Rhombohedral Twinning Research Articles

サファイヤにおける菱面双晶の形成メカニズム

サファイヤにおける菱面双晶の形成メカニズム

Flux syntheses and single-crystal structures of CsNa10 M 4(AsO4)9 (M = Zr, Hf).

The isostructural compounds caesium deca-sodium tetra-zirconium nona-arsenate, CsNa10Zr4(AsO4)9, and caesium deca-sodium tetra-hafnium nona-arsenate, CsNa10Hf4(AsO4)9, arose as unexpected single-crystal products from the reactions of Na2CO3, MO2 (M = Zr, Hf) and As2O5 in a eutectic flux of NaCl and CsCl. They consist of MO6 octa-hedra and AsO4 tetra-hedra sharing vertices to generate three-dimensional polyhedral networks encapsulating the caesium and sodium ions. The MO6 groups share all their vertices with adjacent As atoms but the As atoms have one or two 'terminal' O atoms not bonded to Zr or Hf. The Cs+ ion adopts a squashed octa-hedral geometry and the coordination polyhedra of the partially occupied sodium ions are variously trigonal bipyramidal, tetra-hedral, square pyramidal and trigonal pyramidal. Site symmetries: Cs ; M 3; As 1 and 2; O 1; Na 1, 2 and 3. The M = Zr crystal was refined as an obverse/reverse rhombohedral twin.

Investigation of nanoscratch anisotropy of C-plane sapphire wafer using friction force microscope

In this study, nanoscratch experiments using side-forward multiple scans by friction force microscope with triangular pyramidal monocrystalline diamond tip were conducted on a (0001) plane sapphire wafer substrate to clarify the ductile-regime machining mechanism including its anisotropy. Various characteristics, such as scratch force, depth and specific energy for each scratch direction on C-plane of sapphire, were manifested by a friction force microscope, and the specific scratch energy showed a trend of three-fold symmetry. Subsequently, cutting chips which adhere to the diamond tip exhibited plastic deformations features were testified by a scanning election microscope. Based on slip/twinning systems of sapphire, Schmid factor was calculated for each scratch direction using the resultant force, and the calculated Schmid factors on the rhombohedral planes became the highest. Following the results, the resolved shear stresses along the twinning directions on the rhombohedral planes were calculated using a simple chip formation model, and they were several times larger than the critical resolved shear stress for rhombohedral twinning. As a result, it was found that when the scratch direction is set so that one of the three faces of the diamond tip is close to parallel to one of the rhombohedral planes, the rhombohedral plane acts as the chip shear plane and the specific scratch/cutting energy can be minimized. The cross-sectional transmission electron microscope images of scratched sub-surface also distinctly displayed the existence of subsurface damages consisting of twins and stacking faults relating rhombohedral planes.

Fracture Behavior of Single-Crystal Sapphire in Different Crystal Orientations

In order to study the anisotropy of fracture toughness and fracture mechanism of single-crystal sapphire, the three-point bending tests and the single-edge V-notch beam (SEVNB) were used to test the fracture toughness of A-plane, C-plane, and M-plane sapphire, which are widely used in the semiconductor, aerospace, and other high-tech fields. Fracture morphology was investigated by a scanning electron microscope and three-dimensional video microscopy. The fracture toughness and fracture morphology of different crystal planes of sapphire showed obvious anisotropy and were related to the loading surfaces. C-plane sapphire showed the maximal fracture toughness of 4.24 MPa·m1/2, and fracture toughness decreases in the order of C-plane, M-plane, and A-plane. The surface roughness is related to the dissipation of fracture energy. The surface roughness of the fracture surface is in the same order as C-plane > M-plane > A-plane. The fracture behavior and morphology of experiments were consistent with the theoretical analysis. C-plane sapphire cleavages along the R-plane with an angle of 57.6 degrees and the rhombohedral twin were activated. M-plane and A-plane sapphire cleavages along their cross-section.

Atomic-scale mechanism of rhombohedral twinning in sapphire

Deformation twinning is a fundamental plastic deformation mode in crystals. Upon twinning, individual atoms must move in different directions to satisfy the twin symmetry, which is called atomic shuffling. However, actual atomic motions during shuffling are still unknown, especially for ionic compounds. Here, we report the dynamic twinning behavior dominated by the atomic shuffling in sapphire (α-Al2O3). The propagation and annihilation of twins are revealed to be mediated by migration of step structures on the matrix/twin interfaces. The step migration is driven by cooperative motions of a group of five atoms with relatively few recombination of Al–O bonds. Our findings imply that the atomic shuffling associated with twinning is determined by a collective property of a group of several atoms.

Nanoscale evidence for temperature-induced transient rheology and postseismic fault healing

Abstract Friction-generated heat and the subsequent thermal evolution control fault material properties and thus strength during the earthquake cycle. We document evidence for transient, nanoscale fault rheology on a high-gloss, light-reflective hematite fault mirror (FM). The FM cuts specularite with minor quartz from the Pleistocene El Laco Fe-ore deposit, northern Chile. Scanning and transmission electron microscopy data reveal that the FM volume comprises a <50-μm-thick zone of polygonal hematite nanocrystals with spherical silica inclusions, rhombohedral twins, no shape or crystallographic preferred orientation, decreasing grain size away from the FM surface, and FM surface magnetite nanoparticles and Fe2+ suboxides. Sub–5-nm-thick silica films encase hematite grains and connect to amorphous interstitial silica. Observations imply that coseismic shear heating (temperature >1000 °C) generated transiently amorphous, intermixed but immiscible, and rheologically weak Fe-oxide and silica. Hematite regrowth in a fault-perpendicular thermal gradient, sintering, twinning, and a topographic network of nanometer-scale ridges from crystals interlocking across the FM surface collectively restrengthened fault material. Results reveal how temperature-induced weakening preconditions fault healing. Nanoscale transformations may promote subsequent strain delocalization and development of off-fault damage.

Nanoscale indentation and scratching tests of single crystal sapphire using molecular dynamics simulation

Sapphire is a crystalline aluminum oxide, which has been used for various applications due to its superior thermal, chemical, mechanical, and optical properties. Even though sapphire is a brittle material, its plastic deformation modes have also been studied for decades, mostly in experiments. In this study, we apply the molecular dynamics simulation method to investigate the atomic-scale deformation mechanisms of single crystal sapphire during the indentation and scratching tests. The indentation simulations are carried out in four crystallographic planes (C, A, M, R) and reveal various slip deformations. In particular, the rhombohedral twin structures are formed in the C-plane indentation, and the R-plane indentation triggers most slip systems including the C-, A-, N-, R-, S-planes. Hardness on the four slip planes is calculated during the indentation test and compared with the experimentally measured values. The scratching tests are performed in six different crystallographic directions at three scratching depths of 10 Å, 20 Å, and 30 Å. The simulation results show the deformation modes similar to those found in the indentation tests. In the scratching tests in the two slip directions of the C-plane the basal slip deformation is observed. The normal and scratching forces that are calculated in the scratching test exhibit the orientation dependence such that the C-plane and A-plane have the largest and smallest forces. The atomic displacements and configurations in the rhombohedral twin and basal slip are discussed.

ECCI, EBSD and EPSC characterization of rhombohedral twinning in polycrystalline α-alumina deformed in a D-DIA apparatus

Rhombohedral twinning in alumina (aluminium oxide, α-Al2O3) is an important mechanism for plastic deformation under high-temperature–pressure conditions. Rhombohedral twins in a polycrystalline alumina sample deformed in a D-DIA apparatus at 965 K and 4.48 GPa have been characterized. Three classes of grains were imaged, containing single, double and mosaic twins, using electron channeling contrast imaging (ECCI) in a field emission scanning electron microscope. These twinned grains were analyzed using electron backscatter diffraction (EBSD). The methodology for twin identification presented here is based on comparison of theoretical pole figures for a rhombohedral twin with experimental pole figures obtained with EBSD crystal orientation mapping. An 85°〈02{\overline 2}1〉 angle–axis pair of misorientation was identified for rhombohedral twin boundaries in alumina, which can be readily used in EBSD post-processing software to identify the twin boundaries in EBSD maps and distinguish the rhombohedral twins from basal twins. Elastic plastic self-consistent (EPSC) modeling was then used to model the synchrotron X-ray diffraction data from the D-DIA experiments utilizing the rhombohedral twinning law. From these EPSC models, a critical resolved shear stress of 0.25 GPa was obtained for rhombohedral twinning under the above experimental conditions, which is internally consistent with the value estimated from the applied load and Schmid factors determined by EBSD analysis.

Investigation of the cutting mechanisms and the anisotropic ductility of monocrystalline sapphire

In this study, plunge-cut tests are conducted on single-crystal sapphire to investigate the brittle and ductile deformation mechanisms from the viewpoint of crystal anisotropy. The anisotropic deformation behaviour of the machined sapphire substrate manifests itself in the critical depth of cut and the diverse crack morphologies. Based on a resolved stress model that is adapted to the experimental procedure, weighted resolved stresses are computed, and the tendency of brittle–ductile transition depending on the peculiarities of the low-symmetry hexagonal crystal structure is discussed. Rhombohedral twinning is assumed to dominate the brittle–ductile transition.

EBSD analysis of rhombohedral twinning in hematite crystals of naturally deformed iron formations

The rhombohedral twinning in hematite has an important role in the accommodation of the deformation of hematite single crystals and hematite aggregates. It is a contact twinning and occurs as lamellae parallel to the \{10{\overline 1}2\} planes of hematite as a result of twin gliding on such planes. On account of the recent applications of electron backscatter diffraction (EBSD) techniques in a wide range of microstructural studies, the determination of symmetry operations that relate crystals in a deformed crystalline aggregate is crucial for the full textural characterization. This study presents an EBSD-based crystallographic analysis of the rhombohedral twinning on hematite crystals of a naturally deformed banded iron formation. Manipulations of theoretical pole figures depicting the symmetry relation of the rhombohedral twinning and misorientation and crystallographic data obtained by EBSD are used to establish the rotational relationship between twin and parent crystals. A method for determining pairs of axes and angles of rotation was developed which can be extended to any other twin laws or misorientation patterns in any other crystal system. It was found that the hematite rhombohedral twins are related to the parent crystal by an approximately 85° rotation about the 〈02{\overline 2}1〉 directions. Hence it could be determined that this consists of a macroscopic twinning element which is an alternative to the conventional ones used to describe the symmetry of the twin. It also matches microscopic twinning elements for the rhomb twinning law. Additionally, this method allows the determination of the crystallographic orientation of the twin lamellae and which particular 〈02{\overline 2}1〉 axis satisfies the 85°〈02{\overline 2}1〉 pair of rotation. The use of an unambiguous angle–axis pair of rotation allows the identification of twin boundaries in complex and finely grained aggregates and the distinction of twinning laws in a particular crystal.

Origin of the high performance in GeTe-based thermoelectric materials upon Bi2Te3 doping.

As a lead-free material, GeTe has drawn growing attention in thermoelectrics, and a figure of merit (ZT) close to unity was previously obtained via traditional doping/alloying, largely through hole carrier concentration tuning. In this report, we show that a remarkably high ZT of ∼1.9 can be achieved at 773 K in Ge0.87Pb0.13Te upon the introduction of 3 mol % Bi2Te3. Bismuth telluride promotes the solubility of PbTe in the GeTe matrix, thus leading to a significantly reduced thermal conductivity. At the same time, it enhances the thermopower by activating a much higher fraction of charge transport from the highly degenerate Σ valence band, as evidenced by density functional theory calculations. These mechanisms are incorporated and discussed in a three-band (L + Σ + C) model and are found to explain the experimental results well. Analysis of the detailed microstructure (including rhombohedral twin structures) in Ge0.87Pb0.13Te + 3 mol % Bi2Te3 was carried out using transmission electron microscopy and crystallographic group theory. The complex microstructure explains the reduced lattice thermal conductivity and electrical conductivity as well.

Phase-field analysis of fracture-induced twinning in single crystals

Deformation twinning at the tip of a straight crack or notch is analyzed using a phase-field method that seeks equilibrium twin morphologies via direct minimization of a free energy functional. For isotropic solids, the tendency to twin under mode I or mode II loading is found to depend weakly on Poisson’s ratio and elastic nonlinearity and strongly on surface energy and twinning shear (i.e. eigenstrain). Depending on the coherent twin boundary energy, anisotropy of surface energy is important for mode I loading but less so for mode II. Model predictions for several single crystals are in agreement with experimental observations. Calcite demonstrates a preference for mode I cleavage crack extension over crack tip twinning. Magnesium shows a likelihood for tensile twinning from a pre-existing crack on the basal plane. In sapphire, a preference for rhombohedral twins over basal twins is apparent, with the latter thinner in shape than the former.

Inelastic deformation in shocked sapphire single crystals

To gain insight into orientation-dependent inelastic deformation of shocked sapphire (α-Al2O3) single crystals, resolved shear stresses, applicable for various dislocation slip and twinning systems, were determined for shock compression along different crystal orientations. Results from our anisotropic wave propagation analysis provide an explanation for why the measured elastic limit of shocked r-cut sapphire is lower, compared to c-cut and a-cut sapphire: Shock wave compression of r-cut sapphire favors activation of basal slip and basal twinning. In contrast, shock wave compression of c-cut and a-cut sapphire favors rhombohedral twinning and prismatic slip, respectively. Also, basal slip and/or basal twinning may be important for understanding why r-cut sapphire shocked beyond the elastic limit loses optical transparency gradually, when compared to c-cut and a-cut sapphire.

Analysis of dissociated dislocations in a deformed bicrystal close to the rhombohedral twin orientation in α-alumina

A bicrystal close to a rhombohedral twin orientation in α-alumina has been deformed by compression at high temperature. After deformation the twin contained a periodic array of intrinsic dislocations. This configuration is interpreted by the decomposition of incoming basal lattice dislocations into interfacial disconnections and further interactions between sessile and glissile products. The dislocations are widely dissociated and the separation width between partials being close to 30 Å. The translation state of the interfacial structure between partials is different from those of the perfect twin. Possible structural models are envisaged and simulated using ab initio calculations and the less efficient Streitz and Mintmire modelling. One model in particular fits the experimental image rather well. The interfacial energies are higher than those estimated using elasticity theory.

Microstructure at morphotropic phase boundary in Pb(Mg1/3Nb2/3)O3-PbTiO3 ceramic: Coexistence of nano-scaled {110}-type rhombohedral twin and {110}-type tetragonal twin

For more than half a century, the morphotropic phase boundary (MPB) has drawn constant interest in developing piezoelectric materials, as the phase instability at the region significantly enhances piezoelectricity. However, the local structure/symmetry at the MPB region is still under controversy. The investigation on morphology and origin of the local structure at MPB is of considerable importance to provide a microstructure basis for high piezoelectricity. In the present study, we thus use high resolution transmission electron microscopy to investigate the microstructure feature of MPB at PMN-PT ceramics. The local structure is shown to be the coexistence of nano-scaled {110}-type rhombohedral (R) twin and {110}-type tetragonal (T) twin. Such nano-scaled coexistence can be due to a nearly vanishing polarization anisotropy and low domain wall energy at MPB, which thus facilitates polarization rotation between 〈001〉T and 〈111〉R states and leads to high properties of MPB compositions.

Formation of twins in sapphire under shock wave loading: Atomistic simulations

This work is devoted to molecular dynamics (MD) simulation of shock-wave loading of sapphire (α-Al2O3). Defect free sapphire and sapphire with the microcrack are considered. Homogeneous nucleation and growth of rhombohedral twins are observed in single crystal alumina. A fast mechanism of plastic deformation is revealed under shock-wave loading of sapphire with microcrack. Rhombohedral twins nucleate and grow as a result of a two stage process. At the first stage the formation of a new type of linear defect takes place in the shock wave front, which is initiated at the surface of the microcrack. At the second stage the rhombohedral twins grow from the primary linear defects and combine with each other. The results are confirmed by first principles calculations.

Chromium influence on rhombohedral twinning in sapphire

Mechanical tests have been performed on sapphire doped with four different concentrations of chromium at temperatures between 800 and 1,000 °C. Samples were cut to favor rhombohedral twinning, which is the softest deformation mode of sapphire that inevitably leads to the failure of this material. We have investigated the effect of Cr doping on the rhombohedral twinning. The mechanical test results show that Cr atoms inhibit rhombohedral twinning, which appears to be athermal in the temperature range studied. An increase in the twinning-resolved stress is clearly observed. For 9,540 ppm Cr, the twinning-resolved stress becomes about three times higher than for undoped sapphire, potentially increasing its technological applications in the industry. The examination of lateral surfaces indicates that Cr atoms neither have influence on the twin width nor on the rhombohedral-twinning propagation. All these results have been properly explained within the model of Geipel et al.

HAADF study of the relationship between intergranular defect structure and yttrium segregation in an alumina grain boundary

In order to understand the beneficial role of yttrium in the creep of alumina, Z-contrast high-angle annular dark field (HAADF) imaging in a scanning electron microscope was used to reveal the distribution of yttrium segregation in the core of intergranular dislocations, namely disconnections, in a rhombohedral twin in alumina. The defects accommodate the tilt deviation from twin orientation and present a large step height. In the undoped bicrystal the dislocations appear most often dissociated into partials that delimit grain boundary (GB) segments with alternating structure. In the doped bicrystal, a strong yttrium segregation appears along the step, extending over several planes normal to the twin plane. Yttrium is segregated to the faulted part of the defect. Moreover, it appears segregated to the partial disconnection cores. It does not simply adopt the alumina structure but forms a new structure close to a YAlO 3 compound. The formation of an ordered compound at the GB dislocation core strongly supports the hypothesis that a reduced creep rate results from a decrease in dislocation mobility during GB sliding.

Plasticity of an alumina bicrystal near the rhombohedral twin orientation

A bicrystal slightly deviated from the rhombohedral twin orientation is deformed by creep so as to activate two basal slip systems in each grain. The tilt deviation in the starting bicrystal is accommodated by two parallel arrays of disconnections with the smallest twin Burgers vectors and large associated steps. Dislocations from both grains interact with the grain boundary (GB) and the tilt deviation increases by 3.6°, giving rise to an array of pure edge disconnections with no associated steps. Interfacial defects are interpreted by reactions between incoming dislocations and GB disconnections. Decompositions of dislocations into GB disconnections are followed by glide and climb of products that can annihilate or interact to give a perfect wall of edge disconnections superimposed to the twin boundary perfect structure. Owing to their large Burgers vectors, the final disconnections are always dissociated.

The structural origin of the antiferroelectric properties and relaxor behavior of Na 0.5Bi 0.5TiO 3

This work presents a study of Na 0.5Bi 0.5TiO 3 (NBT) by transmission electron microscopy in the 20–370 °C temperature range. A new orthorhombic intermediate phase between the rhombohedral and the tetragonal phases is proposed to account for the occurrence of 1 2 ( oee) superstructure spots. The phase transition from the rhombohedral to the orthorhombic phase occurs via a modulated phase formed by rhombohedral blocks and orthorhombic sheets. It is shown that these latter represent rhombohedral (0 1 0) twin planes. The modulated phase is proposed to explain the antiferroelectric and relaxor behaviors of NBT.