Do you mean LaB6: https://en.wikipedia.org/wiki/Lanthanum_hexaboride ?

What do you describe as "orthogonal boride cage"?

What do you mean by "remains intact"? Intact under which conditions? Heat? Mechanic stress? Phase transformations?

I would think that 1) LaB6 is a semiconductor, this is why it can be used as cathode material. 2) the melting point is very high > 2000 K which allows to heat it up to high temperatures thus enhancing the electron emitting properties. 3) LaB6 might be described as layered structure, but this has probably not a lot to do with electron emission. 4) The high thermal stability is probably due to the high covalency in the B network. High covalency for elements like B, C, or Si goes usually along with high thermal stability, see e.g. diamond, SiC, BC, ...

Thank you for providing the figure.

You can see the short B-B bonds, the B substructure is highly covalent.

Boron-rich stoichiometries (above LaB6.07) are also reported. In these structures some of the La3+ ions are missing making the material more electron-rich.

Sir thank you for answering me but one more question why Boron atoms are arranged in this fashion.

Sir what is the reason you are saying La3+ ions are missing?

That is a good question. Elemental B has three valence electrons per atom and shows icosahedral arrangements of the B atoms where an individual B atom has 5 or 6 B atoms as neighbors in multicentered covalent bonds. In LaB6 each B atom has slightly more electrons (+1/2 elecron in average), thus the multi-centered bonding is reduced to a lower number of neighbors (all B atoms have 5 neighbors). Maybe this is a reasonable explanation.

If the stoichiometry is LaB6.07 the structure contains less La3+ ions (or La atoms) than in LaB6. This would not change the structure - it would just create some defects (Schottky defects).

The alternative explanation that LaB6.07 contains more B atoms than LaB6 makes no sense - how could B atoms be missing in this structure?

Sir you talked about the defects in this structure It will affect the properties for cathode material for electron gun.

what is LaB6.07?

Citing the previous answer of prof. Axel Klein :

"Boron-rich stoichiometries (above LaB6.07) are also reported. In these structures some of the La3+ ions are missing making the material more electron-rich."

So once every ~100 unit cells in the crystal lattice you can find a defect, namely one cell which does not have the La3+ cation inside.

Concerning the defect structures such as LaB6.07 I can only guess if they are better emitting materials than stoichiometric LaB6.

In Wikipedia they say that LaB6.07 appears blue while LaB6 is violet. If blue represents a smaller band gap than violet, LaB6.07 has a smaller band gap and thus might have a smaller work potential (work function, austrittspotential) than LaB6 with about 2.5 eV. So, I would say it is a better electron emitter.

Daniel, do you agree - you seem to be the expert :-) ?

Concerning the covalent B-B bonding I can add more:

A boron atom with a full extra electron, thus B- makes 4 covalent bonds to its neighbors, thus behaves like a C atom. You can see these in molecules such as BH4-.

Reducing the electron density from B(-) to B(-0.25) and to B(0) increases the need of compensating the lacking electrons through multicentered bonding and increases the numbers of neighboring atoms.

I feel humbled by the compliment, but I am definitely not the expert (yet!). But to elaborate on the electronic structure:

In terms of overall lattice energy, I would suspect LaB6.07 energy to be similar to that of LaB6, or maybe even slightly higher (less negative) due to lowering the local symmetry caused by lattice defects. If that is the case, the work function - which corresponds to energy needed for electron to leave the material - should be lower.

Furthermore, the red shift (a change towards higher wavelengths) of compounds colour signifies smaller energy needed for electron to jump between the HOCO (Highest Occupied Crystal Orbital) and LUCO (Lowest Unoccupied Crystal Orbital) electron bands, which means smaller band gap. Assuming similar electron structure, we can propose one of the three explanations for smaller band gap:

• HOCO orbital energy is higher -> work function decreases
• LUCO orbital energy is lower -> work function doesn't change
• both HOCO and LUCO move -> work function slightly decreases

So this is just my unnecessarily lengthy way to say that I agree.

Dhruv Bhatnagar , let me know If I can still help you anymore with the subject, I'll be glad to if I can!

Edit: You might also want to read the paper Wikipedia refers to. Though there are surely some better articles in this subject by now.Article Structure, defects and properties of some refractory borides

Thank you sir for helping me.

I read the article provided by you In that paper there is homogeneity range they are talking about of LaB6. If you can help me with homogeneity range scenario it will be helpful for me.

Also the boron atom which are arranged in octahedral way it will change because of homogeneity. or vacancy will form this formation of vacancy will be helpful for making material properties better for electron gun.

Axel Klein Daniel Tchoń

I am afraid I do not quite understand your question; If you are confused about the definition of "homogeneity range", than I would assume it means the range of conditions/composition for which an overall crystal structure of investigated compound is preserved. For example the paper mentions:

"Johnson and Daane (ref. 35) found that the homogeneity range extends from LaB6.0 to LaB7.8, using microscopy and density measurements. They did not observe any cell dimension variation within the range of homogeneity but a change in colour of LaB6 was noted."

This suggests that the compound was found to have similar crystal structure up to a point where Lanthanum occupancy was approximately 75%, so roughly every fourth unit cell lacks this metal atom.

If you want to know more about the specific ranges, I unfortunately can't help you - I have never worked with any Boron compounds. I suspect that Li--B series would be a reasonable electron donor within the homogeneity range of LiB6.0, and It would most likely change properties outside of the range (for too low Lanthanum concentration) due to a change of crystal structure. You might want to look into more modern papers on the subject, for example some that cite the publication mentioned here.

Thank you sir. I am trying to understand the crystal structure of LaB6 and it use in thermionic emission of electron gun material.

One more question why in these material boron is multi centred bonded?

What is hybridization state in LaB6 ?

Is there any specific reason which providing some properties because of this bond.