T. Waitz et al. I Acta Materialia 52(2004)137-147 to S=6.7 and annealed at the same temperature (cf. It should be noted that a suppression of a martensitic Figs. 4 and 5). In addition, when the retained crystallites phase transformation was also observed in small particles are not distributed uniformly a nanocrystalline phase and it was proposed that the fraction of particles con- with a heterogeneous distribution of the grain sizes taining a lattice defect suitable for heterogeneous nucle- arises after crystallization (as shown at S and M in ation is decreasing with decreasing grain size [24] Fig 4(b). Finally, as compared to an annealing tem- However, these statistical arguments seem to fail in the perature of 340C the growth rate is expected to be case of FeNi nanoparticles(size from 10-200 nm) since higher at Ta=450C(Ta/Tm=0.46) leading to larger the particles easily transform above RT although both grain sizes(compare Figs. 4(b) and(c)) experimental observations and calculations indicate that heterogeneous nucleation sites are not contained within 4.3. Phase transformations occurring in the nanocrystal he particles; therefore it was proposed that heteroge- neous nucleation sites are provided by the surfaces of the nanoparticles [25]. Similar, in the present case it is con Based on the results of the TEM analysis summarized cluded that in the nanocrystalline NiTi alloy the mar- in Table I it is concluded that in the nanocrystalline Ni- tensitic transformation is not suppressed by a lack of 603at %Ti alloy the martensitic transformation is sup- nucleation sites as the density of heterogeneous nucle- pre grain size. This ation sites provided by the grain boundaries may even transformed volume fraction decreases with decreasing increase with increasing grain boundary area and de- grain size and the onset of the martensitic transforma creasing n size ion is shifted towards lower temperatures. Therefore, Ms drops below the transformation temperature of the 43. 2. Constraints arising by the grain boundaries R-phase(TR)in grains smaller than about 150 nm It is proposed that the grain boundaries impose ading to a two step transformation from the B2 aus- constraints on the growth of the martensite confinin tenite via the R-phase to the B19 martensite. Finally, in the transformed volume fraction in the nanocrystalline grains smaller than about 60 nm the martensitic phase structure. A martensite plate nucleated within a grain transformation is completely suppressed. will be stopped at the grain boundaries acting as ob- Similar results of suppressing Ms were reported in the stacles To propagate the transformation the plate has to case of a cold rolled Ni-498Ti alloy containing a exert stresses that are sufficient to stimulate nucleation nanocrystalline phase [5]. a decrease of Ms below TR is and growth of favourable martensite variants in the also observed in coarse grained NiTi alloys and could be adjacent grains [22]. However, little stresses are expected caused by a high density of dislocations induced during to occur ahead of a small plate bound within an nano- rolling [18] or coherent precipitates induced by aging grain that has a size of less than 100 nm [26]. In addi- [19]. It was proposed that in a nanocrystalline NiTi alloy tion, as deduced from TEM observations in NiTi a the martensitic transformation could be suppressed in restriction was proposed for the autocatalytic nucleation different ways: by the introduction of elastic strains, by of self accommodating plate groups [27]. This is based lattice defects or by crystal refinement [5, 6]. In the on a twin relation of all the martensite variants in the present investigation almost no dislocations and little group which is possible only within a single grain since elastic strains were encountered in the grains(cf Fig 4). martensite variants occurring in adjacent grains have Therefore it is concluded that the grain refinement leads not the required orientation relationship. Therefore, in to the suppression of the transformation. In this context the present case it is concluded that in a volume con aspects concerning nucleation sites, grain boundaries, taining many small grains the ability of spreading the twinning and the R-phase transformation are discussed transformation by autocatalytic nucleation decreases in the following paragraphs with increasing grain boundary area in agreement with the observed decrease of the martensite volume fraction 4.3.1. Nucleation sites in the nanograins Specific dislocation configurations as dislocation walls 4.3.3.(001) Compound twinning or dislocation pile-ups are generally considered as possi As outlined by [28] a martensitic phase transforma- le nucleation sites [20, 21]; in coarse grained NiTi alloys tion will follow a path of almost complete accommo- there is direct experimental evidence that martensite is dation of the transformation shape strains. In coarse nucleating at dislocations tangles in the matrix and near grained NiTi two different mechanisms occurring at grain boundary dislocations[22]. Since in the present case different length scales facilitate the strain accommoda almost no dislocations occur within the nanograins it is tion: Firstly, twinning by(011) type II or (1 1 1)type I oncluded that the grain boundaries act as the heteroge twins(at scale of 30-100 nm) leading to an invariant neous nucleation sites. This is in agreement with experi- plane strain; secondly, at a scale far exceeding 100 nm mental results indicating that in NiTi the grain boundaries self-accommodation of groups of different habit plane can favour the martensitic transformation[23] variants arises [27, 29]. In the present case of theto S ¼ 6:7 and annealed at the same temperature (cf. Figs. 4 and 5). In addition, when the retained crystallites are not distributed uniformly a nanocrystalline phase with a heterogeneous distribution of the grain sizes arises after crystallization (as shown at S and M in Fig. 4(b)). Finally, as compared to an annealing tem￾perature of 340 C the growth rate is expected to be higher at Ta ¼ 450 C ðTa=Tm ¼ 0:46Þ leading to larger grain sizes (compare Figs. 4(b) and (c)). 4.3. Phase transformations occurring in the nanocrystal￾line grains Based on the results of the TEM analysis summarized in Table 1 it is concluded that in the nanocrystalline Ni– 50.3at.%Ti alloy the martensitic transformation is sup￾pressed with decreasing grain size. This means, the transformed volume fraction decreases with decreasing grain size and the onset of the martensitic transforma￾tion is shifted towards lower temperatures. Therefore, Ms drops below the transformation temperature of the R-phase (TR) in grains smaller than about 150 nm leading to a two step transformation from the B2 aus￾tenite via the R-phase to the B190 martensite. Finally, in grains smaller than about 60 nm the martensitic phase transformation is completely suppressed. Similar results of suppressing Ms were reported in the case of a cold rolled Ni–49.8Ti alloy containing a nanocrystalline phase [5]. A decrease of Ms below TR is also observed in coarse grained NiTi alloys and could be caused by a high density of dislocations induced during rolling [18] or coherent precipitates induced by aging [19]. It was proposed that in a nanocrystalline NiTi alloy the martensitic transformation could be suppressed in different ways: by the introduction of elastic strains, by lattice defects or by crystal refinement [5,6]. In the present investigation almost no dislocations and little elastic strains were encountered in the grains (cf. Fig. 4). Therefore it is concluded that the grain refinement leads to the suppression of the transformation. In this context aspects concerning nucleation sites, grain boundaries, twinning and the R-phase transformation are discussed in the following paragraphs. 4.3.1. Nucleation sites in the nanograins Specific dislocation configurations as dislocation walls or dislocation pile-ups are generally considered as possi￾ble nucleation sites [20,21]; in coarse grained NiTi alloys there is direct experimental evidence that martensite is nucleating at dislocations tangles in the matrix and near grain boundary dislocations [22]. Since in the present case almost no dislocations occur within the nanograins it is concluded that the grain boundaries act as the heteroge￾neous nucleation sites. This is in agreement with experi￾mental results indicating that in NiTi the grain boundaries can favour the martensitic transformation [23]. It should be noted that a suppression of a martensitic phase transformation was also observed in small particles and it was proposed that the fraction of particles con￾taining a lattice defect suitable for heterogeneous nucle￾ation is decreasing with decreasing grain size [24]. However, these statistical arguments seem to fail in the case of FeNi nanoparticles (size from 10–200 nm) since the particles easily transform above RT although both experimental observations and calculations indicate that heterogeneous nucleation sites are not contained within the particles; therefore it was proposed that heteroge￾neous nucleation sites are provided by the surfaces of the nanoparticles [25]. Similar, in the present case it is con￾cluded that in the nanocrystalline NiTi alloy the mar￾tensitic transformation is not suppressed by a lack of nucleation sites as the density of heterogeneous nucle￾ation sites provided by the grain boundaries may even increase with increasing grain boundary area and de￾creasing grain size. 4.3.2. Constraints arising by the grain boundaries It is proposed that the grain boundaries impose constraints on the growth of the martensite confining the transformed volume fraction in the nanocrystalline structure. A martensite plate nucleated within a grain will be stopped at the grain boundaries acting as ob￾stacles. To propagate the transformation the plate has to exert stresses that are sufficient to stimulate nucleation and growth of favourable martensite variants in the adjacent grains [22]. However, little stresses are expected to occur ahead of a small plate bound within an nano￾grain that has a size of less than 100 nm [26]. In addi￾tion, as deduced from TEM observations in NiTi a restriction was proposed for the autocatalytic nucleation of self accommodating plate groups [27]. This is based on a twin relation of all the martensite variants in the group which is possible only within a single grain since martensite variants occurring in adjacent grains have not the required orientation relationship. Therefore, in the present case it is concluded that in a volume con￾taining many small grains the ability of spreading the transformation by autocatalytic nucleation decreases with increasing grain boundary area in agreement with the observed decrease of the martensite volume fraction. 4.3.3. (0 0 1) Compound twinning As outlined by [28] a martensitic phase transforma￾tion will follow a path of almost complete accommo￾dation of the transformation shape strains. In coarse grained NiTi two different mechanisms occurring at different length scales facilitate the strain accommoda￾tion: Firstly, twinning by h011i type II or ð1 1
1Þ type I twins (at scale of 30–100 nm) leading to an invariant plane strain; secondly, at a scale far exceeding 100 nm self-accommodation of groups of different habit plane variants arises [27,29]. In the present case of the T. Waitz et al. / Acta Materialia 52 (2004) 137–147 145