Be2Si: Group Symmetry Requirements of a Metal

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In summary, the article by M. Cohen and J. Corkill discusses the structural, bonding, and electronic properties of IIA-IV antifluorite compounds, specifically the imaginary compound Be2Si which is shown to be a metal. The authors use group symmetry requirements and band structure calculations to determine that Be2Si is a metal. They also mention that this compound does not exist in nature and can only be predicted through ab initio calculations. The band structure is used to determine if a compound is a metal or insulator by filling up the lowest energy states with electrons. From this, it can be seen that Be2Si is a metal due to the lack of a band gap after filling 4 bands. However, the
  • #1
Feynmanfan
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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!
 

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  • #2
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.
 
  • #3
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,
 
  • #4
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.
 
  • #5
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.
 
  • #6
Feynmanfan said:
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: [tex] g(\varepsilon) = \sum_{nk} \delta(\varepsilon-\varepsilon_{nk})[/tex] where n is a band index, k is a point in the Brillouin zone, [tex]\varepsilon_{nk}[/tex] is the band energy, and the summation is taken over the whole Brillouin zone. Then [tex]N_{elec} = \int_{-\infty}^{E_f} g(\varepsilon) d\varepsilon[/tex] defines the Fermi energy.
 

1. What is Be2Si?

Be2Si is a chemical compound made up of two beryllium atoms and one silicon atom. It is classified as a metal and has a unique crystal structure.

2. What is the group symmetry of Be2Si?

The group symmetry of Be2Si is P6/mmm, which means it has a hexagonal crystal structure with six-fold rotational symmetry and mirror planes.

3. What are the requirements for a metal to have group symmetry P6/mmm?

A metal must have a hexagonal crystal structure with six-fold rotational symmetry and mirror planes in order to have group symmetry P6/mmm.

4. Why is group symmetry important for metals?

Group symmetry is important for metals because it affects their physical and chemical properties. Metals with higher group symmetry tend to have higher melting points, are more resistant to deformation, and exhibit unique electronic and magnetic properties.

5. How does the group symmetry of Be2Si affect its properties?

The group symmetry of Be2Si contributes to its high melting point and resistance to deformation. It also gives rise to its unique electronic and magnetic properties, making it a promising material for use in electronic devices and magnetic storage media.

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