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By F. L. Fayers, J. W. Sheldon

It has been a matter of concern to the petroleum industry to determine what effect the capillary term has on saturation profiles, since these profiles determine ultimate economic oil recovery. In their original solution of the non-capillary two-phase flow problem, Buckley and Leverett&apos; showed that solutions of the two-phase flow equations became multiple-valued in saturation. Since it is physically unrealistic for saturation to have more than one value at a given position, Buckley and Leverett resolved this difficulty by introducing a saturation discontinuity or "shock". They evaluated the strength and position of the shock from material balance considerations. Recently Sheldon, Zondek and Cardwell&apos; have demonstrated that the method of characteristics can be used to solve this and related problems. Owing to capillarity it is physically unlikely that saturation shocks occur in an oil reservoir. Buckley and Leverett suggested that the effects of interfacial tensions should be included in the fluid flow equations, if the solutions are to give continuous single-valued saturation distributions. An analogy to this problem is encountered in the theory of wpersonic compressible flow where the introduction of the viscous term eliminates shock behavior. However, the mathematical form of the capillary term in the porous medium fluid flow equations differs from the viscosity term in the Navier-Stokes equation. This paper demons~rates that capillarity does eliminate the triple-valued behavior and indicates the magnitude of capillary and gravity effects on the saturation profile for a variety of systems. DERIVATION OF LAGRANGIAN AND EULERIAN FORMS OF THE DISPLACEMENT EQUATION The equations representing capillary, two-phase flow are given by applying Darcy&apos;s law and a material balance condition for each phase. The familiar Darcy and material balance equations are as follows. ^U*^0......<3, ^^r=°......c« S is the saturation of the water phase, and B the inclination of the porous medium. Pressures in the oil and water phases differ by the capillary pressure associated with the interfacial tensions, P.-P.=pAS)..........(5) where p, is determined experimentally. The porous medium is said to be oil-wet if P, > Po and water-wet if P, < Po. If the fluids are incompressible and the total volumetric flow rate, q, is constant, then v, f v,, = q...........(6) By eliminating P.. /»,, and v, from Eqs. 1, 2, 5 and 6 it follows that It is convenient to normalize the variables in the problem after the manner of Handy and Hadley% so that Eqs. 3 and 7 become where j,, = —, the fractional flow of water; (F, is a capillary pressure normalizing constant.) Substitution of Eq. 9 into Eq. 8 gives In this partial differential equation for an initial value

By Stanley D. Michaelson, Norman Weisis

The purpose of beneficiation is to increase the economic value of an ore by elimination of waste rock or by separation of minerals that require separate reduction, without destroying the physical and chemical identity of the minerals. Flotation has replaced older methods of beneficiation to a very great ex- tent, nearly entirely in the case of the copper, lead, and zinc minerals and less completely in the case of such other minerals as iron, coal, and titanium. Flotation is also used to recover barite, fluorspar, feldspar, cement rock, spodumene, vermiculite, silica, beryl, and potash in the nonmetallic field, and cobalt, vanadium, germanium, antimony, mercury, molybdenum, manganese, nickel, gold and silver, cadmium, and bismuth for metals. The rapid growth of flotation to pre-eminence cannot be attributed to its low cost, because gravity, magnetic, and electrical methods may in some cases cost only half as much. But for ores containing finely disseminated minerals, these other methods are successful only in exceptional cases, for example the magnetic taconites or titanium-bearing sands. For low grade ores with coarse texture or spotty mineralization the advantages of low-cost gravity methods and highly efficient flotation are often combined, as in the beneficiation of coal and some ores of lead and zinc, phosphate, tungsten, and manganese. When an ore is responsive to either flotation or non-flotation concentration, or to combinations of the two, the choice depends upon cost of the process only when dealing with ores of low value; in other cases it is dictated by either the process efficiency or the product specification. Generally speaking, flotatio.1 is so efficient as compared with other methods of concentration that process cost is rarely an important factor in its selection. It is said, "The metal in the mill tailing has already been mined." Once the mining cost has been paid it doesn&apos;t increase total costs very much to do a thorough job of milling. With the exception of the few types of ores that are not amenable to flotation, the chief reason for preferring electrical and gravity methods to flotation may lie in the specification of the product. Flotation demands fine grinding, and specifications may not permit this with many nonmetallic ores or coal. Another reason is the size of investment-where capital is hard to obtain or the life of the property is short, the justification for a flotation plant may not exist, and one must be content to skim off the cream. y not exist, and one must be content to skim off the cream. Gravity processes often cost less than flotation because a large part of the waste rockcan be rejected without costly grinding, no chemicals are required,

Jan 1, 1962

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute&apos;s influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger&apos;s argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.&apos; Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute&apos;s influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute&apos;s influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is &apos;uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b&apos;e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970

By E. E. Underwood, L. L. Marsh

Aluminum single crystals, alloyed with 0.042 atomic pet Cu and 0.11 and 1.1 atomic pct Mg, were subjected to constant stress creep tests, tensile tests, and hot hardness measurements within a temperature range of 300° to 866OK. Calculations based on Dorn&apos;s temperature-compensated time parameter, 6, gave a value of DH, = 27,000 cal per mol for the activation energy of early creep in aluminum single crystals. Correlations have been obtained for aluminum alloy single crystals with the parameter E for solid solution strengthening, as well as with the parameter F for solid solution hardening, by using a valence of three for aluminum. Limited measurements on tensile specimens show that the slip band density tends to decrease with increasing temperature and with decreasing solute concentration. INCREASING interest is being shown in the mechanisms of plastic deformation in single crystals during tensile and creep testing. The complexity of deformational processes in polycrystalline materials has led to a search for simpler experimental conditions. Numerous creep and tensile investigations have been conducted with pure, metallic single crystals. To a lesser degree, the effects of alloying elements on the tensile properties of single crystals have been determined. However: the literature dealing with the effects of alloying additions in single crystals under creep conditions is vanishingly small. This paper represents an attempt to narrow this gap in the knowledge of the subject. Previous investigations of creep behavior at the Battelle Memorial Institute1-1 have been of great value in the analysis of the present single crystal data. It is equally desirable, however, to ascertain the extent of correspondence between the behavior of single crystal and polycrystalline materials. For this purpose, correlations, similar to those developed for polycrystalline aluminum alloys by Dorn and co-workers, have been made with the single crystal data. The results from this study have tended to confirm and extend those correlations to the case of alloyed single crystals. Materials and Procedures Three dilute binary aluminum alloys were prepared for this investigation from 99.99 + wt pct Al, 99.8 wt pct Mg, and 99.92 wt pct (electrolytic) Cu. The nominal compositions of the alloys were 0.042 atomic pct Cu, and 0.11 and 1.1 atomic pet Mg. Precautions were taken to avoid contamination of the stock during melting and casting of the alloys. After a heat treatment of 8 hr at 925°F the alloys were extruded, then machined into) threaded tensile specimens with a 3 in. reduced section and a 0.505 in. diam. Spectrographic examination showed less than 47 ppm metallic impurities in each alloy. The single crystals were grown by the strain-anneal method, with a critical strain of about 11/4 pet giving the optimum results. In general, 3 in. crystals were obtained with the Al-Cu alloy, but smaller crystals in the magnesium alloys necessitated the use of 2 in. and 1 in. gage lengths with the low and high magnesium alloy specimens, respectively. After an electrolytic polish, the orientation of that portion of the specimen containing the largest single crystal was determined from Laue back-reflection photographs. Tensile tests were conducted at a constant load rate of about 2 lb per min. Creep runs were made in a constant temperature room, under constant stress at the higher creep temperatures, and constant load at the lower temperatures. The eloneation was measured to within ±5 microin. by a specially designed capacitance extensometer. The ex-tensometer arms were attached to the 3 in. specimens at the shoulders of the test piece or, where the crystals were smaller than 3 in., by knife-edge grips.

Jan 1, 1957

By E. T. Turkdogan

This paper deals with an analysis of the conditions leading to the formation of blowholes and surface and subsurface defects in cast low-carbon steels. The theoretical analysis of the problem is based on the concept of the occurrence of deoxidation reactions during cooling of liquid steel and during its solidification. The reaction equilibrium data are given on deoxidation of steel by carbon, silicon, and manganese. The details of the calculations are given on the simultaneous deoxidation of steel by silico-manganese additions to produce a desired level of deoxidation at certain residual concentrations. Based on an idealized model, an attempt is made to calculate the enrichment of solutes in the solidifying liquid entrapped within the interdendritic cells which are known to be less than 200 µ thick. Formulae are derived for the calculation of the change in the residual oxygen content of the enriched liquid steel, controlled by Si/Mn deoxidation. It is shown that for every particular initial silicon, manganese, and oxygen concentration in steel (as residuals in liquid solution at the beginning of solidification) there is a particular carbon concentration below which carbon monoxide, leading to blowholes or pinholes, is not expected to form. There are a number of independent variables which have a decisive influence on the formation of blowholes. For example, it is shown that the position of the curve depicting the critical relation between initial silicon and carbon content for suppression of the evolution of carbon monoxide) can be shifted to lower silicon or higher carbon levels by: increasing manganese content; decreasing oxygen, hydrogen, or nitrogen content; or increasing external pressure on the solidifying mass. FOR the production of sound castings it is essential to prevent the formation of interdendritic worm-holes or pinholes brought about by gas evolution during solidification. Another major problem encountered in solidification of ingots is the formation of surface defects. These problems are thought to be closely associated with the deoxidation reaction occurring in liquid steel during cooling and subsequent solidification. As the liquid becomes richer in impurities during dendritic solidification of steel, a series of reactions may occur in the liquid phase trapped within the branches of growing dendrite platelets. Because of the strong interaction between dissolved oxygen and impurities in liquid steel, the reactions most likely to occur are of the deoxidation type. However, inherent to the extreme complexity of the problem in question, numerous simplifying assump-

Jan 1, 1965

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy&apos;s law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-

By H. J. Oberson, J. H. Brown

Comminution devices such as rod or ball mills are characteristically nonselective in their operation in that all material fed to a mill is ground to some extent. This is unfortunate when the object of comminution is liberation, for not only is energy expended in breaking pure gangue particles wasted, but, since gangue is frequently the predominant phase, the opportunity for such loss is great. Ideally, in this application a comminuting device should develop fracture only in locked particles. In the present investigation an attempt was made to use the large density difference which may exist between minerals to prevent comminution of one while grinding the other. EXPERIMENTAL MATERIALS AND EQUIPMENT The two minerals used in this work were -8-mesh galena and -8+ 20-mesh quartz. All tests were made on 2000-g charges containing 50 pct by weight of each mineral. Heavy media suspensions consisted of -100-mesh ferrosilicon in water. For grinding, a laboratory mill 10 in. diam by 12 in. long was filled to about 30 pct of its volume with either a ball or a rod charge. The balls ranged in size from 3/8 to 1 1/8 in. in diam; the rods ranged from 5/8 to 1 1/4 in. diam by 11 in. long. EXPERIMENTAL PROCEDURE In all tests employing heavy media, the ground pulps were treated as follows: 1) After recovering the ground charge from the mill but before drying, the pulp was wet screened on 200 mesh. 2) After drying the + 200-mesh product from step 1, the ferrosilicon was removed magnetically. 3) The nonmagnetic quartz and galena product from step 2 was sized on 10-mesh through 200-mesh screens. 4) The mineralogical composition of each screen fraction was determined by measuring its specific gravity. The specific gravity was related to the weight of galena in the fraction through the relationship

Jan 1, 1961

By J. J. Jakosky

All electrical geophysical methods depend for their operation upon the effects produced by the flow of an electric current. By studying these effects it is possible to predict the general axis of current flow. The greater flow of current is in the path of greatest effective conductivity; and since the effective conductivity of a mineralized zone is different from that of its surrounding envelope (usually much greater), it is possible to locate such a mineralized zone by the distribution of current. Due consideration must be given, of course, to geological structure, to type of mineralization, and to other factors. A number of methods are used to cause this flow of current, and various methods arc available for detecting the presence of such current flow and for studying its effects. In a rather detailed way, this paper will discuss the theoretical and practical phases of the inductive methods of geophysical prospecting. Electromagnetic Generation of an Electeomotive Force The inductive method is so named because the current flowing in the conductor is obtained by electromagnetic induction, instead of by the use of ground electrodes through which a current is passed as in the applied potential systems, or by direct contact with the orebody. An alternating current flowing in a coil will create an electromagnetic field around the coil. This field will have the same frequency as the current and will radiate or travel outward from the coil in closed magnetic or flux circuits. These flux circuits (in air or a homogeneous medium) will be perpendicular to the plane of the coil and will extend or travel outward with uniform velocity in every direction. Maximum feld exists in the plane of the coil. Such a coil used for transmitting or as the "energizer" will exhibit similar figure-eight characteristics to those exhibited by the direction-finding coil which will be described in detail later.

Jan 1, 1929

By A. Raman, P. P. Singh

The constitution of the La-Rh system was studied by powder X-ray diffraction, metallopaphic, and differential thermal analysis techniques and an equilibrium diagram is presented. Eleven intermediate phases occur in the system and the crystal structural data for nine of them were determined. La3Rh crystallizes in an orthorhombic structure of undetermined type, whose unit cell is obtained by doubling the &apos;a; and &apos;c,,&apos; edges of an FesC type unit cell. The other intermediate phases of the system are LarRh-3( undetermined structures also occur in the system. LaRh, undergoes a polymorphic phase transformation at 1240°C. LaRh3 and La2Rh7 also exhibit polymorphisnz. The phases Laah and LazRh7 melt congruently. The latter undergoes a eutectoid transformation into LaRh, and Rh at 1205°C. Laah3 is formed by a peritectoid reaction between Laah and La,Rh,,. The other Phases result from peritectic reactions between the liquid and the adjacent rhodium-rich phases. The intermediate Phases of the La-Rh system are compared with those of the La-Co and La-Ni systems. DURING the course of a detailed investigation to study the occurrence of CrB, FeB, A1B2, and related structures in the rare earth alloys it was found that much information is lacking for the rare earth noble metal systems. Although the structures of several rare earth alloys containing the noble metals at the AB and AB2 stoichiometries have been reported, the occurrence of related structures at other stoichiometries has not been studied. We have initiated a project to study the crystal structural features of selected rare earth-rhodium alloys and to map the equilibrium diagrams of representative systems with conventional methods. The results of our investigation in the La-Rh system are presented in this paper. Two phases were known in the La-Rh system. LaRh has the CrB-type structure.&apos; LaRhz is a MgCu2-type Laves phase.z EXPERIMENTAL PROCEDURE Alloys weighing less than 1 g were prepared from commercially pure lanthanum (99.9 pct +), supplied by Lunex Company, Pleasant Valley, Iowa, and rhodium (99.92 pct +), supplied by Engelhardt Industries, Newark, N.J., in a conventional arc melting furnace under argon atmosphere. The buttons were turned upside down and remelted three times to insure homogeneity in the samples. Since negligible loss of material was encountered during melting, a chemical analysis of the alloy buttons was not undertaken. Powder specimens for X-ray diffraction studies in the as cast state were then prepared. The buttons were wrapped in thin molybdenum foils and homogenized by heating in vacuum at suitable high temperatures for more than 1 week. They were then broken into three or four pieces for annealing experiments. The pieces were wrapped in molybdenum foils and annealed at various temperatures in evacuated quartz capsules. The annealing was carried out for 2 hr at or above 1200°C, 1 day at temperatures close to llOO°C, 2 days at 1000°C, and for 1 week at temperatures below 1000°C. After annealing the alloy pieces were again broken and powder specimens for X-ray diffraction were prepared. The powders of the lanthanum rich alloys with more than 80 at. pct La were prepared by filing. The filings were sealed in molybdenum tubings and stress-relieved at 600°C in vacuum. It was not deemed necessary to stress-relieve the powders of the other alloys, since the alloys were very brittle and were ground easily. POWDER X-RAY DIFFRACTION X-ray diffraction photographs of powders (-325 mesh size) of the alloys in the as cast and annealed states were prepared in a Guinier-de Wolff focussing camera with copper K, X radiations. These patterns were studied to identify the stoichiometries and the crystal structures of the intermediate phases. The lattice parameters of the phases were calculated after minimizing the differences between the observed sin2 6 values, calculated from the diffraction angles 8, and the sin2 8 values, calculated using approximate lattice constants obtained from a few lines. These differences were minimized manually to less than 0.0005. The latLice constants are judged to be accurate to *0.005A for values less thp about 10A and to k0.01~ for values greater than 10A. The relative intensities of the lines were calculated using a computer program written by Jeitschko and Parthk.~ No attempt was made to refine the atomic positional parameters in the phases. METALLOGRAPHY The phase equilibria in the investigated alloys in the as cast and annealed states were also studied by metallographic examination. The polished specimen surfaces were etched with 10 pct picric acid in alcohol (alloys up to 25 pct Rh), concentrated picric acid (from 25 to 37.5 pct Rh), 2 pct nital (40 to 50 pct Rh), 10 pct nital (from 50 to 66.7 pct Rh) and with concentrated 48 pct HF for the other rhodium-rich alloys. Selected microstruture~ were then photographed using a Po-laroid Land camera. THERMAL ANALYSIS Differential thermal analysis of the alloys was carried out in DTA-668 Stone differential thermal ana-

Jan 1, 1970

By Henry Fay

THE erosion of guns is a complex problem which can be solved only by a detailed study of all the factors involved. In the present paper it is proposed to submit the results of observations and experiments which have extended over several years. Certain facts have been established and preliminary reports have been published.&apos; Conclusions have been reached since then which, it is believed, are worth presenting for the purpose of promoting discussion, and with the hope that ultimately the whole truth will be known. The particular phase of the problem which will be presented here is the hardening of the inner surface of the gun tube. It has been known for a long time that after firing a large caliber gun for some time, the surface of the metal becomes hard and brittle, cracks, and wears away.2 The character of this phenomenon may be learned by an examination of some results which are typical, obtained from a detailed study of a 12-in. gun. The gun was trepanned and rings representing various sections of the gun were cut out for examination. The first ring represented the metal at the muzzle end, and the other rings were removed at approximately 120, 240, 325 and 337 in., respectively, toward the breech end. The appearance of the surface of the metal in the different sections is shown in Fig. 1. The greatest amount of wear and maximum amount of hard surface layer was found in section marked E, which is nearest the powder chamber and at the beginning of the rifling; the maximum amount of cracking in D; the maximum amount of copper deposition in C. Section B showed heat cracks on both lands and grooves, and section A showed heat cracks on the driving edge of the lands only. There was much flow of metal in both sections E and D, and there was progressively less effect noticeable toward the muzzle end. The polished cross-section of these same pieces is shown in Fig. 2. The

Jan 12, 1916

By C. Gatlin, M. E. Chenevert

The effects of bedding plane orientation on the elastic constants and the yield strengths of three laminated rocks (one sandstone and two shales) and one isotropic rock (a limestone) were studied. The directional dependence of the elastic properties of these rocks was experimentally evaluated using a triaxial compression cell and auxiliary stress-strain measuring equipment. Symmetry of Poisson&apos;s ratios within the bedding plane suggested that horizontal isotropy exists, but the bedding planes do give rise to an appreciable difference between properties in the horizontal and vertical directions. For the three bedded rocks studied, Young&apos;s modulus was lower normal to bedding than along bedding. Yield strengths were determined at confining pressures from 0 to 12,000 psi in a triaxial compression cell. The rocks studied showed strength reductions as high as 40 per cent when the test specimen was oriented at 20°-30° to the bedding planes. The mechanical behavior of these rocks suggested that the rock properties of shear strength and/or coefficient of internal friction can vary with direction, depending on the particular rock tested. Tensile strengths were also measured and found to be lowest when failure occurred along bedding. This work shows that bedded formations exhibit sizable directional variations in both their elastic constants and yield strengths. It is suggested that these variations may be accounted for by using the "elastic laminate" model and the "variable coefficients" failure model. INTRODUCTION The nature of rock deformation at elevated pressures has been studied by many workers; papers by Handin,l,2 and Robinson3 illustrate the present state of knowledge. Most investigators have either chosen rocks which were as isotropic as possible (in order to avoid complications of data interpretation and analysis) or they have oriented their samples so that the effects of anisotropies (such as bedding planes) have been avoided. Of the studies performed, few were concerned specifically with mechanical anisotrop-ies. Griggs4 has presented limited data for specimens cut parallel, normal, and 45° to the bedding plane; he relates the strength anisotropy observed to the fabric (bedding) anisotropy. His tests were primarily concerned with large deformations (20 per cent strain); thus, no directional values of the elastic constants were reported. Handin has reported the results of similar experiments. Bott5has discussed rock strength anisotropies due to faults, cleavage, or bedding. He was concerned primari ly with determining the shear stress on such planes and did not mention the effect of friction. Jaeger6 later generalized Bott&apos;s work by taking friction into account and presented a limited theory for the failure of rocks having a "single plane of weakness", and also for rocks having a constant coefficient of friction, and a shear strength which varies with bedding plane orientation. Donath and Cohen,7 and Donathg have evaluated rock strengths from shale and slate specimens cut normal and parallel to bedding. A dependence of cohesive strength (7,) on the specimen orientation was also shown. Adler9 has also studied this problem and lists similar results. He assumes that all bedded rocks behave according to Jaeger&apos;s single-plane-of-weakness theory. Kalinin and Belorussov10 list results for strength tests parallel and perpendicular to bedding and use this information as a basis for hole deviation analysis. From the literature it is apparent that sedimentary rocks have been tested under widely varying conditions of stress; however, the assumption of isotropy is generally, but not always, made. Since geologic sedimentation often deposits sediments in very definite lavers.,. it seems that more svstema tic attention should be given to the possible effects of this natural bedding. Bedding, as used here, refers to visible regularities of grain size or orientation resulting from depositional processes. The mechanical strength anisotropies, which bedding may present, is not the only anisotronic property to be considered, since the elastic

Jan 1, 1966

By Avnulf Muan, Egil Aukrust

The activity-composition curve for cobalt oxide in (Co,Fe)304 solid solutions with spinel-type stmcture has been determined experimentally by studying the equilibrium between the spinel phase and a coexisting cobaltowüstite phase, "(Co,Fe)O", at 1200°C. A large negative deviation from ideal behavior prevails in the spinel at low cobalt oxide concentrations and a positive deviation at high cobalt oxide concentrations. The activity-composition curve for iron oxide in the solid solution is determined from the above curve by integvation of the Gibbs-Duhem equation along the join Co3O4,-Fe3O4. The standard free energy of formation of cobalt ferrite, CoFe2O4, from the oxide components CoO and Fe2O3 is calculated to be -8.2 kcal. ThERMODYNAMIC properties of (CO,Mn)3O4 solid solutions with spinel-type structure have been presented recently.&apos; The present paper deals with similar relations in another spinel solid-solution phase, that represented by the system Co3O4-Fe3O4. The principles involved in measurements and calculations of thermodynamic properties for the system Co3O4-Fe3O4 are analogous to those used and discussed in detail in the work on (CO,Mn)3O4. A (CO,Fe)3O4 solid solution coexists in equilibrium with a (Co.Fe)Ot solid solution over a considerable Here acOo1.33 and aao are the activities of cobalt oxide in the spinel and the oxide solid solutions, respectively, pO2, is the oxygen pressure of equilibration, and pb, is the oxygen pressure at which CoO and CosO4 coexist in equilibrium in the binary system Co-O at the same temperature. The activity-com position curve for cobalt oxide in the (Co,Fe)O solid solution in contact with metal has been determined in a previous investigation by the present authors.&apos; The system shows a small positive deviation from linear behavior. Because of the large defect concentration in wiistite and in (Co,Fe)O solid solutions, one cannot assume that the activity-composition relations in the oxide phase coexisting with a spinel phase at relatively high oxygen pressures are the same as those prevailing in the oxide solid solution coexisting with metal. However, a Gibbs-Duhem integration over the ternary Co-Fe-0 solution can be used to determine activities of cobalt and iron, and hence of CoO and FeO, from a knowledge of the oxygen potentials. Several papers have dealt with the subject of application of the Gibbs-Duhem equation to multi-component systems. 3-6 In the present case, it was

Jan 1, 1964

By M. E. Nicholson

The effect of boron on the austenitic transformation rate of iron is smaller than on low carbon steels. The influence of austenitizing temperature on B-Fe is the reverse of its influence on steels. THERE have been many studies made of the influence of boron on the hardenability of steel, but apparently none has been made of its influence on the y-a transformation of pure iron. There are several facts suggesting that boron should have a pronounced effect on the transformation rate of iron. First, Simcoe et a1.l indicated that boron reduces the nucleation rate of ferrite and bainite. Second, they showed, along with others,&apos;, " that the lower the carbon content of steel the greater the influence of boron on hardenability. If this trend extends to pure iron, the influence on rate of ferrite formation should be considerably greater for iron than for medium carbon steels. According to Rahrer and Armstrong," the multiplying factor for boron in pure iron should be about 2.40, compared with 1.50 in a 0.35 pet C steel. According to an extrapolation made by Grange and Mitchell,&apos; the effect should be even greater, and the multiplying factor should be about 3.5 in iron. Many investigations of the boron influence&apos;.7, 2, 5 indicated that boron is effective only when in solid solution. On the other hand, Chandler and Bredig" suggested that boron increases hardenability by combining with nitrogen, thereby preventing formation of AlN, which catalyzes the decomposition of austenite. If their hypothesis is valid, boron should have no effect on an alloy free from nitrogen. Digges et al." showed that so far as low nitrogen high purity Fe-C alloys are concerned this is not the case. No experiments, however, have been made on low nitrogen iron. To determine whether or not boron has an effect on low nitrogen iron and, if an effect exists, to determine whether it is as large as predicted from the investigations of boron treated steels, the following work was performed. Because of the rapidity with which iron transforms from austenite to ferrite at even a moderate degree of supercooling, it was decided to study the influence of boron on the transformation rate of iron by determining the effect of quenching rate on the temperature of the beginning of transformation. The technique, essentially that used by Greninger&apos; and Duwez,H consisted of heating small specimens, 0.1 in. sq and 0.010 in. thick, in an atmosphere of purified helium with a resistance heater coil, and then quenching the sample in a jet of helium gas. At the time the jet was applied, the heating coil was removed from around the sample. The sample was suspended in the furnace on 30 gage chrome1 and alumel wires, one welded to each side of the specimen, which also served as a thermocouple for measuring the specimen temperature. Specimens were prepared from vacuum-melted iron obtained from the National Research Corp. which was rolled to a thickness of 0.060 in. and then decarburized in wet hydrogen for 51/2 hr at 700°C. This treatment also removed any boron present in the iron. The resulting iron contained 0.001 pet C. 0.0002 pet N, and 0.005 pet 0. One half of the piece was then boronized by surrounding it with 325 mesh boron powder and heating it for about 2 hr at 900°C in H,. The boronized iron was then homogenized at 1100°C for 24 hr. The iron boride case formed by boronizing was removed by grinding 0.010 in. from each side of the plate, and the piece was finally rolled to a thickness of 0.010 in. The resulting alloy contained

Jan 1, 1957

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-B alloys has been measured up to the solubility limit for the formation of boron nitride. The activity coefficient of nitrogen increases with increasing boron content in the range 0 to 7 wt pct B. From experimen -tal data, values have been calculated for the B-N interaction parameter e3 at temperatures in the range 1550" to 1750°C. A value of 0.038 has been estimated for the boron self-interaction parameter eg at 1550°C. The standard free energy of decomposition of boron nitride into the elements dissolved in liquid iron has been determined to be: ?F° = 45,900 -21.25T in the range from 1550° to 1750°C. The nitride is assumed to be of composition BN. BORON nitride has an unusual combination of properties which make it appear attractive in a wide range of engineering applications. Some of its more important and most recent applications are in the nuclear area, particularly in connection with the liquid-metal cooled reactor concept now receiving considerable emphasis. Boron nitride has a high degree of stability at elevated temperatures. It also has excellent ma-chinability and the ease with which its crystals deform suggests applications as a lubricant. These properties stem from a hexagonal layer-type structure similar to the structure of graphite. One of its primary uses to date has been for seals in liquid-metal pumping systems. It is also used in nuclear reactors as an insulating layer to separate two solid metals which are not themselves compatible under the conditions of temperature and atmosphere in which they are used. Its inertness to liquid metals has also suggested use as a mold-release agent in casting processes. In addition to its excellent machinability and reported inertness to liquid metals such as iron, silicon, aluminum, copper, and zinc, boron nitride has high thermal conductivity and excellent thermal shock resistance. This combination of properties would make it appear ideal as a refractory crucible material for refining of high-purity liquid metals, for example high-quality steels. However, since it is known that concentrations of boron as low as 50 ppm can have a marked effect on the physical properties of certain steels,&apos; in particular on the creep and stress-rupture properties, an investigation was undertaken to define accurately the chemical equilibrium among boron, nitrogen, and liquid iron in the range of steelmaking temperatures. EXPERIMENTAL PROCEDURE Two experimental approaches to this problem were employed: a Sieverts&apos; method and a quenching method. In the first method, the Sieverts&apos; technique was used to measure the equilibrium nitrogen solubility in liquid Fe-B alloys of 0 to 7 pct B as a function of nitrogen gas pressure over the melt. The solubility limit of the boron nitride phase formed was determined by the point of departure of the nitrogen absorption from Sieverts&apos; Law. This technique has been applied to liquid Fe-Ti alloys by Rao and parlee,&apos; to liquid Fe-A1 alloys by Evans and Pehlke,3 and to solid Fe-V alloys by Fountain and Chipman.4 In the second method a melt of liquid iron was held in a crucible of boron nitride under a known partial pressure of nitrogen gas. After thermodynamic equilibrium was attained, the melt was quenched in a stream of helium and then analyzed by wet-chemical methods for boron and nitrogen. The Sieverts&apos; apparatus used in the first method was essentially of the same design as the one described by Pehlke and Elliott.5 The charge materials were vacuum-melted high-purity iron (Ferro-vac E) supplied by the Crucible Steel Co. and -325 mesh boron powder supplied by Cooper Metallurgical Associates of Cleveland, Ohio. The boron contained less than 0.02 wt pct O, according to supplier&apos;s analysis. Recrystallized alumina crucibles were used to contain the melt. Examination of solidified melts showed these crucibles to be satisfactory with no evidence of any reaction or physical penetration of the crucible wall by the melt. The melt temperature was measured by a disappearing filament-type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diam sight hole in the crucible lid. The pyrometer was calibrated against the melting point of pure iron in the same apparatus, taking the emissivity of

Jan 1, 1964

By Michael F. Dunn, Francis S. Kendorski

The fall of rock from strip coal mine highwalls continues to be the largest single source of fatal accidents, so methods to improve highwall stability through improved blasting practices were investigated in the field. This paper covers the results of a project to improve, using existing and proven technology, unstable highwall conditions through better blasting practices in Appalachian strip coal mines. Better borehole blasting agent distribution and optimization of burden, spacing, and delay periods allowing satisfactory breakage with minimal backbreak were the objectives. At a selected field site, geologic conditions were closely examined with regard to joint orientation and spacing, and resulting slope stability considerations. Utilizing surface blasting concepts of trying to achieve flexural failure of the rock mass both horizontally and longitudinally by appropriate relationships between burden, spacing, and hole length, as well as delay time sequence to achieve optimal confinement and breakage, successful results were achieved. A test series of eight blasts was completed and the resultant highwall monitored by repetitive photography. Actual blockfalls could be measured and the stability for each blast design thus quantified. The study of drilling and blasting economics along with equipment performance led to an economic model of blast parameters and the identification of blast design cost benefits. The work demonstrated that small strip mining companies are able to achieve a more stable highwall excavation utilizing presently available technology, equipment, and explosive products at improved operational cost and safety.

Jan 1, 1983

By James Pollock

SUMMARY THE possibility of colloidal deposition of cinnabar has been neglected. In opalite deposits cinnabar exists in particles within or near the colloidal size range. Colloidal processes have been admitted to be operative in hot springs and low-temperature deposits similar to most cinnabar deposits. Mercuric sulphide sols are stable to elevated temperature and pressure, and in nature probably are chiefly affected by the electrolytes in solution, dilution of colloid, and presence of protective colloids as silica. The stability of mercuric sulphide sols to electrolyte is measured, and shown to be greatly increased by dilution and by the protective action of silica. Mercuric sulphide sols follow the Schulze-Hardy valency rule, therefore the precipitating power of complex mixtures of electrolytes can be computed roughly. The stability of mercuric sulphide sols is shown to be greater than the equivalent precipitating power of the electrolytes in a hot spring depositing mercuric sulphide. It is concluded that finely divided or earthy types of cinnabar are colloidally deposited. POSSIBILITY OF COLLODIAL DEPOSITION While colloidal solution has been suggested as a means of transport for a number of minerals, such as the sulphides of antimony, arsenic, and iron, it has been neglected in connection with mercury. This is surprising because there exists positive evidence that cinnabar is present in certain deposits in particles of colloidal or near colloidal size. Colloidal transport could result from either the rapid dilution or neutralization of alkaline sulphide solution bearing mercury coming in contact with deep ground waters, or from colloidal solution near the original source and subsequent flow to the point of deposition unchanged. That the dilution of a mercuric alkaline sulphide solution will precipitate mercury sulphide in colloidal form has been demonstrated a number of times and is easily confirmed. The dilution hydrolyzes the alkaline sulphide Na2S to the corresponding hydroxide and hydrosulphide NaOH and NaHS, and the diminution of the concentration of alkaline sulphide reduces the solubility. It is not the contention of this writer that colloidal deposition is the mode of transport of mercuric sulphide in all mercury deposits, but that the stability of a mercuric sulphide sol, as demonstrated below, in waters that are similar to those that have deposited mercuric sulphide necessitates consideration of this possibility in many deposits, especially those of the hot-spring and so-called opalite type. EVIDENCE OF COLLOIDAL DEPOSITION Ross1 has shown that most deposits of quicksilver are formed at low temperatures and pressures, and probably by solutions that have relatively simple chemical compositions. In most cases the solutions are probably similar to those observed in hot springs, and in two instances-at Steamboat Springs, Nevada, and Sulphur Bank, California-hot springs have been reported by Becker as actually depositing cinnabar.2 Opalite deposits were believed by early investigators to be surface phenomena

Jan 1, 1944

By R. R. Brandenthaler

CONTROLLING -the pressure under which a well produces crude oil has advantages that are ap¬parently not entirely realized by many operators in the Mid-Continent district. The possibilities of utilizing well pressures are indicated by a series of ex-periments recently completed by the Bureau of Mines in which pressure control was successfully applied to 20 wells in, the Davenport field. The flowing period of all of .the wells was lengthened in some instances it was. more than doubled. The daily oil production from approximately one-half of the tested wells was in-creased. The amount of gas produced per barrel of oil was decreased, and this, in addition to a slower rate of decline in production, indicated that the ultimate re-covery had been increased. The successful application of pressure control to flow-ing oil wells must take into consideration the relation-ships existing between pressures in the different parts of the system which, though not equal, are nevertheless more or less interrelated. These relationships, which have such an important bearing on the results obtained by applying pressure control, are as follows: A change in rock pressure will affect the tubing pressure, casing pressure, and differential pressure, but it will not affect the trap pressure. A change in tubing pressure will affect the differential pressure and casing pressure; also, a change in casing pressure will affect the tubing pressure and differential pressure. Trap pressures are not affected by rock pressure, casing pressure, tubing pressure, or differential pressure, unless the traps are required to handle gas and oil beyond their capacity. Trap pressures will affect the differential pressure, tubing pressure, and casing pressure and any changes at the well-head, whether differential pressure, tubing pres-sure or casing pressure, will affect the pressures in the well. Any change in rock pressure results in a change in the tubing pressure, casing pressure, and differential pressure. When any sudden or unusual change in well-head pres-sures occurs (for example, an erratic tubing pressure), and when a sudden decrease in oil or gas takes place, it is al-ways advisable to note whether the trap pressure has changed. If the trap pressure has not changed, note whether the oil line from the trap to the flow-tank has become clogged, as would be evidenced by a rise in the oil level in, the trap. If the oil line is functioning properly, and if the trap pressure has not changed, the flow-line from the well to the trap should be inspected. If it is free from obstructions, then changes in the differential pressure, tubing pressure, and casing pressure must be due to changed well conditions.

Jan 4, 1927

By Y. L. Yao

THE NaT1-type compound may be considered as the penetration of two diamond lattices in such a way that a superstructure of the bcc lattice is formed. Examples of the NaT1-type compound of lithium are LiZn, LiCd, LiA1, LiIn, and LiGa. Except for LiZn and LiCd, each molecule of these equiatomic compounds contains a total of four valence electrons. In LiZn and LiCd it was suspected (for example, see Ref. 1) that the fourth electron was withdrawn from the 18-shell of zinc or cadmium. An incomplete 18-shell would have to show strong paramagnetism. In 1955 Klemm and Fricke2 determined the magnetic susceptibility of LiZn, LiCd, LiA1, and LiIn (also NaTl and NaIn). The molar susceptibility of the outer electrons of LiZn and LiCd was found to be not strongly but weakly positive; that of LiAl and LiIn not negative but weakly positive. Thus they questioned the hypothesis about LiZn and LiCd in particular and the description of the NaT1-type structure in general. However, they did not determine the magnetic susceptibility of LiGa. This note is to report results for all five compounds of lithium. The starting materials are 99.9 pct pure lithium sticks containing less than 0.005 pct Na. 99.9 pct Zn, 99.9 pct Cd, 99.99 pct Al, 99.999 pct In, and 99.999 pct Ga. Weighed amounts of two components were wrapped in tantalum foil and placed in a graphite crucible. It was found that the tantalum sheath minimized the vaporization losses of lithium during melting. The sheath was easily stripped from the alloy rod and the tantalum in the alloy was barely detectable (less than 0.01 wt pct). The melting was performed in a resistance furnace under an argon atmosphere. Alloy specimens were annealed for 1 hr at 400°C in vacuum. The magnetic susceptibility at room temperature was determined by the Faraday Method, using the procedures previously described.&apos; The results are shown in Table I. The interpolated values at 50 at. pct of Li and the average values at 48 to 52 at. pct of Li at 20°C determined by Klemm and Fricke2 are also shown. It is seen that the present value for LiZn and LiCd is slightly more positive but the present value for LiAl and LiIn is slightly less positive than their corresponding values. Also, it is noted there is an abrupt decrease of susceptibility of LiAl from 51.2 to 52.5 at. pct of Li. Klemm and Fricke2 found that the total susceptibility of LiZn, LiCd, LiA1, and LiIn is almost independent of temperature. slater4 gave a working expression for the diamagnetism of the atomic core as follows:

Jan 1, 1964

By Rex B. McLellan

Studies of the eyuilibrzum between ferrite and austenite with gas mixtures (CO + CO2 and H2 + CHe) have been used as a means of deducing the energy and vibrational entropy of carbon atoms in dilute interstitial Fe-C solutions. A simple model for dilute interstitial solutions is given which enables a solubility equation for the equilibrium between the gas mixtures and the solid to be deduced. This solubility equation is used to estimate the partial In this work measurements of the equilibrium between dilute solid solutions of carbon in iron and gaseous mixtures of CO2 + CO and CH4 + Hp have been analyzed using theoretical solubility equations deduced from a knowledge of the thermodynamic parameters of the gas mixtures and an appropriate model for the solid solution. The solubility equations are deduced by equating the chemical potential of carbon atoms in the gas thermodynamic functions of dilute Fe-C solutions from the measured equilibrium between the solid and the gas mixtures. It is shown that the vibra-tional entropy of a carbon atom in a and y iron is smaller than the corresponding entropy 01. a nitrogen atom in solid solution inferrite or austenite and that there is little difference between the vibrational entropies of both nitrogen and carbon atoms in ferrite and austenite. and solid phases. The chemical potential of carbon in the gas is found from a simple statistical mechanical analysis of the gas mixtures utilizing spec-troscopic data while that for carbon in the interstitial solution is found from a model in which the carbon atoms act as bound oscillators distributed in a random fashion in the solution. The solid solution is dilute enough to enable solute-solute interactions to be ignored. Thus the configurational entropy of the solution is ideal but the mixing entropy contains additional excess terms due mainly to the vibrational changes occurring on solution formation. The partial excess entropies (and the partial energies) do

Jan 1, 1965