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A new precipitate phase in a TiNiHf high temperature shape memory alloy
PII:
Acta mater. Vol. 46, No. 1, pp. 273±281, 1998 # 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00187-0
A NEW PRECIPITATE PHASE IN A TiNiHf HIGH TEMPERATURE SHAPE MEMORY ALLOY X. D. HAN1,2{, R. WANG1,3, Z. ZHANG1 and D. Z. YANG2 Beijing Laboratory of Electron Microscopy, Chinese Academy of Sciences, P.O. Box 2724, Beijing 100080, 2Department of Materials Engineering, Dalian University of Technology, Dalian 116024 and 3 Department of Physics, Wuhan University, Wuhan, 430072 P.R. China 1
(Received 19 December 1995; accepted 19 May 1997) AbstractÐA precipitate phase in a Ti36.5Ni48.5Hf15 high temperature shape memory alloy aged at 873K for 150 h has been studied by transmission electron microscopy (TEM) and high resolution electron microscopy (HREM). The precipitate phase of the approximate composition of (Ti0.6Hf0.4)Ni is identi®ed to be face-centered orthorhombic lattice with lattice parameters A = 1.287 nm, B = 0.874 nm and C = 2.622 nm and space group F2/d 2/d 2/d.. The lattice correspondence between the precipitate phase and B2 matrix is determined to be A = 4.17c, B = 2(a + b) and C = 6(ÿa + b), where A, B and C are the basis vectors of the precipitate phase and a, b and c are those of the B2 matrix. The precipitate has an oblate spindle like shape with its habit plane being the (100)Pk(001)B plane. Six orientation variants and translation domains have been observed. These variants are related by those symmetry operations which belong to the B2 matrix but are lost in the precipitate phase. # 1997 Acta Metallurgica Inc.
1. INTRODUCTION
TiNi shape memory alloy (SMA) is one of the best functional materials showing a good shape memory eect (SME). The precipitate phase in TiNi SMA strongly aects the SME and mechanical properties of the alloy and one observed the following precipitation sequence in Ni-rich near equiatomic TiNi binary alloys: b parentphase 4 Ti3Ni4 4Ti2Ni3 4TiNi3 when the aging temperature and time are increased [1±3]. Recently, researchers have paid a great deal of attention to studies of high temperature SMA. Among them TiNiHf is a new type which shows reversible martensitic transformations at the higher temperature range of 470±570 K [4, 5]. In our previous paper, the structure and substructure of the martensite and its transformations in a Ti36.5Ni48.5Hf15 SMA were investigated in detail [6]. Since the precipitation behaviour during aging is very important, we report in the present paper a new precipitate phase found in this TiNiHf SMA after aging, including its crystal lattice, space group, lattice correspondence with B2 matrix and variant relationships.
2. EXPERIMENTAL PROCEDURE
The electrolytic nickel and sponge titanium and hafnium was arc-melted four times. Ingots of the {To whom all correspondence should be addressed at: Department of Physics & Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong. 273
composition Ti36.5Ni48.5Hf15(at.%) were heat-treated at 1273 K for 10 h under vacuum conditions followed by forging at 1273 K. After forging the ingots were annealed in vacuum at 1273 K for 1 h and aged at 873 K for 150 h. Then they were sparkcut into plates of 2 mm thickness. To prepare transmission electron microscopy (TEM) foils, these plates were mechanically polished to 60 mm thickness and then ion-milled. TEM observation was carried out on a Philips EM 420 microscope. Specimens for high resolution electron microscopy (HREM) were the TEM foils which had been heated at 773 K for 5 h in the heating stage of the microscope. The HREM experiment was carried out by using a JEOL 2010 microscope with a point resolution of 0.197 nm.
3. RESULTS
3.1. Crystal lattice of the precipitate After aging at 873 K for 150 h there are many small oblate spindle like precipitates distributed in the matrix as shown in Fig. 1. These precipitates are too small to make a selected-area electron diffraction (SAED) study from a single precipitate. Fortunately the precipitates possess a ®xed orientation relationship with the B2 type matrix, so a series of SAED patterns (EDPs) of the precipitate phase can be easily obtained together with the EDPs of the B2 matrix. Figure 2 shows a set of EDPs covering the whole orientation triangle of the precipitate phase obtained by tilting the foils around the reciprocal vectors [001]*Pk[-1 1 0]*B
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Fig. 1. General morphology of the precipitates in the B2 type matrix.
[Fig. 2(a)±(e)], [0 -1 0]*Pk[1 -1 0]*B [Fig. 2(a), (f), (g) and (h)] and [100]*Pk[001]B [Fig. 2(h), (i), (j), (k) and (e)], respectively. The experimental tilting angles jexp between neighboring EDPs are indicated in the ®gure. These EDPs can be indexed according to the B2 type matrix with a lattice parameter of a = 0.309 nm [6] and an orthorhombic phase with the lattice parameters A = 1.287 nm, B = 0.874 nm and C = 2.622 nm as shown in Fig. 3(a)±(k) arranged according to Fig. 2(a)±(k). In Fig. 3 the zone axis indices [uvw]B and re¯ection indices (hkl)B are relevant to the B2 matrix and other indices are relevant to orthorhombic precipitate. All the experimental dhkl values of the lattice plane distances obtained from the distances Rhkl between the (hkl) re¯ection spots and the central spot in EDPs are in good agreement with the calculated ones. Moreover, as can be seen from Table 1, the experimental angles between two zone axes [U1V1W1] and [U2V2W2] are also in good agreement with the calculated ones which are indicated in Fig. 3. From the EDPs shown in Fig. 2 the reciprocal lattice of the precipitate is reconstructed as shown in Fig. 4(a) which contains 4 4 12 reciprocal unit cells. A part of Fig. 4(a) containing 2 2 2 reciprocal unit cells is selected and shown in Fig. 4(b) from which the following re¯ection conditions can be deduced: h, k, l all odd or h, k, l all even and h + k + l = 4n Table 1. Experimental and calculated angles jexp and jcal between zone axes [U1V1W1] and [U2V2W2] [U1V1W1] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [0 0 -1] [0 0 -1] [0 0 -1] [0 0 -1]
[U2V2W2]
jexp (8)
jcal (8)
[-3 -1 0] [-1 -1 0] [-1 -2 0] [-1 -3 0] [-2 0 -1] [-1 0 -1] [-1 0 -2] [0 -1 -3] [0 -1 -1] [0 -3 -1] [0 -9 -1]
14.1 37.0 55.2 64.4 47.3 64.1 76.2 6.1 18.2 46.2 72.1
12.7 34.2 53.6 63.9 45.5 63.9 76.2 6.3 18.4 45.0 71.6
with n an integer. From this re¯ection condition the space group of the precipitate can be determined as being F 2/d 2/d 2/d. Some EDPs in Fig. 2 need to be interpreted in detail. Figure 2(a) seems to possess a fourfold symmetry but in fact it comes from two orthogonal variants of the precipitates in addition to the spots belonging to [0 0 -1]B zone axis and only the spots belonging to the variant 1 were indexed in Fig. 3(a). Other spots in Fig. 2(a) may be obtained by a fourfold rotation from those of variant 1. Similarly, the [-1 -3 0]P zone axis EDP in Fig. 2(d) is superposed by the [-1 0 -1]P EDP and Fig. 2(k) can be explained as a [0 -9 -1]P EDP superposed by the [0 -1 -1]P EDP, and we only indexed the spots belonging to the [-1 -3 0]P and [0 -9 -1]PEDPs in Fig. 3. 3.2. Orientation relationship and lattice correspondence between the precipitate and B2 matrix In Fig. 2 each EDP of the precipitate is superposed by an EDP of the B2 type matrix; hence it is easy to deduce the orientation relationships between the precipitate and the B2 matrix as follows: 100P k 001B2 010P k 110B2 001P k ÿ110B2
1
which is schematically shown in Fig. 4. Moreover, by measuring the distances from the re¯ection spots of the precipitate and the B2 matrix to the central spot we obtain the following lattice correspondence between the precipitate and the B2 matrix: A 0:24c B 1=4 a b C 1=12 ÿa b
2
where A*, B* and C* are reciprocal basis vectors of the precipitate and a*, b* and c* are those of the B2 matrix. By using the matrix notation the correspondence (2) may be expressed as: 0 1 0 1 A a @ B A Q @ b A 3 C c with
0
0 Q @ 1=4 ÿ1=12
1 0 0:24 1=4 0 A: 1=12 0
4
From (3) it is easy to deduce the relationships for the basis vectors, zone axis indices and lattice plane indices as follows: 0 1 0 1 A a @ B A Qÿ1 @ b A 5 C c
HAN et al.: TiNiHfSMA
275
Fig. 2. Experimental EDPs obtained by tilting the specimen around the [001]*Pk[-1 1 0]*B [(a)±(e)], [0 -1 0]*Pk[-1 -1 0]*B [(a), (f), (g) and (h)] and [100]*Pk[001]*B [(h), (i), (j), (k) and (e)]. The experimental tilting angles jexp are indicated.
0
1 0 1 U u ÿ1 @V AQ @vA W w 1 0 1 H h @ K A Qÿ1 @ k A L l
6
0
7
where the capital and lower case letters are related
to the precipitate and B2 matrix, respectively, and Qÿ1 is the transposed inverse matrix of Q: 0 1 0 0 4:17 ÿ1 @ 2 2 0 A: 8 Q ÿ6 6 0 Noticing that a = b = c = 0.309 nm [6] we deduce the lattice parameters of the precipitate from equations (5) and (8) as follows:
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Fig. 3. Schematical indexing of the EDPs shown in Fig. 2. The zone axis indices [uvw]B and re¯ection indices (hkl)B are relevant to the B2 type matrix, and other indices are relevant to one variant of the face-centered orthorhombic precipitates. The calculated angles jcal between two zone axes [U1V1W1]P and [U2V 2W 2]P are indicated. The symbol indicates extinct re¯ections which appear by multiple diraction.
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Fig. 4. Schematic diagram of the reciprocal lattice of the precipitate reconstructed from Fig. 2. (a) A block sustained by g(400)=g(001)B, g(040)=g(110)B and g(0 0 12)=g(1 -1 0)B; (b) a block sustained by g(200), g(020) and g(002) showing the re¯ection conditions.
A 1:287 nm B 0:874 nm C 2:622 nm: Table 2 lists the correspondence of the zone axes and the re¯ection indices obtained from equations (6) and (7). The indices are indicated in Fig. 3. Because the minor dierence between the lattice constant A for the precipitate and 4a for the B2 matrix, some zone axes of the precipitate, such as [1 -1 0]P, [-1 -2 0]P, [-1 -3 0]P, [-2 0 -1]P and [-1 0 -1]P are not exactly parallel to the relevant zone axes of the matrix, hence the calculated angles jcal between the two zone axes of the precipitate are not always equal to the corresponding calculated angles of the B2 matrix and we indicate the latter in the parentheses in Fig. 3.
Table 2. Correspondences between the zone axis indices [UVW]P and [uvw]B and between the re¯ection indices [HKL]P and [hkl]B for the precipitate (P) and B2 type matrix (B) [UVW]P 0 -3 1 0 -3 -1 -1 0 0 0 -1 0 0 0 -1 -1 -3 0 -1 -2 0 -1 -1 0 -2 0 -1 -1 0 -1 0 -1 -1 0 -9 -1
[uvw]B -1 0 0 0 -1 0 0 0 -1 -1 -1 0 1 -1 0 -6 -6 -4.17 -4 -4 -4.17 -2 -2 -4.17 3 -3 -4.17 6 -6 -4.17 1 -2 0 -1 -2 0
(HKL)
P
0 0 12 0 -4 0 0 -2 6 4 -4 0 4 -2 6 12 -4 0 400 -12 0 24 -12 0 12 -4 0 0 0 -6 6 0 -2 6 0 -2 18 4 -4 12
(hkl)B -1 1 0 -1 -1 0 -1 0 0 -1 -1 0.96 -1 0 0.96 -1 -1 2.88 0 0 0.96 -2 2 -2.88 -1 1 -2.88 0 0 -0.96 -2 -1 0 -1 0 0 -2 1 0 -2 0 0.96
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Table 3. Lattice correspondence variants and habit plane variants of the precipitates
Variant AP [100]P
BP [010]P
CP [001]P
Habit plane (100)P
1 2 3 4 5 6
[110]B2 [1 -1 0]B2 [101]B2 [-1 0 1]B2 [011]B2 [0 1 -1]B2
[-1 1 0]B2 [110]B2 [1 0 ÿ1]B2 [101]B2 [0 -1 1]B2 [011]B2
(001)B2 (001)B2 (010)B2 (010)B2 (100)B2 (100)B2
[001]B2 [001]B2 [010]B2 [010]B2 [100]B2 [100]B2
Long axis direction [100]P [-1 1 0]B2 [110]B2 [1 0 ÿ1]B2 [101]B2 [0 -1 1]B2 [011]B2
3.3. Variants of the precipitate Considering the symmetry of the B2 parent phase, there may exist six orientation variants of the precipitate. The lattice correspondence between these six variants and the B2 parent phase are listed in Table 3. The variants 1 and 2 are related by fourfold rotation around the [001]B2 axis, so do the variants 3 and 4 (around the [010]B2 axis), and the variants 5 and 6 (around the [100]B2 axis). The thin precipitates 1 and 2 indicated in Fig. 1 possess such a relationship. Moreover, the variants 1, 3, 5 are
Fig. 5. (a) Bright ®eld image and (b) EDP when the incident beam is parallel to the [111]B2 axis showing three variants of the precipitates related of threefold rotation around the [111]B2 axis.
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279
Fig. 6. HREM image (a) and the corresponding EDP (b) along the [100]Pk[001]B direction; (c) is the schematic EDP from variant 1.
related by threefold rotations around the [111]B2 axis and so do the variants 2, 4 and 6. Figure 5(a) and (b) shows bright-®eld images with the incidence of [111]B2 and the corresponding [111]B2 zone axis EDP, respectively. By comparing Fig. 5(b) with Fig. 2(c) one can conclude that Fig. 2(c) is a [-1 -2 0]P EDP from a single variant of the precipitate and Fig. 5(b) is composite EDPs from three variants related by threefold rotation around the [111]B2 axis. The three variants are clearly seen in Fig. 5(a). 3.4. High resolution electron microscopy observation HREM observation along the main zone axes of the precipitate and the B2 matrix has revealed some structural detail of the precipitate. Figure 6(a) shows a HREM image along the [100]Pk[001]B direction as indicated by the EDP [Fig.6(b)]. As explained in Section 3.1, the EDP shown in Fig. 6(b) consists of a [0 0 -1]B EDP and two [-1 0 0]P EDPs from the variants 1 and 2 of the precipitate, related by a fourfold rotation around the [001]B direction. Figure 6(c) shows a schematic [-1 0 0]P EDP from variant 1. In Fig. 6(a), the (004)P, (0 -2 2)P and (022)P lattice planes in variant 1 are marked which correspond to the re¯ection spots (004), (0 -2 2) and (022), respectively, in Fig. 6(c). In Fig. 6(a) variant 2 is also marked which is related to variant 1 by a fourfold rotation. Figure 7 shows a HREM image and the corresponding EDP along the [010]P direction which is a little deviated from the [110]B direction. Thus, while the lattice image of the precipitate with its short direction parallel to the [100]P direction can be
clearly seen, the B2 matrix is not correctly orientated. In the precipitate, the (004)P, (202)P and (-2 0 2)P lattice planes are marked which correspond to spots (004), (202) and (-2 0 2), respectively, in the EDP. Figure 8 shows a HREM image and the corresponding EDP along the [120]Pk[111]B axis. In Fig. 8 the (004)P lattice plane is marked which is perpendicular to the long axis direction of variant 1. In Fig. 8 variant 3 is related to variant 1 by a threefold rotation around the [111]B axis, and variant 1' is parallel to variant 1 but has a translation of 0.218 nm along the [001]P direction, i.e. a translation of the (-1 1 0)B plane distance. The long axis direction of the precipitate variants are indicated in Figs 7 and 8, respectively. From Figs 6±8, we know that all the lattice planes relevant to the precipitate have been con®rmed by the HREM observation.
3.5. The composition of the precipitate Quantitative element composition analysis was carried out using an Energy Dispersive X-ray (EDX) spectroscope of the Link System attached at a JEOL JEM-100 CX (II) electron microscope. The spot size was about 30 nm. The results indicate a Hf element enrichment in the precipitates compared with the matrix. Knowing that the composition of the matrix is Ti36.5Ni48.5Hf15, the composition of the precipitates was determined to be nearly (Ti0.6Hf0.4)Ni.
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Fig. 7. HREM image and the corresponding EDP along the [110]P direction. The long axis direction of variants is indicated by double arrows and L.A.; the short axis direction of the precipitates is indicated by short double arrows and S.A..
Fig. 8. HREM image and the corresponding EDP along the [120]Pk[111]B direction. The long axis direction of variant 3 is indicated by double arrows and L.A.; the long axes of variants 1' and 3 are indicated by single arrows, respectively (also by L.A.).
HAN et al.: TiNiHfSMA
3.6. Habit plane of the precipitate By observing the shapes of the (Ti0.6Hf0.4)Ni precipitates imaged along the h100iB, h111iB and h110iB direction we can conclude that most of the precipitates possess an oblate spindle shape with their long axes parallel to the [001]Pk[ÿ1 1 0]B direction and their ¯at planes parallel to the (100)Pk(001)B plane. HREM observation as shown in Figs 7 and 8, which show that the long axis of the precipitate is parallel to the [001]Pk[-1 1 0]B direction and the short axis of the precipitate is nearly parallel to the [100]Pk[001]B direction, con®rmed the conclusion. The (100)P plane of the precipitate is coherent with the (001)B plane and hence may be identi®ed as the habit plane. Thus the present study revealed that the habit plane variants of the (Ti0.6Hf0.4)Ni precipitate are the same as the lattice correspondence variants and they are all listed in Table 3.
4. DISCUSSION AND CONCLUSIONS
It is well known that for the Ti-rich TiNi SMA there exists the precipitation sequence b0(B2 type matrix) 4 Ti3Ni4 4Ti2Ni3 4TiNi3 with increase in the aging temperature and time [1]. According to the binary phase diagrams of Hf±Ni, Hf±Ti and Ti±Ni we know that Ti and Hf form continuous solid solutions and the stable phases at the Ti- or Hf-rich side are Ti2Ni or Hf2Ni. However, Ti2Ni possesses the E93 structure type while Hf2Ni the C16 structure type, hence they cannot form continuous (Ti,Hf)2Ni solid solutions. Similarly, the present study shows that (Ti0.6Hf0.4)Ni possesses a dierent structure type compared with the TiNi phase. Since the (Ti0.6Hf0.4)Ni phase has a rather large unit cell, it is dicult to provide an atomic structure model from the SAED and HREM studies. However, some conclusions can be drawn from the present study. 1. When the Ti36.5Ni48.5Hf15 SMA is aged at 873 K for 150 h, precipitates of composition (Ti0.6Hf0.4)Ni form.
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2. The precipitate possesses a face-centered orthorhombic lattice with lattice parameters of A = 1.287 nm, B = 0.874 nm and C = 2.622 nm and a space group of F 2/d 2/d 2/d (No.70). 3. The precipitate is intimately related to the B2 type matrix with the following lattice correspondence: A = 4.17c, B = 2(a + b) and C = 6(ÿa + b) where A, B and C are the basis vectors of the precipitate and a, b and c are those of the B2 matrix. The precipitate may also be described as a three-dimensional modulated B2 structure, i.e. commensurably modulated in the (001)B plane and incommensurably modulated along the [001]B direction. 4. The shape of the precipitate is oblate spindle like with a habit plane of (100)Pk(001)B and a long axis of [001]Bk[-1 1 0]B. This is consistent with the fact that the lattice of the precipitate is matched very well in the (100)Pk(001)B plane but with a 4% dierence along the [100]Pk[001]B direction. 5. There are six orientationally dierent variants as listed in Table 3. These variants are related by point operations 4h001iB and 3h111iB. In addition, translation domains have also been observed. These variants and domains are related by those symmetry operations which belong to the B2 matrix but are lost in the precipitate phase. AcknowledgementsÐThis work was supported by the National Natural Science Foundation of China. REFERENCES 1. Nishida, M., Wayman, C. M. and Honma, T., Metall. Trans. A,, 1986, 17A, 1505. 2. Miyazaki, S. and Otsuka, K., Met. Trans. A,, 1986, 17A, 53. 3. Nishida, M., Wayman, C. M. and Honma, T., Script Metall., 1984, 18, 1389. 4. Muder, J. H., Mass, J. H. and Beyer, J. Paper presented at ICOMAT-92. California, 1992, p. 869. 5. Han, X. D., Zou, W. H., Jin, S., Zang, Z. and Yang, D. Z., Scripta metall. mater., 1995, 32, 1441. 6. Han, X. D., Zou, W. H., Wang, R., Zhang, Z. and Yang, D. Z., Acta mater., 1996, 44, 3721.
Acta mater. Vol. 46, No. 1, pp. 273±281, 1998 # 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00187-0
A NEW PRECIPITATE PHASE IN A TiNiHf HIGH TEMPERATURE SHAPE MEMORY ALLOY X. D. HAN1,2{, R. WANG1,3, Z. ZHANG1 and D. Z. YANG2 Beijing Laboratory of Electron Microscopy, Chinese Academy of Sciences, P.O. Box 2724, Beijing 100080, 2Department of Materials Engineering, Dalian University of Technology, Dalian 116024 and 3 Department of Physics, Wuhan University, Wuhan, 430072 P.R. China 1
(Received 19 December 1995; accepted 19 May 1997) AbstractÐA precipitate phase in a Ti36.5Ni48.5Hf15 high temperature shape memory alloy aged at 873K for 150 h has been studied by transmission electron microscopy (TEM) and high resolution electron microscopy (HREM). The precipitate phase of the approximate composition of (Ti0.6Hf0.4)Ni is identi®ed to be face-centered orthorhombic lattice with lattice parameters A = 1.287 nm, B = 0.874 nm and C = 2.622 nm and space group F2/d 2/d 2/d.. The lattice correspondence between the precipitate phase and B2 matrix is determined to be A = 4.17c, B = 2(a + b) and C = 6(ÿa + b), where A, B and C are the basis vectors of the precipitate phase and a, b and c are those of the B2 matrix. The precipitate has an oblate spindle like shape with its habit plane being the (100)Pk(001)B plane. Six orientation variants and translation domains have been observed. These variants are related by those symmetry operations which belong to the B2 matrix but are lost in the precipitate phase. # 1997 Acta Metallurgica Inc.
1. INTRODUCTION
TiNi shape memory alloy (SMA) is one of the best functional materials showing a good shape memory eect (SME). The precipitate phase in TiNi SMA strongly aects the SME and mechanical properties of the alloy and one observed the following precipitation sequence in Ni-rich near equiatomic TiNi binary alloys: b parentphase 4 Ti3Ni4 4Ti2Ni3 4TiNi3 when the aging temperature and time are increased [1±3]. Recently, researchers have paid a great deal of attention to studies of high temperature SMA. Among them TiNiHf is a new type which shows reversible martensitic transformations at the higher temperature range of 470±570 K [4, 5]. In our previous paper, the structure and substructure of the martensite and its transformations in a Ti36.5Ni48.5Hf15 SMA were investigated in detail [6]. Since the precipitation behaviour during aging is very important, we report in the present paper a new precipitate phase found in this TiNiHf SMA after aging, including its crystal lattice, space group, lattice correspondence with B2 matrix and variant relationships.
2. EXPERIMENTAL PROCEDURE
The electrolytic nickel and sponge titanium and hafnium was arc-melted four times. Ingots of the {To whom all correspondence should be addressed at: Department of Physics & Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong. 273
composition Ti36.5Ni48.5Hf15(at.%) were heat-treated at 1273 K for 10 h under vacuum conditions followed by forging at 1273 K. After forging the ingots were annealed in vacuum at 1273 K for 1 h and aged at 873 K for 150 h. Then they were sparkcut into plates of 2 mm thickness. To prepare transmission electron microscopy (TEM) foils, these plates were mechanically polished to 60 mm thickness and then ion-milled. TEM observation was carried out on a Philips EM 420 microscope. Specimens for high resolution electron microscopy (HREM) were the TEM foils which had been heated at 773 K for 5 h in the heating stage of the microscope. The HREM experiment was carried out by using a JEOL 2010 microscope with a point resolution of 0.197 nm.
3. RESULTS
3.1. Crystal lattice of the precipitate After aging at 873 K for 150 h there are many small oblate spindle like precipitates distributed in the matrix as shown in Fig. 1. These precipitates are too small to make a selected-area electron diffraction (SAED) study from a single precipitate. Fortunately the precipitates possess a ®xed orientation relationship with the B2 type matrix, so a series of SAED patterns (EDPs) of the precipitate phase can be easily obtained together with the EDPs of the B2 matrix. Figure 2 shows a set of EDPs covering the whole orientation triangle of the precipitate phase obtained by tilting the foils around the reciprocal vectors [001]*Pk[-1 1 0]*B
274
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Fig. 1. General morphology of the precipitates in the B2 type matrix.
[Fig. 2(a)±(e)], [0 -1 0]*Pk[1 -1 0]*B [Fig. 2(a), (f), (g) and (h)] and [100]*Pk[001]B [Fig. 2(h), (i), (j), (k) and (e)], respectively. The experimental tilting angles jexp between neighboring EDPs are indicated in the ®gure. These EDPs can be indexed according to the B2 type matrix with a lattice parameter of a = 0.309 nm [6] and an orthorhombic phase with the lattice parameters A = 1.287 nm, B = 0.874 nm and C = 2.622 nm as shown in Fig. 3(a)±(k) arranged according to Fig. 2(a)±(k). In Fig. 3 the zone axis indices [uvw]B and re¯ection indices (hkl)B are relevant to the B2 matrix and other indices are relevant to orthorhombic precipitate. All the experimental dhkl values of the lattice plane distances obtained from the distances Rhkl between the (hkl) re¯ection spots and the central spot in EDPs are in good agreement with the calculated ones. Moreover, as can be seen from Table 1, the experimental angles between two zone axes [U1V1W1] and [U2V2W2] are also in good agreement with the calculated ones which are indicated in Fig. 3. From the EDPs shown in Fig. 2 the reciprocal lattice of the precipitate is reconstructed as shown in Fig. 4(a) which contains 4 4 12 reciprocal unit cells. A part of Fig. 4(a) containing 2 2 2 reciprocal unit cells is selected and shown in Fig. 4(b) from which the following re¯ection conditions can be deduced: h, k, l all odd or h, k, l all even and h + k + l = 4n Table 1. Experimental and calculated angles jexp and jcal between zone axes [U1V1W1] and [U2V2W2] [U1V1W1] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [-1 0 0] [0 0 -1] [0 0 -1] [0 0 -1] [0 0 -1]
[U2V2W2]
jexp (8)
jcal (8)
[-3 -1 0] [-1 -1 0] [-1 -2 0] [-1 -3 0] [-2 0 -1] [-1 0 -1] [-1 0 -2] [0 -1 -3] [0 -1 -1] [0 -3 -1] [0 -9 -1]
14.1 37.0 55.2 64.4 47.3 64.1 76.2 6.1 18.2 46.2 72.1
12.7 34.2 53.6 63.9 45.5 63.9 76.2 6.3 18.4 45.0 71.6
with n an integer. From this re¯ection condition the space group of the precipitate can be determined as being F 2/d 2/d 2/d. Some EDPs in Fig. 2 need to be interpreted in detail. Figure 2(a) seems to possess a fourfold symmetry but in fact it comes from two orthogonal variants of the precipitates in addition to the spots belonging to [0 0 -1]B zone axis and only the spots belonging to the variant 1 were indexed in Fig. 3(a). Other spots in Fig. 2(a) may be obtained by a fourfold rotation from those of variant 1. Similarly, the [-1 -3 0]P zone axis EDP in Fig. 2(d) is superposed by the [-1 0 -1]P EDP and Fig. 2(k) can be explained as a [0 -9 -1]P EDP superposed by the [0 -1 -1]P EDP, and we only indexed the spots belonging to the [-1 -3 0]P and [0 -9 -1]PEDPs in Fig. 3. 3.2. Orientation relationship and lattice correspondence between the precipitate and B2 matrix In Fig. 2 each EDP of the precipitate is superposed by an EDP of the B2 type matrix; hence it is easy to deduce the orientation relationships between the precipitate and the B2 matrix as follows: 100P k 001B2 010P k 110B2 001P k ÿ110B2
1
which is schematically shown in Fig. 4. Moreover, by measuring the distances from the re¯ection spots of the precipitate and the B2 matrix to the central spot we obtain the following lattice correspondence between the precipitate and the B2 matrix: A 0:24c B 1=4 a b C 1=12 ÿa b
2
where A*, B* and C* are reciprocal basis vectors of the precipitate and a*, b* and c* are those of the B2 matrix. By using the matrix notation the correspondence (2) may be expressed as: 0 1 0 1 A a @ B A Q @ b A 3 C c with
0
0 Q @ 1=4 ÿ1=12
1 0 0:24 1=4 0 A: 1=12 0
4
From (3) it is easy to deduce the relationships for the basis vectors, zone axis indices and lattice plane indices as follows: 0 1 0 1 A a @ B A Qÿ1 @ b A 5 C c
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Fig. 2. Experimental EDPs obtained by tilting the specimen around the [001]*Pk[-1 1 0]*B [(a)±(e)], [0 -1 0]*Pk[-1 -1 0]*B [(a), (f), (g) and (h)] and [100]*Pk[001]*B [(h), (i), (j), (k) and (e)]. The experimental tilting angles jexp are indicated.
0
1 0 1 U u ÿ1 @V AQ @vA W w 1 0 1 H h @ K A Qÿ1 @ k A L l
6
0
7
where the capital and lower case letters are related
to the precipitate and B2 matrix, respectively, and Qÿ1 is the transposed inverse matrix of Q: 0 1 0 0 4:17 ÿ1 @ 2 2 0 A: 8 Q ÿ6 6 0 Noticing that a = b = c = 0.309 nm [6] we deduce the lattice parameters of the precipitate from equations (5) and (8) as follows:
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Fig. 3. Schematical indexing of the EDPs shown in Fig. 2. The zone axis indices [uvw]B and re¯ection indices (hkl)B are relevant to the B2 type matrix, and other indices are relevant to one variant of the face-centered orthorhombic precipitates. The calculated angles jcal between two zone axes [U1V1W1]P and [U2V 2W 2]P are indicated. The symbol indicates extinct re¯ections which appear by multiple diraction.
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Fig. 4. Schematic diagram of the reciprocal lattice of the precipitate reconstructed from Fig. 2. (a) A block sustained by g(400)=g(001)B, g(040)=g(110)B and g(0 0 12)=g(1 -1 0)B; (b) a block sustained by g(200), g(020) and g(002) showing the re¯ection conditions.
A 1:287 nm B 0:874 nm C 2:622 nm: Table 2 lists the correspondence of the zone axes and the re¯ection indices obtained from equations (6) and (7). The indices are indicated in Fig. 3. Because the minor dierence between the lattice constant A for the precipitate and 4a for the B2 matrix, some zone axes of the precipitate, such as [1 -1 0]P, [-1 -2 0]P, [-1 -3 0]P, [-2 0 -1]P and [-1 0 -1]P are not exactly parallel to the relevant zone axes of the matrix, hence the calculated angles jcal between the two zone axes of the precipitate are not always equal to the corresponding calculated angles of the B2 matrix and we indicate the latter in the parentheses in Fig. 3.
Table 2. Correspondences between the zone axis indices [UVW]P and [uvw]B and between the re¯ection indices [HKL]P and [hkl]B for the precipitate (P) and B2 type matrix (B) [UVW]P 0 -3 1 0 -3 -1 -1 0 0 0 -1 0 0 0 -1 -1 -3 0 -1 -2 0 -1 -1 0 -2 0 -1 -1 0 -1 0 -1 -1 0 -9 -1
[uvw]B -1 0 0 0 -1 0 0 0 -1 -1 -1 0 1 -1 0 -6 -6 -4.17 -4 -4 -4.17 -2 -2 -4.17 3 -3 -4.17 6 -6 -4.17 1 -2 0 -1 -2 0
(HKL)
P
0 0 12 0 -4 0 0 -2 6 4 -4 0 4 -2 6 12 -4 0 400 -12 0 24 -12 0 12 -4 0 0 0 -6 6 0 -2 6 0 -2 18 4 -4 12
(hkl)B -1 1 0 -1 -1 0 -1 0 0 -1 -1 0.96 -1 0 0.96 -1 -1 2.88 0 0 0.96 -2 2 -2.88 -1 1 -2.88 0 0 -0.96 -2 -1 0 -1 0 0 -2 1 0 -2 0 0.96
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Table 3. Lattice correspondence variants and habit plane variants of the precipitates
Variant AP [100]P
BP [010]P
CP [001]P
Habit plane (100)P
1 2 3 4 5 6
[110]B2 [1 -1 0]B2 [101]B2 [-1 0 1]B2 [011]B2 [0 1 -1]B2
[-1 1 0]B2 [110]B2 [1 0 ÿ1]B2 [101]B2 [0 -1 1]B2 [011]B2
(001)B2 (001)B2 (010)B2 (010)B2 (100)B2 (100)B2
[001]B2 [001]B2 [010]B2 [010]B2 [100]B2 [100]B2
Long axis direction [100]P [-1 1 0]B2 [110]B2 [1 0 ÿ1]B2 [101]B2 [0 -1 1]B2 [011]B2
3.3. Variants of the precipitate Considering the symmetry of the B2 parent phase, there may exist six orientation variants of the precipitate. The lattice correspondence between these six variants and the B2 parent phase are listed in Table 3. The variants 1 and 2 are related by fourfold rotation around the [001]B2 axis, so do the variants 3 and 4 (around the [010]B2 axis), and the variants 5 and 6 (around the [100]B2 axis). The thin precipitates 1 and 2 indicated in Fig. 1 possess such a relationship. Moreover, the variants 1, 3, 5 are
Fig. 5. (a) Bright ®eld image and (b) EDP when the incident beam is parallel to the [111]B2 axis showing three variants of the precipitates related of threefold rotation around the [111]B2 axis.
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Fig. 6. HREM image (a) and the corresponding EDP (b) along the [100]Pk[001]B direction; (c) is the schematic EDP from variant 1.
related by threefold rotations around the [111]B2 axis and so do the variants 2, 4 and 6. Figure 5(a) and (b) shows bright-®eld images with the incidence of [111]B2 and the corresponding [111]B2 zone axis EDP, respectively. By comparing Fig. 5(b) with Fig. 2(c) one can conclude that Fig. 2(c) is a [-1 -2 0]P EDP from a single variant of the precipitate and Fig. 5(b) is composite EDPs from three variants related by threefold rotation around the [111]B2 axis. The three variants are clearly seen in Fig. 5(a). 3.4. High resolution electron microscopy observation HREM observation along the main zone axes of the precipitate and the B2 matrix has revealed some structural detail of the precipitate. Figure 6(a) shows a HREM image along the [100]Pk[001]B direction as indicated by the EDP [Fig.6(b)]. As explained in Section 3.1, the EDP shown in Fig. 6(b) consists of a [0 0 -1]B EDP and two [-1 0 0]P EDPs from the variants 1 and 2 of the precipitate, related by a fourfold rotation around the [001]B direction. Figure 6(c) shows a schematic [-1 0 0]P EDP from variant 1. In Fig. 6(a), the (004)P, (0 -2 2)P and (022)P lattice planes in variant 1 are marked which correspond to the re¯ection spots (004), (0 -2 2) and (022), respectively, in Fig. 6(c). In Fig. 6(a) variant 2 is also marked which is related to variant 1 by a fourfold rotation. Figure 7 shows a HREM image and the corresponding EDP along the [010]P direction which is a little deviated from the [110]B direction. Thus, while the lattice image of the precipitate with its short direction parallel to the [100]P direction can be
clearly seen, the B2 matrix is not correctly orientated. In the precipitate, the (004)P, (202)P and (-2 0 2)P lattice planes are marked which correspond to spots (004), (202) and (-2 0 2), respectively, in the EDP. Figure 8 shows a HREM image and the corresponding EDP along the [120]Pk[111]B axis. In Fig. 8 the (004)P lattice plane is marked which is perpendicular to the long axis direction of variant 1. In Fig. 8 variant 3 is related to variant 1 by a threefold rotation around the [111]B axis, and variant 1' is parallel to variant 1 but has a translation of 0.218 nm along the [001]P direction, i.e. a translation of the (-1 1 0)B plane distance. The long axis direction of the precipitate variants are indicated in Figs 7 and 8, respectively. From Figs 6±8, we know that all the lattice planes relevant to the precipitate have been con®rmed by the HREM observation.
3.5. The composition of the precipitate Quantitative element composition analysis was carried out using an Energy Dispersive X-ray (EDX) spectroscope of the Link System attached at a JEOL JEM-100 CX (II) electron microscope. The spot size was about 30 nm. The results indicate a Hf element enrichment in the precipitates compared with the matrix. Knowing that the composition of the matrix is Ti36.5Ni48.5Hf15, the composition of the precipitates was determined to be nearly (Ti0.6Hf0.4)Ni.
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Fig. 7. HREM image and the corresponding EDP along the [110]P direction. The long axis direction of variants is indicated by double arrows and L.A.; the short axis direction of the precipitates is indicated by short double arrows and S.A..
Fig. 8. HREM image and the corresponding EDP along the [120]Pk[111]B direction. The long axis direction of variant 3 is indicated by double arrows and L.A.; the long axes of variants 1' and 3 are indicated by single arrows, respectively (also by L.A.).
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3.6. Habit plane of the precipitate By observing the shapes of the (Ti0.6Hf0.4)Ni precipitates imaged along the h100iB, h111iB and h110iB direction we can conclude that most of the precipitates possess an oblate spindle shape with their long axes parallel to the [001]Pk[ÿ1 1 0]B direction and their ¯at planes parallel to the (100)Pk(001)B plane. HREM observation as shown in Figs 7 and 8, which show that the long axis of the precipitate is parallel to the [001]Pk[-1 1 0]B direction and the short axis of the precipitate is nearly parallel to the [100]Pk[001]B direction, con®rmed the conclusion. The (100)P plane of the precipitate is coherent with the (001)B plane and hence may be identi®ed as the habit plane. Thus the present study revealed that the habit plane variants of the (Ti0.6Hf0.4)Ni precipitate are the same as the lattice correspondence variants and they are all listed in Table 3.
4. DISCUSSION AND CONCLUSIONS
It is well known that for the Ti-rich TiNi SMA there exists the precipitation sequence b0(B2 type matrix) 4 Ti3Ni4 4Ti2Ni3 4TiNi3 with increase in the aging temperature and time [1]. According to the binary phase diagrams of Hf±Ni, Hf±Ti and Ti±Ni we know that Ti and Hf form continuous solid solutions and the stable phases at the Ti- or Hf-rich side are Ti2Ni or Hf2Ni. However, Ti2Ni possesses the E93 structure type while Hf2Ni the C16 structure type, hence they cannot form continuous (Ti,Hf)2Ni solid solutions. Similarly, the present study shows that (Ti0.6Hf0.4)Ni possesses a dierent structure type compared with the TiNi phase. Since the (Ti0.6Hf0.4)Ni phase has a rather large unit cell, it is dicult to provide an atomic structure model from the SAED and HREM studies. However, some conclusions can be drawn from the present study. 1. When the Ti36.5Ni48.5Hf15 SMA is aged at 873 K for 150 h, precipitates of composition (Ti0.6Hf0.4)Ni form.
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2. The precipitate possesses a face-centered orthorhombic lattice with lattice parameters of A = 1.287 nm, B = 0.874 nm and C = 2.622 nm and a space group of F 2/d 2/d 2/d (No.70). 3. The precipitate is intimately related to the B2 type matrix with the following lattice correspondence: A = 4.17c, B = 2(a + b) and C = 6(ÿa + b) where A, B and C are the basis vectors of the precipitate and a, b and c are those of the B2 matrix. The precipitate may also be described as a three-dimensional modulated B2 structure, i.e. commensurably modulated in the (001)B plane and incommensurably modulated along the [001]B direction. 4. The shape of the precipitate is oblate spindle like with a habit plane of (100)Pk(001)B and a long axis of [001]Bk[-1 1 0]B. This is consistent with the fact that the lattice of the precipitate is matched very well in the (100)Pk(001)B plane but with a 4% dierence along the [100]Pk[001]B direction. 5. There are six orientationally dierent variants as listed in Table 3. These variants are related by point operations 4h001iB and 3h111iB. In addition, translation domains have also been observed. These variants and domains are related by those symmetry operations which belong to the B2 matrix but are lost in the precipitate phase. AcknowledgementsÐThis work was supported by the National Natural Science Foundation of China. REFERENCES 1. Nishida, M., Wayman, C. M. and Honma, T., Metall. Trans. A,, 1986, 17A, 1505. 2. Miyazaki, S. and Otsuka, K., Met. Trans. A,, 1986, 17A, 53. 3. Nishida, M., Wayman, C. M. and Honma, T., Script Metall., 1984, 18, 1389. 4. Muder, J. H., Mass, J. H. and Beyer, J. Paper presented at ICOMAT-92. California, 1992, p. 869. 5. Han, X. D., Zou, W. H., Jin, S., Zang, Z. and Yang, D. Z., Scripta metall. mater., 1995, 32, 1441. 6. Han, X. D., Zou, W. H., Wang, R., Zhang, Z. and Yang, D. Z., Acta mater., 1996, 44, 3721.