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Structural and Optical transitions in ruby
Collaborators: W. Duan (U. of MN), G. Paiva (USP), & A. Fazzio (USP)Support: NSF, CNPq, and FAPESP
Renata WentzcovitchU of MN
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Invariant Variable Cell Shape MD
h1
h2
)(thiji=vector indexj=cart. index
VPUWmL extDFTji
jiI
IIi
,
2,22
sgs T
hsr o)h(1h hhg T
Wentzcovitch, (91)
•Self-consistent MD (PWPP)Wentzcovitch & Martins, (91),Wentzcovitch et al. (92,93)
•Troullier-Martins pseudopotentials
•LSDA (Ceperley & Alder)
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Typical Computational Experiment
Damped dynamics
)(~ PI),(~ int rffr
P = 150 GPa
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abcxP
K VodPdV
Kth = 259 GPa K’th=3.9
Kexp = 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)
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Thermal EoS
qj B
qjB
qj
qj
TkV
Tk
VVUTVF
)(exp1ln
2)(
)(),(
Volume (Å3)
F (R
y)4th order finite strain equation of state
static zero-point
thermal
MgO
Static 300K Exp (Fei 1999)V (Å3) 18.5 18.8 18.7K (GPa) 169 159 160K´ 4.18 4.30 4.15K´´(GPa-1) -0.025 -0.030
-
-
-
-
Phonons from DFPT
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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)
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X-ray diffraction
• Experimental confirmation (Funamori and Jeanloz, Science (1997))
• Comparison with EDS (Jephcoat, Hemley, Mao, Am. Mineral.(1986))
175 GPa
corundum
Rh2O3 (II)
50/50% mixture
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Phase transitions in Al2O3
Duan, Wentzcovitch, & Thomson, PRB (1998)
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The high pressure ruby scaleForman, 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)
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Optical transitions in ruby
Intra-d transitions in Cr3+ (d3)
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Ab initio calculation of Al2O3:Cr
(80 atoms/cell)
(Duan, Paiva, Wentzcovitch, Fazzio, PRL (1998))
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Structural properties of the color center
Duan, Paiva, Wentzcovitch, & Fazzio, PRL (1998)
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Eigenvalue SpectraCorundum Rh2O3 (II)
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Deformation parameters
Orbital deformation parameters
Multiplet method for d-electrons in X-tal field(Sugano, Tanabe, & Kamimura, 1971)
(Fazzio, Caldas, & Zunger, PRB (1984)
2 2
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Optical transitions X Pressure
(Duan, Paiva, Wentzcovitch,Fazzio, PRL (1998)
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-Cr2O3
AFMTN=308 K=(2.76±0.03) B
dTN/dP=-1.5K/kbar
R3c a = 5.35 A=55.1
o
o
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landau
zzMMUVVUUV 2121122
22
1 ).(
• Free energy expansion:
M1, M2 – (AFM) sub-lattice magnetizations21, MM
ljikikjljlikikjl MMuuu 21
• U = u33 – uniaxial strain; V = uii – hydrostatic; z
MM 21,
• Minimizing (equilibrium)
zzo MMuU 21. zzo MMvV 21.
zzMM 21• = -1,1,0 for AFM, FM, PM
• UPM = (UAFM + UFM)/2 VPM = (VAFM + VFM)/2, therefore … PM lattice parameters are averages of AFM and FM’s
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Compressive behavior of Cr2O3
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Phase transition in Cr2O3
• Corundum Rh2O3 (II) phase transition AFM at 14 GPa, PM at 18 GPa.
• Experimental confirmation: Rheki & Dubrovinsky (2001) unpublished PT = 30GPa, T= 1500 K.
Dobin, Duan, & Wentzcovitch, PRB 2000
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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?