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By John T. Norton, Matthew J. Donachie

Residual lattice strai?zs were produced in 2024 aluminum and ingot iron by uniaxial tensile deformation. These strains were rneasured on the original surface and ulith depth below the surface. The strains conformed approximately to those from a macroscopic stress distribution but they were not truly macroscopic in nature. The exact mechanism which apparently causes the coherently difi9,acting region of each grain to behave as if macroscopically stressed was not determined. MACROSCOPIC stresses in metals produce strains in the lattice which result in X-ray line broadening and line displacements. The latter effect can be utilized in a technique for determining stresses in metals as first shown by Lester and born.' Subsequent advances in technique have enabled the X-ray method of stress measurement to be satisfactorily applied to many problems involving residual stresses of a macroscopic nature, such as those due to welding, grinding, shot-peening, and so forth. In the case of stresses such as those described above, the correlation of X-ray- and mechanically determined data has been generally good. However, plastically extended polycrystalline metals have sometimes been reported2 to show line displacements upon release of the applied tensile load, yet the nature or origin of the residual lattice strains, rls, producing these displacements has never been clear. As will be pointed out, this lack of clarity regarding the macroscopic or microscopic nature and origin of these stresses casts doubt on the validity of results achieved by the commonly accepted techniques of X-ray stress measurement. This anomalous behavior requires clarification to remove the doubts concerning X-ray stress measurement. The present paper is the result of an investigation of the interesting behavior of such plastically extended polycrystalline metal bodies. The studies were originated to carry out the following tasks: 1) Observe whether a residual lattice strain is produced as a result of plastic extension and show whether any residual lattice strains produced can be related to the usual concept of a macrostress. 2) Examine the origin of any residual lattice strains observed. 3) Consider the implications or consequences of the existence of such residual lattice strains on the problem of X-ray stress measurement. THEORY 1) Lattice Strains. The theoretical developments necessary for the treatment of lattice strains and their relation to stresses follow from the classical theory of elasticity and have been adequately covered by arrett. For an isotropic solid under homogeneous deformation, it can be shown that, for uniaxial stresses where Dl is the macrostress acting in the longitudinal direction; E$L is the lattice strain in the plane defined by the surface normal and the longitudinal direction at an angle, , from the surface normal; ET is the similar strain in the transverse plane; E is Young's modulus; and v is Poisson's ratio. Eq. [2] is independent of angle + and Eq. [I] is a linear function of sin2, see Fig. 1, and can be solved analytically for DL if E and u are known and EL is measured. Thus, a uniaxial macrostress will be indicated by a linear E,L vs sinZ plot and a

Jan 1, 1962

By T. S. Lundy, R. E. Pawel, F. R. Winslow, C. J. McHargue

The volume-diffusion coefficients of Nb-95 and Ta-182 in niobium have been measured over the temperature range 878° to 2400°C. High-temperature specimens (T 21500°C) were sectioned by conventional lathe and grinding techniques while low-temperature specimens were sectioned by an anodizing and stripping technique previously described. Over a range of more than ten orders of magnitude in diffusivity, the self-diffusion data is well-represented by the equation: D = (1.1+ 0.2) exp [- (96,000 * 900)/RT ] cm2/sec Upward deviations from this line are explained by short-circuit diffusion in combination with the loss of resolution of the sectioning techniques. Oxygen contamination within the range 100 to 450 ppm was found to have little or no effect on the self-diffusivitj 01 niobium. In a limited number of measurements, the diffusivity of Ta-182 in niobium was found to be about half that of Nb-95 in niobium. These data may be described by D = (I.0+0.90.5)exp [- (99,300 * 2400) /RT ] PREVIOUSLY reported studies of self-diffusion in niobium were by Resnick and Castleman1 and Peart, Graham, and Tomlin.2 The data of Resnick and Castleman over a temperature range 1585" to 2120°C show considerable scatter but. can be represented by D = (12.4 *0.8) exp [-(105,000+3OOO)/RT] cm2/sec The limited data of Peart, Graham, and Tomlin follow the equation D = 1.3 exp (-95,00O/RT) cm2/sec In view of recent diffusion data for ß zirconium3 and 0 titanium4 in which Arrhenius-type plots do not yield straight lines and of the potential high- temperature uses of niobium and its alloys, we thought it important to investigate the diffusion behavior of this bcc refractory metal over a large temperature range. This has recently been done for molybdenum,5 chromium,6 vanadium,"" and tantalum.9 Niobium was a particularly suitable material for this study largely because of the development of an anodizing and stripping sectioning technique which enables diffusivities as small as l0-19' sq cm per sec to be determined accurately.10 In addition to self-diffusion data, data were obtained for the diffusion of Ta-182 in niobium and for the effect of varying oxygen content on self-diffusion. I) EXPERIMENTAL PROCEDURE Materials. The niobium was obtained from three sources: 1) melting stock from Shieldalloy Corp., 2) electron-beam melted single crystals, 1/2 in. diameter, from Semi-Elements, Inc., and 3) oxygen-doped, electron-beam melted single crystals from Materials Research Corp. The melting stock was electron-beam melted and specimens 5/8 in. diameter by 1/2 in. long were machined from the center of the bar. The analysis supplied by the vendor and an interstitial analysis of one of the specimens are given in Table I. The single crystals (type 2 above) were cut with a jeweler's saw to specimens about 3/8 in. long. The interstitial analysis of this material is given in Table 11. This material was used

Jan 1, 1965

By Peter R. Drummond

THE final casting of refined copper has been re-J- stricted for generations by the following sequence of operations: Filling the reverberatory furnace, melting, skimming, blowing or flapping, and poling. The hoped-for 24 hr cycle, producing 300 tons or more, has been taken up largely with the necessary bat time-consuming tasks of cleaning the bath, sulphur elimination, and in turn removal of excess oxygen to produce tough-pitch copper. Incidental to comparatively slow melting under combustion gases, copper oxides react with the furnace lining, and the slag so-formed must be completely recycled. The three-phase arc furnace has eliminated some of the cycle stages, and telescoped the remainder into a continuous operation. Electrical energy, supplied to graphite electrodes enclosed in high grade refractories, rapidly melts copper cathodes and sustains a stream of metal, containing approximately 0.01 pct oxygen, without contamination from fuel. The arc was struck on the first large electric furnace for melting copper in the United States on April 13, 1949. The earliest use of this type of furnace was at Copper Cliff, Ont., in 1936, and an admirable description of their installation has been published? Copper, melted in the Baltimore furnace, is used to cast billets, and the installation differs somewhat from the Canadian, as will be described. The arc furnace is a heavy-duty, three-phase furnace, holding 50 tons, the general outline of which appears on Fig. 1. The steel shell is 15 ft ID with a bottom radius of 14 ft 2 in. The roof, separate and distinct from the body, consists of a 15-ft water-cooled, cast-steel ring of the same outside diameter as the furnace. The center line of the furnace lies 9 ft 6 in. from that of the trunnions, permitting a 5" backward tilt for skimming, and a 40" maximum nose tilt forward for complete draining. Normally, the furnace overflows by displacement, and the use of the forward tilt arrangement is restricted to covering charging delays. The charging slot, 3 ft 8 in. x 5 in., lies on the north center line, the tap hole on the south, and the 30x30 in. skim door 45" to the west of the slot. The original 20-in. graphite electrodes were replaced with 14 in. in December 1949. Three conventional direct current winch drives, governed by electrical controls, position each electrode which has individual mast supports and counterweights. An independent circulation supplies cooling water for the electrode glands, the roof ring, charge slot, and the skim door frame. Arc Furnace Refractories Hearth: Fused-in monolithic bottoms had been used in copper arc furnaces, installed prior to April 1949. These consisted of thin layers of periclase, successively fused in place over preliminary brick courses. Heat was obtained from the arc, using a T-like arrangement of broken electrodes resting directly on the periclase to be fused. The operation, taking weeks to perform, was very expensive. The chemically-bonded magnesite-brick bottom, installed at Baltimore, was the first of its kind and a radical departure from previous practice. It consists of a 1 to 6-in. layer of castable refractory laid on the steel shell, modifying it to a 12 ft 2 in. bottom radius. Two courses of 9x2 % -in. fireclay straights and keys follow. The third course is made of 9-in. magnesite blocks of special shape to form circles of an inverted arch. It was started by a four piece keystone with skew-backs forming the outer course. The fourth course also started on a central keystone, or button, of four 90" segments, 12 in. diam x 13 Vz in. deep, and continued with 13%-in. blocks. Skewbacks at the shell completed the course to produce a horizontal surface for the side walls with a single course of No. 2 arch fireclay against the steel. Dry chrome-magnesite cement was brushed over each course after laying, and a 1-in. expansion space between the brick and the shell was filled with the same mixture. The total bottom thickness, excluding the castable material, was 5 in. of clay plus 22% in. of chemically-bonded magnesite. Tap Hole: A 5-in. OD and 3-in. ID silicon-carbide tube constitutes the tap hole and is set tangential to the upper course of the furnace bottom. Molten metal fills the tube when the furnace is level and filled to capacity. Side Walls: The lining, against the shell, consists of a 9x4Y2x3 in. soldier course of fireclay, using straights and No. 1 arches to turn the circles. A second soldier course of 9x4'/2x2'/2-in. fireclay was laid in a somewhat similar fashion. Three courses of 13Y2x6x3 in. and 9x6~3 in. of final magnesite, laid flat, completed the lining, using Nos. 1 and 2 keys to turn the circles. Cardboard spacers were placed between every two bricks in horizontal courses, and a thin coat of chrome-magnesite cement filled the joints between the firebrick and magnesite. A sprung-arch spanned the skim door with jambs of suitable magnesite shapes. Charge Slot: The slot is 3 ft 8 in. wide x 5 in. high. A silicon-carbide sill of special shapes has a 30" slope to allow cathodes to slide easily into the bath. The original arch was flat, and composed of Nos. 1 and 2 wedge magnesite with a 6-ft radius. It projected 5 in. over the sill, and, being a flat arch, gave an 18 15/16-in. opening between the inner edge and the metal line. The whole assembly was later raised 9 in., and the flat arch replaced with an arch, the lower edge of which maintained the 5-in, width from the outer to inner edges as shown in Fig. 2. A water-cooled, cast-copper jacket protects the steel shell behind the slot.

Jan 1, 1952

H. W. Turner, Portland, Ore. (communication to the Secretary*) :—Mr. Brown's paper on the complicated groups of veins exposed in the workings of the Bodie mine forme a valuable contribution to the literature of the structural features of ore-depoeits. It is much to be desired that managers should put into print the results of their observations of the mines under their charge. These observations, as well as data of production, kind of ores, etc., usually accumulate for years, and unless the mining geologists of the Geological Survey happen along before the mine is worked out, such data seldom get into print. About the year 1899 I went through the mines at Bodie with R. C. Turner, then superintendent, and made some notes on the veins and gangue-minerals, and collected some specimens. Mr. Brown refers to crystals of feldspar (albite) found on fragments of quartz on the surface. I collected a number of specimens of these crystals, mostly from Queen Bee hill, and

Jan 1, 1909

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener's anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,' the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.' THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.' Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969

By K. A. Slagle

Hydraulic analysis of the wellbore has become increasingly inzportant for designing cementing operations and selecting equipment, materials and techniques to complenzent modern well-c-ompletion practices. Non-Newtonian fluid technology has advanced beyond the point where former empirical methods of analysis adequately define the hydraulic system and fluid properties. In view of these factors, this paper describes a series of rheological calculations which have been found practical, through field usage, for assistance in selecting a cementing program. A relatively simple laboratory method using standard viscometric equipment is suggested for determination of the rheological properties of slurries, and clrrta are presented on some of the more common cementitrg conzposition.A. A criterion for divergence from laminar-flow characteristics has been proposed. Usefulness of the calculations is indicated by examples of cementing operations where they have been used. INTRODUCTION With the changing aspects of well-completion practices during the past few years, it has been increasingly important to have a relatively simple method of analyzing the flow conditions existing in the well during cementing operations. This is particularly true in view of the improved economics toward which most of the changes have been directed. Rheological characteristics of slurries used for cementing should be a major consideration in the trend toward smaller casing sizes, either single or multiple strings. Receiving increased attention is the practice advocated in 1948 by Howard and Clark' of attaining turbulent flow with the fluids circulated during a primary cementing operation. While there may still be a difference of opinion concerning this technique, most available information indicates that superior primary-cementing results are generally obtained when high displacement rates are employed. Fluid properties of the slurry to be used must be available, as well as calculation methods, to determine what flow rates should be attained and the probable consequences in terms of frictional pressure and horsepower utilization. It would certainly be inappropriate to attempt high displacement velocities if sufficient pressure might be developed to create lost circulation. Since cementing slurries are non-Newtonian fluids, it is not possible to define their rheological or fluid properties by the single factor of viscosity and then make calculations for the quantities just described. Because the shear stress-shear rate ratio is not constant: it becomes necessary to establish at least two parameters for adequate fluid-flow calculations. It is not the purpose of this paper to delve into the mathematical development of non-Newtonian technology, nor to discuss the arbitrary classification system under which a single fluid may resemble two or three different classes depending upon experimental conditions. Rather, the intention is to present a useful series of calculations based on a concept applicable to both Newtonian fluids and to the preponderance of non-Newtonian fluids encountered in the oil-producing industry. Development of this approach was begun some 32 years ago,' and has most recently been brought to fruition by Metzner and his co-workers at the U. of Deleware. Some non-Newtonian fluids encountered in the petroleum industry, other than cementing slurries, have also had the benefit of this method of analysis."' The two parameters required to define the fluid are usually denoted by the symbols n' and K' and, for the purposes of this discussion, are called "flow behavior index" and "consistency index", respectively. These two slurry properties permit calculation of the Reynolds' number and the "critical" velocity, or the velocity at which departure from laminar flow begins. EXPERIMENTAL DETERMINATIONS The two principal instruments used for rheological studies are the pipeline (capillary-tube) viscometer and the rotational viscometer. When conveniently possible, a capillary-tube viscometer (where the pressure drop and flow rate of the material can be measured) is the better method for rigorous determination of the flow behavior index and consistency index for non-Newtonian fluids. With pressure-drop data at various flow rates, it is then possible to prepare a logarithmic plot of shear rate as the abscissa-shear stress as the ordinate. For fluids which do not exhibit time-dependency, these data will usually produce a straight line. The flow behavior index n' represents the slope of this line, while the consistency index K' becomes the intercept of this line at unity shear rate in accordance with the mathematical derivations associated with this concept of rheology. Due to the difficulties anticipated in maintaining a uniform, pumpable cement slurry for the time interval required to obtain measurements from the pipe viscometer, the n' and K' data reported herein were obtained using a direct-indicating rotational viscometer (Fig. 2). The

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By S. M. Brisbane

THE life of refractory linings in rotary cement kilns can be shortened by uneven or inadequate support of the kiln and its shell and by variations in the conditions of operation. Alteration of these factors may, according to their nature, bring about mechanical deterioration of the lining or promote chemical attack. Chemical attack has been described elsewhere.1-4 The distortion of cement kilns has been discussed in a general manner by Rochow,6 ho indicates the amount of distortion which may occur in an unlined shell, and by Rosenblad: who states that the deformations of the shell are greatest above the trunnions. The present article indicates the extent of the distortion of a kiln to an oval shape in certain selected positions and the deviation from a straight line of the kiln along its length between two supports. The cement kiln is a long, hollow, rotating cylinder consisting of steel plates which may be either welded or riveted together. This shell is supported on tires, frequently 60 ft apart, which roll on trunnions. The large mass of the kiln causes distortion of its cross-section; it becomes slightly oval, i.e., diameters lengthen as they become horizontal and shorten as they become vertical. There is also a tendency for the shell to bow between supporting tires; this bowing may be upwards or downwards depending on the position of the weight forces and the supports. The extent of the deviations from the ideal kiln shape was investigated. Observations described in this paper were made on the shell of the clinkering zone between the first and second tires of two of the kilns at the Geelong works of Australian Portland Cement Pty. Ltd. The kilns were both 400 ft long and 10 ft diam with a welded enlarged burning zone 11 ft 6 in. diam. The shell was fabricated from mild steel and in this section its thickness was 1 in. It was lined with 41/2 in. of chemically bonded magnesite-chrome bricks which were jointed with mild steel plates. The kilns operate on a 4 pct slope and the speed may be varied between 0.75 and 1.68 rpm. The wet process is used; kilns are coal fired and are fitted with integral coolers. Temperatures within the kiln are difficult to determine with any accuracy because of the absence of black body conditions, but surface temperatures are probably in the range 1420° to 1470°C. Average shell .temperatures at the two positions at which the deformation studies were made were 370°C and 355"C respectively. Methods: In determining the ellipticity it was necessary to measure the lengths of the vertical and horizontal diameters while the kiln was in operation; data obtained from a stationary kiln would not have the same practical significance. For this purpose the four points V, W, X, and Y at the ends of two mutually perpendicular diameters were marked on one kiln. The point X is shown in Fig. 1. For the measurement of the length of the vertical diameter a vertical column, to which a horizontally aligned telescope was attached, was placed 10 ft from the kiln. The telescope could be racked up and down in a vertical plane. Two sets of readings were taken, one set when each of the points V, W, X, and Y was at its maximum height above the

Jan 1, 1957

By H. C. Chang, N. J. Grant

REEP studies and measurements in most in-V> stances are based on a relatively gross gage length. Even in some recent theoretical studies on the mechanism of creep, changes were followed by means of X-rays and metallography without regard for the behavior of the individual grains and grain boundaries.'" Analytical studies of creep have frequently indicated that more than one competing process is operative and that the ultimate creep performance depends on the effects of temperature, time, and strain rate as well as grain size.'-" he grains and grain boundaries are known to respond differently to these variables but the extent of the response is still little known, especially in poly-crystalline materials where the relative orientations of grains and grain boundaries are important. This paper reports some experimental observations of the behavior of the grain boundaries and their effect on the deformation in the grains. High purity aluminum was used to avoid complications of aging reactions, second phase, inclusions, etc. Experimental Procedure A small vertical nichrome wound furnace was built to permit direct loading on the test specimen. This furnace is capable of operating up to about 1300°F with reasonable temperature distribution. A ground rectangular quartz window, 1.25x0.5 in., is imbedded in the external stainless steel tube to permit observations of the creep process with a microscope. An argon atmosphere ,was provided to prevent oxidation. The quartz window caused a temperature gradient between the back and front surfaces of the specimen of 15" at 700°F. The temperature gradient could be cut down to 3°F along the length of the specimen by adjusting shunts across the furnace windings. An ordinary metallurgical microscope with a working distance of 14 mm was rebuilt so that it could be moved in three mutual perpendicular directions. Visual examination could be made with either a 30X eyepiece or a 15X filar eyepiece. Using an objective of focal length 24.3 mm and a numerical aperture 0.20 a total magnification of 120X or 240X could be obtained. High purity aluminum rated at 99.995 pct was supplied by the Aluminum Co. of America as % in. then the gage portion was further machined to 3/16 in. diam. The ends were Y4 in. diam and threaded to fit available specimen holders. Two opposite flat surfaces of the gage portion were obtained by milling, giving final dimensions of the gage portion of 3/4x3/16x3/32 in. Machined specimens were first electropolished in Jacquet's solution.' Reference marks were produced by pressing a thin sewing needle into the surface of the specimen. The specimen was then annealed at 900°F for 24 hr and at 1150°F for 12 hr. Typical macrostructures of specimens treated in this manner are shown in Fig. 1. The range of the grain size was 1 to 5.5 mm (see Fig. l), but most of the grains were of 2.5 mm and went through the whole thickness of the specimen. The specimen was re-electropolished and etched electrolytically to reveal the grain boundaries. In order to reveal the orientation difference of the grains, etch pits were produced on the surface of the grains by etching in a mixture of hydrochloric and nitric acids (HC1, 45 pct; HNO,, 10 pct; H,O, 45 , by volume). The specimens were very carefully put into the holders and furnace; yet even with this care, fine slip lines were developed on the specimen surface.

Jan 1, 1953

By C. C. Mattax, J. E. Bobek, M. O. Denekas

ABSTRACT investigations in recent years have shown that rock wettability can exert a profound influence on the displacement of oil by water from oil producing reservoirs. Core analyses frequently show oil recoveries from preferentially water-wet rock to be significantly greater than those from preferentially oil-wet rock. Thus, an accurate prediction of water-drive or waterflood oil recovery is dependent on the evaluation of reservoir rock wettability. Laboratory and field studies have been undertaken to examine and develop methods which may be used to measure rock wettahililiy, to investigate factors which may alter the wettability of reservoir rock, and to determine the wettability of specific reservoirs. It has been found that measurement of the rate and volume of spontaneous imbibition of the wet-ting phase by a rock is a reliable and reproducible test for semi-quantitarive determination of preferential rock wettability. Laboratory tests have shown that the wettability of reservoir rock may depend on both the crude oil composition and the rock type. Field and laboratory tests have indicated that coring flulids and core handling techniques can cause significant changes in the wettability of rock surfaces. However, a few fluids, brine in particular, appear not to affect core wettability and may be used when coring to determine reservoir wettability. Core handling and packing procedures have been developed which preserve core wettability during storage and laboratory testing. The wetfability characteristics of six reservoirs have been evaluated by wettabilify tests performed in the field on fresh cores cut with brine or special water-base muds. The tests indicated that all six reservoirs are water wet; however, the de-gree differed from one reservoir to another. INTRODUCTION Although surface properties of reservoir rock and interfacial characteristics of rock, crude oil, and water systems have been discussed for many years, the full significance of these properties to the production of oil is still in the process of evaluation. It is known, however, that one surface characteristic—preferential wettability of the reservoir rock—-is of paramount importance when the reservoir is being produced by water-flood or water-drive mechanisms. The importance of rock wettability has been pointed out by several authors'.',%* who have found that pref- erentially water-wet cores flood more efficiently than oil-wet cores; that is, more oil is recovered from water-wet cores in the early flooding stages than from oil-wet cores. Other authors'," indicate that waterflood oil recovery from cores of intermediate wettability may be greater than that from either strongly water-wet or strongly oil-wet cores. These recent investigations emphasize that the true wettability of a reservoir must be known before the performance of waterflood or water-drive reservoirs can be accurately evaluated. When reservoir wettability is to be determined by core analysis, precautions must be taken to maintain the original wettability which can be altered readily during coring5 nd testing.' In the coring operation the core may be partially or completely penetrated by the drilling fluid which, if it contains surface active materials, may drastically change the wettability of the core. Also, improper core handling during stcrage and testing may change its wettability because of evaporation of fluids or exposure to oxygen or surface active contaminants. One purpose of this paper is to discuss methods for obtaining, preserving, and testing cores without altering their original wettability. In addition, the results of wettability tests on fresh and preserved cores from six reservoirs are presented where special precautions were taken to obtain samples without altering their wettability during the coring operation.

By Harold M. Mooney

WHEN apparent resistivity data are taken with the symmetrical Wenner 4-electrode spread, a fixed center position is used and readings are taken for values of electrode separation. Basic data consist of apparent resistivity plotted against separation of adjacent electrodes . The interpreter attempts to infer geologic structure, such as the depth to discontinuities and the nature of subsurface earth materials. An earlier paper' described methods for interpreting resistivity data. All of these involve a severe assumption, namely that the earth in the region of interest consists of horizontal layers, electrically homogeneous and isotropic. The actual earth never satisfies this assumption exactly and may deviate from it so much that none of the above methods can be applied. Attempts in three directions have been made to modify the assumption so that it approaches known geologic complexity more closely. First, curves have been calculated for dipping discontinuities. Stern' and Aldredge hose a few widely separated dip angles. Trudu confined his attention to small dips. Berel'kovskiy and Zubanov computed gradient curves for widely separated dip angles. Unz as given the most complete solution, with a brief attempt to treat the three-layer case. Second, anisotropy can be taken into account. It seems geologically probable that layered materials have different vertical and horizontal conductivities. Cagniard, Maillet, and Pirson et up methods for finding an equivalent hypothetical isotropic medium. Standard interpretation methods can be applied to this, and the actual medium can then be deduced. Belluigi'" discounts the practical importance of anisotropy; Geneslay and Rouget do not agree with his conclusion. Third, the effect of variable resistivity in a layer can be considered. Keck and Colby" examine the mathematics of an exponential increase in a surface layer. Several authors, for example, Stevenson,'' consider a continuous variation of resistivity with depth. The present paper deals with a linear variation of resistivity in a surface layer. Geologically, surface variations should be expected. Unconsolidated materials such as glacial drift show marked irregularities over short distances. The effects of weathering change with depth. The moisture content of material above the water table may vary from a dry sand to a saturated clay, and both of these will be changed by rainfall. Figs. 1 to 6 present apparent resistivity curves to show the effect of a variable surface layer. In all cases resistivity varies linearly with depth down to a depth of one unit. Material beneath this depth has constant resistivity. Electrode separation is plotted in depth units. Insets on each figure show the corresponding cross-sections, plotting true resistivity against depth. To illustrate, consider curve A of Fig. 1. The true resistivity of material at the surface of the earth is taken as 0.4 units. Resistivity increases with depth, reaching a value of 1.0 at 0.5 depth units and 1.6 at 1.0 depth units. Below a depth of 1.0, all the material has very low resistivity (zero, for purposes of calculation). Curve A in the main part of Fig. 1 shows how apparent resistivity varies for this case as the electrode spacing is increased. To illustrate further, curve E of Fig. 4 corresponds to true resistivity of 1.2 units at the surface, 1.0 at a depth of 0.5 units, 0.8 at a depth of 1.0, and 1.5 for all depths greater than 1.0. Apparent resistivity curves have been plotted logarithmically so that the shape of the curves becomes independent of the units, giving the curves wide validity. A certain drift-covered area, for example, shows a gradual decrease of resistivity from 230 ohm-meters at the surface to 150 ohm-meters at the bedrock surface, 275 ft down; bedrock resistivity is 800 ohm-meters. Curve E of Fig. 5 indicates that true resistivity decreases from 1.2 units at the surface to 0.8 at a depth of 1.0, then increases abruptly to a constant value of 4.0 units. Since resistivity and depth ratios are the same, this can be used to predict the field curve. For Fig. 5, multiply true resistivity and apparent resistivity by

Jan 1, 1955

By Raymond L. Orr

Calorimetric measurements have been made of the heats of solution of gold axd indium in a number of liquid tin-rich alloys at a temperature of 705°K. Relative partial molar enthalpies of gold were determined as a function of dilute solute concentrations in the binary Au-Sn system and in the ternary Ag-Au-Sn and Au-In-Sn systems. Relative partial molar enthalpies of indium were determined for dilute solute concentrations in the In-Sn, Ag-In-Sn, and Au-In-Sn systems. Through application of the interaction coefficient concept introduced by Wagner and more recently extended by Lupis and Elliott, ualues have been obtained for the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. The results are inte@reted in terms of solute atom distributions through comparisons with the predictions of dilute solution models. INTEREST in the thermodynamic behavior of dilute liquid alloys stems from two primary sources. From a practical viewpoint, it is often of importance to know or to be able to predict the effect that one solute will have on the thermodynamic properties of the other solutes in a multicomponent system. Studies of dilute solutions may also be rewarding from the theoretical point of view. Some of the difficulties arising from the more complex interactions possible in concentrated solutions are avoided, leading to easier interpretations in terms of solutibn models and bonding energies. For example, in a binary alloy the limiting values of the partial molar properties of the solute represent the case for which each solute atom is completely surrounded by atoms of the solvent, and no other interactions are possible. Solute - solute interactions in dilute solutions are conveniently treated by the interaction coefficient concept of ~agner.' Using a Taylor series expansion for the logarithm of the activity coefficient, In yi, of a component, i, in a solution consisting of dilute solutes with atomic fractions xi, xj, xk, and so forth, in a solvent, s, and neglecting the second- and higher-order terms, Wagner obtained the expression: Where Wheyz is the limiting value of yi in the pure solvent, s. The interaction coefficients, e:, e:, and so forth, are defined by: Since yi is related to the excess partial molar Gibbs energy of component i by GfS = RT In yi, E: is re- ferred to as the "Gibbs energy interaction coefficient". Lupis and Elliott~ extended Wagner's treatment to the relative partial molar enthalpy, aHi, and the excess partial molar entropy, qS. They defined the enthalpy interaction coefficient as: and the excess entropy interaction coefficient as: leading to expressions similar to Eq. [I]: The three interaction coefficients are related by? The self-interaction coefficients, E:,qf,and at, represent the effects of interactions between atoms of component i in solvent s; €3, q{, and 03 represent the effects of interactions between i and j atoms in solvent s; and so forth. From the Maxwell-type relationships between partial molar quantities, it may be shown1'2 that e{ = ej, r}\ =tj), and ai - crj. Experimental determination of the interaction coefficients requires extremely precise measurements of the appropriate properties as functions of solute concentrations in very dilute regions. Few such data exist for intermetallic alloys, even for binary systems, because of experimental difficulties. This is especially true with respect to enthalpy data for dilute alloys. Examination of the compilation of data for binary alloys by Hultgren, Orr, Anderson, and ~elle~~ reveals that determination of limiting values of &fii(Xi =0) often requires extrapolations to infinite dilution from xi = 0.05 to 0.10. Direct measurements of the enthalpy interaction coefficient, qi, for multicomponent systems are virtually nonexistent. This quantity is of course subject to direct calorimetric measurement, but its determination must be limited to cases where high experimental precision is possible. The heats of solution of gold and indium in liquid tin can be measured with relatively high precision, which makes determinations of 73 involving these metals as the measured solutes experimentally attractive. This paper presents the results of such determinations of the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. MODELS FOR DILUTE-SOLUTION BEHAVIOR Random-Solution Behavior. In the quasi-chemical treatment of solutions, only nearest-neighbor bonds are considered, and a composition independent value

Jan 1, 1967

By Antonio Marrano, Eda F. Quadros, Diogo Correa [Fo], Paulo T. Cruz

For many years the water pressure test has been used as a normal procedure to investigate the hydraulic characteristics of rock masses and discontinuities. Although the test has given evidence of problematic areas, the nature of flow and the so called equivalent permeability are seldom seriously affected by the testing tecnique. In order to improve the information on these points the Instituto de Pesquisas Tecnológicas de São Paulo - IPT, has developed an extensive program at laboratory and field research on the hydraulics at rock fractures. This paper summarizes the main items related to this research. Is shows that with only small improvements on field tests and some support of laboratory conductivity tests on natural rock joints it is possible to obtain a better understanding of the nature of flow in fractures, improve flow predictions and estimate the opening and hydraulic conductivity, as well as the transmissivity of natural joints or rock discontinuities.

Jan 1, 1982

By F. Rosenblum, P. Spira, F. Kitzinger

The possibility of increasing the efficiency of mineral processing plants by means of computer control has prompted metallurgists to examine their flowsheets more critically in order to develop practical control strategies. Control schemes in use to date generally rely on the automation of traditional and previously manually regulated control loops, e.g., the addition of reagents to maintain a constant assay or a constant pH. This approach is predicated on the availability of well established primary sensors such as pH electrodes or on-stream analyzers. Noranda Research Center, in cooperation with Noranda Group concentrators, has developed a froth level monitor and a pulp density meter adaptable to this type of control. Although some of the basic principles on which they are based have been known for some time, their incorporation into the design of reliable, direct-reading instruments which can be interfaced with a computer is believed to be novel.

Jan 4, 1979

By F. Rosenblum, P. Spira, F. Kitzinger

The possibility of increasing the efficiency of mineral processing plants by means of computer control has prompted metallurgists to examine their flowsheets more critically in order to develop practical control strategies. Control schemes in use to date generally rely on the automation of traditional and previously manually regulated control loops, e.g., the addition of reagents to maintain a constant assay or a constant pH. This approach is predicated on the availability of well established primary sensors such as pH electrodes or on-stream analyzers. Noranda Research Center, in cooperation with Noranda Group concentrators, has developed a froth level monitor and a pulp density meter adaptable to this type of control. Although some of the basic principles on which they are based have been known for some time, their incorporation into the design of reliable, direct-reading instruments which can be interfaced with a computer is believed to be novel.

Jan 1, 1980

By Henry Carlisle

Henry Carlisle: This is November, 1960, and my good friend John Gustafson is sitting on the other side of a tape recorder. I, Henry Carlisle, am going to ask him some questions on the highlights of his life, and he has been good enough to say that he will play this question and answer game with me. Now, John, let's pick out a very interesting period when you went to North Labrador and made a preliminary investigation of the big iron deposits there. You were working for either Timmins or Hollinger, which was it? John K. Gustafson: I was in charge at that time of a Hollinger Exploration Co. office in Toronto. We had acquired options on enough shares to control Labrador Mining and Explorations Co., and through Hollinger North Shore Ltd., another company, we had a 3000 square mile concession in Ungava, Quebec, on the direct extension of the iron ore fields.

Jan 7, 1972

By Norman Visnes

EARLY in 1954, as initial development of the Galena mine was being finished, plans for stoping operations became the foremost consideration of the operating management. The Galena is being operated under lease agreement with the owner, Vulcan Silver-Lead Corp. Started in 1947, the Galena is a deep level development of American Smelting & Refining Co. and Day Mines Inc. under the management of ASARCO, in the Coeur d'Alene mining district. Lead mineralization was found on the 3000 level in 1950. In 1953 development on the 3000 level disclosed a siderite vein, later known as the Silver vein, which contains commercial quantities of silver in Tetrahedrite. This vein was explored on the 2800 and 2400 levels and later on the 3400 level, the lowest in the mine. Work above the 2400 level to date has indicated that the vein dissipates to weak mineralization, and ore values are uncertain above the 2200 horizon.

Jan 1, 1957

By K. R. Evans

The yield and fracture characteristics of a Ti-8 pct A1 alloy have been examined at room temperature as a function of exposure temperatures to 1700°F. Em-brittlenzent of the alloy is observed to occur following exposures below 1280°F, the critical temperature for formation of ordered Ti3Al particles. Presence of Ti3Al particles results in an increase in the yield and flout stresses which, for a given exposure time, are a maximum at the critical temperature. Embrittlement is attributed to the occurrence of plastically induced fracture controlled by the increase inflow stress. This interpretation is compatible with the decreasing ductility and increasing crack popagation rates observed with increasing exposure time below the critical temperature. Slip line observations and measurements of the gain size dependence of the yield stress indicate that the slip character of the alloy is not influenced by exposure treatments below the critical temperature. ThE potential usefulness of Ti-A1 alloys in structural applications has prompted considerable interest in studies of their microstructure and mechanical characteristics. The relatively recent surge of interest in the system and at the same time its complexities are indicated by the fact that despite numerous recent efforts14 there has not even been general agreement upon a phase diagram for the system. However, most of the Ti-A1 alloys of commercial interest range in aluminum content from 5.0 to 8.5 wt pct where most investigators achowledge the existence of the ordered Ti41 phase. Goldak and parrs confirmed the existence of Ti41 from X-ray diffraction analysis of the stoichiometric composition while Blackburn6 has determined its presence in commercial Ti-8 pct A1 alloys by electron diffraction analysis and dark field transmission microscopy. The embrittlement of Ti-8 pct A1 alloys was initially reported by Crossley and carew7 who showed that aging in the temperature range of 750" to 1110°F resulted in extreme brittleness. This behavior was later confirmed and correlated by Soltiss to the presence of long-range order in the commercial Ti-8 pct Al-1 pct Mo-1 pct V alloy (Ti-8-1-1) which exhibited anomalous creep and yield strength behavior at 950°F. This investigation was designed to study the mechanical characteristics of a binary Ti-8 pct A1 alloy in order to further examine the nature of the embrittlement behavior reported for the alloy system. EXPERIMENTAL PROCEDURE A Ti-8 pct A1 binary alloy was obtained from the Wah Chang Co. in the form of 0.050 in. sheet. The chemical composition of the alloy is given in Table I. Heat-treatment of the alloy was conducted in evacuated vycor capsules for the tensile sDecimens (1.25 bv 0.25 in. gage section) and in evacuated stainless steel jackets for the crack growth-rate panels. All specimens were annealed at 1700°F for 24 hr and water quenched before an exposure at elevated temperatures. Tensile testing was conducted at room temperature in an Instron testing machine equipped with a pushbutton control for instantaneous control of the cross-head motion. In this manner the change in stress, Aa, accompanying an increase in strain-rate by a factor of 10 was measured immediately after yielding. The crack growth-rate panels used were 3 by 18 in. with a precrack 0.33 in. long cut into the center of the panel. The panels were cycled at a maximum gross stress of 40,000 psi at a maximum to minimum tension stress ratio of 20. Cycling of the specimens was continued until the crack propagated the width of the panels. The crack length was intermittently measured during slow crack growth. EXPERIMENTAL RESULTS Correlation of Embrittlement to the Critical Temperature for Ordering. Blackburn6 has found that the critical temperature, T,, for the formation of Ti41 in a Ti-8 pct A1 alloy with an interstitial content on the order of that given in Table I is approximately 1245°F. The relationship between the ductility of the binary alloy used in this investigation and T, was estimated from tensile tests on specimens which were exposed for 24 hr at various temperatures followed

Jan 1, 1970

By Rex B. McLellan

A simple model for dilute interslitial solid solutions is set up which enables a solubility equation for the equilibrium between the solid solution and the gaseous solute to be deduced. This solubility equation is used to estimate the partial thermody -namic functions of Ag-O and Fe-N dilute interstitial solid solutions from the measured equilibrium between these solutions and the gas phase. It is shown that the partial excess entropy of the solute atom in solution is a vibrational entropy which is due Principally to the oscillation of the interstitial atom and does not arise from electronic or elastic interaction between the solute atoms and solvent matrix. In this work measurements of the equilibrium between dilute solid interstitial solutions and a gaseous phase are used to deduce the important thermody-namic functions of the solid solution with the aid of a theoretical solubility equation formulated from a knowledge of the thermodynamic functions of the gas and a simple model for the solid solution. The quantity of principal interest which is deduced from the equilibrium data is the change in vibrational entropy occurring when a solute atom (u) is placed in an interstial site in the solvent (u) lattice. This paper forms part of a more general study in which the properties of condensed phases are deduced from measurements of the equilibrium between the condensed phase and a gas. Previous investigations have dealt with the equilibrium between krypton and liquid metals,' a pure metal and its vapor,' and dilute substitutional alloys and the vapor,3 and the subject has been popularly reviewed by McLellan.4 In the latter investigation3 the vapor pressures of very dilute Cu-Ag and Cu-Au alloys were measured with a Knudsen cell technique over a large range of temperatures and the analysis of the vapor-pressure data showed that the relative partial excess entropies were large and positive [ds= -Sudk = 30 for Au-Ag alloys and 150 for Cu-Au alloys; these values should be compared to unity, the value assumed for these exponentials in the quasi-chemical theory of solutions]. For many interstitial solutions experimental data is available for the equilibrium between the solution and a gaseous phase, and this can be used to deduce the vibrational entropies of the solute atoms in solution. The general method employed is to calculate the chemical potential of the solute atoms in the gas and equate this to pi, the chemical potential of solute atoms in the solid, which is deduced from a simple model set up for the dilute interstitial solution (in which the solute atoms act as bound oscillators in interstitial sites). This enables a theoretical solubility equation to be set up. In the case of Ag-O and Fe-N solid solutions the solubility c, is found to vary with temperature according to a relation of the type, where PU2 is the pressure of the O2 or Np molecules. Essentially, the theoretical solubility equation enables the parameter A(T), which gives the vibration entropy, and the parameter AH, which gives the energy of solution of a solute atom, to be estimated from the measured variation of solubility with temperature. The solutions treated are dilute enough to enable solute-solute interactions to be neglected so that the partial energy and excess entropy of solution E, and GS are not functions of composition and the configurational entropy is that of a random solution. Large positive values have been found for sxSu this quantity has not been given sufficient consideration in recent work on interstitial solutions and it is felt that the partial thermodynamic quantities of very dilute solutions should be understood before the thermodynamics of concentrated solutions can be fully appreciated. EXPERIMENTAL DATA 1) The Silver-Oxygen System. The measurements of Steacie and Johnson,= using silver foils, indicate that there is a pronounced minimum in the solubility vs temperature curve for O-Ag solutions. Eichenauer and Miiller6 have recently redetermined the solubility of oxygen in silver using a method developed in the investigation of metal-hydrogen systems.7 The solubility determinations were carried out on compact specimens of differing shapes and sizes and the results indicate a much lower solubility than was obtained by Steacie and Johnson with no minimum at 400°C. Subsidiary experiments showed that the erroneous results of Steacie and

Jan 1, 1964