Materials Sciences and Applicatio n, 2011, 2, 1166-1174
doi:10.4236/msa.2011.28157 Published Online August 2011 (http://www.SciRP.org/journal/msa)
Copyright © 2011 SciRes. MSA
Theoretical Study of the Rare Earth Compounds
LaFe13-xTx (T = Cr, Cu, Ga, Mn, Ni) and Curie
Temperature Variation
Lingping Xiao1,2*, Jiang Shen2
1Jiangxi Blue Sky University, Nanchang, China; 2Institute of Applied Physics, University of Science and Technology, Beijing, China.
Email: *xiaolingping1982@163.com
Received November 25th, 2010; revised January 17th, 2011; accepted June 9th, 2011.
ABSTRACT
The phase stability and site preference of the intermetallics LaFe13-xTx (T = Cr, Cu, Ga, Mn, Ni) with NaZn13-type struc-
ture have been investigated by lattice inversion potentials. The calculated results indicate that each of the stabilizing
elements Cr and Mn significantly decreases the cohesive energy of LaFe13-xTx and plays a role in stabilizing the 1:13
structure. The calculated lattice parameters of LaFe13-xTx (T = Al, Si) compounds are in good agreement with the ex-
perimental data. Qualitative analyses are carried out on the behavior of the Curie temperature and magnetocrystalline
anisotropy. All the results indicate that the pair potentials based on the lattice inversion method can effectively give a
deeper insight into the structure and property of complex materials.
Keywords: Rare Earth Compounds, Interatomic Potentials, Site Preference, Computers Simulation
1. Introduction
Recently rare earth transition metal intermetallic com-
pounds with NaZn13-type structure have attracted con-
siderable attention owing to their potential application
and intriguing magnetic properties [1-4]. In rare earth-
transition metal intermetallic compounds the strong
magnetic coupling between 3d atoms gives rise to the
large magnetization. It seems that the novel R-T inter-
metallic compounds with excellent magnetic properties
are always related to a high content of 3d transition metal.
Among all binary R-M intermetallic compounds only
LaCo13 crystallizes in the cubic NaZn13-type structure
(space group Fm-3c). The LaFe13 compound does not
exist. Generally, the positive heat of alloying between La
and Fe is considered to be the reason why no LaFe13 bi-
nary compound exists. Up to now, many compounds
with NaZn13-type structure have been obtained in R (T,
M) 13 systems (R = rare earth, T = Fe, Co, Ni and M = Al,
Si) by elemental substitution. By now ternary compounds
LaFe13-xSix (1.3 < x < 2.6) [5] and LaFe13-xAlx (1 < x < 7)
[6] are known. Besides, recently the NdFe13-xBex com-
pounds (2< x <4) have been synthesized.
The cubic symmetry of the structure usually implies a
lack of significant magnetocrystalline anisotropy, so that
intermetallic compounds with the NaZn13-type structure
cannot be used for permanent magnets. Much larger
magnetocrystalline anisotropy is expected in materials
with a strong anisotropic crystal structure. It has been
observed that in some range of Si or Al concentrations
the crystal symmetry of the R(M,T)13 compounds trans-
forms from cubic (NaZn13-type) to tetragonal in the
LaCo13-xSix and PrFe13-xSix compounds (Ce2Ni17Si9-type)
[7] or to orthorhombic in the LaFe13-xAlx compounds[8]
and hence creates an opportunity for developing magne-
tocrystalline anisotropy in 1:13 alloys.
In this work, a series of inter-atomic pair potentials in
LaFe13-xTx were determined using a general lattice-inversi-
on technique with a first principles-based crystal cohe-
sive energy calculation. In this way, the stability of
LaFe13-xTx and the site preference were evaluated and
analyzed. Section 2 given an introduction to the method-
ology for the calculation. Section 3 shows the calculated
results and give a comparison with the results of the ex-
periments. The conclusions and the further discussion are
given in the Section 4.
2. Calculation Methods
In general, any interatomic pair potential can be obtained
by a strict lattice inversion of cohesive curve, and the
cohesive energy curves can be obtained either by first
Theoretical Study of the Rare Earth Compounds LaFeT(T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation1167
13-x x
principle calculation or by experimental data fitting. The
lattice inversion theorem is focused on explaining how to
use Chen’s lattice inversion theorem to obtain the intera-
tomic pair potential from the first principle cohesive en-
ergy curve. A brief introduction of the lattice inversion
theorem is proposed as follows [9]: Suppose that the
crystal cohesive energy obtained by the first principle
calculation is expressed as:
E(x) = 00
1
1[()]
2n
rbnx
(1)
where x is the near-neighbor distance, r0(n) is the n
neighbor coordination number, b0(n)x is the distance be-
tween the central reference atom and its nth neighbor,
and [b0(n)x] is the pair potential. A multiplicative
closed semi-group b(n). In the process, a lot of virtual
lattice points are involved, but the corresponding virtual
coordination number is zero. In the b(n), for any two
integers m and n, there is a sole integer k such that b(k) =
b(m) b(n). Hence, equation (1) can be rewritten as
E(x) = 0
1
1[ ()]
2n
rbnx
(2)
where


1
0()
() 0
rbbn n
rn
(3)

0
0
() ()
() ()
bnb n
bnb n
Then the general equation for the interatomic pair po-
tential obtained from the inversion can be expressed as
() 2()[()]
ni
x
InEbnx

(4)
where I(n) has the characteristics of
1
1
()/()
()
() () k
bn bk
bk
Inr bbn






(5)
I(n) is uniquely determined by a geometrical crystal
structure, not related to the concrete element category.
Thus, the interatomic pair potentials can be obtained
from the known cohesive energy function E(x).The in-
teratomic pair potential in distinct atoms can be obtained
by the same inversion method, and they are used to study
the rare earth intermetallics structures. Which are close to
the Morse function, that is:

0
12
0
x= 2
xx
RR
ФDe e


 


 


 

 

0
1
(6)
where D0 is the depth of potential of potential, R0, γ are
parameters. Some important potential are show in the
Table 1.
3. Calculation Results
The structure of LaFe13-xTx (T = Ga, Ni, Mn, Cr, Cu)
compounds are simulated by the energy minimization
process and realized by the conjugate gradient method
with 14 Å as the cut-off radius of the potentials. The re-
sults are taken by the arithmetic average for 30 stochastic
configurations. To avoid statistic fluctuation, the model
is taken as a 2 × 2 × 2 super cell.
3.1. Phase Stability and Lattice Constants of
LaFe13-xTx (T = Cr, Cu, Ga, Mn, Ni)
Although the pure LaFe13 compound is unstable, it can be
considered as the eigentructure of LaFe13-xTx and their
interstitial compounds. In the calculation procedure, the
initial lattice constants of LaFe13 are randomly chosen in
a certain range. Under the control of the interatomic pair
potentials, the energy minimization is carried out by us-
ing the conjugate gradient method. The results show that
the space group maintains Fm-3c or I4/m·cm with
NaZn13-type structure in the tolerance range of 0.001 -
0.1 Å.
In the structure of LaFe13, we first substitute T (T = Cr,
Cu, Ga, Mn, Ni) atom for Fe in each site with different
concentrations and then use the energy minimization
method to relax the systems under the interaction of the
potentials. With different fractions of the third element,
LaFe13-xTx may crystallize in the cubic structure with the
space group Fm-3c or in the tetragonal structure with the
space group I4/mcm. Thus the average cohesive energy
of final structure can be investigated and compared. The
average cohesive energies of different structures are
displayed in Figure 1. It can be seen that the crystal
energy gradually decrease with increasing content of the
ternary element T (T = Cr, Cu, Ga, Mn, Ni). The struc-
ture stability is judged by the energy and tolerance. The
tolerance, which represents the displacement of the
atomic position in order to retrieve the space group, is an
assistant criterion. Numerous calculations show that,
when the tolerance is much large than 0.5 Åthe com-
pounds do not exist in experiments. In fact, the site oc-
cupation is determined by the energy and the too large
tolerance means that the final stable structure has devi-
ated too far from the selected one and that the structure
has been changed.
In the calculation, for LaFe13-xCrx, Cr entering into 96i
site of the cubic structure has the lowest energy and the
tolerance is acceptable for 0 x 3.5. On the other hand,
in the range 0 x 3.5, the tolerance for Cr entering into
16k site of the tetragonal structure is so large that the
tetragonal structure could not exist. However, when 3.5
x 4.0, the tolerance with Cr entering into 16 k site of
the tetragonal structure drops sharply and the tetragonal
Copyright © 2011 SciRes. MSA
Theoretical Study of the Rare Earth Compounds LaFe13-xTx (T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation
Copyright © 2011 SciRes. MSA
1168
structure is acceptable for x 3.75. For LaFe13-xMnx, Mn
entering into 8b site of the cubic structure has the lowest
energy for x 3.25, and the tolerance is acceptable in this
range. However, in the range of 3.25 x 4.0 the toler-
ance with Mn entering into 96i site of the cubic structure
is so large that the cubic structure could not exist, and
Mn entering into 16k site of the tetragonal structure.
From the Figure 1, we can see that Cr, Mn play an im-
portant role in stabilization. But Ni, Cu and Ga cannot
stabilize LaFe13 structure.
Table 1. Some important potential of (LaFe13-xTx) system.
R0(Å) D0(kcal/mol) γ
Fe-Fe 2.73609 17.6177 8.75429
La-La 4.7585 6.7761 6.4607
La-Fe 2.41269 2.38229 6.30159
La-Si 3.4186 13.2643 10.0062
La-Al 3.64488 10.6466 8.89225
Fe-Si 2.7334 15.2938 8.2601
Fe-Al 2.7405 14.9015 9.09675
0123456
-6.25
-6.20
-6.15
-6.10
-6.05
-6.00
-5.95
-5.90
-5.85 (LaFe13-xCrx)
Cohesive Energy (ev/atom)
Cr content (x)
8b
4d
96i
16k
16k(1)
16k(2)
0123456
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(LaFe13-xCrx)
toerlance
Cr content (x)
4d
8b
96i
16k
16k(1)
16k(2)
Theoretical Study of the Rare Earth Compounds LaFeT(T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation1169
13-x x
0123456
-5.8
-5.6
-5.4
-5.2
-5.0
-4.8
-4.6
-4.4 (LaFe13-xCux)
Cohesive Energy (ev/atom)
Cu content (x)
8b
4d
96i
16k
16k(1)
16k(2)
0123456
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 (LaFe13-xCu x)
tolerance
Cu content (x)
8b
4d
96i
16k
16k(1)
16k(2)
0123456
-6.0
-5.8
-5.6
-5.4
-5.2
-5.0
-4.8
-4.6
-4.4
-4.2 (LaFe13-xGax)
cohesive Energy (ev/atom)
Ga content (x)
8b
96i
4d
16k
16k(1)
16k(2)
Copyright © 2011 SciRes. MSA
Theoretical Study of the Rare Earth Compounds LaFeT(T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation
1170 13-x x
0123456
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 (LaFe13-xGax)
tolerance
Ga content (x)
8b
96i
4d
16k
16k(1)
16k(2)
0123456
-6.10
-6.05
-6.00
-5.95
-5.90
-5.85 (LaFe13-xMn x)
Cohesive E ne r gy ( ev /atom )
Mn content (x)
8b
96i
4d
16k
16k(1)
16k(2)
0123456
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(LaFe13-xMnx)
tolerance
Mn c ont ent (x)
8b
96i
4d
16k
16k(1)
16k(2)
Copyright © 2011 SciRes. MSA
Theoretical Study of the Rare Earth Compounds LaFe13-xTx (T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation
Copyright © 2011 SciRes. MSA
1171
0123456
-5.9
-5.8
-5.7
-5.6
-5.5
-5.4
-5.3
-5.2 (LaFe13-xNix)
Cohesieve Energy(ev/atom)
N i con te nt (x)
8b
96i
4d
16k
16k(1)
16k(2)
0123456
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 (LaFe13-xNix)
tolerance
Ni content (x)
8b
96i
4d
16k
16k(1)
16k(2)
Figure 1. The cohesive energy and tolerance variation with the third element content x in LaFe13-xTx (T = Cr, Cu, Ga, Mn, Ni)
with different space group Fm-3c and I4/mcm.
3.2. Fe-Fe Bond Length Change of LaFe13-xTx (T
= Si, Al) tance and the number of nearest neighbors. Here, we will
theoretically study the effects of Fe-Fe bond length
change on the magnetic properties of NaZn13-type inter-
metallic compounds.
In the cubic NaZn13 structure (space group Fm-3c), the
rare earth atoms occupy the single 8a sodium site, while
the Fe atoms are distributed over the two zinc sites, Fe1
(8b) and Fe2 (96i). The Fe1 atoms are surrounded by an
icosahedron of 12 Fe2 atoms and possess a local symme-
try peculiar to an FCC-like lattice. In the tetragonal
structure (space group I4/mcm) the Fe atoms occupy four
different sites. The Fe1 atoms (the 4d site) in icosahedron
centers are surrounded by 12 Fe atoms in the sites
Fe2(16k), Fe3(16l1) and Fe4(16l2). Previous investigations
[10] have shown that the magnetic properties of the
R-Fe-based compounds are determined predominantly by
the Fe-Fe interaction, which is sensitive to the Fe-Fe dis-
In the experiments, LaFe13-xAlx crystallizes the cubic
NaZn13-type structure with the space group Fm-3c in the
range 1.04 x 7.15, and LaFe13-xSix compounds are of
a single phase with the space group Fm-3c in the range
1.4 x 2.6 [11]. According to our previous works, Si
entering into the 96i site could stabilize the cubic struc-
ture of LaFe13-xSix with x < 3.25, and for 3.25 < x < 5.25
Si first enters into the 16l2 site of the tetragonal structure
and with 16l2 full the rest of the Si enters into the 16k site
[12]. Compared with the experiment, the calculated result
is good at illustrating the structure transition. Therefore, it
is also verified that interatomic pair potential are effect-
Theoretical Study of the Rare Earth Compounds LaFeT(T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation
1172 13-x x
Table2. The crystallographic parameters a and c of LaFe13-xTx (Al, Si) in Å, obtained from experiments (exp.) and calcula-
tions (cal.), and Ref. is the source of the experimental data.
x a(cal) c(cal) a(exp) c(exp) Ref.
LaFe13-xSix 2 11.470 11.463 [13]
3 8.035 11.485 7.994 11.363
4 7.997 11.501 7.974 11.542
5 7.967 11.595 7.954 11.720
LaFe13-xAlx 2 11.547 11.668 [14]
3 11.569 11.731
4 11.614 11.794
5 11.688 11.857
6 11.794 11.920
7 11.871 11.983
tive. Table 2 shows the lattice parameters of LaFe13-xTx
(T = Si, Al) obtained from both the experiments [13] [14]
and calculations. The results correspond well to experi-
mental data. The bond lengths of Fe-Fe which play an
important role in magnetic properties can be evaluated.
In this subsection, the dependence of Curie temperature
on the Si/Al concentration is analyzed qualitatively.
In the experiment, the value of TC for the LaFe11.5Si1.5
compound is 188 K. Just as Givord et al. have pointed
out, there are two types of exchange interactions, positive
and negative, which depend on the length of Fe-dumb-
bells. All the exchange interactions could be positive
except the case associated with 96i-96i, 96i-8b, since the
distances between these iron atoms are small.
In order to study the trend of Curie temperature varia-
tion, the distance between special sites and the related
exchange interaction should be investigated. Figure 2
presents the bond lengths in LaFe13-xSix, indicating that
the lengths of 96i-96i are shorter than 2.46 Å which can
be considered as the threshold of switching exchange
interaction. The distances between 96i-96i and 96i-8b
decrease with increasing Si content, which are similar to
that in the experimental trend. Notice that the bond
lengths of 96i-8b are larger than 2.46 Å, then the varia-
tion of exchange interaction from 96i-8b pairs can be
neglected. As far as iron pairs except 96i-96i are con-
cerned, the positive exchange interactions associated
with large bond lengths are weak, even though the intro-
duction of Si atom has the effect of reduction on them.
Then the contribution to the exchange interaction from
these iron pairs can also be neglected. In the next step,
we will focus on the effect of 96i-96i lengths based on
the variation of Curie temperature.
In the above subsection, the analysis of site preference
behavior shows that Si atoms have a pronounced prefer-
ence for occupying 96i site. On the one hand, the number
of 96i-96i (Fe-Fe) dumbbell pairs reduces and the nega-
tive exchange interaction with the increase of Si atom,
and in thus beneficial in improving the Curie temperature.
on the other hand, bond lengths of 96i-96i pairs decrease
with increasing Si content, and thus enhance the negative
exchange interaction and lead to a lower Curie tempera-
ture. So there is a competing mechanism arising from Si
content increase, i.e. the variation of Curie temperature is
not monotonic with the increment of Si concentration.
Givord et al. [15] have shown that the threshold of
switching Fe-Fe exchange interaction is 2.45 Å. In other
words, if the distance of Fe-Fe is shorter than 2.45 Å,
then the exchange interaction would be negative, if it is
larger than 2.45 Å, then it would be positive. In the pre-
sent calculation, the threshold of Fe-Fe exchange interac-
tion is taken as 2.46 Å, instead of 2.45 Å from the ex-
perimental analysis. This difference may be caused by a
systemic error in derivation of these quasi-in-
teratomic potentials.
ab initio
4. Conclusions and Discussions
Pair potentials based on calculations and on
the lattice-inversion method have been used to calculate
the structural properties of a series of LaFe13-xTx (T = Cr,
Cu, Ga, Mn, Ni).The results show that Cr and Mn make
the cohesive energy decrease markedly, indicating that
these atoms can stabilize LaFe13-xTx with the cubic
NaZn13-type or its derivative tetragonal structure.
ab initio
Furthermore, the increase of the Curie temperature of
LaFe13-xTx (T = Si, Al) with increasing Si concentration
can be qualitatively explained in terms of the distance
dependence of the exchange interaction. The presented
results indicate that simple pair potentials are useful for
studying the structural properties of these kinds of inter-
metallics.
5. Acknowledgements
The authors would like to thank the stimulating discus-
sions with Professor N. X. Chen, and Y. Chen. The pre-
sent work is supported by National 973 project
Copyright © 2011 SciRes. MSA
Theoretical Study of the Rare Earth Compounds LaFeT(T= Cr, Cu, Ga, Mn, Ni) and Curie Temperature Variation 1173
13-x x
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
2.42
2.44
2.46
2.48
2.50
2.52
2.54
Fe-Fe distance
Al/Si concentration (x)
96i-96i of LaFe13-xAlx
8b-96i of LaFe13-xAlx
96i-96i of LaFe13-xSix
8b-96i of LaFe13-xSix
Figure 2. Bond lengths (Å) of Fe-Fe pairs with the ternary element (Al/Si) content in LaFe13-xTx (T = Al, Si).
2006CB605101. This work was also supported by the
Young Natural Science Foundation of Jiangxi Blue Sky
University.
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