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By S. D. Dahlgren

ORDERED G.P. zones having the cesium chloride structure were found to exist in the bcc iron-rich grains of an Fe-Au-Cu alloy that had been supersaturated with approximately equal atomic percentages of gold and copper, and aged at 400° and 350°C. Streaks and superlattice spots in electron diffraction patterns revealed the presence of the ordered zones in the aged material. The ordered Ll2 structure is commonly found for precipitates in fcc metals (e.g., Ni3A1 in nickelL7') but it is uncommon to find precipitates in bcc metals having the cesium chloride structure. The formation of the G.P. zones caused age hardening of the grains. Samples containing 3.8 at. pct each of gold and copper (with the remainder being iron) were annealed at 95@ or 1125°C in quartz capsules and were quenched by breaking the capsules under water. X-ray diffraction patterns revealed two solid solutions in the quenched samples. One solid solution was bcc and the other was fcc. The microstructure consisted of iron-rich grains of 0.3 mm diam surrounded by a yellow gold-copper-rich grain boundary network. The Au-Cu phase diagram %hows continuous solid solubility of gold and copper with ordered phases forming below 410°C. None of the ordered Au-Cu phases have the cesium chloride structure. Both Fe-Au and Fe-Cu phase diagrams3 show extended miscibility gaps and only terminal solid-solution phases. Consequently, it is reasonably certain the iron-rich grains consisted of an a-phase terminal solid solution, and the grain boundary network consisted of a gold-copper-rich terminal solid solution. Lattice parameters of the quenched solid solutions were consistent with the suggestion that the quenched phases were terminal solutions. The lattice parameter of the bcc phase (2.879A) obtained upon quenching from 950°C was higher than that (2.866A) for pure iron. The fcc phase in this sample had a lower lattice parameter than that for a 50 at. pct Au and 50 at. pci Cu solid solution, i.e., 3.866 compared to 3.877A. The lattice parameter for the 50 pct Au and 50 pct Cu solid solution was interpolated from data for Cu-Au solid solutions.4 More gold and copper were soluble in iron at 1125°C than at 950°C as indicated by a 0.012A increase in the bcc lattice parameter for a sample quenched from 1125°C. After the alloy had been quenched from 950° and 1125°C, the bcc lattice parameters were 2.879 and 2.891A1 respectively G.P. zones having the cesium chloride structure-which formed during low-temperature aging—were detected by electron diffraction and observed with electron transmission microscopy. In Fig. 1, the asymmetrical streaks parallel to ( 100) directions indicate that platelike G.P. zones had formed parallel to (100) planes of the matrix. The direction of streak asymmetry shows that the bcc unit cell of the G.P. zones was larger than the bcc cell of the matrix. The ordered cesium chloride structure is indicated by low-intensity superlattice spots at 010 positions which are nonallowed for bcc structures. The superlattice spots are streaked; therefore they are from the G.P. zones and are not caused by rel-rod effects of a thin matrix phase. The appearance and size of the zones observed in electron transmission microscopy and the appearance of the asymmetrical streaks in the electron diffraction patterns for the Fe-Au-Cu alloy were the same as those observed for a similarly treated Fe-Au alloy.' Ordered G.P. zones were detected also for an Fe-Au-Cu sample aged only at 400°C. The production of the ordered cesium chloride structure zones by low-temperature aging of super-

Jan 1, 1968

By C. A. Stickels

In a recent paper, Held1 showed that rolling conditions can have a marked effect on the volume fraction of surface texture produced in low-carbon steel. This variation in rolling texture is reflected in the recrys-tallization texture and affects the plastic properties of the annealed sheet. The fact that roll friction can influence the surface deformation texture in iron and steel has been known for some time;'= but the magnitude of the effect has never been shown quite so clearly before. The analogous effect during wire drawing has been recognized for many year.4 Dillamore and Roberts5 examined surface textures in warm- and cold-rolled aluminum and copper. They found that when a surface texture was present it could be described as the interior texture rotated about the transverse sheet direction. The angle of rotation was a function of the type of lubrication, the amount of reduction per pass, and the temperature of rolling. The purpose of the present note is to show that surface textures in cold-rolled iron can also be described as interior textures rotated about the transverse sheet direction. Vacuum-melted electrolytic iron* was straight- rolled 90 pct at room temperature in a two-high rolling mill with 5-in.-diam rolls. Two rolling procedures were used: a) no lubrication with reductions of about 0.035 in. per pass, and b) heavy lubrication with lano-line and reductions of about 0.002 in. per pass. The final sheet thickness was 0.030 in. (110) pole figures were determined by transmission through specimens taken from the sheet surface and sheet midplane. The surface texture of the sheet cold-rolled according to procedure a is shown in Fig. l.* The shapes of the low-intensity contour lines indicate that the texture can be described as a partial fiber texture with a (110) fiber axis normal to the sheet. The approximate range of orientstions present is (011)[211] — (0ll)[100] — (011)[211]. This range of orientations is what one would obtain by rotating the interior texture 90 deg about the transverse sheet direction. The intensity of (110) and (222) reflections from planes parallel to the surface was measured after removing metal from the surface by chemical polishing. The surface texture here was confined to the outer

Jan 1, 1968

By G. Y. Chin, M. T. Dolan, W. L. Mammel

We have obtained by computer methods the solutions of the Taylor analysis1 for axisymmetric flow in bcc metals. Four modes of slip have been treated in detail:2-4 (111), {112}(111), {123}( 111), and a mixture of all three. In addition to obtaining anisotropy of strength data for randomly oriented or textured polycrystalline material,4 we have also obtained the lattice rotation resulting from slip on the predicted systems. The patterns of lattice rotation are essential to an improved understanding of texture development during deformation. The present note shows the results of lattice rotation for 5 pct axisymmetric compression, for fifty-two axial orientations distributed at 5-deg intervals throughout the standard stereographic triangle. The data are presented in Figs. 1 to 4 for the four modes of slip. The lattice rotation is indicated by a vector, the ends of which correspond to the positions before and after the deformation. The different vectors emanated from a given orientation represent different combinations of five slip systems that satisfy Taylor&apos;s minimum shear criterion.&apos; Fig. 1 shows the results for {110}< 111> slip. They are similar to those obtained by Bishop5 for the case of (111 )(110) slip in axisymrnetric tension, since in axisymmetric flow the sense of lattice rotation for {111)( 110) in tension is the same as that for (110) (111) in compression. The pattern of lattice rotation may be divided into three regions: region A in which the rotation is toward [100]; region B, toward [lll]; and region C, toward either [ loo] or L lll]. Although some slip combinations in region C lead to [1101, the latter is not stable as continued activity of the same combinations will eventually move the axis toward [loo] or Llll]. It may also be noted that [loo] is itself not stable. However, close inspection of the vectors in region A shows that it is impossible for an axial orientation within A to rotate outside its boundary. Hence after heavy compression, all orientations from A and some from C are expected to form a diffuse band in the [100] vicinity. By far the largest region is B. Here all orientations rotate to [lll], which is a truly stable position. Thus the [111] texture component is expected to be rather sharp. For the case of (112 }( 111) slip, Fig. 2, region C is enlarged at the expense of A, with B about the same as for {110}( 111) slip. A significant difference, however, is that [loo], as well as [Ill], is now truly stable. Fig. 3 shows the results of slip on {123}( 111) systems. Region B is substantially enlarged at the expense of C, with A being intermediate in size between the {110}(111) and {112}(111) cases. Like the case of {110)( 111) slip, [100] is itself unstable. However, the lattice rotations here are confined to less than 5 deg; hence it may be considered "stable" for practical purposes. Finally, Fig. 4 shows the results of mixed slip. Here region B is the largest, and C the smallest, of all the cases considered. Both [loo] and [ill] are stable. The behavior of the three corner positions is, in fact, identical to the case of {112)( 111) slip, Fig. 2; it turns out that in these positions for the mixed slip case, all the active slip systems (based on Taylor&apos;s criterion) belong to pure {112}( 111) .4 In summing up the results for the four modes of

Jan 1, 1968

By R. W. Armstrong, P. C. Jindal

TABOR1 has indicated for a number of polycrystal-line materials that their hardness should be directly related to their yield strength. For a material showing zero work-hardening, the Meyer hardness, MH, may be calculated in terms of the yield stress, sy, by utilizing slip line theory and the result is: The Meyer hardness corresponds to indenting the surface with a spherical indenter and specifying the ratio of load and projected area of the indentation. The correlation indicated by Eq. [I] is not well-established. It has been verified to some degree by performing hardness tests on materials strained to the maximum nominal stress and taking this stress as the (new) yield stress of a nonwork-hardening material. The dependence of hardness on yield strength for an annealed material capable of showing work-hardening has not been theoretically evaluated but, presumably, the hardness should be greater than that specified above. Marcinkowski, Fisher, and szirmae2 measured the dependence of the Vickers Diamond Pyramid hardness, H,, on yield strength for an annealed Fe-Cr alloy which shows work-hardening and found:

Jan 1, 1968

By G. S. Cole, G. F. Bolling

ThIS note accompanies a study of grain structure changes in metal ingots produced by the alteration of fluid motion.1 Although the Prandtl Number of aqueous solutions is much higher than that for metals, it is quite instructive to see the simulation of freezing, as pointed out by Jackson and coworkers.2-4 Accordingly we have observed the effects of natural thermal convection, the changes induced by a steady-state rotation in one direction, and the changes under oscillation.&apos; Temperature measurements were made under duplicate conditions whenever the visual observations appeared interesting. A solution of 15 pct NH4C1 in water was chosen. In each case the solution was preheated to 90°C in a 4-in.-diam Pyrex beaker filled to a level of about 5-in. depth and covered to prevent convective air cooling. The beaker was then placed in a container of iced brine, suitably arranged on a rotating table for movement about its cylindrical axis. Upon immersion in the brine under static conditions, fluid flow was observed near the wall of the beaker before the onset of crystallization, which generally commenced only after the temperature fell to 51.5"C. The region of flow extended about 1 mm from the wall and could not be observed elsewhere. The measured radial temperature increased sharply within 1 cm from the wall and thus over a distance considerably greater than that observed for the flow. However, we note that this difference of approximately one order of magnitude between hydrodynamic and thermal boundary layers should be expected for aqueous solutions, in contrast to metallic liquids. Beyond this layer the temperature was isothermal at a given height and in general nearly 10°C warmer than at the wall. The overall visual observation was therefore supported quite well by temperature measurement. There was also a vertical temperature gradient of nearly 2°C per cm throughout the liquid increasing from the colder bottom; this of course could not be observed visually. Eventually crystals precipitated from solution. (It

Jan 1, 1968

By W. A. Tiller, W. C. Johnston

A high-temperature electromagnetic stirrer is described in which heating and stirring are accomplished by independently controlled power sources. The appavatus is suitable lor use at temperatures up to 1700°C in a variety of ambient atmospheres. Some typical examples of the homogenizatimz capabilities of the system are given. THERE are few processes in solidification that are not markedly affected by motion in the melt during freezing. In many instances, the mechanisms are diffusion-controlled, and the transport in the melt may be greatly accelerated by deliberately stirring the melt. In zone-refining, stirring1 assists the removal of rejected impurities from the interface, so the process proceeds at a faster rate. The transition from a planar to a cellular interface is caused by constitutional undercooling in the melt ahead of the interface: and stirring delays its onset. Stirring is valuable for homogenization of melts: and chemical reaction with sluggish kinetics may be accelerated. Finally, it has been observed that grain refinement is related to motion in the melt. Fine grain castings are usually produced by the addition of catalysts to the -melt,&apos; catalysts which are thought to act simply as hetereogeneous nucleation centers. Even here motion is important. Richards and Rostoker 5 applied ultrasonic vibration to a solidifying A1-Cu alloy which had been innoculated with a catalyst and found that the grain diameter fell linearly with the amplitude, the peak acceleration and the power input to the melt from the transducer. Finally, mechanical and electrical stirring alone have been used to generate a fine-grained structure.6,7 Johnston ef a1.&apos; have carried out a series of systematic investigations of grain refinement by electromagnetic stirring in a number of low melting point alloys. They found, for example, that the number of grains per unit volume in Pb-Sn alloys could be increased several orders of magnitude by stirring an undercooled melt at the moment of recalescence. In general, a relation AT .H = constant prevailed for a given grain size, where AT was the undercooling of the melt and H the field strength. In more recent work, deliberate homogeneous nucleation of slightly undercooled melts established that the mechanism of refinement must be one involving crystal fragmentation and subsequent multiplication, rather than a "shower" of nuclei effect.9 It is the purpose of this note to describe a stirring device suitable for use up to 1700°C. At low temperatures mechanical stirring and direct-current methods are feasible, but at high temperatures the problem of a protective atmosphere and of electrode corrosion rules out such procedures. The most convenient method for high temperatures is to use externally generated ac fields for both stirring and heating. With rf induction heating alone, considerable stirring and agitation can be achieved, but in general the penetration of field into the melt is small, and the stirring cannot be controlled independently of the heating. In the present experiments, separate power sources of different frequencies for heating and for stirring were used. A susceptor design was chosen so that the 450 kc rf heating field was completely absorbed in the susceptor. The stirring frequency, 400 cps, hereafter called the af field, was chosen so that a high penetration of the melt proper was achieved. EXPERIMENTAL APPARATUS The apparatus, Fig. 1, consists of a quartz tube and end plates, surrounded by an rf induction coil and six equally spaced af stirring coils, four of which are shown in full and a fifth in section. Each af stirring coil is a transformer of which the secondary is a single-turn water-cooled copper loop and the primary is composed of two 10 amp-117 v Variac cores as shown. These cores are cooled by forced air, as each of the six pairs will carry maximum currents of 15 amp for short periods. Each set of Variac windings are connected in series, but opposite sets are connected in parallel with a three-phase 400 cps 400-v source. By properly phasing the coils in this way, a rotating field is produced. Capacitors C1, C2, and C3 in Fig. 2 are used to match this inductive load to the generator. Fig. 3 shows a cutaway view of the quartz tube. The sample (1 in. diam by 1 in. high) is placed in a tapered alumina crucible. An axial W-26 pct Re thermocouple, enclosed by a protection tube, is provided. The cruci-

Jan 1, 1968

By C. E. Brukl, E. Rudy, St. Windisch

The ternary-alloy system Nb-Mo-C was investigated by means of X-ray, melting point, DTA, and metallo-graphic techniques; a complete phase diagram for temperatures above 1500°C was established. Above 1960°C, niobium monocarbide and the cubic (Bl) high-tenzperature phase in the Mo-C system form an uninterrupted series of solid solutions. The ternary range of the pseudocubic q MoCl-, is very restricted. Dimolyb-denum carbide dissolves up to 44 mol pct Nb2C (2240°C), whereas the maximum solid solubility of MO2C in Nb2C does not exceed 5 mol pct. The order-disorder transformation temperatures in Mo2C and Nb2C are lowered by the mutual metal exchanges. Six invariant (p = const) reactzons occur in the ternary system; three correspond to class 11-type four-phase reactions involving a liquid phase, one to a class I (eutectoid)-type, and two further isotherms are associated with limiting tie lines. The results of the Phase diagram investigation are discussed, and the thermodynamic interpretation identifies the low relative stability of the binary sub-carbides in conjunction with the large stability diflerences between niobium and molybdenum carbides as the cause for the formation of a stable equilibrium between the monocarbide and the metal phase in the ternary reson. Due to their refractoriness, the carbides of the high-melting transition metals have received increased interest in recent years as base materials in composite structures for aerospace applications at high temperatures and for the development of self-bonded cutting tool materials; other novel fields of application include power reactors, where operation at high temperatures becomes essential for attaining high power efficiencies. In these applications, the increased reaction rates at high temperatures require a close consideration of the chemical interactions between the alloy constituents. As a consequence, a detailed knowledge of the phase relationships in the alloy systems is required in order to provide a sound basis for developmental -type work. Partly as a result of the considerable experimental difficulties associated with the investigation of this high-melting alloy class, no complete studies of ternary metal-carbon systems have been performed until recently. Even the high-temperature phase relationships in the binary transition metal-carbon systems have been delineated only during the past few years to a degree of accuracy required for a more detailed study of ternary or higher-order alloys. In recent investigations of binary and ternary systems of refractory transition metals with carbon, boron, and silicon,&apos; alloys from the ternary systems Nb-Mo-C became of interest because of the demonstrated possibility2,3 of obtaining compatible composites based on metal + monocarbide combinations. In the meantime, however, studies in other, but related, ternary metal-carbon systems, such as Ta-W-C, have shown that the solid-state equilibria may change significantly toward higher temperatures (>2000°C), and that extrapolations based on low-temperature equilibrium data are, in general, not very reliable. Although the lower-temperature (<2000°C) phase relationships in the Nb-Mo-C system are similar to those found in Ta-W-C, a cursory thermodynamic analysis of the equilibria indicated4 that complete solid-solution formation between Mo2C and Nb2C should not occur at higher temperatures. The present work was conducted in order to experimentally verify these expectations and, in addition, to provide phase equilibrium data in the melting range of the alloys. In the boundary systems, niobium and molybdenum are known to form a continuous series of solid solutions.576 The continuous solubility was also confirmed by Kornilov and Polyakova,7,8 who also observed a minimum melting point at 22 at. pct Mo and 2345°C. The phase diagram investigations of the Nb-C system by Storms and Krikorian9 and Kimura and Sasaki10 were recently supplemented by Rudy et al.11,12 The system contains a high-melting monocarbide with the B1 structure, Table I, and a subcarbide, Nb2C, which exists in at least two different states of sublattice order at low temperatures47"-&apos;3 and a disordered state above approximately 2500°C.11,12 The melting-point measurements by Rudy et al .11,14 are in close confirmation of the data by Kimura and Sasaki.10 The rather complex phase relationships in the Mo-C system were only recently Clarified.15,18 The system is characterized by three congruently melting, intermediate phases, MozC, ? MoC1-x and a Mol-,, Table I, of which only Mo2C is stable at temperatures below 1650°C. Substoichiometric MozC exists in several states of sublattice order which interconvert in homogeneous phase transitions. Hyperstoichiometric compositions cannot exist in the ordered state. Upon cooling through a critical temperature range, the

Jan 1, 1968

By W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.&apos; This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By J. E. Spruiell, F. H. Patterson, B. F. Shuler

The microstructures and textures developed by the working of high-purzly thermochemically deposited tungstem sheet have been inuesligated. Greater than 60 pct reduction was required to deslroy the columnar grain structure which existed in the as-deposited sheet. With increasing reductions the texture gradu-ally charged from the initial as-deposited orientation with (100) parallel to the sheet normal to a (100}(011) ideal ovienlation with some spread about the rolling direction. This texture was retained after recrystalli-zation a1 2000°C. THE processes for depositing tungsten by hydrogen reduction of tungsten hexafluoride have been under development for the past several years.1,2 The nature of the deposition process is such that the as-deposited material contains a highly oriented columnar grain structure perpendicular to the deposition substrate. This well-defined columnar structure may be useful in certain applications293 but a wrought or equiaxed structure may be desired for some components such as tubing. Knowledge of the effects of working ther-mochemically deposited (TCD) tungsten is therefore necessary in order to establish the feasibility of obtaining worked and recrystallized microstructures and textures. The details of a recently developed technique for thermochemically depositing flat, uniformly thick tungsten sheet are presented with emphasis on the effects of deformation by rolling on the microstructure and texture. Although no work has been previously reported on the rolling and the annealing textures of TCD tungsten, there have been some determinations of textures for cold-rolled tungsten foil prepared from powder-metal -lurgy billets.4-8 The general description is that of a predominantly lurgy{100}(011) texture, with some spread about the rolling direction as an axis. pugh5 reports data both for cold-rolled and for annealed foil having about 96 pct initial cold work. He observed no change in texture, except for a decrease in the spread, for annealing treatments of 30 min at temperatures up to 1800°C. On annealing at 1900°C, both the low-temperature components plus new components which were described alternately as {001}(320) plus {001)(230) or as {100}(011) ± 12 deg about the sheet normal were observed. Above 1900°C, the new orientation existed alone, and it was stable up to 2500°C, the highest temperature that Pugh investigated. THERMOCHEMICAL DEPOSITION OF TUNGSTEN SHEET High-purity tungsten sheet was reproducibly deposited on the inner walls of a molybdenum mandrel by the thermochemical reaction WFs(g) + 3H2(g) - W(s) + 6HF(g). The mandrel was heated by a five-zone tube furnace which afforded a controllable fixed-temperature profile. Sheets measuring 1+ by 12 in. have been deposited with uniform thicknesses of up to 0.145 m. As shown schematically in Fig. 1, the purified reaction gases were metered into a mixing chamber at a Hz-to-WF6 ratio of 15 and preheated to 350°C. The flow rate of the WF6 was 300 cu cm per min at stp. These gases were directed through a conical injector into the deposition chamber. Inside this chamber hydrogen reduction of the WF6 to pure tungsten metal occurred on the hot walls of the molybdenum mandrel at a total pressure of 5 Torr. Typical temperatures for the five zones in the chamber were, respectively, 565", 540", 550°, 570°, and 590°C. The hydrogen fluorlde generated from the reaction, the excess hydrogen, and some un-reacted WF6 were pumped on through the scavenger

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2&apos;3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.&apos;&apos;&apos; ~ohatgi&apos; has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-

Jan 1, 1968

By R. P. Agarwala, M. S. Anand

Using residual activity technique, the diffusion of palladium, silver, cadmium, indium, and tin in alunzinum has been studied in the temperature range of 400" to 630°C. The diffusivities (in units of square centimeters per second) have been expressed as: IMPURITY diffusion in aluminum,1-9 silverand lead5 for cases of low solid solubility of the impurity in the host metal has yielded frequency factors in the range of l0-6 to l0-9 sq cm per sec whereas the activation energy is practically half the self-diffusion activation energy value. From the observed values of frequency factor, activation energy, and entropy of activation, it has been suggested&apos; that these solutes are not diffusing by vacancy or interstitial mechanisms but by a mechanism which should be consistent with such low values of the diffusion parameters (Do and Q). However in spite of extensive work on these types of systems, the mechanism of diffusion is still not well understood. The present investigation on the diffusion of palladium, silver, cadmium, indium, and tin in aluminum has been carried out to throw further light on the diffusion mechanism in systems, where the solid solubility is very low (except for the case of silver). The results are discussed on the basis of solid solubility and the structural changes involved owing to the presence of the solutes in aluminum solid solution. An attempt has also been made to apply the existing theories of charge5-8 and size8 difference between the solute and the solvent. EXPERIMENTAL PROCEDURE Specimens (1/2 in. diam by 3/8 in. high) were machined out of pure aluminum (99.995 wt pct) rod obtained from Johnson Mattheys. They were sealed under vacuum in quartz tubes and annealed at 620° C for several hours; the grains thus developed were sufficiently large to eliminate the possibility of diffusion along the grain boundaries. The flat ends were prepared carefully after polishing as described previously,10 Radioactive nitrates of cadmium, indium, and tin and chloride of palladium containing, respectively, cd115, 1n114, sn113, and pd103 were dissolved in distilled water and mixed with 30 pct acetone. By means of a micropipet a drop of this solution was placed on a smoothly polished and lightly etched surface of the specimen. Due care was taken to see that the solution spread uniformly on the surface of specimen without trickling down its sides. Radioactive silver was elec-trodeposited using a AgCN-KCN bath. The amount of sample deposited in all the cases was not more than 0.1 µ thick. The samples were then sealed in quartz tubes in vacuum. The cadmium samples were sealed in a purified argon atmosphere to avoid evaporation. The samples were then diffusion-annealed. The temperature of annealing varied between 400° and 630°C and was controlled to ±5°C. On heating to -400°C,the deposits of cadmium, indium, and tin, which were of the order of 0.1 p in thickness, were converted to their respective oxides. The contribution of oxygen present in the lattice of aluminum due to these oxides has been calculated and found to be less than 10 ppm in all cases. Oxide method has already been used by other workers11&apos;12 in diffusion studies without any controversy on the issue. However, in some of these investigations, metallic deposition was also tried. The diffusivities calculated from these measurements were found to agree very well with the diffusivities obtained by using the oxide method. Thus it is assumed that the measured diffusivities represent true diffusion coefficients. Since palladous chloride decomposes at about 500°C, the deposited samples which were to be diffusion-annealed below 500°C were heated in vacuum for a very short time at 500°C to allow the decomposition of palladous chloride to palladium metal. Time taken in decomposition of nitrates to oxides and chloride to metal was negligibly small as compared to the period of the diffusion anneals. The residual activity technique13 was used to study the diffusion profiles where thin layers from the specimen surface were removed by grinding it parallel to a flat surface on a 600-grade carborundum paper. The specimen was washed, dried, and weighed, the differ -ence of the weight being the measure of the thickness of the layer removed. After each such abrasion and weighing, the total residual activity on the surface of the specimens was measured by counting 0.656, 0.94,

Jan 1, 1968

By E. J. Fasiska, H. Wagenblast

The dilalion of a ivon by interslilial carbon was measured by two independent techniques —dilatometric mesurements at 719 c and X-ray measurments of the urlil cell parameters a1 room temperature after quenching. The relative expansion per increase in cavbon content by both methods is (2.9 + 0.3) x 10-3 pev at. pcl C nrzd is temperature- independent within experimental error. This corresponds to (6.3 5 0.6) cu cm per g-atom for the partial gram-atomic volume of carbon in a iron-only slightly smaller than the atomic volume for iron in the same temperature vange. THE only previous quantitative study of the dilational effect of carbon dissolved in a iron was performed in 1934 by Burns1 which, at the time, generated some discussion of possible sources of experimental error.2 For a system of such widespread importance, we felt that a new investigation was merited. Both X-ray diffraction and dilation measurements were used to determine the expansion of the a iron lattice by dissolved carbon, avoiding as much as possible any previous experimental problems and deficiencies. The dilation method at solution temperature offers not only measurements which are free of residual strain but also, in conjunction with the room-temperature X-ray measurements, a method to detect any large temperature dependence of the partial gram-atomic volume of carbon. To insure that quenching strains did not affect the room-temperature X-ray measurements, wire specimens of constant carbon content but different diameter were examined for such an effect. SPECIMEN PREPARATION The material used for both experimental techniques was "Ferrovac E" iron received in the form of 19-mm-diam rod and stated as having the following impurity contents: C, Cr, Cu, Mn, P, and V, each in the range of 10 to 50 ppm; Co, O, Mo, S, and Si, 60 to 100 ppm; W, 200 ppm; Ni, 230 ppm; N, 4 ppm. The stock material was cold-swaged to 0.71 mm diam for the Debye-Scherrer X-ray camera specimens and portions were cold-rolled from 6.3 mm diam to 0.79- and 0.25-mm sheet for X-ray diffractometer and dilation measurements. The wires were annealed in wet hydrogen for 6 hr at 840°C and 15 hr at 720°C, and then quenched into 0°C water. A chemical analysis for carbon after this treatment gave 0.0046 + 0.0014 at. pct C. Three portions of these wires were subsequently held at 719°C in three different hydrogen + methane mixtures and then quenched, resulting in carbon concentrations of 0.0283, 0.0598, and 0.1067 at. pct C by chemical analysis. After carburizing, the wires were swaged to 0.48 mm and electroplated with silver to prevent carbon loss during subsequent heat treatment. The final heat treatment consisted of holding the wires at 72 1°C for 5 min in a He-2 pct H mixture followed by quenching into 0°C brine. The wires were held at room temperature for a few minutes to remove the silver plating using a phosphoric acid-hydrogen peroxide solution, and then stored in liquid nitrogen until the measurements were made. EXPERIMENTAL TECHNIQUE A) Dilation Measurement. The dilatometer consisted of a gas-atmosphere vertical tube furnace modified so that length changes of a ribbon-shaped specimen could be measured externally. This was done by installing a gas-tight mercury seal at the top of the furnace as shown schematically in Fig. 1. The specimen (21.0 cm long, 1.27 cm wide, and 0.25 mm thick) was suspended in the center of the furnace by 3-mm-diam quartz rods with the upper one passing through the cap of the mercury seal. Above the cap, the upper quartz rod was coupled to a lever exerting a load of about 25 g (-12 lb per sq in.) on the specimen and having a 10 times mechanical magnification. The vertical position of a marker at the other end of the beam was read with a traveling microscope with a precision of 0.01 mm. The temperature gradient of the furnace was meas-

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Dendritic aggregate of ice formed on freezing of aqueous soluitions has been studied. Chlorides of sodium, potassiutn, lithiunz , and hydroget1 were used as solutes. The spacing between ice platelets or den-drites was experimenlally found proportzonal to the square root of freezing time when the freezing rate was constant from beginrting to end of solidification; the constant freezing rates were obtained during freezing of small droplets of aqueous soliitions surrounded by relatively large heat sinks. The transverse growth velocity of the ice platelets is proportional to the square root of the freezing rate. During unidirectional freezing from a constant temperuture chill, the solution at each location is subjected to a spectrum of freezirtg rates. The freezing rate is ini- FREEZING of solutions has been a subject of investigation in many disciplines. Aqueous solutions offer the advantage of transparenty; their study is of special significance due to the increasing interest in freezing processes for desalination. In addition dendritic solidification of aqueous solutions is in many ways analogous to freezing of metallic solutions. Aqueous solutions of most ionic salts freeze with tially low, passes through a maximum, and then decreases until solidificatimz is complete. The den-drite spacing increases linearly with the distance from the chill surface; it is inversely profiortional to the square root of the maximum freezing rate. The dendrite spacings in the two systems (the constanl freezing rate and the varying freezing rate) are equal, when the maximum freezing rate of the varying freezing rate system equals the average freezing vale of the constant freezing rate system. Mass transport in interdendritic liquid duriug solidificatiotz is analyzed; the experimental observations indicate that maximum concentration difference (AC) and supercooling (AT) in the interdendritic liquid are indepexdent of freezing rate. the separation of practically pure ice crystals from the liquid phase; with very few exceptions there is no solid solubility of ionic salts in ice. As an ice crystal grows there is rejection of solute from the moving interface into the liquid. Since the rejected solute moves primarily by diffusion, concentration gradients are established in the liquid. The highest solute concentrations are found in liquid immediately adjacent to liquid-solid interfaces and lowest concentrations farthest from the interface. Two-phase equilibrium obtains only at the solid-liquid interface; at other locations the liquid becomes supercooled because temperature gradients are negligible compared to concentration gradients. This is an immediate consequence of the fact that thermal diffusivities are considerably higher than mass diffusivities.

Jan 1, 1968

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute&apos;s influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger&apos;s argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.&apos; Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute&apos;s influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute&apos;s influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By G. S. Cole, G. F. Bolling

Fluid flow strongly influences ingl structure and the columnar -to-equaaxed transition. Artificial flow patterns siwzilar to the nuturul ones act to induce this transition, while dampening forces act to suppress this transition. It is shown here how simple mechanical forces can be applied to a systerrz in order to induce or slipPvess relative fluid flow and the change both the structure transition and the exact structures obtained. The example used is the effect of slow rotations and oscillations 012 a cooling- ingot (of laboratory scale). The details of rotution and oscillation for various cooling rates, lenlperal~ire gradients, and sizes of ingot are related to other solidzfication variables. THE grain structure of a casting can be changed by altering the fluid motion during solidification. Just how important these changes are depends directly upon the degree to which the fluid motion can be controlled. An early step in understanding the nature and influences of fluid motion was taken by studying natural thermal convection; when a static mechanical device was used to suppress natural flow the result was opposite to that obtained when an electromagnetic device was used to augnlent flow in a pattern similar to the natural one. &apos;&apos;2 Suppression allowed more columnar growth to occur, but "augmented natural convection" brought about an earlier columnar-to-equiaxed transition (CET). Since the solidification of a free ingot must have characteristics somewhere between those displayed during suppression and augmentation, we know that natural convection must influence the CET. Further, since heat transfer in the liquid is always some time-dependent combination of convection and conduction, it can easily be guessed that the temperature gradient in the liquid is the vital factor affecting the CET.1,2 It is obvious that the structure arising from the unadulterated solidification of an ingot, without external influence, is rarely if ever the best possible one. Although the pattern of the natural fluid flow may be considered efficient, the magnitude of the flow and the heat transfer decrease freely from the outset. For a

Jan 1, 1968

By R. A. Flinn, R. D. Pehlke, D. R. Glass, P. O. Hays

Knowledge of the depth of penetralion of an oxygen jet into the bath of the oxygen converter and of the correlation of penetration with driuing pressuve, lance heighl, and nozzle throat area is vital to the understanding of converter operation. If the penetration is too shallow, then severe and hazardous slopping takes place. On the other hand, if the jel penetrates entirely Lhvough lhe bath for an apprcciublc period of time, bottom damage occurs. In addilion to measurement of the penetralion of the jel, knou~ledge of the circulatory movement in the bath is also of interest in order to evaluale various theories oj-concerter operating behavior which have been published. In this investigation, experimental converters were buill of IOU- , 300-, and 4000-lb capacity. Four independent methods were used to determine penelralion: the onset of bottom marking, a nitrogen bubbler probe, observation througlt an optical syslew built into the oxygen lance, and direcl viewing of the jet issuing from the bottom of the vessel. Good correlation zuas obtained, and empirical relalions for pvedicling perletration were found. These relations were conjzrmed by bottom marking tests in 55- and 110-ton vessels. Within the operaling conditions employed in these tests, the depth to which a single oxygen jet penetrated zuas found lo vary according to the relatiorl ThE technical literature is replete with data concerning the successful use of the basic oxygen furnace or converter in steelmaking. Experimental data are lacking, however, on the vital factors of the depth of penetration of the jet into the bath and the induced circulation. Commercial operating conditions usually have been the result of cut and try experiments in lance manipulation until satisfactory results were obtained. There have been, however, two hotly argued opposing theories concerning desirable depth of penetration and these are exemplified by the Schwarz and Miles patents1,2 on one hand and the Suess patent3 on the other. The Schwarz patent teaches that the jet, issuing from the nozzle at supersonic speed, penetrates deeply "so that the reactions between the iron and the oxygen and between the oxygen and the rest of the smelting components take place in the center of the bath". Specific operating suggestions are given by Miles.2 By contrast, the Suess patent calls for surface Circulalion was investigated by lour methods: by direct observation in 200-lb open baths, by the use of graphite rudders in the 300- and 4000-lb converlers, by direct observalion through an oplical system in the lance, and by various models al room temperature. All were in excellent agreement and indicated that the motion of the bath ulas up at the center, radially outluavd at the surface, and down at the sides. Experi-ments in small and in commercial vessels indicate that it is essential to operate with a jet penetration of approximately 50 pct of the bath depth. Surface blowing results in low oxygen eficienty and in hazardous conditions which may render the process inopeuable. RejYactory dartzage al the bottom of the vessel is only encountered when the jet penetrates to the bottom, and this can be avoided by properly applying the penetration formula. The application of this en/pirical formula in commercial peraations is best when limited to combinations of lance size, pressure, and height which are typically encounteved in the use of a single-hole lance. blowing so that "...the oxygen jet does not penetrate deeply into the molten metal bath and is confined to an impingement area at the central portion of the bath surface". These references are given merely to illustrate the basic differences between the two schools of thought and to point out the need for measurement of penetration for the sake of the operator. For example, it is shown later that inefficient and even dangerous conditions can arise if improper blowing conditions are used. Differences are also evident between the two schools of thought as to the mixing, circulation, and agitation which is to be accomplished by the jet. The Schwarz patent states that "surface contact is not sufficient in most cases to bring about quick reaction, the same as the blowing of the gas over the bath surface or the mere blowing of the gas onto the bath surface". The patent goes on to call for active mixing. In contrast the claims of the Suess patent call for "discharging a stream of oxygen ... to an extent to avoid material agitation of the bath by the oxygen stream". In this patent the circulation is said to be downward in the center and up at the sides of the vessel. A number of investigators4-12 have explored penetration and circulation in transparent models. In general, it is agreed in these tests that the circulation is upward at the center (along the sides of the jet cavity),

Jan 1, 1968

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,&apos; there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By L. C. Michels, O. G. Ricketts

The disorientations between s?nall grains, whose growth has been arrested at an early stage of recrys-tallization, and the deformed matrix in cold-rolled aluminum single crystals were determined using transmission Kikuchi line and electron diffraction patterns. The orientations of the recrystallized grains were found to be random, and the disorientations of these grains with the matrix weve found to be intermediate to large. This leads to the conclusion that the observed vecrystallization began in small areas of large disorientation present in the cold-worked structure. heavily cold-worked thin sections of aluminunz single crystals and of polycrystalline aluminum and nickel were produced directly by a mechanical technique. The specinlens thus prepared were heated with the electron beam to bring about vecrystallization during observation in the electron microscope. Motion pictures taken du.ring heating and the electvon, microg.raphs taken both before and aftev heating allowed the recrystallization process to be traced to its ovigin. Re cvystallized grains originated in very s,mall regions of the cold-worked structure and developed through rapid migration of high-angle boundaries. The boundaries either were present as such in the matrix or were formed out of dense dislocation networks. SIGNIFICANT advances have been made in recent years in the study of nucleation of recrystallization using the technique of transmission electron microscopy of thin metal foils. Bollman1 in a study of heavily rolled polycrystalline nickel found support for the Cahn-Cottrell2,3 theory of nucleation. According to this theory nuclei form by the initially slow growth of subgrains formed through polygonization. During this initial period of slow growth (the incubation period) the migrating boundary of the subgrain increases its disorientation with the cold-worked matrix and thereby increases its mobility to become a rapidly migrating high-angle boundary. Bailey4,5 investigated the annealing behavior of several metals deformed both in tension and by rolling and concluded that recrystallization took place through the migration of high-angle boundaries. With low deformations these boundaries were present in the metal before deformation. With high deformation it was not possible to tell whether the boundaries were pieces of the original grain boundaries or were produced either during deformation or by polygonization during ameal- ing. Direct observation during heating of metal foils indicated that subgrains form by polygonization and grow at an uneven rate. The grain size obtained decreased with decreasing foil thickness indicating that the foil surface resists boundary motion. Votava,6 in heating stage experiments on rolled copper, observed nuclei to appear suddenly and grow in jumps of differing magnitude. However, he found no special dislocation configurations where the nuclei appeared. Fujita,7 as a result of a study of subgrain growth in heavily worked aluminum, concluded that the boundary of a recrystallized grain initially forms from the boundary of a group of subgrains. This occurred by a process of deposition of vacancies and dislocations in the group boundary as the boundaries within the group disappear. HU8,9 directly observed a similar process in heating stage experiments on 70 pct rolled Si-Fe single crystals. The growth of subgrains appeared to proceed by a coalescence mechanism. The observed fading away of the boundary between two subgrains was explained by the moving out of dislocations from the disappearing boundary into the connecting or intersecting boundaries around the subgrains. The subgrain size and degree of disorientation with the surrounding structure were thus increased. With the increase in disorientation occurred a corresponding increase in boundary mobility, which eventually allowed the boundary to migrate rapidly. This process was observed to occur within "microbands" consisting of parallel narrow segments disoriented by a few degrees present in the as-rolled structure. The conclusion of Rzepski and Montuelle10 that growth is preceded by the coalescence of blocks through disappearance of their common boundaries supports this view. In contrast to Hu&apos;s coalescence model for nucleation were the conclusions of Walter and ~och.""~ Working with the same material as Hu, of the same orientation and rolled to the same reduction, they concluded that nucleation occurred by the Cahn-Cottrell mechanism. They observed, in agreement with Hu, that recrystallization began in the "microband" regions which they referred to as "transition" bands. Bartuska13 studied subgrain growth in heavily rolled nickel using a beam heating method in the electron microscope. He concluded that nuclei for recrystallization form from the largest most perfect subgrains present in the cold-worked structure by rapid intermittent migration of parts of subboundaries. In rare instances he observed subgrain growth by coalescence. EXPERIMENTAL PROCEDURE The materials used in this study were 99.999 pct A1 supplied by A.I.A.G. Metals, Inc., and 99.999 pct Ni supplied by Johnson and Matthey and Co., Ltd. The Hitachi HU-11 electron microscope, with uniaxial

Jan 1, 1968

By Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.&apos; Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:&apos; where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.&apos; The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:&apos;" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968