Search Documents

By Morris Cohen, Robert C. Ruhl

Fe-Ni-B alloys were inresligated by X-ray diffraclion after splat quenching. Although this rapid cooling did not produce a measurable supersaturation of dissol1ed boron in either binary Fe-B or Ni-B alloys, a marked increase in dissolved boron was achieved by the splal quenching of lernary Fe-Ni-B alloys. Boron additions up to 2.0 wl pcl to Fe-13Ni and Fe-24Ni alloys cause an increase in retained austenite from 0 to 59 pet and to 92 pet, respectively. The martensitic phase in the Fe-13Ni-9 at. pct B alloy is .found to conlain about 0.6 at. pet interstitial boron, as evidenced by the tetragonality of this phase, and about 3.6 at. pct substilutional boron, us deduced from the lattice paratrieler decrease, the balance of the boron being precipitated as (Fe,Ni)aR. The austenitic Fe-Ni-B plznses also contain both interstitial and substitutional boron. Iron-Boron System. The phase diagram and related information about the solid solutions and intermediate phases in the Fe-B system are given by ansen,' Elliott.2 and Pearson.1 The equilibrium solid solubility of boron in both ferrite and austenite is quite small: the maximum solid solubility of 0.02 wt pct B (0.11 at. pct B) occurs in iron at the eutectic temperature of 1150°C. while the maximum solubility in a iron is less than 0.01 wt pct.l There is disagreement in the literature as to whether these solid solutions are substitutional or interstitial. Based on the measured activation energy of boron diffusion in iron, it appears likely that boron moves interstitially in austenite. 4 However, this observation does not rule out the possibility that some of the dissolved boron may also occupy substitutional sites in this phase. Investigations of internal friction of boron in iron have suggested that boron is interstitial there.' Shevelev, 5 on the other hand, reports a decrease in the ferrite lattice parameter with dissolved boron content, thus indicating a substitutional solution. Unfortunately. Shevelev's methods and analysis are unclear. Goldhoff and spretnak6 have measured the lattice parameters of pure iron and an Fe-0.005 wt pct B (0.027 at. pct) alloy at both room temperature (ferrite) and from 920° to 1200°C (austenite). They reporte: a lattice contraction in the ferrite of 0.0003 ± 0.0002 due to boron, thus indicating a predominately substitutional solution. Appreciable (0.0010 to 0.0060) lattice contractions were found in boron-containing austenites, but these effects were much larger than could be accounted for by the substitutional solution of all the boron present. Nickel-Boron System. Elliott 2 gives a summary of thephase diagram and recent work on this system. The solubility of boron in nickel reaches a maximum of 0.03 wt pct at the eutectic temperature of 1080°C. Iron-Nickel System. ansen' presents the equilibrium diagram for this system and also discusses the metastable austenitic and martensitic phases along with the a=? transformations. The lattice parameters of Fe-Ni ferrites have been recently redetermined by Abrahamson and Lopata.7 Their data, Fig. 1, show an unusual change in slope at about 1.7 at. pct Ni. Very few measurements of the lattice parameters of Fe-Ni martensites are available in the literature. The values of Roberts and Owen8 are considerably higher than those measured in the course of the present work: they find that a, is constant at 2.874? from 8 to 30 at. pct Ni. Both the slope change in the ferrite parameters and the occurrence of a maximum plateau in the marten-sitic lattice parameters vs composition denote the

Jan 1, 1970

By R. L. Pober, L. Kaufman, E. V. Clougherty

Composite structure of hafnium, zirconium, and titanium diboride with additions of metals and/or compound phases were prepared by reactive high-pressure hot pvessing and evaluated in air and in mixtures of oxygen and helium at temperatures up to 2400°K and at linear flow rates of 0.1 to 0.2 ft per sec stp. Oxidation characteristics, principally depth of conversion of diboride to dioxide, were determined by a gas analysis method and by postoxidation metallo-graphic analyses. The best oxidation resistance was observed for hafnium diboride-silicon carbide composite which exhibited a 6-mil conversion to dioxide for a 1-hv oxidation in air at 2200°K compared to a 20-mil recession for hafnium diboride with no additive. Analogous improvements in oxidation resistance were observed for the addition of silicon carbide to zirconium. EARLIER investigationof the oxidation behavior of the diborides of the transition elements of Groups IVA and VA in flowing gas mixtures have produced a ranking of these compounds according to which HfB2 is the most oxidation-resistant followed in turn by ZrB2 > TiB2 > TaBz > NbB2. Other ~tudies~-~ have examined the physical, thermal, and thermodynamic properties of these diborides to provide a sound basis for the more detailed and specialized investigations which are required to generate the information needed to assess the usefulness of such materials in high-temperature oxidizing environments. Recent oxidation studies7 have examined the effect of variations of metal and boron content on the oxidation characteristics of zirconium and hafnium diboride in flowing gas mixtures including air and helium plus oxygen. Results obtained in the latter investigation confirmed the superior oxidation resistance of HfB2 over ZrB2. Moreover, metal-rich compositions of hafnium diboride showed improved oxidation resistance over boron-rich compositions at temperatures up to 2000°K; at higher temperatures the differences are not distinguishable. In particular HfBI.7 exhibited a diboride to dioxide conversion depth of 4 mils in 1 hr at 2000°K; HfB2. 2 exhibited a conversion depth of 16 mils for the same exposure.~ Specimens for the study of metal and boron stoichiometry on the oxidation characteristics of HfB2 and ZrB2 were prepared by high-pressure hot pressing, a specialized type of fabrication which produced dense crack-free bodies of the desired compositions with no significant impurity introductions. The purpose of the present investigation was to explore the possibility of further improving the oxidation resistance of the metal-rich ZrB, and HfB2. The plan to accomplish this objective was based in the formulation of several diboride compositions containing other compounds and phases which are generally known to have good oxidation resistance in one or more types of test environment. Ideally, such additives would also enhance or at least not diminish other boride property values principally mechanical strength and those parameters related to thermal stress resistance. The additions selected for HfBz included zirconium, aluminum, and (Ta + TaB2) designed to produce ternary metal diborides, hafnium to form a discrete HfB phase, chromium to provide a metal skeletal phase, (Hf + Si) to form a discrete hafnium silicide phase, and Sic to provide a discrete second phase. Additions to ZrB2 included A1 + B designed to produce a ternary metal diboride, Zr + Si to form a discrete zirconium silicide phase, and Sic to provide a discrete second phase. All the specimens were prepared by high-pressure hot pressing which was used to advantage to fabricate billets of the variety of compositions desired and suitable for oxidation testing. The present investigation also included the evaluation of high-pressure hot-pressed TiB2and TiB2-20 vol pct Sic, conventionally hot-pressed Boride 2,' and KT silicon carbide. Boride

Jan 1, 1969

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, ' the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

By G. Derge, Ling Yang, John Henderson

Self-diffusion coefficients of aluminum have been measured by the capillary reservoir technique in liquids of the CaO-SiO2-Al2O3 system containirg equimolar portions of CaO and SiO2, in the temperature range 1400o to 1520oC. For the melt containing 6.0 mole pct Al2O3 the results can be expressed by the equation D = [(4.3 * 0.3) x 104] exp [(-85,000 * 17,500)/RT]cm~sec-'; for the melt containing 12.5 mole pct Al2O3, by the equation D = (5.4 i 0.2) exp [(-60,000 * 10,00O)/RT] cm2sec-: A concept of the constitution of these melts has been developed which proposes that the ratios O/(Si +Al) and Al2 O3/CaO determine the dominant species present. In recent years considerable work has been done on the system CaO-SiO2-A12O3 with a view to elucidating the structure of liquids of this system. Conductivity,' electromotive force, 3 density,4 and activity5 measurements have all contributed to an understanding of the problem, but as yet there is no entirely satisfactory theory that can account for all the observed experimental results. In principle, measurements of self-diffusion coefficients should give further information which is not obtainable in other ways. Self-diffusion coefficients for calcium, silicon,6 and oxygen7 have been measured. The present investigation extends the series of self-diffusion coefficient measurements to include aluminum and develops a concept of constitution for liquids of this system which is compatible with all the observed experimental results. EXPERIMENTAL The technique used in the measurement of the self-diffusion coefficient of aluminum was the capillary-reservoir method,8 A126 being incorporated in the melt contained in the capillary and inactive aluminum in the reservoir melt. This method was chosen because it minimizes convection currents' in the diffusion zone. It has the further advantage that the boundary conditions are such that a slight modifica- tion of Anderson and saddington's8 solution of Fick's Law yields an equation which requires measurements only of the length and the initial and final average specific activities of the solidified melt within the capillary. where t is the diffusion time, Co is the average specific activity of the melt contained in the capillary at t = O, C is the average specific activity of the melt contained in the capillary at t = t, 1is the length of the capillary, and D is the self-diffusion coefficient. The equation is of somewhat different form than those previously applied to high temperature diffusion studies because the specific activity of the melt in the reservoir was negligible both before and after diffusion. The diffusion apparatus is shown schematically in Fig. 1. It consisted of a silicon carbide resistance furnace containing the inactive melt in a graphite crucible, internal dimensions 7/8 by 4 in., enclosed in a 1 1/4- by 1 1/2- by 30-in. McDanel tube. A 3/8-in. McDanel thermocouple sheath to which graphite radiation shields and a graphite protection tube were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube the capillaries could be lowered into or raised out of the melt. Temperature was measured with a Pt-Pt 13 pct Rh thermocouple which was calibrated periodically against a standard couple. The furnace temperature was controlled to ± 5°C through the thermocouple immersed in the melt. Temperature variation over the depth of the melt was less than ± 3°C. The inactive melts were prepared from pure native quartz, assaying better than 99.9 pct SiO2, A.R. grade A12O3 and A.R. grade CaCO,. The same quartz and CaCO3 were used in preparing the active melts, the

Jan 1, 1962

By C. Gatlin, M. E. Chenevert

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

Jan 1, 1966

By Elmars Ence, Harold Margolin

The titanium-aluminum system has been investigated in the composition region 0 to 34 pct Al in the temperature range 800" to 1450°C. The phases encountered in this region were: a,ß, TiAl3, The reactions observed are as follows: 13 ; L - 6T. A1, 0 (15 pct Al) + 6 (18 pct Al) - yTi Al (16.5 pct Al) at -1170°C andP (7 pctpct Al) + y (9.2 pet Al) - ah(9 pct Al) at - 1060°C. A eutectoid reaction: y — a +d belm 700°C is postulated. THE Ti-A1 system has been the sub.ect of a number of investigations. Several of these1-3 have indicated extensive solubility of A1 in both a and ß titanium. Ence and Margolin, as a result of work on the Ti-A1-0 system:'5 have shown that the a solubility ofalumi-num is considerably restricted, and found that a compound, Ti2A1 existed in the region formerly designated as Q a This structure was identified as hexagonal with c/a = 0.803. Pietrokowsky confirmed the existence of this phase7 and pointed out that the structure was isomorphous with Ti3Sn.8 Although the existence of Ti,A1 has been confirmed by others,9-12 there has been considerable disagreement regarding the composition and mode of formation. A detailed reinvestigation of the Ti-A1 system has been published by Sagel et al.13 The tentative diagram indicated two phases, a, and e, occurring in the former all a region. The a, phase has the same structure as Ti2A1 and was indicated as having a broad region of solubility. Epsilon, a tetragonal phase, was shown to form within the a, solubility region. AS a result of unpublished work,14 Ence and Mugy3 olin disagreed with the interpretation of Sage1 et al., although some common features existed. The present study was conducted in an attempt to clarify prevailing uncertainties. EXPERIMENTAL PROCEDURE Alloy Preparation—Alloys were prepared from iodide titanium (99.9 pct Ti with less than 0.01 pct Zr) or Bureau of Mines electrolytic titanium (BHN-73) and high purity aluminum (99.99 pct). Alloys were arc-melted in argon or helium atmosphere as 15-g buttons in the composition range up to 34 pct Al. Depending on need, alloys were made in increments varying from 0.25 to 2 pct Al. Up to five 15-g buttons of some compositions were made. Weight losses during melting did not exceed about 1 pct of the charge and chemical analysis revealed that both titanium and aluminum were evaporated. In general, nominal and analyzed compositions agreed within 0.5 pct and therefore nominal compositions were used in plotting the data. Unavoidably, some overlap of composition occurred, particularly where small increments of A1 were used. The small increments were primarily used to obtain alloys which would fall into the narrow a -, r region and this purpose was achieved. In general, the data obtained from Bureau of Mines base titanium and iodide titanium alloys were in agreement. Forging—Both as-cast and forged samples were employed. Samples were heated for hand forging by an oxygen-hydrogen torch to the region 1200" to 1300°C. A titanium anvil and cover plate were used to prevent any iron pick-up and consequent formation of a low melting point compound. Frequent reheating kept the temperature in the desired range. Under these conditions, alloys containing up to 15.5 pct could be successfully forged. To check on the depth of contamination, forged alloys were heated slightlybelow the ß transformation temperature. Metal was removed to a depth below the contaminated surface so revealed, and the subsequent results obtained from these samples agreed closely with those secured from as-cast material. Heat Treatment—Prior to heat treatment, all alloys were vacuum annealed to remove hydrogen. Samples

Jan 1, 1962

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen' with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,' indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina' has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,' 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.' Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison' reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity' factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi's solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith' have applied Raimondi's solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,' Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By M. M. Singh, H. L. Hartman

This paper reports on the results of a fundamental investigation of the behavior of rock under impact of a chisel-shaped bit. Drop-tester studies were conducted with strain gauges attached to the rock and striking bit-edge. It was established that rock behaves viscoelastically. Little correlation was found to exist between the strain waveforms detected on the rock surface and in the bit; thus, strain-time curves obtained with transducers mounted on the bit cannot be used to explain the sequence of events in rock breakage. It is estimated that nearly 1 per cent of the total energy of the blow is expended in permanent deformation of the rock. The strain- energy distribution on a rock surface as a result of chisel impact, which follows a simple law, is presented graphically. Experiments also were conducted with gauges embedded in the rock vertically below the line of impact and at an angle of approximately 45' to the vertical. No essential difference was observed in the type of wave obtained with embedded gauges and with gauges on the surface, as may have been anticipated from theory. INTRODUCTION Through the ages great strides have been taken towards improvement of the various techniques applied in the breakage of rock. Indeed, numerous applications of the rock-failure process are an integral part of present-day industry, including oil well drilling. Yet, astonishingly, little is known regarding the behavior of rock under dynamic loading or the mechanism of rock failure. The value of impact loading studies from the point of view of drilling is evident, however, and requires little elaboration because impact of a chisel edge on rock forms the basic action constituting most common methods of drilling. RELATED STUDIES Impact studies of communition and fragmentation conducted by Fahrenwald, et a1,8 Poncelet,l7 Axelson, et a1,2 Piret,16 Hartman and pfleider,ll Charles and deBruyn,5 and others have been of considerable help in understanding rock-breakage phenomena. Further insight into the basic action of drilling and penetration has been obtained by the work of Irving,13 Cherkasov and Shlyapin,6 BOrcherdt,3 Shepherd,19 Shreiner and Pavlova,20 Drilling Research Inc.7 Hartman,10 Appl and Gatley1 and several other investigators. However, knowledge concerning the stresses and strains induced in the rock and bit during impact remains scant. Recent photoelastic studies by Tandanand and Hartman (1961. 1962)22, 23 have shed light on stress distributions and Fracturing produced in plastics by chisel-shaped bits. In the field of transient strain Pulses and their role in rock drilling, the only extensive work has been performed by Drilling Research Inc. (DRI). They attached strain gauges to the shank of a bit and conducted drop-tester studies, using a die-shaped bit to obtain force-time diagrams. Their work led to the conclusion that, for a given rock type, the first peak of force occurs at a fixed level regardless of the total energy in the system, provided it exceeds a certain minimum threshold level. Further, on this basis an explanation was offered for the sequence of events in crater formation as the result of a single blow on rock. PURPOSE OF PRESENT STUDY The investigations reported in this paper were conducted in a manner similar to the DRI approach, but with the objective of determining the strain distribution in the rock around the area of bit impact and, to a limited extent, the strain in the chisel-shaped bit itself. It was expected that a knowledge of the disposition of these strains, along with the rate of attenuation of strain energy in the rock

By A. Kenneth Schellinger

DURING the comminution of a brittle material in the presence of dry air, no known phase change or chemical reaction takes place. The energy changes associated with the comminution are those of the transformation of kinetic energy into heat energy and the energy absorption represented by the actual rupture of molecular and/or ionic bonds. The random nature of the actual grinding process in a tumbling-mill often precludes the effective application of a rupture force on each individual particle of brittle mineral present. The result must be a great deal of useless vibration on an atomic scale in both the brittle mineral and the grinding medium below the elastic limit, which vibration is eventually manifested as heat energy in the mill. The actual rupture of molecular, or ionic, bonds creates new surface on the brittle minerals; each square centimeter of this new surface then must possess a number of potential bonds, each of which could reform theoretically with the release of energy. The sum total of this potential energy of bonding per unit of new surface, minus bond satiation effects of the enclosing gas or liquid, must be the surface energy of the mineral. If the comminution of the brittle mineral were carried out within the chamber of a calorimeter, the energy released as heat could be determined rather accurately. Moreover, the total kinetic energy input to the comminuting mass (mineral and medium) conceivably could be derived by a suitable torquemeter and revolution counter if the whole calorimeter were revolved. The difference between these two energy figures should then represent the net energy (gross energy input—heat enerb output) used in creating new surface, gliding or slip on atomic planes, twinning, and possibly other lattice rearrangements within the mineral. If it be postulated further that with a hard, brittle crystalline material, such as quartz, the energy used to produce gliding, twinning, and other permanent lattice movements is a very small fraction of the total net energy absorbed, then this energy absorption within the grinding calorimeter can be ascribed to the creation of new surface energy alone. Such energy is, from the thermody-namic standpoint, the true effective work of the grinding device, in this case a tumbling-medium mill. The ratio of this effective work (in calories) to the total energy input (in calories) should express the thermodynamic efficiency of the comminution taking place under the conditions used in the grinding calorimeter. This approach to the measurement of the energetics of tumbling-mill grinding was suggested by some previous work by Fahrenwald and coworkers' with a laboratory ball mill and a thermometer. They measured the efficiency of grinding based on the formula: Pct Grinding Efficiency = Energy (calories) — Thermal Energy x 100 1npZ Output (calories) Energy input (calories) Efficiencies thus measured, while grinding quartz sand, ranged from 19.7 pct to 7.4 pct. Cook in 1915,' used this approach to the problem of grinding efficiencies in stamp batteries and obtained the energy input by stamp weights times drop distances and the energy output by means of thermometers and pulp flow rates. He calculated that 80 pct of the input energy to the stamp shoes was wasted as sensible heat in the ore pulp. No other studies of comminution by this method of energy differences came to the author's attention. Reasonable agreement as to the order-of-mag-nitude of comminution efficiencies in tumbling-media mills is lacking in the literature. There is a widespread impression among technical workers that the grinding efficiency of the industrial ball mill may be on the order of 1 pct, or even a fraction

Jan 1, 1952

By A. R. Elsea, E. E. Fletcher

Cast X-40 alloy with the lowest nitrogen content studied had a 100-hr rupture stress at 1500°F about equal to the reported value for the commercial alloy. Increases in nitrogen content progressively decreased the rupture strength, and with about 0.1 to 0.2 pct N a minimum strength was reached, but there was no accompanying change in microstructure. Further increases in nitrogen resulted in the fomzation of progressively increasing amounts of a lamellar, pearlitic-type structure at the grain boundaries, with accompanying increases in rupture strength, and above about 0.25 to 0.33 pct N, the rupture strength exceeded the normally reported values. Two series of melts representing different melting stocks exhibited minimum rupture strengths at different nitrogen contents. This suggests that some unidentwed trace element not removed by vacuum melting has a strong influence on the response of this alloy to variations in nitrogen content. In a series of melts with manganese contents ranging from 0.6 to 3.2 pct, the material with the lowest manganese content had the highest 100-hr rupture strength at 1500°F. The manganese variations had no appreciable effect on the microstructure. CAST cobalt-base alloys such as X-40* exhibit high strengths at elevated temperatures (1500°F and above), but they also show considerable scatter in high-temperature properties. Since the design of parts for critical applications must be based on the minimum expected properties, this broad scatter appreciably lowers the design strength of the alloy. If the relatively poor properties exhibited by a few test parts from any given group could be improved, the spread in properties would be narrowed, and the design stress could more closely approach the average expected properties. The purpose of this research investigation was to learn what were the causes of these erratic properties and, if possible, to find methods for eliminating them. Earlier unpublished work showed that vacuum melting markedly influenced the high-temperature strength of cast X-40 alloy. There were indications that this behavior may have been the result of changes in the nitrogen or manganese content of the castings. Consequently, in the current investigation, the influence of variations in nitrogen and manganese content on the structure and high-temperature properties of cast X-40 alloy was studied. In this program, X-40 melting stock was vacuum melted to produce a base material that was very low in nitrogen content and in volatile trace elements. Additions were then made to this base material to produce alloys of the desired composition. The metal was cast into investment molds producing coupons which were machined into stress-rupture bars. These bars were subjected to stress-rupture tests and me-tallographic study to determine the influence of changes in analyses (nitrogen and manganese content) on the structure and properties. Material—The melting stock used for these experi-ments was in the form of shot from two master heats of commercial X-40 alloy. Only one master heat was used in a given series of melts. Thus, any differences in structure or properties that showed up in the specimens from a given series would be the result only of the intended variations in composition. The certified analyses of the master heats were as follows: C Mn Si Cr Ni Lot No. 2 0.50 0.71 0.66 25.44 10.53 Lot No. 3 0.54 0.73 0.70 25.95 10.00 W Fe Co P S Lot No. 2 7.45 1.34 Bal. 0.011 0.013 Lot No. 3 7.58 1.53 Bal. 0.005 0.016

Jan 1, 1960

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.' In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy's3 equation for nonabsorbing thin films. In Lucy's derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.' The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

By S. J. Matas, R. F. Hehemann, R. H. Goodenow

The hot-stage metallographic method has been employed to determine radial growth rates of upper and lower bainite. Lower bainite appears to grow as individual plates that increase in both length and thickness while upper bainite grows as sheaves of closely spaced plates or needles. A discontinuity in the temperature dependence of the growth rate appears to be associated with the transition from upper to lower bainite and stepped quenching experiments suggest that lower bainite will not continue to grow when the temperature is raised to the upper range. Thus, a single process does not appear to control the growth of both upper and lower bainite. A tentative model based on the forces acting on a dislocation interface is proposed to account for the slow growth of bainite. It has been recognized since the early studies of Davenport and Bain that a close relationship exists between the martensite and bainite transformations in steels. However, diffusion of carbon during the transformation has lead to considerable controversy concerning the reaction mechanism.1-7 Many studies4,5,7-9 have emphasized the structura and kinetic aspects of the bainite reaction and, in particular, the difference observed between the two forms of bainite—frequently termed upper and lower bainite. A kinetic difference between the two types of bainite has been revealed in the activation energy determined from the overall reaction;4,5 however, many difficulties arise in an interpretation of these activation energies since a number of temperature dependent factors contribute to the kinetics of the overall reaction. The displacive surface relief10 accompanying the bainite reaction permits a separation of the nuclea-tion and growth contributions to the reaction and allows the kinetics of the growth process to be examined. Several investigations of this type have been conducted; however, they have been restricted to the low temperature range.3'6'11 Here, bainite plates are observed to grow slowly in both length and width. The present investigation extends such studies to include the upper bainite range. MATERIALS AND PROCEDURE Materials. The composition of the steels studied in this investigation are presented in Table I. The range of composition permitted a study of the effect of carbon content on the growth rate of upper bainite in the 9 pct Ni steels and consideration of both upper and lower bainite in the higher carbon steels. These steels were received as hot-rolled rounds and were forged to approximately 1/2 in. thick plates for preparation of metallographic specimens. In order to produce an essentially zero carbon steel, Steel A was decarburized in wet hydrogen at 1550°F for 15 days with the result tabulated as Steel AD. Experimental Procedure. In order to study the slow growth of the displacive transformation product, a commercially available Leitz hot stage was modified to permit heating of the specimen by its own resistance in a manner similar to that employed by other investigators.6 The furnace chamber was maintained at a pressure of 2 to 3 X 10-5 mm Hg prior to austenitizing at 2000° ± 12° F for 5 min. Samples could be cooled from the austenitizing to the transformation temperature in approximately 15 sec and the progress of transformation was recorded with a 9 cm by 12 cm single frame camera or a 16 mm movie camera. RESULTS AND DISCUSSION Growth Characteristics. The general growth characteristics observed in this investigation were analogous to those reported previously.3,6,11 Typical growth sequences for the high temperature and low temperature forms are illustrated in Figs. 1 to 5. In both temperature ranges, bainite plates increase in length at slow, temperature dependent rates until interrupted by a grain boundary, another plate, or

Jan 1, 1963

By J. E. Neal, C. T. Naber, O&apos

Silicon thin films were deposited by electron beam evaporation in an ultrahigh vacuum onto (0001) and (1102) sapphire substrates. Attempts were made to correlate the structural properties of the deposited silicon films with the following: 1) substrate orientation, 2) substrate surface condition, 3) substrate temperature, and 4) deposition rate. The substrate temperatures were varied between 500° and 1000°C and the deposition rates were varied between approximately 50 and 700A per min. The following sapphire surface treatments were investigated: 1) annealing in the ultrahigh vacuum at 1200° C; 2) heating in a hydrogen atmosphere at about 1350°C; and 3) etching with silicon by evaporating silicon onto sapphire substrates heated to 1200° or 1300°C. Twinned silicon films were occasionally formed at substrate temperatures between the 800° and 1000°C on unprocessed mechanically polished substrates; however, the reproducibility and crystallinity of these films were generally poor. Single-crystal and twinned silicon films were formed at substrate temperatures between 700° and 1000°C on substrates which were silicon-etched at 1300°C prior to deposition. Fiber texture films were formed at substrate temperatures between 500° and 700°C. The (111) lattice plane of the silicon single-crystal films was parallel to the (0001) sapphire plane and the (100) silicon plane was parallel to the (1102) sapphire plane. TECHNIQUES are well-established for growing single-crystal silicon thin films on sapphire by chemical methods.'-* Vacuum epitaxial techniques have a number of advantages over chemical epitaxial techniques in the fabrication of thin film microcircuits.5 One of the most significant is that vacuum techniques are compatible with well-established procedures for forming vacuum-deposited thin-film resistors, capacitors, and interconnections. Salatna, Tucker, and young6 recently reported the formation of relatively poor crystalline-quality silicon films on sapphire by electron beam evaporation in a vacuum of about 7 x 10-7 Torr. The purpose of the investigation described here is to determine the relationships between the structural properties of silicon thin films deposited on sapphire substrates by electron beam evaporation in an ultra-high vacuum and the following: 1) substrate orientation; 2) substrate surface condition; 3) substrate temperature; and 4) deposition rate. The substrate temperatures were varied between 500° and 1000° C and the deposition rates were varied between approximately 50 and 700A per min. Two orientations of sapphire were used: (0001) and (1102). The thick-nesses of the films were between 8000 and 16,000A. The morphology and crystallinity of the deposited films and substrate surfaces were investigated by optical microscopy, electron microscopy, and electron diffraction. APPARATUS AND PROCEDURE A cross section of the ultrahigh-vacuum thin-film evaporator is shown in Fig. 1. The bell jar is stainless steel and copper gaskets are utilized at all seals. High vacuum is attained by a 6001iter per sec ion pump and a titanium sublimation pump. Sorption pumps are used to rough the system to a pressure of about 10 µ prior to starting the ion pump. Vacuums in the 10- 10 Torr range were attained after baking the system at about 250°C for 8 hr. Vacuums in the 10-8 to 10-9 Torr range were maintained during silicon evaporation. The silicon charges, which were cut from p-type single-crystal boules which had resistivities between 2000 and 4500 ohm-cm, were placed in the water-cooled copper crucible of a 180 deg bent-beam 5-kw electron beam evaporator. During evaporation, a molten zone was formed in the top center of the silicon charge, and the portion of the silicon charge in contact with the water-cooled crucible remained solid. The substrate heater, which has been described

Jan 1, 1969

By R. S. Shoemaker, D. L. Harris

PST investigations into the possibility of concentrating the low-grade iron ores of the Gogebic Range in Wisconsin have been hampered by the complex association of the constituent minerals. In part the problem arises from the fact that the iron occurs essentially as two minerals, hematite and goethite, having nearly the same chemical composition but exhibiting different physical properties. Individual grains of these minerals are usually so small that the ore must be ground to a size finer than 325 mesh if substantial liberation of the minerals is to be secured. Appraisal of beneficiation tests on this iron ore requires, therefore, some method of determining quantitatively the contents of constituent minerals in the various products of the beneficiation. Because of the chemical similarity of the two iron minerals, chemical analyses do not provide a means of differentiation. Although the minerals are different physically, they are both opaque and friable, and as the ore must be ground to a very fine size for liberation to be secured, quantitative microscopic methods of analysis are extremely difficult at best. In an effort to overcome these analytical problems, a quantitative X-ray diffraction analysis method has been developed at the University of Wisconsin for the research program on iron ore beneficiation. The X-ray diffraction analysis of chemical compounds of crystalline form has proved of inestimable value for structure studies and rapid qualitative analytical purposes in a number of fields.' In some cases X-ray diffraction analysis has been found suitable for quantitative determinations. H. P. Klug2 found that quantitative procedures for quartz powders when mixed with calcium fluoride were reproducible within ±1.0 pct. Talvenheimo and White3 reported quantitative analyses of clay minerals to be accurate within 10 pct and also detected 1 pct of bentonite in 99 pct illite. In other investigations,'" powders of quartz and mica have been analyzed quantitatively with accuracies from 1 to 5 pct. A powder of tungsten carbide was analyzed similarly by Redmond7 and Rooksby8 reported the determination of small amounts (0.11 pct) of calcium oxide in magnesium oxide. In the most generally practiced use of X-ray diffraction, traces of the diffracted beam are recorded as lines on a film much as lines of elements are recorded on an optical spectrograph film. As with the spectrograph, the darkness of the lines denotes the amount of the constituent in the sample. If the film is replaced by a Geiger tube assembly and a graphic recorder or a scaling unit, the intensity of the diffracted beam can be registered as a peak on a chart or energy impulses per unit of time on the scaler. Several methods of quantitative measurement have been investigated and reported in literature. Klug2 used manual operation of the goniometer and a counting technique to determine the difference in counting rates at the diffracted angle and for the background. In another case3 the area under the recorded diffracted peak was the basis for the determination. In other instances the height of the recorded diffraction peak above background, measured while the goniometer was moving, has been the basis for the measurement. The sizes of particles most suitable for diffraction techniques are reported in the literature as follows: for tungsten carbide a maximum of 40 microns7 and for quartz a maximum of 5 microns.' Very fine sizes of crystals are known to cause a broadening of the diffused beams; hence some workers have set a lower limit of 0.1 micron for quantitative results. Guinier10 has indicated that broadening of the diffracted X-ray beam is not appreciable for crystallites larger than 0.02 to 0.03

Jan 1, 1956

By W. B. Gogarty

With the use of polymer solutions in secondary recovery operations, the need has developed to understand the mobility control mechanism. This study investigated mobility control by considering both permeability and rheological effects. Experiments used a high molecular weight, partially hydrolyzed polyacrylamide polymer. Flow studies took place in reservoir and Berea cores having zero oil saturation. Effective size of the polymer flow unit was inferred from Nuclepore filter tests. Clay studies indicated the particle size capable of decreasing the core permeability. Flushed permeabilities measured the approximate core permeabilities with flowing polymer solutions. These permeabilities were considerably lower than original values. With mobility data and the flushed permeability, maximum effective viscosities were determined for polymer solution flow in a core. Effective viscosities showed that rheological properties play an important part in mobility control with polymer solutions. The study showed that permeabilities decrease and stabilize with polymer flow. At the lower permeabilities, high shear rates exist in the cores. Because of the pseudoplastic character of the polymer solution, the high shear rates caused low effective viscosities. This condition pointed to the inefficient use of the potentially high viscosity of the polymer solution at low shear rates. INTRODUCTION In the oil industry, a great deal of interest is being shown in the use of polymer solutions for secondary recovery and a number of polymer floods are being performed in the United States.1 Some of these floods have become commercial while others have been reported as failures. A number of floods are still in progress and remain to be evaluated. With the advent of polymer flooding, the need developed to understand the mobility control mechanism in porous media. Rheologically, the polymer solutions behave as pseudoplastic fluids. Investigators have studied the rheology for this type of non-Newtonian fluid in porous media?-6 Results have also been reported on the ability of polymer solutions to decrease mobility.7-10 Some investigators indicated that polymer solutions show a different rheological behavior in cores than on the viscometer.7,8 This study is representative of an initiatory investigation on mobility control with polymer solutions. Some effects are considered on a qualitative basis. Mobility control is considered from the standpoint of both permeability and rheology and, to the extent possible, permeability and rheological effects are considered separately. Results show that mobility control occurs from a reduced permeability caused by polymer retention and an effective viscosity determined by the average shear rate in the core. In this respect, rheological behavior is as important in mobility control as permeability. PROCEDURES A high molecular weight, partially hydrolyzed, polyacrylamide polymer was used in the investigation. Solutions of various concentrations were made with this polymer in different types of water. Some solutions used distilled water and others used tap water. The tap water contained approximately 500 ppm dissolved solids. As used in this paper, concentrations in ppm refer to parts by weight solute to one million parts by weight of solvent. In the tap water, calcium and magnesium accounted for from 60 to 80 ppm of the solids, the remainder being mostly sodium chloride. All solutions contained a bactericide, and anti-oxidants and antiprecipitants were added to the tap water. Capillary and concentric-cylinder* viscometers determined the rheological properties of solutions. The capillary viscometer is described elsewhere.6 Berea and reservoir sandstone were used as core materials for this investigation. Cores were 1 in. in diameter by approximately 2 to 3 in. long. Prior to mounting, the Berea cores were heat-treated for 3 hours at 850F. This treatment decreased the water-sensitivity of the clays in the cores. The reservoir cores were cleaned with solvent and

By William C. Hagel

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a PL-IORh chamber, and splzeres of a Fe2O3 containing three or less grains was determined from 9000 to 1250°C. Isotope equilibrum on crystal surfaces appears to be quickly established, and the rate-determining factor is self-difiusion confbvrning to the relation D = 2.04 esp(- 77,900/RT) sq cin sec-'. Changing sphere diameters caused no detectable variation in diffusion coefficients. Oxygen ions diffuse faster than cations at low temperatures, but a crossover may occur at about 1150°C. INVESTIGATIONS by Davies et al.' and Himmel et al2 have suggested that the mechanism of iron oxidation above 600°C involves a predominance of cation migration in the wüstite (FeO) and magnetite (Fe301) layers and oxygen-ion migration in the hematite (a Fe2O3) layer. Evidence for little cation migration during hematite growth consists of: 1) the disappearance of radioactive-silver markers, presumed to vaporize from the oxide-gas interface, and 2) a large discrepancy between parabolic rate constants for magnetite oxidation and those calculated from Lindner's3 data for cation self-diffusion, D:, using Wagner's theory.4 Reversing the calculations gave anticipated self-diffusion coefficients, D:, for oxygen ions of 3.6 x 10-9 sq cm sec-1 at 1100°C and 5.9 x 10-10 sq cm sec-1 at 1000°C. Since then Kingery et a1.5 reported three values for oxygen-ion diffusion in polycrystalline, sintered hematite. These were obtained near 1200°C, at an oxygen pressure of approximately 150 mm Hg, and could be represented by the Arrhenius expression, Dg = 1 x 10 11 exp(-146,000/RT) sq cm sec-1. Extrapolation to temperatures below 1100°C infers that oxygen ions are less mobile than cations. This contradicts the aforementioned oxidation evidence and also coble7s study of the initial sintering of hematite. From the latter, apparent diffusion coefficients for the slowest rate-controlling species could be calculated, and fair agreement was found with an extension of Lindner's data for cation diffusion. Fig. 1 depicts such comparisons graphically. Three points have been included for the determinations of Himmel et al. on cation diffusion in large, natural hematite crystals surrounded by pure oxygen at atmospheric pressure. No dependence on crystal log raphic direction was noted. Since the value of 10-l4 sq cm sec-' at 1000°C actually represents an upper limit, one might interpret that there is a small decrease in D: when single crystals are employed. On the whole, however, cation diffusion appears relatively well-defined,* while the few results tension to lower temperatures. After having gained experience measuring oxygen-ion diffusion in certain glasses7 and in the corundum oxide, a Cr2O3, the purpose of this work was to determine D; values for hematite and thus possibly assist a mechanistic understanding of the kinetics of the oxidation and reduction of solid iron oxides. I) EXPERIMENTAL PROCEDURE A) Material. Hematite powder of moderately high purity was received from the Columbian Carbon Co. An accompanying lot analysis listed 0.03 H2O, 0.008 weight percents, with the remainder Fe2O3. Subsequent treatments were ball milling, drying, prepressing, and hot-pressing for 60 min at 1350°C under 5000 psi. Since graphite dies coated with a slurry of alumina were used for hot-pressing, the surrounding atmosphere at temperature was sufficiently reducing to form some magnetite on the outer surface of each cylinder. After removing any attached alumina, a stabilizing anneal of 50 hr at 1300°C in oxygen was added. The final product was nonmagnetic and exceeded 97 pct of the density (5.24 g cm-3) usually given for FezO3. On polishing cylindrical ends, counts were made of the number of grain boundary intercepts per

Jan 1, 1967

By Keith R. Bock, Norman Parlee, Albert M. Barloga

Coils of pure iron and iron-carbon alloy wire (0.05 to 0.80 pct C) and sufficient sulfur to saturate the solid phase were equilibrated in evacuated or argon filled tubes. After rapid cooling, and removal of the outside nonmetallic layer, the wires were analyzed for carbon and sulfur and the data used to construct an Fe-S binary and isotherms of the Fe-C-S ternary in the range 1149° to 1427°C. THE solid solubility of sulfur in steel is of interest in connection with such phenomena as hot shortness, burning, and so forth. "Burning," the more or less permanent damage that some steels suffer when heated for forging or rolling, has been shown to be related closely to the behavior of sulfur and less closely to carbon and oxygen.' Attempts to interpret burning phenomena in steels fail because of lack of data on the Fe-C-S and the more complex systems in this family. Rosenqvist and Dunicz 2 and Turkdogan, Ignatowicz, and pearson3 have largely elucidated the Fe-S diagram in the region of interest but no information on the Fe-C-S diagram in this region appears to be available in the literature. This paper deals with the elucidation of the Fe-C-S diagram in these interesting ranges. The method employed is different from those used by previous workers2'3 on the Fe-S system. EXPERIMENTAL METHOD Pure iron wires (Ferrovac E) or iron carbon alloy wires of 1 mm in diam were cleaned with acid and acetone, coiled, and placed in silica tubes (7 mm OD and 5 mm ID) previously closed at one end. Enough sulfur was added to assure saturation of the solid iron phase. The filled tubes were either simply evacuated and sealed, or filled with argon at a reduced pressure and sealed. The argon was required at the higher temperatures to prevent collapse of the tubes. The filled and sealed tubes were placed in the middle uniform temperature zone of a Globar tube furnace and equilibrated at temperatures ranging from 2100°F (1149°C) to 2720°F (1493°C). After equilibration the tubes were removed from the furnace and quenched in air or water, the form of quenching being found to have no effect on the results. The tubes were broken open and the coils were placed in a 1 : 1 HC1 solution to remove the sulfide-rich layer. The coils were then cut into small pieces and analyzed for sulfur and carbon. In the early stages of the investigation different equilibration times ranging up to 17 hr were tried and the cores of the wires were analyzed to test for saturation. One hour appeared to be sufficient to reach maximum sulfur content at 1454°C and 2 hr sufficient at 1149°C. The practice adopted was to use at least 3 hr at the higher temperatures and at least 5 hr at the lower temperatures. The iron-carbon alloy wires used were made by carburizing pure iron wire with carbon monoxide gas in a one inch diameter ceramic tube at about 1204°C. Differing carbon contents were obtained by allowing fairly large coils to react with the gas for varying lengths of time at a flow rate of 800 cc per min. The reacting times ranged from 15 min to 4 hr depending upon the amount of carbon desired. The furnaces used were controlled by means of Leeds and Northrup Speedomax Type H instruments with D.A.T. Control attachment. Thermocouples were calibrated against the melting points of gold and copper. The temperatures recorded appear to be accurate within i2.7OC. Starting with run No. 85 and continuing with the

Jan 1, 1962