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Structural and Optical Transitions in Ruby: Insights from Molecular Dynamics Simulations

This study explores the structural and optical transitions in ruby (Al2O3:Cr) under high pressure through molecular dynamics simulations and first-principles calculations. Collaborating with researchers from the University of Minnesota and USP, we investigate phase transformations, specifically the transition to Rh2O3(II) at pressures near 30 GPa. Our findings reveal how pressure affects optical properties and characterizes the behavior of absorption lines in response to structural changes. This research is supported by NSF, CNPq, and FAPESP, providing a deeper understanding of ruby's behavior under extreme conditions.

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Structural and Optical Transitions in Ruby: Insights from Molecular Dynamics Simulations

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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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