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By H. J. Modi, P. L. De Bruyn

IN recent years interest has been aroused in flotation rate studies both from a technical and a more practical aspect. With increasing fineness of grind becoming a necessity in treatment of low grade ores, difference:; in flotation rates of various size ranges will assume importance in the evaluation of overall recovery results. Theoretical analysis of flotation kinetics was initiated by Schuhmann,' who sought to define flotation rate of a given mineral and specified size range in terms of certain physical variables of the flotation system. Using as a basis for his analysis the bubble-particle encounter hypothesis previously advanced by Gaudin,' Schuhmann writes for the rate of flotation (R,.) of particles of average size x, Rx = PcPa(x) V F. [1] In this relation Pc and Pa represent, respectively, the probability of collision between particle and gas bubble in a given time interval and the probability of adhesion of particle to the bubble after collision. Rigorously speaking, the term PC does not have the significance of a probability factor, since it depends on the time interval and therefore can be numerically greater than unity. The term c(x) expresses the concentration of particles of an average size x in the flotation cell in weight per unit volume of pulp, and V denotes the total volume of pulp in the cell. The product, P,c(x)V, defines the frequency of particle-bubble collisl.on, and when it is multiplied by P,, the number of collisions per unit time resulting in successful adherence is obtained. The factor, F, measures the froth stability and is introduced because after fruitful bubble-particle contact some particles may still riot reach the froth launder. Coalescence of bubbles in the froth column or too short a bubble life could account for this effect. Schuhmann also introduced the concept of "specific flotation rate" (Q) to allow for the relative abundance of different mineral species in the flotation pulp. The specific flotation rate, having the dimension of reciprocal time, is defined as Eq. 2: Qx =Rx/c(x)v [2] and it also follows from Eq. 1 that Qx = PcPaF. [31 The theoretical aspects of flotation kinetics were also considered by Sutherland,3 who tried to improve Eq. 1 by expressing the probability factors in terms of such physical variables as particle radius (x), bubble radius (X), velocity of bubble relative to particle (v), the number of bubbles per unit volume of pulp (N) and the induction period (A) necessary for air-mineral adhesion. According to Sutherland's treatment, the rate equation, Eq. 1, transforms to R, = [3pX x v N] [sech2 (3 v ?/4 X) ] ?c(x) V [4] where the first term in brackets on the right-hand

Jan 1, 1957

By John Birkinbine

Secretary's Note.—In printing this paper in the present volume, the figures given in the pamphlet edition have been brought more nearly up to date, the product of 1899 being in many instances inserted. Iron-Ore Resources. In a paper presented to the Institute in 1897,* I discussed the iron-resources of the United States as then developed, calling attention to some principal sources upon which other countries depended. The following statement will give a general idea of the amounts, as compiled from the latest official records, of ores won, and metal produced, in the nations which are important contributors to the world's output. Unfortunately these are not all contemporaneous, since in some countries the statistics do not appear until after one or more years. The statement covers not only pig-iron and iron-ore, but also manganese-ore —the manganese mined being principally used in the production of spiegeleisen or ferro-manganese, and these alloys being generally included in the pig-iron output. Table I, which epitomizes the present situation, shows respectively the countries and the quantities of iron-ore and man-

Jan 1, 1901

By Zay Jeffries

From the title of this chapter the reader could expect an attempt to out- line the anticipated shape of things to come, mineralwise. We have no crystal ball and if we possessed one we could claim no expertness in its use. In the first place no one can tell the future status of man. No one has any way of knowing to what extent peace will prevail, nor to what extent changes may occur in national sovereignties or forms of government or in international relationships. So future man is an uncertainty. Nor can we predict new developments that may result in significant changes in man's status or in the mineral industry or both. If, for example, this chapter had been written in the middle 1930's, nearly everything that has happened since in the fields of atomic energy and space technology would have been missed. Yet what vast changes these I have made in the status of man! Also the changes in the mineral industry have been important. A writer would have been bold indeed had he prophesied that uranium would play such an important role. But we need not confine our foggy vision to these fields. The steep rise in the use of aluminum, titanium, and germanium reflects the unpredictable in what may be thought of as the more normal pursuits. This should not discourage one from using the past and currently observable trends as bases for limited predictions. To do this, however, it is desirable to make certain assumptions about man's status without pretense that these assumptions have a high probability of fulfillment: 1. Only minor changes will occur in the geographical boundaries of the nations of the world. 2. World War III will not take place in the near future. 3. As a consequence of (2), man will not destroy himself by wanton use of atomic weapons. 4. Disarmament will take place, if at all, gradually rather than all at one time. Under the above assumptions the world will enjoy a period of relative peace even though the status may be one of an armed truce. The assump-

Jan 1, 1964

By W. F. de Lange, M. I. Brittan

A mathematical model of the Western Holdings gold concentrator in South Africa was generated by multiple regression analysis of routine plant operating data. Interpretation of the computer results and application of the model indicated that significant economic improvement in gold recovery could be realized by relatively minor modifications to the circuit. The modifications made are described and the economic benefits resulting from the increased gold production are assessed. Comparison, of the projections of the mathematical model with actual plant performance is illustrated.

Jan 1, 1976

By J. de la Vergne, L. O. Cooper

The hydrostatic steel mine shaft liner (HSL) Provides a permanent wall lining for drilled shafts. It is watertight and suitable for bad ground conditions. After a shaft has been drilled to its full depth, the HSL is lowered into it and secured in place with cement grout. The liner consists of a cylindrical steel shell usually reinforced with exterior stiffening rings. The shell is basically designed for compressive strength and the rings are provided to give the shell added resistance to buckling. There are no published standards for the correct procedures to design an HSL. This paper gives a method that appears logical. A design solution can be complex with increased opportunity for error. This paper presents simple formulas to produce sufficient accuracy for construction design. Two new concepts are presented, referred to as transition pressure and critical pressure. An example demonstrates use of the formulas and concepts presented. To facilitate comprehension and use of the formulas, Greek letters are avoided and most of the English alphabet symbols used refer by association to their definitions. An appendix shows derivation of the formulas.

Jan 1, 1984

By Desmond De Villiers Oxford, Peter H. Williams

Nchanga Consolidated Copper Mines, Ltd., is one of the four mines operated by the Anglo American Corp. in Northern Rhodesia, now the independent nation of Zambia. Today Nchanga is the second largest single producer of copper in the world, accounting for more than 200,000 long tons of copper annually at a monthly milling rate of 430,000 tons of ore. The average mill-head grade is about 5.20% total copper, of which approximately 60% is copper sulfide. The remainder, referred to as "acid soluble," is copper oxide. Nchanga mines three separate orebodies varying in grade and sulfide-to-oxide ratio. Ore is processed in two separate grinding circuits feeding into three separate flotation circuits. A fourth flotation circuit treats leach plant residue for additional recovery of sulfides.

Jan 1, 1965

By J. J. De Witte, J. G. Cazort

The Paranam plant in Surinam (formerly Dutch Guiana) was built during 1939-40 to supply crushed and dried bauxite for the growing U.S. aluminum industry, supplementing production from the Suriname Aluminum Co.'s Moengo works, which began operation in 1922. A subsidiary of Aluminum Company of America, Suralco's total annual production from these two plants averages 2.55 million dry metric tons of various grades of bauxite. Starting in 1941 with bauxite from mines on the west side of the Suriname River, annual production at the Paranam plant has varied from a low of approximately 450,000 tons to more than 1 million tons in 1949. High production rates during World War II and the late 1940's rapidly depleted these reserves, and in 1950 plans were made to mine the known deposits on the east bank of the river, about five miles downstream from the original Paranam plant.

Jan 11, 1960

By L. H. de Wald, J. Walter Scott

It is usual practice in the copper industry to use open horizontal molds for casting tough-pitch copper wire bars.' A wire bar cast in this manner is partly characterized by heavy wrinkles and a comparatively deep skin of oxide on the top of the bar, corresponding to the open side of the mold. On the theory that the rough, high-oxide surface might have an adverse effect on the rolling and drawing properties of a wire bar and might account for some of the irregularities of mill behavior, several bars which had been planed to remove the wrinkled surface were processed into wire. These bars responded to mill treatment more satisfactorily than did the regular wire bars. Realizing that machining the surface of one face of each bar would not be commercially feasible, it was decided that casting the metal into a vertical mold and cropping off the pouring end would accomplish approximately the same result. Several wire bars of commercial size (250 Ib.) were so cast and processed into wire for comparative test with bars cast in the usual horizontal molds. It is the purpose of this paper to present the results obtained from this investigation, in which commercial bar sizes and processing technique were used throughout. The results show that in general copper wire bars cast vertically are superior to those cast horizontally. Experimental Procedure A horizontally cast bar and a vertically cast bar were obtained from each of several regular reverberatory furnace heats of copper which had been refined and poled to tough-pitch metal in accordance with usual methods.' Both bars were cast from the same part of the melt and within five minutes of each other, in order to produce as nearly as possible, in each case, wire bars of identical composition.

Jan 1, 1930

By L. H. de Wald, J. Walter Scott

The removal of lead by fire refining methods from copper of electrolytic quality is growing in importance. Particularly is this true of the refining of secondary copper and copper cathodes obtained from electrolytic cells where lead is used as the anode material, as in the electrolysis of ore-leaching solutions and foul electrolyte. When investigating the removal of small amounts of lead from molten copper in a reverberatory furnace during the refining of secondary copper of otherwise electrolytic copper quality,' it was found necessary first to know something about the distribution of the lead throughout the bath. The authors believe that it is not generally known how small amounts of lead as an impurity are distributed in a molten copper bath; that is, whether the lead is concentrated at the bottom or at the top, or whether it occurs more or less uniformly throughout the bath. The data contained in this report may help, therefore, in the development of a satisfactory fire refining method for the removal of this obstinate element from a molten copper bath. The first step was the development of a method for taking samples from various locations in the bath, at the surface and at various depths. The sampling device used, shown in Fig. 1, consisted of a 10-gram fireclay assay crucible fitted into a ring on the end of a steel rod handle of suitable length. A fireclay scorifier, 2 in. dia., with a ½-in. hole bored in the

Jan 1, 1930

By W. O. Philbrook, C. W. McCoy

The reduction of chromous oxide from lime silica alumina slags by carbon-saturated iron behaves as a first-order process having a rate of 0.001 grams Cr min 1 cm 2 (pct Cr ) , substantially independent of slag composition and temperature over an important range for iron smelting. The equilibrium ratio (pct Cr)/[pct Crl is below 0.04 for slags having lime-silica ratios above 0.6. MANY studies have been conducted on chromium in slag-metal systems under oxidized conditions. The Purpose of these investigations has been twofold; namely, (1) to determine those conditions which lead to greater chromium recovery in electric-furnace and open-hearth practice, and (2) to determine the nature of oxide inclusions and de-

Jan 1, 1959

In situ mining techniques have become prominent in recent years due to declining ore grades, rising costs, and increasing concern for miners' health and safety. Current practices depend heavily on the effective and uniform fragmentation of the ore zone of interest, which not only provides for proper media flow but also exposes additional surface areas to react with the processing system. Specifically, current applications have focused on blasting to a mined-out opening or, in the case of shallow de- posits, blasting to the surface void. In the former case, several obstacles are encountered, including proper initiation, uniform fragmentation, and a lack of swell space for the blast, which tend to produce less desirable results in the zone of' interest.

Jan 3, 1979

By J. M. Cabal, M. Chica Olmo, J. P. Laille

One of the main goals of a simulation of a coal deposit mining is to predict a series of parameters considered by the miner to be useful, e.g. ash content, sulphur content, seam thickness etc). The idea is to simulate different ways of mining a multi-seam brown coal deposit (the Mine Puentes de Garcia Rodriguez deposit, ENDESA, Spain ), which is exploited by several bucket-wheel-excavators (BWE) . Two mining models are used: a geostatistical model which provides a numerical way of re- presenting the three-dimensional ore-body, then a deterministic model, consisting of simulating the technical aspects of the mining. The main purpose of this simulation is to show how the mining operations can be reproduced using these two techniques.

Jan 1, 1983

SULFURIC ACID U.S. 4,070,260 - Sulfuric acid leaching of willemite, hemimorphite, or other zinc silicate ore. Ore is leached with at least a stoichiometric amount of a IN to 6N sulfuric acid solution at a temperature near its boiling point to form a gelatinous mass of hydrated silica and zinc sulfate, the water in the mass partially evaporated to crystallize all of the silica, the mass treated with hot water to dissolve substantially all of the zinc sulfate, the suspension filtered, and zinc values recovered from the filtrate by electrolysis. N. Dreulle, assigned to Compagnie Royale Asturienne des Mines. Jan. 24, 1978. 3 pp. (204-119). Filed: 2-10-76 (656,966) . Priority: France, 2-14-75 (75/04594) .

Jan 1, 1979

By AIME AIME

WINFIELD SCOTT MORRIS, known from Coast to Coast within the petroleum industry as "Buck" Morris, is and has been for several years an outstanding man in the Petroleum Division of the A.IM.E., so it is most natural to have him as the Chairman of the Division. "Buck" has been such a vociferous promoter of everything TEXAS that most of his friends believe him to be a "Longhorn" by birth-but the records show he was born at Wilmington, N. C., on July 29, 1901. He worked his way through college and graduated from the University of North Carolina in 1924 with a B.S., followed by a C.E. in 1927. His graduation thesis was entitled "De¬sign of a Modern Oil Refinery."

Jan 1, 1944

By L. A. Bromley, A. W. Petersen

The van Arkel-deBoer method for producing ductile titanium by thermal decomposition of Til, vapor and deposition on an electrically heated filament is modified by film boiling Til liquid on a heated filament, resulting in similar titanium deposition on the filament and liberation of gaseous iodine. The deposition rate is higher and the energy requirement smaller than in the van Arkel process. Many problems must be solved before the process is commercially feasible. TITANIUM of 99.9 pct purity, called ductile titanium, has been produced by a modification of the van Arkel-deBoer&apos; method. In the van Arkel-deBoer method, an electrically heated wire is suspended from two electrodes, which are placed in a container holding TiI, vapor at a low&apos; vapor pressure (usually <5 mm Hg). The vapor diffuses to the hot wire, usually maintained at 1100" to 1600°C,&apos; and decomposes according to the reaction liberating gaseous atomic iodine and depositing solid crystalline titanium on the wire. Estimations based on the data of Runnalls and Pidgeon,&apos; indicate that the rate-control ling step is the diffusion of atomic iodine away from the wire. There appears to be nearly thermodynamic equilibrium at the wire with TiI, and iodine as the main gaseous species. TiI, is almost certainly an important gaseous species in the cooler regions.&apos; The liberated iodine diffuses to a heated source of crude titanium and reacts to form more TiI, vapor, which again diffuses to the hot wire and completes the cyclic process. The foregoing process may be modified by suspending the hot wire in liquid TiI,, instead of the vapor, and obtaining film boiling. This type of boiling is characterized by the formation of a continuous film of vapor over the wire surface. Since only vapor contacts the wire sul.face, the temperature of this surface may be raised as high as desirable, within the limit of mechanical strength requirements for the wire. By properly adjusting the input voltage. the temperature of the wire may be maintained above U0C"C; and by evacuating the vessel holding the liquid TiI, and maintaining a suitable condenser temperature, the vapor pressure of TiI, may be held low. Thus, the conditions of operation of the van Arkel-deBoer method may be approximated with film boiling; and hence, it is postulated that ductile titanium may be produced by this method. Preparation of Til, There are many methods available for the preparation of TiI,; that used in this research was prepared by the direct reaction of titanium sponge in controlled amounts with liquid iodine. Although no difficulty was encountered with this reaction, it has since been pointed out that this method is sometimes dangerous and should be used with caution. The resulting TiI, was purified by distillation. First Film Boiling Experiments Apparatus: The apparatus shown in Fig. 1 was used for film boiling TiI, on short wire filaments. The current to the filament was supplied through a bank of three 5 kva transformers connected in parallel. The current was controlled by adjusting the voltage over a 0 to 67.5 v range with a 7 kva variable transformer on the low voltage side of the bank of transformers. The current and voltage were measured by Weston meters. The sealed-in-glass tungsten electrodes were hard-soldered to the filament for the film boiling of TiI,. The bottom part of the reactor, containing TiI,, was wrapped with ni-chrome heating wires to maintain the TiI, in the liquid state. An ice or liquid nitrogen trap, for solidifying I, vapor and any TiI, not condensed, was attached to the low pressure side of the air-cooled condenser. A Megavac vacuum pump was used. Procedure: A 0.010 in. diam tungsten filament was hard-soldered to the tungsten electrodes. TiI, was melted (mp 156°C) and poured into the reactor chamber; the top of the reactor chamber, containing the electrodes, was replaced. Freezing of the TiI, was prevented by controlling the current to the ni-chrome wires wrapped around the reactor with a 1 kva variable transformer. The mechanical vacuum pump was started and the system evacuated to about 2 mm Hg TiI, vapor pressure. The current to the filament was turned on and the impressed voltage slowly increased with the variable transformer. A sudden drop in current at nearly constant im-

Jan 1, 1957

By M. King Hubbert, David G. Willis

A theoretical examination of the fracturing of rocks by means of pressure applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should be horizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. INTRODUCTION The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the petroleum industry in a paper by J. B. Clark,&apos; of the Stanolind Oil and Gas Co. in 1948, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed. The technique itself is mechanically related to three other phenomena concerning which ah extensive literature had previously developed. These are: (1) pressure parting in water injection wells in secondary-recovery operations, (2) lost circulation during drilling, and (3) the breakdown of formations during squeeze-cementing operations, all of which appear to involve the formation of open fractures by pressure applied in a wellbore. The most popular interpretation of this mechanism has been that the pressure had parted the formation along a bedding plane and lifted the overburden, notwithstanding the fact that in the great majority of cases where pressures were known they were significantly less than those due to the total weight of the overburden as determined from its density. Prior to 1948, this prevalent opinion had already been queried by Dickey and Andresen,2 in a study of pressure parting; and by Walker,"&apos; who, in studies of squeeze cementing, pointed out that the pressures required were mostly less than those of the overburden, and inferred that the fractures should be vertical. J. B. Clark,&apos; in his paper introducing hydraulic fracturing, and later Howard and Fast," and Scott, Bearden, and Howard," also of Stanolind, postulated that the entire weight of the overburden need not be lifted in producing horizontal fractures, but that it was only necessary to- lift an "effective overburden," requiring a correspondingly lower pressure. Hubbert,7 in discussing the paper by Scott and associates, pointed out that the normal state of stress underground is one of unequal principal stresses; and in tectonically relaxed areas, characterized by normal faults, the least stress should be horizontal. Therefore, in most cases, fracturing should be possible with pressure less than that of the overburden and, moreover, such fractures should be vertical. Harrison, Kieschnick, and McGuire,8 also on the expectation that the least principal stress should be horizontal, argued strongly in favor of vertical fracturing. Scott, Bearden, and Howard6 observed that, when

Jan 1, 1958

G. D. Kneip, Jr., and J. 0. Betterton, Jr. (Union Carbide & Carbon Corp., Oak Ridge, Tenn.)—The authors have contributed to the theory of zone melting by considering the effects of the solidification of the final zone on the distribution curves for the finite length bar. However, they do not consider in sufficient detail the restrictions imposed by the particular metals involved. Eq. 4 has the analytical solution which is equivalent to Pfann&apos;s&apos; equation for normal solidification of the final zone. For distribution coefficients less than one, it is apparent from this form of the equation that, as the solidification approaches completion, the concentration attains extremely large values which are inconsistent with the density of physical materials. The necessary restrictions then are that the solute concentration cannot exceed the density of the alloy, or more frequently, the solubility limit in the solid phase. Secondly, the distribution coefficient cannot be constant from 0 to 100 pet solute unless the liquidus and solidus coincide over this whole region. It would thus be more correct to impose limits on the solubility such as would be indicated by a typical eutectic diagram. Furthermore, in this case the assumption that the distribution coefficient remains constant is more likely to be realized. Eq. 4 should then be replaced by the following C,,(x) =k/L-x [ ?11 3 C11 (x)Ddx - ?11 4 Cn(x)dx= k[Cn (L-l)/k] [ L-x/l]x-1 L-l = x = L-l [kCenterlie/Cn (L-l)]1/k-1 The typical shape for the distribution curve in the final zone is indicated schematically in Fig. 12 for the simple eutectic case. The solidification proceeds according to Pfann&apos;s&apos; expression until the concentration reaches the maximum solubility in the solid phasc. At this point, the concentration changes abruptly to the eutectic composition and remains at this value for the duration of the solidification. The width of the flat region, and the back reflection of this effect into the concentration curve on subsequent passes, depends upon the ratio of the eutectic concentration to the original concentration, upon the distribution coefficient, and upon the number of passes. Similar effects on the concentration curves in the first zone length would be expected in many systems for which the distribution coefficient is greater than one, and where the maximum solubility is not too much larger than the original concentration. The discussers agree with the authors that the assumption that the liquid is uniform in concentration should be considered with caution. Kneip and Better-ton&apos; have shown, however, that in floating zone refining of zirconium, using induction heating, the distribution of iron agrees with theory which assumes a uniform liquid composition. Hence, in this case, the experimentally realized distribution coefficient agrees with the present phase diagram within the experimental uncertainty. L. Burris, Jr., C. H. Stockman, and I. G. Dillon (authors&apos; reply)—The authors are happy to have received the comments of G. D. Kneip, Jr., and J. 0. Betterton, Jr., which provide additional insight into the zone refining process. It is true that the equations developed are inapplicable if the solute solubility in the solid phase is exceeded. However, this restriction on the use of the equations was clearly stated in the paper. A closer approach to

Jan 1, 1957

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel&apos;s paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel&apos;s attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,&apos;, y uranium, and perhaps zirconim.&apos; The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors&apos; reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato&apos;s value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,&apos;&apos; and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener&apos;s predictions.28 We have no quarrel with Hagel&apos;s placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By H. Larson, J. Chipman

The ferrous and ferric oxide concentrations of slags, expressed as j = Fe+++/(Fe+++ + Fe++), have been established through gas-slag equilibrium at 1550°C in a range of oxygen pressure of 10-I to 10-9 equilibriumatm. The value of j is increased by basic additions (BaO, CaO, MgO, MnO) and decreased by acidic oxides (SiO2 and TiO2). Oxygen pressure is shown graphically as a function of composition for slags which are analogous to those at the slag-gas interface of the open hearth furnace. THE progress which has been made in recent years in understanding the chemistry of metallurgical slags has been based largely on studies of slag-metal and slag-gas equilibria. There is a considerable body of knowledge which is applicable to reactions occurring at the slag-metal interface in open hearth steelmaking. There is little information concerning reactions of the slag with the furnace atmosphere and hence little basis for an understanding of the transfer of oxygen, sulphur, or hydrogen between gas and slag. The oxygen pressure of the open hearth atmosphere is normally of the order of 10-1 to 10-3 atm which differs by several orders of magnitude from that of about 10" atm at the slag-metal interface. The chemical properties of the slag, for example, the ratio of ferric to ferrous iron and the ability of the slag to hold sulphur in solution, are greatly affected by changes in oxygen pressure. This investigation was undertaken to enlarge our knowledge of the effect of oxygen Pressure on steel-making slags. Using air or controlled mixtures of CO a CO2 a range of oxygen Pressures from 10.&apos; to 10.&apos; was covered. Review of the Literature There are only a few references in the literature which pertain directly to this investigation. The most important is that of Darken and Gurry1,2 on the system iron-oxygen. This work included the determination of the phase diagram of the system and also a study of the field of homogeneous melts and their oxygen pressures. Their apparatus and procedure were very similar to that used in this study. Iron oxide was melted in a platinum crucible under an atmosphere of CO2:CO, CO2:H2, H2O, CO2, air or O2 depending upon the partial pressure of oxygen desired. After equilibrium was reached, the sample was quenched and analyzed for ferrous and ferric oxide. By appropriate calculations these authors were able to determine the oxygen and iron activities in the various slags, heats of formation of the oxides of iron, and heats of solution of iron and oxygen in the liquid slags. In a subsequent paper&apos; the same authors made a less thorough investigation of the effects of additions of lime and manganese oxide on the composition of iron oxide melts. Only a few experiments were made and those in a narrower range of temperature and oxygen pressure. Darken&apos; has investigated the fusion temperature of iron oxide in contact with silica under various atmospheres. He found that the temperature changes from 1120° to 1447°C as the gas composition changes from CO2/CO equal to 20.8 to pure oxygen. A comprehensive paper by White" predates the work of Darken and Gurry. The decomposition of ferric oxide into oxygen and lower oxides of iron was studied from 1000° to 1650°C and under oxygen pressures from 2 to 76 cm of mercury. The effect of

Jan 1, 1954

By M. B. Bever, A. K. Jena

Equations for the heat effects of additions of mixtures of multicomponent phases to a solution have been derived in terms of the enthalpy interaction coefficients. By these equations and the measured composition dependence of the heat effects on addition of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions, values of the enthalpy in-teraction coefficients in tin-rich solutions at 541°K have been obtained. Analysis of these results in terms of the regular solution theory and the quasichemical theory suggests that near the melting point of the solvent association in the solution becomes important. SEVERAL recent papers have discussed the nature of dilute solutions on the basis of measured enthalpy interaction coefficients. l-3 These coefficients contribute to the understanding of the constitution of solutions and can be used for the evaluation of thermo-dynamic data of multicomponent systems. Their experimental determination, however, is laborious. This communication reports values of the enthalpy interaction coefficients of silver, cadmium, and gold in liquid tin-rich solutions obtained from the measured heat effects of additions of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions. These measurements were made in the course of the determination of the heats of formation of Ag-Cd solid solutions reported in a concurrent publication.4 THE HEAT EFFECT OF AN ADDITION TO A SOLVENT This analysis is concerned with the addition of a mixture of multicomponent phases from the temperature To to a solvent of known composition at temperature T. If Nmixture << Nsolvent, where N designates the gram-atoms involved, the heat effect per g-atom of mixture added can be expressed as (HT - HT )i = difference in heat contents of component element i in the mixture at T and To Q = heat effect on solution of the mixture at temperature T Also1 Q = S Xi [2] where ?Hi ,T,x = relative partial enthalpy per g-atom of i in solution at temperature T and composition of the solution x x = average of the atom fractions of the added material in solution before and after the addition The relative partial enthalpy ?Hi per g-atom of an element i in a dilute solution composed of a solvent 1 and the solutes j = 2, ... m is related to the interaction coefficients by the following equation5 ?Hi - ?Hi-?Hi,x1-1 + S n1ixj+ . . . +S...S...S nrixn2... Xnji...Xnmm+... [3] vhere Xj = atom fraction of solute j in the solution nri = the rth order enthalpy interaction coefficients, which can also be represented by the more general designation5 L(i)n2,n3...nm and nj may have any positive integral value or zero. For identification of various rth order interaction coefficients, nri is written as nn2i2,...nij,...nmm. Eqs. [1], [2], and [3] combine to give the following general equation for the heat effect on addition of a small quantity of a mixture to a large quantity of a dilute solution n = _?ga ?Ha,To + ? Xi(HT - HT o)i a. i + ?xi?Hi,X,i?1 + ??xnjixj + . . . + ???. . .?. . .?xinrix2n2. . . xnji. . . xnmm+ . . . [4] The first term on the right-hand side of this equation is the heat of decomposition at the addition temperature of the phases present in the mixture, the second term is the heat required to raise the temperature of

Jan 1, 1970