鞋潊敳桰删-EquationofState.pptVIP

Equation of State Thermal Expansion Bulk Modulus Shear Modulus Elastic Properties Equation of State (EoS) a = coefficient of thermal expansion (K-1) b = compressibility KT = 1/b = isothermal bulk modulus K’T = (?K/?P)T Ks = adiabatic bulk modulus Ks = Kt(1+ agT) g = Thermal Gruneisen parameter G Shear Modulus Volume thermal expansion Thermal expansion at zero pressure V = V0 (1 + aT) a(T) = a0 + a1T + a2T2 Can be measured by XRD or mechanically. Fei Y. (1995) Mineral Physics and Crystallography, AGU Reference Shelf 2, 29-44. Ultrasonics Transducers generate acoustic signal (MHz or GHz) Interferometry allows measurement of velocities to one part in 104. Precision increases with frequency Transducer is hexagonal ZnO and generates P or S waves. But S waves don’t go beyond MHz Recently Hartmut’s group has developed a GHz S-wave generator. Elastic Properties Stress is a second rank tensor, sij Strain is a second-rank tensor, eij The elastic tensor is fourth-rank cijkl c can be represented as 6x6 matrix for cubic c11 = c22 = c33, c44 and c12 are non-zero Elastic Moduli Cubic (3terms) c11, c44, c12 Tetragonal (6 or 7) c11, c33, c44, c66, c12, c13, c23, (c16) Hexagonal(5) c11, c33, c44, c12, c13 Trigonal(6 or 7) c11, c33, c44, c12, c13, c14, (c15) Orthorhombic: (9) c11, c22, c33, c44 c55 c66, c12, c13, c23 Monoclinic(13) c11, c22, c33, c44, c55, c66, c12, c13, c23, c15, c25, c35, c46 * Thermal Expansion Thermal Expansion Four-Circle Diffractometer Static Compression Static Compression Static Compression Static Compression Static Compression * * * Sheet16 Sheet15 Sheet14 Sheet13 Sheet12 Sheet11 Sheet10 Sheet9 Sheet8 Sheet7 Sheet6 Sheet5 Sheet4 Sheet3 Sheet2 Sheet1 Chart1 CS28 F-f plot P s(P) V/V0 s(V/V0) V0/V fE s(fE) sn sd s FE s(FE) K=155.8 K=5.54 K=159.2 K=3.1 Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page 3.00E-03 5.00E-03 1.00 8.00E-05 1.00 4.33E-05 .67 1.00 2.00