Be2Si: Group Symmetry Requirements of a Metal

[Feynmanfan]

Dear friends,

I'm having trouble understanding an article by M. Cohen and J. Corkill (Structural, bonding, and electronic properties of IIA-IV antifluorite compounds).

In this article Be2Si (an imaginary compound) is shown to be a metal. The argument used is GROUP SYMMETRY :... group symmetry requirements produce a band along Delta that crosses the fermi level...

My question is: what are these group symmetry requirements? How do they know the Fermi level is there?

I show you the band structure if you want to have a look.

Thanks!

 

[Astronuc]

Why would one consider Be₂Si and imaginary compound, and I assume they've (authors) made such materials. Silicides are quite common, but most are considered intermetallic compounds.

I would expect that Be₂Si is considered a metal based on mechanical, electrical and thermophysical properties, e.g. electrical and thermal conductivities.

 

[Feynmanfan]

Sorry Astronuc, that's the point of the article: no Be2Si is found in nature and it's predictions are base on ab initio calculations.

It is a metal and this can be deduced from the band structure. Please help me interpret the band structure.

The article says that it is a metal because of group symmetry considerations.

best,

 

[Astronuc]

Rather than say 'imaginary', we might say 'artificial'. Most metals are not found in their elemental forms in nature, and certainly all alloys are not found in nature, but we like to manipulate nature and extract metals and make alloys, and then we fight nature to mitigate corrosion.

Anyway, does one have a similar band structure for a known metal or alloy system?


There is an interesting patent on reacting vaporous metal with SiO2.

US patent - 3012902 It includes perhaps one way to produce Be₂Si.

 

[Feynmanfan]

THanks for your comment but what I want to know (whether it exists or not) is how we can infer from the band structure that the fermi level is where it is and that the Be2Si is a metal.

 

[kanato]

THanks for your comment but what I want to know (whether it exists or not) is how we can infer from the band structure that the fermi level is where it is and that the Be2Si is a metal.

You can tell if something is a metal or insulator from the band structure by filling up the lowest energy states with electrons. For instance, look at the band structure for Be2C. They are using pseudopotentials, so C has 4 electrons (2 2s + 2 2p) and Be has 2 electrons (the 2 2s electrons), so that's 8 electrons total. Each band holds two electrons, since they are doing spin unpolarized calculations. So 8 electrons fill the bottom 4 bands. If you count up 4 bands from the bottom, you see that once those bands are filled there is a gap. So you have an insulator (or semi-conductor, if the gap is less than 2eV or so).

In Be2Si, you don't see a gap after filling 4 bands. Actually there are band crossings so you can't fill either of the upper bands completely. So this way you know you have a metal.

You can't tell exactly where the Fermi level for a metal is going to be from looking at the band structure. From the above procedure you can roughly see where it will be, but you really need to look at the density of states: $$g(\varepsilon) = \sum_{nk} \delta(\varepsilon-\varepsilon_{nk})$$ where n is a band index, k is a point in the Brillouin zone, $$\varepsilon_{nk}$$ is the band energy, and the summation is taken over the whole Brillouin zone. Then $$N_{elec} = \int_{-\infty}^{E_f} g(\varepsilon) d\varepsilon$$ defines the Fermi energy.