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By E. T. Turkdogan, Klaus Schwerdtfeger

OelSEN and Maetz1 detected some 20 years ago the existence of a miscibility gap in iron oxide-CaO-P2O5 slags melted in iron crucibles at about 1400°C. Because of the importance of this system for the dephos-phorization of steel in the basic Bessemer process, equilibria between liquid iron and selected iron oxide-CaO-P2Q slags have been measured since by numerous investigators.2-5 When in equilibrium with metallic iron, the iron oxide of the slag is present mainly as FeO. In connection with oxygen-blowing steelmaking processes, it is useful to know the phase relations in the slag system at higher oxygen pressure, when major parts of the iron oxide are present as Fe2O3. This problem was investigated by Turkdogan and Bills7 by equilibrating the oxide mixtures contained in platinum crucibles with CO2-CO mixtures at 1550°C. It was found that increasing the Fe2O3 content decreases the composition range of the miscibility gap strongly so that the miscibility gap has almost disappeared at pco2/pco = 75. This result was refuted by the careful work of Olette et a1.,''' who equilibrated their slags with controlled Ha-H2-Ar gas mixtures. Their equilibrium measurements, at 1600°C and at oxygen pressures of 5 x 10"* and 10"5 atm, showed that the oxidation state of the iron has almost no influence on the formation of the miscibility gap. The present experiments were undertaken to check the previous results of Turkdogan and Bills. The experiments were performed at 1625°C in the strongly oxidizing atmosphere of air (PO2 = 0.20 atm) for which no experimental data are available. About 10 g of slag were melted in platinum crucibles and held at constant temperature for 1 hr. After equilibration, the crucible was rapidly pulled out of the furnace and cooled in air. The platinum crucible was removed from the sample. The two slag layers were carefully separated with a small diamond disc, and the surface of the top layer, which may have changed its oxidation state during cooling, was removed. The slags were crushed and analyzed chemically for CaO, P2O5, Fe2+, and Fetotal. The starting mixtures were prepared by sintering the desired amounts of reagent-grade 2CaO . P2O5 - H2O, CaCO3, and Fe2O3. Sintering and subsequent crushing were done three times to ensure homogenization. Molybdenum wire resistance heating was used. The furnace was provided with a recrystallized alumina reaction tube which was left open to air at the top. The temperature was controlled electronically. The reported temperature was measured with a Pt/Pt-10 pct Rh thermocouple and is estimated to be accurate within +5°C. The composition of the equilibrated melts is given in Table I. For the graphical illustration of these quaternary slags the type of projection suggested by Trömel and Fritze10 was used. In this representation, Fig. 1, the composition point of a mixture within the tetrahedron Fe2O3-CaO-P2O5-FeO is projected into the Fe2O3-CaO-P2O5, triangle (triangle I) so that the direction of projection is parallel to the side FeO-Fe2O3, and into the triangle Fe2O3-P2O,-Fe0 (triangle 11) so that the direction of projection is parallel to the side CaO-P2O5, of the tetrahedron. The projected point has the coordinates wt pct CaO, wt pct P205, and wt pct (FeO + Fe2O3) in triangle I and wt pct FeO, wt pct Fe2O3, and wt pct (CaO + PzO5) in triangle 11. Both triangles are turned into the same plane around the Fe203-P20, side of the tetrahedron. An illustration of the projection of a quaternary point in the present system is shown in Fig. 1. The advantage of this type of projection is that all four components for an equilibrium curve can be read directly from the diagram. The present results are shown graphically in Fig. 2. The curves depicting the miscibility gap are dashed in parts where no experimental points were obtained. The composition range covered by the miscibility gap

Jan 1, 1968

By W. P. Blake

Forging under the hydraulic press, which was introduced by Haswell in the year 1861, at the machine shops of the Imperial State Railway Company of Austria, has since been greatly improved, so that at the present time there are very few parts of machines which cannot be produced in this way, and at no greater cost than iron castings. The process is now used at Vienna chiefly for such parts of locomotives as cross-heads, link-bars, axle-box frames, etc., especially where the form is intricate, and there are many angles and projections. These objects weigh from 50 to 150 lb. or more, and it is claimed for them that they are not only much cheaper than ordinary forgings, but are much more regular in form and stronger. The results which Mr. Haswell has attained, after years of patient experimenting, were well shown in the Austrian Department of the Vienna Exhibition by a collection of the pressed objects in iron and steel, just as they left the moulds, with some of them cut asunder longitudinally and the surfaces etched, so as to show the internal structure or direction of the grain. Through the courtesy of Mr. Haswell and his son I saw the hydraulic presses in full operation at the works, drawing down large Bessemer ingots, cutting them up into blocks of convenient size, and forming various park of locomotives. They have two large hydraulic presses in use; the largest, with a piston 24 inches diameter, gives 1200 tons pressure, and the second, with an 18-inch piston, gives 600 tons pressure. The pressure in the pumps is 600 atmospheres. The action is vertical; the piston descends upon the work, and for forging ingots is armed with a hammer-like head. An ingot of No. 7 soft Bessemer steel, which was forged in my presence, weighed 2030 lbs. One end being placed upon the anvil, the piston is brought slowly down and crowded into the mass as if it were putty or dough, forcing it each way, but chiefly in the direction of the length of the ingot, this being the narrowest section of the anvil and hammer. The piston is then raised and the ingot is moved forward for a second squeeze, and so on, until the first half of the ingot has been reduced in thickness, when it is turned on edge and the operation is repeated. The ingot is then turned end for end and forged until the whole length has been re-

By H. Cecil Spicer

THE results described in this article are based on field work conducted during the periods April-May, 1939, and May-July, 1940. The United States Potash Co. is mining potash on Government land under a permit from the Department of the Interior and the geophysical investigation was completed under a cooperative arrangement made between that company and the Conservation Branch of the Geological Survey. The writer, a member of the Section of Chemistry and Physics of the Geologic Branch, was assigned to this investigation. Four definite objectives were in mind for the geophysical work in the studies over the salt deposits. The first was to determine the measure of success that could be attained in this type of work with the resistivity methods that were to be employed. These methods had been introduced into the work of the Conservation Branch by Benjamin E. Jones for the investigation of dam sites, and have been used under his direction by the author for such work. If the method proved to be applicable, an effort was to be made to contour the top of the salt beds and also the other formation boundaries known to be present in this area. Salt-water aquifers were to be studied in an effort to determine their boundaries, and an attempt was to be made to delineate the potash-bearing beds. EARLIER STUDIES Others have made, and reported, resistivity studies over saliferous deposits in different areas. Friede1 and Messrs. Schlumberger2 reported geophysical work performed in the discovery of the salt domes of Alsace; Carrette and Kelly3 described the geology of the same area. Leonardon and Kelly4 published a resistivity curve obtained over the Hettenschlag dome, and a further discussion of this same area was given by the Messrs. Schlumberger5 in a communication. Messrs. Alty6 described studies on salt deposits in which the single-probe method was used. Sinerez7 mentions that electrical methods were tried over salt deposits in Spain. Geoffrey and Charrin8 show a resistivity curve obtained over marl, gypsiferous marl and salt which is similar to that obtained over the New Mexico salt deposits. Kelly9 reported resistivity work performed with the ground comparator of Zuschlag over the salt deposits near Syracuse, N. Y., where the Salina formation is at a depth of 700 to B00 ft. Some structural studies on the potash basin of Alsace are described by Poldini.10 Another single-probe resistivity study, made over salt deposits in New Mexico, is briefly described by Heiland,11 through the courtesy of Harry Aurand, of the Midwest Refining Co.

Jan 1, 1941

By H. Cecil Spicer

THE results described in this article are based on field work conducted during the periods April-May, 1939, and May-July, 1940. The United States Potash Co. is mining potash on Government land under a permit from the Department of the Interior and the geophysical investigation was completed under a cooperative arrangement made between that company and the Conservation Branch of the Geological Survey. The writer, a member of the Section of Chemistry and Physics of the Geologic Branch, was assigned to this investigation. Four definite objectives were in mind for the geophysical work in the studies over the salt deposits. The first was to determine the measure of success that could be attained in this type of work with the resistivity methods that were to be employed. These methods had been introduced into the work of the Conservation Branch by Benjamin E. Jones for the investigation of dam sites, and have been used under his direction by the author for such work. If the method proved to be applicable, an effort was to be made to contour the top of the salt beds and also the other formation boundaries known to be present in this area. Salt-water aquifers were to be studied in an effort to determine their boundaries, and an attempt was to be made to delineate the potash-bearing beds. EARLIER STUDIES Others have made, and reported, resistivity studies over saliferous deposits in different areas. Friedel1 and Messrs. Schlumberger2 reported geophysical work performed in the discovery of the salt domes of Alsace; Carrette and Kelly3described the geology of the same area. Leonardon and Kelly4 published a resistivity curve obtained over the Hettenschlag dome, and a further discussion of this same area was given by the Messrs. Schlumberger5 in a communication. Messrs. Alty6 described studies on salt deposits in which the single-probe method was used. Sinerez7 mentions that electrical methods were tried over salt deposits in Spain. Geoffrey and Charrin8 show a resistivity curve obtained over marl, gypsiferous marl and salt which is similar to that obtained over the New Mexico salt deposits. Kelly9 reported resistivity work performed with the ground comparator of Zuschlag over the salt deposits near Syracuse, N. Y., where the Salina formation is at a depth of 700 to 8oo ft. Some structural studies on the potash basin of Alsace are described by Poldini.10 Another single-probe resistivity study, made over salt deposits in New Mexico, is briefly described by Heiland,11 through the courtesy of Harry Aurand, of the Midwest Refining Co.

Jan 1, 1941

By J. L. Meijering

Oxidation hardening of cylindrical and spherical specimens first decreases with depth below the surface, but then increases again as the center is approached. This is in agreement with the view that this change in hardness is mainly determined by the change in velocity of the oxidation boundary, which affects the dispersion of the oxide. WHEN a thick slab of silver containing 0.3 pct Mg by weight is internally oxidized, the hardness measured on a cross section is found to decrease considerably with distance from the surface.&apos; This phenomenon has been attributed to the diminution of the velocity of the oxidation boundary. The smaller this velocity is, the more slowly the free-oxygen concentration rises towards the concentration in equilibrium with the oxygen gas. And a small 0 concentration favors dissociation and thus conglomeration of the oxide. For instance, the hardness decreases more rapidly during long annealings in nitrogen than in air.&apos; Measurements by Gregory and Smith3 on sections through internally oxidized Al-silver wire showed a smaller variation in hardness, probably because the wire diameter was only 0.9 mm. Wood4 found a drop in hardness with depth in internally oxidized Al-copper strip, and also—by electron microscopy—the concomitant increase in Al2O3 particle size. Under certain circumstances internal oxidation leads to formation of rather irregular inner oxide films in the midst of dispersed oxide. This special sort of conglomeration—discussed in Ref. 5—is also favored by greater depth below the surface.3,5 In this paper hardness measurements in large diameter cylindrical and spherical specimens are described. Here the oxidation velocity* goes through ness initially decreases with depth but increases again towards the center. Normally, the diffusion coefficient D1 of oxygen is very large compared to D2, that of the dissolved metal. If, furthermore, the atomic fraction c2 of the latter is much larger than the O-solubility cl- but c2D2 << c1D1- the velocities in question are easily calculated2 to be: for the cylinder and for the sphere. Here p is the radial coordinate of the oxidation boundary and R the specimen radius, which in dilute silver alloys is constant, as no external oxidation occurs. These equations have been derived for a divalent solute; for nondivalent solutes c2 has to be multiplied by half the valency. The equations are not valid near the center. For which can be considered as a standard case,2 the Eqs [I] and [2] begin to yield U-values which are appreciably too high for p/R = 0.05 and 0.15, respectively. But at the v-minima they are still very good approximations. These minima lie at p = emlR= 0.37R in the cylinder and p = 1/2 R in the sphere. Other factors besides the velocity v will also influence the hardness. The oxide concentration cox is constant in a flat strip, apart from a narrow region in the middle,2 but in cylindrical and spherical specimens cox decreases steadily with depth. When C1 << c2 and c1D1 >> c2D2 one can calculate

Jan 1, 1961

By R. M. Hudson

The removal of nitrogen from a nitrogenized low-carbon sheet steel that contained 0.011 wt pct N was determined during heat treatment in Hz-N, mixtures. TIze process followed a first-order rate law; that is, plots of the logarithm of nitrogen content in steel were linear with the time of treatment at a given temperature. The rate of removal increased with an increase in temperature from 900" to 1300°F. By 1400°F the rate in dry hydrogen had decreased to a value intermediate between the rates at 1200" and at 1300°F; in wet (2.47 vol pct water vapor) hydrogen the rate at 1400°F was less than the rate at 1300°F and nearly the same as the rate at 1200OF. The rate at a given temperature increased as the 3/2 power of hydrogen concentration in the atmosphere. While wet atmosplzeres were generally more effective than the corresponding dry atmosplzeres, the effect of water vapor was much less pronounced than the influence of hydrogen content. NITROGEN is the principal agent in the strain aging of ferrite, the effect of carbon being secondary.&apos; To eliminate the return of the yield point after straining and aging, it is claimed2 that the amount of nitrogen in solution in steel must be reduced to 0.0002 wt pct. Strong nitride-forming elements (titanium, vanadium, zirconium, and aluminum) can act to eliminate strain aging by combining with nitrogen. It is extremely difficult to decrease the nitrogen content in commercial steels to the low level required by conventional coil annealing because of the poor contact between the strip surface and the reactive atmosphere. However, a variety of gas-metal reactions can be effected by use of the open-coil annealing method,3 in which the metal surface is fully exposed to the atmosphere. With this possibility in mind, the Applied Research Laboratory has studied the influence of time, temperature, and atmosphere composition on the removal of nitrogen from low-carbon sheet steel. MATERIALS AND EXPERIMENTAL WORK Samples from a commercial nitrogenized low-carbon steel (0.010 in. thick) in the cold-reduced condition were used. The chemical composition of this steel is given in Table I. The gas mixtures used are listed in Table 11. The moisture content in the "wet" annealing atmospheres was controlled at a +70°F dew point (2.47 vol pct water vapor) by passing the gas mixture through a glass tube packed with a solid mixture of 10 pct anhydrous oxalic acid and 90 pct oxalic acid dihydrate held at 127°F; this technique has been described previously.4 For "dry" atmospheres, the gas mixtures were passed through a cold trap immersed in liquid nitrogen. A hinged-top Hevi-Duty electric furnace was used with a Vycor-glass furnace tube. When the furnace was at the desired temperature, the gas mixture was passed through the furnace at a flow rate between 1.1 and 1.2 cfh; coupons (size 3 by 3/4 in.) of the steel were pulled into the center of the Vycor-glass

Jan 1, 1964

By John Chipman, Carl F. Floe

A year ago the authors published a paper on the solubility of sulphur dioxide in molten copper.l The data in that paper agreed closely with that obtained by previous investigators, which, however, did not agree with the theoretical predictions for solubility of triatomic gases of this type. It has generally been assumed that the reaction of solution is: 6Cu(l) + SO2(g) = Cu2S (in Cu) + 2 Cu2O (in Cu) [I] _ (CU2S)(CU2O)2 K = (Cu)6(Pso2) [2] Neglecting the slight change in copper concentration and considering that the concentrations of sulphur and oxygen are both proportional to the volume of gas absorbed, it follows that this volume should be proportional to the cube root of the pressure. It was found that a plot of the volume absorbed versus the cube root of the pressure gave a straight line, but that this line did not pass through the origin. Calculations of the equilibrium constant for the reaction showed that it was fairly constant for pressures above 100 mm. but that actually it approached zero at lower pressures. The conclusion was made therefore that the solubility as determined could not be expressed by Eq. I or by any other simple equation, particularly at low pressures. Other investigators have concluded that the solubility of sulphur dioxide in copper as well as in several copper alloys is more nearly proportional to the square root of the pressure.* Such a conclusion, however, does not satisfactorily account for the results, even when rather complicated mechanisms for the solution are assumed. The highly improbable speculations of Lepp2 and of Schneider and Esch3 based upon hypothetical dissociation pressures of Cu2O and CU2S dissolved in copper illustrate the type of reasoning that has been used to account for the discrepancy. In the discussion of the previous paper, the authors pointed out that the discrepancy might possibly be due to impurities in the copper, although the purest form available was used. Further consideration of the problem suggested that the impurities likely to have the greatest effect on the solubility of so2 in copper were oxygen, sulphur and carbon. Accordingly, further experiments have been made to show the effects of these elements. Experimental Methods The apparatus used for measuring solubility was essentially the same as that shown in the previous paper. However, since it was desired to make measurements at low pressures, a McLeod gauge was added and 6-mm. glass tubing was substituted for the capillary. This increased the "hot volume" considerably but was necessary in order to obtain good vacuums in a reasonable length of time. A mercury diffusion pump was also installed.

Jan 1, 1942

By E. S. Tankins, G. R. Belton

A simple solution model, based upon the formation of molecular species, is developed for strongly electronegative dilute solutes in liquid binary-metallic solvents. Two approximations are considered for the relative concentrations of the species: the random and the quasi-chemical. Equations are presented for the partial molar free energy, enthalpy, and entropy of mixing of the solute. An experimental study has been made of equilibrium in the reaction H2 6) +0 (dissolved) = H2O(g))for the liquid Cu-Co alloys. The standard free energy of solution of oxygen is presented as a function of composition for the alloys at 1550°C and as a function of temperature for five of the alloys. The experimental results for these alloys and also for Cu-Ni alloys are shown to be in reasonable agreernent with the theory in the random approximation. A knowledge of the thermodynamic behavior of dilute solutes in liquid metals and alloys is of importance in understanding and designing refining and alloy-making processes. Accordingly, several attempts have been made to derive suitable solution models to forecast the effect of a third component on the activity coefficient of such a solute in a metal. Alcock and Richardson&apos; reviewed the literature prior to 1958 and also showed that a regular solution model gave a reasonable description in the case of metallic solutes but failed to account for the behavior of the more electronegative solutes sulfur and oxygen. These same authors2 later modified their model by using the quasi-chemical approximation3 to calculate the average composition of the first coordination shell surrounding each solute atom. This modified model was shown to lead to a better qualitative description of the behavior of the electronegative solutes; however, quantitative agreement with experimental data for oxygen in alloys could only be achieved by assuming a very small coordination number. The authors concluded that the major source of error in the model was the assumption that pairwise interaction energies were independent of composition. Substitutional and interstitial random solution models by Wada and saito4 are essentially similar to the first model except that the required interchange energies were derived from the modified solubility parameter equation of Mott, instead of from experimental binary data. Most recently Hoch5 has presented a statistical model for interstitial solutions and has applied the model to the Fe-C-O system. However, as the various interaction energies needed in the model had to be derived from the ternary data, the model does not promise well as a means of forecasting ternary behavior. Each of the above models carries the assumption that the strongly electronegative solutes have the same configurational environment as metallic solutes; i.e., the solute can be treated as a substitutional or interstitial atom in a quasi-crystalline lattice and is surrounded by a normal coordination shell of solvent atoms. There are, however, a number of facts which suggest that this is unlikely. First, the heats of solution are large, being more typical of molecule formation rather than alloying. For example, the heats of solution of monatomic oxygen and sulfur in liquid iron are -90 kea16,8 and -74 kea1,7, 8 respectively. These are to be compared with maximum heats of solution of metallic solutes in liquid iron of about -13 keal (silicon is an exception with -28.5 kea17). The large depression of the surface tension of liquid iron by trace amounts of the electronegative solutes oxygen, sulfur, and selenium9 suggests, by analogy with aqueous systems, the possible existence of polar molecules in the liquid. The effect of these solutes is at least three orders of magnitude greater than normal metal solutes.10 As has been pointed out by Richardson,11 the electron affinities and ionization potentials of oxygen and sulfur are such that it is likely that they exist in metallic solution as negatively charged ions. If this is so, and it is assumed that electrostatic forces play an important role in determining the configuration, it is unlikely that the stable configuration will be that of an isolated ion surrounded by a symmetrical coordination shell of solvent ions. It is more likely that the energy of the system would be lowered by the formation of solute-solvent screened dipoles. The above arguments suggest the formation of "molecular species" between solute and solvent atoms. The idea of the existence of molecular species in such solutions is not new, however&apos;, for Marshall and chipman12 have explained in a semi-quantitative manner the C-O equilibrium in liquid iron by postulating the species CO. Chen and Chip-man13 interpreted their measurements on the Cr-O equilibrium in iron in terms of the species CrO. Zapffe and sims14 have also postulated the existence of such species in liquid-iron alloys.

Jan 1, 1965

By Carl F. Floe, John Chipman

A year ago the authors published a paper on the solubility of sulphur dioxide in molten copper.l The data in that paper agreed closely with that obtained by previous investigators, which, however, did not agree with the theoretical predictions for solubility of triatomic gases of this type. It has generally been assumed that the reaction of solution is: 6Cu(l) + SO2(g) = Cu2S (in Cu) + 2 Cu2O (in Cu) [I] _ (CU2S)(CU2O)2 K = (Cu)6(Pso2) [2] Neglecting the slight change in copper concentration and considering that the concentrations of sulphur and oxygen are both proportional to the volume of gas absorbed, it follows that this volume should be proportional to the cube root of the pressure. It was found that a plot of the volume absorbed versus the cube root of the pressure gave a straight line, but that this line did not pass through the origin. Calculations of the equilibrium constant for the reaction showed that it was fairly constant for pressures above 100 mm. but that actually it approached zero at lower pressures. The conclusion was made therefore that the solubility as determined could not be expressed by Eq. I or by any other simple equation, particularly at low pressures. Other investigators have concluded that the solubility of sulphur dioxide in copper as well as in several copper alloys is more nearly proportional to the square root of the pressure.* Such a conclusion, however, does not satisfactorily account for the results, even when rather complicated mechanisms for the solution are assumed. The highly improbable speculations of Lepp2 and of Schneider and Esch3 based upon hypothetical dissociation pressures of Cu2O and CU2S dissolved in copper illustrate the type of reasoning that has been used to account for the discrepancy. In the discussion of the previous paper, the authors pointed out that the discrepancy might possibly be due to impurities in the copper, although the purest form available was used. Further consideration of the problem suggested that the impurities likely to have the greatest effect on the solubility of so2 in copper were oxygen, sulphur and carbon. Accordingly, further experiments have been made to show the effects of these elements. Experimental Methods The apparatus used for measuring solubility was essentially the same as that shown in the previous paper. However, since it was desired to make measurements at low pressures, a McLeod gauge was added and 6-mm. glass tubing was substituted for the capillary. This increased the "hot volume" considerably but was necessary in order to obtain good vacuums in a reasonable length of time. A mercury diffusion pump was also installed.

Jan 1, 1942

By Harold Markus, Gerhard Derge

THE first paper1 of this series described a technique of careful surface preparation by means of which reproducible results may be obtained from potential measurements of the behavior of tin in carbonate solutions with a pH range from 8.4 to 11.2. It then went on to establish the behavior of pure tin electrodes under these conditions and showed that the metal remains active at all times, though the steady potential attained after several hours decreases from I.I2[t] volts at a pH of 12.6 to 0.6 volts at a pH of 8.4. This behavior may serve as a norm with which all other data can be compared. In the second paper,2 small amounts of other anions were added to the carbonate solutions and the conclusion was reached that the common impurities encountered in alkaline materials packaged in tin do not increase corrosion. In fact, in some cases these anions may actually promote the formation of protective films. The present paper rounds out this survey by presenting data on the influence of cations added to the carbonate solutions, as well as the effect of alloy additions to the tin. In many cases the potential data are supplemented with weight-loss measurements. Information is also presented on the effects of some additional anions, the influence of gases above the electrolyte, the behavior of high-purity tin, and the effect of atmospheric oxidation on the corrosion resistance of the above-named alloys. Analysis of the entire body of data discloses some general rules applicable to corrosion in carbonate solutions. The experimental methods used are the same as those previously described. EXPERIMENTAL DATA Cations.-The carbonates of the cations K+, Li+, NH4+, which are soluble, were studied in the same way as the anions, by adding 0.01 mol of the metal carbonate to one liter of 0.2 M sodium carbonate solution, pH 11.2, or to 0.1 M sodium bicarbonate, pH 8.4. The other metallic carbonates are only slightly soluble, of the order of 0 7-3 mols per liter or less, and the sodium carbonate solutions were saturated by adding excess reagent several days before the experiment, shaking frequently, and filtering just before use. The chemicals were c.p. grade in each case except the indium salt. This salt was prepared by solution of the metal in hydrochloric acid and precipitation by addition of Na2CO3. These cations may be divided into two classes, according to their effect on the potential behavior of the tin: (I) normal, (2) passive. To offer a basis of comparison, curves I of Figs. I and 2 are given to illustrate the behavior of tin in carbonate solutions saturated with CaCO3. These curves are the

Jan 1, 1941

By R. E. Ogilvie, J. I. Goldstein, R. E. Hanneman

The interdiffusion coefficients for the Fe-Ni system were determined as a function of composition in both the a and y phases at 1 atm pressure. The inter diffusion coefficients were also determined in the y phase at 40 kbar pressure. The concentration gradients were measured with an electron probe, and the diffusion coefficients were calculated by the Matano analysis. At 1 atm, Ey increases with nickel content up to 65 at. pct Ni. The relationship of Dy with temperature and nickel concentration, up to 50 at. pct Ni, is given by the equation DY-l atm = exp(.0519 CN~ +1.15) MANY of the transformations that occur in the solid state are diffusion-controlled, especially those involving precipitate growth in most metallurgical systems. Multicomponent diffusion is usually expressed in terms of a chemical or an inter diffusion The activation energy Q at 1 atm decreases from pure iron to 60 to 70 at. pct Ni and decreases from pztre nickel to 60 to 70 at. pct Ni. The Kirkendall marker movement indicates that DFe is greater than DNi zcp to about 60 at. pct Ni. Above 60 at. pct Ni, however, DNi becomes peater than DFe The inter diffusion coefficients were also compared with those calculated from self-diffusion data. A comparison between calculated and measured coefficients shows only rough agreement. The effect of 40 kbar pressure is to decrease DyPl atm by an order of magnitude. The activation volumes for high-pressure diffusion are in favorable agreement with theoretical models developed for self-diffusion. coefficient which determines the rate at which material is transferred from the matrix phase to the precipitate and hence determines the growth rate of the precipitate. Since the numerical values of the diffusion coefficients differ widely as a function of the metallic system, temperature, and pressure, the diffusion coefficients must be determined for each particular environmental condition. Of long-standing interest is the growth of the classic Widmanstatten pattern in metallic (Fe-Ni) meteorites. The growth rate of the pattern is controlled by the diffusion coefficients in the Fe-Ni system. Since these coefficients are essential to calculating the growth rate of the pattern, we found it necessary to determine the diffusion coefficients

Jan 1, 1965

By J. W. Gwinn

The underground haulage system in the lead-silver mine of the Bunker Hill & Sullivan Co., situated at Kellogg, Idaho, is the most extensive in the Cæur d&apos;Alene district, comprising about 35,000 ft. of tunnels, drifts, and cross-cuts where locomotive haulage is in use. The main working adit, known as the Kellogg tunnel, or No. 9 level, is approximately 10,000 ft. in length from the portal to the main working shaft and extends beyond that about 4,500 ft. in each of two directions. On this level all the ore from the Bunker Hill & Sullivan, the Sierra Nevada Consolidated, and the Caledonia Mining Co.—an average of 44,600 tons per month—is hauled to the mills, located a short distance from the portal. Electric haulage by the trolley-type locomotive is used on this level throughout. Below this level, at intervals of 200 ft. vertically, are five other working levels (Nos. 10, 11,12,13, and 14); and the total haulage distance on these, where electric locomotives are used, is approximately 16,000 ft. No. 13 level has but recently been opened up and is not working to capacity; while the main cross-cut on No. 14 has just been started, and has no need of power haulage. Of the four levels equipped with electric haulage, Nos. 11, 12, and 13 have storage-battery locomotives, and No. 10 still retains the trolley type by reason of the small and decreasing tonnage produced. Electrification - Electric power is supplied to the mine by two systems. The first, the 500-volt direct-current trolley, was installed in 1897 when the Kellogg tunnel was started, and was extended as the tunnel advanced, being used for the first trainload of ore on Nov. 17, 1902, since which time it has been in continuous service. The current for the line is transmitted on a No. 00 copper wire as far as the shaft, and on No. 0 wire throughout the remaining length of the Kellogg tunnel; and until the installation of the storage-battery locomotives it was used in practically all the cross-cuts and drifts on each level below No. 9.

Jan 1, 1915

By Roland Blanchard

Recent discovery at Mount Isa of copper mineralization in commercial amount at a depth of 1000 ft., coinciding with downward termination of ore at about the same depth within the larger silver-lead-zinc lenses that have been the standby of Mount Isa&apos;s production to date, has been cited as an example in support of mineral zoning. A previous paper by the author and Graham Hall1 furnished a detailed description of the geology of the ore at Mount Isa as exposed up to that time, but necessarily dealt mainly with the silver-lead-zinc mineralization. Most of the geologic facts that constitute the first half of the present paper were set forth in the previous one in much greater detail, with full supporting evidence for the facts cited. The large amount of underground development (approximately 20 miles) and the extensive exploration carried out by diamond drilling (100,000 ft.) at Mount Isa, added to extensive microscope work conducted over a period of years, both by the company&apos;s staff and by others, had made possible the calculation within fairly close limits of mineralogical composition of the principal mineralized block of ground down to 1000-ft. depth, and had established closely the mineral succession, with reasons for deposition of the various minerals in the patterns now occupied by them. The geologic facts as outlined in the previous paper remain as stated; but because substantial development within the new copper ore body and further exploratory diamond drilling within the new silver-lead-zinc area (Racecourse) have taken place since that paper was written, statements and figures relating to those two areas in the present paper supersede those furnished in the previous one. The recent work likewise has established more clearly the paragenetic relationship between the chalco-pyrite and galena. Evidence confirming the relationship is furnished in the present paper. The facts of ore occurrence at Mount Isa show Accepted Zonal Succession Silver sulphantimonides Galena Sphalerite Tetrahedrite Arsenical sulphides Chalcopyrite Pyrrhotite Mount Isa Succession I In the main but prob- Silver sulphantimonides ably not wholly Tetrahedrite I contemporaneous Galena Pyrrhotite Sphalerite Arsenical sulphides They show further: (I) that instead of the silver-lead minerals yielding to increased zinc in depth, the zinc yields to increased silver-lead; (2) no dovetailing of the silver-lead-zinc sulphides into chalcopyrite takes place; (3) despite the large amount of pyrrhotite deposited in the district (estimated at upward of 100,000,000 tons), its deposition took place under moderately low temperature conditions; (4) no evidence has been found for increase in temperature of deposition, with depth, to deepest exploration in ore (1475 ft.). The anomalous condition at Mount Jsa, both as to the unorthodox mineral succession and the largely unorthodox patteru of mineral distribution, is explained in the present paper,

Jan 1, 1949

By Roland Blanchard

Recent discovery at Mount Isa of copper mineralization in commercial amount at a depth of 1000 ft., coinciding with downward termination of ore at about the same depth within the larger silver-lead-zinc lenses that have been the standby of Mount Isa&apos;s production to date, has been cited as an example in support of mineral zoning. A previous paper by the author and Graham Hall1 furnished a detailed description of the geology of the ore at Mount Isa as exposed up to that time, but necessarily dealt mainly with the silver-lead-zinc mineralization. Most of the geologic facts that constitute the first half of the present paper were set forth in the previous one in much greater detail, with full supporting evidence for the facts cited. The large amount of underground development (approximately 20 miles) and the extensive exploration carried out by diamond drilling (100,000 ft.) at Mount Isa, added to extensive microscope work conducted over a period of years, both by the company&apos;s staff and by others, had made possible the calculation within fairly close limits of mineralogical composition of the principal mineralized block of ground down to 1000-ft. depth, and had established closely the mineral succession, with reasons for deposition of the various minerals in the patterns now occupied by them. The geologic facts as outlined in the previous paper remain as stated; but because substantial development within the new copper ore body and further exploratory diamond drilling within the new silver-lead-zinc area (Racecourse) have taken place since that paper was written, statements and figures relating to those two areas in the present paper supersede those furnished in the previous one. The recent work likewise has established more clearly the paragenetic relationship between the chalco-pyrite and galena. Evidence confirming the relationship is furnished in the present paper. The facts of ore occurrence at Mount Isa show Accepted Zonal Succession Silver sulphantimonides Galena Sphalerite Tetrahedrite Arsenical sulphides Chalcopyrite Pyrrhotite Mount Isa Succession I In the main but prob- Silver sulphantimonides ably not wholly Tetrahedrite I contemporaneous Galena Pyrrhotite Sphalerite Arsenical sulphides They show further: (I) that instead of the silver-lead minerals yielding to increased zinc in depth, the zinc yields to increased silver-lead; (2) no dovetailing of the silver-lead-zinc sulphides into chalcopyrite takes place; (3) despite the large amount of pyrrhotite deposited in the district (estimated at upward of 100,000,000 tons), its deposition took place under moderately low temperature conditions; (4) no evidence has been found for increase in temperature of deposition, with depth, to deepest exploration in ore (1475 ft.). The anomalous condition at Mount Jsa, both as to the unorthodox mineral succession and the largely unorthodox patteru of mineral distribution, is explained in the present paper,

Jan 1, 1949

By L. Leibowitz, M. G. Chasanov, L. W. Mishler

A drop calorimeter system is described for use in measuring enthalpies to 3600°K. Data are presented for tungsten between 2800" and 3600°K. The enthalpy of tungsten in cal per mole between 2000° and 3600°K can be represented by the equation HºT- Hº298 = - 1.7622 X 103 + 5.7772T + 8.9861 where T is in degrees Kelvin. A tabulation of com -puted values is presented for heat capacity, entropy, and free energy function. A drop calorimeter has been constructed to carry out enthalpy measurements at temperatures to 3600°K. Samples are heated by induction1 and dropped into a commercial adiabatic calorimeter, modified for this purpose. The experimental temperature is limited by the melting point of container materials and compatibility of the container and its contents. Several high-temperature drop calorimeters have been described in the literature1-5 but none has been used at temperatures as high as those in the present work; our measurements of the enthalpy of tungsten range from 2800" to 3600°K. DESCRIPTION OF EQUIPMENT An overall schematic view of the equipment is shown in Fig. 1. Power for the induction coil is supplied by a 25-kw 250 kHz Ther-Monic generator coupled to an iron core RF transformer. The Sample capsule is suspended in the work coil by 10-mil diam tungsten wires which are wrapped around a horizontal 5-mil diam tungsten wire. The horizontal suspension wire is clamped between two massive copper electrodes which are fixed in an x-y motion device that allows adjustment of the position of the heated capsule from outside the vacuum chamber. The copper electrodes are connected by flexible copper straps to a 1250-joule (5 kv, 100 pfarad) condenser bank. When it is desired to release the capsule, the condensers are discharged through the horizontal suspension wire causing it to vaporize rapidly. Very reliable and precise release of the capsule is achieved in this manner. Experiments have shown that no heat correction is required for this discharge energy. As part of the temperature measuring system, two prism holders have been incorporated in the apparatus. The upper prism holder is in the main vacuum chamber itself, whereas the lower one is in a side arm attached to the drop tube below the gate valve. The upper prism is mounted on a rotary vacuum feed-through, and may be moved under a protective shield when not in use. This prevents deposition of vapors on the prism surfaces when temperature measurements are not being made. Similarly, the lower prism is mounted on a push-pull vacuum feed-through, and when not in use may be pulled into its side tube. The prism mountings are fitted with guides and stops so that they may be moved precisely into the desired position. The aim throughout is to minimize the time the prisms are exposed to vapors from the hot samples. At the high temperatures reported in this paper, only the lower prism was used. The upper prism holder in these cases was fitted with an additional radiation shield. By using a prism and viewport, the lower surface of the samples can be observed by an optical pyrometer. The measurements discussed in this paper were obtained with a Leeds and Northrup 8622-C-S series manual pyrometer which is estimated to be accurate to 0.5 pct. Pyrometer calibrations and prism and window corrections were carried out in the conventional manner6 using tungsten strip lamps calibrated by the National Physical Laboratory, Teddington, England. Prism corrections were rechecked after each use. All work to date has been done in vacuum, and no measurable change has been observed in the prism correction below -2300°K for the upper prism and below -2800°K for the lower one. The total time of exposure of the prisms is about 50 sec per run. At high temperature, the final temperature reading is corrected by using the final A value for the prism; see Ref. 6 for details of this procedure. The calorimeter is a modified Parr Instrument Co. (Moline, lll.), Series 1230 adiabatic calorimeter with automatic jacket control. Other authors5 have used a similar calorimeter with good results. The calorimeter jacket cover and calorimeter cover are attached to the drop tube which contains a radiation shield. This shield is a gold-plated copper disc which can be operated manually from outside the calorimeter. The receiver is attached below the radiation shield and is lined with tungsten. In a typical experiment, the calorimeter and its jacket water temperatures were adjusted to 0.000°K temperature difference. The sample was allowed to equilibrate in the furnace at the desired temperature for about 20 min. The initial calorimeter temperature was then recorded, the sample dropped, and appropriate shutters closed. After about 3 min, the drop tube and receiver were filled with helium to 60 torr. The final calorimeter temperature was recorded after it had remained constant over a 5-min period. The equilibration time in the calorimeter was about 25 min. Thermistor probes are used to operate a hot and cold water supply system to maintain the jacket temperature equal to the calorimeter temperature. For actual measurements of the calorimeter temperatures, a quartz thermometer was used (Hewlett Packard Dymec Thermometer, Model #2801A). This thermome-

Jan 1, 1970

By R. N. Dokken, J. F. Elliott

A high-temperature solution calorimeter was used to measure directly the partial molar heat of mixing of nickel in the Cu-Ni system, 0 to 15 at. pct Ni and 1200°C; of silver in the Cu-Ag system, 0 to 50 at. pct Ag and 1100°C; and of cobalt in the Cu-Co system, 0 to 6 at. pct Co and 1200°C. The heats of fusion of copper and silver were also detervnined directly. The results of these investigations are as follows: Cu-Ni: HM = [2.64 + 0.25Xm JXNiXCy kcal/g-U~OI Cu-Ag: HM =[4.00 + 0.31XAglXAgXCu kcal/g-atom Cu-Co: HF~ = [8- 5X~,]X& kcal/g-atotn Cu, AH, = 3290 * 275 cal/g-atom Ag, AH, = 2890 * 250 cal/g-atom The performance of the calorimeter was enhanced by improving the operational and control procedures, particularly the temperature-wieasuren~ent method and the solute-addition practice. The interpretation of the experimental data was improved by developing machine computational techniques that increased the speed, flexibility, and accuracy of the treatment of the data. THIS paper reports further measurements of the heats of solution of liquid metals with the high-tem- perature solution ca1orimeter.l Measurements were made of the partial molar heats of mixing in the following liquid alloys: Cu-Ni, Cu-Ag, and Cu-Co. In addition the heats of fusion of copper and silver were also determined. The apparatus and the experimental procedure were essentially those of Benz and Elliott.2 Several modifications in the experimental method and the means for interpreting the data were incorporated in this study to improve the results. The operation of the calorimeter and its characteristics will be described only briefly here. The

Jan 1, 1965

By D. F. Stein

In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Because of this limited success, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. As a result of these calculations, it was concluded that autoradiograPhy is a rather insensitive technique to measure grain boundary segregation. The range (energies) of the emitted particles (ß and a) must be low, and the concentration of the radioactive speczes at the grain boundary must be (in general) two or three orders of magnitude greater than the concentration within the grain. Because of these very restricted conditions , the limited success of the technzque is not surprising. In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Sulfur segregation in iron1 and possibly polonium segregation in Pb-5 pct B1 2 alloys are the only autoradi-ography experiments that have demonstrated segregation to grain boundaries in metals without the formation of a second phase. Segregation to a boundary without the formation of a second phase is often called Gibbs&apos; absorption and is discussed by McLean in Chapter 5 of Ref. 10. There are several394 experiments showing grain boundary diffusion of a radioisotope, but this type experiment is not representative of equilibrium between the concentration of an element at a grain boundary and that in bulk, so it will not be discussed in this paper. In an attempt to determine if temper embrittle ment of low-alloy steels was associated with segregation of antimony to grain boundaries, a program to use auto-radiography (using Sb-125) was initiated. Even though other measurements strongly suggest that segregation is occurring during embrittlement, no evidence of grain boundary segregation was observed in the auto-radiography experiments. An attempt was also made to detect segregation of carbon (using C-14) to grain boundaries in iron during slow cooling. There is again strong indirect evidence7 that segregation occurs during such a treatment, but the autoradiography experiment gave no evidence of such segregation. Because of the failure of these experiments and the general lack of success by our metallographic unit in measuring grain boundary segregation using autoradi-ography, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. MODEL SYSTEM The model system is illustrated in Figs. 1 and 2. It is a semi-infinite bicrystal with a single grain boundary perpendicular to the top face. The width of the grain boundary, W, is defined as the region to which segregation has occurred and it is assumed that this region is of constant composition. The assumption of an infinite dimension is for mathematical reasons but the results of such an analysis (as will be demonstrated later) are valid for even very small specimens. It also is assumed that the measurement is not limited by means of detecting the radiation (photographic emulsions, counters, and so forth) but that the means of detecting radiation is linearly sensitive to the radiation and has infinite resolving power. The distance y is the perpendicular distance from the center of the grain boundary to the point at which the background radiation is measured and x is the integration variable. CALCULATION FOR BETA PARTICLES Two values of the intensity of radiation will be calculated, the intensity at the center of the grain boundary and the intensity far from the grain boundary. The radiation at the center of the grain boundary can be calculated in the following way. Assume a grain boundary of width W having a uniform concentration equal to Cgb + Cb where CGb is the excess concentration of the element under consideration at the grain boundary and Cb is the bulk concentration. The intensity of radiation, IgB, at the center of the grain boundary, is a consequence of the amount of radioactive material, decay rate, absorption, and geometrical factors which can be represented mathematically by the following expression:

Jan 1, 1968

By D. H. Thompson, A. W. Tracy

Season-cracking is a type of failure of brass that results from the simultaneous effect of stress and certain corrodants. The object of this paper is to present data that will aid in a more complete understanding of the mechanism of season-cracking and related phenomena. Results presented show that certain high copper alloys are susceptible to season-cracking or stress-corrosion cracking, and possible explanations are discussed. Starting at least as far back as 1906, many papers have been devoted to this subject but the symposium1 held in Philadelphia in 1944 is the richest source of information. In order to study season-cracking, several of the many variables were held constant so as to learn the effects of others. Season-cracking is generally understood to refer to the corrosion cracking of brass having internal stresses;²,³ it is a special case of the general stress-corrosion cracking. Inasmuch as applied stresses are more readily produced and controlled, they were used exclusively in this research and the resulting phenomenon must he called stress-corrosion cracking.²,³ Only constant tensile stresses were used. The agents believed to be most frequently responsible for season-cracking are ammonia. amines and compounds containing then]. Both moisture and oxygen also appear to he necessary. Therefore, an atmosphere containing ammonia, water-vapor and air was selected for these tests. Briefly, the work consisted of exposing sheet metal specimens, having a reduced section ¼ by 0.050 in., of copper-base alloys to the effect of static tensile stresses between 5,000 and 20,000 psi and simultaneous contact with a. continuously renewed atmosphere containing 80 pct air, 16 pct ammonia and 4 pct water vapor at 35°C. The gas mixture and the speci- mens were maintained above the dew-point. The time-to-failure in minutes was the primary measure of results. In order to limit the experiment to finite time, it was considered that a specimen which had neither failed nor undergone microscopically detectable cracking in 40,000 min. (4 weeks) while under a stress of 10,000 psi or more could be considered immune to cracking. This is merely a convenient limit and is not to be considered proof of immunity. Supplementary tests in the absence of stress using weight loss or microscopical appearance as measures of attack were made. Apparatus The apparatus used in this research is shown in Fig 1. To facilitate the description it may conveniently be divided into six parts: stress-producing units, test chamber, gas train, electrical controls, timers and gas analysis device. A stress-producing unit is shown in an exploded view at the left in Fig 2. At the right is an assembled unit with a specimen in place in the lower portion; it is this part that remains in the ammonia atmosphere during a test. The upper part contains a spring, a central threaded rod, a large nut and necessary washers, pins, and so forth. Stress is produced in the specimen by screwing down the top nut against the spring, thus putting a tensile load on the central rod and so on the specimen. The wrench that turns the nut by extending through the upper cap, is seen at the upper right of the figure. The magnitude of the load is gauged by measuring from the pin that extends through the side of the tube, to a fixed point on the large flange. Measurement is made with a vernier beam caliper, shown at the right of the figure. The necessary spring compression to give a desired stress is calculated from the calibration curve of the spring and the dimensions of the specimen. The test chamber, center Fig 1, consists of a thermally insulated steel box 32 in. long by 10 in. high by 7 in. wide. A horizontal baffle reaching nearly to each end divides the chamber equally. Below this baffle are inlets for air and ammonia, a heating coil and a fan. Thus the gases are warmed and mixed in the lower level and flow past the specimens in the upper level. A thermo-regulator and thermometer project into the upper space. The top is pierced by 12 ports flanked by 3/8 in. threaded studs. A test starts when a port is opened and a unit containing a stressed specimen is thrust through it and bolted down against a neoprene gasket. The test chamber is held at 35°C. The gas train, right rear Fig 1, carries ammonia and air continuously to the test chamber. Tank ammonia passes through two reducing valves, a needle valve, a flow meter and into the test chamber. The air from either the plant compressor or a small laboratory compressor passes through wool towers and flow controls to the flow-meter. It then bubbles through water at 34°C and through a heated line to the test chamber. Electrical controls, left rear, Fig 1, provide rectifiers and mercury relays for the test-chamber and humidifier-heating-control circuits and outlets for

Jan 1, 1950

By Paul Weir

FOR the first time in 1938, bituminous coal production for the week ending Nov. 19 surpassed that of the corresponding week in 1937, and indexes of industrial activity indicated the possibility that the remaining weeks of 1938 would run ahead of the corresponding weeks of the preceding year. But regardless of this year-end pickup, total production in 1938 was approximately 25 per cent less than in 1937. The estimate of 340 million tons for 1938 places the bituminous industry slightly above the production level of 1933 and approximately 10 per cent above the modem low of 1932. Anthracite production is not subject to the same extent as is bituminous coal to fluctuations arising out of the rate of industrial activity, hence the decline from 1937 has not been so great being approximately 14 per cent under 1937. The estimate for 1938 production is approximately 45 million tons, but this represents the lowest level reached in the last fifty years with the possible exception of several strike years.

Jan 1, 1939

By Hiroshi Oikawa, A. G. Guy

Recent experimental evidence has shown that it is often incorrect to neglect the reactions occurring at an interface with respect to the diffusion reactions. By introducing reaction-rate constants and k for the transfer of components 1 and 2 between the a and b phases, a phenomenological description has been devised for the coupled processes of diffusion and in-terfacial reaction. An illustrative example has been analyzed with the aid of a suitable computer program. The results indicate that for kab values on the order of 10&apos;1 cm per sec and Ð values of about 10¯10 sq cm per sec, the interfacial reactions are significant during the first 10 2 to l0 6 sec of a diffusion experiment. Among the observable effects of the interfacial reactions in this case appear to be the burying Kirkendall markers and an anomaly in the initial shifting of these markers. THE study of diffusion between two phases is especially important because of its direct connection to phase transformations. For example, the transformation of austenite to ferrite involves diffusion in the a and ý phases and also an interfacial reaction (trans formation) at the a/? interface. If ferrite and aus-tenite are the two members in a diffusion couple, the same two reactions occur during the diffusion process. The numerical values obtained for the diffusion coefficients and interfacial-reaction constants from diffusion experiments can then be employed to predict phase-transformation behavior. Refinement of the calculations of phase transformation is also suggested by the present method for treating two-phase diffusion. In the recent paper by Nolfi et al.&apos; only the solute com ponent is considered in the interfacial reaction accompanying a phase transformation. The present analysis demonstrates that both components must be considered. It is generally recognized that reactions of some kind must occur at the interface in a two-phase diffusion couple, but usually it is assumed that the interface reaction occurs so rapidly that its effect on the overall process is unobservable because the slower diffusion process determines the kinetics of the process. However, Seith and Heumann 2 pointed out that effects of the interfacial reaction should always occur in the early stages of diffusion, and recently Eifert et al. 3 have shown that interfacial reactions influence the composition and motion of the interface in a/ß Al-Cu diffusion couples during the entire course of prolonged, high-temperature treatments. A general procedure for handling the combined processes of interfacial reaction and diffusion in a binary, two-phase system is to introduce kinetic coefficients for the interface reactions and to develop the system of equations governing the interlinked processes of diffusion and interface reaction. The resulting equations, although not amenable to solution in closed form, can be usefully manipulated by a digital computer. INTERFACIAL REACTIONS IN TWO-PHASE DIFFUSION Consider the general case of diffusion between two solid solutions, a and ß, which are adjacent phases in a binary system, Fig. 1. Two semiinfinite bars having compositions c1 and c0ß are jointed at x = 0. If concentrations are expressed in volume fraction,4

Jan 1, 1970