Systematic errors lattice constants

For nanocrystals, the interpretation of lattice parameter shifts is complicated by the very small dimensions of the crystallites. Because of the small crystal dimensions, the diffraction peaks are broadened as described by the Debye-Scherrer equation (106), making accurate assessment of small shifts more challenging. Systematic errors such as zero-point or sample-height offsets can also cause artificial shifts in lattice constants (107). The inclusion of an internal... 

Despite the great variety of calculational schemes employed, relativistic band structure codes have by now achieved a high level of accuracy. While for example the calculated lattice constant of fcc-Th in early publications covered a broad range of values (Fig. 1), a number of state-of-the-art relativistic full potential methods give reliable values very close to each other, about 2.5 percent below the experimental lattice constant (which is the systematic error of the LDA functional used in the calculations). Moreover, the most accurate schemes coincide in their total energies within a few mHartree per atom, a level of accuracy almost comparable to non-relativistic band structure schemes. 

Whenever HF and standard (LDA/GGA) DFT functionals yield systematically errors with opposite sign with respect to experiment, the formulation of hybrid functionals improves the accuracy of the calculations. This is the case for band gaps, phonon spectra, magnetic coupling constants, and all properties that depend on the extent of electronic localisation at either perfect or defective lattice sites. This feature is particularly important at lattice defects that break the translational symmetry of the crystal in this case, non orbital-dependent DFT functionals appear unable to localise the defect states, even in simple matrices as MgO. 

The calculated values of k ff. using RNDF/B-IV data and the HAMMER code system, are shown in Table I. Overall, the experimental results are predicted well by the data and calculational method employed. In all cases studied, calculated values of k s decrease as the mod-erator-to-fiiel volume ratio increases (for a constant rod size) or as the lattice pitch incieases. A typical result is shown in Fig. 1. Thus, it is seen that the use of U and U cross-section data from ENDF/B-IV leads to reasonable results, but systematic error trends in predicting LWR benchmark experiments. 

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