min: 0.07
max: 64.16
h=3.00
h=5.00
h=10.00
The following are valence charge density iso-surface plots of 22 crystals at their stress-free ground-states calculated using VASP. Click on 'movie' to see the animations where the contour values are varied from minimum to maximum (movie +) and from maximum to minimum (movie -) valence charge density ( h = rho x Vcell ). Three snapshots are taken in each movie and are shown on the right. Click on the thumbnail for larger view.
From these ab initio calculation results, bond-localized valence charge densities are seen in Si, C, and SiC. Non-nuclear maxima are seen in Al, Mo, and W. Cuboidal shaped charge densities (and also significant interstice charge densities) are seen in Fe and TiAl. Very significant interstice charge densities are seen in Mg. All these materials manifest relatively large shearability.
In comparison, charge densities in Au, Ag, Cu, and Zn are very close to the "muffin-tin" picture, and the iso-surfaces remain predominantly spherical throughout. These materials in turn are located at the bottom end on the shearability spectra.
Charge density iso-surfaces are also quite spherical in ionic crystals CaO, KBr, MgO, and NaCl, but there is an extra unscreened Coulomb term in the bonding energy, which makes ionic solids having moderately large shearability (in between directionally-bonded metals and covalent solids) in fully relaxed shear, but abnormally large shearability (see Table II) if constrained. This suggests ionic solids have the potential to be much more brittle than even covalent solids.
|
Ag min: 0.07
|
h=3.00 |
h=5.00 |
h=10.00 |
|
Al min: 0.08
|
h=1.76 |
h=2.89 |
h=3.36 |
| Movies: Al vs. Cu densities, Al vs. Cu iso-surfaces in {111}<112> shear. |
|
Au min: 0.08
|
h=4.00 |
h=6.00 |
h=13.00 |
|
C min: 0.88
|
h=2.40 |
h=6.70 |
h=11.50 |
|
CaO min: 0.00
|
h=6.00 |
h=16.00 |
h=44.00 |
|
Cu min: 0.05
|
h=3.00 |
h=9.00 |
h=20.00 |
| Movies: Al vs. Cu densities, Al vs. Cu iso-surfaces in {111}<112> shear. |
|
Fe (FM) (spin up + spin down) min: 2.77
|
h=3.00 |
h=5.00 |
h=18.00 |
|
Fe (FM) (spin up - spin down) min: -0.26
|
h=0.00 |
h=4.00 |
h=16.00 |
|
KBr min: 1.55
|
h=4.00 |
h=7.00 |
h=38.00 |
|
Mg min: 1.00
|
h=2.50 |
h=3.70 |
h=4.20 |
|
MgO min: 0.00
|
h=8.00 |
h=11.00 |
h=23.00 |
|
Mo min: 0.06
|
h=4.30 |
h=5.80 |
h=8.60 |
|
NaCl min: 0.17
|
h=9.00 |
h=18.00 |
h=184.00 |
|
Ni (NM) min: 0.03
|
h=3.00 |
h=4.00 |
h=13.00 |
|
Ni (FM) (spin up + spin down) min: 0.03
|
h=3.22 |
h=3.66 |
h=8.99 |
|
Ni (FM) (spin up - spin down) min: -0.13
|
h=0.0 |
h=4.0 |
h=6.0 |
|
Si min: 0.21
|
h=2.00 |
h=5.00 |
h=17.00 |
|
SiC min: 0.02
|
h=3.00 |
h=7.00 |
h=10.00 |
|
a-Si3N4 min: 0.86
|
h=59.00 |
h=117.00 |
h=210.00 |
|
b-Si3N4 min: 0.49
|
h=29.00 |
h=57.00 |
h=100.00 |
|
Ti min: 5.11
|
h=7.00 |
h=9.00 |
h=61.00 |
|
Ti3Al min: 0.29
|
h=24.00 |
h=29.00 |
h=36.00 |
|
TiAl min: 0.13
|
h=11.00 |
h=13.00 |
h=19.00 |
|
W min: 0.06
|
h=4.36 |
h=5.64 |
h=7.63 |
|
Zn min: 2.89
|
h=7.00 |
h=10.00 |
h=62.00 |