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By Thomas R. Stauffer

The principle that conventional schemes for taxing petroleum or mineral resources are "inefficient" is illustrated using simulation calculations tested against an "ideal" system. Inefficiency is defined as the relative success in maximizing expected government revenues from the resources. Most systems fail because: 1) they leave oil in limbo, i.e. unproduced because of excessive fiscal burden; or 2) they unnecessarily increase the variance in the explorationist'c, rate of return by undertaxing large fields and overtaxing smaller but infra-marginal fields. This increases his discount rate and reduces taxable surplus. An "ideal" tax system is specified which maximizes government revenues while minimizing risk to the operator. Two criteria are developed: 1) the tax falls to zero on fields which yield only the minimum necessary rate of return ("marginal" fields); and 2) the after-tax present value of all fields is the same for all fields above a threshhold size. In particular, marginal fields, while contrib- uting little to expected values, do contribute to reducing variance and hence risk praemia by distributing the exploration costs over a higher probability of successful outcomes.

Jan 1, 1982

By Francois Clerf

IRON ORE fields are situated in both the East and West of France (see maps). The eastern deposit is by far the most important from a tonnage point of view, not only in France, but in all Europe. The ores of this region are known as minette, and are situated in the Lorraine ore fields and the Briey plateau. The iron ores of the West are those of Normandy, Anjou and Brittany. Before the war, a large number of important German companies had acquired considerable interests in these western fields and a heavy trade with Westphalia had begun. Recently, however, conditions have changed and some of the mines of Brittany and Anjou are now idle. From a geological point of view, in Anjou and Brittany, a series of synclines extends from the northwest to the southeast, containing a number of seams of varying thickness and generally intercalated in Silurian and sometimes in Devonian formations. The ore is generally a hematite or a magnetite. The composition varies from 48 to 52 per cent of iron and from 8 to 12 per cent of silica. Con¬servative estimates indicate a con¬siderable tonnage of workable ores (150,000,000 metric tons).

Jan 1, 1936

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By S. Wiederhorn

The energy and force of interaction between a crack and a slip band have been calculated. When the distance between the crack and the slip band is greater than the dislocation spacing of- the slip band, the force on the cgrack is perpendicular to the slip band. The energy needed to propagate a crack against this force can be lawe enough to pevmit crack propagation parallel to noncleavage planes. SEVERAL recent experiments have demonstrated the occurrence of crack-slip band interaction in ionic crystals having a NaC1-type structure. Stokes, Johnston, and Lil have studied the nucleation and growth of cracks in MgO. From their observations, they conclude that slip bands have the ability to halt and stabilize cleavage crack nuclei. Gilman2 has shown that a crack, propagating along a (100) cleavage plane in a previously deformed LiF crystal, tends, at certain points within the crystal, to switch to (110) planes. He reasons that plastic deformation reduces the cohesive energy of the (110) planes below that of the (1130) planes, making possible (110) crack propagation. Keh3 has demonstrated that when indentations are made in MgO, crkcks form along (110) planes at the indentations. Gilman2 attributes the formation of these cracks to plastic cieformation. There is some doubt as to the formation of cracks on (110) planes. Kuznetsov4 in his discussion of crack propagation in rock salt, shows that splitting along (110) planes requires 1.76 times as much energy as splitting along a stepped (100) surface. Therefore, the observed (110) cracking in LiF and

Jan 1, 1962

By T. Rosenqvist

From the chemical, metallurgical, and mineralogical points of view, the importance of thermodynamic data for metal-sulphides and sulphur dissolved in molten metal has long been realized. Such data will give a basis for thermo-dynamic calculations of processes such as roasting and the distribution of sulphur between molten metal and slags. Furthermore, it will help us understand the chemical forces which tie sulphur to the metal and to the melt. Thermodynamic studies of solid sulphides and the equilibria between solid sulphides and metals have been carried out in a rather large number of cases by several investigators. An excellent review of this work is given by Kelley.1 On the other hand, very little is known about the thermodynamic properties of molten sulphides and of sulphur dissolved in molten metal. The only system which previously has been investigated in this respect is the iron/sulphur system. The purpose of the present investigation was primarily to obtain further data for metalisulphur melts and the system silver/sulphur was chosen, not because this system was expected to be of special interest in itself, but because the silver/sulphur system is a typical example of a metal/sulphur system. Because of the low melting temperatures, the work could be carried out without appreciable furnace and refractory difficulties. The sulphur in this system possesses a rather high escaping tendency compared to most other metal/sulphur systems. By the method employed (reaction with hydrogen to form hydrogen sulphide) this gives ratios Ph2s/Ph2 up to 0.30, which may be determined accurately. 'rhermodynamic investigations of the heterogeneous reaction Ag2S +H2 —+ 2Ag + H2S have previously been carried out by Pelabon,2 Keyes and Felsing,3 Jellineb and Zakowski,4 Wat-anabe,6 and Britzke and Kapustinsky.6 Their results are in rather poor agreement. Experimental Part PRINCIPLE In the present invehgation the escaping tendency of sulphur from the condensed phase was determined by the reaction: S + H2 = H2S The ratio Ph2s/Ph2 is at constant temperature, directly proportional to the escaping tendency of sulphur and to its chemical activity in the condensed phase. (This ratio will subsequently be denoted by H2S/H2.) From this ratio and its variation with temperature and with change in the com- position of the condensed phase, thermodyrlamic quantities such as free energy and heat of reaction can be derived. The apparatus used is shown in Fig 1. The silver/sulphur alloy was placed in a crucible inside a refractory tube and mounted inside the furnace to the left. The tube was a part of a closed, gas-tight system in which the gas mixture could circulate until equilibrium was established. Circulation was maintained by the glass propeller to the right, driven by an external magnet, and promoted by the chimney action of the furnace. The gas passed up through the furnace, down into the crucible where it came in contact with the alloy, passed rapidly up through a narrow tube and out of the hot zone. After equilibrium was established between the gas and the condensed phase, the composition of the gas mixture was determined from its density. In its circulation, the gas mixture passed through a chamber (lower right on Fig 1) containing a buoyancy-balance, where the density of the gas was determined by magnetic balancing. From the measured density,

Jan 1, 1950

By B. Post, D. Moskowitz, F. W. Glaser

Lattice parameters of various hafnium compounds, two borides, a carbide and a nitride were determined. Some physical properties were measured and comparisons with the properties of the corre-sponing zirconium compounds were drawn. A LTHOUGH borides of transition metals have A been extensively investigated in recent years, there are few references in the literature to borides of hafnium. This is not surprising, in view of the extreme scarcity and great cost of the purified metal. Becker' reported the existence of a boride, carbide, and nitride of hafnium; he listed the formulas as HfB, HfC, and HfN. However, in his work no mention was made of chemical analyses of the reaction products. In this paper results of a study of various hafnium compounds, including borides, carbides, and nitrides, are reported. It was expected, of course, that these compounds would closely resemble their zirconium analogues, which have previously been extensively investigated. Three borides of zirconium are known: ZrB,² ZrB,² and ZrB212.4 In addition, one carbide, ZrC,5 and one nitride, ZrN,5 have been reported. It should be noted that ZrB and ZrB12 are stable phases only in relatively high-temperature regions, unlike ZrB2, which is stable from room temperature to its melting point." It was felt that hafnium would yield corresponding borides, carbides, and nitrides with similar stability ranges. Experimental Procedures and Results A quantity of hafnium metal that was better than 97 pct pure, with zirconium as its major impurity, was furnished by the Argonne National Laboratories. The boron powder used was approximately 96.5 pct pure. In general, the procedure involved mixing the metal and boron powders in the desired proportions, and subsequently hot pressing them. The resulting specimens were analyzed chemically and phases present were identified by X-ray diffraction methods. A Philips Norelco Geiger counter spectrometer was used for identification of components and for measurement of lattice constants. Filtered copper radiation was used for all X-ray work. Electrical resistivity and density measurements were carried out at room temperature. The stable diboride, HfB2, will be described first. Stoichiometric quantities of boron and metal were heated to approximately 2000°C during hot pressing. The reaction product was shown by X-ray diffraction methods to be isomorphous with ZrB2 (space group Dlgh; P6/mm). Values of lattice constants of HfB2 compared with those of ZrB2 are shown in Table I. The calculated density of HfB2 is 11.2 g per cc, compared with a measured (pycnometric) value of 10.5 g per cc. HfB2 specimens prepared under a wide variety of conditions (including variations in initial Hf-B ratios) showed only insignificant variations in lattice constants, indicating a very narrow range of homogeneity. Like ZrB2,7 HfB2 is an excellent electrical conductor. The resistivity at room temperature of hot-pressed samples, approximately 85 pct dense, is 12 microhm-cm. This compares favorably with the electrical resistivity of 10 mi-

Jan 1, 1954

By C. Ernest Birchenall, Robert F. Mehl

APPLICATION of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion coefficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner1 derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smiths on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 ACTIVITIES IN BRASS9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by azn = Pza/Pzn° [I]

Jan 1, 1947

By R. K. Buhr, H. Thresh, M. Bergeron, F. Weinberg

The microsegregation of nickel and chromium in directionally solidified AISI 4340 steel castings has been measured using electron probe microanalysis. Minimum concentrations were observed to occur at the center of the dendrite stalks, as reported previously. However, the position of the maximum concentrations could not be determined from the dendrite configuration. An etching technique has been developed which shows the position of maximum concentration. Measurements were made of the distribution of nickel and chromium in the dendritic structure. The ratio of maximum to minimum concentration was determined as a function of primary dendrite arm spacing for both as-cast and partially homogenized materials. The results are compared with observations reported in the literatuve. A S part of an investigation of solute segregation in directionally solidified AISI 4340 steel casting, electron probe microanalysis was used to measure the distribution of nickel and chromium in the dendritically segregated material. This complemented the observations on the segregation of radioactive phosphorus obtained by autoradiographic techniques in the same castings.' Kattamis and I?lemings2 have reported similar measurements, using electron probe microanalysis, on dendritically segregated AISI 4340 steels. They found minimum solute concentrations occurred at the center of dendrites, maximum concentrations occurred in the center of interdendritic regions, for symmetrically oriented dendrites, and a regular variation of concentration within dendrite arms. The ratio of maximum to minimum concentration was found to be essentially independent of position in the castings, except near the chill surface where it was somewhat higher. Assuming complete diffusion in the liquid and no diffusion in the solid during freezing, they considered that isoconcentration curves in the steel were homothetic. As a result, isoconcentration curves of the various elements, contour surfaces of dendrites produced by isothermal-transformation studies, and the contour of the solid-liquid interface would all be similar, and could be superimposed by a uniform expansion or contraction of the contours. Preliminary results of the present investigation suggested that isoconcentration curves were not homothetic. It was also evident that points of maximum concentration could not be predicted from the dendrite configuration. Since the ratio of maximum to minimum concentration appeared to be an important parameter in defining the overall segregation in a casting, other techniques for determining the point of maximum concentration were investigated. In addition the overall solute distribution associated with the dendritic structure was examined for both nickel and chromium, and the consistency of the distribution for neighboring dendrites was determined. METHOD Fifty-pound heats of AISI 4340 steel were cast in a manner similar to that used by Flemings et al3 with a water-cooled copper base plate and exothermic sides and top. The nominal composition of the material was C, 0.41 pct; Mn, 0.66; Si, 0.35; S, 0.012; P, 0.010; Ni, 1.88; Cr, 0.95; Mo, 0.28. The steel solidified directionally from the chill surface, with a dendritic structure which increased in dendrite arm spacing with increased distance from the chill. Results of the general investigation of the cast structure and segregation of radioactive phosphorus in these castings have been reported elsewhere.' For the present measurements, sections were cut from the casting at several distances from the chill surface. The sections were subsequently heat-treated, mounted, and then polished on a plane perpendicular to the general freezing direction of the casting. Electron probe microanalysis was carried out with the JEOL-JXA3 microprobe using a voltage of 25 kev and beam current of 0.15 µa. The take-off angle is 22 deg. Quartz crystals were used in the spectrometers and measurements made for Ka radiation from both nickel and chromium simultaneously. A thin layer of carbon was deposited on all specimen surfaces prior to examination in the microprobe. Early measurements were made on polished surfaces, with indentation marks produced by a hardness tester to indicate the area of interest. It was found desirable to use etched surfaces, as opposed to polished surfaces, to reduce sample preparation time and more readily relate the microprobe scan to the structure. To determine if this could be done, without introducing significant errors, a series of measurements were made on polished and etched surfaces of the same specimen. Both polished and etched surfaces produced similar results within normal scatter as shown in the observations. Subsequent measurements were then made on etched surfaces. Measurements with the microprobe analyzer were made by point counting, for periods of 100 sec, at 10-µ intervals. Ten-second counts were made on pure nickel and chromium standards, incorporated in the specimen mount before and after each set of measurements. The results were adjusted for background, then corrected for dead time using the expression:

Jan 1, 1969

By Edmund J. Korber, Donald E. Raab, Frank A. Burns

During the early 1960s, the advent of self- advancing longwall roof supports triggered serious consideration by Bethlehem management to introduce the technique of longwall mining at one of our central Pennsylvania coal mines. Although longwall mining was initially justified as a means to cope with the severe roof conditions at our Mine 32 (Watson, B., 1971), the result of the endeavor has been a consistent and reliable level of coal production, first from Mine 32 and then later from Mine 33, over a period of fifteen years. Longwall production from the Cambria Division has been the mainstay of the low volatile coal required by Bethlehem Steel for steel production. Let us review the events that led to this accomplishment, as well as where we stand today.

Jan 1, 1981

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by

By H. A. Doerner

PROPOSALS to use hydrocarbon or natural gases for the reduction of zinc from oxide materials may be traced back through Patent Office files to the early years of the present century. Natural gas at rates cheap enough to compete with solid fuels has been available at or near one major zinc district for more than a decade. That the seemingly meritorious and economically interesting applications of these proposals have not devel-oped into workable processes for direct production of zinc by natural gas cannot be completely ascribed to the proverbial conservatism of the zinc industry. It is possible to produce spelter commercially in normal times from zinc oxide and carbonaceous reducing agents without having a very precise understanding of the chemistry of the process. The reduc-tion by hydrocarbons is not, however, in this class, and the technical complexity of this reduction metallurgy and chemistry prohibits solution of the inherent difficulties by the "hit and miss" methods that are some-times thought to be practical. In a thermodynamic study of the chemistry of zinc smelting, Maier1 made a preliminary study of the chemistry of the use of methane for reducing zinc oxide by thermodynamic means, pointing out that the following reactions, the limits of which could be theoretically predicted, were important: ZnO + CH4 = Zn(gas) + CO + 2H2 [1] CH4 = C -I- 2H2 [2] ZnO + CO = Zn(gas) + CO2 [3] ZnO + H2 = Zn(gas) + H2O [4] Other possible reactions, not discussed in the reference quoted, are: CO2 + CH4 = 2CO + 2H2 [5] H2O + CH4 = CO + 3H2 [6]

Jan 1, 1933

By C. Wagner

When an alloy solidifies and the composition of the solid differs from the composition of the liquid, atoms of the alloying elements rejected at the solid-liquid interface have to diffuse toward the bulk liquid. Diffusion may be supported by convection. Theoretical calculations have been made for a liquid without convection, for a liquid involving natural convection, and for solidification of a liquid alloy at the surface of a rotating disk as an example of forced convection. WHEN an alloy solidifies, the equilibrium composition of the originating solid phase differs in general from the composition of the liquid phase. Thus, segregation may take place, i.e., the composition of the solid phase formed at different times differs from the bulk composition. The degree of segregation depends on several factors such as the partition ratio of the alloying elements between the liquid and the solid phase, the rate of solidification, and convection. To clarify, a theoretical analysis has been worked out. The following presuppositions are made: 1—Calculations are confined to the solidification of binary alloys in which the concentration of component A (solvent) is much greater than that of component B (solute). 2—The equilibrium concentration of the alloying element B is assumed to be lower in the solid phase than in the coexisting liquid phase. 3—At the solid-liquid interface, partition equilibrium is assumed. 4—The dependence of the partition ratio of the solute between the liquid and the solid phase on concentration and temperature is disregarded since only small concentrations of the solute are considered. 5—The concentration of the alloying element B in the solid phase is supposed to be lower than the saturation concentration for the formation of a second solid phase. 6—diffusion in the solid phase is disregarded, since diffusion rates in the solid state are comparatively low. When the partition ratio of the solute between the liquid and the solid phase is greater than unity, a part of the solute is rejected at the solid-liquid inter- face and has to diffuse toward the bulk liquid. Thus there is necessarily a concentration difference in the liquid between the solid-liquid interface and the bulk liquid as has been pointed out by Hayes and Chipman,' Rutter and Chalmers,' Tiller, Jackson, Rutter, and Chalmers, and others (see Fig. 1). In view of the concentration gradient in the liquid phase, the ratio of the concentration of the solute in the solid phase to that in the bulk liquid differs from the equilibrium ratio, although at the solid-liquid interface, partition equilibrium is assumed. Under certain limiting conditions, the solid may even have virtually the composition of the bulk liquid as is shown below. General Equations Let u be the linear crystallization velocity in cm per sec, D the diffusion coefficient of component B in the liquid phase in cm2 sec-', c',, and c", the concentrations of component B in the liquid and the solid phase, respectively, in mol per cm", and s the distance from the solid-liquid interface toward the bulk liquid at a given time t. The partition ratio is assumed to be equal to a partition constant K. Thus. The difference in the specific volume between the liquid and the solid phase may be disregarded. In view of the discontinuity of the concentration of the solute at the interface according to Eq. 1, u(c', — c",), , , = tic', (S = 0)(1 — K) gram-atoms B per unit area per unit time are rejected at the interface and have to diffuse toward the bulk liquid. From Fick's first law it follows that uc',,(s = 0) (1 ~K) == - D(dc',,/?>s). _-„. [2] The concentration profile in the liquid near the interface depends on the interplay of diffusion and convection as is discussed in the following sections. A schematic concentration profile is shown in Fig. 1. The "effective thickness of the diffusion boundary

Jan 1, 1955

By Stephen G. Wright

Jan 1, 1985

By E. T. Hayes, A. H. Roberson, M. H. Davies

ZIRCONIUM has been produced on a pilot-plant scale for only a few years, but the potential uses have led a large number of research establishments to engage in a thorough study of the metal and its alloys. The work described in this paper is part of a cooperative project between the Bureau of Mines and the Air Materiel Command. The Zr-Cr system was one of the first investigated because of the possibilities of improving the properties at elevated temperatures, the chemical corrosion resistance, and the mechanical properties of zirconium in a manner similar to the enhancement of the properties of titanium by additions of chromium. There is no published work on the Zr-Cr system but from the similarity of the metals involved it was expected that it would be similar to the Zr-Fe' and Ti-Cr' systems. The materials used in this investigation were prepared in the Bureau of Mines laboratory at Albany, Ore. Zirconium was produced by magnesium reduction of zirconium tetrachloride, and a typical analysis is as follows: Fe, 0.06 pct; Ox, 0.08; N?, 0.01; C, 0.02; and other impurities such as Al, Pb, Ni, Ti, and Si less than 0.01 pct each. High purity chromium was prepared by treating crushed electrolytic chromium in a stream of dried and purified hydrogen." The resulting powder contained about 0.01 pct 0 and about 0.1 pct total metallic impurities. All alloys were prepared by arc-melting 50 g briquetted compacts of the desired composition in a Kroll-type" arc furnace using an inert atmosphere. The furnace was evacuated twice and backfilled with helium, which was gettered by melting a center zirconium button immediately before the alloys were melted. Alloys were remelted at least once to insure greater uniformity of composition and subsequently were annealed in vacuum at 1250°C for 48 hr. Fairly homogeneous alloys were obtained by this means; a slight loss of chromium from the surface by evaporation during the high temperature homogenization was noted. All alloys were analyzed for chromium and gave results in good agreement with the nominal composition. Spot checks on tungsten and nitrogen showed pick-up of these elements to be negligible. Over 70 alloys were prepared for use in this investigation; only the critical ones are shown in Table I. Alloys containing up to 10 pct Cr were amenable to hot working at 850°C and a number of these were sheath rolled to 1/16 in. thickness. Specimens were cut from the sheet for use as metallographic samples. For the thermal analysis a differential couple was used in conjunction with an X-Y recorder, the temperature of the specimen and the difference in ternperature between it and the standard nickel body were recorded simultaneously. Heating and cooling rates of 5°C per min were used. The sensitivity of the instrument was such that a difference in temperature between the specimen and standard equivalent to 0.1 mv produced a deflection of 1 in. on the recording chart. The chromel-alumel thermocouples were checked against a Bureau of Standards calibrated thermocouple. Melting-point determinations were made in a high vacuum induction furnace using an optical pyrometer. The pyrometer, calibrated against nickel, copper, and zirconium (iodide process) under near black body conditions, was focused on the base of a hole drilled in cylindrical samples. A North American Philips Geiger counter X-ray spectrometer was used for all diffraction studies. This instrument, in addition to supplying precise intensity measurements of planar reflections, has an added advantage in that metallographic specimens mounted in bakelite can be used directly, and this

Jan 1, 1953

By B. R. Coil

One executive writing on capital equipment re- placement stated: "We keep extremely close watch over repair costs and when we reach the point of uneconomical operation, we replace the machine." This, of course, is most elementary, but a very basic premise. However, it seems advisable to set forth several equally obvious principles, so that all discussion will start from the same point. The subject is intended to deal with the point of uneconomical operation due to high operating costs in general and high repair costs in particular. This is not concerned with a similar problem of high costs because of an insufficient number of machines, be they trucks, shovels, or dozers.

Oct 1, 1955

By W. Hodge, A. F. Haskins, R. M. Evans

Refractory boron compounds are shown to resist corrosion by molten zinc. Coatings were made from ferroboron and manganese boron by several methods: welding, hard facing, and pack diffusion; and techniques of coatings are very important. Mechanical failure of the diffusion coatings can be partially eliminated by applying them to type 416 chromium steels rather than carbon steels. Welded coatings made with a tungsten arc are better than those made by other welding methods. Sintered compacts of mixtures of iron and chromium borides developed strengths of about 30,000 psi. They resisted corrosion of zinc at 600°C and oxidation at higher temperatures. MOLTEN zinc rapidly attacks common metals of construction. The rate of attack is greatly amplified at temperatures over 500°C. However, there are many applications where it is necessary, or at least advantageous, to use metal construction, such as for galvanizing pots and zinc smelter equipment. Condensers and agitator linings used in continuous zinc smelting processes are eroded and corroded by violently agitated molten zinc. Pumps, tubing, and other parts to permit transfer of molten zinc would be desirable in many zinc handling operations. The development of metallic materials which are resistant to molten zinc also might permit its use as a heat-transfer medium in modern high efficiency power plants. In reviewing previous work on zinc-resistant metals, it was evident that most of the available data refer to corrosion at temperatures just above the melting point. Tungsten and high Mo-Fe alloys containing more than 80 pct Mo resist corrosion by molten zinc.', ' Imhoff states that because chromium is not attacked by zinc, chromium plating improves galvanizing pot life." Nitrided cast iron has been used in die-casting machines' where the molten alloy is 96 pct Zn and 4 pct Al. Other metals that have been suggested as of possible value for zinc resistance are columbium, tantalum, and titanium.V he corrosion of steel by zinc has been discussed by many authors,z, "2 None of these materials resisted corrosion by molten zinc at the temperatures used in this investigation, i.e., 600" to 700°C. I. Exploratory and Resistant-Coating Tests To make a study of zinc-resistant metals, exploratory tests were conducted to sort out roughly those materials which seemed most worthy of further development. This preliminary study included both solid metals and surface coatings. Exploratory Corrosion Tests in Molten Zinc—In initiating a study of this problem, numerous samples of metals and alloys were evaluated by dynamic corrosion tests made at 440 °C. Each metal was tested in its most readily available form, which, because of shape and size, was often unsuited for standard corrosion testing. The equipment used for dynamic corrosion testing of all materials, except in a few initial experiments, is shown in Fig. 1. Samples were tied to tungsten rods with tungsten wire, immersed in the zinc, and revolved at 12 rpm about the circumference of a 4 in. diam circle. Speed of travel was about 12.5 fpm. The molten zinc was protected from oxidation by an atmosphere of carbon monoxide, or, at a later period in the program, by a 9:1 mixture of nitrogen and hydrogen. When the effect of both molten metal and atmosphere was desired, the zinc level was lowered. Special high grade zinc was used in all of the corrosion tests. Corrosion losses for materials tested are shown in Tables I and 11. Whenever the materials were available in suitable form, the losses are reported in mils per year. It was recognized that weight losses on irregularly shaped specimens did not show the corrosion rate but the important consideration—poor resistance to corrosion—could be determined readily.

Jan 1, 1956

By Oliver S. North

Reserves of perlite rock in the western section of the United States are immense. A geological report prepared for the Union Pacific RR showed proved tonnage of over 400 million tons in southern Nevada alone. Yet the perlite industry is not large, and most of the mines are relatively small. There are indications that perlite processing, thus far largely in the hands of relatively small com¬panies, is becoming concentrated in a few large companies. For economic reasons the bulk of perlite sold in crude form has come from three or four pro¬ducers, although many individual operators have sold small quantities to limited lists of purchasers. Perlite is one of ultra-lightweight aggregates. Owing to its outstanding qualities as an aggregate, variety of uses, and ultimate economy of use, it has enjoyed considerable popularity in this country in recent years. Marked foreign interest also has been evinced in this material.

Jan 2, 1955

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method' for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By Sylvain J. Pirson

The question of the interpretation of apparent resistivity curves is still a much disputed subject although the discussion has been going on for several years, mainly since Gish and Rooneyl made their first measurements on the Tidal Basin at Washington, D. C. As a first approximation, they interpreted the depth to a horizontal discontinuity in terms of the electrode spacing at which a maximum or a minimum occurs in the resistivity curve. Later on, Lancaster-Jones2 proposed a closer approximation of depth determination by evaluating the depth to a horizontal discontinuity as the two-thirds of the electrode spacing at which a point of inflection occurs in the resistivity curve. An accurate determination of the depth was recently proposed by Tagg3 for a two-layer problem. It is a graphic solution of the problem by means of charts calculated from the formula of the apparent resistivity based on the theory of electrical images. Tagg's method is theoretically sound but the fact that the layers have been assumed to be homogeneous and isotropic must not be overlooked. Abusive use of the method has been made by geologists who have failed to recognize the fact that nature offers only few cases where the conductivity of the rocks may be assumed to be the same parallel and perpendicular to the bedding plane. Actually the ratio of the two resistivities in those directions may take values ranging from one (isotropic medium) to three for shales. In such conditions Tagg's method leads to disappointments. A method recently advocated by Manhart4 and Tattam6 forces Tagg's method to give a solution where manifestly the case under

Jan 1, 1934

THE Nominating Committee appointed at the Division meeting in October and consisting of Frank A. Herald, A. W. Peake, C. R. McCollom, Joseph Jensen, H. W. Camp, C. P. Watson, F. Julius Fohs, George Otis Smith, J. B. Umpleby, J. M. Lovejoy and A. W. Ambrose, have presented the following ticket for the year 1929: Chairman, Joseph B. Umpleby; associate chairman, A. C. Rubel; secretary-treasurer, R. Van A. Mills; vice-chairman for Economics, Warren A.. Sinshein~er; vice-chairman for Engineering Education, H. C. George; vice-chairman for Engineering Research, Harry H. Hill; vice-chairman for Production, C. P. Watson;vice-chairman for Refinery Engineering, A. D. David. For Production Engineering Charles V. Millikan. is named vicechairman, with ,Charles E. Beecher, Glenn D. Robertson and W. W. Scott as associate vice-chairmen. The Executive Committee named is to consist of Joseph B. Umpleby, chairman with A. W. Ambrose, Charles E. Beecher, A. D. David, Glenn D. Robertson, H. C. George, Harry H. Hill, John M. Lovejoy, Charles V. Millikan, R. Van A. Mills, Earl Oliver, A. W. Peake, A. C. Rubel, W. W. Scott, Warren A. Sinsheimer and .C. P. Watson, members. Ballots will be mailed to members of the Division.

Jan 1, 1928