Introduction to the Theory of Lattice Vibrations and their Ab Initio Calculation
Ion Errea Lope University of the Basque Country
Ion Errea holds a degree (2007) and PhD (2011) in Physics from the University of the Basque Country (UPV/EHU). He was a post-doctoral researcher at the Pierre and Marie Curie University in Paris and the Donostia International Physics Centre (DIPC). He was shortlisted for the 2015 Volker Heine Young Investigator Award and was selected Emerging Leader by the Journal of Physics: Condensed Matter. Since 2018, he has led the research group on Quantum Theory of Materials at the Centre for Material Physics (CSIC-UPV/EHU). His research focusses on the development of theoretical methods of calculating complex properties of solids and has been published in prestigious scientific journals including Nature, P. N. A. S, Nano Letters and Physical Review Letters. He has also been a guest speaker at dozens of international conferences.
Session2 (2 hours): Lectures and Exercises: 19:00 – 21:00 (Beijing time, BJT)[12:00-14:00, CET; 8:00-10:00, UYT]
Check the program for the newest time. Some courses will be hold at different times.
Program: on-line meetings via ZOOM and Tencent Meeting
Day 1
Feb 1, 2022, Tuesday
Session 1: 15:00-17:00 (MN)
Crystal pattern Crystal lattice vs. crystal pattern and crystal structure. Symmetry directions in a lattice .Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D. Crystal families. Symmetry groups and types of symmetry in direct space: morphological symmetry; symmetry of physical properties; symmetry of lattices; symmetry of the unit cell content; symmetry of crystallographic patterns.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MN)
Crystallographic point groups Stereographic projection and the morphology of crystals. Hermann-Mauguin symbols for point groups. Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem.
Crystallographic point groups (Cont.) Group actions: conjugation and normalizers. Wyckoff positions for point groups. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups. Overview of crystallographic point groups. Coset decomposition of the space group with respect to its translation subgroup.
Tutorial session (optional) (19:00-19:40)
Session 2: 19:40-21:40 (MN)
Space groups – general introduction: Periodic structure of the crystalline matter: lattices and their basic properties.
Space groups and their descriptions (cont.): Exercises on orthogonal projections of space groups 2.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MIA)
Space groups and their descriptions (cont.): Space groups and their description in International Tables for Crystallography, Vol. A: Matrix-column formalism in the description of space-group symmetry. Isometries and crystallographic symmetry operations. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets.
Transformations of the coordinate systems: Change of origin and orientation. Conventional and non-conventional descriptions of space groups; ITA-settings. Bilbao Crystallographic Server: Computer databases and access tools to crystallographic symmetry data for space groups
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (MIA)
Subgroups of space groups: types of subgroups of space groups. Maximal subgroups in International Tables for Crystallography, Vol. A1. Hermann theorem. Maximal subgroups; series of isomorphic subgroups. Coset decomposition.
Group-subgroup relations between space groups (cont.) Domain-structure analysis in structural phase transitions. Relations of Wyckoff positions for a group-subgroup pair.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00(LS)
Reciprocal space Crystallographic calculations in reciprocal space. Introduction to diffraction.
Diffraction symmetry Laue classes, Friedel’s law, resonant scattering. Integral, zonal and serial reflection conditions and their use to determine the space-group type. Special reflection conditions.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MIA)
Group-subgroup relations between space groups (cont.) Computer databases and access tools to crystallographic symmetry data for space groups. Maximal subgroups data and related computer application in the Bilbao Crystallographic Server.
Crystal-structure tools of the Bilbao Crystallographic Server Crystal-structure descriptions. Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal structure descriptions (the programs EQUIVSTRU and COMPSTRU). Crystal-structure descriptions compatible with symmetry reduction (the program TRANSTRU). Hands-on practicals with the computer tools for crystal-structure descriptions
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (LS)
Crystal-structure tools of the Bilbao Crystallographic Server (cont.) Crystal-structure relationships. Family trees (Baernighausen trees) of crystal structures: aristotype (basic) and hettotypes (derivative) structures). Hands-on practicals with the program STRUCTURE RELATIONS.
Crystal-structure tools of the Bilbao Crystallographic Server (cont.) Structural pseudosymmetry. Pseudosymmetry search for new ferroics. Application in structural phase transitions. Hands-on practicals with the program PSEUDO.
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (MIA)
General remarks on representations Representations of discrete groups: definition and basic properties. Reducible and irreducible representations. Equivalence of representations. Theorem of orthogonality. Characters of representations and character tables. Subduced and direct-product representations
Representations of point groups Representations of Abelian groups: cyclic groups and direct products of cyclic groups. Character tables of representations of point groups. Database of Bilbao Crystallographic Server on point-group representations.
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (ZS)
Crystal-field theory Group theory-based selection rules, energy level splitting on symmetry degradation, crystal-field potentials of point groups.
RODRIGUEZ-CARVAJAL Juan is the author of FullProf, one of the most used powder diffraction computer programs in the world. (More than 6400 citations, WoS, of the article Physica B 192, 55 (1993); about 12000 citations of the use of the program in Google Scholar)
Juan works at the Institute Laue-Langevin as Staff Scientist. He has full experience in the following areas: Powder and single crystal x-rays and neutron scattering; Symmetry analysis, crystallography and magnetism; Oxides presenting remarkable properties(superconductivity, giant magnetoresistance, charge, spin & orbital ordering.); Computer programming and data analysis.; Neutron diffraction instrumentation.
This course is sponsored by International Office of University of Science and Technology Beijing, as part of the “Go Beyond International Course”.
Due to the course capacity, only 40 participants will be engaged in the ZOOM live course, in which they could ask for guidance and explanations from Juan. Please fill in the form and you will be informed about the remaining vacancies.
The course will also be simultaneously broadcasted via Tencent meeting.
The latest news and the Tencent meeting ID will updated in this webpage.
Ming Zhao+, Zhiyu Yang+, Lixin Ning*, Zhiguo Xia*, Tailoring of White Luminescence in a NaLi3SiO4:Eu2+ Phosphor Containing Broad-Band Defect-Induced Charge-Transfer Emission, Adv. Mater.,2021. [DOI: 10.1002/adma.202101428]
Ming Zhao, Qinyuan Zhang, Zhiguo Xia*, Narrow-Band Emitters in LED Backlights for Liquid-Crystal Displays,Mater. Today, 2020, 40, 246. [DOI: 10.1016/j.mattod.2020.04.032]
Ming Zhao, Zhiguo Xia*, Xiaoxiao Huang, Lixin Ning*, Romain Gautier, Maxim S. Molokeev, Yayun Zhou, Yu-Chun Chuang, Qinyuan Zhang, Quanlin Liu, Kenneth R. Poeppelmeier*, Li Substituent Tuning of LED Phosphors with Enhanced Efficiency, Tunable Photoluminescence and Improved Thermal Stability, Sci. Adv., 2019, 5, eaav0363. [DOI: 10.1126/sciadv.aav0363]
Ming Zhao, Hongxu Liao, Maxim S. Molokeev, Yayun Zhou, Qinyuan Zhang, Quanlin Liu and Zhiguo Xia*, Emerging Ultra-Narrow-Band Cyan-Emitting Phosphor for White LEDs with Enhanced Color Rendition, Light. Sci. Appl., 2019, 8, 38. [DOI: 10.1038/s41377-019-0148-8]
Ming Zhao, Kun Cao, Mengjia Liu, Jing Zhang, Rong Chen*, Qinyuan Zhang, and Zhiguo Xia*, Dual-Shelled RbLi(Li3SiO4)2:Eu2+@Al2O3@ODTMS Phosphor as a Stable Green Emitter for High-Power LED Backlights, Angew. Chem. Int. Ed., 2020, 59, 12938–12943. [DOI: 10.1002/ange.202003150]
Ming Zhao, Zhiguo Xia*, Maxim S. Molokeev, Lixin Ning*, Quanlin Liu, Temperature and Eu2+ Doping induced Phase Selection in NaAlSiO4 Polymorphs and the Controlled Yellow/Blue Emission, Chem. Mater., 2017, 29, 6552–6559. [DOI: 10.1021/acs.chemmater.7b02548]
Ming Zhao+, Yayun Zhou+, Maxim S. Molokeev, Qinyuan Zhang, Quanlin Liu, Zhiguo Xia*, Discovery of New Narrow-Band Phosphors with the UCr4C4-Related Type Structure by Alkali Cation Effect, Adv. Opt. Mater., 2019, 7, 1801631. [DOI: 10.1002/adom.201801631]
Ming Zhao, Qinyuan Zhang, Zhiguo Xia*, Structural Engineering of Eu2+-Doped Silicates Phosphors for LED Applications, Accounts Mater. Res., 2020, 1(2), 137. [DOI: 10.1021/accountsmr.0c00014]
Hongxu Liao+, Ming Zhao+, Yayun Zhou+, Maxim S. Molokeev, Quanlin Liu, Qinyuan Zhang, and Zhiguo Xia*, Polyhedron Transformation toward Stable Narrow-Band Green Phosphors for Wide-Color-Gamut Liquid Crystal Display, Adv. Funct. Mater.,2019, 29, 1901988. [DOI: 10.1002/adfm.201901988]
Hongxu Liao+, Ming Zhao+,Maxim S. Molokeev, Quanlin Liu, Zhiguo Xia*, Learning from a Mineral Structure toward an Ultra-narrow Band Blue-emitting Silicate Phosphor RbNa3(Li3SiO4)4:Eu2+, Angew. Chem. Int. Ed., 2018, 57, 11902-11905. [DOI: 10.1002/ange.201807087]
([+] These authors contributed equally to this work)
1. Zhou, D. D.; Song, Z.; Zhou H.; Liu, Q. L. Enhanced persistent luminescence via Si4+ co-doping in Y3Al2Ga3O12:Ce3+,Yb3+,B3+. J. Lumin. 2020, 222, 117190. [DOI: 10.1016/j.jlumin.2020.117190]
2. Song Z.; Zhou, D. D.; Liu, Q. L. Tolerance factor and phase stability of the garnet structure. ACTA CRYSTALLOGRAPHICA SECTION C-STRUCTURAL CHEMISTRY, 2020, 76, 311. [DOI: 10.1107/S2053229619011975]