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By D. H. Desy, L. C. Fincher

The magnesium-rich end of the Mg-Ti phase diagram was investigated. The liquidus, solidus, and solvus boundaries to 1 pct Ti were established. All alloys were prepared by saturating molten magnesium with titanium in a consumable titanium crucible under inert gas maintained at 230 psig. The liquidus of the Mg- Ti system was determined by analysis of dip samples taken from 700° to 1300°C under equilibrium conditions in a pressurized inert atmosphere furnace and by analysis of small ingots rapidly poured and quenched from 1400° to 1500°C. The solubility of titanium in magnesium ranged from 0.018 wt pet Ti at 700°C (0.012 wt pet at 650°C by extrapolation) to 1.035 wt pet Ti at 1500°C. The solidus for compositions ranging from 0.03 to 1.00 wt pet Ti was determined to be 650° ± 1°C by thermal analysis. The titanium solid solubility values ranged from 0.08 wt pet at 350°C to 0.19 wt pet by extrapolation to 650°C. The freezing reaction is peritectic. No intermetallic compounds were found in the system; the phase in equilibrium with molten magnesium saturated with titanium was found to be titanium with magnesium in solid solution. Solid titanium will dissolve at least 1.32 wt pct Mg. PREVIOUS investigations of the Mg-Ti system have shown considerable disagreement on the solubility of titanium in liquid magnesium. Furthermore, the solid solubility of titanium in magnesium has not been well established. Liquidus curves for previous work and for the present investigation are shown in Fig. 1. Aust and Pidgeon1 used a dip-sampling method on molten magnesium held in equilibrium with solid titanium under a protective atmosphere to determine the solubility and found that it ranged from 0.0025 wt pet Ti at 651°C to 0.015 wt pet Ti at 850°C. Eisenreich2 introduced titanium into molten magnesium by means of TiCL4 adsorbed on BaCl2. Ingots were then cast at various temperatures. Making the assumption that only the titanium dissolved in magnesium at the time of casting was soluble in H2SO4, Eisenreich determined the solubility of titanium in molten magnesium to range from 0.003 wt pet at 655°C to 0.115 wt pet at 800°C. Eisenreich also determined the solid solubility of titanium in magnesium to be 0.015 wt pet at room temperature and 0.045 wt pet at 500°C. Since the solid solubility just below the freezing temperature for the bulk of the alloy was much larger than the liquid solubility just above the freezing temperature, Eisenreich concluded that the freezing reaction was peritectic. Obinata et al.3 equilibrated molten magnesium with titanium in hermetically sealed titanium containers which were then furnace-cooled. The titanium content of the magnesium was then determined and found to range from 0.170 wt pet at 700°C to 0.85 wt pet at 1200°C. No intermetallic compound was found in the system. The Armour Research Foundation4 determined two points on the solvus by electrical resistivity methods: 0.00057 wt pet at 200°C and 0.0008 wt pet at 300°C. At higher temperatures, data were meaningless with no trends observable. The authors of this report believed that the lack of significant data at the higher temperatures was due to variations in specimen geometry, although there was no positive evidence to verify this supposition. The present investigation was undertaken to clarify the uncertainty in both the liquidus and solvus of the magnesium-rich end of the Mg-Ti system. EQUIPMENT AND MATERIALS The equipment used in this investigation, with some modifications, was essentially that used by Crosby and Fowler5 in their determination of part of the Mg-Zr phase diagram. The equipment, as modified for this work, is shown in Fig. 2. It consists of a sealed furnace chamber which can be pressurized with inert gas so that melts can be made above the boiling point of magnesium at atmospheric pressure. Melts are made by induction heating in a titanium crucible which, after diffusion of sufficient magnesium into the walls of the crucible to saturate the titanium at the sampling temperature, comprises the solid phase in equilibrium with the molten magnesium. Dip samples may be taken with the sampling tube, or the entire furnace may be tilted so that ingots may be poured into a mold in the side chamber. The principal difference from the earlier apparatus is in the thermocouple, which in the present equipment is enclosed in a protection tube and immersed directly in the melt. The tips of both the thermocouple protection tube and the sampling tube, which dip into the melt, are made of high-purity titanium. The 4 1/2-in.-long titanium tip of the sampling tube is threaded into a steel tube, O in Fig. 2, which extends through the top of the furnace. To determine whether the temperature at the tip of

Jan 1, 1969

By J. E. Worthington, W. H. Spence, I. T. Kiff

Gold was discovered at the Haile mine in Lancaster County, South Carolina, in 1827 or 1828, and since that time the mine has been worked intermittently by both open-pit and underground methods until its forced closure in 1942 by World War II. Production figures are incomplete, especially for the early years, but the total gold produced is estimated to have been greater than 200,000 oz. Thus, the Haile mine has been the most productive gold mine in the eastern United States. The upper, residually enriched ores were relatively rich, but the bulk of the production has come from the mining of lower grade ores. General Geology The Haile mine is located in late Precambrian or early Paleozoic rocks of the Carolina slate belt at the edge of the Atlantic Coastal Plain [(Fig. 1)]. The metamorphic grade is lower greenschist facies and the rocks have been folded into a sequence of northeast-trending isoclinal folds. The gold is associated with siliceous, pyritic, and kaolinized felsic pyroclastic and tuffaceous rocks in an interbedded volcanic and volcanoclastic sequence of felsic to mafic tuffaceous rocks and argillaceous sediments [(Fig. 2)]. The ore bodies occur in two northeast trending zones approximately 500 m apart; each zone is 30-70 m wide and 600 m or more in length, with possible extensions to the east beneath the Coastal Plain sediments. Mineralogy. Gold in the Haile mine is always associated with siliceous and/or pyritic ores. The gold occurs in at least three states: As native gold as originally deposited; as residual gold derived from the breakdown of pyrite; and as gold included in pyrite. Major associated minerals in addition to quartz and pyrite are kaolinite, sericite, and iron oxides. Minor molybdenite, arsenopyrite, pyrrhotite, copper sulfides, sphalerite, rutile, and topaz are also present. Petrology. The gold-bearing ore zones vary from highly siliceous rocks to pyritic massive sulfide lenses. This variation is most easily seen today along strike from the Haile pit to the Red Hill pit. Ore grade material still exposed in the wall of the Haile pit consists of a highly siliceous and very thinly bedded rock containing minor pyrite. Along strike, the character of the mineralization changes to pyritic massive sulfide lenses occurring interbedded with siliceous horizons at the Red Hill pit. The siliceous rocks vary from the thinly-bedded material as just described from the Haile pit to silicified fragmental-appearing rocks to totally recrystallized cherty rocks lacking any recognizable primary features. Scattered, apparently at random, throughout the very thinly-bedded and very fine-grained ore face of the Haile pit are seemingly anomalous silica-rich clasts or concretions up to 5 cm in diameter which will be discussed later in this paper. Alteration. One of the most striking features of the Haile deposit is the alteration mineral assemblage which is intimately associated with the siliceous and pyritic ores. This altered material has been intersected in drill core at depths greatly exceeding the modern weathering profile and is, therefore, of hydrothermal origin rather than from supergene processes. This "sericite," actually a fine-grained mixture of sericite, kaolinite, and quartz, can be shown to stratigraphically underlie the gold- quartz-pyrite zone, and is well exposed in the open pit just southeast of the Haile and Bumalo pits. Relict textures indicate that this highly altered material was originally a felsic ash flow. Other similar alteration zones have been found in outcrop and drill core underlying the remaining ore bodies. Thus each of the mineralized zones consists of two parts: A siliceous and/or pyritic gold-bearing ore zone which is stratigraphically underlain by a zone of high alumina minerals, in this case sericite and kaolinite along with variable amounts of quartz. A green chrome mica, presumably fuchsite, is present in trace amounts in the high alumina zone. Genesis An adequate model to explain the origin and distribution of the gold deposits in the Carolina slate belt is presently lacking. Worthington and Kiff1 suggested a volcanogenic origin for certain gold deposits in the North Carolina slate belt from the waning exhalations of felsic volcanic piles. They also pointed out that such an origin has similarities to many epithermal precious metal deposits located in more recent volcanic piles in the western United States. A further key to the understanding of the genesis of the gold mineralization at the Haile mine is the close association of the mineralization in siliceous and sulfidic horizons to the genetically related and stratigraphically underlying high alumina alteration. Such high-alumina alteration is common around felsic volcanic centers in the Carolina slate belt and the mineralogy as seen today consists of some combination of kaolinite, sericite, pyrophyllite, kyanite, andalusite or sillimanite depending on the local prevailing grade of metamorphism. Accompanying the high-alumina alteration are large quantities of pyrite and iron-oxide minerals as well as characteristic minor accessory minerals often including base metal sulfides, fluorine-bearing minerals (topaz, fluorite, apatite), titanium-bearing minerals (ilmenite, rutile),

Jan 1, 1981

By R. T. Hukki

John F. Myers (Consulting Engineer, Greenwich, Corm.)—Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity. It is also constructive that such able investigators give to the students of comminution their interpretation of their laboratory results in terms of large-scale operation. History shows that it takes a lot of time for such radically new ideas to be absorbed by the industry. Typical of this is the present-day activity of cyclone classification in primary grinding circuits. The idea of cyclone classification has been kicking around for 30 or 40 years. Certainly we all suspect that the ponderous grinding mills of today, and their accessory apparatus, large buildings, etc., will ultimately give way to small fast units, just as this has occurred in other industries over the past 50 years. At the moment there is no evidence that ball and liner wear is prohibitively high. In fact, at the time Fahrenwald was demonstrating his high-speed horizontal machine at the meeting of the American Mining Congress, several years ago, he assured this writer that the balls retained their shape much longer than they do in conventional tumbling mills. Rods and balls that slide (as some operators in uranium plants are experiencing) get flat. Apparently the balls have a rolling action. Mr. Hukki's references to the processing capacity of the Tennessee Copper Co. mills is adequate. Those studying this subject will be greatly interested in the paper presented by Richard Smith of the Cleveland-Cliffs Iron Co. at the annual meeting of the Canadian Institute of Mining and Metallurgy in Vancouver April 24, 1958. This paper will be published during the latter part of 1958 in the Canadian Institute of Mining and Metallurgy Bulletin. Hukki's pioneering spirit is to be commended. R. T. Hukki (author's reply)—It has been heartening to read the objective discussion by J. F. Myers. The sincerity of his opinions is further strengthened by the fact that the article he has discussed contradicts in a major way the parallel achievements of his life work. Myers is right in his opinion that in general it takes a long time before new ideas are accepted by the industry. On the other hand, revolutions usually take place at supercritical speeds. There are many indications at present that both the unit operation of grinding and the related subject of size control are now just about ripe for a revolution. In grinding, brute force must ultimately give way to science. Rapid progress can be anticipated in the following fields: 1) Autogenous fine grinding at supercritical speeds will be the first advance and the one that will gain recognition most easily on industrial scale. At this moment, little Finland appears to be leading the world. Crocker recently made a statement that in nine cases out of ten, your own ore can be used as grinding medium more effectively and far more economically than steel balls. This is true. The present author would like to introduce a supplementary idea: In eight cases out of the nine cited above, it can be done at the highest overall efficiency in the supercritical speed range. Fine grinding must be based on attrition, not impact. The path of attrition may be vertical, horizontal, even inclined. 2) In coarse grinding, the conventional use of rods is sound practice. However, even the rods can be replaced by autogenous chunks large enough to offer the same impact momentum as the rods. To obtain the momentum, the chunks must be provided with a free fall through a sufficient height in horizontal mills operated at supercritical speeds. Coarse grinding must be based on impact. Detailed analysis of the subject may be found in a paper entitled "All-autogenous Grinding at Supercritical Speeds" in Mine and Quarry Engineering, July 1958. 3) All conventional methods of classification, including wet and dry cyclones, are inefficient in sharpness of separation. Continuous return of huge tonnages of finished material to the grinding unit with the circulating load is senseless practice. In the near future the present methods will be either replaced or supplemented by precision sizing. These three fields are also the ones to which J. F. Myers has so admirably contributed in the past. Fine Grinding at Supercritical Speeds. By R. T. Hukki (Mining EnGineERInG, May 1958). Eq. 9, page 588, should be as follows: T , c, (a — 6') n D Ltph On page 584 of the article the captions for Figs. 4 and 5 have been placed under the wrong illustrations and should be interchanged.

Jan 1, 1959

By W. M. Robertson

The formation of grain boundary grooves on surfaces of poly crystalline samples of cobalt and iron immersed in liquid lead has been studied. The grooves form by volume diffusion of the solutes cobalt and iron in the liquid. The diffusion coefficients of the solutes in liquid lead are derived from the measured rate of grooving. The diffusion coefficients are described by the relation D = Do exp (-Q/RT), with, for cobalt, Do = 4.6 x 10-4 sq cm per sec and Q = 5300 ± 800 cal per mole, and for iron, DO = 4.9 x 10-3 sq cm per sec and Q = 10,500 ± 1500 cal per mole. LIQUID metal-solid metal interactions occur at solid-liquid interfaces. Interfacial energy provides a driving force to change the morphology of the interface. Mullins1,2 has derived expressions for the kinetics of interface morphology changes driven by capillarity. These expressions can be applied to an isothermal system of a solid in equilibrium with a liquid saturated with the solid. Surface profile changes can occur by volume diffusion of the solute in the liquid, by volume self-diffusion in the solid, and by interfacial diffusion at the liquid-solid interface. A groove will form at the intersection of a grain boundary with a solid-liquid interface, reducing the total interfacial free energy of the system. The solid-liquid interfacial energy ? must be greater than half the grain boundary energy of the solid ?6 for Mullins' calculations to apply. If ? is less than ?b/2, then the liquid penetrates the boundaries, separating the grains rather than forming grooves. Boundary penetration did not occur in the work described here. where CO is the equilibrium volume concentration of the solid in the liquid, Dv the volume diffusion coefficient of the solid in the liquid, ? the interfacial free energy of the solid-liquid interface, O the atomic volume of the solid crystal, k Boltzmann's constant and T the absolute temperature. Eqs. [1] and [2 ] also apply to grooving by volume self-diffusion in the solid,1 with CoODv = D Self, where DSelf is the volume self-diffusion coefficient of the solid. For a grooving mechanism of interfacial diffusion at the solid-liquid interface, the groove width is given by2 where CS is the interfacial concentration of the diffusing species, and DS is the interfacial diffusion coefficient. Eqs. [1] and [3] can be used to determine the mechanism of groove growth. A t1/3 dependence of the growth indicates volume diffusion and t1/4 indicates interfacial diffusion. In some cases, volume diffusion and interfacial diffusion both can contribute substantially to the grooving process, causing the time dependence to be intermediate between t 1/3 and t1/4.3 For these cases, the relative contributions of the two processes can be separated.4 However, in many cases, one process will be dominant, and the data can be analyzed on the basis of Eq. [1] or Eq. [3] alone. The time dependences for volume diffusion in a liquid and volume self-diffusion in a solid are the same. However, the self-diffusion contribution of the solid is usually negligible compared to volume diffusion in the liquid. After the grooving mechanism has been determined, Eq. [1] or Eq. [3 ] yields the kinetic parameter A or B. The kinetic parameter can be used to calculate values for the unknown quantities in the product CD?. Usually C is known or can be estimated. If ? is known, then D can be calculated. In a measurement of grain boundary grooving of copper in liquid lead,' the time dependence indicated volume diffusion in the liquid. The quantities Co, Dv, and ? were obtained from the literature, giving excellent agreement between the observed values of A and the values calculated from Eq. [2 ].5 In a study of the grooving of several refractory metals in liquid tin and liquid silver, A1len6 educed that grooves formed by volume diffusion in the liquid. In a study of nickel in a nickel sulfide melt, Steidel, Li, and spencer7 found volume diffusion grooving kinetics. Both Dv and ? were unknown, so they could not obtain either one separately, though they did obtain a reasonable value for the temperature dependence of the product Dv ?. Several methods have been used to obtain surface profiles. It can be done by sectioning through the interface7 or by chemically removing the liquid from the solid surface after solidification of the liquid.6 However, if the liquid dewets the solid on removing the solid from the melt, then the interface can be observed directly. This method was used previously' and was utilized also in the present study. EXPERIMENTAL PROCEDURE Lead of 99.999 pct purity was obtained from American Smelting and Refining Co. Cobalt sheet was obtained from Sherritt-Gordon Mines, Ltd., with a nominal purity of 99.9 pct, the principal impurities being nickel, iron, copper, carbon, and sulfur. The sheet was

Jan 1, 1969

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By John Chipman

The concentration of a solute in a dilute ),zetallic solution may be measured by any of several parame- ters including weight percent, atom fraction, atom ratio, and lattice ratio. The ratio of filled to unfilled interstitial sites is useful for interstitial solutes. A variable 2 proportional to this ratio is used as a measuve of concentration. For component 2 irz a bitzary solution z2 = n2/Ym - nz/b) where b is the numberber of interstitial sites per lattice atom. For a t~lul-ticortzporzent solution this becomes zz = n2/(nl + Cvjnj) in which Vj = - l/b for an interstial solute and +1 for a substitulional solute. In the infinitely dilute solution the activity of an interstitial solute 2 is proportional lo z2. At finile concentration the departure from this limiting law is expressed us an activity coefficient, his coefficient is a function of concentra1io)z expressed as tevactiolz coeffcient 8; is analogous to the jark~iliar e£ bul is found to be independent of concentvation in certain solutions for which data are available. It is found that the same equations may be used to express the activity of a nonmetallic solute, sulfur, in liquid solutions of iron containing other solutes, both metallic and nonmetallic. For a nonmetallic solute or for one which strongly increases the actiuity of sulfur, it is convenient to assign arbitvarily a value vj = — 1. When this is done the derivative is found to be constant in each of the ternary solutions studied. The activity coefficient of sulfur in a complex liquid iron solution may be expressed as where nk is a second-order cross product determined in the quaternary solution Fe-S-j-k. The equation is used to calculate tlze activity of sulfur i)z three sevetl- component solutions. IN thermodynamic calculations concerning dilute solutions it is unnecessary to invoke laws and relations which extend across the concentration range to include concentrated solutions. In most binary metallic systems, as arkeen&apos; has recently pointed out, there exist two terminal composition regions of relatively simple behavior, connected by a central region of much greater complexity. When the solute is a nonmetal there is only one such region and in many systems the concentration range is extremely limited. It is the purpose of this paper to suggest a method for the calculation of activities in such a terminal region in which one or more solutes are dissolved in a single solvent of predominantly high concentration. HENRY&apos;S LAW In the usual textbook statement of Henry&apos;s law, concentration is stated in mole fraction. This has the advantage that it makes Henry&apos;s law thermodynamically consistent with Raoult&apos;s law. Since all measures of concentration at infinite dilution are related by simple proportion it follows that mole fraction, molality, atom ratio, weight percent, or any other unit of concentration can be used with the appropriate constant. At finite concentrations, however, calculations based on the law depend upon the unit employed. Deviations from Henry&apos;s law at finite concentrations depend upon the composition variable employed. They are evaluated in terms of activity and interaction coefficients2 which have become familiar features of metallurgical thermodynamics. It is the purpose of this paper to propose a measure of concentration for metallic solutions containing interstitial or nonmetallic solutes by means of which the calculation of activities in complex solutions may be simplified. The discussion will be restricted to free-energy interaction coefficients3 typified by Wagner&apos;s c|a BINARY SOLUTIONS The several measures of concentration which are to be considered are shown in line a of Table I. The corresponding activity coefficients are in line b and the deviation coefficients, sometimes called self-interaction coefficients, are in line c. Henry&apos;s law simply states that the activity coefficient approaches a constant value at infinite dilution. By adoptihg the infinitely dilute solution as the reference state and defining the "Henrian" activity as equal to the concentration in this state, the activity coefficient is always unity at infinite dilution. This convention is far sim~ler and more useful in dilute solution than emploiment of the &apos;Raoultian" activities and it will be used in the following discussion. The several definitions and equations of Table I will be referred to by means of their coordinates in the table. Early observations of deviations from Henry&apos;s law in metallic solutions were shown graphically4 rather than analytically. For the case of sulfur in liquid iron5 the slope of a plot of logfs vs (%S) was constant in the range 0 to 4.8 pct S, indicating constancy of eh2&apos; in Ic. He was proposed by wagnerz and has been widely adopted. The a function of IIIc recently employed by ~arkenl was designed specifically for dilute solutions. Darken has shown that the value of a12 remains essentially constant for many binary solutions within a substantial range of compositions. The atom ratio is directly proportional to the molalitv.<, a conventional measure of concentration. IVb and C served as the basis for smith&apos;s6 classic studies of

Jan 1, 1968

By P. N. Richards, M. K. Ormay

Commercially hot-rolled low-carbon steel strip may have one of two basic types of orientation texture, depending upon the amount of a iron which was present during the finishing passes. The changes in these textures with varying amounts of cold reduction up to 95 pct have been determined for the sheet surface plane and for parallel planes down to the mid-plane. The development of cold reduction textures has been reassessed on the basis of (200), (222). and (110) stereographic pole figures and pole density or inverse pole figure values. In agreement with the literature, it is shown that the textures can be described in terms of partial fiber textures but alternative descriptions are given for one of the fiber textures, in order to more closely correlate with experimental data. One partial fiber texture consists of orientations of the type (hkk)[011] extending from (100)[011] to {322}(011) in agreement with the literature. At moderate amounts of cold reduction, a second partial fiber texture forms with a <331> fiber axis inclined 20 deg to the sheet normal and a range of orientations centered on one close to (1 11)[112] and reaching to (232)[101] or (322)[011]. An alternative description involves a (111) fiber axis parallel to the sheet normal but capable of rotation about the rolling direction with rotation about the fiber axis. ORIENTATIONS developed in low-carbon steel strip after cold reduction are of commercial importance because they control, in part, the final preferred orientations after subsequent annealing. The method of control however is not understood completely. Some preliminary work indicated that the cold-reduced orientations and the subsequent annealing textures of commercial low-carbon steel were dependent on the orientations present in the material before cold reduction, that is, those present in the hot-rolled strip but, to date, the effects of initial orientations have not been extensively investigated. For this reason, much of the information given in the literature on development of preferred orientation is difficult to assess as details of initial texture and processing conditions are often inadequate or are altered by a subsequent heat treatment such as normalizing.&apos; It is known2 that anomalous results for near surface orientations may be obtained if lubrication during cold rolling is not adequate but whether lubricant was used during the experiments has not always been given, nor has the exact depth below the surface at which determinations have been made. A comprehensive review of cold rolling textures has been made recently by Dillamore and Roberts&apos; and more restricted recent reviews are due to stickels4 and Abe.5 Based largely on the experimental work of Bennewitz,1 reviewers have accepted that the preferred orientations produced on cold reducing low-carbon steel can be described in terms of two partial fiber textures as follows: Partial Fiber Texture A which has a (011) direction in the rolling direction and includes orientations within the spread from (211)[011] through (100)[Oll] to (211)[011.]; there is some controversy as to whether it extends as far as the orientation (111)[011]. As Dillamore6 has observed, the extent of this partial fiber texture depends on the intensity levels selected. Partial Fiber -texture B which has a (011) direction located 60 den from the rolling direction in the plane containing the rolling direction and the sheet normal. There are two directions which satisfy these conditions and orientations in this partial fiber texture extend from (21l)[0ll] through (554)[225] to (121)[101]. The orientations {211}(011) are members of both partial fiber textures A and B and it can be noted that a variant of {554)<225> is within 6 deg of a variant of {111}(112). Barrett7 had postulated earlier that, in addition to orientations which would fall into partial fiber texture A, a true fiber texture with a (111) direction in the sheet normal was present after heavy cold reduction. This fiber texture would include orientations such as {111}(011) and {111}(112). Later investigators, notably Bennewitz,&apos; have discounted this, mostly on the ground that the partial fiber textures A and B, as described above, contain all the strong orientations that have been observed. However in other work it has been reported2 that (222) pole density or inverse pole figure values show a continuing increase with increasing reduction by cold rolling and give values considerably greater than for any other low indices plane. Thus it could be inferred that a (111) fiber texture as described by Barrett would be one which becomes more dominant with increasing cold reduction, whereas Bennewitz&apos; concluded that components such as {554)(225) in partial fiber texture B began to decrease in intensity at high reductions. Following Bennewitz, one would expect a decreasing (222) pole density value (parallel to the sheet normal) with increasing cold reduction. Because fiber textures consist of grains with a range of orientations that have one axis in common, it has been inferred that during deformation the crystal orientations rotate about the fiber axis&apos;74 and that the orientations of crystals that at one stage belong to one fiber texture can rotate on further cold reduction into the other fiber texture through an orientation in which the two fiber textures intersect.&apos; For example,

Jan 1, 1970

By W. F. Chiao

With the application of dislocation damping theory an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. A ductile steel was compared with a brittle stee1 by simultaneously measuring the ultrasonic attenuation and velocity during tensile test, and the density of free dislocations and their mean loop length were then calculated as a function of strain. The results showed that in the ductile steel there was always a large generation of dislocations and great extension of loop length occurring at some stage within the early plastic region. In contrast, the brittle steel showed very little or no such sudden changes in dislocation dynamic states after the onset of plastic deformation. Furthermore, a strong temperature dependence of dislocation dynamic states was also observed in the ductile steel and a hypothesis was suggested that a thermally activated process of dislocation rearrangement could occur at higher deformation temperatures. The activation energy of dislocation rearrangement at room temperature was estimated as about 2030 cal per mole.C. DUCTILITY is an indispensible property in the application of engineering materials, especially steel. During the past two decades the theoretical and experimental approach to the understanding of flow and fracture of metals has been constantly undergoing changes and progress." while the fracture behavior of metals can be influenced by many factors such as chemical Composition,3 second-phase particle mor-phology,4 and dislocation arrangement,5 it is now a general belief that the fundamental understanding of the ductile-brittle fracture phenomena of solid materials must stem from the study of dislocation dv-namics developed under stress conditions.6,7 Most of the traditional ductility tests, such as Charpy impact test, slow bend test, and tensile fracture test, cannot by themselves reveal directly the mechanisms of ductile to brittle transition of materials. In the experimental investigation of tensile ductility it would be ideal to be able to study directly the dynamics of dis-locations in a bulk specimen during the process of deformation. Since the ultrasonic pulse technique is the only satisfactory method for studying dislocations and the fine details of deformation characteristics in metals in the course of a tensile test, it would appear that a comparative study of ultrasonic attenuation changes during tensile tests of metallic materials exhibiting different ductility might be very informative. So far no work comparable to this study has appeared in the literature. Recent progress in both theory and experiment has indicated the feasibility of studying the dislocation mechanisms of ductility behaviors by ultrasonic measurements during tensile test. Granato and Lucke8 have developed a quantitative theory that enables the calculation of dislocation density and their average loop length from the measurements of ultrasonic attenuation and velocity, and several investigators, including Chiao and Gordon,9&apos;10 have shown that simultaneous ultrasonic measurements can be successfully made during a tensile test. Furthermore, many investigators11-13 have repeatedly proposed in the past several decades that deformation and fracture are mutually self-exclusive, and that the ability or inability of a material to deform plastically, i.e., to generate dislocations, is a major factor in determining whether the material will be ductile or brittle. Thus, in the present work an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. This article is principally concerned with the study of the relation between the propagation of ultrasonic waves and tensile deformation in a steel series which displays quite different toughness at room tempera-turk. changes in attenuation and velocity of ultrasonic waves have been measured as a function of strain during the deformation process. The results have been interpreted in terms of the vibrating string model for dislocation damping as developed by Granato and Lucke, and it has been found that some of the more subtle predications of the model are in good agreement with the experiments. This would be especially meaningful because most of the previous experiments in testfying the model were carried out with single crystals of high-purity materials and little work has been done with polycrystalline steel alloys. EXPERIMENTAL PROCEDURES AND RESULTS Specimen Materials. The tensile specimens used throughout this experiment were of two compositions selected from a series of Fe-Mo-0.77 pct Mn-0.22 pct C steels prepared for a ductile-brittle fracture transition study. One steel contains 0.21 pct Mo and the other 1.03 pct Mo. These two compositions were chosen for the present study because they possess quite different toughness properties at room temperature. The 0.21 pct Mo steel is quite ductile while the 1.03 pct Mo steel is rather brittle, as measured by the standard Charpy impact test. The alloys had been prepared by vacuum induction melting and chill casting in steel molds. The ingots were hammer-forged into 1/2-in.-sq bars from which tensile specimen blanks were cut. These blanks were first normalized under argon atmosphere at 1700°F and then reaus-tenitized and isothermally transformed at 1050°F to a bainitic microstructure. The chemical compositions, heat treatments, hardness measurements, and Charpy transition temperatures of the two steels are listed in Table I.

Jan 1, 1970

By M. J. Richards, A. Szirmae, G. R. Speich

The formation of austenite from ferrite, ferrite plus retastable carbide, spheroidite, and pearlite has been studied in a series of irons, Fe-C alloys, and plain-carbon steels using fast heating techniques. In the absence of carbide, austenite nucleates at ferrite/ferrite grain boundaries; nucleation is followed by the rapid growth characteristic of a massive transfornation. The trarnsformation occurs at 950°C at heating rates of 106º C per sec and cannot be suppressed. Metastable carbide dissolves before austenite forms and does not influence the transformation kinetics. For spheroidite structures, austenite nucleates preferentially at the jinction between carbides and ferrite grain boundaries. Growth from these centers proceeds until the carbide is completely enveloped; subsequent growth occurs by carbon diffusion through the austenite envelope. For pearlite structures, austenite nucleates preferentially at pearlite colony intersections. Carbide la)?zellae dissolve at the advancing austenite interface but complete solution of carbide does not occur; the residtial carbide is eventually dissolvled or spheroid-ized depending on the carbon cuntent. The magnitude and temperature dependence of the austenite growth rate into Fe-C pearlite when incomplete carbide dissolution is assumed are satisfactorily explained by an approximate colume diffusion model. The impurities present in plain-carbon steel reduce the growth rate of austenite in comparison to that jound in an Fe-C alloy. The formation of austenite has been studied in much less detail than the decomposition of austenite. This is primarily a result of the importance of harden-ability in determining the mechanical properties of steel. Recently, more interest in the kinetics of austenite formation has resulted from the discovery by Grange1 that rapid heating techniques strengthen steel by refining the austenite grain size. Although the strengthening effect is not large, it is accompanied by no loss in ductility. In addition, interest continues in rapid heat treatment of low-carbon steel sheet for tin plate applications.2,3 Among the few systematic studies of austenite formation are the early work of Roberts and Mehl4 on formation of austenite from pearlite and recent work of Molinder5 and of Judd and paxton6 on formation of austenite from spheroidite. Also, Boedtker and Duwez7 and Haworth and paar8 have recently studied the formation of austenite from ferrite in relatively pure iron, Kidin et al.9,10 have studied the formation of austenite in 8 pct Cr steels, and Paxton has recently discussed various aspects of austenite formation in steels." The present work was undertaken to determine the kinetics of austenite formation for a variety of starting structures including ferrite, ferrite plus metastable carbide, ferrite plus spheroidal cementite, and ferrite plus pearlitic cementite. Emphasis was placed on determining the active sites for austenite nucleation, determining the temperature and time range of austenite formation, and in the case of pearlite a careful study of the growth rate of austenite was made in the absence and presence of impurities. By using a variety of heating techniques including laser-pulse heating, it has been possible to study austenite formation in an isothermal fashion over a wide range of temperatures. EXPERIMENTAL PROCEDURE The alloys studied in the present work are a zone-refined iron with 4 pprn C, an Fe-C alloy with 130 pprn C, 2 Fe-C alloys with 0.77 and 0.96 wt pct C, and a plain carbon steel with 0.96 wt pct C. The zone-refined iron and Fe-C alloys contained 60 pprn and 200 pprn total substitutional impurities, respectively. The plain carbon steel contained 2400 pprn Si, 2000 pprn Mn, and 900 pprn Cr. Various heat treatments were given to these alloys to produce different starting structures of equiaxed ferrite, ferrite plus metastable carbide, fine pearlite, and spheroidite. These heat treatments are given in Table I. A wide range of heating rates were employed in this work because many of the reactions occur so quickly at temperatures in the austenite range that they are completed during the initial heating cycle unless very fast heating rates are used. Essentially the same heating techniques employed by Speich et a1.12 and Speich and Fisher13 were used in this work. For time intervals of 2 sec to 20 hr, simple hand immersion of 0.010-in. thick specimens in a Pb-Bi bath was employed. These specimens were quenched in a 10 pct NaC1, 2 pct NaOH aqueous bath. For time intervals of 100 m-sec to 2 sec, an automatic dunking and quenching device was employed with 0.002-in. thick specimens. Again, liquid Pb-Bi baths were used for a heating medium but now helium gas quenching was employed. For time intervals of 2 to 100 m-sec a laser heating device was employed with 0.002-in. thick specimens; a helium plus fine water-droplet spray was now used for quenching. Additional information on heating times shorter than 2 m-sec was obtained by study of the zones around the centrally heated laser spot. Here diffusion of heat from the centrally heated zone raises the temperature of the specimen locally to all temperatures between ambient and the peak temperature, but for times of the order of microseconds. All the heat-treated specimens were examined by

Jan 1, 1970

By A. D. Zunkel, A. H. Larson

Equilibrium arsenic contents of Pb-As alloys in contact with PbO-As2O3 slags containing less than 30 mol pct As2O3, were determined at 650°, 700: and 750 C in an inert at?rzosphere. In this temperature range, the arsenic content of the alloy increased with increasing temperature in the single-phase liquid slag region and decreased with increasing temperature in the two-phase slag region and the single-phase solid-solution slag region. The PbO-As2O3 phase diagram below 22 mol pct As2O3 was determined by thertrzal analysis and by application of a log ?As2O3/?PbO vS log XAs2o3 /x3pbO plot determined from the equilibrium actiuity data. The resulting phase diagram was not well-defined since the eutectic temperature was not detected in the thermal analysis experiments, although a region of terminal solid solubility of As2O3 was found. Results from the phase diagram determination are compared with an existing diagram in the literature. THIS experimental investigation is an extension of a study by the authors1 on the slag-metal equilibria in the systems concerned with commercial lead refining processes such as softening and dross fuming. The first part of this investigation was a study of the slag-metal equilibria in the Pb-PbO-Sb2O3 system. The only experimental work previously done on the Pb-PbO-As2O3 system was by Pelzel2,3 in which the phase diagram for the PbO-As2O3 system was determined below 50 wt pct As2O3 and the equilibrium constant for the reaction 3Pb + As2O3 + 3PbO + 2As was determined as a function of temperature. No slag-metal equilibrium data have been determined. It is due to the scarcity of information regarding the Pb-PbO-As203 system that this work was undertaken. This paper describes the determination of the slag-metal equilibria in the Pb-PbO-As203 system by equilibrating Pb-As alloys with PbO-As2O3 slags in an inert atmosphere, the effect of 1 wt pct additions of bismuth and copper on the slag-metal equilibria, and the PbO-As2O3 phase diagram both by thermal analysis and the use of the slag-metal equilibria data. EXPERIMENTAL Materials. The materials used in this investigation were analytical reagent-grade and assayed as follows: 1) 99.8 pct PbO (0.014 pct insoluble in CHJCOOH, 0.02 pct not precipitated by H2S, 0.1 pct CaO, and 0.08 pct SiO2); 2) 99.95 pct As2O3; 3) 99.99 pct Pb; 4) 99.0 pct As; 5) 99.99 pct Cu; and 6) 99.97 pct Bi. Room-temperature X-ray patterns revealed no detectable impurities in any of these materials. Apparatus for Equilibrium and Thermal-Analysis Determinations. The resistance-heated crucible furnace used in this investigation employed nichrome elements and was mounted so that it could be raised to surround the reaction tube during each experiment and, subsequently, lowered. A schematic diagram of the apparatus is shown in Fig. 1. Each charge was heated in a 3+-in.-OD by 31/2-in.-high 416 stainless-steel crucible placed in a 41/4-in.-1D by 18-in.-long fused-silica reaction tube which was closed at one end. On a shoulder around the crucible was placed a 3: -in.-OD by 12-in.-long open-end fused-silica condenser tube. The open end of the reaction tube was covered by a water-cooled brass cap with ports for 1) admitting an inert atmosphere to the system through a stopcock, 2) introducing a stainless-steel, motor-driven, paddle stirrer into the crucible, 3) evacuating the system with a mechanical vacuum pump, and 4) sampling the melt with Vycor sampling tubes. The brass cap was fitted to the open end of the reaction tube with a silicone gasket and collar clamp. The furnace temperature was controlled by a Barber-Coleman Capacitrol controller and a chromel-alumel thermocouple. Due to the corrosiveness of the melt, the controlling thermocouple also served as the measuring thermocouple. The temperature of the melt was calibrated against the controller temperature and was checked periodically during each test with a Vycor-enclosed calibrated chromel-alumel thermocouple. The temperature measurement and control can be considered accurate to ±3°C. Procedure. The charge placed in the crucible for each experiment consisted of 1000 g of Pb-As alloy and 300 g of PbO-As2O3 slag. The crucible was then placed in the reaction tube, the condenser tube was placed on the shoulder of the crucible, the silicone gasket and brass cap were fitted on the open end of the reaction tube, and the entire system was evacuated and filled with argon ten times. After the last flushing, a positive argon pressure of 1 psig was impressed on the system. The furnace was then raised to sur-

Jan 1, 1968

By R. Grierson, L. J. Bonis

The high-temperature Strength oF TD nickel has been observed to be dependent upon the previons thermal and mechanical history of the material. Variations in both the level and the anisotropy of strength have been observed. 01 this paper- these variations are correlated with the storing of annealing resistant elastic strain energy in the matrix of the TD nickel. An x-vay line -broadening tecknique is used to measure the maLrTis elastie strain. THE inclusion of a finely dispersed second phase into a ductile matrix has long been recognized as an extremely effective method of strengthening the matrix both at high and at low homologous temperatures. It has been found, however, that the factors which determine the high-temperature strength are not the same as those which are important at low temperatures. Below 0.5 Tm the size and distribution of the second phase particles are of prime importance in determining the strength,&apos;)&apos; while above this temperature the strength is mainly dependent upon the previous thermal and mechanical history of the alloy,3-7 This paper is primarily concerned with explaining the response of the high-temperature mechanical strength of one of these alloys (DuPont&apos;s TD nickel) to various thermo-mechanical treatments. It will be shown that this response is not associated with the occurrence of any form of dislocation substructure within the matrix of the alloy. It has been found, however, that a correlation does exist between the elastic strain level in the matrix and the previous thermomechanical history of the alloy and that the observed changes in elastic strain level parallel the measured changes in high-temperature strength. It therefore must be concluded that variations in high-temperature strength are a direct result of the variations in elastic strain level. MATERIAL TD nickel contains approximately 2 vol pct of Tho2 in an unalloyed nickel matrix. It is formed, as a powder, by a chemical technique and this powder is compacted to form ingots which are then extruded to give 21/2-in.-diam rod. Rod of smaller diameter is prepared from the as-extruded rod by swaging. In the studies reported in this paper, 1/2-in.-diam rod was used. This rod received an anneal of 1 hr at 1100°C prior to being used in any of these studies. EXPERIMENTAL TECHNIQUES Two methods were used to examine the structure of the nickel matrix of the TD nickel. These were: 1) transmission electron microscopy; 2) the analysis of the position and profile of X-ray diffraction lines obtained using the nickel matrix as the diffracting media. To prepare thin foils for electron-microscopical examination, slices of TD nickel approximately 0.050 in. thick were cut from the as-received 1/2-in.-diam rod. These were then chemically polished down to 0.045 in., rolled to 0.009 in., given a predetermined heat treatment, and thinned, using a modified Bollman technique, to provide the foils for observation. All observations were carried out at 100 kv, using a Hitachi HU-11 electron microscope. Specimens of the undeformed rod were prepared by grinding down the 0.050-in.-thick slices to approximately 0.015 in. and then thinning chemically and electrolytically to give the thin foils. The X-ray specimens were prepared by rolling 0.375-in.-thick rectangular blocks down to 0.075 in. The surfaces of the rolled material were ground flat, chemically polished to remove the layer disturbed by the grinding, and given a predetermined anneal in an inert atmosphere. They were then ground lightly to check their flatness and given a final chemical polish prior to being examined. The X-ray diffraction line profiles were measured using an automated Picker biplane diffractometer. A special specimen holder was built to allow a more accurate and reproducible positioning of the specimen. The line profiles were determined by carrying out intensity measurements at intervals of either 1/30 deg or 1/60 deg over a range of 3 deg on either side of the nickel peaks of interest. A piece of pure nickel which had been recrystallized to give a large grain size was used as a standard to give the X-ray line profile generated by a strain-free matrix. The analysis of the X-ray diffraction line profiles is a modification of that due initially to Warren and Aver-bach8and has been described elsewhere.3 This analysis gives a measurement of two parameters associated with the structure of the nickel matrix. These parameters are: 1) the size of the coherently diffracting domains within the nickel matrix; 2) the magnitude of the elastic strains in these domains. Both of these parameters are first determined in terms of a Fourier series. These series are obtained from other Fourier series which describe the measured profile of the X-ray diffraction lines. Thus, for both the coherently diffracting domain size and the elastic strain level, it is possible to plot Ft (the Fourier coefficient) against t (the term in the Fourier series), where t can be expressed in terms of a distance L and the Fourier coefficient Ft(S) (associated with elastic strain level) can be expressed in terms of the root mean square strain (e2)1/2. Thus a plot of (F 2)1/2 vs L can be obtained. Plots of this type are shown graphically in Figs. 6 and 8. Interpretation

Jan 1, 1968

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-&apos; the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:&apos; and, if some simplifying assumptions about particle shape are allowed, the total number of particles.&apos;2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.&apos; Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By F. F. Craig

Many full-scale waterflooding operations are preceded by pilot floods, one purpose of which is to provide an estimate of recoverable oil. A laboratory model study was made to determine the influence of the producing wells&apos; effective productivity on the oil recovery efficiency of single five-spot pilots, as well as single injection well pilot floods. The effective productivity is indicated by the value of Condition Ratio, defined as the actual well productivity to that of on undamaged and non-stimulated, normal-sized well in the same formation. The effects of initial gas satrcration and mubility ratio on recovery eficiency were also investigated in this model study. Model test results skowed that at favorable mobiliry ratios, a five-spot pilot flood can provide a direct quantitative estimate of the recoverable oil in the pilot area. If the pilot producer&apos;s Candition Ratio is 2.2 or more, upwards of 90 per cent of the recoverable oil in the pilot area is recovered from the inside producer, regqrdless of the mobility ratio or initial gas saturation. This Condition Ratio can be achieved with preyent fracturing techniques. Model studies also showed that over the range of imposed injection pressure differences and regional pressure gradients normally encountered in field operations, there was no effect on the recovery efficiency of a five-spot pilot waterflood. Model studies of single injection well pilot waterfloods showed that with no initial gas saturation, the total oil recovery at the offset producing wells can indicate the oil recovery possible by full-scale waterflooding. It is essential that the Condition Ratios of the offset wells be above 1.4. If an initial gas saturation exists prior to water injection, the recoverable oil cannot be directly evaluated by a single injection well pilot flood. However, the production per formance of such a flood can be used to provide information on volumetric sweep efficiency. INTRODUCTION Oil reservoirs are conlplex structures and cannot always be fully studied in the laboratory. Therefore, many operators consider it prudent to evaluate a waterflood prospect by means of a pilot flood. Pilot waterfloods generally involve one of two well arrangements: a single five-spot pilot waterflood, involving four injectors and an internal pilot producing well; and a single injection well pilot flood (sometimes called an inverted five-spot pilot) having one injector and four sur- rounding pilot producers. Some pilot floods are composed of multiple five-spot pilot patterns. To yield information applicable to field-wide performance, the pilot must be located in a representative portion of the reservoir. Pilot floods generally are conducted for one or more of the following reasons: (1) to determine whether water could be injected at desirably high rates, (2) to determine whether an oil bank or zone of increased oil saturation is formed by water injection, and (3) to estimate the oil recovery by waterflooding. Many of the early pilot water-floods were conducted for only the first two reasons. As soon as a buzz in oil production was obtained in the pilot, water injection was initiated throughout the entire lease or field. A number ot laboratory studies have been directed toward determining conditions under which a pilot flood could yield a quantitative estimate of the oil recovery possible by full-scale pattern flooding. One of the early studies of single five-spot pilot flooding&apos; showed that well damage to the inside pilot producer could reduce the total amount of oil recovered. In a study of the single injection well pilot flood pattern,&apos; the results indicated that if the model boundaries were no closer than a half-well spacing beyond the pilot pattern, the pilot performance in the laboratory is unaffected by these boundaries. In another study,? he effect of initial gas saturation and mobility ratio on the ratio of production to injection rate for various groupings of five-spot patterns was defined by mathematical and analog methods. In a study4 involving both potentiometric and flow model experiments at a mobiliry ratio of unity, four different pilot patterns were studied. These included a single five-spot, a single injection well pilot, a cluster of four single injection well pilots and six inverted five-spots. In this study the ratio of well diameter to the distance between injection and producing wells was held constant at 1:1000. The effect of the 7 ratio-—the ratio of the pressure drawdown at the producing wells to the pressure build-up at the injection wells on the pilot performance-was studied. The values of 7 ratio ranged from 0 to 0.34. Results showed that both the total oil recovery and the total fluid production from the pilot relative to the cumulative injection increased with increasing values of the 7 ratio. The effect of both the ratio of injection to producing rates and mobility ratio on the oil recovery performance of a liquid-saturated single five-spot pilot flood was studied in a series of flow model tests.5 Rate ratios ranged from one to four, and mobility rates ranged from 0.1 to 10. Resulls of these tests showed that at low rate ratios, the pilot producers may recover up to four times the recover-

Jan 1, 1966

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&apos;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&apos;s law c = Kp1/2, and substitution therewith into Eq. [4] gives directly Eq. [I] where ? = DK. Integration of Fick&apos;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 C. Feng, W. E. Krul

A study was made of the development of texture and the anisotropy in plastic flow of Ti-8Al-1Mo-1V alloy. Based on Pole figure determinations, the shifting of texture induced by rolling at approximately 400°C was found to be due primarily to slip rotation for the major Portion of the material. Grain boundary shear is believed to be an important factor. The anisotropy of the textured alloy was examined in terms of the variations of yield stress under tension and the ratio of bi -axial strain increments µp, in the temperature range 25" to 290°C. The results were related to Hill&apos;s theory on plastic anisotropy. The Schmid factors of (1100)[1120], (1101)[1120/, and (1101)[1120] slip systems were analyzed and found to be compatible with the observed anisotropy. Cross-slip between these planes was proposed as a possible deformation mode. In a number of published articles, considerable interest has been directed to the possible achievement of texture hardening in hcp metals. Following Backofen, Hosford, and Burke,&apos; this phenomenon was related to the yield criteria of the material and was expressed in terms of the biaxial strain ratio, r = d?w/d?l. The higher the value of r, the greater is the expected potential for texture hardening under certain loading conditions. For a given material, r varies with direction. Such variation can be traced to the anisotropy in plastic flow and can be explained within the framework of the various modes of deformation. Hatch2 found that a high r value coincides with a texture whereby the (0001) pole is closely aligned with the surface normal for sheet materials, Based on the analysis of the slip on the {1010}, {1011}, and (0001) planes, Lee and Backofen3 and Avery, Hosford, and Backofen4 concluded that the resistance to thinning is reduced by the operation of the (0001) <1120> slip system; with this reasoning they were able to explain the low r values (i.e., r « 1) observed in magnesium alloy sheets in the rolling direction and in commercially pure titanium in the transverse direction. The general equation, dealing with plastic flow in a polycrystalline aggregate has been used to correlate the plastic anisotropy and texture. In this expression, T and s are shear and normal stresses, and dri and d? are shear and normal strain increments, respectively. Assuming that five slip systems are operative within each grain and applying the principle of maximum work,5,6 one can determine the m value among the available systems. On this basis, Hosford7 and Chin, Nesbitt, and Williams&apos; were able to correlate m with yield stress under plane-strain compression, and Svensson9 was able to predict the variation of yield stress in textured aluminum. These workers made their analyses from materials in which slip operation is known to be associated with plastic flow. Questions remain regarding the derivation of Hill&apos;s theory on plastic anisotropy,10,11 since it was formulated on von Mises&apos; yield criterion.&apos;&apos; Its ability to deal with other forms of deformation has been in doubt.13 Others have discussed the validity of Hill&apos;s quadratic equation relating strain and yield stress.14&apos;15 For hcp titanium, deformation by various modes of slip and twinning operations has been reported.16-20 If all possible modes of deformation operate and contribute substantially to the plastic flow, it is difficult to imagine how the quadratic expression can suitably describe the anisotropic plastic flow of titanium alloys. Backofen and Hosford15 considered that Hill&apos;s is a macroscopic theory and implied that the major mode of deformation by slip mechanism will adequately describe anisotropy of the material. In the present investigation, slip operation will be shown to play the major role in the development of sheet texture induced by rolling of a commercial titanium alloy. Although twinning and other modes of deformation may also operate, their operation is believed to be secondary. The anisotropic properties of the sheet, which can be expressed in terms of directional variation of r, µp = -d?w/d?l and the yield stress will be shown to be governed primarily by slip operation. MATERIALS AND EXPERIMENTAL TECHNIQUES The titanium alloy chosen for the present investigation had a nominal composition of 8 wt pct Al, 1 wt pct Mo, 1 wt pct V, and 0.1 wt pct interstitial impurities. Sheets varying between 0.1 and 0.15 in. thickness were used. The alloy was received in a condition which was prepared by rolling at 900°C and annealing at 700°C. Subsequently, the sheets were subjected to further reduction in thickness by rolling at 400°C. A total reduction in thickness of 65 to 70 pct was obtained by a series of quick passes in a rolling mill with intermediate reheating. Further reduction in thickness was not possible due to cracking developed at the edges of the sheets. X-ray measurements were conducted in a Siemens and a Norelco unit to determine the texture of the sheets. Reflection techniques were used exclusively with CuK, radiation and a nickel filter. The loss of X-ray intensity due to geometric defocusing was calibrated with a technique described previously." The (0001), (1010), and (1071) pole figures were plotted from 0 to 80 deg, and to present the texture elements quantitatively, inverse pole figures were constructed following the technique described by Jetter, McHargue, and Williams.22 Tensile experiments were carried out at 25", 175",

Jan 1, 1970

By C. J. McHargue, J. C. Ogle

Lightly deformed columbiun single crystals which contained only parallel hoins or purullel and intersecting trains were annealed at 1000&apos; and 1600"C. No re-crystallizntion occurred in specimens hawing only parallel twins. Only noncoherent twin boundaries nzipated at 1000°C but both coherent and noncoherent ones moved al 1600°C. Recrystallization occurred within a few minutes at twin intersections at 1000°C. The orientation 01 the recrystallized grains differed front that of both the matrix and deformation twins, but could he derired by (110) and/or(112) rotations. ALTHOUGH twinning in metals has been extensively studied, there have been no definitive studies of the annealing behavior of crystals containing deformation twins. Some effects observed after annealing deformation twins have been summarized by Cahn1 and Hall2. Any or all of these phenomena are observed: 1) The twins may contract so that the sharp edges of the lens become blunted, and eventually the twin may disappear entirely. 2) The twins may balloon out at an edge, giving rise to a large grain having the same orientation as the twin. 3) The specimen may recrystallize; i.e., new grains are nucleated and grow at the expense of the twins and the crystal immediately adjoining the twin. Such grains have orientations which are not present before. Contraction has been observed in iron,3 titanium,3, 4 beryllium,5 zinc,8, 7 Fe-A1 alloy,&apos; and uranium.9 Long anneals at high temperatures are required to have any appreciable effect in these metals and only thin twins are absorbed. Lens-shaped twins are absorbed from the edges: the thin, almost parallel-sided twins are usually punctured in several places and each piece contracts independently. Absorption is very gradual and no sudden cooperative jumps have been observed. The expansion of a twin into a larger grain of identical orientation is unusual, but such growth has been observed in iron,"&apos;" zinc,6 and uranium." Crystals which have been deformed simultaneously by slip and twinning recrystallize first in the area adjacent to the twin. New grains appear faster where the twins intersect: but isolated twins, especially if thick, can also give rise to new grains. This type of recrystallization occurs in zinc.6, 7, 12, 13 and beryllium.14 Reed-Hill noted, in a single crystal of magnesium, the nucleation of a recrystallized grain at a twin intersection which had the same orientation as the second-order twin and which grew into the highly strained matrix.15 Short-time annealing has been reported to cause no change in the deformation twins in vanadium,16 columbium, 17, 18 tantalum,19 tungsten,&apos;&apos; and zinc.7 The purpose of this investigation was to note the effects of annealing on the coherent and noncoherent boundaries of deformation twins in columbium and to locate the nucleating sites for recrystallization. The orientation relationships, which the new recrystallized grains have with the parent crystal and the deformation twins, were also determined. EXPERIMENTAL PROCEDURE Single crystals of columbium were obtained by cutting large grains from electron-beam-melted buttons which contained 10 to 50 ppm C, 10 to 100 ppm O,, 1 to 10 ppm H2, and 10 to 15 ppm N2. The crystals were hand-ground and chemically polished until all grain boundaries were removed. The specimens were mounted in an epoxy resin and a face of each crystal was mechanically polished on a Syntron polisher using Linde A and then Linde B polishing compounds. After all faces were mechanically polished, the crystal was electrolytically polished to remove all distortion due to cutting and grinding. Laue photographs were taken of all faces of the crystals to determine the quality and orientation of each crystal. The crystals were compressed about 10 pct at -196 C in a specially constructed compression cage with an Instron tensile machine. Each crystal was separated from the top and bottom anvils by teflon films which acted as a lubricant. With the specimen crystal in position, the entire cage was cooled to -196°C by being submerged in a Dewar containing liquid nitrogen. The crystals were compressed at a rate of 0.02 in. per min and the load was recorded on a strip-chart recorder. After deformation the crystals were mechanically polished on 600-grit paper and Pellon cloth with Linde A and Linde B polishing compounds. The crystal faces were chemically polished and then etched. The twin planes were identified metallographically from an analysis of the twin traces on two surfaces. Annealing was carried out by placing each crystal in a columbium bucket made from the same electron-beam-melted material as the crystal itself and suspending the bucket by a tantalum wire in a quartz tube. After a vacuum of 10-7 Torr was attained, a furnace at 1000" or 1600 C was raised into position and the crystals held for various lengths of time. The crystals were repolished and etched after annealing to remove any surface contamination. Approximately 0.010 in. was removed during this process. The resulting surface was examined metallographically for microstructural changes due to annealing. A microbeam Laue camera mounted on a Hilger Micro-focus X-ray unit was used to determine the Orientstions of the recrystallized grains. This X-ray micro-beam camera had a 0.002-in.-diam collimator and incorporated the ideas of both and and chisWik21 and Cahn.22

Jan 1, 1967

By Donald Warren, J. F. Libsch

HIS investigation originated as a result of a pre-vious experimental study&apos; of the magnetic properties of Fe-Co alloys fabricated by the powder metallurgy technique. Densities of powder compacts prepared for the magnetics investigation varied from 7.45 to 7.70 g per cu cm or from 93 to 95 pct of the experimental value of 8.08 g per cu cm for a fused alloy of the same composition.&apos; While this range of density is considered sufficiently high for most applications, the highest possible density is to be desired for maximum magnetic properties. By applying a technique similar to the one described above to a pure electrolytic iron powder, Rostoker³ was able to achieve a density of 7.895 g per cu cm, which is the highest density ever reported for sintered iron. While Rostoker&apos;s work involved the sintering of an elemental powder rather than a mixture, it was believed that higher densities should also have been obtained for alloys using the above technique because of the recoining operation and the high sintering temperature. Consequently, it was decided to investigate the various factors affecting the density of this alloy with the idea that such a study might lead to higher densities and, as a result, powder alloys having magnetic properties identical with those of the fused alloys. It was believed that the principal reason that near-theoretical densities for the powdered alloy were not obtained was the interference of gases with the normal sintering mechanism. When present during the sintering operation, gases can exert several harmful effects: they can remain on the particle surface and interfere with surface diffusion and plastic flow; they can be released and, under certain conditions, expand the void spaces through gas pressure; or they can remain trapped in the pores and exert a hydrostatic pressure that retards elimination of the pores. Jones,4 Rhines,5 Goetzel," and others have given the effect of gases in the sintering of powder compacts an extensive treatment. Among the more important sources of gases in the sintering process are dissolved gases, adsorbed gases, air entrapped during pressing, and gaseous products of chemical reactions. During sintering adsorbed gases are partly released at a relatively low temperature, while those gases entrapped during pressing cannot escape until their pressure is increased sufficiently through increasing temperature to expand the interpartjcle openings. The remaining adsorbed gases, gaseous reduction products, and dissolved gases produce a similar effect at the higher temperatures. If, in the sintering process, gas evolution occurs after the interpore channels have been sealed, an exaggerated expansion of the void spaces results. This is particularly true if the temperature is high enough for extensive plastic flow. In his fabrication of powder bars from tantalum, Balke7 had to consider the effect of adsorbed hydrogen and provide for its escape during sintering by limiting the compacting pressure to a maximum of 50 tons per sq in. The effect of gases entrapped during pressing was first noted by Trzebiatowski8 when he found that gold and silver powders decrease in density with increasing sintering temperature if pressed at 200 tsi, while they exhibit the usual increase when pressed at 40 tsi. Recent investigators9-11 have also noted that entrapped gases have an effect on the expansion of copper compacts during sintering. Proper provision for the escape of gaseous products of reduction must be made in order to avoid deleterious effects. Myers" states that in the sintering of electrolytic tantalum powder, the temperature was gradually raised to 2600°F with a pause at 2000°F to permit reduction of the oxides. Experimental Details For the present study, 50 pct Co-50 pct Fe compacts in the form of circular disks 1½ in. in diam and 0.15 in. thick were fabricated by the pressing and sintering of a mixture of the elemental powders. It was decided to follow the sintering process by means of liquid permeability measurements, because it was thought that such measurements might serve as a measure of relative pore sizes, as well as a possible indication of the point at which most of the interpore channels become sealed. However, since the permeability as measured by the flow of a liquid, such as ethylene glycol, does not give an absolute indication of the point where the pores have become isolated, a method for determining the percentage of pores connected to the surface was set up. As an additional cross check on the permeability measurements, metallographic methods were used to study the relative pore size. Finally, the property of ultimate interest, the density, was measured. Raw Materials: The powders used consisted of an annealed, 99.9 pct pure, —150 mesh grade of electrolytic iron powder, and a 98 pct pure, —200 mesh grade of reduced and comminuted cobalt powder. The cobalt powder was not further processed either by hydrogen reduction or annealing. The screen analyses for the iron and cobalt powders are given in Table I, while the chemical analyses for each type of powder are listed in Table 11. Table 111 gives the hydrogen loss measurements for the powders according to the M.P.A. Standard Method and for a higher temperature as well. Preparation of Compacts: Equal amounts of the elemental powders were mixed by rotation for 1 hr and then pressed into compacts approximately 0.15

Jan 1, 1952

By E. S. Fisher, L. C. R. Alfred

The elastic anisotropy factors, c4,/c6,, c3,/cll, and c12/cl,, for hcp metal crystals vary significantly among the dgferent unalloyed metals. Significant variations with temperature are also found. The effects of elastic anisotropy on the dislocation in an elastic continuum with hexagonal symmetry have been investigated by computing the elasticity factors for the self-energies of dislocations in fourteen different metals at various temperatures where the elastic moduli have been reported. For most of the metals the effects of the orientation of the Burgers vector, dislocation line, and glide plane are small and isotropic conditions can be assumed without significant error. Significant effects of anisotropy are, however, found in Cd, Zn, Co, Tl, Ti, and Zr. The elasticity factors have been applied in the calculations of dislocation line tensions, the repulsive forces between partial dislocations, and the Peierls-Nabarro dislocation widths. It is predicted that the increase in elastic anisotropy with temperature in titanium and zirconium makes edge dislocations with (a), (a + c), and (c) Burgers vectors unstable in basal, pyramidal, and prism planes, respectively. The probability of stacking faults forming by dissociation of Shockley partials in basal planes also decreases with increasing c4,/c6, ratio, when the stacking fault energy is greater than 50 ergs per sq cm. The widths of screw dislocations with b = (a) in titanium and zirconium increase very significantly in prism planes and decrease in basal planes as c4,/c6, increases. The effects of elastic anisotropy on various dislocation properties in cubic crystals have received considerable attention during the past few years. In the case of cubic symmetry the departure from isotropic elasticity depends entirely on the shear modulus ratio, A = 2c4,/(cl, —c12); i.e., the medium is elastically isotropic when A = 1. Foreman1 showed that an increase in the ratio A produces a systematic lowering of the dislocation self-energy for a given orientation and Poisson&apos;s ratio. ~eutonico~, has shown that large anisotropy can have a marked effect on the formation of stacking faults by the splitting of glissile dislocations in (111) planes of fcc and (112) planes of bcc crystals. ~iteK&apos; made similar calculations for (110) planes of bcc metals. Both studies of bcc metals showed that the large A values encountered in the alkali metals tend to reduce the repulsive forces between Shockley partial dislocations. In fcc metals, however, A does not vary over the large range encountered in bcc metals; consequently, the effect of A on the forces between Shockley partials is masked somewhat by the differences in Poisson&apos;s ratio between metals. The effect of A on the line tension of a bowed out pinned dislocation has also been investigated for cubic crystals, first by dewit and Koehler5 and more recent- ly by Head.6 In both cases the line energy model is applied and the core energy is not taken into account, thus making the conclusions somewhat tenuous with regard to the physical interpretation. Nevertheless, the fact that a large A decreases the effective line tension is clearly evident and the tendency for large A to produce conditions that make a straight dislocation unstable (negative line tensions) also seem evident. Head, in fact, shows visual microscopic evidence that stable V-shaped dislocations occur in 0 brasse6 For hcp metals the definition of elastic anisotropy is more complex and, furthermore, significant deviations from an isotropic continuum are found among a number of real hcp metals, especially at higher temperatures. The present work was carried out to survey the effects of elastic anisotropy on the elasticity factors, K, that enter into the calculations of the stress fields around a dislocation core. Some isolated analytical calculations have previously been carried out for several hcp metals but they are restricted in the dislocation orientations and temperature.8&apos;9 The present computations are based on single-crystal elastic moduli that have appeared in the literature and consider various orientations requiring numerical computations. The results are then applied to survey the effects of temperature on the dislocation line tension and dislocation splitting in hcp metals. PROCEDURE Anisotropy Factors. The degree of elastic anisotropy in hcp crystals cannot be described by a single parameter, such as the A ratio in cubic crystals. The following three ratios must be simultaneously equal to unity in order to have an elastically isotropic hexagonal crystal: The magnitudes of these ratios at several temperatures, as computed from the existing data for the elastic moduli of unalloyed hcp metals, are given in Table I. There are no cases of complete elastic isotropy, but the large anisotropy ratios encountered in the cubic alkali metals are also missing. There are, however, several significant differences among the hcp metals, the most notable being the relatively small A and B ratios in zinc and cadmium and the differences in the magnitudes and temperature dependences of A. It has been noted that the temperature dependence of A has a consistent relationship to the occurrence of the hcp — bcc tran~formation. For cadmium, zinc, magnesium, rhenium, and ruthenium, A is less than unity at 4&apos;~ and, with exception for rhenium, decreases with increasing temperature. In the case of rhenium, A has essentially no temperature dependence between 923&apos; and 1123"~, so that it is clear that A does not approach unity at higher temperatures. Cobalt is similar to the above-mentioned group of metals in that it also does

Jan 1, 1969

By J. J. Frawley, W. J. Childs

The dynamic nucleation of supercooled bismuth and Bi-Sn alloys has been studied over a frequency range of 15 to 20,000 cps. For low-frequency vibration, a minimum vibrational energy was required for enhancement of nucleation. Above this critical energy, the dynamic supercooling was less than static supercooling showing that vibration promoted nucleation. The amount of dynamic supercooling continued to decrease with increasing vibrational energy until a minimum or threshold value was reached. This minimum value of supercooling for nucleation remained constant joy all further increases in vibrational energy. For higher frequencies, similar results were observed. This behavior has been related to the necessity of cavitation for dynamic nucleation. When a liquid is cooled to a temperature below its equilibrium melting point, the solid phase is more thermodynamically stable. However, for solidification to occur, a two-step process, nucleation and subsequent growth of the solid phase, must occur. When a liquid is supercooled, that is cooled below the equilibrium melting point, the controlling process for solidification to begin is the rate of nucleation. Once nucleation has occurred, the solidification process is controlled by the rate of growth. Nucleation can be induced by two factors: either by a catalyst or by the use of mechanical shock. Numerous investigators1-4 have studied the effect of nucleation catalysis but much less systematic study has been made of nucleation by mechanical shock waves. The influence of vibrations on grain size in castings and ingots has been studied by many authors but no clear understanding of the mechanism or accurate prediction of the effect has been presented.5 It would be intuitively expected that the further the departure from equilibrium (i.e., the greater the supercooling), the easier it would be to induce nucleation. This has been quantitatively demonstrated both by walker6 and later by Stuhr,7 that the greater the degree of supercooling the easier it is to nucleate by a shock wave. Stuhr also attempted to obtain the mechanical energy required for nucleation of bismuth as a function of supercooling. He vibrated a crucible containing supercooled metal at low frequencies and various amplitudes and noted the corresponding dynamic supercooling obtained. The amount of supercooling was inversely proportional to the mechanical energy applied. Limitation of his experiment was the problem of the confinement of the liquid in the crucible without splashing and minimizing other unwanted modes of vibration. Tiller et al.8,9 did similar work on tin and Sn-Pb alloys using an electromagnetic stirring device. Their conclusions were that the magnitude of the magnetic field strength did not affect the amount of undercooling at which nucleation was initiated. While conclusive experimental results have been lacking to explain this effect of mechanical vibration on inducing nucleation, a number of theories have been proposed. Two of these theories are discussed below. 1) The Change in Melting:- Point Locally Due to the Change in Pressure (Clapeyron Equation). According to Vonnegut10 the most plausible explanation for the nucleation of a supercooled melt by cavitation is the effect of changing the melting point by a change in pressure. For materials where the volume decreases on solidification, an increase in pressure raises the melting point; for materials which expand on solidification, the melting point is raised for a decrease in pressure, i.e., rarefaction. Using the Clapeyron equation, the melting point of a metal can be calculated as a function of pressure. If it is assumed that the equation can also be used to calculate the temperature of nucleation of a supercooled melt as a function of pressure (i.e., the temperature of heterogeneous nucleation will increase with pressure at the same rate as the melting point), the amount of supercooling required for nucleation will be constant at all pressures as shown in Fig. 1. It is obvious that an isothermal change which results in an increase in melting point results in an equal increase in supercooling. This increase in supercooling may now be sufficient for nucleation. A pressure of 80,000 atm was calculated, using the Clapeyron equation, as the pressure required to increase the temperature of nucleation of nickel by 200°C. According to Lord Rayleigh,11 this very large pressure could be generated for a very brief period of time by the collapse of a cavity. This pressure wave is radiated in all directions from the collapsed cavity. If the temperature of the melt is slightly below its equilibrium melting temperature at atmospheric pressure, stable growth can follow; that is, once nucleation occurs, growth becomes the main driving force of the solidification process. This proposal has been extended to water which expands on freezing by assuming that nucleation occurs during rarefaction following the pressure pulse. This negative pressure pulse should follow immediately after the positive pressure pulse with its magnitude approaching the critical tensile strength of the liquid. The negative pressure developed during this period would raise the melting point of water and thus promote nucleation. Hunt and jackson12 have suggested this for water. Similarly, it could be postulated that bismuth which also expands on freezing could be nucleated during the negative pressure pulse. 2) Nucleation by a High-pressure Phase. An extension of the Clapeyron equation to systems where density decreased on freezing at atmosphere pressure has been proposed by Hickling.13 The phase diagram for water initially shows the well-known decrease in

Jan 1, 1969