Research
Davor Balzar, Ph.D. Condensed-Matter Physics
My interests are mainly in studies of materials' properties by diffraction methods. The focus is on strain and defect studies by diffraction-line-broadening analysis, residual strain/stress, and texture. Take a look at selected publications and recent presentations for more information. You can also see several photographs of our diffraction equipment.
Some of the recent studies are described below.
Elastic-strain tensor by Rietveld refinement
Lately, we work on problems of accurate determination of bulk strain/stress and texture. The complete texture information allows calculations of orientation-distribution function (ODF) and consequent weighting of monocrystal elastic constants. The polycrystalline elastic constants are needed to calculate accurate elastic stresses from the measured elastic strains. A simultaneous determination of complete strain tensor and texture is possible by Rietveld refinement of diffraction measurements collected at different specimen orientations. Therefore, all the strain and texture parameters can be obtained along with structural, microstructural, compositional, and other information for all the crystalline phases. The method is generally applicable and especially suitable for determination of stress and texture in multiphase materials.
The method to obtain strain tensor is explained in the following publication:
The following publication proposes a method to determine texture-weighted strain/stress orientation distribution function and average strain/stress tensors by Rietveld refinement for arbitrary crystal symmetry:
Strain and defects by analyzing diffraction-line broadening
Many crystalline lattice imperfection will cause diffraction-line broadening. Dislocations, vacancies, interstitials, substitutions, and similar defects manifest themselves through the lattice strain. If a crystal is broken into smaller incoherently diffracting domains by dislocation arrays, stacking faults, twins, or another extended imperfections, then domain-size broadening occurs. By analyzing angle dependence of the line broadening it is possible to distinguish and quantify these defects. However, although the understanding for these basic facts exists for a relatively long time, there is no single coherent theory which would be applicable irrespectively of crystalline symmetry, degree of diffraction-line broadening, and so on.
The following reviews explain more thoroughly the current status in this field:
Phenomenological approaches to line-broadening analysis assume that the size-broadened and strain-broadened line profiles can be approximated by simple analytical functions. During decades of research, it became more and more obvious that neither Lorentz (Cauchy) nor Gauss functions can adequately model either size or strain effect. However, the Voigt-function (a convolution of Lorentz and Gauss functions), as a model for both size-broadened and strain-broadened profiles ("double-Voigt" method), may be more realistic and accurate. On assumption of Gaussian distribution of strains, the relationship between parameters obtained by the Warren-Averbach approximation and integral-breadth methods becomes possible. Moreover, some common occurrences in Warren-Averbach analysis, particularly the "hook" effect, functional dependence of mean-square strain on averaging distance, and ratio of volume-weighted to the are-weighted domain size, all follow from the "double-Voigt" model.
The "double-Voigt" model is covered in the following publications:
Applications of line-broadening analysis
Ferroelectrics
We studied changes of residual stress and defects that occur upon poling of ferroelectric BaTiO3 polycrystals by high-resolution synchrotron-radiation diffraction. BaTiO3 polycrystals are studied increasingly because the particle size, which has important influence on structure and physical properties, is controlled easily. The existence of a distinct severely textured and strained surface layer was detected. Most likely, this layer has the same tetragonal structure as the main fraction. Diffraction-line-broadening analysis shows large microstructural changes, especially along the direction of spontaneous-polarization and poling-field vector. The inhomogeneous strain upon poling is about the same order of magnitude as the strain caused by electrostriction during poling and indicates a substantial increase of the dislocation density. Dislocations play an important role in bulk microstructural changes that occur upon poling. The dislocation density is on the order of 109/cm2 and an associated strain-energy increase of about 20 kJ/m3. This implies that the application of an external poling field generates defects in the structure and increases the internal stress. The increase of internal stress influences the ferroelectric and phase-transition temperatures. Moreover, the increase of both internal stress and defect concentration may have adverse consequences on both polycrystalline and epitaxial thin films through the accelerated degradation of dielectric properties. Because some dislocation reactions lead to microcracking, this may even result in the mechanical failure.
We also studied pristine, W and Mn 1% doped Ba0.6Sr0.4TiO3 epitaxial thin films grown on the LaAlO3 substrate that were deposited by pulsed-laser deposition (PLD). Dielectric and ferroelectric properties were determined by the capacitance measurements and X-ray diffraction was used to determine both residual elastic strains and defect-related inhomogeneous strains by analyzing diffraction line shifts and line broadening, respectively.We found that both elastic and inhomogeneous strains are affected by doping. This strain correlates with the change in Curie-Weiss temperature and can qualitatively explain changes in dielectric loss. To explain the experimental findings, we model the dielectric and ferroelectric properties of interest in the framework of the Landau-Ginzburg-Devonshire thermodynamic theory. As expected, an elastic-strain contribution due to the epilayer-substrate misfit has an important influence on the free-energy. However, additional terms that correspond to the defect-related inhomogeneous strain had to be introduced to fully explain the measurements.
High-Tc superconductors
Most high-Tc superconductors contain numerous crystalline defects, such as substitutions, vacancies, twin and stacking faults, and dislocations simultaneously. Both point and extended defects relate closely to their physical properties. Moreover, superconductors show weak diffraction-line broadening (due to high annealing temperatures) and high degree of peak overlapping (because of relatively low crystal symmetries), which makes it very difficult to analyze both presence and abundance of defects by classical diffraction methods. Diffraction line-broadening analysis of (La-M)2CuO4 and Bi-Cu-O series of superconductors was carried out. In the former, the strains originate from dislocations and from different sizes of host and dopant ions. Domain sizes of all compounds are larger in the c-direction than in the a-b plane, which indicates existence of stacking faults and twins. In the latter, larger strains exist in the c-direction than in the a-b plane, which measures stacking disorder perpendicular to the two-dimensional weakly-bonded BiO double layers.
An overview of the method and applications to high-Tc superconductors is given here:
Reactor-pressure-vessel ferritic steels
In low-alloyed bcc steels, the most important origin of strain-related line broadening may be twofold: second-phase precipitates and dislocations. If precipitates are small, impurity atoms have to assume the crystalline structure of the host lattice, that is, the precipitates are coherent with the matrix. If the radii of impurity and host atoms are different, this causes a distortion of the host lattice close to the precipitate-matrix interface. In a simple isotropic elastic-continuum misfit-sphere approximation, precipitates cause an overall expansion of the host lattice, which would result in the change of lattice parameters. However, the effect of local distortion of the host lattice in the vicinity of precipitates is an inhomogeneous (local) strain that causes diffraction-line broadening.
A particular problem in low-alloyed bcc steels used for reactor-pressure vessels is embrittlement caused by formation of copper-rich precipitates (CRP). The formation of small (1-2 nm) CRPs is greatly facilitated by large neutron-irradiation damage. Because the CRPs are so small, it is difficult to monitor the kinetics of their formation and growth directly. However, small CRPs are coherent with the bcc matrix, which causes local matrix strain and interaction with the dislocation strain fields, thus impeding the dislocation mobility. As CRPs grow, coherency strain and dislocation density and their arrangement changes. At some critical size of CRPs, the bulk crystal structure of copper (fcc) is achieved and CRPs are no longer coherent with the matrix, which relieves the matrix strain. Thus, it is possible to monitor the changes of mechanical properties (strength, hardness, ductility, embrittlement) through microstructural parameters, such as strain and defect abundance and arrangement.