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Discussion of the paper of K. Huessener, (Trans., vol. 53, pp. 402 to 4333, and of the papers of Linn Bradley, H. D. EGbert and W. W. Strong, pp. 303, 319. R. J. WysoR, So. Bethlehem, Pa. (communication to the Secretary*). —At our plant (Bethlehem Steel Co.), we have had several Bradshaw burners under course of construction and erection for some time, but up to the present we have not had opportunity to put them in service. I regret that I can not take part in the discussion with some actual results from these burners. Mr. Huessener properly emphasizes the importance of obtaining the highest combustion temperature practicable in boiler practice, which demands a near approach to perfect combustion conditions. The ideal burner is the one which, while meeting the various mechanical requirements, fulfills the above condition under a wide range of gas pressure. The question as to the relative value of hot raw gas and cold washed gas for boiler use is a very interesting one. I think that in the past the importance of low temperature of washed gas sometimes has been overemphasized. Mr. Huessener has pointed out that so far as temperature is concerned, no advantage accrues in washing gas below 100" F. In many plants, there is a notable operating economy in using furnace cooling water, which is appreciably warmer than the supply water. However, in a given type of washer, other conditions being constant, the lower the exit gas temperature the lower will be the dust content; this is equivalent to saying that the more washing water is used, other conditions being constant, the lower will be the dust content of the exit gas. For each type of washer there is a certain desired average temperature difference between inlet water and exit gas, concomitant with known average dust and moisture contents, and with economical operation. With the present tendency toward smaller stove checkers, it is generally agreed that gas for stove use should be cleaned to a dust content of 0.20 grain or less. The method employed and extent of gas cleaning are clearly problems for individual furnace plants. As a general proposition, wet washing is decidedly more attractive for furnaces smelting soft, fine Lake ores than for those reducing chiefly hard, lumpy ores, such as the foreign and domestic magnetites. In the former case the average moisture content of the gas is probably 35 grains per cubic foot, the dust content is relatively high and the top temperature relatively low. In our plant, the ore mixtures consist almost exclusively of hard magnetites. The average dust content of the gas leaving the dust catcher will average only about 2 grains and the moisture about 12 grains per cubic foot, corresponding to saturation at about 83" F. The temperature is fully 100" F. higher

Jan 1, 1917

By M. J. Pool, C. E. Lundin

THE relative partial molar enthalpies of aluminum, gallium, and indium in liquid tin have been measured at 750°K by liquid-metal solution calorimetry. The measured heat effects and the calculated relative partial molar heats of solutions at infinite dilution are listed in Table I along with the relative heat contents of the solutes calculated from the data of Kelley. All of the values are referred to 750°K even though the calorimeter temperature fluctuated by +1°K during the entire series of experiments. The effect of this small temperature variation on the experimental values should be less than the experimental error. The limits of error given in Table I represent the standard deviations of all values from the mean. In no case was the experimental deviation greater than the listed error limits. The reported error estimates only apply to the estimated precision of experimental values and not to their accuracy. Systematic errors could be present in the calorimeter which would affect the absolute values given. Moreover the heat-content data used could also be in error and this would affect the end results. The relative enthalpies used were listed in Table I so that future corrections could be made if necessary. The relative partial molar heats of solutions of aluminum in liquid tin and dilute A1-Sn liquid solutions are large and positive. The value at infinite dilution is given in Table I. In the dilute-solution region investigated the relative partial molar heat of solution was a linear function of composition. A least-squares analysis of the data gave the following expression at 750°K: Atf^ = 6195 - 12,160 A:A1(cal/g-atom) where XA1 is the mole fraction of aluminum in the alloy. This can be compared with the data of Cohen, Howlett, and ever' who obtained the expression: 1SM = 6075 - 10,750 XM at 573°K Apparently both the partial molar heat of solution at infinite dilution and the concentration dependence increase with increasing temperature. This same

Jan 1, 1964

By N. Jaffe, J. E. Dorn

The effect of stress on the creep rate of high-purity poly crystalline aluminum in the intermediate temperature range was investigated by conducting creep tests at a series of different stresses and by decreasing the stress abruptly during the course of primary and secondary creep. Three series of decreases in stress tests were conducted: the stress was decreased in primary and secondary regions of creep at 347.5°K and the stress was decrensed in primary creep at 327°K. The results demonstrate the effects of structure and temperature on the stress dependence of the creep rate. The trends in the creep rate after a drop in stress are complicated and show that recovery takes place. The experimental results were compared with Friedel's theory for cross-slip, the experimentally determined energy for a constriction being in good agreement with the theoretical estimate proposed by Stroh. PREVIOUS investigations have shown that the ap-- parent activation energy for creep of polycrystalline aluminum, over the range from about 250° to 380°K, is approximately 27,400 cal per mole,' a value that is to a first approximation insensitive to the applied stress, the creep rate, and the creep strain. Several facts strongly support the thesis that creep, in this temperature range, is controlled by the rate-determining mechanism of cross-slip: 1) Recovery of the cold-worked state can take place by a number of mechanisms prominent among which is climb and cross-slip. Astrom2 reported rapid recovery of cold-worked polycrystalline aluminum at 340° to 370°K giving an activation energy of 28,000 cal per mole and additional recovery at the higher temperatures of 455° to 478°K giving an activation energy of 36,000 cal per mole. Whereas the latter process was clearly identified with the climb mechanism, the former process. which has an activation energy in good agreement for that of creep in the same temperature range, is most likely due to recovery by thermally-activated cross-slip. 2) Single crystals of aluminum exhibit sharp slip-

Jan 1, 1962

By Charles R. Simcoe

The stress-strain curves in the microyield region for various Fe-C solid solutions shown by Davies and Ku are typical examples of parabolic curves defined by the expression a = kEn 111 These data, when replotted on log-log coordinates, as shown in Fig. 9, exhibit three essentially parallel straight lines. It is apparent that carbon increases the flow stresses, but does not affect the exponent n. In other words, the only factor in Eq. [1] affected by in in carbon content is the constant k. As Eq. [1] is written k is the stress at a strain of 1.0. This is unsatisfactory for examining data in the microyield region. Therefore, the equation can be altered to the form: to permit the use of the authors' microyield stress at a strain of 10-6 as k. Extrapolating the curves in Fig. 9 to a strain of 10-6 gives stress values of 2000, 3200, and 5400 psi for 0.008, 0.014, and 0.02 pct C, respectively. These values do not agree exactly with the authors' measured values, but this will not affect the following discussion. The effect of carbon content on the slopes of the stress-strain curves shown in Fig. 2 of the paper by Davies and Ku can be analyzed by differentiating Eq. [2] with respect to strain. Thus: where n is always less than 1.0. Since n is essen- tially constant as a function of carbon content for the data under discussion, the slopes of the stress-strain curves depend only on k and E. If the slopes are examined at various selected Plastic strains. i.e., 10-6, 10-5, and so forth, it follows from Eq. [3] that the dif-ferent slopes for the different carbon contents depend only on the different values of ke=10-6. Thus, the larger ke=10-6, the steeper the linear stress-strain curve will rise with increasing plastic strain. This

Jan 1, 1969

By Reuben B. Ellestad, Fremont F. Clarke

In the early days of the lithium industry most of the production was from lepidolite, zinnwaldite, and amblygonite. Nearly all the early extraction processes described in the literature involve heating the finely ground mineral with sulphuric or hydrochloric acid. On subsequent water leaching most of the bases present in the mineral (especially aluminum) are dissolved as sulphates. As a result, the leach solution required extensive chemical purification before the lithium could be precipitated as carbonate. Following the remarkable growth of the lithium industry to its present size, zinnwaldite and amblygonite ores must be considered of minor importance only. Attention is now focused on spodumene, abundant enough in North America to be a major source of supply, and there are important supplies of lepidolite and petalite in Africa. The extraction processes described below all apply to spodumene, although several will also operate on other lithium minerals, such as petalite. Base Exchange with Alkali Sulphates: A distinct advance was made with the disclosures of Wadman and von Girsewalt. In these methods the finely ground silicate ore (spodumene or lepidolite) is intimately mixed with an excess of alkali sulphate (usually K2S04) in at least a 1 to 1 proportion, and the mixture was heated to a relatively high temperature. Base exchange results, with the formation of lithium sulphate. A water leach dissolves the lithium sulphate, together with the excess potassium sulphate. Successful operation of this type of process requires very thorough grinding and mixing, as well as careful temperature control. The use of K,SO, is objectionable from cost considerations since purification of lithium carbonate re- quires the use of potassium carbonate, if the K2S04 is to be recovered and recycled. The lower solubility of K,SO, as compared with Na,SO, is also objectionable, since it limits the concentration of the Li,SO, solution to be precipitated by K,CO,. Early laboratory-scale investigation of this process by Lithium Corp. was not encouraging

Nov 1, 1955

By Thomas C. Wilder

The activities of both components and the partial and integral molar thermodynamic properties of mixing for the liquid Al-Ge system at 1200°K and for the gertnanium-rich Al-Ge liquidus have been determined from data for eighteen alloys of compositions in the range 0.0593 < 0.880 using the reuersible gal-vanic. cell in the temperature interval 9320 to 1258°K. The liqui-dus compositions above 93 2 °K loere also ve determined by observing the discontinuities in the C us T plots for the high-melting alloys. This system shows moderate negative deviation from ideality throughout, the values for y° being 0.212 and 0.189 for aluminum and germanium, respectively, at 1200°K. Pavtial molar Properties of aluminum on the germanium-rich solidus and at infinite dilution in Ge(s) oboue 932°K were estimated from the foregozng measurements and the equlibrium data of previous investzgators. RECENT compilations of data1" have shown an increasing demand for knowledge of the thermodynamic properties of mixing of metallic alloy systems. In the case of binary-liquid systems where one of the components is a semiconductor this information is useful because, primarily, properties of the second (dopant) component on the liquidus, solidus, and at infinite dilution may be determined more accurately than from calculations based on the phase diagram. In this investigation a reversible galvanic cell was used to determine the chemical potential of aluminum in the two-phase region, liquid + [Ge], on the germanium-rich side of the A1-Ge system in the temperature range 932" to 1193°K. In addition, similar measurements for homogeneous liquid A1-Ge alloys for the entire composition range were obtained for the temperature interval 932" to 1258°K. The cell used was: The experimental technique and the treatment of the data were essentially the same as described earlier394 and are elaborated upon only briefly here. Each cell consisted of a liquid aluminum anode and three A1-Ge alloy cathodes of different composition which were held in Morganite alumina crucibles. The alloys were made up from aluminum and germanium weighed to the nearest 0.1 mg to a total weight of 5 to 10 g. Aluminum was a gift of Aluminum Co. of America and had a purity of 99.995+ pct. Germanium of transistor grade was a gift of Bell Telephone Laboratories. The four electrodes were contained in a larger alumina crucible which also held the prepurified fused chloride electrolyte. Contact to the electrodes was made by tantalum wire leads sheathed in alumina. The tantalum leads were centered in the electrodes by suitable positioning of an alumina radiation shield which fitted on the top of the - alulnina crucible. Two chrome l-alumel thermocouples, sheathed in quartz wells, completed the internal cell arrangement. The entire assembly was enclosed in an alumina tube, fitted with a water-cooled copper head so the system could be evacuated and then flushed with purified argon. *

Jan 1, 1967

By H. W. Schadler

Single crystals of tungsten, which were grown by electron bombardment floating zone refining, were strained 2 pet in tension and bending at 298°, 77°, and 20°K to determine the modes and crystallography of the plastic deformation of these temperatures. At 77° and 20°K plastic deformation occurs by slip on systems of the type (011) [111] and by twinning on (112)-type planes. For crystals strained at 298°K, deformation occurs by slip in [111] directions on either (Oil)- or (112)-type planes. CURRENT models for the initiation of brittle fracture in crystalline materials are based on a knowledge of the details of their plastic deformation.1 Body-centered cubic tungsten exhibits brittle failure at temperatures below about 500 °K yet the modes and crystallography of its plastic deformation have not been studied below 1000°K. In 1924, Goucher2 reported that tungsten single crystals with a total impurity content of less than 0.01 wt pet deformed by slip on the (112) [111] system in the temperature range 1000° to 3000°K. He also observed (001) [010] slip in one crystal which was constrained by the presence of a large fissure. According to Barrett3 tungsten also deforms by twinning on the (112) plane in the [111] direction, but he gives no details on the tendency for twin formation or the temperature range in which twinning occurs. Therefore, as a necessary part of a study of the factors influencing the brittle fracture of tungsten, the modes and crystallography of the plastic deformation were determined at 298°, 77°, and 20°K. Tungsten single crystals, grown using the electron-bombardment zone-refining technique first described by Calverly,4 were deformed to between 1 and 2 pet plastic strain in tension and bending. The surface offset resulting from slip or twinning was observed with an optical microscope to determine the crystallography of the deformation. The existence of twins was proven by the standard polishing and etching technique; and the crystallography of dislocation motion was followed using the dislocation etchant described by Wolff.5 Some observations on the fracture characteristics of tungsten single crystals are included. EXPERIMENTAL TECHNIQUES Growth, Purity, and Perfection of the Crystals-Several years ago Calverly, Davis, and Lever4 dem-onstrated the feasibility of growing tungsten single crystals by the electron-bombardment floating zone-refining technique, and Carlson6 showed that crystals produced in this way had a high degree of purity and were ductile at room temperature. Tungsten single crystals produced by this technique in equipment similar to that described by Carlson were used in this study. The starting material, a powder metallurgy product, was obtained in the form of a swaged 1/8-in. rod from the General Electric Wire Plant in Cleveland, Ohio. The crystals were grown from this material in a vacuum of 10"4 mm of Hg by passing a molten zone 1/8 in. long down the rod twice at a speed of 3 mm per min. At this zone speed

Jan 1, 1961

By John M. Campbell, W. E. Portman

A series of correlating charts have been prepared to enable the field engineer to predict the amount of stock tank fluid produced by stabilization of first stage separator fluid. The charts shown are particularly convenient for estimating the relative effect of temperature and pressure in economic studies. Further work is planned to investigate the factors affecting stage separation&apos; yo supplement this preliminary work. The direct correlation of separation variables is dictated as a convenience to eliminate the trial and error calculation necessary when using the standard flash vaporization equations. These are obtained by a material balance using the equilibrium vaporization ratio K, and have appeared in the following, or similar. form many times in the literature. where La = mols of any component n in the separator liquid Ko — equilibrium vaporization ratio for any component at separator pressure and temperature Fa = mols of any component n in the feed Vn = mols of any component n in the vapor V = total mols of separator vapor These equations may of course be effectively and accurately solved by use of digital and analog computers. However, these are not usually readily available in field offices and the need often arises for fast results during routine operational problems. Consequently, many methods have been devised in an attempt to simplify the basic calculation.2-14 The methods proposed are generally satisfactory, but do not eliminate trial and error methods and the necessity of subsequent calculations to obtain the answer in volume terms. The purpose of this work. therefore, was to develop accurate charts that would give the result directly in gallons. When using stage separation the recoveries would be lower than those shown, for stabilization usually gives about 95 + per cent recovery on the potential stock tank components in the separator liquid. The recoveries are shown in terms of a 14 psi Reid Vapor Pressure product which has a true vapor pressure of 14.7 psia at 98°F. Consequently, this product represents a stable stock tank liquid under normal storage conditions. To estimate natural gasoline re- coveries by stabilization the volume shown may be multiplied by 1.20 for 18 Ib RVP natural gasoline and 1.36 for 26 lb RVP natural gasoline. PROCEDURE The five analyses shown in Table 1 were chosen since they were representative of wellstream compositions often found and had almost the same propanes plus liquid content, expressed in gallons per 1,000 std. cu ft of wellstream. The distribution of the components though is widely variant. A temperature range of 0-100°F. and a pressure range of 200 to 1,250 psia was chosen inasmuch as most separations fall within these limits The K values used were modified values of those originally published by Katz and Hachmuth.&apos; In the range chosen these have generally given good results when predicting fluid recoveries. The choice was somewhat arbitrary, for the authors&apos; personal experience has shown that

Jan 1, 1957

By Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x Y x 100 ? x/A A [1] A+ B x + A/B(100-x) X _ 100yA 100y [2] yA+(100-y)B or y+A(100-y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are&apos; time consuming if several conversions have to be made. In 1931 Water-man&apos; constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Olander2 has proposed a graphic method simpler than Waterman&apos;s and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation:

Jan 1, 1933

By Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x or 1 x/A+100-x/B B(100-x) _ 100yA 100y [2] X. yA + (100 - y)B or y (100 - y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are time consuming if several conversions have to be made. In 1931 Water-man1 constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Ölander2 has proposed a graphic method simpler than Waterman&apos;s and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation

Jan 1, 1933

By W. R. Hibbard

THE classical work on the electrical conductivity of alloys was carried out by Matthiessen and his coworkers1 in the early 1860&apos;s. He attempted to correlate the electrical conductivity of alloys with their constitution diagrams, but the information regarding the latter was too meager for success. Guertler2 reworked Matthiessen&apos;s and other conductivity data in 1906 on the basis of volume composition (an application of Le Chatelier&apos;s principle with implications as to temperature and pressure effects), and obtained the following relationships between specific conductivity and phase diagrams (plotted as volume compositions) : 1—For two-phase regions, electrical conductivity can be considered as a linear function of volume composition, following the law of mixtures. 2—For solid solutions, except intermetallic compounds, the electrical conductivity is lowered by solute additions first very extensively and later more gradually, such that a minimum occurs in systems with complete solid solubility. This minimum forms from a catenary type of curve. Intermetallic compound formation with variable compound composition results in a maximum conductivity at the stoi-chiometric composition. Landauer" has recently considered the resistivity of binary metallic two-phase mixtures on the basis of randomly distributed spherical-shaped regions of two phases having different conductivities. His derivation predicts deviations from the law of mixtures which fit measurements on alloys of 6 systems out of 13 considered. Volency (Ionic Charge) Perhaps the first comprehensive discussion of the electrical resistivity of dilute solid-solution alloys was presented by Norbury&apos; in 1921. He collected sufficient data to show that the change in resistance caused by 1 atomic pct binary solute additions is periodic* in character. The difference between the period and/or the group of the solvent and solute elements could be correlated with the increase in resistance. Linde5-7 determined the electrical resistivity (p) of solid solutions containing up to about 4 atomic pct of various solutes in copper, silver, and gold at several temperatures. He reported that the extrapolated"" increase in resistance per atomic percent addition is a function of the square of the difference in group number of the solute and solvent as follows: ?p= a + K(N-Ng)2 where a and K are empirical constants and N and Ng are group numbers of the constituents. This empirical relation was subsequently rationalized theoretically by Mott,8 who showed that the scattering of conduction electrons is proportional to the square of the scattering charge at lattice sites. Thus, the change in resistance of dilute alloys is propor-t,ional to the square of the difference between the ionic charge (or valence) of the solvent and solute when other factors are neglected. Mott&apos;s difficulty in evaluating the volume of the lattice near each atom site where the valency electrons tend to segre-gate: limited his calculations to proportionality relations. Recently, Robinson and Dorn" reconfirmed this relationship for dilute aluminum solid-solution alloys at 20°C, using an effective charge of 2.5 for aluminum. In terms of valence, Linde&apos;s equation becomes ?P= {K2 + K1 (Z8 -Za)2} A where K1 and K2 are coefficients, A is atomic percent solute, Z, is valence of solvent, and Zß, is valence of solute. Plots of these data for copper, silver, gold, and aluminum alloys are shown in Fig. 1. The values of K1 and K2 are constant for a given chemical period (P), but vary from period to period. The value of K, increases irregularly with increasing difference between the period of the solvent and solute element (AP), being zero when AP is zero. The value of K, appears to have no obvious periodic relationship. All factors other than valence that affect resistivity are gathered in these coefficients. Because of the nature of the coefficients, Eq. 1 is of limited use in estimating the effects of solute additions on resistivity unless a large amount of experimental data are already available on the systems involved. It is the purpose of the first part of this report to investigate the factors that may be included in the coefficients of Linde&apos;s equation. On this basis, it is hoped that the relative effects of solute additions on resistivity can be better estimated from basic data, leading to a more convenient alloy design procedure. It is well 10,11 that phenomena that decrease the perfection of the periodic field in an atomic lattice, such as the introduction of a solute atom or strain due to deformation, will also increase the electrical resistivity. Thus, in an effort to relate changes in electrical resistivity to alloy composition, it appears appropriate to consider the atomic characteristics related to solution and strain hardening

Jan 1, 1955

By William Marsh Baldwin

[Two of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Hencky1-3 and the St. Venant7-10 equations. HUBER-VON MISES-HENCKY EQUATION The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,? al, a2, and a3 satisfy the equation: (s1 - s2)2 + (s 2 - s 3)2 + (s 1 ? s3)2 = 2K2 [I] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities a1, a2, and a3 are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4,5 (Fig. I). The radius of this cylinder is v2/3K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values s 1/K = si, s 2/K = s2, s 2/K = s3 to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (s1 - S2)2 + (S2 - S3)2 + (Sl - S3)2 = 2 [2] and the radius of the cylinder becomes 2/3v. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elastically, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates s1, s2, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordi¬nate axes). Let us now pass a line through the point on the circle and the point on the axis.]

Jan 1, 1946

By K. S. Milliken

NORMAN W. Lord&apos; has shown that the resultant impurity distribution after n zone passes is given by in the ingot section OSa<N—n, where a is the displacement in zone lengths, N is the ingot length in zone lengths, C,, is the initial uniform impurity concentration, k is the segregation constant = Ceoll C,,,,,,,, at equilibrium, and The foregoing expression is formidable in respect to computational labor. However, the triple sum can be reduced as follows is better if computing for only a single value of n. For k<l, it can be shown that this last equation is equivalent to The infinite series is useful only when k is small enough to force rapid convergence. In such cases, the absence of subtraction from unity has the definite advantage of preserving accuracy. Acknowledgments It is a pleasure to acknowledge stimulating correspondence with Dr. Howard Reiss of Bell Telephone Laboratories Inc. This note is published by permis-sion of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By G. Wakefield, A. H. Daane, D. H. Dennison, F. H. Spedding

Preparation of pure scandium metal was accomplished by calcium reduction of the fluoride by two methods; a low-temperatzdre alloy process and direct reduction with subsequent distillation of the product. The following properties were determined: melting point: 1181OK; boiling point (calculated): 3000°K; lattice constants at 298°K (hexagonal lattice): a = 3.308 * 0.001 A, c = 5.267 * 0.003A; calculated density at 298°K, g per cm3: 2,990 + 0.007; electrical resistivity, ohm-cm: 299°K, 66.6 ± 0.2 x 10 -6; 373oK, 77.4 * 0.2 x 10 -6; thermal coefficient at 299°K, ohm-cm per deg: 5.4 X x; heat of sublimation at 298°K, kcal pel- mole: 80.79. The vapor pressure was determined as a function of temperature between 1505o and 1748°K, with the data fitted to a straight line shielding the equation: Log Pmm = -1.718 X 104/ToK + 8.298. SCANDIUM, element number 21, was first discovered by Nilson in 1879 and was recognized as the Ekaboron as predicted by Mendeleff. As it is in group III of the periodic table, the general properties are a little like aluminum and also resemble quite closely the properties of yttrium and the rare-earth metals, in both the metallic and ionic form. Although the earth&apos;s crust contains approximately 5 ppm of scandium (the element is as abundant as arsenic and twice as abundant as boron) it generally occurs so widely distributed that it has earned the reputation of being very rare. The one exception to this is the mineral thortveitite, which has been found in Madagascar (20 pct Sc2O3) and in Norway (35 pct Sc2O3). Scandium also occurs in small but distinct amounts in uranium and rare-earth ores; the recent larger scale processing of these materials has made some scandium available from these sources. As with other naturally-occurring monoisotopic elements (except Be), scandium contains an odd number of protons and an even number of neutrons. Scandium metal was first prepared by Fischer and coworkers1 in 1937 by electrolysis of scandium chloride in a molten eutectic mixture of lithium and potassium chlorides, using molten zinc as a cathode and collector of the scandium metal produced. The zinc was removed from the Zn-2 pct Sc alloy by vacuum distillation, leaving a product reported to be 94 to 98 pct Sc, with the main impurities being iron and silicon. They reported a melting point of 1400° C for this material. Scandium has also been prepared by the reduction of scandium chloride with potassium metal in a glass apparatus by Bommer and Hohmann in 1941,&apos; resulting in a mixture of metal and potassium chloride; these workers did not isolate the metal proper, but the X-ray diffraction of the slag-metal mixture showed it to be hexagonal with a = 3.30A, c = 5.45A. petru3, 4 and coworkers have recently reported the preparation of the metal in a compact form by the reduction of either ScF3 or ScC13 with calcium metal and subsequent distillation of the product. This process probably yielded a metal of high purity, but they list no chemical analysis nor do they list any of the properties of their product. Previous related work in this Laboratory has been concerned with the production of yttrium and the rare-earth metals and the determination of their physical properties. Because of its similarity to these metals, scandium is being included in this study. PREPARATION OF SCANDIUM METAL The preparation of yttrium and the rare-earth metals may be accomplished by reduction of their fluorides with calcium metal in tantalum crucibles.5 This process leads to the introduction of tantalum (up to 0.5 pct) as an impurity in the higher melting rare earths, but since the tantalum occurs as dendrites, uncombined with the rare-earth metals, its presence is not objectionable in some cases. The preparation of scandium metal in this manner, however, was found to yield a product containing 2 to 5 pct Ta. To obtain a purer product, the following two methods were developed for the reduction of scandium fluoride with calcium metal: i) a low-temperature process utilizing zinc to form a low

Jan 1, 1961

By D. E. Peacock, B. Harris

Thermal-expansion and electrical-resistivity measurements have been carried out below 400°K on niobium and two niobium alloys containing tungsten. For anonaly in the expansion us temperature curve below aboct 300°K. This reslt is consistent with an earlier obsercation that Young&apos;s modilus joy Cb-132 lms an unusiully strong -tenperati-e dependence below roon temperature. No anonulous behavior was observed in the resistiuity vs temperature curve for either alloy or in the magnetic susceptibility us tenperature curve for Cb-132. These results are disclssed in terms of various electronic and bonding theories of the transition metals and their alloys, but it has not been possible to reach any definite conclusion as to the cause of the results obtained. ALONG with investigations of the low-temperature mechanical behavior of niobium and its alloys, some of the physical properties of these materials have also been studied. In the work described here, thermal expansion and electrical resistivity were measured below 400°K for niobium and two of its alloys, Cb-132 and D-43. In addition, the magnetic susceptibility of Cb-132 was measured over the same temperature range. The alloys are representative of two distinct tion-hardened alloy such as might find service as a turbine blade, while D-43 (Nb, 5.3 at. pct W, 1.1 at. pct Zr. and 0.08 at. pct C) is a solution- and dispersion-hardened alloy, of considerably lower strength than Cb-132. which is a potential vane material. Their significant common feature is the presence of tungsten as the principal source of solution hardening. EXPERIMENTAL TECHNIQUES Thermal-expansion measurements were made with a quartz-tube dilatometer using baths of liquid nitrogen, liquid bromoethane, and a liquid polyalkylene glycol derivative to cover the range 80 to 400 K. Results are recorded as expansion relative to that of quartz, and the probable maximum error in any value of relative expansion. All, is about il pct. The metallurgical condition of the specimens, which were in rod form. will be discussed in the section dealing with experimental results. Resistivity was measured on recrystallized wires 0.030 in. in diam using a potentiometric technique. The same baths were used for temperatures between 80&apos; and 400°K as were used for the expansion measurements. and in addition the resistance of D-43 and Cb-132 was measured at 4.2 K by immersion in liquid helium. The maximum expected experimental error in any resistivity value is about 3 pct and that in any change in resistivity about i0.05 pct. Temperatures in both sets of experiments were measured with liquid-in-glass thermometers with an accuracy usually better than 1°K. EXPERIMENTAL RESULTS 1) Thermal Expansion. In Fig. 1 is shown the relative linear expansion of recrystallized niobium. D-43. and Cb-132. The curve for Cb-132 is composed of results from several runs on three different samples. Two of the samples were annealed for an hour at 1500°C to cause recrystallization and the third was annealed for an hour at 2000&apos;C to remove some mi-crosegregation of tungsten which was known to be present in the wrought alloy received from the manu-

Jan 1, 1967

By C. C. Herrick

The vapor pressure of indium has been measured by the torque-effusion technique, as a function of temperature between 1102o and 1422oK. For liquid indium, the vapor pressure (in atmospheres) can be represented by the equation -R In P = 5.782 x104/T - 25.29from 1000o to 1422oK. Extrapolation yields a calculated normal boiling point of 2329°K and a heat of vaporization at 298 oK of 58.09 kcal per mole by the third-law method and of 58.39 kcal per mole by the second-law method. Calculations indicate that the free-energy functions of Hultgren are to be preferred to those of Guruich. BECAUSE of the potential uses of liquid metals, it is important that convenient experimental methods be developed which will lead to a sufficient body of thermodynamic data so that reasonable estimates of properties of liquid metals can be made. Indium is particularly well-suited to investigation, since it remains liquid over a long temperature interval, it alloys readily, suitable containers for it are easily procured, and relatively few investigations of its thermodynamic properties in the region above 1000°K have been made. PREVIOUS RESEARCH The first determination of the vapor pressure of indium was made by Anderson,&apos; using the Knudsen method and silica-lines stainless-steel cells. Kohlmeyer and spandau2 determined the normal boiling point, and a mass-spectroscopic investigation has been made by Lyubimov and Lyubitov.3 (Unfortunately, only an equation representing the data of the latter investigators has been available to us.) Hultgren et al.4 and Gurvich5 have published discordant tables of the free-energy functions for indium. EXPERIMENTAL METHOD The torsion-effusion principle has been described amply in the literature.8,7 With this method, one observes the angular deflection induced by effusion of vapor from a multihole effusion cell which is suspended from a filament producing a small rotational restoring force. The pressure within the effusion cell can be computed from the relation ziaifiai where k is the torsion constant of the filament, 6 is the observed angular deflection, and ai, fi, and qi are the area, force factor, and moment arm of the ith effusion orifice. The force factor f is analogous to the Clausing factor,&apos; and corrects for the reduction in effusive force attributable to the finite geometry of the effusion orifice. Schultz and Searcy&apos; have tabulated the force factors for various tube geometries. EXPERIMENTAL APPARATUS The physical arrangement employed in this study is shown in Fig. 1. The furnace elements are six Globar heat rods with 15-in. hot zones. Temperature is maintained to * 1°K by a Beck mechanism driving two 26-amp Powerstats in parallel. A Pt (Pt, Rh 10 pct) thermocouple serves as the sensing element. Four inner tubes act as vibration isolators; the air pressure required for maximum isolation was determined empirically, and is maintained by a solenoid valve. The tungsten fiber, 9 by 0.002 in., is joined to an 0.008-in. tungsten wire or graphite rod via a machined lightweight chuck.

Jan 1, 1964

By L. W. Davies

ONE of the most important applications of the zone-melting process of Pfann1 concerns the refining of materials with respect to impurities whose distribution coefficient k differs from unity. The repeated passage of molten zones along an ingot concentrates the impurities for which k < 1, for example, towards the end to which the zones move. It is desirable to know the ultimate distribution of impurity after the passage of an infinite number of zones of constant length; this is also the distribution which is unchanged by the passage of a further molten zone.

Jan 1, 1959

By G. B. Craig, B. Ramaswami

The temperature and strain rate dependence of the flow stress ratio and the stvain rate dependence qi the flow stress of annealed polycrystalline a zirconiur were determined over the temperature range 30 0" to 1000°K. Some evidence was found for strain aging and discontinuous flow in the temperature ranges 520" to 650°Kand650" to 760°K, respectively. The Cottvell-Stokes relationship was obtained when deformation occurred by twinning as well as slip. The flow stress ratio showed a strong dependence on temperature and strain rate above 800°K. The expevirnental evidence indicated that the rate-controllitzg mechanism for the deformation of a zirconium above 800°K was dislocation climb, and that the deformation was not thermally activated in the range 520" to 800°K. The stacking-fault energy of a zirconium was estimated to be about 250 ergs per sq cm. A knowledge of the temperature and strain rate dependence of the applied stress necessary to deform a crystalline solid is essential for understanding the thermally activated processes occurring during deformation.&apos; Several experimental techniques have been developed for studying these processes.273 One of the techniques is the deter mi nation of the strain rate dependence of the flow stress at constant temperature. In close-packed crystals, it has often been observed that the change in stress due to a change in the strain rate varies linearly with the flow stress, (~1,&apos; This relationship, known as the Cottre ll-Stokes law, is obeyed when deformation occurs by glide alone. However, when deformation occurs by twinning as well as glide, there is disagreement among different investigators on whether the Cottrell-Stokes law is observed. Whereas Thornton et ~1.~find departures from Cottrell-Stokes law when twinning occurs in copper, ~avis~ and sasinski? find that Cottrell-Stokes law is obeyed when deformation occurs by twinning as well as slip in cadmium and magnesium, respectively. One of the main objectives of this study is to determine whether the Cottrell-Stokes law is obeyed when deformation occurs by twinning as well as slip. The second technique that has been used extensively to study the thermally activated deformation of crystals is the determination of the ratio of the flow stresses, at identical dislocation structures and con-

Jan 1, 1968

By Y. A. Chang

Heat content values of tantalum monocarbide and tungsten monocarbide have been determined from 325" to 985°K by means of a drop-type diphenyl ether calorinzeter. Based on the values obtained in the present study and those available in the literature, best values lected and computed from 298. 15°K to temperatures close to their respectiue melting points. At temperatures higher than 1700°Kfor TaC and 27000 K for WC, values of Cp and related thermodynamic quantities were extrapolated based on the two Debye parameters: one corresponds to the metal sublattice and the other to the carbon sublattice. The contrzbutzon In the total specific heat due to lattice dilation was evaluated using the Nernst-Lindemann relalionship. The calculated values of Cp were in good agreement with the In view of their refractoriness, tantalum monocar-bide (TaC) and tungsten monocarbide (WC) are of con- experimentally determined ualues. Furthermore, the calculated values of the absolute entropies at 298.15"K were 5.03 and 4.15 in comparison to the experimental values of 5.05 and 4.15, all expressed in the unit of cal per degg-atom. Using the same Debye parameters, values of the linear coefficients of ther mal expansion for TaC and WC were calculated from absolute zero to their respective melting points using the Grüneisen equation. The calculated values are in excellent agreement with the experimental values available in the literature. Finally, the values of the bulk modulus of TaC from room tenzperature to temperature near its melting Point were also calculated using the equation recently derived by Anderson. No cot~ipari-son between the calculated and experimental values can be made due to lack of experimental data. siderable practical interest. In order to completely define these materials, it is necessary to know their thermal properties as a function of temperature. Tantalum rnonocarbide having a NaCl structure (B-1 type) melts congruently at 4250PK,1 while tungsten monoearbide with a simple hexagonal structure (Bh type) melts per itectically at 3049°K into melt and graphite.2 In the present study, the heat content values (from which

Jan 1, 1968