81829 - Introduction to Physics of Condensed Phase

Learning outcomes

At the end of the course, the student will acquire some basic concepts of condensed matter physics: Simmetry and order/disorder effects in atoms aggregates; mechanical properties of solids; the concept of lenght scale and its influence on the properties of condensed matter. How a solid nucleates and grows. Phase diagrams.

Course contents

Recommended prerequisites/prerequisites

Knowledge of: classical mechanics and thermodynamics are requirements for successful attendance of the course. Mathematical analysis. Knowledge at least at an introductory level of quantum theory or simultaneous attendance of a quantum physics course.

The course is experimental and phenomenological in nature and is aimed mainly but not exclusively at students of Materials Science, at students interested in the future achievement of a master's degree in Materials Physics and Nanoscience and at those interested in Physics of the Earth system or Science of Climate . During the lessons, scientific videos and images regarding the phenomena discussed are shown. The aim of the course is to introduce the student to natural phenomena and important effects regarding the condensed states of matter and some quantum phenomena that occur in matter in the solid state. The technological applications of the phenomena considered are highlighted.

The aim of the course is also to introduce students to some of the most current and interesting research areas in the Physics of Condensed States. The course is divided into various parts, which are connected to each other.Contents

1 Sets of atoms and molecules.

The concept of symmetry and symmetry breaking is introduced, with particular emphasis on the symmetry breaking that occurs in the transition from one condensed state to another. The types of rigid symmetries in the plane and in space arise. Examples of symmetries in nature and their breaking are therefore presented: drops of water falling into a puddle; circles in the wheat fields, the trunk of a tree, the deformation of a can.

Periodic systems
A very important case of symmetrical arrangement is that of Crystals. Bravais lattices will then be illustrated and the reciprocal lattice will be defined, with examples of crystals and regular solids, with particular attention to cubic lattices.
The classification of crystals and solids in general also requires analyzing the type of bond established between the atoms and/or molecules that make up the solid. A classification of solids based on bonds will be presented, providing the main characteristics of each.
A macroscopic solid is hardly a single large crystal. Polycrystalline solids and nanometric crystals will therefore be introduced, showing how the mechanical, optical and electrical properties of a polycrystal change compared to those of a single crystal. In particular, the properties of solids made up of nanometric crystals will be discussed. To conclude, Carbon and its phases will be examined: diamond, graphite, fullerenes, nanotubes, graphene.

Aperiodic and disordered systems.

Not all solids and certainly not liquids can be described as periodic aggregates. In some cases the solid cannot be described as a Bravais lattice. Quasi-Crystals are then presented and the problem of tessellations is discussed, firstly presenting the problem of the aperiodic Penrose tessellation of the plane. We subsequently discuss the recent discovery of the Einstein (not Albert) tile which allows an aperiodic covering of the plane with a single type of tile. The structure of amorphous substances such as glass is then described and compared with that of liquids. Finally, multi-phase systems are presented. As an example, we will illustrate the case of airgel, which is a material less dense than air and with exceptional thermal insulation properties, used both in NASA missions and in building cladding.

2 Energy/Surface tension

In liquids, surface tension is an important phenomenon and is crucial in many phenomena. This concept and the associated one of surface energy are introduced. The wonders of soap bubbles are shown and superhydrophobic surfaces are discussed. The behavior of a drop falling into water and the phenomenon of wine tears will be shown. You will discover how spiders and water striders walk on water.

3 Nucleation theory.

Having previously described the types of solids, we will now discuss how they are formed. The process by which a new condensed phase originates is more complex than is commonly imagined. Whether the solid will be a single crystal, a polycrystal or an amorphous depends on a number of factors that will be examined. We will illustrate the essence of the theory of Nucleation, which can be homogeneous or, much more commonly, heterogeneous. This is of particular importance in phenomena such as cloud formation and precipitation. As a particular case, the formation of snowflakes will be described, a problem that has fascinated great scientists such as Kepler, who was the first to scientifically describe this phenomenon, also making a conjecture on the regular aggregation of atoms in solids which has only been proven a few years ago be true.

4 Binary phase diagrams

Phase diagrams for pure substances are introduced in introductory thermodynamics courses. However, many substances are made up of 2 or more components. Important examples are metallic alloys and rocks. This leads us to consider binary phase diagrams. In a binary phase diagram the system is usually described as a function of composition and temperature. In the case of solids and liquids, the pressure dependence is not particularly relevant and in any case these are systems that are usually at ambient pressure. The main phenomena that appear in a binary phase diagram are presented: coexistence of solid and liquid in a range of temperatures; presence of eutectics; phase separation in both the liquid and solid phases. The phase diagram of water and salt (Sodium Chloride) and that of steel are described as illustrative and particularly important cases. You will understand why the twin towers in New York collapsed and why ice chimneys (brinicles) form.

5 Mechanical properties of solids.

Why don't we sink into the floor? Why is glass (usually) fragile and metals are ductile? In this part of the course we investigate which factors determine the fragility, hardness and ductility of solids. We will first understand why the elastic constants of solids do not have much to do with the resistance of a material. The elastic modulus and yield strength of a solid will be defined. The various types of defects in solids will be illustrated and in particular the concept of dislocation will be introduced, a true deus ex machina of the mechanical properties of materials. We will describe how defects greatly influence not only the mechanical but also the optical and electromagnetic properties of solids, starting with those of semiconductors. Finally we will mention shape memory materials. These substances possess very particular mechanical properties thanks to a deformation mechanism that is completely different from that of other substances. You will see a crumpled Nitinol wire that returns to its initial shape, motors based on martensitic deformation and metal alloys with an elastic deformability comparable to that of a polymer rubber band.

6. Collective quantum phenomena

Introduction to collective quantum phenomena in condensed matter. Physical properties of ferromagnetic materials, superconductors, superfluids and their applications.

7. Quantum materials and quantum technologies

Materials for quantum computing and quantum sensors.

8. The new frontiers of research in the Physics of Matter

The course will include a cycle of introductory lectures on some current research topics in the field of condensed state physics, from quantum materials to nanomaterials.

Readings/Bibliography

For each part of the program, some articles and review will be given to the students.

Teaching methods

Lessons and demonstrations. Assignment for reading and discussion of articles.

Assessment methods

Oral exam/practical test.

In order to take the exam, a written essay (about 15 pages) is required on a topic agreed upon with the teacher. The topic can be presented in approximately 20 minutes, in one of the following two different ways.

a) Oral presentation, also with the aid of a projector (approximately 15 slides).

b) Preparation and practical demonstration during the examination of one or more experiments related to the topics covered in the course. In addition to the quality of the presentation and writing of the thesis, the final evaluation will be based on the degree of depth and understanding of both the topic presented and the basic concepts of the physics of condensed states addressed in the course.

Teaching tools

Scientific video will be used as a support of the concepts explained at lesson.

Office hours

See the website of Enrico Gianfranco Campari

See the website of Samuele Sanna