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By Rex B. McLellan, W. A. Oates

FROM a consideration of the application of the Gibbs-Duhem equation to multicomponent systems arken' derived the following equation applying to dilute solutions of a solute, 2, dissolved in a binary solution, 1-3:

Jan 1, 1969

By M. S. Seltzer

In a previous paper1 it was shown that activation energies for steady-state creep in lead sulfide single crystals varied with the concentration of electronic defects. For n-type lead-excess crystals, values for the creep activation energy, Qc, decreased from 2.9 to 2.2 ev as the carrier concentration increased from 1017 to 1017 electrons per cu cm, while Q, increased from 1.6 to 2.3 ev for p-type sulfur-excess crystals as the concentration of holes increased from 6 X 1017 to 1018 per cu cm. It was also shown in Ref. 1 that the Q, values could best be correlated with the sum of the self-diffusion activation energies in PbS, i.e., for a given concentration of electrons or holes Q, = QPb + Qs, where Qpb and QS are the activation energies for diffusion of pb210 and s35 in PbS. This result suggests that creep rates are controlled by at least two atomic defects, one for lead migration and one controlling sulfur transport. It would be most desirable to interpret these creep energies in terms of an atomic defect disorder model for lead sulfide. Studies of creep rates as a function of sulfur pressure2 indicate that the defects controlling creep rates are singly ionized lead and sulfur vacancies, VPb and Vs. This hypothesis can be more firmly established by determination of Q, under conditions of constant atomic defect concentration rather than constant electronic defect concentration as has been previously done. Therefore, several measurements have been made of Q, on crystals whose con- centration of lead vacancies or sulfur vacancies has been fixed by equilibration under appropriate sulfur pressure and temperature. It was indicated in Ref. 2 that high-temperature isotherms are available which show how the concentrations of various atomic point defects in PbS vary with composition over the entire homogeneity range for the compound. Two such isotherms are shown in Fig. 1 for 900" and 1000°K. Utilizing these isotherms the concentration of a given defect, say Vbb, may be held constant over a particular temperature range by adjusting the sulfur pressure as the temperature is changed. Thus the concentration of one defect suspected of controlling creep rates may be held constant while other defect concentrations vary. The apparent activation energy for formation of these defects can be obtained from the isotherms giving their concentration as a function of sulfur pressure. Activation energies for creep obtained under conditions of constant defect concentration can then be compared with defect formation energies and certain possible atomic defects can be eliminated as creep-controlling species. We have performed creep experiments as a function of temperature at a stress of 244 g per sq mm under conditions which fixed the lead vacancy concentration, V', at 1016, 3.2 x 1016, and 3.2 x 1017 cm-3, and one were the sulfur vacancy concentration, Vs, was held at lo17 cm-3. The results are presented in Fig. 2 as creep rate, k, vs reciprocal of absolute temperature, 1/T. Specimens 34, 35, and 36 were deformed under constant lead vacancy concentration while specimen

Jan 1, 1969

By Carl F. Cline, Richard R. Vandervoort, Willis L. Barmore

THE objective of this investigation was to determine the high-temperature plastic deformation behavior of stoichiometric uranium mononitride as a function of stress and temperature. Interest in the properties of this material stems from its potential use in high-temperature nuclear reactor systems. The creep of other refractory compounds containing uranium (e.g., U02, UC) has been studied by various investigators.1"4 Fassler et al.4 have studied the creep of UN in vacuum from 1100° to 1350°C at stresses of 6000 and 8000 psi. In the present work, the creep of stoichiometric UN was investigated from 1500° to 1800°C at stresses from 2000 to 5000 psi in a partial pressure of 200 mm of nitrogen. The specimens were prepared by hot isostatic pressing of UN powder into cylinders of $ in. diam by about 1 in. high. After pressing, the specimens were heat-treated in nitrogen at 1900°C for 50 hr. The densities of individual specimens were determined by the water displacement method. All specimens were theoretically dense, based on a value of 14.32 g per cu cm.5 Principal metallic impurities in ppm by weight were: Ca, 50; Cu, 5; Fe, 30; Mg, 5; Ni, 10; and Si, 20. Oxygen content was 400 ± 50 pprn and carbon content was 100 i25 ppm. The nitrogen content was 5.56 ±0.05 wt pct. The average grain size for five specimens, as determined by the intercept method, was 0.14 i 0.01 mm. One specimen had a grain size of 2.0 mm. This large grain size is an anomaly, since all specimens had the same chemical and thermal histories. Specimens of 1/4 in. diam by 1/2 in. high were creep-tested in compression in a clam shell furnace heated by W-25 pct Re sheet elements. Temperature was measured to ilODC by an optical pyrometer which had been calibrated by a standard source. The distance between fiducial marks on the specimen was measured before placement into the furnace. The furnace chamber was evacuated to 10-5 Torr and back-filled to 200 mm N2. After heating rapidly to temperature, the load was applied and controlled to ±2 pct by an Instron testing machine. Upon initial loading, the specimen was deformed until a constant crosshead rate was obtained, then quenched to room temperature, remeasured, and replaced in the furnace. Upon subsequent reloading at temperature, the crosshead rate was constant for the selected condition indicating steady-state creep.

Jan 1, 1969

By O. A. Cheadle, F. E. Lane

ThE computer program for arbitrary crystal systems reported by Camp and Clum' has been modified to make it more convenient for hexagonal crystals. The program' uses the Miller indexes (hkl) which can be confusing for hexagonal crystals while the modified program uses the Miller-Bravais indexes with four axes; e.g., the angles between the (110) planes, Fig. 1, are 0 and 90 deg but in the (hkil) system the angles between the (1150) planes are 0 and 60 deg. If a Laue photograph is taken of a crystal oriented with the prismatic planes nearly parallel to the film then the spots on the stereo graphic projection will be from high-index planes. The probable positions of the low-index planes, e.g., (0001) plane, can only be obtained from the intersection of zones and this is not accurate to 1 or 2 deg. The number of planes considered by the program (card 1)' has to be limited to the ones of low index or the program time is excessive but a solution will not be obtained if one of the spots has an index that is not being considered. To overcome this problem the program1 was modified so that if no fit was obtained at *1 deg (card 3) of the tabulated angles then ±2 or ±3 deg was tried. If still no solution was obtained either due to one of the angles not being measured correctly to ±3 deg or because one of the spots was from a high-index plane, then the last spot was discounted and a fit tried for the remaining spots at i1 deg, and so forth. The minimum number of spots that the program will try to fit is five. If the limit on any individual index is 4 (card 1) and (h + k + l + 1) is six then twenty-three planes are considered and there are over 1000 interplanar angles. Many pairs of planes have very similar interplanar angles and with the errors previously mentioned the program will often produce several alternative solutions to a group of spots particularly at ±2 or ±3 deg. However without the program the alternative solutions would probably not have been found. If a large number of spots are used the number of possible fits is reduced. In the example shown in Fig. 2, if only spots which are on the film are used (case 1) the program gives six possible solutions, Table I. However if points 7 and 8 are also used (case 2) the program gives only one fit which also agrees with a standard projection of the crystal. In addition to time-saving the program ensures that a correct solution is obtained since it is unlikely that all the alternatives would have been gound manually; the first would probably be assumed to be the correct solution. The program has been used for zirconium crystals but is equally suitable for other hexagonal materials.

Jan 1, 1969

By D. Kunstelj, M. Stubicar, A. Tonejc, A. Bonefacic

A. Bonefafcic, D. Kunsfeli, M. Stubicar, and A. Tonejc The present communication is concerned with the variation of the texture in aluminum wires with die angle and temperature, at constant speed of extrusion. Experiments were carried out concurrently on refined samples, with a stated purity of 99.997 pct pure A1 and commercial samples of 99.5 pct Al. Ingots of refined aluminum samples were machined to 30-mm-diam by 150-mm-long billets. These billets were transformed to 5-mm-diam wires by drawing. The final form, suitable for examination, was obtained by extrusion through conical-face dies with a 1-mm hole diam and extrusion ratio 5:l in diam. The initial form of the commercial aluminum samples was drawn wire 5 mm in diam. These samples showed a poorly defined texture with (111) as a major and (001) as a minor component. A similar defined texture appeared in the refined aluminum samples after drawing to 5 mm diam. Conical-face dies with different angles (defined by the axis and the generating line of the cone) were used in our experiments. The values of the angles were 27, 35, 45, 57, 63, and 90 deg. The extrusion container was fitted with a heating element and controller permitting temperatures up to 600°C to be maintained within i5"C. Extrusion was performed at 250°, 300°, 350°, 400°, and 500°C at constant speed (approximately 1 mm per sec) and constant die reduction. The extrusion product was a wire 1 mm in diam and approximately 20 cm long. In order to remove the surface layer with the "conical" texture and to reduce the absorption by the X-ray examination of the samples, the extruded wire was etched to 0.22 mm in diam. Experiments were performed in the middle sections of the 20-cm-long wires. In addition to the die of l-mm hole diam, dies with a 1.5-, 0.7-, 0.6-, 0.5-, and 0.4-mm hole diam and 63-deg die angle were constructed. In our experiments we did not find in these ranges any important difference concerning the texture of the extruded wires and we continued our work solely on the 1.0-mm die. The diffracted X-rays (Cu K radiation) were recorded photographically. Diffracted intensities were measured on the (111) reflection with a microphotometer. The relative amounts of texture components were determined from the areas under the diffracted maxima. We found the texture of extruded aluminum wires to be strongly influenced not only by the temperature of extrusion and the purity of the sample but also by the form of the die. It is generally admitted that cold-drawn aluminum wires have mainly a (111) texture with a small amount of (001) component, Table I of Ref. 1. In our experiments with wires extruded in conditions represented by Fig. 1, in some cases a single (001) texture was obtained. If these wires were drawn repeatedly at room temperature, X-ray measurements revealed a duplex (001)-(111) fiber texture. Further drawings increased the (111) and decreased the (001) texture component. In Fig. 1 the percentage of material oriented with (001) parallel to the extrusion direction is represented as a function of the temperature and the die angle (a), for commercial and refined aluminum samples, respectively. From these diagrams we may draw the following conclusions. The slope of the die (a) influenced more strongly the texture at the lower rather than the higher temperatures. Again, a stronger influence was found in the case of the commercial in comparison with refined aluminum samples. In the case of the commercial aluminum samples the amount of material with (001) texture increases with increasing wire temperature in an approximately linear manner. This effect is less pronounced in the pure aluminum samples, with the exception of the die with a = 45 deg. In this case the (001) texture decreases with increasing temperature, as shown in Fig. 1. Component (001) is more pronounced in higher-purity aluminum samples. Our experiments led to the conclusion that both (001) and (111) components are essentially stable in extruded aluminum wires. As we obtained a single (001) texture starting with a sample of drawn wire in which the (001) component was very weak, our experiments revealed that the (001) component is not a remnant of the initial texture; this is in disagreement with the findings of Vandermeer and McHargue.1 We gratefully acknowledge discussions with Professor M. Paic. 1 R. A. Vandermeer and C. J. McHargue: Trans. 7MS-AME, 1964, vol. 230, p. 667.

Jan 1, 1969

By C. P. Kempter

AS part of a continuing program of liquid metals research, the densities of liquid lead, tin, zinc, cadmium, and indium have been measured by a pycnometric method. The pycnometers are made of high-density graphite to the design illustrated in Fig. l(a). In pursuing this research program, emphasis has been placed on detailed experimental care. As a result, claims are made for densities accurate to within ± 0.05 pct over temperature ranges varying from about 100± to 200°C above the melting point. A paper reporting the densities of tin, lead, and Pn-Sn alloys has recently been published,' while papers dealing with

Jan 1, 1969

By A. F. Crowley, D. W. G. White

AS part of a continuing program of liquid metals research, the densities of liquid lead, tin, zinc, cadmium, and indium have been measured by a pycnometric method. The pycnometers are made of high-density graphite to the design illustrated in Fig. l(a). In pursuing this research program, emphasis has been placed on detailed experimental care. As a result, claims are made for densities accurate to within ± 0.05 pct over temperature ranges varying from about 100° to 200°C above the melting point. A paper reporting the densities of tin, lead, and Pn-Sn alloys has recently been published,' while papers dealing with

Jan 1, 1969

By T. O. Massalski, J. D. Ayers

A massive transformation, 0 —am, takes place in a number of copper-based systems where the ß phase field at high temperatures extends to compositions that are slightly less solute-rich than the limits of the a phase field that exists at lower temperatures. Consequently a solid-state transformation becomes possible that does not involve a change of composition. Within this narrow range of composition the massive am phase can be usually produced in two ways: by a fast quench from the ß phase through the a phase field, or by pulse heating into the a phase field of an undecomposed ß phase retained at room temperature by a prior quench. In the Cu-Ga system the occurrence of a massive am phase has been also observed in alloys whose composition falls outside the equilibrium a phase field1 but not in the Cu-Zn system.2 We have recently observed the occurrence of the ß — am transformation also in two silver-based systems, Ag-Zn and Ag-Cd. The a and 0 phase fields in these systems again slightly "overlap" in a narrow composition range. In the Ag-Zn system this range falls between 36.7 and 40.2 at. pct Zn, and in the Ag-Cd system between approximately 41 and 42.5 at. pct Cd. Alloys were prepared from high-purity materials and cast in quartz tubes under inert atmosphere. No significant change of composition occurred during casting. After homogenizing in the 0 phase field, small pieces of each alloy were reheated at the homogenizing temperatures for a few minutes and quenched into various media. There were examined metallographic-ally after removal of surface layers that may have suffered from contamination or from the loss of the solute element. In the Ag-Zn system extensive areas of the am phase (identified by selective etching, observation of the slip trace variants, and occurrence of twinning) were observed in a comparatively low-zinc alloy (37.8 at. pct Zn) for all quenching media employed: iced

Jan 1, 1969

By E. N. Pugh, J. V. Craig

WhILE it has been established that well-defined microhardness impressions can be produced in germanium by room-temperature indentation,1-3 the role of dislocations in the process is the subject of continuing discussion.4-7 Recently, Carroll and ~anaka'

Jan 1, 1969

By M. J. Pool, P. J. Spencer, J. R. Guadagno

THE present work was carried out as part of a general program to study the magnitude and concentration dependence of exothermic heats of solution of various metals in liquid tin. Thermodynamic data for the Te-Sn system are very limited, particularly for dilute alloys. Indeed, apart from the prior heat of solution determinations of Pool,1 the only other published values are those of McAteer and seltz2 who carried out electromotive force measurements on solid alloys of compositions from 75 to 95 at. pct Te at temperatures between 543° and 668° K, of Colin and Dro-wart3 who made mass-spectrometric studies of the vapor in equilibrium with solid SnTe, and of Robinson and Bever4 who determined the heat of formation of SnTe by solution calorimetry. The present work thus provides further thermodynamic information for this system, specifically in a temperature range where the solubility of tellurium is very limited. The liquid metal solution calorimeter used in this investigation has been described previously.' No further discussion of its design or operation will therefore be given here. For each series of measurements a tin bath consisting of approximately 70 g of 99.99 pct pure Sn was carefully weighed out and inserted in the calorimeter which was maintained at the desired temperature to within ± 1/4°c. Tellurium, of 99.999 pct purity, was supplied by Atomergic Chemetals Co., a division of Gallard-Schlesinger Chemical Manufacturing Corp. Approximately 0.0006 to 0.001 g-atom specimens of tellurium were used for each experimental run and these were added to the calorimeter from a temperature of 273" K. Heat of solution values were calculated by analysis of a strip-chart recorder plot of the heat effect accompanying the solution of each sample in the tin bath. The heat capacity of the latter was determined at regular intervals during a series of tellurium drops by using pure tin or tungsten calibration samples, the heat contents of which were obtained from the standard compilation of Hultgren et al5 The composition of the bath was calculated after each drop from a knowledge of the weights of tin and tellurium added. Values of the heat of solution of tellurium at 725" and 775° K are listed in Table I together with the corresponding tellurium contents of the alloys. The data are also plotted as a function of tellurium concentration in Fig. 1, which includes the equivalent data obtained by pool' at 750° K. It can be seen that the heat of solution remains

Jan 1, 1969

By R. C. Dorward

DIFFUSION considerations are necessary to describe many technologically important metallurgical and physical processes. Since most commercially important alloys are comprised of more than two components, diffusion calculations applicable to binary systems are often unjustified. However, in many instances the more general equations valid for three-component systems may be employed. The phenom-enological description of ternary diffusion is now well-established,1-4 and the theory has been applied with some success to a few practical situations.5"7 The flux equations for the solutes (components 1 and 2) of a ternary solution may be expressed by:

Jan 1, 1969

By Hsun Hu, R. S. Cline

In an earlier publication1 it was shown that a single crystal of Cu-4 wt pct Al cold-rolled in the (110)[112] orientation was stable up to 95 pct reduction, although the orientation spread was considerable larger than in a similarly oriented and cold-rolled copper single crystal. When rolled to 99 pct reduction, the copper crystal retained its initial orientation and a high degree of sharpness of texture, whereas the Cu-4 pct

Jan 1, 1969

By D. F. DeSante, A. S. Tetelman

MICROCRACKS are often introduced into commercial metals during fabrication processes such as swaging, cold rolling, deep drawing, and welding. These microcracks act as strain concentrators and may be capable of causing premature catastrophic failure of a component or weld. The present investigation was undertaken to determine whether high-temperature annealing treatments may be capable of reducing or negating the detrimental effects of such existing microcracks. Internal microcracks, ranging from 0.1 to 0.85 mm in length and averaging 0.23 mm, were introduced into polycrystalline Fe-3 pct Si tensile specimens (0.155 mm grain size) by the cathodic charging of hydrogen.1'2 The typical appearance of such microcracks and their associated strain patterns (made visible by the technique of dislocation etch pitting3) is shown in Fig. 1. The stress fields of the dislocation loops formed during plastic relaxation stabilize the microcracks so that, when the internal hydrogen pressure is removed: the microcracks stay open, rather than disappear as perfectly elastic cracks would be expected to do.' As shown in Fig. 2, such stopped microcracks cause a 36 pct decrease in the macroscopic cleavage fracture strength at -196°C.

Jan 1, 1969

By H. C. Fiedler

X HE development of the cube-on edge secondary re-crystallization texture in Si-Fe strip requires that normal grain growth be restrained. It has been shown that the degree of restraint and hence the completeness of secondary recrystallization depends upon the size and number of second-phase particles, which in turn is dependent upon the prior processing history.1y2 The purpose of this note is to show that, for heats in which manganese sulfide particles are providing the restraint to grain growth, the choice of hot rolling temperature depends upon the manganese content. The making and processing of the heats to the final gage of 0.012 in. has been described.3 The compositions are given in Table I. Apparent in Fig. 1 is the decrease in the ability of strips hot-rolled from 1175°C to undergo secondary recrystallization as the manganese content increases. It has been shown that 1175°C is below the solubility temperature of 0.014 pet S in even the 0.038 pct Mn alloy: and the observed behavior is attributed to an increasing fraction of the sulfur forming large manganese sulfide particles at the heating temperature for hot rolling. This fraction of the sulfur is thus unavailable to subsequently form the small, uniformly dispersed particles which are needed to restrain normal grain growth. Since the sulfur is completely in solution at 1325°C,3 strips from all three alloys show strong secondary recrystallization behavior when hot-rolled from that temperature.

Jan 1, 1969

By J. Campbell

Long freezing range casting alloys are particularly susceptible to a type of porosity which is observed to form in layers parallel to the supposed position of the isotherms in the solidifying casting. Under favorable conditions (which appear to be typified by low-temperature gradients in the casting giving rise to a wide and more or less uniform pasty zone, and which arise from several factors, particularly: a) wide freezing range alloy, b) high thermal conductivity of metal, c) low thermal conductivity of mold, and d) high mold temperature3) layer porosity has been observed in many different casting alloys: copper,' aluminum, magnesium,' steels, and high-temperature alloys.3 Baker4,5 and later cibula6 argue that layer porosity occurs because of thermal contraction, in a manner analogous to hot tearing. In outline, the theory consists of the establishment of a coherent dendrite network by the impinging of dendrite tips. Subsequent shrinkage imposes tensile stresses on the network which tears perpendicularly to the stress, i.e., parallel to the isotherms. If these tears are not filled by the inflow of residual liquid then layers of porosity result. Baker7 attempted to test whether the porosity was the result of thermal contraction by casting test pieces in a mold designed to accentuate hot tearing. However, no significant increase in porosity was observed. This negative result of Baker's critical experiment appears to be substantiated by numerous observations, particularly the experiments by Lagowski and Meier8 on Mg-Zn alloys covering the range of zinc contents up to 30 pct Zn. These clearly reveal that the maxima for the incidence of hot tearing and layer porosity are well-separated, occurring at 1 and 6 pct Zn, respectively. Furthermore, the thermal contraction maximum occurred at 1 pct Zn, indicating that hot tearing is associated with contraction in the solid state, and not with porosity. These observations are further substantiated by the elementary consideration that the thermal contraction of the casting is likely to produce (if anything, since the temperature difference across casting of high thermal conductivity, such as aluminum and copper, is likely to be negligible) a compressive stress on the

Jan 1, 1969

By N. A. D. Parlee, M. T. Utine

ThE kinetics of absorption of oxygen by induction-stirred liquid silver (at constant Po2 and T) has received some study here.''2 This paper describes a study of the kinetics of effusion (non-bubble-forming), and some additional work on absorption. A Sieverts type of apparatus was used. The kind of reaction tube assembly has been described.4 The same 25-kw, 450-kc induction unit was used as in earlier absorption work1'2 but the "coupling" was different. The runs were made under the following conditions: i) saturation at 1 atm, effusion at 0.81 atm;

Jan 1, 1969

By N. Standish

By contrast with viscometry and sedimentation, no actual measurements of the applicability of Stokes' law to steelmaking have ever been reported; instead, the proof for and against Stokes' law has been inferred from the frequently observed phenomenon that inclusions collect in the top scum and the bottom of ingots. As such proof is unsatisfactory, continued reference to Stokes' law in steelmaking, even as a model for calculating the terminal velocities of rising inclusions, should be avoided. In fact, all conclusions that have been reached regarding size, density, and viscosity on the flotation of inclusions could be made more rationally without Stokes' law. A worthwhile exception is that of Mitsche1 who in 1934 used Stokes' law to show not only the expected effects of size, density, and viscosity on flotation but also the beneficial effects of i) melting under a slag layer (now Electro Slag Refining); ii) treating melts with synthetic slags (Ref. 2 gives recent applications); iii) bubbling an inert gas through the melt (recent applications in Refs. 3 and 4); and iv) altering the solid/ liquid interface characteristics. At this point, it should again be emphasized that the boundary conditions for which Stokes' law was derived place enormous restrictions on the law but its application, as noted earlier, can yield useful results in some fields under certain conditions and within well-defined limits. When compared with inclusions, which may be solid or liquid, spherical or irregular, dispersed or coagulated, interacting between themselves and the melt, floating in a liquid which is in a state of motion of varying intensity5 and contained in vessels of various shapes and sizes that may change with time as in a solidifying ingot, the conclusion is obvious-Stokes'

Jan 1, 1969

By A. Mitchell, M. Etienne

VARIOUS'-3 reports on the electroslag remelting process refer to the "thin skin of slag" existing around the slag pool and the solidifying ingot, but none considers the various mechanisms by which this layer forms and thus influences the surface quality of the ingot. A vertical section4,5 of the Cao-CaF2-Al2O3 diagram is shown in Fig. 1 between CaF2 and 6Al2.CaO3 From this, it is seen that a typical "70:30" CaF2:A1a3 slag will solidify to produce 6Al2O3.CaO primary phase in a eutectic matrix. The commercial slags contain sufficient CaO to produce* this composition by both the

Jan 1, 1969

By R. W. Smith, G. W. Delamore, J. A. Spittle

RECENT work by the authors1 has demonstrated that the crystals constituting the equiaxed zone in small ingots originate, on quenching, in the chilled liquid. Whether any partial remelting2 takes place of the den-drites nucleated in the chilled region was not examined. However, the claim3 that this normally occurs, leading to crystal multiplication, has been disputed.4 Thus, for an equiaxed zone to form in the central region of an otherwise columnar ingot, it is necessary to transport crystallites from the chill zone to this region. In view of the work of Uhlmann et al.,5 it was considered desirable to examine the transport process further. Experimental Technique and Results. In the earlier experiments by the authors.1 a stainless-steel crucible 17/8 in. diam, 41/2 in. high, ad containing an alloy of A1-4 wt pct Cu, was quenched from 660°C into a bath of Wood's metal maintained at 100°C. Under these conditions a central zone of equiaxed crystals was obtained. However, if a 2250-G unidirectional magnetic field was applied for 2 sec immediately following the instant of quenching, or subsequently, the equiaxed zone did not appear. Careful thermal analysis showed that the short application of the field had virtually no effect on the thermal conditions of the melt. It thus appeared that the crystallites which were ultimately to grow large enough to form the equiaxed zone existed in the liquid immediately ahead of the interface, occlusion being prevented by the convective fluid flow induced by freezing from the walls of the cylinder. When this relative movement was prevented by the Lorenz forces induced by the application of the magnetic field, the crystallites were caught up in the rapidly advancing dendrite solid-liquid interface. To test this assumption, a small ingot of super-purity aluminum was partially melted and poured into a heated stainless-steel mold which was then immediately quenched into molten Wood's alloy. The resulting structure is shown in Fig. 1, and consists of columnar grains with a central fine-grained zone. Thus the unmelted solid present at the beginning of solidification had been transported ahead of the columnar interface. Discussion. There appears to be little or no information available on the interaction of suspended particles with a metallic solid/liquid interface. However, some information is available for transparent organic sys-

Jan 1, 1969

By J. C. M. Li

A dislocation model is constructed for a cylindrical tilt boundary of which the axis of tilt is parallel to the axis of the cylinder. The strain energy per unit area calculated from this model agrees with thut of an infinite vertical wall of edge dislocations. Based on this model, a dislocation mechanism for the shrinking of such a cylindrical boundary is proposed. The power relation between the grain boundary velocity and the driving force is accounted fm by the stress dependence of dislocation velocity. The activation area for grain boundary motion is found to correlate with that .for Creep in aluminum. In the preceding paper' the velocity of a curved grain boundary is found to be a power function of the driving force, [1] where M is the velocity at unit driving force, y is the grain boundary energy, and p is the radius of curvature. This finding adds another nonlinear rate equation to metallurgical phenomena. While a macroscopic theory for the steady state as just presented2 can be used to understand the shape of the moving boundary, such theory usually does not provide any information about the atomistics of the process. It is attempted in this paper to discuss the nonlinear rate equation in terms of a dislocation mechanism. A DISLOCATION MODEL FOR A CYLINDRICAL TILT BOUNDARY Before a dislocation mechanism can be proposed for the motion of a cylindrical tilt boundary, it is necessary to construct a dislocation model for the boundary. For simplicity, a tilt boundary in a simple cubic lattice will be examined. Although this does not represent the situation in aluminum, it is expected that the general features will be similar. The details of the model in the fcc lattice can be constructed when a refinement of the simple model is called for. A cylindrical low angle tilt boundary in a simple cubic lattice is shown in Fig. 1. Two sets of edge dislocations are needed as shown. A schematic representation is shown in Fig. 2(a). In terms of a continuous distribution of dislocations, the density of dislocations n, of Burgers vector b, in the small segment ds of the grain boundary is Similarly the density of dislocations n, of Burgers vector bz in the same segment ds is where is the tilt angle of the grain boundary. Based on this continuous distribution of dislocations in the grain boundary, it can be shown that the interaction between a small segment of the boundary and the rest of it is zero. Furthermore, the stress produced at any point inside or outside the cylinder is also zero. This shows that the model is acceptable in the sense that the boundary has no long-range stresses. Since the model of continuous distribution of dislocations in the grain boundary does not reveal the interactions among individual dislocations, a discrete dislocation model has to be used for such purpose. For simplicity, an equivalent model is shown in Fig. 3. This arises because the total Burgers vector is, from

Jan 1, 1970