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Normally to prepare input file (structure of materials) for Quantum Espresso/VASP, I searched the corresponding CIF file from this website (http://www.crystallography.net/cod/result.php), after that I use Vesta to get the relevant atomic positions and lattice parameter. I have a question regarding that. Most of the CIF files cell temperature are at 298 K, so if we use the structural data from that CIF (298 K) and run Quantum Espresso/VASP to find electronic properties (e.g, density of states, fermi level), Are the output data of quantum espresso represent the temperature of 0 K?

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  • $\begingroup$ Please, check here. $\endgroup$
    – Camps
    Commented May 15 at 18:20

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This is slightly difficult to answer, since temperature has several effects and in DFT these can be accounted for in different ways. Probably the main four direct effects are:

  • Thermal expansion (or contraction)
    As the temperature increases, most materials and fluids expand (although some contract); this may be accompanied by an internal atomic relaxation as well. This change in the material structure affects the DOS and band-structures, and the band-gap and magnetic properties are particularly sensitive to this.\

  • Atomic motion
    As well as the overall lattice change, the atoms might change their equilibrium positions, which can even change the crystal symmetry. This has a direct effect on the band-structure, DOS and magnetic properties, even in the Born-Oppenheimer approximation (i.e. even when the motion itself is neglected).

    This effect is especially important for materials with internal degrees of freedom (e.g. GaN), or soft phonon modes which may become unstable. For lighter elements you may also need to take zero-point motion into account; the perovskite SrTiO$_3$, for example, requires modelling of zero-point motion to get the oxygen positions correct and, hence, the rotations of the TiO$_3$ octahedra.

  • Fermi-level broadening
    The quasi-particles, whose states we usually approximate by the Kohn-Sham eigenstates in DFT, gain thermal energy as the temperature increases. The main effect is to broaden the Fermi-level, causing thermal excitation of the quasi-particles across the band-gap. This leads to partial occupancies of the bands near the Fermi level, as upper valence bands start to empty and lower conduction bands start to fill. This is not usually very important at room temperature unless the band-gap is very small, since room-temperature $k_bT$ is only $\sim$ 25 meV, but it is important at higher temperatures. This can be modelled with a Fermi-Dirac smearing function (on top of any broadening used for the Brillouin zone integration).

  • Ground state thermal disorder
    If the material has a degenerate (or near-degenerate) ground state, then at finite temperature these different atomic configurations may all be present in the experimental sample. Most experimental structures are obtained by diffraction, so they will average over all these effects. For example, you might have an OH group which could be aligned either O-H or H-O in a particular direction, and these might have the same energy. In the experimental structure, the results will have been averaged over these configurations, which leads to a structure with the symmetry of the thermal average positions (H-O-H in my example). This is particularly confusing when the stated crystal symmetry cannot be satisfied by any atomic configuration! Sometimes the experimental structures indicate this by fractionally occupying atomic sites, in which case you will need to create a supercell to model it and almost certainly have to lower the symmetry from the one stated in the experimental structure.

Using an experimental structure

In general, you should always model a material at the ground state of the model, i.e. you should optimise your simulation geometry. For most 3D materials, thermal expansion is the most important effect to account for when you take an experimental lattice structure and try to model it in DFT (or any other ab initio method), so you could start with a basic variable-cell geometry optimisation.

When you optimise the atomic coordinates, remember that the symmetry could change as the cell expands (or contracts). Adding a little noise to the atomic positions will usually break all the symmetries, and then you can see whether the atoms relax back to the Wyckoff sites for the previous symmetry. The noise should be relatively small so that the atoms are in the quadratic energy well and optimisation is quick, but remember that it needs to be large enough for the forces to be above the geometry optimisation force tolerance, and if you can't turn off the symmetry finder you'll also need the displacement to be larger than the symmetry tolerance.

Remember also that the experimental structure is not "true", it is someone's best attempt at a complicated non-unique inversion procedure, taking a 2D diffraction pattern and inferring a 3D structure from it. One common problem is that, in X-ray diffraction (XRD), atoms which don't have many electrons are virtually invisible, and hydrogen positions in particular are usually generated from classical modelling in the "experimental" structures. I recommend always optimising hydrogen positions, even if you're convinced that the experimental structure is very good.

If you expect your system to be magnetic, remember that many experimental methods are not sensitive to this and will give you the structural unit cell, not the magnetic unit cell. Antiferromagnetic materials are the classic example, where the primitive cell you need for modelling is twice the primitive cell most experimental methods will give.

Other effects

I've assumed here that the crystal phase you're studying is still stable at the different temperatures, but at some point the phase will change as you increase temperature. Some materials have several different solid phases (e.g. perovskites), and at some point the material will melt and then boil (or sublime).

The coupling between electrons and phonons is usually neglected, since we use the Born-Oppenheimer approximation, but it can be calculated perturbatively and it does depend on temperature. The acoustic phonons have zero frequency (energy) at the $\Gamma$-point (the zone centre) and have a linear dispersion, so they can be important even when most phonon modes may be neglected safely. Lower dimensional materials also have very low-frequency flexural phonon modes, which would also need to be considered alongside the acoustic modes. These flexural modes effectively replace some of the acoustic modes the 3D material would have, and they have a quadratic dispersion which means their frequency typically remains low across more of the Brillouin zone.

In a magnetic material, the magnetic phase may change as temperature increases, and spins also become more disordered, eventually causing the material to demagnetise (at the Curie/Neel temperature). This is not captured in standard DFT approaches, it is another electron-phonon coupling effect. More complicated magnetic phase changes are also possible, for example different sublattices may demagnetise at different temperatures, and other phenomena such as the formation and movement of domain walls can also occur.

A real material will have defects, and some of these will start to migrate at higher temperatures - particularly vacancies and surface adatoms.

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  • $\begingroup$ So, the CIF files (at room temperature, experimental) atomic positions need to be optimized ( to make ground state model) before preparing the input files for QE/VASP? For example: Optimizing atomic positions (relax.in), optimizing Unit cell (vc-relax.in). If I performed the above two steps, then the structure represents the ground state model? $\endgroup$ Commented May 16 at 14:14
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    $\begingroup$ @Md.JahidHasanSagor in general, yes they need to be fully optimised (positions and lattice). It's safer to optimise atoms and lattice together usually, but as long as you are careful you'll get the right answer doing them separately, as long as you check, e.g. relax positions, then lattice, then positions - and only stop if that last step doesn't change anything. Just remember to check the symmetries are OK before you impose any! $\endgroup$ Commented May 16 at 14:47
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    $\begingroup$ Therefore, I can start optimizing 1) the positions, then lattice 2)again positions, then lattice If I see step 2 represent the similar data as step 1, then I will stop. If not, I will be doing same thing until the last step same as previous one, right? $\endgroup$ Commented May 16 at 14:58
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    $\begingroup$ @Md.JahidHasanSagor yes, that should be safe (as long as you're careful with the symmetry). In fact I usually optimise the lattice, then optimise the positions and lattice together from then on. Either way, it sounds like a lot of computer time, but the whole point is that the later steps shouldn't have to do much! $\endgroup$ Commented May 16 at 21:45

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