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

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## Materials Theory and Mineral Physics

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**Materials Theory and Mineral Physics**Renata Wentzcovitch CEMS, U of MN • 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**• Born-Oppenheimer approximation (1927)**Ions (RI ) + electrons (ri ) BO approximation phonons forces stresses Molecular dynamics Lattice dynamics**dft1**Electronic Density Functional Theory (DFT) (T = 0 K) • Hohemberg and Kohn (1964) • Kohn and Sham(1965)(auxiliary non-interacting system) DFT1 energy minimization...**dft2**• Kohn-Sham equations: (one electron equation) with and • Local density approximation (LDA) Quantum Monte Carlo Ceperley and Alder, 1980**Pseudopotentials**1.0 3s orbital of Si rRl (r) 0.5 Pseudoatom Real atom 0.0 -0.5 0 1 2 3 4 5 Radial distance (a.u.) V(r) 1/2 Bond length r Nucleus Core electrons Valence electrons Pseudopotential Troullier-Martins (1991) Ion potential**Fictitious molecular dynamicsH. C. Andersen (1978)**(N,H,P) (N,E,V)**Invariant Variable Cell Shape MD**Wentzcovitch, (1991) i=vector index j=cart. index**Typical Computational Experiment**Damped dynamics (Wentzcovitch, 1991) P = 150 GPa**Lattice**(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)**Elastic Waves**P-wave (longitudinal) S-waves (shear) n propagation direction Yegani-Haeri, 1994 Wentzcovitch et al, 1995 Karki et al, 1997 within 5%**Amorphization in Quartz under Pressure**tridymite quartz cristobalite stishovite coesite 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**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) Comparison**New phase**New Phase**Nature of P induced coordination change**• Stolper & Ahrens, GRL (1987) • Gradual increase in density • Occurs at room T • Changes are reversible**Polyhedra**o Si-O distances (A) 1.531 1.607 1.624 1.683 1.673 1.680 1.714 1.763 1.683 1.752 1.768 1.726 1.760 1.813 1.797 2.030 1.817**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 (Al2O3:Cr)**• PIB (Cynn et al.-1990 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**• Comparison with EDS (Jephcoat, Hemley, Mao, Am. Mineral.(1986)) 175 GPa 50/50%mixture corundum Rh2O3 (II) •Experimental confirmation (Funamori and Jeanloz, Science (1997))**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)**Optical transitions in ruby**Intra-d transitions in Cr3+ (d3)**Ab initio calculation of Al2O3:Cr**(Duan, Paiva, Wentzcovitch, Fazzio, PRL (1998)) (80 atoms/cell)**Corundum**Eigenvalue Spectra Rh2O3 (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**(Sugano, Tanabe, & Kamimura, 1962) (Fazzio, Caldas, & Zunger, 1984) (Duan, Paiva, Wentzcovitch,Fazzio, PRL (1998)**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.**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 • 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 CaSiO3 5000 Mw (Mg,Fe)SiO3 4000 HA Core T solidus T (K) 3000 Mantle adiabat 2000 peridotite (Zerr, Diegler, Boehler, 1998) 0 20 40 60 80 100 120 P(GPa) Collaborators: B.B. Karki (UMN), S. de Gironcoli & S. Baroni (SISSA)**Phonon dispersion in MgO & MgSiO3 perovskite**(Karki, Wentzcovitch, Gironcoli, Baroni, PRB 2000) Calc Exp Calc Exp - 0 GPa Exp: Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994] Exp: Sangster et al. 1970**Quasiharmonic approximation**4th order finite strain equation of state MgO - static zero-point - F (ry) - thermal - 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)**Thermal expansivity of MgO & MgSiO3-pv**(Karki, Wentzcovitch, Gironcoli and Baroni, GRL in press) (10-5 K-1) (10-5 K-1)**MgSiO3-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)**KS at Lower Mantle P-T**300 K 1000 K 2000 K 3000 K**LM Geotherms**Pv Tc Solidus Pyrolite Isentropes CMB |**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

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