Strain energy density in the x-ray powder diffraction from mixed crystals and alloys

Rosenberg, Yu.; Machavariani, V Sh; Voronel, A.; Garber, S. R.; Rubshtein, A. P.; Frenkel, Anatoly I.; Stern, E. A.

doi:10.1088/0953-8984/12/37/307

Cited by 96 publications

(52 citation statements)

References 12 publications

(18 reference statements)

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“…This method defines the crystallite size in terms of a mean effective size of the coherently scattering region normal to the reflecting planes [35]. The Scherrer relation between crystallite size and integral breadth is given by:…”

Section: Scherrer Methodmentioning

confidence: 99%

X-ray diffraction line profile analysis of KBr thin films

2016

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In the present work, the microcrystalline characteristics of KBr thin films have been investigated by evaluating the breadth of diffraction peak. The Williamson-Hall, the Size-Strain Plot and the single line Voigt methods are employed to deconvolute the finite crystallite size and microstrain contribution from the broaden X-ray profile. The texture coefficient and dislocation density have been determined along each diffraction peak. Other relevant physical parameters such as stress, Young's modulus and energy density are also estimated using Uniform Stress Deformation and Uniform Deformation Energy Density approximation of Williamson-Hall method.

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Section: Scherrer Methodmentioning

confidence: 99%

X-ray diffraction line profile analysis of KBr thin films

2016

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“…We suggest that these three methods are also suitable models for the evaluation of the crystallite size of ZnO nanoparticles. Rosenberg et al [28] observed that for metallic samples with cubic structures, the uniform deformation energy model is suitable. We have made a comparison of the estimated microstrain e values of ZnO nanoparticles annealed at 450°C reported by Dole et al [29] by W-H models, with that of our present values.…”

Section: Size-strain Plot (Ssp)mentioning

confidence: 99%

Estimation of lattice strain in ZnO nanoparticles: X-ray peak profile analysis

2014

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ZnO nanoparticles were synthesized from chitosan and zinc chloride by a precipitation method. The synthesized ZnO nanoparticles were characterized by Fourier transform infrared spectroscopy, X-ray diffraction peak profile analysis, Scanning electron microscopy, Transmission electron microscopy and Photoluminescence. The X-ray diffraction results revealed that the sample was crystalline with a hexagonal wurtzite phase. We have investigated the crystallite development in ZnO nanoparticles by X-ray peak profile analysis. The Williamson-Hall analysis and size-strain plot were used to study the individual contributions of crystallite sizes and lattice strain e on the peak broadening of ZnO nanoparticles. The parameters including strain, stress and energy density value were calculated for all the reflection peaks of X-ray diffraction corresponding to wurtzite hexagonal phase of ZnO lying in the range 20°-80°using the modified form of Williamson-Hall plots and size-strain plot. The results showed that the crystallite size estimated from Scherrer's formula, Williamson-Hall plots and size-strain plot, and the particle size estimated from Transmission electron microscopy analysis are very much inter-correlated. Both methods, the X-ray diffraction and Transmission electron microscopy, provide less deviation between crystallite size and particle size in the present case.

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“…However, in nanoparticles the strain is not uniform in all directions, so uniform stress deformation model & uniform energy density deformation model take into account of the anisotropic nature of Young modulus of the crystal and are hence more realistic [29]. The isotropic lattice strain, ε hkl in UDM is replaced σ/E hkl , where E hkl is the young modulus in the direction perpendicular to the set of planes (hkl).…”

Section: Uniform Stress Deformation Modelmentioning

confidence: 99%