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Grain refinement of TiAl-based alloys: The role of TiB2 crystallography and growth
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Acta Materialia 58 (2010) 6744–6751 www.elsevier.com/locate/actamat
Grain refinement of TiAl-based alloys: The role of TiB2 crystallography and growth D. Gosslar a,⇑, R. Gu¨nther a, U. Hecht b, C. Hartig a, R. Bormann a a
Hamburg University of Technology, Institute of Material Science and Technology, Eissendorfer Strasse 42, 21073 Hamburg, Germany b ACCESS Materials and Processes, RWTH-Aachen, Access e.V., Intzestrasse 5, 52072 Aachen, Germany Received 9 August 2010; received in revised form 31 August 2010; accepted 31 August 2010 Available online 25 September 2010
Abstract A crystallographic model is used to predict the nucleation potencies of TiB2 particles during solidification of TiAl-based alloys. Two nucleation scenarios are investigated. In scenario 1, primary TiB2 grows in the melt before formation of the body-centred cubic b phase. In scenario 2, secondary TiB2 precipitates after the first b phase but before formation of the hexagonal close-packed a phase. The model predicts high a and b nucleation potencies of TiB2 in both scenarios. However, pre-existing b grains in scenario 2 are predicted to be preferred a nucleation sites. The experimentally observed b refinement by primary TiB2 agrees with the model predictions. Grain refinement in scenario 2 is attributed to a nucleation on b, which is interleaved with secondary TiB2. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium aluminides; Casting; Grain refining; Edge-to-edge matching; Crystal growth
1. Introduction TiAl-based alloys are an attractive material class if a combination of low weight and high-temperature properties is desired [1]. Casting of these alloys is an important production route for automobile and aircraft parts [2]. A certain amount of boron is required in order to obtain a homogeneous and refined as-cast microstructure [3]. However, the exact grain refinement mechanism is not clear due to the complex solidification sequence. The thermodynamic description of the system Ti–Al–B [4] enables a new investigation of this grain refinement mechanism in terms of alloy composition and phase formation. It has been shown that in case of low-boron content, nucleation of the hexagonal close-packed (hcp) a phase on borides appears to be the grain refinement mechanism [5]. At high boron contents borides are stable in the melt and may also serve as nucleation sites for the primary body⇑ Corresponding author. Tel.: +49 40 42878 3145; fax: +49 40 42878 4070. E-mail address: [email protected] (D. Gosslar).
centred cubic (bcc) b phase. This raises the issue of heterogeneous b nucleation on borides. The magnitude of the a and b nucleation potencies of borides should therefore be a key aspect of the grain refinement mechanism. The aim of this paper is to apply the crystallographic model of Kelly and Zhang [6,7] to predict the nucleation potency of TiB2 for different nucleation scenarios, which occur during solidification of TiAl-based alloys. The model predictions are compared to experimental results in terms of grain refinement and TiB2 morphologies. 2. Experimental Two TiAl-based alloys of composition Ti–45Al– 0.5B at.% (4505B) and Ti–45Al–2B at.% (452B) were cast centrifugally into 16 mm diameter Y2O3 moulds. The casting temperature was approximately 1505 °C (30 °C superheat). 1.5 at.% B of the alloy 452B is achieved by inoculation via a novel Ti–Al–TiB2 master alloy. Details regarding this are described in Ref. [8]. Thermodynamic calculations predict the following transformation pathways [4]:
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.08.040
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1. L ? L + b ? L + b + TiB2 ? a + TiB2 (alloy 4505B) 2. L ? L + TiB2 ? L + TiB2 + b ? a + TiB2 (alloy 452B)
ically in a Ti–Al–B melt [15], the habit plane prediction is omitted.
In pathway (1), TiB2 precipitates after the first b phase at 1485 °C but before the peritectic formation of the a phase starts at 1472 °C. In pathway (2), TiB2 precipitates primarily in the melt at 1550 °C. The as-cast microstructure was investigated by optical metallography and by scanning electron microscopy (SEM). The staining technique described in Ref. [9] was applied to highlight TiB2 particles in the microstructures. Deep etching of the microstructures by a Kroll solution (25 ml H2O, 3 ml HNO3, 2 ml HF) for 2 min was used to reveal the TiB2 morphologies. The size of lamellar a2(Ti3Al)/c(TiAl) colonies was determined by the average line interception method.
3.1. a Nucleation on TiB2 and on b grains
3. The edge-to-edge matching model The edge-to-edge matching model has been developed by Kelly and Zhang [6,7]. This model predicts from first principles the orientation relationship (OR) between two phases. The underlying physical principle is minimization of the interfacial energy which governs formation of an OR. This is achieved by matching of close or relatively close-packed atom rows at the interface. These atom rows have to be contained in close-packed or relatively closepacked planes in order to maximize the atom row matching. Close-packed or relatively close-packed atom rows become matching rows if the interatomic misfit is below 10%. Close-packed or relatively close-packed planes become matching planes if the interplanar mismatch (d-value mismatch) is below 6%. In case of heterogeneous nucleation in the melt, a maximum d-value mismatch of 10% is also accepted [10]. Atom row matching is, however, more important than plane matching. Correspondingly, the interatomic misfit is more important than the d-value mismatch. An OR with a smaller interatomic misfit is therefore preferred over one with a larger interatomic misfit. In addition, the arrangement of atoms within one row is considered by the model. The general rule is that matching between straight atom rows is favoured over matching between zigzag atom rows. Application of the edge-to-edge model predicts successfully the nucleation potency and thereby the grain refinement potential of several ceramic inoculants in Mg and Al alloys [11–13]. Hereby, the nucleation potency is evaluated by the size of the interatomic misfit and d-value mismatch of the predicted OR. In this paper the edge-to-edge model is used to predict the potency of a and b nucleation on TiB2 in accordance to the transformation pathways described in Section 2. In particular, the a nucleation potency of TiB2 is compared to the one of pre-existing b grains. The edge-to-edge model is also capable of predicting the exact habit plane of an OR in absence of growth anisotropies [14]. Since TiB2 does grow highly anisotrop-
The a phase has a simple hcp structure. a forms during the peritectic reaction L + b ? a + TiB2 at the end of solidification of, for example, Ti–45Al at.% alloys with boron contents larger than 0.5 at.% [16]. The peritectic temperature is 1472 °C. The b phase has a simple bcc structure. TiB2 has a hexagonal C32 structure [17]. According to the peritectic reaction, both b grains and TiB2 particles offer possible a nucleation sites. The edge-to-edge model is applied to determine a nucleation potencies of both sites. The close-packed or relatively close-packed directions and planes of a and b have been identified in Ref. [18] and of TiB2 in Ref. [11]. At the beginning of the peritectic reaction the a and b compositions are Ti–46Al–0.02B at.% and Ti–44Al– 0.15B at.%, respectively. High Al solute contents in both phases change the lattice parameters, whereas the influence by the small boron contents is neglected. In this case the lattice parameters of a can be calculated directly by Vegard’s law [19]. In contrast, the lattice parameter of b cannot be determined directly for high Al concentrations, because it decomposes into a upon cooling. The atomic volume remains nearly constant during this transformation. Therefore, the lattice parameter of b can be calculated indirectly from the a lattice parameters [20]. Thermal expansion of a, b and TiB2 are calculated by thermal expansion coefficients published in Refs. [21–23], respectively. Thus, the calculated lattice parameters for the peritectic reaction at 1472 °C are: a = 0.288 nm and c = 0.462 nm for a, a = 0.325 nm for b and a = 0.307 nm and c = 0.328 nm for TiB2. In addition, the lattice parameters are calculated for the Al concentration range 0– 50 at.%. The resulting variation of interatomic misfit and d-value mismatch of a/TiB2 direction and plane pairs is shown in Figs. 1 and 2. Fig. 1 shows that the interatomic misfit of the direction pair h1 1 2 0ia=h0001iTiB2 is in excess of 10%. It is unlikely to become a matching direction pair if 10% is considered as the maximum misfit. The two plane pairs f1 1 0 1ga=f1 1 0 1gTiB2 and f1 1 0 0ga=f1 1 0 0gTiB2 in Fig. 2 are possible matching plane pairs if the same 10% criterion is applied to the d-value mismatch. The plane pair f0 0 0 2ga=f1 1 0 0gTiB2 barely fulfils this 10% criterion at higher Al concentrations. The matching direction pairs h1 1 0 0ia=h1 1 0 0iTiB2 and h1 1 2 3ia=h1 0 1 0iTiB2 are not contained in the matching plane pairs of Fig. 2. Therefore, they are excluded from formation of reproducible ORs. Only the matching direction pair h1 1 2 0ia=h1 1 2 0iTiB2 remains, which leads to the following ORs: OR1-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð1 1 0 1Þa=ð1 1 0 1ÞTiB2 : 5.9%
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Fig. 1. Interatomic spacing misfit of a/TiB2 direction pairs as a function of Al concentration.
Fig. 3. Interatomic spacing misfit of a/b direction pairs as a function of Al concentration.
Fig. 2. d-value mismatch of a/TiB2 plane pairs as a function of Al concentration.
Fig. 4. d-value mismatch of a/b plane pairs as a function of Al concentration.
OR2-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð1 1 0 0Þa=ð1 1 0 0ÞTiB2 : 6.6% OR3-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð0 0 0 2Þa=ð1 1 0 0ÞTiB2 : 10.6% The interatomic misfits and d-value mismatches of OR1-a/TiB2, OR2-a/TiB2 and OR3-a/TiB2 are calculated for the peritectic a composition (Figs. 1 and 2). Due to the lower d-value mismatch OR1-a/TiB2 and OR2-a/TiB2 should be preferred over OR3-a/TiB2. The variation of interatomic misfit and d-value mismatch with Al concentration of a/b direction and plane pairs is shown in Figs. 3 and 4. The lattice parameter of b is kept constant, since a nucleation on pre-existing b grains is being considered. Fig. 3 shows that the interatomic misfit of the direction pair h1 1 2 0ia=h1 0 0ib exceeds the 10% misfit criterion for higher Al concentrations. This makes it an unfavourable matching direction pair in the
case of a nucleation. The plane pairs f1 1 0 1ga=f1 1 0gb and f0 0 0 2ga=f1 1 0gb in Fig. 4 have d-value mismatches well below 10%. Thus, they become matching planes. The plane pair f1 1 0 0ga=f1 1 0gb does not contain any additional matching direction pair of Fig. 3 and it has the largest d-value mismatch. Therefore, it is not considered for the prediction of ORs. The predicted ORs are: OR1-a/b ½1 1 2 0a=½1 1 1b: 2.2% ð0 0 0 2Þa=ð1 1 0Þb: 0.4% OR2-a/b ½1 1 2 3a=½1 1 3b: 0.9% ð1 0 1 1Þa=ð1 1 0Þb: 4.8% OR1-a/b contains straight atom rows (½1 1 2 0a and ½1 1 1b), whereas OR2-a/b contains zigzag atom rows (½1 1 2 3a and ½1 1 3b). This makes the formation of OR1-a/b preferred over that of OR2-a/b, even though the interatomic misfit of OR2-a/b is slightly smaller.
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OR1-a/b is identical to the Burgers OR, which is known from the solid state a ? b transformations in Ti-based alloys [24]. According to Ref. [18], OR2-a/b is very close to OR1-a/b (Burgers OR). They are related by a rotational angle of <0.5°. This makes it difficult to distinguish both ORs by selected-area diffraction. Considering this uncertainty, the prediction of OR1-a/b is in agreement with experimental findings, since the Burgers OR is confirmed by electron backscatter diffraction measurements in the case of a nucleation on b grains [5]. 3.2. b Nucleation on TiB2 TiB2 precipitates prior to b in the melt of, for example, Ti–45Al at.% alloys with boron contents larger than 1.5 at.% [4]. b forms via the eutectic reaction L ? b + TiB2 at 1485 °C during solidification of such alloys. The edgeto-edge model is applied to determine the b nucleation potency of TiB2. The close-packed or relatively close-packed directions and planes of b and TiB2 are given in Section 3.1. The composition of the initially formed b phase is Ti–43Al– 0.17B at.%. The high Al solute content changes the lattice parameter of b. The influence of the small boron content is neglected. Under these conditions the calculated lattice parameters at 1485 °C are: a = 0.325 nm for b and a = 0.307 nm and c = 0.328 nm for TiB2. In addition, the lattice parameters are calculated for the Al concentration range 0–50 at.%. The resulting variation of interatomic misfit and d-value mismatch is shown in Figs. 5 and 6, respectively. The selected direction pairs do not violate the 10% criterion of maximum interatomic misfit, which makes them become matching directions. The plane pair f2 0 0gb=f1 1 2 0gTiB2 can be considered as a matching plane pair if the 10% is applied to the d-value mismatch. The plane pair f1 1 0gb=f1 1 0 1gTiB2 barely fulfils this 10% criterion at higher Al concentrations. The matching direction pairs h1 1 3ib=h1 1 0 0iTiB2 and h1 1 1ib=h1 1 2 0iTiB2 are not contained in matching plane pairs with a reasonably low
Fig. 6. d-value mismatch of b/TiB2 plane pairs as a function of Al concentration.
d-value mismatch. Thus, only the matching direction pairs h0 0 1ib=h0 0 0 1iTiB2 and h1 1 0ib=h1 1 2 3iTiB2 can form reproducible ORs: OR1-b/TiB2 ½0 0 1b=½0 0 0 1TiB2 : 0.9% ð2 0 0Þb=ð1 1 2 0ÞTiB2 : 5.7% OR2-b/TiB2. ½1 1 0b=½1 1 2 3TiB2 : 2.4% ð1 1 0Þb=ð1 0 1 1ÞTiB2 : 10.3% The interatomic misfit and d-value mismatch of OR1-b/ TiB2 and OR2-b/TiB2 have been calculated for the composition of initial b formation (Figs. 5 and 6). The much higher d-value mismatch of OR2-b/TiB2 should lead to OR1-b/TiB2 being preferred. OR1-b/TiB2 has also been confirmed indirectly by Inkson et al. [25] and Godfrey and Loretto [26], who measured the interfacial relationship between TiB2 and the ordered bcc b phase (B2) in cast TiAl-based alloys. Alloying additions stabilized in this case the ordered B2 structure of b at room temperature. The interfacial OR is ½0 1 0bðB2Þ=½0 0 0 1TiB2 and ð0 0 1Þb ðB2Þ=ð1 0 1 0ÞTiB2 . The matching direction pair is identical to OR1-b/TiB2 and the matching plane pair ð2 0 0Þb= ð1 1 2 0ÞTiB2 of OR1-b/TiB2 intersects the matching direction pair. Thus, the prediction of OR1-b/TiB2 agrees with experimental findings. 4. Experimental results
Fig. 5. Interatomic spacing misfit of b/TiB2 direction pairs as a function of Al concentration.
Figs. 7 and 8 show the as-cast microstructure of the alloy Ti–45Al–0.5B at.% (4505B) and Ti–45Al–2B at.% (452B), respectively. The cooling rate at the beginning of solidification is approximately 3 K s1. The size of the lamellar a2(Ti3Al)/c(TiAl) colonies (grains) is 127 ± 67 lm for 4505B and 133 ± 74 lm for 452B. The measured grain sizes confirm the well-known microstructure refinement via TiB2 inoculation [27]. Interestingly the grain size
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Fig. 7. Microstructure of alloy 4505B. Polarized light contrasts lamellar colonies.
Fig. 8. Microstructure of alloy 452B. Polarized light contrasts lamellar colonies.
is almost the same for both alloys. Thus, TiB2 precipitation prior to b in case of alloy 452B does not increase the grain refinement. The stained microstructure of alloy 4505B (Fig. 9) reveals ribbon borides, which decorate the boundaries of large columnar b dendrites in the size range of cm. Additionally, interdenritic regions are stained, exposing a high boride density. These interdendritic regions must be enriched by Al, which arises from the last stage of solidification. Thus, the applied staining technique is also sensitive to Al segregation. Staining of the microstructure of alloy 452B (Fig. 10) shows blocky borides. The highlighted interdendritic (Al-rich) regions suggest in this case a globular b grain morphology in contrast to alloy 4505B. This indicates refinement of b dendrites, once TiB2 is stable before b formation (alloy 452B). Figs. 11 and 12 show the typical morphologies of TiB2 particles in the alloys 4505B and 452B, respectively. TiB2 forms completely via the eutectic reaction L ? TiB2 + b in alloy 4505B (cf. Section 2). This leads to formation of the flake morphology in Fig. 11, which stems from the
Fig. 9. Stained microstructure of alloy 4505B. Thin dark ribbons correspond to TiB2 along columnar former b dendrites. Additionally, Al rich interdenritic areas are stained.
Fig. 10. Stained microstructure of alloy 452B. Small dark spots correspond to TiB2. The few larger dark spots (>20 lm) are pores. Additionally, Al rich interdenritic areas are stained.
Fig. 11. SEM mircograph of deep etched microstructure of alloy 4505B revealing flake TiB2 morphology.
interleaved growth of b and TiB2 with prismatic facets of type f1 1 0 0g [25,26]. TiB2 grows almost unconstrained in
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Fig. 12. SEM mircograph of deep etched microstructure of alloy 452B revealing a blocky TiB2 morphology.
the melt of alloy 452B before b formation. The preferred growth direction is h0 0 0 1i, which leads to a blocky morphology in Fig. 12 with dominant prismatic facets of type f1 1 0 0g [15]. It seems that the f1 1 0 0g facets are bounded by smaller basal facets of type f0 0 0 1g (Fig. 12). The TiB2 particles of alloy 452B exhibit many surface steps. These steps originated presumably from growth in the melt. 5. Influence of TiB2 growth on nucleation potencies The edge-to-edge model is applied to determine how the observed TiB2 morphology affects the a and b nucleation potencies of TiB2. Two requirements have to be met if the edge-to-edge matching is to occur on a certain facet [28]: (i) the facet must contain the matching direction and (ii) the corresponding matching plane must intersect the same facet at the particular matching direction. The prismatic f1 1 0 0g facets of TiB2 in alloys 4505B and 452B fulfil the requirements of OR1-a/TiB2, i.e. the h1 1 2 0iTiB2 matching direction is contained in this facet and the f1 1 0 1gTiB2 matching plane intersects this facet. The other a/TiB2 ORs cannot be established, since the matching planes do not intersect at the h1 1 2 0iTiB2 matching direction. The prismatic f1 1 0 0g facets also meet the conditions of the predicted b/TiB2 ORs (OR1-b/TiB2 and OR2-b/TiB2), since the matching directions h0 0 0 1iTiB2 and h1 1 2 3iTiB2 are contained in the facet and the corresponding matching planes intersect at these directions. The additional basal facets of TiB2 in alloy 452B do not contain the matching direction of the predicted b/TiB2 ORs, which makes establishment of these ORs impossible. All of the predicted a/TiB2 ORs are possible on these basal facets, since the common matching direction h1 1 2 0iTiB2 is contained in these facets and it intersects the different matching planes. 6. Discussion The edge-to-edge matching model is applied to predict approximated ORs for (i) a nucleation on either TiB2
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particles or b grains and (ii) b nucleation on TiB2 particles. The nucleation potency is judged on the basis of the interatomic misfit and d-value mismatch of the predicted OR. ORs with low interatomic misfit and d-value mismatch are expected to indicate a high nucleation potency, which should result in grain refinement. For alloy 4505B only a nucleation is of interest, since TiB2 precipitates after the first b phase (secondary TiB2), but before the peritectic reaction L + b ? a + TiB2 starts. Thus, the experimentally observed grain refinement of alloy 4505B should depend only on a nucleation. The low interatomic misfit and d-value mismatch of the predicted OR1a/TiB2 suggest a high nucleation potency by secondary TiB2, i.e. prismatic f1 1 0 0g facets of secondary TiB2 fulfil the matching requirements. Thus, the TiB2 nucleation potency is not limited by these facets. Hyman et al. [15] observed the development of another type of prismatic facets f1 1 2 0g, which do not meet the matching requirements of the favourable OR1-a/TiB2 since they do not contain the h1 1 2 0iTiB2 matching direction (cf. Section 5). Therefore, these facets would limit the a nucleation potency and thereby the grain refinement. However, the subsequent independent investigations of Inkson et al. [25] and Godfrey and Loretto [26] support the formation of f1 1 0 0g facets. A comparison to the predicted ORs for a on b nucleation (Burgers OR) shows that pre-existing b grains should be the preferred a nucleation sites, i.e. the Burgers OR has the smallest interatomic misfit and d-value mismatch. However, Hecht et al. [5] proved experimentally that a on b nucleation leads to a coarse microstructure if a precipitates after the initial b formation. This is in contradiction to the refinement of alloy 4505B. Therefore, TiB2 particles seem to act as potent nucleation sites, even though the predicted OR for a on TiB2 nucleation is less favourable. This discrepancy highlights the interleaved eutectic growth of TiB2 and b in the case of alloy 4505B. This interleaved grown b might be the actual a nucleation site, due to the predicted high a nucleation potency of b. Following this hypothesis eutectic b nucleation/formation on TiB2 could therefore be responsible for a grain refinement. Alternatively, nucleation of monoborides on TiB2 is observed during the solidification of TiAl-based alloys [29,30] and cannot be excluded in the present case. It is possible that this monoboride nucleation leads to ORs with interatomic misfits and d-value mismatches of the order of the Burgers OR, resulting in enhancement of the a nucleation potency. Details regarding this will be published in a forthcoming paper. For alloy 452B both a and b nucleation is of interest, since TiB2 precipitates primarily in the melt. The predicted OR for b nucleation on TiB2 (OR1-b/TiB2) suggests a high b nucleation potency, which is in agreement with the observed refinement of b grains in the microstructure. The TiB2 morphology is blocky with dominant prismatic f1 1 0 0g facets, which fulfil the matching requirement of the predicted OR1-b/TiB2 (cf. Section 5). Thus, the
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f1 1 0 0g facets do not constrain the high b nucleation potency of TiB2. The absence of flake type TiB2 (alloy 4505B) suggests that the eutectic TiB2 fraction nucleated on primary TiB2 instead of growing interleaved with b. As stated for alloy 4505B, the prismatic facets also permit a nucleation by OR1-a/TiB2. Additionally, the smaller basal f0 0 0 1g facets allow for a nucleation by all of the predicted a/TiB2 ORs (cf. Section 5) OR1-a/TiB2. In this context it is surprising that the grain refinement of alloy 452B is not more pronounced, i.e. refinement of both a and b grains by primary TiB2. This contradiction can be explained by the absence of interleaved b on TiB2 facets in contrast to TiB2 in alloy 4505B. Pre-existing b grains are predicted to be the favourable a nucleation sites (Burgers OR) and furthermore a refinement is not obtained. Further investigations are currently being undertaken by both modeling and experiment to investigate the role of a nucleation in more detail. Finally, the role of surface steps on prismatic f1 1 0 0g facets of primary TiB2 is addressed. These steps are of basal type character (Fig. 12), since the preferred growth direction is h0 0 0 1i. The matching direction h0 0 0 1iTiB2 of OR1-b/TiB2 is not contained in the basal facets, which is expected to hinder growth of b along the prismatic facets as can be seen schematically from Fig. 13. This limits the effective b nucleation site area. For example, an area limitation down to at least 20% can be justified by Fig. 12. Free growth model calculation of the b grain size shows that this size effect leads to a much coarser grain size [31]. Thus, the b grain refinement performance of TiB2 could be enhanced if the development of such growth steps would be suppressed. In contrast, a nucleation on basal facets is not hindered by prismatic f1 1 0 0g surface steps since the matching
direction h1 1 2 0iTiB2 of the predicted ORs is contained in f1 1 0 0g plane (Fig. 14). 7. Conclusions
The edge-to-edge model predicts energetically favourable ORs for a and b nucleation on TiB2. In the case of a nucleation, the predicted Burgers OR suggests the highest a nucleation potency on pre-existing b grains. The morphology of primary TiB2 (stable prior to b and peritectic a formation) enables establishment of the predicted b OR on prismatic f1 1 0 0gTiB2 facets. Experiments confirm b refinement in this case. The observed grain refinement by secondary TiB2 (stable prior to peritectic a formation) seems to be caused by a nucleation on interleaved b rather than on f1 1 0 0gTiB2 facets. The absence of this interleaved b on primary TiB2 limits the maximum achievable refinement, since a nucleation should occur in the last stage of solidification on preexisting b grains, which does not lead to additional refinement via a. The development of basal f0 0 0 1g growth steps on prismatic f1 1 0 0g facets limits the effective b nucleation site area, since the TiB2 matching direction of the predicted b OR is not contained here. Acknowledgements Financial support of the DFG (German Research Foundation) within the priority programme SPP1296 is gratefully acknowledged. References
Fig. 13. b Nucleation on a prismatic f1 1 0 0g facet with a basal f0 0 0 1g surface step.
Fig. 14. a Nucleation on a basal f0 0 0 1g facet with a prismatic f1 1 0 0g surface step.
[1] Appel F, Oehring M, Wagner R. Intermetallics 2000;8:1283. [2] Noda T. Current status of mass production of gamma titanium aluminide alloy turbine rotors in turbocharges and future challenges. In: Kim Y-W, Morris D, Yang R, Leyens C, editors. Structural aluminides for elevated temperature: gamma titanium and other metallic aluminides. New Orleans (LA): TMS; 2008. p. 7. [3] Christodoulou JA, Flower HM. Adv Eng Mater 2000;2:631. [4] Witusiewicz VT, Bondar AA, Hecht U, Zollinger J, Artyukh LV, Velikanova TY. J Alloy Compd 2009;474:86. [5] Hecht U, Witusiewicz A, Drevermann A, Zollinger J. Intermetallics 2008;16:969. [6] Kelly PM, Zhang MX. Mater Forum 1999;23:41. [7] Zhang MX, Kelly PM. Prog Mater Sci 2009;54:1101. [8] Hartig C, Gu¨nther R, Gosslar D, Bormann R. Int J Mater Res 2010;101:572. [9] Hyman ME, McCullough C, Valencia JJ, Levi CG, Mehrabian R. Metall Trans A 1989;20:1847. [10] Qiu D, Zhang H-MF, Kelly PM, Taylor JA. Philos Mag Lett 2007;87:505. [11] Zhang M-X, Kelly PM, Easton MA, Taylor JA. Acta Mater 2005;53:1427. [12] Zhang MX, Kelly PM, Qian M, Taylor JA. Acta Mater 2005;53:3261. [13] Qiu D, Zhang MA, Taylor JA, Kelly PM. Acta Mater 2009;57: 3052.
D. Gosslar et al. / Acta Materialia 58 (2010) 6744–6751 [14] Kelly PM, Zhang MX. Metall Trans A 2006;37A:833. [15] Hyman M, McCullough C, Levi C, Mehrabian R. Metall Trans A 1991;22:1647. [16] Eiken J, Apel M, Witusiewicz VT, Zollinger J, Hecht U. J Phys: Condens Matter 2009;21:1. [17] Villars P, Calvert LD. Pearson’s handbook of crystallographic data for intermetallic phases, vol. 2. Materials Park (OH): ASM International; 1991. p. 1646. [18] Zhang MX, Kelly PM. Acta Mater 2005;53:1073. [19] Bumps ES, Kessler HD, Hansen M. J Met 1952;4:609. [20] Shao G, Tsakiropoulos P. Mater Sci Eng A 1999;271:286. [21] Souvatzis P, Eriksson O, Katsnelson MI. Phys Rev Lett 2007;11:99. [22] Senkov ON, Chakoumakos B, Jonas JJ, Froes FH. Mater Res Bull 2001;36:1431.
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[23] Okamoto NL, Kusakari M, Tanaka K, Inui H, Otani S. Acta Mater 2010;58:76. [24] Burgers WG. Physica 1934;1:561. [25] Inkson BJ, Boothroyd CB, Humphreys CJ. Acta Metall Mater 1995;43:1429. [26] Godfrey AB, Loretto MH. Intermetallics 1996;4:47. [27] Bryant JD, Christodoulou L, Maisano JR. Scripta Metall Mater 1990;24:33. [28] Zhang MX, Kelly PM. Scripta Mater 2006;55:613. [29] DeGraef M, Lo¨fvander JPA, McCullough C, Levi CG. Acta Metall Mater 1992;40:3395. [30] Kitkamthorn U, Zhang LC, Aindow M. Intermetallics 2006;14:759. [31] Gosslar D, Hartig C, Gu¨nther R, Hecht U, Bormann R. J Phys: Condens Matter 2009;21:1.
Acta Materialia 58 (2010) 6744–6751 www.elsevier.com/locate/actamat
Grain refinement of TiAl-based alloys: The role of TiB2 crystallography and growth D. Gosslar a,⇑, R. Gu¨nther a, U. Hecht b, C. Hartig a, R. Bormann a a
Hamburg University of Technology, Institute of Material Science and Technology, Eissendorfer Strasse 42, 21073 Hamburg, Germany b ACCESS Materials and Processes, RWTH-Aachen, Access e.V., Intzestrasse 5, 52072 Aachen, Germany Received 9 August 2010; received in revised form 31 August 2010; accepted 31 August 2010 Available online 25 September 2010
Abstract A crystallographic model is used to predict the nucleation potencies of TiB2 particles during solidification of TiAl-based alloys. Two nucleation scenarios are investigated. In scenario 1, primary TiB2 grows in the melt before formation of the body-centred cubic b phase. In scenario 2, secondary TiB2 precipitates after the first b phase but before formation of the hexagonal close-packed a phase. The model predicts high a and b nucleation potencies of TiB2 in both scenarios. However, pre-existing b grains in scenario 2 are predicted to be preferred a nucleation sites. The experimentally observed b refinement by primary TiB2 agrees with the model predictions. Grain refinement in scenario 2 is attributed to a nucleation on b, which is interleaved with secondary TiB2. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium aluminides; Casting; Grain refining; Edge-to-edge matching; Crystal growth
1. Introduction TiAl-based alloys are an attractive material class if a combination of low weight and high-temperature properties is desired [1]. Casting of these alloys is an important production route for automobile and aircraft parts [2]. A certain amount of boron is required in order to obtain a homogeneous and refined as-cast microstructure [3]. However, the exact grain refinement mechanism is not clear due to the complex solidification sequence. The thermodynamic description of the system Ti–Al–B [4] enables a new investigation of this grain refinement mechanism in terms of alloy composition and phase formation. It has been shown that in case of low-boron content, nucleation of the hexagonal close-packed (hcp) a phase on borides appears to be the grain refinement mechanism [5]. At high boron contents borides are stable in the melt and may also serve as nucleation sites for the primary body⇑ Corresponding author. Tel.: +49 40 42878 3145; fax: +49 40 42878 4070. E-mail address: [email protected] (D. Gosslar).
centred cubic (bcc) b phase. This raises the issue of heterogeneous b nucleation on borides. The magnitude of the a and b nucleation potencies of borides should therefore be a key aspect of the grain refinement mechanism. The aim of this paper is to apply the crystallographic model of Kelly and Zhang [6,7] to predict the nucleation potency of TiB2 for different nucleation scenarios, which occur during solidification of TiAl-based alloys. The model predictions are compared to experimental results in terms of grain refinement and TiB2 morphologies. 2. Experimental Two TiAl-based alloys of composition Ti–45Al– 0.5B at.% (4505B) and Ti–45Al–2B at.% (452B) were cast centrifugally into 16 mm diameter Y2O3 moulds. The casting temperature was approximately 1505 °C (30 °C superheat). 1.5 at.% B of the alloy 452B is achieved by inoculation via a novel Ti–Al–TiB2 master alloy. Details regarding this are described in Ref. [8]. Thermodynamic calculations predict the following transformation pathways [4]:
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.08.040
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1. L ? L + b ? L + b + TiB2 ? a + TiB2 (alloy 4505B) 2. L ? L + TiB2 ? L + TiB2 + b ? a + TiB2 (alloy 452B)
ically in a Ti–Al–B melt [15], the habit plane prediction is omitted.
In pathway (1), TiB2 precipitates after the first b phase at 1485 °C but before the peritectic formation of the a phase starts at 1472 °C. In pathway (2), TiB2 precipitates primarily in the melt at 1550 °C. The as-cast microstructure was investigated by optical metallography and by scanning electron microscopy (SEM). The staining technique described in Ref. [9] was applied to highlight TiB2 particles in the microstructures. Deep etching of the microstructures by a Kroll solution (25 ml H2O, 3 ml HNO3, 2 ml HF) for 2 min was used to reveal the TiB2 morphologies. The size of lamellar a2(Ti3Al)/c(TiAl) colonies was determined by the average line interception method.
3.1. a Nucleation on TiB2 and on b grains
3. The edge-to-edge matching model The edge-to-edge matching model has been developed by Kelly and Zhang [6,7]. This model predicts from first principles the orientation relationship (OR) between two phases. The underlying physical principle is minimization of the interfacial energy which governs formation of an OR. This is achieved by matching of close or relatively close-packed atom rows at the interface. These atom rows have to be contained in close-packed or relatively closepacked planes in order to maximize the atom row matching. Close-packed or relatively close-packed atom rows become matching rows if the interatomic misfit is below 10%. Close-packed or relatively close-packed planes become matching planes if the interplanar mismatch (d-value mismatch) is below 6%. In case of heterogeneous nucleation in the melt, a maximum d-value mismatch of 10% is also accepted [10]. Atom row matching is, however, more important than plane matching. Correspondingly, the interatomic misfit is more important than the d-value mismatch. An OR with a smaller interatomic misfit is therefore preferred over one with a larger interatomic misfit. In addition, the arrangement of atoms within one row is considered by the model. The general rule is that matching between straight atom rows is favoured over matching between zigzag atom rows. Application of the edge-to-edge model predicts successfully the nucleation potency and thereby the grain refinement potential of several ceramic inoculants in Mg and Al alloys [11–13]. Hereby, the nucleation potency is evaluated by the size of the interatomic misfit and d-value mismatch of the predicted OR. In this paper the edge-to-edge model is used to predict the potency of a and b nucleation on TiB2 in accordance to the transformation pathways described in Section 2. In particular, the a nucleation potency of TiB2 is compared to the one of pre-existing b grains. The edge-to-edge model is also capable of predicting the exact habit plane of an OR in absence of growth anisotropies [14]. Since TiB2 does grow highly anisotrop-
The a phase has a simple hcp structure. a forms during the peritectic reaction L + b ? a + TiB2 at the end of solidification of, for example, Ti–45Al at.% alloys with boron contents larger than 0.5 at.% [16]. The peritectic temperature is 1472 °C. The b phase has a simple bcc structure. TiB2 has a hexagonal C32 structure [17]. According to the peritectic reaction, both b grains and TiB2 particles offer possible a nucleation sites. The edge-to-edge model is applied to determine a nucleation potencies of both sites. The close-packed or relatively close-packed directions and planes of a and b have been identified in Ref. [18] and of TiB2 in Ref. [11]. At the beginning of the peritectic reaction the a and b compositions are Ti–46Al–0.02B at.% and Ti–44Al– 0.15B at.%, respectively. High Al solute contents in both phases change the lattice parameters, whereas the influence by the small boron contents is neglected. In this case the lattice parameters of a can be calculated directly by Vegard’s law [19]. In contrast, the lattice parameter of b cannot be determined directly for high Al concentrations, because it decomposes into a upon cooling. The atomic volume remains nearly constant during this transformation. Therefore, the lattice parameter of b can be calculated indirectly from the a lattice parameters [20]. Thermal expansion of a, b and TiB2 are calculated by thermal expansion coefficients published in Refs. [21–23], respectively. Thus, the calculated lattice parameters for the peritectic reaction at 1472 °C are: a = 0.288 nm and c = 0.462 nm for a, a = 0.325 nm for b and a = 0.307 nm and c = 0.328 nm for TiB2. In addition, the lattice parameters are calculated for the Al concentration range 0– 50 at.%. The resulting variation of interatomic misfit and d-value mismatch of a/TiB2 direction and plane pairs is shown in Figs. 1 and 2. Fig. 1 shows that the interatomic misfit of the direction pair h1 1 2 0ia=h0001iTiB2 is in excess of 10%. It is unlikely to become a matching direction pair if 10% is considered as the maximum misfit. The two plane pairs f1 1 0 1ga=f1 1 0 1gTiB2 and f1 1 0 0ga=f1 1 0 0gTiB2 in Fig. 2 are possible matching plane pairs if the same 10% criterion is applied to the d-value mismatch. The plane pair f0 0 0 2ga=f1 1 0 0gTiB2 barely fulfils this 10% criterion at higher Al concentrations. The matching direction pairs h1 1 0 0ia=h1 1 0 0iTiB2 and h1 1 2 3ia=h1 0 1 0iTiB2 are not contained in the matching plane pairs of Fig. 2. Therefore, they are excluded from formation of reproducible ORs. Only the matching direction pair h1 1 2 0ia=h1 1 2 0iTiB2 remains, which leads to the following ORs: OR1-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð1 1 0 1Þa=ð1 1 0 1ÞTiB2 : 5.9%
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Fig. 1. Interatomic spacing misfit of a/TiB2 direction pairs as a function of Al concentration.
Fig. 3. Interatomic spacing misfit of a/b direction pairs as a function of Al concentration.
Fig. 2. d-value mismatch of a/TiB2 plane pairs as a function of Al concentration.
Fig. 4. d-value mismatch of a/b plane pairs as a function of Al concentration.
OR2-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð1 1 0 0Þa=ð1 1 0 0ÞTiB2 : 6.6% OR3-a/TiB2 ½1 1 2 0a=½1 1 2 0TiB2 : 6.6% ð0 0 0 2Þa=ð1 1 0 0ÞTiB2 : 10.6% The interatomic misfits and d-value mismatches of OR1-a/TiB2, OR2-a/TiB2 and OR3-a/TiB2 are calculated for the peritectic a composition (Figs. 1 and 2). Due to the lower d-value mismatch OR1-a/TiB2 and OR2-a/TiB2 should be preferred over OR3-a/TiB2. The variation of interatomic misfit and d-value mismatch with Al concentration of a/b direction and plane pairs is shown in Figs. 3 and 4. The lattice parameter of b is kept constant, since a nucleation on pre-existing b grains is being considered. Fig. 3 shows that the interatomic misfit of the direction pair h1 1 2 0ia=h1 0 0ib exceeds the 10% misfit criterion for higher Al concentrations. This makes it an unfavourable matching direction pair in the
case of a nucleation. The plane pairs f1 1 0 1ga=f1 1 0gb and f0 0 0 2ga=f1 1 0gb in Fig. 4 have d-value mismatches well below 10%. Thus, they become matching planes. The plane pair f1 1 0 0ga=f1 1 0gb does not contain any additional matching direction pair of Fig. 3 and it has the largest d-value mismatch. Therefore, it is not considered for the prediction of ORs. The predicted ORs are: OR1-a/b ½1 1 2 0a=½1 1 1b: 2.2% ð0 0 0 2Þa=ð1 1 0Þb: 0.4% OR2-a/b ½1 1 2 3a=½1 1 3b: 0.9% ð1 0 1 1Þa=ð1 1 0Þb: 4.8% OR1-a/b contains straight atom rows (½1 1 2 0a and ½1 1 1b), whereas OR2-a/b contains zigzag atom rows (½1 1 2 3a and ½1 1 3b). This makes the formation of OR1-a/b preferred over that of OR2-a/b, even though the interatomic misfit of OR2-a/b is slightly smaller.
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OR1-a/b is identical to the Burgers OR, which is known from the solid state a ? b transformations in Ti-based alloys [24]. According to Ref. [18], OR2-a/b is very close to OR1-a/b (Burgers OR). They are related by a rotational angle of <0.5°. This makes it difficult to distinguish both ORs by selected-area diffraction. Considering this uncertainty, the prediction of OR1-a/b is in agreement with experimental findings, since the Burgers OR is confirmed by electron backscatter diffraction measurements in the case of a nucleation on b grains [5]. 3.2. b Nucleation on TiB2 TiB2 precipitates prior to b in the melt of, for example, Ti–45Al at.% alloys with boron contents larger than 1.5 at.% [4]. b forms via the eutectic reaction L ? b + TiB2 at 1485 °C during solidification of such alloys. The edgeto-edge model is applied to determine the b nucleation potency of TiB2. The close-packed or relatively close-packed directions and planes of b and TiB2 are given in Section 3.1. The composition of the initially formed b phase is Ti–43Al– 0.17B at.%. The high Al solute content changes the lattice parameter of b. The influence of the small boron content is neglected. Under these conditions the calculated lattice parameters at 1485 °C are: a = 0.325 nm for b and a = 0.307 nm and c = 0.328 nm for TiB2. In addition, the lattice parameters are calculated for the Al concentration range 0–50 at.%. The resulting variation of interatomic misfit and d-value mismatch is shown in Figs. 5 and 6, respectively. The selected direction pairs do not violate the 10% criterion of maximum interatomic misfit, which makes them become matching directions. The plane pair f2 0 0gb=f1 1 2 0gTiB2 can be considered as a matching plane pair if the 10% is applied to the d-value mismatch. The plane pair f1 1 0gb=f1 1 0 1gTiB2 barely fulfils this 10% criterion at higher Al concentrations. The matching direction pairs h1 1 3ib=h1 1 0 0iTiB2 and h1 1 1ib=h1 1 2 0iTiB2 are not contained in matching plane pairs with a reasonably low
Fig. 6. d-value mismatch of b/TiB2 plane pairs as a function of Al concentration.
d-value mismatch. Thus, only the matching direction pairs h0 0 1ib=h0 0 0 1iTiB2 and h1 1 0ib=h1 1 2 3iTiB2 can form reproducible ORs: OR1-b/TiB2 ½0 0 1b=½0 0 0 1TiB2 : 0.9% ð2 0 0Þb=ð1 1 2 0ÞTiB2 : 5.7% OR2-b/TiB2. ½1 1 0b=½1 1 2 3TiB2 : 2.4% ð1 1 0Þb=ð1 0 1 1ÞTiB2 : 10.3% The interatomic misfit and d-value mismatch of OR1-b/ TiB2 and OR2-b/TiB2 have been calculated for the composition of initial b formation (Figs. 5 and 6). The much higher d-value mismatch of OR2-b/TiB2 should lead to OR1-b/TiB2 being preferred. OR1-b/TiB2 has also been confirmed indirectly by Inkson et al. [25] and Godfrey and Loretto [26], who measured the interfacial relationship between TiB2 and the ordered bcc b phase (B2) in cast TiAl-based alloys. Alloying additions stabilized in this case the ordered B2 structure of b at room temperature. The interfacial OR is ½0 1 0bðB2Þ=½0 0 0 1TiB2 and ð0 0 1Þb ðB2Þ=ð1 0 1 0ÞTiB2 . The matching direction pair is identical to OR1-b/TiB2 and the matching plane pair ð2 0 0Þb= ð1 1 2 0ÞTiB2 of OR1-b/TiB2 intersects the matching direction pair. Thus, the prediction of OR1-b/TiB2 agrees with experimental findings. 4. Experimental results
Fig. 5. Interatomic spacing misfit of b/TiB2 direction pairs as a function of Al concentration.
Figs. 7 and 8 show the as-cast microstructure of the alloy Ti–45Al–0.5B at.% (4505B) and Ti–45Al–2B at.% (452B), respectively. The cooling rate at the beginning of solidification is approximately 3 K s1. The size of the lamellar a2(Ti3Al)/c(TiAl) colonies (grains) is 127 ± 67 lm for 4505B and 133 ± 74 lm for 452B. The measured grain sizes confirm the well-known microstructure refinement via TiB2 inoculation [27]. Interestingly the grain size
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Fig. 7. Microstructure of alloy 4505B. Polarized light contrasts lamellar colonies.
Fig. 8. Microstructure of alloy 452B. Polarized light contrasts lamellar colonies.
is almost the same for both alloys. Thus, TiB2 precipitation prior to b in case of alloy 452B does not increase the grain refinement. The stained microstructure of alloy 4505B (Fig. 9) reveals ribbon borides, which decorate the boundaries of large columnar b dendrites in the size range of cm. Additionally, interdenritic regions are stained, exposing a high boride density. These interdendritic regions must be enriched by Al, which arises from the last stage of solidification. Thus, the applied staining technique is also sensitive to Al segregation. Staining of the microstructure of alloy 452B (Fig. 10) shows blocky borides. The highlighted interdendritic (Al-rich) regions suggest in this case a globular b grain morphology in contrast to alloy 4505B. This indicates refinement of b dendrites, once TiB2 is stable before b formation (alloy 452B). Figs. 11 and 12 show the typical morphologies of TiB2 particles in the alloys 4505B and 452B, respectively. TiB2 forms completely via the eutectic reaction L ? TiB2 + b in alloy 4505B (cf. Section 2). This leads to formation of the flake morphology in Fig. 11, which stems from the
Fig. 9. Stained microstructure of alloy 4505B. Thin dark ribbons correspond to TiB2 along columnar former b dendrites. Additionally, Al rich interdenritic areas are stained.
Fig. 10. Stained microstructure of alloy 452B. Small dark spots correspond to TiB2. The few larger dark spots (>20 lm) are pores. Additionally, Al rich interdenritic areas are stained.
Fig. 11. SEM mircograph of deep etched microstructure of alloy 4505B revealing flake TiB2 morphology.
interleaved growth of b and TiB2 with prismatic facets of type f1 1 0 0g [25,26]. TiB2 grows almost unconstrained in
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Fig. 12. SEM mircograph of deep etched microstructure of alloy 452B revealing a blocky TiB2 morphology.
the melt of alloy 452B before b formation. The preferred growth direction is h0 0 0 1i, which leads to a blocky morphology in Fig. 12 with dominant prismatic facets of type f1 1 0 0g [15]. It seems that the f1 1 0 0g facets are bounded by smaller basal facets of type f0 0 0 1g (Fig. 12). The TiB2 particles of alloy 452B exhibit many surface steps. These steps originated presumably from growth in the melt. 5. Influence of TiB2 growth on nucleation potencies The edge-to-edge model is applied to determine how the observed TiB2 morphology affects the a and b nucleation potencies of TiB2. Two requirements have to be met if the edge-to-edge matching is to occur on a certain facet [28]: (i) the facet must contain the matching direction and (ii) the corresponding matching plane must intersect the same facet at the particular matching direction. The prismatic f1 1 0 0g facets of TiB2 in alloys 4505B and 452B fulfil the requirements of OR1-a/TiB2, i.e. the h1 1 2 0iTiB2 matching direction is contained in this facet and the f1 1 0 1gTiB2 matching plane intersects this facet. The other a/TiB2 ORs cannot be established, since the matching planes do not intersect at the h1 1 2 0iTiB2 matching direction. The prismatic f1 1 0 0g facets also meet the conditions of the predicted b/TiB2 ORs (OR1-b/TiB2 and OR2-b/TiB2), since the matching directions h0 0 0 1iTiB2 and h1 1 2 3iTiB2 are contained in the facet and the corresponding matching planes intersect at these directions. The additional basal facets of TiB2 in alloy 452B do not contain the matching direction of the predicted b/TiB2 ORs, which makes establishment of these ORs impossible. All of the predicted a/TiB2 ORs are possible on these basal facets, since the common matching direction h1 1 2 0iTiB2 is contained in these facets and it intersects the different matching planes. 6. Discussion The edge-to-edge matching model is applied to predict approximated ORs for (i) a nucleation on either TiB2
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particles or b grains and (ii) b nucleation on TiB2 particles. The nucleation potency is judged on the basis of the interatomic misfit and d-value mismatch of the predicted OR. ORs with low interatomic misfit and d-value mismatch are expected to indicate a high nucleation potency, which should result in grain refinement. For alloy 4505B only a nucleation is of interest, since TiB2 precipitates after the first b phase (secondary TiB2), but before the peritectic reaction L + b ? a + TiB2 starts. Thus, the experimentally observed grain refinement of alloy 4505B should depend only on a nucleation. The low interatomic misfit and d-value mismatch of the predicted OR1a/TiB2 suggest a high nucleation potency by secondary TiB2, i.e. prismatic f1 1 0 0g facets of secondary TiB2 fulfil the matching requirements. Thus, the TiB2 nucleation potency is not limited by these facets. Hyman et al. [15] observed the development of another type of prismatic facets f1 1 2 0g, which do not meet the matching requirements of the favourable OR1-a/TiB2 since they do not contain the h1 1 2 0iTiB2 matching direction (cf. Section 5). Therefore, these facets would limit the a nucleation potency and thereby the grain refinement. However, the subsequent independent investigations of Inkson et al. [25] and Godfrey and Loretto [26] support the formation of f1 1 0 0g facets. A comparison to the predicted ORs for a on b nucleation (Burgers OR) shows that pre-existing b grains should be the preferred a nucleation sites, i.e. the Burgers OR has the smallest interatomic misfit and d-value mismatch. However, Hecht et al. [5] proved experimentally that a on b nucleation leads to a coarse microstructure if a precipitates after the initial b formation. This is in contradiction to the refinement of alloy 4505B. Therefore, TiB2 particles seem to act as potent nucleation sites, even though the predicted OR for a on TiB2 nucleation is less favourable. This discrepancy highlights the interleaved eutectic growth of TiB2 and b in the case of alloy 4505B. This interleaved grown b might be the actual a nucleation site, due to the predicted high a nucleation potency of b. Following this hypothesis eutectic b nucleation/formation on TiB2 could therefore be responsible for a grain refinement. Alternatively, nucleation of monoborides on TiB2 is observed during the solidification of TiAl-based alloys [29,30] and cannot be excluded in the present case. It is possible that this monoboride nucleation leads to ORs with interatomic misfits and d-value mismatches of the order of the Burgers OR, resulting in enhancement of the a nucleation potency. Details regarding this will be published in a forthcoming paper. For alloy 452B both a and b nucleation is of interest, since TiB2 precipitates primarily in the melt. The predicted OR for b nucleation on TiB2 (OR1-b/TiB2) suggests a high b nucleation potency, which is in agreement with the observed refinement of b grains in the microstructure. The TiB2 morphology is blocky with dominant prismatic f1 1 0 0g facets, which fulfil the matching requirement of the predicted OR1-b/TiB2 (cf. Section 5). Thus, the
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f1 1 0 0g facets do not constrain the high b nucleation potency of TiB2. The absence of flake type TiB2 (alloy 4505B) suggests that the eutectic TiB2 fraction nucleated on primary TiB2 instead of growing interleaved with b. As stated for alloy 4505B, the prismatic facets also permit a nucleation by OR1-a/TiB2. Additionally, the smaller basal f0 0 0 1g facets allow for a nucleation by all of the predicted a/TiB2 ORs (cf. Section 5) OR1-a/TiB2. In this context it is surprising that the grain refinement of alloy 452B is not more pronounced, i.e. refinement of both a and b grains by primary TiB2. This contradiction can be explained by the absence of interleaved b on TiB2 facets in contrast to TiB2 in alloy 4505B. Pre-existing b grains are predicted to be the favourable a nucleation sites (Burgers OR) and furthermore a refinement is not obtained. Further investigations are currently being undertaken by both modeling and experiment to investigate the role of a nucleation in more detail. Finally, the role of surface steps on prismatic f1 1 0 0g facets of primary TiB2 is addressed. These steps are of basal type character (Fig. 12), since the preferred growth direction is h0 0 0 1i. The matching direction h0 0 0 1iTiB2 of OR1-b/TiB2 is not contained in the basal facets, which is expected to hinder growth of b along the prismatic facets as can be seen schematically from Fig. 13. This limits the effective b nucleation site area. For example, an area limitation down to at least 20% can be justified by Fig. 12. Free growth model calculation of the b grain size shows that this size effect leads to a much coarser grain size [31]. Thus, the b grain refinement performance of TiB2 could be enhanced if the development of such growth steps would be suppressed. In contrast, a nucleation on basal facets is not hindered by prismatic f1 1 0 0g surface steps since the matching
direction h1 1 2 0iTiB2 of the predicted ORs is contained in f1 1 0 0g plane (Fig. 14). 7. Conclusions
The edge-to-edge model predicts energetically favourable ORs for a and b nucleation on TiB2. In the case of a nucleation, the predicted Burgers OR suggests the highest a nucleation potency on pre-existing b grains. The morphology of primary TiB2 (stable prior to b and peritectic a formation) enables establishment of the predicted b OR on prismatic f1 1 0 0gTiB2 facets. Experiments confirm b refinement in this case. The observed grain refinement by secondary TiB2 (stable prior to peritectic a formation) seems to be caused by a nucleation on interleaved b rather than on f1 1 0 0gTiB2 facets. The absence of this interleaved b on primary TiB2 limits the maximum achievable refinement, since a nucleation should occur in the last stage of solidification on preexisting b grains, which does not lead to additional refinement via a. The development of basal f0 0 0 1g growth steps on prismatic f1 1 0 0g facets limits the effective b nucleation site area, since the TiB2 matching direction of the predicted b OR is not contained here. Acknowledgements Financial support of the DFG (German Research Foundation) within the priority programme SPP1296 is gratefully acknowledged. References
Fig. 13. b Nucleation on a prismatic f1 1 0 0g facet with a basal f0 0 0 1g surface step.
Fig. 14. a Nucleation on a basal f0 0 0 1g facet with a prismatic f1 1 0 0g surface step.
[1] Appel F, Oehring M, Wagner R. Intermetallics 2000;8:1283. [2] Noda T. Current status of mass production of gamma titanium aluminide alloy turbine rotors in turbocharges and future challenges. In: Kim Y-W, Morris D, Yang R, Leyens C, editors. Structural aluminides for elevated temperature: gamma titanium and other metallic aluminides. New Orleans (LA): TMS; 2008. p. 7. [3] Christodoulou JA, Flower HM. Adv Eng Mater 2000;2:631. [4] Witusiewicz VT, Bondar AA, Hecht U, Zollinger J, Artyukh LV, Velikanova TY. J Alloy Compd 2009;474:86. [5] Hecht U, Witusiewicz A, Drevermann A, Zollinger J. Intermetallics 2008;16:969. [6] Kelly PM, Zhang MX. Mater Forum 1999;23:41. [7] Zhang MX, Kelly PM. Prog Mater Sci 2009;54:1101. [8] Hartig C, Gu¨nther R, Gosslar D, Bormann R. Int J Mater Res 2010;101:572. [9] Hyman ME, McCullough C, Valencia JJ, Levi CG, Mehrabian R. Metall Trans A 1989;20:1847. [10] Qiu D, Zhang H-MF, Kelly PM, Taylor JA. Philos Mag Lett 2007;87:505. [11] Zhang M-X, Kelly PM, Easton MA, Taylor JA. Acta Mater 2005;53:1427. [12] Zhang MX, Kelly PM, Qian M, Taylor JA. Acta Mater 2005;53:3261. [13] Qiu D, Zhang MA, Taylor JA, Kelly PM. Acta Mater 2009;57: 3052.
D. Gosslar et al. / Acta Materialia 58 (2010) 6744–6751 [14] Kelly PM, Zhang MX. Metall Trans A 2006;37A:833. [15] Hyman M, McCullough C, Levi C, Mehrabian R. Metall Trans A 1991;22:1647. [16] Eiken J, Apel M, Witusiewicz VT, Zollinger J, Hecht U. J Phys: Condens Matter 2009;21:1. [17] Villars P, Calvert LD. Pearson’s handbook of crystallographic data for intermetallic phases, vol. 2. Materials Park (OH): ASM International; 1991. p. 1646. [18] Zhang MX, Kelly PM. Acta Mater 2005;53:1073. [19] Bumps ES, Kessler HD, Hansen M. J Met 1952;4:609. [20] Shao G, Tsakiropoulos P. Mater Sci Eng A 1999;271:286. [21] Souvatzis P, Eriksson O, Katsnelson MI. Phys Rev Lett 2007;11:99. [22] Senkov ON, Chakoumakos B, Jonas JJ, Froes FH. Mater Res Bull 2001;36:1431.
6751
[23] Okamoto NL, Kusakari M, Tanaka K, Inui H, Otani S. Acta Mater 2010;58:76. [24] Burgers WG. Physica 1934;1:561. [25] Inkson BJ, Boothroyd CB, Humphreys CJ. Acta Metall Mater 1995;43:1429. [26] Godfrey AB, Loretto MH. Intermetallics 1996;4:47. [27] Bryant JD, Christodoulou L, Maisano JR. Scripta Metall Mater 1990;24:33. [28] Zhang MX, Kelly PM. Scripta Mater 2006;55:613. [29] DeGraef M, Lo¨fvander JPA, McCullough C, Levi CG. Acta Metall Mater 1992;40:3395. [30] Kitkamthorn U, Zhang LC, Aindow M. Intermetallics 2006;14:759. [31] Gosslar D, Hartig C, Gu¨nther R, Hecht U, Bormann R. J Phys: Condens Matter 2009;21:1.