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Mechanical properties of TiNbTa single crystals at cryogenic temperatures
PII:
Acta mater. Vol. 46, No. 8, pp. 2705±2715, 1998 # 1998 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)00475-8
MECHANICAL PROPERTIES OF TiNbTa SINGLE CRYSTALS AT CRYOGENIC TEMPERATURES TAKESHI KAWABATA1, SATOSHI KAWASAKI2 and OSAMU IZUMI3 ATOM Materials Research Laboratory, Hitokita 1-27-35, Taihaku-ku, Sendai 982-02, Japan, 2Honda Research and Development Co. Ltd., Shimotakanezawa 4630, Haga-machi, Haga-gun, Tochigi 321-33, Japan and 3Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 98077, Japan 1
(Received 13 August 1997; accepted 19 November 1997) AbstractÐMechanical properties of b.c.c. TiNbTa alloy single crystals, which have excellent superconducting properties, were studied by compression tests at cryogenic temperatures. A {332} twin occurred at 4.2 K in the as-annealed specimens of alloy 1 (Ti±40.3Nb±13.3Ta in wt%) at w = ÿ 158 and alloy 2 (Ti±26.4Nb±34.2Ta in wt%) at w = 08 in which slip deformation also occurred. The specimens with other orientations in alloys 1 and 2 at 4.2 K and whole orientations at 77 and 290 K deformed by {112} slip. (101) slip was not observed. Curves of the yield or twinning stress vs w at 4.2 and 77 K were dierent from those of typical b.c.c. metals and alloys. A new dislocation model for the {332} twinning mechanism is proposed whereby that after a pair of stacked twinning dislocations move, shuing of an atomic group consisting of three atoms occurs, forming one elementary twinned layer of four {332} planes. This model could well explain the shape of the twin. The analysis of the twin interface coincides with observations of dense dislocation structures within the twin and on the twin interfaces. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
TiNbTa alloys have excellent superconducting properties with regards to critical temperature (Tc) and upper critical ®eld (Hc2). At 4.2 K, a compositional region with a Hc2 above 11 T was found at nearly 50 wt% Ti, 20±40 wt% Nb and 10±30 wt% Ta [1]. At 2 K, a high Hc2 of about 15 T was observed at higher Ta compositions than those at 4 K [1]. It is important that superconducting materials have better mechanical properties against stress eects such as fracture or micro-cracking of multi-®laments, lowering of Tc and Hc2 by martensitic transformation, and failure of stabilizing material [2]. At cryogenic temperatures the decreased speci®c heat results in unstable mechanical properties, i.e., adiabatic deformation characteristic which is a serrated load±time curve [3]. The {332} deformation twinning was observed by Blackburn and Feeney [4] as a stress induced product in a Ti±Mo alloy by transmission electron microscopy (TEM). The mechanism of {332} deformation twinning was proposed by Crocker [5] as one of the possible twin mechanisms in a ferrous martensitic structure. The twinning elements are K1={332}, Z1=h113i, K2={112}, Z2=h111i and the magnitude of shear is s = 1/23/200.35. In this twinning, a shuing mechanism was considered in which part of atoms move to dierent directions from h113i; the magnitude of shear is a half of h111i{112} deformation twinning. The general shuf¯ing mechanism has been discussed in detail by Christian [6] and also by Hirth and Lothe [7].
It was found that the stress induced product in metastable b phase of Ti alloys is martensite a' of the h.c.p. structure with a habit plane near (344)b [8±10]. But the stress induced product in stable b phase of Ti alloys is {112} twinning [11]. The {344} plane makes an angle of 2.78 with the {332} plane, so that it is dicult to distinguish between {344} and {332} by a two surface trace analysis. In the present study, mechanical properties of single crystal TiNbTa ternary alloys with better superconducting properties were studied at 4.2, 77 K and room temperature (RT 0290 K) in compression tests. In order to explain the shape of twins and dislocation structures in the twin and on twin interfaces, the authors propose a new dislocation model for the {332} twinning mechanism and analyze the twin interface structure. 2. PROCEDURE
From iodide Ti of 99.9% purity and Nb of 99.8% and Ta of 99.9% purity, puri®ed in vacuum by a ¯oating zone melting method in an electron beam furnace, two high Hc2 alloys were made using an arc furnace with a non-consumable tungsten electrode. The prepared composition of alloy 1 was Ti±40.0Nb±12.6Ta (in wt%; composition determined by chemical analysis was Ti±40.3Nb±13.3Ta) and that of alloy 2 was Ti±26.4Nb±34.2Ta (in wt%). Button ingots with a diameter of 50 mm and a thickness of 15 mm were cold rolled to plates of
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Fig. 1. The notation of the angle w between (101) and the plane M with the maximum shear stress and the angle c between (101) and an actual slip plane S for b.c.c. alloys. A, B and C show the compressive orientations, w = ÿ 15, 0 and 158, respectively.
4±5 mm thickness. The plates were cut to a width of 5±7 mm by a precision resinoid cutter. Single crystals were grown by the strain anneal method at 1623 K for 86 ks (24 h) at a pressure of 7 10ÿ5 Pa (5 10ÿ7 Torr). The slip plane S, and the plane M with the maximum shear stress containing a primary slip direction [111], are shown by the angles w and c from the (101) plane, respectively, Fig. 1, related with the compression axis, e.g., C. w and c have values between ÿ30 and 308. In the present study, we chose the three compressive orientations of w = ÿ 15, 0 and 158 which are called orientations A, B and C, respectively. Direction cosines of these Table 1. Burgers vector, slip plane, Schmid factor and character of possible slip or twinning systems for the three orientations tested Burgers vector
Slip plane
Schmid factor
Character
Orientation A (direction cosine [ÿ0.0598, 0.212, 0.974]) 112 ÿ0.494 anti-twinning 112 ÿ0.478 anti-twinning 112 ÿ0.408 anti-twinning 112 ÿ0.369 anti-twinning 332 ÿ0.472 twinning 332 ÿ0.429 twinning Orientation B (direction cosine [ÿ0.141, 0.405, 0.906]) 1 [111] 211 ÿ0.437 twinning 2 1 112 ÿ0.431 anti-twinning 2[111] 1 332 ÿ0.479 twinning 22[113] 1 332 ÿ0.409 twinning 22[113] Orientation C (direction cosine [ÿ0.197, 0.550, 0.809]) 1 211 ÿ0.482 twinning 2[111] 1 211 ÿ0.355 twinning 2[111] 1 332 ÿ0.418 twinning 22[113] 1 332 ÿ0.358 twinning 22[113] 1 2[111] 1 2[111] 1 2[111] 1 2[111] 1 22[113] 1 22[113]
orientations are shown in Table 1. Single crystals with a square cross-section of 2 mm and a length of 5 mm were cut using a spark erosion machine from coarse grains of 5±7 mm after determination of the orientation by X-ray back re¯ection Laue technique with an accuracy of 218. The specimens were solution treated at 1273 K for 7.2 ks (2 h) and then quenched in iced water. The specimens were chemically etched by a solution of HF:H2SO4:HNO3=1:1:1. Compression tests were performed at 4.2, 77 and 290 K in liquid helium, in liquid nitrogen and in air, respectively, using an Instron type testing machine at a cross-head speed of 8.3 10ÿ6 m/s (strain rate = 2 10ÿ3± ÿ4 ÿ1 5.5 10 s ). Slip traces were observed by optical microscopy (OM) with a Nomarski type dierential interference imaging method and also by scanning electron microscopy (SEM, JEOL-T20) for two surface trace analysis. Deformed microstructures were observed by TEM (JEOL-200B). Specimens for TEM were cut on a plane normal to the compression axis by a spark erosion machine to a thickness of 0.6 mm, thinned by emery paper to a thickness of 0.3±0.4 mm and chemically etched by a solution of HF:H2SO4:HNO3:H2O = 1:1:1:1 at 0278 K. The annealed alloys were con®rmed as single phase of the body centered cubic (b.c.c.) structure by TEM.
3. RESULTS
3.1. Orientation dependence of yield or twinning stress At 4.2 K, the load±time curve linearly increased and then the load rapidly dropped to 2/3 01/3 of the peak value. From the peak value of the load, the yield or twinning stress was determined. At other temperatures, the yield stresses were determined at 0.2% plastic strain. The orientation dependence of the yield or twinning stress and the critical resolved shear stress (CRSS) are shown together in Fig. 2. At 4.2 K, the yield or twinning stress of alloy 1 decreased with increasing w. At this same temperature, the yield or twinning stress vs w curve of alloy 2 shows a maximum at orientation B (w = 0). At 77 K, the yield stress at w = ÿ 158 was lower than those at w = 0 and 158. On the other hand, the yield stresses of orientations B and C at 77 K were larger than those at 4.2 K. The shapes of the stress vs w curves at 4.2 and 77 K have an upward convexity, which is opposite to those for typical b.c.c. metals and alloys [12]. At 290 K, the shape of the yield stress vs w curve has a small downward convexity and the stress level was nearly 1/3 of those at 4.2 and 77 K. The CRSS was determined based on observations of the slip plane which will be shown in a later section. The shape of the CRSS vs w curve of alloy 1 at 4.2 K has a small
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 2. The yield or twinning stress and the critical resolved shear stress (CRSS) vs w for slip or twin of alloy 1 at 4.2, 77 and 290 K and of alloy 2 at 4.2 K.
downward convexity and those of alloy 2 at 4.2 K and of alloy 1 at 77 K have an upward convexity. 3.2. Observations of twinning and slip traces 3.2.1. Alloy 1. Four specimen surfaces of alloy 1, at orientation A, deformed at 4.2 K were observed by OM, Fig. 3(a±d). Coarse traces in Fig. 3(b) are (332) and (332) twins. These twins crossed each other. A strong localized shear deformation made a slip-o along a (332) twin. Slip deformation was also observed. The Burgers vector, slip plane, Schmid factor (SF) and character of possible slip or twinning systems in orientations A, B and C with direction cosines are shown in Table 1. Fine slip traces were observed near crossing points of twins or at a front of twins, which contributes to stress relaxation. Figure 3(e) shows an enlarged OM photograph at the center portion, arrow e, in Fig. 3(d) representing the crossing points of (332) and (332) twins. Twin interfaces with a small radius of curvature and a steep change of twin width are frequently observed. There exists a very thin midrib, like a slip trace, parallel to the twinning planes (332) and (332) near the center of twins, indicated by arrows 1 and 1', respectively. Many ®ne slip traces initiated from near the midrib trace and propagated through the (332) twin at nearly right angle to the midrib trace and ran into the neighboring parent making a kink at the twin interface, which is seen at the upper middle portion in Fig. 3(e) (arrow 2). Curved ®ne slip traces were observed at the
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upper left side, arrow 3. The slip traces consisting of coarse and straight lines were mixed with those consisting of ®ne and curved lines. Planes of most ®ne slip traces could not be determined because they were short and their orientations did not have the same direction. Figure 3(f) and (g) show the slip traces observed by SEM and the result of a trace analysis, respectively, at the portion near the lower end, arrow f in Fig. 3(d). The h and k traces were connected by a curved line and their slip systems were determined as [111](112) and [111](211), respectively. (211) and (112) traces were also observed. Figure 3(h), which is an SEM micrograph enlarged near the center of Fig. 3(b) indicated by arrow h, shows the accommodation slip traces of [111](112) slip system observed at the intersections of midrib traces in [113](332) twin with [111](112) slip. On the newly appeared slip-o plane, wavy markings along the shear direction and other types of markings which may be formed by {332} twinning and {112} slip were observed. At 77 K, ®ne slip traces were, contrary to 4.2 K, uniformly distributed on whole specimen surfaces. At 290 K, ®ner and more uniformly distributed traces than those at 77 K were observed. In orientation A at 290 K, the conjugate slip traces were observed, which was deduced as the (112) plane. It was dicult to determine strictly the slip planes for the large plastic strain giving rise to the curved traces. 3.2.2. Alloy 2. A small amount of (332) deformation twins as well as a large local shear deformation, i.e., slip-o, along (211) plane were observed at 4.2 K in orientation B. In other orientations, A and C, the deformation was by slip. Slip markings frequently appeared at the compressed planes or corners of the specimen. 3.3. Stereographic projection of slip and twinning planes Stereographic projections of slip and twinning planes at 4.2 K for alloys 1 and 2 are shown in Fig. 4. The open and right-®lled marks show the twinning deformation of alloys 1 and 2, respectively, and the ®lled and left-®lled marks show the slip deformation of alloys 1 and 2, respectively, and circle, triangle and square marks show the results of orientations A, B and C, respectively. At 4.2 K, for orientation A of alloy 1, two twinning systems [113](332) and [113](332) and three slip systems of [111](112), [111](112) and [111](112) were active (Fig. 4 and see also Table 1). But for orientation A of alloy 2 the conjugate [111](112) slip system in addition to the main [111](112) slip system were operative and {332} twins were not observed. At orientation B of alloy 1 the active slip system was only [111](211), but for alloy 2 a small amount of [113](332) twinning as well as a strong [111](211) slip were observed. At orientation C of
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Fig. 3ÐContinued on facing page
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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Fig. 3. Optical photographs showing (a±d) four specimen surfaces tested at 4.2 K, in orientation A of alloy 1, (e) the enlarged OM photograph near the center of (d) showing the cross points of {332} twins and slip traces, (f) and (g) the enlarged SEM photograph showing slip traces at the lower end in (d) and the sketch of the slip traces in (f), respectively, and (h) the enlarged SEM photograph at the center portion of (b) showing the interaction of slip-like midrib trace in twins and (112) slip, making an accommodation slip on (112).
alloys 1 and 2, (211) slip was operative. The specimen axes rotated to the [001]±[111] line in orientation B of alloy 1, to [111] in B of alloy 2, and to [011] in C of alloy 2, and did not rotate in A of alloys 1 and 2 and in C of alloy 1 (which are shown by arrows in the basic triangle [001, 011, 111] in Fig. 4). At 77 K, (112) and (112) slips were active at orientation A, and (211) slip was active at orientations B and C. At 290 K, the active slip planes for orientations B and C were the same as those at
77 K but only (112) slip was active at orientation A. At 77 and 290 K, compressive axes rotated to [011] in orientation A and to [001]±[111] line in orientations B and C. 3.4. Transmission electron microscopy From the region of w in Fig. 5(a), a diraction pattern of the twin was taken, which was very near to the [111] zone axis. The [001] zone diraction patterns were taken at b and d in Fig. 5(a). The (322) twin rotates the direction of [001] by an angle
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Fig. 4. The stereographic projection of twinning and slip planes tested at 4.2 K for alloys 1 and 2.
of 50.58 to [667] and the angle between [111] and [001] is 54.78 (see Appendix). The calculated lattice rotation by (332) twin coincides with the lattice rotation observed in Fig. 5(b) and (c). The contrast of the {332} twin interfaces was very dark. Very dense and straight line-like morphology was present in the twin (T in Fig. 5(a)) and on the twin interfaces (W in Fig. 5(a)) nearly at right angle to the interface line. The very dense and curved dislocation structure is seen in a strain contour, Fig. 6, indicated by a small arrow, near a (332) twin (g = 110 which is shown by a large arrow). 4. DISCUSSION
4.1. A new dislocation model of {332} twinning From TEM observations, it seems that the {332} twinning process intrinsically makes many dislocations in the twin and on the twin interfaces. Thus we will consider the origin of these dislocations based on the formation mechanism of {332} twin and the twin interface structure. Figure 7 shows the newly proposed (332) twinning mechanism on the (110) plane. The ®lled and open circles show the projection of atomic arrangements on the plane of the paper and upper or lower planes, a/21/2 apart from the paper plane, respectively (a = the lattice ~ is 1/2[110], AC ~ constant). The vector, AB is 1/ ~ 2[001] and AD is 1/2[113] (Fig. 7(a)). Horizontal lines I1 and I2, or I1 and I3 show the mirror plane of (332) twin (Fig. 7(c) or (d), respectively). q = 0 represents the twin interface plane and q = 0 04 correspond to one set of processing (332) layers. q = 00ÿ 4 are the corresponding parent layers.
Two (332) planes are separated by the absolute value of the vector 1/22[332]. In order to understand easily, the twinning process is divided into three steps. The ®rst step is (a) the transfer of atomic groups from L, M and N to L', M' and N', respectively, by a shear of the vector 1/22[113] on S1 plane parallel to (332) plane: The second step is (b) shuing of the atomic groups from L', M' and N' to L0, M0 and N0, respectively, by the transferring vectors 1/11[332] and 1/11[332] for atoms at L' and N' sites, respectively. The third step is (c) a second shear of 1/22[113] on S2, completing one elementary layer of twin structure (Fig. 7(c)). By repeating an equivalent sequence to Fig. 7(a±c), a second layer of the twin can be produced above the ®rst one, Fig. 7(d). After a twinning dislocation b1 passages on S1, Fig. 7(a), an interface with a displacement vector b1 is made. The interface has a large energy and is unstable, because the displacement b1 is one ®fth or one sixth of a perfect twinning shear displacement of 5/22[113] (anti-twinning direction) or 3/11[113] (twinning direction), respectively, which is a shear vector from a parent lattice site to a twin lattice site without shuing, on (332) plane. The atomic shuf¯ing will reduce the interface energy, but this shuf¯ing also make the same high energy interface on S2 as that made on S1 after the movement of b1. Then the following twinning dislocation b2 will run on S2 resulting in a complete (332) twinned unit layer consisting of four (332) atomic planes. Namely, the ®rst dislocation movement, the second atom shuing and the following third dislocation
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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Fig. 5. TEM photographs showing (a) the bright ®eld image of (332) twin and the selected area electron diraction patterns of (b) (001) taken at b in (a), (c) very near (111) taken at c and (d) (001) taken at d.
movement are a sequence of cooperative operations. Therefore, we consider as follows: it is more reasonable that a pair of stacked twinning dislocations b1 and b2 move together to produce this equivalent structure. I1, I2 and I3 show the interfaces of each elementary layer of twin structure, and S1±S4 represent the sheared interlayer (332) planes (Fig. 7(d)). The transferring vector from the
atomic site L to L0 is 1/22[557] and that from N to N0 is 1/22[771]. M is transferred to M0 by the vector 1/22[113]. E0 and F0 in Fig. 7(c) represent the atomic sites transferred by 1/11[113] due to the double shears on S1 and S2. When a pair of stacked twinning dislocations b1 and b2 stop at a certain position on a twin interface, a ledge is formed (Fig. 7(d)). The ledge produces a weak strain ®eld in the neighboring parent
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Fig. 6. A TEM micrograph of a (332) twin taken by g = 110 (long arrow), showing a curved and very dense dislocation structure in the parent plane near a twin interface (short arrow).
phase, at the upper region of the twin, because of the small Burgers vector of twinning dislocations. The square of the Burgers vector 1/22[113] is 1/44 and that of the perfect dislocation 1/2h111i is 3/4. Therefore, the strain energy around a pair of the stacked twinning dislocations will be less than 0.06 that of a perfect lattice dislocation. The step height of the ledge is the absolute value of the vector 2a/ 11[332], i.e. 0.853a. The distance between two dislocations forming a ledge is 3a/221/2, i.e. 0.640a. Therefore, the interface of the {332} twin can possess a rather small radius of curvature and the twin width can also be changed steeply (Fig. 3(e)), because of the rather large step height and the weak strain ®eld around the ledge, forming an interface with dense twinning dislocations. The twin will grow by the movement of a pair of stacked twinning dislocations. As soon as the stacked twinning dislocations pass through an atomic group (L, M and N) on S1 and S2, atomic shuing occurs by
the interatomic interaction forces operating among atoms in the processing region and atoms in the neighboring twin and parent, complete the twinning. The atomic shuing considered in the proposed model does not change the atomic density within the twin. The minimum atomic distance between two atoms existing on the sides of the twin interface is 221/2/11 and the distance between the nearest neighbor atoms in the parent phase is 31/2/2. Thus, the minimum at atomic distance near the twin interface is 0.492 times that of the nearest neighbors. This is too short to exist in the actual lattice. Dislocations with a mixed character, therefore, may be produced on the interlayer of S1 plane (with line vector [113]) (Fig. 7(d)) on which the Burgers vector may not be present. These interface dislocations will be stable only on the interface and cannot move into parent or twin. Screw dislocations with a Burgers vector 1/ 2[111] may also be produced along a line connecting atom sites L0±L0 in the ®rst and second layers of the twin structure. The angle between the line, L0±L0, and the line representing (332) plane in the (110) projection plane is 808 (Fig. 7(d)). When the dislocations are produced at every corresponding atomic site (perhaps the mixed dislocations on the interface and the screw dislocations at 808 to the interface will be alternately produced), the distance between the dislocations is the absolute value of the vector va/2[113]v 01.66a. The results of analysis on the above coincide with the observations of the dislocation structure shown in Section 3.4. The direction of the Burgers vector of twinning dislocations is important in {332} deformation twinning. Even though the Schmid factor of a {332} twinning system is extremely large, the {332} twinning does not appear if the direction of the Burgers vector corresponds to anti-twinning. If the (332) twin is made only by shearing, without shuing, a shear S is of 5/21/2 or 3 21/2 producing a lattice rotation of 121.0 or 129.58, respectively. The shear by the shuing model is 1/ 23/2 producing an actual lattice rotation of 20.058. The careful observation of steps on the specimen surfaces and also the consideration on the strain energy at the twin interface supported the shuing model.
Fig. 7. The proposed dislocation model for (332) twinning on the (110) plane showing (a) a twinning shear of 1/22[113] on the S1 plane, (b) shuing of atomic groups from L', M' and N' to L0, M0 and N0 1 1 [332] and 11 [332] for L' and M' atoms, respectively, and (c) the sites by the transferring vectors of 11 1 [113] on the S2 plane completion of twinning for one elementary twinned layer by a second shear of 22 and (d) formation of a second twinned layer on the ®rst one by movement of a pair of stacked twinning dislocations which produces an equivalent structure to the sequence (a±c), and the ledge structure on the twin interface and a strain ®eld around the ledge. The twinning dislocations b1 and b2 (equal to 1 22[113]) make a ledge with a step height of 0.853a. By the movement of a pair of stacked twinning dislocations to the right the twin can grow. The ®lled and open circles show the atomic arrangements on the plane of the paper and the upper or lower planes apart by a/21/2, respectively. q = 0 is the twin interface and 004 and 00ÿ 4 show the atomic layers for a processing atomic group in twin and a corre~ is 1[001] and AD ~ is ~ is 1[110], AC sponding atomic group in parent, respectively. The vector of AB 2 2 1 [113]. 2
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Fig. 7
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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That the twinning stress was higher than the yield stress by slip in alloys 1 and 2 and the presence of the midrib might be related with the initiation of {332} deformation twinning. The midrib in a {332} deformation twin, which was described as if a slip trace in Section 3.2.1, might be a {332} twin by a perfect twinning displacement of 3/11h113i without shuing, the internal structure of which is the same as a {332} twin by a shear displacement of 1/22h113i including an atomic shuing. The magnitude of 3/11h113i is 1.04 times that of 1/2h111i perfect lattice dislocation and is six times that of 1/22h113i. At the middle point of 3/ 11h113i displacement, some atoms close on a distance of 661/2a/11 which is 0.853 times of an atomic distance between nearest neighbors, during shearing on a {332} plane. Problems of the large shear vector and the short atomic distance during shearing suggest that the {332} twin by 3/11h113i is dicult to occur without lattice instability along a {332} plane. An end of {332} twin midrib makes a step with a large angle, e.g., 129.58 on a grain boundary (when the angle between h113i and grain boundary normal is 63.78) so that growth of the {332} twin midrib will be con®ned to a thin thickness. The 3/ 11h113i twinning dislocation can rarely stop on a twin interface at an intermediate distance, and runs to a grain boundary, a free surface or slip bands because the step by the twinning dislocation on the interface has a large energy, resulting in a thin layer with almost the same thickness. Then, the {332} twin by the 1/22h113i shear with atomic shuing will grow on the {332} twin by the shear of 3/ 11h113i. The interface between (332) twins by 3/ 11[113] and 1/22[113] cannot be observed by TEM, but may be observable by OM due to the dierence of shear displacements, which is coincident with the experimental results in the present study. The magnitude of shear vector 1/6h111i for a {112} deformation twin is 1.915 times that of shear vector 1/22h113i for a single twinning dislocation but is 0.957 times that of 2 (1/22)h113i for a pair of stacked twinning dislocations in a {332} deformation twin. A ratio of strain energies for 1/6h111i, 1/22h113i and 2 (1/22)h113i can be roughly estimated from squares of those shear vectors to be 1:9/33:18/33, namely, 1:0.273:0.545. When a strain energy canceling within an area between stacked twinning dislocations is considered, the energy of a pair of stacked {332} twinning dislocations may be further smaller than a half that of the {112} twinning dislocation. From the above energy consideration, that not the {112} twin but the {332} twin was observed in the present study is reasonable. 4.2. Orientation and temperature dependence of deformation mechanism The Schmid factor of (332) twinning for orientation B is a little larger than that for orientation A. In alloy 1, (332) twinning was not observed in
orientation B but was observed in orientation A. These results are related to both magnitudes of the shear vector and the Schmid factor for (211) slip and (332) twinning, and also to the instability of the metastable b phase. For alloy 2, (332) twinning was observed in orientation B, which results mainly from a large Schmid factor (Table 1). Slip planes deviated largely to {112} from the planes where the maximum shear stress was operative and (101) slip was not observed. When {332} twins occurred, the twinning stress was larger than the yield stress by slip. These phenomena were the characteristic properties for slip or twinning in the alloys studied. 4.3. Composition dependence of deformation mechanism Additions of elements Nb and Ta stabilize the b phase of Ti alloys. The deformation twin occurs even at RT in TiNb binary alloys with similar Ti/ Nb composition ratios to those in alloys 1 and 2. The addition of Ta stabilizes the b phase. Thus, deformation twinning occurred only at 4.2 K and at restricted orientations. Increasing the amount of Ta caused an increase of CRSS of alloy 2 at 4.2 K to the CRSS level of alloy 1 at 77 K.
5. CONCLUSIONS
Single crystals with orientations A, B and C (w = ÿ 15, 0 and 158, respectively) for Ti±40.3Nb± 13.3Ta (in wt%, alloy 1) and Ti±26.4Nb±34.2Ta (in wt%, alloy 2) were tested in compression at 4.2, 77 and 290 K. Structural observations by optical microscopy, scanning and transmission electron microscopy were performed. The results were as follows. (1) Shapes of the yield or twinning stress vs w curves at 4.2 and 77 K were dierent from those of typical b.c.c. metals and alloys. (2) The {332} deformation twinning appeared at 4.2 K in orientation A of alloy 1 and orientation B of alloy 2. Under the other conditions, deformation occurred by {112} slip. (101) slip was not observed. (3) At 4.2 K in the as-quenched specimens, localized strong shear deformation, namely slip-o, occurred along nearly a (332) plane after twinning in orientation A, and along a (211) plane in orientations B and C. (4) The shape of {332} twins was, sometimes, similar to a tree leaf with a small radius of curvature and the twin width often changed steeply. A midrib trace parallel to the {332} plane was observed within the twins. (5) A dense dislocation structure with a straight morphology was observed in the twins and on the twin interfaces, which was considered to be intrinsically related with the interface structure of the {332} twin.
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
(6) A new dislocation model for {332} twinning is proposed. The movement of a pair of stacked twinning dislocations, with Burgers vector 1/22[113] on (332) planes (the separated distance between two twinning dislocations is 3a/221/2, a: the lattice constant), and atomic shuing by the vectors 1/11[332] and 1/11[332] form an elementary (332) deformation twin with a thickness of four (332) layers. The theoretical considerations of {332} twinning could well explain the experimental observations concerning the twin shape and dislocation structures with straight morphology within the twin and on the twin interfaces.
6. Christian, J. W., The Theory of Transformations in Metals and Alloys. Pergamon Press, Oxford, 1965, p. 743. 7. Hirth, J. P. and Lothe, J., Theory of Dislocations, 2nd ed., Wiley, New York, 1982, p. 811. 8. Weinig, S. and Machlin, F. S., Trans. A.I.M.E., 1954, 191, 1280. 9. Liu, Y. C., Trans. A.I.M.E., 1956, 206, 1036. 10. Gaunt, P. and Christian, J. W., Acta metall., 1959, 7, 534. 11. Paris, H. G., LeFevre, B. G. and Starke, E. A., Metall. Trans., 1976, 7A, 273. 12. Kroupa, F. and Vitek, V., Can. J. Phys., 1967, 45, 945.
APPENDIX
REFERENCES 1. Larbalestier, D. C., Adv. Cryog. Engng Mater. , 1980, 26, 10. 2. Collings, E. W., Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys. Plenum Press, New York, 1983. 3. Wigley, D. A., Mechanical Properties of Materials at Low Temperatures. Plenum Press, New York, 1971, p. 84. 4. Blackburn, M. J. and Feeney, J. A., J. Inst. Metals, 1971, 99, 132. 5. Crocker, A. G., Acta metall., 1962, 10, 113.
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The orientation or plane Pm in parent transforms to that in twin Pt by the transformation tensor Tt of (332) twin, Pt Pm Tt :
A:1
Here, Tt
9, 1 2, 11 6,
2, 6 9, 6 : 6, 7
A:2
The [001] orientation changes to [6,6,7] by rotation of (332) twinning. The angle between [6,6,7] and [111] is 4.38.
Acta mater. Vol. 46, No. 8, pp. 2705±2715, 1998 # 1998 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)00475-8
MECHANICAL PROPERTIES OF TiNbTa SINGLE CRYSTALS AT CRYOGENIC TEMPERATURES TAKESHI KAWABATA1, SATOSHI KAWASAKI2 and OSAMU IZUMI3 ATOM Materials Research Laboratory, Hitokita 1-27-35, Taihaku-ku, Sendai 982-02, Japan, 2Honda Research and Development Co. Ltd., Shimotakanezawa 4630, Haga-machi, Haga-gun, Tochigi 321-33, Japan and 3Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 98077, Japan 1
(Received 13 August 1997; accepted 19 November 1997) AbstractÐMechanical properties of b.c.c. TiNbTa alloy single crystals, which have excellent superconducting properties, were studied by compression tests at cryogenic temperatures. A {332} twin occurred at 4.2 K in the as-annealed specimens of alloy 1 (Ti±40.3Nb±13.3Ta in wt%) at w = ÿ 158 and alloy 2 (Ti±26.4Nb±34.2Ta in wt%) at w = 08 in which slip deformation also occurred. The specimens with other orientations in alloys 1 and 2 at 4.2 K and whole orientations at 77 and 290 K deformed by {112} slip. (101) slip was not observed. Curves of the yield or twinning stress vs w at 4.2 and 77 K were dierent from those of typical b.c.c. metals and alloys. A new dislocation model for the {332} twinning mechanism is proposed whereby that after a pair of stacked twinning dislocations move, shuing of an atomic group consisting of three atoms occurs, forming one elementary twinned layer of four {332} planes. This model could well explain the shape of the twin. The analysis of the twin interface coincides with observations of dense dislocation structures within the twin and on the twin interfaces. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
TiNbTa alloys have excellent superconducting properties with regards to critical temperature (Tc) and upper critical ®eld (Hc2). At 4.2 K, a compositional region with a Hc2 above 11 T was found at nearly 50 wt% Ti, 20±40 wt% Nb and 10±30 wt% Ta [1]. At 2 K, a high Hc2 of about 15 T was observed at higher Ta compositions than those at 4 K [1]. It is important that superconducting materials have better mechanical properties against stress eects such as fracture or micro-cracking of multi-®laments, lowering of Tc and Hc2 by martensitic transformation, and failure of stabilizing material [2]. At cryogenic temperatures the decreased speci®c heat results in unstable mechanical properties, i.e., adiabatic deformation characteristic which is a serrated load±time curve [3]. The {332} deformation twinning was observed by Blackburn and Feeney [4] as a stress induced product in a Ti±Mo alloy by transmission electron microscopy (TEM). The mechanism of {332} deformation twinning was proposed by Crocker [5] as one of the possible twin mechanisms in a ferrous martensitic structure. The twinning elements are K1={332}, Z1=h113i, K2={112}, Z2=h111i and the magnitude of shear is s = 1/23/200.35. In this twinning, a shuing mechanism was considered in which part of atoms move to dierent directions from h113i; the magnitude of shear is a half of h111i{112} deformation twinning. The general shuf¯ing mechanism has been discussed in detail by Christian [6] and also by Hirth and Lothe [7].
It was found that the stress induced product in metastable b phase of Ti alloys is martensite a' of the h.c.p. structure with a habit plane near (344)b [8±10]. But the stress induced product in stable b phase of Ti alloys is {112} twinning [11]. The {344} plane makes an angle of 2.78 with the {332} plane, so that it is dicult to distinguish between {344} and {332} by a two surface trace analysis. In the present study, mechanical properties of single crystal TiNbTa ternary alloys with better superconducting properties were studied at 4.2, 77 K and room temperature (RT 0290 K) in compression tests. In order to explain the shape of twins and dislocation structures in the twin and on twin interfaces, the authors propose a new dislocation model for the {332} twinning mechanism and analyze the twin interface structure. 2. PROCEDURE
From iodide Ti of 99.9% purity and Nb of 99.8% and Ta of 99.9% purity, puri®ed in vacuum by a ¯oating zone melting method in an electron beam furnace, two high Hc2 alloys were made using an arc furnace with a non-consumable tungsten electrode. The prepared composition of alloy 1 was Ti±40.0Nb±12.6Ta (in wt%; composition determined by chemical analysis was Ti±40.3Nb±13.3Ta) and that of alloy 2 was Ti±26.4Nb±34.2Ta (in wt%). Button ingots with a diameter of 50 mm and a thickness of 15 mm were cold rolled to plates of
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KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 1. The notation of the angle w between (101) and the plane M with the maximum shear stress and the angle c between (101) and an actual slip plane S for b.c.c. alloys. A, B and C show the compressive orientations, w = ÿ 15, 0 and 158, respectively.
4±5 mm thickness. The plates were cut to a width of 5±7 mm by a precision resinoid cutter. Single crystals were grown by the strain anneal method at 1623 K for 86 ks (24 h) at a pressure of 7 10ÿ5 Pa (5 10ÿ7 Torr). The slip plane S, and the plane M with the maximum shear stress containing a primary slip direction [111], are shown by the angles w and c from the (101) plane, respectively, Fig. 1, related with the compression axis, e.g., C. w and c have values between ÿ30 and 308. In the present study, we chose the three compressive orientations of w = ÿ 15, 0 and 158 which are called orientations A, B and C, respectively. Direction cosines of these Table 1. Burgers vector, slip plane, Schmid factor and character of possible slip or twinning systems for the three orientations tested Burgers vector
Slip plane
Schmid factor
Character
Orientation A (direction cosine [ÿ0.0598, 0.212, 0.974]) 112 ÿ0.494 anti-twinning 112 ÿ0.478 anti-twinning 112 ÿ0.408 anti-twinning 112 ÿ0.369 anti-twinning 332 ÿ0.472 twinning 332 ÿ0.429 twinning Orientation B (direction cosine [ÿ0.141, 0.405, 0.906]) 1 [111] 211 ÿ0.437 twinning 2 1 112 ÿ0.431 anti-twinning 2[111] 1 332 ÿ0.479 twinning 22[113] 1 332 ÿ0.409 twinning 22[113] Orientation C (direction cosine [ÿ0.197, 0.550, 0.809]) 1 211 ÿ0.482 twinning 2[111] 1 211 ÿ0.355 twinning 2[111] 1 332 ÿ0.418 twinning 22[113] 1 332 ÿ0.358 twinning 22[113] 1 2[111] 1 2[111] 1 2[111] 1 2[111] 1 22[113] 1 22[113]
orientations are shown in Table 1. Single crystals with a square cross-section of 2 mm and a length of 5 mm were cut using a spark erosion machine from coarse grains of 5±7 mm after determination of the orientation by X-ray back re¯ection Laue technique with an accuracy of 218. The specimens were solution treated at 1273 K for 7.2 ks (2 h) and then quenched in iced water. The specimens were chemically etched by a solution of HF:H2SO4:HNO3=1:1:1. Compression tests were performed at 4.2, 77 and 290 K in liquid helium, in liquid nitrogen and in air, respectively, using an Instron type testing machine at a cross-head speed of 8.3 10ÿ6 m/s (strain rate = 2 10ÿ3± ÿ4 ÿ1 5.5 10 s ). Slip traces were observed by optical microscopy (OM) with a Nomarski type dierential interference imaging method and also by scanning electron microscopy (SEM, JEOL-T20) for two surface trace analysis. Deformed microstructures were observed by TEM (JEOL-200B). Specimens for TEM were cut on a plane normal to the compression axis by a spark erosion machine to a thickness of 0.6 mm, thinned by emery paper to a thickness of 0.3±0.4 mm and chemically etched by a solution of HF:H2SO4:HNO3:H2O = 1:1:1:1 at 0278 K. The annealed alloys were con®rmed as single phase of the body centered cubic (b.c.c.) structure by TEM.
3. RESULTS
3.1. Orientation dependence of yield or twinning stress At 4.2 K, the load±time curve linearly increased and then the load rapidly dropped to 2/3 01/3 of the peak value. From the peak value of the load, the yield or twinning stress was determined. At other temperatures, the yield stresses were determined at 0.2% plastic strain. The orientation dependence of the yield or twinning stress and the critical resolved shear stress (CRSS) are shown together in Fig. 2. At 4.2 K, the yield or twinning stress of alloy 1 decreased with increasing w. At this same temperature, the yield or twinning stress vs w curve of alloy 2 shows a maximum at orientation B (w = 0). At 77 K, the yield stress at w = ÿ 158 was lower than those at w = 0 and 158. On the other hand, the yield stresses of orientations B and C at 77 K were larger than those at 4.2 K. The shapes of the stress vs w curves at 4.2 and 77 K have an upward convexity, which is opposite to those for typical b.c.c. metals and alloys [12]. At 290 K, the shape of the yield stress vs w curve has a small downward convexity and the stress level was nearly 1/3 of those at 4.2 and 77 K. The CRSS was determined based on observations of the slip plane which will be shown in a later section. The shape of the CRSS vs w curve of alloy 1 at 4.2 K has a small
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 2. The yield or twinning stress and the critical resolved shear stress (CRSS) vs w for slip or twin of alloy 1 at 4.2, 77 and 290 K and of alloy 2 at 4.2 K.
downward convexity and those of alloy 2 at 4.2 K and of alloy 1 at 77 K have an upward convexity. 3.2. Observations of twinning and slip traces 3.2.1. Alloy 1. Four specimen surfaces of alloy 1, at orientation A, deformed at 4.2 K were observed by OM, Fig. 3(a±d). Coarse traces in Fig. 3(b) are (332) and (332) twins. These twins crossed each other. A strong localized shear deformation made a slip-o along a (332) twin. Slip deformation was also observed. The Burgers vector, slip plane, Schmid factor (SF) and character of possible slip or twinning systems in orientations A, B and C with direction cosines are shown in Table 1. Fine slip traces were observed near crossing points of twins or at a front of twins, which contributes to stress relaxation. Figure 3(e) shows an enlarged OM photograph at the center portion, arrow e, in Fig. 3(d) representing the crossing points of (332) and (332) twins. Twin interfaces with a small radius of curvature and a steep change of twin width are frequently observed. There exists a very thin midrib, like a slip trace, parallel to the twinning planes (332) and (332) near the center of twins, indicated by arrows 1 and 1', respectively. Many ®ne slip traces initiated from near the midrib trace and propagated through the (332) twin at nearly right angle to the midrib trace and ran into the neighboring parent making a kink at the twin interface, which is seen at the upper middle portion in Fig. 3(e) (arrow 2). Curved ®ne slip traces were observed at the
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upper left side, arrow 3. The slip traces consisting of coarse and straight lines were mixed with those consisting of ®ne and curved lines. Planes of most ®ne slip traces could not be determined because they were short and their orientations did not have the same direction. Figure 3(f) and (g) show the slip traces observed by SEM and the result of a trace analysis, respectively, at the portion near the lower end, arrow f in Fig. 3(d). The h and k traces were connected by a curved line and their slip systems were determined as [111](112) and [111](211), respectively. (211) and (112) traces were also observed. Figure 3(h), which is an SEM micrograph enlarged near the center of Fig. 3(b) indicated by arrow h, shows the accommodation slip traces of [111](112) slip system observed at the intersections of midrib traces in [113](332) twin with [111](112) slip. On the newly appeared slip-o plane, wavy markings along the shear direction and other types of markings which may be formed by {332} twinning and {112} slip were observed. At 77 K, ®ne slip traces were, contrary to 4.2 K, uniformly distributed on whole specimen surfaces. At 290 K, ®ner and more uniformly distributed traces than those at 77 K were observed. In orientation A at 290 K, the conjugate slip traces were observed, which was deduced as the (112) plane. It was dicult to determine strictly the slip planes for the large plastic strain giving rise to the curved traces. 3.2.2. Alloy 2. A small amount of (332) deformation twins as well as a large local shear deformation, i.e., slip-o, along (211) plane were observed at 4.2 K in orientation B. In other orientations, A and C, the deformation was by slip. Slip markings frequently appeared at the compressed planes or corners of the specimen. 3.3. Stereographic projection of slip and twinning planes Stereographic projections of slip and twinning planes at 4.2 K for alloys 1 and 2 are shown in Fig. 4. The open and right-®lled marks show the twinning deformation of alloys 1 and 2, respectively, and the ®lled and left-®lled marks show the slip deformation of alloys 1 and 2, respectively, and circle, triangle and square marks show the results of orientations A, B and C, respectively. At 4.2 K, for orientation A of alloy 1, two twinning systems [113](332) and [113](332) and three slip systems of [111](112), [111](112) and [111](112) were active (Fig. 4 and see also Table 1). But for orientation A of alloy 2 the conjugate [111](112) slip system in addition to the main [111](112) slip system were operative and {332} twins were not observed. At orientation B of alloy 1 the active slip system was only [111](211), but for alloy 2 a small amount of [113](332) twinning as well as a strong [111](211) slip were observed. At orientation C of
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KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 3ÐContinued on facing page
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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Fig. 3. Optical photographs showing (a±d) four specimen surfaces tested at 4.2 K, in orientation A of alloy 1, (e) the enlarged OM photograph near the center of (d) showing the cross points of {332} twins and slip traces, (f) and (g) the enlarged SEM photograph showing slip traces at the lower end in (d) and the sketch of the slip traces in (f), respectively, and (h) the enlarged SEM photograph at the center portion of (b) showing the interaction of slip-like midrib trace in twins and (112) slip, making an accommodation slip on (112).
alloys 1 and 2, (211) slip was operative. The specimen axes rotated to the [001]±[111] line in orientation B of alloy 1, to [111] in B of alloy 2, and to [011] in C of alloy 2, and did not rotate in A of alloys 1 and 2 and in C of alloy 1 (which are shown by arrows in the basic triangle [001, 011, 111] in Fig. 4). At 77 K, (112) and (112) slips were active at orientation A, and (211) slip was active at orientations B and C. At 290 K, the active slip planes for orientations B and C were the same as those at
77 K but only (112) slip was active at orientation A. At 77 and 290 K, compressive axes rotated to [011] in orientation A and to [001]±[111] line in orientations B and C. 3.4. Transmission electron microscopy From the region of w in Fig. 5(a), a diraction pattern of the twin was taken, which was very near to the [111] zone axis. The [001] zone diraction patterns were taken at b and d in Fig. 5(a). The (322) twin rotates the direction of [001] by an angle
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KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 4. The stereographic projection of twinning and slip planes tested at 4.2 K for alloys 1 and 2.
of 50.58 to [667] and the angle between [111] and [001] is 54.78 (see Appendix). The calculated lattice rotation by (332) twin coincides with the lattice rotation observed in Fig. 5(b) and (c). The contrast of the {332} twin interfaces was very dark. Very dense and straight line-like morphology was present in the twin (T in Fig. 5(a)) and on the twin interfaces (W in Fig. 5(a)) nearly at right angle to the interface line. The very dense and curved dislocation structure is seen in a strain contour, Fig. 6, indicated by a small arrow, near a (332) twin (g = 110 which is shown by a large arrow). 4. DISCUSSION
4.1. A new dislocation model of {332} twinning From TEM observations, it seems that the {332} twinning process intrinsically makes many dislocations in the twin and on the twin interfaces. Thus we will consider the origin of these dislocations based on the formation mechanism of {332} twin and the twin interface structure. Figure 7 shows the newly proposed (332) twinning mechanism on the (110) plane. The ®lled and open circles show the projection of atomic arrangements on the plane of the paper and upper or lower planes, a/21/2 apart from the paper plane, respectively (a = the lattice ~ is 1/2[110], AC ~ constant). The vector, AB is 1/ ~ 2[001] and AD is 1/2[113] (Fig. 7(a)). Horizontal lines I1 and I2, or I1 and I3 show the mirror plane of (332) twin (Fig. 7(c) or (d), respectively). q = 0 represents the twin interface plane and q = 0 04 correspond to one set of processing (332) layers. q = 00ÿ 4 are the corresponding parent layers.
Two (332) planes are separated by the absolute value of the vector 1/22[332]. In order to understand easily, the twinning process is divided into three steps. The ®rst step is (a) the transfer of atomic groups from L, M and N to L', M' and N', respectively, by a shear of the vector 1/22[113] on S1 plane parallel to (332) plane: The second step is (b) shuing of the atomic groups from L', M' and N' to L0, M0 and N0, respectively, by the transferring vectors 1/11[332] and 1/11[332] for atoms at L' and N' sites, respectively. The third step is (c) a second shear of 1/22[113] on S2, completing one elementary layer of twin structure (Fig. 7(c)). By repeating an equivalent sequence to Fig. 7(a±c), a second layer of the twin can be produced above the ®rst one, Fig. 7(d). After a twinning dislocation b1 passages on S1, Fig. 7(a), an interface with a displacement vector b1 is made. The interface has a large energy and is unstable, because the displacement b1 is one ®fth or one sixth of a perfect twinning shear displacement of 5/22[113] (anti-twinning direction) or 3/11[113] (twinning direction), respectively, which is a shear vector from a parent lattice site to a twin lattice site without shuing, on (332) plane. The atomic shuf¯ing will reduce the interface energy, but this shuf¯ing also make the same high energy interface on S2 as that made on S1 after the movement of b1. Then the following twinning dislocation b2 will run on S2 resulting in a complete (332) twinned unit layer consisting of four (332) atomic planes. Namely, the ®rst dislocation movement, the second atom shuing and the following third dislocation
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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Fig. 5. TEM photographs showing (a) the bright ®eld image of (332) twin and the selected area electron diraction patterns of (b) (001) taken at b in (a), (c) very near (111) taken at c and (d) (001) taken at d.
movement are a sequence of cooperative operations. Therefore, we consider as follows: it is more reasonable that a pair of stacked twinning dislocations b1 and b2 move together to produce this equivalent structure. I1, I2 and I3 show the interfaces of each elementary layer of twin structure, and S1±S4 represent the sheared interlayer (332) planes (Fig. 7(d)). The transferring vector from the
atomic site L to L0 is 1/22[557] and that from N to N0 is 1/22[771]. M is transferred to M0 by the vector 1/22[113]. E0 and F0 in Fig. 7(c) represent the atomic sites transferred by 1/11[113] due to the double shears on S1 and S2. When a pair of stacked twinning dislocations b1 and b2 stop at a certain position on a twin interface, a ledge is formed (Fig. 7(d)). The ledge produces a weak strain ®eld in the neighboring parent
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KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
Fig. 6. A TEM micrograph of a (332) twin taken by g = 110 (long arrow), showing a curved and very dense dislocation structure in the parent plane near a twin interface (short arrow).
phase, at the upper region of the twin, because of the small Burgers vector of twinning dislocations. The square of the Burgers vector 1/22[113] is 1/44 and that of the perfect dislocation 1/2h111i is 3/4. Therefore, the strain energy around a pair of the stacked twinning dislocations will be less than 0.06 that of a perfect lattice dislocation. The step height of the ledge is the absolute value of the vector 2a/ 11[332], i.e. 0.853a. The distance between two dislocations forming a ledge is 3a/221/2, i.e. 0.640a. Therefore, the interface of the {332} twin can possess a rather small radius of curvature and the twin width can also be changed steeply (Fig. 3(e)), because of the rather large step height and the weak strain ®eld around the ledge, forming an interface with dense twinning dislocations. The twin will grow by the movement of a pair of stacked twinning dislocations. As soon as the stacked twinning dislocations pass through an atomic group (L, M and N) on S1 and S2, atomic shuing occurs by
the interatomic interaction forces operating among atoms in the processing region and atoms in the neighboring twin and parent, complete the twinning. The atomic shuing considered in the proposed model does not change the atomic density within the twin. The minimum atomic distance between two atoms existing on the sides of the twin interface is 221/2/11 and the distance between the nearest neighbor atoms in the parent phase is 31/2/2. Thus, the minimum at atomic distance near the twin interface is 0.492 times that of the nearest neighbors. This is too short to exist in the actual lattice. Dislocations with a mixed character, therefore, may be produced on the interlayer of S1 plane (with line vector [113]) (Fig. 7(d)) on which the Burgers vector may not be present. These interface dislocations will be stable only on the interface and cannot move into parent or twin. Screw dislocations with a Burgers vector 1/ 2[111] may also be produced along a line connecting atom sites L0±L0 in the ®rst and second layers of the twin structure. The angle between the line, L0±L0, and the line representing (332) plane in the (110) projection plane is 808 (Fig. 7(d)). When the dislocations are produced at every corresponding atomic site (perhaps the mixed dislocations on the interface and the screw dislocations at 808 to the interface will be alternately produced), the distance between the dislocations is the absolute value of the vector va/2[113]v 01.66a. The results of analysis on the above coincide with the observations of the dislocation structure shown in Section 3.4. The direction of the Burgers vector of twinning dislocations is important in {332} deformation twinning. Even though the Schmid factor of a {332} twinning system is extremely large, the {332} twinning does not appear if the direction of the Burgers vector corresponds to anti-twinning. If the (332) twin is made only by shearing, without shuing, a shear S is of 5/21/2 or 3 21/2 producing a lattice rotation of 121.0 or 129.58, respectively. The shear by the shuing model is 1/ 23/2 producing an actual lattice rotation of 20.058. The careful observation of steps on the specimen surfaces and also the consideration on the strain energy at the twin interface supported the shuing model.
Fig. 7. The proposed dislocation model for (332) twinning on the (110) plane showing (a) a twinning shear of 1/22[113] on the S1 plane, (b) shuing of atomic groups from L', M' and N' to L0, M0 and N0 1 1 [332] and 11 [332] for L' and M' atoms, respectively, and (c) the sites by the transferring vectors of 11 1 [113] on the S2 plane completion of twinning for one elementary twinned layer by a second shear of 22 and (d) formation of a second twinned layer on the ®rst one by movement of a pair of stacked twinning dislocations which produces an equivalent structure to the sequence (a±c), and the ledge structure on the twin interface and a strain ®eld around the ledge. The twinning dislocations b1 and b2 (equal to 1 22[113]) make a ledge with a step height of 0.853a. By the movement of a pair of stacked twinning dislocations to the right the twin can grow. The ®lled and open circles show the atomic arrangements on the plane of the paper and the upper or lower planes apart by a/21/2, respectively. q = 0 is the twin interface and 004 and 00ÿ 4 show the atomic layers for a processing atomic group in twin and a corre~ is 1[001] and AD ~ is ~ is 1[110], AC sponding atomic group in parent, respectively. The vector of AB 2 2 1 [113]. 2
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Fig. 7
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
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KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
That the twinning stress was higher than the yield stress by slip in alloys 1 and 2 and the presence of the midrib might be related with the initiation of {332} deformation twinning. The midrib in a {332} deformation twin, which was described as if a slip trace in Section 3.2.1, might be a {332} twin by a perfect twinning displacement of 3/11h113i without shuing, the internal structure of which is the same as a {332} twin by a shear displacement of 1/22h113i including an atomic shuing. The magnitude of 3/11h113i is 1.04 times that of 1/2h111i perfect lattice dislocation and is six times that of 1/22h113i. At the middle point of 3/ 11h113i displacement, some atoms close on a distance of 661/2a/11 which is 0.853 times of an atomic distance between nearest neighbors, during shearing on a {332} plane. Problems of the large shear vector and the short atomic distance during shearing suggest that the {332} twin by 3/11h113i is dicult to occur without lattice instability along a {332} plane. An end of {332} twin midrib makes a step with a large angle, e.g., 129.58 on a grain boundary (when the angle between h113i and grain boundary normal is 63.78) so that growth of the {332} twin midrib will be con®ned to a thin thickness. The 3/ 11h113i twinning dislocation can rarely stop on a twin interface at an intermediate distance, and runs to a grain boundary, a free surface or slip bands because the step by the twinning dislocation on the interface has a large energy, resulting in a thin layer with almost the same thickness. Then, the {332} twin by the 1/22h113i shear with atomic shuing will grow on the {332} twin by the shear of 3/ 11h113i. The interface between (332) twins by 3/ 11[113] and 1/22[113] cannot be observed by TEM, but may be observable by OM due to the dierence of shear displacements, which is coincident with the experimental results in the present study. The magnitude of shear vector 1/6h111i for a {112} deformation twin is 1.915 times that of shear vector 1/22h113i for a single twinning dislocation but is 0.957 times that of 2 (1/22)h113i for a pair of stacked twinning dislocations in a {332} deformation twin. A ratio of strain energies for 1/6h111i, 1/22h113i and 2 (1/22)h113i can be roughly estimated from squares of those shear vectors to be 1:9/33:18/33, namely, 1:0.273:0.545. When a strain energy canceling within an area between stacked twinning dislocations is considered, the energy of a pair of stacked {332} twinning dislocations may be further smaller than a half that of the {112} twinning dislocation. From the above energy consideration, that not the {112} twin but the {332} twin was observed in the present study is reasonable. 4.2. Orientation and temperature dependence of deformation mechanism The Schmid factor of (332) twinning for orientation B is a little larger than that for orientation A. In alloy 1, (332) twinning was not observed in
orientation B but was observed in orientation A. These results are related to both magnitudes of the shear vector and the Schmid factor for (211) slip and (332) twinning, and also to the instability of the metastable b phase. For alloy 2, (332) twinning was observed in orientation B, which results mainly from a large Schmid factor (Table 1). Slip planes deviated largely to {112} from the planes where the maximum shear stress was operative and (101) slip was not observed. When {332} twins occurred, the twinning stress was larger than the yield stress by slip. These phenomena were the characteristic properties for slip or twinning in the alloys studied. 4.3. Composition dependence of deformation mechanism Additions of elements Nb and Ta stabilize the b phase of Ti alloys. The deformation twin occurs even at RT in TiNb binary alloys with similar Ti/ Nb composition ratios to those in alloys 1 and 2. The addition of Ta stabilizes the b phase. Thus, deformation twinning occurred only at 4.2 K and at restricted orientations. Increasing the amount of Ta caused an increase of CRSS of alloy 2 at 4.2 K to the CRSS level of alloy 1 at 77 K.
5. CONCLUSIONS
Single crystals with orientations A, B and C (w = ÿ 15, 0 and 158, respectively) for Ti±40.3Nb± 13.3Ta (in wt%, alloy 1) and Ti±26.4Nb±34.2Ta (in wt%, alloy 2) were tested in compression at 4.2, 77 and 290 K. Structural observations by optical microscopy, scanning and transmission electron microscopy were performed. The results were as follows. (1) Shapes of the yield or twinning stress vs w curves at 4.2 and 77 K were dierent from those of typical b.c.c. metals and alloys. (2) The {332} deformation twinning appeared at 4.2 K in orientation A of alloy 1 and orientation B of alloy 2. Under the other conditions, deformation occurred by {112} slip. (101) slip was not observed. (3) At 4.2 K in the as-quenched specimens, localized strong shear deformation, namely slip-o, occurred along nearly a (332) plane after twinning in orientation A, and along a (211) plane in orientations B and C. (4) The shape of {332} twins was, sometimes, similar to a tree leaf with a small radius of curvature and the twin width often changed steeply. A midrib trace parallel to the {332} plane was observed within the twins. (5) A dense dislocation structure with a straight morphology was observed in the twins and on the twin interfaces, which was considered to be intrinsically related with the interface structure of the {332} twin.
KAWABATA et al.: MECHANICAL PROPERTIES OF TiNbTa
(6) A new dislocation model for {332} twinning is proposed. The movement of a pair of stacked twinning dislocations, with Burgers vector 1/22[113] on (332) planes (the separated distance between two twinning dislocations is 3a/221/2, a: the lattice constant), and atomic shuing by the vectors 1/11[332] and 1/11[332] form an elementary (332) deformation twin with a thickness of four (332) layers. The theoretical considerations of {332} twinning could well explain the experimental observations concerning the twin shape and dislocation structures with straight morphology within the twin and on the twin interfaces.
6. Christian, J. W., The Theory of Transformations in Metals and Alloys. Pergamon Press, Oxford, 1965, p. 743. 7. Hirth, J. P. and Lothe, J., Theory of Dislocations, 2nd ed., Wiley, New York, 1982, p. 811. 8. Weinig, S. and Machlin, F. S., Trans. A.I.M.E., 1954, 191, 1280. 9. Liu, Y. C., Trans. A.I.M.E., 1956, 206, 1036. 10. Gaunt, P. and Christian, J. W., Acta metall., 1959, 7, 534. 11. Paris, H. G., LeFevre, B. G. and Starke, E. A., Metall. Trans., 1976, 7A, 273. 12. Kroupa, F. and Vitek, V., Can. J. Phys., 1967, 45, 945.
APPENDIX
REFERENCES 1. Larbalestier, D. C., Adv. Cryog. Engng Mater. , 1980, 26, 10. 2. Collings, E. W., Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys. Plenum Press, New York, 1983. 3. Wigley, D. A., Mechanical Properties of Materials at Low Temperatures. Plenum Press, New York, 1971, p. 84. 4. Blackburn, M. J. and Feeney, J. A., J. Inst. Metals, 1971, 99, 132. 5. Crocker, A. G., Acta metall., 1962, 10, 113.
2715
The orientation or plane Pm in parent transforms to that in twin Pt by the transformation tensor Tt of (332) twin, Pt Pm Tt :
A:1
Here, Tt
9, 1 2, 11 6,
2, 6 9, 6 : 6, 7
A:2
The [001] orientation changes to [6,6,7] by rotation of (332) twinning. The angle between [6,6,7] and [111] is 4.38.