chemical structure. This conclusion was also corroborated by our
analysis of the rather broad bondangle distribution (see Supplemen
tary Fig. S4).
On the other hand, despite the large number of the geometrically
distinct polyhedron types, certain polyhedra appeared with high
frequencies (20–40%; see Fig. 4). A closer inspection suggests that
they are Kasper polyhedra, which are the deltahedra that involve the
minimum number of disclinations
30,31
. The atomic packing con
figurations of different Kasper polyhedra are shown in Fig. 3. In the
Ni–P glass, the percentages of the Z10 (Z
¼
CN) Kasper polyhedron
(the bicapped square archimedean antiprism, BSAP, with Voronoi
index
k
0,2,8,0
l
), and the Z11 Kasper polyhedra (with
k
0,2,8,1
l
) are
16.2% and 10.6%, respectively, while in the Ni
81
B
19
MG, the
Z9 Kasper polyhedron (TTP, with
k
0,3,6,0
l
) and the Z10 Kasper
polyhedra are dominant (at 17.8% and 7.1%, respectively). In
comparison, prominent icosahedral local order is found in the
Zr
84
Pt
16
MG, where the occurrences of the Z12 and Z11 Kasper
polyhedra are 14.1% and 9.0%, respectively. Therefore, it is evident
that the Kasper polyhedron SRO is the main underlying topological
SRO in the MGs.
The preference for a particular type, as seen in Fig. 3 together with
the shift of the main peak, is controlled by the effective atomic size
ratio between the solute and solvent atoms,
R
*. With decreasing
R
*,
the preferred polyhedra type changes from the Frank–Kasper
32
type
(for
R
*
.
1.2) to the icosahedral type (
R
*
<
0.902, as for Zr–Pt
with
R
*
¼
0.90), and then to the BSAP type (
R
*
<
0.835, as in Ni–P
with
R
*
¼
0.78), and then to the TTP type (
R
*
<
0.732, as in
Ni–B with
R
*
¼
0.69); see Figs 3 and 4. As pointed out above,
some MGs, notably TM–metalloid systems (Ni–B, Pd–Si and so on),
indeed exhibit the TTP local order, similar to that in corresponding
crystalline compounds
33
. But this should be understood as a geo
metrical consequence and only specific to a small number of MGs
that meet the
R
* requirement for the formation of TTP (
R
*
<
0.732).
Our results not only validate the important role of the relative size
Figure 3

CN distribution of the solute atoms in several representative
MGs, obtained from
ab initio
calculations.
The average CN changes with
the effective atomic size ratio, and for each glass the majority of the solute
atoms (
.
75% of total) have two dominant CNs. Also shown are the Kasper
polyhedra corresponding to the different CNs. The Kasper polyhedra are the
dominant coordination polyhedra in the relaxed MGs.
Figure 4

The occurrences of different coordination polyhedra (with
different Voronoi indices) of the solute atoms in the MGs.
The bars
outlined in red show the frequency of the dominant Kasper polyhedra. Note
that only the polyhedra with a population of
.
2% are shown.
NATURE

Vol 439

26 January 2006
ARTICLES
421