies electrical contact between the gold cylinder and the brass spindle was made by means of a gold strip covered with plastic. The anodic dissolution of gold was studied by immersing the electrode in a solution containing known concentrations of KCN and KAu(CN)2 but free of oxygen, and by passing an anodic current through the gold electrode. The pH of the solution was maintained between 10.5 to 11.0 in these and all other tests by addition of KOH. The pH was measured before and after each test by means of a glass-elec-

Jan 1, 1955

By J. Weijdema, D. N. Dietz

In the conventional underground combustion process (dry combustion) much heat is left behind in the swept formation and goes to rva.rte. Econonmy can be improved by heat recuperation through water injection. This is most advantageous if done at the earliest opportunity before much heat is dissiputed to cap and base rock. Water injected simultaneously with the air will flash to superheated steam, which passes through the combustion front together with the nitrogen from the air. A condensation front traveling up to three times as fast as the combustion front drives out the oil. In this type of wet combustion, the water evaporates before it reaches the combustion zone. The evaporation front travels more slowly than the combustion zone. If so much water is injected that the evaporation front overrun the combustion front, combustion in that spot will be quenched and some unburned fuel will be left behind. Air reacts with the oil farther down-stream where steam temperatures occur; at steam temperature, the air reacts rapidly with the oil. Velocity of the combustion front is increased thereby and is governed essentially by the water-injection rate. In the extreme case of high water-injection rate, a short heat wave of constant length is driven through the formation by water injection. Once this wave has been established, no more heat need be generated than that required to make up the heat losses from the short heat wave; a relatively low rate of air injection will suffice. The feasibility of partially quenched combustion has been confirmed in tube experiments. A heat wave at steam temperature is observed. Chemical analyses of flue gas indicate preferential burning of hydrogen while a carbonaceous residue is left in the formation. Introduction A disadvantage of so-called dry in situ combustion is that air-compression costs are rather high. An air consumption of about 400 std cu m/cu m (400 scf/cu ft) of formation swept is an accepted figure. This high consumption is mostly wasted since much heat is left behind in the depleted oil sand. Methods were investigated for recuperating as much as possible of the heat left behind. This paper deals only with basic principles and is confined mainly to one-dimen- sional flow without lateral heat losses; experiments were conducted in relatively narrow, well insulated tubes. If some water is injected with the air, it will turn to superheated steam in an evaporation front, which should travel behind the combustion front. The steam having passed the combustion front causes a steam drive by a condensation front that can travel faster than the combustion front. The latter needs to travel only part of the distance covered by the oil-displacing condensation front, and thus consumes less air. The water-air ratio would seem limited to that at which cold water overruns the combustion. This limitation was deliberately exceeded considerably in theory and experiments. It was found that combustion is then indeed quenched, but only locally. Farther downstream, the oxygen finds residual oil at steam temperature, which is suficiently high to ensure rapid oxidation. Thus, the combustion front uses only part of the available fuel because it is chased through the formation faster than its normal velocity. No heat is left behind. This new process is called "partially quenched combustion". At the upper limit of the water-air ratio, a small heat slug is moved through the formation by the flow of water and steam. Only a small flow of air is needed since it has only to generate sufficient heat to make up for the lateral heat losses of the short heat slug. Theory Although many factors complicate underground combustion, the processes will be presented in their simplest form. For this reason, one-dimensional flow without lateral heat losses is assumed. Heat conduction in the direction of flow also is disregarded. Under these conditions, dry combustion causes very high temperatures. The heat-carrying capacity of the gas stream is small. Heat generated by oxidation of a residual oil saturation is retained in the sand. The available fuel determines the air requirement and the temperature obtained. Accepting the often-mentioned air consumption of 400 std cu m/cu m (400 scf/cu ft) formation, we calculate a temperature of the swept sand of 1,200C (2,192F) (Fig, I). If water is injected at a modest rate with the air, it will flash to superheated steam upon contact with the heated sand. One cu m (35.31 cu ft) of hot formation will evaporate about 0.5 cu m (17.66 cu ft) of water, and thereafter will accommodate (at an estimated 0.80 saturation and an assumed 0.40 porosity) another 0.3 cu m (10.59 cu ft) of water in cold condition. As long as less than 0.5 + 0.3 = 0.8 cu m (28.25 cu ft) of water is injected for every 400 std cu m (14,125 scf) of air (water-

Jan 1, 1969

By G. W. Ostroot, S. Shryock

Cementing deep, high-temperature oil wells where static temperatures range from 350 to 400F has become routine in the part decade. In the United States there were 271 wells drilled deeper than 15,000 ft during 1963. Many of these wells had static temperatures higher than 400F. Bottom-hole static temperatures near 700F are now realities in the geother-mal (steam producing) wells of California's Salton Sea area. The detailed planning initiated prior to drilling the wells is discussed together with the methods, materials and equipment used in solving the cementing problems which are encountered. Data are also presented that lead to development of cementing compositions that provide adequate thickening time, do not retrogress in strength, and maintain low permeability under these extreme temperature conditions. Field data include the cementing programs used on eight relatively trouble-free geothermal steam wells in the Salton Sea area. INTRODUCTION Not too many years ago cementing oil wells with temperatures in the range of 300F caused considerable anxiety. In some areas of the United States it is now fairly common to cement wells having bottom-hole static temperatures in excess of 400F. We are now confronted with the problem of cementing wells with temperatures ranging from 500 to 700F. Temperatures in this order of magnitude are often found in geothermal steam wells. From where does this extreme heat emanate? There are many theories as to the source of this steam flow. The most widely held views are: (1) heat- ing of ground water fairly close to the surface by an intrusive mass of hot rock; (2) steam generation from a reservoir of metamorphic rock, normally found below 25,000 ft and not at the shallower depths of the Salton Sea reservoir; and (3) high-temperature gases (water vapor) escaping and migrating from molten or semi-molten rock (magma) at a considerable depth. Of these. No. 3 seems to be the most generally acceptable explanation. Heat from springs and fumaroles has been used for years as a means of heating and cooking; however, significant progress in harnessing the vast power of underground steam reservoirs has been relatively slow. The first large-scale attempt to use the heat generated by steam from wells was made in Italy around the beginning of the 20th century. In excess of 250,000 kw of electrical power is now being produced from holes around Larde-rello, Italy. Another very active drilling program was initiated in the volcanic area of New Zealand in 1949.' Natural steam for power projects in the United States began in the early 1920's. An early commercial steam field is located at the Geysers, approximately 75 miles north of San Francisco, an area discovered in 1847 and used for many years as a health resort. Steam originates from 15 wells that have been drilled since 1957. The present output from this project is 25,000 kw. Success of the Geysers operation has been responsible for several companies taking a careful look at the feasibility of producing steam for power generation in the Salton Sea area of Southern California's Imperial Valley. Geothermal steam activity in this latter area began in 1961 when O'Neill, Ashmun and Hilliard completed Sportsman No. 1, at that time the hottest wellbore in the world.' Since its References given at end of paver. completion seven additional wells have been successfully completed in this area. Many problems encountered in drilling steam wells had to be overcome to make the ventures successful. Formation temperatures encountered in the Salton Sea seemed to be a straight-line function (a gradient of 13F per 100 ft of depth).' This imposed severe conditions on all aspects of drilling and completion. This varied, to some extent, from gradients in the older geothermal areas. Not to be overlooked is the effect of these temperatures on casing creep or elongation by thermal expansion (Table I), because standard API flanged wellhead equipment makes no provision for this kind of performance. Floating equipment was redesigned, and changes in types of downhole equipment were made in an effort to eliminate anticipated problems. In the later completed wells, standard oil-well cementing equipment has been used. During the early development of geothermal steam wells there were some problems resulting from blowouts. However, these were eliminated in the deeper Salton Sea wells and no problems were encountered with the drilling mud. A sodium surfactant mud was used on the Sportsman No. 1 to drill from 2,690 to total depth. Nevertheless, it was necessary that a cooling system be added and the mud cooled before circulating it back into the well. The difficulty in evaluating the size of the steam area and its potential in terms of pounds of steam and years of productivity still has not been resolved. Economic complexities have also entered into the steam play in the Salton Sea. The wells at the Geysers were drilled at a cost of $15,000 to $20,-000, whereas the Salton Sea wells will cost more than $150,000. This cost differential has to some extent been accounted for because of the heavily

Jan 1, 1965

By O. D. Gaither

This paper is an analytical study of the flow of fluids through small vertical conduits. Small conduits are defined as 11/4-in. nominal diameter tubing size and smaller, and approximately twice this area for annular conduits (i.e., 1- X 21/2-in. annulus and smaller). Experimental data are presented for the 1-X2-in. and 11/4- X 2%-in. annuli, and the I-in. and 11/4-in. tubing, since these represent the small conduit sizes and configurations generally encountered in oilfield applications. Data have been gathered for these conduits for single-phase water, single-phase gas and two-phase water-gas mixtures, with particular emphasis on high gas-liquid ratios. Water rates in excess of 2,000 BID and gas rates in excess of 2.5 MMcf/D, and two-phase flow ratios in between these two, represent the scope of the data gathered. Existing equations have been applied to predict flowing pressures and compared with experimental data. New correlations have been developed. INTRODUCTION The increased economic pressure on the domestic oil industry in the United States has constantly required the use of new techniques and equipment designed to reduce the cost of finding and producing oil and gas. Since tangible items are most readily apparent in economic analysis, the advent of lower-cost well completions was inevitable. One of the methods used to reduce costs which has received widespread attention is the slim-hole completion technique where tubing is used as the well casing and in which small conduits are used for tubing if necessary. Small conduits, defined by Kirkpatrick1 as "11/4-in. diameter nominal tubing and smaller for tubing flow and less than twice the 11/4-in. diameter nominal tubing internal flow area for annulus flow", have also found widespread usage as siphon strings for de-watering gas wells and as "kill" strings in deep high-pressure oil and gas wells. The growing use of small-diameter tubing has resulted in an increased need for development of improved methods to measure or predict flowing bottom-hole pressures since the physical dimensions generally preclude the use of subsurface-recording pressure gauges. Even in the cases where small bombs are available, the relatively high velocities encountered at nominal flow rates make it necessary to use excessive weight bars or special hold-down devices. Attempts to use recognized correlations to accurately predict flowing or gas-lift performance in wells equipped with small conduits have been generally unsuccessful. Insufficient field data were available to allow the development of a correlation on this basis, and an experimental approach was applied in an attempt to obtain a workable relation. The experimental approach used to obtain the data presented in this paper was actually a compromise between a field installation and a laboratory study. A test well 1,000 ft in length was used to obtain flow data on single-phase liquid, single-phase gas and two-phase water-gas flowing mixtures. Liquid rates up to 2,200 B/D and gas rates up to 3 MMcf/D were used in the single-phase flow studies. Two-phase flow rates from 100 to 600 B/D with gas-liquid ratios from 500 to 8,000 cu ft/bbl were recorded. Experimental data were obtained for single- and two-phase flow through 1-in and 11/4-in. nominal tubing, and through the annuli between 1- and 2-in. and 11/4- and 2%-in. nominal tubing strings. Experimental results for the two-phase flow are compared to the Poettmann-Carpenter correlation2 which is widely used as a comparative standard for development of multiphase flow predictions in flowing and gas-lift wells. Correlations developed by Tek,3 Baxendell and Thomas" were also investigated. The experimental data recorded herein fell in between the two flow regimes as defined by Ros," and this correlation also failed to yield satisfactory results. The fact that existing correlations failed to confirm the experimental data led to the need for development of a new correlation. Although a two-phase flow study was the primary objective of this investigation, data were also recorded for single-phase flow of water and gas, and constants were developed relating to pipe roughness and equivalent diameters for annular flow. These single-phase studies assisted materially in the development of certain of the two-phase flow results. Considerable previous work has been published which presented relationship of surface measurements to bottom-hole condition. The works of Buthod and Whiteley,6 Jones,' Poettmannb and the Texas Railroad Commission" are classic examples of the successful use of mathematical relationships which allow acceptable predictions of subsurface pressures, when gas is the flowing fluid. Darcy and others have derived relationships which may be used with minor modifications to predict subsurface flowing conditions in injection and water-supply wells. As previously stated, the application of the single-phase flow relationships

By A. W. H. Morris, G. H. Laurie, J. N. Pratt

Using- galvanic cells of the form Sn(liq)/Sn" (LiCl-KC1-SnCl,)/Sn-Ag (alloy), measurements have been made of relative thermodynamic properties of the a, C, E, and liquid phases of the Ag-Sn alloy system. Partial heats of solution of the components in the liquid alloys lzave also been observed by direct cal-orimetric measurement in an isoperibol calorimeter. The thermodynanzic quantities are disczlssed in relation to structural and other properties and the existence of anomalous minor fluctuations in the partial heats and entropies of solution in liquid alloys is tentatively suggested. In the course of a recent electro motive-force study of the thermodynamic properties of Sn-Ag-Pd liquids,' some measurements were also performed on the Ag-Sn binary system. Most previous thermodynamic studies of this system have been concerned with the liquid state. Measurements confined to the limiting heat of solution of silver in liquid tin have been made by many calorimetric workers2 while high-temperature calorimetric measurements of the heats of formation of the full range of liquid alloys are reported in the early work of Kawakami~ (1323°K) and more recently by Wittig and Gehrin~(1248°K). Electromotive-force studies on liquid alloys have been made by Yanko, Drake, and Hovorka' (606" to 686°K; 86 to 99.4 at. pct Sn) and by Frantik and Mc Donald' (900°K; 30 to 90 at. pct Sn). The only known measurements on the solid state are of heats of formation of the a, £, and c phases; these values were obtained using tin-solution calorimetry, at 723"K, by Kleppa,~ whose investigation also yielded heats of formation of liquid alloys containing more than 64 at. pct Sn. The present experiments on the Ag-Sn alloys include a re-examination of the liquid phase and, because of the dearth of free-energy data for the solid state, attempted measurements on the a, c, and E phases. The principal new feature of electromotive-force results obtained for the liquid phase was an indication of anomalous fluctuations in the partial heats and entropies of solution of tin at certain compositions. However, since the values for these thermodynamic quantities were determined from the temperature coefficients of cell potentials, which are commonly subject to considerable error, confirmation by calorimetric measurements was considered desirable. A detailed investigation of the partial heats of solution of the components in the binary liquids was made using a liquid metal solution calorimeter. I) GALVANIC CELL STUDIES a) Experimental Details. Measurements were made, as a function of alloy composition and temperature, of the potentials of reversible galvanic cells of the form: ~n(liq)/~n++/~n-Ag (solid or liquid alloy) Details of the apparatus and experimental techniques have been given elsewhere.' so that a brief account will suffice here. Molten salt, 58 mole pct LiC1-42 mole pct KC1, containing small amounts (1 to 2 mole pct) of stannous chloride was used as the electrolyte. The salts were dehydrated by pre-electrolysis and vacuum -drying techniques. Cells were established under an argon atmosphere by immersing tin and alloy electrodes in the molten salt contained in a large silica tube, heated in a vertical resistance furnace. The tube was sealed at the top by a head plate provided with openings permitting the simultaneous insertion of six electrodes, a central thermocouple sheath, and connections to vacuum and argon lines. Temperatures were controlled to *0.2"C over prolonged periods, with maximum variation over the electrodes at any time of 0.l°C. Temperatures were measured with a standardized Pt/13 pct Rh-Pt couple. The electromotive force of this and the cell potentials were measured on a Cambridge Vernier potentiometer and short-period galvanometer. Alloys were prepared from Pass "S" tin (99.999 pct) and Johnson-Matthey high-purity silver (99.999 pct) by melting in evacuated silica capsules and quenching in cold water. For liquid phase experiments, pieces of the resulting alloys were remelted into prepared silica electrode units, while solid electrodes were prepared by remelting into 3-mm bore tubing, inserting a cleaned molybdenum lead wire, and quenching to produce uniform rods about 3 cm in length, with soundly attached leads. In all cases remelting was done under an argon atmosphere. The solid electrodes were subsequently annealed in evacu ated silica tubes for 14 days at about 20°C below the solidus and quenched. Analyses showed that these techniques produced uniform electrodes with no significant change from weighed out compositions. b) Results and Discussion. Measurements were made on about forty alloys in the solid and liquid states, over varying ranges of temperature between 550" and 1050°K. Stable, mutually consistent, and reproducible electromotive-force data were obtained with most liquid alloys and these are shown in Fig. 1. Investigations were extended below the liquidus tem-

Jan 1, 1967

By Tell Ertl

TODAY'S mining industry is witnessing a transition in labor utilization. The drill-jumbo operator, the mucking-machine operator, the blasting crew, the scaling and timbering crew are all specialists. The all-around miner is rapidly disappearing. As mechanization has resulted in a higher order of underground skills; specialization of labor has been a natural consequence, as has the need for more supervision and engineering. Mines now are cleaner, neater, safer, and have a greater productivity per man-shift than ever before. Nothing spectacular like the continuous miner has yet come to the underground metal mines, but t a gradual improvement in methods, equipment, and technical knowledge is achieving the increased efficiency. With the exhaustion of the rich ores and large profits and who-cares-about-the-costs, mining has become a business; that of producing low value ores at costs below selling price. Charles A. Chase, patriarch of Colorado mountain mining men, manager of the Shenandoah-Dives, was one of the first to preach and prove his preachings that mining is a business. He has been mining a lead-copper-zinc-gold-silver ore, much from elevations above 1.3,000 ft, for a quarter century without a shutdown.-The ore is of such low value that most engineers and investors still would consider it foolhardy. Yet he has kept Silverton, Colo., alive, has paid wages without a lapse, has produced $25 million of new wealth and maintained a steady return to the investors. This type of responsibility is increasingly apparent in the mining business and is one feather that can be worn proudly. .Much emphasis is being placed on improving, the productive mining operations-breaking, loading and transportation. Breaking in underground metal mining is done by drilling and blasting. To the writer's knowledge, no chain or rotary-type machine has been developed for mining strong, abrasive rock. Drilling Percussion drills are still the standard drilling machines underground. Diamond drills, that: were the rage a decade ago for drilling long holes, are being superseded by the rock drill. The development of the hard abrasion-resistant carbide bit permits full-gage long holes to be drilled by percussion drills at a lower cost than diamonds. The change in the use of percussion drills is chiefly in the method of mounting. The column and arm are disappearing and the jackleg and rubber-tired or track-layer jumbo mountings are taking its place. At the Homestake mine .lightweight jackhammers mounted• on pneumatic legs using 7/8-in. hexagonal drill. rods and 1 1/2-in, tungsten-carbide detachable bits have been found more portable and maneuverable. They have less air consumption, lowered, dynamite consumption, and more footage and tonnage per man-shift than with 3 1/2-in. drifters on a column mounting. Drills now are mounted on longer feed carriages, drilling up to 20 ft without changing steel. These mountings result in great savings because the driller can set up quickly, drill the entire depth of the hole without changing the drill rod or bit using carbide and one-use bits, and can move his machine quickly to the next hole. One man to the machine is becoming general practice. The result is longer rounds rounds drilled at a lower cost than the previously used short rounds. A jumbo developed in the Tri-State can be extended to mine ore left in the roof up to 65 ft above the floor. Drill-rod life was formerly considered to be about 250 min of actual use. The increase in the drilling time per rod per day has gone up considerably with the development of the jumbo and the long-feed carriage, resulting in which is apparently more rod breakage., Consequently, a great deal of research is being done in the attempt to develop an alloy-steel rod with longer service life to offset the greater cost. Some reports indicate that alloy steel or Swedish steel results in cheaper drilling than conventional drill rod. However, several tests have shown only slightly increased life for alloy drill rod. Undoubtedly, the blow of the rock drill, the length of the drill rod, and the resiliency of the rock being drilled are important factors in the life of drill rod, so it follows that alloy steel might work well in some mines and result in no savings in others. The bit forged on the drill rod is seldom encountered and steel detachable bits are not as common as in the recent past. The one-use bit is gaining popularity because of. the difficulty in rehardening reconditioned steel bits satisfactorily. It is thought that the, carbie-insert bit is most applicable to drilling hard 'rock' where the steel bit is unable to drill out a full change, for instance, in extremely abrasive

Jan 1, 1952

By D. F. Atkins, B. A. Rogers

The constitutional diagram presented herein is relatively simple. Complete mutual solid solubility exists for an interval below the solidus line, a continuous curve with a flat minimum near 22 pct Cb and 1740°C. Upon cooling, the solid solution breaks up, except at the columbium-rich side, from two causes: zirconium-rich alloys transform under the influence of the ß-a transformation in zirconium; alloys of intermediate composition decompose into two solid solutions below 1000°C. The combined effect is the formation of a eutectoid at a temperature of 610°C and a composition of 17.5 pct Cb. The eutectoid horizontal extends from 6.5 to 87.0 pct Cb. Some age hardening effects have been observed in the zirconium-rich alloys but the positions of the solvus lines remain uncertain. IN recent years, zirconium has been produced in much larger quantities than were available previously. Correspondingly, the incentive for studying its alloy systems has increased, as the number of recent publications on alloy systems testifies. However, only a partial diagram of the Zr-Cb system has been published and relatively few references have been made to alloys of the two metals. Hodge' investigated the Zr-Cb system up to about 25 pct Cb. His data on melting points were not sufficiently numerous to distinguish with certainty between the alternatives of a narrow eutec-tic horizontal and a wide flat minimum in the solidus curve. Although Hodge considered his results on transformations in the solid state to be only tentative, he suggested that the eutectoid in the zirconium-rich alloys lay at about 625 °C and 10 pct Cb and estimated that the solubility of colum-bium in zirconium at 625 °C was near 6 pct. According to Simcoe and Mudge,2 less than 0.5 pct Cb is soluble in zirconium at 800°C. These authors observed an increased strength in both the 0.5 and I pct Cb alloys made with hafnium-containing zirconium. According to Keeler,3 the strength of zirconium is increased by addition of columbium to a content of at least 3 pct. Keeler' also observed a maximum in hardness at about 10 atomic pct Cb and commented on the brittleness of alloys of this composition. Anderson, Hayes, Rober-son, and Kroll5 investigated the tensile properties of Zr-Cb alloys containing 5.1 and 12.9 pct Cb at room temperature and at 343°C. The 12.9 pct alloy had a high tensile strength at room temperature but also a low percentage of elongation. All alloys had high elongation at 343 °C. Littona measured strength and elongation values of annealed alloys containing up to 27.5 pct Cb and found low elongation values for all of the alloys of high columbium content. Some observations on the resistance of Zr-Cb alloys to corrosion in water at high temperature have been published by Lustman, De Paul, Glatter, and Thomas' who found that additions of columbium up to 1 pct had only a minor effect on the corrosion resistance of zirconium. Preparation of the Alloys Raw Material: Zirconium of a relatively good grade was available for making the alloys. It was obtained as scrap pieces that had been left over from an operation that included production by the iodide process, melting under a protecting atmosphere, and fabrication to plates. The individual pieces had hardness values of 24 to 32 Ra and a typical analysis is shown in Table I. The columbium also was scrap trimmed from sheets. It was furnished by the Fansteel Metallurgical Corp. and had a high ductility but its analysis was known only approximately. The metal probably contained about 0.5 pct Ta, perhaps 0.25 pct C, and a few hundredths percent each of iron, silicon, and titanium. Melting: The alloys were melted in a tungsten-electrode copper-crucible arc furnace similar to units that have been described recently in the metallurgical journals.'.' The crucible of this furnace is provided with a cavity in which a getter charge can be melted before the melting of the alloy charges. Hardness measurements on the ingots indicate that the getter charge takes up a considerable fraction of the oxygen and nitrogen from the helium atmosphere of the furnace. The alloys used in the investigation are given with their intended compositions, hardness, and melting points in Table 11. Fabrication: All alloys of the Zr-Cb system appear to be amenable to fabrication. At least, all of the compositions listed in Table II could be reduced to wires in a rotary swaging machine. The starting material was either slabs cut from ingots and ground by hand to rough cylinders or narrow strips trimmed from sheets made by cold rolling slabs. However, not all of the alloys could be fabricated satisfactorily by the same method. From 0 to 4 pct Cb and from 20 to 30 pct Cb or more, the alloys could be swaged cold from ¼ in. cylinders to 0.80 mm wires with only one intermediate annealing, sometimes with none. From 40 to 90 pct Cb, the alloys were difficult to swage either hot or cold but could

Jan 1, 1956

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962