Acta Materialia 220 (2021) 117336 Contents lists available at ScienceDirect Acta Materialia journal homepage: www.elsevier.com/locate/actamat Strong strain gradients and phase coexistence at the metal-insulator transition in VO2 epitaxial films Laura Rodríguez a, Felip Sandiumenge b, Carles Frontera b, José Manuel Caicedo a, Jessica Padilla a, Gustau Catalán a,c, José Santiso a,∗ a Catalan Institute of Nanoscience and Nanotechnology, ICN2, CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, 08193 Bellaterra, Barcelona. Spain b Institut de Ciència de Materials de Barcelona (ICMAB-CSIC). Campus UAB, 08193 Bellaterra, Catalonia. Spain c ICREA - Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Catalonia. Spain a r t i c l e i n f o a b s t r a c t Article history: The proximity of a thermodynamic triple point and the formation of transient metastable phases may Received 25 June 2021 result in complex phase and microstructural trajectories across the metal-insulator transition in strained Revised 8 September 2021 VO2 films. A detailed analysis using in-situ synchrotron X-ray diffraction unveils subtle fingerprints of Accepted 15 September 2021 this complexity in the structure of epitaxial films. During phase transition the low-temperature mono- Available online 26 September 2021 clinic M1 phase is constrained along the {111}R planes by the coexisting high-temperature R phase do- Keywords: mains, which remain epitaxially clamped to the substrate. This geometrical constraint induces counter- Metal-insulator transitions acting local stresses that result in a combined tilt and uniaxial in-plane compression of M1 domains, and Phase coexistence a concomitant anomalous cR -axis elongation. This mechanism progressively transforms the M1 phase into Martensitic transitions the transitional triclinic phase (T), and ultimately into the monoclinic M2 phase, generating strong strain Local strain fields and tilt gradients that remain frozen after the complete transformation of the R phase upon cooling to RT. The transformation path of VO2 films, the complex competition between stable and metastable VO2 polymorphs and its impact on the structure of the low temperature monoclinic state, provide essential insights for understanding the electronic and mechanical properties of the films at the nanoscale, as well as to control their use in functional devices. © 2021 The Authors. Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 1. Introduction temperature M1 phase resulting from the alternate displacement of V ions from the central position of the VO6 octahedra columns, VO2 is a strongly correlated electron material that in bulk form forming zig-zag chains of dimers, while the high-temperature R presents a first-order metal-insulator transition (MIT) at about 68 phase consists of straight chains with equal V-V distances. How- °C, with several orders of magnitude change in electrical con- ever, it is well established that under uniaxial tensile strain along ductivity as well as in infrared optical transmittance [1–4]. These cR -axis [9], or compressive uniaxial strain along the [110]R direc- properties make VO2 attractive in applications like thermochromic tion [10], there appears a monoclinic insulating phase, M2, con- smart windows [5] and in field-effect transistors [6–8]. The MIT sisting of two types of V chains parallel to the cR direction al- is accompanied by a displacive structural transition from a low- ternating straight V-V dimers or zig-zag non-dimerized V chains. temperature monoclinic phase (M1, with space group P21 /c) to a This separation into two different V-V chains results from the com- high-temperature tetragonal conducting phase (isostructural to ru- pression of one column set of VO6 octahedra oriented with their tile R phase, space group P42 /mnm). The most important struc- axis connecting apical O atoms along the [110]R direction, while tural feature of this transition, which relates to the electronic lo- the other column set of VO6 octahedra are longitudinally stretched calization and the opening of a 0.6 eV gap, is the formation of along the [1-10]R direction. In equilibrium conditions, these three two characteristic V-V distances along the cR direction in the low- phases, M1, M2 and R, may coexist at the transition tempera- ture in a solid-state triple point of the phase diagram [11,12]. Be- sides these polymorphs, there exist transient, metastable phases ∗ Corresponding author. playing bridging roles between them, namely, 1) a triclinic (T) E-mail address: jose.santiso@icn2.cat (J. Santiso). (also referred to as M3) phase forming at the transition between https://doi.org/10.1016/j.actamat.2021.117336 1359-6454/© 2021 The Authors. Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 the M1 and M2 structures, [12–14], and 2) metallic monoclinic 2. Experimental methods phases bridging the R and M1 structures [15–17], which, alto- gether, illustrate the complexity and adaptive nature of the VO2 VO2 films were grown on TiO2 (001) single crystal substrates by system. pulsed laser deposition from a V2 O5 ceramic target. The ablation The richness of the phase diagram, combined with the was performed by using a KrF excimer laser (Lambda Physik COM- ferroelastic-martensitic character of VO2 , makes the pathway of Pex 201, λ= 248 nm wavelength). Film growth conditions were the transformation from the low-temperature (M1) to the high- 400 °C deposition temperature, 10 mTorr gas pressure of pure O2 , temperature (R) ground states strongly dependent on geometrical laser fluence of 0.8 J•cm−2 and target-to-substrate distance of 55 constraints and strain fields, which may induce different forms of mm. The cooling down step was at 15 °C•min−1 keeping the same phase coexistence and multiscale microstructures below and across gas pressure. All the samples shown in this work were grown un- the transition. There are multiple examples in the literature con- der the same PLD growth conditions, with thicknesses between 40 cerning the observation of mesoscale domains in VO2 single crys- nm up to 120 nm by varying the number of pulses (growth rate ∼ tals and epitaxial films consisting of various phases and differ- 0.03 nm•pulse−1 ). Films were analysed by XRD by using a 6-angle ent domain arrangements. For instance, in 2D nanoplatelets [18,19] goniometer diffractometer at the KMC2 line at Helmholtz-Zentrum and 1D nanobeams [20], different ferroelastic domain configura- Berlin synchrotron radiation with a Vantec 20 0 0 2D GADDS de- tions have been reported which depend on the size and orien- tector (with 2048 × 2048 pixels) at energy selected to λ=1.54 Å, tation of the crystals, as well as M1/R phase coexistence during as well as in a lab diffractometer with 4-angle goniometer (MRD the transition [21]. Even more complex scenarios are observed in X’Pert Pro from Malvern-Panalytical) and Cu Kα tube and 2 x nanobeams under stress, with the formation of the M2 polymorph Ge(110) monochromator. In both XRD setups the sample tempera- at the interface between M1 and R domains during the transition ture was controlled by using a sample stage for non-ambient anal- [22–24]. Similar T and M2 domains were also observed in inter- ysis (DHS1100C from Anton Paar). Slight temperature differences facial regions between M1 and R in polycrystalline films on Si3 N4 (± 5°C) could result from the different sample holder setup of both membranes [25] or epitaxial films on Al2 O3 (0 0 01) substrates [26]. experiments. In epitaxial VO2 films grown on TiO2 (001) substrates experimen- We analysed a collection of VO2 and TiO2 HKL reflections by tal evidences reported so far, indicate that, due to the large cell measuring conventional 2θ /ω scans and reciprocal 2D maps in the parameter change during phase transition, films tend to generate lab diffractometer. More detailed analysis of the reciprocal space microcracks as a strain relaxation mechanism [27–29]. As a conse- reflections was performed by measuring 3D reciprocal space maps quence, it is observed that the phase and microstructural trajec- in the synchrotron source. The 3D maps were constructed by mak- tories during the transition of VO2 /TiO2 (100) films become spa- ing use of the 2D information in each frame (2D detector) mea- tially heterogeneous. In the proximity of the cracks, the film is sured by scanning either different φ angles (azimuthal angle), or relaxed, thus evolving from M1 ground state to R upon transi- η angles (incidence angle). We chose reflections which contained tion without intermediate phases [11,12,30]. On the other hand, information about out-of-plane cell parameters (such as 002R ), as the regions between cracks have been observed to retain an in- well as in-plane components (112R , 101R , and 1/2 0 3/2R ). plane biaxial compressive strain up to thicknesses above 80nm The evolution of the reflections with temperature was followed [27,30]. Under such strain conditions the strain-Temperature phase by heating at small steps starting from room temperature up to the diagram predicts the absence of intermediate phases between M1 completion of the phase transition (about 70 °C depending on the and R phases during transition [11,12]. However, recent investi- sample thickness). Measurements on synchrotron source with 2D gations by this group have shown that strained VO2 films may detector provide a fast overview of the 3D reciprocal space even develop very fine pre-transitional tweed textures prior to relax- for weak reflections. However, peak positions depend on a care- ation and condensation of the low temperature M1 ground state ful sample alignment and detector calibration. For accurate lattice [17]. Such textures look tetragonal on average, and are promoted parameter determination, the 2D maps measured at diffractometer by the nucleation of a transient metallic monoclinic phase (x3M), lab were used (Figure S6 and S7). and evolve with film thickness towards multicomponent tweeds incorporating the x3M, M1 and M2 structures on a rutile-like scaf- 3. Results and discussion fold [17]. At that stage, the nanoscale phase intermixing of those domains precludes any differentiation of existing phases from X- All deposited films consist of pure VO2 epitaxially oriented on ray diffraction experiments, since the peak commonly assigned to TiO2 (001) substrates, with the [001]R -axis perpendicular to the the rutile phase in fact encompasses variable levels of those poly- substrate plane, and [100]/[010]R directions parallel to the equiv- morphs, macroscopically keeping an average tetragonal symmetry. alent in-plane axes of the TiO2 substrate. X-ray diffraction 2θ /ω During the transition, however, those bridging phases are expected scans at different temperatures, from 25 °C to 70 °C, are depicted to evolve, eventually growing in size, within measurable levels. in Fig. 1 a. They show the evolution of the 002 VO2 film and TiO2 Similarly, a recent review on VO2 claim that local perturbations substrate peaks during the phase transition for a 80 nm thick sam- of the strain state induced by the presence of defects or ferroelas- ple. Fig. 1b shows a characteristic electrical transport measurement tic domains may produce deviations from the expected equilibrium of a similar film with a clear insulating to metal transition at about phases landscape [31]. The present study focusses on the tempera- 50 °C, with a change of resistivity of more than two orders of mag- ture evolution of VO2 film phase coexistence and microstructure nitude. The transport curve presents some hysteretic behavior in by synchrotron X-ray diffraction in-situ analysis. Despite the in- the heating and cooling cycles as typically shown in MIT transi- herent presence of microcracks in the films, the accurate study of tions. the intensity distribution around the corresponding main Bragg po- The XRD scan obtained at 25 °C, below the transition, shows a sitions allows to unravel a transformation path through adaptive broad peak with maximum at 2θ = 65.2°, and a shoulder on the distortions of the monoclinic phase upon the transition from the left side of the peak. When heating up, at 35-40 °C a second max- high-temperature rutile phase, involving the formation of T and imum appears at 2θ = 65.7°. These two peaks correspond to the M2 phase tilted domains. These distortions, which in fact result 402̄M1 and 002R reflections of the monoclinic (M1) and rutile (R) from varying degrees of V-V dimerization, remain frozen at room VO2 phases, respectively. Note that the monoclinic 402̄M1 reflec- temperature in virtually perfect films of the low-temperature insu- tion corresponds to the same 002R orientation when expressed in lating M1 phase. the tetragonal setting of the parent rutile structure. At higher tem- 2 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 Fig. 1. (a) High resolution XRD 2θ /ω scans in the region of 002 TiO2 , 402̄M1 and 002R VO2 reflections for an 80 nm thick sample. (b) Resistivity versus temperature for a similar sample (60nm thick) showing the transition from the insulating to the metallic phase for heating and cooling cycles (indicated by arrows). Table 1 maps shown below are presented in a logarithmic intensity scale. Measured and reported pseudo-tetragonal lattice parameters for M1 and R Fig. 2a shows the evolution of the 002R film reflection as seen on phases different projections (3D maps overview in Figure S1, Suppl. Info). Phase Lattice constants [Å] Strain [%] The vertical Qxy Qz projection corresponds to a slice following the bulk film ε⊥ ε // [110]∗ R direction, including the substrate reflection, while horizon- tal Qx Qy maps integrate a slice around the VO2 film peak only. The M1 cR = 2.872 cR = 2.858 - 0.5 + 1.5 aR = 4.516 // [100]R aR = 4.592 c) diffuse inverted-V shape, already observed at 30 °C, combined with = 4.528 // [010]R a) the horizontal Qx Qy projection, indicates that the VO2 intensity is R cR = 2.860 cR = 2.839 - 0.7 + 0.78 distributed in four main branches following the [110]∗ R /[1-10]∗ R aR = 4.556 b) aR = 4.592 c) directions in the horizontal plane, and pointing downwards at a certain angle with the vertical axis. As can be observed in Fig. 2a, a) from ref [37]; b) ref [14]; c) at this stage (40 °C) both phases are assumed the intensity maximum is in the central axis at Qx =Qy =0. This is to be fully strained to the substrate, so this value is taken from in-plane TiO2 (001) crystal consistent with the observation of the linear scan in Fig. 1a which indicates a single peak at the Qz position expected for the strained M1 phase. The peak asymmetry, with a smoother intensity decay peratures, the monoclinic peak intensity decreases while the rutile at lower 2θ angles, observed in that scan, thus can be attributed intensity increases, and this progressive unbalance extends over to the contribution of those diffuse intensity branches. At 30 °C a wide range of temperatures, from 35 to 55 °C, which approxi- one can only distinguish one peak corresponding to the M1 phase, mately coincides with the transition range observed in the trans- but at 40 °C and 50 °C the R peak is observed in the Qxy Qz maps port measurement. at a higher Qz value and Qx =Qy =0, indicating the transformation At 40 °C, when the two coexisting phases yield about the same into the rutile phase. At this stage the M1 component progressively maximum intensity, the measured d002 interplanar distances corre- splits into four peaks away from the central Qx =Qy =0 position fol- spond to the pseudo-rutile out-of-plane unit cell parameters 2.858 lowing the [110]∗ R /[1-10]∗ R directions, as indicated by yellow ar- Å and 2.839 Å, for M1 and R phases, respectively, as shown in rows. It can be observed that, upon increasing the temperature, the Table 1. These unit cell parameters are -0.5 % and -0.7 % shorter centroid positions of the M1 split components progressively shift than reported bulk parameters, 2.872 Å for (402̄)-oriented M1, and along the inverted-V intensity traces. From the symmetric 002R re- 2.860 Å for (001)-oriented R phases, respectively. This contrac- flection one can only gather information about out-of-plane com- tion results from the elastic response to the tensile in-plane bi- ponents, while a more complete insight into the in-plane compo- axial stress of the VO2 layer on the (001)TiO2 single crystal sub- nents requires at least one reflection with H,K = 0 components. strate. Looking at the bulk in-plane unit cell parameters of the re- Fig. 2b shows selected projections of 3D reciprocal space maps ported M1 phase, 4.516 Å and 4.528 Å, along the [100]R and [010]R at the 112R reflection. The vertical maps correspond to slices in pseudo-tetragonal rutile directions (average in-plane value is 4.522 two orthogonal directions: one following the [110]∗ R axis (Qxy Qz Å), the average mismatch is about +1.5 %, while for rutile VO2 , it map), as above, and another one following the perpendicular [1- is about +0.78 %. The large difference between the mismatch of 10]∗ R axis (Qx-y Qz map). The horizontal Qx Qy maps show again the M1 and R phases induces the formation of microcracks above four main branches with projections following the [110]∗ R /[1-10]∗ R a critical thickness of about 15 nm, as previously reported. [27– directions. This crossed pattern is centered in the same (Qx ,Qy ) po- 29] and also discussed in the supplementary information (Fig. S9). sition as the TiO2 substrate 112 reflection. Splitting of the M1 max- imum along these branches is clear at 40 °C and 50 °C, (indicated 3.1. Evolution of lattice distortions during the phase transition with yellow arrows) but only incipient at 30 °C. In the horizontal maps, contrary to the splitting observed in the 002R reflection, the A deeper insight into the evolving VO2 microstructure was ob- branches following the [110]∗ R direction show asymmetric splitting tained by performing XRD 3D reciprocal space maps during heat- from the central (Qx ,Qy ) position: the centroid position indicated ing from room temperature up to 50 °C across the phase transition with the yellow arrow shows a larger shift than the opposite split on a 120 nm thick film. Since the distortions analyzed in this work component. Instead, along the [1-10]∗ R direction, the splitting re- produce only weak diffuse signatures around main reflections, all mains symmetric (as indicated by red arrows). This difference is 3 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 even clearer in the vertical cuts. While the Qx-y Qz maps show a symmetric arrangement similar to that observed in the 002R re- flection, the Qxy Qz map is clearly asymmetric already at 30 °C. The two branches seem to follow the same oblique direction, although the one pointing towards larger Qxy values is clearly more elon- gated than the opposite one. With increasing temperature the cen- troids of the split components shift apart following the trajectory of the pre-existing branches, as indicated by yellow arrows. At each temperature the in-plane magnitude of the splitting is the same for both directions parallel and perpendicular to [110]∗ R (distance be- tween red or yellow arrows). However, their average position along Qxy in the asymmetric branch (middle position between the two yellow arrows) is displaced from the central position. The behaviour described above can be interpreted as follows. The progressive splitting of the M1 components is consistent with an increasing domain tilting, while the asymmetric displacement from the central Qxy position is due to a progressive variation of the in-plane reticular spacing along the [110]∗ R direction. Impor- tantly, both distortions increase with the progress of the transi- tion to the rutile phase. It is worth noting that the lowering of the Qz position for both M1 components in the vertical maps shown in Fig. 2a and 2b, indicates an increase of the out-of-plane unit cell parameter, contrary to the elastic response expected for the in-plane tensile strain imposed by the substrate. In contrast with this behaviour, in all the maps, the corresponding R component (intense peak appearing above 30 °C at larger Qz in vertical maps) does not show any significant change, while its in-plane parame- ter remains coherent with that of TiO2 substrate. Altogether, these results point to the build-up of severe internal stresses which se- lectively affect the monoclinic phase embedded in the rutile film, and that the stress level increases as its volume fraction decays during the transition. The evolution of reciprocal space maps ob- tained around the 1/2 0 3/2R reflection is shown in Fig. 2c. This reflection, arising from the unit cell doubling caused by the V-V dimerization, can in principle be attributed to either the M1 or M2 structures. It can be indexed as either 302̄M1 or 130/1̄30M2 . As can be observed in Fig. 2c, at 30 °C it shows a main peak at the same (Qx ,Qy ) position than that expected for a perfectly coherent VO2 film on the TiO2 substrate, along with diffuse branches. However, the horizontal Qx Qy projection clearly defines a pattern of only two main branches, instead of four, along [110]∗ R and [1-10]∗ R direc- tions. Because of the four-fold symmetry of the substrates, the ap- pearance of M2 domains would imply the existence of a couple of 130/1̄30M2 equal intensity reflections for each 1/2 0 3/2R position (following (100)/(010)R mirror planes). This would necessarily gen- erate a four-branch arrangement at the position of each half-order reflection, which is not observed. Instead, a set of M1 domains ar- ranged following the 4-fold symmetry of the substrate may consist of one single 302̄M1 reflection at each ±Qx ,±Qy quadrant in recip- rocal space, compatible with the experimental observations. There- fore, the main contribution to the observed half-order reflections comes from crystal domains compatible with the M1 structure. We note that a small proportion of T or M2 phases could generate mir- ror branches that could go unnoticed due to the weakness of this reflection. In fact, a close look at the 50 °C Qx Qy map shows a very weak signal attributable to such mirror branches but they are too fade to extract any conclusion. An additional important observation in the horizontal Qx Qy map of the 1/2 0 3/2R reflection at 40 °C concerns the peak split- Fig. 2. XRD reciprocal space maps of different VO2 reflections obtained at 30, 40 ting, which is even more evident at 50 °C. Contrary to previous and 50 °C during the phase transition: (a) vertical Qxy Qz and horizontal Qx Qy 2D 002R and 112R vertical cuts shown in Fig. 2a and 2b, these maps projections of the 002R reflection; (b) vertical Qx-y Qz , Qxy Qz and horizontal Qx Qy do not show any intensity at the central (Qx ,Qy ) position. This 2D projections of the 112R reflection; and (c) vertical Qx-y Qz , Qxy Qz and horizon- confirms the previous assignment of the central position to the tal Qx Qy projections of the 1/2 0 3/2R reflection. The horizontal projections contain only VO2 film reflections. The arrows indicate the split M1 components (red and R phase. The corresponding vertical Qx-y Qz and Qxy Qz maps also yellow arrows indicate symmetric and asymmetric splitting, respectively). Qx,y show meaningful differences with respect to the 002R and 112R corresponds to a range of ±0.025Å−1 for (a) and (b), and ±0.015Å−1 for (c). The reflections. The split components (indicated by yellow and red ar- complete T range, acquired with 5 °C steps, is depicted in Fig. S2, S3 and S4 (Suppl. Info) for the 002R , 112R and 1/2 0 3/2R reflections, respectively. 4 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 rows) and the diffuse branches appear only in the higher Qx part of the maps. Again, upon heating up, the centroid positions shift apart from central position following the corresponding branches trajectory. The explanation for the selection of the higher Qxy trace follows in the next paragraph. Similar splitting was also observed in other reflections, like 101R shown in Figure S5 (of suppl. Info). 3.2. Geometrical model for the coexistence of M1 and R phases Before considering in detail the microstructure reflected by the above results, we first recall the ferroelastic properties of VO2 . From group theory, the number of symmetry-degenerated domain orientations is equal to the order of the prototypic point group (4/mmm, order 16) divided by the order of the ferroelastic point group (2/m, order 4) [32]. Therefore, in the M1 phase there are four equivalent domain orientations, which can be generated by 90° rotations around the cR -axis, as illustrated in Fig. 3 a. The per- missible, low index, wall orientations separating these domains are (100)R , (010)R , (001)R , (110)R and (1-10)R (in addition, there is an- other set of permissible walls whose orientation depends on the values of the spontaneous strain components). [33] Due to the monoclinic shear, the clamping of monoclinic domains at the do- main walls requires a tilt which further increases the number of orientation variants, as actually seen in diffraction experiments. For instance, for {110}R -type walls, A domains in Fig. 3a, rotate around the [110]R or [1-10]R directions to satisfy the clamping on the (1- 10)R or (110)R planes, with adjacent B and D domains respectively, defining two new variants, A’ and A’’, as depicted in Fig. 3b. In this way, eight M1 variants are generated. On the other hand, the tetragonal R phase remains epitaxially-oriented with respect to the TiO2 substrate axes (as il- lustrated in the center of the sketch). From these considerations it is possible to anticipate the spot distribution arising from the coex- istence of the different M1 variants in reciprocal space. A scheme of such arrangement is shown in Fig. 3c to 3f. As starting point, ig- noring domain clamping at domain walls (i.e. c∗ R remains parallel to the [001]R direction). Fig. 3c shows a horizontal section of recip- rocal space for one single set of ferroelastic A domains (red dots), Fig. 3. (a) Top view sketch of the different variants of M1 domains arranged in four untilted ferroelastic domains (A, B, C and D) relative to the prototype R struc- which for simplicity includes only 01LR , 10LR and 11LR -type reflec- ture. The yellow arrows indicate the monoclinic shear direction along the [100]R or tions (with L any integer number different from zero). The sketch [010]R prototype axes for each domain. (b) Scheme of the eight different M1 vari- also includes the half order reflection -1/2 0 L/2R , which, as the ants obtained after rotation around the [110]R and [1-10]R directions, required to 1/2 0 3/2R one measured in this study, is characteristic of the M1 satisfy clamping on the {110}R domain walls. The yellow arrow corresponds to the tilt of the corresponding c∗ R -axis along either the [110]R or [1-10]R directions. (c) structure. Each M1 variant will have a unique -1/2 0 L/2R set of re- Schematics of an horizontal reciprocal space cut including a selection of HKL re- flections along the direction of the M1 shear distortion, related to flections for untilted A domains; (d) for A’/A’’ tilted domains; and (e) including an the unit cell parameter doubling induced by the V-V dimerization. additional uniaxial compression of A’/A’’ domains along the [110]∗ R and [1-10]∗ R di- As mentioned before, asymmetries in reciprocal space maps rections, respectively (note the shift in individual positions from previous tilted po- may be accounted for by applying a uniaxial compression perpen- sitions indicated by transparent symbols). (f) Complete arrangement of reflections for A’/A’’, B’/B’’, C’/C’’ and D’/D’’ variants (different colors are used for each variant). dicular to the clamping rotation about the [110]∗ R or [1-10]∗ R axes (i.e. perpendicular to the domain walls). This compression is in- corporated into the model as sketched in Fig. 3e for A’/A’’ do- mains. The position of the spots in reciprocal space is shifted away the HHL and 00L reflections in the reciprocal space allow for direct from the corresponding rotation axis (in the direction of the ar- determination of the corresponding cell parameters, as depicted in rows). This situation is the same for the rest of the B’/B’’, C’/C’’ and Fig. 4a. The appearance of a monoclinic shear distortion, with an- D’/D’’ variants. The spot distribution resulting from the combined gle α shear , induces a splitting of certain HKL reflections for the twin domain tilts and compression is depicted in Fig. 3f. Squared re- A’/A’’ variants. If one considers that c∗ R remains perpendicular to gions correspond to the areas analyzed in this work. This model the substrate surface for both domains, as in the sketch in Fig. 4b, is qualitatively consistent with the experimental observations of the splitting is produced in the vertical direction of the HHL re- the symmetric crossed pattern in Qx Qy maps of the 002R reflec- flections, and the magnitude of the splitting should correspond to tion (Fig. 2a), as well as of the asymmetric cross pattern in Qx Qy 2α shear . Further rotation of the A’/A’’ domains in opposite direc- maps of the 112R reflection (Fig. 2b). The model also reproduces tions, with magnitude α rot , shifts the HKL reflection positions ac- the two-branch asymmetric Qx Qy maps of the 1/2 0 3/2R reflec- cordingly, as depicted in Fig. 4c. tion observed in Fig. 2c. This shear and rotation, along with the uniaxial compression, Similarly, one can draw the model for the vertical projections also reproduce the main features observed in the vertical cuts of of reciprocal space, as depicted in Fig. 4. In epitaxial domains with the 002R , 112R reflections, shown in Fig. 2, as well as that in 101R tetragonal structure, i.e.: with no monoclinic shear and no rotation reflection (i.e. the splitting and asymmetry of maps in Figure S5, from substrate plane, the out-of-plane and in-plane coordinates of in SI). However, despite the qualitative agreement, this interpreta- 5 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 Fig. 4. Schematic of the distribution of 11L and 00L reflections in vertical projections of the reciprocal space for A’/A’’ variants with different distortion: (a) no shear and no rotation of crystal domains, (b) with monoclinic shear angle α shear ; and (c) additional rotation of domains in opposite direction with angle α rot . Filled and empty spots correspond to A’ and A’’ variants, respectively. tion, based on a pure ferroelastic behaviour, fails to account for the corrections are applied. More details of the calculation of the unit actual strain and tilt values extracted from the diffraction data. In cell parameters are given in the supplementary info (Figure S6 and the next section, the analysis incorporates the martensitic charac- S7). Fig. 5a indicates the XRD intensity of both R and M1 com- ter of the transformation by including the geometrical constrains ponents obtained from the corresponding 002R maps, which can associated to the coexistence of the R and M1 structures. By do- be taken as an estimate of the relative concentration of M1 and ing so, it is evidenced that these constrains are, in fact, responsible R phases in the film. At room temperature the film is apparently for a complex interplay between strain and phase stability which pure M1 and upon increasing temperature, the R fraction increases accurately accounts for the intensity distribution observed in the abruptly above 30 °C reaching a value of about 90 % already at reciprocal space maps. 40 °C. Above this temperature the M1 phase is still present but in a much reduced amount. From the M1/R ratio one can consider that the transition takes place in a broad temperature range be- 3.3. Martensitic character: Interplay between strain and phase tween 30 and 40 °C. This reduced transition temperature, well be- stability low Tc = 68 °C for bulk VO2 , results from the epitaxial strain on TiO2 (001) which stabilizes the rutile structure against the mono- In order to check the validity of this model, we determined the clinic one [11]. out-of-plane and in-plane unit cell parameters for the M1 and R The measured out-of-plane unit cell parameters are depicted in phases, as well as the monoclinic shear and domain tilt angles of Fig. 5b as extracted from the 002R , 112R , and 103R reflections. The the M1 domains, as a function of temperature up to 60 °C. These coincidence between the values extracted from these reflections is values were extracted from the main peak positions in the XRD a proof of the validity model, except for the measurement at T= maps assigned to the different domains according to the previously 35 °C, at the onset of transition, where there were difficulties in described model, and are collected in Fig. 5. Different reflections resolving the different M1 components and large errors are ex- were analyzed: 002R (in two different in-plane azimuthal angles, pected. At room temperature, out-of-plane cR values of 2.854 Å and either parallel to [100]∗ R or [110]∗ R ), and 1̄1̄2R (along [110]∗ R ) or 2.837 Å were measured for M1 and R phases, respectively. These 1̄03R (along [100]∗ R ) reflections. Essentially, the calculation directly values are consistent with those measured from the linear scans extracts the rotation angle from the in-plane splitting of 002R re- of 002R reflections in Fig. 1a. Up to 35 °C no substantial changes flections. The rotation angle can be also calculated from the 1̄1̄2R are observed, but above 35 °C a change in the slope of the out- and 1̄03R reflections as the necessary tilt to bring twin variants of-plane expansion of the M1 phase is clearly observed. A qualita- to a common in-plane coordinate in reciprocal space. Therefore, tively similar dependence was already observed in a previous re- the remaining vertical splitting corresponds uniquely to the mono- port on epitaxial films of VO2 /TiO2 (001) [34]. In that T range the clinic shear. The average in-plane and out-of-plane cell parameters apparent thermal expansion coefficient derived from our data is are therefore calculated once the corresponding shear and rotation 6 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 Fig. 5. Structural evolution of the R and M1 phases during the transition. (a) Intensity of 002R contributions; (b) Out-of-plane cell parameters extracted from the 002R , 112R and 103R reflections; (c) In-plane unit cell parameters extracted from the 112R reflection; and (d) Tilt angles (empty symbols) and monoclinic shear angles (filled symbols) of M1 domains. 353 10−6 K−1 , which clearly contrasts with the much lower ther- of α rot =1.25° at 60 °C, far exceeding α rot =0.23° corresponding to mal expansion coefficient of about 55 10−6 K−1 measured for the R {110}R -type twin domains in the bulk M1 phase. This anomalous phase. A comparison with reported values for rutile VO2 , of about behavior clearly indicates that the observed domain tilting does 30 10−6 K−1 [35,36], indicates that the thermal expansion mea- not result from the twin structure expected for the ferroelastic M1 sured here for epitaxial rutile VO2 is not far from reported values phase. of bulk samples. On the other hand, the out-of-plane M1 phase ex- In order to get insights into the origin of the distortion, we de- pansion considerably deviates from reported bulk values. In fact, at coupled the domain tilt angle from its corresponding monoclinic 60 °C, the M1 phase attains a cR -axis parameter of about 2.887 Å, shear angle. Fig. 5d shows the shear angle values derived from the which surpasses the bulk value, cR = 2.872 Å. [37] This expansion splitting of 112R reflections (measured along [110]∗ R direction), and is contrary to the elastic response expected for the in-plane tensile of 103R reflections (along [100]∗ R direction). Below 35 °C the mea- strain imposed by the TiO2 substrate, and should be related to a sured shear angles are about 0.2-0.3°, which do not deviate much phase change rather than to thermal expansion. The correspond- from the monoclinic shear angle α shea r = 0.32° along the [100]∗ R ing in-plane unit cell parameters extracted from the positions of direction (0.23° if measured along [110]∗ R direction) of the M1 bulk the different M1 components of the 112R reflection are depicted structure. However, above 35 °C, in the temperature interval dom- in Fig. 5c. In the direction perpendicular to [110]R , the M1 do- inated by the coexistence of M1 and R phases, the variations in mains show an in-plane interplanar distance, d1-10 , similar to that shear strain evidence a discrepancy with both monoclinic M1 and of the R phase, of about 3.242 Å, which also matches that of the M2 phases. Altogether these observations indicate that the larger TiO2 substrate as expected for a fully strained state. However, in the fraction of the rutile phase, the more pronounced the distor- the direction parallel to [110]R , the interplanar d110 distance suf- tion of the remaining M1 domains, far from their bulk equilibrium fers a sudden compression of about -1.2 %, from 3.242 Å to 3.203 structure. In fact, the enlargement of the cR parameter observed in Å at 40 °C. Above this temperature it continues decreasing linearly Fig. 5b, and the uniaxial compression along the [110]R direction, down to 3.180 Å at 60 °C, well below the reported bulk value of suggest a progressive transformation of the M1 structure towards d110 = 3.198 Å.[37] Therefore, the M1 phase changes from an in- the reported values of the M2 phase, as indicated in the graph plane tensile strained state to a compressive state along the [110]R (cR =3.898 Å, and d[110] =3.150 Å, d[1-10] =3.255 Å [14]). Moreover, direction, while it maintains a tensile strained value in the orthog- the progressive, rather than abrupt, evolution of the crystal struc- onal [1-10]R direction. This large uniaxial in-plane distortion can- ture is consistent with the formation of the transitional T phase, not be explained neither in terms of mere thermal expansion, nor reported to bridge the M1 and M2 phases through a progressive as an elastic response to the biaxial epitaxial strain. Besides, if one dimerization of V ions [10]. looks at the M1 domain tilt angle derived from the splitting of the 002R , 112R and 103R reflections from M1 phase along the [110]R 3.4. Dynamical model of M1 and R phase coexistence direction, depicted in Fig. 5d, it is clear that below 30 °C there is no detectable tilt angle, while above 35 °C there is a sudden Fig. 6 shows the 002R reflection, in a Qxy Qz map (projection change followed by a linear increase reaching a maximum value along the [110]∗ R direction), obtained from a 50 nm thick film at 7 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 Fig. 6. a) XRD reciprocal space map of the 002R reflection, obtained at 35 °C from a 50nm thick film, projected along the out-of-plane [001]∗ R and in-plane [110]∗ R directions. The arrows indicate the positions of the epitaxial R component, along with the tilted M1, T and M2 components forming the inverted-V shape. The red dots in the graph indicate the trajectory of the centroid position corresponding to the T domains between 30 to 60 °C. Note the clear definition of the M2 spot at the end of the arms (red arrows). b) Reciprocal space projections of the 002R , 112R and 222R reflections (expressed in the rutile setting) along the out-of-plane [001]∗ R and in-plane [110]∗ R directions at increasing temperatures. The red arrows indicate the position of the tilted M2 components, while the yellow arrows point to the centroid positions of the evolving T- phase at different stages of the transformation, from M1 to M2. Note the asymmetry between the left and right arms at the 112R and 222R reflections. The red circles in the 222R maps indicate the absence of the right arm for the M1 (and M2) components across the transition, which overlap with the R component, indicating matching between the R, M1, T, and M2 structures on the (111)R planes. c) Schematic detail of the relative orientation between the R and M1 phases with common matching (111)R planes, showing the tilt and compression along the [110]R direction of the M1 (T and M2). domains. d) Sequence (from  1 to 4 ) of monoclinic phase nucleation and evolution through the M2 and T phases during cooling down from the rutile phase. Some parts in the vicinity of M2 domains retain a strain gradient accommodated in the T phase, 3 , even when the film has fully transformed into the M1 ground state (T-phase strain gradient in  4 ). 35 °C, when the majority phase is already R but still a clear sig- occurs on preferred crystallographic planes minimizing the co- nal from M1 domains is observed. This map is very similar to that herency strains between the two structures. In this situation, the previously presented in Figure 2a for a thicker film, and shows the large difference between the unit cell parameters of the two inverted V-shape with symmetric branches at both sides of the phases is likely to result in the build-up of large stresses during central axis at Q[110] = 0. The splitting of M1 002R peaks is al- cooling down across the phase transition. In this sense, it is inter- ready resolved at this temperature (indicated with a yellow arrow). esting to note that the evolution of the 112R M1 components in Particularly apparent in this map is the existence of an intensity the Qxy Qz and Qx Qy maps shown in Fig. 2b indicates that the peak peak at the extreme positions of the diffuse branches (indicated closer to the central position along the [110]∗ R direction shows a with a red arrow), which is consistent with tilted domains with very small shift compared to the other components. This suggests the unit cell parameters of the M2 phase (040M2 reflection). The the occurrence of an invariant R/M1 matching which constrains the continuous trace between the M1 and M2 reflections can be ex- rotation and distortion of M1 domains. In order to check this hy- plained by the formation of a progressive transitional state in the T pothesis, different HHL maps (H= 0, 1, 2, L =2) were measured phase (indicated by orange labels). Thus, this observation indicates on the 50nm thick film at T= 35, 45 and 55 °C. Fig. 6b shows that even at room temperature, when the film has transformed to vertical Qxy Qz cuts of the 3D maps parallel to the [110]∗ R direc- M1, there are still residual strain gradients corresponding to the tion. The maps show R (central axis) and M1 (inverted “V”-shape) frozen structural trajectory of the metastable T phase. The graph components analogous to those previously shown in Fig. 2. Qxy Qz also shows superimposed the centroid positions of the split T com- maps of the 002R reflection are symmetric, while the Qxy Qz cuts ponents measured at different temperatures, from 30 to 60 °C, on of the 112R and 222R reflections show asymmetric branches. The the same sample. It is apparent that, as the temperature increases, yellow arrows indicate the evolution with temperature of the cen- the centroid positions of the split components follow exactly the troid positions of residual M1 tilted domains, similar to that ob- same trajectory as the preexisting intensity traces caused by the served in the 002R reflection, while the red arrow corresponds to reverse transformation during cooling from the growth tempera- the extreme position of the tilted M2 domains. An interesting fea- ture. This indicates that the structural path through the T phase is ture arises from the extent of the branches of these asymmetric reversible. Qxy Qz maps. It is apparent that, in the 112R reflection, the right Considering the martensitic character of the transition, it is rea- branch is considerably reduced with respect to that observed in sonable to think that the contact between the R and M1 phases the 002R maps and, for the 222R reflection, the right branch is no 8 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 longer observed. This behavior is consistent with the occurrence of one set of (111)R planes belonging to the M1 phase, namely (210)/(21̄0)M1 , being parallel to the (111)R planes of the R phase, as shown in the scheme depicted in Fig. 6c, and with strain gradients developing perpendicularly to that contact plane. The same con- tact plane, (111)R // (221)M2 , has been previously shown to provide favorable matching between R and M2 domains in VO2 microcrys- tals.[38] These are equivalent to the (210)/(21̄0)M1 planes in the M1 structure, and therefore are expected to provide also favorable matching with the (111)R planes of the rutile structure. A calcula- tion of the mismatch for different possible contact planes between the R and M1 bulk structures (see supplementary info, Fig. S8 and Table S1) indeed indicates that the best matching is obtained be- tween the (111)R and (210)/(21̄0)M1 planes, both equivalent in the Fig. 7. Scheme of the VO2 transformation path followed by the main film domains (thick red arrow) as well as interfacial regions (dashed orange line) across the cR - pseudo-rutile representation of the M1 structure. Other interface axis strain vs Temperature phase diagram as reported in [11]. The blue arrow in- orientations such as (001)R // (010)M2 or (021)R // (011)M2 , equiv- dicates the prevailing strain gradient at RT crossing stability regions of T and M2 alent to (001)R // (20-1)M1 or (021)R // (22-1)M1 , respectively, also phases. reported in [38] to produce a low mismatch between R and M2 in VO2 microcrystals, were not observed in this case. Upon heating, as rutile becomes the dominant phase, the mi- nority M1 phase is assumed to be confined in increasingly smaller domains, which thus become elastically softer, capable to ro- tate and compress along the [110]R direction to keep the com- the direction of the tilt axis. Therefore, a uniaxial in-plane strain mon (111)R planes. This situation is equivalent to that observed is induced onto the M1 nuclei along the [1-10]R direction, which in other oxides with tetragonal structure, like mixed c/a-axis ori- can stabilize intermediate structures between M1 and M2 in the T ented Pb(Zr,Ti)O3 thin films [39], where partial strain relaxation phase by adjusting the out-of-plane and in-plane lattice parame- is achieved by domain tilting of the minority phase, resulting in ters and domain rotation, generating a continuous track reflected different orientation variants. In this case, the four possible {111}R in the diffuse intensity branches (Fig. 6 a), as depicted in sequence planes determine four orientational variants of the M1 phase, fol- 1 and  2 . In fact, these are size effects associated to varying de- lowing the <110>R directions, and the different shear directions grees of V dimerization. As the transition proceeds, in sequence  2 of the M1 domains along <100>R result in eight orientational to  3 , T domains grow in size and become less elastic, with a con- variants fully equivalent to the model shown in Fig. 3b. Although comitant reduction in domain rotation, progressively transforming the M1 domain arrangement scheme was introduced based on the into the equilibrium M1 structure. The transition is completed at possible existence of ferroelastic {110}R -type walls between M1 do- about 30-35 °C, in sequence  4 , when most of the film volume mains, the present coupling between R and M1 domains repro- has transformed into the M1 phase. This transformation is fully re- duces the same pattern. However, the experimental values of the versible when increasing temperature above Tc . M1 domain tilt, up to α rot =1.25°, indicate a much larger tilt of M1 As schematized in Fig. 6d, this mechanism carries the build-up domains, which is not compatible with the domain tilt caused by of very high stresses along the (111)R planes, stabilizing M2 do- {110}R-type walls, limited to a maximum value of the shear strain mains (depicted in red color). This implies a further elongation of of the monoclinic structure (α shear =0.32°). Instead, domain tilt due the cR axis (d001 =2.898 Å, +1.3 % relative to the R phase), which in to the coupling between (111)R planes in the R and M1 structures turns requires a larger rotation with respect to the R matrix (up to (and ultimately with M2) has much wider limits and nicely ac- α rot =1.3°). To depict the phase transformation path Fig. 7 shows a counts for the experimental data. scheme of the c-axis strain versus Temperature phase diagram, as Once established the structural constrains controlling the co- reported in [11]. In this diagram the extent of T phase is enlarged existence of the M1 and R phases this part discusses about the for clarity. Note that the original in-plane biaxial tensile strain state phase distribution and their evolution during transition. Any at- of the film at the deposition temperature is expected to produce a tempt to directly observe the different phases’ distribution across compressive strain along c-axis (negative value). Therefore, upon the film surface by micro-Raman spectroscopy resulted non con- cooling down VO2 would follow a main path, below the triple clusive because of the large overlap with the TiO2 substrate as well point, where R transforms into M1 phase, without the formation as the very subtle changes of the observable low frequency phonon of additional phases. However, once the first M1 domains are nu- modes in the M1, M2 and T structures (as explained in Fig. S10 cleated within the R matrix the build-up of uniaxial stresses coun- in the supplementary information). However, based on the X-ray teract the epitaxial stress by inducing a cR -axis expansion (positive diffraction results, a model of the microstructural evolution across strain value), turning some interfacial regions of the VO2 film into the phase transition can be sketched as shown in Fig. 6d. At a tem- M2 phase, as depicted in the vertical trajectory of the dashed line perature well above the transition, the whole volume of the film in the scheme. Further cooling down to RT would transform the corresponds to the rutile structure, fully strained by the TiO2 sub- M2 domains into the transitional T phase and eventually to the strate. Upon cooling down, at the onset of the transition, in  1 , nar- stable M1. The observation of the M2 phase at room temperature row M1 domains start to nucleate on the equivalent (111)R planes indicates that such stresses prevail after the transformation, and of the rutile structure. In fact, this mechanism is fully consistent are responsible for the frozen strain gradients, bridging R and M1 with the transition being driven by V ion displacements perpen- structures through the T-phase, observed in virtually pure M1 films dicular to those planes [40]. Their small volume makes them elas- well below the transition temperature, in stage  4 of Fig. 6d. This tically softer with respect to the surrounding R matrix, and there- mechanism explains the persistence of inverted V-shape intensity fore the elastic energy increase due to the nucleation of the M1 traces in the XRD reciprocal space maps. Finally, it is worthy to phase within the R matrix can be partially released by rotating the note that these phase transformation mechanisms very likely com- formed nuclei around a common [1-10]R axis. However, this rota- pete with crack formation in the relaxation of the high stress levels tion of M1 domains does not accommodate the elastic strain in developed in these epitaxial films. 9 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 4. Conclusions References In summary, this work uncovers the interplay between intrin- [1] F.J. Morin, Oxides which show a metal-to-insulator transition at the neel tem- perature, Phys. Rev. Lett. 3 (1959) 34–36, doi:10.1103/PhysRevLett.3.34. sic strains and phase stability in VO2 epitaxial films deposited on [2] C.N. Berglund, H.J. Guggenheim, Electronic properties of VO2 near the TiO2 (001) across its martensitic-like metal-insulator transition. 3D semiconductor-metal transition, Phys. Rev. 185 (1969) 1022–1033, doi:10.1103/ reciprocal space maps obtained from virtually perfect insulating PhysRev.185.1022. [3] J.B. Goodenough, The two components of the crystallographic transition M1 films exhibit weak diffuse intensity traces that represent the in VO2 , J. Solid State Chem. 3 (1971) 490–500, doi:10.1016/0022-4596(71) trajectories of Bragg reflections resulting from strong strain gradi- 90091-0. ents frozen in the films after cooling from the growth temperature. [4] A.S. Barker, H.W. Verleur, H.J. Guggenheim, Infrared optical properties of vana- dium dioxide above and below the transition temperature, Phys. Rev. Lett. 17 In situ experiments show that, upon heating, these Bragg reflec- (1966) 1286–1289, doi:10.1103/PhysRevLett.17.1286. tions follow the reverse trajectory along the preexisting intensity [5] T.D. Manning, I.P. Parkin, R.J.H. Clark, D. Sheel, M.E. Pemble, D. Vernadou, tracks, indicating a reversible behavior. The analysis of these traces Intelligent window coatings: atmospheric pressure chemical vapour deposi- tion of vanadium oxides, J. Mater. Chem. 12 (2002) 2936–2939, doi:10.1039/ shows that they result from a combination of normal strains and B205427M. domain tilts which exceed by far those expected from the ferroe- [6] D. Ruzmetov, G. Gopalakrishnan, C. Ko, V. Narayanamurti, S. Ramanathan, lasticity of VO2 . This complex behavior is explained by consider- Three-terminal field effect devices utilizing thin film vanadium oxide as the ing the martensitic character of the transition and the subtle in- channel layer, J. Appl. Phys. 107 (2010) 114516, doi:10.1063/1.3408899. [7] M. Nakano, K. Shibuya, D. Okuyama, T. Hatano, S. Ono, M. Kawasaki, Y. Iwasa, terplay between strain and phase stability in the proximity of the Y. Tokura, Collective bulk carrier delocalization driven by electrostatic surface VO2 triple point. Particularly, it is shown that the coexisting R and charge accumulation, Nature 487 (2012) 459–462, doi:10.1038/nature11296. M1 phases share their common (111)R planes during the transi- [8] Z. Yang, C. Ko, S. Ramanathan, Oxide electronics utilizing ultrafast metal- insulator transitions, Annu. Rev. Mater. Res. 41 (2011) 337–367, doi:10.1146/ tion. This geometrical constrain, coupled with the epitaxial match- annurev- matsci- 062910- 100347. ing, results in domain tilts about the <110>R axes and the build- [9] N.F. Quackenbush, H. Paik, M.J. Wahila, S. Sallis, M.E. Holtz, X. Huang, up of uniaxial compressive stresses perpendicular to them, caus- A. Ganose, B.J. Morgan, D.O. Scanlon, Y. Gu, F. Xue, L.-Q. Chen, G.E. Sterbin- sky, C. Schlueter, T.-L. Lee, J.C. Woicik, J.-H. Guo, J.D. Brock, D.A. Muller, ing the formation of the M2 phase. Moreover, it is shown that the D.A. Arena, D.G. Schlom, L.F.J. Piper, Stability of the M2 phase of vanadium diffuse intensity traces reflect varying degrees of V-V dimerization dioxide induced by coherent epitaxial strain, Phys. Rev. B. 94 (2016) 85105, accommodated within the metastable triclinic T phase bridging the doi:10.1103/PhysRevB.94.085105. [10] J.P. Pouget, H. Launois, J.P. D’Haenens, P. Merenda, T.M. Rice, Electron localiza- M1 and M2 structures. These results provide new insights into the tion induced by uniaxial stress in pure VO2, Phys. Rev. Lett. 35 (1975) 873–875, microstructural consequences of the extreme sensitivity of VO2 to doi:10.1103/PhysRevLett.35.873. strain, unveiling the existence of remnant dimerization disorder in [11] J. Cao, Y. Gu, W. Fan, L.Q. Chen, D.F. Ogletree, K. Chen, N. Tamura, M. Kunz, C. Barrett, J. Seidel, J. Wu, Extended mapping and exploration of the vana- virtually perfect insulating M1 films. This insight may have strong dium dioxide stress-temperature phase diagram, Nano Lett 10 (2010) 2667– implications on the local electronic properties of the material, as 2673, doi:10.1021/nl101457k. well as for the understanding of the correlation between film mi- [12] J.H. Park, J.M. Coy, T.S. Kasirga, C. Huang, Z. Fei, S. Hunter, D.H. Cobden, Mea- crostructure and mechanical properties. surement of a solid-state triple point at the metal–insulator transition in VO2 , Nature 500 (2013) 431–434, doi:10.1038/nature12425. [13] J.P. Pouget, H. Launois, T.M. Rice, P. Dernier, A. Gossard, G. Villeneuve, P. Ha- genmuller, Dimerization of a linear Heisenberg chain in the insulating phases Declaration of Competing Interest of V1-x Crx O2 , Phys. Rev. B. 10 (1974) 1801–1815, doi:10.1103/PhysRevB.10.1801. [14] M. Marezio, D.B. McWhan, J.P. Remeika, P.D. Dernier, Structural aspects of the The authors declare that they have no known competing finan- metal-insulator transitions in Cr-doped VO2 , Phys. Rev. B. 5 (1972) 2541–2551, cial interests or personal relationships that could have appeared to doi:10.1103/PhysRevB.5.2541. [15] J. Laverock, V. Jovic, A.A. Zakharov, Y.R. Niu, S. Kittiwatanakul, B. Westhenry, influence the work reported in this paper. J.W. Lu, S.A. Wolf, K.E. Smith, Observation of Weakened V—V dimers in the monoclinic metallic phase of strained VO2 , Phys. Rev. Lett. 121 (2018) 256403, doi:10.1103/PhysRevLett.121.256403. Acknowledgments [16] F. Grandi, A. Amaricci, M. Fabrizio, Unraveling the Mott-Peierls in- trigue in vanadium dioxide, Phys. Rev. Res. 2 (2020) 13298, doi:10.1103/ PhysRevResearch.2.013298. This work was supported in part by the Spanish Ministry [17] F. Sandiumenge, L. Rodríguez, M. Pruneda, C. Magén, J. Santiso, G. Catalan, of Economy, Industry and Competitiveness (projects MAT2016- Metallic diluted dimerization in VO2 tweeds, Adv. Mater. 33 (2021) 2004374, 77100-C2-1-P and PID2019-108573GB-C21), and by the Catalan doi:10.10 02/adma.2020 04374. AGAUR agency (project: 2017-SGR-579). ICN2 is funded by the [18] A. Tselev, V. Meunier, E. Strelcov, W.A. Shelton, I.A. Luk’yanchuk, K. Jones, R. Proksch, A. Kolmakov, S.V Kalinin, Mesoscopic metal−insulator transition at CERCA programme/Generalitat de Catalunya and by the Severo Ferroelastic domain walls in VO2 , ACS Nano 4 (2010) 4412–4419, doi:10.1021/ Ochoa programme (SEV-2017-0706). LR acknowledges the support nn1004364. of Severo Ochoa programme and ICN2 for her PhD grant. Part of [19] A. Tselev, E. Strelcov, I.A. Luk’yanchuk, J.D. Budai, J.Z. Tischler, I.N. Ivanov, K. Jones, R. Proksch, S.V Kalinin, A. Kolmakov, Interplay between Fer- the measurements were carried out at the KMC-II instrument at roelastic and metal−insulator phase transitions in strained quasi-two- Helmholtz-Zentrum Berlin für Materialien und Energie. Besides, we dimensional VO2 Nanoplatelets, Nano Lett 10 (2010) 2003–2011, doi:10.1021/ would like to thank Dr. D. Többens for assistance during the KMC- nl1008794. [20] J. Wu, Q. Gu, B.S. Guiton, N.P. de Leon, L. Ouyang, H. Park, Strain-induced self II experiment. The research leading to this result has been partially organization of metal−insulator domains in single-crystalline VO2 Nanobeams, supported by the project CALIPSO plus under the Grant Agreement Nano Lett 6 (2006) 2313–2317, doi:10.1021/nl061831r. 730872 from the EU Framework Programme for Research and In- [21] J. Cao, E. Ertekin, V. Srinivasan, W. Fan, S. Huang, H. Zheng, J.W.L. Yim, D.R. Khanal, D.F. Ogletree, J.C Grossman, J Wu, Strain engineering and one- novation HORIZON 2020. F.S. acknowledges the Spanish Ministry dimensional organization of metal-insulator domains in single-crystal vana- of Industry, Economy and Competitiveness (MINECO) for financial dium dioxide beams, Nat. Nano. 4 (2009) 732–737, doi:10.1038/nnano.2009. support through the “Severo Ochoa” programme for Centers of Ex- 266. [22] J.I. Sohn, H.J. Joo, D. Ahn, H.H. Lee, A.E. Porter, K. Kim, D.J. Kang, M.E. Welland, cellence in R&D (SEV-2015-0496) and project no. RTI2018-098537- Surface-stress-induced mott transition and nature of associated spatial phase B-C21. The authors acknowledge the support of Dr. E. del Corro for transition in single crystalline VO2 nanowires, Nano Lett 9 (2009) 3392–3397, the micro-Raman analysis of the films. doi:10.1021/nl900841k. [23] S. Zhang, J.Y. Chou, L.J. Lauhon, Direct correlation of structural domain for- mation with the metal insulator transition in a VO2 Nanobeam, Nano Lett 9 Supplementary materials (2009) 4527–4532, doi:10.1021/nl9028973. [24] M. Liu, S. Xie, L. Wei, M. Galluzzi, Y. Li, Q. Wang, X. Zhou, Y. Wang, J. Li, Quan- titative functional imaging of VO2 metal-insulator transition through interme- Supplementary material associated with this article can be diate M2 phase, Acta Mater 195 (2020) 720–727, doi:10.1016/j.actamat.2020. found, in the online version, at doi:10.1016/j.actamat.2021.117336. 06.014. 10 L. Rodríguez, F. Sandiumenge, C. Frontera et al. Acta Materialia 220 (2021) 117336 [25] L. Vidas, C.M. Günther, T.A. Miller, B. Pfau, D. Perez-Salinas, E. Martínez, [33] J. Sapriel, Domain-wall orientations in ferroelastics, Phys. Rev. B. 12 (1975) M. Schneider, E. Gührs, P. Gargiani, M. Valvidares, R.E. Marvel, K.A. Hallman, 5128–5140, doi:10.1103/PhysRevB.12.5128. R.F. Haglund, S. Eisebitt, S. Wall, Imaging Nanometer phase coexistence at de- [34] H. Qiu, M. Yang, Y. Dong, H. Xu, B. Hong, Y. Gu, Y. Yang, C. Zou, Z. Luo, C. Gao, fects during the insulator–metal phase transformation in VO2 thin films by The tetragonal-like to rutile structural phase transition in epitaxial VO2 /TiO2 resonant soft X-ray holography, Nano Lett 18 (2018) 3449–3453, doi:10.1021/ (001) thick films, New J. Phys. 17 (2015) 113016, doi:10.1088/1367-2630/17/11/ acs.nanolett.8b00458. 113016. [26] Y. Ji, Y. Zhang, M. Gao, Z. Yuan, Y. Xia, C. Jin, B. Tao, C. Chen, Q. Jia, Y. Lin, [35] D. Kucharczyk, T. Niklewski, Accurate X-ray determination of the lattice Role of microstructures on the M1-M2 phase transition in epitaxial VO(2) thin parameters and the thermal expansion coefficients of VO2 near the tran- films, Sci. Rep. 4 (2014) 4854, doi:10.1038/srep04854. sition temperature, J. Appl. Crystallogr. 12 (1979) 370–373, doi:10.1107/ [27] L. Rodríguez, E. del Corro, M. Conroy, K. Moore, F. Sandiumenge, N. Domingo, S0021889879012711. J. Santiso, G. Catalan, Self-pixelation through fracture in VO2 thin films, ACS [36] K.V.K. Rao, S.V.N. Naidu, L. Iyengar, Thermal expansion of tetragonal phase of Appl. Electron. Mater. 2 (5) (2020) 1433–1439, doi:10.1021/acsaelm.0c00199. VO2 , J. Phys. Soc. Japan. 23 (1967) 1380–1382, doi:10.1143/JPSJ.23.1380. [28] K. Kawatani, H. Takami, T. Kanki, H. Tanaka, Metal-insulator transition with [37] G. Andersson, J. Paju, W. Lang, W. Berndt, Studies on vanadium oxides. I. Phase multiple micro-scaled avalanches in VO2 thin film on TiO2 (001) substrates, analysis, Acta Chem. Scand. 8 (1954) 1599–1606, doi:10.3891/acta.chem.scand. Appl. Phys. Lett. 100 (2012) 173112, doi:10.1063/1.4709429. 08-1599. [29] T. Yajima, Y. Ninomiya, T. Nishimura, A. Toriumi, Drastic change in electronic [38] J.D. Budai, A. Tselev, J.Z. Tischler, E. Strelcov, A. Kolmakov, W.J. Liu, A. Gupta, domain structures via strong elastic coupling in VO2 films, Phys. Rev. B. 91 J. Narayan, In situ X-ray microdiffraction studies inside individual VO2 micro- (2015) 205102, doi:10.1103/PhysRevB.91.205102. crystals, Acta Mater 61 (2013) 2751–2762, doi:10.1016/j.actamat.2012.09.074. [30] M. Liu, A.J. Sternbach, M. Wagner, T.V Slusar, T. Kong, S.L. Bud’ko, S. Kitti- [39] K.S. Lee, J.H. Choi, J.Y. Lee, S. Baik, Domain formation in epitaxial Pb(Zr,Ti)O3 watanakul, M.M. Qazilbash, A. McLeod, Z. Fei, E. Abreu, J. Zhang, M. Goldflam, thin films, J. Appl. Phys. 90 (2001) 4095–4102, doi:10.1063/1.1404424. S. Dai, G.-X. Ni, J. Lu, H.A. Bechtel, M.C. Martin, M.B. Raschke, R.D. Averitt, [40] J.D. Budai, J. Hong, M.E. Manley, E.D. Specht, C.W. Li, J.Z. Tischler, D.L. Aber- S.A. Wolf, H.-T. Kim, P.C. Canfield, D.N. Basov, Phase transition in bulk single nathy, A.H. Said, B.M. Leu, L.A. Boatner, R.J. McQueeney, O. Delaire, Metalliza- crystals and thin films of VO2 by nanoscale infrared spectroscopy and imag- tion of vanadium dioxide driven by large phonon entropy, Nature 515 (2014) ing, Phys. Rev. B. 91 (2015) 245155, doi:10.1103/PhysRevB.91.245155. 535–539, doi:10.1038/nature13865. [31] J.-P. Pouget, Basic aspects of the metal{\textendash}insulator transition in vana- dium dioxide VO2 : a critical review, Comptes Rendus. Phys. 22 (2021) 37–87, doi:10.5802/crphys.74. [32] K. Aizu, Possible species of ferromagnetic, ferroelectric, and Ferroelastic crys- tals, Phys. Rev. B. 2 (1970) 754–772, doi:10.1103/PhysRevB.2.754. 11