5 3 5 3
New Phase Transitions for Er Sb and Tm Sb
Table 1. Some Crystal Data and Refinement Parameters for YB-Er
Y- and YB-Tm Sb , and YB-Lu Sb
5
Sb
3
,
as core orbitals containing 12 electrons. Reciprocal space integra-
tions to determine self-consistent charge densities, density of states
5
3
5
3
3
0
Tm Sb
5 3
(DOS) curves, and crystal orbital Hamilton population (COHP)
Er Sb
5 3
Lu Sb
5 3
3
1
(
YB)
(YB)
1209.90
(Y)
(YB)
analyses were performed by the tetrahedron method using 112
k-points in the irreducible wedges of the corresponding Brillouin
zones.
formula weight 1201.55
crystal system
1240.10
orthorhombic
5 3
Total electronic energies of the two forms of Tm Sb as well as
a potentially intermediate structure were calculated as a function
of volume using the Vienna ab initio simulation package
space group, Z
Pnma, 4
cell dimensions, Å
a
b
7.9646(9)
9.176(1)
11.662(1)
852.2(3)
9.363
7.9262(5)
9.1375(6)
11.6034(5)
9.1077(4)
11.6013(7) 7.9841(4)
7.8847(4)
9.0770(5)
11.5055(6)
823.44(8)
10.003
32-34
(
VASP).
All calculations were performed using projector
35
augmented-wave (PAW) pseudopotentials and the Perdew-Burke-
Ernzerhof generalized gradient approximation (GGA-PBE). A 7
c
3
36
volume, Å
840.2(1)
9.564
1105/0/44
1.187
843.76(7)
9.524
1086/0/44
1.385
3
37
F (cal), g/cm
×
7 × 7 Monkhorst-Pack k-points grid was used to sample the
data/res/param
1115/0/44
1.488
1064/0/44
1.092
2
first Brillouin zone for the reciprocal space integration. The energy
cutoff of the plane wave basis was 215 eV. With these settings,
the total energy converged to less than 1 meV per unit cell. At
first, energy vs volume calculations were carried out for both the
low-temperature and the high-temperature structures. The atomic
positions were taken directly from the crystallographic data, and
the volumes of the unit cells were varied isotropically. A set of
GoF on F
R
1
[
, wR
I > 2σ(I)]
, wR (all data)
2
0.034, 0.041 0.023, 0.030 0.0241, 0.0609 0.0218, 0.0428
R
1
2
0.0252, 0.0612 0.0264, 0.0444
a
Table 2. Atomic Coordinates and Isotropic-Equivalent Displacement
Parameters (Å × 10 ) for the Tm
2
3
5
Sb
3
Structures
b
x
y
z
U(eq)
“
intermediate atomic positions” relative to the two standard types
YB-Tm
0.0598(1)
1/4
1/4
1/4
5 3
Sb
was established by averaging the atomic coordinates of the low-
temperature and high-temperature structures in the standard setting
of space group Pnnm. (For the lattice of the space group Pnma,
the corresponding space group of the intermediate would be Pnmn
along with a change of origin.) These atomic positions were then
optimized within the unit cells of both structures.
Tm1
Tm2
Tm3
Tm4
Sb1
0.1948(1)
0.0286(1)
0.1860(1)
0.3544(1)
0.0660(1)
0.4129(2)
0.0606(1)
0.5093(1)
0.7798(1)
0.2864(1)
0.3265(1)
0.5409(1)
12(1)
9(1)
14(1)
17(1)
13(1)
10(1)
0.0029(1)
1/4
Sb2
Y-Tm
0.0584(1)
1/4
1/4
1/4
5 3
Sb
Tm1
Tm2
Tm3
Tm4
Sb1
Sb2
a
0.0664(1)
0.0047(1)
0.2284(1)
0.2914(1)
0.3255(1)
0.4766(1)
0.1908(1)
0.5251(1)
0.8248(1)
0.3435(1)
0.0639(1)
0.5960(2)
b
8(1)
7(1)
10(1)
9(1)
8(1)
8(1)
Results and Discussion
Syntheses and Structure Type Distributions. Synthetic
explorations among the binary R Sb phases for R ) Y,
5 3
Gd-Ho confirmed the reported formation of hexagonal
M-type structures with, in most cases, substantially the same
lattice dimensions as reported in the literature, which came
0.0093(1)
1/4
8
d Wyckoff site for R1 and Sb1, 4c for other atoms. U(eq) is defined
as one-third of the trace of the orthogonalized Uij tensor.
samples were held between two fused silica rods within a tightly
fitting outer silica tube, and the assembly was sealed under helium,
as before. The raw data were corrected for the susceptibilities of
the containers and the diamagnetic contributions of the atom cores.
Electronic Structure Calculations. Electronic structures for the
primarily from powder diffraction data. The same is true for
M-type bismuthides of Gd
38,39
and YB-types for Y and
2
1
Tb-Er. Reaction details, products, and lattice dimensions
are given in Table 3 for one reaction for each compound
and structure type, although more extensive investigations
Y- and YB-types of Tm
the tight-binding linear muffin-tin-orbital (TB-LMTO) method
within the atomic sphere approximation (ASA) using the Stuttgart
5 3
Sb were calculated self-consistently by
4
0
22-25
were completed. Some reported unit cell volumes deviate
3
from ours by up to (0.7% (∼5-7 Å ), particularly for those
26
from the older literature, but none of the differences suggest
that substantial interstitial impurities had been involved
earlier, in contrast to our experiences with divalent cations
and hydrogen. A few R (Sb,Bi) Z compositions were also
code. Exchange and correlation were treated in a local spin density
approximation (LSDA), and scalar relativistic effects were taken
into account. The radii of Wigner-Seitz (WS) spheres were
optimized according to an automatic procedure. One empty sphere
in an 8-fold general site was required for each. The WS radii so
determined were 1.75-1.84 Å for Tm, 1.77-1.87 Å for Sb, and
.11-1.20 Å for the empty sphere. The basis set included 6s, 6p,
d, and 4f functions for Tm, 4s and 4p functions for Sb, and a 1s
27
28
29
5
3
investigated for Z ) F or H, namely for Y
Gd (Sb,Bi) (F,H), and Er (Sb,Bi) F, but in only one case did
a meaningful change appear. This was the repeated appear-
5 3
(Sb,Bi) F,
5
3
5
3
1
5
function for the empty spheres. The Tm 4f functions were treated
(
(
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Inorganic Chemistry, Vol. 48, No. 10, 2009 4365