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By K. U. Snowden, J. N. Greenwood

EARLY studies by Gough and sopwith' have shown that the fatigue resistance of certain metals increased when the test was carried out in a partial vacuum; lead showed this effect to a marked degree. This communication describes surface deformation differences between high-purity lead fatigued in air and in a vacuum of approximately 5 X l0-3 mm Hg. Both air and vacuum tests were carried out by the same alternating flexure machine at a frequency of 500 cpm. Flat cantilever-bend specimens with tapered sides were cut from strip, annealed at 100°C, and chemically polished.

Jan 1, 1959

By O. J. Huber, P. D. Frost, H. A. Robinson

URANIUM is a (ß-stabilizing, eutectoid-forming element when alloyed with titanium. Udy and Boulger1 have reported that an alloy of 48.6 pet uranium in titanium retains ß-phase when quenched from the ß-region, while compositions of approximately 30 pet uranium transform to martensite during such quenching. Since the eutectoid reaction is rather sluggish, titanium-uranium alloys should be capable of being strengthened by the ß — a trans-

Jan 1, 1959

By R. A. Meussner, R. T. DeHoff, F. N. Rhines

ZINC diffuses through copper more rapidly than does tin. Accordingly, when a ternary diffusion couple is made, by bringing an 0 copper-zinc brass into contact with an a copper-tin bronze at fixed high temperature, it is to be expected that zinc will diffuse into the bronze faster than tin diffuses into the brass. Adjacent to the brass side of the couple the total alloy content (zinc plus tin) should diminish, therefore, while next to the bronze side the alloy content should increase. Since the path of compo- sition change must be continuous, in a single-phased alloy, it should follow a curved and, in general, an S-shaped course. The realization of this prediction is demonstrated in Fig. 1, where the composition paths of two ternary diffusion couples are plotted on the appropriate isotherm of the copper-tin-zinc phase diagram. The diffusion couples were both made from a binary copper-tin alloy analyzing 5.0 pct tin placed against binary copper-zinc alloys analyzing 18.9 and 29.3 pct Zn, respectively. These alloys were produced from electrolytic grades of copper and zinc and a pure grade of straits tin, melted under borax in clay-graphite crucibles and cast in a vertical iron mold. Cylindrical pieces 1 in. in diam and 1 % in. long were machined from the casting and were faced by metallographic polishing to good matching end surfaces. Pairs of the cylindrical pieces were held

Jan 1, 1959

By L. O. Brockway, W. C. Bigelow, J. A. Amy

Specimens of Inconel-X alloy solution-treated at 2050°F and aged for periods of 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F have been examined by electron microscopy and by electron and X-ray diffraction. Four minor phases were identified: titanium nitride, niobium nitride, an M23C6 complex carbide, and the intermetallic ? phase. The two nitrides were found in all of the aged specimens and in the solution-treated alloy, the y' phase formed at all aging temperatures, while the M23C6 carbide formed only on aging at 1200° and 1400°F. Variations in the hardness, rupture strength, creep strength, and yield strength of the alloy have been shown to be related to variation in the size and distribution of the particles of the y' phase within the matrix grains of the alloy, with maximum values of these properties occurring when there is a maximum amount of the phase present and a fine state of dispersion of the particles prevails. THE nickel-chromium alloys containing titanium and aluminum are widely used in applications requiring high strength at elevated temperatures. Studies on relatively simple ternary and quaternary alloys'-4 have indicated that the favorable high-temperature properties of these alloys are related to the precipitation of an intermetallic ?'-phase having a structure based On that of the Ni3A1 phase of the nickel-aluminum system. The present investigation was undertaken to identify the minor phases and to study the microstructural changes occurring in one of the more complex commercial alloys as a result of aging in the service temperature range, with particular emphasis on investigating the role of the ?' -phase. The microstructural changes were studied by electron microscopy and the minor phases were identified by X-ray and electron diffraction. MATERIALS AND METHODS Inconel-X alloy was selected for this investigation because the previous studies of Frey, Freeman, and white6 provided extensive information on the variations in metallurgical properties of this alloy resulting from high-temperature aging treatments. Specimens aged 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F were made available for the present use. These were taken from 1-in. round-bar stock of a commercial heat having the following weight composition: 0.04 C, 0.56 Mn, 6.59 Fe, 0.007 S, 0.38 Si, 0.03 Cu, 73.22 Ni, 14.97 Cr, 0.78 Al, 2.38 Ti, and 1-02 Nb. They were solutjon-treated at 2050 for 4 hr and then water-quenched prior to aging. Powder X-ray diffraction patterns were obtained from insoluble minor phases which were separated from the alloys by digestion in the reagent of Mahla and Nielsen.6 Back-reflection patterns were obtained from electrolytically polished surfaces of the bulk search to detect the ?'-phase' Cu-K a radiation was used in both cases. In the electron-diffraction studies, the general method developed by Heidenreich, Sturkey, and

Jan 1, 1959

By M. Metzger, T. A. Read

The strengthening effects of hydroxide and synthetic plastic films in the creep of cadmium crystals were studied. The results were broadly consistent with the naive mechanical model. The dislocation-film reactions and the significance of the macroscopic stresses associated with certain films are discussed in the paper. ALTHOUGH a number of studies have been made of the strengthening of metal single crystals produced by surface films usually less than Ir in thickness, the mechanisms underlying this phenomenon are still not well established. Roscoe' first noted the critical shear stress and the stress-strain curve of cadmium-crystal wires to be raised markedly by the presence of oxide films. Subsequent investigators2-' have confirmed the effect for several metals and films including a number of plated poly-crystalline metal films. Harper and Cottrel1" with a thin film on zinc presumed to have formed as a result of etching and washing treatments) did not detect a strengthening at a rate of extension of 10 ' sec-' although at lo-' sec-' the film raised the flow stress by 7 pct at 0.0005 extension and by 22 pct at 0.01. The marked strengthening at moderate strains thus appeared to be the result of a dynamical effect dependent on the rate and amount of plastic flow. Other observations'. " are consistent with this view. The large effects of films on the tensile creep rate of single crystals were demonstrated when the observation of Andrade and Randall," that the creep rate of cadmium crystals increased on immersion in aaueous solutions of certain cadmium salts. was shown' * to hold only when a film was present initially and was explained by the attack of the solution on the film and the removal of its strengthening effect. Changes in the creep rate interpretable in terms of the removal or formation of various films have been observed by other investigators.3,8,10,31 Certain other experiments have been reported in which surface films or liquid environments have affected the plastic behavior of metals, but these are not within the scope of the present work which deals with the effect of solid films on single-crystal slip. Possible Mechanisms—The film does not significantly reduce the load on the crystal in the elastic range (the elastic moduli of film and crystal are not too greatly different and the area of the film is so small that its share of the load is negligible) so that the initial operation of internal Frank-Read sources is not affected. However, as Fisher" has pointed out, a source terminating on the crystal surface requires only half the critical stress for activation as an internal source of the same length and a relatively strong film (even a very thin one) would pin the free ends of the surface sources so that, if surface sources are responsible for plastic flow in a clean crystal. such a film would increase by roughly a factor of 2 the stress necessary for generation of dislocation loops at a given rate. The other general possibility is that the film resists the passage to the crystal surface of internally generated dislocations. If the film is adherent and if the specimen is to exhibit slip of the same general character as a film-free specimen, the film must deform or fail in shear at the active slip planes. The naive mechanical model, where shear-stress relaxation across the active slip plane in the metal transfers load to the film until it deforms and slip can

Jan 1, 1959

By E. S. Bartlett, D. N. Williams

QUANTITATIVE values for the oxidation rate of unalloyed molybdenum in air at temperatures above the melting point (1460°F) of the characteristic oxide are contained in the literature as a result of previous investigations. Lustman' reported values corresponding to 0.36 in. penetration per day (IPD) at 1500 and 1600°F in still air, noting essentially no variation in rate with temperature. Jones, Spretnak, and Speiser' reported values corresponding to 0.14 and 0.13 IPD at 1500 and 1800°F, respectively, in still air, attributing the decreased oxidation rate at higher temperatures to a lesser accumulation of the corrosive molten oxide on the surface at the higher temperature as a result of increased volatilization rate. Harwood3 ecently summarized work in the field, presenting generalized data corresponding to 0.48 to 0.96 IPD at 1800°F and 0.55 to 0.83 IPD at 1700°F in slowly flowing air. In a recent program at Battelle, it became desirable to know more about the characteristic oxidation behavior of molybdenum under varying conditions of temperature and atmosphere. Using oxidation-test apparatus designed for dynamic, continuous recording of weight change during testing,' values for the oxidation rate of molybdenum were obtained at temperatures from 1400 to 2150°F. In addition the effect of air flow on the oxidation rate was studied briefly at temperatures of 1600, 1800, and 2000°F. Exhaust of the contaminated atmosphere from the oxidation chamber was effected by an impeller pump attached to a 3/16-in.-diam opening in the oxidation chamber. The volumetric exhaust rate (cubic feet per hour) was normally maintained slightly in excess of the input rate to avoid condensation of MOO,,' on the sample suspension rod. The entering atmosphere was preheated prior to admission to the oxidation chamber by a 1 1/2-in.-diam cup packed with shredded asbestos. The experimental data are presented in Table I. Comparing conditions 2 and 3 (taking into account the temperature difference) and conditions 8 and 9. shows that in the absence of forced exhaust an atmosphere of moving air results in greater oxidation rate than a stagnant atmosphere. The use of forced exhaust, as shown by comparing conditions 3 and 4 and conditions 14 and 15: resulted in an even greater increase in oxidation rate. By virtue of the size of the atmosphere input and exhaust openings, it was calculated that the exhaust velocity was about 60 times that of the input velocity for essentially equal volumetric flow rates. Because of the proximity (about 3/4 in.) of the exhaust port to the specimen, it is logical to assume that cleansing of the atmosphere immediately surrounding the specimen was accomplished much more efficiently by the exhaust flow than by the input flow at a constant-volumetric flow rate. Also, it can be seen by comparing conditions 4 through 7 and conditions 11 through 13 that increasing the rate of atmosphere flow (by increasing input velocity with a proportional increase in exhaust velocity) above some optimum value has little, if any, further effect on the oxidation rate. These results suggest that there is a maximum oxidation rate for molydenum at a given temperature which is obtained when conditions are maintained such that the partial pressure of MOO3 in the atmosphere surrounding the specimen is at a low value. By controlling the partial pressure of MOO, surrounding the sample, it is possible to control the rate of volatilization of MOO:, from the surface. This, in turn, affects the rate of oxidation, since the thickness of the MOO3 layer determines the amount of oxygen which will be able to reach the reaction surface.' When the liquid oxide layer is less than some critical thickness, i.e., when the volatilization rate is high, enough oxygen is transported to the active surface to permit oxidation to proceed at the maximum rate allowed by the kinetics of the oxidation reaction. However, if the volatilization of MOO,, is suppressed, the thickness of the layer of MOO3 on the surface increases, and the diffusion of oxygen through the oxide layer becomes the rate-controlling step in the oxidation process. The lack of agreement between the present results and those of previous investigators is presumed to be due to differences in removal of the oxidation product (Moo,) from the immediate vicinity of the sample. By comparing conditions 1, 5, 10, 12 and 14, it is seen that when forced exhaust was used the oxidation rate of molybdenum increased with increasing temperature. A rapid increase was observed between 1400 and 1600°F, attributable to the effects

Jan 1, 1959

By P. G. Shewmon

THIS paper is concerned with the redistribution of a second phase when a 2-phase solid alloy is annealed in a temperature gradient. An examplewhich is discussed in detail is the redistribution of carbides in a low-carbon steel annealed in a temperature gradient below the A, temperature. As a result of such a treatment, the carbides at the cooler side disappear, while those at the hotter side grow in size. In a 2-phase zirconium-hydrogen alloy, the amount of hydride will tend to be increased at the cold end and decreased at the hot end. That such an effect can occur in solid metals is not generally appreciated. However, with the trend toward higher operating temperatures in several fields, this phenomenon will become more important in the future. Actually, such effects should be rather common in the core of nuclear power reactors where the op- erating temperatures are high and temperature gradients are an order of magnitude higher than in previous high-temperature applications of alloys. The purpose of this paper is to point out the existence of such an effect, to discuss the manner in which one predicts whether a redistribution of the second phase will occur in a given system, whether the second phase will go to the hot or cold face, and how rapidly the redistribution will occur. One aspect of this problem has been discussed by pfam and Wernick2who considered the migration of a small liquid region through a solid. In their case, the diffusivity in the liquid is much larger than in the solid and they have interpreted their results successfully by using Fick's first law as the flux equation in the liquid, and taking the concentration gradient from the phase diagram. For all the cases they have studied, this type of analysis predicts that the liquid region migrates from the cold end to the hot end, and this is what was found ex-

Jan 1, 1959

By C. F. Lucks, W. D. Wood, H. W. Deem

Electrical ad thermal-conductivity measurements have been made on titanium and 6 titanium alloys. The following expression was derived for calculating thermal conductivity from electrical conductivity: K = 0.626 s T x 10-8 + 0.00497 where K = thermal conductivity, cal sec-1 cm-2 cm0C-1 s = electrical conductivity, ohm-]cm-1 T = temperature, deg Kelvin This expression gives calculated thermal conductivities that are not in error by more than 10 pct from the experimental values for A-55 titanium and the 6 alloys measured; namely, A-110AT, C-110M, C-130AM, Ti-6A1-4V, Ti-140A, and Ti-155A, which are representative of the presently available commercial a and a-ß titanium alloys. THERMAL conduction in a gas, liquid, or amorphous solid is accomplished by energy diffusion from molecule to molecule, a relatively slow process. For this reason, such materials have a low thermal conductivity. When a material is crystalline, there is in addition a heat transfer by a vibratory motion of the crystal lattice. It is the contribution of this lattice conduction that makes a crystal a much better conductor than a gas, liquid, or amorphous solid. Lattice conduction, however, does not account for the relatively enormous thermal conductivity of a metal. This is explained by the freedom of movement of valence electrons. These valence electrons drift in a metal in a direction toward a drop in electrical potential and, to a lesser degree, in the direction of a temperature drop in the metal. Since both the electrical and thermal conductivities of a metal depend upon the presence of free electrons, there should be some relatively simple relation between the two. Wiedemann and Franz in 1653 first discovered an approximate empirical relation between the electrical and thermal conductivities of metals at the same temperature. This ratio varies appreciably with temperature, and Lorenz later showed that by adding a temperature factor to the Wiedemann-Franz ratio the value of K/(s T) is constant, where K is the thermal conductivity, a the electrical conductivity, and T the absolute temperature. This Lorenz constant shows a greater variation for alloys than it does for pure metals, the ratio increasing slightly as the proportion of alloying elements increases. It has been found that a closer correlation between electrical conductivity and thermal conductivity can be obtained by means of an equation of the form K - A s T + B [1] where A and B are constants. In this equation the term AsT is the contribution of electronic conduction and B is the contribution of lattice conduction to the total thermal conductivity. EXPERIMENTAL MEASUREMENTS Electrical-resistivity and thermal-conductivity measurements on titanium and 6 titanium alloys serve as the basis for determining an equation of the K = AsT + B type for titanium alloys. Specimens—Table I shows nominal compositions of the 7 metals on which electrical and thermal conductivities were measured. The electrical and thermal-conductivity specimens for each alloy were taken from stock of the same heat and usually from adjacent sections of the same bar. All of the metals measured were in a mill-annealed condition. Methods—Electrical-resistivity measurements

Jan 1, 1959

By J. O. Betterton, D. S. Easton

A detailed investigation was made of the phase diagram of silver-zirconium, particularly in the region 0 to 36 at. pct Ag. The system was found to be characterized by two intermediate phases Zr2Ag and ZrAg and a eutectoid reaction in which the -zirconium solid solution decomposes into a-zirconium and Zr2Ag. It was found that impurities in the range 0.05 pct from the iodide-type zirconium were sufficient to introduce deviations from binary behavior, and that with partial removal of these impurities an increase in the a-phase solid solubility limit from 0.1 to 1.1 at. pct Ag was observed. The phase diagram of the silver-zirconium system is of interest as an example of alloying a transition metal from the left side of the Periodic Table with a Group IB element. Silver would normally act as a univalent metal, its filled 4d-shell remaining undisturbed during the alloying. However, there is a possibility that some of the 4d electrons might transfer to the zirconium. An insight into such a question can occasionally be obtained by comparison of phase diagrams. The silver-zirconium system forms part of a more complete review of various solutes in zirconium in which these valency effects were studied.' Earlier work on the silver-zirconium system was done by Raub and Enge1,2 who investigated the silver-rich alloys. After the start of the present experhents, work on this system was reported by Kemper3 and by Karlsson4 which for the most part agrees with the phase diagram presented here. EXPERIMENTAL PROCEDURE The alloys were prepared by arc casting on a water-cooled, copper hearth with a tungsten electrode and in a pure argon atmosphere. Uniform solute composition was attained by multiple melting on alternate sides of the same ingot. Progressive improvements in the vacuum conditions inside the apparatus during the course of the experiments reduced the Vickers hardness increase of the pure zirconium control ingot from 10 to 20 points, observed initially, to negligible amounts at the end of the experiments. Such hardness changes in zirconium are a well known indication of purity. For example, -01 wt pct additions of oxygen, nitrogen, and carbon increase hardness by 6, 10, and 3 VPN respectively. '9' Further verification that the final casting technique did not add a significant quantity of impurities was obtained when pure zirconium was arc cast and then isothermally annealed in the vicinity of the allotropic transition. The transition was always observed to take place over the same temperature range as in the original crystal bar. The alloy ingots were annealed in sealed silica capsules for times and temperatures which varied between 1 day at 1300°C and 60 days at 700°C. The best method found to prevent the reaction of the zirconium with the silica was foil wrapping of molybdenum or tantalum. With this method, samples of pure zirconium were found to be unchanged in hardness after annealing for 3 days at 1200°C. In most of the experiments the protection of these foils was supplemented by an additional layer of zirconium foil inside the molybdenum or tantalum foil. The alloys, foil, and the capsule were outgassed at pressures in the range 10 to l0-7mm Hg in the temperature range 800" to 1100°C before each anneal in order to remove hydrogen and other impurities, and to provide a suitable container for the high purity, inert atmosphere, which is essential in the annealing of zirconium. The temperature measurements were made with Pt/Pt + 10 pct Rh thermocouples calibrated frequently during the experiments against the melting points of zinc, aluminum, silver, gold, and palladium. For the longer anneals the sum of various temperature errors was generally well within ± 2°C. For short-time anneals and during thermal analysis the overall temperature error is considered to be within ± 0.5°C. The compositions of the alloys from the quenching experiments were determined by chemical analysis at Johnson Matthey and Company, Ltd., under the direction of Mr. F. M. Lever. The actual metallo-graphic samples were individually analyzed in every case, and prior to the analyses two or more sides of each specimen were examined to insure that the specimen was not segregated. The sum of the solute and solvent analyses was in each case within the range 99.9 to 100.1 pct. In the course of the experiments, minor impurities in the range 0 to 500 ppm were found to have significant effects on the zirconium-rich portion of the phase diagram. Similar effects had been encountered previously in other zirconium phase-

Jan 1, 1959

By A. G. Metcalfe, Koeneman

A study of the structure of chemically deposited nickel by Goldenstein, Rostoker, Scpssberger, and Gutzeit has been reported recently. In this work it was shown that the nickel deposit produced by the catalytic nickel-reduction process was an amorphous solid. Crystallization occurred at elevated temperatures when the original powder pattern which showed only a diffuse ring with a d-spacing of 2.01A became sharp, revealing nickel and nickel-phosphide lines. The phosphide was indexed provision%lly on a tetragonal lattice of parameters a = 9.01A and c = 4.42A, which is in reasonable agreement with the structure of Ni3P proposed by No-wotny and Henglein.3 The transformation from the amorphous to the solid state occurs abruptly (e.g., after 7 min holding at 400°C) with the evolution of considerably more than 1000 cal per gm-mole. A more detailed analysis of these effects requires a knowledge of the solubility of phosphorus in nickel. Konstanti-now3 mapped out the phase diagram in 1908 but did not determine the solid solubility. The eutectic was placed at 11 pct P and 880°C. The purity of typical catalytic nickel deposits is very high.' Spectrographic analysis for heavier elements showed only trace amounts of aluminum, calcium, iron, magnesium, lead, and silicon. The term "strace" is a qualitative definition for less than 0.1 pct and probably less than 0.01 pct. Analysis for the interstitial elements yielded 0.04 pct C, 0.0023 pct 0, 0.0005 pct N, and 0.0016 pct H. Some of this material with 7.5 pct P was used in the present work. EXPERIMENTAL METHODS Alloys were prepared from carbonyl-nickel shot and a master composition containing 7.5 pct P. Cold-crucible, nonconsumable-arc melting was used.

Jan 1, 1959

By A. H. Cottrel

SINCE metallurgy exists to provide strong, tough, engineering materials it must inevitably be perpetually concerned with the problem of brittle-ness. The steel-making industry was created because chemically unrefined iron is brittle. The steel-working and alloy-steel industries exist partly because hardness and ductility are mutually exclusive qualities in structurally unrefined steel. Yet, in spite of these immense industries, the brittle failure of steel ships hulls, bridges, pressure vessels, and pipelines, is still a contemporary problem. In fact, brittleness is a normal property of most solids, including metals and alloys, at low temperatures. Only face-centred cubic metals are commonly ductile at the lowest temperatures, and even here exceptions are known.'," Expensive are-melting processes. under inert gases or vacuum, have been developed to overcome brittleness in titanium, zirconium, columbium. and molybdenum. Polycrystal-line zinc, magnesium, and uranium have little ductility at room temperature. Beryllium, chromium, and tungsten have even less; similarly for antimony, bismuth, germanium, silicon, intermetallic compounds, and metallic carbides, nitrides, silicides, and borides. Oxides and other ceramics would be ideal creep-resistant materials but for their extreme brittleness when cold, and great efforts have been made to overcome this problem by mixing ceramics with metals. In fact, the traditional use of the name metallurgy for what is really the science of engineering materials is a recognition that most non-metallic solids have so far been precluded, by their extreme brittleness, from use as major structural materials in mechanical engineering. Most of what we know about brittleness in metals has come from studies of structural steel, and it is this material that shall mainly be considered. The things we have learned from it have a wider application, at least to other body-centred cubic transition metals, although the extent to which similar ideas can be applied to hexagonal metals and other materials is not yet clear. Fracture and Plastic Deformation The theoretical breaking strength of an ideal solid, about E/10 where E is Young's modulus, has been approached reasonably closely in experiments on fibres. But large specimens break at much lower stresses. For example, brittle cracks in large structural steel assemblies have been observed to spread catastrophically at speeds of 6000 ft per sec under stresses of about 10,000 psi, i.e. about E/3000. There are two sources of weakness; stress concentrations, and chemical agents in grain boundaries or on crack faces that lower the surface energy y of the material. Although we shall deal mainly only with the first of these, much of the discussion is also applicable to the second when different values of y are used. Griffith's well-known formula p = [ 2Ey/p(1 - v2)c]1/2 [1] gives the smallest tensile stress p able to propagate an atomically sharp surface crack of length c or interior crack of length 2c through a thick plate (compared with c) of elastically isotropic material of

Jan 1, 1959

By J. C. M. Li

This exploratory survey was undertaken to repeat some experiments- in which anomalous results were reported1 for bismuth and to measure the thermoelectric power of some bismuth alloys and inter-metallic compounds. sato1 reported that the thermoelectric power of bismuth depends on the temperature gradient. This seems rather unreasonable especially when the Benedicks effect' has not been detected. Even if the material is not homogeneous, the observed thermoelectric power can be represented by

Jan 1, 1959

By R. Bakish, C. S. Barnett

IN experiments on tantalum strained in tension, Bechtold did not observe deformation-twinning even at a temperature as low as that of liquid air.' This is an unexpected behavior for a metal of body-centered-cubic structure. Therefore, it is desirable to determine whether the lack of twinning is an inherent characteristic of this particular metal, or whether the reluctance to twin can be overcome under suitable conditions. The following experiments were performed under conditions favorable to twinning and cleavage in their competition with slip, namely, with impact loading on large-grained sheet at low temperatures. The crystallography of cleavage in tantalum sheet was also investigated carefully because of the remarkable ductility of tantalum at low temperatures and because recent tests on oxygen-embrittled tantalum had disclosed unusual cleavage behavior for a metal of this structure: cleavage primarily on (110) planes and only occasionally on {100}.2 The tantalum, supplied by Fansteel, was of 99.9 pet purity, with the chief impurities being iron (0.03 pet) and carbon (0.03 pet). Coarse grains were produced by the strain-anneal method, the anneal being 4 hr at 2000°C in a vacuum of 10-3 mm Hg, followed by furnace cooling. Impact deformation was applied in various ways: a) by hammer blows on an anvil, the specimen and anvil being immersed in liquid nitrogen ( —196°C), b) by driving a precooled center-punch into the sheet, and c) by bending around a crystallographically determined axis with a hammer blow. The impact-deformation produced bands and slip lines on the surface, Fig. 1. The bands have every appearance of being deformation twins, a) They are tilted with respect to the untwinned surface. b) They have the appearance of Neumann bands in iron, thin lens shape, some having serrated edges. c) The orientation in each is different from that of the surrounding matrix and uniform within a given band, see slip lines within them in Fig. 1. d) Upon repolishing and etching, the difference in orientation and the resemblance to Neumann bands is again evident, Fig. 2. (In this micrograph the slight bend in the bands as they cross grain boundaries was noted frequently and results from the high degree of preferred orientation in the sheet.) e) The bands persist after annealing treatments that would have removed them had they been a low-temperature martensitic phase, e.g., after an anneal of 1/2 hr at 900°C. When back-reflection Laue data were plotted for single-surface analysis of several grains, every trace of the bands in each grain could be explained by (112) planes. In addition, two of the bands were located in space by traces on two surfaces, and these also were found to lie on (112) planes within the error of the stereographic plot. Since (1 12) is the anticipated composition plane for deformation twins in body-centered-cubic metals it is felt that the observations listed above are conclusive evidence for the identification of the bands as twins. Similar tests with impact at —77° and at 25°C produced no twinning. It is concluded that the critical shear stress for slip at the rates of straining used was always low enough to prevent the applied stress from reaching the value required for twinning at these temperatures. It was noted that the serrations along the edges of the twin bands exhibited parallel crystal facets. Several similarly oriented notches are visible in Fig. 1, and a remarkable set is shown in Fig. 3. It appears from Fig. 1 and similar areas that notches are frequently associated with the intersection of a slip line with a twin, although not all such intersections are at notches. In some instances a slip line appears to enter the twin, cross it, reflect from the opposite side and recross it, producing a pattern resembling a notch but without producing the notch itself, see Fig. 1. It is suggested that the stress concentration at the end of a slip line is responsible for these details. The strain energy associated with the pile-up of dislocations at a twin boundary may be lessened by untwin-ning or failing to twin a portion of the twin band, or

Jan 1, 1959

By W. D. Robertson, W. L. Phillips Jr.

Stress-strain curves were obtained for single crystals of alpha brass in tension and in direct shear. Specimens were strained various amounts in a given slip direction, unloaded, and immediately strained in a second slip direction 60°, 120°, or 180&apos; from the original slip direction. Crystals strained in tension and direct shear had comparable critical resolved shear stresses and stress-strain curves. The density of slip lines in direct shear and in tension was essentially the same. The stress-strain curves obtained in shear were independent of initial orientation, choice of {111 } slip plane, choice of <110> slip direction, prior annealing temperature, and rate of cooling after annealing. There was no recovery after annealing for 4 hr at room temperature or 200°C; recovery was observed after 4 hr at 400°C. The crystals showed no asterism and mechanical properties were completely recoverable up to 20 pct strain. It was found that there is a barrier to slip in all latent close-packed directions, and that the magnitude of these barriers, evaluated at 3 pct strain, is proportional to prior strain and independent of the choice of latent direction in the {111} plane. The formation of Cottrell-Lomer barriers is discussed as a possible explanation for the hardening of the latent systems. AN idealized concept of plastic deformation indicates that a single crystal should yield at some stress that is dependent on crystal perfection and it should then continue to deform plastically by the process of "easy glide," which is characterized by a linear stress-strain curve and a low coefficient, ds/dE, of work-hardening. Hexagonal metal crystals generally conform to this ideal concept of laminar flow. In face-centered cubic metals the range of easy glide is always restricted in magnitude and it is strongly dependent on orientation, composition, crystal size, shape, surface preparation, and temperature. Since one of the principal differences between the two crystal systems, both of which deform by slip on close-packed planes, is the existence of secondary (latent) slip planes in the face-centered cubic crystals, it has been proposed that the transition from easy glide to turbulent flow, characterized by rapid linear hardening, is due to slip on secondary planes intersecting the primary plane.&apos;-.; However, the characteristic differences between individual face-centered cubic metals remain to be explained; in particular, it is not clear why the range of easy glide should vary so greatly in different metals and alloys similarly oriented for single slip. An investigation and comparison of different metals with respect to latent hardening on the primary slip plane should provide some of the information required to specify the necessary and sufficient conditions governing the transition from easy glide to turbulent flow. But, in order to accomplish this purpose, plastic strain must be produced by simple shear in a chosen plane and in a predetermined direction by some form of directed shear apparatus, the results of which must be correlated with the corresponding tension experiments. Two such experiments have been performed previously with zinc and with aluminum. Edwards, Washburn, and Parker" and Edwards and Washburn7 found that the strain-hardening coefficients in two latent directions in the basal plane of zinc were the same as in the primary direction. However, to initiate and propagate slip in either the [2110] or the [1210] direction, following primary slip in the [1l20] direction, it was necessary to increase the stress above that required to continue slip in the primary direction; when the direction of shear was reversed 180 deg plastic strain began at a much lower stress than that required to initiate slip in the original direction and the stress to propagate slip in the reverse direction was lower than the stress to continue slip in the forward direction, indicating a permanent loss of strain-hardening. Rohm and Kochendorfer observed softening in aluminum for all latent close-packed planes and directions. They also found that the critical resolved shear stress obtained from their direct shear apparatus was 50 pct lower than the value obtained from conventional tension tests, that the stress-strain curve was linear at 50 pct plastic strain, and that slip lines were not visible at strains less than 30 pct. At present it is uncertain whether these diverse results correspond to real differences in work-hardening characteristics of the close-packed planes of aluminum and zinc or to differences in experimental technique. In view of Read&apos;s analysis &apos;" of the stress distribution in the experimental arrangement of Rohm and Kochendorfer, there is some reason to question the significance of the latter results. In order to resolve this problem it is necessary to re-valuate the direct-shear technique and either repeat the previous measurements or investigate a third system. The latter choice seemed most likely to produce significant results with respect to work-hardening, and accordingly, it was decided to examine the hardening characteristics of the latent slip directions in alpha-brass. The choice of alpha-brass was dictated by the fact that easy glide is more extensive in this alloy than in any other face-centered cubic metal or alloy and, presumably, more nearly like the idealized hexagonal system. Experimental Procedure Crystals were made in graphite by the Bridge-man method in the form of cylinders, 11/2 in. diam and 8 to 9 in. long. Material for the crystals was 70/30 brass containing the following impurities:

Jan 1, 1959

By L. R. Shoenberger

Boron has been used to produce nonaging low-carbon sheet steel. Retention of the necessary minimum amount of about 0.006 pet partially killed the steel. Amounts exceeding about 0.012 pet increased the degree of deoxidotion, piping tendencies, and possibility of hot tearing in primary rolling. Semikilled practice resulted in good ingot yields and satisfactory surface quality. Aluminum added with the boron provided a protective de-oxidizer. Good drawobility was indicated by performances of the steel in a limited number of deep-drawing trials. Some problems with hot-tearing and boron-analysis procedures were overcome. Metal lographically, the boron semikilled steels revealed some structures not usually found in plain low-carbon steels. IN 1943 Low and Gensamer1 reported that strain aging, which hardens and embrittles ordinary low-carbon rimmed steel, was due to nitrogen and carbon, and that oxygen played a relatively unimportant role. Since then, many investigators have substantiated their findings and indicated that nitrogen is particularly potent. Commercially, today&apos;s most widely produced non-aging sheet steels for deep drawing are either aluminum killed or vanadium rimmed types. The difference in deoxidation practice, alone, is evidence that oxygen is apparently not an important consideration in control of strain aging. The fact that nitrogen is important is apparent in the consideration that has been given, knowingly or unknowingly, to the amount combined with aluminum and vanadium. Patents were granted to Hayes and Griffis2 for the processing of aluminum-killed steel, and to Epstein" for the manufacture of vanadium rimmed material. Certain prescribed steps in producing these steels can be correlated with the formation of the respective nitrides within certain temperature ranges below the usual hot-finishing temperatures. The potential nonaging properties of either type can be reduced or suppressed by cooling too rapidly to permit the aluminum or vanadium to combine with nitrogen. Subsequent suberitical annealing of the cold-rolled strip, however, normally forms the nitrides and produces the resistance to strain aging. Titanium-killed nonaging steel, described by Comstock,1 forms a nitride in the molten state and is essentially nonaging throughout its processing. Zirconium-killed steel, which was investigated briefly by the author,* appeared to have similar nitride- forming characteristics. It is known" that chromium can produce nonaging rimmed steel, but relatively little is known of the potentialities of some of the other nitride-forming elements such as boron, silicon, columbium, and cerium. In attempting to develop a new nonaging cold-rolled sheet steel with good drawability, the following factors were considered pertinent. Such a steel would necessarily have a low carbon content and therefore have a relatively high degree of oxidation when made in a basic open-hearth furnace. If the denitriding element were also a deoxidizer, a part of the addition would be lost as oxide. The degree of deoxidation would determine whether the steel is rimmed, semikilled or killed, and also could be expected to have an important bearing on ingot yields and ultimate surface quality. Assuming that the pattern for the production of cold-rolled sheets would not be changed to any great extent, the nitride must form in the molten steel, in hot rolling, in subsequent cooling, or in annealing. The nitride, once formed, should resist dissociation and be stable in the final product. Usually an excess of the nitride-forming element is required to combine with sufficient nitrogen. If the element used is a strong ferrite strengthener, a small excess may markedly decrease drawability. With aluminum and vanadium, about 0.03 to 0.05 pct in the steel is preferred. Epstein has said" that about 0.30 pct chromium is required. Titanium nonaging steels are hard unless a sufficient amount (about 0.30 pct) is added also to combine with the carbon. The cost of the necessary amounts of these latter two elements discourages commercial acceptance. Silicon was considered as a possible nitride former, but since amounts up to 0.10 pct in rimmed and semikilled steels do not induce marked resistance to strain aging, larger amounts are apparently required, which would tend to harden and strengthen the ferrite. Of the other elements mentioned, all but boron are expensive heavy-metal elements. Stoichi-ometrically, almost an equal weight of boron would be required to combine with the nitrogen—-ordinarily about 0.003 to 0.006 pct in scrap-practice open-hearth steels. Boron is a slightly stronger deoxidizer than carbon but is less powerful than zirconium, aluminum, or titanium. Thus a rimmed-steel practice might be possible. There is much in the technical literature concerning the hardenability effects of minute amounts of boron in killed steels but very little about its behavior in low-carbon material—particularly as a ferrite strengthener. The available data indicated a need for better information concerning the effects of boron in low-carbon strip steels. Experimental Work Development of a Boron-Treated Nonaging Strip Steel—Initial attempts to produce a boron-rimmed strip steel employed 3-ton basic open-hearth heats which could be teemed into molds large enough to sustain a normal rimming action. Boron as ferro-boron was added to the ladle in small amounts because of the reported hot-short character of aluminum-killed heat-treating grades containing more than about 0.005 pct boron. Actually, the amounts used, i.e., 1/8 and 1/4 lb per ton, would be large for

Jan 1, 1959

By J. F. Martin, J. E. Friedline, L. M. Melnick, G. E. Pellissier

A method has been developed for determining gases in steel in which the gases are extracted by vacuum fusion and analyzed by mass spectrometry. This method is especially applicable for determining small amounts of oxygen and nitrogen. The lower limit of detection for both oxygen and nitrogen is 0.0001 pct with an average deviation of about 0.0001 pct for oxygen and 0.00008 pct for nitrogen. Hydrogen analyses by this method are in good agreement with analyses by vacuum tin-fusion. A complete analysis of all gases extracted from a steel sample can be accomplished in 40 min. It has long been known that certain of the gaseous elements exert particular effects on the physical and mechanical properties of steel. With the recent advent of new experimental steelmaking practices it is now possible to obtain steels with extremely low contents of such elements as oxygen and nitrogen. Present methods for determining these two gases are of insufficient sensitivity as applied to steels made by these newer practices, and therefore a new technique was considered necessary. A review of the literature showed that the conventional vacuum-fusion method1 was the procedure most suitable for modification to obtain a sensitive method for determining the gaseous elements present in steel simultaneously. However, for trace amounts of gases it is impractical to increase the sample size because of the physical limitations of the apparatus and the increased degassing time which would be necessary. Also, when only one of the desired gases is present in trace amounts, quantitative separation by conventional vacuum fusion is almost impossible. Since small analytical mass spectrometers are now commercially available, it was decided to use this instrument in conjunction with conventional vacuum fusion for both qualitative examination and quantitative determinations of the gaseous elements in steel. This technique has already been used with success for the analysis of copper and lanthanum.2"4 APPARATUS A vacuum-fusion unit was first designed and built, Fig. 1. This unit was designed especially for the determination of small amounts of nitrogen and/or oxygen in steel since an acceptable method (vacuum tin-fusion)5 was already in use for the determination of hydrogen in steel. The vacuum system was con- structed of Pyrex glass throughout. Mercury check valves were used in place of stopcocks in the high-vacuum section of the system. Ferromagnetic samples are normally introduced into the vacuum system through a mercury lift. In case of a break in the lift, the mercury is prevented from entering the furnace by a self-locking, mercury safety check valve, Fig. 2. This check valve, developed at our laboratory, is a modified T/S ball-and-socket joint placed in the sample inlet system between the mercury and the furnace. A sudden entry of mercury or air pushes this valve into the closed position, completely blocking the top of the mercury lift. The check valve is held in the closed position by the vacuum of the apparatus. A separate entrance tube also was placed in the system, so that samples which would amalgamate with mercury, or which are nonmagnetic, could be introduced into the furnace. A slightly modified Guldner-Beach furnace is used in this system.8 The optical flat was connected to the system by a ground-glass joint to facilitate cleaning, a quartz delivery tube was substituted for Pyrex, and the crucible was used uncovered. Fusion takes place in a high-purity graphite crucible insulated by — 200-mesh high-purity graphite powder. The crucible set (crucible and funnel) is suspended in a quartz crucible. The furnace envelope and the sample inlet system are exhausted by 2 single-stage, mercury-diffusion pumps in series. The first of these is a high-speed pump, which will work only with a very low backing pressure. This pump is used to exhaust the gases from the furnace as rapidly as possible. The second mercury-diffusion pump is used as a backing pump for the first; the capacity of this pump is much lower. However, it will work efficiently against a back pressure of 3 mm of mercury. To assure positive pumping, a modified Naughton and Uhlig condenser7 is used. With the use of proper valving the second pump is also used as a circulation pump in the catalyst system.

Jan 1, 1959

By N. A. Gokcen

The construction and operation of a simple and accurate vacuum-fusion apparatus are described in detail. Absolute accuracy of the oxygen analysis has been determined by the reduction of oxides weighed to 20.01 mg. The Bureau of Standards steel samples have been analyzed repeatedly, and their inadequacy for the acceptable range of oxygen is presented. The limits of interference of manganese, aluminum, and titanium, and the effects of tin and water-cooling of the furnace tube have been investigated in detail. ANALYSIS by the vacuum-fusion method consists of melting a sample in a degassed graphite crucible under high vacuum and extracting oxygen as carbon monoxide, and nitrogen and hydrogen as gaseous elements. The resulting gas mixture is analyzed for its constituents, from which oxygen, nitrogen, and frequently hydrogen may be determined within 1/2 hr or less. The history and summary of methods1-4 and extensive reviews of literature&apos;.&apos; for the determination of gases in metals have been published in detail. The foundation of the modern vacuum-fusion method of analysis was laid by Jordan and Eckman,11 and Oberhoffer and his associates.1, 10 Diergarten,11, 12 Meyer,13 Thanheiser et al.,14, 15 Ericson and Benedicks,16 Ziegler,17, 18 Sloman,16-23 Thompson et al.,24 and later many others contributed to the improvement, accuracy, and limitations of the method. In some investigations, however, the limitations of the procedure and the errors involved in the analysis require further critical examination and evaluation. In many apparatuses, lunnecessarily complicated and cumbersome features and elaborate precautionary measures do not have conclusive advantages. The purpose of this invest:igation was, therefore, a) to construct a very simple and accurate apparatus, b) to determine the absolute accuracy of results, c) to establish the limits of interference of manganese. aluminum, and titanium, d) to reexamine critically the reduction and recovery of oxygen from oxide powders of various sizes, and e) to evaluate critically the eight steels of the Bureau of Standards."&apos; Apparatus The apparatus used in this investigation is shown in Fig. 1. It has been used for over three years, during which several modifications were made. A brief description of the apparatus is as follows. The transparent silica or Vycor tube, E, is joined to the Pyrex head, B, by mean of a face to face ground joint sealed with mercury. A similarly sealed ball and socket joint would also have been satisfactory. A standard tapered ground joint, successfully used by some investigators, was tried, but in the absence of grease or vacuum cement it was very difficult to disassemble the joint. The graphite crucible, G, 15/16 or l 1/8 in. OD, 2 1/2 or 3 in. high, 1/10 in. wall, shown enlarged in Fig. 3a, is made from the rods containing less than 0.08 pet ash. Two baffles, overlapping sufficiently to prevent spattering, are inserted in two opposite slots cut on a band saw. Two small holes in the baffles permit the temperature measurement of the melt. A second type of crucible, Fig. 2, G, shown enlarged in Fig. 3b, is also satisfactory, though not as convenient as the crucible shown in Fig. 3a. Somewhat similar but more elaborate crucibles with baffles were first tried by Ericson and Benedicks,&apos;" but were abandoned in favor of a crucible with a stopper and a peripheral graphite powder filter. Various versions of their crucible with a stopper have later been used by other analysts, 10-27, 27-30 The crucible is packed directly in E, Figs. 1 and 2, with —35 + 48 graphite powder for shielding and insulation. A minimum layer of 7 mm of powder is necessary for keeping E cool and minimizing the blank. The first use of graphite powder was made by Sloman,10-23 Who found that —200 mesh was the most satisfactory. The author tried various size powders from +20 to —100 mesh and found that a) particles of 28 mesh or larger were not sufficiently insulating and were heated by the induction current, b) the powder finer than 60 mesh packed too much and did not readily permit the escape of gases even when the crucible was heated very slowly; hence, the powder was occasionally blown out of the side in the crucible and in the mercury pump. The optimum size powder is, therefore, 35 to 48 mesh size or 0.4 mm in average diameter. The furnace is designed to eliminate excessive amounts of

Jan 1, 1959

By G. Ostberg

OXYGEN has frequently been considered responsible for phenomena in the metallurgy of cast iron which are not sufficiently explained by the presence of other elements. Oxygen and oxides have been regarded as critical factors, particularly for the solidification process, and specifically in the formation of graphite. However, the evidence for an influence of oxygen has mostly only been indirect or qualitative. Furthermore, quantitative data on the oxygen content of cast iron presented in the literature have often been less conclusive as being apparently determined with insufficient regard for the difficulties associated with the sampling and analysis. These problems, experimental and theoretical, have been studied in this investigation. An attempt is made to bring the views on the soluble amount of oxygen in cast iron on a level with the present understanding of the thermodynamics of these types of alloys. Although there are no experimental data on the complete multicomponent cast-iron alloys some conclusions have been drawn from investigations on simpler systems. The order of magnitude of the solubility of oxygen in cast iron is considered in the first part of the paper. The second part deals with the oxygen content actually present under practical conditions. First the possible sources of errors in sampling and analyzing methods are examined. Finally some observations on the oxygen and oxide content of malleable iron during the production process are made. THERMODYNAMICS OF OXYGEN SOLUBILITY When cast iron is saturated with oxygen the saturation phase is essentially carbon monoxide or silicon dioxide depending upon the composition of the iron, the temperature, and the rates of formation of the oxides.* The latter occurs accordiw to the O + C = CO, Kc0 - a COa J 20 + Si = SiO2, Activities are used here instead of weight pct concentrations, since activities are believed to show more sensitively the effects of the interaction of all the alloying elements. Calculations involving activities are, however, seriously hampered by lack of experimental data on the interactions between the components encountered in the multi component cast-iron system Fe-O-C-Si-Mn-P-S- and so on. In order to make an estimate of the oxygen solubility reason-

Jan 1, 1959

By S. R. Seagle, R. Schuhmann, N. A. Parlee

Rates of CO evolution and CO absorption were measured for liquid-iron alloys containing from 0.15 to 4.4 pet C, using a modified Sieverts apparatus. The alloys were held in alumina crucibles, so that both crucible-metal and gas-metal reactions occurred simultaneously. The data are interpreted on the hypothesis that the C-O reaction rate is controlled by oxygen diffusion across the boundary layers at the gas-metal and crucible-metal surfaces. CARBON-monoxide evolution from liquid Fe-C-0 alloys is a key reaction in steelmaking processes, both in the steelmaking furnace and in the ingot mold. Also, this reaction probably is an essential step in the desulfurization of iron under blast-furnace conditions, for which carbon is the principal reducing agent or deoxidizer present in the iron. The thermodynamic properties of the solutions of C and 0 in Fe and the equilibria of these solutions with gaseous CO and CO, have been investigated in some detail and are reasonably well understood. However, while these equilibrium data have accumulated in the laboratory, other data have accumulated to show that equilibrium conditions are often not achieved under plant operating conditions. Thus, an understanding of the rate and mechanism of the carbon-oxygen reaction not only has theoretical interest, but ultimately may assume considerable practical importance. Reaction Mechanisms and Rate Equations The over-all reaction under consideration is C (in liquid Fe) + 0 (in liquid Fe) + CO (gas) [I] Although this appears to be a straightforward heterogeneous reaction, involving just two phases (liquid metal and gas), a wide variety of reaction mechanisms has been proposed. Different authors have expressed divergent views as to the nature of the rate-controlling steps. Accordingly, a brief discussion of the possible reaction steps will be given. 1) Homogeneous Reaction Within Liquid Iron— Feild&apos; and Jette2 have applied chemical reaction-rate theory as if the C-0 reaction were a homogeneous, second-order reaction occurring within the liquid-metal phase. This mechanism necessarily produces CO "molecules" dissolved in liquid iron. In order to yield CO gas, the dissolved CO must nucleate CO gas bubbles, and the dissolved CO also must be transported to the bubble surface where it enters the gas phase. However, this mechanism is inconsistent with present concepts of the structure of liquid-metal solutions. 2) Reaction at Gas-Metal Interface—At the surface of contact between gas and metal, a second-order reaction between dissolved C and 0 may occur to produce a CO molecule which enters the gas phase. This reaction presumably involves an "activated complex" structure in the interface. Some such surface mechanism appears essential because the carbon and oxygen do not occur in the same species in the two phases and therefore must react in some way at the surface. At liquid-iron temperatures, calculations based on reaction-rate theory indicate that the surface reaction must proceed extremely rapidly and thus cannot be a rate-determining step in the C-O reaction under ordinary conditions.3 ccordingly when the over-all reaction is measurably slow, the surface reaction may be considered at equilibrium; that is Cc* Co* = m&apos;Pco [2] in which Co* and Co* are the concentrations of carbon and oxygen (weight per unit volume of metal), respectively, in the liquid-metal phase at the interface, Poo* is partial pressure of CO in the gas phase at the surface (atmospheres), and m&apos; is the mass-action constant for Reaction [I]. Since activities of C and 0 are not strictly proportional to concentrations, m&apos; is not a true thermodynamic equilibrium constant but varies with carbon content.&apos; 3) Mass Transport—If the reaction is to proceed at the gas-metal surface, as described above, dissolved carbon and oxygen in the liquid iron must come to the surface and gaseous carbon monoxide must move away from the surface. Details of the mass-transport mechanisms depend on the kind of system under consideration. For a stirred metal bath in contact with a CO gas phase, the transport of C and 0 to the surface can be described by 1 Do Mols CO evolved per sec = — 1/16— Do/do Agm (CO-Co*) = 1/12 Do/do Agm *(Co-Co*) [3] In this equation, Do and D, are the diffusion constants for oxygen and carbon in liquid iron, 6, and 6,. are the boundary-layer thicknesses, A,,,, is the

Jan 1, 1959

By Thierry Coléou

In this paper, we consider open pit optimization. At present, most methods specify the economic parameters and then find the corresponding optimal pit. But as the economic environment varies (which it does regularly these days), the "optimal" pit changes and quite often changes markedly. The questions are: by how much does it change and which parameters are most influential? The functional approach of Technical Parameterization of Reserves, devised by Matheron in 1975, gives the set of all the different optimal pits, under any economic condition. It separates technical design and economic assumptions and thus permits the use of several optimality criteria when choosing the final pit, and not just the maximization of an additive profit formula. Very efficient specific algorithms are presented to obtain all the potentially optimal pits. Fluctuations in the parameters induce changes in the optimum design. Inclusion relations that exist generate very tight bounds and hence very quickly detect optima, even when using a classical adaptation of maximization techniques (graph theory, moving cone, dynamic programming ...). The advantage of Technical Parameterization of Reserves over other methods is that it provides a nested sequence of optimal pits which can then be used for mine scheduling. Many possible mining schedules can be obtained by using the family of technically optimal projects to split up the orebody. The "optimal" schedule, which is in fact a compromise between the different requirements of the economists, the mine planner and the metallurgist, can be chosen from within the wide scope of possibilities. A practical example of mine scheduling for a chromite mine is presented in detail.

Jan 1, 1989