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Structural and Optical transitions in ruby

Structural and Optical transitions in ruby. Renata Wentzcovitch. U of MN. Collaborators: W. Duan (U. of MN), G. Paiva (USP), & A. Fazzio (USP) Support: NSF, CNPq, and FAPESP. Invariant Variable Cell Shape MD. Wentzcovitch , (91). •Self-consistent MD (PWPP)

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Structural and Optical transitions in ruby

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  1. Structural and Optical transitions in ruby Renata Wentzcovitch U of MN Collaborators: W. Duan (U. of MN), G. Paiva (USP), & A. Fazzio (USP) Support: NSF, CNPq, and FAPESP

  2. Invariant Variable Cell Shape MD Wentzcovitch, (91) •Self-consistent MD (PWPP) Wentzcovitch & Martins, (91), Wentzcovitch et al.(92,93) •Troullier-Martins pseudopotentials •LSDA (Ceperley & Alder) i=vector index j=cart. index

  3. Typical Computational Experiment Damped dynamics P = 150 GPa

  4. abcxP (a,b,c)th < (a,b,c)exp ~ 1% Tilt angles th - exp < 1deg Kth = 259 GPa K’th=3.9 Kexp = 261 GPa K’exp=4.0 ( Wentzcovitch, Martins, & Price, 1993) ( Ross and Hazen, 1989)

  5. Thermal EoS MgO - static zero-point - F (Ry) - thermal - 4th order finite strain equation of state Static300KExp (Fei 1999) V (Å3) 18.5 18.8 18.7 K (GPa) 169 159 160 K´ 4.18 4.30 4.15 K´´(GPa-1) -0.025 -0.030 Volume (Å3) Phonons from DFPT

  6. Structural Transitions in Ruby • PIB (Cynn et al.-1980 and Bukowinski – 1994). Between 4 and 148 GPa • LAPW (Marton & Cohen – 1994) 90 GPa • Pseudopotentials (VCS-MD) (Thomson, Wentzcovitch, & Bukowinski), Science (1996)

  7. X-ray diffraction • Comparison with EDS (Jephcoat, Hemley, Mao, Am. Mineral.(1986)) 175 GPa 50/50%mixture corundum Rh2O3 (II) • Experimental confirmation (Funamori and Jeanloz, Science (1997))

  8. Phase transitions in Al2O3 Duan, Wentzcovitch, & Thomson, PRB (1998)

  9. The high pressure ruby scale Forman, Piermarini, Barnett, & Block, Science (1972) (R-line) Bell, Xu,& Mao, in Shock Waves in Condensed Matter, ed. by Gupta (1986) Mao, Xu, & Bell, JGR (1986)

  10. Optical transitions in ruby Intra-d transitions in Cr3+ (d3)

  11. Ab initio calculation of Al2O3:Cr (Duan, Paiva, Wentzcovitch, Fazzio, PRL (1998)) (80 atoms/cell)

  12. Structural properties of the color center Duan, Paiva, Wentzcovitch, & Fazzio, PRL (1998)

  13. Corundum Eigenvalue Spectra Rh2O3 (II)

  14. Multiplet method for d-electrons in X-tal field Deformation parameters (Sugano, Tanabe, & Kamimura, 1971) (Fazzio, Caldas, & Zunger, PRB (1984) Orbital deformation parameters 2 2

  15. Optical transitions X Pressure (Duan, Paiva, Wentzcovitch,Fazzio, PRL (1998)

  16. -Cr2O3 AFM TN=308 K =(2.76±0.03) B dTN/dP=-1.5K/kbar R3c a = 5.35 A =55.1 o o

  17. • Free energy expansion: landau M1, M2 – (AFM) sub-lattice magnetizations • U = u33 – uniaxial strain; V =  uii – hydrostatic; • Minimizing  (equilibrium) • = -1,1,0 for AFM, FM, PM • UPM = (UAFM + UFM)/2 VPM = (VAFM + VFM)/2, therefore … PM lattice parameters areaverages of AFM and FM’s

  18. Compressive behavior of Cr2O3

  19. Phase transition in Cr2O3 Dobin, Duan, & Wentzcovitch, PRB 2000 • Corundum  Rh2O3 (II) phase transition AFM at 14 GPa, PMat 18 GPa. • Experimental confirmation: Rheki & Dubrovinsky (2001)unpublished PT = 30GPa, T= 1500 K.

  20. Conclusions • Calculated P-induced optical shifts in ruby agree well with experiments • Phase transformation should affect mainly the U and Y absorption lines • New interpretation of observed anomalies in absorption lines • Prediction and confirmation of corundum to Rh2O3 (II) transition in Cr2O3 near of below 30 GPa • To be clarified: Study of Y line above 30 GPa NEXAFS under pressure… • …also: Pressure dependence of TN and Is there hysteresis in this Neel transition?

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