Matches in SemOpenAlex for { <https://semopenalex.org/work/W11962172> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W11962172 abstract "Lattice models based upon empirical two-body potential functionsare used to predict the elastic constants of “mantle-candidate” mineralsat high pressures for direct comparison with seismic velocity profiles.The method of long waves, originally formulate d by Born and his coworkers,has been applied to solids in the rock salt, spinel, and rutilestructures. Calculations for NaCl (rock salt), MgO (rock salt), Al_2MgO_4(spinel), and TiO_2 (rutile) are compared with recent high-precisionultrasonic data. The effect of van der Waals forces and second-neighboranion-anion interactions is shown to be small. The NaCl and MgO dataare best fit with an exponential cation-anion repulsive potential. Theelastic constants of MgO cannot be well fit unless the ionicity (valenceproduct) is lowered to 0.7 of its full ionic value. For NaCl this is notrequired. The shear instability (C_(44) = 0) is predicted for both NaCl andMgO, but the exact pressure is sensitive to the details of the potential. Using the Mg-O two-body potential found for periclase, Al_2MgO_4spinel was investigated using only two pieces of input datum, K and ρ.Although the predicted elastic constants were in good agreement with thedata, the pressure derivatives were not. The discrepancy is caused bya large contribution from the internal deformations which occur in allnon-centro symmetric structures. The same result was found for TiO_2. Arelaxation of the rigid-ion and central-force approximations may correctthis discrepancy. Using the Mg-O bond parameters found for periclase and theSi-Q bond parameters found from K and ρ of stishovite, the elasticproperties of the high-pressure polymorph δ–Mg_2SiO_4 spinel werepredicted. The predicted equilibrium density was in agreement withprevious experimental extrapolations; the predicted μ parameter wasin agreement with prior estimates based on bond-length arguments, andthe predicted bulk modulus was in agreement with prior systematicsestimates. However, the internal deformation contribution againdominated the pressure derivatives and caused both the predicted V_pand V_s to be lower than the corresponding seismic velocities in thespinel region of the mantle. A comparison of MgO (rock salt) andSiO_2 (stishovite) with the seismic profiles for the post-spinel lowermantle shows a discrepancy in both absolute value and gradient. Unlikethe silicate spinel, this is not obviously caused by the internal deformations.The lattice models predict that both TiO_2 and stishovite willbecome unstable in shear (1/2 (C_(11) – C_(12) = 0) at high pressure. Other methods of using laboratory data to interpret seismicprofiles are reviewed. Birch's formulation of isotropic finite straintheory is corrected and used to test the homogeneity and adiabaticityof the lower mantle of recent earth-inversion models. Systematics areshown to be insufficient to treat the shear properties. Although latticemodels are limited by empirical approximations to the complex bondingforces, the empiricism is on a more basic level than that of velocitydensity systematics previously used to interpret seismic profiles. Byusing lattice models, one gains the natural dependence of both the compressionaland shear properties on the crystal structure." @default.
- W11962172 created "2016-06-24" @default.
- W11962172 creator A5018706842 @default.
- W11962172 date "1971-01-01" @default.
- W11962172 modified "2023-09-24" @default.
- W11962172 title "Seismological applications of lattice theory" @default.
- W11962172 doi "https://doi.org/10.7907/s6b1-6n30." @default.
- W11962172 hasPublicationYear "1971" @default.
- W11962172 type Work @default.
- W11962172 sameAs 11962172 @default.
- W11962172 citedByCount "2" @default.
- W11962172 crossrefType "dissertation" @default.
- W11962172 hasAuthorship W11962172A5018706842 @default.
- W11962172 hasConcept C121332964 @default.
- W11962172 hasConcept C145148216 @default.
- W11962172 hasConcept C168900304 @default.
- W11962172 hasConcept C178790620 @default.
- W11962172 hasConcept C185592680 @default.
- W11962172 hasConcept C191897082 @default.
- W11962172 hasConcept C192562407 @default.
- W11962172 hasConcept C199289684 @default.
- W11962172 hasConcept C2776230739 @default.
- W11962172 hasConcept C2777889555 @default.
- W11962172 hasConcept C2778758504 @default.
- W11962172 hasConcept C2780942940 @default.
- W11962172 hasConcept C2984729377 @default.
- W11962172 hasConcept C97355855 @default.
- W11962172 hasConceptScore W11962172C121332964 @default.
- W11962172 hasConceptScore W11962172C145148216 @default.
- W11962172 hasConceptScore W11962172C168900304 @default.
- W11962172 hasConceptScore W11962172C178790620 @default.
- W11962172 hasConceptScore W11962172C185592680 @default.
- W11962172 hasConceptScore W11962172C191897082 @default.
- W11962172 hasConceptScore W11962172C192562407 @default.
- W11962172 hasConceptScore W11962172C199289684 @default.
- W11962172 hasConceptScore W11962172C2776230739 @default.
- W11962172 hasConceptScore W11962172C2777889555 @default.
- W11962172 hasConceptScore W11962172C2778758504 @default.
- W11962172 hasConceptScore W11962172C2780942940 @default.
- W11962172 hasConceptScore W11962172C2984729377 @default.
- W11962172 hasConceptScore W11962172C97355855 @default.
- W11962172 hasLocation W119621721 @default.
- W11962172 hasOpenAccess W11962172 @default.
- W11962172 hasPrimaryLocation W119621721 @default.
- W11962172 hasRelatedWork W1901421741 @default.
- W11962172 hasRelatedWork W1969854712 @default.
- W11962172 hasRelatedWork W1972773998 @default.
- W11962172 hasRelatedWork W1979549076 @default.
- W11962172 hasRelatedWork W1990019041 @default.
- W11962172 hasRelatedWork W1996100216 @default.
- W11962172 hasRelatedWork W2004928367 @default.
- W11962172 hasRelatedWork W2027146594 @default.
- W11962172 hasRelatedWork W2028901741 @default.
- W11962172 hasRelatedWork W2035837012 @default.
- W11962172 hasRelatedWork W2041825588 @default.
- W11962172 hasRelatedWork W2058180080 @default.
- W11962172 hasRelatedWork W2068607469 @default.
- W11962172 hasRelatedWork W2087023901 @default.
- W11962172 hasRelatedWork W2094564640 @default.
- W11962172 hasRelatedWork W2139604341 @default.
- W11962172 hasRelatedWork W2255781310 @default.
- W11962172 hasRelatedWork W2315149106 @default.
- W11962172 hasRelatedWork W3041134640 @default.
- W11962172 hasRelatedWork W33592996 @default.
- W11962172 isParatext "false" @default.
- W11962172 isRetracted "false" @default.
- W11962172 magId "11962172" @default.
- W11962172 workType "dissertation" @default.