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By A. H. Daane, W. J. Wunderlin, B. J. Beaudry

In an earlier study at this laboratory,' the authors investigated the solid solubility of holmium in copper, silver, and gold, and also the melting point of the first eutectic on the noble-metal-rich side in these systems. In a more recent study of the solubility of rare-earth metals in gold at this laboratory. Rider, Gschneidner, and McMasters2 noted that the reported eutectic temperature in the Ho-Au system was lower than the corresponding eutectics in systems of dysprosium and erbium with gold. A redetermination of the eutectic temperature in the Ho-Au system with the same alloy used in the original study showed the eutectic temperature to be 810°C instead of 778°C as originally reported. (The eutectic temperatures in the Ho-Ag and Ho-Cu systems were also redetermined and were found to be 795" and 864°C compared to 787° and 868°C, respectively, which were reported originally.) Since this large change in eutectic temperature made the solubility data appear questionable, new alloys were prepared, heat-treated, and examined metallographically. The procedure of sample preparation and heat treatment used in the original work' was followed except longer heat treatments were used ranging from 7 days at 600°C to 6 hr at 900°C. The results obtained are shown in Fig. 1. There is good agreement between the two studies in the maximum solubility of holmium in gold. Since the slope of the solvus is less pronounced in the present study, the extrapolation to 550°C shows a solubility of 1.6 wt pct Ho in gold compared with 1.0 wt pct in the original work. Since additional data were obtained and longer heat treatments were used in the present study, the larger value is believed to be more accurate. The authors wish to express their appreciation to P. Rider and K. A. Gschneidner. Jr., for bringing this discrepancy to their attention, and also to D. Thompson for assisting in the present study.

Jan 1, 1965

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By D. P. Harris

This paper surveys a few of the quantitative exploration models that might be of interest to an ex-plorationist seeking to apply methods of operations research to mineral exploration. A general development of each model is presented, and the model is evaluated relative to the exploration activity. Finally, a philosophy of exploration and mineral resources is presented, and a possible exploration strategy incorporating concepts of some of these models consistent with this philosophy is proposed. The high cost of conducting an effective exploration program has generated an increasing interest in methods of optimizing the allocation of the resources of a firm engaged in mineral exploration. As a step towards this, mathematical models have been formulated which are designed to quantify those variables of mineral exploration in such a manner that they can be integrated with all phases of the firm's operations so as to optimize its profit objective. QUANTITATIVE MODELS General: Exploration models express at least two concepts: mineral occurrence and effectiveness of search. In simplest terms, an exploration model might be formulated mathematically as follows: P(X) = F(X) . G(X), where P(X) = the unconditional probability of discovery of X deposits, F(X) = the probability of occurrence of X deposits, and G(X) = the probability of discovery of X deposits, conditional upon their existence in the search area. With these general models as a basis of reference, some of the specific exploration models are examined below. The Allais Model: DEVELOPMENT - M. Allaisl performed the first study in which a philosophy of exploration was formulated into a probability framework. His objective was to estimate the economic profitability of the exploration of the Algerian Sahara. Allais divided the Algerian Sahara into blocks of land (called cells) 10 km square and defined the random variable, X, as the number of mining districts per cell. Thus, F(X) would describe the probability of 1, 2, or n mining districts occurring within any cell of the search area. Allais reasoned that his best information as to the form of the distribution, F(X), was the number of mining districts per cell that had been found in well explored areas in the world, such as the Western States of the U.S. He found that the Poisson function produced a reasonably good fit to the distribution of districts in these explored areas: where? is a parameter, such as the average number of districts per cell. Thus, by determining the value

Jan 1, 1968

By R. W. Raymond

THE Brüclrner roasting-cylinder is well known as an apparatus which has done good work in the desulphnrization, particularly of refractory silver ores, in the western districts of this country. A paper by Mr. J. M. Locke, of Cincinnati, describing the cylinders, as constructed by Messrs. Lane & Bodley, in that city, may be found at p. 295, vol. ii., of the Transactions of the Institute; and a paper by Mr. N. H. Cone, vol. iv., p. 226, gives an account of their operation in Colorado. The purpose of the present paper is to present an .improved construction, designed by Mr. Brückner. This is clearly shown in the accompanying plate, which scarcely needs explanation. It will be seen at once that this construction involves two cylinders, instead of one. Mr. Brückner thinks that three cylinders might be better yet, as securing an exact mechanical reproduction of the work of the well-known three-hearth Fortschaufelungsofen, the most perfect of the reverberatories in which delicate roasting is performed with hand-labor. THE APPARATUS. Erection of the Cylinders.—Although the cylinders may he put lip at any locality, or added to existing works, it is preferable, if possible, to choose the site on a hill sloping naturally, say about 30' or 33. Two excavations are made, one 8 to 12 feet higher up than the other; and each is protected by a wall with a batter of about 1 inch to the foot, to prevent slides of stone and earth. Each cylinder being 20 feet long and 7 feet in diameter, the total excavation should be 60 to 70 feet along the hill, and 15 to 25 feet wide. On each level a building is erected 35 feet long by 20 feet wide and 12 feet high, with the roof containing a ventilator against the hill. When both buildings are on the same level, there should preferably be a solid frame-work of very heavy timber, to carry the four rollers which bear the upper cylinder. The four rollers carrying the lower cylinder should preferably rest on two very heavy pieces of timber, strongly braced together and laid to their top in a foundation made of stone or brick and cement. Foundations are necessary only under each two opposite rollers, but they must be made carefully,

Jan 1, 1886

By H. I. Aaronson, H. A. Domian, A. D. Brailsford

A current study of the growth kinetics of k (hcp) plates in a Cu-Si (fcc)' has generated a requirement for data 02 the chemical interdiffusion coefficient in a (termed D,) as a function of temperature at the composition of the a/a + k pJase boundary. Rhines and Mehl 2 have determined D, as a function of composition at lower silicon contents by making Matano analyses of concentration-penetration curves. However, the accelerating increase in B, which they demonstrated as the phase boundary composition is approached at constant temperature and the rapidly diminishing accuracy of this analysis as the limiting compositions of a diffusion couple are approached (the silicon-rich component of their couples contained appreciably less silicon than is permitted by the solubility limit) indicate that the required information cannot be safely obtained by extrapolation of their data. Although the quite different method employed in this study is not exact, it will be shown that the approximations made are not serious ones, particularly from the viewpoint of the prgcipal application anticipated for these data. D, was determined from the migration kinetics of the a :k boundaries formed in sandwich-type diffusion couples produced by welding a block of high-purity copper to opposite sides of a cube (* in. on edge) of homogenized high-purity Cu-5.82 wt pct Si alloy. The alloy is pure k in the temperature range employed. The surfaces of the couple components which were normal to the diffusion direction were machined accurately flat and parallel, lightly polished, and carefully cleaned. Welding was then accomplished by means of the vacuum-encapsulated pressure jig technique previously employed.3 Welding was always conducted at the intended diffusion temperature; thus the welding anneal also served as the first diffusion anneal. Subsequent diffusion anneals were performed in evacuated Vycor capsules. Following the welding anneal, one of the surfaces parallel to the diffusion direction was machined, ground, and polished flat; additional material was removed from this surface after each diffusion anneal in order to avoid any effects of composition changes. After etching,4 the average distance between a : k boundaries was measured by means of a traveling microscope with an accuracy (per measurement) of better than 1 p. Satisfactory results were obtained at four temperatures in the range 775° to 655°C; attempts to obtain data at two lower temperatures were unsuccessful, evidently as the result of the interference of surface contamination during the welding process.

Jan 1, 1969

By Maynard H. Jameson

EARLIER investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.1 The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,2 and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. THEORY Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredge3 determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities po, pi, and p2 are involved, and the source I is located at the interface of the media (po) and (pi). The perpendicular depth of the lower interface is h,? is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: [ ] As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is ?, the angle measured from the horizontal to the first image is 2? to the second image it is 4?,, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1941

By D. E. Light, J. Y. Somnay

The use of alkyl acid phosphates and their alkali salts as collectors for the uranium minerals brannerite and uranothorite was investigated. In particular a detailed flotation study was carried out using isooctyl acid phosphate as a promoter. Tests were conducted on an Elliot Lake ore analyzing 0.11% U 3 O 8, chiefly as brannerite, and approximately 9% pyrite. Pyrite was floated with conventional reagents; the flotation of brannerite from the sulfide tails was studied to determine the optimum pH and pulp density to employ with isooctyl phosphate. 4 uranium recovery of over 90% was possible with a selectivity index of 8.95 when these tails were floated at 17% solids and a pH of 1.7. The effect of various modifying agents was also investigated. Aluminum sulfate, lactic acid and sodium silicate improved the selectivity of collection yielding selectivity indices of 9.5 to 11.5. Ferric chloride was found to be a depressant for brannerite. A Bancroft ore which analyzed 0.13% U308, and contained uranothorite was also amenable to flotation using isooctyl acid phosphate. The composite uranium concentrate obtained assayed 0.41% U308 at a recovery of 95.3% and a ratio of concentration of 3.24. Previous investigations1,2 on the flotation of brannerite, pitchblende, uraninite and/or uranothorite from various Canadian ores showed that fatty acids, including oleic acid and tall oils, petroleum sulfo-nates and alkyl acid phosphates, were suitable collectors for these uranium minerals. Additional work carried out by the Mines Branch in Ottawa on brannerite ores from the Elliot Lake area3 used the tall oil Acintol FA-1, or FA-2, as a collector. A recovery of 92% of the uranium in a concentrate which contained about 55% of the weight and assayed 0.2% U3O8 was obtained from a feed of 0.1% U308 in this latter instance. Eigeles et a1.4 carried out flotation on pitchblende ores and found that the most promising results were obtained with alkyl acid phosphates and their alkali salts as collectors. Within the homologous series of alkyl phosphates, the best flotation characteristics were displayed by isooctyl phosphates. Further, isooctyl phosphate derivatives were much less sensitive to hardness forming salts than oleic acid, enabling all flotation tests to be made with tap water. This paper describes tests employing alkyl acid phosphates for the flotation of ores containing brannerite and uranothorite. The flotation work described herein was conducted in conjunction with the development of a leaching process for Elliot Lake, Ontario, brannerite ores. In this process pyrite in the ore was concentrated by flotation and roasted, providing sulfur dioxide which was used to produce sulfuric acid in situ in a liquid-solid extraction process. A 40% conversion to sulfuric acid was indicated at a leaching temperature of 80°C; this resulted in the extraction of 93% of the total uranium after a contact period of 6 hr. A rotary kiln was used as a leaching vessel. Preconcentration by flotation was studied in conjunction with the above process to reduce the bulk of solids for leaching and, consequently, capital expenditure. The materials and methods used in this study will be described initially. Then the results will be presented in two sections, the first dealing with the brannerite ore, and the second with the uranothorite. Finally an economic analysis of the results on the brannerite material will be made. MATERIALS AND METHODS The two ore samples examined were from uranium-producing mines. One was a brannerite ore, a uraniferous quartz pebble conglomerate from the Elliot Lake area, which contained 0.11% U3O8, 4.3% S and 4.5% total Fe. Mineralogical studies of similar samples indicated the presence of quartz, microcline, sericite, pyrite and minor quantities of rutile, pyrrho-tite and zircon. The other ore was from a biotite-rich pegmatite in the Bancroft area; feldspar, quartz and biotite formed the major gangue components. Uranothorite was the principal uranium mineral; the head assay was 0.13% U 3 O 8. Preparation of Feed: The ores were crushed to —10

Jan 1, 1963

By F. Garofalo

It has been shown by various investigators that during constant stress creep the dependence of minimum creep rate, 6,, on stress, o, is given by em = A onat low stress levels, md by 6, = A' exp [ß s] at high stress levels. In these relations A, n, A', and ß are constant at constant temperature. A single relation has been found which satisfies conditions for both high and low stresses and agrees well with experimental results. This relation is 2, = AN (sinh a s)n, where A" is a constant at constunt temperature and a = p/n. This relation also satisfies the linear relation, 6, = k s, found at temperatures near the melting point at low stresses. EXPERIMENTAL creep results have led to a number of empirical relationships between minimum creep rate, 6,, and the applied stress, s. Under conditions of constant stress it is generally found that at low-stress levels,'-' the dependence of minimum creep rate is given by 6, = Asn. At high-stress levels'74 the experimental results fit the relation, 6, = A' exp [po l. In these relations A, n, A' and ß are constant at constant temperature. A model based on climb-of-edge dislocations from a pile-up array leads to a relation similar to that found experimentally at low stresses.' On the other hand. theories based on chemical-reaction rate,5 nonconservatively moving dislocation jogs, and jog migration and climb-of-edge dislocations4 lead to a relation similar to that found experimentally at high stresses. No difference in mechanism between low and high stress levels has been clearly defined; it is questionable whether such a difference really exists. In any event, the major argument usually given in substantiation of a change in mechanism from low to high stresses is that no single relation exists for defining the stress dependence of the creep rate over wide ranges in stress. However, such a relation has been found and is of the form, dm = A" (sinh a s)n, where A" is a constant at con- stant temperature and a = ß/n. This relation agrees well with experimental results over wide ranges in stress and temperature for copper, aluminum, an A1-3.1 pct Mg alloy, and an austenitic stainless steel. STRESS DEPENDENCE OF MINIMUM CREEP RATE At low stress levels the minimum creep rate, gm, depends on the stress, 0, under conditions of constant stress creep through the relation em=Aon [1] The quantities A and n have been defined previously. In the range in which this relation applies, a linear dependence is found in a log em,-log o plot. Above the stress range of application of relation [I], the minimum creep rate increases much mar; rapidly than predicted by relation [I]. This behavior is shown in Fig. 1 for a series of creep tests on copper4 at various temperatures ranging from 673 o to 973°K. Relation [I] is satisfied at the lower stresses, although the results at 973°K are quite limited. In all cases the transition beyond the applicable range of relation [I] is a gradual one indicating no abrupt change in mechanism. For all test temperatures, values of n have been determined from the results in Fig. 1. These are reported in Table I under Alog tm/hlog o. At high stress levels the stress dependence of minimum creep rate under conditions of constant stress is given by im = A' exp [ß a] 2] All factors have been defined previously. In a log em-0 plot, relation [2] predicts a linear function. Experimentally, a pronounced deviation from the prediction of relation [2] is found at lower stresses. As the stress is lowered, the minimum creep rate decreases more rapidly than predicted by relation [2]. This shown for copper in Fig. 2. Again it is found that the transition from high to low stresses is gradual and no really sharp change is found. Values of p determined from the high stress results are given in Table I. The dependence of minimum creep rate on stress at constant temperature for all ranges in stress

Jan 1, 1963

By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy's law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy's law' has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy's law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.'s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.' To others,' turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy's law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.' In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy's law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy's law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy's law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy's law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy's law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By Arthur F. Taggart

A general awakening of interest among mill men concerning the mechanical efficiencies of their crushing machines is evident from a perusal of the recent files of mining publications. Considering the large part of the power bill which must be debited to the crushing department, such interest is natural. When, however, the articles on the subject are read, the only statement upon which the writers agree is that fine grinding consumes a large amount of power, and that the machine which, from a concentration standpoint, offends as a slime producer is, for that reason, a serious offender in wasting power. When the mill man attempts to find a method for measuring the power wasted, or to compare the efficiency of one machine with that of another for the same work, he is confronted with a choice of methods which lead to conflicting results. There are two reasons why the work of crushing is not more generally understood. In the first place, experimental data are difficult to obtain; and in the second place, before these data can be put in general form certain assumptions must be made. A difference in these assumptions by different investigators has led to conflicting conclusions. This conflict has resulted in the proposal of two laws. The first of these is the so-called Rittinger's law, which is variously stated as follows: "The work of crushing is proportional to the reduction in diameter."—R. H. Richards: Ore Dressing, p. 304 (1903). "The work required to crush rock is very nearly proportional to the reciprocals of the diameters crushed to."—A. Del Mar: Engineering and Mining Journal, vol. xciv, No. 24, p. 1129 (Dec. 14, 1912). "The work done in crushing is proportional to the surface exposed by the operation, or better expressed for this purpose, the work done on a given mass of rock is proportional to the reciprocal of the diameter of the final product, assuming that all the mass has been reduced to one exact size, which is only theoretically possible."— A. 0. Gates: Engineering and Mining Journal, vol. xcv, No. 21, p. 1039 (May 24, 1913). ' ' " Of this law as variously stated above H. Stadler says (Grading Analyses and Their Application, Author's Reply to Discussion, Transactions of the Institution of Mining and Metallurgy, vol. xx, p. 426 [1910-111):

Jan 1, 1915

By B. G. Reisdorf

This paper describes the microstructural changes that occur when quenched ultrahigh-strength steels containing OA pet C and various amounts of nickel, silicon, and cobalt are tempered. The changes that occur in hardness, yield strength, and martensite diffraction-peak widths when these steels are tempered are related to the precipitation of the carbide phases. An unea$ectedly high silicon content (about 30 pct) was found in the E -carbide phase in a steel containing only 1.5 pct Si. TEMPERED martensitic steels have such wide-spread utility that they have been the subject of numerous investigations, and a sizable amount of literature has developed on this subject.M This investigation, which is a part of a larger program to correlate microstructure with mechanical properties at a variety of strength levels, is limited to the microstructural changes that occur when a quenched 0.40 pct carbon steel (USS Airsteel X-200 steel) is tempered, and to the effects of the alloying elements—nickel, cobalt, and silicon—on these microstructures. Used in this investigation were electron microscopy, electron-diffraction identification of the carbide phases, electron-probe micro-analysis of the carbides, X-ray determinations of retained austenite, and measurements of martensite X-ray diffract ion-peak widths. MATERIALS AND METHODS The chemical analyses of the eight heats examined eats No. 30 through 37) are shown in Table L Heat No. 30 has the chemical com~osition of Airsteel X-200, and the remaining seven heats contain various amounts of nickel, chromium, cobalt, and silicon. The heats were air-melted in an induction furnace and cast into 8 by 8 in. ingots that were subsequently heated to 2300 and rolled to 1-in.-thick plate. Oversize 0.505-in.-diam tensile specimens were rough-machined from the plates and austenitized in air at 1700° F for half an hour and oil-quenched. The specimens were then tempered in air at temperatures of 400° to 1000 for tempering times of 1, 4, and 16 hr, and finish-machined to 0.505-in.-diam tensile specimens. Electron micrographs were prepared from Formvar replicas of the midthickness of tensile-specimen shanks that had been electrolytically polished and etched in nital. Electron-diffraction patterns were obtained from carbon-extraction replicas. The replicas were prepared by etching the sample surface in the same manner as for microscopy, evaporating carbon on the etched surface, and re-etching the sample to free the carbon film and the precipitate particles. Electron-probe microanalysis was performed on some of the extraction replicas. To obtain adequate fluorescent X-ray intensities, several thicknesses of replica were exposed to the electron beam so that the results represent an average composition of the extracted particles rather than an analysis of single precipitate particles. The retained austenite contents of the specimens were determined by an empirical X-ray diffraction

Jan 1, 1963

By W. P. Sykes

IN CONNECTION with a study of tungsten steels, Honda and Murakami1 reported an investigation of the system iron-tungsten. This report included a tentative equilibrium diagram, photomicrographs of various alloys in the series, and qualitative measurements of hardness and magnetic properties. The present investigation originally had as its object the study of the hardness and tensile properties of a series of carbon-free iron-tungsten alloys. But, as the work progressed it became evident that the system possessed other features of interest, so the scope of the investigation was enlarged. MATERIALS The iron powder used in preparing the alloys was obtained as follows: Iron oxalate was precipitated from a ferrous-sulfate solution by the addition of a solution of oxalic acid. This oxalate, after thorough washing, was ignited to iron oxide, which after reduction in hydrogen at about 1000° C. yielded iron powder containing but about 0.2 per cent. iron oxide and about 0.005 percent. carbon. Tungsten metal in the form of powder, such as is used in the manufacture of filaments for incandescent lamps, was the other constituent. This material analyzed 99.8 per cent. tungsten and contained no carbon, The metal powders, in the desired proportions, were mixed by tumbling and formed, under pressure of 20 tons per sq. in., into rods 3/8 by 3/8 by 10 in. To form the alloys without contamination, sections of the pressed rods were placed on alundum slabs and heated in an alundum tube wound with a tungsten resistor and packed in heat-insulating material. While the resistor was heated, a stream of hydrogen was continually passed through both the tube and the case containing it. The tungsten winding on the tube, as well as the material heated within the tube, was thus protected from oxidation. Such a furnace will operate constantly

Jan 2, 1926

By W. M. Yim

Experimental results are presented which indicate that transverse striations in horizontal zone-leveled Bi-Sb alloy crystals are due to irregular growth rate resulting from thermal fluctuations in the melt (Iring gowth. Thc thermal fluctutations arose from two different sources. The first type was brought about by periodic fluctuations in the furnace temperature. The second type can be attributed to turbulent therrrol conlcclion in the trzelt near the solid-liquid inteyace. Tile arrzplitlcde ond fvequency of the tetiperaticre fluctlrations vesultity from llle lhevnal con1,ecrrell. The striation spacings in Lhe crystals covvelale well with the periodicity 0.f the tempevature flueluatiors. Altliough the strialiors represenl corrlpositiozul inhoiHogeneity oh a rzicroscule, less than f.z cil. be1 S6 in Best's as deterrirzed by electron-pro be chalq'sis, the slriations roerre fbund to ILUL' no rrleusuanble effect on electical vesistirity rwr on weak field macgnetoresistance of. the Bi-Sb a1lu.y in the ternpevutue ),unge 4.Polo 300°K. DURING the course of an investigation on the horizontal growth of semimetals,' it was found that crystals of Bi-Sb alloys contained many closely spaced parallel arrays of striations. These striations occurred perpendicular to the growth direction and parallel to the solid-liquid interface. We shall refer to them as transverse striations, or just striations'', to distinguish them from lineage substructures or longitudinal striations which form parallel to the growth direction and have been known to be associated with cellular structures.' Similar transverse striations have been reported previously to occur in other materials prepared by horizontal growth: metals,4 semiconductors,5 as well as their alls. - Various methods of crystal preparation have apparently little effect on the occurrence of the transverse striations. They form whether the crystals were grown by the vertical Czochralski technique, withe1' or without'3- rotation, or by the horizontal zoning methd.- Thus, the transverse striations are not limited to any one class of materials, nor to any particular method of preparation. It is likely, therefore, that all of the observed transverse striations may have some common cause. Previously, workers agreed that periodic changes in the growth rate bring about the striations. However, no agreement exists as to the origin of the growth-rate fluctuations. Some attributed the discontinuous growth to a purely external cause, such as fluctuations in the furnace temperature, jerky motions in the crystal pulling mechanism, or a nonsymmetrical temperature distribution in the melt (in the case of crystals grown by the Czochralski technique with rtation). Others looked for the cause in some fundamental property of the growth process itself. For instance, a certain degree of supercooling is required to initiate growth from the melt. But, with further growth, the degree of supercooling decreases because of the liberation of the heat of solidification at the solid-liquid interface. Thus, crystal growth would be brought to a halt until sufficient supercooling is resotred and the cycle begins again.3'11 According to this model, periodic fluctuations in the melt temperature should exist at the solid-liquid interface. Since the periodic fluctuations in growth rate would result in changes in the segregation coefficient of solute atoms, crystals containing the transverse striations may, in some cases, show a periodic impurity fluctuation along the length, resulting in a degradation of electrical properties. The resistivity striations in doped germanium'9-10 or lnsbB are well-known examples of this microsegregation. The present work was undertaken to explain the exact origin of the transverse striations, and to assess the extent of their effect on chemical homogeneity as well as on electrical properties of Bi-Sb alloy crystals. Results from our previous study of the crystal growth of Bi-Sb alloys1 indicated that the transverse striations may arise from the temperature fluctuations in the melt during growth. This paper will show that the melt temperature fluctuations are indeed responsible for the occurrence of the transverse striations. I) EXPERIMENTAL Although the transverse striations have been observed in all slow-grown Bi-Sb alloys across the entire compositional range, we selected a composition, Big3Sbs, for the present study in view of the extensive data available on the crystal growth of this alloy from a previous study.' High-purity bismuth and antimony, both a 6-nine grade by the manufacturer's emission spectrographic analysis, were used throughout. Independent mass-spectrographic analysis showed, however, that the starting materials were more nearly a 5-nine grade. each containing metallic impurities of approximately 10 ppm atomic. In zone-leveled Big5Sb5 alloys, the total metallic-impurity content was slightly lower, about 7 ppm atomic, indicating that some degree of purification was achieved during the growth. None of the electrically active impurities, such as tin and lead (acceptors) and tellurium and selenium (donors), were present in significant quantity in undoped Bi95Sb5. Typical analysis of the undoped Bi95Sb5 alloy is shown in Table I. Nonmetallic impurities, such as carbon and oxygen, were detected, sometimes as much as 100 ppm, in both the starting materials and the zone-leveled alloys: but the data were only qualitative. Temperature fluctuations in the melt were monitored over 1 or more days by means of a 5-mil chromel-

Jan 1, 1967

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation' y = 100 (x/k)a [1] in which y — cumulative percent finer, x = particle size, a -= distribution modulus, and k = size modulus. Charles3 found that the energy consumption in comminution is usefully expressed by another empirical relation, E = Ak(1-D) [2] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; (1-n) is the slope of a plot of log E vs log k. Holmes3 has presented energy equations similar to Eq. 2. The constants a and n in Eqs. 1 and 2 have been shown to depend both on the nature of the material and on the comminuting device. Moreover, Charles showed that within experimental error a and n are a — n+1 = 0 [3] Combining Eqs. 2 and 3, E = A k-a [4] In the first sections of this article it is shown that the energy equation, Eq. 4, can be derived directly from the size distribution equation for the fine sizes, Eq. 1. The derivations are made without assuming any of the specific relationships between energy and particle size which have been common in previous literature. For comminution processes in which Eqs. 1 and 4 adequately represent the experimental data, the constant A in Eq. 4 is found to be a simple and useful inverse measure of grindability. That is, A is the energy consumption per unit volume of comminution product finer than unit size as determined from the straight line portion of the log-log plot of the size distribution. These considerations all lead to a unifying hypothesis of comminution mechanism from which both Eq. 1 and Eq. 4 can be derived. Finally, it is pointed out that this hypothesis raises serious questions as to the significance of the Rittinger hypothesis, the Kick hypothesis, and other theories in which energy numbers are systematically assigned to various size fractions of comminution products in order to calculate theoretical energy consumptions. Derivation of the Energy Equation from the Size Distribution Equation: For simplicity, consider the comminution of 100 volumes of a feed material of relatively uniform particle size. The comminution process may be considered as the summation of many individual and independent comminution events. The extent of comminution is most easily expressed as the number of comminution events, z. In the first derivation, the key assumption is that the characteristics of the comminution events in a given crushing or grinding process are substantially constant and do not vary with the progress of the comminution process. Accordingly the characteristics of an average comminution event may be defined. In one such event, a quantity of energy $E is applied to a single particle of size f and volume $v. The crushing of this particle produces fine particles with a size distribution similar to that given by Eq. 1: yw=100(x/ka)a0 [51 In this equation yo, a0, and k0 are used to characterize the product of an individual comminution event rather than the product of the comminution process as a whole. In using Eq. 5, we will not be concerned with values of x close to the feed size f and will therefore assume only that the equation is applicable to the finest sizes of the material. In 100 volumes of total product, the actual volume of product finer than x from a single comminution event, or dy, is given by The total volume of material below size x, resulting from z events, is then given by y = z(dy) =z(dv) (x/ka)a0 =" Eq. 7 reduces to Eq. 1 when we let a, = a and [8a] z =100/dv (ka/k )1 or k = ka (zdv/100)-1/a [8b] Eq. 8a shows that the distribution modulus of the comminution product is the same as for the product of an individual comminution event. Eq. 8b shows how the size modulus of the comminution product k varies with the extent of comminution as measured by the number of events, z, or as measured by the fraction of the feed actually subjected to com- minution1 zdv/100. The energy input to 100 volumes of total feed, or 100E, is the sum of the energy inputs for all the comminution events: 100E =z (dE) [9]

Jan 1, 1961

W. P. Blake, Shullsburg, Wis.: I desire to express my admiration of Prof. Posepny's memoir, and particularly of the charming manner and spirit of the introduction. With respect to his mention of the ore-deposits of Missouri and Wisconsin, reference may be made to my paper presented at this meeting (Trans., xxii., 621)) showing the existence of dislocations and breaks in the bedding, and their apparent close relation with the localization of the ore-deposits as claimed by Dr. James G. Percival, and also so claimed by Dr. Jenney in his paper before us (Trans., xxii., 171). I have in my paper given reasons for believing that the zinc- and lead-ores in the strata above the compact Trenton limestones were formed by lateral secretion and concentration from above downwards, substantially as shown by Prof. J. D. Whitney, and not by the ascent of solutions through the fissures, as Prof. Posepny (p. 304) seems inclined to believe. In regard to the contemporaneity of the ore and the rocks, and in favor of a later introduction of ore through fault-fissures, Prof. Posepny (p. 310) cites the influence of these fissures. In my paper, already referred to, I have endeavored to show how faults may have influenced the deposition of ore without being themselves channels for the flow of mineral solutions, and how they may have caused the contemporaneous formation of metallic sulphides from sea-water in the body of a forming rock; the faulting fissure being formed at an early period in the foundation rocks, and probably continuing to be a plane of break and movement in the deposits of later formation.

Jan 1, 1894

By Edward B. Dismukes, Walter R. Dickson

Measurements of current efficiency at an iron anode during the electrolysis of FeO-CaO-SiO2 melts contained in an iron crucible indicate that compositions of high SiO5 content conduct current almost entirely by ionic mechanisms. Hozueuer, compositions of high metal oxide content give euidence for considerable nonionic conduction that can be attributed to p-type semicon-duction. Measurements of transference numbers in a Hittorf-type cell show that both calcium and iron ions are important contributors to ionic conduction. ELECTROCHEMICAL properties such as conductance, transference numbers. and oxidation or reduction at an electrode have been studied as means of delineating the structure of simple silicate melts that are related to the more complex slags encountered ir steelmaking processes.' Measurement of these properties has strengthened the concept that molten silicates are constituted of metal ions and of silicate networks. Typically, the magnitude of electrical conductivity and the extent of agreement with Faraday's law have given evidence for ionic structures, and transference numbers have shown cations to be the exclusive carriers of electrical charge. However, melts containing oxides of iron, FeO in particular, have been found to exhibit nonionic conduction of curx,ent. The work by Inouye, Tomlinson, and chipman' demonstrated semiconduction, presumably of the p-type, in molten wüstite. Simnad, Derge, and George3 and Dukelow and Derge,4 in studying the electrolysis of FeO-SiO2 and FeO-MnO-SiO2 melts, concluded that p-type semi-conduction occurs in these systems, although ionic conduction is generally favored by increased percentages of MnO or SIO2. Previous research on the electrochemistry of

Jan 1, 1962

By D. N. Dietz

A method for determining average reservoir pressure is presented, which is simpler to apply than that devised by Matthews. Brons and Hazebroek. For bounded reservoirs, identical results are obtained if stabilized-flow conditions prevail. The present method yields inferior results in the transient state. The method can, with a slight modification, also be used for water-drive reservoirs. INTRODUCTION In the method proposed by Matthews, Brons and Haze-broek' for determining average reservoir pressure in a multi-well reservoir, the cumulative production (the production time of each well) enters twice: once when the buildup is plotted against In (t + t)/At to arrive at p*, and a second time when the correction, p*-p is determined with one of the several formulas for differently shaped drainage areas. Once a steady state has been attained, however, the previous production history should be immaterial. The same pressure distribution could have been arrived at after different cumulative productions of the individual wells. In principle, therefore, it should be possible to determine average pressures without referring to cumulative productions. In the following paragraphs an expression is presented for the difference between the pressure in a producing well and the average pressure of its drainage area. Then the build-up time needed to overcome this difference is indicated. CASE OF A CIRCULAR DRAINAGE AREA AND A CENTRAL WELL PRESSURE DISTRIBUTION BEFORE SHUT-IN The general differential equation of radial flow (see Muskat, Eq. 10.2) may be written In the steady state, the rate of production of the well is equal to the rate of expansion of the fluid contained in the the drainage area; thus

Jan 1, 1966

First Session BRASS Wednesday, A.M., Nov. 29 Co-Chairmen: CARTER S. COLE, Staff Engineer, A.S.T.M. E. A. ANDERSON, Chief of Metals Section, Research Div., New Jersey Zinc Co. (of Pa.) Second Session BRASS Wednesday, P.M., Nov. 29 Co-Chairmen: D. K. CRAMPTON, Director of Research, Chase Brass and Copper Co., Inc. A. W. TRACY, Metallurgist, The American Brass Co. Dinner and Technical Session Wednesday Evening, Nov. 29 Toastmaster: N. L. MOCHEL, Manager Metallurgical Engineering, Westinghouse Electric Corp. Talk on "How Do Things Look Today and For the Future" RALPH KELLY, President, Baldwin Locomotive Works Technical Paper on Stress-Corrosion Cracking E. H. Dix, JR., Assistant Director of Research and Chief Metallurgist, Aluminum Company of America Third Session BRASS Thursday, A.M., Nov. 30 Co-Chairmen: W. B. PRICE, Director of Research, Scovill Manufacturing Co. A. L. JAMIESON, Associate Metallurgist, Frankford Arsenal First Session LIGHT METALS Thursday, P.M., Nov. 30 Co-Chairmen: L. L. WYMAN, Metallurgist, General Electric Co. M. A. HUNTER, Professor of Metallurgical Engineering and Head, Dept. of Metallurgical Engineering, Rensselaer Polytechnic Institute Second Session LIGHT METALS Thursday Evening, Nov. 30 Co-Chairmen: R. T. WOOD, Chief Metallurgist, American Magnesium Corp. J. D. HANAWALT, Director, Metallurgical Dept., Dow Chemical Co. First Session STEEL Friday A.M., Dec. I Co-Chairmen: H. S. RAWDON, Chief, Division of Metallurgy, National Bureau of Standards A. L. FEILD, Director of Research, Rustless Iron and Steel Corp. First Session MISCELLANEOUS METALS Friday P.M., Dec. I Co-Chairmen: E. A. ANDERSON, Chief of Metals Section, Research Div., New Jersey Zinc Co. (of Pa.) CARTER S. COLE, Staff Engineer, A.S.T.M.

Jan 1, 1945

By W. H. Hough, P. B. Leavenworth

Development in the upper Texas Gulf Coast during 1944 resulted in the discovery of 19 new fields as compared with 11 during 1943. These discoveries include 10 oil fields, one dry gas field, and eight gas-condensate fields. Drilling During the year 590 wells were drilled as compared with 418 drilled during 1943. Of these operations, 485 wells were drilled in proven fields, with the following results: 281 oil wells, 22 condensate wells, one dry gas well and 141 dry holes. The remaining 105 wells were wildcats, of which 19 were producers. The geological distribution of these discoveries was as follows: In 1944, production amounted to 178,-522,630 bbl., which was an increase of some 31,670,384 bbl. over the 1943 figure of 136,852,246 bbl. These figures include both condensate and oil production, as separate figures are not available. Wildcatting in the area was more successful during 1944 than in 1943 as the following comparison of number of wells drilled illustrates: Discoveries during 1944 Smith Point, Chambers County.—Standard Oil Company of Texas completed its No. I State, sec. 109, on Feb. 15, 1944, in a Frio sand at 8135 to 8146 ft. The well flowed 250 bbl. of 42º gravity oil through an 1/8-in, choke. Gas-oil ratio was 800 to I; tubing pressure, 1100 bbl. Four other oil wells and one gas well were completed during the year. This discovery does not appear to be of major importance. The producing area lies on the upthrown side of a large fault. North Winnie, Chambers County.—Sun Oil Co. completed No. I P. E. Dougherty on Apr. 27, 1944, from the Frio, through perforations at 8757 to 8759 ft. The initial production was 154 bbl. of 38.3º gravity oil through an 1/8-in. choke. Gas-oil ratio Was 2526 to 1; tubillg Pressure, 2280 1b.; casing Pressure, 1225 lb.; total depth, 9519 ft. Three other wells were drilled during the Year. This discovery is on the downthrown side of the major Winnie Stowell fault, and increases in magnitude the already large producing area along this fault. Mayes Field, Chambers County.—Humble Oil and Refining Company's No. I Mary Etta Mayes was completed on Dec. 24, 1944, in a Frio sand, at 8166 to 8169 ft. through 1/4-in. for 768 bbl. of 40.3º gravity

Jan 1, 1945

By R. Raring, W. J. Harris, J. A. Rinebolt

The effects of additions of alloying elements on the true-stress, true-strain characteristics of 0.30 pct C, 1.00 pct Mn, 0.30 pct Si pearlitic steel were studied. The alloying elements investigated were C, Mn, Si, P, The alloys are compared on the basis of fracture stress, fracture strain, energy to fracture, rate of strain hardening, strain hardening exponent, height of the flow curve, and lower yield point. IN the past, nearly all studies of the effects of alloying elements on the tensile properties of metals have compared the conventional engineering parameters, namely, tensile strength, yield strength, elongation, and reduction of area. Recently, however, the true-stress, true-strain method of recording results from the tension test has been used; Lacy and Gensamer,' Hollomon," and French and Hibbard- are used this method to study the effects of composition on strength and ductility of metals. In this paper, the effects of certain alloying elements on true-stress, true-strain curves of steels with nearly constant grain size and pearlite spacing are presented. The notation employed in this paper is given in Table I. Since the definitions of stress and strain and the analytical geometry of the stress-strain curve have been explained previously, for example by Gensamer,' they will not be reviewed here. However, the method used for the determination of energy to fracture, E,, requires mention. These energy values were calculated on the assumption that the flow curve followed the idealized equation:' corresponds to the specific energy absorption to that strain value. There is justification for preferring the use of eq 1 for the determination of the energy to a particular strain rather than the area under the experimental stress-strain curve, since Gensamer showed that the use of the Bridgman correctione for stress at the neck of a tensile specimen brought the corrected experimental curve nearer to the idealized power-law curve than to the uncorrected experimental curve. However, it should be noted that the difference between the areas under the idealized curve and the experimental curve is not great for strain of less than 1.0, as can be seen from Fig. 1. In this figure, the true-stress, true-strain curve for a 0.01 pct C, 1.00 pct Mn steel is plotted through the experimental data points. From the value of a,, from this curve and the value of n as determined by the Inm-

Jan 1, 1952