English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Small displacement methods have been successfully used to calculate thelattice dynamical properties of crystals. It involves displacing atoms by asmall amount in order to calculate the induced forces on all atoms in asupercell for the computation of force constants. Even though these methods arewidely in use, to our knowledge, there is no systematic discussion of optimaldisplacement directions from the crystal's symmetry point of view nor arigorous error analysis of such methods. Based on the group theory and pointgroup symmetry of a crystal, we propose displacement directions, with anequivalent concept of the group of $k$, deduced directly in the Cartesiancoordinates rather than the usual fractional coordinates, that maintain thetheoretical maximum for the triple product $V$ spanned by the threedisplacements to avoid possible severe roundoff errors. The proposeddisplacement directions are generated from a minimal set of irreducible atomicdisplacements that keep the required independent force calculations to aminimum. We find the error in the calculated force constant explicitly dependson the inverse of $V$ and inaccuracy of the forces. Test systems such as Si,graphene, and orthorhombic Sb2S3 are used to illustrate the method. Ourdisplacement method is shown to be very robust in treating low-symmetry cellswith a large `aspect ratio' due to huge differences in lattice parameters, useof a large vacuum height, or a very oblique unit cell due to unconventionalchoice of primitive lattice vectors. It is expected that our displacementstrategy can be used to address higher-order interatomic interactions toachieve good accuracy and efficiency.

Efficacious symmetry-adapted atomic displacement method for lattice dynamical studies