Structural rigidity

Abstract: Series Preface. Preface. Rigidity Theory. Generic and Abstract Rigidity B. Servatius, H. Servatius. Rigidity of Molecular Structures: Generic and Geometric Analysis W. Whiteley. Tensegrity Structures: Why Are They Stable? R. Connelly. The Role of Tensegrity in Distance Geometry T.F. Havel. Applications to Networks. Comparison of Connectivity and Rigidity Percolation C.F. Moukarzel, P.M. Duxbury. Rigidity Percolation on Trees P.L. Leath, C. Zeng. Rigidity as an Emergent Property of Random Networks: A Statistical Mechanical View P.M. Goldbart. Granular Matter Instability: A Structural Rigidity Point of View C.F. Moukarzel. Rigidity and Memory in a Simple Glass P. Chandra, L.B. Ioffe. Constraint Theory, Stiffness Percolation and the Rigidity Transition in Network Glasses J.C. Phillips. Topologically Disordered Networks of Rigid Polytopes: Applications to Noncrystalline Solids and Constrained Viscous Sintering P.K. Gupta. Rigidity Constraints in Amorphization of Singly- and Multiply-Polytopic Structures L.W. Hobbs, et al. Floppy Modes in Crystalline and Amorphous Silicates M.T. Dove, et al. Generic Rigidity of Networks Glasses M.F. Thorpe, et al. Rigidity Transition in Chalcogenide Glasses P. Boolchand, et al. Rigidity, Fragility, Bond Models and the `Energy Landscape' for Covalent Glassformers C.A. Angell. Entropic Rigidity B. Joos, et al. Applications to Proteins. Molecular Dynamics and Normal Mode Analysis of Biomolecular Rigidity D.A. Case. Efficient Stochastic Global Optimization for Protein Structure Prediction Y. Zhou, R. Abagyan. Flexible and Rigid Regions in Proteins D.J. Jacobs, et al. Flexibly Screening for Molecules Interacting with Proteins V. Schnecke, L.A. Kuhn. Studying Macromolecular Motions in a Database Framework: From Structure to Sequence M. Gerstein, et al. List of Participants. Index.

Abstract: The average and local structure of the oxides Ba2SiO4, BaAl2O4, SrAl2O4, and Y2SiO5 are examined to evaluate crystal rigidity in light of recent studies suggesting that highly connected and rigid structures yield the best phosphor hosts. Simultaneous momentum-space refinements of synchrotron X-ray and neutron scattering yield accurate average crystal structures, with reliable atomic displacement parameters. The Debye temperature ΘD, which has proven to be a useful proxy for structural rigidity, is extracted from the experimental atomic displacement parameters and compared with predictions from density functional theory calculations and experimental low-temperature heat capacity measurements. The role of static disorder on the measured displacement parameters, and the resulting Debye temperatures, are also analyzed using pair distribution function of total neutron scattering, as refined over varying distance ranges of the pair distribution function. The interplay between optimal bonding in the structure, s...