Materials Theory and Mineral Physics Overview of methods Amorphization of quartz under pressure Structural transitions in ruby and the ruby pressure scale Thermoelasticity of LM minerals and the problem of LM temperature and composition Epilog Renata Wentzcovitch CEMS, U of MN

BO approximation Born-Oppenheimer approximation (1927) Ions (R I ) + electrons (r i ) Molecular dynamicsLattice dynamics forces stresses phonons

Electronic Density Functional Theory (DFT) (T = 0 K) Hohemberg and Kohn (1964) Kohn and Sham(1965) (auxiliary non-interacting system) energy minimization... DFT1 dft1

Kohn-Sham equations : (one electron equation) with and Local density approximation (LDA) Quantum Monte Carlo Ceperley and Alder, 1980 df t2

Pseudopotentials Nucleus Core electrons Valence electrons V(r) Radial distance (a.u.) Troullier-Martins (1991) rR l (r) s orbital of Si Real atom Pseudoatom r Ion potential Pseudopotential 1/2 Bond length

Fictitious molecular dynamics H. C. Andersen (1978) (N,E,V) (N,H,P)

Invariant Variable Cell Shape MD i=vector index j=cart. index Wentzcovitch, (1991)

Typical Computational Experiment Damped dynamics (Wentzcovitch, 1991) P = 150 GPa

Lattice 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)

Yegani-Haeri, 1994 Wentzcovitch et al, 1995 Karki et al, 1997 within 5% S-waves (shear) P-wave (longitudinal) n propagation direction Elastic Waves

Amorphization in Quartz under Pressure quartz cristobalite tridymite coesite stishovite Collaborators: C.R.S. da Silva (UMN), J. Chelikowsky (UMN), N. Binggeli (EPFL)

Hemley, Prewitt, Kingma, in Reviews in Mineralogy, 29 (1996) (Hemley,1987)

Microstructure of  -quartz during amorphization Kingma, Maede, Hemley, Mao, & Veblen, Science (1993) Q – Quartz Q’- Quartz-like * - New peaks

Mechanical instability of quartz under pressure Binggeli & Chelikowsky, PRL 1993 (shear instability) Chapplot & Sikka, PRL 1993 (phonon softening)

quartz  -Quartz

Comparison Quartz - 0 GPa (exp) Quartz - 0 GPa (calc) K-phase – 33 GPa (calc) New phase – 25.5 GPa (exp) New phase – 26 GPa (calc) New phase – 27.4 GPa (exp)

New phase New Phase

Nature of P induced coordination change Stolper & Ahrens, GRL (1987) 1)Gradual increase in density 2)Occurs at room T 3)Changes are reversible

Polyhedra Si-O distances (A) o

Conclusions Nature of the intermediate phase of silica seems to be understood Properties: produced by a soft mode structure consists of 6-, and 5-fold Si at 33 GPa it is 10% denser than quartz (  H ~ 0.1 eV/atom) Amorphous could be the result of a generalized phonon stability

Optical transitions in ruby across the corundum to Rh2O3 (II) phase transformation Collaborators: W. Duan (U. of MN), G. Paiva (USP), & A. Fazzio (USP) Support: NSF, CNPq, and FAPESP

Structural Transition in Ruby (Al 2 O 3 :Cr) PIB (Cynn et al and Bukowinski – 1994). Between 4 and 148 GPa LAPW (Marton & Cohen – 1994) 90 GPa Pseudopotentials (VCS-MD) (Thomson, Wentzcovitch, & Bukowinski), Science (1996)

Suggestive X-ray diffraction pattern 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

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 Cr 3+ (d 3 )

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

Eigenvalue Spectra Corundum Rh 2 O 3 (II)

Multiplet method for e - ’s in X-tal field (Fazzio, Caldas, & Zunger, PRB (1984) (Sugano, Tanabe, & Kamimura, 1962) [ [

Deformation parameters Racah parameters B and C Orbital deformation parameters

Optical transitions X Pressure (Duan, Paiva, Wentzcovitch,Fazzio, PRL (1998) (Sugano, Tanabe, & Kamimura, 1962)(Fazzio, Caldas, & Zunger, 1984)

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

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 Need more experiments: Study of Y line above 30 GPa NEXAFS under pressure…

Thermoelasticity of LM minerals and the problem of LM temperature and composition Core T Mantle adiabat solidus HA Mw (Mg,Fe)SiO 3 CaSiO 3 peridotite P(GPa) T (K) (Zerr, Diegler, Boehler, 1998) Collaborators: B.B. Karki (UMN), S. de Gironcoli & S. Baroni (SISSA )

Phonon dispersion in MgO & MgSiO 3 perovskite Calc Exp (Karki, Wentzcovitch, Gironcoli, Baroni, PRB 2000) 0 GPa - Exp: Sangster et al Exp: Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994]

Quasiharmonic approximation 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 ) K (GPa) K´ K´´(GPa -1 )

Thermal expansivity of MgO & MgSiO 3 -pv (Karki, Wentzcovitch, Gironcoli and Baroni, GRL in press)  ( K -1 )

MgSiO 3 -perovskite and MgO Exp.: [Ross & Hazen, 1989; Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996; Chopelas, 1996; Gillet et al., 2000; Fiquet et al., 2000]

Elastic moduli of MgO at high P and T (Karki et al. 1999, 2000)

K S at Lower Mantle P-T 300 K 1000 K 2000 K 3000 K

LM Geotherms Pv Solidus Isentropes Pyrolite CMB | TcTc

Me “…At depths greater than 1200 km, the rate of rise of the bulk modulus is too small for the lower mantle to consist of an adiabatic and homogeneous layer of standard chondritic or pyrolitic composition. Superadiabatic gradients, or continuous changes in chemical composition, or phase, or all are required to account for the relatively low bulk modulus of the deeper part of the LM,….” (Wentzcovitch, 2001)

Epilog Beyond QHA and beyond elasticity (rheology) Transition metal (Fe) bearing systems Alloy systems Press on to Gbars…

Thanks to … Bijaya B. Karki Shun-I. Karato G. David Price