Subido por Miguel Angel Sánchez Monroy

2001-jalcom

Anuncio
Journal of Alloys and Compounds 322 (2001) 45–54
L
www.elsevier.com / locate / jallcom
The electronic structure of the Laves phase intermetallics LnM 2
(Ln5Y, La–Lu, M5Mg, Al) and the LaMg 2 H 7
and CeMg 2 H 7 hydrides
Emilio Orgaz*
´
´
´
´
´
´
´ , Mexico
´
, Facultad de Quımica
, Universidad Nacional Autonoma
de Mexico
, CP 04510, Coyoacan
,
Departamento de Fısica
y Quımica
Teorica
D.F. Mexico
Received 23 November 2000; accepted 28 February 2001
Abstract
We present our results of the electronic structure of rare earth–non-magnetic metal intermetallic Laves phase compounds LnM 2
(Ln5Y, La–Lu, M5Mg, Al) along with the recently discovered LaMg 2 H 7 and CeMg 2 H 7 hydrides. By means of the full potential linear
augmented plane wave method within the generalized gradient approximation for the exchange and correlation energy, we determined ab
initio the energy bands and density of electronic states for these compounds. We investigated the trends in the electronic structure and
chemical bonding characteristics of both series of intermetallic compounds and closely related hydrides.  2001 Elsevier Science B.V.
All rights reserved.
Keywords: Rare earth compounds; Hydrogen absorbing materials; Electronic band structure
1. Introduction
The systematic study of the magnetic binary Laves
phase intermetallics containing rare earths is a growing
field of interest owing it to the variety of complex
properties shown by these materials. In particular, the
description of the magnetic behavior is a challenging issue
since the early sixties. We focused our attention onto Laves
phase derived intermetallics containing rare earths and
non-magnetic metals such as aluminum and magnesium.
These intermetallic compounds seem to be simpler than
those containing transition metals. This simplicity is just
apparent in virtue of their complex magnetic behavior,
which is not yet well understood. Moreover, Gingl and
coworkers [1] recently found new high hydrogen density
hydrides derived from two Laves phase intermetallics:
LaMg 2 H 7 and CeMg 2 H 7 . The crystal structure was determined by neutron diffraction techniques, but the physical and chemical properties of these materials are up to
today unknown. This is important owing to the variety of
the properties that such kind of materials can exhibit, going
from insulating to metallic behavior [2–5], and the real and
*Corresponding author.
E-mail address: Orgaz@eros.pquim.unam.mx (E. Orgaz).
potential applications [6]. Reviewing the literature, it is
noteworthy the lack of a theoretical systematic study
regarding the electronic properties of the LnAl 2 and
LnMg 2 Laves phases intermetallic series. Band structure
studies exist only for some selected compounds [7–19].
This is understandable because of the intrinsic limitations
of the standard local density approximation (LDA) methods to describe the electronic structure of these strongly
correlated f-electron systems. Buschow [20] extensively
reviewed most of the research done on rare earth–nonmagnetic metal intermetallic compounds up to the late
1970s. In recent years, some of the most prominent
aluminum–rare earth compounds: CeAl 2 , PrAl 2 , EuAl 2 ,
DyAl 2 and YbAl 2 have been revisited. However, few
reports concerning the rare earth–magnesium intermetallics have been published [20]. In general, these rare earth
intermetallic compounds exhibit a complex magnetic behavior. For example, the LnAl 2 series are all ferromagnetic
at low temperatures, excepting CeAl 2 which shows an
antiferromagnetic transition at around 4.6 K. All of them
show a crystal field induced magneto-crystalline anisotropy. In DyAl 2 and ErAl 2 [21,22], an anomalous magnetocaloric effect has been recently investigated by means
of a Hamiltonian model containing the crystal field and
exchange interactions. A single crystal of GdAl 2 has been
0925-8388 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved.
PII: S0925-8388( 01 )01212-9
46
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
investigated by NMR techniques [23], where the anisotropy of the magnetic hyperfine interaction for Al has been
determined, and the role of orbital polarization of the
conduction electrons has been discussed. LnM 2 compounds shown systematically a large electronic specific
heat coefficient. For example, for CeAl 2 g 5274 mJ K 22 22
mole [24,25], for YbAl 2 g 516.8 mJ K -mole [26], for
22
LuAl 2 , g 55.6 mJ K -mole [27].
In this article we present our systematic investigation of
the electronic structure of the LnM 2 (Ln5Y, La–Lu,
M5Mg, Al) series of compounds along with the recently
discovered hydrides LaMg 2 H 7 and CeMg 2 H 7 . In the
following sections we will outline the essentials of the
computation method. Next, we will describe the most
important aspects of the electronic structure of this family
of compounds.
in the localized f states [13,15]. In our study, we neglect
this interaction mainly due to the lack of information about
the magnetic moment orientation with respect to the lattice
for both series of compounds. Self-interaction corrections
(SIC) [30] to the LSD approximation are not yet implemented in the LAPW code. However, it seems that the
GGA to the exchange and correlation energy yield similar
results to those obtained within the LSD-SIC approach.
This is at least true for elemental Pr as quoted by Svane et
al. [30]. Spin polarizations were introduced from the
beginning of the iterative calculations without any particular choice for the atomic magnetic moment. Finally, it
is important to note that the convergence scheme necessitate a small mixing parameter owing to the strong sensitivity
of the f-bands occupancies.
3. Results
2. Calculation details
We have computed the electronic energy bands of the
complete series LnM 2 (Ln5Y, La–Lu; M5Al, Mg) and
recently discovered LaMg 2 H 7 and CeMg 2 H 7 hydrides, by
means of the full potential-linear augmented plane waves
(FPLAPW) method [28]. The total density of states (DOS)
as well as the angular momentum resolved DOS at each
atomic site were computed. The exchange part of the
crystal potential was modeled by means of the generalized
gradient approximation (GGA) [29] to the local spin
density (LSD) theory. Samples of 120 k-points of the
irreducible wedges of the face centered cubic (fcc) and
hexagonal Brillouin zones were selected. For this set of
points, we computed ab initio the energy eigenvalues
converged to 1 mRy for the valence states. The muffin–tin
(MT) radii were selected as large as the crystal structure
permits and kept similar for all the series. This selection
allow us to compare directly the electron occupancies and
derived properties along the intermetallic compound series.
The MT radii were selected in the following manner. For
the intermetallic compounds, we fixed the MT radius of Al
˚ The corresponding Ln MT radii
(Mg) to 1.32 (1.46) A.
were then scaled to the maximum value that the structure
permits. This procedure yields a Ln / M radius ratio ranging
from 1.10 to 1.25 along the lanthanide series. For the
hydrides, the values of the MT radii were fixed to 1.46,
˚ for Ln, Mg and H atomic spheres,
1.27 and 0.64 A
respectively, for both hydrides. The atomic orbitals of the
atoms were separated into core, semi-core and valence
during the calculations. For Mg and Al the 1s and 2s
orbitals were handled as core states, while the 2p orbitals
as semi-core ones. For the lanthanides the 4d, 5s and 5p
orbitals were treated as semi-core. All the calculations
were performed in the semi-relativistic approach, neglecting the spin–orbit interaction. The spin–orbit interactions
are important because they introduce the multiplet splitting
Before describing the results of the band structure
calculations, we briefly outline some features of the crystal
structure of these compounds. LnAl 2 series crystallize in
the C15 (Fd3m) fcc structure, where the Ln atoms occupy
]
the 8a sites of 43m symmetry, while the Al atoms are
]
located at the 16d sites of 3m symmetry. The crystal
structure of the LnMg 2 intermetallic compounds is C15
when Ln is La, Ce, Pr, Nd, Sm and Gd. The C14 structure
is shown by the remaining compounds of the LnMg 2
series. The C14 structure is hexagonal (P6 3 /mmc) with Ln
atoms located at the 4f sites of 3m symmetry. The Mg
]
atoms occupy both 2a and 6h sites of 3m and mm2
symmetry, respectively. The LaMg 2 H 7 and CeMg 2 H 7
hydrides are both isostructural belonging to the complex
tetragonal space group P4 1 2 1 2. This structure is a distorted
tetragonal version of the fcc C15 one. The Ln atoms
occupy the 4a sites of 2 symmetry, while the Mg atoms the
8b sites of 1 symmetry. The hydrogen atoms occupy four
different sites in the structure. While the LnM 2 (M5Al,
Mg) series show both close packed structures, these
hydrides exhibit an open structure with an interstitial
volume close to 60%.
3.1. LnM2 ( Ln 5 Y, La–Lu; M 5 Al, Mg) series
The LnAl 2 and LnMg 2 compound series do not follow
Vegard’s rule. In both series the cell volume decreases
monotonically with the atomic number, reflecting the wellknown lanthanide contraction. However, two exceptions
appear clearly in both series when Ln is Eu or Yb [20]. It
has been argued that these anomalous behaviors are due to
the mixed-valence character frequently observed in Ce,
Sm, and particulary in Eu and Yb compounds.
We have partially optimized the geometry of some
selected intermetallics by means of FPLAPW total energy
calculations. In these calculations we searched for a
minimum in the total electronic energy by varying the
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
lattice parameters, keeping the ideal relative atomic positions unchanged. We found that the equilibrium (theoretical) lattice parameters differ less than 1.5% of the
experimental values. All the results described below were
obtained by considering the experimental crystal data. In
the case of the LnMg 2 series we performed some additional total energy calculations for EuMg 2 in the C15 structure.
We found that the experimentally observed C14 structure
is clearly more stable than the C15 one by 3.65 eV/
formula. To our knowledge, the crystallographic data for
LuMg 2 has not been reported, so we did not consider this
intermetallic in the present investigation.
For the LnAl 2 series, we plotted, in Fig. 1(a) the
calculated values of the magnetic moment ( m 5
]]]
gJœJ(J 1 1)) at the Ln site obtained from the band
structure, along with the free ion (Ln 13 ) and the experimental [20] values. We found a similar behavior for the
LnMg 2 compounds (not shown). The agreement between
the two calculated magnetic moments and the experimental
value is quite good. It must be noted the anomalous
Fig. 1. (a) Magnetic moment of the Ln-4f (in mB ) for the LnAl 2 series,
open squares for the Ln 13 ion, dark circles for our results in the solid and
open triangles for the experimental values. (b) Total spin (in spin /
formula) versus the free ion spin value.
47
behavior of EuM 2 . Sm and Eu ions show systematically a
multiplet structure in which the first energy states differ by
less than kT. This implies that a statistical occupation of
these states must be taken into account [20,31]. It is
interesting to note that the energy interval between the
ground state multiplet and the first excited states is
systematically smaller for Eu than for Sm. In the case of
the intermetallic compounds studied in this paper, only
EuM 2 show these phenomena. It is important to note that
the total magnetic moment of these compounds is dominated by the Ln contributions, in Fig. 1(b), we plot the spin
value obtained by the difference in the spin up and spin
down band occupancies, versus the expected value for the
Ln 13 free ion. We observe that the correlation is good with
only one exception; YbM 2 . We obtained a diamagnetic
band structure while the Yb 13 free ion shows a small
magnetic moment. We will come back to this point later.
We show in Fig. 2 the total DOS for some selected
LnAl 2 intermetallic compounds. The plots for the LnMg 2
intermetallic compounds are not shown. In Figs. 3 and 4
we plotted the partial DOS (PDOS) for LaMg 2 and CeMg 2
intermetallics. The PDOS is the DOS projected into the
atomic sites, decomposed by angular momentum contribution. In these figures we separated the f-electron PDOS
contribution for the lanthanides (Ln-f), which appears in
the inserts. All the computations were performed introducing a spin polarization. The self-consistent procedure
yields diamagnetism for the Y, La, Yb and Lu compounds.
In Table 1 we show, for both series of intermetallic
compounds, the total DOS and PDOS for each contribution
of the spin at the Fermi energy. In Table 2, the charge
analysis at the muffin–tin spheres is summarized. A first
observation of the total DOS permits to state some
expected trends. From the beginning of the series up to
NdM 2 , it is a common feature that the main Ln-f structures
show pronounced peaks with relatively wide structures.
These f-band widths decrease monotonically and from
SmM 2 to the end of the series, are clearly narrower,
showing peaks strongly pronounced. On the other hand,
the position of the spin up and spin down peaks of the total
DOS shifts to lower energies owing to the filling of the
f-bands. The spin polarization is larger at the middle of the
series, as it is expected. It has been largely discussed [13]
that density functional based theories are not able to
predict spectroscopic observed positions of the f-bands and
the multiplicities. However, we obtain, within the generalized gradient approximation [29] to the exchange and
correlation potential, the expected trends for the behavior
of the f-bands along the lanthanide series. The PDOS
plotted in Figs. 3 and 4, show common features among the
intermetallic compounds. In general, the main characteristics are maintained along the series, particularly for the Al
or Mg atom and the Ln-s, Ln-p and Ln-d contributions. It
should be noted, however, that the spin polarization of the
Ln-f bands induces a small one in the Ln-d contributions
as it can be appreciated in the PDOS plots and Table 2.
48
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
Fig. 2. Total density of states in (states / eV-formula) for selected intermetallics (a) NdAl 2 , (b) SmAl 2 , (c) GdAl 2 and (d) HoAl 2 .
However, these contributions to the total magnetism are
small. It should be noted that, in both series of compounds,
Al and Mg do not show an appreciable spin polarization.
The very small contributions arise from the M-p and M-d
(M5Al or Mg) states.
In the cubic C15 structures, we expect that the f-states
split into the irreducible representations of the cubic O h
point group a 2u ^ t 1u ^t 2u . At the center of the fcc
Brillouin zone, G, we have the full symmetry of the O h
point group and it is possible to identify the main orbital
contributions to each energy band. By inspecting the wave
function coefficients at G point (not shown) we can outline
the origin of the occupied states.
The general form of the band structure and ordering of
the energy states are similar among the lanthanide series.
Particularly, LaAl 2 results obtained in this research are in
good agreement with the previous results of Jarlborg and
coworkers [8–10]. In the case of LaMg 2 , as well as for the
entire LnMg 2 series, the overall band width is smaller than
for the LnAl 2 compounds (Fig. 3(a) and (b)). This is
primarily due to the smaller number of electrons in the
LnMg 2 unit cell. This produces a shift of the Fermi level to
lower energies. On the other hand, the cell volume, and the
Ln–Ln and Ln–Mg distances, are larger in the LnMg 2
series with respect to the LnAl 2 one. However, the
ordering of the electronic states is similar for both LnAl 2
and LnMg 2 series.
The PDOS for CeAl 2 is in good agreement with earlier
reports [8–10]. In the spin up part of the PDOS of CeAl 2
and CeMg 2 , we observe a small contribution of the Ce-f
states to the occupied band which is also evident in the
wave function coefficients. This Ce-f contribution yields a
f-electron occupancy of 0.97 and 0.94 electrons per Ce
atom for CeAl 2 and CeMg 2 , respectively. This estimate is
in good agreement with previous reports. The Ce–Ce
˚ (3.78 A).
˚
distance (d Ce – Ce ) in CeAl 2 (CeMg 2 ) is 3.49 A
Both d Ce – Ce values are close to the critical Ce–Ce distance
˚ which separate the Pauli paramagnets
d crit 53.4 A,
(d Ce – Ce ,d crit ) from the magnetic ordered compounds in a
Hill plot [33]. However, as Pickett pointed out [7], the f–f
overlap interaction between first Ce neighbors is small in
this compound. This is also the case in our results and is
expected for the rest of the lanthanide series. The total
DOS of CeAl 2 compares quite well with the experimental
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
Fig. 3. Partial density of states (in states / eV-atom) for LaMg 2 , (a) La, (b)
Mg.
data of UV photoelectron spectroscopy [34]. While the
spectra show peaks at 3.8, 1.8 and 0.8 eV below the Fermi
energy, we obtain a double peaked structure at 24.3 and
23.8 eV followed by two peaks at 21.67 and 20.83 eV. It
is useful to point out here that these peaks are mainly due
to the Al-s,p / Ce-d interactions.
GdAl 2 has been investigated by means of the LMTO
method [14]. The general aspects of DOS (band widths
and peaks) are close to our results. They found a total DOS
at Fermi energy of 1.000 states / eV-formula. However, our
result, 1.639 states / eV-formula, is larger than the experimental value obtained from Bremsstrahlung Isochromat Spectroscopy [32] which is 1.125 states / eV-formula. The spin polarization of the Gd-f states yield similar
values to those reported in Table 2. We obtained the PDOS
at Fermi energy, at the Al site, smaller than those
computed with the LMTO method. YbAl 2 and LuAl 2 have
been recently investigated by means of the tight-binding
LMTO (TB-LMTO) method [15]. In these calculations the
spin–orbit interactions have been considered. Their results
are in general agreement with those obtained in this report.
The splitting between the 4f 5 / 2 and 4f 7 / 2 states of both Yb
49
Fig. 4. Partial density of states (in states / eV-atom) for CeMg 2 , (a) Ce, (b)
Mg.
and Lu are explicit in their total DOS and PDOS. The
values of these splittings are 1.6 and 1.5 eV for YbAl 2 and
LuAl 2 , respectively. Our calculations neglect the spin–
orbit interaction, however, the positions of the 4f 5 / 2 and
4f 7 / 2 peaks are close to those obtained for the DOS in this
work. For YbAl 2 , a narrow peak appears at ¯ 0.5 eV
below the Fermi level compared to 0.2 and 1.8 eV in the
work of Lee and coworkers. For LuAl 2 a single f-peak
appears in the total DOS and PDOS at ¯ 5.3 eV below the
Fermi level, to be compared to the two peaks at 4.0 and 5.5
eV in the work of Lee et al. The estimated values of g
(7.81 mJ K 22 mole and 4.08 mJ K 22 mole, respectively,
for YbAl 2 and LuAl 2 ) are in good agreement with those
found in this work. As we pointed out, Yb can show II, IV
and mixed valence states. The energy bands and DOS for
both YbAl 2 and YbMg 2 intermetallics indicate that Yb
adopt a II valence state since both systems appear to be
diamagnetic after our calculations.
3.2. LaMg2 H7 and CeMg2 H7 hydrides
As it was pointed out in the beginning of this section,
both hydrides show a distorted structure close to the C15
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
50
Table 1
Total DOS (in states / eV-formula) and PDOS (in states / eV-atom) at Fermi energy for the LnM 2 (Ln5Y, La–Lu, M5Al, Mg) series; for the LnMg 2 series,
the index 1(2) in magnesium atoms holds for the 2a(6h) sites of the C14 (P6 3 /mmc) structure, respectively; in the compounds where two entries appear, the
first (second) correspond to the spin up (down) contribution
LnAl 2
Total
Ln-s
Ln-p
Ln-d
Al-s
Al-p
Al-d
Y
1.976
0.014
0.038
0.484
Ln-f
0.004
0.012
0.156
0.048
La
2.230
0.008
0.074
0.340
0.080
0.018
0.205
0.040
Ce
5.317
1.210
0.007
0.006
0.013
0.027
0.142
0.125
4.193
0.317
0.009
0.010
0.055
0.089
0.025
0.018
Pr
17.244
0.754
0.001
0.003
0.010
0.015
0.117
0.104
16.110
0.056
0.005
0.010
0.084
0.073
0.015
0.015
Nd
8.648
0.558
0.010
0.003
0.062
0.011
0.301
0.073
6.683
0.019
0.014
0.010
0.174
0.059
0.040
0.013
Sm
14.660
0.454
0.009
0.001
0.013
0.006
0.082
0.043
13.714
0.008
0.024
0.013
0.080
0.062
0.019
0.010
Eu
1.629
0.743
0.005
0.005
0.016
0.011
0.143
0.068
0.764
0.007
0.012
0.017
0.085
0.091
0.017
0.017
Gd
0.493
1.146
0.005
0.004
0.008
0.015
0.142
0.120
0.003
0.301
0.002
0.010
0.025
0.095
0.012
0.022
Tb
0.839
3.955
0.007
0.003
0.015
0.027
0.203
0.155
0.005
2.568
0.005
0.009
0.062
0.172
0.021
0.032
Dy
1.154
14.567
0.004
0.009
0.030
0.006
0.238
0.061
0.007
13.809
0.009
0.003
0.105
0.023
0.024
0.026
Ho
0.661
31.007
0.003
0.002
0.014
0.027
0.118
0.128
0.007
29.875
0.010
0.007
0.067
0.035
0.017
0.018
Er
0.650
16.519
0.003
0.024
0.014
0.008
0.112
0.140
0.010
15.277
0.010
0.016
0.066
0.061
0.017
0.042
Tm
0.548
4.488
0.005
0.013
0.009
0.022
0.080
0.133
0.032
3.535
0.010
0.018
0.056
0.097
0.015
0.027
Yb
2.241
0.016
0.024
0.202
0.742
0.030
0.172
0.042
Lu
1.847
0.020
0.038
0.423
0.006
0.014
0.154
0.050
LnMg 2
Total
Ln-s
Ln-p
Ln-d
Mg 1 -s
Mg 1 -p
Mg 1 -d
Mg 2 -s
Mg 2 -p
Mg 2 -d
Y
3.204
0.016
0.098
0.805
0.004
0.018
0.270
0.042
0.021
0.265
0.042
La
3.181
0.025
0.038
0.746
0.121
0.028
0.209
0.041
Ce
12.782
1.099
0.012
0.001
0.022
0.011
0.301
0.187
10.855
0.187
0.013
0.011
0.105
0.087
0.026
0.011
Pr
9.125
1.165
0.017
0.002
0.034
0.016
0.337
0.192
7.322
0.041
0.039
0.011
0.133
0.128
0.025
0.013
Nd
29.180
2.034
0.019
0.017
0.055
0.043
0.296
0.250
27.090
0.037
0.024
0.018
0.057
0.254
0.033
0.020
Sm
10.959
1.951
0.006
0.021
0.013
0.043
0.109
0.216
10.282
0.014
0.020
0.018
0.036
0.254
0.010
0.022
Eu
1.418
1.227
0.007
0.015
0.027
0.024
0.030
0.010
0.000
0.000
0.012
0.011
0.105
0.157
0.001
0.001
0.015
0.017
0.121
0.138
0.013
0.011
Gd
2.457
1.521
0.003
0.002
0.063
0.015
0.725
0.152
0.005
0.572
0.011
0.011
0.171
0.110
0.026
0.013
Tb
1.543
12.802
0.008
0.015
0.043
0.020
0.318
0.160
0.006
11.527
0.009
0.004
0.150
0.118
0.021
0.019
0.011
0.017
0.147
0.084
0.020
0.023
Dy
1.262
37.334
0.009
0.010
0.034
0.024
0.228
0.155
0.006
35.431
0.012
0.009
0.123
0.081
0.020
0.040
0.014
0.010
0.131
0.113
0.017
0.036
Ho
1.246
15.768
0.009
0.011
0.036
0.029
0.206
0.131
0.010
14.529
0.012
0.008
0.124
0.095
0.021
0.023
0.015
0.014
0.133
0.115
0.017
0.017
Er
0.986
21.372
0.009
0.014
0.027
0.026
0.143
0.185
0.008
19.790
0.006
0.015
0.099
0.120
0.017
0.029
0.014
0.016
0.120
0.111
0.014
0.030
Tm
0.809
5.058
0.008
0.006
0.023
0.005
0.090
0.044
0.026
4.688
0.006
0.000
0.102
0.024
0.011
0.009
0.013
0.003
0.104
0.033
0.012
0.007
Yb
1.772
0.018
0.042
0.148
0.177
0.017
0.209
0.018
0.029
0.184
0.020
Ln-f
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
51
Table 2
Population analysis (in electrons / atom) inside the muffin–tin spheres for the LnM 2 (Ln5Y, La–Lu, M5Al, Mg) series; for the LnMg 2 series, the index
1(2) in magnesium atoms holds for the 2a(6h) sites of the C14 (P6 3 /mmc) structure, respectively; the data for Ln5Y, La, Yb and Lu are not spin polarised;
for Ln5Ce–Tm, the data is spin polarised; the values set into parentheses correspond to the spin down contribution. Otherwise, the spin up and spin down
contributions are essentially the same
LnAl 2
Ln-s
Ln-p
Ln-d
Ln-f
Al-s
Al-p
Al-d
Y
La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
0.11
0.07
0.04
0.04
0.04
0.04
0.05
0.06
0.06
0.06
0.06
0.07
0.07
0.14
0.18
0.16
0.19
0.09
0.09
0.08
0.06
0.07
0.08
0.08
0.07
0.07
0.07
0.07
0.13
0.15
0.75
0.64
0.38 (0.31)
0.36 (0.36)
0.32 (0.23)
0.21 (0.14)
0.25 (0.15)
0.46 (0.24)
0.40 (0.24)
0.32 (0.25)
0.27 (0.23)
0.26 (0.24)
0.23 (0.21)
0.38
0.69
0.01
0.10
0.79 (0.18)
2.09 (0.06)
3.26 (0.04)
5.46 (0.01)
6.57 (0.01)
6.89 (0.40)
6.90 (1.22)
6.90 (2.33)
6.89 (3.45)
6.89 (4.45)
6.86 (5.60)
13.5
13.9
0.78
0.79
0.39
0.39
0.39
0.39
0.40
0.39
0.39
0.40
0.40
0.40
0.40
0.80
0.78
0.93
0.85
0.43
0.44
0.44
0.39
0.42
0.46
0.46
0.46
0.46
0.46
0.46
0.89
0.95
0.12
0.09
0.05
0.06
0.05
0.04
0.05
0.06
0.06
0.06
0.06
0.06
0.06
0.11
0.13
LnMg 2
Ln-s
Ln-p
Ln-d
Ln-f
Mg 1 -s
Mg 1 -p
Mg 1 -d
Mg 2 -s
Mg 2 -p
Mg 2 -d
Y
La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
0.20
0.10
0.06
0.06
0.07
0.08
0.08
0.10
0.10
0.11
0.11
0.11
0.12
0.23
0.15
0.11
0.05
0.05
0.06
0.06
0.05
0.07
0.07
0.06
0.07
0.06
0.06
0.11
0.72
0.73
0.41 (0.33)
0.35 (0.26)
0.35 (0.20)
0.29 (0.15)
0.22 (0.00)
0.46 (0.22)
0.32 (0.21)
0.25 (0.22)
0.23 (0.19)
0.19 (0.19)
0.16 (0.17)
0.24
0.01
0.08
0.84 (0.10)
2.12 (0.03)
3.85 (0.01)
5.91 (0.01)
6.97 (0.00)
6.31 (0.16)
7.39 (1.39)
7.15 (2.62)
6.95 (3.25)
6.95 (4.58)
6.82 (5.94)
12.79
0.57
0.58
0.30
0.29
0.30
0.30
0.28
0.29
0.29
0.29
0.29
0.29
0.30
0.60
0.56
0.49
0.25
0.24
0.26
0.26
0.24
0.27
0.27
0.27
0.28
0.27
0.28
0.55
0.06
0.05
0.03
0.03
0.03
0.03
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.06
0.58
0.54
0.06
0.29
0.23
0.02
0.30
0.30
0.30
0.30
0.31
0.58
0.26
0.26
0.27
0.26
0.26
0.45
0.03
0.03
0.03
0.03
0.03
0.05
one shown by the parent LnMg 2 intermetallic compound.
In both hydrides the Ln–Ln (Mg–Mg) distances increase
about 5% (4%) with respect to the values found in the
corresponding LnMg 2 system. However, it is remarkable
that the Ln–Mg distances decrease about 2.5% (4%) for
La–Mg (Ce–Mg) distances with respect to the LnMg 2
systems, which is indicative of a compression stress in the
hydride.
The metal–hydrogen distances are in general of the
same order with those found in other transition metal
Laves phase hydrides, but larger than those commonly
observed in ternary alkali (alkaline earth), transition metals
hydrides [3,4,35,36]. In the present hydrides, rare earths
shows 12-fold hydrogen coordination (4 3 H ( 1 ) , 4 3 H (2 ) ,
4 3 H ( 3 ) ) with eight different Ln–H distances ranging from
˚ On the other hand, magnesium atoms show
2.36 to 2.55 A.
a eight-fold hydrogen coordination (2 3 H ( 1 ) , 2 3 H (2 ) ,
2 3 H ( 3 ) , 2 3 H ( 4 ) ) with eight different Mg–H distances
˚ This variety of first neighbors
ranging from 1.91 to 2.59 A.
Ln–H and Mg–H distances reflect the distortion of this
system and the lowering of the point group symmetry with
respect to the ideal fcc C15 structure.
In Fig. 5 we outline the total and partial DOS for the
hydride LaMg 2 H 7 . The inspection of the total DOS plot of
LaMg 2 H 7 (Fig. 5(a)) indicates that this hydride is a
semiconductor with an energy gap of 2.6 eV. This gap is
indirect between the G and M k-points as it can be
appreciated in the energy bands plot (not shown). Both
hydrides contain six types of non-equivalent atoms.
Besides the low point group symmetry of these compounds, the analysis of the structures appearing in total
DOS, as well as in the PDOS plots are difficult to perform.
However, the inspection of the wave function coefficients
at G point (not shown) permit to state some general trends.
In the total DOS plot (Fig. 5(a)), at the bottom of the
energy scale, it appears two peaks that are mainly dominated by the Mg-s / H 4 -s contributions (Fig. 5(c) and (d)).
The La and the other hydrogen atom contributions are
small in this energy range. At higher energies, it appears a
wide structure in the total DOS plot. This structure arises
from the interactions between the La-d (Fig. 5(b)), Mg-p
(Fig. 5(c)) and H-s (Fig. 5(d)) orbitals. The PDOS of the
hydrogen atoms show a large energy dispersion covering
all the valence band. This behavior is similar to that shown
52
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
Fig. 5. (a) Total density of states (states / eV-formula) and (b)–(d) partial density of states (in states / eV-atom) for LaMg 2 H 7 .
by the metallic hydride [3] SrPdH 3 . This hydride shows a
˚ similar to the Mg–H distances in
Pd–H distance of 1.92 A,
LaMg 2 H 7 . However, in the case of quasi-molecular (insulating) hydrides, as K 3 MnH 5 [4], with a Mn–H distance
˚ or even hydrides as K 2 PtH 4 [37], with smaller
of 1.80 A,
˚ the PDOS of the hydrogen atoms
Pt–H distances (1.58 A),
are clearly more localized in energy.
In Fig. 6, we plotted the total DOS and the PDOS for
CeMg 2 H 7 . This hydride shows a magnetic moment localized in the Ce atom ( ¯ 2.60 mB ) as it can be appreciated in
the electron population analysis summarized in Table 3.
The essential features of the band structure, energy bands
(not shown) and DOS, is very similar to that obtained for
the LaMg 2 H 7 hydride. In both spin contributions the lowlying energy bands are well separated from those concerning the Ce-f contributions. The main difference with
respect to LaMg 2 H 7 arises from the Ce-f bands position.
The Fermi energy cuts the beginning of the spin up f-band
containing around one electron. This can be appreciated in
the spin up contribution to the total DOS (Fig. 6(a)) and
the Ce site projected PDOS (Fig. 6(b)), which appear 1.9
eV above the top of the other valence band contributions.
The spin down contribution to the DOS exhibits the
unoccupied f-bands above the Fermi energy and separated
from the top of the (spin down) valence band by 2.56 eV.
Below the Fermi energy it stands up, as in the case of
the CeMg 2 parent intermetallic, a non-negligible complex
Ce-f hybrid contribution to the DOS. The Mg and H atoms
do not show induced magnetization in both LnM 2 series.
This can be observed in the PDOS (Fig. 6(c) and (d)) and
the population analysis in Table 3. In spite of the similarities, the electronic structure of CeMg 2 H 7 , as well as
LaMg 2 H 7 , exhibit strong differences with respect to the
LnMg 2 parent compounds induced by covalent Mg–H and
Ln–H interactions. The covalent character appears more
clearly in the wave function coefficients analysis; the
Ln-d / H-s and Mg-s / H-s states show a strong mixing.
However, the population analysis not necessarily reflects
this situation owing to the dependence of these values on
the muffin–tin radii. It is remarkable the increase of the
bandwidths compared to that of the corresponding LnMg 2
intermetallics. It should be stressed that the shift of the
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
53
Fig. 6. (a) Total density of states (states / eV-formula) and (b)–(d) partial density of states (in states / eV-atom) for CeMg 2 H 7 .
DOS and PDOS structures of the hydrides towards lower
energies (energy stabilization) relative to the peak’s positions of the DOS in the respective intermetallics.
4. Conclusions
Intermetallic compounds of rare earths and non-magnetic metals have attracted interest since the early sixties
owing to it their variety of magnetic properties. Recently,
high hydrogen density hydrides have been discovered in
two of these intermetallics. This fact opened the oppor-
tunity to reexamine the general trends of the electronic
structure of such intermetallics, as well, the electronic
properties of the new respective hydrides. We found that
the general behavior of the LnM 2 series is controlled by
the characteristics of the Ln-f band as the energy width and
relative position to the Fermi level. The analysis of the
magnetic moment of the paramagnetic phases yields a
good agreement with the experimental values. The general
trends of the chemical bonding features as well as the
characteristics of the energy bands and density of states
have been outlined. In the case of the investigated hydrides, LaMg 2 H 7 and CeMg 2 H 7 , we found that they both
Table 3
Population analysis (in electrons / atom) inside the muffin–tin spheres for the LaMg 2 H 7 and CeMg 2 H 7 hydrides; the indexes 1, 2 and 3 in hydrogen atoms
hold for the 8b sites while the index 4 for the 4a sites of the P4 1 2 1 2 structure; the values set into parentheses correspond to the spin down contribution;
otherwise, the spin up and spin down contributions are essentially the same
LaMg 2 H 7
CeMg 2 H 7
Ln-s
Ln-p
Ln-d
Ln-f
Mg-s
Mg-p
Mg-d
H 1 -s
H 2 -s
H 3 -s
H 4 -s
0.08
0.04
0.30
0.14
0.60
0.33 (0.31)
0.17
0.96 (0.12)
0.27
0.14
0.32
0.16
0.12
0.06
0.61
0.30
0.62
0.30
0.60
0.30
0.65
0.33
54
E. Orgaz / Journal of Alloys and Compounds 322 (2001) 45 – 54
show important differences in the electronic properties
with respect to the parent intermetallic compound. While
LaMg 2 H 7 appears to be semi-conducting in agreement
with experiments, in CeMg 2 H 7 the Fermi level cuts the
Ce-f band indicating the possibility of metallic conduction.
We hope that more experimental investigations will be
performed regarding the transport and magnetic properties
in these series of intermetallics and their hydrides. Particulary, it should be interesting to investigate if other
isostructural rare earth’s–magnesium hydrides exists.
Acknowledgements
´ General de
We would like to thank DGSCA (Direccion
´
´
Servicios de Computo
Academico)
of UNAM (Univer´
´
sidad Nacional Autonoma
de Mexico)
for providing us
with the supercomputing facilities for the work presented
in this paper. Financial support was provided under
´
CONACYT (Consejo Nacional de Ciencia y Tecnologıa–
´
Mexico)
Grant No. 3634326-E.
References
[1] F. Gingl, K. Yvon, T. Vogt, A. Hewat, J. Alloys Comp. 253 (1997)
313.
[2] M. Gupta, L. Schlapbach, in: L. Schlapbach (Ed.), Topics in Applied
Physics, Hydrogen in Intermetallic Compounds, Vol. 63, Springer,
Berlin, 1988.
[3] E. Orgaz, V. Mazel, M. Gupta, Phys. Rev. B 54 (1996) 16124.
[4] E. Orgaz, Phys. Rev. B 61 (2000) 7989.
[5] M. Gupta, Int. J. Quantum Chem. 77 (2000) 982.
[6] P. Dantzer, in: H. Wipf (Ed.), Topics in Applied Physics, Hydrogen
in Metals III, Vol. 73, Springer, Berlin, 1997.
[7] W.E. Pickett, B. Klein, J. Less-Common Met. 93 (1983) 219.
[8] T. Jarlborg, A.J. Freeman, D.D. Koelling, J. Phys. (Paris) 43 (1982)
c7.
[9] T. Jarlborg, A.J. Freeman, D.D. Koelling, J. Appl. Phys. 53 (1982)
2140.
[10] T. Jarlborg, A.J. Freeman, D.D. Koelling, J. Magn. Magn. Mat. 60
(1986) 291.
¨
[11] J.C. Fuggle, F.U. Hillebrecht, Z. Zolniereck, R. Lasser,
Ch.
¨
Freiburg, O. Gunnarsonn, K. Schohammer,
Phys. Rev. B 27 (1983)
7330.
´
[12] F. Lopez-Aguilar,
J. Costa-Quintana, Phys. Stat. Sol. B 132 (1985)
485.
´
[13] J. Costa-Quintana, F. Lopez-Aguilar,
S. Balle, R. Salvador, Phys.
Rev. B 41 (1990) 7096.
[14] M. Magnitskaya, G. Chelkowska, G. Borstel, M. Neumann, H. Ufer,
Phys. Rev. B 49 (1994) 1113.
[15] S.J. Lee, Y. Hong, I.R. Fisher, P.C. Canfield, B.N. Harmon, D.W.
Lynch, Phys. Rev. B 61 (2000) 10076.
[16] R. Stiller, H. Merz, W. Drewes, H.-G. Purwins, J. Phys. (Paris) 48
(1987) 997.
[17] Yu.P. Smirnov, A.E. Sovestnov, G.I. Terekhov, A.V. Tyunis, V. A
Shaburov, Sov. Phys. Solid State 30 (1988) 2021.
[18] A. Hasegawa, A. Yanase, J. Magn. Magn. Mater. 15 (1980) 887.
[19] H. Adachi, H. Ino, H. Miwa, Phys. Rev. B 59 (1999) 11445.
[20] K.H.J. Buschow, Rep. Prog. Phys. 42 (1979) 1373.
˜
[21] P.J. von Ranke, I.G. de Oliveira, A.P. Guimaraes,
X.A. da Silva,
Phys. Rev. B 61 (2000) 447.
[22] P.J. von Ranke, V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. B
58 (1998) 12110.
[23] H. Bauer, M.S.S. Brooks, E. Dormann, Phys. Rev. B 48 (1993)
1014.
[24] J.L. Gavilano, J. Hunziker, O. Hudak, T. Sleator, F. Hulliger, H.R.
Ott, Phys. Rev. B 47 (1993) 3438.
[25] O. Hudak, J.L. Gavilano, H.R. Ott, Z. Phys. B 99 (1996) 587.
[26] A.C. Gossard, V. Jaccarino, J.H. Wernick, Phys. Rev. 133 (1964)
A881.
[27] F.U. Hillebrecht, M. Campagna, in: K.A. Gschneidner Jr., L. Eyring,
¨
S. Hufner
(Eds.), Handbook on the Physics and Chemistry of Rare
Earths, Vol. 10, North-Holland, Amsterdam, 1987, Chapter 70.
[28] P. Blaha, K. Schwarz, J. Luitz, Comput. Phys. Commun. 59 (1990)
399.
[29] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996)
3865.
[30] A. Svane, W.M. Temmerman, Z. Szotek, J. Lægsgaard, H. Winter,
Int. J. Quantum Chem. 77 (2000) 799.
[31] J. Crangle, The Magnetic Properties of Solids, Edward Arnold,
London, 1977.
[32] A. Slebarski, W. Zipper, J. Auleytner, J. Phys. F 13 (1983) 2643.
[33] H.H. Hill, Nucl. Metall. 12 (1970) 2.
[34] M. Croft, J.H. Weaver, D.J. Peterman, A. Franciosi, Phys. Rev. Lett.
46 (1981) 1104.
[35] K. Yvon, P. Fischer, in: L. Schlapbach (Ed.), Topics in Applied
Physics, Hydrogen in Intermetallic Compounds, Vol. 63, Springer,
Berlin, 1988.
[36] K. Yvon, in: R.B. King (Ed.), Encyclopedia of Inorganic Chemistry,
J. Wiley, NY, 1994.
[37] E. Orgaz, M. Gupta, Int. J. Quantum Chem. 80 (2000) 141.
Descargar