Spinodally decomposed nanostructures in a TiO2–VO2 crystal Z. Hiroi, T. Yoshida, J. Yamaura, and Y. Okamoto Citation: APL Materials 3, 062508 (2015); doi: 10.1063/1.4919764 View online: http://dx.doi.org/10.1063/1.4919764 View Table of Contents: http://scitation.aip.org/content/aip/journal/aplmater/3/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nanostructured VO2 film with high transparency and enhanced switching ratio in THz range Appl. Phys. Lett. 104, 071903 (2014); 10.1063/1.4863408 Direct observation of giant metallic domain evolution driven by electric bias in VO2 thin films on TiO2(001) substrate Appl. Phys. Lett. 101, 243118 (2012); 10.1063/1.4772211 Metal-insulator transition sustained by Cr-doping in V2O3 nanocrystals Appl. Phys. Lett. 100, 043103 (2012); 10.1063/1.3679396 Effect of annealing on the microstructure and optical properties of ZnO / V 2 O 5 composite Appl. Phys. Lett. 98, 111904 (2011); 10.1063/1.3566997 Spectroscopic evidence of the formation of (V,Ti)O2 solid solution in VO2 thinner films grown on TiO2(001) substrates J. Appl. Phys. 109, 043702 (2011); 10.1063/1.3549835
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APL MATERIALS 3, 062508 (2015)
Spinodally decomposed nanostructures in a TiO2–VO2 crystal Z. Hiroi,a T. Yoshida, J. Yamaura,b and Y. Okamotoc Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277–8581, Japan
(Received 18 March 2015; accepted 23 April 2015; published online 6 May 2015) We have prepared a single crystal of Ti0.4V0.6O2 which forms a solid solution crystallizing in the rutile structure at high temperatures and undergoes phase separation due to the spinodal decomposition when cooled to room temperature. The spinodally decomposed crystal consists of a self-assembled, mega stack of alternate Ti- and Vrich layers with an approximate period of 33 nm along the c axis. The unidirectional microstructure causes a large anisotropy in resistivity and a small one in thermal conductivity. A sharp metal–insulator transition as well as a structural transition to a monoclinic structure is observed in the thin V-rich layers. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4919764]
Microstructures associated with phase separations are often important in determining the mechanical and electric properties of actual materials. To obtain a hard steel, for example, it is crucial to control eutectoid reactions in the Fe–C system from high-temperature austenite (γ-Fe) to a mixture of ferrite (α-Fe) and cementite (Fe3C): the hardness depends on the size, amount, and distribution of hard cementite grains.1 In a more recent trend of thermoelectric applications, self-assembled lamellar structures of PbTe and Sb2Te3 were prepared utilizing a eutectic reaction between them.2 The spinodal decomposition (SD) is one of the phase separation mechanisms, in which a solid solution becomes thermodynamically unstable against a minimal composition fluctuation, and a nearly sinusoidal composition modulation occurs and develops upon cooling or with time duration after quenching from high temperatures.3 Finally, completely phase-separated microstructures with square-wave like composition modulations are obtained. The SD is a general phenomenon ubiquitously observed in various systems such as alloys, polymers, glasses, oxides, and even in the beginning of the universe.4,5 Since the SD initially takes place “uniformly” with a long-range spatial correlation, quasi-periodic, self-assembled two-phase mixtures with various kinds of morphologies are obtained at the nanometer scale. Actually, the mechanical properties of some alloys and polymer blends are affected by the SD morphologies containing lamellas or bubbles.4 The TiO2–SnO2 system gives a typical example for SD in oxides.6,7 Both the component oxides crystallize in the tetragonal rutile structure (Fig. 1) and form a complete solid solution above 1723 K. The SD takes place below this temperature, resulting in modulated structures composed of Ti- and Sn-rich phases with periods of 10–100 nm. A unique feature of this SD system is the strong anisotropy:8,9 a composition modulation occurs only along the c axis, reflecting the tetragonal symmetry as well as a smaller lattice mismatch along the a axis (1.5%) than the c axis (3.7%); the modulation direction should be chosen so as to minimize the elastic strain energy at the interface between two phases. This is a great advantage to obtain a well-ordered, natural superlattice by SD. Note that most SDs in cubic alloys or polymer blends possess no such preference in direction,
a Author to whom correspondence should be addressed. Electronic mail: [email protected] b Present address: Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama, Kanagawa
226–8503, Japan.
c Present address: Department of Applied Physics, Nagoya University, Chikusa-ku, Nagoya 464–8603, Japan.
2166-532X/2015/3(6)/062508/8
3, 062508-1
© Author(s) 2015
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FIG. 1. Schematic representation of a spinodal decomposition in the TiO2–VO2 system. A solid solution crystal between the two components is stable above 830 K, which crystallizes in the rutile structure with Ti/V atoms statistically occupying the position surrounded octahedrally by six oxide atoms. A spinodal decomposition occurs at lower temperatures, resulting ideally in such a natural superlattice crystal having a mega stack of alternate Ti- and V-rich layers along the c axis with periods of 5–50 nm.
resulting in isotropic mixtures of two phases. For applications, the dielectric and gas-sensing properties of spinodally decomposed (Ti,Sn)O2 thin films were investigated.10,11 Recently, we have shown that the TiO2–VO2 system is another example of SD in the rutile family.12,13 A phase diagram with a miscibility gap was determined in a series of polycrystalline samples. We are interested in this system because of distinct differences in their chemical and physical properties: TiO2 without d electrons is a wide band-gap insulator and shows a photocatalytic activity,14,15 while VO2 with one d electron is a metal at high temperatures and becomes an insulator at low temperatures; a metal–insulator (MI) transition takes place at TMI = 342 K upon heating.16 VO2 is potentially important for applications as ultrafast resistive or optical switching devices,17,18 because conductivity and optical absorption change dramatically across the transition. These large differences in properties between the two constituents make the TiO2–VO2 system exceptional; in other SD systems, two constituents possess quite similar properties in all aspects. Therefore, it is intriguing to investigate the properties of spinodally decomposed composites in the system. The MI transition of VO2 is dramatic: a large electrical discontinuity of more than several orders of magnitude is observed across the transition.16,19 It is a first order transition accompanied by a structural transition from the high-temperature tetragonal (P42/mnm) rutile (r) structure to the low-temperature monoclinic (P21/c) structure. A striking feature of this low-temperature structure called M1 is the presence of V–V pairs in the strands of edge-sharing octahedra along the c axis of the tetragonal structure: alternate V–V separations are 2.65 and 3.12 Å in place of the regular 2.87 Å spacing in the tetragonal structure near the transition.19 Since all the 3d electrons are trapped
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by these dimers in their bonding molecular orbitals, the MI transition takes place simultaneously at the structural transition. The mechanism of the MI transition has been greatly debated for decades from various perspectives.19–23 Very recently, one of the authors has proposed that the driving force has nothing to do with electron correlations nor Peierls instability as previously believed but is a structural instability to form a “molecular orbital crystal” by generating a direct metal–metal bonding.13 In the present paper, we report on microstructures generated by SD in a single crystal of Ti0.4V0.6O2. A mega stack of alternate Ti- and V-rich layers with a period of approximately 33 nm along the c axis is observed in the mm-size crystal. A large anisotropy is observed in resistivity owing to the anisotropic microstructure. A MI transition occurs in the thin V-rich layers together with a structural transition to the M1 structure at a reduced temperature of 322 K compared with the bulk value of 342 K. The thermoelectric property is also examined. Single crystals of Ti0.4V0.6O2 were prepared by the floating zone method. A starting polycrystalline sample was synthesized as reported previously12 and was sintered into a dense rod at 1623 K in an argon gas flow for 24 h. The rod was partially melted in a high-pressure argon gas of 5 atm in a four-mirror image furnace (Crystal Systems Corp.) and slowly moved downward so that a crystal grew at a speed of ∼1 mm h−1. A solid-solution crystal was obtained by annealing an as-grown crystal at 1323 K in a quartz tube filled with 1 atm argon gas and then by rapidly quenching into ice water. A completely phase-separated crystal was prepared by further annealing the solid-solution crystal at 673 K for 24 h. Microstructures of as-grown crystals were examined in a transmission electron microscope (JEOL 2010-F). A specimen for observation was prepared by the argon ion milling method. The crystal structure was determined by the single crystal x-ray diffraction (XRD) method using a Mo Kα radiation in a triple-axis diffractometer (Rigaku AFC6S). Resistivity, Seebeck coefficient, and thermal conductivity were measured in a Physical Property Measurement System (Quantum Design). Figure 2(a) shows a photograph of typical crystals picked up from a crushed boule of as-grown crystal. They have cleavages along the (110) and (001) planes (the Miller indices are based on the tetragonal cell). The (110) cleavage is typical for the rutile family of compounds, coming from the crystal structure itself, while the (001) cleavage is rare and thus probably due to layered microstructures by SD. Since the crystals were slowly cooled after solidification from a melt, an SD has already occurred in these as-grown crystals. This is directly evidenced by electron microscopy observations on a thin piece of crushed crystal. Figure 2(b) shows a typical image taken from an edge of crystal, in which bright bands (Ti-rich layers) and dark bands (V-rich layers) appear alternately
FIG. 2. (a) Photograph of pieces of the as-grown Ti0.4V0.6O2 crystal grown by the floating-zone method and (b) electron micrograph showing a lamellar structure in which Ti-rich layers (bright bands with ∼20 nm thickness) and V-rich layers (dark bands with ∼15 nm thickness) alternate with an average periodicity of 33 nm along the c axis.
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along the c axis. The thickness of each layer is 10–20 nm, and the average periodicity is 33 nm. Note that the way of stacking is not perfect but there are “stacking faults” from place to place. We have noticed in later experiments that this irregularity is going to be removed by annealing a solid-solution crystal at 673 K for 24 h. The crystal structure of the as-grown crystal has been examined by means of reciprocal lattice mapping of XRD intensity at room temperature below the TMI. Figure 3(a) shows an intensity map around the 004 reflection in the h0l plane; the index is based on a rutile-type tetragonal unit cell with a = 4.5504 Å and c = 2.8988 Å. Observed in the h0l scan are two spots with nearly same h values and different l values, indicating the presence of two components having different lattice spacings only along the c axis: the spots with smaller and larger l values are assigned to Ti- and V-rich layers, respectively. On the other hand, the h4l scan around the 040 reflection [Fig. 3(b)] shows a single spot, which means a perfect lattice matching along the layers. We have also examined specific reflections that are forbidden in the rutile structure but allowed in the monoclinic M1 structure, such as 0 1/2 7/2 shown in Fig. 3(c). A weak but clear spot is observed only at an l value corresponding to the V-rich layer. Thus, the V-rich layer takes the M1 structure at room temperature below the TMI, while the Ti-rich layer takes the rutile structure. Lattice constants determined from these peak positions are listed in Table I. A relation between the two unit cells is depicted in Fig. 4: am ≈ 2cr, bm ≈ ar, cm ≈ (ar2 + cr2)1/2, where subscripts m and r refer to the monoclinic and rutile structures, respectively. Note that the monoclinic distortion takes place as a result of dimerization of V atoms: the dimerization patterns along the cr or am axis are almost antiphase along the [100]r direction, while in-phase along the [010]r direction perpendicular to the paper in Fig. 4, which gives the monoclinic unit cell. As a result, V dimers are aligned along the [10-1]r or cm direction. Since associated atomic movements mostly occur along the cr axis, a lattice matching can be easily achieved within the cr plane, which is evidenced by the reciprocal mapping of Fig. 3. This is also the reason why the SD occurs with the composition modulation only along the cr axis: a smaller elastic strain energy is achieved at the cr plane. Moreover, this gives a persuasive explanation why the MI transition can take place in such thin lamellas in SD samples12,13 and also in ultrathin VO2 layers in artificial superlattice films.24 It is intriguing to notice that the diffraction spots in Fig. 3 exhibit characteristic broadenings. Either of the 004 spots from the two layers is heavily elongated along the [101]r∗ direction. Moreover, the 0 1/2 7/2 spot from the V-rich layer shows a similar elongation. These elongations are probably related to strain or disorder in the arrangements of V dimers, because the (101)r pane is
FIG. 3. Reciprocal maps of x-ray diffraction intensity for reflections with indices of (a) 004, (b) 040, (c) 0 1/2 7/2, and (d) 004 on the basis of the rutile structure (a = 4.5504 Å and c = 2.8988 Å) for an as-grown Ti0.4V0.6O2 crystal. Shown in (a), (b), and (c) are hl scans at k = 0, 3.99, and 0.50, respectively, and a hk scan at l = 3.92 in (d); the hk scan at l = 3.92 in (d) corresponds to a cross section of the 004 spot from the Ti-rich layers in (a). The x-ray intensity in count per second is plotted by color contour in the scale shown at the bottom. The 0 1/2 7/2 reflection is not observed from Ti-rich layers in the rutile structure but from V-rich layers in the monoclinic M1 structure.
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TABLE I. Structural parameters of Ti- and V-rich layers in an as-grown Ti0.4V0.6O2 single crystal.
Crystal structure a r (Å) c r (Å) Vr (Å3) Ti composition x b a ss(x) (Å)c c ss(x) (Å)c Thickness (nm)d
Ti-rich layer
V-rich layer
Tetragonal rutile 4.567 2.954 61.61 0.65 4.57 2.95 18
Monoclinic M1a 4.567 2.856 59.57 0.11 4.54 2.89 15
constants of the original monoclinic unit cell are a m = 5.712 Å, b m = 4.567 Å, c m = 5.421 Å, and β = 122.6◦. from the Vr–x relation established in solid solutions in the polycrystalline form.12 c Lattice constants of the corresponding solid solutions. dThickness of each layer when the total thickness is 33 nm. a Lattice
bEstimated
the lattice plane along which V dimers are aligned, as mentioned above (Fig. 4). It is likely that the structural coherence is disturbed by certain misplacements of V dimers or a disorder in phase among dimer rows along the cr axis in the V-rich layer, which are caused by the Ti substitution. Interestingly, the fact that a similar elongation is present in the 004 spot from the Ti-rich layer suggests that the Ti-rich layer suffers a strain from the adjacent V-rich layers. Alternatively and more likely, V dimers are locally generated to induce a short-range order toward the M1 structure in the Ti-rich layer containing ∼35% of V atoms (see below) even if the global symmetry is kept tetragonal. Furthermore, there is another elongation for the 004 spot from the Ti-rich layer [Fig. 3(d)], where an hk scan at l = 3.92 is shown, that is, a cross section of the 004 spot in Fig. 3(a). The spot is elongated about 4 times along the [010]r∗ direction compared with that along the [100]r∗ direction. The reason is not clear but may be due to a misfit strain caused by lattice matching between the square lattice of the Ti-rich layer and the essentially orthorhombic lattice of the V-rich layer at the interface. Note that the lattice matching can be easily attained along the [100]r direction by adjusting the β angle, but not so along the [010]r direction, as shown in Fig. 4. The composition of each layer is estimated by using the relation between the unit cell volume Vr of the rutile structure and the Ti composition x, which has been obtained in the previous study on polycrystalline samples: Vr/Å3 = 59.02(4) + 5.0(2)x − 1.6(2)x 2.12 This relation is also valid for spinodally decomposed samples; the volume seems to be decided only by the composition, irrespective of strain. The estimated compositions of the Ti- and V-rich layers in the present Ti0.4V0.6O2
FIG. 4. Atomic structure near an interface (broken line) between a Ti-rich layer crystallizing in the rutile structure (left) and a V-rich layer in the M1 structure (right). The positions of metal atoms are based on those of pure TiO2 and VO2, respectively, and oxide atoms are omitted. The atoms colored faint are located half of the unit cell below the paper. The lattice matching at the interface occurs so as to adjust the interatomic distances parallel to the interface: a r = c m sin β = bm. Note that the Ti(V) atoms in the Ti(V)-rich layer are partially and statistically replaced by V(Ti) atoms.
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crystal are Ti0.65V0.35O2 and Ti0.11V0.89O2, respectively, which are consistent with the spinodal decomposition curve in the phase diagram.12 In addition, the lattice constants of the corresponding solid solutions, which should be natural lattice constants under no strain, are calculated also based on the relations established in the previous study: ar/Å = 4.530(1) + 0.064(2)x and cr/Å = 2.877(2) + 0.153(1)x − 0.07(1)x 2,12 as listed in Table I. Then, the thicknesses of the two layers are obtained to be 18 and 15 nm, respectively, provided that the average periodicity of composition modulation is 33 nm from the electron micrograph of Fig. 2. A comparison in the lattice constants between the layers in the crystal and the corresponding solid solutions reveals that they are nearly the same for the Ti-rich layer, while significantly different for the V-rich layer: the ar is elongated and the cr is compressed from the natural values of the solid solution. This situation is schematically depicted in Fig. 5. The lattice matching at the interface is achieved mostly by deforming the thinner and possibly softer V-rich layer. This strain effect may be important in reducing the TMI of VO2, as mentioned in the next paragraph. In order to investigate the MI transition of VO2, we have measured resistivity on Ti0.4V0.6O2 single crystals heat-treated in various ways. As shown in Fig. 6, an as-grown crystal exhibits a large jump of 3–4 orders of magnitude due to the MI transition taking place in the V-rich layers. Note that there is a difference between two measurements performed with electrical currents running parallel to the cr axis and the [110]r direction. Moreover, the TMI’s are 322 and 326 K upon heating and cooling, respectively, which are about 20 K lower than those of bulk VO2. This reduction is not due to the Ti substitution, because the Ti substitution increases the TMI in solid solutions up to x = 0.2 (x = 0.11 in the present crystal). Therefore, it must be due to a strain effect mentioned above and noted in the previous study.12,25 After the crystal was annealed at 1323 K and then quenched rapidly into ice water, the MI transition disappears completely; no transition is expected for an x = 0.4 solid solution. Then, the quenched crystal was further annealed at 673 K for 12 h, which should induce a spinodal decomposition. In fact, the MI transition is recovered with much reduced overall resistivity and an enhanced anisotropy compared with the as-grown crystal: the resistivity above TMI is about 1000 times larger for current running along the cr axis than along the [110]r direction. This large anisotropy is apparently because the semiconducting (more insulating) Ti-rich layers tend to prevent a current flow among the metallic (less insulating) V-rich layers above (below) TMI. Plausibly, certain irregularities present in the as-grown crystal such as stacking faults as observed in the electron micrograph of Fig. 2(b) have been removed, and more complete lamellar structures are attained in the annealed crystal. It is also noted that the TMI’s are now 315 and 322 K upon heating and cooling, respectively, several Kelvins further reduced. In addition, the thermal hysteresis becomes larger after annealing. These mean that the misfit strain effect has been enhanced as more perfect lattice matching is achieved. The dramatic change between the solid-solution and phase-separated crystals is perfectly reversible. The thermoelectric property of the spinodal crystal has been investigated by means of resistivity, Seebeck coefficient, and thermal conductivity. They were measured on one as-grown crystal
FIG. 5. Schematic drawing of Ti- and V-rich layers in a phase-separated Ti0.4V0.6O2 crystal due to the spinodal decomposition. Lattice matching makes them deform so as to fit with each other at the interface perpendicular to the c r axis. The size difference is exaggerated for clarity.
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FIG. 6. Resistivities of Ti0.4V0.6O2 crystals heat-treated in various ways; an as-grown crystal, a quenched crystal from 1323 K, and an annealed crystal at 673 K after the quenching. For each crystal, two measurements were carried out with electrical currents running along the [001]r direction (I //c) and the [110]r direction (I //ab).
at the same time, as shown in Fig. 7. The Seebeck coefficient is always negative, reflecting that the carriers are electrons, and shows a sudden jump to a larger negative value at TMI, indicating an annihilation of the electron carriers in the V-rich layers. In addition, the thermal conductivity becomes small below TMI, as a contribution from conducting carriers is lost. The lattice thermal conductivity of 15–20 mW K−1 cm−1 in the insulating state is quite small compared with the bulk values at 300 K (85 and 50 mW K−1 cm−1 for TiO2 and VO2, respectively26,27), which approaches that of a glass, 5–7 mW K−1 cm−1. It is also noted that the thermal conductivity remains nearly constant in a wide temperature range at 100–300 K, in contrast to the conventional behavior: the thermal conductivity of most compounds increases with decreasing temperature in this temperature range; actually, that of TiO2 and VO2 at 100 K becomes 230 and 160 mW K−1 cm−1, respectively. One may expect that this low and temperature-independent thermal conductivity is related to the spinodal microstructure, as the stacking of the two kinds of layers can serve as a scatterer for acoustic phonons, as observed in artificial superlattice films made of PbTe and Pb(Se,Te).28 Certainly, the thermal conductivity with heat flow perpendicular to the multilayer interface is slightly smaller than the parallel one. However, since the difference between the two measurements is small, the spinodally decomposed microstructures may not be the main source for this small thermal conductivity, but a randomness
FIG. 7. (a) Resistivity, (b) Seebeck coefficient, and (c) thermal conductivity of an as-grown Ti0.4V0.6O2 crystal. In each figure, two kinds of datasets are shown with electrical current/heat flow parallel to the c axis or the [110]r direction.
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effect arising from substitutions must dominate.29 Unfortunately, the spinodal microstructure of the TiO2–VO2 system may not be helpful in improving the thermoelectric efficiency. Nevertheless, it would be interesting to examine other SD systems composed of metallic compounds with large thermoelectric power factors from the viewpoint of low thermal conductivity in heterogeneous structures. In summary, we prepared a single crystal of Ti0.4V0.6O2 and have examined microstructures induced by a spinodal decomposition by means of electron microscopy, single-crystal XRD, and transport properties. The crystal is characterized by a mega stacking of alternate Ti- and V-rich layers: they have approximate compositions of Ti0.65V0.35O2 and Ti0.11V0.89O2 and thicknesses of 18 and 15 nm, respectively. Significant effects of the misfit strain at the interface are revealed as broadening of diffraction spots in the XRD experiments as well as a reduction in TMI. 1
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APL MATERIALS 3, 062508 (2015)
Spinodally decomposed nanostructures in a TiO2–VO2 crystal Z. Hiroi,a T. Yoshida, J. Yamaura,b and Y. Okamotoc Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277–8581, Japan
(Received 18 March 2015; accepted 23 April 2015; published online 6 May 2015) We have prepared a single crystal of Ti0.4V0.6O2 which forms a solid solution crystallizing in the rutile structure at high temperatures and undergoes phase separation due to the spinodal decomposition when cooled to room temperature. The spinodally decomposed crystal consists of a self-assembled, mega stack of alternate Ti- and Vrich layers with an approximate period of 33 nm along the c axis. The unidirectional microstructure causes a large anisotropy in resistivity and a small one in thermal conductivity. A sharp metal–insulator transition as well as a structural transition to a monoclinic structure is observed in the thin V-rich layers. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4919764]
Microstructures associated with phase separations are often important in determining the mechanical and electric properties of actual materials. To obtain a hard steel, for example, it is crucial to control eutectoid reactions in the Fe–C system from high-temperature austenite (γ-Fe) to a mixture of ferrite (α-Fe) and cementite (Fe3C): the hardness depends on the size, amount, and distribution of hard cementite grains.1 In a more recent trend of thermoelectric applications, self-assembled lamellar structures of PbTe and Sb2Te3 were prepared utilizing a eutectic reaction between them.2 The spinodal decomposition (SD) is one of the phase separation mechanisms, in which a solid solution becomes thermodynamically unstable against a minimal composition fluctuation, and a nearly sinusoidal composition modulation occurs and develops upon cooling or with time duration after quenching from high temperatures.3 Finally, completely phase-separated microstructures with square-wave like composition modulations are obtained. The SD is a general phenomenon ubiquitously observed in various systems such as alloys, polymers, glasses, oxides, and even in the beginning of the universe.4,5 Since the SD initially takes place “uniformly” with a long-range spatial correlation, quasi-periodic, self-assembled two-phase mixtures with various kinds of morphologies are obtained at the nanometer scale. Actually, the mechanical properties of some alloys and polymer blends are affected by the SD morphologies containing lamellas or bubbles.4 The TiO2–SnO2 system gives a typical example for SD in oxides.6,7 Both the component oxides crystallize in the tetragonal rutile structure (Fig. 1) and form a complete solid solution above 1723 K. The SD takes place below this temperature, resulting in modulated structures composed of Ti- and Sn-rich phases with periods of 10–100 nm. A unique feature of this SD system is the strong anisotropy:8,9 a composition modulation occurs only along the c axis, reflecting the tetragonal symmetry as well as a smaller lattice mismatch along the a axis (1.5%) than the c axis (3.7%); the modulation direction should be chosen so as to minimize the elastic strain energy at the interface between two phases. This is a great advantage to obtain a well-ordered, natural superlattice by SD. Note that most SDs in cubic alloys or polymer blends possess no such preference in direction,
a Author to whom correspondence should be addressed. Electronic mail: [email protected] b Present address: Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama, Kanagawa
226–8503, Japan.
c Present address: Department of Applied Physics, Nagoya University, Chikusa-ku, Nagoya 464–8603, Japan.
2166-532X/2015/3(6)/062508/8
3, 062508-1
© Author(s) 2015
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FIG. 1. Schematic representation of a spinodal decomposition in the TiO2–VO2 system. A solid solution crystal between the two components is stable above 830 K, which crystallizes in the rutile structure with Ti/V atoms statistically occupying the position surrounded octahedrally by six oxide atoms. A spinodal decomposition occurs at lower temperatures, resulting ideally in such a natural superlattice crystal having a mega stack of alternate Ti- and V-rich layers along the c axis with periods of 5–50 nm.
resulting in isotropic mixtures of two phases. For applications, the dielectric and gas-sensing properties of spinodally decomposed (Ti,Sn)O2 thin films were investigated.10,11 Recently, we have shown that the TiO2–VO2 system is another example of SD in the rutile family.12,13 A phase diagram with a miscibility gap was determined in a series of polycrystalline samples. We are interested in this system because of distinct differences in their chemical and physical properties: TiO2 without d electrons is a wide band-gap insulator and shows a photocatalytic activity,14,15 while VO2 with one d electron is a metal at high temperatures and becomes an insulator at low temperatures; a metal–insulator (MI) transition takes place at TMI = 342 K upon heating.16 VO2 is potentially important for applications as ultrafast resistive or optical switching devices,17,18 because conductivity and optical absorption change dramatically across the transition. These large differences in properties between the two constituents make the TiO2–VO2 system exceptional; in other SD systems, two constituents possess quite similar properties in all aspects. Therefore, it is intriguing to investigate the properties of spinodally decomposed composites in the system. The MI transition of VO2 is dramatic: a large electrical discontinuity of more than several orders of magnitude is observed across the transition.16,19 It is a first order transition accompanied by a structural transition from the high-temperature tetragonal (P42/mnm) rutile (r) structure to the low-temperature monoclinic (P21/c) structure. A striking feature of this low-temperature structure called M1 is the presence of V–V pairs in the strands of edge-sharing octahedra along the c axis of the tetragonal structure: alternate V–V separations are 2.65 and 3.12 Å in place of the regular 2.87 Å spacing in the tetragonal structure near the transition.19 Since all the 3d electrons are trapped
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by these dimers in their bonding molecular orbitals, the MI transition takes place simultaneously at the structural transition. The mechanism of the MI transition has been greatly debated for decades from various perspectives.19–23 Very recently, one of the authors has proposed that the driving force has nothing to do with electron correlations nor Peierls instability as previously believed but is a structural instability to form a “molecular orbital crystal” by generating a direct metal–metal bonding.13 In the present paper, we report on microstructures generated by SD in a single crystal of Ti0.4V0.6O2. A mega stack of alternate Ti- and V-rich layers with a period of approximately 33 nm along the c axis is observed in the mm-size crystal. A large anisotropy is observed in resistivity owing to the anisotropic microstructure. A MI transition occurs in the thin V-rich layers together with a structural transition to the M1 structure at a reduced temperature of 322 K compared with the bulk value of 342 K. The thermoelectric property is also examined. Single crystals of Ti0.4V0.6O2 were prepared by the floating zone method. A starting polycrystalline sample was synthesized as reported previously12 and was sintered into a dense rod at 1623 K in an argon gas flow for 24 h. The rod was partially melted in a high-pressure argon gas of 5 atm in a four-mirror image furnace (Crystal Systems Corp.) and slowly moved downward so that a crystal grew at a speed of ∼1 mm h−1. A solid-solution crystal was obtained by annealing an as-grown crystal at 1323 K in a quartz tube filled with 1 atm argon gas and then by rapidly quenching into ice water. A completely phase-separated crystal was prepared by further annealing the solid-solution crystal at 673 K for 24 h. Microstructures of as-grown crystals were examined in a transmission electron microscope (JEOL 2010-F). A specimen for observation was prepared by the argon ion milling method. The crystal structure was determined by the single crystal x-ray diffraction (XRD) method using a Mo Kα radiation in a triple-axis diffractometer (Rigaku AFC6S). Resistivity, Seebeck coefficient, and thermal conductivity were measured in a Physical Property Measurement System (Quantum Design). Figure 2(a) shows a photograph of typical crystals picked up from a crushed boule of as-grown crystal. They have cleavages along the (110) and (001) planes (the Miller indices are based on the tetragonal cell). The (110) cleavage is typical for the rutile family of compounds, coming from the crystal structure itself, while the (001) cleavage is rare and thus probably due to layered microstructures by SD. Since the crystals were slowly cooled after solidification from a melt, an SD has already occurred in these as-grown crystals. This is directly evidenced by electron microscopy observations on a thin piece of crushed crystal. Figure 2(b) shows a typical image taken from an edge of crystal, in which bright bands (Ti-rich layers) and dark bands (V-rich layers) appear alternately
FIG. 2. (a) Photograph of pieces of the as-grown Ti0.4V0.6O2 crystal grown by the floating-zone method and (b) electron micrograph showing a lamellar structure in which Ti-rich layers (bright bands with ∼20 nm thickness) and V-rich layers (dark bands with ∼15 nm thickness) alternate with an average periodicity of 33 nm along the c axis.
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along the c axis. The thickness of each layer is 10–20 nm, and the average periodicity is 33 nm. Note that the way of stacking is not perfect but there are “stacking faults” from place to place. We have noticed in later experiments that this irregularity is going to be removed by annealing a solid-solution crystal at 673 K for 24 h. The crystal structure of the as-grown crystal has been examined by means of reciprocal lattice mapping of XRD intensity at room temperature below the TMI. Figure 3(a) shows an intensity map around the 004 reflection in the h0l plane; the index is based on a rutile-type tetragonal unit cell with a = 4.5504 Å and c = 2.8988 Å. Observed in the h0l scan are two spots with nearly same h values and different l values, indicating the presence of two components having different lattice spacings only along the c axis: the spots with smaller and larger l values are assigned to Ti- and V-rich layers, respectively. On the other hand, the h4l scan around the 040 reflection [Fig. 3(b)] shows a single spot, which means a perfect lattice matching along the layers. We have also examined specific reflections that are forbidden in the rutile structure but allowed in the monoclinic M1 structure, such as 0 1/2 7/2 shown in Fig. 3(c). A weak but clear spot is observed only at an l value corresponding to the V-rich layer. Thus, the V-rich layer takes the M1 structure at room temperature below the TMI, while the Ti-rich layer takes the rutile structure. Lattice constants determined from these peak positions are listed in Table I. A relation between the two unit cells is depicted in Fig. 4: am ≈ 2cr, bm ≈ ar, cm ≈ (ar2 + cr2)1/2, where subscripts m and r refer to the monoclinic and rutile structures, respectively. Note that the monoclinic distortion takes place as a result of dimerization of V atoms: the dimerization patterns along the cr or am axis are almost antiphase along the [100]r direction, while in-phase along the [010]r direction perpendicular to the paper in Fig. 4, which gives the monoclinic unit cell. As a result, V dimers are aligned along the [10-1]r or cm direction. Since associated atomic movements mostly occur along the cr axis, a lattice matching can be easily achieved within the cr plane, which is evidenced by the reciprocal mapping of Fig. 3. This is also the reason why the SD occurs with the composition modulation only along the cr axis: a smaller elastic strain energy is achieved at the cr plane. Moreover, this gives a persuasive explanation why the MI transition can take place in such thin lamellas in SD samples12,13 and also in ultrathin VO2 layers in artificial superlattice films.24 It is intriguing to notice that the diffraction spots in Fig. 3 exhibit characteristic broadenings. Either of the 004 spots from the two layers is heavily elongated along the [101]r∗ direction. Moreover, the 0 1/2 7/2 spot from the V-rich layer shows a similar elongation. These elongations are probably related to strain or disorder in the arrangements of V dimers, because the (101)r pane is
FIG. 3. Reciprocal maps of x-ray diffraction intensity for reflections with indices of (a) 004, (b) 040, (c) 0 1/2 7/2, and (d) 004 on the basis of the rutile structure (a = 4.5504 Å and c = 2.8988 Å) for an as-grown Ti0.4V0.6O2 crystal. Shown in (a), (b), and (c) are hl scans at k = 0, 3.99, and 0.50, respectively, and a hk scan at l = 3.92 in (d); the hk scan at l = 3.92 in (d) corresponds to a cross section of the 004 spot from the Ti-rich layers in (a). The x-ray intensity in count per second is plotted by color contour in the scale shown at the bottom. The 0 1/2 7/2 reflection is not observed from Ti-rich layers in the rutile structure but from V-rich layers in the monoclinic M1 structure.
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TABLE I. Structural parameters of Ti- and V-rich layers in an as-grown Ti0.4V0.6O2 single crystal.
Crystal structure a r (Å) c r (Å) Vr (Å3) Ti composition x b a ss(x) (Å)c c ss(x) (Å)c Thickness (nm)d
Ti-rich layer
V-rich layer
Tetragonal rutile 4.567 2.954 61.61 0.65 4.57 2.95 18
Monoclinic M1a 4.567 2.856 59.57 0.11 4.54 2.89 15
constants of the original monoclinic unit cell are a m = 5.712 Å, b m = 4.567 Å, c m = 5.421 Å, and β = 122.6◦. from the Vr–x relation established in solid solutions in the polycrystalline form.12 c Lattice constants of the corresponding solid solutions. dThickness of each layer when the total thickness is 33 nm. a Lattice
bEstimated
the lattice plane along which V dimers are aligned, as mentioned above (Fig. 4). It is likely that the structural coherence is disturbed by certain misplacements of V dimers or a disorder in phase among dimer rows along the cr axis in the V-rich layer, which are caused by the Ti substitution. Interestingly, the fact that a similar elongation is present in the 004 spot from the Ti-rich layer suggests that the Ti-rich layer suffers a strain from the adjacent V-rich layers. Alternatively and more likely, V dimers are locally generated to induce a short-range order toward the M1 structure in the Ti-rich layer containing ∼35% of V atoms (see below) even if the global symmetry is kept tetragonal. Furthermore, there is another elongation for the 004 spot from the Ti-rich layer [Fig. 3(d)], where an hk scan at l = 3.92 is shown, that is, a cross section of the 004 spot in Fig. 3(a). The spot is elongated about 4 times along the [010]r∗ direction compared with that along the [100]r∗ direction. The reason is not clear but may be due to a misfit strain caused by lattice matching between the square lattice of the Ti-rich layer and the essentially orthorhombic lattice of the V-rich layer at the interface. Note that the lattice matching can be easily attained along the [100]r direction by adjusting the β angle, but not so along the [010]r direction, as shown in Fig. 4. The composition of each layer is estimated by using the relation between the unit cell volume Vr of the rutile structure and the Ti composition x, which has been obtained in the previous study on polycrystalline samples: Vr/Å3 = 59.02(4) + 5.0(2)x − 1.6(2)x 2.12 This relation is also valid for spinodally decomposed samples; the volume seems to be decided only by the composition, irrespective of strain. The estimated compositions of the Ti- and V-rich layers in the present Ti0.4V0.6O2
FIG. 4. Atomic structure near an interface (broken line) between a Ti-rich layer crystallizing in the rutile structure (left) and a V-rich layer in the M1 structure (right). The positions of metal atoms are based on those of pure TiO2 and VO2, respectively, and oxide atoms are omitted. The atoms colored faint are located half of the unit cell below the paper. The lattice matching at the interface occurs so as to adjust the interatomic distances parallel to the interface: a r = c m sin β = bm. Note that the Ti(V) atoms in the Ti(V)-rich layer are partially and statistically replaced by V(Ti) atoms.
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crystal are Ti0.65V0.35O2 and Ti0.11V0.89O2, respectively, which are consistent with the spinodal decomposition curve in the phase diagram.12 In addition, the lattice constants of the corresponding solid solutions, which should be natural lattice constants under no strain, are calculated also based on the relations established in the previous study: ar/Å = 4.530(1) + 0.064(2)x and cr/Å = 2.877(2) + 0.153(1)x − 0.07(1)x 2,12 as listed in Table I. Then, the thicknesses of the two layers are obtained to be 18 and 15 nm, respectively, provided that the average periodicity of composition modulation is 33 nm from the electron micrograph of Fig. 2. A comparison in the lattice constants between the layers in the crystal and the corresponding solid solutions reveals that they are nearly the same for the Ti-rich layer, while significantly different for the V-rich layer: the ar is elongated and the cr is compressed from the natural values of the solid solution. This situation is schematically depicted in Fig. 5. The lattice matching at the interface is achieved mostly by deforming the thinner and possibly softer V-rich layer. This strain effect may be important in reducing the TMI of VO2, as mentioned in the next paragraph. In order to investigate the MI transition of VO2, we have measured resistivity on Ti0.4V0.6O2 single crystals heat-treated in various ways. As shown in Fig. 6, an as-grown crystal exhibits a large jump of 3–4 orders of magnitude due to the MI transition taking place in the V-rich layers. Note that there is a difference between two measurements performed with electrical currents running parallel to the cr axis and the [110]r direction. Moreover, the TMI’s are 322 and 326 K upon heating and cooling, respectively, which are about 20 K lower than those of bulk VO2. This reduction is not due to the Ti substitution, because the Ti substitution increases the TMI in solid solutions up to x = 0.2 (x = 0.11 in the present crystal). Therefore, it must be due to a strain effect mentioned above and noted in the previous study.12,25 After the crystal was annealed at 1323 K and then quenched rapidly into ice water, the MI transition disappears completely; no transition is expected for an x = 0.4 solid solution. Then, the quenched crystal was further annealed at 673 K for 12 h, which should induce a spinodal decomposition. In fact, the MI transition is recovered with much reduced overall resistivity and an enhanced anisotropy compared with the as-grown crystal: the resistivity above TMI is about 1000 times larger for current running along the cr axis than along the [110]r direction. This large anisotropy is apparently because the semiconducting (more insulating) Ti-rich layers tend to prevent a current flow among the metallic (less insulating) V-rich layers above (below) TMI. Plausibly, certain irregularities present in the as-grown crystal such as stacking faults as observed in the electron micrograph of Fig. 2(b) have been removed, and more complete lamellar structures are attained in the annealed crystal. It is also noted that the TMI’s are now 315 and 322 K upon heating and cooling, respectively, several Kelvins further reduced. In addition, the thermal hysteresis becomes larger after annealing. These mean that the misfit strain effect has been enhanced as more perfect lattice matching is achieved. The dramatic change between the solid-solution and phase-separated crystals is perfectly reversible. The thermoelectric property of the spinodal crystal has been investigated by means of resistivity, Seebeck coefficient, and thermal conductivity. They were measured on one as-grown crystal
FIG. 5. Schematic drawing of Ti- and V-rich layers in a phase-separated Ti0.4V0.6O2 crystal due to the spinodal decomposition. Lattice matching makes them deform so as to fit with each other at the interface perpendicular to the c r axis. The size difference is exaggerated for clarity.
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FIG. 6. Resistivities of Ti0.4V0.6O2 crystals heat-treated in various ways; an as-grown crystal, a quenched crystal from 1323 K, and an annealed crystal at 673 K after the quenching. For each crystal, two measurements were carried out with electrical currents running along the [001]r direction (I //c) and the [110]r direction (I //ab).
at the same time, as shown in Fig. 7. The Seebeck coefficient is always negative, reflecting that the carriers are electrons, and shows a sudden jump to a larger negative value at TMI, indicating an annihilation of the electron carriers in the V-rich layers. In addition, the thermal conductivity becomes small below TMI, as a contribution from conducting carriers is lost. The lattice thermal conductivity of 15–20 mW K−1 cm−1 in the insulating state is quite small compared with the bulk values at 300 K (85 and 50 mW K−1 cm−1 for TiO2 and VO2, respectively26,27), which approaches that of a glass, 5–7 mW K−1 cm−1. It is also noted that the thermal conductivity remains nearly constant in a wide temperature range at 100–300 K, in contrast to the conventional behavior: the thermal conductivity of most compounds increases with decreasing temperature in this temperature range; actually, that of TiO2 and VO2 at 100 K becomes 230 and 160 mW K−1 cm−1, respectively. One may expect that this low and temperature-independent thermal conductivity is related to the spinodal microstructure, as the stacking of the two kinds of layers can serve as a scatterer for acoustic phonons, as observed in artificial superlattice films made of PbTe and Pb(Se,Te).28 Certainly, the thermal conductivity with heat flow perpendicular to the multilayer interface is slightly smaller than the parallel one. However, since the difference between the two measurements is small, the spinodally decomposed microstructures may not be the main source for this small thermal conductivity, but a randomness
FIG. 7. (a) Resistivity, (b) Seebeck coefficient, and (c) thermal conductivity of an as-grown Ti0.4V0.6O2 crystal. In each figure, two kinds of datasets are shown with electrical current/heat flow parallel to the c axis or the [110]r direction.
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effect arising from substitutions must dominate.29 Unfortunately, the spinodal microstructure of the TiO2–VO2 system may not be helpful in improving the thermoelectric efficiency. Nevertheless, it would be interesting to examine other SD systems composed of metallic compounds with large thermoelectric power factors from the viewpoint of low thermal conductivity in heterogeneous structures. In summary, we prepared a single crystal of Ti0.4V0.6O2 and have examined microstructures induced by a spinodal decomposition by means of electron microscopy, single-crystal XRD, and transport properties. The crystal is characterized by a mega stacking of alternate Ti- and V-rich layers: they have approximate compositions of Ti0.65V0.35O2 and Ti0.11V0.89O2 and thicknesses of 18 and 15 nm, respectively. Significant effects of the misfit strain at the interface are revealed as broadening of diffraction spots in the XRD experiments as well as a reduction in TMI. 1
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