In this course the basic elements necessary to describe the microscopic properties of crystalline

matter are presented. The first topic introduces the necessary elements for a classification based

on the geometric ordering of atoms. The next topic discusses the classification of solids based on

the valence electronic structure of the atoms. The third theme describes the physical properties

and the effect of symmetry on them. Finally, the bases of crystal diffraction are presented as a

technique for the determination of crystalline structures.

- To know and to handle the physical and mathematical fundamentals of the diffraction of

X-rays and electrons for the structural analysis of matter.

- Development of skills to visualize three-dimensional structures and recognize different

structures.

- Identify the symmetry-elements and operations, lattice-types, crystalline systems,

point-groups and space-groups, as well as notation systems.

Structural Properties of Solids (6ECTS, optional, 4th year)



Syllabus



Crystal symmetry

1. Introduction to the structure of solids. Symmetry-elements and transformations. Proper and

improper operations. Helical axes and sliding planes. Bravais lattice. Point groups. Crystal

systems and Bravais lattices in 2 and 3 dimensions. Wigner-Seitz lattice. Space groups.

Setting standard. Transformations between different settings. Symmorphic and

non-symorphic groups. Chirality and enantiomorphism. Wickoff positions. Type structures.

2-Classification of solids and cohesion energy

Molecular bonds. Molecular, ionic and covalent solids. Ionic radii. Stability of ionic

structures. Hydrogen bond. Cohesion, general concepts. The noble gas solids. Lennard-Jones

potential. Madelung’s constant. Cohesion energy in metals.

3-Physical properties of solids

Crystal anisotropy. Tensor physical properties. Symmetry of physical properties: reduction

of tensors. Curie-Neumann principle. Rank 1 tensors: polarization. Rank 2 tensors: tension

and deformation. Propagation of elastic waves: elastic constants. Piezoelectricity.

Thermodynamic properties of crystals: thermoelastic effect, heat of deformation, direct

effects, coupled effects. Pyroelectricity. Examples of optical tensors.

4-Diffraction and solid structure determination

Physical bases of diffraction. Reciprocal lattice. X-rays, neutrons and electrons. Diffraction

geometry. Diffraction by gases, liquids and solids. Laue equations. Bragg’s law. Structure

factor.

The development of course content will be done through in-class lessons. The resolution of

exercises will be done by the teacher and students will have to do the presentation of their work.

The course is complemented with the contents presented in the corresponding course in Egela,

where collections of exercises and exams from previous courses can be found.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Realization of Practical Work (exercises, cases or problems) (%): 50
  • Exhibition of works, readings ... (%): 50

P : Participation in classroom practice sessions. It includes periodic delivery of exercises resolved

in class.

T : Exhibition of works carried out individually or in groups.

E: Final exam.

Three options are considered for the calculation of the final grade:

Option 1: Continuous evaluation 1: P + T

Option 2: Continuous evaluation 2: (P + T ) × 0.7 + E × 0.3

Option 3: Final exam: E.

By default, option (1) will be assumed. To take advantage of option (3) the intention to renounce

continuous assessment must be communicated in writing to the teacher before November 15.

People who appear on the day of the exam without having renounced the continuous evaluation

will take advantage of option (2).

Final exam, whose result will be 100 % of the final grade.

Curso en Egela: https://egela.ehu.eus/course/view.php?id=21799

Basic bibliography

- Malgrane, C., Ricolleau, C., Schlenker, M., Physical Properties of Crystals. Ed. Springer

2014, ISBN 978-94-017-8993-6 (eBook).

- Ashcroft, N.W., Mermin, N.D. Solid State Physics. Holt, Rhinehart and Winston 1976.

- Giacovazzo, C., Fundamentals of Crystallography Oxford Univ Press, 1992.

- Nye, J.F., Physical Properties of Crystals: Their Representation by Tensors and Matrices

Oxford Univ Press, 1985.

Web addresses

Bilbao Crystallographic Server: www.cryst.ehu.eus
Inorganic Crystal Structure Database (ICSD): webbdcrista1.ehu.es/icsd/index.php
Materials Project: materialsproject.org