Twin Walls Research Articles

Microstructure dynamics in orthorhombic perovskites

Anelastic loss mechanisms associated with phase transitions in ${\text{BaCeO}}_{3}$ have been investigated at relatively high frequency $\ensuremath{\sim}1\text{ }\text{MHz}$ and low stress by resonant ultrasound spectroscopy (RUS), and at relatively low frequency $\ensuremath{\sim}1\text{ }\text{Hz}$ and high stress by dynamic mechanical analysis (DMA). Changes in the elastic moduli and dissipation behavior clearly indicate phase transitions due to octahedral tilting: $Pnma\ensuremath{\leftrightarrow}Imma\ensuremath{\leftrightarrow}R\overline{3}c\ensuremath{\leftrightarrow}Pm\overline{3}m$ structures at 551 K, 670 K, and 1168 K, and strain analysis shows that they are tricritical, first-order, and second-order phase transitions, respectively. Structures with intermediate tilt states ($R\overline{3}c$ and $Imma$ structures) show substantial anelastic softening and dissipation associated with the mobility of twin walls under applied stress. The $Pnma$ structure shows elastic stiffening which may be due to the simultaneous operation of two discrete order parameters with different symmetries. In contrast with studies of other perovskites, ${\text{BaCeO}}_{3}$ shows strong dissipation at both DMA and RUS frequencies in the stability field of the $Pnma$ structure. This is evidence that ferroelastic twin walls might become mobile in $Pnma$ perovskites and suggests that shearing of the octahedra may be a significant factor.

Anelastic loss behaviour of mobile microstructures inSrZr1 − xTixO3 perovskites

Anelastic loss mechanisms associated with phase transitions inSrZr1 − xTixO3 perovskites(x = 0.375, 0.450, 0.550, 0.775) have been investigated by dynamic mechanical analysis between 128and 723 K at frequencies of 0.1–50 Hz. Distinctive patterns of changes in the elastic modulidue to octahedral tilting transitions correlate closely with data for the shear modulusobtained previously by resonant ultrasound spectroscopy at high frequencies (∼0.5 MHz). The transition is first order and has a characteristic minimum in the shear modulus and Young’s modulus.For x = 0.450 and 0.550, a dissipation peak occurs at the transition temperature, the maximum ofwhich varies with frequency according to a power law relationship of the formtanδ = Afn, withn≈ − 0.3. Debye-like dissipation peaks in the stability field of theImma structureat x = 0.375 havea frequency and temperature dependence consistent with twin wall pinning by defects with an activationenergy ∼ 184 kJ mol − 1. These results indicate that there is diversity of pinning and relaxation processesfor transformation twin walls and interfaces in different perovskites withI4/mcm,Imma andPnma structures.

Trapping of oxygen vacancies in the twin walls of perovskite

The binding and pairwise interaction of oxygen vacancies in the ferroelastic (100) twin walls of the orthorhombic phase of ${\text{CaTiO}}_{3}$ perovskite $(Pbnm)$ have been investigated by numerical simulations using empirical force fields. An oxygen vacancy finds it energetically favorable to reside inside a twin wall, particularly when bridging two titanium ions located in the twin-wall plane. In such case, the binding energy of the vacancy to the wall is $0.7\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{eV}$, the error bar reflecting variability within two different force fields. A different disposition of the vacancy in the wall sees its binding energy reduced by a factor of 2. This implies that depending on the relative time scales for twin-wall motion and for oxygen-vacancy diffusion, anelastic motion of twin walls can display two different energy dissipation mechanisms associated to these point defects. The strongest interactions among oxygen vacancies in a twin wall are due to short-range repulsion so that no defect clusters were found. The vacancy-wall binding energy is found to increase substantially with pressure.

Nanoscale properties of thin twin walls and surface layers in piezoelectric WO3−x

Reduced WO3 single crystals have been investigated by conductive and piezoresponse force microscopy. The reduced crystals show a piezoelectric active surface layer with a noncentrosymmetric tetragonal structure which is different from the bulk of the crystal. The domain walls carry a high current while the bulk remains insulating. Twin-related interfaces are atomically thin, the upper bound being less than 10 nm. The reduced surface layer remained in the piezoelectric state even after several weeks, while the current in the twin boundaries was reduced by re-oxidization. This layer shows a significant piezoelectric activity with a piezoelectric coefficient of about 7.9 pm/V.

Elastic relaxations associated with the – transition in LaAlO3: III. Superattenuation of acoustic resonances

Resonant ultrasound spectroscopy has been used to characterize elastic softening andanelastic dissipation processes associated with the transition in single crystal and ceramic samples ofLaAlO3. Softening of the cubic structure ahead of the transition point is not accompanied by anincrease in dissipation but follows different temperature dependences for the bulk modulus,, and the shear components, and C44, as if the tilting instability contains two slightly different criticaltemperatures. The transition itself is marked by the complete disappearanceof resonance peaks (superattenuation), which then reappear below∼700 K in spectra from single crystals. Comparisons with low frequency, high stress data fromthe literature indicate that the dissipation is not due to macroscopic displacement of needletwins. An alternative mechanism, local bowing of twin walls under low dynamic stress, ispostulated. Pinning of the walls with respect to this displacement process occurs below∼350 K. Anelasticity maps, analogous to plastic deformation mechanism maps, are proposed todisplay dispersion relations and temperature/frequency/stress fields for different twinwall related dissipation mechanisms. These allow comparisons to be made ofanelastic loss mechanisms under mechanical stress with elastic behaviour observed bymeans of Brillouin scattering at high frequencies which might also be related tomicrostructure.

Antiferromagnetic spin and twin domain walls govern hysteretic expressions of exchange anisotropy

The present study shows that antiferromagnetic spin and twin domain walls govern the hysteretic expressions of exchange anisotropy at low and high fields, respectively, using annealed NiO single crystals and Co. In the presence of twin walls, spin walls are shown to be a geometrical necessity in the antiferromagnetic NiO. A threshold field $(\ensuremath{\sim}10\text{ }000\text{ }\text{Oe})$ exists below which twin walls are frozen, and rotational hysteresis is dominated by losses due to spin walls. Above the threshold field, twin walls become mobile, resulting in a sharp increase in rotational hysteresis. Remarkably, rotational hysteresis associated with spin walls is similar to that of an ordinary ferromagnet---as the field strength increases, rotational hysteresis tends toward zero. However, unlike an ordinary ferromagnet where rotational hysteresis becomes zero above its saturation field, rotational hysteresis in antiferromagnet drops but then sharply increases once the threshold field for twin wall motion is exceeded. In crystals without spin walls, low-field rotational hysteresis is zero or negligible. Domain imaging of twin walls in antiferromagnet and Weiss walls in ferromagnet reveals a one-to-one spatial correlation even though twin walls are considered to have no net dipoles. This surprising result is explained by the fact that crystallographic interfaces in real crystals are not atomically sharp or ideal, and the defective interface invariably results in net moment across the finite width of the twin wall. The field dependence of domain walls in Co film exchange coupled to NiO shows global similarities to previously reported behavior of Co films deposited on nanocrystalline NiO [H. D. Chopra, D. X. Yang, P. J. Chen, H. J. Brown, L. J. Swartzendruber, and W. F. Egelhoff, Jr., Phys. Rev. B 61, 15312 (2000)]. In both cases, domain wall motion is not the dominant mode of magnetization reversal (wall motion is entirely absent in the present study while wall motion was only occasionally observed in the previous study), reversal occurs abruptly and different regions switch at different fields, and the observed pinning sites are frozen in the applied field range. Despite vastly different underlying microstructure of NiO in these two studies (annealed NiO single crystal with a fixed orientation across the NiO-Co interface in the present study versus nanocrystalline NiO in the previous study), the observed similarities may be understood by recognizing that, just as crystallographically imperfect twin interfaces serve as pinning sites for walls in Co film, other defects can play a similar role. Practically, results provide means of tuning rotational hysteresis by varying the type and the density of domain walls in NiO and by tuning the saturation field of the ferromagnet relative to the threshold field for the twin wall motion.

Mural Sovereignty: From the Twin Towers to the Twin Walls

After the demolition of the Berlin Wall (1989), the construction of the Palestinian Wall from 2002 and the passing of The Secure Fence Act of 2006 (governing the US–Mexico border) enact a return to mural forms of sovereignty: walls are both without and within law, ‘old solutions’ to problems newly-made. While the Berlin Wall is considered a Cold War monument, both the Palestinian Wall and the ‘Secure Fence’ concretize the paradoxical reappearance of ancient territorializing strategies in a post-Cold War New World Order. These paradoxes are related to the coincidence of intensive and extensive forms of contemporary sovereignty: the contraction of a narrowed sovereign border accompanied by the projection of an extended sovereign power. These mural structures are considered in the context of the renovation of Ground Zero, Franz Kafka’s story ‘The Great Wall of China’, and Dan Perjovschi’s mural ‘What Happened to US?’ (Museum of Modern Art 2007).

The intrinsic elasticity of twin walls: Ferrielectric twin walls in ferroelastic CaTiO3

Computer simulation of ferrielectric domain walls in ferroelastic CaTiO3 demonstrate that twin walls possess almost the same compressibility as the bulk. The Ti–Ti repetition length inside the wall is approximately 0.2% greater than the equivalent lattice parameter of the bulk. A slight reduction in the uniaxial compressibility perpendicular to the twin wall is compared with predictions of various theoretical models which give either large softening or large hardening. Simple spring models predict correctly that any change is expected to be small for relevant potentials far from the ferroelastic transition point.

Elastic anomalies associated with transformation sequences in perovskites: II. The strontium zirconate–titanateSr(Zr,Ti)O3 solid solution series

The sequence of phase transitions due to octahedral tilting across theSr(Zr,Ti)O3 solid solution series has been investigated by resonant ultrasoundspectroscopy at high and low temperatures using ceramic samples. The elasticbehaviour associated with phase transitions as a function of composition inSr(Zr,Ti)O3 at room temperature is proposed to be analogous to that as a function of temperature inSrZrO3, with the transition at SrZr0.57Ti0.43O3, at SrZr0.35Ti0.65O3, and at SrZr0.05Ti0.95O3. Changes in elastic constants and acoustic dissipation with temperature have beenanalysed for samples across the compositional range. The intermediate phases,I4/mcm and what isassumed to be Imma, appear to have stability fields across the full compositional range and both show largedissipation effects, most probably due to twin wall mobility. In contrast, the Zr-richPnma phase, which should contain transformation twin walls, is an unexpectedly stiff andnon-dissipating material, similar to the high temperature and/or Ti-rich phase. In the case of Pnma, this is attributed to coupling between the two order parameters, which could impederelaxation responses to an applied stress. The structure is a classically stiff cubic perovskite and no transformation-related dissipationprocesses are expected.

Elastic anomalies associated with transformation sequences in perovskites: I. Strontium zirconate,SrZrO3

Elastic behaviour associated with the hierarchy of tilting transitions inSrZrO3 has been examined using resonant ultrasound spectroscopy on a ceramic sample attemperatures between 153 and 1531 K. Changes in slope of the evolution of resonancefrequencies with temperature indicate that phase transitions occur at 1038 K (), 1122 K (), and 1367 K (). Strain analysis of previously recorded neutron diffraction data shows that the and transitions are close to tricritical in character, and that is first order. Deviations from the form of the elastic behaviour predicted byLandau theory are found. In particular, elastic softening in the vicinity of the transition suggests that local dynamical fluctuations between individual tilt systems occur, rather thana discontinuous switch from one phase to another. Determinations of the mechanical quality factor,Q, showthat SrZrO3 in the phase is a classically high-Q (i.e. non-dissipating) cubic material.I4/mcm and Imma phases both have much greater dissipation (lowQ), which is tentatively attributed to the mobility of twin walls. The room temperaturePnma phase is unexpectedly much stiffer than bothI4/mcm andImma phases andhas high Q. It appears that when two separate tilt systems operate, as inPnma, they can interact to reduce strain/order parameter relaxations.

Effect of ferroelastic twin walls on local polarization switching: Phase-field modeling

Local polarization switching in epitaxial ferroelectric thin films in the presence of ferroelastic domain walls was studied using phase-field approach. The nucleation bias profile across a twin wall was analyzed, and the localization of preferential nucleation sites was established. This analysis was further extended to a realistic domain structure with multiple twin boundaries. It was observed that the local nucleation voltage required for a 180° domain switching is closely related to the number of such local defects.

Ferrielectric Twin Walls inCaTiO3

Sizeable spontaneous polarization has been found in the (100) twin walls of CaTiO3, a definitely nonpolar material. Theoretical simulations of these walls show an extremely rich texture of the local polarization at and close to the walls, including a strong antiferroelectric component, and local nonzero contributions perpendicular to the wall plane, which do not contribute to the net dipole. Individual Ti displacements of 2 pm off the octahedron center give rise to a net polarization corresponding to a displacement of 0.6 pm in the direction of the bisector of the twin angle.

Elastic and anelastic anomalies in (Ca,Sr)TiO 3 perovskites: Analogue behaviour for silicate perovskites

Values of bulk modulus ( K), shear modulus ( G) and mechanical quality factor ( Q) have been determined for polycrystalline samples across the CaTiO 3 (CST0)–SrTiO 3 (CST100) solid solution by resonant ultrasound spectroscopy. Because of similarities with low frequency elastic and anelastic anomalies due to twin wall motion reported in previous studies, a working hypothesis is developed in which dissipation processes are interpreted in terms of twin wall displacements. At high temperatures in CST50 the stability field of the I4/ mcm structure is marked by the disappearance of all resonance peaks (superattenuation). This is attributed to anelastic domain wall sliding. At room temperature the I4/ mcm phase of CST70 and CST80 has values of G which are lower than those of cubic or orthorhombic phases, and a concomitant drop in Q is interpreted as implying that the domain wall pinning process reported elsewhere to occur below ∼400–450 K is only partial. A similar drop in G and Q was found in CST95 below the P m 3 ¯ m ↔ I 4 / m c m transition at ∼238 K. The I4/ mcm ↔ Pbcm transition in CST70 at ∼230 K is marked by an abrupt increase in Q, suggesting that mobile twins in crystals with the I4/ mcm structure become effectively immobile in antiferroelectric crystals with the Pbcm structure. The I4/ mcm ↔ Pnma transition in CST50 is marked by a similarly abrupt increase in Q, consistent with twin walls becoming effectively immobile also in crystals with the Pnma structure. A fall in Q below ∼800 K in CST0, however, could imply that a degree of twin wall mobility might develop in Pnma crystals if the tetragonal spontaneous strain departs significantly from zero. The remarkable attenuation behaviour of crystals with the I4/ mcm structure at the relatively low stress conditions which apply during resonances of a parallelepiped with edge dimensions of ∼2–4 mm, is consistent with the view that a characteristic signature for tetragonal CaSiO 3 in the Earth's lower mantle should be a marked attenuation of seismic waves.

Investigation of Interface Properties by Nanoscale Elastic Modulus Mapping

We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinity of interfaces. The method is demonstrated on twin walls in PbTiO(3) single crystals. It is revealed that the region near the twin wall is significantly softer than the two domains surrounding it. A comparison with finite element simulations relates this effect to an anelastic relaxation due to point defect accumulation around the twin wall. Local softening around the twin wall can affect the overall elastic modulus in thin films and nanostructured ferroelectric materials, in which the average distance between twin walls is smaller than the thickness of the softer region.

Investigation of twin boundary thickness and energy in CuAlNi shape memory alloy

The nanometer-scale thickness and energy of twin boundaries govern the martensitic twin structure and its dynamics, which are responsible for the actuation and superelasticity of shape memory alloys. In this letter the authors apply a method, which has been recently developed for investigating twin wall structures in ferroelectric crystals, on a shape memory alloy crystal. Fittings of simulated displacement fields to atomic force microscopy measurements allow them to extract the thickness of type-I twin boundaries in CuAlNi. Further, a relation between the twin boundary thickness and energy is developed and used for evaluating the twin boundary energy.

Effect of internal friction on transformation twin dynamics in perovskiteSrxBa1−xSnO3(x=0.6,0.8)

The dynamics of transformation twins in ${\mathrm{Sr}}_{x}{\mathrm{Ba}}_{1\ensuremath{-}x}\mathrm{Sn}{\mathrm{O}}_{3}$ $(x=0.6,0.8)$ perovskite has been studied by dynamical mechanical analysis in three-point bend geometry. This material undergoes phase transitions from orthorhombic to tetragonal and cubic structures on heating. The mechanical loss signatures of the transformation twins include relaxation and frequency-independent peaks in the orthorhombic, and tetragonal phases, with no observed energy dissipation in the cubic phase. The macroscopic shape, orientation, and relative displacements of twin walls have been calculated from bending and anisotropy energies. The mechanical loss angle and distribution of relaxation time are discussed in terms of bending modes of domain walls.

Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part III. Experimental investigation of polycrystalline samples

Bulk and shear moduli of polycrystalline samples of perovskites with different compositions across the CaTiO3-SrTiO3 solid solution have been measured at ambient conditions and in-situ at high pressures by pulse-echo ultrasonic methods. The samples were prepared as dense pellets by hot pressing synthetic powders at {approx}7.5 GPa and {approx}1000 C. Any variations of bulk modulus due to phase transitions are small, but significant anomalies have been observed in the shear modulus at ambient conditions. These are associated with a sequence of symmetry changes PmFormulam -> I4/mcm -> Pbcm -> Pnma with increasing CaTiO3 content. Comparison with variations in elastic properties predicted using Landau theory suggests that a substantial part of the elastic softening observed in tetragonal samples could be due to anelastic contributions from transformation twin walls. This additional softening does not occur in orthorhombic samples, and the transition from tetragonal to orthorhombic symmetry results in a stiffening of the shear modulus. No overt evidence was found for a phase transition I4/mcm {leftrightarrow} Pnma at high pressures in Ca0.35Sr0.65TiO3 but small changes in the trends of both bulk and shear moduli in the range 2.5-3 GPa could be due either to a different transition or a change in compression mechanism.more » A PmFormulam {leftrightarrow} I4/mcm transition at {approx}2 GPa in Ca0.05Sr0.95TiO3 shows the same form of softening as observed for the transition as a function of composition. A simple model of twin wall contributions to the compliance of tetragonal samples failed to match the observed variations that, alternatively, seem to follow {Delta}G {proportional_to} q4 where {Delta}G is the change in shear modulus and q4 the driving order parameter for the PmFormulam {leftrightarrow} I4/mcm transition. Analogous elastic behavior is expected to occur in (Mg,Fe)SiO3 and CaSiO3 perovskites at high pressures and temperatures.« less

Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part II. Calibration for the effects of composition and pressure

A Landau free energy expansion has been developed in a first attempt to describe the Pm 3 m ↔ I 4/ mcm octahedral tilting transition in perovskite across a complete binary solid solution, CaTiO 3 − SrTiO 3 (CST). Only two parameters, the critical temperature and the coefficient, λ 4 , for coupling between the order parameter and the tetragonal strain are given a composition-dependence. The best match between observed and calculated variations of the tetragonal strain as a function of temperature in CaTiO 3 (CST0) and as a function of composition at room temperature is found for a model of the solid solution in which the transition is close to tricritical for the composition range CST0 to ~CST90. The change in transition character from second order (246 potential) to tricritical is accounted for by an increase in |λ 4 | between SrTiO 3 (CST100) and ~CST90. The Landau potential is used to calculate the variations of single-crystal and bulk elastic constants through the Pm 3 m ↔ I 4/ mcm transition as functions of both pressure and composition. This model for the CST solid solution permits the classical softening effects of strain/order parameter coupling to be separated quantitatively from the much larger superelastic softening observed for twinned crystals of tetragonal SrTiO 3 and CST. Data from the literature for relative changes of elastic properties measured at low frequencies have been rescaled to absolute values for comparison with calculated values of Young’s modulus. These appear to show that, below the temperature for domain wall pinning, some 5–10% of softening of the isotropic Young’s modulus could still be due to the effects of twin wall movements.

Effect of 90 deg ferroelastic twin walls on lattice dynamics of nanocrystalline tetragonal ferroelectric perovskites

A combined transmission electron microscopy (TEM) and Raman spectroscopy study has been performed on nanocrystalline Ba0.9Sr0.1TiO3 (BST) crystals and tubes. TEM investigations revealed the existence of 90 deg ferroelastic twins in the materials. Raman spectra showed an obvious shoulder (∼750 cm-1) from the broad band at ∼720 cm-1 that nominally represents the quasimode of E(LO4) and A1(LO3). The intensity of this shoulder increases with the twin population in the nanocrystalline materials, suggesting a correlation between the lattice dynamical characteristics and the long-range ferroelastic strain of the twin wall. The ferroelastic strain is mainly constrained along the c-axis of the BST unit cell, and the effect of this constraint is more pronounced in nanocrystalline materials than in bulks due to a significant wall volume ratio in twinned nano-materials. A1 phonons showing collective ion dynamics along the c-direction could be then hardened by the strain, while E symmetry exhibiting vibrations perpendicular to the c-axis would be less affected. The theoretically predicted giant LO–TO coupling in tetragonal ferroelectric perovskites [18] suggests that the hardening of the softest A1(TO1) mode in A1 symmetry is accompanied by that of the hardest A1(LO3) phonon. Consequently, the shoulder could be ascribed to the ferroelastic strain induced hardening of the quasimode with a considerable contribution from the A1(LO3) phonon.

Anelastic behaviour of leucite KAlSi 2O 6

An examination of the anelastic response of leucite, KAlSi 2O 6, to frequency modulated stress is presented. Leucite is a naturally occurring open framework aluminosilicate closely related to analcime (a zeolite compound) and is found in the earth's crust. It shows two phase transitions at ( T c 1 ) 665 °C and ( T c 2 ) 645 °C, from cubic Ia3 d through I4 1/ acd to I4 1/ a. Consequently the low temperature I4 1/ a phase contains both lamellar and merohedral twins; the intermediate I4 1/ acd phase contains lamellar twins only. Leucites typically show a high density of twin walls. Recent studies have shown that lamellar microstructures can give rise to anelastic softening via twin wall motion [R.J. Harrison, S.A.T. Redfern, J. Appl. Phys. 95 (2004) 1706–1717; R.J. Harrison, S.A.T. Redfern, E.K.H. Salje, Phys. Rev. B 69 (2004) 144101-1–144101-10; R.J. Harrison, S.A.T. Redfern, J. Street, Am. Mineral. 88 (2003) 574–582]. This could be a mechanism for seismic attenuation in crustal and mantle rocks. We propose that this process also occurs in leucite on the basis of results of dynamical mechanical analysis. A frequency modulated stress (0.4–16 Hz) was applied in three point bend geometry to single crystals of leucite containing twins. The dynamic modulus and tan δ functions have been measured, though these are partially obscured by the presence of the higher temperature phase transition. The apparent activation energies for twin wall motion (600 kJ mol −1 or more) are unusually high, suggesting possible dependence on silicon diffusion within the aluminosilicate framework. Softening of the modulus in the high-temperature cubic phase, on cooling towards the Ia3 d to I4 1/ acd transition, is consistent with coupling to optic modes which show strong dispersion with three phonon branches softening equally in all directions.