Environmental Engineering Reference
In-Depth Information
Tab l e 1 . 2 .
Structural properties of the lanthanides.
Element Structure
Lattice const.
Atomic rad. Density Melt.point
a (A)
c (A)
(g/cm
3
)
(300 K)
S
(a.u.)
( )
La
dhcp
3.774
12.171
3.92
6.146
1191
Ce(
β
)
dhcp
3.681
11.857
3.83
6.689
1071
Ce(
γ
)
fcc
5.161
3.81
6.770
Ce(
α
)
fcc
4.85 (77 K)
3.58
8.16
Pr
dhcp
3.672
11.833
3.82
6.773
1204
Nd
dhcp
3.658
11.797
3.80
7.008
1294
Pm
dhcp
3.65
11.65
3.78
7.264
1315
Sm
rhom
3.629
26.207
3.77
7.520
1347
Eu
bcc
4.583
4.26
5.244
1095
Gd
hcp
3.634
5.781
3.76
7.901
1586
Tb
hcp
3.606
5.697
3.72
8.230
1629
Dy
hcp
3.592
5.650
3.70
8.551
1687
Ho
hcp
3.578
5.618
3.69
8.795
1747
Er
hcp
3.559
5.585
3.67
9.066
1802
Tm
hcp
3.538
5.554
3.65
9.321
1818
Yb
fcc
5.485
4.05
6.966
1092
Lu
hcp
3.505
5.549
3.62
9.841
1936
although the hcp allotrope of Yb is only stable at low temperatures, and
Ce has two separate fcc phases in addition to its dhcp form.
The heavy rare earths are all hcp, while the dhcp structure pre-
dominates among the lighter metals. These structures may be produced
by stacking close-packed layers in the sequences ABAB and ABAC re-
spectively, as shown in Fig. 1.3. The fcc structure corresponds to the
stacking sequence ABCABC, while the Sm structure is ABABCBCAC.
The latter has rhombohedral symmetry but it is frequently more conve-
nient to consider it as hexagonal. The crystallographic
a
-axis is taken
along the direction joining a pair of nearest neighbours in the hexagonal
plane, the
c
-axis is normal to the plane, and the
b
-axis is orthogonal to
the other two. The local, i.e. nearest-neighbour, symmetry in the fcc
and hcp structure is, of course, cubic and hexagonal respectively. The
dhcp structure, on the other hand, has two types of site and, for an
'ideal'
c/
2
a
ratio of 1.633, their
local
symmetry alternates between cubic
and hexagonal in the sequence chch, while the Sm structure corresponds
to chhchh. As may be seen from Table 1.2, however, the
c/
2
a
ratio is
consistently smaller than the ideal value, so the 'cubic' sites have only
approximate local cubic symmetry.
Search WWH ::
Custom Search