Elastic Relaxation Effects Research Articles

First principles phase diagram calculation for the 2D TMD system [formula omitted

First principles phase diagram calculations, that included van der Waals interactions, were performed for the bulk transition metal dichalcogenide system (1−X)·WS2−(X)·WTe2. To obtain a converged phase diagram, a series of cluster expansion calculations were performed with increasing numbers of structural energies, (Nstr) up to Nstr=435, used to fit the cluster expansion Hamiltonian. All calculated formation energies are positive and all ground-state analyses predict that formation energies for supercells with 16 or fewer anion sites are positive; but when 150⪅Nstr⪅376, false ordered ground-states are predicted. With Nstr≥399, only a miscibility gap is predicted, but one with dramatic asymmetry opposite to what one expects from size-effect considerations; i.e. the calculations predict more solubility on the small-ion S-rich side of the diagram and less on the large-ion Te-rich side. This occurs because S-rich low-energy metastable ordered configurations have lower energies than their Te-rich counterparts which suggests that elastic relaxation effects are not dominant for the shape of the miscibility gap.

Investigating elastic relaxation effects on the optical properties of functionalised calcium carbonate compacts using optics-based Heckel analysis

Heckel analysis is a widely used method for the characterisation of the compression behaviour of pharmaceutical samples during the preparation of solid dosage formulations. The present study introduces an optical version of the Heckel equation that is based on a combination of the conventional Heckel equation together with the linear relationship defined between the effective terahertz (THz) refractive index and the porosity of pharmaceutical tablets. The proposed optical Heckel equation allows us to, firstly, calculate the zero-porosity refractive index, and, secondly, predict the in-die development of the effective refractive index as a function of the compressive pressure during tablet compression. This was demonstrated for five batches of highly porous functionalised calcium carbonate (FCC) excipient compacts. The close match observed between the estimated in-die effective refractive index and the measured/out-of-die effective THz refractive index supports the validity of the proposed form of the equation. By comparing the measured and estimated in-die tablet properties, a clear change in the porosity and hence, the effective refractive index, due to post-compression elastic relaxation of the FCC compacts, has been observed. We have, therefore, proposed a THz-based compaction setup that will permit in-line monitoring of processes during tablet compression. We envisage that this new approach in tracking powder properties introduced in this preliminary study will lead to the onset of further extensive and detailed future studies.

Evolution of the activation energy spectrum and defect concentration upon structural relaxation of a metallic glass determined using calorimetry and shear modulus data

We performed high precision shear modulus and calorimetry measurements on a model Pd-based glass subjected to different annealing treatments below the glass transition temperature Tg. Applying the Interstitialcy theory, we found that structural relaxation-induced heat release/absorption below and near Tg can be precisely described using shear modulus data confirming thus the generic relationship between the heat and elastic relaxation effects in metallic glasses. The same approach is used for the reconstruction of underlying activation energy spectra. It is found that the spectra derived from calorimetry and shear modulus data are very close. Integration of these spectra gives the change of the concentration of frozen-in defects and its absolute value for different stages of structural relaxation.

Analyse du contraste d'un sous-joint de torsion (0 0 1) dans le silicium en MET à deux ondes

A quantitative analysis of the image of a low angle (0 0 1) twist boundary in silicon is performed using the two-beam dynamical theory of electron diffraction. The contrast features are discussed as functions of the thickness of the foil and possible elastic relaxation effects of the low angle twist boundary in the thin foil. To cite this article: R. Bonnet et al., C. R. Physique 3 (2002) 657–663.

The Effect of Elastic Relaxation on the Indentation Size Effect in Tungsten Carbide

where a is the apex half-angle of the pyramidal indenter, P is the indenting load in kgf and d is the indentation diagonal in mm. The diagonal, d, is measured by means of an optical microscope after unloading the indenter, while the apex half-angle of the indentation, a, is assumed to be constant at all applied loads and equal to the apex half-angle of the indenter, i.e., half of the angle between opposite triangular faces of the indenter (standard a ˆ 688). It is well established that in most materials the microhardness measured by means of indentations decreases with increasing indenting load down to a constant value, which coincides with the macrohardness of the material [1]. This phenomenon is called indentation size effect (ISE) and has been observed in many materials, including tungsten carbide (WC) single crystals [2]. This work aimed at assessing the role of elastic relaxation in the observed ISE. For this purpose, a (0 0 0 1) face of a WC crystal was indented at 25, 50, 100, 200 and 500 3 10y3 kg and, after unloading the indenter, the depth and diagonal lengths of the indentations were measured by atomic force microscopy (AFM). The results were compared with the depth and diagonal of the indentations before unloading, which were calculated from the geometry of the indenter. The indenter was a standard Vickers indenter, i.e., a square pyramid of apex half-angle equal to 688. For the calculation of the size of the indentation before unloading, it was assumed that the intrinsic hardness of the WC (0 0 0 1) surfaces was 2000 kgf mmy2, i.e., the macrohardness measured at loads of 1 kg or higher [3]. Fig. 1 shows the percentage change in the depth and the diagonal length of the indentations before and after unloading each of the ®ve indenting loads, as well as the percentage change in Vickers microhardness, relative to the known macrohardness. The percentage change decreases in all cases with increasing indenting load. The microhardness tends to the macrohardness value, and the percentage change in diagonal length tends to zero, but the change in depth tends to approximately 30%. The half-angle â between two opposite edges of the indentation, which, before unloading, is related to the apex angle a by the equation tan ⠈  2 p tan a (2)

Self-Assembly of Quantum-Dot Molecules: Heterogeneous Nucleation of SiGe Islands on Si(100)

We report on the formation of clusters of self-assembled quantum dots (termed quantum-dot molecules). Each cluster, typically consisting of four closely spaced SiGe islands, is formed by preferential nucleation around the edges of square pits. Uniform-sized pits are directly formed by controlled deposition of Si and C on the initial Si(100) surface, followed by the growth of a thin Si buffer layer. Formation of ${105}$ pit walls as precursors to island formation and elastic relaxation effects near the pits appear to influence island nucleation. Quantum-dot molecules may have potential applications in nanoelectronic devices and may exhibit novel electronic and optical properties.

Role Of Surface Instability And Anisotropy On Strain Relaxation Of Sige On Si(110)

AbstractSiGe alloys (< 1.5 % mismatch) were grown on Si (110) substrates at 700°C by molecular beam epitaxy. The structure and surface morphology were studied as a function of SiGe coverage (1.5mn–9nm) using atomic force microscopy, transmission electron microscopy and RHEED. A very high density of nanoscale SiGe ledges (less than 1 nm high and 1 μm long) were observed to form on the step terraces created during buffer layer growth. An interesting phenomenon is that the step bunches generated by the buffer growth and SiGe ledges are aligned along the elastically hardest <111> direction on the Si (110) surface. With increasing alloy thickness, the nanoscale SiGe ledges become longer and straighter. The effects of the surface instability and elastic anisotropy on the elastic relaxation effects are discussed.

Effects of elastic relaxation on aspect ratios during island growth of isotropic films

The effect of misfit strain on the equilibrium aspect ratio of isotropic islands has been investigated by using numerical calculations of the elastic strain energy of spherical caps on a substrate. The effects of three dimensionless quantities were investigated: the ratio of the surface energy to strain energy, the modulus mismatch and the ratio of the interfacial energy to the surface energy of the island. It was shown that values of these parameters that tended to increase the strain energy dominance resulted in larger equilibrium aspect ratios (height-to-width ratio). The effect of modulus mismatch was also studied. It has been shown that as the modulus of the substrate increases relative to the island (keeping all other parameters constant), the aspect ratio increases. Furthermore, it has also been shown that island-to-island interactions occur over very short ranges, becoming negligible when the midpoint of the islands are separated by more than two diameters.

Effects of elastic relaxation on large-angle convergent-beam electron diffraction from cross-sectional specimens of GexSi1−x/Si strained-layer superlattices

Abstract A large-angle convergent-beam electron diffraction pattern with fine diffraction lines from a cross-sectional specimen of Gexsi1−x/Si strained-layer superlattices can give much information on local strain and misfit stress relaxation. The diffraction lines in the GeSi layers are shifted from those in the Si layers by the misfit strain and the strain relaxation. In this paper we shall demonstrate that the effects of elastic relaxation and the residual strains can be separated.

Transmission electron microscopy of elastic relaxation effects in Si-Ge strained layer superlattice structures

Transmission electron microscopy of elastic relaxation effects in Si-Ge strained layer superlattice structures

Transmission electron microscopy of elastic relaxation effects in Si–Ge strained layer superlattice structures

A series of Si/GexSi1−x (x≂0.2–0.4) strained layer superlattices have been grown by molecular-beam epitaxy on (100) oriented substrates in order to study elastic relaxation effects. In the bulk of a Si–Ge strained layer system grown on a relatively massive substrate, the elastic misfit strain resulting from unit-cell expansions and contractions is accommodated in the GexSi1−x alloy layers. However, it is known that these stresses can be significantly relaxed near surfaces of the bulk or in thin foils prepared for cross-sectional transmission electron microscopy. It has been found that this stress relaxation introduces a number of electron diffraction effects which are superimposed on structure factor or other contrast effects associated with layered structures. We derive equations describing the relaxation strain field for GexSi1−x alloy layers ≂10 nm in thickness present on relatively massive substrates (>100 nm) based on the solution of a line force acting on an elastic half-space. This predicts a long-range stress relaxation.

On the Propagation of Twin-Fault-Induced Stress in Platelet Fau-Framework Zeolites

AbstractA model describing the propagation of a rhombohedral distortion in platelet CSZ–1 zeolites is presented. It is proposed that internal stress gradients grown into CSZ–1 platelets at synthesis are responsible for this distortion of the cubic FAU framework, where the spacings of 111 planes parallel to the platelet surfaces are elongated relative to the {111} planes. The presence of inhomogeneities is suggested by the presence of thin bands of twin faults which are invariably observed near the central layers of each platelet. Elastic modelling confirms that the effects of any stress associated with such twin faults will be most pronounced in the thinnest platelets, where the effects of elastic relaxation are minimal, and where the width of the fault zone relative to the platelet thickness is maximal. Platelet CSZ–3 and Y-type zeolites, which are considerably thicker, are therefore not expected to show significant rhombohedral distortion despite the presence of similar twin fault bands.

The effects of elastic relaxation on transmission electron microscopy studies of thinned composition-modulated materials

Composition modulations in defect-free crystalline materials are generally accompanied by a lattice distortion where unit cell dimensions are not characteristic of the local composition. The distortion originates from the constraint that the interatomic spacings perpendicular to the modulation direction be commensurate from one layer to the next. Thus there is an internal stress field set up in the material which attempts to suppress unit cell expansions and contractions in these perpendicular directions. A well-known example is the tetragonal distortion observed in bulk, cubic strained layer superlattices, and spinodally decomposed alloys. However, it is frequently overlooked that these stresses can be significantly relaxed near surfaces of the bulk material, particularly those surfaces lying perpendicular to the modulation direction. This relaxation can be a dominating effect in materials which have been thinned in cross section for study by TEM. Lattice plane bending near the specimen surfaces can cause strong diffraction contrasts, and the local lattice spacings are representative of neither the bulk, tetragonally distorted material, nor the unstressed material. In this paper we discuss how this important, and oft-neglected relaxation affects TEM bright-field and dark-field image contrasts, high resolution lattice images, and interpretation of selected area diffraction data. We also derive expressions, relevant for all sample thicknesses, describing the relaxation strain field in cubic anisotropic materials, thinned perpendicularly to the modulation direction. The results are discussed in the context of two classes of modulated materials, namely spinodally-decomposed InGaAsP alloys and GeSi/Si strained layer superlattices.

The effect of elastic relaxation on the local structure of lattice-modulated thin films

Shear stresses in lattice-modulated bulk materials, such as spinodally decomposed alloys, distort considerably the local unit cell dimensions. We show that the distortion changes appreciably in thin films because of elastic relaxation near the surfaces, giving rise to a significant thickness dependence to this effect. It is emphasized that these distortions can be large and must be allowed for if high resolution electron microscopy is to be used as a technique for deducing local composition or unit cell dimensions in composition-modulated materials.

Internal friction in hydrogen-charged palladium

The work has been suggested by the fact that in pure metals with dislocations, the point defects, such as impurity atoms, may give rise to thermally activated elastic relaxation effects. Palladium has been chosen as metal basis and hydrogen as interstitial because palladium is absorbent of hydrogen, which may be introduced with an electrolytical process and degassed with the electrolytical opposite process, without any change of dislocation density in the material. The experiments show that an electrolytic charge of hydrogen atoms of the order of 0.4.10-3 per palladium atom modify theQ−1(T) curve of the permanently strained material at low temperatures. The characteristic relaxation effects due to the dislocation motion (Bordoni peaks) disappear, while a new relaxation is introduced. A structural explanation of the relaxation is proposed that is based on an interaction mechanism between impurities and dislocations.