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By George F. Comstock

It has been reported recently1 that the hardenability and toughness of forging steels may be improved appreciably by the use of complex deoxidizers containing titanium, aluminum, and vanadium. In the light of these results, an investigation of similar deoxidizers containing various hardening and grain-refining elements was proposed. These deoxidizers included three manganese-silicon-aluminum-titanium al- loys with and without boron and calcium, three titanium-aluminum ferroalloys with vanadium, molybdenum and zirconium, respectively, an aluminum-zirconium ferroalloy, and plain ferroboron. Their approximate compositions are given in Table I, and the results obtained so far in the investigation of their effects on steel are presented in the later parts of this paper. Method of Using Deoxidizers The deoxidizers listed in Table I were used in three series of 0.40 per cent carbon steels, which were melted in a small basic-lined induction furnace and cast in the form of I7-lb. ingots about 2.75 in. square. The basic charge for each heat was 10 lb. Armco iron and 6 lb. of clean low-carbon sheet-steel scrap. When melted, this charge was deoxidized with 15 grams of ferrosilicon, then about 500 grams of pig iron was added to give the desired carbon content. After the pig iron was dissolved, nickel shot and high-carbon ferrochromium were added if required, and additions of 80 per cent high-carbon ferromanganese and 50 per cent ferrosilicon were made to provide the proper amounts of those elements. Aluminum was added to every heat 2 min. after the silicon, for grain-size control and preliminary deoxidation. One minute later the special deoxidizer was added to the clean bare surface of the molten steel, and 2 min. afterward the steel was poured into the ingot mold, using a hot-top and pipe-preventing compound after pouring to decrease the depth of the shrinkage cavity. The special deoxidizers were used mostly in the form of about ½ to¾-in. lumps,

Jan 1, 1942

By George F. Comstock

IT has been reported recently1 that the hardenability and toughness of forging steels may be improved appreciably by the use of complex deoxidizers containing titanium, aluminum, and vanadium. In the light of these results, an investigation of similar deoxidizers containing various hardening and grain-refining elements was proposed. These deoxidizers included three manganese-silicon-aluminum-titanium al- [ ] loys with and without boron and calcium, three titanium-aluminum ferroalloys with vanadium, molybdenum and zirconium, respectively, an aluminum-zirconium ferro-alloy, and plain ferroboron. Their approximate compositions are given in Table I, and the results obtained so far in the investigation of their effects on steel are presented in the later parts of this paper. METHOD OF USING DEOXIDIZERS The deoxidizers listed in Table I were used in three series of 0.40 per cent carbon steels, which were melted in a small basic-lined induction furnace and cast in the form of I7-lb. ingots about 2.75 in. square. The basic charge for each heat was 10 lb. Armco iron and 6 lb. of clean low-carbon sheet-steel scrap. When melted, this charge was deoxidized with 15 grams of ferrosilicon, then about 500 grams of pig iron was added to give the desired carbon content. After the pig iron was dissolved, nickel [ ] shot and high-carbon ferrochromium were added if required, and additions of 80 per cent high-carbon ferromanganese and 50 per cent ferrosilicon were made to provide the proper amounts of those elements. Aluminum was added to every heat 2 min. after the silicon, for grain-size control and preliminary deoxidation. One minute later the special deoxidizer was added to the clean bare surface of the molten steel, and 2 min. afterward the steel was poured into the ingot mold, using a hot-top and pipe-preventing compound after pouring to decrease the depth of the shrinkage cavity. The special deoxidizers were used mostly in the form of about ½ to ¾ -in. lumps,

Jan 1, 1942

By George F. Comstock

It has been reported recently1 that the hardenability and toughness of forging steels may be improved appreciably by the use of complex deoxidizers containing titanium, aluminum, and vanadium. In the light of these results, an investigation of similar deoxidizers containing various hardening and grain-refining elements was proposed. These deoxidizers included three manganese-silicon-aluminum-titanium al- loys with and without boron and calcium, three titanium-aluminum ferroalloys with vanadium, molybdenum and zirconium, respectively, an aluminum-zirconium ferroalloy, and plain ferroboron. Their approximate compositions are given in Table I, and the results obtained so far in the investigation of their effects on steel are presented in the later parts of this paper. Method of Using Deoxidizers The deoxidizers listed in Table I were used in three series of 0.40 per cent carbon steels, which were melted in a small basic-lined induction furnace and cast in the form of I7-lb. ingots about 2.75 in. square. The basic charge for each heat was 10 lb. Armco iron and 6 lb. of clean low-carbon sheet-steel scrap. When melted, this charge was deoxidized with 15 grams of ferrosilicon, then about 500 grams of pig iron was added to give the desired carbon content. After the pig iron was dissolved, nickel shot and high-carbon ferrochromium were added if required, and additions of 80 per cent high-carbon ferromanganese and 50 per cent ferrosilicon were made to provide the proper amounts of those elements. Aluminum was added to every heat 2 min. after the silicon, for grain-size control and preliminary deoxidation. One minute later the special deoxidizer was added to the clean bare surface of the molten steel, and 2 min. afterward the steel was poured into the ingot mold, using a hot-top and pipe-preventing compound after pouring to decrease the depth of the shrinkage cavity. The special deoxidizers were used mostly in the form of about ½ to¾-in. lumps,

Jan 1, 1942

By C. A. Stetefeldt

Jan 1, 1895

By C. D. King

A QUARTER century ago this country was producing an extraordinary quantity of iron and steel, with a decisive influence on the outcome of the first World War. Today this country is again demonstrating its industrial capacity with telling results. If this lapse of time has confirmed the opinion that man learns little from experience with respect to human relationships, at least we can derive some consolation from the knowledge that in the same period we have made huge strides industrially, and particularly in the steel industry. The differences represented by 25 years are striking, and have resulted from a multitude of changes that have contributed to the present-day high state of our pig iron and steel manufacture.

Jan 1, 1944

By Amitava Gangulee, Michael B. Bever

The order-disorder transition in Ag-Mg alloys in the range 17 to 26 at. pct Mg was investigated and some thermodynamic, electrical and mechanical properties of ordered Ag-Mg alloys were measured. A modification of the phase diagram is proposed on the basis of measured transition temperatures. The stability of the ordered structure is analyzed in terms of the quasichemical theory. Kinetic aspects of the order-disorder transition were also investigated. The energies of ordering at 273°K of Ag-Mg alloys were measured by liquid metal solution calorimetry. The electrical resistivities and the tensile Properties of the ordered alloys were measured. The exothermic energy of ordering increased with magnesium concentration up to the composition Ag3Mg; it is discussed in terms of the quasichemical theory. Pronounced order hardening was observed and can be explained by several strengthening mechanisms, which are particularly effective because of a change in crystal structure associated with the ordering transition. IN silver-rich solid solutions containing approximately 17 to 26 at. pct Mg, long- range ordering may occur during appropriate therma1 treatments. Clare-brough and Nicholas1 first detected such long-range order in the solid solution of composition Ag3Mg and suggested that the unit cell of the superlattice contained 256 atoms. x-ray2 and electron diffraction3 investigations confirmed the occurrence of long-range order, but indicated a shifted Ll2-type structure. On the basis of recent X-ray measurements the crystal structure of ordered Ag3Mg has been confirmed as type D023.4 The present paper is concerned with the order-disorder transition in silver-rich Ag-Mg solid solutions and some thermodynamic, electrical, and mechanical properties of the ordered alloys. The effects of short-range order on the properties of silver-rich solid solutions containing up to 26 at. pct Mg are discussed in a concurrent paper.5 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Specimens. Specimens of Ag-Mg alloys containing from 18 to 26 at. pct Mg were prepared in the form of 1.0-mm-diam wires as described in Section 1.1 of Ref. 5. Disordered specimens were prepared by annealing at 773°K for 1 hr and quenching into iced brine. Ordered specimens were prepared by annealing at 773°K for 1 hr and slowly cooling to room temperature over a period of 15 days. The specimens were stored at 78°K. 1.2) Resistivity Measurements. Electrical resistivi- ties were measured by a potentiometric method.' Equilibrium values were obtained at several temperatures. The kinetics of ordering were investigated by following the time-dependent changes of the resistivity of initially disordered specimens during annealing. The specimens were enclosed in copper capsules and immersed in salt pots; the heating up was accelerated by injecting preheated helium into the capsules. 1.3) Calorimetry. The energies of ordering of the alloys were measured in a tin solution calorimeter as the difference between the heat effects of additions of completely ordered and disordered specimens of the same composition. The procedure and the method of calculation have been described.6 Magnesium was used for thermal compensation in most calorimetric runs in order to improve the accuracy.677 1.4) Mechanical Tests. Tensile tests were carried out with wire specimens at room temperature as described in Section 1.5 of Ref. 5. Microhardness measurements were also made.? 2) RESULTS AND DISCUSSION The characteristics of the order-disorder transition of silver-rich Ag-Mg solid solutions will be discussed first. Some thermodynamic, electrical, and mechanical properties of the ordered alloys will then be considered and compared with the corresponding properties of dis-disordered alloys. 2.1) The Order-Disorder Transition. 2.1.1) Thermodynamic and Structural Aspects. The transition temperatures Tt were determined from discontinuities in the slope of the equilibrium resistivity vs temperature curves. Normalized curves for three compositions are shown in Fig. 1. The transition temperature increases with the magnesium concentration and reaches a maximum at the stoichiometric composition Ag3Mg. The transition temperature of the alloy Ag3Mg was measured as 665° ± 2°K and compares with published values of 660°,1 663°,8 and 66°k.3 In the slopes of the resistivity vs temperature curves of alloys containing 22.2 and 22.5 at. pct Mg, discontinuities were observed at two temperatures. Such upper and lower discontinuities indicate a two-phase field. A modified form of the published phase diagram9 is shown in Fig. 2. A two-phase field was found only on the low-magnesium side of the composition Ag3Mg. On the high-magnesium side, the existence of a two-phase field could not be established because of insufficient resolution, but such a field must be present. This part of the phase diagram can be made complete by a eutec-toid-type reaction a = (a' + ß). The existence of a boundary between the two-phase fields (a + ß) and (a' + ß) is also in accord with published lattice parameters.3 The crystal structure of ordered Ag3Mg (type Do23)

Jan 1, 1969

By John J. Cioston

THE steadily rising flood of gold production from all parts of the world has created an avalanche of rumors regarding the stability of the present price of this metal. Markets have been unsettled from Johannesburg to London from New York and Toronto to Melbourne, despite repeated denials from, American and British authorities of any immediate intention to alter the price. Various economists and financial writers have blossomed forth with predictions that the price would be set at the old level of $20.67 per oz.; some have even been so brash as to state That a price of $15 would be necessary to bring production within control. These effusions, based entirely upon monetary theories and with no regard to production costs, serve to confuse rather than clarify the situation.

Jan 1, 1937

By GEORGE O. SUMAN

IN THE operation of oil properties there are various difficulties with pumping wells which can often be overcome or greatly lessened if sufficient attention is, directed towards pump and tubing problems. The difficulties referred to are the wearing out of pumps, sanding up of pumps, and the sanding up of the hole. As the perforations in the oil strings are large and the oil and sand loose and unconsolidated considerable trouble is often encountered in pumping wells due to the ease with which' the sand can come into the holes. DETERMINING FLUID LEVEL In determining the proper depth at which to tube a well it is essential to first find out something about the behavior of the fluid in 'the hole: Facts in regard to this natter can be obtained by finding the fluid level on pulling the tubing, by making a pumping test on the well tubed to various depths, and by bailing tests during cleaning out work. In ordinary oil field operations it is customary to take the fluid level at the time of pulling the tubing. This 'can only be done when the pump is not sanded up. There are two methods used in obtaining the fluid level. One method is to note where the outside of the tubing starts, to be covered with fluid when pulling the

Jan 1, 1925

By Mark R. Lamb

THE treatment of slime is of special interest to those engaged in cyaniding gold- and silver-ores. The usual practice is to make as small a percentage of slime as possible. In many instances the slime is given no treatment, but is impounded in dams in the hope that the future will develop some method of economically treating this product. The filter-press was the first step upward from ordinary decantation, but, on account of heavy labor-charge and high cost, its use has been limited to high-grade material. The slime at the Combination mill at Goldfield averages perhaps $20 per ton, and although the values are quickly dissolved the filter-press installation was not entirely satisfactory, resulting in the erection of the canvas-cell filter, developed by Chas. Butters and his staff. This filter is a great improvement over the filter-press, and the following description of it will be of interest to those engaged in treating slime produced in crushing ores, especially in view of the fact that, by the use of this filter, slime can be treated at a lesser cost and with a higher percentage of gold- or silver-extraction than in the ordinary treatment of sand; and, moreover, the initial outlay for an all-sliming plant is less than that for the ordinary sand- and slime-plant. The economy of construction of the Butters filter-plant is clearly shown in Figs. 1 and 2, which illustrate the 20-frame filter of 40 tons capacity, now being installed by the Nevada Goldfield Reduction Co. In this construction the slime-pump is so connected that it can pump to or from either tank or the filter by changing the valve-settings-a combination which is necessary in this particular installation, since sufficient fall is not available for filling and discharging the filter by gravity. Ordinarily, a slime-plant comprises: a filter-box with frames

Jan 1, 1907

By Michael Perch

The fact that coal is a complex organic material and heterogeneous in composition has made its study extremely difficult, particularly in regard to obtaining a fundamental concept of the processes involved in the formation of coke. It has been stated recently that coals are natural polymers and that in a complex reaction such as occurs during carbonization the differences between coals are quantitative and not qualitative. Such being the case, it would be expected, therefore, that a series of coals subjected to exactly the same conditions of coking would produce results that should be related quantitatively to the chemical analyses of the individual coals. In the past, however, this fact was not generally recognized and consequently many empirical test methods were devised for testing coals. The interpretation of the results obtained depended upon comparing a set of data with other data on coals of known characteristics. The testing procedure had to be con- ducted in precisely the same manner each time and not the least requirement in making the interpretation was experience. The test methods varied from those utilizing a gram of coal to the plant-scale tests in which one or more ovens were charged with the test coal. The aim had been principally to find some simple, inexpensive means by which the coke-making and other properties of coal could be predicted. It is not necessary to emphasize the importance of these endeavors, for anyone acquainted with the problems involved in the selection of coals for making coke is well aware of the time and expense involved in making a series of definitive tests.

Jan 1, 1949

By E. V. Murphree

CREATION of atomic energy, aside from its influence on war or peace, has posed these basic questions for the world: How soon can energy from atoms be harnessed to do man's daily work? How much of this power will there be, to what degree will it supplant present fuels, and what does it imply for the future of civilization? Answers to these questions may be found in part in analysis of just what atomic energy is and how far its development has come. The answers are encouraging. One of the first questions encountered in considering the application of atomic reactions is whether such reactions can be controlled. Fortunately, this has been adequately demonstrated by the operation of the Government plutonium plants at Hanford, Wash. Here nuclear reactions are carried out on a large scale involving liberation of about a billion B.t.u. per hour. This hourly heat liberation is equivalent to that obtained from about 7100 gallons of fuel oil. It has been possible to operate these plants day in and day out with the reaction controlled at the intensity desired. There should therefore be no question that, under proper conditions, reactions involving nuclear fission can be controlled.

Jan 1, 1946

By C. A. Meissner

THE following is a further discussion of the paper of James Gayley, " The Application of Dry-Air Blast to the Manufacture of Iron " (Trans., xxxv., 746), with special reference to his sup-plementary paper (Bi-Monthly Bulletin, No. 4, July, 1905, pp. 797 to 819), and. to the paper of J. E. Johnson, Jr., "Notes on the Physical Action of the Blast Furnace " (Bi-Monthly Bulletin, No. 5, September, 1905, pp. 1111 to 1146). Mr. Gayley's paper has been discussed also by E. Windsor Richards, R. W. Raymond, E. H. Saniter, W. J. Foster, H. M. Howe, V. Pendred, B. H. Thwaite, James Gayley and Alexander Pourcel (Trans., xxxv., pp. 1022 to 1042), Joseph W. Richards (Bi-Monthly Bulletin, No. 4, July, 1905, pp. 703 to 718); T. W. Robinson (Bi-Monthly Bulletin, No. 4, July, 1905, pp. 788 to 796) ; C. B. Dudley, R. W. Raymond, J. E. Johnson, Jr., W. F. Mattes, James Gayley, David Baker, John Birkinbine and F. E. Bachman (Bi-Monthly Bulletin, No. 5, September, 1905, pp. 1147 to 1152);.E. de Mille Campbell (Bi-Monthly Bulletin., No. 1, January, 1906, pp. 25 to 50) ; John Birkinbine (Bi-Monthly Bulletin, No. 1, January, 1906, pp. 137, 138). At the Washington meeting of the Institute, May, 1905, a very instructive and interesting paper was presented by Mr. J. E. Johnson, Jr., entitled " Notes on the Physical Action of the Blast Furnace,"' in which reference is made to Mr. Gayley's dry-blast process. A few of Mr. Johnson's conclusions, as summarized in the last pages of his paper, do not appear to me to be in complete accordance with the results obtained at the Isabella furnaces; and I therefore present the following notes which may throw further light on this subject: Mr. Gayley has called attention to the fact that the moisture in the air is an extremely variable and uncertain factor; and

May 1, 1906

By James V. Thompson

SINCE it was introduced in 1943 to recover chromite from Oregon beach sands, the Humphreys spiral concentrator has proved successful in several fields of wet mineral beneficiation. By the end of 1957, 9390 Humphreys spirals had been manufactured. Most of these are still in service. The spiral does not offer a panacea for all mineral dressing problems. Its proper application can best be determined by test work. Spirals present a unique advantage for the metallurgist to make tests in a full-size machine rather than a miniature model, without the risk involved in scaling up results. With only 10 to 40 lb of sample, the operator of a closed circuit test unit employing a full-size Humphreys spiral can conduct preliminary tests with full-scale loadings of 0.5 to 2.5 tph. With larger samples, from 300 to 500 lb, he can run longer multi-stage tests to obtain reliable data for the next step-pilot plant design. The manufacturer of the Humphreys spiral concentrator maintains a fully equipped ore dressing laboratory and by insisting on test work prior to sales has largely prevented misapplication of the spiral.

Jan 1, 1958

By J. T. Ryan

POISONOUS, irritating, or explosive gases are found in almost every industry, and manufacturers of gas masks are called upon to provide gas mask protection for a great variety of conditions, such as operators in horseradish factories, fumigators of homes and ocean liners, and men engaged in the manufacture of tetra-ethyl-lead, the new motor fuel. The modern type of gas mask and respirator, to provide protection against all such industrial gases, is an outgrowth of the gas mask developed during the World War to protect the soldiers against the poisonous war gases. So far, it has been possible to develop ample mask protection from all known noxious gases and fumes present in atmospheres encountered in mines, metallurgical works, and chemical and other industries, so long as there is sufficient oxygen present to support the flame of an oil lamp. The most important development of the gas mask was in providing protection against carbon monoxide- which is the noxious gas that mining men are most concerned with and, in fact, is the noxious gas that man is most frequently exposed to. This paper will be con- fined largely to the discussion of masks for underground use in metal mines. Gases that contaminate the normal air in mines can be divided into two classes: those that are given off normally by the workings, and those that are produced in mine operation.

Jan 1, 1926

By H. M. Chance

Jan 1, 1886

By S. Weinig, E. S. Machlin

IN a previous study of the grain boundary stress relaxation phenomenon,' the authors had arrived at the conclusion that two successive steps were involved in the complete relaxation of stress at a grain boundary. These two steps were grain boundary migration and grain boundary slip. It was further suggested that the slower of these two processes is rate controlling. In an attempt to ascertain the validity of the above, a study of grain growth kinetics on the same alloys used for the previous study was undertaken. Separate wire specimens, 0.030 in. diam, in the same as-deformed state (99 pct reduction in area) as in the previous investigation were heated to the various temperatures for a sequence of times. The compositions used and the temperatures of testing are summarized in Table I. A statistical determination of grain size was then made on each specimen, using the average length of traverse between boundaries as a measure of the grain size. Examples of typical results obtained are shown in Figs. '1 and 2. The grain growth law D = ktn was found to fit most of the data. Using this relation, values of the grain growth exponent n were calculated and the inter -esting dependence of n on solute content shown in Figs. 3 and 4 was then obtained. Also, it was found that the constant K which was obtained from extrapolation is roughly independent of solute content. (K is uncertain to within ±25 pct.) An estimate of the activation energy for grain growth was made using the technique of Burke? This method utilizes the plot of the reciprocal of time necessary for the grain size to increase from a definite starting size Do, to a final size D, for each isothermal heat treatment. The slope of this curve corresponds to the heat of activation for the process. In Fig. 5 the rate of grain growth is plotted against the reciprocal of absolute temperature. The activation energies were obtained from these curves and are summarized in Fig. 6. Discussion It is interesting to note that the same saturation in the variability with concentration has been found for the grain growth exponent n in this research as was found in the previous researches on both grain boundary stress relaxationa and internal friction of dislocation origin." The significant feature is that saturation in the variation of these properties has been found to occur at about the same level of solute concentration, namely, between 0.1 and 0.5 atomic pct. The only characteristic common to these different quantities is that solute adsorption at grain boundaries and dislocation can take place and affect these values in a similar fashion. Thus, it is concluded that the grain growth exponent n depends upon solute adsorption at the grain boundaries. It appears, therefore, that theoretical considerations leading to the contrary conclusions5,6 have not treated the real process by which solute atoms exert their effect on grain growth. Prior to the analysis of the observed activation energies, certain of the aspects of the aforementioned grain boundary stress relaxation investigation will be briefly reviewed. It was found that with the addition of solute atoms the grain boundary stress relaxation peak (internal friction vs temperature) decreased in intensity. Simultaneously a second peak was observed which increased with increasing solute atoms. Both of these peaks were shown to be the result of grain boundary stress relaxation. They have been termed, respectively, poire peak and solute peak. It was suggested that the solute peak was dependent upon grain boundary migration, whereas the pure peak was a manifestation of grain boundry slip. Activation energies for both peaks were obtained as a function of Solute content. The value of the activation energy in the temperature range corresponding to the solute peak was

Jan 1, 1958

By R. M. Brick, Arthur Phillips, A. J. Smith

A PREVIOUS publication1§ has described the effect of quenching stresses on the lattice parameter values of high-purity aluminum-copper alloys particularly with reference to the solution and precipitation of CuA12. A similar study has been made of the aluminum-rich aluminum-magnesium alloys. Attention has been directed in the present investigation. to the magnitude of the quenching stresses as affected by the specimen size and shape, the number of solute atoms and the quenching rate. The effect of cooling stresses in causing plastic deformation or cracking has been considered in relation to the physical properties of the alloy. On reheating alloys in the two-phase field, the time required for precipitation to occur has been observed in connection with the degree of supersaturation, the rate of diffusion of the solute atoms as a function of the comparative atomic radii, degree of strain, temperature of reheating and grain size. A few qualitative comparisons on the relative effect of these factors have been drawn between the aluminum-copper alloys and the aluminum-magnesium alloys. STRAIN IN SOLID-SOLUTION ALLOYS A 10 per cent magnesium alloy in the form of chill-cast bars was furnished by the Aluminum Company of America through the courtesy of L. W. Kempf. Additional alloys were prepared using aluminum (99.95 per cent Al) and high-grade magnesium. The alloys listed in Table 1 were melted in an Acheson graphite crucible under a flux of fused MgCl2, CaC12, NaCl. Chill-cast rods were sealed under vacuum

Jan 1, 1935

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

By S. W. Zehr, G. S. Murty, W. A. Backofen

AN observation by Squires, Weiner, and phillipsl has stimulated interest in a mechanism of deformation at high temperature (above -0.5 of the absolute melting point) that is not usually thought to be involved in the creep of metals. They found precipitate-free or "denuded" zones along grain boundaries normal to the stress axis in tensile specimens of a hydrided Mg-1/2 wt pct Zr alloy after slow straining at 450° and 500°C. Their suggestion that the zones were a result of directional diffusion of magnesium atoms was supported with calculations from Harris and Jones2 which also tended to identify the process as Nabarro-Herring (N-H) creep3,4—a process that is characterized by Newtonian viscosity, with stress (o) directly proportional to strain rate (C), and one that proceeds by lattice diffusion. Material transport by diffusion along grain boundaries is an alternative basis for Newtonian viscosity, as demonstrated by Coble,5 and is favored over N-H creep for fine grain size and lower temperature.6 In either case, the strain rate sensitivity of flow stress, defined as m = d log o/d log E (which commonly appears in the empirical a = KEW), is unity. The experiments to be described here gave metallo-graphic indications of diffusional creep which were no less clear than those just cited, but the associated m (as measured by the method of Ref. 7) was much more like that of a Bingham material. For true Bingham behavior, (a — ao) E, where oo is an initial yield stress. Therefore, even if flow after yielding should occur by diffusional transport, m must increase from 0 as < is raised to reach unity only in the limit as One result is that the resistance to tensile necking conferred by Newtonian viscosity is lost, which would become increasingly apparent through the formation of more sharply defined necks as 6 is lowered. That trend appeared in these experiments. Most of the work was done on an extremely finegrained alloy of magnesium with -6 wt pct Zn and ½ wt pct Zr (Mg ZK60); the initial mean-intercept grain diameter, L, was 0.55 µ. Shown in Fig. l(a) is a germanium-shadowed carbon replica of the surface of a specimen that was coated with silicone oil,* heated to 270°C under a helium atmosphere, and then stretched locally -200 pct at an initial E = 3.3 x 10-5 sec-1. Under

Jan 1, 1969