Room temperature deformation of single crystals of Ti5Si3 with the hexagonal D88 structure investigated by micropillar compression tests

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Since the gas inlet temperature of the advanced turbine systems already exceeds 1700 °C that is much higher than the melting temperature (~ 1350 °C) of Ni-based superalloys, there is an ever-increasing demand for developing ultra high-temperature structural materials that can withstand at temperatures well above the maximum operating temperatures of Ni-base superalloys in severe oxidizing atmosphere 1,2 . Silicides with the chemical formula of TM 5 Si 3 formed with transition-metals (TMs) are of interest, as most of them exhibit the highest melting temperature in each of the corresponding TM-Si binary phase diagrams and a reasonably good oxidation property due to the high Si content 3 . Indeed, Nb 5 Si 3 and Mo 5 SiB 2 with the tetragonal D8 l structure and Mo 5 Si 3 with the tetragonal D8 m structure have intensively been investigated in the last several decades as the strengthening phases of Nb- [4][5][6][7] and Mo-8-10 based refractory alloys, respectively. Ti 5 Si 3 with the hexagonal D8 8 structure, on the other hand, has been investigated initially as a constituent phase of Ti-Ti 5 Si 3 in-situ composites 11 and in recent years as the strengthening phase of Mo-Mo 5 SiB 2 based alloys because the creep strength and oxidation resistance are significantly improved by replacing a large amount of Mo with Ti so as to incorporate Ti 5 Si 3 as the constituent phase of Mo-Mo 5 SiB 2 based alloys [12][13][14][15][16][17] . Because of some excellent properties as a promising structural material for ultra-high temperature applications [the high melting temperature (2130 °C) and low density (4.32 g/cm 3 )], the deformation behavior of monolithic Ti 5 Si 3 has been investigated with polycrystals 11 and single crystals 18,19 . Frommeyer et al. 11 reported that Ti 5 Si 3 is extremely brittle at low temperatures as expected from the complex crystal structure of the D8 8 type (Pearson symbol: hP16, Space group: P6 3 /mcm). Plastic flow is observed only above 1000 °C in polycrystals, while Umakoshi and Nakashima 18 reported plastic flow carried by deformation twinning of the {1102} < 1101 > -type at high temperatures above 1300 °C in single crystals with some limited orientations. Then, Kishida et al. 19  www.nature.com/scientificreports/ Recently, micropillar compression testing that utilizes small specimens of the micron-meter scale has been recognized as a powerful method to investigate the plastic deformation behavior of hard and brittle materials at a low temperature (for example, room temperature) well below their onset temperatures (above 1000 °C for most of these materials) for plastic flow in the bulk form. Those hard and brittle materials include intermetallics with complex crystal structures 20-25 , semiconductors [26][27][28][29][30][31] and ceramics [32][33][34][35] . We have investigated the room-temperature plastic deformation behavior of various hard and brittle materials including D8 l -Mo 5 SiB 2 24 , D8 l -Nb 5 Si 3 25 , 6H-SiC 31 and so on [21][22][23] and have successfully identified operative slip systems and their critical resolved shear stress (CRSS). Of particular interest to note is that slip systems that do not participate in the high temperature deformation in the bulk form do participate in the room-temperature deformation in the micropillar form 24,25,31 and that completely different dislocation dissociation schemes are observed at high (bulk) and low (micropillar) temperatures even when the same slip system operates. Thus, the CRSS at a low temperature obtained in the micropillar form is plotted far away from the extrapolation of the temperature-dependent CRSSs obtained at high temperatures in the bulk form 31 . Such information about the room-temperature deformation behavior must be very important to conceive a strategy to improve the brittleness at low temperatures of these hard and brittle materials.
In the present study, we investigate the room-temperature deformation behavior of single crystals of Ti 5 Si 3 with the hexagonal D8 8 structure as a function of specimen size and loading-axis orientation by micropillar compression tests, to get information that might be useful for the improvement of the brittleness at low temperatures. flat portion corresponding to a strain burst is commonly observed soon after elastic loading in many stressstrain curves regardless of the loading-axis orientation. Although a strain burst is followed by a load drop in most cases, that is not included in Fig. 1. As observed in other micropillar compression tests of single crystals of www.nature.com/scientificreports/ metallic materials [36][37][38][39][40] , the occurrence of a strain burst in stress-strain curves in Ti 5 Si 3 is considered to be plastic flow caused by dislocation motion in avalanches, as in the case of Mo 5 SiB 2 24,37,40 . Being consistent with the occurrence of plastic flow caused by dislocation motion in avalanches, most micropillar specimens exhibit slip plane (shear) failure, accompanied by giant steps on the slip plane along the slip direction ( Fig. 2). Deformation microstructures with the three orientations are shown in Fig. 2a-c for some specimens in which micropillar testing was successfully interrupted before instantaneous slip plane failure occurs. For the [2205] orientation ( Fig. 2a), analysis of slip traces that appeared on two orthogonal side-surfaces has identified the slip plane to be (1100). Because shear deformation occurs so as to maintain the ( 1120) side-surface flat, the shear direction is contained in the ( 1120) plane and is determined to be [0001]. The slip system operative in [2205]-oriented micropillar specimens is thus identified to be (1100)[0001], as observed in the same orientation of bulk single crystals at above 1300 °C 19 .

Compression deformation behavior.
For the [431 0] orientation, deformation markings corresponding to slip on (1101) are observed on two orthogonal side faces. On the assumption that slip on this plane occurs along either a or a + c direction (when expressed with the hexagonal lattice parameters), the possible slip vectors in the [431 0] orientation are [1120], [21 13 ] and [1213 ], the latter two of which have the identical Schmid factors. Of the three, [112 0] is ruled out, since deformation markings are clearly observed also on the (0001 ) side-surface that contains the [112 0] direction (Fig. 2b). The slip system identified in [4310]-oriented micropillar specimens is thus identified to be {1101} < 21 13 > . This slip system has never been identified to operate in bulk single crystals. In bulk single crystals with the same [431 0] orientation, {2112} < 2113 > pyramidal slip was identified to operate above 1400 °C 19 .
Fracture toughness. Micro-cantilever bend tests on chevron-notched micro-beam specimens were conducted to evaluate the fracture toughness. The load-displacement curves obtained for chevron-notched microbeam specimens with a notch plane parallel to (0001) and (1100) are shown in Fig. 3a. The loading directions were set parallel to [1100] and [0001] for (0001)-and (1100)-notched micro-beam specimens, respectively. The load-displacement curves (Fig. 3a) exhibit no sign of apparent plastic deformation before failure occurs. In addition, a fairly flat fracture surface observed in the SEM image for the (0001)-notched micro-beam specimen indicates the occurrence of brittle cleavage fracture (Fig. 3b). The values of fracture toughness can then be evaluated simply from the maximum load and geometrical parameters of the chevron-notched specimens based on the model proposed by Deng et al. 41 , details of which were described in our previous papers 24 . The fracture toughness values of Ti 5 Si 3 are evaluated to be 0.45 and 0.73 MPa m 1/2 respectively with the notch plane parallel to (0001) and (1100), both of which are considerably lower than those for D8 l -Mo 5 SiB 2 (2.43 MPa m 1/2 ; notch plane // (100)) and D8 l -Nb 5 Si 3 (1.79 MPa m 1/2 ; notch plane // (001)) evaluated by the same method 24,25 .

Discussion
The CRSS values (τ CRSS ) for the three slip systems identified in the present study are calculated with yield stresses defined as the stress at which the first strain burst occurs and the corresponding Schimid factors as plotted in Fig. 4a as a function of specimen size (the edge length L). The CRSS values for all slip systems are extremely high exceeding 2.6 GPa regardless of specimen size and exhibit the so-called "smaller is stronger" trends, following an inverse power-law relationship, τ CRSS ∝ L −n (n: the power-law exponent), as commonly observed in micropillar compression of single crystals of many metallic materials, ceramics, semiconductors and intermetallic compounds [22][23][24][25][30][31][32][33]35,36,38,39,42,43   where m is the stress exponent and k is the Boltzmann constant 44 . Apparently, the room-temperature bulk CRSS values estimated for {1100}[0001] prism slip, {2112} < 2113 > pyramidal slip are much lower than those expected from the extrapolation of the ln τ CRSS − (1/T) relations for the deformation modes operative at high temperatures. This suggests that the deformation mechanism that governs the CRSS for {1100}[0001] prism slip and {21 12} < 2113 > pyramidal slip varies depending on testing temperature. One possible explanation for the different deformation mechanisms operating at high and low temperatures is that the room-temperature bulk CRSSs estimated in the micropillar form is determined by the nucleation of new dislocations from specimen surfaces of micropillars, as we discussed previously for 6H-SiC 31 and α-Nb 5 Si 3 25 because virtually no grown-in dislocation is expected to exist in micropillar specimens of Ti 5 Si 3 single crystals when judged from the brittleness and high CRSSs. However, more detailed studies including dislocation analysis by TEM are definitely needed to prove this.
The expected orientation-dependent operative slip systems are calculated based on the estimated bulk CRSS values for the three slip systems identified in micropillar compression tests and are shown in the stereographic projection of Fig. 4c 19 . The absence of {2118} < 8443 > twinning at room temperature is easily understood from the fact that {21 18} < 8443 > twinning requires very complicated atomic shuffling to restore the crystal structure during deformation twinning, so that it can happen only at sufficiently high temperatures at which sufficient atomic diffusion   (1101)), generalized stacking fault energy (GSFE) for < 2113 > slip on (211 2) and (1101) were calculated by first-principles DFT calculations. Figure 5 plots the GSFE curves and their derivatives (the gradient of the GSFE curve corresponding to the ideal shear strength, τ th ) for the two pyramidal slip systems of (2112)[2113 ] and (1101) [2113 ]. For (211 2) and (1101) slip planes, there exist four and three different possible slip planes to be considered, respectively (see, the insets of Fig. 5a). Among the possible slip planes, only the calculation results for the slip planes exhibiting the lowest ideal shear strength and unstable stacking fault energies are indicated in Fig. 5. The selected slip planes are indicated with red and blue lines respectively, while the others are indicated with dashed black lines in the insets of Fig. 5a. To be noted in Fig. 5 is that the GSFE curves and their derivative curves are asymmetric on both slip planes with respect to the [2113 ] slip direction and that the displacement along the positive direction gives rise to compression strain for the [0001] orientation while that along the negative direction does so for the [431 0] orientation. Table 1 summarizes the results of the GSFE calculations. For both orientations, the ideal shear strength and unstable stacking fault energy are both lower  www.nature.com/scientificreports/ on (211 2) than on (1101), suggesting the preference for the (211 2) slip plane for both orientations. This situation does not change even the ideal shear strength is normalized to the corresponding Schmid factors for each loading orientation (the normalized ideal shear strength, τ th /m in Table 1). . We believe that the difference in τ th /m is too small to draw a final conclusion for the slip plane preference for this orientation. One more thing to be noted in Table 1 is that the magnitude correlation for the ideal shear strength (τ th ) for the (211 2) and (1101) slip planes (22.5 and 16.8 GPa) is opposite to that for the bulk CRSS values deduced from micropillar experiment (1.90 and 2.32 GPa). We believe that this discrepancy comes from the fact that no dislocation dissociations, especially those accompanied by non-collinear Burgers vectors, are taken into account in the above discussion based on the GSFE calculations. In view of the large magnitude (about 0.906 nm) of the Burgers vectors of 1/3 < 2113 > , the 1/3 < 2113 > dislocation is expected to dissociate into partial dislocations with shorter Burgers vectors. In order to deduce the possible dissociation scheme for 1/3 < 2113 > dislocation, construction of full gamma surfaces on (211 2) and (1101) planes must be made, because experimental identification of the dissociation scheme is extremely difficult with the occurrence of instantaneous shear failure in micropillar specimens. The construction of gamma surface is currently in progress in the authors' research group to draw the final conclusion on the slip plane preference.

Methods
A single crystal rod of Ti 5 Si 3 was grown from an ingot with a nominal composition of Ti − 37.5 at.% Si by directional solidification with an optical floating-zone furnace at a growth rate of 6 mm/h. Characteristics in the atomic arrangement and crystal structure of Ti 5 Si 3 are detailed in our previous paper 19 Table 1 of our previous paper 19 . After the mirror finishing of specimen surface by mechanical polishing with diamond paste, micropillar specimens with a square cross-section having an edge length L ranging from 0.5 to 3.6 μm and a specimen height-to-L ratio of 1:3-1:5 were fabricated by the focused-ion beam (FIB) machining with a JEOL JIB-4000 FIB milling and imaging system operated at 30 kV. Micropillar compression tests were conducted at room temperature under the displacement-rate controlled mode (a nominal strain rate of 1 × 10 -4 s −1 ) with an Agilent Technologies Nano Indenter G200 nanomechanical tester equipped with a flat-punch diamond indenter tip. Microstructures of micropillar specimens before and after the compression tests were investigated by scanning electron microscopy (SEM) in order to measure dimensions and analyze slip traces, respectively. SEM observations were made along the direction inclined by 30° from the loading axis. Single cantilever bend tests were conducted with chevronnotched micro-beam specimens to evaluate the fracture toughness, as the details of the experimental procedures are described in our previous paper 24 . Generalized stacking fault energy (GSFE) for 1/3 < 2113 > slip on (211 2) and (1101) were calculated by firstprinciples DFT calculations using the Vienna ab-initio simulation package (VASP) code [45][46][47] . The generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) was used to treat the exchange-correlation functional 48 . We used supercells for the GSFE calculations for (211 2) and (1101) planes respectively containing 192 and 96 atoms, in each of which the Ti:Si atomic ratio was fixed at 5:3 so as to maintain the stoichiometry of Ti 5 Si 3 . The in-plane units of the supercells were defined by unit vectors along [2113 ] and [011 0] for the (211 2) supercell and by those along [2113 ] and [1213] for the (1101) supercell. A vacuum layer with a total thickness of 1.5 nm (when measured along the slip plane normal) is included in each supercell. Monkhorst-Pack k-point meshes of 10 × 8 × 2 and 8 × 8 × 2 were used for the (211 2) and (1101) supercells, respectively 49 . An energy cutoff of 500 eV was used throughout the calculations. All atoms were relaxed only along the direction perpendicular to the glide plane so as to minimize the energy of the supercell with a given in-plane displacement 24 .

Conclusions
The room-temperature deformation behavior of Ti 5 Si 3 was investigated by micropillar compression tests as a function of loading-axis orientation and specimen size and micro-cantilever bend tests with chevron-notched specimens. The results obtained are summarized as follows. with chevron-notch planes parallel to (0001) and (1100), respectively. The fracture toughness values are considerably lower than those for D8 l -Mo 5 SiB 2 (2.43 MPa m 1/2 ; notch plane // (100)) and D8 l -Nb 5 Si 3 (1.79 MPa m 1/2 ; notch plane // (001)) evaluated by the same method, indicating much more significant inherent brittleness of Ti 5 Si 3 compared to the other transition-metal silicides of the TM 5 Si 3 type.