Nuclear Energy and Safety Research Department Laboratory for Waste Management Structure of Cement Phases Structure of Cement Phases from ab initio Modeling Modeling from ab initio Crystalline C- -S S- -H H Crystalline C Sergey V. Churakov Sergey V. Churakov sergey.churakov@psi.ch sergey.churakov@psi.ch Laboratory for Waste Management Laboratory for Waste Management Paul Scherrer Institute Paul Scherrer Institute Switzerland Switzerland Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Cement Phase Composition Cement Phase Composition C- -S S- -H Solid Solution Model H Solid Solution Model C C- -S S- -H H C C- -S S- -H H C Lothenbach &Winnefelf(2006) after Lothenbach &Winnefelf(2006) after Kulik Kulik & & Kersten Kersten (2001) (2001) Lothenbach et al. (2008) et al. (2008) Lothenbach Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Possible end- -Members Members Possible end for Amorphous C- -S S- -H Solid Solutions H Solid Solutions for Amorphous C × 5H 2x × C- -S S- -H (I): H (I): Anomalous Anomalous – – Normal Tobermorite Normal Tobermorite Solid Solution Solid Solution CSH (I): C Tobermorite Solid Solution Ca 5 Si 6 O 17 (OH) 2x 5H 2 O CSH (I): Tobermorite Solid Solution Ca x Si 6 O 2x (OH) 2 O 5- -x 17- -2x Ca/Si = 0.60 – – 0.75 0.75 Ca/Si = 0.60 Ca/Si = 0.60 – Ca/Si = 0.60 – 0.75 0.75 × 5H × 5H 2 × (OH) × Ca 4 Si 6 O 15 (OH) 2 × 5H 5H 2 O – – Ca 4.5 Si 6 O 16 × 5H 5H 2 O Ca 4 Si 6 O 15 (OH) 2 × 2 O Ca 4.5 Si 6 O 16 (OH) (OH) × 2 O Ca 4 Si 6 O 15 (OH) 2 5H 2 O – – Ca 4.5 Si 6 O 16 5H 2 O Ca 4 Si 6 O 15 (OH) 2 O Ca 4.5 Si 6 O 16 (OH) 2 O C- -S S- -H (II): H (II): Normal Tobermorite Normal Tobermorite – – Jennite Jennite Solid Solution Solid Solution C Ca/Si = 0.75 – – 1.50 1.50 Ca/Si = 0.75 × 5H × 8H (OH) × 6 × Ca 4.5 Ca 4.5 Si Si 6 6 O O 16 16 (OH) 5H 2 2 O O – – Ca Ca 9 9 Si Si 6 6 O O 18 18 (OH) (OH) 6 8H 2 2 O O Further relevant C- -S S- -H Phases H Phases Further relevant C Xonotlite: Xonotlite : Ca 6 Ca 6 Si Si 6 6 O O 17 17 (OH) (OH) 2 2 Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Basic Structural Elements of C- -S S- -H Phases H Phases Basic Structural Elements of C Xonotlite 11 Å Tobermorite Jennite 11 Å Jennite Ca 6 Si 6 O 17 (OH) 2 Ca 4+x Si 6 O 15+2x (OH) 2-2x × 5H 2 O Ca 9 Si 6 O 18 (OH) 6 × 8H 2 O Silicate chain Silicate chain 7 Å 7 Å 11 Å 11 Å Ca- -Layer Layer Ca c c c b c b a a b b b b Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Method Method Molecular Dynamics (MD) Molecular Dynamics (MD) Newton Equation Newton Equation ∂ 2 d R U ( R ) = − k Must be known Must be known M ∂ k 2 dt R k & Γ Ensemble of position and velocities of position and velocities ({ R }, { R }) Ensemble k k Average over Ensemble Ensemble Average over Structure: Thermodynamics: Dynamics: • Bond distances • Energies • IR spectra • Crystallographic positions • Temperature • Diffusion • … • … • … Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Interaction Potentials Interaction Potentials • Ab Initio methods 2 h Solve Schrödinger equation − ∇ Ψ + Ψ = Ψ 2 U E to obtain energy and forces 2 m • Empirical force field methods intra- molecular : harmonic bond stretching, bending … inter- molecular: electrostatic and van der Waals interaction Ab Initio Initio <=> Ab <=> Empirical Empirical � Computationally expensive ☺ Fast computation ☺ Valid for any P-T conditions and chemistry � Must be calibrated for the system of interest � Fail to describe bond breaking/forming ☺ Correct description of bond breaking/forming � up to ~ n × 10 2 atoms ☺ up to ~ n × 10 6 atoms � up to ~ n × 10 ps ☺ up to ~ n × 10 2 ns Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Density functional theory Density functional theory Hohenberg & Kohn, 1964; Kohn & Sham 1965; Schrödinger Equation Ψ = Ψ • Exact Hamiltonian H ( R ) E ( R ) 3 N 3 N • 3N dimensional problem far too complex :-(( Kohn-Sham Equation ⎧ ψ = ε ψ KS KS H ( r ) ( r ) 1 3 1 1 3 ⎪ • Approximate Hamiltonian ⎨ ......... • 3 dimensional problem ⎪ ψ = ε ψ but can be solved ! :-)) KS KS ⎩ H ( r ) ( r ) N 3 N N 3 Kinetic Energy Coulomb Interactio n Coulomb Interactio n of Electrons 6 7 8 − Nuclei 6 4 7 Electrons 4 8 Electrons 6 4 7 4 8 Quantum 6 4 7 4 effects 8 1 = − ∇ + + ρ + ρ ˆ ˆ ˆ KS 2 el el H V ( R ) V [ ] V [ ] 1 4 2 4 3 ext nuc Hartree xc 2 1 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 3 Approximat ion Exact ∑ ρ = ψ 2 el ( r ) ( r ) Major uncertainty i i Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Approximations for Exchange and Correlation functional Approximations for Exchange and Correlation functional ˆ • local density approximation (LDA) ˆ xc ρ homogeneous electron gas el V [ ( r )] V ρ ∇ ρ ˆ xc el el • generalized gradient approximation (BLYP, PBE, ....) V [ ( r ), ( r )] xc Pseudopotential approximation Pseudopotential approximation an example for Si atom all electro vs. pseudo wavefunctions Radial Electron Wavefuctions in Si Atom Valence Region Core Region Core Region Valence Region 1s 3s 3s pseudowavefunction 2s 3s true wavefunction 0 1 2 3 4 0 1 2 3 4 R [bohr] R [bohr] Basis set Basis set Plane Waves Gaussian basis set ∑ ∑ − ψ = kr ψ = μ ϕ i c , e c ϕ μ α = − α 2 r l m n k μ ( , l , m , n ) Ne x y z i i i i , μ k Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management DFT approach used in this work DFT approach used in this work • CPMD code (used for oblique supercell) • Plane Wave basis set • 70 Ry cut-off • BLYP functional, MT-pseudopotentials • Car-Parrinello MD • CP2K/Quickstep code (used for orthogonal supercell) • Gaussian and Plane Wave basis set • Triple- ζ basis for O and H, double- ζ for Si and Ca • PBE functional, Goedeker - pseudopotentials • Born Oppenheimer MD Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Xonotlite Experimental Observations Xonotlite Experimental Observations Ca 6 Si 6 O 17 (OH) 2 NMR: NMR: Ideal structure from X- -ray studies: ray studies: Ideal structure from X 3 and Q 1 sites • Presence of both Q Presence of both Q 2 , Q 3 and Q 1 sites • 2 , Q • Presence OH with different environment Presence OH with different environment Q 3 • and molecular H 2 O Q 2 and molecular H 2 O IR and TG/DTA: IR and TG/DTA: • Presence of molecular H Presence of molecular H 2 O • 2 O EDS: EDS: Calculated IR spectra Calculated IR spectra • Ca:Si • Ca:Si > 1.0 in disordered samples > 1.0 in disordered samples Experimental Experimental arb. units Possible defect formation mechanism Possible defect formation mechanism {Si} { Si} X X Si + 2H + 2H 2 2 O ={4H} O ={4H} X X Si + SiO + SiO 2 2 Si Si 4000 3000 2000 3800 3600 3200 2800 2400 2000 ν Η [cm ] -1 CPMD, BLYP, MT-PP, 80 Ry Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
Nuclear Energy and Safety Research Department Laboratory for Waste Management Assumed Defect Formation Mechanism Assumed Defect Formation Mechanism {Si} Si} X + 2H 2 O ={4H} X + SiO 2 { X Si + 2H 2 O ={4H} X Si + SiO Si Si 2 Δ 57 kJ/mol Δ 57 kJ/mol Δ 40 kJ/mol Δ 40 kJ/mol Δ 5 kJ/mol Δ 5 kJ/mol Δ 0 kJ/mol Δ 0 kJ/mol {4H} x {4H} x {8H} x {8H} x {4H} x {4H} x {8H} x {8H} x Q3 Q3 Q2 Q2 {Q3,Q3} {Q3,Q3} {Q2,Q3} {Q2,Q3} CPMD, BLYP, MT-PP, 80 Ry Churakov & Mandaliev Mandaliev (2008) CCR (2008) CCR Churakov & Paul Scherrer Institut • 5232 Villigen PSI 14 October, 2008, Le Croisic Croisic 14 October, 2008, Le
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