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1、The role of first principles calculations in geophysics,Renata WentzcovitchUniversity of MinnesotaMinnesota Supercomputing Institute,ASESMA10,The role of first principles calculations in geophysics,Acknowledgements,K.Umemoto(GEO,U of MN),Z.Wu(USTC,Hefei,PRC),Y.Yu(U of MN),T.Tsuchiya,J.Tsuchiya(Ehime
2、 U.,Japan)S.de Gironcoli(SISSA,Trieste),M.Cococcioni(U of MN),ASESMA10,How well can we describe minerals by first principles?,What property?Is it a solid solution or an end member?Does it have iron or hydrogen bonds?What is the PT range?DFT within LDA,GGA(PBE),and DFT+UVariable cell shape MD(VCS-MD)
3、Density functional perturbation theoryQuasiharmonic approximation(QHA)(Quantum ESPRESSO),ASESMA10,Typical Computational Experiment,Damped dynamics,P=150 GPa,(Wentzcovitch,Martins,and Price,PRL 1993),Perovskite and the Earths mantle,Perovskite and the Earths mantle,ASESMA10,The Contribution from Seis
4、mology,Longitudinal(P)waves,Transverse(S)wave,from free oscillations,Bulk()wave,ASESMA10,PREM(Preliminary Reference Earth Model)(Dziewonski&Anderson,1981),0,24,135,329,364,P(GPa),ASESMA10,+,Mineral sequence II,Lower Mantle,(Mgx,Fe(1-x)O,(Mgx,Fe(1-x)SiO3,ASESMA10,TM of lower mantle phases,Core T,Mant
5、le adiabat,solidus,HA,Mw,(Mg,Fe)SiO3,CaSiO3,peridotite,P(GPa),0,40,20,60,80,100,120,2000,3000,4000,5000,T(K),(Zerr,Diegler,Boehler,Science1998),Thermodynamics Method,VDoS and F(T,V)within the QHA,N-th(N=3,4,5)order isothermal(eulerian or logarithm)finite strain EoS,IMPORTANT:crystal structure and ph
6、onon frequencies depend on volume alone!.,ASESMA10,Validity of the QHA,ASESMA10,Tsuchiya et al.,J.Geophys.Res.,110(B2),B02204/1-6(2005).,equilibrium structure,kl,re-optimize,Thermoelastic constant tensor CijS(T,P),ASESMA10,cij,(Wentzcovitch,Karki,Cococciono,de Gironcoli,Phys.Rev.Lett.2004),300 K1000
7、K2000K3000 K4000 K,(Oganov et al,2001),Cij(P,T),ASESMA10,Effect of Fe alloying,(Kiefer,Stixrude,Wentzcovitch,GRL 2002)(Mg0.75Fe0.25)SiO3,4,+,+,+,|,ASESMA10,Comparison with PREM,Pyrolite(20 V%mw)Perovskite,Brown&Shankland T(r),38 GPa,100 GPa,(Wentzcovitch et al.Phys.Rev.Lett.2004),Wentzcovitch,Karki,
8、Cococciono,de Gironcoli,Phys.Rev.Lett.92,018501(2004),Phys.Rev.Lett.92,018501(issue of 9 January 2004),9January2004,Whats Down There?,L.H.Kellogg et al.,Science 283,1881(1999),copyright AAAS,Lava lamp.A new calculation suggests geophysicists still dont know exactly what the Earths mantle is made of.
9、Other research suggests that there are slow but complex flows in the mantle,even though its entirely solid.,Like bats using echolocation to navigate through the night,geophysicists rely on seismic waves for information on the Earths deep interior.Almost everything known about that inaccessible regio
10、n is inferred from the speed of sound waves generated by earthquakes.In the 9 January PRL,however,a team describes a calculation of the properties of the Earths lower mantle starting from basic physics principles.The results disagree slightly with seismic data and suggest that the structure of miner
11、als in the Earths lower mantle is more complex than geophysicists have assumed.,The Earth has an iron core surrounded by a dense layer called the mantle,which is capped with a thin rind of rocky crust.Seismic measurements reveal the density and elasticity of the mantle,but not much about its composi
12、tion.Perovskite,the mineral that dominates the lower mantle,contains mainly magnesium,silicon,and oxygen,but researchers suspect that a lot of iron and aluminum are present as impurities.Exactly how much isnt known,nor how these impurities would affect the elasticity of the rock.To further complicat
13、e the mystery,minerals often behave in unexpected ways at the extreme pressures found 1000 kilometers underground.Iron,for example,becomes non-magnetic and may tend to migrate from perovskite toward another mineral called magnesiumwustite,as the pressure rises.,Thermoelasticity of MgSiO3 Perovskite:
14、Insights on the Nature of the Earths Lower MantleR.M.Wentzcovitch,B.B.Karki,M.Cococcioni,and S.de GironcoliPhys.Rev.Lett.92,018501(issue of 9 January 2004),ASESMA10,(M.Murakami and K.Hirose,private communication),Drastic change in X-ray diffraction pattern around 125 GPa and 2500 K,Pbnm Perovskite,U
15、NKNOWN PHASE,ASESMA10,MgSiO3 Perovskite,-Most abundant constituent in the Earths lower mantle-Orthorhombic distorted perovskite structure(Pbnm,Z=4)-Its stability is important for understanding deep mantle(D”layer),ASESMA10,Ab initio exploration of post-perovskite phase in MgSiO3,Perovskite,-Reasonab
16、le polyhedra type and connectivity under ultra high pressure-,ASESMA10,Lattice system:Bace-centered orthorhombicSpace group:CmcmFormula unit Z:4(4)Lattice parameters a:2.462(4.286)120 GPa b:8.053(4.575)c:6.108(6.286)Volume 120 GPa 3:121.1(123.3)()perovskite,Pt,Crystal structure of post-perovskite,AS
17、ESMA10,Structural relation between Pv and Post-pv,Deformation of perovskite under shear strain 6,Perovskite,ASESMA10,High-PT phase diagram,1000 K,D”,Tsuchiya,Tsuchiya,Umemoto,Wentzcovitch,EPSL 224,241(2004),Sidorin,Gurnis,Helmberger(1998)6 MPa/K,ASESMA10,D Layer Demystified,MONTREAL-Deep within Eart
18、h,where hellish temperatures and pressures create crystals and structures like none ever seen on the surface,a strange undulated layer separates the mantle and the core.The composition of this region,called the d layer(pronounced dee double prime),has puzzled earth scientists ever since its discover
19、y.Now,a team of researchers believes they know what the d layer is.,24 March 2004,Strange stuff.Post-perovskite owes its odd crystal structure to the intense heat and pressure at the boundary between the mantle and core.CREDIT:RENATA WENTZCOVITCH,Three thousand kilometers deep in Earth,the solid roc
20、k of the mantle meets the liquid outer core.At this juncture,seismic waves from earthquakes traveling through Earth suddenly change speed,and sometimes direction.These sudden shifts trace the border of the d layer,which rises and falls in ridges and valleys.Researchers suspected that the layer marks
21、 a change in the crystal structure of the rock,which might happen at different depths depending on the temperature.This would explain the rises and dips of the boundary.But what could account for the sudden speed shifts of the seismic waves?,The explanation may lie in an entirely new kind of crystal
22、 structure,according to presentations by Jun Tsuchiya and Taku Tsuchiya here 23 March at a meeting of the American Physical Society.They and colleagues at the University of Minnesota in Minneapolis collaborated with a team from the Tokyo Institute of Technology led by Motohiko Murakami.The Tokyo tea
23、m used a diamond anvil to squeeze and heat a grain of perovskite,the dominant mineral deep within the earth.They then took an x-ray image to see what happened to the molecular structure of the mineral in conditions like those in the d layer.The Minnesota group then analysed the x-ray.Only one crysta
24、l structure fit the x-ray data,and it was like nothing anyone had seen before.,http:/sciencenow.sciencemag.org/archives.shtml,Deep mantle observables from regional studies,Lay,Garnero,Williams PEPI,2004,in press,ASESMA10,Lay,Garnero,Williams 2004,PEPI,ASESMA10,Large-scale lengths:Lowermost mantle he
25、terogeneity,From:Lay,Garnero,AGU/IUGG Monograph(2004),Lay,Garnero,Williams,PEPI(2004),ASESMA10,Aggregate Elastic Moduli of Perovskite,Bppv Bpv Gppv Gpv,Aggregate Elastic Moduli of Post-perovskite,(Wentzcovitch et al.,PRL 2004),ASESMA10,Seismic velocity of Perovskite,Longitudinal,Shear,Bulk,Seismic v
26、elocity of Post-perovskite,Contrast in S waves is larger than in P waves.,(Wentzcovitch et al.,PRL 2004),ASESMA10,V(%),Velocity discontinuity along the phase boundary,Wentzcovitch,Tsuchiya,Tsuchyia,Proc.Natl.Acad.103,543(2006),ASESMA10,Lay,Garnero,Williams 2004,PEPI,ASESMA10,ASESMA10,Wentzcovitch et
27、 al.,Proc.Natl.Acad.103,543(2006),ASESMA10,Large-scale lengths:Lowermost mantle heterogeneity,From:Lay,Garnero,AGU/IUGG Monograph(2004),Lay,Garnero,Williams,PEPI(2004),ASESMA10,Comparison with PREM,Pyrolite(20 V%mw)Perovskite,Brown&Shankland T(r),38 GPa,100 GPa,(Wentzcovitch et al.Phys.Rev.Lett.2004
28、),Summary,Post-perovskite transition has changed the way geophysicists look at the Earth The crystal structure of post-perovskite and its properties were obtained by first principles and experiments confirm our V vs P relation and more The computed elastic properties of perovskite and pos-perovskite
29、 help to interpret large scale velocity anomalies in the D”region First principles theory has won the hearts and minds of geophysicists since then.,ASESMA10,ASESMA10,http:/www.minsocam.org/,Other resources on mineral physics:My web pages:http:/www.cems.umn.edu/research/wentzcovitch/http:/www.vlab.msi.umn.edu/COnsortium on Materials Properties Research in Earth Sciences(COMPRES)http:/compres.us/Please joint us!,
