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By Frederick Laist

F. N. FLYNN, Clifton, Ariz.-I would like to ask Mr. Mathewson what percentage of his leaching liquor is wasted at this time? It has a bearing on the question in connection with the New Cornelia, and I think it is a very important question. E. P. MATHEWSON, Anaconda, Mont.-I am not sure what the percentage is now, but we don't discard the strong liquors. Something like 25 per cent. of the wash water taken out each day is sent over a special set of scrap iron tanks, and the copper recovered there. We had a little trouble at first. We did not proceed to use the sponge iron for the reason that the plant we originally contemplated was abandoned for flotation. Our original idea was to use a leaching process on all the tailings of the mill, but we found it would take a great deal of time to build a plant; and the cost of operating the plant we estimated to be about the same and the recovery the same. It was a question of time with us, and we decided to adopt flotation. That changed our plans. We now have the leaching plant, treating the tailings of the old dump, and the flotation applied to the current tailings. The sponge iron was figured for the large plant. We can get all the scrap iron necessary for the small plant-plenty from the scrap produced in the main plant of the smelter.

Jan 12, 1916

By O. D. Gonzalez

Existing measurements for the steady-state permeation of hydrogen in a iron above 100°C have been examined for contribution of determinate errors. The analysis leads to a recommended equation for the permeability of hydrogen in a iron: o= (2.9 ±0.5) x 10-3 exp - (8400 ± 400)/RT cu cm (ntp H2) cm-1 sec-1 atm-1/2 THE permeability of a iron to hydrogen has been the subject of numerous investigations over the past 40 years, and at present there are thirteen sets of published results for the rate of steady-state permeation of hydrogen in a iron above 100°C. The numerical values in each set of results are entirely self-consis-tent, but the spread among the sets is too large to be attributed solely to experimental error, i.e., to error other than in the specimen itself. Several reasons have been advanced to explain the disparities, but to date the relative importance of experimental inaccuracy to the spread remains uncertain. The purpose of this report is to examine in detail the sources of determinate errors inherent in the experiments and to assess as far as possible the contribution of the errors to the results. The ultimate goal is the selection of values for the permeability and heat of permeation most nearly representative of hydrogen in a iron. The analysis is limited to those experiments in which the permeation rate was observed at steady state—a condition in which traps for hydrogen within the metal are filled to a fixed level15 so that the trapping mechanism is not reflected in the rate of passage of the gas. Furthermore only data are examined in which surface processes are judged to have little or no influence on the flow. It is hoped with these restrictions to obtain values of the permeability and the heat of permeation which will be as closely related as possible to the mechanism of lattice diffusion. I) DEFINITION OF TERMS; UNITS In this report the data for permeation are given in terms of a coefficient oj permeability, ?, which is defined by the equation: jt=?A/?x{p1/2-po1/2) [1] where jt is the total flow of gas normal to the surface of a membrane of planar geometry, e.g., a disc, of area A and thickness ?x; pi and po are the pressures in the input and output sides, respectively. For flow radial to the walls of a membrane of cylindrical geometry, e.g., a tube, the corresponding equation is: where 1 is the length of the cylinder, and ri and ro are the inner and outer radii, respectively. The flux normal to the surface is given by Fick's law: j= -D(dc/dx) [3] At steady state the concentration gradient will be constant, and integration of Eq. [3] gives for the total flow through a disc of area A and thickness Ax: h =-DA(co - ci) [4] where c, and ci are the concentrations of solute at the output and input surfaces, respectively. When surface control is absent, co and ci are given by Sievert's law c = Kp1/2, and substitution therewith into Eq. [4] gives directly Eq. [I] where ? = DK. Integration of Fick's Eq. [3] in cylindrical coordinates will give Eq. [2] where again ? = DK and is thus shown to be independent of geometry (provided that surface control is negligible). The coefficient of permeability, or simply the permeability,* must be expressed in proper units. In *The term permeability will refer in this report always to the coefficient defined above; permeation will be used to specify the general phenomenon of gas passage through a membrane. this report ? will be expressed in the units of cu cm (ntp H2) cm-1 sec-1 atm-1/2. The variations of D and K with temperature are given by D = Do exp(-Ea/RT) and K = KO exp(-?Hs/RT) where E, is the activation energy for diffusion and AH, the heat of solution, each usually expressed in calories per mole of solute. The variation of permeability with temperature will thus be given (for conditions where surface control is negligible) by ? = ?o exp(-?Hp/RT) where ?0 = DoKo and ?Hp = Ea + ?Hs. The units of ?0 are the same as those of 6, and??Hp will be expressed in calories per mole H. 11) SUMMARY OF PERMEABILITY RESULTS Table I gives the values reported to date for the permeability of H2 in a iron in terms of ?o and ?Hp. Except where noted the parameters listed were taken directly from the numbers reported by the various investigators with only a change in units. The temperature limits within which the listed ?o and ?Hp hold are given in column 7; the limits marked in parentheses in this column indicate the entire temperature range covered in each investigation. The listed values of ?o and ?Hp are those giving a linear plot of ln? against T-1 at the higher temperatures in each set of measurements, and thus presumably represent the case for which surface control was negligible. Column 6 gives values of 9 at a representative tem-

Jan 1, 1970

By D. P. Morton

SINCE 1023, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (I) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.' This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as loo, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods. Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. 2 (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should he the same. It is neces-

Jan 1, 1941

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

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

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

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

ALEXANDER, JOHN S, M,'74-6,'81-3 ASHBURNER, C A, M, '85-7 ASMUS, GEORGE, Dl, '78-80 BACON, D H , M, '00-2 BAYLES, JAMES C , M,'80-2,'91-3 P, '84-5, V,'88-9 BIRKINBINE, JOHN, M, '83-5, V, 'S7-J, P, '91-2 BLAIR, THOMAS S , M, '74-43 BLAKE, WILLIAM P , V,'71-4,'76-7,'05-6 BLANDY, JOHN F, V,'71-3,'78-9 BLOW, A A, C, '05-7 BOWIE, A J , JR, V,'93-4 BRAMWELL, J H , A1, '89-91 BROOKS, THOS B , M, '72 BRUNTON, D W , V, 97-8 BUCK, STUART M , M, '83-5 BURDEN, JAMES A, V,'80-1 BURNHAM, WILLIAM, M, '82-4. CAMPBELL, H H, M, '93-5 CHAMBERLAIN, H S , V, '96-7 CHANNING, J PARKE, V,'08 CHRISTY, S B , V. '91-2, '07-8 CHURCH, JOHN A, M, '79-8l,'94-6, V, '07-8 COGSWELL, W B, V, '74-5,'86-7

Jan 1, 1910

By G. R. Speich, Morris Cohen

The growth rate of bainite has been determined by hot-stage metallography in five hypereutectoid high-purity iron-carbon, iron-carbon-chromium, and iron-carbon-nickel alloys. The studies have been confined essentially to lower bainite. The growth rate is independent of time at constant temperature, but both the edgewise and sidewise growth rates increase with increasing temperature. Increasing the carbon content, or adding chromium or nickel, decreases the growth rate without greatly affecting the temperature dependence. The results lead to separate diffusion-controlled models for the edgewise and sidewise growth rates. ALTHOUGH bainite has been subject of many detailed investigations,1,2 the growth mechanism of this intermediate transformation product of steel remains unclear. One difficulty has been that practically all the kinetic measurements have been restricted to studies of the overall reaction rate. Only a limited amount of information3, 4-6 is available on the growth process itself. The purpose of the present work was to investigate the effect of time, temperature and composition on the growth rate of bainite using hot-stage metallography. This method makes it possible to observe continuously the isothermal growth of individual bainitic units because of the surface upheavals accompanying their formation.3 This information is needed to test the existing growth models and to obtain a better understanding of the factors controlling the bainitic transformation. EXPERIMENTAL PROCEDURE Alloys—The compositions of the alloys used in the present work are shown in Table I. The five alloys were vacuum-melted and cast, and were prepared from high-purity materials. The three iron-carbon alloys were available from the work of Roberts et al.7 in the form of 3/8-in. diam rods.* To facilitate machining, the rods were ing. The rods were then tempered for 3 hr at 650°C to allow machining. The iron-carbon alloys in Table I were selected for investigating the effect of carbon on the bainitic growth rate. Due to the rapidity of the transformations involved, it was not feasible to measure the growth rates in iron-carbon alloys having carbon contents much less than 0.9 pct C. The iron-carbon-chromium and iron-carbon-nickel alloys were selected to study the influence of chromium and nickel on the growth rate at a carbon level of about 1.1 pct C, since this carbon content was intermediate among the iron-carbon alloys. The concentrations of chromium and nickel were chosen to match isothermal trans formation diagrams in the literature.8'9 Hot-Stage—Since the iron-carbon alloys had such low hardenabilities, it was necessary to quench the hot-stage specimens drastically from the austentiz-ing temperature to the isothermal transformation temperature to prevent the formation of pearlite or proeutectoid constituents. A rapid-quenching metal-lographic hot-stage was built for this purpose. A maximum temperature of about 1100°C and quenching rates up to 500°C per sec could be attained with this equipment. The details of the apparatus are described in a recent publication. After being polished and mounted on the hot-stage, the specimen (0.020 in. thick) was protected from oxidation and decarburization during austenitizing by a vacuum of 10-4 to 10-5 mm. The quench to the reaction temperature was accomplished with a helium blast, and the isothermal run at this temperature was conducted in a helium atmosphere. A fine-wire thermocouple spot-welded to the sample and a high-speed

Jan 1, 1961

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of- liquid Mg-Pb allojs have been determined by an isopiestic method from 18 to 42 at. pct Pb and by a thevmodynumic analysis of the phase diagram frofiz 0 to 100 at. pct Pb. In the overlapping composition range the magneszupn activity values derived by the two methods are in excellent agreement, thus mutually supporting the correctness of the Mg-Pb phase diagram previously determined by the authors and of the acticitzes deriz~ed isopiestically. SEVERAL studies have been made of the thermody-namic properties of liquid Mg-Pb alloys. Wagner and Engelhardt,1 Lantratov,2 Knappwost,3 Sryvalin et al.* and Wilson5 used the electromotive-force method, Scheil and Wolf8 and Schmahl and Sieben" applied the transpiration technique, and the present authors8 utilized the phase diagram to determine the activity of magnesium in the Mg-Pb system. The results of these studies are not in very good agreement and could not be incorporated into a general systematic analysis of the thermodynamic properties of the homologous series of the Mg-Group IV B systems Mg-Pb,8 Mg-Sn,° Mg-Ge,10and Mg-Si.11 The thermodynamic properties of the Mg-Pb system were therefore re investigated by an isopiestic technique which has been developed for similar studies in the Mg-SnB and Mg-Ge10 systems- Lead specimens, contained in iron or graphite crucibles, were heated in a temperature gradient in an evacuated and sealed titanium reaction tube and equilibrated with magnesium vapor of known vapor pressure to form alloys of compositions which depended on their temperatures, the temperature of the magnesium vapor source, and the thermodynamic properties of the system. EXPERIMENTAL PROCEDURE Magnesium (Dominion Magnesium Ltd., Toronto, Canada) of 99.99+ pct purity and lead (American Smelting and Refining Co.) of 99.999 pct purity were used. In the early experiments, Runs 2 and 3, the alloys were contained in uncovered high-purity iron crucibles. Alloys formed in the uncovered iron crucibles had to be chemically analyzed owing to the slight volatility of lead under the imposed experimental equilibration conditions. The compositions of these alloys were determined by a gravimetric analysis of lead as lead chromate. To avoid this problem, the remaining runs were made in covered graphite crucibles machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non- i reactivity of graphite with lead and magnesium has been previously established,' and the experimental procedure has been described in full detail.' In the runs using covered graphite crucibles it was found that the weight increases of the crucibles and their contents after equilibration equaled the magnesium contents of the alloys within the accuracy of the chemical analysis (i0.3 at. pct Pb). Clearly, the small lid openings of the graphite crucibles prevented significant lead losses during a run, and the weight increase was therefore taken as the magnesium content of the alloys. EXPERIMENTAL RESULTS At thermodynamic equilibrium the magnesium partial pressure of the specimens equaled that of the reservoir. Since the magnesium reservoir was always maintained at the temperature minimum of the system, the activity of magnesium of any specimen was given by the ratio of the magnesium reservoir pressure to the vapor pressure of pure magnesium at the specimen temperature. The standard state was chosen as liquid magnesium and the vapor pressure of liquid magnesium

Jan 1, 1968

By D. C. Ganow, N. J. Grant, I. R. Silver, A. R. Chaudhuri

The structural changes that result when a metal is "cold worked" lead to higher values of yield and tensile strength on subsequent deformation at room temperature. Further it has been shown that the beneficial effects of cold work are, to some extent, maintained even at elevated temperatures. The strength improvements from prior cold work decrease as the temperature is raised and are a function of grain size, amount of cold work, and strain rate (or time of test). If recrystallization occurs during test, the cold-worked material may even show weaker stress-rupture properties than the annealed material. A question that arises is whether there is a significant effect on the subsequent creep behavior if the prior deformation is performed under creep conditions at high temperatures not too different than the test temperature, but at significantly different strain rates and for various amounts of strain. An answer to this question was sought in the work described in the present paper. PROCEDURE Two materials were used in this work, high-purity aluminum and a solid-solution A1 2 pct Mg alloy. The compositions are shown in Table I. The grain size in the two materials was 0.2 to 0.3 mm. The deformation for both the prestraining and for the creep tests was at constant stress. The procedure adopted was to prestrain a specimen to the desired elongation, remove the load, and cool to room temperature rapidly by spraying. the test bar with cold water. The specimen was then placed in a creep machine, held at the test temperature for less than 5 min, and loaded. Less than 15 min was required to bring the specimen to temperature. The creep stress was based on the diameter resulting from the prior strain, and values of elongation at fracture listed in the tables do not include the respective elongations resulting from the prestrain. The choice of the stresses for the prestrain and for the creep tests was made so that the tests could be completed in relatively short times to maximize any effect of prestrain. The specimens had a gage length of 1 in., the pure aluminum specimens having a diameter of 0.150 in. and the alloy specimens a diameter of 0.125 in. For pure aluminum, prestrain was at 400' and 600°F with testing at 500°F; for the alloy, prestraining was at 700°F and testing at 600°F. RESULTS The prestrain conditions for the aluminum and the alloy specimens are shown in Tables I1 and IV. In addition to showing the time required to achieve the desired prestrain, the expected rupture Lives are given which would have resulted had the creep prestrain been continued to fracture. The prestrained and the annealed specimens were then tested in creep to fracture; the temperature and stress for the pure aliminum specimens being 500o F and 1800 psi and for the alloy, 600' F and 3400 psi. The creep curves for the prestrained and the annealed specimens of pure aluminum showed all three stages of creep; hence in addition to the effect of prestraining on the rupture life, it was also possible to determine the effect of prestraining on the minimum creep rate, and on the time and elongation at the end of each of the three creep stages. The results are shown in Fig. 1 and Table 111.

Jan 1, 1960

By C. R. Claus, G. A. Standish

Since March. 1945, the Magnolia Petroleum CO. has drilled 39 wells in Southwest Coastal Louisiana. All wells were drilled within a comparatively small radius, but the area provides a large variety of problems. The deepest well drilled was 13,518 ft, and the total depth averaged 10,977 ft. Throughout this period drilling mud control and types of mud handled were: (I) phosphate, (2) red lime (late conversion), (3) red lime starch (early conversion), (4) red lime starch oil emulsion, (5) precision controlled low alkalinity-low lime content. and (6) gel muds for completion purposes. Improvement has been obtained in effecting some or all of the following: (I) more rapid penetration, (2) reduction in drilling hazards, (3) better evaluation of cores and logs, and (4) better completions. The geological sequence of zones penetrated range from recent sediments at the grass roots through the Frio section. Anticipation of high-pressure zones and incompetent formations entails precision control of drilling mud weights, and the unconsolidated nature of the various zones requires constant attention to the filtrate, viscosity, and gel strength values. In the Chalkley field, particularly, this combination of problems exists, where the formation pressures and overburden weight density values are in very close proximity. Design of casing and drilling mud programs must be modified to fit each well. INTRODUCTION Field and research work on drilling fluids has made constant progress, enabling operators to prospect progressively deeper horizons. Numerous papers have been written on the theoretical aspects of drilling fluid devel- opment, but in the field engineers have found it difficult to evaluate the role of specific mud constitutents when dealing in terms of thousand barrel mud systems. For that reason field data is somewhat lagging in technical report writing. However, applications of new techniques in the field have usually paralleled, and in numerous instances preceded, research work. The information obtained by Magnolia Petroleum Co. in the course of drilling 39 wells within a comparatively small area in Southwest Coastal Louisiana provides an excellent opportunity of reviewing a specific example of drilling mud evolution. A large variety of problems has been coped with, the most important result being that every well was successfully drilled to its projected total depth. The discussion begins with the advent of deep drilling in this area in March, 1945, and is concluded with a resume of recent drilling operations in the Chalkley field. The primary purpose of this paper is to describe the evolution in types of drilling fluids as it occurred and its application in the solution of various drilling problems. All of this information and experience resulted in the successful drilling of the three wells in the Chalkley field, where a combination of the most sound techniques was necessary in carrying drilling operations to the projected total depths. Other operators along with service company engineers have contributed considerably through the interchange of ideas and information to this paper, but the data and conclusions which are contained are based on first-hand observation of Magnolia Petroleum Company's drilling operations. The 39 wells drilled by Magnolia Petroleum Co. average in depth 10,977 ft per well, while the maximum depth penetrated was 13,518 ft. The cost of drilling fluids have varied from $8,700 to $165,000, with the over-all drilling costs ranging from $74,000 to $543,000 per well. This wide variance illustrates the unpredictable nature of each well and the effects on over-all cost when high density muds are required to control

Jan 1, 1955

By B. D. Smith, K. H. Coats

Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 50 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. INTRODUCTION Axial dispersion — the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relativeiy recent studiesl-13 and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles. In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentallv determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model. In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and johnston14 for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: The dispersion coefficient D for unconsolidated systems is correlated by u is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand.l4 Eq. 3 holds for 2 For a Do homogeneous (regular) type of packing, should be 1 or less.6 Aris and Amundson6 and Carberry and Bretton consider o to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm.15 For v /Do less than about 2, the effect of molecular diffusion must be considered and the total dispersion coeffi-

Jan 1, 1965

By J. A. Hren, G. Thomas

A high-temperature stage has been used to study precipitation and dissolution in thin foils of Al-20pct Ag alloy directly in the electron microscope. The results show that the aging characteristics are similar to those observed for bulk materials, and in addition, direct evidence is presented for clustering at the solid solution temperature. The limit of solubility of G. P. zones is-350°C. The heterogeneous precipitation, the growth and dissolution of ?&apos;have been studied in detail. Growth of ?&apos; parallel to the basal planes, occurs by continuous motion of inter -facial partial dislocations. Growth stops at intersecting particles due to formation of sessile a/6 <110> interfacial dislocations. Growth normal to the habit plane occurs by the spontaneous nucleation of partial dislocations on alternate (111) planes and the thickening rate is --10-3= times the lengthening rate. The precipitates dissolve in layers and the final product is a whole a/2 <110> dislocation . The nucleation -growth -dissolution processes are thus completely reversible. Kinetic data obtained from the dissolution rates of ?&apos;particles enable the diffusion coefficient to be determined and the activation energy is found to be 37.5(±4) kcal mol-1, which is that expected for dzffusion of silver in aluminum. The velocity of the interfacial dislocations is thus dependent solely on the rate of diffusion of silver atoms. RECENTLY it was demonstrated that a high-temperature stage could be effectively used in the electron microscope to follow directly the processes of precipitation and dissolution in thin foils of A1-4 pct Cu alloy.&apos; These experiments also provided kinetic data which enabled the diffusion coefficient to be estimated. This new development of electron metallography opens up many fruitful areas of research and it was decided to investigate the aging behavior in thin foils of A1-20 pct Ag alloy, particularly the mechanism of heterogeneous precipitation (i.e., precipitation on lattice defects). This system was chosen because the aging characteristics of bulk specimens are now well known,2"7 and because we wished to obtain more details of the role played by partial dislocations and stacking faults in the nucleation growth and dissolution of the hcp ?&apos; phase. This is of interest for the general case of fcc-- hcp transformations. Part of the A1-Ag phase diagram is shown in Fig. 1. The use of a high-temperature stage also enables a study to be made of the clustering process (formation of G. P. zones) and to determine the structure of the solid solution prior to the usual quenching and aging procedures. It is also possible to obtain kinetic data from measurements of the rates of dissolution of precipitate particles. Unlike the results of previous experiments on A1-4 pct CU 1 where much of the initial precipitation occurred on the foil surfaces, the results on the A1-20 pct A1 alloy were identical to those reported for bulk specimens6,7 and no surface precipitation was ever observed. Thus, it was possible to follow the aging sequence: G.P. zones — ?&apos; — ? directly in the thin foils. This paper is concerned with the formation and dissolution of zones and the ?&apos; phase, and no attempt has been made so far to follow the mode of discontinuous precipitation of ?. I) EXPERIMENTAL DETAILS The high-purity A1-20 pct Ag alloy was prepared by the Aluminum Co. of America in the form of 0.001-in.-thick sheets. These were cold rolled with intermediate anneals to a thickness of 0.0004 in.,

Jan 1, 1963

By H. P. Stuwe

It is investigated whether a model of sphere packing permits the computation of the lattice parameters and their variation with concentration in various a phases; it does, except in phases containing silicon. Several observations indicate that a particular role is played by the "E-atoms" in the lattice. THE phase is formed by many alloys of the transition elements.&apos;-&apos; Its structure has been described by Bergman and Shoemaker,5,8 Dickins, Douglas, and Taylor,7 and Kasper, Decker, and elanger.&apos; There are five kinds of crystallographically equivalent positions for the 30 atoms in the unit cell which have been designated by these authors I, 11, 111, IV, and V or, in the same sequence, A, B, C,D, and E, as shown in Fig, 1. For the purposes of the present paper two elements of the lattice will be discussed separately: The lattice planes perpendicular to the c-axis which are made up by the atoms A, B, C, and D and which determine the a-parameter; and the close-packed "vertical rows" of E-atoms which determine the c-parameter. asper,9 and Frank and kasper10 described the a phase and other complex structures as sphere packings. In these papers particular attention is paid to the coordination polyhedra. Lattice positions with an equal number of nearest neighbors are considered equivalent regardless of their crystallo-graphic description. This seems to work very well for the explanation of ordering phenomena in the a phase as far as information on this is available." If the description of the phase as a sphere packing is valid it should be possible to draw two further conclusions: 1) It should be possible to calculate the lattice parameters from the atomic radii of the components, and 2) It should be possible to predict the variation of the lattice parameters with concentration within one phase field. Both points are discussed in this paper. PROCEDURE Measurements of lattice constants were done with a symmetrical back-reflection X-ray camera. With Cr-radiation, about a dozen a1 lines could be observed with most samples. From the (550/710)- and 720-lines the a-value was computed. With this value the c-parameter was calculated from the (333)- and (413)-lines. Finally, the position of all the other lines was computed from the lattice parameters thus obtained. In this way the validity of the indexing could be checked and, at the same time, this proce- dure gave an estimate of the accuracy of the lattice parameters. A correction was made for film shrinkage. The atomic radii used in the computations are the Goldschmidt radii for coordination number 12. Actually, some of the atoms have a coordination number of 14 or 15, but the error thereby introduced is small. * For the computation of lattice constants from the atomic radii an "average atomic radius" of all components was used, i.e., complete disorder was assumed. Although this seems to be true for some systems like OS-Cr,4 it is not true in others.11,13,14 The ordering model, however, which has been suggested by Kasper on the basis of extensive research lets both kinds of atoms contribute to both the &apos;&apos;vertical rows" and the lattice planes perpendicular to them, so that even with ordering of this kind the assumption of complete disorder cannot introduce a very serious error in calculating lattice parameters. RESULTS Bergman and shoemaker6 gave a table of the interatomic distances in the Fe-Cr phase. If we disre-

Jan 1, 1960

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation&apos;s supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation&apos;s need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation&apos;s supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation&apos;s need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By K. P. Gupta

The Cb-rich boundary of the (Cb,Al) a phase field at 1250OC is near 41 pct Al. The Al atoms tend to occupy the C. N. 12 sites in this structure. A homologous (Ta,Al)a phase was identified. No a phase was found in the Mo-Al system at 1200°C. The first binary o-phase with a non-transition element as a major component was found1,2 in the Cb-Al system. The composition of this phase was reported2 as approximately 34 at. pct Al, based on X-ray diffraction patterns taken of alloys in the as-cast condition. Further study of the composition of this o-phase, therefore, appeared desirable. Since Si was previously found3,4 to occupy preferentially the lowest C.N. sites (I and IV) in the a phase, and preliminary resultsa indicated that Al may show similar ordering, one of the aims of the present work was to obtain more complete information on ordering in (Cb, Al) o. Among the binary systems of Al with Ti-, V-, and Cr-group elements, the Ti-Al, Zr-Al, V-Al, and Cr-Al systems are known to comprise no o-phase. In the present work a Ta-Al and a Mo-Al alloy were studied in an effort to find additional o phases with Al as a major component. EXPERIMENTAL PROCEDURES AND RESULTS An alloy with the intended composition of Ta + 40 at. pct Al was prepared by arc melting in He atmosphere. In both the as-cast condition and after annealing for 10 days at 1250°C and quenching in cold water this alloy consisted of two phases, as seen in the X-ray pattern and the microstructure. One of these phases was identified as the o-phase; the observed and calculated d-spacings are shown in Table I. The lattice parameters of this o-phase are a = 9.972 A, c = 5.214 A and c/a =0.5228, as determined from a Debye-Scherrer pattern using Fe K a radiation. The d-spacings for the unknown second phase are given in Table 11. The alloy contained approximately 25 pct of the unknown phase after annealing, as estimated on the basis of microscopic examination. A Mo-Al alloy was prepared by arc melting, with an intended Al-content of 35 at. pct. The alloy button was annealed for 7 days at 1200°C and water quenched. The X-ray pattern of the alloy in both the as-cast and the annealed state showed the reflections of Mo3Al (Cr30 type structure) and an unknown phase different from a. Six Cb-Al alloys were prepared in the composition range 30 to 50 pct Al. All alloys were arc melted in He atmosphere. After annealing for three days at 1175oC in evacuated silica capsules and quenching in water, the alloys with 30 to 40 pct Al contained three phases, namely the o-phase, Cb3Al (Cr3O-type structure) and an unknown phase. The alloys with more than 40 pct Al contained two phases, namely, what appeared metallographically, the o-phase and the same unknown phase. In the alloys containing less that 38 pct Al, the unknown phase was not present after annealing for 4 days at 1250°c,

Jan 1, 1962

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.&apos; Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train&apos; The &apos;ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961