Hex, Bugs and More Physics | Emre S. Tasci

Golden Remark: "If you assume formula and Pearson Symbol (along with the Space-group number) together are sufficient to identify a structure, then there is a 488 in 53766 (0.9%) probability that you are wrong. And that probability is more than enough to spoil the fun."

Been there, experienced it first hand yesterday.

Moral of the story : If you happen to be involved with any of the following beauties, just make sure that their twins aren’t swapping with your sweetheart. Otherwise, it is very likely that you’ll get your heart broken into two (actually into three for the ones marked with *). Checking their height-width-and shoe number works well (or directly check the volume, so to speak…)

As2O3,mP20,14
As4S3,oP28,62
AsS,mP32,14*
B2O3,hP15,144
BiI,mS16,12
BN,hP4,194
C,hP4,194
CdI2,hP18,164
CdI2,hP21,156*
CdI2,hP24,156*
CdI2,hP30,156*
CdI2,hP33,156
CdI2,hP39,156
Co2Si,oP12,62
Cr3C2,oP20,62
FeB,oP8,62
GaS,hP8,194
HgCl2,oP12,62
ICl,mP16,14
LiO,hP8,194
N2O4,cI36,204
NbSe2,hP12,187
NbTe4,tP60,75
PbI2,hP21,156
Pr5O9,mP112,14
Rh12As7,hP22,176
Se,mP32,14
SiC,hR102,160*
SN,mP8,14*
TeO2,oP24,61
Ti4O7,aP22,2
U3O8,oS22,38
U3O8,oS44,63
UF5,tI48,122
VO2,mS24,12
WO3,mP16,14
ZrO2,mP12,14

I see that it has been some time since my last entry but I hope I will be more informative from now on…

The Fourteen Bravais Lattices

When one relaxes the restriction to point operations and considers the full symmetry group of the Bravais lattice, there turn out to be fourteen distinct space groups that a Bravais lattice can have. Thus, from the point of view of symmetry, there are fourteen different kinds of Bravais lattice. This enumeration was first done by M.L. Frankenheim (1842). Frankenheim miscounted, however, reporting fifteen possibilities. A. Bravais (1845) was the first to count the categories correctly.

(…)

The seven crystal systems and fourteen Bravais lattices described above exhaust the possibilities. This is far from obvious (or the lattices would have been known as Frankenheim lattices).

Ashcroft, Mermin  Solid State Physics Saunders 1976 Ch. 7

I don’t understand why you materials scientists are so busy in working out experimentally the constitution [crystal structure and phase diagram] of multinary systems. We know the structure of the atoms [needing only Atomic Numbers], we have the laws of quantum mechanics, and we have electronic calculation machines, which can solve the pertinent equation rather quickly!

J.C. Slater, 1956 as quoted by Villars et al. Journal of Alloys and Compounds 279 (1998) 1