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By K. M. Goldman, Lo-Ching Chang

The kinetics and mechanism of transfer of a constituent across a slag-metal interface are fundamentally important because many metallurgical processes involve the existence of a slag phase and a metal phase. Industrial processes seldom proceed to equilibrium, and information of the rates and modes of reactions are therefore often of greater practical importance than equilibrium data. A study of the kinetics of sulphur transfer across a slag-metal interface under reducing conditions will contribute a great deal toward a better understanding of desulphurization in the blast furnace process. The general principles existing in the transfer of a constituent, such as sulphur, across a slag-metal interface can be extended to similar transfer phenomena in other metallurgical processes. The present paper will demonstrate how such studies will lead to fruitful results from both the practical and theoretical standpoints. EXPERIMENTAL METHOD The apparatus used was, simple. A graphite crucible 15/8-in. id, a wall 1/8-in. thick, and a depth of 4 in., was packed in an outer fused silica tube with powdered magnesia. The crucible assembly was rotated at a speed of 235 rpm inside an in- duction coil. A charge of 250 g of Armco ingot iron was introduced into the graphite crucible and melted by induction heating. The melt was held at a desired temperature for 3-5 "'in., aftcr which 7.5 g of granular ferrous sulphide was added and the bath was held for another 3-5 mi11. A metal sample was then taken by means of a fused silica tube and a rubber suction bulb. Immediately after the metal sample was taken, 30 g of a prefused and crushed slag were introduced. The slag reached the ternperature of the furnace in 1 to 1 1/2 min. Slag

Jan 1, 1949

By David Kramer, Cecil G. Rhodes

Critical transport currents were measured as a function of perpendicular external magnetic field in Ti-22 at. pct Nb wire samples. These samples were heat-treated to yield w Phase precipitates at denslties ranging from 10 to 10 17cm-3. The Precipitates are ellipsoids of revolution with major axes of 50 to 1300A. Flux-Pinning by w precipitates is responsible for the high critical transport currents that were ob- ThE ability of a type II superconductor to sustain a zero-resistance transport current (Jc) in an external magnetic field (H) is due to the presence of micro-structural features which can impede the motion of magnetic flux penetrating the superconductor under the influence of a Lorentz force. Such features are referred to as pinning sites. The pinning strength is tained. A sample cooled from 800°C and annealed 1 hr at 450°C carried a critical tramport current of 10 amp per sq cm at 30 kG. Variations in the current-carrying ability of this alloy are due to changes in its pinning strength which is a function of precipitate density and composition and of the composition of the matrix. the reaction of the bulk superconductor to the Lorentz force and depends on the efficiency of the individual pinning sites and on their volume density. The super -current density increases with pinning strength, other things being equal. The above concepts are discussed in detail in a comprehensive review by Livingston and Schadler.' In Ti-Nb alloys, as in other binary titanium alloys, the metastable hexagonal w phase usually forms below the p/a + p phase boundary near the titanium side of the phase diagram. Stiegler et a1.' have summarized much of what is known about w phase in titanium and zirconium binary alloys. The present work deals with

Jan 1, 1968

By C. H. Mathewson, E. M. Thalheimer

In planning the present experiments, we have made a particular effort to secure that adjustment of working conditions which would render the forthcoming tests most serviceable by way of indicating the comparative properties of the three different commercial grades of copper used. More specifically, we have endeavored to obtain certain definite information with respect to the relative behavior under test of ordinary electrolytic copper and furnace-refined lake copper containing (a) a moderate percentage of arsenic and (b) a rather large percentage of arsenic, in addition to the usual content of silver and other impurities. These comparisons were made systematic and comprehensive by testing throughout a series of (eight) reductions running from 0 to 70 per cent. in the case of cold-rolled metal, and throughout a series of (15) temperatures running from 100' C. to 1,000" C. in the case of annealed metal. In other words, a survey of properties similar to that made by Grard,' in the case of electrolytic copper, was here repeated (with modifications) and extended to two other commercial varieties of copper. The great importance of copper both as a material of construction and as the base of our most important alloys (aside from steel) has led to innumerable investigations of its properties, particularly in commercial forms. Naturally, the merits of furnace-refined lake coppers us. those of the very pure electrolytic product have furnished the subject of much experimental work and animated discussion, wherein the effect of arsenic has by no means been overlooked. In the literature of the past 10 years,

Jan 1, 1917

By N. I. Fisher, J. Shepherd

Statistical studies have been carried out on structural geological data collected across a large zone of roof failure 600 m (1968 ft) wide and at least 800 m (2642 ft) long in the Greta coal seam at Aberdare East Colliery. Two swarms of hundreds of minor, normal faults with throws commonly between 3 and 300 mm in the room and pillar workings are broadly coincident with roof failure. The faults have been classified into dip slip and oblique and strike slip types. Roof conditions have been classified into good; troublesome with subclasses scaly, heavy, gutter falls and wide, flat-roofed falls; and severely failed with subclasses very heavy roof, gutter falls and dome falls. Troublesome conditions are defined as those in which the height of the fall is less than or equal to 0.3 m, and severely failed conditions as those in which the fall height is greater than 0.3 m. Comparison of faults, roof condition and mining rate on a shift basis indicates that faults and roof failure are much more important than machine breakdowns in reducing mining rate. The effect of faults on roof conditions has been quantified using a concept called the "zone of influence," a rectangular area around a fault in which the fault has potentially deleterious effects. The spatial comparison of fault "zones of influence" with areas of roof failure wing Spearman's rank correlation coefficient shows that, while normal dip slip faults do not appear to be associated with roof failure, oblique slip and strike slip faults appear to be associated with roof classed as severely failed. The "zone of influence" of an oblique slip fault may extend up to 3 m on each side of it in the headings and up to 1.14 m in the cut-throughs. The fault "zone of influence" has geomechanical implications for the design of mine openings and Possibly represents the maximum length of a cantilevered roof beam likely to fail during mining, owing to a fault. Roof conditions could Possibly be predicted in blocks of &gin coal if the type of fault could be identified in oriented drill cores.

Jan 1, 1979

By L. S. Darken, H. A. Wriedt

In a previous paper,1 an experimental study of nitrogen dissolved in a cold-rolled ad heat-treated, low-carbon steel at 300° to 450°C yielded the equilibrium solubility relations and the concentrations of the two types of deject sites involved. In this paper, the probable identities of the defects that absorb nitrogen are restricted from the available evidence to screw dislocatioms for B sites, and to either micro crack surfaces or edge In a previous paper.' we reported an experimental study of the excess nitrogen solubility in a low-carbon steel produced by a combination of plastic deformation and nonrecrystallizing heat treatment. The concentrations of the defect sites that absorb the excess nitrogen were measured in terms of their capacities for nitrogen. Also measured were the equilibria of nitrogen distribution among the sites. Several problems and questions arise from these measurements. We should like a physical identifi- dislocations for A sites. The concentrations of these defects in experimental steel specimens are estimated from the concentrations of defect sites. finally, the influence of chemical composition upon the nitrogen-trapping defects—the relative numbers generated in deformation, the relative numbers surviving as temperature is raised, the apparent numbers observed, and the distribution equilibria-is discussed. cation of the defects involved and of the two kinds of nitrogen-absorbing sites, called A and B types, upon those defects; the concentrations of the defects themselves could then be computed. We should also like to know how exclusively the findings apply to the "X steel" used in the experiments and to what extent they apply to cold-rolled steel given no subsequent treatment. By considering the data already given, together with results from a few specific tests which will be reported as they are invoked, we are able to eliminate some interpretations altogether and to secure an acceptable though limited interpretation from among the remaining possibilities.

Jan 1, 1965

By C. H. Mahoney, A. L. Tarr, P. E. Le Grand

Magnesium, it is now generally realized, differs in some important aspects from most other structural metals, not excepting even its close neighbors, the aluminum-base alloys. This is particularly true with respect to the effects of elevated temperatures on the two light metals when in the molten state. Aluminum, 0' the one hand, should not be raised above its melting point any higher than is absolutely necessary if one is to avoid danger of gas absorption and a tendency toward grain growth in the resultant casting.' Magnesium alloys, in sharp contrast, actually benefit by being heated to temperatures considerably above their melting point, It is a commonly accepted practice to establish the desired fine grain in the industrial magnesium alloys of the aluminum-hearing group by raising the temperature of the melt after the refining treatment to some 250°C (482°F.) above the melting range. To recall briefly the typical practice for magnesium alloys, the molten metal is refined by fluxing at about 730°C. (I350°F.), and after the melt has been covered with a suitable flux, the temperature is raised to between 870°C. (I600°F.) and 930°C. (1700°F.). It is then cooled as quickly as possible to the casting temperature. This superheating, as it is called, results in a fine-grained cast metal structure which has superior mechanical properties, enhanced amenability to 'solution heat-treatment, and better machinability than cast metal that has not been superheated. The minimum temperature of superheating varies to some extent with the composition of the alloys to be treated and usually increases with the percentage of magnesium in alloys containing the same constituent metals.' It should be noted that the grain-refining effect of superheating is markedly apparent only in connection with the alloys containing aluminum as an alloying Constituent—the binary alloy containing 1.5 per cent manganese, for example, is not refined in grain to any noticeable extent by a superheating effort. While the phenomenon of superheating is well known in the magnesium industry, the mechanism of the process has remained a mystery During the superheating cycle something occurs that forces a fine grain upon the solidifying metal. The process has been controlled in an empirical manner, and occasionally, especially on large-scale melts, and for no apparent cause, no grain refinement is obtained from a superheating treatment. Only a few papers of importance have been published on the subject. Of these, one of the most helpful is the paper by Achenbach, Nipper and Piwowarski,3 which gives considerable data concerning the effect of superheating on various properties such as fluidity, shrinkage and hot crack

Jan 1, 1945

By John C. McDonald

CONTROLLED cold work is used between solution heat treatment and precipitation heat treatment for producing certain tempers of the commercial aluminum base alloy 2219 (designation of the Aluminum Association, U.S.A.) which contains 6.3 pet Cu as the major ingredient responsible for the age hardening. The complete composition limits for this alloy are listed in Table I. The alloy has been described in detail,' and the control of the heat treatment has also been published.2 Beneficial effects of such cold work in other alloys have also been pointed out.3'4 NO data have been published on the effects of varying amounts of cold work under fixed aging conditions. In connection with an investigation of the possibility of providing the desired cold work by explosively generated shock waves, it became desirable to investigate the effect of variable cold work, and to compare the re -sults with those obtained from explosives. The general principles of explosive hardening are well-described in the literature.' All material used was guaranteed by the supplier

Jan 1, 1968

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By K. M. Kolobova, E. Z. Kurmayev, A. Z. Menshikov, S. A. Nemnonov, V. A. Trapeznikov

The present work represents a review of our intestigations into the X-ray spectra of solids, which have been carried out by us along two lines of upproach: 1) St@ of the electronic structure of high -rnelting compounds of transition metals; 2) stzddy of the interatomic binding forces by the fine structure of absorption spectra under varying temperature and concentration conditions. With this in mind, int>estigations hare been made into the emission and absorption spectra of the K-series of atoms of transition elements in alloys and compounds. In the problem concerned with the electronic structure of high-melting compounds of transition metals, considerable importance is attached to the question of ascertaining the role played by 3d4sp electrons of metal and 2p electrons of metalloid in the formation of chemical bonds and of giving, on the strength of this data, an explanation of the properties which seem to be contradictory at first sight: good conductivity inherent in metals and high brittleness and high-melting characteristics typical of covalent compounds. Over the last few decades this question has attracted the attention of many investigators whose studies were devoted to this type of compound. Many works, both of theoretical1-3 and experimental4- l5 nature , have contributed much to the elucidation of the physical character of the phenomenon referred to. Alongside the investigations in the field of electric resistance, Hall effect, paramagnetic susceptibility, electronic heat capacity, and the temperature of transformation into a superconducting state, we should particularly emphasize the studies on X-ray spectra, which have played a significant role in the development of the zonal theory for high-melting compounds. This fact has become highly evident after the theoretical calculation of the energy spectrum has been made and the density of states curve in Tic, TiN, and Ti0 has been plotted by Ern and Switendick3 who used the method of augmented plane waves. Correlation of the results of the theoretical calculation of the band structure in the compounds listed above with the data obtained by X-ray spectroscopy studies showed that X-ray spectra can be a source of valuable information on the electronic structure of high-melting compounds within a wide range of ener- gies. It is well known that X-ray emission spectra basically give a direct picture of the occupied excited states above the Fermi level of a solid (valence band, conduction band) and that the absorption spectra (region of initial absorption) give a similar picture of states corresponding to the unoccupied levels near the Fermi surface. Full information on the density distribution of electronic states by energies can be obtained by combining the emission and absorption spectra. Such an opportunity arises from investigation

Jan 1, 1970

By R. O. Williams

Measurements have been made of the internal energy of deformation in a Cu-A1 alloy and a Cu-Zn alloy as the deference between the work and the released heat. The method required the rapid compression of samples to reduce thermal interactions. The rate of energy storage is low initially but then becomes almost linear with strain. Both alloys stored about 60 cal per mole at a strain of 0.4 in the recrystallized condition. The fractional rate of storage increases at low strains reaching about 0.25 at a strain of 0.15 and then decreases slowly with increasing strains. As do pure metals, these alloys release appreciable energy immediately following deformation; in contrast with pure metals, however, the release continued for extended periods of time. This energy release is somewhat sensitive to the amount of deformation, the deformation temperature, and prior thermal & eatment. It is believed that this release is a composite of that observed in pure metals which has been attributed to dislocations and that due to the motion of vacancies which produces increased short-range order. IT is expected that changes brought about by deformation of a pure metal can be understood in terms of the three defects—dislocations, vacancies, and interstitials—along with the interactions possible between these defects. Frequently stacking faults are created and must also be considered. 1t is not immediately clear whether or not the stress fields which are created should be regarded as independent of dislocations. For alloys there is the important additional effect of atomic configuration, for example short-range order, which must also be considered and will, in general, interact with each of the above defects. While it is true that a complete understanding of pure metals is not yet possible, it would seem very valuable to establish the similarities and differences between pure metals and alloys. Such knowledge could contribute to the understanding of both. A study of the changes in internal energy resulting from deformation of two alloys is reported here. Although some information has been available for alloys almost as long as for pure metals, the volume of work has been substantially less. Sato' and Quinney and Taylor' were responsible for the earlier work, both using brass and annealing calorimetry. tizhnova' studied stored energy in Cu-Ni alloys by a method somewhat similar to the one reported here. Bever and his co-workers have made extensive studies of Au-Ag alloys4'5 and more recently CU-AU'U' using solution calorimetry. Clarebrough et a1.' have recently studied brass using annealing calorimetry. EXPERIMENTAL METHOD The present results were obtained by the rapid, adiabatic compression of a sample about 1/4 in, diam by 1/2 in. long between two tungsten carbide hammers. A vacuum provided thermal isolation and oil provided effective lubrication between the sample and hammers. The increase in internal energy is the difference between the mechanical energy and the heat liberated within the sample. The mechanical energy was determined from the velocity of the hammers (calculated from the height through which the hammers traveled) and was essentially constant for each deformation cycle. The heat was determined from the temperature increase of the sample which was measured by an embedded thermocouple. Specific heat data were calculated from Neumann's rule using tabulated data for pure metals.9 Since the fraction of the energy which is stored is large compared to that for pure metals, specific heat data of high accuracy are not required. Successive increments of deformation were carried out by repeating the procedure, the limit being determined mostly by the decreasing accuracy caused by the increasing corrections and the decreasing storage of energy. About five cycles were used to give a true strain of about 0.5 while the time interval between cycles was 1 to 2hr.

Jan 1, 1963

By Miroslaw Hajdasinski

Estimation of the economic effectiveness of industrial development projects including mining ones is generally made on the basis of the discrete model of the value changes in time, although the character of these changes is similar to the continuous model. In this paper an attempt has been undertaken to investigate the problem of the value equivalence of both models exemplified by a construction of an underground coal mine. An effort has been made to determine the errors which for different estimation criteria appear in result of the application of the discrete model. Theoretical considerations have been supplemented with practical conclusions.

Jan 1, 1977

By B. H. Lehnhard, C. J. Cecil

The paper describes the use of the Electric Pilot in the Permian Basin for making permeability surveys of wells and for the selective acidization of wells. A general summary of the information obtained from the many permeability surveys run in this area is given, and the possible application of this information to reservoir control problems is discussed. The application of the Electric Pilot on specific wells, involving well completion, acidizing and workover operations is also included. Introduction The Electric pilot is a comparatively new tool in oil-producing areas. From the beginning, the possibilities of this new service caught the imagination of many of the oil operators and acidizing engineers. Through the continued and ever increasing use of the pilot during the past year, and the close cooperation of the oil operators who have used this service, the efficiency and utility of the Electric Pilot service has been increased to a point where it is now a well established and recognized service. There are two major uses for the Electric Pilot: (I) permeability survey; (2) selective acid treatments. Permeability surveys are made to determine the thickness of the various permeable sections at the borehole, the vertical position of these zones at the bore hole, and the relative capacities of the various zones. Nomenclature Data obtained from the permeability survey are used to calculate three different indexes that pertain to the volume of fluid injected into the various permeable zones. A nomenclature for these various indexes has been set up, which correspond with the various productivity indexes, except that they are a measure of injected fluid rather than produced fluid. The nomenclature and definition of the indexes used in connection with a permeability survey by the Electric Pilot are as follows: 1. Capacity.—The volume of water injected into an individual permeable zone, in gallons Per minute. 2. Capacity Index.—The volume of water injected into an individual permeable Zone, in gallons Per minute Per pound Per Square inch differential Pressure. 3. Specific Capacity Index.—The volume of water injected into an individual permable zone in gallons Per minute Per pound per square inch differential per foot of thickness of the zone at the borehole. Capacity is the most generally used index, and for planning initial acidizing procedures and most workover jobs it is sufficient. For comparing permeability surveys on the same well before and after

Jan 1, 1945

By C. Hertzler

The difference of means of milling characteristics by rock and ore type is tested in a statistical manner in the paper. The null hypothesis being tested is that the sample means of two different populations are equal. It is assumed that the null hypothesis is true when performing the test. Because of this, acceptance of this hypothesis leads to the conclusion that the sample means of the two different populations are equal (or there is no significant difference between the sample means), not that the samples come from the same population, as the author asserts. Rejection of the null hypothesis leads to the conclusion that the sample means of the two different populations are not equal. A P value for this test is reported in Table 2 and is incorrectly identified as the probability that the two samples came from different populations. Actually, what was recorded was 100(1 - p) where p is the usual p-value. The usual p-value measures, on a scale of zero to one, the extent to which the data agree with the null hypothesis. It is the probability of observi" a value of the test statistic (Z score) that is at least as contradictory to the null hypothesis as the one computed from the sample data (McClave and Dietrich 11, 1982). The author makes no mention of the fact that were these tests to be conducted together, the chances of determining that the null hypothesis is not true when it is really true are increased considerably (Snedecor and Cochran, 1980). This is a multiple comparisons problem and should be dealt with accordingly. The usual methods involve adjusting the level of the individual tests. Table 2 reports an incorrect 100(1 - p) value in the comparison of concentrate grades for other rock types with .30 to .69% Cu vs other rock types with .70 + % Cu; 86% should be 98.6%. Although the article can be criticized for poor data presentation and discussion of that data, the point the author makes regarding the use of these statistics in the ore reserve estimation process is well taken. It does not appear that inaccuracies in the statistical interpretations have hindered that usefulness.

Jan 1, 1985

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Wei-Kao Lu, G. Bitsianes

An improved general rate equation for a one-ditnensional gas-solid system has been derived. Fov the veversihle interfacial chemical reaction, there are concentrations of gaseous reactant and product at the reacting zone to be considered. They have been calculated with the velations fuvnished by the constraints on the system, namely, quasi-steady state and equimolal counterdiffusion of the gases. The results of the diffusiori study of Evans, Watson, and ,Mason based on the "dusty gas" model have been applied here. The interfacial chemical reaction is taken as first-order with respect to the concentration of the gases involved. The equation has proper dependence on gas composition and on solid structure through the relative values of Knudsen and normal diffusivities. The existence of the total pressure gradient inside the specimen has been predicted and confirmed experimentally. In a previous communication' we introduced a general rate equation for gas-solid reactions by considering the contributions of chemical reaction at inter- phase boundaries and diffusion through the solid product layer simultaneously. These equations, for one-dimensional and spherical specimens, take care of the whole range continuously from purely diffusion control to purely chemical reaction control. In this paper we study only the one-dimensional system. The corresponding rate equation is reproduced here: Of the two terms on the right-hand side of Eq. [I], the first represents the contribution of interfacial chemical reaction and the second that of gaseous diffusion. The shortcomings of Eq. [I] are that in its derivation the interfacial chemical reaction was assumed to be irreversible and the diffusion rate of gaseous product was not considered. Any pressure effects building up within the porous media were also neglected. Evidently. these simplifying assumptions will limit the general applicability of these equations. The rate of reduction of iron oxide by hydrogen, for instance, is very sensitive to the concentration of water vapor in the main gas stream, as has been reported by cewan' and by Quets et a1.3 Furthermore, the gaseous phase at the reacting interface will contain an appreciable amount of the gaseous product of reaction. If this were not true, a sufficiently high concentration gradient for the outward diffusion of the gaseous product could not be maintained. With these shortcomings in mind, Eq. [1I cannot be rigorously ap-

Jan 1, 1967

By R. Costantini

A. Brebner (Chairman, Dept. of Civil Engineering, Queen's University, Kingston, Ont., Canada) — Under the heading of friction losses, the author, in Eq. 10, gives the relationship

Jan 1, 1962

Jan 1, 1895

By W. T. Bishop, G. A. Crowe

While the literature in the United States on general polarographic technique is extensive, very little appears to be directly applicable to the analysis of flotation tailings. For this reason, it seemed worth while to present a few polarographic methods of ore analysis that have been in constant use in the laboratories of the Hercules Experiment Station for the past few years. At the time of our initial investigation of the polarographic method, there was little or no mention of its specific application to flotation tailings. It was therefore necessary for us to establish suitable conditions for the analysis of our flotation tailings and to consider possible interfering constituents. The polarograph, or dropping mercury electrode, method was discovered in 1925 by J. Heyrovsky and M. Shikata,1 of the Charles University, Prague. This method has since received extensive development and the literature contains many articles on the use of the polarograph for the quantitative determination of metals as well as anions, oxygen in solution, and reducible organic compounds. Kolthoff and Lingane,² by the publication of their book, "Polarography," in 1941 did much to advance the knowledge and use of the polarograph. In chapter 25 of that book, methods for the polarographic analysis of brass, steel and iron products, alloys, and zinc ore are given. Aluminum,³ cadmium,³,4 cobalt,4 cop-per,³-9 gold,10 iron,3,11 lead,³,l2,l³ molybdenum,14 nickel,4,8,9 tin," and zinc³,4,5,7 in ores have been analyzed by the polarograph. However, most of the work on tailing samples has been published in Russian journals and translations are not yet readily available. In this paper we will describe the method that was developed and used in our laboratory for the determination of copper, zinc, and lead in flotation tailings. Principle OF the Method The polarograph is an instrument for applying a potential to a mercury pool and a dropping mercury electrode separated by a solution, and for measuring the resultant electrical current. The procedure is essentially a small-scale electrolysis, in which the voltage required to reduce or oxidize the material identifies it qualitatively and the current measures the concentration quantitatively. Different constituents in a sample may often be determined simultaneously provided they reduce at sufficiently different voltages. An example is the determination of copper and zinc in the same solution. The reduction potentials are quite far apart, as shown in Fig. I. The polarographic method is particularly useful in the range of concentration between those normally determined by spectographic and chemical methods. In

Jan 1, 1947