Formula for Interplanar Distance in Cubic Lattice

  • Thread starter Thread starter potatowhisperer
  • Start date Start date
potatowhisperer
Messages
31
Reaction score
1
i am trying to find the formula for the inter-planar distance for the cubic .
i do know that it's :d (h,k,l)= a /√ (h² +k²+l²), i am only able to get to : 2π/(√a*²(h²+k²+l²)) , with a* being the parameter of the reciprocal lattice , the explanation given to how to go from a* to a , is that for all cubic lattices : a* = 2π/a , and this is what i don t understand , a = a* , only in the case of the simple cube , for body centered cube for example : we find a* = (2π/a)( j+k )with a*, j,k vectors ,a : parameter of the elementary lattice ; so calculating the modulus we find a*= √2 2π/a ;
and i am feeling frustrated , i know i am missing something but i don t know what .
 
Last edited:
Physics news on Phys.org
It looks like you need to clarify the definitions of a and a*.
 
a refers to the parameter of the elementary lattice , as a, b, c , of the simple cubic lattice .
lattice_parameters.gif

a* is the parameter of the reciprocal lattice , as in a* , b* , c* .
crystal-structure-analysis-46-638.jpg

a* , b* , c* are deduced from the parameters of the primitive lattice, a1 , a2 and a3 .
in the second pic a* is b1 , b*is b2 , c* is b3 , .
you can see that the modulus of a* = b 1 , is not 2π/a .
 
after a lot of searching , i noticed something , they do not actually mention the modulus of the vectors themselves but the lattice constant , i don t exactly understand what the difference is .
lattice constant is defined as the physical dimension of unit cells in a crystal lattice. so how is that different from the modulus of the lattice vector ?
 
i think i finally understood what is going on : you see i have always assumed that they were talking about the primitive vectors , for example to calculate the reciprocal vectors in the case of body centered we had to look for the primitive lattice ( which is a simple cube ) , but doing that means we re calculating the primitive reciprocal vectors . not just the reciprocal vectors .
and so if we actually try to calculate the reciprocal vectors of the actual body centered lattice,without going through the primitive lattice , we find 2π/a , and that is true for all cubic lattices .
uhhhh finally . all because of one word : primitive .
 
From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...
Hi. I have got question as in title. How can idea of instantaneous dipole moment for atoms like, for example hydrogen be consistent with idea of orbitals? At my level of knowledge London dispersion forces are derived taking into account Bohr model of atom. But we know today that this model is not correct. If it would be correct I understand that at each time electron is at some point at radius at some angle and there is dipole moment at this time from nucleus to electron at orbit. But how...
Back
Top