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Chemical Bond: Catalysis, Materials, Nanotechnology

Explore the nature of chemical bonding and its applications in catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy. This lecture series covers topics such as perovskite structures, charges in molecular dynamics simulations, and QEq equations.

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Chemical Bond: Catalysis, Materials, Nanotechnology

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  1. Lecture 19, November 17, 2009 Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy Course number: KAIST EEWS 80.502 Room E11-101 Hours: 0900-1030 Tuesday and Thursday William A. Goddard, III, wag@kaist.ac.kr WCU Professor at EEWS-KAIST and Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Senior Assistant: Dr. Hyungjun Kim: linus16@kaist.ac.kr Manager of Center for Materials Simulation and Design (CMSD) Teaching Assistant: Ms. Ga In Lee: leeandgain@kaist.ac.kr Special assistant: Tod Pascal:tpascal@wag.caltech.edu EEWS-90.502-Goddard-L15

  2. Schedule changes Nov. 9-13 wag lecturing in Stockholm, Sweden; no lectures, TODAY Nov. 17, Tuesday, 9am, L19, as scheduled Nov. 18, Wednesday, 1pm, L20, additional lecture room 101 Nov. 19, Thursday, 9am, L21, as scheduled Nov. 24, Tuesday, 9am, L22, as scheduled Nov. 26, Thursday, 9am, L23, as scheduled Dec. 1, Tuesday, 9am, L24, as scheduled Dec. 2, Wednesday, 3pm, L25, additional lecture, room 101 Dec. 3, Thursday, 9am, L26, as scheduled Dec. 7-10 wag lecturing Seattle and Pasadena; no lectures, Dec. 11, Friday, 2pm, L27, additional lecture, room 101 EEWS-90.502-Goddard-L15

  3. Last time EEWS-90.502-Goddard-L15

  4. Electrostatic balance principle-Illustration, BaTiO3 A number of important oxides have the perovskite structure (CaTiO3) including BaTiO3, KNbO3, PbTiO3. Lets try to predict the structure without looking it up Based on the TiiO2 structures , we expect the Ti to be in an octahedron of O2-, STiO = 2/3. The question is how many Ti neighbors will each O have. It cannot be 3 since there would be no place for the Ba. It is likely not one since Ti does not make oxo bonds. Thus we expect each O to have two Ti neighbors, probably at 180º. This accounts for 2*(2/3)= 4/3 charge. The Ba must provide the other 2/3. Now we must consider how many O are around each Ba, nBa, leading to SBa = 2/nBa, and how many Ba around each O, nOBa. Since nOBa* SBa = 2/3, the missing charge for the O, we have only a few possibilities: EEWS-90.502-Goddard-L15

  5. Prediction of BaTiO3 structure nBa= 3 leading to SBa = 2/nBa=2/3 leading to nOBa = 1 nBa= 6 leading to SBa = 2/nBa=1/3 leading to nOBa = 2 nBa= 9 leading to SBa = 2/nBa=2/9 leading to nOBa = 3 nBa= 12 leading to SBa = 2/nBa=1/6 leading to nOBa = 4 Each of these might lead to a possible structure. The last case is the correct one for BaTiO3 as shown. Each O has a Ti in the +z and –z directions plus four Ba forming a square in the xy plane The Each of these Ba sees 4 O in the xy plane, 4 in the xz plane and 4 in the yz plane. EEWS-90.502-Goddard-L15

  6. BaTiO3 structure (Perovskite) EEWS-90.502-Goddard-L15

  7. How estimate Charges?-Charge Equilibration First consider how the energy of an atom depends on the net charge on the atom, E(Q) Including terms through 2nd order leads to • Charge Equilibration for Molecular Dynamics Simulations; • K. Rappé and W. A. Goddard III; J. Phys. Chem. 95, 3358 (1991) (2) (3) EEWS-90.502-Goddard-L15

  8. Charge dependence of the energy (eV) of an atomassume a quadratic fit about charge=0 E=12.967 E=0 E=-3.615 Cl+ Cl Cl- Q=+1 Q=0 Q=-1 Harmonic fit Get minimum at Q=-0.887 Emin = -3.676 = 8.291 = 9.352 EEWS-90.502-Goddard-L15

  9. QEq parameters EEWS-90.502-Goddard-L15

  10. Interpretation of J, the hardness Define an atomic radius as RA0 Re(A2) Bond distance of homonuclear diatomic H 0.84 0.74 C 1.42 1.23 N 1.22 1.10 O 1.08 1.21 Si 2.20 2.35 S 1.60 1.63 Li 3.01 3.08 J is related to the coulomb energy of a charge the size of the atom EEWS-90.502-Goddard-L15

  11. The total energy of a molecular complex Consider now a distribution of charges over the atoms of a complex: QA, QB, etc Letting JAB(R) = the shielded Coulomb potential of unit charges on the atoms, we can write Taking the derivative with respect to charge leads to the chemical potential, which is a function of the charges or The definition of equilibrium is for all chemical potentials to be equal. This leads to EEWS-90.502-Goddard-L15

  12. The QEq equations Adding to the N-1 conditions The condition that the total charged is fixed (say at 0) Leads to the condition Leads to a set of N linear equations for the N variables QA. We place some conditions on this. The harmonic fit of charge to the energy of an atom is assumed to be valid only for filling the valence shell. Thus we restrict Q(Cl) to lie between +7 and -1 and for C to be between +4 and -4 Similarly Q(H) is between +1 and -1 EEWS-90.502-Goddard-L15

  13. The QEq Coulomb potential law We need now to choose a form for JAB(R) A plausible form is JAB(R) = 14.4/R, which is valid when the charge distributions for atom A and B do not overlap Clearly this form as the problem that JAB(R)  ∞ as R 0 In fact the overlap of the orbitals leads to shielding The plot shows the shielding for C atoms using various Slater orbitals Using RC=0.759a0 And l = 0.5 EEWS-90.502-Goddard-L15

  14. QEq results for alkali halides EEWS-90.502-Goddard-L15

  15. QEq for Ala-His-Ala Amber charges in parentheses EEWS-90.502-Goddard-L15

  16. QEq for deoxy adenosine Amber charges in parentheses EEWS-90.502-Goddard-L15

  17. QEq for polymers Nylon 66 PEEK EEWS-90.502-Goddard-L15

  18. Perovskites Perovskite (CaTiO3) first described in the 1830s by the geologist Gustav Rose, who named it after the famous Russian mineralogist Count Lev Aleksevich von Perovski crystal lattice appears cubic, but it is actually orthorhombic in symmetry due to a slight distortion of the structure. Characteristic chemical formula of a perovskite ceramic: ABO3, A atom has +2 charge. 12 coordinate at the corners of a cube. B atom has +4 charge. Octahedron of O ions on the faces of that cube centered on a B ions at the center of the cube. Together A and B form an FCC structure EEWS-90.502-Goddard-L15

  19. Ferroelectrics The stability of the perovskite structure depends on the relative ionic radii: if the cations are too small for close packing with the oxygens, they may displace slightly. Since these ions carry electrical charges, such displacements can result in a net electric dipole moment (opposite charges separated by a small distance). The material is said to be a ferro-electric by analogy with a ferro-magnet which contains magnetic dipoles. At high temperature, the small green B-cations can "rattle around" in the larger holes between oxygen, maintaining cubic symmetry. A static displacement occurs when the structure is cooled below the transition temperature. Illustrated is a displacement along the z-axis, resulting in tetragonal symmetry (z remains a 4-fold symmetry axis), but at still lower temperatures the symmetry can be lowered further by additional displacements along the x- and y-axes. EEWS-90.502-Goddard-L15

  20. Phases BaTiO3 c Domains separated by domain walls a Six variants at room temperature <111> polarized rhombohedral <110> polarized orthorhombic <100> polarized tetragonal Non-polar cubic 120oC -90oC 5oC Temperature Different phases of BaTiO3 Ba2+/Pb2+ Ti4+ O2- Non-polar cubic above Tc <100> tetragonal below Tc EEWS-90.502-Goddard-L15

  21. Bulk Ferroelectric Actuation s s V 0 V s s Strains, BT~1%, PT~5.5% Apply constant stress and cyclic voltage Measure strain and charge In-situ polarized domain observation US Patent # 6,437, 586 (2002) Eric Burcsu, 2001 EEWS-90.502-Goddard-L15

  22. Application: Ferroelectric Actuators Must understand role of domain walls in mediate switching 1.0 E 2 Experiments in BaTiO3 Strain (%) Domain walls lower the energy barrierby enabling nucleation and growth 0 1 -10,000 0 10,000 90° domain wall Electric field (V/cm) Switching gives large strain, … but energy barrier is extremely high! Essential questions: Are domain walls mobile? Do they damage the material? In polycrystals? In thin films? Use MD with ReaxFF EEWS-90.502-Goddard-L15

  23. Ti atom distortions and polarizations determined from QM calculations. Ti distortions are shown in the FE-AFE fundamental unit cells. Yellow and red strips represent individual Ti-O chains with positive and negative polarizations, respectively. Low temperature R phase has FE coupling in all three directions, leading to a polarization along <111> direction. It undergoes a series of FE to AFE transitions with increasing temperature, leading to a total polarization that switches from <111> to <011> to <001> and then vanishes. EEWS-90.502-Goddard-L15

  24. Space Group & Phonon DOS EEWS-90.502-Goddard-L15

  25. Phase Transitions at 0 GPa, FE-AFE R O T C 1. G. Shirane and A. Takeda, J. Phys. Soc. Jpn., 7(1):1, 1952 EEWS-90.502-Goddard-L15

  26. EXAFS & Raman observations d (001) α (111) 26 • EXAFS of Tetragonal Phase[1] • Ti distorted from the center of oxygen octahedral in tetragonal phase. • The angle between the displacement vector and (111) is α= 11.7°. PQEq with FE/AFE model gives α=5.63° Raman Spectroscopy of Cubic Phase[2] A strong Raman spectrum in cubic phase is found in experiments. • B. Ravel et al, Ferroelectrics, 206, 407 (1998) • A. M. Quittet et al, Solid State Comm., 12, 1053 (1973) EEWS-90.502-Goddard-L15

  27. Polarizable QEq Proper description of Electrostatics is critical Allow each atom to have two charges: A fixed core charge(+4 for Ti)with a Gaussian shape A variable shell charge with a Gaussian shape but subject to displacement and charge transfer Electrostatic interactions between all charges, including the core and shell on same atom, includes Shielding as charges overlap Allow Shell to move with respect to core, to describe atomic polarizability Self-consistent charge equilibration(QEq) Four universal parameters for each element: Get from QM EEWS-90.502-Goddard-L15

  28. Validation • H. F. Kay and P. Vousden, Philosophical Magazine 40, 1019 (1949) • H. F. Kay and P. Vousden, Philosophical Magazine 40, 1019 (1949) ;W. J. Merz, Phys. Rev. 76, 1221 (1949); W. J. Merz, Phys. Rev. 91, 513 (1955); H. H. Wieder, Phys. Rev. 99,1161 (1955) • G.H. Kwei, A. C. Lawson, S. J. L. Billinge, and S.-W. Cheong, J. Phys. Chem. 97,2368 • M. Uludogan, T. Cagin, and W. A. Goddard, Materials Research Society Proceedings (2002), vol. 718, p. D10.11. EEWS-90.502-Goddard-L15

  29. Free energies for Phase Transitions Common Alternative free energy from Vibrational states at 0K We use 2PT-VAC: free energy from MD at 300K Velocity Auto-Correlation Function Velocity Spectrum System Partition Function Thermodynamic Functions: Energy, Entropy, Enthalpy, Free Energy EEWS-90.502-Goddard-L15

  30. Free energies predicted for BaTiO3 FE-AFE phase structures. Free Energy (J/mol) Temperature (K) AFE coupling has higher energy and larger entropy than FE coupling. Get a series of phase transitions with transition temperatures and entropies Theory (based on low temperature structure) 233 K and 0.677 J/mol (R to O) 378 K and 0.592 J/mol (O to T) 778 K and 0.496 J/mol (T to C) Experiment (actual structures at each T) 183 K and 0.17 J/mol (R to O) 278 K and 0.32 J/mol (O to T) 393 K and 0.52 J/mol (T to C) EEWS-90.502-Goddard-L15

  31. Nature of the phase transitions Displacive Order-disorder Develop model to explain all the following experiments (FE-AFE) EEWS-90.502-Goddard-L15

  32. Next Challenge: Explain X-Ray Diffuse Scattering Cubic Tetra. Ortho. Rhomb. Diffuse X diffraction of BaTiO3 and KNbO3, R. Comes et al, Acta Crystal. A., 26, 244, 1970 EEWS-90.502-Goddard-L15

  33. X-Ray Diffuse Scattering Photon K’ Phonon Q Photon K Cross Section Scattering function Dynamic structure factor Debye-Waller factor EEWS-90.502-Goddard-L15

  34. Diffuse X-ray diffraction predicted for the BaTiO3 FE-AFE phases. The partial differential cross sections (arbitrary unit) of X-ray thermal scattering were calculated in the reciprocal plane with polarization vector along [001] for T, [110] for O and [111] for R. The AFE Soft phonon modes cause strong inelastic diffraction, leading to diffuse lines in the pattern (vertical and horizontal for C, vertical for T, horizontal for O, and none for R), in excellent agreement with experiment (25). EEWS-90.502-Goddard-L15

  35. FE-AFE Explains X-Ray Diffuse Scattering Cubic Tetra. Ortho. Rhomb. Experimental Cubic Phase (001) Diffraction Zone Tetra. Phase (010) Diffraction Zone Rhomb. Phase (001) Diffraction Zone Ortho. Phase (010) Diffraction Zone experimental Diffuse X diffraction of BaTiO3 and KNbO3, R. Comes et al, Acta Crystal. A., 26, 244, 1970 EEWS-90.502-Goddard-L15

  36. Domain Walls Tetragonal Phase of BaTiO3Consider 3 cases + + + + + + + + + + + + + + + + + + + - - - - + + + + - - - - P P P P P P - - - - - - - - - - - - - - - - - - - - - + + ++ - - - - + + + + + + + + + + + + + + + + + + + + + + + - - - - + + + + - - - - E=0 E - - - - - - - - - - - - - - - - - - - - - + + ++ - - - - + + + + CASE I CASE II CASE III experimental Polarized light optical micrographs of domain patterns in barium titanate (E. Burscu, 2001) • Open-circuit • Surface charge not neutralized • Domain stucture • Short-circuit • Surface charge neutralized • Open-circuit • Surface charge not neutralized EEWS-90.502-Goddard-L15 36

  37. 180° Domain Wall of BaTiO3 – Energy vs length z o y Type I Type II Type III 37 Ly EEWS-90.502-Goddard-L15

  38. 180° Domain Wall – Type I, developed z o y C A D A B Wall center Transition layer Domain structure A A B B C C D D 38 Ly = 2048 Å =204.8 nm Displacement dY Zoom out Displace away from domain wall Displacement dZ Displacement reduced near domain wall Zoom out EEWS-90.502-Goddard-L15 38

  39. 180° Domain Wall – Type I, developed z o y Wall center: expansion, polarization switch, positively charged Transition layer: contraction, polarization relaxed, negatively charged Domain structure: constant lattice spacing, polarization and charge density 39 L = 2048 Å Polarization P Free charge ρf EEWS-90.502-Goddard-L15 39

  40. 180° Domain Wall – Type II, underdeveloped z A C o y B D A B C D 40 L = 128 Å Polarization P Displacement dY Displacement dZ Free charge ρf Wall center: expanded, polarization switches, positively charged Transition layer: contracted, polarization relaxes, negatively charged EEWS-90.502-Goddard-L15 40

  41. 180° Domain Wall – Type III, antiferroelectric z o y 41 L= 8 Å Displacement dZ Polarization P Wall center: polarization switch EEWS-90.502-Goddard-L15 41

  42. 180° Domain Wall of BaTiO3 – Energy vs length z o y Type I Type II Type III 42 Ly EEWS-90.502-Goddard-L15

  43. 90° Domain Wall of BaTiO3 z L o y Wall center Transition Layer Domain Structure L=724 Å (N=128) • Wall energy is 0.68 erg/cm2 • Stable only for L362 Å (N64) EEWS-90.502-Goddard-L15 43

  44. 90° Domain Wall of BaTiO3 z L o y Wall center: Orthorhombic phase, Neutral Transition Layer: Opposite charged Domain Structure L=724 Å (N=128) Displacement dY Displacement dZ Free Charge Density EEWS-90.502-Goddard-L15

  45. 90° Domain Wall of BaTiO3 z L o y L=724 Å (N=128) Polarization Charge Density Free Charge Density Electric Field Electric Potential EEWS-90.502-Goddard-L15

  46. Summary III (Domain Walls) 180° domain wall • Three types – developed, underdeveloped and AFE • Polarization switches abruptly across the wall • Slightly charged symmetrically 90° domain wall • Only stable for L36 nm • Three layers – Center, Transition & Domain • Center layer is like orthorhombic phase • Strong charged – Bipolar structure – Point Defects and Carrier injection EEWS-90.502-Goddard-L15 46

  47. Mystery: Origin of Oxygen Vacancy Trees! 0.1μm Oxgen deficient dendrites in LiTaO3 (Bursill et al, Ferroelectrics, 70:191, 1986) EEWS-90.502-Goddard-L15

  48. Aging Effects and Oxygen Vacancies Vz c a Vx Vy • Problems • Fatigue – decrease of ferroelectric polarization upon continuous large signal cycling • Retention loss – decrease of remnant polarization with time • Imprint – preference of one polarization state over the other. • Aging – preference to relax to its pre-poled state Pz Three types of oxygen vacancies in BaTiO3 tetragonal phase: Vx, Vy & Vz EEWS-90.502-Goddard-L15

  49. Oxygen Vacancy Structure (Vz) Ti Ti O O O O 2.12Å 2.12Å O O 1.93Å 1.84Å Ti O Ti O O O 2.12Å O 4.41Å 1.93Å Ti O O O O Ti 2.12Å O 1.85Å O 1.93Å Ti 2.10Å O O O O Ti P P P O O Ti 1 domain No defect defect leads to domain wall 1.93Å O 2.12Å O O Remove Oz Ti 1.93Å O 2.12Å O O Ti 1.93Å O 2.12Å O O Ti P Leads to Ferroelectric Fatigue EEWS-90.502-Goddard-L15

  50. Single Oxygen Vacancy TSxz(1.020eV) TSxy(0.960eV) TSxz(0.011eV) Vy(0eV) Vx(0eV) Diffusivity Mobility EEWS-90.502-Goddard-L15

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