T. Waitz et al. Acta Materialia 52(2004)137-14 nanocrystalline NiTi the mean grain size(30-160 nm, cf to grain boundaries. Also the grain boundaries might Figs. 4 and 5)represents a length scale of the same order even trigger the formation of twins [34] as that of the twinning period and smaller than that of inally, it was proposed recently that during the r the self-accommodating groups in a coarse grained al- phase to B19 transformation(00 1)compound twinning loy. Therefore, in the nanograins the constraints of the could give rise to an invariant plane strain under the grain boundaries suppress the formation of self-accom- condition of a critical value aR <86.20[29]. In the present modating variants. As a consequence within the nano- case the martensitic transformation is preceded by the grains a different path of the transformation occurs that formation of R-phase as required for(00 1) compound is leading to the required decrease of the transformation twinning acting as lattice invariant strain. As deduced strains by the formation of very fine(00 1)compound from Fig. 6(c)the measured RT values of aR(88.50+0.69 twins(cf. Figs. 7-9). This is outlined as follows: it was and 87.8+0.6)are somewhat larger than the calculated smaller strain energy as compared to (011) type II annealed coarse grained NiTi where aR >89o r2s case of proposed that (00 1)compound twinning leads to a critical angle but the agreement is better than in the ca twinning [29, 30]. In addition, a decrease of the twinning period d1+d2 decreases the elastic energy Awe(strain 4.3.4. R-phase transformation energy per unit transformed volume)[31]. However, It is concluded that the constraints of the grain with decreasing d the twin boundary area At and boundaries should have little effect on the B2 to R-phase therefore the twin boundary energy A,7t of the trans- transformation since in this case the transformation formed volume increase. From the observed very small shape strain is significantly smaller (roughly 1% as twinning period it can be concluded that the specific compared to 10% in the case of the B2 to B19 trans- twin boundary energy it of the(00 1) compound twins formation). This is in agreement with the present results must be very small. It should be mentioned that in the since on cooling the r-phase precedes the martensite in present case (cf. Fig. 9) the thinnest lamellae of the the small grains. The critical diameter of nuclei of the r compound twins contain two martensite unit cells (i.e. phase was estimated to be about 4-8 nm by in situ TEM four(002) lattice planes yielding d=0.9 nm). Since the analysis [36]. Therefore, the R-phase transformation separations of the twin boundaries are comparable to expected to be completely suppressed in very small the interatomic distance the nanotwinned martensite grains as shown in Table 1. In grains having a size in the may be regarded as an adaptive martensite phase as range from 15 to 50 nm small strains could be present proposed by [28]. Finally, experimental results found in prior to the transformation that may help to accom the literature [29, 30, 32] indicate that a variety of modate a single variant of the R-phase elastically In the constraints as dislocations, grain boundaries and pre- grains larger than 50 nm, however, the shape strains cipitates that may inhibit self-accommodation lead to have to be accommodated by twins that have a small the same preferred mode of the transformation involv- width to decrease Awe(cf. Fig. 6(a). Therefore as ex- ing(001)compound twinning to decrease the strain pected, caused by the constraints of the grain bound energy aries the width of the twins(20-50 nm) is significantly The experimental results show that in grains smaller smaller in the nanograins as compared to that of about than 60nm(cf. Table 1)no thermally induced martensitic 300 nm measured in coarse grained NiTi alloys[371 phase transformation occurs. It is proposed that this is caused by the decrease of self-accommodation with de- creasing grain size since per unit of transformed volume 5. Conclusions an increasing chemical driving force-Ag(<O)i.e a larger undercooling is required to overcome an increasing en- 1. A NiTi alloy was subjected to HPt deformation lead ergy barrier Agnc(>0)including elastic(Awe)and surface ing to amorphization. Nanocrystalline debris is re- (At,)energy. The present conclusions are in agreement tained in the amorphous phase; the size and the with calculations of Agne carried out for ZrO2 nanopar- number of the retained crystallites is decreasing with ticles containing twinned martensite [33]. Similar to the increasing HPT strain present case smaller particles are more stable against the 2. The amorphous phase shows low thermal stability. It martensitic transformation than larger ones is concluded that heterogeneous crystallization is trig- It should be mentioned that previously (00 1)com gered by the retained crystallites that have survived pound twins of the martensitic phase were considered as the hpt deformation deformation twins only since they do not agree with the 3. Isothermal annealing is leading to nanocrystalline phenomenological theory of the B2 to B19 transfor- structures with grain sizes in the range of 5-350 nm mation in NiTi as no invariant habit plane can occur depending on the annealing temperature and the den [29]. In the nanocrystalline alloy the presence of an in- sity of the heterogeneous nucleation sites present in variant habit plane is less important for the transfor the amorphous phase. This leads to the conclusion mation since the bl9 phase will mainly occur attached that the strain of the hpt deformation determinesnanocrystalline NiTi the mean grain size (30–160 nm, cf. Figs. 4 and 5) represents a length scale of the same order as that of the twinning period and smaller than that of the self-accommodating groups in a coarse grained al￾loy. Therefore, in the nanograins the constraints of the grain boundaries suppress the formation of self-accom￾modating variants. As a consequence within the nano￾grains a different path of the transformation occurs that is leading to the required decrease of the transformation strains by the formation of very fine (0 0 1) compound twins (cf. Figs. 7–9). This is outlined as follows: it was proposed that (0 0 1) compound twinning leads to a smaller strain energy as compared to h011i type II twinning [29,30]. In addition, a decrease of the twinning period d1 + d2 decreases the elastic energy Dwe (strain energy per unit transformed volume) [31]. However, with decreasing d the twin boundary area At and therefore the twin boundary energy Atct of the trans￾formed volume increase. From the observed very small twinning period it can be concluded that the specific twin boundary energy ct of the (0 0 1) compound twins must be very small. It should be mentioned that in the present case (cf. Fig. 9) the thinnest lamellae of the compound twins contain two martensite unit cells (i.e. four (0 0 2) lattice planes yielding d ¼ 0:9 nm). Since the separations of the twin boundaries are comparable to the interatomic distance the nanotwinned martensite may be regarded as an adaptive martensite phase as proposed by [28]. Finally, experimental results found in the literature [29,30,32] indicate that a variety of constraints as dislocations, grain boundaries and pre￾cipitates that may inhibit self-accommodation lead to the same preferred mode of the transformation involv￾ing (0 0 1) compound twinning to decrease the strain energy. The experimental results show that in grains smaller than 60nm (cf. Table 1) no thermally induced martensitic phase transformation occurs. It is proposed that this is caused by the decrease of self-accommodation with de￾creasing grain size since per unit of transformed volume an increasing chemical driving force)Dgc (<0) i.e. a larger undercooling is required to overcome an increasing en￾ergy barrier Dgnc (>0) including elastic (Dwe) and surface (Atct) energy. The present conclusions are in agreement with calculations of Dgnc carried out for ZrO2 nanopar￾ticles containing twinned martensite [33]. Similar to the present case smaller particles are more stable against the martensitic transformation than larger ones. It should be mentioned that previously (0 0 1) com￾pound twins of the martensitic phase were considered as deformation twins only since they do not agree with the phenomenological theory of the B2 to B190 transfor￾mation in NiTi as no invariant habit plane can occur [29]. In the nanocrystalline alloy the presence of an in￾variant habit plane is less important for the transfor￾mation since the B190 phase will mainly occur attached to grain boundaries. Also the grain boundaries might even trigger the formation of twins [34]. Finally, it was proposed recently that during the R￾phase to B190 transformation (0 0 1) compound twinning could give rise to an invariant plane strain under the condition of a critical value aR 6 86:2 [29]. In the present case the martensitic transformation is preceded by the formation of R-phase as required for (0 0 1) compound twinning acting as lattice invariant strain. As deduced from Fig. 6(c) the measured RT values of aR (88.5  0.6 and 87.8  0.6) are somewhat larger than the calculated critical angle but the agreement is better than in the case of annealed coarse grained NiTi where aR P89 [35]. 4.3.4. R-phase transformation It is concluded that the constraints of the grain boundaries should have little effect on the B2 to R-phase transformation since in this case the transformation shape strain is significantly smaller (roughly 1% as compared to 10% in the case of the B2 to B190 trans￾formation). This is in agreement with the present results since on cooling the R-phase precedes the martensite in the small grains. The critical diameter of nuclei of the R￾phase was estimated to be about 4–8 nm by in situ TEM analysis [36]. Therefore, the R-phase transformation is expected to be completely suppressed in very small grains as shown in Table 1. In grains having a size in the range from 15 to 50 nm small strains could be present prior to the transformation that may help to accom￾modate a single variant of the R-phase elastically. In the grains larger than 50 nm, however, the shape strains have to be accommodated by twins that have a small width to decrease Dwe (cf. Fig. 6(a)). Therefore as ex￾pected, caused by the constraints of the grain bound￾aries the width of the twins (20–50 nm) is significantly smaller in the nanograins as compared to that of about 300 nm measured in coarse grained NiTi alloys [37]. 5. Conclusions 1. A NiTi alloy was subjected to HPT deformation lead￾ing to amorphization. Nanocrystalline debris is re￾tained in the amorphous phase; the size and the number of the retained crystallites is decreasing with increasing HPT strain. 2. The amorphous phase shows low thermal stability. It is concluded that heterogeneous crystallization is trig￾gered by the retained crystallites that have survived the HPT deformation. 3. Isothermal annealing is leading to nanocrystalline structures with grain sizes in the range of 5–350 nm depending on the annealing temperature and the den￾sity of the heterogeneous nucleation sites present in the amorphous phase. This leads to the conclusion that the strain of the HPT deformation determines 146 T. Waitz et al. / Acta Materialia 52 (2004) 137–147