Microsegregation and crystal perfection in metals

656

Journal of Crystal Growth 3, 4 (1968) 656—662 © North-Holland Publishing Co., Amsterdam

MICROSEGREGATION AND CRYSTAL PERFECTION IN METALS M. D. HUNT Foseco International Ltd., Birmingham, England and I. A. SPITFLE and R. W. SMITH Department ofPhysical Metallurgy and Science of Materials, University of Birmingham, Birmingham, England

The generation of low angle boundaries in melt-grown crystals is examined and it is concluded that these boundaries principally arise following the rearrangement of dislocations resulting from constitutional and thermal stresses. Homogenisation of cellular segregation takes place readily in

systems with solutes having a segregation coefficient, k < I but with difficulty when k > I. This results in the generation of a coarse array of large misorientation subboundaries in the former case and the converse for the latter.

1. Introduction

However, a surface

Elbaum’) has listed five mechanisms by which dislocations can be introduced into a crystal during growth: (1) propagation of dislocations into the growing crystal from the seed crystal; (2) thermal stresses; (3) constitutional stresses; (4) dendritic growth and (5) vacancy supersaturation. Once introduced, their number may be augmented by multiplication under the action of mechanical stresses or reduced by annihilation. In particular, mechanisms (2), (3) and (5) have been examined in this laboratory. 2. Collapsed vacancy discs The contribution of mechanism (5) to lineage structures2) has been estimated by Frank3), using thermal equilibrium values in order to derive the concentration of excess vacancies generated as a crystal cools from the melt. These vacancies are supposed to coalesce and collapse to form dislocation loops. The loops “climbup” the temperature gradient and finally intersect the interface to give a pair of edge dislocations which then separate by climb. A further loop subsequently nucleates in the “tensile” region between them. Thus the total dislocation content is set by the balance between dislocation generation and annihilation. More recently, Schoeck and Tiller4) have shown that the vacancy excess normally obtainable is insufficient to nucleate vacancy discs and, should dislocation loops be present, they would be unable to reach the interface. Thus they totally reject Frank’s proposed mechanism.

the so-called

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“vacancy pitting”, and the results ofcertain Mössbauer absorption experiments8), suggested that an anomalously high vacancy concentration exists in a metal at, or near, its melting point. In view of this suggestion, measurements of self-diffusion in tin were carried out 9) to within 0.05 °Cof its melting point but no effects attributable to the presence of an anomalously high vacancy concentration were observed. Thereupon, the Mössbauer experiments were repeated1 0) and the earher anomalous results were shown to be due to partial melting brought about by impurities. It is thus apparent that lineage structures cannot be generated by vacancy condensation in the bulk of a crystal, although it has been suggested 7) that vacancy interaction with a screw dislocation which intersects the solid—liquid interface could lead to extensive dislocation multiplication. 3. Constitution stresses When solute segregates during crystal growth, lattice misfit usually leads to the incorporation of strain accommodating dislocations”2). Subsequent solute dispersal, as the result of diffusion processes occurling behind the interface as crystal growth proceeds, liberates these dislocations which then migrate and form low angle crystal boundaries, or suffer annihila~j~fl~2_l

5).

In order to examine further the effect of the homogenisation of cellular segregation on crystal perfection, crystals have been grown’ 6) in horizontal graphite

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657

MICROSEGREGATION AND CRYSTAL PERFECTION IN METALS

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fact, traces of substructure were Often observed in the as-grown crystals. Cellular segregation was examined by chemically etching the electropolished sections of crystals cut with an acid saw’ 7) and by electron-probe analysis. Low angle boundaries were also examined by chemical etching, together with a modified Schulz X-ray technique. For crystals containing k < 1 type solute, and grown in a horizontal graphite boat, considerable homogenisation was observed to have taken place only a short distance from a decanted solid/liquid interface, asshown earlier’3” 5). For instance, 2 mm behind the interface of a 0.1 at % Pb in Sn alloy, the cellular pattern had completely disappeared (fig. 1), the lead appearing at cell nodes and also outlining “super-cell” boundaries. At 1 cm behind the interface, only discrete Pb-rich globules could be observed. As the Pb-content was increased so the progressive structural breakdown was pushed further behind the interface. However, for Pbcontents in excess of approx. at%, “wavy” plates of the lead-rich phase outlined 0.6 “super-cell” boundaries

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(fig. 2). It is considered that these super-cells form by dislocation rearrangement in the solid to form low

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Fig. 1. 0.1 at 00 Pb in Sn, growth rateR — 0.0014cm/sec. GL = 15 °C/cm;0.2 cm behind interface, transverse view x 140. The Pb is segregated at cell nodes and along “super-cell” (striation) boundaries.

boats and by “pulling” from a stirred melt, using conventional techniques and an argon atmosphere. Tin and zinc have been used as solvents and, to these, small additions of solutes (Pb in Sn, Cd in Zn) having segregation coefficients, k, < 1, and solutes (Sb in Sn, Cu in Zn) having k> 1, were made. The solvent metals were zone-refined to at least a purity of 99.9999 % and the solute additions were spectrographically pure. Usual inert gas melting practices were followed to produce master alloys which were subsequently diluted. Since horizontal growth is characterised by smallternperaturegradients inboth liquid(GL) and solid (G 5), typically 10°C/cmconsiderable homogenisation had usually taken place by the time growth was terminated and thus well-developed substructures were usually observed. In contrast, crystals pulled from stirred melts normally experience large temperature gradients which, with the use of a liquid nitrogen “after-cooler”, may exceed 100 C/cm. Thus little solute dispersal would be expected to occur in vertically-grown crystals but, ~ C

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Fig. 2. 0.7 at 0 Pb in Sn grown as fig. 1. 0.6 cm behind interface, transverse view x 140. Wavy Pb plates in “super-cell” walls.

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658

M. D. HUNT, J. A. SPITTLE AND R. W. SMITH

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0.5 at % Sb in Sn, R = 0.0025 cm/sec, GL = 8 °Cfcm; the decanted solid—liquid interface x 140.

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Fig. 4. As fig. 3; several microns behind the interface, transverse x 140. Lowangle boundary appears independent ofcell walls.

Fig. 6. 0.1 at % Cd in Zn, R = 0.002 cm/sec. GL = 12 °C/cm; oblique section, Schulz X-ray micrograph showing striation boundaries x 5.

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MICROSEGREGATION AND CRYSTAL PERFECTION IN METALS

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fore being examined using the Schulz technique’8), fig. 6. Only coarse striation boundaries were observed and these had rnisorientations varying from 6’ to 1.5°. The cellular pattern persisted strongly in the Cu in Zn alloys (k > 1), as shown in fig. 7. A Schulz examination, fig. 8, showed a fine striation substructure to be present, misorientations being 1’ to 20’, i.e. markedly different from the k < 1 situation.

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Fig. 7. 0.15 at % Cu in Zn grown as fig. 6. 1.4 cm behind the interface transverse view x 140. Well defined cellular pattern.

angle walls which eventually gain intersection with the interface at cellular troughs. The wavy plates result from the freezing as a divorced eutectic of the heavilyenriched liquid in the very deep and narrow interface troughs. It is apparent from figs. 1 and 2 that the striation substructure becomes finer with increasing solute concentration. The Sb in Sn alloys, i.e. a k > 1 type system, when grown horizontally, exhibited remarkably different homogenisation characteristics to those of the k < 1 type solute systems. This is clearly demonstrated in figs. 3, 4 and 5 for a 0.5 at% Sb in Sn alloy. It is noted that little segregation apparently takes place during growth and that striation boundaries do not “follow” cellular boundaries. The cell boundaries were shown to be virtually free from solute, using the electron-probe. Changes in the cellular pattern similar to the Pb in Sn alloys were observed in horizontally grown Cd in Zn alloys. Since striation boundaries could not be clearly rendered visible by chemical etching, in these alloys, crystals were sectioned 1 cm. from the interface, acidplaned and finally polished with Gilman’s reagent be-

Czochralski-grown crystals. However, as before, the As expected little homogenisation occured in the the k < 1 type systems but not where k> 1. In the striation boundaries coincided with cell boundaries for case of a 0.1 at °,/~Pb in Sn alloy, the cell structure was still well defined 5 cm behind the interface. Crystals of Sb in Sn, grown by the Czochralski technique, showed a number of unique features. Representative of these are figs. 9—11. The first of these micrographs shows that a crystal array, centred on the cell nodes (fig. 9), lies beneath the decanting film. However this array soon breaks up, first to a series of parallel linear boundaries and then, fig. 10 changing to a more “chunky” structure, presumably due to easy dislocationrearrangement inthe relatively solute-free cell walls.

Fig. 8.

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As fig. 10; oblique section Schulz X-ray micrograph x 4.

660

M. D. HUNT, J. A. SPITTLE AND R. W. SMITH

hand, the pulled-crystal (R

0.015 cm/sec, G5 > 80 °C/cm), was composed of an array of low angle subboundaries, the misorientations varying from 3.5’ to 3°. It is thus apparent that thermal stresses can play a significant part in dislocation generation, probably by multiplication.

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5. Conclusions

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It is clear that marked solute homogenisation would be expected to takethe place in horizontally-grown 2) and hence observed behaviour of k crys< I tals’ systems takes place. However, the homogenisation results for the k > 1 type solutes do not appear to fit these expectations. Therefore, in an attempt to explain these apparent anomalies, the diffusion coefficient for Sb in Sn was measured for a small range oftemperature near the melting point of tin. It was found to be an order of magnitude less than for Pb in Sn (ref. 20).

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It would thus appear that the coarse striation boundary array in the case of k < 1 type solutes, relative to the fine one for k > 1 type solutes, stems mainly from the ease with which solute diffuses and which allows

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Fig. 9. 0.2 at ?. in Sb in Sn, Czochralski-grown, R = 0.008 cm/see, G 5 = 80 °C/cm, electropolished and etched, decanted interface x 140. Dislocation sub-boundaries are seen to outline the cells.

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Only 0.2 cm behind the interface the crystal substruc ture has vanished. The origin of the “dribblings” or

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cellular segregation in fig. 11 is puzzling. Similar rnicr~ graphs were obtained over the whole length of the crystal. These dribblings may be analogous to the solute trails observed in Czochralski-grown doped-germanium crystals and ascribable to temperature gradient-zone melting’~).stresses

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In order to be able to compare the results obtained from the horizontally-grown crystals with those pulled vertically from a stirred melt, crystals of zone-refined zinc were grown by each method, and then examined using the Schulz technique. For the horizontally-grown crystal, fig. 12 (R = 1 x iO~cm/sec, GL <•9 °C/cm) no evidence of a striation array was obtained. (A strong sub-boundary of 19’ misorientation is present in fig. 13.) On the other XV

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As fig. 9; 0.1 cm behind interface, transverse view >< 140. Some crystal structure still visible.

661

MICROSEGREGATION AND CRYSTAL PERFECTION IN METALS TABLE

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Dislocation content of horizontally-grown dilute zinc crystals

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of the Cdin Zn alloys. The fact that striation size decreases with increase in solute concentration is cornpatible with increased dislocation locking23) at high solute concentration and therefore reduced migration distances.

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As for fig. 9; 0.2cm behind interface, transverse view x 140. “Dribblings” moving into most cells.

easier dislocation rearrangement. However, it should be noted that the severity of segregation in the case of k > 1 type solute is set by the initial alloy concentration (i.e. the composition range to the pure component) and so is usually small, whereas in the case of k < 1, liquid of eutectic composition is easily generated. Thus cell grooves would be expected to be shallow in the case of the former and deep for k < 1 as observed by Weinberg2 1). This presumably accounts for the greater ease with which large-angle striation boundaries migrate from cell walls on decanted interfaces for k > 1 type systems22). Although the striation boundaries are finer for k> 1 type systems than for k < 1, the dislocation content of the latter crystals is usually greater. This is shown in table 1, the data being derived from the Schulz micrographs. Although there is a larger atomic size-factor in the case of Cd in Zn (+l2%) than Cu in Zn (—4%), it is considered that the higher overall dislocation density results principally from the increased segregation XV

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Fig. 12. Zone-refined zinc, horizontally-grown, R = I x lO~ cm/see, GL < 9 C/cm, oblique section, Schulz X-ray micrograph < 3.5.

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662

M. D. HUNT, J. A. SPITTLE AND R. W. SMITH

stitutional stresses, and, whilst excess thermal vacancies may influence this rearrangement2 6) they play little part in dislocation generation. References 1) C. Elbaum, Progr. Metal Phys. 8 (1959) 203. 2) E. Teghtsoonian and B. Chalmers, Can. J. Phys. 29 (1951) 270. 3) F. C. Frank, Deformation and Flowof Solids, in: I. U. T.A.M. Colloquium, Madrid, 1956. 4) G. Schoeck and W. A. Tiller, Phil. Mag. 5 (1960) 43. 5) P. E. Doherty and R. S. Davis, Acta Met. 7 (1959) 118. 6) P. E. Doherty and R. S. Davis, Trans. AIME 221 (1961) 737. 7) P. E. Doherty and B. Chalmers, Trans. AIME 224 (1962) 1124. 8) A. J. F. Boyle, D. St. P. Bunbury, C. Edwards and H. E. Hall, Proc. Phys. Soc. (London) 77 (1961) 129. 9) R. H. Packwood, Ph. D. Thesis, Birmingham University, 1964. 10) G. L. Longworth and R. H. Packwood, Phys. Letters 14 (1965) 75. 11) A. J. Goss, K. R. Benson and W. G. Pfann, Acta Met. 4 (1956) 333. 12) W. A. Tiller, J. Appi. Phys. 29 (1958) 611. 13) V. V. Damiano and G. S. Tint, Acta Met. 9 (1961) 177. 14) P. Kratochvil and H. Sichova, Acta Met. 10 (1962) 682. 15) H. Biloni and G. F. Bolling, Trans. AIME 227 (1963) 1351. 16) M. D. Hunt, Ph. D. Thesis, Birmingham University, 1965. 17) M. D. Hunt, J. A. Spittle and R. W. Smith, J. Sci. Instr. 44 (1967) 230. 18) L. G. Schulz, J. Metals 6 (1954) 1082. 19) W. Bardsley, J. M. Callan, H. A. Chedzey and D. T. J. Hurle, Solid-State Electron. 5 (1962) 395. 20) R. D. Packwood and R. W. Smith, to be published.

Fig. 13. Zone-refined zinc, Czochralski-grown, R = 0.015 cm/ see, G~> 80 °C/cm, oblique section, Schulz X-ray micrograph

that thermal stresses can significantly influence the dislocation contents of carefully-grown metal “single” crystals. Such stresses usually arise during Czochralski-

21) F. Weinberg, in: Crystal Growth, Ed. H. S. Peiser (Pergamon, Oxford, 1967) p. 639. 22) M. D. Hunt and R. W. Smith, Can. I. Phys. 40 (1962) 1245. 23) R. F. Sekerka, G. F. Bolling and W. A. Tiller, Can. J. Phys.

growth2 5) but can be avoided by the careful selection of an “after-heater”. In summary, it may be stated that crystal substructures in melt-grown crystals arise from the rearrangement of disiccations introduced by thermal and/or con-

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38 (1960) 883. 24) W. A. Tiller, Acta Met. 10 (1962) 682. 25) K. G. Davis and P. Fryzuk, Acta Met. 12 (1964) 950. 26) K. R. Evans and W. F. Flanagan, Phil. Mag. 14 (1966) 1131.

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