1. 1 4.1 Introduction to CASTEP (1)  CASTEP is a state-of-the-art quantum mechanics-based program designed specifically for solid-state materials science. CASTEP employs the density functional theory plane-wave pseudo-potential method, which allows you to perform first-principles quantum mechanics calculations that explore the properties of crystals and surfaces in materials such as semiconductors, ceramics, metals, minerals, and zeolites.  Typical applications involve studies of surface chemistry, structural properties, band structure, density of states, and optical properties. CASTEP can also be used to study the spatial distribution of the charge density and wave functions of a system.

2. 2 4.1 Introduction to CASTEP (2)  CASTEP can be used effectively to study properties of both point defects (vacancies, interstitials, and substitutional impurities) and extended defects (e.g., grain boundaries and dislocations) in semiconductors and other materials.  Furthermore, the vibrational properties of solids (phonon dispersion, total and projected density of phonon states, thermodynamic properties) can be calculated with CASTEP using either the linear response methodology or the finite displacements technique. The results can be used in various ways, for instance, to investigate the vibrational properties of adsorbates on surfaces, to interpret experimental neutron spectroscopy data or vibrational spectra, to study phase stability at high temperatures and pressures, etc. The linear response method can also be used to calculate the response of a material to an applied electric field - polarizability for molecules and dielectric permittivity in solids - and to predict IR spectra.

3. 3 4.2 Modeling Figure 4.1. Model for the motion energy calculation. (a)Supercell with an extra oxygen vacancy. (b)Supercell with a oxygen ion located at the saddle point.

4. 4 4. 3 Choosing Parameters  The structural parameters were calculated by geometry optimization with high accuracy from first principles.  Calculations of the total energy of the systems were carried out using the pseudo-potential method.  All static calculations were performed using the CASTEP code with ultra soft pseudo-potentials and the Perdew-Burke-Ernzerhof (PBE) GGA exchange correlation term.  The ultra-find convergence of the total energy and the energy cutoff were chose.  Spin polarization was taken into account in this study.

5. 5 4. 4 Examples  Example 1: migration energy of oxygen ion in the BaCo 0.875 B 0.125 O 3 (B= Sc, Mn, Ni, Fe, Co, Y, Nb, In, Sn) Figure 4.2 Migration energy of oxygen ion in the BaCo 0.875 B 0.125 O 3 system

6. 6 4. 4 Examples  Example 2:migration energy of oxygen ion in the Ba 0.875 A 0.125 CoO 3 (A= La, Sr, Ba, Ca) Figure 4.3 Migration energy of oxygen ion in the Ba 0.875 A 0.125 CoO 3 system

7. 7 4. 4 Examples  Example 3: Calculation for oxygen ion migration in SrBO 3  The aim of calculation was to choose a better element as a B-site dopant in SrTiO 3 to lower the oxygen ion migration energy and thus increase the oxygen ion conductivity. The ion migration energy was referred to as the activation energy for oxygen ion conduction. The ion migration energies in SrBO 3 (B=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, As, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Cd, In, Sn and Sb)

8. 8 Figure 4.4 Migration energy of oxygen ion in the SrBO 3 system X. Li et al. / Electrochemistry Communications 10 (2008) 1567 – 1570

9. 9 4.5 Testing Methods  Electron-blocking method  Thermogravimetric testing  Concentration cell  Chemical titration