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Anelastic spectra corresponding to curves 1, 2 and 5 of Fig. 1, measured on the 1st (circles) and 5th (lines) modes.
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The complex elastic compliance s11(ω,T) of SrTiO3−δ has been measured as a function of the O deficiency δ<0.01. The two main relaxation peaks in the absorption are identified with hopping of isolated O vacancies over a barrier of 0.60 eV and reorientation of pairs of vacancies involving a barrier of 1 eV. The pair binding energy is ≃0.2 eV, and ind...
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Citations
... Even though peaks P1-P3 are considerably broader than Debye relaxations, they are clearly caused by well-defined defects with quite different activation barriers E. It would be tempting to make parallels with the anelastic relaxation spectra of other defective perovskites, like O deficient SrTiO 3−δ [38] and partially decomposed (TMCM)MnCl 3 [31], but the present situation is different. Oxide perovskites are quite stable compounds and may loose only O atoms at high temperature in a reducing atmosphere. ...
... The charge compensation in SrTiO 3−δ from the loss of O 2− anions can be achieved by the reduction of 2δ Ti 4+ cations to Ti 3+ . The resulting defects are V O and small polarons and the anelastic spectra of SrTiO 3−δ and BaTiO 3−δ show peaks due to their hopping, with clearly distinct peaks for vacancies that are isolated and paired [38,39]. ...
... Therefore, jumps between strongly inequivalent positions, like those required to form and separate a defect pair, produce relaxation processes distinct from those cited above, and with a much depressed intensity. This type of relaxation between inequivalent states is hardly distinguishable in SrTiO 3−δ with δ 0.01, where a small but distinct peak can be attributed to the partial dissociation of pairs of V O [38]. ...
We measured the anelastic, dielectric and structural properties of the metal-free molecular perovskite (ABX3) (MDABCO)(NH4)I3, which has already been demonstrated to become ferroelectric below TC= 448 K. Both the dielectric permittivity measured in air on discs pressed from powder and the complex Young’s modulus measured on resonating bars in a vacuum show that the material starts to deteriorate with a loss of mass just above TC, introducing defects and markedly lowering TC. The elastic modulus softens by 50% when heating through the initial TC, contrary to usual ferroelectrics, which are stiffer in the paraelectric phase. This is indicative of improper ferroelectricity, in which the primary order parameter of the transition is not the electric polarization, but the orientational order of the MDABCO molecules. The degraded material presents thermally activated relaxation peaks in the elastic energy loss, whose intensities increase together with the decrease in TC. The peaks are much broader than pure Debye due to the general loss of crystallinity. This is also apparent from X-ray diffraction, but their relaxation times have parameters typical of point defects. It is argued that the major defects should be of the Schottky type, mainly due to the loss of (MDABCO)2+ and I−, leaving charge neutrality, and possibly (NH4)+ vacancies. The focus is on an anelastic relaxation process peaked around 200 K at ∼1 kHz, whose relaxation time follows the Arrhenius law with τ0 ∼ 10−13 s and E≃0.4 eV. This peak is attributed to I vacancies (VX) hopping around MDABCO vacancies (VA), and its intensity presents a peculiar dependence on the temperature and content of defects. The phenomenology is thoroughly discussed in terms of lattice disorder introduced by defects and partition of VX among sites that are far from and close to the cation vacancies. A method is proposed for calculating the relative concentrations of VX, that are untrapped, paired with VA or forming VX–VA–VX complexes.
... Notice that isolated V X do not have an electric dipole and therefore do not cause dielectric relaxation, while pairs of cation and anion vacancies have both elastic and electric dipoles. Even though peaks P1-P3 are considerably broader than Debye relaxations, they are clearly due to well defined defects with quite different activation barriers E. It would be tempting to make parallels with the anelastic relaxation spectra of other defective perovskites, like O deficient SrTiO 3−δ [26] and 10 of 19 partially decomposed (TMCM)MnCl 3 [18], but the present situation is different. Oxide perovskites are quite stable compounds and may loose only O atoms at high temperature in reducing atmosphere. ...
... The charge compensation in SrTiO 3−δ from the loss of O 2− anions can be achieved by the reduction of 2δ Ti 4+ cations to Ti 3+ . The resulting defects are V O and small polarons and the anelastic spectra of SrTiO 3−δ and BaTiO 3−δ show peaks due to their hopping, with clearly distinct peaks for vacancies that are isolated and paired [26,27]. Figure 10. ...
... Therefore, jumps between strongly inequivalent positions, like those for forming and separating a defect pair, produce relaxation processes distinct from those cited above, and with a much depressed intensity. This type of relaxation between inequivalent states is hardly distinguishable in SrTiO 3−δ with δ 0.01, where a small but distinct peak can be attributed to the partial dissociation of pairs of V O [26]. ...
We measured the anelastic, dielectric and structural properties of the metal-free molecular perovskite (ABX$_{3}$) (MDABCO)(NH$_{4}$)I$_{3}$, which has already been demonstrated to become ferroelectric below $T_{\text{C}}=$ 448~K. Both the dielectric permittivity measured in air on discs pressed from powder and the complex Young's modulus measured on resonating bars in vacuum show that the material starts deteriorating with loss of mass just above $T_{\text{C}}$, introducing defects and markedly lowering $T_{\text{C}}$. The elastic modulus softens of 50\% when heating through the initial $T_{\mathrm{C}}$, contrary to usual ferroelectrics, which are stiffer in the paraelectric phase. This suggests improper ferroelectricity, where the primary order parameter of the transition is not the electric polarization, but the orientational order of the MDABCO molecules. The degraded material presents thermally activated relaxation peaks in the elastic energy loss, whose intensities increase together with the decrease of ~$T_{\mathrm{C}}$. The peaks are much broader than pure Debye, due to the general loss of crystallinity, also apparent from X-ray diffraction, but their relaxation times have parameters typical of point defects. It is argued that the major defects should be of the Schottky type, mainly due to the loss of (MDABCO)$^{2+} $ and I$^{-}$, leaving charge neutrality, and possibly also (NH$_{4}$)$^{+}$ vacancies. The focus is on an anelastic relaxation process peaked around 200~K at $\sim 1$~kHz, whose relaxation time follows the Arrhenius law with $\tau $$_{0}$~$\sim $\ $10^{-13}$\ s and $E\simeq 0.4$~eV. This peak is attributed to I vacancies (V$_{\text{X}}$) hopping around MDABCO vacancies (V$_{\text{A}}$) and its intensity presents a peculiar dependence on temperature and content of defects. The phenomenology is thoroughly discussed in terms of lattice disorder introduced by defects and of partition of V$_{\text{X}}$ among sites that are far from and close to the cation vacancies. A method is proposed for calculating the relative concentrations of V$_{\text{X}}$, that are untrapped, paired with V$_{\text{A}}$ or forming V$_{\text{X}}$--V$_{\text{A}}$--V$_{\text{X}}$ complexes.
... Being the fastest among the point defect jumps, it may contribute to the relaxation process with the lowest activation energy, R1. Notice that, in cubic perovskites, the hopping of an isolated V X does not produce dielectric relaxation, because it has two nearest neighbour B atoms in opposite directions, and no electric dipole is created [37]. Moreover, in the hexagonal perovskites with columns of BX 6 octahedra, V X are bound to diffuse within the same column, unless the A cations support missing or excess X. ...
... A final remark on the expected abundance of isolated V X is due. In inorganic oxide perovskites, relatively large amounts of V O can be reversibly created and eliminated with thermal treatments in reducing or O 2 atmospheres, without affecting the perovskite framework of metallic cations, and the hopping and clustering of V O can, therefore, be observed [37]. In the hybrid metal-organic perovskites, there are no quantitative studies on the formation of these defects; however, the organic cations are certainly less stable than metallic A cations, and it is perhaps impossible to create V X without an equal or even larger amount of V A . ...
... Finally, we comment on the fact that R2, even though identified with point defect relaxation, is considerably broader than a Debye relaxation. For comparison, in the cubic perovskite oxide SrTiO 3−δ , isolated V O diffuse with an activation energy of 0.60 eV, while the reorientation of pairs of V O requires 1.0 eV, and both the anelastic relaxation peaks are close to single-time Debye relaxations (α ≥ 0.95), at least up to δ ∼0.01 [37]. The point is that, in hexagonal perovskites with large molecular A cations, the distances between A and X are larger than in cubic perovskites, and due to the columnar geometry of the BX 6 octahedra, there are several X sites facing an A site with distances that differ little from each other. ...
We present dielectric and anelastic spectroscopy measurements of the molecular piezoelectric TMCM-MnCl3 and TMCM-Mn0.95M0.05Cl3 (M = Cu, Fe, Ni; TMCM = trimethylchlorometylammonium), whose powders were pressed into discs and bars and deposited as films on Si by Matrix-Assisted Pulsed Laser Evaporation (MAPLE). As in other molecular ferroelectrics, the dielectric permittivity ϵ′ drops at the structural transition temperature TC, below which the number of directions that the polar TMCM molecules visit is reduced, with the formation of ferroelectric domains. Concomitantly, the Young’s modulus E starts increasing and the elastic energy loss has a step-like increase, attributable to the motion of the domain walls. Both the dielectric and elastic anomalies indicate the improper character of the ferroelectric transition, where the ordering of the molecular orientations is not driven by the cooperative interaction of their electric dipoles. Below room temperature, at least two thermally activated relaxation processes appear both in the dielectric and anelastic spectra, whose real and imaginary parts measured at several frequencies can be fit with the Havriliak–Negami formula. The microscopic parameters so-obtained indicate that they are due to point defects, and it is argued that they are Cl vacancies and their complexes with TMCM vacancies. The considerable width of these relaxation maxima is explained by the geometry of the hexagonal perovskite structure. The partial substitution of Mn with 5% Ni has little effect on the anelastic and dielectric spectra, while Cu and, especially, Fe cause a large enhancement of the losses attributed to domain wall relaxation, with substantial contributions also above TC. The condensation of water from the humidity in the powders compacted by cold pressing was observed and discussed. The piezoelectric activity of the films was assessed by PFM.
... For the kMC and MD simulations, we considered oxygen-vacancy diffusion in SrTiO 3 , primarily because it is a system that has been extensively studied, so that there is excellent agreement from a variety of methods (chemical diffusion, 32 nuclear spin relaxation, 33 tracer diffusion, 34 anelastic relaxation, 35 and classical MD simulations 36 ) as to the absolute magnitude of the vacancy diffusivity and its activation enthalpy (of 0.62 eV). Furthermore, this value of the migration barrier is also obtained from static supercell simulations based on densityfunctional-theory (DFT) calculations with sufficiently large cells containing an even number of perovskite formula units in all three spatial dimensions. ...
Analysis of the mean squared displacement of species k, <r_k²>, as a function of simulation time t constitutes a powerful method for extracting, from a molecular-dynamics (MD) simulation, the tracer diffusion coefficient, D_k*. The statistical error in D_k* is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of <r_k²(t)> curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D_k* depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity–the number of k particles that have jumped at least once–we derive a closed-form expression for the relative uncertainty in D_k*. We confirm the accuracy of our expression through comparisons with self-generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.
... The attention comes from SrTiO 3 being a (comparatively simple) model system, and hence the knowledge required when investigating oxygen surface exchange is available. To be specific, there is deep understanding of oxygen diffusion in the bulk phase [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and there is detailed quantitative knowledge of charge carrier concentrations as a function of thermodynamic variables (temperature, oxygen activity, doping level). [2,3,5,6,11,17,[21][22][23][24][25] In studying oxygen surface exchange on SrTiO 3 , researchers have concentrated on the effect of compositional changes, [15,[26][27][28][29][30][31][32] but they have also looked at the effect of water vapor, [31,[33][34][35][36][37] UV radiation, [26,38] and surfaces layers of metals [39] or alkaline-earth oxides. ...
... This value agrees well with literature data from both experimental and computational studies of (0.62 to 0.67) eV. [2,4,9,13,15,[18][19][20] The O * D data can be used-with the help of Equation (11) D are reported in literature, one from a computational study [18] and the other from an analysis of various experimental datasets. [1,2,15] The computational study reported ...
18O2/16O2 exchange experiments on terminated (100), (110), and (111) oriented samples of single‐crystal SrTiO3 are used to study the effect of surface orientation on the oxygen surface exchange coefficient kO∗\[k_{\rm{O}}^*\] and the surface space‐charge potential Φ0. Isotope exchanges are carried out at temperatures 922 < T/K < 1073 at an oxygen activity aO2 = 0.2 in dry conditions (aH2O < 10−7.7); isotope profiles are measured subsequently by secondary ion mass spectrometry. Isothermal kO∗$k_{\rm{O}}^*$ values are found to vary by less than one order of magnitude, with kO∗(111)≈kO∗(110)>kO∗(100)$k_{\rm{O}}^*(111) \approx k_{\rm{O}}^*(110){\bm{ > }}k_{\rm{O}}^*(100)$. All kO∗$k_{\rm{O}}^*$ data are consistent with a change in the activation enthalpy of surface exchange from 3.0 eV at high temperatures to 1.8 eV at lower temperatures. The transition is attributed to a change from a charge‐transfer mechanism at high temperatures to a mechanism involving surface OH species. The transition temperature depends on the surface orientation, Ttr(111) ≈ Ttr(110) > Ttr(100). Values of Φ0 obtained varied between 0.50 V and 0.37 V, with isothermal values obeying Φ0(111) ≈ Φ0(110) < Φ0(100). Φ0 data is analysed to obtain the OH− surface coverage for the low‐temperature regime. Similarities between the behavior of Φ0 and that of kO∗$k_{\rm{O}}^*$ are highlighted. 18O/16O exchange experiments combined with time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) analysis are used to determine the surface space‐charge potential Φ0 and the oxygen surface exchange coefficient kO∗$k_{\rm{O}}^ * $ on (100), (110), and (111) oriented samples of single‐crystal SrTiO3.
... It is possible that the oxygen vacancies are the cause of this difference between crystalline and amorphous top layers. This could be either through the vacancies themselves, as they can form linear clusters in STO, 40,41 or through an interaction with the walls separating different domains, where the formation energy of oxygen vacancies is lower than the bulk in certain ferroelectrics. 42 The exact interaction between vacancies and domains in a-LAO/STO is unclear, but our data indicate that domains should only gradually affect the current flow as the carrier density is reduced. ...
The two-dimensional electron system found between LaAlO3 and SrTiO3 hosts a variety of physical phenomena that can be tuned through external stimuli. This allows for electronic devices controlling magnetism, spin-orbit coupling, and superconductivity. Controlling the electron density by varying donor concentrations and using electrostatic gating are convenient handles to modify the electronic properties, but the impact on the microscopic scale, particularly of the former, remains underexplored. Here, we image the current distribution at 4.2 K in amorphous-LaAlO3/SrTiO3 using scanning superconducting-quantum-interference-device microscopy while changing the carrier density in situ using electrostatic gating and oxygen annealing. We show how potential disorder affects the current and how homogeneous 2D flow evolves into several parallel conducting channels when approaching the metal-to-insulator transition. We link this to ferroelastic domains and oxygen vacancies. This has important consequences for micro- and nanoscale devices with low carrier density and fundamental studies on quantum effects in oxides.
... Moleculardynamics simulations constitute an optimal method [44,[49][50][51] for obtaining D v (T). Indeed, classical molecular-dynamics simulations that employ the empirical pair-potentials of Pedone et al. [52] have been shown [44,49] to reproduce experimental diffusion rates of oxygen vacancies in SrTiO 3 [19,27,[53][54][55] and BaTiO 3 [38,56,57] extraordinarily well, not only in terms of the activation enthalpy of oxygen-vacancy migration but also the absolute rate of vacancy diffusion. Here, we used molecular-dynamics simulations with the empirical pair-potentials of Pedone et al. [52] to calculate D v (T) in BaSnO 3 for four different cases: All simulation cells contained a fixed number of oxygen vacancies (40 distributed randomly over 8232 oxygen-ion sites) and either a background charge or the appropriate number (to compensate the oxygen vacancies' charge) of barium vacancies, barium antisites, or tin vacancies. ...
The high‐mobility, wide‐bandgap perovskite oxide BaSnO3 is taken as a model system to demonstrate that the native point defects present in un‐doped, epitaxial thin films grown by hybrid molecular beam epitaxy can be identified and their concentrations at the ppm level determined quantitatively. An elevated‐temperature, multi‐faceted approach is shown to be necessary: oxygen tracer diffusion experiments with secondary ion mass spectrometry analysis; molecular dynamics simulations of oxygen‐vacancy diffusion; electronic conductivity studies as a function of oxygen activity and temperature; and Hall‐effect measurements. The results indicate that the oxygen‐vacancy concentration cannot be lowered below 1017.3 cm−3 because of a background level of barium vacancies (of this concentration), introduced during film growth. The multi‐faceted approach also yields the electron mobility over a wide temperature range, coefficients of oxygen surface exchange and oxygen‐vacancy diffusion, and the reduction enthalpy. The consequences of the results for the lowest electron concentration achievable in BaSnO3 samples, for the ease of oxide reduction and for the stability of reduced films with respect to oxidation, are discussed. Miniscule amounts of two different small bits of nothing: barium vacancies and oxygen vacancies. Oxygen vacancies are found through a powerful combination of experimental and computational techniques to arise from oxide reduction or to compensate a ppm background level of barium vacancies.
... 409 They can contribute to the electrical conductivity (in SrTiO 3 they form an impurity state in the bandgap, just below the conduction band) 573,582 and modify the oxidation state of neighboring cations. Furthermore, oxygen vacancies are mobile, with an activation energy of the order of 0.6-1 eV for the perovskite titanates, [583][584][585] and can be displaced under the action of an applied electric field, or migrate at high temperature to the interface to screen the ferroelectric polarization, 586 where the subsequent pileup at one electrode interface and depletion at the other can contribute to resistance degradation, imprint effects, and fatigue in ferroelectric capacitor structures. 583,587 It has been inferred that the high density of free carriers in thin PZT ferroelectric layers may be a consequence of the formation of oxygen vacancies induced at the temperature of growth in order to screen the surface ferroelectric polarization (self-doping). ...
Ferroelectric interfacial devices consist of materials systems whose interfacial electronic properties (such as a 2D electron gas or an interfacial magnetic spin configuration) are modulated by a ferroelectric layer set in its immediate vicinity. While the prototypical example of such a system is the ferroelectric field effect transistor first proposed in the 1950s, only with the recent advances in the controlled growth of epitaxial thin films and heterostructures, and the recent physical understanding down to the atomic scale of screening processes at ferroelectric-semiconducting and -metallic interfaces made possible by first principles calculations, have the conditions been met for a full development of the field. In this review, we discuss the recent advances in ferroelectric interfacial systems with emphasis on the ferroelectric control of the electronic properties of interfacial devices with well ordered (epitaxial) interfaces. In particular, we consider the cases of ferroelectric interfacial systems aimed at controlling the correlated state, including superconductivity, Mott metallic-insulator transition, magnetism, charge, and orbital order, and charge and spin transport across ferroelectric tunnel junctions. The focus is on the basic physical mechanisms underlying the emergence of interfacial effects, the nature of the ferroelectric control of the electronic state, and the role of extreme electric field gradients at the interface in giving rise to new physical phenomena. Such understanding is key to the development of ferroelectric interfacial systems with characteristics suitable for next generation electronic devices based on controlling the correlated state of matter.
... These vary considerably in existing literature concerned with the STO defect chemistry, however, for example at 600 • C, the present model yields a vacancy mobility of 6.98 × 10 − 5 cm 2 V − 1 s − 1 , which is still in good agreement with the value of 2.5 × 10 − 5 cm 2 V − 1 s − 1 , derived from the general expression of the vacancy diffusion coefficient by De Souza et al. [42]. At this point it is worth mentioning, that oxygen vacancy trapping at lattice defects and impurities has been reported for SrTiO 3 [77][78][79]. However, this mechanism will not be included in this analysis, as the dopant concentration in the present samples is very low and only very small amounts of complex defects including oxygen vacancies could be detected by PALS measurements (see below). ...
The defect chemistry and electronic trapping energies in undoped single crystalline SrTiO3 were examined by electrochemical impedance spectroscopy at low (25-160 ∘C) and intermediate (500-700 ∘C) temperatures. Electronic and ionic conductivity as well as chemical capacitance values were obtained with a transmission line equivalent circuit. Impedance spectroscopy at low temperatures was used to quantify trapping energies of main ionic defects. Particularly the chemical capacitance is shown to be a highly valuable, though hardly used tool for establishing a defect model based solely on electrochemical measurements. It is very sensitive for minority charge carriers and can thus unveil otherwise hardly accessible defect concentrations. The chemical capacitance analysis yields a valence dependent acceptor concentration in the ppm range for the investigated samples. Complementary positron annihilation lifetime spectroscopy (PALS) suggests existence of Ti vacancies and both methods (chemical capacitance and PALS) agree in their quantification of the corresponding vacancy concentration (6 ppm). Beyond successfully predicting acceptor defect concentrations in undoped SrTiO3, the method is sensitive for electronically relevant defects in sub-ppm concentrations.
... In spite of the considerable literature studying V O in perovskites or simply invoking them as the cause of many effects, simple properties like their hopping rate and fractions as free or paired or otherwise aggregated V O are not known with certainty. The best known case is SrTiO 3 , which remains cubic down to 105 K and where selective probing of isolated and aggregated V O has been obtained with anelastic spectroscopy [5], in that case the complex Young's modulus E versus temperature T and frequency ω∕2π. The anelastic spectra of SrTiO 3−δ reveal several thermally activated relaxation processes, appearing as Debye-like peaks in the elastic energy loss = Q E E 1 versus T. The maxima of these peaks occur at the temperatures at which the conditions ωτ ≃ 1 are verified, so allowing the precise determination of the specific defect relaxation times τ and their activation energies by varying frequency. ...
... The analysis of the anelastic spectra with varying O deficiency δ in SrTiO 3−δ gives a different picture from that generally accepted, according to which in SrTiO 3 , and by extension in oxide perovskites, V O are isolated and hop over a barrier of ≃ 1 eV, though an extremely broad spectrum of activation energies exists in the literature even for SrTiO 3 alone. Instead, the isolated V O in SrTiO 3−δ diffuse over a barrier of only 0.6 eV, but form pairs and larger clusters, possibly chains, already for δ ~0.005, and the generally measured activation energy of ~1 eV is associated with clustered V O [5]. ...
... The situation of BaTiO 3 and other perovskite ferroelectrics is also more confused, since the V O mobility in the FE state is affected by the lowering of symmetry, by internal fields and domain walls. In view of the anelastic study on SrTiO 3−δ [5], which evidences how the mobility of V O involves processes with quite different mobilities, it would be desirable to probe and discriminate the various processes also in undoped BaTiO 3−δ . The main difficulty in probing the hopping of free V O in BaTiO 3−δ is that the expected relaxation maxima at kHz frequencies are below T C = 400 K, and therefore are completely masked by the losses from the domain wall motion. ...
The diffusion and aggregation of oxygen vacancies (VO) in perovskites are still poorly understood, even though they are involved in a wide range of applications and phenomena, from solid-state electrolytes for fuel cells to ferroelectric fatigue. In strontium titanate it has been possible, by measuring the complex elastic modulus, to identify peaks in the elastic energy loss versus temperature due to hopping of isolated and paired VO and evaluate all the relevant kinetic and thermodynamic parameters. We present similar experiments in barium titanate, where the ferroelectric transition at TC = 400 K partially hides the anelastic relaxation processes due to VO. The introduction of VO, however, depresses TC, and it has been possible to lower it enough to reveal all the relaxation processes due to free and clustered VO. The resulting anelastic spectra are similar to those of SrTiO3−δ but there are also important differences. In BaTiO3−δ the anisotropy of the elastic dipole of the isolated VO is about three times larger, the anelastic and relaxation peaks markedly shift to lower temperature with doping, the activation energy for the diffusion of the isolated VO is 0.72 eV, larger than 0.60 eV in SrTiO3, while that for the pair reorientation is smaller, 0.86 eV compared to 0.97 eV. All these observations are explained by taking into account that, unlike in SrTiO3, Ti is dynamically disordered over eight off-centre positions. A strong indication in this sense comes from the temperature dependence of Young’s modulus, with anharmonic stiffening perfectly linear in temperature down to 200 K in SrTiO3, and with anomalous softening already below 750 K in BaTiO3.
