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Cremons, Daniel R. Specimen holders capable of being heated to over °C have provided insight into myriad kui kasi on haiget teinud, including nanoscale thermal transport, structural phase transitions, and catalytic reactions.
In order for such studies to be accurate and precise, direct determination of the specimen temperature — rather than the heating-element temperature — is critical. Further, such methods should be versatile in that any temperature across a wide range may be measured, irrespective of single-indicator properties specific to the specimen e.
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Here, we describe a rigorous approach to direct, in situ thermometry of TEM specimens that exploits lattice thermal expansion and the resultant decrease in diffraction-vector magnitude in reciprocal space.
Via sub-pixel measurement of reciprocal-lattice-vector magnitudes, picometer increases in lattice parameters are measured over a continuous temperature range and compared to those expected from the coefficient of thermal expansion.
Statistical treatment of several experimental trials conducted on nanostructured aluminum thin films shows excellent agreement with both theory and indirect measurement of the in situ heating holder.
Additionally, we illustrate how uncontrolled, thermally-induced variation in single-crystal orientation leads to modulation of the excitation error and, therefore, the Bragg-spot intensities resulting in a convolution of heating and tilting effects, thus complicating temperature determination via the Debye—Waller effect.
Mexico ; Cadena A, A. Mexico ; Kryvko, A. Mexico The texture analysis using X-ray diffraction XRD implies measurement of pole figures Pf from the diffracted intensities considering the model of kinematical dispersion.
The extinction phenomenon results in a decrease of diffracted intensity and that in turn in a decrease of pole densities Pds. The phenomenon appears in the kinematical theory of XRD as the primary extinction and the secondary extinction to characterize the loss of intensity of kinematical dispersion. In turn, the static Debye-Waller factor is an integral characteristic of defects in crystals that is introduced in the kinematical theory of XRD and also is used in dynamical theory of XRD.
In this work the correlation between the primary extinction coefficient and the static Debye-Waller factor in the case of textured nickel was determined.
The value of static Debye-Waller factor was determined from the value of the calculated primary extinction coefficient. For the evaluation there were used Pds in the maxima of Pf obtained for and reflections with Mo Kα radiation, and the Pds in the maxima of Pf obtained for the first and second orders of these reflections with Cu Kα and Co Kα radiations.
Cremons, Daniel R.
There were calculated the dislocation densities in grains using values of static Debye-Waller factor and the extinction coefficients. The dislocation densities calculated from these two characteristics are practically equal. DWFs are presented in terms of cumulant expansion up to the fourth order and the many-body effects are taken into vesanna spin valutab in the present one-dimensional model based on the first shell near neighbor contribution approach used in the derivations of the anharmonic effective potential and XAFS cumulants where Morse potential is assumed to describe the single-pair atomic interaction.
Analytical expressions for the dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants have been derived based on the many-body perturbation approach. Thermodynamic properties and anharmonic effects in XAFS of vesanna spin valutab crystals described by the obtained cumulants have been in detail discussed.
The advantage and efficiency of the present theory are illustrated by good agreement of the numerical results for Mo, Fe and W with experiment.