Critical rare-earth free La2Fe14B (2:14:1) has the potential to be a gap permanent magnet. However, La2Fe14B decomposes into La, α-Fe, and LaFe4B4 phases below 1067 K. The phase stability and coercivity have been studied in La2Fe14B magnet using first principles DFT (density functional theory) calculation and micromagnetic simulation. For a perfect La2Fe14 B cube (edge length of 256 nm) without any structural defects and soft magnetic secondary phases, the coercivity (8.5 kOe) is reduced to ∼40% of its magnetocrystalline anisotropy field (HA = 20 kOe). Further, the coercivity sharply reduces to 3.2 kOe upon forming a thin layer (2 nm) of α-Fe on the surface of the La2Fe14B cube particle. The DFT calculations indicate that a partial replacement of La by other rare-earth (RE) elements can enhance the structural stability of 2:14:1. The gains in cohesive energy are 0.75, 0.10, and 0.33 eV per formula unit in (La0.5RE0.5)2Fe14B with RE = Ce, Pr, and Nd, respectively. Stabilizing the 2:14:1 structure and mitigating the formation of soft magnetic structural defects or impurity phases such as α-Fe is necessary to develop La2Fe14B based magnet, which can be moderately achieved via partial substitution of La by other rare earth elements such as Ce, Pr, and Nd.

Nd2Fe14B permanent magnets are widely applied in many fields, including electric/hybrid vehicles, wind power generation, and electronics, because of their excellent magnetic performance.1–5 The growth of the rare earth (RE) magnet industry results in a supply shortage of critical RE metals such as Pr, Nd, Dy, and Tb, while La and Ce co-produced with Pr and Nd are oversupplied. Using La and Ce can help balance the use of rare earth resources, hence reducing the costs of permanent magnets. The magnets RE2Fe14B (2:14:1) with RE = La and Ce have attracted intensive research in recent years.6–10 Although Ce can form a stable phase of 2:14:1, the La2Fe14B phase is metastable. Hadjipanayis et al.11 found that the 2:14:1 phase can be obtained in as-cast La16Fe76B8 alloys with heat treatment at 1073 K. It was also reported that the 2:14:1-type phase does not exist in melt-spun La-Fe-B alloy with/without heat treatment.12 Li et al.13 found that La2Fe14B is a high-temperature stable ternary compound. The phase is unstable and decomposes into La, α-Fe, and LaFe4B4 phases at a temperature below 1067 K. The phase melts as α-Fe, Fe2B, and liquid phase at a temperature above 1200 K. In other words, the La2Fe14B phase is only stable in a small temperature range (1067 K to 1200 K).

The thermal instability of La2Fe14B limits the choice of potential processing routes to prepare La-Fe-B ternary magnets. Unlike La, all other RE2Fe14B (RE = Ce, Pr, Nd, Sm, Gd-Lu, and Y) are stable phases. It is expected that the partial replacement of La by other RE = Ce, Pr, and Nd will stabilize the 2:14:1 structure. Zhang et al.12 reported that the substitution of La by 40% of Nd could significantly enhance the formation of the 2:14:1 phase. However, the metastable behavior of La2Fe14B may still cause local segregation of RE elements in La-RE-Fe-B magnets and promote the formation of structural defects and/or impurity soft magnetic phases under high-temperature processing conditions. Theoretical and experimental works confirm that the La atoms prefers to segregate to the grain boundary phase in La-Nd-Fe-B.14–17 These defects or impurity phases may deteriorate the magnetic properties, such as reducing coercivity. Tang et al. reported that the partial substitution of Nd by La (40%) reduced the coercivity from 11 kOe to 0.1 kOe in Nd-Fe-B sintered magnet.14 Further, the magnetocrystalline anisotropy field of La2Fe14B (HA = 20 kOe at 300 K) is inferior to those of Nd2Fe14B (HA = 70 kOe).18 This makes its coercivity more sensitive to the structural defect and/or soft magnetic secondary phases.

As part of our endeavor to develop La-Fe-B base magnet, we investigated the effect of the potential impurity soft ferromagnetic phase due to the instability of La2Fe14B on the coercivity using micromagnetic simulation. Further, we studied the effect of the partial replacement of La by RE = Ce, Pr, and Nd on the phase stability of 2:14:1 from a first principle DFT (Density Functional Theory) calculation. Finally, we discuss the pathway to develop La2Fe14B-based permanent magnets.

The micromagnetic simulation is based on Landau–Lifshitz–Gilbert equation (LLG), and has been an effective method at the continuum level to model the static and dynamic magnetic properties in ferromagnetic materials. The principles of micromagnetic simulation have been well documented in previous literature.19–21 It has been widely used to study the magnetic properties of Nd2Fe14B based magnet.22–25 We perform micromagnetic modeling using a finite difference (FD) micromagnetic code MuMax3.26,27 Here, the finite-difference cell size is 1 × 1 × 1 nm for all the calculations. For the calculation of the magnetic hysteresis loop, we adopted a field step of 2 mT. The total energy minimization was performed using a conjugate gradient method with a converge criterion of normalized magnetization change less than 10−6. The materials parameters18,28 for micromagnetic simulation are listed in Table I.

TABLE I.

Materials parameters of magnetization (Ms), magneto-crystalline anisotropy constant (K1), and exchange constant (Aex) for micromagnetic simulation.18,28

MaterialsMs (kA/m)K1 (MJ/m3)Aex (pJ/m)
La2Fe141098 1.1 
α-Fe 1710 0.048 22 
MaterialsMs (kA/m)K1 (MJ/m3)Aex (pJ/m)
La2Fe141098 1.1 
α-Fe 1710 0.048 22 

The first principle DFT total energy calculations were performed using the OpenMX code.29,30 The pseudoatomic-orbital basis sets and norm-conserving pseudopotentials are used. The Perdew–Burke–Ernzerhof (PBE) functional31 was employed to approximate the exchange correlation. The 4f electrons of Nd and Pr are treated using the DFT + U method.32,33 The U values for Pr and Nd are selected as 6.0 eV and 5.9 eV, respectively.32 Starting with the experimental parameters of unit cell size and atomic positions,13 the geometry was fully relaxed with the convergence of the total energy and the force better than 10−6 Hartree and 10−5 Hartree/Bohr, respectively. The number of k points is 7 × 7 × 5 for the total energy calculation. The cohesive energy (i.e., atomization energy) has been defined as the difference between the total energy of the RE2Fe14B phase E(RE2Fe14B) and that for each atom in the 2:14:1 formula unit.

Ec=2ERE+14EFe+EBE(RE2Fe14B)

As a starting point, we perform a micromagnetic simulation to study the effect of size and morphology on the coercivity of La2Fe14B particle without any structural defects and secondary soft magnetic phase. To mimic the different particle morphologies, we selected the particles with cube and sphere shapes. Figure 1 shows the coercivity of La2Fe14B as a function of particle size. With decreasing particle size, the coercivity, Hci, increases. For the same volume, the particles with a sphere shape has higher coercivity than the ones with cube shape. For example, the La2Fe14B cube with an edge length of 32 nm has a coercivity of 15.1 kOe, and the spherical particle with the same volume has a coercivity of 17.9 kOe. As expected, these values are less than the effective magnetocrystalline anisotropy field (HA = 20 kOe) due to the inhomogeneous magnetization reversal near surface. The sharp edge of the cube has a stronger demagnetization effect and further reduces the coercivity.

FIG. 1.

Calculated coercivity of La2Fe14B particles with a shape of sphere (black circle) and cube (red square), respectively, as a function of edge length of the cube (the sphere has the same volume of the corresponding cube).

FIG. 1.

Calculated coercivity of La2Fe14B particles with a shape of sphere (black circle) and cube (red square), respectively, as a function of edge length of the cube (the sphere has the same volume of the corresponding cube).

Close modal

Figure 2 displays the demagnetization field and magnetization distribution of a La2Fe14B cube with an edge length of 128 nm at a magnetic remanent state (external field H = 0). The magnetization orientation deviates from the magnetic easy-axis (here, x-direction or horizontal direction, Fig. 2) near the surface and edge of the particle. This is driven by the demagnetization field (magnetostatic field) with a direction opposite to the magnetization. The magnetization reversal is driven by the combined contributions of the demagnetization and external fields. The strong local demagnetization field at the surface and sharp edges of the particles reduce the coercivity, hence changes its value with morphology. In polycrystalline bulk magnets, the grains are typical polyhedrons. The related demagnetization field cannot be avoided entirely. However, appropriately tailoring the grain morphology can reduce the local demagnetization and enhance coercivity.

FIG. 2.

The demagnetization field (a) and magnetization (b) distribution in a La2Fe14B cube with an edge length of 128 nm at a magnetic remanent state (external field H = 0). Here, the arrow is the magnetization or demagnetization direction. The easy-axis is along the x-direction (horizon direction).

FIG. 2.

The demagnetization field (a) and magnetization (b) distribution in a La2Fe14B cube with an edge length of 128 nm at a magnetic remanent state (external field H = 0). Here, the arrow is the magnetization or demagnetization direction. The easy-axis is along the x-direction (horizon direction).

Close modal

As discussed in Sec. III, La2Fe14B is stable at a small temperature range (1067 K to 1200 K) and tends to decompose into α-Fe, La, and LaFe4B4 phases. To mimic the effect of the potential structural defect and impurity soft magnetic phase (e.g., α-Fe) on the coercivity, we set up a “defect cube” model with a La2Fe14B cube (defect-free core) enclosed with an α-Fe layer (shell) with a thickness of 2 nm. The edge length of the defect cube is 256 nm. The calculated magnetic hysteresis loop (J-H) of the defect cube-shaped La2Fe14B particles is shown in Fig.3. For comparison, we also calculated the J-H loop of a La2Fe14B “ideal cube” particle (edge length 256 nm) without any structural defects and soft magnetic secondary phase. The computed coercivity (Hci = 8.5 kOe) of the “ideal cube” is reduced to about 40% of its magnetic anisotropy field (Ha = 20 kOe) due to the local demagnetization field. However, the coercivity sharply reduces to 3.2 kOe in the La2Fe14B defect cube. Eliminating or minimizing the impurity soft magnetic phase such as α-Fe is necessary to obtain high coercivity in the La2Fe14B magnet.

FIG. 3.

Calculated demagnetization curve (J-H) of a La2Fe14B particle (256 nm) without any structural defects (black, circle) and that of the La2Fe14B particle with a thin layer (2 nm) of α-Fe on the surface (red, triangle).

FIG. 3.

Calculated demagnetization curve (J-H) of a La2Fe14B particle (256 nm) without any structural defects (black, circle) and that of the La2Fe14B particle with a thin layer (2 nm) of α-Fe on the surface (red, triangle).

Close modal

Figure 4 shows the unit cell of La2Fe14B. The unit cell is created using the VESTA package.34 The tetragonal 2:14:1 phase has a space group of P42/mnm (No. 136) and four formula units, 68 atoms in each unit cell. There are six crystallographically inequivalent Fe sites, two inequivalent La sites, and one B site. It should be noted that different site notations exist. Here, we use Herbst’s notation.18 

FIG. 4.

Unit cell of La2Fe14B (a) and the slab at the z = 0 position (b). The big red and green atoms are La at 4f and 4g, respectively. The B atom is a small black ball. The moderate size blue ball is the Fe atom at the 8j2 site. The medium size gold balls are other Fe atoms. All the images are generated using VESTA package.34 

FIG. 4.

Unit cell of La2Fe14B (a) and the slab at the z = 0 position (b). The big red and green atoms are La at 4f and 4g, respectively. The B atom is a small black ball. The moderate size blue ball is the Fe atom at the 8j2 site. The medium size gold balls are other Fe atoms. All the images are generated using VESTA package.34 

Close modal

In the 2:14:1 unit cell, all the La and B atoms are at crystal plane of z = 0 and z = 1/2 (Fig. 4(a)). The La atom at 4f site is surrounded by a polyhedron consisting of 16 Fe atoms. On the other hand, La at the 4g site was enclosed by a polyhedron including 16 Fe atoms and one boron atom (Fig. 4(b)). The 2:14:1 phase can be considered as the alternative packing of the 4f La- and 4g La-centered polyhedrons in three-dimension space (Fig 4(b)). The stability of these polyhedrons will affect the phase stability of 2:14:1. Thermodynamics calculation indicate that the enthalpy of mixing for La-Fe is positive over the whole composition range,35 in agreement with the fact that none of the La-Fe intermetallic phases exist in the La-Fe binary system. The results imply that the chemical bond between La and Fe is very weak, which is partially responsible for the metastable behavior of La2Fe14B. Conversely, the enthalpy of mixing for Fe and other light rare earth elements such as Ce, Pr, Nd, and Sm are negative. Stable binary compounds such as RE2Fe17 with RE = Ce, Nd, Pr, and Sm exist.35 Since all the RE2Fe14B with RE = Ce, Pr, Nd, Sm, Gd-Lu, and Y are stable phases,18 partial replacement of La by other RE elements is expected to enhance the phase stability of (La, RE)2Fe14B. Our first principle DFT calculation confirms this hypothesis, as further discussed.

As shown in Table II, the replacement of La by other RE = Ce, Pr, and Nd increases the cohesive energy of 2:14:1. A 50% La replaced by Ce, Pr, and Nd results in a cohesive energy increment of 0.75, 0.10, and 0.33 eV per formula unit, respectively. The resultant improvement in the stabilization of the 2:14:1 structure would eliminate or reduce the phase decomposition of La2Fe14B during the synthesis process. In addition, the total energy calculations indicate that the atoms of Ce, Pr, and Nd prefer to replace the La atom at the 4f site, which has a smaller site volume than the La 4g site. As shown in Table II, the Wigner–Seitz (WS) cell analysis36 indicates that the 4f- and 4g-La site has a WS volume of 31.0 Å3 and 32.1 Å3 in La2Fe14B, respectively. This volume effect is partially responsible for the preferential site occupation. i.e., the larger-sized La and smaller Ce/Pr/Nd atoms prefer to enter the 4g and 4f sites, respectively. The calculated total magnetic moments are also listed in Table II. Except for Pr and Nd, only the contributions from the spin moment for La, Ce, Fe and B are included in the calculated total magnetic moment. The orbital moments from La and Ce are around 0.07–0.12 µB while that from Fe atoms ranges from 0.01 to 0.05 µB. The contribution from boron can be ignored (less than 0.001 µB). The size of orbital moment from the 4f electrons of Pr and Nd are comparable to their spin moments. We treat the 4f electrons of Nd and Pr with a Russel-Saunders model, (i.e., the orbital contribution is its theoretical value and couples with spin moment following a Hund rule) and include their contributions to the total magnetic moments (Table II). As expected, the substitution of La by Ce reduces the total magnetic moment due to the reduced unit cell volume. On the other hand, in (La,RE)2Fe14B with RE = Pr and Nd, the total magnetic moment increases due to the contribution of Pr and Nd magnetic moment.

TABLE II.

Calculated lattice constants a (Å) and c (Å), Wigner–Seitz volume (WSV, Å3), Cohesive energy Ec (eV/f.u.) and magnetic moments M (µB/f.u.) in (La0.5RE0.5)2Fe14B (RE = Ce, Pr, and Nd). The RE atoms of Ce, Pr and Nd are at the 4f sites.

RELaCePrNd
a 8.8197 8.7886 8.8130 8.810 
c 12.3350 12.2406 12.2861 12.270 
Ec 82.744 83.492 82.841 83.071 
M 30.9 30.0 38.0 38.3 
WSV (4f31.0 29.0 30.8 30.8 
WSV (4g32.1 32.2 32.2 32.2 
RELaCePrNd
a 8.8197 8.7886 8.8130 8.810 
c 12.3350 12.2406 12.2861 12.270 
Ec 82.744 83.492 82.841 83.071 
M 30.9 30.0 38.0 38.3 
WSV (4f31.0 29.0 30.8 30.8 
WSV (4g32.1 32.2 32.2 32.2 

Further, the Ce is more effective than Pr and Nd in stabilizing 2:14:1, i.e., higher cohesive energy (Table II). However, the partial replacement of La by Pr or Nd can also enhance the magnetocrystalline anisotropy in addition to improving the phase stability. For example, substituting La by 50% of Nd will improve the magnetocrystalline anisotropy field from 20 kOe to ∼55 kOe.17 It is expected that the higher magnetocrystalline anisotropy field would reduce the sensitivity of coercivity to structural defects or the minor secondary soft magnetic phases.

The magnetic performance of a permanent magnet is determined by the multiscale structure at atomic, particle, grain and bulk levels. To develop a stable La2Fe14B phase, there is need to overcome the limitation imposed by its narrow stable temperature range (1067 K to 1200 K). This can be accomplished by a partial replacement of La by other RE atoms such as Pr and Nd which, in turn, will enhance the low (20 kOe) MCA. At the grain or particle size level, the morphology, size, and surface defect will modify the magnetization reversal behavior and affect the coercivity. Optimizing grain size and morphology is crucial for the magnetic phase with low MCA, such as La2Fe14B. Considering the metastable behavior of La2Fe14B, proper design of composition and processing conditions to eliminate or mitigate the formation of soft magnetic defects or impurity phases, such as α-Fe, is a challenging task. Finally, when the particles or grains of La2Fe14B are assembled into the bulk magnet, the grain boundary and/or grain boundary phase should be appropriately engineered to minimize the inter-grain magnetic interactions.

In summary, La2Fe14B has the potential to be a gap permanent magnet, although it is metastable. The coercivity depends on the grain size and morphology. According to micromagnetic simulation, it is susceptible to forming impurity soft magnetic phases on the surface of La2Fe14 B grains. The DFT calculations indicate that the partial replacement of La by other rare-earth (RE) elements such as Ce, Pr, and Nd can enhance the structural stability of 2:14:1. Stabilizing the 2:14:1 structure and mitigating the formation of soft magnetic impurity phase such as α-Fe is necessary to obtain high coercivity in La2Fe14B based magnet, which can be moderately achieved via the partial substitution of La by other rare earth elements such as Ce, Pr, and Nd.

This work is supported by the Critical Materials Institute (CMI), an Energy Innovation Hub funded by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. The work was performed at Ames National Laboratory, operated for the U.S. Department of Energy by Iowa State University of Science and Technology under Contract No. DE-AC02-07CH11358.

The authors have no conflicts to disclose.

X. B. Liu: Conceptualization (equal); Investigation (lead); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). I. C Nlebedim: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request and approval from Critical Materials Institute, US-DOE.

1.
J. J.
Croat
,
J. F.
Herbst
,
R. W.
Lee
, and
F. E.
Pinkerton
,
Journal of Applied Physics
55
,
2078
(
1984
).
2.
M.
Sagawa
,
S.
Fujimura
,
N.
Togawa
,
H.
Yamamoto
, and
Y.
Matsuura
,
Journal of Applied Physics
55
,
2083
(
1984
).
3.
O.
Gutfleisch
,
M. A.
Willard
,
E.
Brück
,
C. H.
Chen
,
S. G.
Sankar
, and
J. P.
Liu
,
Advanced Materials
23
,
821
(
2011
).
4.
S.
Sugimoto
,
Journal of Physics D: Applied Physics
44
,
064001
(
2011
).
5.
R. W.
McCallum
,
L.
Lewis
,
R.
Skomski
,
M. J.
Kramer
, and
I. E.
Anderson
,
Annual Review of Materials Research
44
,
451
(
2014
).
6.
E. J.
Skoug
,
M. S.
Meyer
,
F. E.
Pinkerton
,
M. M.
Tessema
,
D.
Haddad
, and
J. F.
Herbst
,
Journal of Alloys and Compounds
574
,
552
(
2013
).
7.
X.
Fan
,
S.
Guo
,
K.
Chen
,
R.
Chen
,
D.
Lee
,
C.
You
, and
A.
Yan
,
Journal of Magnetism and Magnetic Materials
419
,
394
(
2016
).
8.
T.
Ma
,
W.
Zhang
,
B.
Peng
,
Y.
Liu
,
Y.
Chen
,
X.
Wang
, and
M.
Yan
,
Journal of Physics D: Applied Physics
51
,
055003
(
2018
).
9.
H.
Chen
,
R.
Han
,
J.
Qu
,
Y.
Yao
,
J.
Liu
,
W.
Li
,
S. P.
Ringer
,
S.
Dong
, and
R.
Zheng
,
Journal of Alloys and Compounds
846
,
156248
(
2020
).
10.
J.
Jin
,
Z.
Wang
,
G.
Bai
,
B.
Peng
,
Y.
Liu
, and
M.
Yan
,
Journal of Alloys and Compounds
749
,
580
(
2018
).
11.
G. C.
Hadjipanayis
,
Y. F.
Tao
, and
K.
Gudimetta
,
Applied Physics Letters
47
,
757
(
1985
).
12.
Z. Y.
Zhang
,
L. Z.
Zhao
,
J. S.
Zhang
,
X. C.
Zhong
,
W. Q.
Qiu
,
D. L.
Jiao
, and
Z. W.
Liu
,
Materials Research Express
4
,
086503
(
2017
).
13.
X.
Li
,
Z.
Lu
,
Q.
Yao
,
Q.
Wei
,
J.
Wang
,
Y.
Du
,
L.
Li
,
Q.
Long
,
H.
Zhou
, and
G.
Rao
,
Journal of Alloys and Compounds
859
,
157780
(
2021
).
14.
W.
Tang
,
S.
Zhou
, and
R.
Wang
,
Journal of Applied Physics
65
,
3142
(
1989
).
15.
W.
Tang
,
Y. Q.
Wu
,
K. W.
Dennis
,
N. T.
Oster
,
M. J.
Kramer
,
I. E.
Anderson
, and
R. W.
McCallum
,
Journal of Applied Physics
109
,
07A704
(
2011
).
16.
X. B.
Liu
,
Z.
Altounian
,
M.
Huang
,
Q.
Zhang
, and
J. P.
Liu
,
Journal of Alloys and Compounds
549
,
366
(
2013
).
17.
Z.
Li
,
W.
Liu
,
S.
Zha
,
Y.
Li
,
Y.
Wang
,
D.
Zhang
,
M.
Yue
, and
J.
Zhang
,
Journal of Rare Earths
33
,
961
(
2015
).
18.
J. F.
Herbst
,
Reviews of Modern Physics
63
,
819
(
1991
).
19.
W. F.
Brown
, Jr.
, in
Micromagnetics
(
Wiley
,
New York
,
1963
).
20.
H.
Kronmüller
,
R.
Fischer
,
M.
Seeger
, and
A.
Zern
,
Journal of Physics D: Applied Physics
29
,
2274
(
1996
).
21.
J.
Fidler
and
T.
Schrefl
,
Journal of Physics D: Applied Physics
33
,
R135
(
2000
).
22.
H.
Sepehri-Amin
,
T.
Ohkubo
,
M.
Gruber
,
T.
Schrefl
, and
K.
Hono
,
Scripta Materialia
89
,
29
(
2014
).
23.
G. A.
Zickler
,
P.
Toson
,
A.
Asali
, and
J.
Fidler
,
Physics Procedia
75
,
1442
1449
(
2015
).
24.
D.
Liu
,
T. Y.
Zhao
,
R.
Li
,
M.
Zhang
,
R. X.
Shang
,
J. F.
Xiong
,
J.
Zhang
,
J. R.
Sun
, and
B. G.
Shen
,
AIP Advances
7
,
056201
(
2017
).
25.
J.
Fischbacher
,
A.
Kovacs
,
M.
Gusenbauer
,
H.
Oezelt
,
L.
Exl
,
S.
Bance
, and
T.
Schrefl
,
Journal of Physics D: Applied Physics
51
,
193002
(
2018
).
26.
A.
Vansteenkiste
,
J.
Leliaert
,
M.
Dvornik
,
M.
Helsen
,
F.
Garcia-Sanchez
, and
B.
van Waeyenberge
,
AIP Advances
4
,
107133
(
2014
).
27.
A.
Vansteenkiste
and
B.
Van de Wiele
,
Journal of Magnetism and Magnetic Materials
323
,
2585
(
2011
).
28.
H.
Kronmüller
, in
Materials Science and Technology
(
American Cancer Society
,
2019
), pp.
1
43
.
29.
T.
Ozaki
,
Physical Review B
67
,
155108
(
2003
).
30.
T.
Ozaki
and
H.
Kino
,
Physical Review B
69
,
195113
(
2004
).
31.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Physical Review Letters
77
,
3865
(
1996
).
32.
D.
van der Marel
and
G. A.
Sawatzky
,
Physical Review B
37
,
10674
(
1988
).
33.
M. J.
Han
,
T.
Ozaki
, and
J.
Yu
,
Physical Review B
73
,
045110
(
2006
).
34.
K.
Momma
and
F.
Izumi
,
Journal of Applied Crystallography
44
,
1272
(
2011
).
35.
B.
Konar
,
J.
Kim
, and
I.-H.
Jung
,
Journal of Phase Equilibria and Diffusion
37
,
438
(
2016
).
36.
E.
Koch
and
W.
Fischem
,
Zeitschrift Für Kristallographie - Crystalline Materials
211
,
251
(
1996
).