quick start

2 Topics
setting the stage

11 Topics
density functional theory

24 Topics
crystallography

8 Topics
geometry optimization

18 Topics
electronic structure

9 Topics
chemical bonding

7 Topics
elasticity

9 Topics
precision and accuracy

6 Topics
phonons and temperature

4 Topics
band gaps

2 Topics
let’s play!

17 Topics
project

8 Topics
As elastic constants are not easily measured experimentally, there are by now many more crystals for which there are DFT values than crystals for which there are experimental values.

Read this paper by de Jong et al., on a database of ab initio computed elastic constants (alternative download here, in case your institute does not subscribe to this journal). Focus on the first 4.5 pages of the pdf, plus the discussion of Fig. 2. Try to connect the information you read there with the information in the videos on elastic properties you just studied.

The paper mentions the “Voigt-Reuss-Hill average” of elastic constants and derived properties. This connects the ideal world of DFT on single crystals to the real world of polycrystalline solids. The Voigt procedure is a way to convert the computed single crystal information into estimated polycrystalline information, and this procedure is known to provide an upper bound of the values that you can experimentally expect. The same applies to the Reuss procedure, which results in a lower bound. The Voigt-Reuss-Hill average is the average of the Voigt and Reuss values, which results in fair approximations of the experimental polycrystalline values. Table 1 in de Jong et al. gives the formulae for the Voigt-Reuss-Hill averages of the major elastic moduli. If you want to read more about this, this paper is a possible starting point.

Afterwards, go to www.materialsproject.org (where this database of elastic constants is stored), and look up the full elastic tensor of molybdenum carbide. Mind that it gives you the Voigt-Reuss-Hill averages of the elastic moduli right away. As an illustration to the power of this information, consider that now you’re able to answer the question “What’s the speed of sound in molybenum carbide ?” — that would be really hard to answer having only experimental information.

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