Crystal structure prediction for a given chemical composition has long been a challenge in condensed-matter science. We have recently shown that experimental powder x-ray diffraction (XRD) data are helpful in a crystal structure search using simulated annealing, even when they are insufficient for structure determination by themselves [Tsujimoto et al., Phys. Rev. Mater. 2, 053801 (2018)]. In the method, the XRD data are assimilated into the simulation by adding a penalty function to the physical potential energy, where a crystallinity-type penalty function, defined by the difference between experimental and simulated diffraction angles was used. To improve the success rate and noise robustness, we introduce a correlation-coefficient-type penalty function adaptable to XRD data with significant experimental noise. We apply the new penalty function to SiO2 coesite and ɛ-Zn(OH)2 to determine its effectiveness in the data assimilation method.
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According to the definition of the correlation coefficient, DCC can take values from 0 to 2. However, the correlation coefficient only becomes negative if calculated XRD pattern is inversely proportional to the experimental one. Intensity of XRD pattern never shows a negative value. In addition, the averaged intensity, is negligible compared to that of the peaks in a discrete XRD pattern. Therefore, DCC hardly becomes larger than 1 in practice.
The potential energy for the obtained ɛ-Zn(OH)2 structures (≈–190.3 eV) is slightly larger than that of reference ɛ-Zn(OH)2 (–190.4 eV). This suggests that the hydrogen bond orientation in the obtained structure does not perfectly agree with that of the reference. However, this energy difference is considered to be within the range of error, because this energy difference (2.5 meV/atom = 0.1 eV for 40 atoms) is much smaller than thermal energy at 300 K (=25 meV/atom = 1 eV for 40 atoms). In addition, in terms of XRD pattern, we can hardly distinguish the obtained structure from the reference one, since DCC is about 10−5. Therefore, here, we regard the obtained structure with total energy at around –190.3 eV as ɛ-Zn(OH)2.
