Direction-dependent elastic grain-interaction models – a comparative study

Mechanical and diffraction (X-ray) elastic constants (diffraction (X-ray) stress factors for macroscopically elastically anisotropic specimens) can be calculated for polycrystalline specimens from single-crystal elastic data by employing elastic grain-interaction models. Traditionally, only so-called isotropic grain-interaction models are considered: all directions in the polycrystal are taken equivalent with respect to the grain interaction. Only recently, so-called direction-dependent, i.e. anisotropic grain-interaction models, have been proposed. These models can express the effects of the reduced dimensionality of thin films, of the surface anisotropy of bulk polycrystals and of a grain-shape (morphological) texture on the elastic properties of polycrystals. In this work, the available, recently proposed direction-dependent grain-interaction models will be compared, in particular on the basis of numerical calculations of diffraction and mechanical elastic constants, of variances of certain orientation-dependent stress and strain tensor components and of the distributions of strains in the Euler (orientation) space. It will be demonstrated that the so-called Vook–Witt and inverse Vook–Witt models become (but only approximate) equivalent to the Eshelby–Kröner model for certain grain-shape textures.     

Mechanical elastic constants and diffraction stress factors of macroscopically elastically anisotropic polycrystals: the effect of grain-shape (morphological) texture

The effect of the grain-shape (‘morphological’) texture of a polycrystal on the mechanical elastic constants and diffraction (X-ray) stress factors is investigated. To this end, the Eshelby–Kröner grain interaction model originally devised for polycrystals consisting of spherical grains is extended to ellipsoidal grain morphology. Results obtained for the mechanical elastic constants show that a polycrystal consisting of ellipsoidal grains with their principal axes aligned along common directions (i.e. when an ideal grain-shape texture occurs) is macroscopically elastically anisotropic. Also the diffraction (X-ray) stress factors are affected by the grain-shape texture; they reflect the macroscopic elastic anisotropy by resulting in nonlinear so-called sin²?ψ plots. In general, a grain-shape texture can have a moderate effect on the mechanical elastic constants and a pronounced effect on the diffraction elastic constants, depending on the crystal symmetry and single-crystal elastic anisotropy.     

Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.     

Elastic mechanical grain interactions in polycrystalline materials; analysis by diffraction-line broadening

Abstract

Experimental investigations have revealed that the Neerfeld–Hill and Eshelby–Kröner models, for grain interactions in massive, bulk (in particular, macroscopically isotropic) polycrystals, and a recently proposed effective grain-interaction model for macroscopically anisotropic polycrystals, as thin films, provide good estimates for the macroscopic (mechanical and) X-ray elastic constants and stress factors of such polycrystalline aggregates. These models can also be used to calculate the strain variation among the diffracting crystallites, i.e. the diffraction-line broadening induced by elastic grain interactions can thus be predicted. This work provides an assessment of diffraction-line broadening induced by elastic loading of polycrystalline specimens according to the various grain-interaction models. It is shown that the variety of environment, and thus the heterogeneity of the stress–strain states experienced by each of the individual grains exhibiting the same crystallographic orientation in a real polycrystal, cannot be accounted for by traditional grain-interaction models, where all grains of the same crystallographic orientation in the specimen frame of reference are considered to experience the same stress–strain state. A significant degree of broadening which is induced by the heterogeneity of the environments of the individual crystallites is calculated on the basis of a finite element algorithm. The obtained results have vast implication for diffraction-line broadening analysis and modelling of the elastic behaviour of massive polycrystals.     

Effective dielectric and piezoelectric constants of thin polycrystalline ferroelectric films

The averaged dielectric, piezoelectric, and elastic constants of thin polycrystalline barium titanate and lead titanate films are calculated within a modified effective-medium approximation, which takes fully into account piezoelectric interactions between crystallites. Films with c-or a-type crystal texture resulting from mechanical interaction with the substrate are considered when the film becomes ferroelectric under cooling of the heterostructure. The dependences of the effective material constants of textured films on the residual macroscopic polarization of a film are described. An analysis is made of the effect of two-dimensional clamping of a film on a thick substrate on measurements of dielectric and piezoelectric constants. Fiz. Tverd. Tela (St. Petersburg) 40, 2206–2212 (December 1998)     

Synthesis and optical characterization of nanocrystalline CdTe thin films

From several years the study of binary compounds has been intensified in order to find new materials for solar photocells. The development of thin film solar cells is an active area of research at this time. Much attention has been paid to the development of low cost, high efficiency thin film solar cells. CdTe is one of the suitable candidates for the production of thin film solar cells due to its ideal band gap, high absorption coefficient. The present work deals with thickness dependent study of CdTe thin films. Nanocrystalline CdTe bulk powder was synthesized by wet chemical route at pH≈11.2 using cadmium chloride and potassium telluride as starting materials. The product sample was characterized by transmission electron microscope, X-ray diffraction and scanning electron microscope. The structural characteristics studied by X-ray diffraction showed that the films are polycrystalline in nature. CdTe thin films with thickness 40, 60, 80 and 100 nm were prepared on glass substrates by using thermal evaporation onto glass substrate under a vacuum of 10⁻⁶ Torr. The optical constants (absorption coefficient, optical band gap, refractive index, extinction coefficient, real and imaginary part of dielectric constant) of CdTe thin films was studied as a function of photon energy in the wavelength region 400–2000 nm. Analysis of the optical absorption data shows that the rule of direct transitions predominates. It has been found that the absorption coefficient, refractive index (n) and extinction coefficient (k) decreases while the values of optical band gap increase with an increase in thickness from 40 to 100 nm, which can be explained qualitatively by a thickness dependence of the grain size through decrease in grain boundary barrier height with grain size.     

Mechanical properties of sol-gel derived lead zirconate titanate thin films by nanoindentation

Lead zirconate titanate (PZT) thin films are deposited on platinized silicon substrate by sol-gel process. The crystal structure and surface morphology of PZT thin films are characterized by X-ray diffraction and atomic force microscopy. Depth-sensing nanoindentation system is used to measure mechanical characteristics of PZT thin films. X-ray diffraction analyses confirm the single-phase perovskite structures of all PZT thin films. Nanoindentation measurements reveal that the indentation modulus and hardness of PZT thin films are related with the grain size and crystalline orientation. The increases of the indentation modulus and hardness with grain size are observed, indicating the reverse Hall-Petch effect. Furthermore, the indentation modulus of (1 1 1)-oriented PZT thin film is higher than those of (1 0 0)- and random-oriented films. The consistency between experimental data and numerical results of the effective indentation moduli for fiber-textured PZT thin films using Voigt-Reuss-Hill model is obtained.     

Microstresses in textured polycrystals studied by the multireflection diffraction method and self-consistent model

A new version of the X-ray diffraction method for determining macrostresses and microstresses in textured polycrystalline material is presented. In this method the lattice strains for various orientation of the scattering vector as well as for various crystallographic planes {hkl} are measured. The interpretation of the experimental data is based on the least-squares fitting procedure, in which the diffraction elastic constants and theoretical values of microstresses are used. The diffraction elastic constants and the microstresses are calculated by the self-consistent model. The new method was successfully applied for stress determination in one- and two-phase steels subjected to elastoplastic deformation, and the significant anisotropy of the incompatibility stresses was observed in textured samples.     

Optical constants of Na-doped ZnO thin films by sol-gel method

The structural and optical properties of pure and Na-doped ZnO thin films have been investigated by X-ray diffraction (XRD), atom force microscopy and UV-Vis spectrophotometer. The crystal structure of all the thin films is the hexagonal wurtzite. The average grain size and surface roughness increases with the increase of the Na/Zn ratio. The optical band gap of the thin films decreases from 3.26 to 3.12 eV by increasing the Na/Zn ratio from 0.0 to 0.10. Transmittance spectra were used to determine the optical constants of the thin films, and the effect of Na/Zn ratio on the optical constants was investigated. With the increase of Na/Zn ratio, the refractive index decreases and the extinction coefficient increases in the 380-700 nm spectral range.     

Electrical conductivity of YSZ film grown by pulsed laser deposition

Yttria-stabilized zirconia (YSZ) thin films, 0.6–1.5 μm, were deposited on Pt and sapphire substrates by a pulsed laser deposition (PLD) method. Their structural and transport properties have been studied by means of X-ray diffraction and electrical conductivity measurements. The in-plane and the perpendicular-to-plane conductivities (hereafter, “across-plane” conductivity) of thin films were measured and compared to that of bulk sample. X-ray diffraction and electron microscopy results showed that the films on Pt and sapphire were polycrystalline cubic with a columnar structure. Both the across-plane and the in-plane conductivities of YSZ thin film were close to that of bulk specimens. Thus no conductivity enhancement was found for the present nano-crystalline YSZ films (grain or column size, 60∼100 nm).     

Resonant-ultrasound spectroscopy for studying annealing effect on elastic constant of thin film

In this paper, we study the elastic property of thin films using resonant-ultrasound spectroscopy (RUS). RUS determines the elastic constants of a solid from its resonance frequencies of free vibration. There were two problems to be solved for applying RUS to thin films: accurate measurement of the resonance frequencies and mode identification of each resonance frequency. We solve these problems using the tripod needle transducers and the laser-Doppler interferometry (LDI). In this paper, we describe the RUS/LDI measurement setup we developed, and show the relationship between the elastic constant and annealing temperature for Cu thin films. Then, we discuss the effects of recrystallization and recovery on the elastic constant referring the X-ray diffraction measurement.     

Structural and morphological characterization of chemically deposited silver films

Silver thin films were deposited on glass slide substrates at room temperature by the chemical bath deposition (CBD) technique, using silver nitrate (AgNO₃) as Ag⁺¹ source and triethanolamine [(N(CH₂CH₂OH)₃)] as the complex reductor agent. We determined the conditions of the CBD process to obtain homogeneous, opaque silver films with good adhesion to the substrate and white coloration. The silver films were studied by X-ray diffraction, scanning electron microscopy, and atomic force microscopy. The results show that the films are composed of several layers with different morphology depending on the deposition time. In all the cases, the crystalline structure of the films was the face cubic centered phase with a moderate [111] texture. Strains and stresses were calculated by the Vook-Witt grain interaction model.     

An atomistic assessment of the impact of flaw orientation on the elastic and failure behavior of single-crystal Si nanometre-thick slabs

Abstract

Failure of nanoscale Si thin films was examined using molecular dynamics (MD) simulations that employed the modified embedded atom method (MEAM) interatomic potential. Specifically, nanometre-thick slabs of different crystallographic orientations containing asymmetric, high aspect ratio surface flaws were subjected to uniaxial tensile strains with the strain applied perpendicular to the flaw major axis. The ensuing elastic response and failure behaviour were examined as a function of variation in crystallographic orientation relative to the surface flaw. For certain flaw orientations, crack propagation was accompanied by slip along preferred directions, while in other cases, failure was purely brittle. In addition, a significant dependence of the computed elastic constants and yield stress, on the relative orientation of the surface flaw was observed. This work offers new insights into the role of surface flaws on the mechanical failure of silicon-based, nanoscale, engineered structures.     

Internal stresses and stability of the tetragonal phase in zirconia thin layers deposited by OMCVD

Zirconia thin films were deposited by OMCVD (organo-metallic chemical vapour deposition) at various temperatures and oxygen partial pressures on a AISI 301 stainless steel substrate with Zr(thd)₄ as precursor. The as deposited 250 nm thin zirconia films presented a structure consisting of two phases: the expected monoclinic one and also an unexpected tetragonal phase. According to the literature, the stabilization of the tetragonal phase (metastable in massive zirconia) can be related to the crystallite size and/or to the generated internal compressive stresses.To analyze the effect of internal and external stresses on the thin film behaviour, in-situ tensile experiments were performed at room temperature and at high temperature (500 °C).Depending on the process parameters, phase transformations and damage evolution of the films were observed. Our results, associated to XRD (X-ray diffraction) analyses, used to determine phase ratios and residual stresses within the films, before and after the mechanical experiments, are discussed with respect to their microstructural changes.     

Effect of thickness on structural, optical and electrical properties of nanostructured ZnO thin films by spray pyrolysis

Transparent conducting zinc oxide thin films were prepared by spray pyrolytic decomposition of zinc acetate onto glass substrates with different thickness. The crystallographic structure of the films was studied by X-ray diffraction (XRD). XRD measurement showed that the films were crystallized in the wurtzite phase type. The grain size, lattice constants and strain in films were calculated. The grain size increases with thickness. The studies on the optical properties show that the direct band gap value increases from 3.15 to 3.24 eV when the thickness varies from 600 to 2350 nm. The temperature dependence of the electrical conductivity during the heat treatment was studied. It was observed that heat treatment improve the electrical conductivity of the ZnO thin films. The conductivity was found to increase with film thickness.     

Unusual elastic behavior of nanocrystalline diamond thin films

This Letter studies the relationship between the elastic constants and the microstructure of nanocrystalline diamond thin films deposited by the chemical vapor deposition method doping various concentration of N2 gas. The elastic constants were measured by resonant ultrasound spectroscopy and picosecond laser ultrasounds. The increase of N2 gas decreases the diagonal elastic constants, but increases the off-diagonal elastic constants. The micromechanics calculation can explain this unusual elastic behavior, and it predicts thin graphitic phases at grain boundaries.     

Bulk-wave and guided-wave photoacoustic evaluation of the mechanical properties of aluminum/silicon nitride double-layer thin films

The development of devices made of micro- and nano-structured thin film materials has resulted in the need for advanced measurement techniques to characterize their mechanical properties. Photoacoustic techniques, which use pulsed laser irradiation to nondestructively induce very high frequency ultrasound in a test object via rapid thermal expansion, are suitable for nondestructive and non-contact evaluation of thin films. In this paper, we compare two photoacoustic techniques to characterize the mechanical parameters of edge-supported aluminum and silicon nitride double-layer thin films. The elastic properties and residual stresses in such films affect their mechanical performance. In a first set of experiments, a femtosecond transient pump–probe technique is used to investigate the Young’s moduli of the aluminum and silicon nitride layers by launching ultra-high frequency bulk acoustic waves in the films. The measured transient signals are compared with simulated transient thermoelastic signals in multi-layer structures, and the elastic moduli are determined. Independent pump–probe tests on silicon substrate-supported region and unsupported region are in good agreement. In a second set of experiments, dispersion curves of the A₀ mode of the Lamb waves that propagate along the unsupported films are measured using a broadband photoacoustic guided-wave method. The residual stresses and flexural rigidities for the same set of double-layer membranes are determined from these dispersion curves. Comparisons of the results obtained by the two photoacoustic techniques are made and discussed.     

Studies on pyrolytically sprayed SnO2 and Sb-SnO2 thin films for LPG sensor applications

Undoped and antimony doped tin oxide thin films of different thicknesses were prepared on mineral glass substrate by spray pyrolysis method via sol-gel route. Both the films show good transmittance in the visible region. Band gap energy of both films lies between 3 to 3.5 eV. X-ray diffraction studies of undoped and antimony doped tin oxide thin films for various annealing temperature show polycrystalline tetragonal structure of SnO₂ with preferred orientation of (110) and (101), respectively and from the XRD data, grain size were also evaluated. AFM images of Undoped and antimony doped tin oxide thin films annealed at 375 °C depict the film thickness and indicate uniform surface pattern without dark pits and with strains of some ups exceeding the specified limit. The prepared films were tested in a specially developed test rig for Liquefied Petroleum Gas detection at different operating temperatures. The response characteristics of the films for LPG detection show maximum sensitivity and minimum response time at the operating temperature 400 °C. Studies indicate that antimony doped tin oxide thin film are one among the suitable candidates for LPG detection with a detection sensitivity and response time (t90) of 11 and 140 seconds, respectively. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

A mathematical model to predict the grain size of nanocrystalline CdS thin films based on the deposition condition used in the sol–gel spin coating method

Design of experiment (DOE) based on central composite design (CCD) has been employed for the development of a mathematical model correlating the important process parameters like thiourea concentration (U), annealing temperature (A), rotational speed (S), and annealing time (T) of the spin coating process for the preparation of CdS thin films. The experiments were conducted as per the design matrix. Nanocrystalline CdS thin films have been prepared using cadmium nitrate and thiourea as precursors by sol gel spin coating method using the results of the mathematical model. The prepared CdS films have been characterized and the crystal structure and grain size of the samples were analyzed using X-ray diffraction technique. The adequacy of the developed models was checked by analysis of variance (ANOVA) technique. The accuracy of prediction has been carried out by conducting confirmation test. Using this model, the main effect of process parameters on grain size of CdS films have been studied. These parameters were optimized to obtain minimum grain size using the Microsoft excel solver. The results have been verified by depositing CdS films using the optimized conditions. These films have been characterized using X-ray diffraction technique and the grain size is found to be 8.8 nm. The high resolution transmission electron microscopy (HRTEM) analysis showed the grain size of the prepared CdS film to be ∼7 nm. UV–vis spectroscopy analysis revealed that CdS films exhibited quantum confinement effect.     

Influence of 120 MeV Si9+ ion irradiation on ZnTe semiconductor thin films

ABSTRACT

ZnTe (Zinc Telluride) is a potential semiconducting material for many optoelectronic devices like solar cells and back contact material for CdTe-based solar cells. In the present study, ZnTe thin films were prepared by thermal evaporation technique and then irradiated with 120?MeV Si⁹⁺ ions at different fluences. These films are characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and UV–Visible spectroscopy techniques. XRD study confirms increased crystallinity and grain growth for post-irradiated ZnTe thin films for fluences, up to 1?×?10¹¹ ions cm^?2. However, the grain size and crystallinity decreased for higher fluence-exposed samples. SEM images confirm the observed structural properties. Modification of the surface morphology of the film due to the ion irradiation with different fluences is studied. Optical band gap of film is decreased from 2.31?eV (pristine) to 2.17?eV after irradiation of Si⁹⁺ ions.