Matches in SemOpenAlex for { <https://semopenalex.org/work/W2019468024> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W2019468024 endingPage "A160" @default.
- W2019468024 startingPage "A152" @default.
- W2019468024 abstract "The condition that a given lattice model be stable against all small deformations is that all the eigenvalues of all the dynamical matrices be positive. The stability of several lattices is studied by calculating the dynamical matrices for a large number of wave vectors in the Brillouin zone. Central potential interactions represented by Lennard-Jones and Rydberg forms are used, and the nearest-neighbor distance $ensuremath{epsilon}$ is allowed to vary throughout a range of ifmmodepmelsetextpmfi{}10% of the value ${ensuremath{epsilon}}_{0}$ which minimizes the static lattice potential. The fcc and hcp lattices are stable for all central potentials and all values of $ensuremath{epsilon}$ studied; the bcc is stable for all values of $ensuremath{epsilon}$ for long-range central potentials; and the diamond is stable for a range of $ensuremath{epsilon}>{ensuremath{epsilon}}_{0}$ for all central potentials studied. The sum of the static lattice-potential plus the harmonic zero-point energy is minimized as a function of $ensuremath{epsilon}$, and it is found for all stable models except diamond that this procedure increases $ensuremath{epsilon}$ from ${ensuremath{epsilon}}_{0}$ by about ${ensuremath{epsilon}}_{0}ensuremath{kappa}$, where $ensuremath{kappa}=frac{ensuremath{hbar}}{{M}^{frac{1}{2}}{D}^{frac{1}{2}}{ensuremath{epsilon}}_{0}}$, with $M=mathrm{mass}mathrm{of}mathrm{ions}$ and $D=mathrm{static}mathrm{lattice}mathrm{binding}mathrm{energy}$. For diamond, however, there is no minimum in the range of $ensuremath{epsilon}$ for which the lattice is stable, for physically reasonable values of $ensuremath{kappa}$. Born has suggested that if a lattice is stable for long waves, it is stable for short waves; a counterexample has been found in the present study for the diamond lattice. A comprehensive table of accurate lattice sums is given in an Appendix." @default.
- W2019468024 created "2016-06-24" @default.
- W2019468024 creator A5054858207 @default.
- W2019468024 creator A5063034831 @default.
- W2019468024 date "1965-01-04" @default.
- W2019468024 modified "2023-09-25" @default.
- W2019468024 title "Stability of Crystal Lattices" @default.
- W2019468024 cites W1966230776 @default.
- W2019468024 cites W1974864168 @default.
- W2019468024 cites W1981507340 @default.
- W2019468024 cites W1982953458 @default.
- W2019468024 cites W2003693856 @default.
- W2019468024 cites W2004366174 @default.
- W2019468024 cites W2019225100 @default.
- W2019468024 cites W2022846310 @default.
- W2019468024 cites W2026374723 @default.
- W2019468024 cites W2029362311 @default.
- W2019468024 cites W2037859325 @default.
- W2019468024 cites W2066669004 @default.
- W2019468024 cites W2091980807 @default.
- W2019468024 cites W2121762031 @default.
- W2019468024 cites W2796590481 @default.
- W2019468024 cites W2798070843 @default.
- W2019468024 cites W2798153371 @default.
- W2019468024 cites W4255670186 @default.
- W2019468024 doi "https://doi.org/10.1103/physrev.137.a152" @default.
- W2019468024 hasPublicationYear "1965" @default.
- W2019468024 type Work @default.
- W2019468024 sameAs 2019468024 @default.
- W2019468024 citedByCount "24" @default.
- W2019468024 countsByYear W20194680242012 @default.
- W2019468024 countsByYear W20194680242013 @default.
- W2019468024 countsByYear W20194680242016 @default.
- W2019468024 countsByYear W20194680242017 @default.
- W2019468024 countsByYear W20194680242018 @default.
- W2019468024 countsByYear W20194680242020 @default.
- W2019468024 countsByYear W20194680242021 @default.
- W2019468024 countsByYear W20194680242023 @default.
- W2019468024 crossrefType "journal-article" @default.
- W2019468024 hasAuthorship W2019468024A5054858207 @default.
- W2019468024 hasAuthorship W2019468024A5063034831 @default.
- W2019468024 hasConcept C114614502 @default.
- W2019468024 hasConcept C121332964 @default.
- W2019468024 hasConcept C153015087 @default.
- W2019468024 hasConcept C158693339 @default.
- W2019468024 hasConcept C159985019 @default.
- W2019468024 hasConcept C16291881 @default.
- W2019468024 hasConcept C186370098 @default.
- W2019468024 hasConcept C192562407 @default.
- W2019468024 hasConcept C24890656 @default.
- W2019468024 hasConcept C26873012 @default.
- W2019468024 hasConcept C2776921476 @default.
- W2019468024 hasConcept C2781204021 @default.
- W2019468024 hasConcept C33923547 @default.
- W2019468024 hasConcept C37914503 @default.
- W2019468024 hasConcept C62520636 @default.
- W2019468024 hasConceptScore W2019468024C114614502 @default.
- W2019468024 hasConceptScore W2019468024C121332964 @default.
- W2019468024 hasConceptScore W2019468024C153015087 @default.
- W2019468024 hasConceptScore W2019468024C158693339 @default.
- W2019468024 hasConceptScore W2019468024C159985019 @default.
- W2019468024 hasConceptScore W2019468024C16291881 @default.
- W2019468024 hasConceptScore W2019468024C186370098 @default.
- W2019468024 hasConceptScore W2019468024C192562407 @default.
- W2019468024 hasConceptScore W2019468024C24890656 @default.
- W2019468024 hasConceptScore W2019468024C26873012 @default.
- W2019468024 hasConceptScore W2019468024C2776921476 @default.
- W2019468024 hasConceptScore W2019468024C2781204021 @default.
- W2019468024 hasConceptScore W2019468024C33923547 @default.
- W2019468024 hasConceptScore W2019468024C37914503 @default.
- W2019468024 hasConceptScore W2019468024C62520636 @default.
- W2019468024 hasIssue "1A" @default.
- W2019468024 hasLocation W20194680241 @default.
- W2019468024 hasOpenAccess W2019468024 @default.
- W2019468024 hasPrimaryLocation W20194680241 @default.
- W2019468024 hasRelatedWork W1667758839 @default.
- W2019468024 hasRelatedWork W197112097 @default.
- W2019468024 hasRelatedWork W1974691889 @default.
- W2019468024 hasRelatedWork W2010688092 @default.
- W2019468024 hasRelatedWork W2047937054 @default.
- W2019468024 hasRelatedWork W2094307869 @default.
- W2019468024 hasRelatedWork W2161763076 @default.
- W2019468024 hasRelatedWork W2203645648 @default.
- W2019468024 hasRelatedWork W2584118035 @default.
- W2019468024 hasRelatedWork W2952629275 @default.
- W2019468024 hasVolume "137" @default.
- W2019468024 isParatext "false" @default.
- W2019468024 isRetracted "false" @default.
- W2019468024 magId "2019468024" @default.
- W2019468024 workType "article" @default.