Lattice Strain Distribution Research Articles

The influence of interdiffusion on the lattice misfit of epitaxial structures

The concept of lattice misfit and strain distribution at a heterointerface is reconsidered, taking into account the interdiffusion of substrate and layer components. Based on calculated compositional profiles for multicomponent solid solutions, the respective lattice-parameter profiles and stress profiles in the interface region of an epilayer system have been derived. For different diffusion coefficients and different influences of substrate and layer components on the lattice parameters, stresses develop due to interdiffusion during growth although the natural lattice matching is perfect. The stresses are formed both in the substrate and the layer and change their sign near the interface. Depending on the diffusion of substrate and layer components and on the sign of the natural misfit more than one stress-free plane can occur. They are shifted away from the interface either into the substrate or into the layer, the distance depending on the diffusion time. The model was applied to LPE-grown (Hg,Cd)Te on different substrates.

ＣｒＫα線およびＭｏＫα線による冷間圧延集合組織材のＸ線応力測定

In the case of X-ray stress measurement of textured materials, the lattice strain distribution usually shows a nonlinear relation against sin2ψ because of the elastic anisotropy of crystals. In the present study, CrKα and MoKα characteristics X-rays were used for the investigation of cold-rolled low carbon steels. The non-linearity of sin2ψ diagram which is observed on the 211 diffraction was examined after plastic elongation as well as under elastic loading.The non-linearity of d-sin2ψ diagram for 211 diffraction by CrKα radiation was intensified with increasing elastic loading. Furthermore, the non-linearity was found to be more remarkably than that expected from the elastic anisotropy when the specimen was once suffered plastic elongation. On the other hand, it was found that the lattice strain distribution obtaind from the 732+651 diffraction by MoKα radiation showed good linearity in the sin2ψ diagram because of deep penetration depth of MoKα radiation and a high multiplicity factor of highly indexed diffraction plane. It was also found that the X-ray elastic constants for 732+651 diffraction clearly depended on the rolled ratio and sample orientation to the rolled direction of the specimen.

The residual stress in TiN films deposited onto cemented carbide by high-rate reactive sputtering

The lattice parameters, lattice strain distribution and residual stress on different planes in tiN films deposited onto cemented carbide by reactive sputteringsputtering are studied by X-ray diffraction methods as a function of sputter target input power at a constant bias voltage of –100 V. The residual stress shows remarkably large differences between the values measured on different planes in a film. The form of the various sin 2ψ vs. lattice parameter plots (sspp) also shows differences and can, for example, be linear for the (422) peak but shows ψ splitting for the (220) peak. These results together with differences in the behavior of the parameters and diffraction peak broadening allow two distinct types of behavior to be isolated. They are not understood but are conjectured as being related to plastic flow, lattice deffects and possibly even ultramicrocracking on specific lattice planes.

Determination of non-symmetric secondary creep behaviour of ceramics by residual stress measurements using neutron diffractometry

e.g. c~ ~ 7 was reported for hot-pressed silicon nitrides [31. In Equation 2 the same exponent n for tension and compression was assumed. Chuang [4] used a relationship with different n-values. The coefficient c~ can be determined directly from creep tests using tensile loads. Unfortunately, such tests are not easy to perform. An alternative is given by bending creep tests on a specimen of trapezoidal cross-section. The stationary creep rates are expected to be different if the narrow side is subject to tensile or to compressive stresses. Formulae for the evaluation of ~ from the observed creep rates can be taken from [2]. Another method of determining ~ is based on measurements of the dimensional changes of a bending bar produced by the creep test as described in [5]. Both methods yield rather rough values of a. In this letter we present a method which is based on the determination of the residual stress distribution in a crept bending bar by neutron stress analysis. This method was found to be rather simple and yields a-values of superior precision. Creep tests were performed on specimens with dimensions 3 .5mm x 4 .5mm x 45ram made from the following materials: an AlzO3 ceramic containing 2.7% SiO2, 1.3% MgO, 0.02% CaO and 0.02% Fe203 (V38, Feldmiihle AG, Plochingen, FRG) and hotpressed silicon nitride (HPSN), containing 2.5% MgO. Due to the additives, a grain boundary glass phase is obtained in these materials after sintering. This is why creep can occur at relatively low temperatures. For these materials the Nor ton exponent was determined to ben = 2.25 (A1203) [5] and n = 2 (HPSN) [6]. The bending creep tests were performed with a load corresponding to an initial outer fibre bending stress of a0 = 60MPa (A1203) and o 0 = 135MPa (HPSN). The specimens crept for 100 h at 1100°C (A1203) and 1200° C (HPSN) were cooled under load and unloaded at room temperature. High-resolution neutron diffractometers were used to determine the residual stress distribution in the samples after unloading. Neutron stress analysis is analogous to the well-known method of X-ray stress analysis, i.e. it is based on precise measurements of lattice strain distributions. This technique has been described in previous publications [7-9], and therefore we confine ourselves here to giving some important details. Preliminary measurements were performed on a triple-axis spectrometer located at the Melusine Research Reactor, Grenoble, France. The final data sets were taken on the high-resolution diffractometers D I A at the high-flux reactor of the ILL, Grenoble. Slits in the incident and the diffracted beam restricted the irradiated volume to 0.4ram x 3 mm x 3mm, with the smallest dimension in the y-direction (see Fig. 1). For the A1203 ceramic the d-spacings were measured on the { 1 1 3} planes, whereas for HPSN the {1 1 1} and {2 1 1} planes were chosen. With a neutron wavelength of 2 = 0.298 nm the corresponding Bragg angles 20 were between 80 and 105 ° . The lattice strains were determined in the central part of the samples for the strain components G and ez as a function of y. Under the assumption that the residual stresses G are uniaxial and directed along the x-direction, the strain components investigated are related to the residual stresses G by

Dynamical x-ray diffraction from nonuniform crystalline films: Application to x-ray rocking curve analysis

A dynamical model for the general case of Bragg x-ray diffraction from arbitrarily thick nonuniform crystalline films is presented. The model incorporates depth-dependent strain and a spherically symmetric Gaussian distribution of randomly displaced atoms and can be applied to the rocking curve analysis of ion-damaged single crystals and strained layer superlattices. The analysis of x-ray rocking curves using this model provides detailed strain and damage depth distributions for ion-implanted or MeV-ion-bombarded crystals and layer thickness, and lattice strain distributions for epitaxial layers and superlattices. The computation time using the dynamical model is comparable to that using a kinematical model. We also present detailed strain and damage depth distributions in MeV-ion-bombarded GaAs(100) crystals. The perpendicular strain at the sample surface, measured as a function of ion-beam dose (D), nuclear stopping power (Sn), and electronic stopping power (Se) is shown to vary according to (1−kSe)DSn and saturate at high doses.

The molecular glass state in KBr1-x (CN)x

Structural and dynamic properties of the molecular glass KBr1-x (CN)X are reported. The low temperature state can be characterized as an averaged crystal, where clusters of correlated frozen-in CN- ions yield a distribution of frozen-in lattice strains which destroy the rigorous center-of-mass periodicty of the high temperature phase. The freezing process measured via cusps in the dipolar and quadrupolar susceptibilities is a relaxional phenomenon and depends sensitively on the timescale of the experiment.

The strong APR spectrum from trigonal Cr2+in GaAs

The authors report a study of the intense acoustic paramagnetic resonance spectra observed in semi-insulating or illuminated n-type chromium-doped gallium arsenide. The experimental data are compared with a Jahn-Teller model for Cr2- ions occupying substitutional sites but subject to a large trigonal distortion as well as to random lattice strains (Cr2-II). Despite the lack of a detailed knowledge of this lattice strain distribution, a satisfactory fit to the major experimental features is obtained after noting that the four equivalent directions for the trigonal strain are not magnetically equivalent for an arbitrary magnetic field direction. The origin of this large trigonal distortion present at a small fraction of the Cr sites is, however, unexplained.

Stress Evaluation on Materials Having Non-Linear Lattice Strain Distributions

AbstractThe state of the art of stress evaluation on materials having non-linear lattice strain distributions is presented.New results on heterogeneous materials with measurements conducted on both phases of the material show compensation of the shear stress components σ13 in ground surface layers of (α+β) brass. There is only the compensation of normal components σ11 of (α+γ) steel after plastic straining.The fundamental aspects and the evaluation of macro- and microresidual stresses on materials having preferred orientation are broadened. The use of Mo-Ka-radiation shows linear lattice strain distributions, as a result of minimizing the influence of micro residual stresses causing oscillations. The interplanar distance- or strain-polefigure shows similarities with the intensity polefigure.The knowledge of the theoretical influence of stress distribution with depth from the surface of the material is extended. The experimental procedure should use either different radiations having different penetration depths or a low-penetrating radiation in combination with removal of surface layers.

A Useful Guide for X-Ray Stress Evaluation (XSE)

AbstractThis paper summarizes experiences available for the measurement of lattice strains in different materials with different wavelengths to evaluate stresses by means of X-rays. The recommendations given are based on previous statements. Some principles of fundamentals of X-ray physics for the recording of interference lines with Ω and ψ-diffractometers are dealt with. Methods applicable for the determination of the peak position of the interference lines, the assessment of linear and non-linear lattice strain distributions, and tine calculation of stresses are outlined. For iron, aluminium, copper, nickel and titanium the constants for practical X-ray stress evaluation (XSE) and the parameters of measurement are tabled.

Acoustic relaxation due to Ni3+ions in Al2O3

The authors have obtained an expression for the acoustic relaxation loss due to the ion Ni3+ in Al2O3 including the effects of lattice strains. In the absence of a magnetic field the six lowest-lying levels of this system reduce to two uncoupled three-level systems which can be treated exactly using the current dynamic Jahn-Teller model to obtain both the relaxation loss and the associated relaxation times. It is predicted that there is no loss in the absence of lattice strains, but that in the presence of a distribution of lattice strains the loss is given by the classical expression for a two-level system reduced by a number of strain-dependent factors. Their expression has the correct dependence on acoustic model and greatly improves agreement with the experimentally observed magnitudes. Comparisons between the calculated and observed relaxation times enable an estimate of the second moment of the lattice strain distribution and a value for the Jahn-Teller reduction factor r to be obtained.

Lattice strain and misfit dislocations in GaAs-GaAlAsP heterojunctions

The lattice strain and misfit dislocations in a GaAs-GaAlAsP heterojunction were examined. The change in lattice strain with the composition ratio or the position of the crystal was measured, and it was found that some of the misfit dislocations introduced in the heterojunction were edge-type dislocations. The critical thickness of the epitaxial layer for the generation of misfit dislocations was also measured. The critical differential strain between the atomic layers was on the order of several angstroms. The distribution of lattice strain was analyzed by a two-dimensional simple cubic lattice model, and the distribution of differential strain was examined.

Angular variation of the EPR linewidths of ions in tetragonal symmetries; Mn 2+IN CaWO 4

The angular dependence of the EPR linewidths of Mn 2+ in tetragonal crystals is calculated under the assumption of a random distribution of lattice strains. A change in this angular dependence for different tetragonal groups is found. Data obtained for Mn 2+ in CaWO 4 support the theory.

Substructure strengthening in dispersion-strengthened nickel alloys

Pure nickel, 80 pct Ni-20 pct Cr, 98 pct Ni-2 pct ThO2, and 78 pct Ni-20 pct Cr-2 pct ThO2 were studied in a wide range of thermomechanical conditions to identify strengthening mechanisms in the dispersion-strengthened materials. An X-ray line profile technique was used to determine the distribution of lattice strain, the crystallite domain size and the incidence of twins and stacking faults. Transmission electron microscopy was carried out, and tensile tests were done at room temperature and at an elevated temperature. It was found that cold deformation of Ni−ThO2 did not produce lattice strains as large as was the case with pure nickel and Ni−Cr. However, deformation of Ni−Cr−ThO2 did generate high lattice strains, due it is thought to the influence of chromium on cross-slip. The materials containing high lattice strains recrystallized more readily on annealing or testing at high temperature. It was concluded that room temperature strength was related to domain size without regard to composition in the series investigated. Strengthening by particle-dislocation interaction was not thought to be applicable when the domain size was small compared to the interparticle spacing, or at elevated temperatures. High temperature strength was determined primarily by the presence of a polygonized dislocation substructure which was stabilized by the thoria dispersion.

On the Measurement of Strain Distribution in Wood under the Axial Tension Force by X-Ray Diffraction

Under the axial tensile force in the fiber direction the distribution of crystal lattice strain in the b-axis direction of the cellulose (I) in the cell wall of tracheids were measured by the X-ray diffraction technique using (040) reflection of cellulose micelles.In this study the transit X-ray method was used and the diffraction profiles were obtained by 40sec fixed time and θ-2θ method. The macroscopic surface strains of the specimens in the fiber direction were measured by the electrical strain meter and resistance type strain gage, pasted on both sides of the specimens.The lattice strain in the fiber direction was a little smaller than the surface strain of the specimens, but the average ratio of the lattice strain to the surface strain was in the range of 0.90∼0.97 below the surface strain level of 3000×10-6.The lattice strains decreased with the increasing inclination from the fiber axis.In the inclined direction from the fiber axis, the lattice strains were a little smaller than the normal strains of the specimen calculated from Eq. (10), of homogeneous orthogonal anisotropic body, but the appearance of distribution of lattice strains in the cell wall was similar to that of the normal strains of the specimens.From those results it is considered that the micelles which were arranged in the cell wall have actually taken over a portion of the applied stress and acted an effective role in the mechanical properties of wood.It is qualitatively observed that the micelles have largely been improved in their orientation by the axial extension in the fiber direction.

The Application of X-ray Line Broadening to a Study of Substructure Strengthening in Dispersion Strengthened Alloys

AbstractA refined x-ray line profile analysis was used to determine the lattice strain distribution and crystallite domain size in nickel and a series of alloys, Ni-Cr, Ni-ThO2 and Ni-Cr-ThO2 in a wide range of thermo-mechanical conditions. Corrections were made for instrumental broadening and doublet broadening according to Stokes and Rachinger respectively, for errors due to the “hook effect”, for terminal errors in the series arising from Instability of the components, and for the presence of stacking faults and twins on the basis of peak shift and asymmetry. The internal consistency of the x-ray data was reviewed critically and good agreement was found. The values of lattice strain and domain size were used to evaluate the presence of a dislocation substructure and the degree of polygonization of the subgraln boundaries.It was concluded that the thoria-free materials developed much higher lattice strains during cold rolling than did the Ni-ThO2, due it is thought to the operation of multiple slip in the latter. The Ni-Cr-ThO2 also developed high lattice strains during cold rolling, similar to those of the thoria-free lattices, and this was explained by the influence of chromium on cross-slip. It was postulated that the regions of high lattice strain act as driving forces in the process of recrystallization and promote grain growth during heat treatment following cold rolling.The x-ray results were correlated with transmission electron microscopy and tensile data in a parallel study in which models for room temperature and high temperature strengthening were proposed.

Determination of Residual Stress of Aluminum Alloys by X-Rays

The distribution of residual lattice strains or lattice spacings and residual stresses in plastically extended aluminum alloys were measured by various characteristic X-rays. Then, the scattering of the distribution of the residual lattice strains vs. sin2ψ were investigated precisely in each stage of plastic strains, and the wave length and lattice plane dependency of the residual stresses were discussed.Hot rolled sheets of Al-1.2 Mn (3003) and Al-4.5 Cu-1.5 Mg-0.6 Mn (2024) alloy were used in this experiment. The shape and dimensions of specimens are shown in Fig. 1. The chemical composition, heat treatment and mechanical properties are indicated in Table 1, 2. To prevent the diffraction lines of these specimens from becoming spotty, the specimen holder8) was equipped with horizontally and vertically oscillating mechanism, by which sufficiently continuous diffraction patterns were obtained (Fig. 2).In order to make sure of the wave length and diffraction plane dependency of the residual stress, the data for several planes by CuKα, CoKα and CrKα radiation were sought and obtained (Fig. 5). On the observation of the distribution of residual lattice strains by sin2ψ method, the direction of the incident X-ray beam to the specimen surface ψ0 is devided at intervals of 5°in the range of 0°∼45°and their diffraction lines on the side of ψ0+η were observed (Fig. 3, 4). The results obtained in this study are summarized as follows.(1) In order to examine the detailed distribution of the lattice strains or lattice spacings, it is necessary to obtain many lattice strains vs. sin2ψ and to observe always only the sharp diffraction lines on the side of ψ0+η precisely.(2) It is confirmed that the distributions of the lattice strains vs. sin2ψ of annealed specimens are nearly linear, but scatter evidently in the early stage of the plastic strain about 2%, and aproach linear relation again with increase of the plastic strain. From these configuration, it is considered that the stress of a second kind9) in terms of Heyn intergranular stress takes place in the residual lattice strain.(3) The residual stresses are independent of the wave length but depend mainly on the lattice planes.

Lattice Strain Measurements on Deformed FCC Metals

AbstractIn this work experiments have been undertaken to determine the type of residual stresses of plastically deformed polycrystals of aluminum, copper, and nickel which cause a shift of the X-ray interference lines. In order to get accurate stress values, the lattice strain distribution has been measured in special planes of the deformed specimens, using the sin2 ψ technique. The surface stresses were determined as a function of the macroscopic plastic strain of cylindrical specimens. With increasing strain, the residual surface stress component parallel to the direction of deformation increases. The stresses observed are compressive ones after tension and tensile ones after compression.The changes in the residual lattice strain distributions which arise on progressive thinning of the plastically deformed specimens have been measured. From the stress values determined in each new surface layer, the stress distribution originally present in the uodestroyed specimen was calculated. Tensile stresses in the interior of the specimens are in equilibrium with compressive stresses in the surface areas. The formation of residual stresses on specimens with a work-hardened surface layer is found to be quite different from that of well-annealed samples.The results of this work seem to show that in uniaxially deformed cylindrical specimens, residual macrostresses arise which may be a consequence of a macroscopic inhomogeneity of work-hardening between the surface layers and the interior of the polycrystals.