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By Tedsen L. F., Dorn J. E., A. E. Flanigan

since aluminum-alloy sheet may be used occasionally at moderately elevated ternperatures, the effects of temperature on the mechanical properties are of interest. Recently the short-time tensile properties of several high-strength materials have been studied at temperatures up to 3750°F.l This paper deals with stress-rupture and creep properties at the same temperatures. The work was done at the University of California as a portion of the project NRC-548. It was financed by the War Production Board and was supervised by the Office of Production Research and Development. This paper has been released for publication by the latter agency. The following materials were studied, all in the form of 0.040-in. sheet: Alclad 24s-T Alclad 24s-T8I Alclad 24s-T86 Alclad 75s-T R3oI-T (clad) Specimens were loaded in tension in the cross-grain direction. Testing temperatures included 94°F., 2II°F., 300°F., and 375°F. Stress levels were selected to cause rupture in times ranging from several minutes to 1000 hr. In each test the following data were obtained: (I) fracture time, (2) elongation at fracture, (3) the complete strain-versus-time curve (creep curve), (4) creep rate (defined in a later section). Materials Materials for specimens were obtained from the manufacturers' commercial

Jan 1, 1947

By Tedsen L. F., Dorn J. E., A. E. Flanigan

since aluminum-alloy sheet may be used occasionally at moderately elevated ternperatures, the effects of temperature on the mechanical properties are of interest. Recently the short-time tensile properties of several high-strength materials have been studied at temperatures up to 3750°F.l This paper deals with stress-rupture and creep properties at the same temperatures. The work was done at the University of California as a portion of the project NRC-548. It was financed by the War Production Board and was supervised by the Office of Production Research and Development. This paper has been released for publication by the latter agency. The following materials were studied, all in the form of 0.040-in. sheet: Alclad 24s-T Alclad 24s-T8I Alclad 24s-T86 Alclad 75s-T R3oI-T (clad) Specimens were loaded in tension in the cross-grain direction. Testing temperatures included 94°F., 2II°F., 300°F., and 375°F. Stress levels were selected to cause rupture in times ranging from several minutes to 1000 hr. In each test the following data were obtained: (I) fracture time, (2) elongation at fracture, (3) the complete strain-versus-time curve (creep curve), (4) creep rate (defined in a later section). Materials Materials for specimens were obtained from the manufacturers' commercial

Jan 1, 1947

By Daniel N. Beshers, Ralph H. Condit

An expression for the diffusion coefficient of inlerstitial atoms in the bcc lattice is derived which takes account of jumps between tetrahedral and octahedral interstices. The results are applied to the case of carbon diffusion in iron to find values for jump frequencies of the types, octahedral-tetrahedral, tetra-hedral-tetrahedral, and tetrahedral-octahedral. ThERE has been renewed discussion1-5 concerning the mechanism of diffusion of interstitial atoms in the bcc lattice. This lattice has both octahedral and tetrahedral interstices, and it has been pointed out that the interstitial atoms may make jumps of the octahedral-octahedral type, hereafter called o-o, octahedral-tetrahedral, o-t, and tetrahedral-tetrahedral, t-t. Doubt has been cast on the applicability of snoek's8 model for internal friction to some interstitial migrations in bcc lattices wherein he proposed 0-0 jumps as the principal mechanism of migration. Also, the anomalous excess diffusion of carbon in iron at high temperatures4 has been ascribed to t-t jumps,2,3 even though the sites normally occupied are octahedral. In this paper an expression is derived for the diffusion coefficient, taking account of the three types of jump mentioned. The relationship of the coefficient to the corresponding internal friction relaxation time is found for the limiting case corresponding to Snoek's model. These results are applied to the case of carbon in iron. In Fig. 1, the structure is shown with the locations of the interstices. Each o site has four t site neighbors coplanar with it, and each t site lies halfway between two o sites. There are four t site first neighbors of a t site lying at the vertices of a tetrahedron. Let the average fraction of atoms occupying o sites and t sites be No and Nt, respectively. Since there are six o and twelve t interstices per unit cell having a lattice parameter, a, the concentration of interstitial atoms will It will be assumed that three types of jumps may be distinguished, t — t, t — o, o — t,for which the jump

Jan 1, 1968

By Howard I. Smith

THE mineral trona was discovered on Government land in 1938, about 18 miles west of the town of Green River, Wyo., in the core of the John Hay, Jr., well, a test well drilled for oil by the Mountain Fuel Supply Co. in sec. 2, T. 18 N., R. 11o W., sixth principal meridian. Although no oil or gas was reported, the drilling led to a discovery of great potential economic importance and exceptional scientific interest. Trona is a relatively rare mineral found at various places in playa deposits but not previously found at any great depth. It is composed of hydrous sodium carbonate and sodium bicarbonate (Na2CO3.NaHCO3.2H2O). Pure trona contains the equivalent of 70.35 per cent of sodium carbonate. Total sodium computed to carbonate times 1.42 equals the percentage of trona in the absence of other sodium carbonate minerals in the sample. ANALYSES Two short pieces of core sent to the author a few days after the completion of the Hay well were analyzed by R. C. Wells† and found to be exceptionally pure trona. A brief article on this discovery has already been published.1 Arrangements were then made through W. T. Nightengale‡ for the author to inspect and sample the core. The company log of the well included notations of sodium salt crystals from a depth of 1190 to 1820 ft. Not being able to identify all the minerals present, the author selected several specimens of the core for petrographic examinations and sampled the sections of trona for analysis. J. J. Fahey, of the Geological Survey, examined the specimens and reported most of the crystals to be a new anhydrous sodium carbonate and calcium carbonate mineral (Na2CO3.2CaCO3), which he named shortite,2 after Maxwell N. Short.* He analyzed the samples of trona, with the results shown in Table i. [ ] In addition to the 10 ft. I in. of trona in the first section, it is reasonable to assume that the 9 ft. 8 in. for which no core was available for sampling is either mostly trona or some other soluble salt, but it should not be included in calculating reserves. In the part of the core between 1590 ft. 3 in. and 1600 ft. 4 in. the material insoluble in cold water, amounting to about 5 per cent, was estimated petrographically to contain 70 per cent clay, 25 per cent shortite, and 5 per cent pyrite. ACCOMPANYING MINERALS Fahey later secured about 600 ft. of the core for a detailed examination and study

Jan 1, 1942

By T. H. Alden

BaCKOFEN, Avery, and Turner have shown"2 that the large tensile elongation in superplastic metals is correlated with a high strain-rate sensitivity of the flow stress. At present, the reported superplastic materials are complex eutectic or eutectoid systems with a large solubility range in at least one of the terminal phases. This note describes the behavior of a solid-solution alloy (at 22°C)5,= Sn-1 wt pct Bi, which has been processed in order to produce a fine grain size.2,3,6 The chill-cast, 1/2-in.-diam ingot was homogenized for 1 week at 130°C, extruded at O°C to 0.083 in. diam, quenched within 15 sec, and stored at -196°C. Samples were warmed to room temperature 16 hr prior to mechanical testing or metallography. During tension testing at room temperature, it was found that the flow stress reached a steady-state value which depended on the imposed elongation rate and was independent of strain to an error of about ±5 pct. In Fig. 1 is plotted log a vs log e where a is the measured steady-state flow stress and i the imposed strain rate. These quantities were calculated using "instantaneous" area and length to an accuracy in the sample diameter of ±5 x 10-4 in. The log a-log 1 curve is sigmoidal. The strain-rate sensitivity, which may be given by d log old log 6,' has a maximum value of about 0.48 between i = 5 x 10-4 and 5 x 10-3 per min. The value is well above frequently measured values for metals at creep temperatures (0.1 to 0.3) and comparable to the rate sensitivity for Pb-Sn solder: which has been shown to be superplastic.2,3 Note, however, that below or above the strain rate of 10-3 per min the rate sensitivity of Sn-1 pct Bi decreases and at high rates is more nearly like that of conventional metals. The grain size of this material is relatively uniform, Fig. 2, and may be specified by an average linear intercept i.' Grain growth occurs at room temperature but after 16 hr, L = 5. Tensile elongation was measured on finer-grain-size specimens, which had been at room temperature 15 min prior to testing. After 15 min, the samples are fully recrystallized. Three strain rates, 5 x 10-3, 10-2, and 2.5 x 10-2 per min, were employed for which the measured elongations varied from 425 to 500 pct. These results would seem to justify the term superplastic, applied to this alloy, although the ductility is inferior to that of the Sn-Bi eutectic.3 The Sn-1 pct Bi alloy, which is a single-phase material with equiaxed, fine grains, is an excellent one on which to make an estimate of the Nabarro-Herring9 creep rate. According to the model of Avery and Backofen2 a substantial part of the deformation must be accomplished by N-H creep in the strain rate-temperature regime in which d log a/d log 1 = 0.5. The maximum N-H creep rate is given by9 L2kT where v is the atomic volume and D the self-diffusion coefficient. For this test v = 3.O x 10-23 cu cm, D = 1.4 e-23,300/RT = 2.5 x 10-l7 sq cm per sec,7 L = 5x 10+4 cm, T = 295°K, and a = 2000 lb per sq in. = 1.38 x 10' dyne per sq cm. The calculated creep rate is E= 4 x 10-11 per sec which may be compared with the measured creep rate at this stress, Fig. 1, of 6.7 x 10-5 per sec. The N-H creep rate is seen to be negligible. Earlier consideration2 of this question was in error because incorrect diffusion coefficients were used. The assistance of R. R. Russell in metallography is acknowledged gratefully.

Jan 1, 1967

By A. M. Kivari

Operations at the cement plant of the Permanente Corporation, in the hills about 45 miles south of San Francisco and 12 miles west of San Jose, are interesting to the members because of the adoption of modern hydrometallurgical methods for handling and beneficiating raw materials. Closed-circuit grinding, classification, hy-droseparation, flotation, agitation, and thickening are familiar terms at this cement plant. These methods make it possible to process refractory limestone into suitable materials for the mallufacture of modern cements. Construction of the plant, having originally a design capacity of 7000 bbl. of cement per day, was started in June 1939, and the first clinker was ground on the following Christmas Day. At present the capacity is about 12,000 bbl. of finished cement per 24 hr., most of the production being low-heat cement. † About 3I30 tons of limestone, 620 tons of clay and I00 tons of gypsum are required daily for this output. Occasionally iron oxide is added to the clay to obtain the desired composition. This, together with the gypsum, is purchased from outside sources. up to the present time, the ccrporation has produced low-heat, normal, moderate-heat, moderate-sulphate-resisting, high-early-strength, oil-well, modihed-oil-well, and plastic cements. Most of the present production is for Shasta Dam, near Red- ding, Calif., the total demand being 5,800,000 bbl. of cement. Following are some of the cement require ments of the Shasta Dam specifications: Per Cent Chemical composition: Loss in ignition.......... 2.25 Insoluble residue......... 0.75 SO3.................... 2.25 MgO................... 5.'' Uncombined lime in clinker (CaO)......... I.25 Percentage of iron oxide to alumina ratio....... I.5 Compound composition: Tricalcium silicate (3CaO.SiO2)........... Not more than 35 Dicalcium silicate (zCaO.SiO2)........... Not less than 40 and not more than 65 Tricalcium aluminate (3CaO.Al2O3).......... Not more than 7 Tetracalcium aluminofcr- rite (4CaO.Al²O³.Fe²O³) Not more than 20 Fineness: The average specific surface in the bin sampled shall be not less than 1800 sq. cm. per gram and no individual sample less than 1600 sq. centimeters. Compressive strength: The average compressive strength in pounds per square inch of three mortar cubes composed of one part cement and 2.75 parts fine testing sand, by weight, shall be equal to or greater than the following:

Jan 1, 1942

By A. M. Kivari

Operations at the cement plant of the Permanente Corporation, in the hills about 45 miles south of San Francisco and 12 miles west of San Jose, are interesting to the members because of the adoption of modern hydrometallurgical methods for handling and beneficiating raw materials. Closed-circuit grinding, classification, hy-droseparation, flotation, agitation, and thickening are familiar terms at this cement plant. These methods make it possible to process refractory limestone into suitable materials for the mallufacture of modern cements. Construction of the plant, having originally a design capacity of 7000 bbl. of cement per day, was started in June 1939, and the first clinker was ground on the following Christmas Day. At present the capacity is about 12,000 bbl. of finished cement per 24 hr., most of the production being low-heat cement. † About 3I30 tons of limestone, 620 tons of clay and I00 tons of gypsum are required daily for this output. Occasionally iron oxide is added to the clay to obtain the desired composition. This, together with the gypsum, is purchased from outside sources. up to the present time, the ccrporation has produced low-heat, normal, moderate-heat, moderate-sulphate-resisting, high-early-strength, oil-well, modihed-oil-well, and plastic cements. Most of the present production is for Shasta Dam, near Red- ding, Calif., the total demand being 5,800,000 bbl. of cement. Following are some of the cement require ments of the Shasta Dam specifications: Per Cent Chemical composition: Loss in ignition.......... 2.25 Insoluble residue......... 0.75 SO3.................... 2.25 MgO................... 5.'' Uncombined lime in clinker (CaO)......... I.25 Percentage of iron oxide to alumina ratio....... I.5 Compound composition: Tricalcium silicate (3CaO.SiO2)........... Not more than 35 Dicalcium silicate (zCaO.SiO2)........... Not less than 40 and not more than 65 Tricalcium aluminate (3CaO.Al2O3).......... Not more than 7 Tetracalcium aluminofcr- rite (4CaO.Al²O³.Fe²O³) Not more than 20 Fineness: The average specific surface in the bin sampled shall be not less than 1800 sq. cm. per gram and no individual sample less than 1600 sq. centimeters. Compressive strength: The average compressive strength in pounds per square inch of three mortar cubes composed of one part cement and 2.75 parts fine testing sand, by weight, shall be equal to or greater than the following:

Jan 1, 1942

By Howard I. Smith

The mineral trona was discovered on Government land in 1938, about 18 miles west of the town of Green River, Wyo., in the core of the John Hay, Jr., well, a test well drilled for oil by the Mountain Fuel Supply Co. in sec. 2, T. 18 N., R. IIO W., sixth principal meridian. Although no oil or gas was reported, the drilling led to a discovery of great potential economic importance and exceptional scientific interest. Trona is a relatively rare mineral found at various places in playa deposits but not previously found at any great depth. It is composed of hydrous sodium carbonate and sodium bicarbonate (Na2CO3 NaHCo3.2H2O). Pure trona con-tains the equivalent of 70.35 per cent of sodium carbonate. Total sodium computed to carbonate times 1.42 equals the percentage of trona in the absence of other sodium carbonate minerals in the sample. Analyses Two short pieces of core sent to the author a few days after the completion of the Hay well were analyzed by R. C. Wells† and found to be exceptionally Pure trona. A brief article on this discovery has already been published.1 Arrangements were then made through W. T. Nighten-gale‡ for the author to inspect and sample the core. The company log of the well included notations of sodium salt crystals from a depth of 1190 to 1820 ft. Not being able to identify all the minerals present, the author selected several specimens of the core for petrographic examinations and sampled the sections of trona for analysis. J. J. Fahey, of the Geological Survey, examined the specimens and reported most of the crystals to be a new anhydrous sodium carbonate and calcium carbonate mineral (Na2CO 3.2 CaCO3), which he named shortite,² after Maxwell N. Short." He analyzed the samples of trona, with the results shown in Table I. In addition to the 10 ft. 1 in. of trona in the first section, it is reasonable to assume that the 9 ft. 8 in. for which no core was available for sampling is either i mostly trona or some other soluble salt, but it should not be included in calculating | reserves. In the part of the core between i 1590 ft. 3 in. and 1600 ft. 4 in. the material insoluble in cold water, amounting to about 5 per cent, was estimated petrographically I to contain 70 per cent clay, 25 per cent shortite, and 5 per cent pyrite. Accompanying Minerals Fahey later secured about 600 ft, of the core for a detailed examination and study

Jan 1, 1942

By Howard I. Smith

The mineral trona was discovered on Government land in 1938, about 18 miles west of the town of Green River, Wyo., in the core of the John Hay, Jr., well, a test well drilled for oil by the Mountain Fuel Supply Co. in sec. 2, T. 18 N., R. IIO W., sixth principal meridian. Although no oil or gas was reported, the drilling led to a discovery of great potential economic importance and exceptional scientific interest. Trona is a relatively rare mineral found at various places in playa deposits but not previously found at any great depth. It is composed of hydrous sodium carbonate and sodium bicarbonate (Na2CO3 NaHCo3.2H2O). Pure trona con-tains the equivalent of 70.35 per cent of sodium carbonate. Total sodium computed to carbonate times 1.42 equals the percentage of trona in the absence of other sodium carbonate minerals in the sample. Analyses Two short pieces of core sent to the author a few days after the completion of the Hay well were analyzed by R. C. Wells† and found to be exceptionally Pure trona. A brief article on this discovery has already been published.1 Arrangements were then made through W. T. Nighten-gale‡ for the author to inspect and sample the core. The company log of the well included notations of sodium salt crystals from a depth of 1190 to 1820 ft. Not being able to identify all the minerals present, the author selected several specimens of the core for petrographic examinations and sampled the sections of trona for analysis. J. J. Fahey, of the Geological Survey, examined the specimens and reported most of the crystals to be a new anhydrous sodium carbonate and calcium carbonate mineral (Na2CO 3.2 CaCO3), which he named shortite,² after Maxwell N. Short." He analyzed the samples of trona, with the results shown in Table I. In addition to the 10 ft. 1 in. of trona in the first section, it is reasonable to assume that the 9 ft. 8 in. for which no core was available for sampling is either i mostly trona or some other soluble salt, but it should not be included in calculating | reserves. In the part of the core between i 1590 ft. 3 in. and 1600 ft. 4 in. the material insoluble in cold water, amounting to about 5 per cent, was estimated petrographically I to contain 70 per cent clay, 25 per cent shortite, and 5 per cent pyrite. Accompanying Minerals Fahey later secured about 600 ft, of the core for a detailed examination and study

Jan 1, 1942

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 Takeyasu Ito, Mayumi Someno, Kazuhiro Goto

SINCE the pioneering work by Kiukkola and Wagner,1 many experiments have been reported on solid electrochemistry at elevated temperatures. However, the studies have been confined to experiments under isothermal conditions. One may conceive many situations under nonisothermal conditions. With two different temperatures T1, and T2 at the two electrodes, the electromotive force, E of a Galvanic cell will be expressed by the following equation under a steady state heat transfer in solid electrolytes of zirconia-lime and thoria-lime. E = ^ $ l&-dGO2+a(T2-Ti) [1] where tO2- is the transference number of oxygen ions in the electrolyte, Go, is the chemical potential of oxygen, and a is the coefficient of the thermoelec-tromotive force due to the temperature difference. The objective of the present study was to evaluate the coefficient of the thermoelectromotive force for zirconia-lime and thoria-lime under isobaric condition. The physical meaning of this coefficient is out of the scope of the present communication. The experimental cell assembly is schematically shown in Fig. 1. The zirconia-lime electrolyte tube and thoria-lime electrolyte tube were 8.0 mm OD and 5.0 ID, from commercial sources with chemical analyses of 94.8 wt pct ZrO2, 3.85 pct CaO, 0.83 pct SiO2, 0.25 pct TiO2, and 0.05 pct Fe2O3; and 95.0 pct ThO2, 4.0 pct CaO and rare earth metal oxides, respectively. The specific gravity was 5.5 g per cu cm for zirconia-lime and 9.8 g per cu cm for thoria-lime. Original powder size before shaping and sintering the tube was several microns for both electrolytes. The distance separating the two electrodes was 4.0 or 5.0 cm. Platinum wire of 0.5 mm diam was used for the electrodes. The temperature gradient was controlled by heating one electrode with a small heating coil of nichrome wire. The temperatures at the two electrodes were measured with two calibrated Pt-13 pct Rh:Pt thermocouples, directly contacting the two platinum electrodes. The atmosphere was either air or pure oxygen. The partial pressure of oxygen in air was considered equal at the vicinities of the two electrodes, with negligibly small thermal segregation in the gas phase. The difference of the chemical potential of oxygen was controlled only by the temperature difference at the two electrodes and not by the oxygen pressure difference. The temperature ranges were 600" to 1200°C for zirconia-lime and 850" to 1200°C for thoria-lime electrolytes. Fig. 2 shows the relation of the measured electromotive force and the difference of the oxygen chemical potential at the two electrodes for zirconia-lime and thoria-lime electrolytes. The electromotive forces in the figure were measured by a *0.05 mv potentiometer. The chemical potential difference was calculated by the following equations.'

Jan 1, 1970

By Finn Ouchterlony

A simple bilinear R-curve description of crack extension resistance is applied to the testing of sub-size rock core specimens. The K-curve consists of a linear sub-critical part and a flat post-critical part. Formulas for the apparent energy rate resistance quantities Gm, Jm, and [R] are developed. Experiments on notched cores of Ekeberg marble, Bohus granite, and Stripa granite are compared with these predictions. The R-curve model gives reasonable results for Gm -data but fails essentially to describe the Jm and [R]-data. Another model with a sharply increasing linear post-critical part could possibly account for the [R]-data, but direct R-curve measurements seem a better approach.

Jan 1, 1982

By G. P. Marino

The "conductivity ", Kr, of a spherical void in a linear temperature gradient due to radiation is calculated by integration of the general expression for diffuse radiation between two gray surfaces of arbitrary orientation. The spherical geometry allows an exact evaluation of the phenomenon without resorting to up-proximate expressions for the radiant heat flux. The resulting expression for Kr is three quarters of the approximate value obtained by Loeb. IN the determination of the thermal conductivity of porous materials such as sintered UO2 and ThO2 fuel pellets, the magnitude of the thermal conductivity in the pores due to radiative heat transfer across the pore, Kr, may be important in assessing the total conductivity of the pellets. Loeb' has calculated Kr for various pore geometries by approximating the net flux of heat between two surfaces of temperature difference AT as 4eT~AT and obtained: K,=4yoet3odp [1] where a is the Stefan-Boltzmann constant, E is the emissivity of the radiating surface, To is the average absolute temperature of the region across which radiation occurs, dp is the largest dimension of the gap in the direction of heat flow, and y is a geometric factor. That is: y = 1 for laminar pores and cylindrical pores with axes parallel to the heat flow direction, y = 2/3 for spherical pores, y = /4 for cylindrical pores with axes perpendicular to heat flow direction. It was the purpose of this work to obtain an exact expression for K, in spherical pores by integration of the general expression for the net heat transfer between two incremental areas on the surface of a spherical pore. This procedure yields a value of Kr 3/4 of that obtained by Loeb. I) CALCULATION OF Kr Fig. 1 illustrates the general geometry which defines the problem. The total emissive power for a gray body is given by: E = EoT4 [2] where E is the radiated energy per unit area of the radiation surface per unit time, T is the absolute temperature, o is the Stefan-Boltzmann constant (o = 5.67 X lo- '' watt per sq cm-"K1), and E is the emissivity of the surface. Although Eq. [2] gives the exact expression for the total emissive power of any gray body, all practical problems involve the net exchange of thermal radiation between a body and surrounding bodies. The two major considerations in the solution of such problems are a) shape and relative position of the surfaces and b) the emissivities of the surfaces. In this work it shall be assumed that all incremental areas on a pore have the same emissivity and, further, that little or no reflection occurs (i.e., the radiation hitting a surface is either absorbed or transmitted). Thus, the solution of the stated problem requires only that consideration a be satisfied. Consider two incremental surface areas dA 1 and dA2 of the same material in a general orientation to one another. Let dAl be at temperature TI and dAz be at T2. Fig. 2 illustrates the geometrical parameters involved. That is, 71, is the normal of dA, n2 the normal of dA2, r the line connecting the centers of each area, 81 the angle between nl and r, and Q2 the angle between 7,2 and r. Using Eq. [2] and the Lambert cosine law of diffuse radiation it is easily shown that:293 WdAf- dA, = ecr T*------^fpi------" dAidA2 [ 3a 1 and

Jan 1, 1970

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3') a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;' hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.' This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By J. P. Zannaras

If we assume that testing of the model started at time t1, that time t2 was the instant at which the elastic limit of the material was passed at the points of the maximum stress, and that at time t3 the failure of the model was completed as shown in the typical photograph (Fig. I), then actually the photograph shows the final results of what took place between time t2 and t3. By the principle of similitude all conclusions drawn from the behavior of the model were applicable and valid for actual mine roofs up to the time t2 after time t2 motions and friction came into play during the destruction of the model. The events between t2 and t3 and the photograph itself are not representative of the events expected in an actual mine roof unless corrections imposed by the principle of similitude are made. It can therefore be stated that all conclusions and observations of the author from the photographs are applicable only to his small-scale experiments and not to actual mine roofs. Without investigation of the true stresses or the combined maximum stress induced in the beds it has been assumed by the author that failure occurred solely due to bending stress caused by loading of the beds. (The author states that D was taken to be the theoretical strain given by elementary beam theory.) Fig. 1 shows that the beds were clamped together. This clamping was necessary to prevent slipping of the beds due to the horizontal shear. However, this clamping caused an uncontrolled and undertermined com-pressive stress S at the end of the beds, and this com-pressive stress caused a true tensile stress ?S (? PoiS-son ratio). This true tensile stress combined with the tensile stress produced at the end of the beds due to loading (fixed beam uniformly loaded), and the horizontal shear which is maximum at the end appears to be the most probable maximum stress produced in the beds. It is therefore evident that the author in performing this experiment has introduced stresses in the model not existing or dissimilar to actual mine roofs, and therefore his conclusions may be applicable to his small-scale experiments but inapplicable to actual mine roofs. Louis A. Panek (author's reply)—The discusser's difficulty is related to mechanics of materials rather than similitude. The effect of time did not enter into the tests in any way, being simply excluded from consideration in this study, because all quantitative results entering into the design equations are based on measured (between time t1 and time t2) bending strains that are well below the breaking strain (i.e., in the elastic range) for the model material. Time does not become a significant factor until the rock stress reaches 80 to 90 pct of the breaking stress." The objective of this investigation was not to predict that bolted roof will fail after time t, but was instead to develop a safe roof, that is, roof in which the bending strain is much less than (say less than 50 pct of) the breaking strain. The models tested to failure had no direct bearing on the design equations. Although for some rocks time may influence the magnitude of stress or strain at which fracture occurs, breaking stress or breaking strain values were not employed for any purpose in this investigation. Tests to failure were made only to obtain additional evidence regarding the behavior of the bolted laminae' as evinced by the locations of the cracks. As stated in the last paragraph of the paper, if one wishes to predict the time or stress conditions for which the roof will fail, additional information is required. The reason for clamping the laminae is to make them behave liked clamped beams, which closely approximate the clamped-plate condition of the actual mine roof beds (Ref. 5, p. 1; Ref. 6). The writer has previously demonstrated that the bending stresses induced by centrifugal loading in a clamped model beam are in agreement with those predicted by theory;' hence clamping has no significant effect on the bending ,trains measured during a test. Moreover, actual ,in, roof beds are likewise subject to a clamping effect due to weight of superincumbent strata carried by the pillars or ribs on each side of the opening. It is emphasized that this study was restricted to evaluating only the reinforcing effect produced by the bolts. Procedures employed in the experiments and in the data analysis were such as to deliberately exclude the effects of other factors. The objections offered are therefore invalid,

Jan 1, 1957

By Walter R. Crane

PAGE I. Apparatus and Methods.......... 406 1. The Magnetic Circuit...........406 2. Apparatus Employed in the Traction-Method...... 406 a. The Coils............409 b. The Pole-Pieces..........409 3. Methods of Testing Fields Produced by Different Pole.Pices.. ..409 c. Testing with a Search.Coil........410 d. Testing with Iron-Filings and Glass Tube.. .. .410 4. General Forma of Pole-Pieces.........411 e. Flat Poles............411 f. Conical Poles........... 411 g. Spherical Poles...........411 h. Chisel-Edged (Chamfered) Poles.......412 II. Magnetic Fields...........412 5. Methods of Testinq for Magnetic Permeability...... 421 i. The Rod-Method..........423 j. Method Employed in These Experiments......424 k. Difference in the Results of the Two Methods..... 425 l. The Traction-Method.........427 m. Effect of Loosening the Charge.......430 n Corrections...........432 6. Theory.............433 o. Effect of Varying Weight on Tractive Force..... 434 p. Effect of Varying Pole-Distance.......436 q. Effect of Varying Magnetization.......436 T. Effect of Varying Size.. .......437 a. Summary,........... 441 III. The Relative Magnetic Permeability of Various Minerals,. 443 The form and strength of magnetic fields have attracted much attention. especially in connection with the designing of dynamo-electric machinery—an art which has been revolution-

Jan 1, 1902

By Falih Ergunalp

REGULAR production of chrome in Turkey started in 1860 with the operation of the Bursa deposits (5, Fig. I). Others were discovered at Makri, near Fethiye (3, Fig. I). For 33 years Turkey remained the principal source of this mineral. While new discoveries were coming in elsewhere, Turkey's output declined until 1921, as a result of four successive wars, which ruined the economics of the country. In 1927 a revival came with the production of 18,000 tons. In that year the Société Minière de Fethiye was formed. This company now operates mines in the Vilayets of Aydin, Denizli, Burdur and Mentese, and it has reached a maximum production of between 80,000 and 90,000 tons annually. The Turkish output therefore increased from 29,000 tons in 1930 to 55,000 tons in 1931; and to 119,009 tons in 1934. The second phase in the increase in chrome production in Turkey came about in 1935, when the Government decided to reorganize and control the mineral industry of the country according to the principles of "government control" of the present regime. Up to that time the mineral resources of the country had been exploited by private concerns. In 1935, the M.T.A. (Maden Tetkik ve Arama) Institute (Institute of Mining Research and Geological Survey) was established by the Government to do the geological and geophysical survey work and discover new mineral resources for the country. Before the establishment of the M.T.A. Institute, the chief chrome-producing region was Fethiye (3 and 4, Fig. I). As a result of the extensive work of this bureau, many new chrome deposits have been discovered and are now in production. The operational field of the mineral industry was given to Eti Bank, another Government-sponsored and Government-controlled establishment. Eti Bank gradually took over the exploitation of existing mines by purchasing them from privately operated companies. Attention was first given to the Zonguldak collieries and to the different chrome deposits scattered over the country. The Guleman mines (14, Fig. 1) were developed and put in operation in 1936. Since then the bulk of Turkish chrome output has come from this mine, which yields the highest grade ore in the world (averaging 52 per cent Cr2O3). In 1939, the recently discovered chrome deposits to the north of Eskisehir went into production, yielding ore having a Cr2O3 content of 51 to 52 per cent. Today, more than ever, the efforts of both the M.T.A. Institute and the Eti Bank are concentrated on finding new deposits and placing them in operation. There are still many promising regions of the country that merit systematic surveying and prospecting for chrome ores. Thus it is probable that Turkey will continue to make noteworthy progress in chrome output. As the annual chrome production of

Jan 1, 1944

By C. E. Van Orstrand

AN intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it will be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. H. Emmons,1 minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. MATHEMATICAL THEORY In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be assumed that the intrusive is a large parallelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, t = o), which has the same thermal properties as the intrusive, is2,3 [ ] In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. 'v = temperature at point x, y, z, time t. vo = initial temperature throughout the intrusive, t = o. K = coefficient of thermal diffusivity. a, ß, ? are variables of integration. Put n = m in Eq. I, and we have [ ]

Jan 1, 1944

By K. A. Grange, W. S. Holt, E. T. Tkac

Quantitative knowledge of the time clement involved in austenite transformation in a particular steel provides a sound basis for understanding and planning heat-treatment. Such knowledge is conveniently obtained by measurement of austenite transformation as it occurs at each of a series of temperature levels. The results of these measurements usually are summarized in the form of the now familiar isothermal transformation diagram (I-T diagram, TTT diagram, or S-curve). Although a considerable number of such diagrams already have appeared in the literature, there remain many compositions of commercial importance for which no I-T diagram is available. The diagram for many such steels may be predicted from published data with sufficient accuracy for most practical purposes, but for others no satisfactory prediction can be made because the effect on austenite transformation of one or more of the important alloying elements present is not well enough known. Such a steel is Nitralloy, Type 13s-Modified, which, containing about 1.25 per cent aluminum, differs from any whose I-T diagram has been published. This paper presents results of a study of the isothermal transformation behavior of a sample from a commercial heat of this aluminum-chromium-molybdenum steel, together with pertinent supplementary data including the equilibrium transformation temperatures (Aeaand Ae,), the temperature range of martensite formation, and the end-quench harden-ability. These data are directly applicable to the hcat-treatment of this type of steel and are of interest in revealing some of the fundamental effects of aluminum as an alloying element in steel. Material All specimens were prepared from a 1 1/4 i-in. diam bar forged from a 5 by 5-in. billet from a commercial heat made in an electric arc furnace. The composition of the bar was; C, 0.41 per cent: AIn, 0.57: P, 0.016: S, 0.005: Si, 0.24: Ni, 0.17: Cr, I.j7: Mo, 0.36: All 1.26. The forged bar was normalized from r750°F (95s°C) and then tempered for one hour at rzoo°F (650°C), this tempering treatment having been given to facilitate the machining of specimens. Equilibrium Transformation Temperatures In hypoeutectoid steel the minimum temperature at which austenite is completely stable, Aep, and the maximum temperature at which austenite is completely unstable, Ael, are of great significance in heat-treatment. Since these temperatures are dependent upon com-

Jan 1, 1948

By W. S. Holt, K. A. Grange, E. T. Tkac

Quantitative knowledge of the time clement involved in austenite transformation in a particular steel provides a sound basis for understanding and planning heat-treatment. Such knowledge is conveniently obtained by measurement of austenite transformation as it occurs at each of a series of temperature levels. The results of these measurements usually are summarized in the form of the now familiar isothermal transformation diagram (I-T diagram, TTT diagram, or S-curve). Although a considerable number of such diagrams already have appeared in the literature, there remain many compositions of commercial importance for which no I-T diagram is available. The diagram for many such steels may be predicted from published data with sufficient accuracy for most practical purposes, but for others no satisfactory prediction can be made because the effect on austenite transformation of one or more of the important alloying elements present is not well enough known. Such a steel is Nitralloy, Type 13s-Modified, which, containing about 1.25 per cent aluminum, differs from any whose I-T diagram has been published. This paper presents results of a study of the isothermal transformation behavior of a sample from a commercial heat of this aluminum-chromium-molybdenum steel, together with pertinent supplementary data including the equilibrium transformation temperatures (Aeaand Ae,), the temperature range of martensite formation, and the end-quench harden-ability. These data are directly applicable to the hcat-treatment of this type of steel and are of interest in revealing some of the fundamental effects of aluminum as an alloying element in steel. Material All specimens were prepared from a 1 1/4 i-in. diam bar forged from a 5 by 5-in. billet from a commercial heat made in an electric arc furnace. The composition of the bar was; C, 0.41 per cent: AIn, 0.57: P, 0.016: S, 0.005: Si, 0.24: Ni, 0.17: Cr, I.j7: Mo, 0.36: All 1.26. The forged bar was normalized from r750°F (95s°C) and then tempered for one hour at rzoo°F (650°C), this tempering treatment having been given to facilitate the machining of specimens. Equilibrium Transformation Temperatures In hypoeutectoid steel the minimum temperature at which austenite is completely stable, Aep, and the maximum temperature at which austenite is completely unstable, Ael, are of great significance in heat-treatment. Since these temperatures are dependent upon com-

Jan 1, 1948