Intermetallics 22 (2012) 68e76
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Solidification and grain refinement in Ti45Al2Mn2Nb1B D. Hu a, *, C. Yang a, A. Huang b, M. Dixon b, U. Hecht c a
Interdisciplinary Research Centre in Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Rolls-Royce Plc, Derby DE24 8BJ, UK c ACCESS Materials and Processes, Intzestrasse 5, 52072 Aachen, Germany b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2011 Received in revised form 31 October 2011 Accepted 1 November 2011 Available online 26 November 2011
The solidification process of Ti45Al2Mn2Nb1B (Ti4522-1B) was studied together with the baseline alloy Ti45Al2Mn2Nb (Ti4522) through directional solidification. Boron addition at 1 at% was found to have a strong limiting effect on beta dendrite growth, resulting much finer beta dendrites than in the boronfree alloy. Boron addition at that level was also found to have changed the orientation relationship of peritectic alpha with beta dendrites. The peritectic alpha has the Burgers orientation relationship with the beta dendrites in Ti4522 whilst is randomly oriented in Ti4522-1B. The peritectic alpha in Ti4522-1B was likely to be inoculated by boride precipitates at the beta/liquid interfaces. Formation of randomly oriented peritectic alpha during solidification, boride precipitate-induced randomly oriented alpha during beta-to-alpha transformation and fine beta dendrites contribute to grain refinement in Ti4522-1B. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: A. Titanium aluminide, based on TiAl B. Phase identification B. Phase transformation C. Crystal growth D. Microstructure
1. Introduction Ti45Al2Mn2Nb1B (Ti4522-1B) is one of the first alloys with fine grains in as-cast state [1,2]. In the as-cast state the grain/lamellar colony size is in the range of 50e100 mm and there is, therefore, no need for any grain refinement heat treatment after casting. Grain refinement during solidification by addition of boron is effective in many TiAl alloys [3]. It was revealed by early studies that there is a switch on/off effect by boron addition for grain refinement with a minimum boron concentration, i.e. the critical boron concentration, of about 0.5e0.7 at%, depending on alloy composition. Below the critical concentration boron addition will not lead to grain refinement during solidification and interestingly there is no significant further grain refinement with further increasing boron addition above the critical level [4]. The outcome from recent work on grain refinement through low boron addition in beta-solidifying TiAl alloys suggests that such switch on/off effect should only exist in TiAl alloys with a peritectic reaction, i.e. with Al concentration of 45 at% and above since the grains were refined in some betasolidifying alloys with as low as only 0.1 at% boron [5,6]. A few universal grain refinement mechanisms have been proposed so far to account for the grain refinement observed in alloys like Ti45221B and none of them could explain many the features of grain
* Corresponding author. Tel.: þ44 1214147840. E-mail address:
[email protected] (D. Hu). 0966-9795/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2011.11.003
refinement satisfactorily. Those mechanisms are lack of support from clear experiment evidence [1,7e9]. Directional solidification technique has recently been used to study solidification process in TiAl alloys and has been proven powerful and effective [6,10e13]. Ti4522-1B was developed around 1990 and has been studied as a potential turbine blade material since then. However, the solidification process of Ti4522-1B has never been properly studied. Furthermore, the grain refinement mechanism in boron-containing alloys with a peritectic reaction during solidification has not been identified despite of some already proposed universal grain refinement mechanisms [7,8]. The purpose of this paper is to present the results from a deliberate study on solidification of Ti4522-1B and to throw new light into understanding the grain refinement mechanism in peritectic TiAl alloys with boron addition. 2. Experimental Unidirectional solidification was used in this study. The samples were prepared using the BridgmaneStockbarger technique in ACCESS Materials and Processes at a constant growth rate V of 8.33 105 ms1 and a constant temperature gradient in liquid at the solideliquid interface GL of 2 104 km1. Crucible tubes made of densely sintered yttria were used to minimise oxygen pickup during experiment. Solidification process was frozen by liquid metal quenching with a cooling rate of about 100 Cs1. Details of the setup of the furnace and other parameters can be found in ref.6.
D. Hu et al. / Intermetallics 22 (2012) 68e76
The Ti45Al2Mn2Nb1B feedstock was machined from a 200 mm diameter ingot and the boron concentration was 0.8 at%. A boronfree alloy, Ti45Al2Mn2Nb, was used as a comparison. Its feedstock was prepared from a plasma arc melted button ingot. The oxygen in the two alloys was about 500 wtppm. The Bridgman specimens were sliced longitudinally and polished using the common method form preparing SEM samples. The interested areas were analysed using scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD). 3. Results 3.1. General description of microstructures The scanning electron microscopy (SEM) images of the solidification zones (mushy zone) in the Bridgman specimens of Ti45221B and Ti4522 are shown in Fig. 1. They were taken in the backscatter electron (BSE) mode and thus the contrast was mainly compositional. Two significant differences can be seen by comparing the solidification zones of the two alloys. The first is the length of the solidification zone. It is about only 2.4 mm long in the Ti4522-1B whilst about 4 mm in Ti4522. The second is that the size of the dendrites, both in length and width, varies significantly in the two alloys, with those in Ti4522-1B being much finer than those in Ti4522. It seems both the differences can be attributed to the boron addition since the two Bridgman specimens were prepared under the same conditions. The white large particles are yttria from the contamination by the crucible material. Detailed microstructures of the solidification zone of Ti4522-1B are shown in Fig. 2. Fig. 2a was taken from the middle of the solidification zone (‘A’ in the Ti4522-1B montage in Fig. 1 indicates its position along the growth axis in the solidification zone) with the longitudinal direction of the Bridgman specimen lying vertically. It is featured with dendrites in different sizes. The coarse dendrites should have formed early during solidification and those fine dendrites should have formed after the coarse ones and are in between of them. Bright ridges can be seen in all the dendrites, especially in the coarse ones. Those bright ridges are the telling signs of the beta-to-alpha transformation. During beta-to-alpha transformation the beta stabilising elements, here the Nb, was expelled from the newly formed alpha to the remaining beta. Those areas are enriched with beta stabilising elements even after they eventually transformed into alpha entirely, which thus gives rise to bright contrast in BSE images. The bright ridges were formed during the final quenching of the Bridgman specimen preparation and their existence tells that those parts of dendrites were beta phase before quenching. Titanium boride precipitates are evident in the solidification zone. Those boride precipitates embedded within the dendrites are long and thick and with bright contrast.
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Some of them are parallel to the stems of the dendrites indicating that they should have formed during solidification process and should have co-grown with the dendrites. Such boride precipitates can also be observed in the area where dendrite formation just started from the liquid (the left side of the solidification zone in Fig. 1), which indicates that the solidification of the primary titanium boride and the beta phase could start at the same time in this alloy or the difference between them could be too small to be distinguished by this technique. Fine curvy titanium boride precipitates are found in the interdendritic areas and they were formed during quenching. The microstructure shown in Fig. 2b was taken from the area (its relatively longitudinal position in the mushy zone is marked by ‘B’ in the Ti4522-1B montage in Fig. 1) where solidification was almost completed. Still, within those dendrites are the bright ridges which were formed during quenching. Those bright ridges are mainly located in the stems of dendrites. Most part of the secondary dendritic arms (e.g. the arrowed area) is free from the bright ridges. It implies that they were alpha already before quenching and quenching only had the alpha phase transformed into alpha2 and retained (or transformed into fine gamma lamellae in the interdendritic areas). The existence of the alpha in the interdendritic areas suggests that the L þ b / a peritectic reaction should have occurred [11,12]. 3.2. Peritectic transformation According to the TieAl binary phase diagram there is a peritectic reaction/transformation, L þ b / a, in alloys with Al concentration of 44.8e49.4 at% [14]. Both Ti4522-1B and Ti4522 fall into this composition range. In fact the deviation from the binary phase diagram by additions of 2Mn2Nb(1B) has never been measured but it is assumed that the low alloying would not cause a large departure from the binary system. In this study the peritectic alpha phase was studied using electron back-scatter diffraction technique in the solidification zones of the Bridgman specimens. 3.2.1. In Ti4522 A BSE image showing the microstructure of an interdendritic area of the Ti4522 Bridgman specimen is shown in Fig. 3a. The analysed area is located in the middle of the Ti4522 montage in Fig. 1 and its relative position along the length of the mushy zone is marked with a ‘C’. The EBSD alpha2 orientation map of this area, Fig. 3c, shows that there are two large alpha2 grains, the red to the right and the purple to the left. In Fig. 3a they are separated by a thin dotted line. They were formed through the beta-to-alpha transformation during quenching as indicated by the bright ridges in them. From the centre of the interdendritic area to the stem of the dendrites several regions can be defined according to
Fig. 1. SEM BSE image montages showing the microstructures of the solidification zone in Ti4522-1B (top) and Ti4522 (bottom) Bridgman specimens. The withdraw direction is to the right.
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D. Hu et al. / Intermetallics 22 (2012) 68e76
Fig. 2. SEM BSE images showing the microstructures in the solidification zone of Ti4522-1B Bridgman specimen at the positions of (a) about 1/3 from the left and (b) about in the middle of the Fig. 1. The withdraw direction is downward.
the phase and morphology. The interdendritic areas are lamellar and the two double headed arrows show the lamellar interface trace directions in the two grains. Fig. 3b shows an enlarged image of the interdendritic area of grain II and the lamellar interface traces can be clearly seen. The lamellar region encompassed by the white dashed lines was formed by decomposition of peritectic alpha into alpha2 þ gamma lamellae and thus labelled as PAL. The regions outside the white solid lines are alpha2 formed via beta-to-alpha transformation during quenching and labelled as BA. The narrow belts between the white solid and dashed lines are the lamellar regions formed from the alpha phase BA which was formed during quenching from the beta dendrites. Such regions are labelled as BAL. The BAL regions contain bright ridges and the PAL does not, which suggests that the PAL regions would not have experienced a beta-to-alpha transformation during solidification and quenching. The EBSD gamma orientation map in Fig. 3d shows that the centres of the PAL regions are gamma lamellae due to the high concentration of Al in the interdendritic areas.
The orientation relationship between the grains and regions were determined and the results are shown in the pole figures in Fig. 4. The pole figure to the left shows the (0001) direction of the two alpha2 grains. The angle between them was measured from the pole figure as 60 . Apparently the two alpha2 grains are from the same beta dendrite. Detailed analysis of their orientation relationship proved that they were two Burgers alpha variants when formed. The method used for determination of Burgers alpha variants based on EBSD pole figures is given in Appendix I. The pole figures in the middle and to the right are the (111) directions of gamma phase from the two PAL regions. As mentioned earlier the lamellae are mainly gamma and the signals from the alpha2 lamellae, if there is any, were too weak to yield clear and definite spots in the pole figures. There are two distinguishable gamma twin variants in the gamma lamellae and each of them yield four spots for {111} planes. The superimposed spot, circled or squared, is from the lamellar interface plane. According to the Blackburn orientation relationship between alpha2 and gamma, it should be parallel to
Fig. 3. SEM BSE images showing the microstructure in the middle of the solidification zone of Ti4522 Bridgman specimen. (b) is an enlarged image of the interdendritic area to the left. (c) and (d) are the EBSD orientation maps of the alpha2 and gamma phases.
D. Hu et al. / Intermetallics 22 (2012) 68e76
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Fig. 4. Pole figures showing (0001) orientation of the two alpha2 grains and the interfacial {111} orientation of the interdendritic lamellar colonies. The lamellar interfaces are parallel to the basal planes of the alpha2 grain surrounding them.
the (0001) basal plane of the parent alpha grain within which the lamellae were formed. Indeed, the observed lamellar interface (111) is parallel to the (0001) alpha2 basal plane as shown in the pole figure. The PAL region was mainly transformed from the peritectic alpha and the lamellar interface (111) plane was the basal plane of the peritectic alpha. Since the surrounding alpha2 grain was transformed from the beta dendrite and has the Burgers OR with the prior beta dendrite, it is clear that the peritectic alpha had a Burgers OR with the beta dendrite on/into which it grew. 3.2.2. In Ti4522-1B An area in the middle of the solidification zone in Ti4522-1B Bridgman specimen was chosen for detailed analysis. The BSE image and the EBSD alpha2 orientation map of this area are shown in Fig. 5. The coloured areas in the orientation map represent the alpha2 grains and the black is for gamma. The dendrites in this area are up to about 100 mm in width and a few hundred microns in length. Upon quenching some parts of the beta dendrites transformed into alpha (alpha2 afterwards), which can be told from the bright ridges within the dendrites. In some parts of the dendrites there are no bright ridges. A few alpha2 grains are delineated out at the left part of the long dendrite at the bottom of the image where the white solid lines are the alpha2/gamma interface and the dashed lines separate the alpha2 grain within the dendrite. Those lines were drawn according to the alpha2 orientation map. All the numbered alpha2 grains except for No.9 have bright ridges inside. Alpha2 grain 9 and the area below grain 22 have no bright ridges at all although they were parts of the dendrite. Considering the phase transformation history it can be established that they were alpha2 whist other parts of the dendrite were beta before quenching. Those alpha areas before quenching should be the peritectic alpha or at least related to the peritectic alpha. The peritectic alpha, such as the area below grain 22 at the edge of the dendrite, had a high Al concentration which made it unstable during quenching and transformed into gamma.
The alpha2 orientation map shows an interesting feature. Several alpha2 grains surrounding the same interdendritic area have the same colour although they are located on different sides. Those alpha2 grains have the same orientation. Probably they are actually a single alpha2 grain and only shown in this way due to the intersection with sample surface. Underneath the sample surface they may still be connected to each other. Each group of parallel alpha2 grains are assigned with the same number and it can be seen such alpha2 grains are throughout the whole analysed area. The (0001) orientation of those alpha2 grains was analysed using EBSD data and it was found that those alpha2 grains are randomly oriented. The pole figure from the whole area is shown in Fig. 6a. To determine the orientation relationship between alpha2 grains in the same dendrite six alpha2 grains, numbered 9 and 20e24, were selected for further analysis. The (0001) pole figure of the whole dendrite is shown in Fig. 6b and the spots from the 6 grains are indicated. The angle between c-axes of any two grains was measured from the pole figure and the values are given in Table 1. The purpose of this exercise is to find out whether those alpha2 grains have Burgers orientation relationship with the prior beta dendrite. It can only be found out through the interrelationship between alpha2 grains since the beta phase is no longer there. From the Burgers orientation relationship between beta and alpha/ alpha2 it can be easily worked out that the angle between the caxes of any two alpha grains can only be 0, 60 or 90 and this is only the first criterion for Burgers alpha variants. There are only two pairs having the specific angle values, being 60.4 for pair 9e23 and 89.1 for pair 21e23. All the others deviate a lot from the specific angles. However, having the angles of 0, 60 or 90 between the c-axes is only necessary but sufficient for being Burgers alpha variants. The angles between the a-axes of two Burgers alpha variants must match certain values which are specified in Appendix I. The {11 2 0} pole figures from the two alpha2 grain pairs with the angle between (0001) orientation close to either 60 or 90 were extracted
Fig. 5. Detailed microstructure in the middle of the solidification zone of Ti4522-1B and its EBSD alpha2 orientation map.
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D. Hu et al. / Intermetallics 22 (2012) 68e76
Fig. 6. Alpha2 (0001) pole figures from (a) the whole area and (b) the selected grains. The {11 2 0} pole figures from alpha2 grain pairs (c) 9e23 and (d) 21e23 and the circled are from grain 23.
from the EBSD data and are shown in Fig. 6c and d. The angles between their a-axes are measured and given in Tables 2 and 3. None of them matches with those in the Appendix. Thus, it can be concluded that the selected alpha2 grains have no Burgers orientation relationship with the prior beta dendrite although they were formed within it. All the other numbered alpha2 grains in the whole area were analysed in the same way and a same conclusion was reached. 3.3. Titanium boride Titanium boride precipitates can be observed throughout the Ti4522-1B Bridgman specimen and their size and morphology vary with their thermal history. All the observed boride precipitates are the primary boride, i.e. formed in the liquid. The relatively straight long and coarse boride precipitates with grey contrast were formed during slow solidification of the specimen whilst those fine curvy ones in the interdendritic areas were formed during quenching. Those coarse long boride precipitates were identified using EBSD
technique as having a B27 crystal structure (orthorhombic with a ¼ 0.611 nm, b ¼ 0.305 nm and c ¼ 0.456 nm) with [010] being the longest direction. An orientation relationship was observed between some boride precipitates and some alpha2 grains next to them. The orientation relationship is <11 2 0>a2//[010]B27, (0001)a2//(001)B27. Fig. 7 shows an area selected from Fig. 5 and its corresponding EBSD alpha2 orientation map. Several long boride ribbons are highlighted by white arrows. The alpha2 grains numbered 1 to 4 in the orientation map have been found to have the above orientation relationship with the boride ribbons (represented by the white lines) within/next to them. Those alpha2 grains are believed to be inoculated by the boride during solidification or solid phase transformation. Out of the four boride ribbons two of them, 1 and 3, inoculated alpha grains within prior beta dendrites and the others, 2 and 4, inoculated alpha2 grains at both sides of the interdendritic area. Nevertheless the orientation relationship between alpha2 grains and boride is the same. The pole figures showing such an orientation relation are given in Fig. 8 and they are from alpha2 grain 1 and the boride ribbon next to it. The pole
Table 1 Angle between c-axes of any two selected alpha2 grains.
20 21 22 23 24
9
20
21
32.2 42.9 40.8 60.4 42.2
74.8 47.3 49.6 51.0
64.5 89.1 62.5
22
26.5 4.1
23
29.0
Table 2 Angles between the a-axes of alpha2 grains 9 and 23.
a1(23) a2(23) a3(23)
a1(9)
a2(9)
a3(9)
26.5 60.1 67.7
36.0 86.6 42.7
84.7 63.6 69.2
D. Hu et al. / Intermetallics 22 (2012) 68e76 Table 3 Angles between the a-axes of alpha2 grains 21 and 23.
a1(23) a2(23) a3(23)
a1(21)
a2(21)
a3(21)
28.3 45.2 79.1
42.0 53.8 80.4
83.3 83.8 89.6
figures show that the (0001) basal plane of that alpha2 grain is parallel to the (001) plane of the B27 boride and one of the {11 2 0} planes is parallel to (010) of B27 boride. The latter is equivalent to the two directions, one of the <11 2 0> and [010], being parallel to each other. 4. Discussion There are a few interesting new observations related to boron addition in this work. One is the limiting effect of boron on beta dendrite growth. This effect appeared in both longitudinal and latitudinal directions. The average width of the dendrites in the boron-containing alloy is only about a quarter of that in the boron-free alloy. Boron was found to be a strong growth limiter for the beta solid in liquid titanium due to its strong partitioning tendency to the liquid from the solid [15]. Its growth limiting effect is through building up a boron-enriched layer in the liquid titanium in front of the beta solid. Actually it is the second strongest growth limiter in the 30 elements studied by Bermingham et al, only being next to beryllium [15]. It seems that the growth limiting effect of boron in TiAl alloys is as strong as in titanium and titanium alloys. The length of the beta dendrites was also significantly reduced by boron addition. In the solidification zone of Ti4522-1B the length of beta dendrites is up to 400e500 mm whilst in Ti4522 it is at the order of millimetres. Such long dendrites are a common feature in other directly solidified TiAl without or only with very low level of boron despite of the variations in composition and experimental conditions [6,10e13]. By comparing the dendrite size and morphology it can be seen that in Ti4522-1B the continuous dendrite growth along the withdraw direction was frequently interrupted by new dendrites incidentally nucleated in the liquid front which blocked the growth of existing dendrites. Also the longitudinal direction of dendrites in Ti4522-1B is diversified. In view of the fact that many dendrites were found to have long coarse titanium boride ribbons along their stems, the diversity in dendrite growth direction could be resulted from the possibility of dendrites having been nucleated by existing boride precipitates as indicated by Fig. 2a. Apart from those mentioned above boron
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addition at 1% could have changed the width of the liquid þ beta phase field since the solidification zone is markedly shorter in Ti4522-1B than in Ti4522. Actually, with boron addition the L þ b phase field in boron-free alloys has been replaced by the L þ b þ TiB phase field [16e18]. Thus the change in the solidification zone is not unreasonable. This may account for the improved castability observed in boron-containing TiAl alloys. Certainly it merits further investigation. Peritectic reaction is a rarely touched topic in TiAl research but it was indeed observed in some directionally solidified high Nb, Ta-containing TiAl alloys [11,12]. The peritectic alpha was expected to have some orientation relationship with the beta dendrites since the latter in fact act as the substrates for peritectic alpha nucleation during peritectic reaction. Thus, the orientation of the beta dendrite crystals should be able to pass onto peritectic alpha. This rationale has been confirmed by the observation in Ti4522 and the Burgers orientation relationship is prevailing. The peritectic alpha was speculated by some researchers to have a grain refinement effect since it could have various orientations even within the same interdendritic area [12]. Indeed differently oriented peritectic alpha grains can form within the same interdendritic area and they can influence the orientation when the adjacent beta dendrite transforms into alpha but grain refinement in this way has not been observed yet. Moreover this is not an ideal grain refinement situation because those peritectic alpha grains are still the Burgers alpha variants from the same parent beta crystal. A larger population of Burgers alpha grains (transforming into textured lamellar colonies later) can only have very limited effect in improve tensile ductility despite of their fine grain size [19]. Also the number of variants is limited if no other factors, such as fast cooling and inoculants, come into play and the resulting microstructures could only be the coarse Widmanstätten microstructures as shown in the right end of the Ti4522 montage in Fig. 1. An ideally grain refined microstructure should be composed of not only fine but also randomly oriented grains. The situation in Ti4522-1B is entirely different. The prevailing character of the alpha2 grains in this boron-containing alloy is their random orientation. As shown in Fig. 3 the alpha grains in the long dendrite have no orientation relationship with their parent beta dendrite. For some grains it can be directly attributed to boride inoculation, as shown in Fig. 7, but for others, especially those close to the edges of beta dendrites the process is not that simple. The common characters of the numbered grains in Fig. 3 are that they were formed in the dendrites via beta-to-alpha solid phase transformation and they have the same orientation at different sides of the interdendritic areas. It is not surprising for
Fig. 7. A selected area from Fig. 5 showing some titanium boride precipitates and the alpha2 grains surrounding them, together with the EBSD alpha2 orientation map.
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D. Hu et al. / Intermetallics 22 (2012) 68e76
Fig. 8. Pole figures showing the (11 2 0)//(010), (0001)//(001) orientation relationship between B27 titanium boride precipitates and the alpha2 grains. They were taken from alpha2 grain no.1 and the long boride ribbon next to it.
the second character if the parallel alpha grains were formed around an interdendritic area between the secondary dendritic arms of the same dendrite or between two parallel dendrites. The same orientation of their parent beta phase can be passed onto them. However, in the case shown in Fig. 3 many parallel alpha2 grains are located around interdendritic areas between different dendrites, which means that their parent beta phase had different orientation. Thus, those alpha2 grains acquired orientation from something else rather than their parent phase. The fact of the parallel alpha grains being distributed around the interdendritic areas strongly suggests that they grew from something like a continuous thin layer coated on beta dendrites surfaces and that layer was a single crystal. The thin layer acted as a seed for the beta-to-alpha transformation, passing its orientation to the alpha formed within beta dendrites. The peritectic alpha is formed between the liquid and the beta dendrites as thin layers. If there are some boride precipitates at beta/liquid interfaces, the peritectic alpha might nucleate on boride and have an orientation defined by the boride rather than the beta dendrites. In fact, titanium boride precipitates are readily available in the interdendritic areas of Ti4522-1B. In this way the parallel alpha grains can form around interdendritic areas regardless of the prior beta dendrite orientation. This is why such parallel alpha2 grains were only found in Ti4522-1B not in Ti4522. It seems that the grain refinement in Ti4522-1B is a combined result of fine beta dendrites, boride inoculating alpha during solid phase transformation and more importantly formation of random oriented alpha around interdendritic areas probably though boride inoculating peritectic alpha.
5. Summary Boron addition at w1 at% to Ti4522 can significantly reduce the beta dendrite size during solidification. Primary titanium boride precipitates were observed in the interdendritic areas in the solidification zone and in the dendrites in Ti4522-1B. Titanium boride precipitates were found to inoculate alpha during beta-toalpha solid phase transformation and there is an orientation relationship between the B27 TiB and inoculated alpha/alpha2 which is <11 2 0>a2//[010]B27, (0001)a2//(001)B27. In Ti4522 the Burgers orientation relationship is obeyed between the peritectic alpha and beta dendrites whilst no orientation relationship was found between the two phases in Ti4522-1B. The loss of Burgers OR was attributed to the process that the peritectic alpha was inoculated by the boride precipitates at beta/liquid interfaces during peritectic reaction and the misoriented peritectic alpha grew into beta dendrites during further cooling. Acknowledgement The financial support from the EPSRC through the Strategic Partnership is gratefully acknowledged. Appendix I. The method of determining Burgers alpha/alpha2 variants During solid phase transformation between hcp and bcc phases the orientation relationship should be (0001)hcp//{110}bcc
D. Hu et al. / Intermetallics 22 (2012) 68e76
and <11 2 0>hcp//<111>bcc. There could be 12 hcp variants at maximum when the bcc phase transforms into the hcp phase with two on each {110} bcc planes and six {110} planes altogether. When the hcp variants and their parent bcc phase coexist, direct measure can be carried out. However, direct measurement is impossible if all the bcc phase transforms into the hcp phase. In this case the only way is to analyse the interrelationship between the hcp grains to ascertain whether they are Burgers variants. The definition of the Burgers variants is that the hcp crystals are from the same bcc parent grain and obey the Burgers OR.
For 0º-related hcp variants (º)
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The first criterion for being Burgers variants is that the angle between the c-axes of the hcp crystals must be 0, 60 or 90 , which was derived from the angles between the {110} plane in the bcc phase. The angles can easily be measured from the (0001) pole figure generated from the EBSD data. The second criterion is that for any two hcp variants their a-axes must form certain angles which is defined by the second part of the Burgers OR, <11 2 0>hcp// <111>bcc. The value of the angles can be expressed using a 3 3 matrix. All the possible a-axes angle matrices are given below. During calculation of the angle between two axes the supplementary angle value was used if it was greater than 90 .
For 60º-related hcp variants (º) (1)
a11
a12
a13
a11
a12
a13
a21
10.5
70.5
49.5
a21
0
60
60
a22
49.5
10.5
70.5
a22
60
51.3
82.3
a23
70.5
49.5
10.5
a23
60
82.3
51.3
a11
a12
a13
a21
10.5
49.5
70.5
(2) For 90º-related hcp variants (º)
a11
a12
a13
a22
55.2
89.8
54.9
a23
65.6
49.1
76.1
a11
a12
a13
a21
18.2
44.9
76.1
a22
44.9
82.3
54.9
a23
76.1
54.9
70.5
a21
7.4
65.4
54.9
a22
65.4
80.0
76.5
a23
54.9
76.5
70.5
(3)
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D. Hu et al. / Intermetallics 22 (2012) 68e76
Example: Alpha2 grains I and II in Fig. 3a have a 60 angle between their c-axes. Their {11 2 0} pole figure is shown in Fig. A1 and the measured angles are given in Table A1. It can be seen that the measured angle matrix matches one of those for 60 -related hcp variants. Therefore, alpha2 grains I and II are Burgers variants.
Table A1 The angles between the a-axes measured from Fig. A1.
a21 a22 a23
a11
a12
a13
0 59.4 59.9
60.8 51.6 82.4
58.6 83.7 50.2
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
Fig. A1. {11 2 0} pole figure from alpha2 grains I and II in Fig. 3.
[18] [19]
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