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

Invariant Variable Cell Shape MD

h1

h2

)(thiji=vector indexj=cart. index

VPUWm

L 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)

Typical Computational Experiment

Damped dynamics

)(~ PI),(~ int rffr

P = 150 GPa

abcxP

K Vo

dP

dV

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)

Thermal EoS

qj B

qjB

qj

qj

Tk

VTk

VVUTVF

)(exp1ln

2

)()(),(

Volume (Å3)

F (

Ry)

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

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)

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

Phase transitions in Al2O3

Duan, Wentzcovitch, & Thomson, PRB (1998)

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)

Optical transitions in ruby

Intra-d transitions in Cr3+ (d3)

Ab initio calculation of Al2O3:Cr

(80 atoms/cell)

(Duan, Paiva, Wentzcovitch, Fazzio, PRL (1998))

Structural properties of the color center

Duan, Paiva, Wentzcovitch, & Fazzio, PRL (1998)

Eigenvalue SpectraCorundum Rh2O3 (II)

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

Optical transitions X Pressure

(Duan, Paiva, Wentzcovitch,Fazzio, PRL (1998)

-Cr2O3

AFMTN=308 K=(2.76±0.03) B

dTN/dP=-1.5K/kbar

R3c a = 5.35 A=55.1

o

o

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

Compressive behavior of Cr2O3

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

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?