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A first-Principles Study of Mechanical Properties of Ta 2 O 5

A first-Principles Study of Mechanical Properties of Ta 2 O 5

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A first-Principles Study of Mechanical Properties of Ta 2 O 5

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  1. A first-Principles Study of MechanicalProperties of Ta2O5 Hai-Ping Cheng Department of Physics University of Florida Workshop on Optical Coatings in Precision Measurements Cal Tech, Paseadena CA March 20-21, 2008

  2. Thermal Noise and Mechanical Properties The power spectral density of displacement or position noise caused by thermal noise in the mirror coatings is eff: effective mechanical loss angle of the mirror; kB, Boltzmann’s constant, T: temperature,  : radius of the Gaussian laser beam, d: thickness of the coatings, Y: Young’s modulus,  : the Poisson ratio of the substrate. quantities without subscript are properties of the substrate, and the parallel/perpendicular subscripts represent the coating material properties parallel/perpendicular to the face of the substrate. The critical parameter is the effective loss angle eff which includes contributions from the substrate ( ) and the coatings. Harry et al.

  3. Thermal Noise in glasses Relaxations of glasses affect: Neutron and light scattering Sound wave attenuation Dielectric loss A direct relation between a microscopic quantity V and a macro-scopic measurement ” is (Wiedersich et al. PRL (2000) 2718 : light scattering scattering susceptility, V: barrier, Q-1: internal friction g(V): barrier distribution, : relaxation time Thermal noise relates to Q via Young’s modules, Poisson ratio,… G. Harry et al. Class Quantum. Grav. 19 (2002) 897-927 Recent reference: G.Harry talk in LIGO/Virgo Thermal Noise Workshop October 2006

  4. Methods for molecular modeling Quantum calculations: solving equations for electrons and then nuclei Classical simulation: solving equations for nuclei with empirical force fields

  5. Computational Methods VASP plane-wave code  Self-consistent density functional theory  Projector augmented wave (PAW) potentials  Perdew-Wang 91 GGA exchange correlation functional  Cutoff kinetic energy for the plane-wave basis set: 520 eV  All configurations explicitly relaxed and calculated Models  Low-temperature Ta2O5: - and -phases  High-temperature Ta2O5: Tetrahedral-structure and octahedron-hexagonal bi-pyramid-octahedron molecular building block

  6. Bulk Modulus -Ta2O5 – Orthorhombic Structure * Sahu et al. Phys. Rev. B69, 165202 (2004)

  7. Bulk Modulus -Ta2O5 – Hexagonal Phase Unit cell: 4 Ta and 10 O atoms * Sahu et al. Phys. Rev. B69, 165202 (2004)

  8. Bulk Modulus High Temperature -Ta2O5 (Tetragonal Structure) Unit cell: 12 Ta and 32 O atoms * Liu et al. Acta Materialia 55, 2385 (2007)

  9. Ta O Another High Temperature -Ta2O5 • The structural model is based on edge sharing of an oxygen octahedron-hexagonal bi-pyramid-octahedron molecular building block unit that repeats 4 times per unit cell.* * Makovec et al. Journal of Solid State Chemistry 179, 1782 (2006)

  10. Relaxed Structure Unit cell: 12 Ta and 28 O atoms Unit Cell 2x2x2 Cell along [100] direction

  11. Bulk Modulus * Makovec et al. Journal of Solid State Chemistry 179, 1782 (2006)

  12. Stress in the thin film Young’s modulus and Poisson’s ratio for the film Temperature Thermal expansion coefficients of the film and the substrate Hollman et al. Surf. Coat. Technol. 90, 234 (1997); Roazaud et al. Thin Solid Films, 270, 270 (1995); Perry et al. Surf. Coat. Technol. 81, 17 (1996); Read et al. Meas. Sci. Technol. 9, 676 (1998); Tien et al. J. Mod. Opt. 47, 1681 (2000). Elastic’s Modulus (Experiments) • Proposed methods to determine elastic modulus of thin film: • Direct measurements – tensile testing method , bending tests , mechanical deflection method ; • Non-contact measurements based on interferometric principles (not to damage the tested materials) ; • Phase shifting interferometry (PSI) technique . Stress-temperature measurements on Ta2O5 films deposited on two different substrate materials with known thermal expansion coefficients, Young’s moduli and Poisson’s ratios:

  13. HT- Ta2O5 (Tetragonal Structure) Y = 337 GPa -Ta2O5 (Hexagonal Phase) Y = 758 GPa HT- Ta2O5 (4 Octahedron-Hexagonal Bi-Pyramid-Octahedron Building Blocks) Y = 232 GPa Young’s Moduli (First-Principles Calculations)

  14. Elastic Moduli & Ta-O Binding Energies *Crooks et al. Class Quantum Grav. 23, 4953 (2006)

  15. About Silica Bottle neck: locating 10n barriers Need new agorithms or different approaches

  16. Silica: Bond angle distribution