Introduction to Crystal Growth

In this module, an introduction to crystal growth is given, ranging from the fundamental physical concepts to techniques as they currently used in both research and industrial production. In addition to teaching the thermodynamic principles, this involves in particular coverage of day-to-day business in laboratories for crystal growth. The module has the following content:

• Thermodynamics of alloys (phases and phase transitions, equations of state, thermodynamics potentials and equilibria, phase diagrams, Gibbs’ phase rule, …)
• Treatment of one- and two-component systems in ideal and non-ideal solution
• Metallurgical phase diagrams (binary, pseudo-binary, ternary) and their application to crystal growth
• Crystal growth, nucleation, grain selection
• Transport phenomena (material, momentum, heat) and growth kinetics
• Techniques for the growth of volume and thin-film samples from solid state, melt, gas phase, and solution
• Phase analysis and structure determination of single-crystal and polycrystal specimens (diffraction, spectroscopy, microscopy, indirect methods, …)

After successful participation, the students are able to explain the basic thermodynamics involved in crystal growth. Moreover, they can discuss processes relevant for crystal growth, such as nucleation and grain selection, in a phenomenological manner. They can interpret metallurgical phase diagrams, inferring basic information on the growth kinetics as well as suitable growth techniques.

For this purpose, the students developed an overview over single crystal growth techniques as they are used throughout research and industrial applications. In particular, the students can describe the underlying physical processes and the key (dis-)advantages of these techniques. Furthermore, the students possess basic knowledge of methods used for the metallurgical characterization of single-crystal and polycrystal samples.

No preconditions in addition to the requirements for the Master’s program in physics.

During the lecture the basics of both, theory and experimental methods are explained and elucidated by tangible examples. Digital handwriting is used to maintain an adequate pace while developing the basic principles. Functional relationships are illustrated using interactive graphics and short example programs. Open discussions with the students are an important integral part of the lecture. In the examples, experiment and theory are treated on an equal footing, highlighting their close integration.

During the exercises the knowledge is deepened by applying the learned concepts to selected examples. In addition to classical exercises, this includes in particular discussions on examples taken from the topical research as well as visits of crystal growth laboratories.

Digital handwriting using Tablet-PC

Lecture slides, dynamic graphics, videos

Lecture notes with literature references

Exercises and examples

K.-T. Wilke and J. Bohm “Kristallzüchtung”

L. Schultz and J. Freudenberger “Physikalische Werkstoffeigenschaften”

P.R. Sahm, I. Egry and T. Volkmann “Schmelze, Erstarrung, Grenzflächen“

R.-E. Reed-Hill “Physical Metallurgy Principles“

A. Smakula “Einkristalle”

B.R. Pamplin (Ed.) “Crystal Growth”

D.T.J. Hurle (Ed.) “Handbook of Crystal Growth”

W.A. Tiller “The Science of Crystallization”

H. Okamoto “Phase Diagrams for Binary Alloys”

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions, sample calculation, and discussions on the basis of sketches, diagrams, and formulas.

For example an assignment in the exam might be:

• Which forms of enthalpy may play a role in a growth from the melt?
• Using the relation of Clausius-Clapeyron, explain how changes of pressure or temperature may influence the chemical potential.
• What is the difference between an ideal and a non-ideal solution?
• What consequences for the single crystal growth of Ce2Ni7 do you infer from the provided phase diagram of the Ce-Ni system? Which growth technique would you use?
• A pressed pellet, consisting of powders of yttrium oxide, barium oxide, and copper oxide, was reacted in a furnace at 900°C. When trying to metallurgically characterize the specimen, which methods would you use? Explain your approach.