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By M. Hoch

Equations are derived from statistical considerations to represent the activities of each component of an interstitial solution, and of a compound with a wide homogeneity range as a function of composition and temperature, based on the interaction energies between the various components, Eij. The equations are checked on the binary systems Fe-C, Ta-H, and Y-H, the ternary systems Ti-O-H, liquid Fe-C-0, and the compounds TiO, MnO, COO, and YH,. In all cases the present model represents the experimental data well. THE aim of this paper is to derive from statistical considerations the thermodynamic behavior of non-substitutional solid solutions. "Nonsubstitutional solid solution" means either an interstitial solid solution (carbon in iron, oxygen and hydrogen in hexagonal and bcc titanium, and so forth) or deviation from stoichiornetry in compounds (introduction of vacancies—removal of atoms in one or both lattice sites of compounds FeO, MnO, TiO, NbO, YH2). wagnerl and Fowler and Guggenheim considered the theory of compounds with small deviation from stoichiometry; Anderson includes larger deviations from stoichiometry, the defect being present in one component only, as vacancy and interstitial. Rees considers only vacancies in one of the components and introduces various kinds of sites for the component where the defect occurs; the various sites interact with different energies, thus giving isotherms with two or more plateaus. Both Rees and Anderson are mainly occupied in determining the limits of two-phase regions, and the defect interaction energy is determined from the critical point. Darken and Gurry5 gave a brief treatment of carbon solution in iron; Speiser and spretnak calculated the configurational entropy for binary interstitial solid solutions by assuming that each interstitial atom in the solution excludes a certain number of neighboring interstitial sites from occupancy. Use will be made of this concept later. Hoch et al treated transition metal oxides of the NaCl-type structure, and also oxygen solution in titanium.' The main aim was to determine the behavior of the activity of one of the components as a function of the composition in the single-phase region. In the present paper, the various interaction energies are discussed in detail and the similarity between interstitial solid solutions and deviation from stoichiometry in ionic compounds is shown. Both types of systems have in common that at least on one kind of lattice site only one kind of atom occurs; this gives a fixed frame to the system, permitting a much easier statistical treatment than for the substitu-tional solid solutions. (The theory is also applied to ternary systems.) The difference between an interstitial solution and deviation from stoichiometry can be explained as follows. In an interstitial solution in the pure or standard state the host atom or host structure is present alone and all the interstitial sites which are going to be filled when the interstitial atom is introduced are empty. The interstitial solution is now created by introducing atoms into this empty lattice. In the deviation from stoichiometry, both kinds of lattice sites are already occupied in a special fashion (all lattice sites occupied, or the same fraction of lattice sites empty, or one kind completely filled, the other only two-thirds). Deviation from stoichiometry removes atoms from lattice sites, adds them, or removes atoms from one kind of lattice site and introduces them on the other lattice site. Though both cases (interstitial solution and deviation from stoichiometry) lead almost to the same equations, they are treated separately. The treatment given below corresponds to the "regular solution"10 treatment of substitutional solid solutions. Speiser and spretnak's6 treatment is similar to the athermal solution in the substitutional use. a) INTERSTITIAL SOLID SOLUTIONS Theory. It will be assumed that there are N lat-tice sites occupied by the host atom (denoted by 1). Corresponding to those N lattice sites there are N octahedral and EN tetrahedral interstitial sites. If only one kind of interstitial atom is added, this in-

Jan 1, 1964

By Oliver B. Knight

The producing formation in the South Field, or "Golden Lane" structure of Mexico, is a buried ridge of reef limestone of Comanchean age overlain unconformably with sediments of Upper Cretaceous, Eocene and Oligocene. The structure extends in a long sweeping arc, with the convex side toward the west, from San Geronimo, Vera Cruz, to San Isidro, south of the Tuxpam River, which it crosses at the town of Alamo. It is 52 miles long and averages 3/4 mile in width. The surface of the producing formation of El Abra limestone consists of a series of minor parallel highs which are separated longitudinally by synclinal troughs and laterally by structural saddles. The presence of these highs has been of utmost importance in the development of the field, especially in recent years when the salt-water level has risen above the synclines and confined the oil to the isolated highs. In many cases, faulty information and interpretation of the subsurface has resulted in drilling costly dry holes and salt-water wells. Development The development of the Golden Lane was started by the Mexican Eagle Oil Co. in 1906. San Diego No. 3, usually known as Dos Bocas, the first producing well on the structure, was completed on July 4, 1908. This well came in unexpectedly for an estimated daily production of 129,000 bbl., and, as the casing was not properly set, the well flowed wild into the Tamiahua Lagoon, causing a loss of several million barrels of oil. In flowing wild the well formed a crater which covers an area of 48 acres, out of which salt water and small quantities of gas still flow. Casiano No. 2, the Huasteca Petroleum Co., which yielded 200 bbl. of oil daily, and which was completed in November, 1909, was the next producing well to be drilled on the structure. In 1910, the same company completed Casiano No. 7, with an initial production of 50,000 bbl. daily, and Casiano No. 1, which produced 200 bbl. daily. In the same year, the Mexican Eagle Oil Co. completed its Potrero del Llano wells 1, 2 and 4, with initial productions of 500, 400 and 100,000 bbl. respectively. From 3910 to the latter part of 1919, development proceeded

Jan 1, 1931

By Alexander R. Troiano, Taylor Lyman

Studies of the transformation of aus-tenite at constant subcritical temperatures have been numerous since the work of Davenport and Rain.' Considerable information has been obtained on low-alloy steels and on high-carbon alloys containing undissolved carbide or graphite at the austenitizing temperature. Little is known of the isothermal transformation of aus-tenite containing in solution large amounts of both carbon and a single alloying element. In this investigation four steels containing one per cent carbon and with chromium in the range 3 to 9 per cent have been examined with the view to establishing the fundamental character of the isothermal reactions when all carbon and chromium are initially in solution in austenite. Experimental Procedure Alloys The chemical compositions of the steels investigated are given in Table I. The 4 per cent Cr alloy is a commercial steel. The other steels were made by the Carpenter Steel Co. as 50-lb., induction-furnace heats and rolled to 5/8 -in. round bars. Bars were softened at 650' to 700°C. before the specimens were cut. Most of the lines on the transformation diagrams presented here have been placed on the basis of the microscopic examinatioll of partially reacted specimens, Thees specimens were approximately 1/2 by 1/4 by 1/8 in. ill size, specimens of the 9 per cent cr steel were held 10 to 12 hr, at 1200°to 1225°C. before quenching to the various subcritical temperatures. The other steels were held for 2 to 2 1/2 hr. at 12ooOC. before quenching. These treatments, carried out in an atmosphere of purified nitrogen, produced an austenite grain size larger than A.S.T.M. So. I, some grains being 1 to 2 mm. in diameter. There were a few undissolved carbide particles in some specimens of the 9 per cent Cr steel. It is believed, however, that any errors in the results due to incomplete solution of carbon and chromium in austenite are negligible; that is, austenite compositions may be considered as being those listed ill Table I. X-ray Methods Constituents were identified and mar-tensite axial ratios determined from Debye

Jan 1, 1945

By Robert D. Pehlke, Weldon L. Daines

The reduction of manganese oxide from a basic slag by silicon dissolved in liquid iron at steelmaking temperatures was studied to determine the rate-controlling step for the process. The experiments were carried out under an argon atmosphere in a resistance-heated vertical-tube furnace. The two liquid phases, slag and metal, were held in zirconia crucibles. Sampling and chemical analysis of the slag phase led to time-concentration curves for the system. Results obtained by varying parameters such as temperature, stirring rate, concentration, and melt geometry defined the limiting reaction mechanism. The reduction of manganese oxide by silicon is a fast reaction and reached equilibrium within 90 min. The rate of stirring has a marked effect on the reaction rate, while, on the other hand, the effect of temperature is very small. This identifies the rate-controlling step as diffusion rather than interfaciul chemical reaction. The variation of other parameters revealed that a) diffusion of manganese in the iron phase is the slow step, b) the value of D/6 for manganese in iron at 1550°C is 7x 10-4 cm per sec, c) the energy of activation for the apparent rate constant is 7 kcal per mole, and d) increasing the amount of silicon in the iron decreases the diffusion coefficient of manganese. THE equilibrium relations pertinent to the reduction of manganese oxide from a steelmaking slag by silicon dissolved in liquid iron have been studied, but little is known about the mechanisms that control the rate of the process. The purpose of the present investigation was to study the rate of reduction by silicon and to determine the rate-limiting step. The effects of stirring rate, temperature, composition, and melt geometry were investigated as a means of identifying the controlling step. On the laboratory scale, relatively little work has been done in the area of slag-metal kinetics, primarily because of the problems confronted in attempting to contain liquid slags and metals in laboratory crucibles at steelmaking temperatures. Since graphite is an ideal material for a crucible, several investigations have been carried out on the reduction of various oxides from a slag by carbon in graphite-saturated iron and on the transfer of sulfur between a slag and graphite-saturated iron. Most of this work has been performed in induction furnaces. Studies where the container was not graphite are extremely limited. A single kinetic study of manganese transfer between molten iron and basic slags was carried out by Sano, Shiomi, and Matsushita.' These investigators prepared calcium oxide and titanium oxide crucibles to contain the two-phase system. Only a few experiments were carried out and the results had to be treated qualitatively. Despite the paucity of kinetic data, a large quantity of information is available in the literature concerning the thermodynamics2-12 and physical properties'3-21 of the slags containing manganese oxide and the dilute liquid iron alloys containing manganese and silicon which were involved in this research program. EXPERIMENTAL METHOD A vertical-tube resistance-heated furnace was used in this investigation to study the slag-metal reaction Although most previous slag-metal studies were carried out in induction furnaces, a resistance furnace has several advantages including better control of temperature and stirring rate. Hence, a resistance furnace was selected for this study, and its design is shown schematically in Fig. 1. Slip-cast, fine-grained, low-porosity, lime-stabilized cubic zirconia crucibles were used for the kinetic experiments. The crucibles were 4 1/2 in. high and 2 1/8 in. OD with a 1/16-in. wall. The crucibles were only slightly

Jan 1, 1969

By E. W. Dewing

The nature of solid solutions of sodium in non-paphitic carbon at temperatures near 1000°C has been investigated by an electrolytic technique. The activity coefficient is found to vary strongly with the heat-treatment temperature of the carbon, and an analysis of the energy terms involved suggests that this is due to variations in the Fermi level. The diffusion coefficient for sodium is in the range implying that the sodium atoms (or ions) are not bound to specific sites on the carbon, in agreement with lack of evidence for specific compounds in the activity -composition curves. In the light of These results phenomena occurring in aluminum reduction cell linings are dis-cussed. It is concluded that sodium migrates by diffusion through the carbon lallice and not the pores, and that A14C9 is formed within the lining hy The excess of NaF invariably found in used linings is formed by this reaction and by air oxidation: There has recently been much interest in the swelling of carbon which occurs when it is made cathodic in an aluminum electrolysis cell, and there is general agreement that the phenomenon is due to the penetration of sodium atoms, derived from the reaction on the carbon lattice. (NaF and AlF3 are constituents of the fused-salt electrolyte.) The low-temperature lamellar compounds of potassium with graphite are well-known, and one compound between sodium and graphite has been reported.4 There is, however, virtually no information on the basic chemistry of the interaction of sodium with nongraphitic carbon at high temperatures, although Dell3 has made some fundamental studies of rates of penetration. At the time the present work was carried out these were not available. Rapoport and samoilenkol had measured rates of physical expansion in a dilatometer, using the fractional increase in length of a carbon specimen after electrolysis in a cryolite bath for 2 hr as an index of susceptibility to cathodic swelling. Work here with a similar apparatus showed that expansion (of a 1.5-in.-diam cylindrical specimen) ceased in less than 20 hr, and that the final expansion was much more reproducible than the value at some intermediate time. This suggested that an equilibrium was being set up, and that a thermodynamic approach was required. The results obtained are not as accurate as had been hoped, but they are the only ones of their type available and have enabled useful conclusions to be drawn. The experimental work was divided into two parts: an investigation of the activity-concentration diagram for sodium in carbon, and a rough determination of the diffusion rate. For the former, most of the experiments were made with petroleum coke even though this is not a form of carbon used in cell linings. It has the advantages, however, that it is a homogeneous material, that it is low in ash, and that its structure is reasonably well understood. Anthracites and coal cokes gave results of the same type as obtained with petroleum coke, but the reprodu-cibility from specimen to specimen was extremely poor. EXPERIMENTAL 1) The Activity-Composition Diagram for Sodium in Carbon. The petroleum coke was ground, pressed at 40,000 psi into plates 19 by 9 by 2 mm without added binder, and heat-treated. The sodium activities were established by an electrolytic technique. The carbon was made anodic in a cryolite bath with an aluminum cathode, and a controlled potential, E, applied so that the sodium activity at the anode was given by ln Na = 1n asa - EF/RT [21 where as, is the sodium activity generated by Reaction [I]. The relative activity is sufficient for many purposes and is simply given by The value of Na not at present known, but when the thermodynamics of the Na-A1 system have been worked out it can be derived from the equilibrium

Jan 1, 1963

By H. P. Greenwald, H. C. Howarth

The rapidly increasing use in coal mines of portable auxiliary fans, which are generally 'blowers" employed in connection with canvas tubing, raises questions concerning the hazards of such equipment, especially where the practices are opposed to established methods of ventilating face workings. Half a dozen or more coal-mine explosions and some fires have been attributed to the use of auxiliary fans; moreover, competent mining engineers have found many dangerous installations and methods of use-for example, intermittent running of the fans in gassy mines with consequent accumulations of firedamp at the faces. These facts have led the U. S. Bureau of Mines to issue this recommendation: "In the interest of safety, the Bureau of Mines, Department of Commerce, recommends that auxiliary fans or blowers should not be used in coal mines as a substitute for methods of regular and continuous coursing of the air to every face in the mine." The comparatively recent introduction of new types of mining machines, mechanical loaders, face conveyors, and slabbing machines has encouraged the trial of new systems of face mining, all of which have for their object the rapid advance of the faces. Although the latter has certain economic advantages, in gassy mines the rate at which gas is given off is generally found to increase in proportion to the speed of advance into new territory, which in turn increases the difficulties of efficient ventilation of the face workings. Some of the systems of advance mining being tried in connection with new mechanizing methods practically compel the use of blower fans and tubing, as single narrow places arc now driven 300 ft. or more without crosscuts. In some instances a series of parallel headings are driven without crosscuts pre-

Jan 1, 1928

By Jim D. Mote, Eugenia M. Howard, Willis L. Barmore, John E. Dorn

The effect of stress and temperature on the creep rate of Ag-33 at. pct A1 and Ag-33 at. pct Al-1 at. pct Zn for prismatic slip was determined over a range of temperatures from 440º to 700°K. The alloys exhibited a brief initial inverted transient creep over which the creep rate increased slightly to a steady-state value which depended only on the stress and temperature, regardless of the previous strain history. The steady-state creep rates were found to be given by: where the activation energy is independent of the stress and strain and agrees fairly well with that estimated for diffusion. The observed creep behavior was shown to be in qualitative agreement with a model based on the stress-induced local disordering in the vicinity of a dislocation. OVER the past fifteen years, considerable progress has been made in correlating the experimen-entally observed plastic behavior of pure metals over each temperature range with one or more of a series of theoretical strain-rate controlling dislocation mechanisms. Despite the current interest in the plastic behavior of intermediate phases and inter metallic compounds, however, very little has been done in identifying the operative dislocation mechanisms in these materials. It is anticipated that the plastic behavior of intermediate phases can be rationalized in terms of the same dislocation mechanisms that are appropriate to pure metals and a solid solutions, provided the additional complexities arising from crystal structure, bonding, long-range order, short-range order, and defect lattices are taken into account. As part of a more extensive investigation on the plastic behavior of intermediate phases, Mote, Tanaka, and Dorn1 recently reported on the effect of temperature on the yield strength for prismatic slip in the hexagonal Ag-33 at. pct A1 intermediate phase as recorded in Fig. 1: Over Region I the deformation was observed to take place as a result of the thermally-activated Peierls mechanism, and over Region II the athermal disordering mechanism applied. The experimental data at that time, however, were not sufficiently extensive to identify the thermally activated mechanisms operative over Region III. It is the purpose of this investigation to attempt to identify the mechanisms that are operative over this high-temperature region. It will be shown that the same mechanism operates all over Region Ill, although the activation energy for this mechanism is in good agreement with that for diffusion, the process cannot be attributed either to the motion of jogged screw dislocations or the climb of edge dislocations. The results, however, are in good qualitative agreement with stress-induced disordering localized at dislocations. EXPERIMENTAL PROCEDURE The alloys studied in this investigation were prepared from silver, aluminum, and zinc (each of purity greater than 99.995 pet) by induction melting under an argon atmosphere and chill casting in a copper mold. Rectangular bar single crystal specimens (1/4 by 1/8 in. in cross-sect ion) of Ag-33 at. pct Al were grown in vacuum by a modified Bridgman technique. Similar Ag-33 at. pct Zn specimens were produced by an identical technique employing an argon atmosphere. The specimens were so oriented that the angle 90-Xo between the tensile axis and the normal to the prismatic plane and the angle A, between the tensile axis and the slip direction were 45 ± 1 deg. The effect of a change in temperature on the creep rate and a change in stress on the creep rate were determined over the temperature range

Jan 1, 1963

By A. Gemperle

Electron diffraction and transmission electron microscopy on foils at room temperature were used to investigate the ordering of Fe-Si alloys containing 10 to 23 at. pct Si. A certain degree of DO3 order was found in all alloys. With the exception of the lowest silicon concentration for which the antiphase domains could not be clearly resolved, the alloys have a domain structure of two-domain type with boundaries having 1/4a01<111> displacement vectors for less than 12.3 at. pct Si and with boundaries having 1/2 a0<100> displacement vectors for more than 12.3 at. pct Si. The alloys with 12.3 at. pct Si have a domain structure consisting of fine domains with 1/2a&apos;o<100> boundaries within much larger domains with 1/4a&apos;o<111> boundaries. The development of these structures can be explained by transition of the alloy from the disordered state into the B2-type order and then into the D03-type order by the mechanism proposed previously for the FeSAl alloys. The existence of the B2 structure in the lower part of the investigated concentration range reported in some articles can be explained by fine domains with 1/2a&apos;o<100> boundaries formed by several disordered planes within large domains with 1/4a&apos;o<111> boundaries. The ordered structure predicted by the theory —with practically no domain boundaries —is found in the alloys having 12.3 at. pct Si where it develops in the B2 structure region. ORDERING in Fe-Si alloys was first studied by phragmenl who found that beginning with 13 at. pct Si the DO3 (Fe3Si) superlattice reflections appear in the diffraction patterns. The equilibrium diagrams constructed later by corson2 and Haughton3 from various measurements proposed the existence of a homogeneous solid solution (a phase) in the range from 0 to 25 at. pct Si. Jette and Greiner4 and Farquhar et al.5 measured the relation between lattice parameter and composition and they considered the break in the curve at 9 to 10 at. pct Si to be caused by the ordered solution a"(Fe3Si). Glaser and Ivanick6 Determined critical ordering temperatures of the alloys containing from 10.9 to 27.9 at. pct Si from the measurement of the electric resistivity of quenched samples. In all cases the critical temperature was lower than the melting point and it was highest for 25 at. pct Si. Lihl and Ebel7 measured the lattice parameter curves at various temperatures up to 1000°C. The region between two breaks on these curves, corresponding to 10 to 12.5 at. pct Si at room temperature, was considered by them to be two-phase (a + a"). They concluded by extrapolation of the measured values that a" in the alloy having 25 at. pct Si is stable up to the melting point. Davies8 studied superlattice reflections in the X-ray diffraction patterns of an alloy containing 8.7 at. pct Si. He found the B2 structure and short-range order in the slowly cooled samples and the DO3 A. GEMPERLE is Research Scientist, Institute of PhysicS, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. __Manuscript submitted January 2, 1968. IMD structure in the quenched and annealed samples. This investigation first reports the presence of the B2 structure, phase a&apos;: in Fe-Si alloys. Meinhardt and krisement9,10 also found its existence in Fe-Si alloys by neutron diffraction. No order was detected by them in the alloy containing 8 at. pct Si. The onset of B2 order was observed at a composition of 9.2 at. pct Si. They found almost perfect B2-type order with partial DO3-type order at room temperature in the 10 to 12.5 at. pct Si range and almost perfect DO3-type order in the 12.5 to 25 at. pct Si range. They established the critical temperatures Tc of both the structures through measurement at higher temperatures. The critical temperature for the B2 structure was found to be always higher than the critical temperature for the DO3 structure of the same alloy. They extrapolated the curves of the critical temperatures and concluded that the alloys with more than 17 at. pct Si have the B2 structure up to the melting point and the alloys with more than 23 at. pct Si have the DO3 structure up to the melting point. The results of Meinhardt and krisement9,10 were confirmed by Dokken&apos;s measurement" of the temperature dependence of the electrical resistivity in the 10.8 to 15 at. pct Si range. On the other hand chessin12 detected by X-ray diffraction a considerably lower degree of order in the 12.7 at. pct Si alloy. ANTIPHASE DOMAIN STRUCTURE IN ALLOYS WITH B2- AND DO$-TYPE ORDER The ordered structures B2 and DO3 can be described in terms of a subdivision of the bcc lattice into four fcc sublattices with a parameter double that of the bcc lattice. Following Marcinkowski13 we will label them I. 11, 111, IV. The B2 structure in the AB alloy is formed by placing A atoms on sublattices I and II and B atoms on sublattices III and IV. In a non-stoichiometric perfectly ordered alloy having concentration (A) > (B), A atoms occupy sublattices I and 11. and A and B atoms distributed at random occupy sublattices III and IV. The DO3 structure in an A3B alloy is formed by placing A atoms on sublattices I, 11, and 111, and B atoms on sublattice IV. In a nonstoichiometric, perfectly ordered alloy having concentration (A)/3 > (B), A atoms occupy sublattices I, 11, and 111, and A and B atoms distributed at random occupy sublattice IV. As further shown in Ref. 13, two types of domains are possible in the B2 superlattice and the antiphase domain structure has associated with it boundaries with displacement vectors 1/4 a&apos;o<ll1> only. Four types of domains are possible in the DO3 superlattice and the antiphase domain structure has associated with it boundaries with displacement vectors 1/4a&apos;o<111> and 1/2a&apos;o<l00>. Bethe14 suggested on the basis of theoretical considerations that in a structure with two sublattices at low temperatures only one domain should be present in the whole crystal at equilibrium. Similarly Bragg15 concluded that at low temperatures the domain struc-

Jan 1, 1969

By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966

By A. E. Perkins

fractured ingot will show a complete diagonal structure. If the temperature is lowered, the equi-axed zone is larger and the pine tree growth is less. A small ingot, though, is prone to this columnar structure, even though the casting temperature is kept down. The speed of cooling after solidification is slower in the hollow ingot than in the solid, therefore the granulation, which takes place after the crystals have formed from the liquid metal, is apt to produce larger grains than in the solid ingot. This is not a detriment. The original crystal size is of much more importance. The size of the grains due to this granulation constantly varies in response to mechanical work and subsequent heat treatment. Surface weakness, as shown by seaming and checking on the exterior when working or by cracking in hardening, is in some measure the result of the surface stresses of the ingot when cast. The temperature of the ingot mold or speed of freezing of the exterior of the ingot is of great importance and much seamy and cracked steel is caused by a too quickly cooled skin. Ingots that are turned or milled all over will not seam very much in working, in fact they are practically free from seams, whereas an ingot rolled without a preliminary machining operation is full of seams and cracks, some long and some short. It has been said that these short seams and cracks in the surface of the bar are the result of elongated depressions in the surface of the ingot and that if an ingot is cast very smooth it should give fewer surface defects. This is partly true, but an ingot cast very hot and having a very smooth skin will crack and seam very badly in the mill, as will the surface of an ingot poured very cold, which is very crinkly, because of the low temperature of the metal. The cause of the cracks and seams in one is not the cause of the cracks and seams in the other. The tube method of hollow drill steel manufacture is superior to the older method because of: (1) Greater freedom from external and internal straining; (2) the inherent small crystal size; (3) absence of harmful segregation, resulting in weakness of wall of hole. (4) less liability for steel to crack in inside of hole during forging or hardening; (5) toughening effect, arising from mild steel wall of hole limiting the intense hardening on quenching. Breakage and Heat Treatment or Rock-drill Steel By A. E. Perkins, Pittsburgh, Pa. Actual figures showing the superiority of one section or another are difficult to obtain. In a given size of steel, however, the cruciform sec -tion shows the most breakage; it is inherently a weak section. It contains less steel per foot than any other standard section of the same size and when rolled the wings tend to cool off setting up cooling stresses.

Jan 1, 1922

By L. S. Castleman, H. A. Froot

A study was made of the growth kinetics of B-brass layers in a-brass us y-brass diffusion couples in which both phases were saturated in the 6 phase. It was found that useful estimates can be made of the difhsion coefficients at the ß-phase interfaces from interface displacement data, which are relatively easy to measure experimentally; also, a useful estimate can be made of the mean heat of activation for diffusion from layer growth data. The effects of pressure on layer growth kinetics were explored and found to be consistent with a vacancy model for diffusion in 6 brass in both the disordered and ordered temperature range. 1 HE study of multiphase diffusion receives relatively little attention in comparison with that devoted to diffusion in homogeneous materials. Of the hundred or so papers on diffusion written each year,&apos; only a few are devoted to the subject, and it is the rare review article2,3 that devotes any space to multiphase diffusional phenomena. This is unfortunate, since the metallurgist frequently encounters practical situations involving cementation processes such as cladding, protective coating of metals, and so forth in which he needs guidance of a fundamental nature. The investigation of multiphase diffusion phenomena is complicated by the fact that one must consider reactions at phase interfaces as well as the migration of atoms within the individual phases; these reactions cause the interfaces to be displaced within the diffusion zone. The relative displacement of two adjacent interfaces corresponds to the growth of an intermetallic layer, and it is not difficult to determine experimentally the kinetics of layer growth. In the past few years it has been pointed out4,5 that valuable fundamental information may be gained about diffusion coefficients and the concentrations at interfaces through a study of their motion. Accordingly, it is the purpose of this paper to report the results of an investigation of interface motion in a simple multiphase binary system. In the work reported herein, attention was focussed on the growth of a 6 -brass layer in a diffusion couple prepared from a- and y-brass compositions saturated with respect to the 6 phase. This particular system was chosen for a number of reasons. First, the bcc ß-brass phase is disordered for all compositions at temperatures above 468°C and becomes increasingly long-range ordered for all compositions at temperatures below 454° C;6,7 thus, the effects of a variation in order on interface displacement could be determined. Second, diffusion coefficients have already been obtained as a function of temperature in the ß phase both in the ordered and disordered Re- and a theoretical picture of the mechanism of diffusion in this and other ordered solutions is emerging.11&apos;12 Third, some thermodynamic data are available for the a-, ß-, and ?-brass phases,13,4 and these data could be used to gain insight into questions of phase equilibria and concentrations at phase interfaces.

Jan 1, 1963

By J. Suiter, H. F. Ryan

H. F. Ryan and J. Suiter (CSIRO)—In this paper the authors have presented "a physical model which has as its central hypothesis the solution strengthening of regions along grain boundaries in the order of tens of angstroms thick", and their calculations have used 40Å as the zhalf-width of this boundary region. Selection of this value by the authors suggests that they were unaware of a number of recent field-ion microscope observations of grain boundary structures (e.g., Refs. 29 and 30). The accompanying figure, Fig. 9, shows a portion of an ion micrograph of a tungsten specimen containing a grain boundary, and the regular arrangement of atoms in various crystal planes in each grain can be seen, except in the boundary zone which is not more than two atom diameters in width. Since it is expected that solute atoms will segregate only to the region where the lattice is disturbed, it would seem that a value of 4Å for the half-width of the boundary region would be more appropriate than the value of 40Å assumed by the authors. If the former value is used in Eq. [8] of their paper to obtain curves showing solute concentration in the grain boundary as a function of temperature, the resulting curves differ significantly from those obtained by the authors. Although there are only relatively slight changes in the regions corresponding to higher temperatures (i.e., grain boundary concentrations of approximately 1 at. pet), at lower temperatures the curves are no longer realistic. For example, the curve corresponding to u = 7000 cal per mole gives a solute grain boundary concentration in excess of 100 pet at a temperature of approximately 360°K, and "flattens out" at a grain boundary concentration of about 300 pet! Similar results are obtained with each of the other curves. Ion microscopy of dilute solid-solution alloys has shown that solute atoms give rise to image points which in most cases are of higher intensity than those of the solvent atoms.31 If the same behavior occurs when the solute atoms are present in much lower concentrations then ion microscopy should provide a sensitive tool for studying the segregation of impurities to the grain boundary regions. Although many grain boundaries in tungsten have been examined after different thermal and mechanical treatments, there has not been, as yet, any systematic study of such segregation. In general the micrographs show no clear indications of marked grain boundary segregation, but occasionally areas are found where the grain boundary contains an appreciable number of image points of high intensity in a very narrow zone, see Fig. 9. If it is assumed that these correspond to impurity atoms then it is possible to estimate the impurity concentration both in the grain boundary and within the body of the grains. Application of this method (to a larger area

Jan 1, 1965

In reply to inquiries and comments which have reached me since the publication of this paper, and in explanation of some seeming discrepancies between my statements in the text concerning the amount of displacement of the faults, on one hand, and certain figures in the plates on the other hand, I give here, with some additional remarks, my measurements of the displacements in the different sections, which it originally seemed unnecessary to print : By displacement, I mean neither the throw, i.e., the vertical distance apart of the two edges of a faulted bed (what Mr.

Jan 1, 1896

By B. Silliman

THE remarkable outflow of natural gas recently developed in Western Pennsylvania, and along the valley of the Ohio and its tributaries, has called attention to an important series of patents for improvements in glass-fnrnaces and the manufacture of glass, which the brothers Siemens have made since 1872. The basement-patent of this series, is No. 127,806 of the U. S. Patent office, and is of date June 11th, 1872. This has been followed by eleven other patents (including one re-issue), all for improvements in glass-furnaces, or methods of manufacture, of which the latest is of date July 11th, 1882. Nine of these patents were issued in 1880-82. The following is the list of these patents, in order of dates, viz.: 1872. June 11th. No. 127,806 (U. S. office), Improvement in glass-furnaces; 17 sheets drawings, 5 pages text. This is the basement-patent. 1877. April 17th. No. 139,800. Improvement in the manufacture of glass; 3 sheets drawings, 2 pages text. Boats and floating vessels swimming in the liquid glass of the tank-furnace. Re-issued in 1880. q. v. 1880. April 27th. No. 226,931. Furnace for annealing and tem pering glass. " July 13th. No. 220,846. Glass-melting-furnace. " August 3d. No. 230,668. Glass-melting-furnace; 4 sheets drawings, 2 pages text.

Jan 1, 1885

GWILLIAM H. CLAMER* (Philadelphia, Pa.).-Sulphur is not so detrimental in its effect if oxygen is also present, so that in sulphur-carrying bronzes and brasses, it is advantageous to maintain a certain percentage of oxygen. As a matter of fact, it would be possible sometimes to correct difficulties by actually adding oxygen. If the cathodes were charged directly into an electric furnace in a neutral or reducing atmosphere, a very high grade of copper would result by a simple melting operation. This would very largely eliminate the loss occasioned by melting in a reverberatory furnace. In such a furnace a large amount of slag is produced during the oxidizing stage of refining. Notwithstanding the fact that melting in an electric furnace might be somewhat more expensive than melting in a fuel furnace, the ultimate result would be a saving and the production of a very high grade of copper.

Jan 1, 1919

By Warren E. Wilson

The transportation of solids in pipe lines is a matter of deep concern in many fields of engineering. Much experimental and theoretical work has been done in an effort to devise means of designing pipe lines that will satisfactorily transport given solid loads, but there remain many unanswered questions in this field. The present discussion will be confined to a rather narrow portion of this field and will endeavor to point out certain factors that may well be considered when comparing the relative economy of various installations. The data have been presented previously but a new interpretation was prompted by a suggestion in a paper by Professor O&apos;Brien,&apos; of the University of California, that the friction work per pound of dry material should be considered in determining the relative efficiency of various installations. This method of considering relative economy in various pipe lines leads to some rather unexpected conclusions, especially with reference to the economy of large pipe sizes. A previous suggestion by the writer concerning the economy of a rather peculiar type of installation is strengthened. It is not believed that the considerations set forth herein apply directly in the case of dredge lines, where economy is largely a matter of a high rate of pumping in order to reduce the unit overhead charge. However, it is believed that some value may be gained from these considerations in cases involving the disposal of a fixed amount of solids per unit time with a minimum expenditure of energy and at a low cost for replacement of worn pipes. Such situations are not uncommon in the disposal of mill tailings and the disposal of solids deposited from irrigation waters. It was found that data leading to general conclusions for various pipe sizes were not available but certain definite trends are indicated and methods of analyzing available data are presented in the hope that they may be of assistance in preparing engineering estimates on designs of pipe lines of the type described above. Energy Requirements Carrying out the idea contained in Professor O&apos;Brien&apos;s paper concerning the method of computing energy required to transport solids, the following analysis leads to some rather interesting conclusions. Let us represent: Solids load in terms of mass per unit time by w Ratio of mass of suspended solids to total mass of mixture flowing by p Volume rate of flow of mixture by Q Length of pipe by L Slope of energy grade line by s Mass per unit volume of solids by m8. Mass per unit volume of liquid by mi Mass per unit volume of mixture by 11 We then have as an expression for the solids load: w = pqmm The work done per unit mass, p, on the mixture to move it along the pipe the

Jan 1, 1947

By Warren E. Wilson

The transportation of solids in pipe lines is a matter of deep concern in many fields of engineering. Much experimental and theoretical work has been done in an effort to devise means of designing pipe lines that will satisfactorily transport given solid loads, but there remain many unanswered questions in this field. The present discussion will be confined to a rather narrow portion of this field and will endeavor to point out certain factors that may well be considered when comparing the relative economy of various installations. The data have been presented previously but a new interpretation was prompted by a suggestion in a paper by Professor O&apos;Brien,&apos; of the University of California, that the friction work per pound of dry material should be considered in determining the relative efficiency of various installations. This method of considering relative economy in various pipe lines leads to some rather unexpected conclusions, especially with reference to the economy of large pipe sizes. A previous suggestion by the writer concerning the economy of a rather peculiar type of installation is strengthened. It is not believed that the considerations set forth herein apply directly in the case of dredge lines, where economy is largely a matter of a high rate of pumping in order to reduce the unit overhead charge. However, it is believed that some value may be gained from these considerations in cases involving the disposal of a fixed amount of solids per unit time with a minimum expenditure of energy and at a low cost for replacement of worn pipes. Such situations are not uncommon in the disposal of mill tailings and the disposal of solids deposited from irrigation waters. It was found that data leading to general conclusions for various pipe sizes were not available but certain definite trends are indicated and methods of analyzing available data are presented in the hope that they may be of assistance in preparing engineering estimates on designs of pipe lines of the type described above. Energy Requirements Carrying out the idea contained in Professor O&apos;Brien&apos;s paper concerning the method of computing energy required to transport solids, the following analysis leads to some rather interesting conclusions. Let us represent: Solids load in terms of mass per unit time by w Ratio of mass of suspended solids to total mass of mixture flowing by p Volume rate of flow of mixture by Q Length of pipe by L Slope of energy grade line by s Mass per unit volume of solids by m8. Mass per unit volume of liquid by mi Mass per unit volume of mixture by 11 We then have as an expression for the solids load: w = pqmm The work done per unit mass, p, on the mixture to move it along the pipe the

Jan 1, 1947

By B. Chalmers, L. Bäckerud

The growth temperature of dendrite tips has been measured in a binary alloy system, Al-Cu, as a function of rate of formation of solid phase. Metallographic examination has rerealed the dendritic structure dereloped during different stages of the freezing process and factors influencing the undercooling, such as solute buildup, surface tension, and kinetic effects, have been estimated. Practical implications of the results are discussed. THE development of a dendritic growth pattern during the solidification of metals and alloys has an influence at least equal to that of grain size on the properties of the casting or ingot being produced. and consequently much interest has been devoted to the study of this phenomenon. A review of the knowledge gathered up to 1964 has been given by Chalmers.&apos; Among recent publications in the area the works of Jackson et al 2 and Flemings and his coworkers3,4 are of special interest. This work is an experimental study of the factors which influence the development of a dendritic pattern during the solidification of a typical binary alloy system, A1-Cu, when there is no heat source in the liquid. This means that the temperature and the temperature gradient are controlled by the heat extraction from and latent heat evolved by the growing crystals. EXPERIMENTAL PROCEDURE Samples were prepared from a master alloy made up of aluminum, 99.995 pct, and copper. 99.99 pct, of the concentrations given below and of sufficient size to fill cylindrical graphite molds of 35 mm ID and 35 mm height. Bottom. wall. and lid of the graphite molds were all of 6 mm thickness, Fig. 1. Thin ceramic thermocouple shields could be introduced at different positions in the sample through holes in the lid. The assembly was heated in a small vertical resistance furnace to a suitable temperature. 700° to 720°C. which is well above the melting point of the sample. It was thereafter taken out of the furnace and chilled at selected rates, and the temperature changes in the sample were recorded. For high sensitivity in the temperature recordings, a reference thermocouple was held in a solidifying pure aluminum melt. which was very well insulated and therefore was at a constant temperature. 660°C, for nearly half an hour. The thermocouples were connected so that the difference voltage was fed into the recorder of which the most sensitive range was 1 mV. Temperature variations could be read to within 0.l°C. The thermocouples used were of the Chromel-Alumel type (28- or 38-gage wires) and the recorder a two-pen Moseley strip chart recorder. The different rates of chilling were obtained in the following way. a) The graphite crucible was wrapped in one or two layers of an insulating. feltlike material (Fiberfrax paper from the Carborundum Co.). The drop in temperature per unit time after complete solidification could thereby be varied from 8" to 18°C per min. This corresponds to a rate of heat extraction in the given samples from 0.08 to 0.17 cal cm-&apos; sec-I. 6) The bare graphite mold was placed free on a piece of firebrick. The measured temperature drop was around 50°C per min (-0.5 cal cm-" &apos; sec- I). c) By blowing compressed air through a tube with many holes surrounding the mold in a ring shape. the rate of heat transfer could be raised to 150&apos; to 200°C per min (-1.7 cal cm-3 sec- I). d) Cooling rates around 1000 C per mill (-9.4 cal cm-3 sec-l) were obtained by substituting the air in the device used in c by water. The range of cooling rates used in these experiments correspond to technical casting processes from slow solidification as obtained in sand molds to very rapid freezing which occurs in some continuous casting and welding processes. EXPERIMENTAL RESULTS The A1-Cu system was chosen for the experiments: the relevant part of the phase diagram is reproduced in Fig. 2. Observation of the Center Temperature. When a thermocouple is inserted in the center of the melt. the type of cooling curves obtained at slow solidification rates differs little from numerous published curves from similar systems. and the solidification pattern

Jan 1, 1970

By Keith Leonard Sutherland

THIS paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C. being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate-free.&apos;&apos; Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. PURITY OF REAGENTS The xanthates were purified in the usual manner.1 Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes. This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystal-line powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. RESULTS The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1942

By W. P. Saunders, W. R. Hibbard, G. H. Eichelman

Interest in the various products of the austenite eutectoid transformation in iron-carbon alloys, particularly as produced by the isothermal sub-critical techniques introduced by Davenport and Bain,&apos; has resulted in the application of similar heat treatments to other eutectoid transformations. Studies o f the beta copper-aluminum alloy eutectoid transformation revealed microstructures very similar to those found in iron-carbon alloys. Investigations5t6 of the kappa phase in the copper-silicon alloy system have established the eutectoid type transformation of this phase into terminal alpha and intermediate gamma phases. This transformation has been reported5 as forming a eutectoid type structure in a very sluggish manner by a long time isothermal treatment. The purpose of the present investigation is to study the products of the kappa eutectoid transformation as affected by transformation temperatures by means of microscopic and hardness methods. Preparation of Alloys The copper-silicon alloy equilibrium diagram is shown in Fig 1. The kappa field converges to a minimum silicon solubility at the eutectoid composition and all other completely kappa alloys are hypereutec-toid. Thus, kappa decomposition involves first the proeutectoid precipitation of gamma, followed by the eutectoid transformation of a lower silicon content kappa (5.2 pct) Smith6 has indicated that alloys containing between 5.4 and 5.7 pct silicon could be hot rolled, but that the latter composition was desirable in order to permit a wider kappa temperature range. The alloy was prepared by adding Baker&apos;s commercially pure silicon to an ingot of copper-silicon alloy containing 2.34 pct silicon remaining from the investigation of Brick, Martin and Angier.&apos; Following the casting techniques of Krynitsky, Saunders and Stern,s the ingot was melted under a heavy layer of dried charcoal in a clay-graphite crucible in a gas-fired pot furnace. Small lumps of silicon were held under thc melt surface with a graphite rod. After the silicon had dissolved, the alloy was chill-cast and then remelted without a cover, stirred thoroughly, skimmed and poured into a preheated cast iron mold. The cast microstructure is shown in Fig 2. The casting, 10 X 4 X K in., was annealed at 750°C for 21 hr and furnace cooled, About }{& in. was milled from all surfaces. The plate was cut in half longitudinally and the bottom half analyzed by A.S.T.M. and The composition by weight was as follows: copper 94.24 pct, silicon 5.56 pct, iron 0.11 pct.

Jan 1, 1949