Rhombohedral Twinning Research Articles

Interpretation of Atomic Resolution Eels Signals at Interfaces

Introduction: Atomically resolved chemical analysis by means of electron energy (core-) loss spectroscopy has been postulated since the technical availability of highly focused sub-nm STEM beams. We study the feasibility of this approach, as compared to the alternative of spatial difference spectra, where interfacial resolution is achieved by subtracting boxes at and apart from the interface. A nanobeam EELS signal is generated by the dynamical propagation of a conical wave through the specimen. This wave acts as 3D-excitation envelope for inelastic scattering and is needed to link the ab-initio calculated atom- and angular-momentum-projected density-of-state (DOS) functions to measurable EELS signals.Projected DOS: For the rhombohedral twin grain boundary in sapphire (FIG 1) as model system, DOS for p states in oxygen have been calculated 4 as described in , for the most stable twin structure obtained by ab-initio calculations.

Quantitative atomic-scale analysis of interface structures: transmission electron microscopy and local density functional theory.

Transmission electron microscopy (TEM) and local density functional theory (LDFT) are combined to analyze the microscopic structure of the rhombohedral twin interface in alpha-Al2O3. LDFT provides interfacial energetics and atomic and electronic structures for three competing models. With high-resolution TEM the atomic structure at the interface is imaged quantitatively along two orthogonal zone axes. Electron energy loss spectroscopy in TEM with nanoscale spatial resolution yields the interfacial electronic structure. Both experiments confirm the theoretically preferred model quantitatively.

Influencia de la densidad de dislocaciones en la tensión de maclado romboédrico del zafiro (α-Al<sub>2</sub>O<sub>3</sub>)

The influence of dislocations on the stress to induce rhombohedral twinning has been examined in α-Al 2 O 3 ) single crystals. Dislocation densities have been modified by basal slip induced by compression at temperatures between 1.000 and 1.300 °C, at stresses up to 400 MPa. As a consequence of this pre-deformation, sapphire is more resistant to twinning at 900 °C, the hardening corresponding to a stress increase by a factor of 10. The twin structure is strongly influenced by the dislocations which impede the motion of twin boundaries; therefore, for high dislocation density very thin twin lamellae are formed contrary to the case for low density.

The effect of titanium doping on the high-temperature rhombohedral twinning of sapphire

C-axis compressive strengths of pure and titanium-doped sapphire were measured at 600°C in air. Single crystal sapphire was doped with both titanium (3+) and titanium (4+) ions from mixtures initially containing 0.05% wt. to 0.25% wt. Ti2O3 in Al2O3. It was shown that both valence state and concentration of titanium were important in slowing down twin boundary movement under c-axis compression. Titanium (4+) doping did not adversely affect the thermal conductivity and infrared optical properties of sapphire.

Microscopic structure and bonding at the rhombohedral twin interface in α-Al2O3

The local interfacial structure and bonding at the rhombohedral twin interface in α-Al2O3 (corundum) was studied by means of first-principles electronic-structure calculations based on the local density functional theory. Two sets of geometrical interface models were selected, one with a terminating oxygen layer at the interface, the other with a termination by interstitial vacancies of the corundum structure. Optimized interface configurations were obtained by minimization of the total internal energy with respect to relative translation states of the adjoining grains and relaxations of all atomic positions.One vacancy-terminated configuration was found with a very low interface energy, a well-defined relative translation state with screw-rotation symmetry and a highly ordered atomic structure, which minimizes the mutual repulsion between the neighboring like-charged ions. A second metastable configuration with vacancy termination and a higher interface energy was also obtained as well as a metastable oxygen-terminated structure with an interface energy between those of the two vacancy-terminated configurations. The theoretical results for the interfacial structures and translation states are discussed with respect to recent experimental investigations of the twin interface by high-resolution transmission electron microscopy. Furthermore, the calculated interfacial site-projected densities of electron states (PDOS) display significant differences from the bulk-crystal PDOS in the conduction bands.

Dislocations and twinning activated by the abrasion of Al 2O 3

Defects generated at the surface of single crystal Al 2O 3 during abrasion on diamond have been analysed by high spatial resolution cross-sectional electron microscopy. Plastic deformation predominantly occurs by basal twinning and pyramidal slip 1/3〈11 2 0〉{ 1 101}. Basal twins have platelet morphologies, with widths d 0001=2 n ∗1/6[0001] and ∣ d 0001∣≪100 nm, aspect ratios d 1010/ d 0001 or d 1120/ d 0001>10, and ABCBA stacking of (0006)Al planes across twin interfaces. Basal twins and dislocations occur clustered around steps in macroscopic (0001) abraded surfaces, whereas ±{11 2 0} and ±{10 1 0} prismatic plane abrasion results in a more uniform 1–5% deformation twin cover with basal twin penetration≫that for basal abrasion. Extensive microcracking along {1 1 02} rhombohedral and (0001) twin habit planes occurs, but no widespread rhombohedral twinning, prism glide or non-basal dislocation Burgers vectors were observed. Implications for surface preparation of Al 2O 3 are discussed.

Near Coincidence Grain Boundary in Alumina

The rhombohedral twin orientation in alumina has been obtained by diffusion bonding and studied by transmission electron microscopy. It corresponds to a Σ7 near coincidence orientation with a grain boundary plane parallel to (0112). The grain boundary contains two arrays of dislocations with the same line direction and alternately distributed Burgers vectors which are translation vectors of the DSC lattice. The associated step vectors are large, up to 1.75nm. Starting from symmetry considerations on the various dichromatic complexes, all possible unrelaxed atomic configurations are constructed. Oxygen terminated grain boundary structures as well as those passing through non occupied aluminium sites are selected on the basis of optimal compacity at the interface. Correlations between simulated and experimental high resolution images favor the structures based on empty octahedral sites at the interface. The most probable structure has a two fold screw axis at the interface and leaves Al-O bonds with very little distorsions from the perfect coordination in alumina.

Evolution of Specimen Shape for Uniaxial Compression of Single Crystals

Compression tests for the study of plastic deformation of single crystals have been widely used, especially for those materials which are brittle and/or difficult to machine in the form of specimens. The present work was stimulated by unexpected observations of the shape evolution of sapphire specimens after a few per cent deformation by basal slip. The crystals were oriented to avoid rhombohedral twinning, using an orientation quite different from previous studies. Here, the authors examine the shape changes for a parallelepiped specimen subjected to a homogeneous strain in compression; it is based on a simple geometrical approach derived from previous calculations. The key parameters are the initial angle {var_phi}{sub 0} between the slip plane and the compression face and the deformation represented by the homogeneous shear strain {gamma} or the specimen shortening (l/l{sub 0}) (l and l{sub 0} are the final and initial lengths).

Basal slip in sapphire (α-Al 2O 3)

Plastic deformation of sapphire has been performed along three different compression axes to activate (0001) basal slip along one or two 〈20〉 directions. One of the orientations is identical to that used in earlier experiments, with the activation of one glide direction, or Burgers vector. We also investigated two new orientations which permit activation of two Burgers vectors. We have shown that for one of these orientations, rhombohedral twinning is difficult to activate and large deformations, for unpolished specimens, can be reached by basal slip down to 900°C. Basal glide along 〈010〉 was observed; the yield stress values are the same for 〈010〉 and <010〉 directions.

Temperature and stress dependence of rhombohedral twinning in sapphire

Temperature and stress dependence of rhombohedral twinning behavior of sapphire single crystals was investigated. Specimens were deformed in compression along the c-axis with an Instron universal testing machine below 1100 °C in order to avoid basal twinning and dislocation slip. Rhombohedral twinning formation can be explained by nucleation of a double kink in the twinning dislocation, while twin growth can be treated as a twinning dislocation movement which is driven by atomic diffusion at elevated temperatures and by mechanical slip at relatively low temperatures. The activation enthalpy and activation volume of rhombohedral twinning dislocation and also the activation energy of twinning dislocation movement were measured using Smidt's empirical equation and Arrhenius' equation, respectively.

Stress-strain modes of rhombohedral twinning in α-Al2O3 single crystals

The plastic deformation of α-Al2O3 due to rhombohedral twinning was investigated. Specimens were deformed in compression along the c axis with an Instron universal testing machine below 1100 °C in order to avoid basal twinning and dislocation slip. Six different types of stress-strain modes were obtained in rhombohedral twinning. Four of these showed that the stress drops accompanied twin formation. From the Instron stress-crosshead displacement charts, the relative twin growth rate (TGR) versus temperature was determined. As the temperature increased, the twin growth rate increased.

A zonal dislocation mechanism for rhombohedral twinning in sapphire (α-Al 2O 3)

HRTEM investigations of rhombohedral twins in sapphire ( α- Al 2 O 3) indicate that they are “screw twins”; the twin axis η 1 is [0 1 11] and involves a 1 6[0 111] translation in addition to the 2-fold rotational symmetry. Based on this data, a zonal dislocation mechanism for rhombohedral twinning in sapphire is proposed which predicts the correct shear strain s = 0.202. This mechanism only requires movements of the Al and O ions of less than 50% of the closest AlAl or OO distances in the ideal crystal, although some ions have to move against the shear.

Slip and Twinning in Sapphire (α‐Al2O3)

The plastic deformation of sapphire (α‐Al2O3) has been studied under hydrostatic confining pressure at temperatures below the ambient pressure brittle‐to‐ductile transition temperature. Samples oriented for prism plane slip (Type I samples) were deformed via dislocation slip at temperatures as low as 200°C. Samples oriented for basal slip (Type II samples) could be plastically deformed at temperatures as low as 400°C but showed more complicated deformation behavior, inasmuch as the sample orientation also allowed for the activation of basal twinning and two of the three rhombohedral twin systems. The temperature dependence of the critical resolved shear stress (τcrss), ln τcrss= ln τ0– M·T for basal slip was significantly greater than that for prism plane slip (Bbasal &gt; Bprism plane), causing the latter system to be the easy slip system below ∼600°C (basal slip is the easy slip system at elevated temperatures). Type II samples deformed primarily by basal twinning in preference to both rhombohedral twinning and basal slip. The different temperature dependence of τcrss for basal and prism plane slip is attributed to details of the dislocation core structure; prism plane dislocations, having a large Burgers vector (∣bPP∣= 0.822 nm), can dissociate into three collinear par‐tials (∣bP∣= 0.274 nm) separated by relatively low‐energy stacking faults, whereas the comparable dissociation of basal dislocations (∣bB∣= 0.476 nm) produces two ncncol‐linear partials separated by a relatively high energy stacking fault. Thus, dissociation of basal dislocations is most likely restricted to the dislocation core, which is manifested in a higher Peierls stress at low temperatures for basal slip compared to prism plane slip.

Structural features of boron nitride dense phase formation from rhombohedral modification under high static pressure

The real structure of boron nitride (BN) polycrystals after high-pressure treatment was investigated by X-ray and transmission electron microscopy methods. Different stages of boron nitride polycrystal evolution under high quasistatic pressure and high temperature were fixed, involving rhombohedral boron nitride twinning, one-dimensionally disordered structure, 2H, 4H, 3C dense phase formation and 3C-BN recrystallization. A new structural scheme of BNr-BNw transition is proposed.

CSL descriptions of rhombohedral twinning in TIBiTe2

Rhombohedral twins of the ternary semiconductor TIBiTe2 have been studied and it has been found that they were either coherent or non-coherent. By an appropriate approximation of the rhombohedral angle by a pair of integersp andq, the rhombohedral twins can be described by the coincidence site lattice (CSL) model. Since the best description for reflection twins is to note the lattice plane (hkl) acting as a mirror plane, the (hkl) description has been used. It has been found that the coherent twins are described by a CSL with low multiplicity ∑, and the non-coherent ones by a CSL with high multiplicity ∑.

Rhombohedral Twin Structure in Hematite (α-Fe2O3)

Electron optical imaging of the structure of haematite ( α-Fe2O3) in two projections has allowed the microscopic twinning elements of rhombohedral twins to be determined. A systematic analysis of alternative structural models, using computer-simulation and image-matching considerations, as well as crystallochemical arguments, is presented. The twin has a screw operation consisting of a pure rotation of 180� about [0111], the twinning direction, combined with a parallel translation of (1/22) [0111]. The twinning plane (0112) forms a coherent interface, consisting of face-and edge-shared octahedra , with no change in the normal nearest-neighbour coordination.

Theoretical and experimental descriptions of grain boundaries in rhombohedral α-Al2O3

Abstract Tables are given of all coincidence orientations with multiplicity Σ ≤ 36 for rhombohedral lattices with axial ratios in the range of corundum type structures (2.696 < c/a < 2-765). Measurements of the relative orientation of 133 pairs of neighbouring grains in sintered a-alumina showed that near-coincidence boundaries (14 cases) and one-dimensional coincidence boundaries (17 cases) occurred more frequently than would be the case for randomly distributed orientations and that many of these special boundaries contained periodic arrays of grain boundary dislocations. Their Burgers vectors have been determined for a rhombohedral twin boundary in order to decide which one among three possible coincidence descriptions best represents the boundary structure.

Microscopic rhombohedral twinning elements of haematite

Abstract Electron optical structure imaging of haematite (α-Fe2O3) in two projections has allowed the microscopic twinning elements of rhombohedral twins to be determined. The twin is a pure 180° rotation about [0111], the twinning direction, combined with a parallel translation of ⅙[0111]. The twinning plane (0112) forms a perfectly coherent interface, consisting of face and edge-shared octahedra with no change in nearest-neighbour coordination. A search for alternative structural models yielded none which could reproduce the experimental images.

Surface mass transport of alumina

The kinetics of thermal grooving at the intersection of rhombohedral twin boundaries with the\((10\bar 10)\) plane in aluminium oxide were measured from 1773 to 2273 K. Analysis of the data using the model of Mullins showed that surface diffusion was the dominant mechanism for mass transport. The results were compared with other similar published work on alumina, and the following equation for surface diffusion was determined: $$D_s (cm^2 sec^{ - 1} ) = 4.05 x 10^5 exp - (452kJ mol^{ - 1} /RT).$$

The crystallography of annealing twins in alumina ceramics

The crystallography of basal and rhombohedral annealing twins in polycrystalline alumina ceramics has been analysed by selected area electron diffraction, and secondary grain boundary dislocations (SGBDs) within those boundaries have been analysed. The twins arise from misorientations of the high coincidence fraction ∑, and the SGBDs have Burgers vectors from the displacement shift complete lattice (DSCL). The basal twin is unique to the rhombohedral system. A O lattice calculation is used to show that the rhomhohedral twin is similar to the ∑ = 7 〈210〉 boundary in hexagonal metals.