The New Laves Phase Na2Ba
G. Jeffrey Snyder3, Arndt Simon*
Max-Planck-Institut für Festkörperforschung, D -70569 Stuttgart, Germany
Z. Naturforsch. 49b, 1 8 9 - 192 (1994); received September 20, 1993
Sodium Barium, Intermetallic C om pound, H exagonal Laves Phase
The crystal structure o f N a 2Ba was determined from single crystal X-ray diffraction data. It
is isostructural with the hexagonal Laves phase Zn2Mg; P 6 3/m mc, a = 739.3(4) pm, c =
1199.9(9) pm. The compound N a 4Ba reported in the phase diagram literature is actually
N a2Ba. Comparisons are made with other Laves phases using a strain parameter diagram.
Introduction
After preliminary investigations o f the B a - N a N system, resulting in the discovery o f the first
sub-nitride N aB a3N [1], we decided to examine
more closely the intermetallic phases formed by
the two metals, leading to the discovery o f the new
Laves phase N a2Ba.
The literature contains a variety o f conflicting
reports concerning N a -B a intermetallic phases.
The standard references for binary phase diagrams
[2,3] show for N a -B a quite different liquidus
curves and binary phases. The work of Remy [4], re­
produced in [2], contains three phases N a 12Ba,
N a6Ba, and NaBa, based on differential thermal
analyses. The prim ary source of [3] is the work of
Stevens and K anda [5], who deduce from X-ray
powder diffraction and thermal d ata that two
phases NaBa and N a4Ba exist up to 197 °C and
65 °C, respectively. The structures are, however,
not given but only observed X-ray powder reflec­
tions without intensities, and tentative lattice con­
stants. Addison [6] reproduced these results from
resistivity measurements, with only slightly varied
positions of the equilibrium lines. In an earlier
work from the K anda group [7], N a2Ba5 or
(N a4Ba9), as well as N a2Ba forming peritectically
at 175 °C, are described. The Laves phase N a2Ba
that we report was observed only below 86 °C and
its X-ray diagram conforms to 17 of the 28 report­
ed diffraction lines given for N a4Ba. Some o f the
remaining lines m atch well with the diffraction
a Present address: Department o f Applied Physics, Stan­
ford University, Stanford CA 94305, U .S .A .
* Reprint requests to Prof. Dr. A. Simon.
V erlag der Z eitschrift für N atu rfo rsch u n g ,
D-72072 T übingen
0 9 3 2 -0 7 7 6 /9 4 /0 2 0 0 -0 1 8 9 /$ 01.00/0
pattern of N a5Ba3N which also vanishes at nearly
the same temperature.
Experimental
Barium metal was distilled and sodium metal fil­
tered following [8]. All transfers were carried out,
using the technique o f Schlenk [8], under flowing
argon purified with molecular sieves, titanium
sponge at 900 K, and oxisorb catalyst [9], in glass­
ware evacuated to better than 10~5 mbar. Because
N a -B a melt wets glass, possibly due to traces of
oxide or nitride impurity, sealed X-ray size sam­
ples could not be made in the usual way [10]. A
Pyrex glass tube with a 19 mm diam eter outer
ground-glass joint was narrowed to a diam eter of
0.1 to 0.5 mm, drawn to a length of approximately
500 mm, and finally sealed with a small bubble at
the end to serve as a gas reservoir. Sodium and
barium metal, 0.0550 g and 0.0806 g, respectively
(80.4 mole % Na), were placed at the opening of
this capillary. They melted together with the capil­
lary heated to 190 °C, while under one atm osphere
of argon pressure to minimize N a evaporation.
The apparatus was then evacuated, and argon
pressure quickly reapplied to fill the capillary with
the liquid metal. At this tem perature the sample
appeared homogeneous and there was no visible
reaction o f the liquid metal with the glass. After
cooling, approximately 100 mm lengths of capil­
lary were cut under flowing argon into a Schlenk
tube. This Schlenk tube had an additional open­
ing, through which pieces, typically 20 mm long, of
capillary were inserted into standard X-ray capil­
laries and sealed under argon. To minimize con­
tam ination, the ends of the capillary pieces were
freshly cut just before insertion. Crystals were then
grown by cooling the samples from 200 °C to
room tem perature at l°/h, in an aluminum metal
core furnace, which increases tem perature uni­
formity.
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190
G . J. S n y d e r-A . Sim on ■The New Laves Phase N a 2Ba
The structure o f N a2Ba was determined from
X-ray diffraction o f a single crystal found in the
middle o f such a sample. The crystal was oriented
such that the hexagonal c-axis was collinear with
the capillary axis. It was clear from the rotation
and axial photographs that other crystals and
some powder were also in the X-ray beam. In o r­
der to statistically minimize inaccuracies due to
stray reflections from other crystals, 1646 reflec­
tions were collected, of which 177 were unique.
D ata were collected using the ortho-hexagonal set­
ting (737.9(2) pm, 1197.6(3) pm, 1278.3(1) pm,
89.96(2)°, 90.02(2)°, 89.98(2)°) and empirical ab­
sorption calculated using mmm symmetry. F u r­
ther experimental details are given in Table I.
The space group was determined to be P 63/mmc
and the structure solved by direct methods.
SHELXTL-93, which minimizes a weighted
squared residual “w R 2 ” from all data using struc­
ture am plitudes |F |2 rather than structure factors
F, was used for structure refinement. The standard
residual “ R 1” is calculated purely for comparison.
M easured intensities more than two sigma below
zero (seven independent reflections) were sup­
pressed for refinement purposes. The lattice con­
stants were taken from powder diffraction data,
using a Stoe capillary diffractom eter at room tem­
perature with silicon as a standard. Atomic coordi­
nates and anisotropic thermal param eters are giv­
en in Table II.*
Empirical formula
Formula weight
Temperature
W avelength
Crystal system
Space group
U nit cell dimensions
Volume
Z
D ensity (calculated)
A bsorption coefficient
F(000)
6 range for data collection
Index ranges
Reflections collected
Independent reflections
Refinement method
Data/restraints/parameters
G oodness-of-fit on F 2
Final R indices [I > 4 cr(I)]
R indices (all data)
Largest diff. peak and hole
Pos
Ba
N a (l)
N a(2)
Ba
N a (l)
N a(2)
* Further crystal and refinement details may be ob­
tained from the Fachinformationszentrum Karlsruhe,
G esellschaft für wissenschaftlich-technische Informa­
tion m bH , D-76344 Eggenstein-Leopoldshafen (Ger­
m any) on quoting the depository number C SD 57845,
the names o f the authors and the journal citation.
Table I. Crystal data and structure re­
finement for N a 2Ba.
N a 2Ba
183.32
293(2) K
71.073 pm
hexagonal
P 63/mmc
a = 739.3(4) pm
c = 1199.9(9) pm
0.5680(6) nm 3
4
2.144 M g/m 3
6.960 m m -1
312
3.18 to 22.93°
+ 8 < /7 < 0 , - 7 < / t < 8 , 0 < / < 1 3
1646
177 (R mi = 0.0960)
Full-matrix least-squares on F 2
170/0/10
1.266
R 1 = 0.0336, w R 2 = 0.0751
R 1 = 0.0401, w R 2 = 0.0894
603 and -6 5 0 e.nm “ 3
y
z
Ueq
0.0620(1)
1/4
39(1)
51(2)
51(3)
4f
6h
2a
1/3
0.8293(6)
0
2/3
2*
0
U ll
U 22
U 33
U 2 3 = U 13
U 12
36(1)
48(3)
51(4)
U ll
47(4)
U ll
44(1)
59(3)
52(6)
0
0
0
1/2 U l l
1/2 U 2 2
1/2 U l l
0
Table II. Atomic coordinates and an­
isotropic
displacement parameters
(pm 2 x l 0 -1) for N a 2Ba. U eq is defined
as one third o f the trace o f the orthogonalized Uy tensor. The anisotropic dis­
placement factor exponent takes the
form:
- 2 n2 [(ha*)2U „ + - + 2 h ka*b*U l2\.
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191
G. J. Snyder-A. Simon • The New Laves Phase N a2Ba
B a -B a
B a -N a (l)
B a -N a (2 )
N a ( l) - N a ( l)
B a -B a -B a
0*)
(3 x )
(3 * )
(2 x )
(3 x )
451.2(4)
428.4(5)
433.3(2)
378.5(13)
109.21(3)
B a -B a
B a -N a (l)
N a ( l) - N a ( l)
N a (l) -N a ( 2 )
B a -B a -B a
(3 x )
(6 x )
(2 x )
(2 x )
(3 x )
Film data, taken with a Guinier-Simon camera
[11] showed that the N a2Ba in these samples m elt­
ed completely at 64 °C and started to reform at
60 °C.
Discussion
N a2Ba is isostructural with the hexagonal Laves
phase Zn 2Mg. The packing o f the atoms is nearly
ideal for spheres of different sizes, with no signifi­
cant contribution due to hom opolar or heteropolar bonding. All the sodium atom s are twelve coor­
dinate, with six sodium and six barium near neigh­
bors. The barium atom is sixteen coordinate,
having twelve sodium near neighbors and a nearly
perfect tetrahedron of four barium near neighbors.
Whereas for the cubic Laves phases A2B (C u2Mg
structure type), interatomic distances are equal
within each category, A - A , A -B , and B -B , the
deviation of the ratio c/a, 1.623, from the ideal val­
ue of 1.633, as well as some free atomic positional
parameters, o f N a2Ba lead to a range of interatom ­
ic distances (Table III) for each category.
Both the Pauling electronegativities of N a and
Ba and the more finely graded (adjusted) w ork
functions according to Miedema [12], 2.70V and
2.32V for N a and Ba respectively, suggest only a
slight transfer o f electrons rom Ba to Na.
The radius ratio rBa/rNa = 1.174 (using twelve
coordinate elemental radii [13]) is only slightly
smaller than the “ideal” value for Laves phases of
V 3/2 = 1.225 [14]. The radius ratio of N a2Ba is in
a range where both m olar volumes and interatom ­
ic distances closely correspond to the weighted
sums of atom ic volumes and radii, respectively
[15]. In fact, the m olar volume of N a2Ba is 99.67%
that of the metals, 2VNa + VBa, further indicating
that there is little chemical interaction between the
elements. On the basis o f a stoichiometrically
weighted sum of radii [15], one calculates the val­
ues:
dNa-Na = °-604 (rBa+ 2 rNa) = 366 pm
dNa-Ba = °-708 (r Ba+ 2 rNa) = 429 pm
d Ba-Ba = 0.740 (rBa+ 2 rNa) = 449 pm
452.0(2)
433.1(2)
360.8(13)
371.1(5)
109.73(3)
Table III. Selected bond lengths [pm] and
angles [ ] for N a 2Ba.
which are close to the average experimental values
of 370.4, 432.0, and 451.8 pm, respectively.
Recent interest focussed on aspects of chemical
bonding in Laves phases [16-18] which are a p ar­
ticularly well suited target to analyze geometric
(atomic size) factors on one hand, and electronic
factors on the other. Due to the weak metallic
bonding N a2Ba provides an example for a struc­
ture which is mainly governed by geometrical fac­
tors. For the characterization o f com pounds AnB
purely from the point of view of packing, Pearson
has introduced the strain param eter diagram
(dBB- 2 r B)/2 rA vs. r B/rA [13], where d BB is a contact
distance between B atoms. Figure 1 is a plot o f the
strain param eter versus the radius ratio for hexag­
onal Laves phases containing only alkali or alka­
line earth elements. These com pounds are well de­
scribed by the line (dBB- 2 r B)/2 rA = 0.63(3) rB/rA0.75(4), which is very near to the experimental line
determined for the alkali metal Laves phases,
N a 2K, N a 2Cs, and K 2Cs, alone [19]. Within stand­
ard deviations, this line coincides with that calcu­
lated for cubic Laves phases allowing for the adap­
tion of atomic sizes to different effective coordina­
tion numbers [15].
The authors thank Dr. Paul Rauch and Dr.
Horst Borrmann for their help, and the Hertz
Foundation for financial support.
S tra in P a ra m e te r
R a d iu s R a tio
Fig. 1. Strain parameter diagram for hexagonal Laves
phases containing only alkali or alkaline earth elements.
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G. J. Snyder-A . Simon • The New Laves Phase N a2Ba
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