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By G. W. Thomas

A mathematical tnodel of forward combustion in an oil reservoir is treated in this paper. The model describes a radial system having a vertical section of essentially infinite thickness, all of which is permeable to gas flow. Combustion, however, is presumed initiated over a limited thickness of the total vertical section. In the interval supporting cotnbustion, the mechanisms of radial conduction, convection and heat generation are taken into account. Above and below the burning interval, heat transport in the radial direction is by cottduction and convection. Vertical heat losses from the ignited interval are accounted for by conduction alone. A general solution is presented for the temperature distribution caused by radial movement of the combustion front. The results show that no feedback of heat occurs into the ignited interval when convection and conduction are acting in the bounding media. Peak temperatures are also 5 to 10 per cent higher than in the case where heat transport in the bounding media is by conduction alone. We arbitrarily define vertical coverage to be that fraction of the total ignited interval which is at 600F above atnbient, or greater, at any given time. The radial distance at which the vertical coverage becomes zero is the propagation range of the combustion front. It was found that an increase in vertical coverage results when the oxygen concentration, fuel concentration or gas-injection rate is increased. Moreover, the combustion front can be propagated 10 to 15 per cent further than in the case where only conduction is acting above and below the ignited interval. INTRODUCTION In the theoretical treatment of forward combustion in a radial system, one of the problems encountered is the determination of the transient temperature distributions caused by an expanding cylindrical heat source. Bailey and Larkin' and Ramey' simultaneously presented analytical solutions to the problem assuming heat transport by conduction alone. In a subsequent publication, Bailey and Larkin3 included the effects of both conduction and convection while treating linear and radial models. In this latter work, however, vertical heat losses were largely neglected. Selig and Couch' dealt with a radial model in which both conduction and convection were acting. Only a limiting case involving vertical heat losses was considered, however. Namely, temperatures on the boundary of the bed of interest were set equal to zero. Solutions thus obtained were representative of a system having a maximum vertical heat flux. Chu5 recently treated a more general case in which a permeable bed was considered bounded by impermeable media. Conduction and convection took place within the bed, and only conduction outside of the bed. The effects of vertical heat losses were included in his study. Solutions were obtained by numerical techniques. This paper is an extension of the theoretical work of other authors pertaining to forward combustion in a radial system. In particular, a mathematical model of the process is treated in which heat generation occurs over a small vertical interval of a larger permeable section. In the interval supporting heat generation, and above and below this interval, the mechanisms of radial conduction and convection are also presumed acting. Heat losses from the ignited interval are accounted for by vertical conduction. An analytical solution for the temperature distribution caused by radial movement of the burning front is presented. The effects of certain process variables are indicated and comparisons with Chu's results are made. THEORY To render the mechanism of forward combustion tractable to mathematical treatment, we idealize the problem to the extent of assuming continuous reservoir media possessing homogeneous and isotropic properties. The following additional assumptions are implicit in this analysis. 1. The thermal parameters, i.e., heat capacities, thermal conductivities and thermal diffusivities are invariant with temperature and pressure. Moreover, the bounding media possess the same thermal properties as the bed of interest. 2. The temperatures of the porous media and its contained fluids at any point and at any time are equal. 3. The reaction rate between the oxidant gas and the fuel is infinite. This assumption implies that the incoming oxygen concentration instantaneously goes to zero within an infinitesimal distance, i.e., the width of the combustion zone is negligible. 4. The rate of gas injection is constant and corresponds to the average rate throughout the lifetime of the project. 5. The fuel concentration is constant throughout the volume of rock swept out by the burning zone. 6. There is complete burnoff of fuel. This assumption demands that the rate of propagation of the burning front equals the rate of fuel burnoff. In a radial system, with a

By J. B. Newsom

DURING July and August, 1931, the Bloomington Limestone Co.,. at Bloomington, Ind., ran a single wire saw on ledge No. 2 at Maple Hill quarry. The ledge was hard rock, much harder than the average Indiana limestone. It was opened at two ends for a depth of about 20 ft., leaving a 130-ft. section between. During the tests 21 cuts were made in this ledge, to an average depth of 10.42 ft., for a total effective cutting area 028,445 sq. ft. The actual area sawed was about 20 per cent higher, as we did not level down in the center, preferring to cut deeper on the ends. The various cuts were carefully, logged, and the results plotted. A study of these results is interesting, as it enables a forecast of probable future costs to be made, and also because it points out the limitations of wire saws, and the lines development should logically take. Some of the inferences to be drawn are discussed below. Best Length of Cut.-No. trouble was due to length of cut, except that we could not easily level down a long cut, and it is probable that longer cuts, say up to 200 f t., can be made. Obviously, longer cuts will result in a higher sawing rate, in square feet per hour if- they do not cause stoppages. Working Higher Ledges.-The cuts averaged 10.42 ft. high by 130 ft. long. A study of several logs indicated that during only about 15 per cent of the cutting time was the saw cutting to its full efficiency; that is, during about 85 per cent of the time the saw was bedding in at the ends and not cutting well in the center, or the ends were below the floor line and only part of the wire was doing effective cutting. This does not mean that the wire was cutting to only 15 per cent of its capacity, but it means that during about 85 per cent of the time part of the cutting was being wasted. If higher ledges had been worked, the wire would have cut to its full efficiency a large part of the time, as it would have had a greater distance; to saw after it had bedded in to the ledge before the ends went down below the floor level. The exact saving to be expected cannot be calcu-lated, but it would be large, if really high cuts were made.

Jan 1, 1932

By W. O. Brown

A laboratory investigation was conducted to determine quantitatively the extent to which connate water was contacted and displaced by invading flood water. In these experiments the connate water in unconsoli-dated sand packed columns was completely displaced by injecting water. The nature of this displacement was similar to that previously described for single-phase miscible fluid displacement studies, and thus the presence of a non-wetting immiscible phase did not appreciably change the nature of the displacement. The effects of water injection rate, column length, and oil viscosity on connate water displacement were investi-gated. It is concluded that the connate water in a reservoir is the water which actually displaces oil from the pores of the rock during a water flood. During a water flood the connate water forms a zone which separates the invading flood water from the continuous oil phase. The size and shape of connate water bank is chiefly dependent oil the oil viscosity and the column length. INTRODUCTION Water flooding is one of the most widely used techniques for the secondary recovery of oil. Presently, however, it is still not possible to recover all the oil in a reservoir by water flooding. The research described in this paper was conducted as part of a study to determine the conditions under which 100 per cent oil recovery could be attained by water flooding. The particular objective of this work was to determine if any chemical agent, regardless of its nature, placed in the flood water could be effective in influencing the mechanism of displacement of the oil by water. It has been known for many years that water does not displace all the oil in a reservoir because a portion of the oil is "trapped" and held immobile by capillary forces. This oil is trapped within the pores of a water-wet rock when it becomes broken into discontinuous globules. Initially, when oil is present at high saturations within the pores of a water-wet rock, the connate water forms rings around the points of contact of the sand grains and may even completely fill small cavities between grains, whereas the oil occupies the larger void spaces between the grains.' Under these conditions, the oil in these spaces is in the form of irregular but continuous filaments, the diameters of which depend on the geometry of the sand pores. The filaments are formed by the oil contained in the small cells which are formed between the sand grains and are connected to their neighboring cells by channels or tunnels formed by pendular rings of water. At a high oil saturation, the oil filaments conform approximately to the shape and size of the cells and their connecting tunnels. Starting with this distribution, as the water saturation is increased the water layers in the small cavities and on the surface of the grains grow. As this occurs, the water rings grow and the diameters of the oil filaments decrease. When an oil filament is reduced to a critically small diameter, the filament breaks, and its tunnel fills completely with water. Any oil which remains within a cell after all its connecting tunnels have been water-filled is trapped as a discontinuous globule. Once the oil has become trapped, the capillary forces oppose distortion of the globules and may prevent their being squeezed through the water-filled tunnels. Only a very small pressure gradient is sufficient to keep oil moving as a continuous filament. On the other hand, once the filament has broken into discontinuous oil droplets a relatively large force is required to distort the surface of a drop and move it through a water-

Jan 1, 1958

By Allen D. Gorrison

EFFORT to develop fundamental quantitative information and improved technique in the production of petroleum has long been faced with difficulties of a particularly evasive nature, owing to a combination of circumstances. In the first place, petroleum comes from far below the ground, out of sight, so that information derived from indirect observations must be extrapolated to reservoir conditions. If one does not force the analogy too far, the petroleum engineer may be said to be somewhat in the position of the astronomer. The actual phenomena which he wishes to observe in detail appear at a place so deep in the earth?s crust that personal observations and direct experiments are impossible.

Jan 1, 1942

By H. J. Stehli

The first sintering of zinc ores was done at the Bartlesville plant of the National Zinc Co., under the auspices of the late Otto Rissman. Mr. Rissman, who had had a long experience in the treatment of zinc ores, well realized all the difficulties of satisfactorily roasting zinc concentrates, which were becoming finer and dustier as each year went by—thus increasing the difficulties of roasting them in the existing forms of roasters, which were furnaces of the Ropp, Hegeler or similar types. Mr. Rissman's idea of the advantages of sinter was expressed in this way: in a zinc ore dead-roasted in a mechanical furnace there are many particles that are just like an egg; that is, they have a hard and impervious film of fused material on the outside, and in the retorting this completely cuts off access of the reducing gases to the center of the egg until a temperature has been reached at which this shell of the egg can be broken down through fusion. A particle of sintered zinc sulphide, on the contrary, is exactly like a piece of sponge. The moment the retort reaches the temperature at which the reactions can take place, they begin, because the reducing gases have ready access to the interior of the particles by means of the pores of the '" sponge." His faith in the advantages of sinter was amply borne out by the results obtained at the pioneer sintering plant for zinc ores installed by the National Zinc Company. Early Method of Sintering The method of procedure at Bartlesville was to roast the zinc concentrates down to somewhere in the neighborhood of 8 per cent residual sulphide sulphur; to cool these, then to wet them down to the proper moisture and mix them in the mixer of the sintering plant; then to sinter them by means of the heat available from the residual sulphides. The sulphur contents of the roast varied considerably, of course, as it was difficult with the furnaces in use to control the roasting exactly at any point short of dead roast. Hence at times the concentrates were roasted a little too low to sinter readily, and at such times the lack of sulphur was made up by the addition of raw concentrates to the sintering-machine charge in suitable amount.

Jan 1, 1937

By Zay Jeffries

THIS paper will include a brief discussion of Prof. Howe's paper on The Supposed Reversal of Inheritance of Ferrite Grain Size from that of Austenite.1 The general subject of grain refining in steel and iron will also be treated. The conclusions reached are stated in the following hypotheses which are discussed more in detail below. 1. The ferrite grain size in pure iron, the ferrite and pearlite grain size in hypoeutectoid steel, the pearlite grain size in eutectoid steel and the cementite and pearlite grain size of hypereutectoid steel are not inherited from the grain size of the mother austenite. 2. The only structural feature that is generally inherited from the austenite of hypo- and hypereutectoid steels on cooling through their transformation ranges is the position of the excess ferrite or cementite at the austenite grain boundaries, sometimes causing complete and sometimes incomplete networks which outline the old austenite grain boundaries. Rapid cooling through the transformation range will cause the non-inheritance of this structural (network) feature. 3. The austenite grain boundaries themselves are nearly always effaced in all steels and also in pure iron during the Ar transformations. 4. The grain-size refining of steel and iron is brought about by the combined. effect of non-inheritance of the transformation products on either heating or cooling, i.e., the austenite transformation .products do not inherit their grain size from the austenite on cooling through the transformation range for does austenite inherit its grain size from the products which form austenite on heating. 5. In general, in both iron and carbon steel the larger the austenite ,grain size, the larger will be the grain size of the transformation products on cooling. This, of course, assumes all other conditions constant except the austenite grain size. An exception is found to this general rule in very pure iron such as electrolytic iron. 1n this instance small austenite grains may form very large ferrite grains on cooling through Ar3.

Jan 11, 1917

By J. D. Edwards

When Charles Martin Hall invented the electrolytic process for the production of aluminum, one basic requirement was a supply of pure alumina. Now, more than 50 years later, the same requirement still holds, and there are no technical straws in the wind to indicate that this situation is likely to change. Long ago, Aluminum Company of America took a number of steps to see that this country should not face shortages of alumina and aluminum in time of emergency. As one step to this end, the Company developed and used a supply of bauxite in South America in order to conserve dwindling Arkansas reserves. Another, and more a program than a step, was to investigate every type of process that might bear the possibility of utilizing the low-grade ores of aluminum that are more plentiful than bauxite. It is a long story, but the investigation included electric-furnace processes, acid extraction processes and alkaline extraction processes, with or without preliminary furnace and sinter treatments. Some of the processes developed were operated in commercial production. This work has been continuous since the first World War. The turn of the wheel came sooner than was expected when, in 1942, bauxite shipmerits through the caribbean became uncertain and hazardous through the operation of submarines. The tremendous requirements of aluminum for the war effort were consuming high-grade bauxite at an alarming rate and a national search for substitutes began. High-grade bauxites, for technical and economic reasons, have been defined as those containing about 7 per cent or less of silica. While bauxite of this grade was limited in amount in the United States, there was in sight a substantially greater volume of low-grade, high-silica bauxite not amenable to economic treatment by the Bayer process, but richer in alumina than the clays or other available low-grade ores. It was at this point, and after several years of intensive research on this particular phase of the problem, that Aluminum Research Laboratories brought to completion the invention of one of its research staff, which made practical the utilization of large reserves of low-grade bauxite in America. Bayer Process The Bayer process has been almost universally used for the production of alumina from bauxite. This process, in outline, comprises the digestion of hely ground bauxite in a solution of caustic soda (NaOH) under pressure and at an elevated temperature. Alumina in the bauxite goes into solution as sodium alumi-"ate and the impurities—oxides of iron, titanium and silicon—remain undissolved. The undissolved residue, known as "red mud,'' from its color, is separated and run to waste. AluKlinum hydrate (A12O3.3H2O) is precipitated from the solution of sodium aluminate, and the liquor containing the caustic soda and some alumina is returned to the Process for digesting more bauxite. The aluminum hydrate, after washing, is calcined at a high temperature to produce

Jan 1, 1949

By Josef Intrater

A dilatometric determination of the a + ß region temperature limits was performed on vacuum melted Zircaloy-2. The temperature of transformation for a-a+ß and a+ß — ß on heating and cooling as a function of rate of heating and heat treating history was studied. The limits were found to be 815° to 830°C to 975° to 995°C on heating and from 960° to 930°C to 785° to 770°C on cooling. A 5° to 15°C increase was observed for a- a + ß with increased rate of heating and a 20° to 30°C decrease for ß - a + ß with increased rate of cooling. 1 HE transformation temperature for pure zirconium has been determined by many investigators1-5 using metallography, electrical resistivity measurements, and dilatometry. The effect of the rate of cooling on the transformation temperature of zirconium has been studied by Hayes and Kaufmann6 and Duwez,7 and the effect of alloying elements by pfei18 and McGeary.13 Since the development of Zircaloy-2, the limits of the a + ß region for that alloy have been also determined. The first reported temperature for the a — a + a transformation in Zircaloy-2 was 900°C and for a + ß - ß 1000C Subsequent studies by Picklesimer and damson" indicated the beginning of the transformation at 810°C, and the metallographic study by the Technology Group of the Special Materials Section at the Westinghouse Bettis plant1' suggested that 820°to 830°C is the temperature of transformation. The dilatometric investigation by the latter group yielded 830°C for the beginning of the transformation. Thomas and Forscher12 set the beginning of the transformation at 900 °C on heating and the end of the transformation at 870°C on cooling. The above investigators stated in their paper that the dilatometric curve exhibits features caused by a eutectoid reac-

Jan 1, 1962

By R. E. Ogilvie, H. C. Gatos, R. E. Hanneman

The ejj-ect of high pressures on chemical inter-diffusion in the Fe-V system was determined by analyses of concentration vs distance profiles of atmospheric and high-pressure diffusion couples. Diffusion data were obtained as a function of tern -perature and composition. Activation energies, activation volumes, and frequency factors were determined at 1 atm, 20 kbars, and 40 kbars as a function concentration in the a and y phases. The A great deal of research has been carried out in the measurement and understanding of binary chemical inter diffusion in solids. Studies of the effects of high pressure on interdiffusion in binary systems, however, have been virtually nonexistent until the present work. This paper gives a detailed account of the effect of high pressure on interdiffusion and the Kirkendall effect in the Fe-V system. The present data are compared to existing theo- Kirkendall effects were measured at 1 atm and 40 kbars. At 1 atm Dy > DFe at the marker concentration; however, Dv approaches DFe under pressure, and at 40 kbars the values are approximately equal. The high-pressure and atmospheric diffusion data are evaluated on the basis of theoretical models. Chemical analyses of the diffusion -couple profiles were made using an electron microbeam probe. retical treatments of pressure dependence of diffusion which are based upon self-diffusion studies. THEORY The rates of atomic migration in metals and alloys are regulated by the repulsive forces exerted on an atom during its motion from one equilibrium lattice site to another and by the availability of a jump site. Application of high pressure is expected to decrease diffusion rates because it decreases interatomic distances as well as defect concentrations. A number of theoretical treatments have been focused on the problem of calculating self-diffusion coefficients in solids under atmospheric pressure. In general, the vacancy mechanism of diffusion appears to be dominant at high temperatures in most metallic systems. The migration of an atom by this

Jan 1, 1965

By Douglas Muir, Chas. A. Chase

The Aztec mine is not widely known, by reason of its isolation and the relative insignificance of its tonnage; financially, however, it has an enviable record and geologically it is extremely interesting. The town of Baldy, Colfax County, the mine camp, at an elevation of 10,000 ft. (3048 m.) is 8 mi. west of Ute Park, the terminus of a branch of the A. T. & S. I?. Ry. The mining tract was designated by the Maxwell Land Grant Co. as the Aztec Reservation, and lies on the east slope of Mt. Baldy, the summit of which, 12,491 ft. (3807 m.), is one of the highest in the state. Rich copper float was found on the northeast slope of the mountain in 1865, and discovery work was begun the next year. At the same time, gold placers were found on Willow Creek, on the southwest side of the mountain, and the Elizabethtown settlement followed shortly. Gold washing lasted many years. In 1867, placer gold was found also on Ute Creek, the tracing of which to its source led to the locating of the Aztec mine by Lynch, Dogherty, and Fosley in the following year. The early production came from the contact of shale and sandstone or from sandstone immediately above the contact. Exact record of production is lacking, but L. C. Gratonl gives estimates ranging between $1,250,000 and $1,500,000, of which about $1,000,000 was taken out in the first four years. After the exhaustion of the early bonanza, production continued intermittently until 1909, when the Maxwell Land Grant Co, undertook systematic development, through four adits at intervals of 75 ft. vertically or approximately 100 ft. on the dip of the contact, which was thought to contain generally a quartz-pyrite vein. The two intermediate adit? almost immediately reached ore, the most southeasterly in Fig. 2. This ore, however, was not mined until 1911-12; its grade was about $20 and

Jan 1, 1923

By Douglas Muir, Chas. A. Chase

The Aztec mine is not widely known, by reason of its isolation and the relative insignificance of its tonnage; financially, however, it has an enviable record and geologically it is extremely interesting. The town of Baldy, Colfax County, the mine camp, at an elevation of 10,000 ft. (3048 m.) is 8 mi. west of Ute Park, the terminus of a branch of the A. T. & S. I?. Ry. The mining tract was designated by the Maxwell Land Grant Co. as the Aztec Reservation, and lies on the east slope of Mt. Baldy, the summit of which, 12,491 ft. (3807 m.), is one of the highest in the state. Rich copper float was found on the northeast slope of the mountain in 1865, and discovery work was begun the next year. At the same time, gold placers were found on Willow Creek, on the southwest side of the mountain, and the Elizabethtown settlement followed shortly. Gold washing lasted many years. In 1867, placer gold was found also on Ute Creek, the tracing of which to its source led to the locating of the Aztec mine by Lynch, Dogherty, and Fosley in the following year. The early production came from the contact of shale and sandstone or from sandstone immediately above the contact. Exact record of production is lacking, but L. C. Gratonl gives estimates ranging between $1,250,000 and $1,500,000, of which about $1,000,000 was taken out in the first four years. After the exhaustion of the early bonanza, production continued intermittently until 1909, when the Maxwell Land Grant Co, undertook systematic development, through four adits at intervals of 75 ft. vertically or approximately 100 ft. on the dip of the contact, which was thought to contain generally a quartz-pyrite vein. The two intermediate adit? almost immediately reached ore, the most southeasterly in Fig. 2. This ore, however, was not mined until 1911-12; its grade was about $20 and

Jan 1, 1923

R. W. Raymond, New Pork City: It seems questionable to me whether Mr. Mezger's identification of the rock-structure he describes, as the Augengneiss of previous authors, is warranted by the definitions given by them. Naumann (1854)t describes Augengneiss as a porphyry-like variety, " which has assumed, by reason of single large kernels or granular concre-

Jan 1, 1896

By E. S. Tankins, G. R. Belton

A simple solution model, based upon the formation of molecular species, is developed for strongly electronegative dilute solutes in liquid binary-metallic solvents. Two approximations are considered for the relative concentrations of the species: the random and the quasi-chemical. Equations are presented for the partial molar free energy, enthalpy, and entropy of mixing of the solute. An experimental study has been made of equilibrium in the reaction H2 6) +0 (dissolved) = H2O(g))for the liquid Cu-Co alloys. The standard free energy of solution of oxygen is presented as a function of composition for the alloys at 1550°C and as a function of temperature for five of the alloys. The experimental results for these alloys and also for Cu-Ni alloys are shown to be in reasonable agreernent with the theory in the random approximation. A knowledge of the thermodynamic behavior of dilute solutes in liquid metals and alloys is of importance in understanding and designing refining and alloy-making processes. Accordingly, several attempts have been made to derive suitable solution models to forecast the effect of a third component on the activity coefficient of such a solute in a metal. Alcock and Richardson' reviewed the literature prior to 1958 and also showed that a regular solution model gave a reasonable description in the case of metallic solutes but failed to account for the behavior of the more electronegative solutes sulfur and oxygen. These same authors2 later modified their model by using the quasi-chemical approximation3 to calculate the average composition of the first coordination shell surrounding each solute atom. This modified model was shown to lead to a better qualitative description of the behavior of the electronegative solutes; however, quantitative agreement with experimental data for oxygen in alloys could only be achieved by assuming a very small coordination number. The authors concluded that the major source of error in the model was the assumption that pairwise interaction energies were independent of composition. Substitutional and interstitial random solution models by Wada and saito4 are essentially similar to the first model except that the required interchange energies were derived from the modified solubility parameter equation of Mott, instead of from experimental binary data. Most recently Hoch5 has presented a statistical model for interstitial solutions and has applied the model to the Fe-C-O system. However, as the various interaction energies needed in the model had to be derived from the ternary data, the model does not promise well as a means of forecasting ternary behavior. Each of the above models carries the assumption that the strongly electronegative solutes have the same configurational environment as metallic solutes; i.e., the solute can be treated as a substitutional or interstitial atom in a quasi-crystalline lattice and is surrounded by a normal coordination shell of solvent atoms. There are, however, a number of facts which suggest that this is unlikely. First, the heats of solution are large, being more typical of molecule formation rather than alloying. For example, the heats of solution of monatomic oxygen and sulfur in liquid iron are -90 kea16,8 and -74 kea1,7, 8 respectively. These are to be compared with maximum heats of solution of metallic solutes in liquid iron of about -13 keal (silicon is an exception with -28.5 kea17). The large depression of the surface tension of liquid iron by trace amounts of the electronegative solutes oxygen, sulfur, and selenium9 suggests, by analogy with aqueous systems, the possible existence of polar molecules in the liquid. The effect of these solutes is at least three orders of magnitude greater than normal metal solutes.10 As has been pointed out by Richardson,11 the electron affinities and ionization potentials of oxygen and sulfur are such that it is likely that they exist in metallic solution as negatively charged ions. If this is so, and it is assumed that electrostatic forces play an important role in determining the configuration, it is unlikely that the stable configuration will be that of an isolated ion surrounded by a symmetrical coordination shell of solvent ions. It is more likely that the energy of the system would be lowered by the formation of solute-solvent screened dipoles. The above arguments suggest the formation of "molecular species" between solute and solvent atoms. The idea of the existence of molecular species in such solutions is not new, however', for Marshall and chipman12 have explained in a semi-quantitative manner the C-O equilibrium in liquid iron by postulating the species CO. Chen and Chip-man13 interpreted their measurements on the Cr-O equilibrium in iron in terms of the species CrO. Zapffe and sims14 have also postulated the existence of such species in liquid-iron alloys.

Jan 1, 1965

By R. Kossowsky

USING etch-pit techniques, Johnston and Gilman' have shown that the stress dependence of dislocation velocity can be represented by the expression where r, is the dislocation velocity, a is the applied stress, and oa, is the stress to produce a unit velocity. Noble and Hul12 showed that the exponent m is strain-dependent and increases rapidly in the work-hardening region. This was explained by arguing that in the work-hardened material the applied stress required for any given velocity will be greater than in the annealed material by an amount equal to a back stress due to work hardening. schadler3 has stressed the importance of substructure as a possible source of error in dislocation velocity measurements, and took care to make velocity measurements in which dislocations moved such short distances that interactions with boundaries were avoided. schadler3 also pointed out that, if standard testing equipment is used, measurements of m from flow stress data could be seriously in error in materials with a high initial work-hardening rate. Noble and Hu112 have further argued that, due to the strain dependence of m , the extrapolation to zero strain4 to obtain the true value of m can be justified only in the preyield region. Microstrain experiments in high-purity iron5,6 have led to the conclusion that aiA (Ref. 5) (defined as the stress to first produce a permanent set of 10-6 in. per in.) and oflow are not controlled by the same deformation mechanism. It has been proposed5,6 that aA is governed by the lattice resistance to the motion of screw dislocations in a given slip plane and that oflow is controlled by the lattice resistance to a full-scale cross slip. The purpose of this note is to extend Noble and Hull's argument further and to show that measurements of m from flow stress data can be in error due to the rapid increase in stress in the microstrain region6 when stress is increased beyond aA. Double z-one-refined single crystals of molybdenum (with the (101)[ 111] slip system operating and a Schmidt factor of 0.475) were used in an experimen-

Jan 1, 1968

By Jaakko Kajamaa

Neutron diffraction was applied to determine sheet textures by the transmission method. Cold-rolled and recrystallized copper sheets were investigated. The amount of cube texture was determined for three compositions, in which the phosphorus content was, respectively, 0, 0.005, and 0.03 wt pct. The heat treatment was in every case 8 sec at 650°C. In the two latter cases the cube texture was prevented. In addition a comparison with the X-ray diffraction transmission method was made with the 96 pct cold-rolled copper sheet. Outer parts of both (111) pole figures can be considered to be rather identical. This is seen from the fact that the intensity ratio ITD/120" was 0.45 for neutron diffraction and 0.40 for X-ray diffraction. Differences between the methods were discussed in detail. Features peculiar to neutron and X-ray diffraction in texture studies were listed and compared. In this work neutron diffraction was applied to determine sheet textures. Specifically, it was desired to ascertain whether this method can be used to reveal differences when compared to other methods. In addition, the amount of the cube texture in copper sheets was determined as a function of phosphorus content. Previous applications of neutron diffraction to texture problems include the following: nickel wires,' wire of some bcc metals,' and uranium bars.3 In the neutron diffraction technique the greatest difference is in the sample—its method of production and its volume. A sample needs no treatment and its volume is roughly 105 times larger than the volume of an X-ray diffraction sample. The cold-rolled sheet was investigated both by neutron diffraction and by X-ray diffraction, because it is expected that, due to large number of defects, possible differences in the results of the two methods would be revealed. It is a well-known fact that X-ray lines show broadening when cold-worked. Analysis has shown that this is based chiefly on small crystalline size, micro-stresses, and/or faults.4'5 Neutrons are sensitive to the above-mentioned disturbing factors as well, but circumstances in diffraction are different from the X-ray case. Because the sample represents a larger volume, the result is an average over that volume. In addition, it can be assumed that the sample has preserved its original structure, because it needs no special preparation. The particular limitation of neutrons is the relatively low neutron intensity available from nuclear reactors. This decreases the resolution as compared to the X-ray diffraction methods. Furthermore, absorption mainly reduces diffracted X-ray intensity, while multiple scattering effects, i.e., secondary extinction, disturb neutron diffraction. SO neutrons and X-rays behave in a different way when interacting with matter. As in other structural investigations, one can utilize this difference in texture studies as well. One cold-rolled and three recrystallization textures in copper sheets were investigated by neutron diffraction. The samples were produced at the Outokumpu copper factory to the specifications shown in Table I. The paper is divided into five parts. The first deals with the theory of the measurement. In the second, experimental procedures are described. Results are presented in the third part. Both cold-rolled and re-crystallized samples are studied. Discussion is in the fourth part, and finally in the fifth part some conclusions are drawn. 1) THEORETICAL CONSIDERATIONS Properties peculiar to neutron diffraction are the following: a) the scattering length varies greatly between one element and another; b) many of the elements do not absorb neutrons appreciably. In this connection it is of primary interest to know the interaction of neutrons with lattice imperfections. As with X-rays this problem leads to diffraction analysis of deformed and recrystallized metals. From the physical point of view the main difference is that neutrons are scattered by nuclei (magnetic scattering is not considered here), whereas X-rays are scattered by electrons. The features peculiar to neutron and X-ray diffraction methods in texture studies are listed in Table 11. Pole figures are an important tool in performing structural analysis of deformed or recrystallized metal. Present texture research technology requires pole figures which are as precise as possible. The choice between these two methods depends on the technical information which is required. The X-ray diffraction transmission technique may give results which are not necessarily representative of the average physical state of the sample. Although foil samples normally contain enough crystallites for diffraction, they may not necessarily represent the whole structure. An example of this problem is the frequently observed difference between the "surface" and the "inside" texture of a sample. The production of foil samples may disturb the original structure of the parent material. The selection and orientation of the foil from the sample is quite arbitrary. Normally, a highly deformed piece of metal has several texture components. Different components are deformed in a slightly different manner. This is a re-

Jan 1, 1969

By I. R. Kramer

[The final paper in the diffusion symposium was given by I. R. Kramer. The author called attention to the diffusion characteristics of chromium deposited on the surface of steel by treatment with chromium chloride and alloyed with the surface layer of the steel by thermal treatment. As the data cited were previously published in the paper " Chromizing of Steel," by I. R. Kramer and Robert H. Hafner (Metals Technology, October 1942, and in the Transactions, volume 154, 1943, pages 415-420), it is unnecessary to reproduce these data here. The following paragraphs are taken from the author's presentation.— Editor.] Aside from the well-known practical application of the diffusion phenomena to carburizing and calorizing, -diffusion also finds application in adding alloying elements to the surfaces of steel parts. The chromizing of steels is a process by which the surface of a low-alloy steel may be enriched with chromium to form a highly corrosion-resistant case; This chromized case differs from an electroplated coat in that it is a diffused layer integral with the base metal and has all of the properties of a high-chromium steel. Recently a method of chromizing has been developed in Germany by Daeves, Becker and Steinberg in which gaseous chromium chloride and hydrogen are passed over the steel at temperatures of 1650° to 1800°F. The chromium chloride reacts with the iron to give chromium and iron chloride. The chromium atoms are deposited on the surface and diffuse in as the iron atoms diffuse out, forming a layer rich in chromium. The principal role of hydrogen is to remove the carbon from. the surface of the steel. Of the two mechanisms, chemical reaction and diffusion, the one operating at the slower rate will determine the rate of formation of the layer. In this case, diffusion is slower and therefore any factors influencing its rate will affect the process. The rate of diffusion is influenced by the temperature and crystal structure of the parent metal. Depth-concentration studies show that the concentration falls off gradually for a considerable distance and then drops sharply at about 13 per cent chromium, the point coincident with the boundary of the gamma loop. The influence of the composition of the base metal upon diffusion is quite important. The depth of penetration of the chromium decreases as the carbon content increases and, of more importance, the chromized layer becomes brittle and is likely to spa11 if the carbon content is too high. It appears that in order to chromize successfully the carbon must be fixed by strong carbide-forming elements such as chromium or molybdenum, which decrease the diffusion of carbon. If this is not done, the carbon will diffuse from the interior faster than the chromium can diffuse inward, thus forming a carbide barrier. The corrosion resistance of the chromized layer is high, and these steels offer some unique advantages over other corrosion-resisting coating or alloys. While chromizing is not meant to replace stainless steels, it may serve in the saving of alloying elements. The chromizing process uses soft or low alloyed steels that can be easily hot or cold formed and since the chromized layer is soft and firmly adherent, chromized parts can be subjected to cold deformation without spalling or chipping and without loss of corrosion resistance.

Jan 1, 1944

By I. R. Kramer

[The final paper in the diffusion symposium was given by I. R. Kramer. The author called attention to the diffusion characteristics of chromium deposited on the surface of steel by treatment with chromium chloride and alloyed with the surface layer of the steel by thermal treatment. As the data cited were previously published in the paper " Chromizing of Steel," by I. R. Kramer and Robert H. Hafner (Metals Technology, October 1942, and in the Transactions, volume 154, 1943, pages 415-420), it is unnecessary to reproduce these data here. The following paragraphs are taken from the author's presentation.— Editor.] Aside from the well-known practical application of the diffusion phenomena to carburizing and calorizing, -diffusion also finds application in adding alloying elements to the surfaces of steel parts. The chromizing of steels is a process by which the surface of a low-alloy steel may be enriched with chromium to form a highly corrosion-resistant case; This chromized case differs from an electroplated coat in that it is a diffused layer integral with the base metal and has all of the properties of a high-chromium steel. Recently a method of chromizing has been developed in Germany by Daeves, Becker and Steinberg in which gaseous chromium chloride and hydrogen are passed over the steel at temperatures of 1650° to 1800°F. The chromium chloride reacts with the iron to give chromium and iron chloride. The chromium atoms are deposited on the surface and diffuse in as the iron atoms diffuse out, forming a layer rich in chromium. The principal role of hydrogen is to remove the carbon from. the surface of the steel. Of the two mechanisms, chemical reaction and diffusion, the one operating at the slower rate will determine the rate of formation of the layer. In this case, diffusion is slower and therefore any factors influencing its rate will affect the process. The rate of diffusion is influenced by the temperature and crystal structure of the parent metal. Depth-concentration studies show that the concentration falls off gradually for a considerable distance and then drops sharply at about 13 per cent chromium, the point coincident with the boundary of the gamma loop. The influence of the composition of the base metal upon diffusion is quite important. The depth of penetration of the chromium decreases as the carbon content increases and, of more importance, the chromized layer becomes brittle and is likely to spa11 if the carbon content is too high. It appears that in order to chromize successfully the carbon must be fixed by strong carbide-forming elements such as chromium or molybdenum, which decrease the diffusion of carbon. If this is not done, the carbon will diffuse from the interior faster than the chromium can diffuse inward, thus forming a carbide barrier. The corrosion resistance of the chromized layer is high, and these steels offer some unique advantages over other corrosion-resisting coating or alloys. While chromizing is not meant to replace stainless steels, it may serve in the saving of alloying elements. The chromizing process uses soft or low alloyed steels that can be easily hot or cold formed and since the chromized layer is soft and firmly adherent, chromized parts can be subjected to cold deformation without spalling or chipping and without loss of corrosion resistance.

Jan 1, 1944

By Frank R. Milliken, Robert Goodwin

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By Robert Goodwin, Frank R. Milliken

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By J. J. Kantner

CREEP investigators have made extensive studies to determine the interrelation of stress, temperature and the tensile creep rates of metals. It has been suggested that at small stresses the secondary or constant creep rates obey a simple viscous law. Building upon this suggestion, departure from pure viscosity as stress increases may be expressed mathematically as a consequence of reversibly altered viscosity or "flowability" in the same sense that temperature change reversibly alters viscosity. From the index to alteration of viscosity, a value for the energy of secondary creep may be derived having the magnitude of the free energy of vaporized metal. The suggestion is made that applica-tion of stress alters the energy of secondary creep. Strain energy is argued to be but a minor factor in the energetics of secondary creep. A deformation mechanism involving the large energy associated with secondary creep implies a sort of solid self-diffusion process. Evidence indicates that creep strain above the recrystallization temperature takes place by crystallographically directed self-diffusion at grain boundaries and points of crystal defects. A self-diffusion theory of secondary creep is proposed, embracing the principles of the Dushman-Langmuir theory of solid diffusion. An equation is suggested whereby the rate of tensile creep may be related directly to the physical and struc-tural character of the solid metal.

Jan 1, 1937