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

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

3. Typical Computational Experiment Damped dynamics P = 150 GPa

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

5. Thermal EoS Volume (Å 3 ) F (Ry) 4 th order finite strain equation of state staticzero-point thermal MgO Static 300K Exp (Fei 1999) V (Å 3 ) 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 - - - - 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 Experimental confirmation (Funamori and Jeanloz, Science (1997)) Comparison with EDS (Jephcoat, Hemley, Mao, Am. Mineral.(1986)) 175 GPa corundum Rh 2 O 3 (II) 50/50% mixture

8. Phase transitions in Al 2 O 3 Duan, Wentzcovitch, & Thomson, PRB (1998)

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

10. Optical transitions in ruby Intra-d transitions in Cr 3+ (d 3 )

11. Ab initio calculation of Al 2 O 3 :Cr (80 atoms/cell) (Duan, Paiva, Wentzcovitch, Fazzio, PRL (1998))

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

13. Eigenvalue Spectra Corundum Rh 2 O 3 (II)

14. Deformation parameters Orbital deformation parameters Multiplet method for d-electrons in X-tal field (Sugano, Tanabe, & Kamimura, 1971) (Fazzio, Caldas, & Zunger, PRB (1984) 22

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

16.  -Cr 2 O 3 AFM T N =308 K  =(2.76±0.03)  B dT N /dP=-1.5K/kbar R3c a = 5.35 A  =55.1 o o

17. landau Free energy expansion: M 1, M 2 – (AFM) sub-lattice magnetizations U = u 33 – uniaxial strain; V =  u ii – hydrostatic; Minimizing  (equilibrium) = -1,1,0 for AFM, FM, PM U PM = (U AFM + U FM )/2 V PM = (V AFM + V FM )/2, therefore … PM lattice parameters are averages of AFM and FM’s

18. Compressive behavior of Cr 2 O 3

19. Phase transition in Cr 2 O 3 Corundum  Rh 2 O 3 (II) phase transition AFM at 14 GPa, PM at 18 GPa. Experimental confirmation: Rheki & Dubrovinsky (2001) unpublished P T = 30GPa, T= 1500 K. Dobin, Duan, & Wentzcovitch, PRB 2000

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 Rh 2 O 3 (II) transition in Cr 2 O 3 near of below 30 GPa To be clarified: Study of Y line above 30 GPa NEXAFS under pressure… …also: Pressure dependence of T N and Is there hysteresis in this Neel transition?