substance: boron compounds
property: structural properties of hexaborides with B6 octahedra
The unit cell of the cubic structure contains one formula weight of MB6 (Fig. 1). The boron atoms form regular
octahedra positioned at the corners of the unit cell, whose center is occupied by the metal atom. All rare-earth
metals and moreover Ca, Sr, Ba, Tl and Pu form isostructural hexaborides (see [77E)]. Often these structures are
denoted as CaB6-type.
Alkali hexaborides are semiconductors. Hexaborides with divalent metals have been predicted to be
semiconductors or insulators, while hexaborides with trivalent metals are assumed to be metallic. Sm ions
exhibit an intermediate valence.
Representatives of metal hexaborides [94K, 85E]
(dM−M, metal-metal interatomic distance; rM, metallic radii sum; dM−M, rM in Å)
Compound
dM−M
∆ = a – 2rM
Conductivity type
M+1B6
NaB6
NaxBa1−x B6
NaxTh1−x B6
NaB5C
54B
76N
76N
98A
M+2B6
CaB6
SrB6
BaB6
EuB6
YbB6
LaB6
TbB6
GdB6
NdB6
PrB6
4.1525
4.1897
4.269
4.1849
4.1479
0.204
−0.114
−0.077
0.195
0.268
semiconductor
semiconductor
semiconductor
semiconductor
semiconductor
86I
92C
77N
95B
95B
82B
82B
83S
83S
79P
4.1332
0.513
gap at EF
93T
4.113
4.1466
4.1396
4.1319
4.1259
0.493
0.419
0.500
0.492
0.498
metal
metal
metal
metal
metal
77N
93O
89B
92C
94M,
95B
4.1105
0.510
metal
77N
Sm+2.6 B6 (intermediate valence)
SmB6
M+3B6
YB6
LaB6
CeB6
PrB6
NdB6
M+4B6
ThB6
Lattice parameters of metal hexaborides compared with the atomic radii of the metal atoms in Fig. 2 [87P].
Lattice parameters of metal hexaborides (lattice constants, bond lengths, mean square displacement) in Figs. 3
and 4 [99T].
X-ray diffraction of CaB6, LaB6, YbB6 and ThB6 in [82B].
MeB6 lattice constant depending on the metal atomic number in [87P].
Preparation with the aluminium-flux method [83G].
Temperature dependence of the lattice parameters of CaB6, Sm0.05Ca0.95B6, Sm0.4Ca0.6B6, SmB6,
Sm0.5La0.5B6, LaB6 determined by neutron scattering in Fig. 5 [88A, 91A].
Comparison of calculated and measured lattice constants and interoctahedral B-B distances in [97R].
Correlation between B charge and valence electron concentration in Fig. 6 [97R].
Lattice distortion in mixed crystals of some rare earth hexaborides [99K1].
Preparation of hexaborides solid solution single crystals by zone melting [99K2].
Force constants for some hexaborides [mdyn Å−1] [90Y]. (numerical parameters of a MVFF treatment to fit the
observed IR and Raman spectra).
Compound B – B
intraoctahedral
Bondbond
Bondbond
Bondbond
Bondbond
60°
90°
non ||
||
M–B
B–B
B–B–B
interoctahedral
bend 135°
CaB6
1.464
0.147
−0.071
−0.184
−0.325
0.192
1.708
0.275
SrB6
1.278
0.148
−0.022
−0.135
−0.269
0.180
1.395
0.589
LaB6
1.348
0.145
−0.033
−0.174
−0.337
0.144
1.664
0.168
NdB6
1.434
0.150
−0.038
−0.175
−0.334
0.113
1, 743
0.174
GdB6
1.503
0.156
−0.058
−0.179
−0.428
0.095
1.827
0.190
TbB6
1.560
0.159
−0.060
−0.179
−0.490
0.096
1.860
0.195
DyB6
1.614
0.175
−0.087
−0.180
−0.510
0.089
1.885
0.220
YbB6
1.408
0.147
−0.062
−0.174
−0.302
0.185
1.688
0.428
11B
The magnitude of the
nuclear electric quadrupole interaction in divalent and trivalent-metal hexaborides and
mixed-valent SmB6 depending on the lattice parameter in Fig. 7 [86B].
Linear relation between the variation in the interoctahedral B-B force constant and the lattice constant in [93N].
Work function and effective magnetic moment in Fig. 8 [59S].
Reflectivity spectra of LaB6, SmB6, EuB6 up to 42 eV in Fig. 9 [81S].
Reflectivity spectra of pure YB6, LaB6, CeB6, SmB6, Sm0.8B6 and TbB6 in Fig. 10 [99W].
Spectroscopic investigation of lattice vacancies in hexaborides [93B].
IR diffuse reflectance spectra of MB6 compounds with two-valent Yb, Sr and Ca and three-valent Nd, Gd, La,
and Dy metal atoms in Fig. 11 [88T, 93Y].
Representative Raman spectra of hexaborides with twofold and threefold ionized metal atoms in Fig. 12 [88T, 93Y].
Frequencies of the phonon symmetry modes A1g, Eg, T2g and T1u for several metal hexaborides in Fig. 13 [86Z].
Phonon frequencies from IR absorption vs. lattice parameter of some metal hexaborides in Fig. 14 [99W].
Magnetic susceptibility of DyB6, TbB6 and HoB6 in Fig. 15 [97T].
Thermal conductivity and magnetic susceptibility of alkali and rare earth hexaborides in [65L].
Observed vibrational wavenumbers ν/c (in cm−1) of metal hexaborides [93Y].
SrB6
Raman
1400
1300
1225
IR
1450
1330
1200
1190
YbB6
Raman
1400
1340
1258 s
IR
1480
1310
1200
1170...
1090
CaB6
Raman
1475
1500
1270 s
IR
1430
1340
1260
1125...
1095
DyB6
Raman
1510
1400
1314 s
IR
1470
1330
Assignments
ν5+tr (comb)
1310
1160...
1100
ν1 A1g (s)
ν2 F1u (b)
1085
1020
1192 sh
1160 sh
1154 sh
1160 w
ν2 Eg (s)
1105
1122 m
1125 s
1180 s
1078
1091 m
1081 w
960...
810
730...
685
960
800 m
ν7 F2u (b)
935 w
845 w
860 w
775 s
762 sh
773 m
715 sh
792
740...
685
770 s
752 sh
760 s
732 sh
ν4 F2g (b)
730
685
470 w
465 w
480
475
510 w
420 w
128
TbB6
Raman
1460
1380
1298
520
460
526 w
485 w
250
150
GdB6
Raman
1430
1350
IR
1410
1375
1280
1155...
1085
1168 s
1100 sh
1142 w
918 w
845 w
806
790
1290 s
330
250
NdB6
Raman
1490
1395
IR
1430
1330
1260
1160...
1100
1156 w
1285 s
790
500 w
480
475
IR
1480
1320
1260
1165...
1095
LaB6
Raman
1440
1330
1242
ν3 F1g (r)
ν6 F1u (t)
262
180
1145 s
1136 sh
940 w
842 w
520
470
IR
1430
1340
Assignments
ν5+tr (comb)
1240
1170...
1095
ν1 A1g (s)
ν2 F1u (b)
ν2 Eg (s)
1152 s
1112 sh
928
778
790
690
790
700
ν7 F2u (b)
680
715 sh
692 m
680 w
685 s
ν4 F2g (b)
782 w
690 sh
670 m
490
480
248
185
523
460
560 w
530
242
175
500
460
500 w
210
170
533
ν3 F1g (r)
ν6 F1u (t)
s = strong; m = medium; w = weak; sh = shoulder; (s) = stretch; (b) = bend; (r) = rotation; (t) = translation
Multichannel Raman studies of binary alkaline borides MB6 (M = Ca, La, Sr, Sm) (abstract only) in [86Y].
The micromechanical properties of metal hexaborides [79P].
Study of the electronic structure of rare earth hexaborides (La, Ce, Pr, Nd, Sm, Eu, Gd, Yb, Y) [85G].
Phonon and specific heat analysis in rare-earth hexaborides [99K2].
Charge carriers per Ln atom derived from Hall effect and XCS (X-ray chemical shift) measurements
Compound
n(Hall)
n(XCS)
LaB6
CeB6
NdB6
PrB6
EuB6
GdB6
YbB6
YB6
0.93
1.06
0.88
0.84
0.03
0.94
0.05
0.96
0.86(3)
1.00(5)
1.01(5)
0.82(8)
≤ 0.05
1.0(1)
≤ 0.05
1.00(2)
85G
Bipolaron formation in icosahedral and octahedral borides [98E].
Pressure dependence of the electrical resistivity; ρ(p)/ρ(0) vs. hydrostatic pressure p for some metal hexaborides
in Fig. 16 [81K, 91S].
Pressure dependence of the thermoelectric power S for LaB6, YbB6 and EuB6 in Fig. 17 [81K].
Vacancies and thermal vibrations of atoms in the crystal structure of rare earth hexaborides [94K].
Boron-boron bond lengths vs. lattice parameter for some metal hexaborides in Fig. 18 [94K].
Characteristic Einstein temperatures of the RE atoms vs. atomic number of the RE element in Fig. 19 [94K].
Variation of the atomic equivalent temperature factors (normalized by a2) vs. the atomic number of the RE
element in Fig. 20 [94K, 99T.
Entropy of LaB6, ferromagnetic EuB6 and antiferromagnetic EuB6 in Fig. 21 [80F].
The working reliability and structure stability of thermoemission lanthanum hexaboride elements in stationary
plasma thruster hollow cathode [98P].
High temperature hardness of single crystals of LaB6, CeB6, PrB6, NdB6 and SmB6 [99O].
Review papers
General review article [85E].
On the physical properties of intermediate valent hexa- and dodecaborides [87W].
On band structure calculations of metal hexaborides [87A].
References:
54B
59S
65L
76N
77E
77N
79A
79P
80F
81K
81S
82B
83G
83S
85E
85G
86B
86I
86Y
86Z
87A
87P
87W
88A
88T
89B
90Y
91A
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J. Less-Common Met. 82 (1981) 211. (Proc. 7th Int. Symp. Boron, Borides and Rel. Compounds,
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Dudnik, E.M.: Phys. Status Solidi (b) 128 (1985) 591.
Bray, P.J.: in: Boron-Rich Solids (AIP Conf. Proc. 140), Albuquerque, New Mexico 1985, D. Emin,
T.L. Aselage, C.L. Beckel, I.A. Howard ed., American Institute of Physics: New York, 1986, p. 142.
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86, Eugene, OR, USA,, Peticolas, W.L.; Hudson, B.; ed., Univ. Oregon: Eugene, OR, USA, 1986, p.
11(abstract only).
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Armstrong, D.R.: in: Proc. 9th Int. Symp. Boron, Borides and Rel. Compounds, University of
Duisburg, Germany, Sept. 21 - 25, 1987, H. Werheit ed., University of Duisburg: Duisburg, 1987, p.
125.
Paderno, Yu.B., Konovalova, E.S.: in: Proc. 9th Int. Symp. Boron, Borides and Rel. Compounds,
University of Duisburg, Germany, Sept. 21 - 25, 1987, H. Werheit ed., University of Duisburg:
Duisburg, 1987, p. 65.
Wachter, P.: in: Proc. 9th Int. Symp. Boron, Borides and Rel. Compounds, University of Duisburg,
Germany, Sept. 21 - 25, 1987, H. Werheit ed., University of Duisburg: Duisburg, 1987, p. 166.
Alekseev, P.A., Konovalova, E.S., Lasukov, V.N., Lyukshina, S.I., Paderno, Yu.B., Sadikov, I.P.,
Udovenko, E.V.: Fiz. Tverd. Tela 30 (1988) 2024 (in Russian).
Turrell, S., Yahia, Z., Huvenne, J.P., Lacroix, B., Turrell, G.: J. Mol. Struct. 174 (1988) 455.
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309.
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Sadikov, I.P., Konovalova, E.S., Paderno, Yu.B.: in: Boron-Rich Solids, Proc. 10th Int. Symp. Boron,
Borides and Rel. Compounds, Albuquerque, NM 1990 (AIP Conf. Proc. 231), D. Emin, T.L. Aselage,
A.C. Switendick, B. Morosin, C.L. Beckel ed., American Institute of Physics: New York, 1991, p. 318.
91S
92C
93B
93N
93O
93T
93Y
94K
94M
95B
97R
97T
98A
98E
98P
99K2
99K1
99K2
99O
99T
99W
Sidorov, V.A., Stepanov, N.N., Ziok, O.B., Chvostanzev, L.G., Smirnov, N.A., Korsukova, M.M.:
Fiz. Tverd. Tela 33 (1991) 1271(in Russian).
Chernychev, V.V., Aslanov, L.A., Korsukova, M.M., Gurin, V.N.: (cited in 94K 11).
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(1993) 133.
Nagao, T., Kitamura, K., Iizuka, Y., Oshima, C., Otani, S.: Surf. Sci. 290 (1993) 436.
Otani, S., Honma, S., Yajima, Y., Ishizawa, Y.: J. Cryst. Growth 126 (1993) 466.
Trounov, V.A., Malyshec, A.L., Chernyshov, D.Yu., Korsukonva, M.M., Gurin, V.N., Aslanov, L.A.,
Chernychev, V.V.: J. Phys.: Condens. Matter 5 (1993) 2479.
Yahia, Z., Turrel, S., Mercurio, J.P., Turrel, G.: J. Raman Spectroscopy 24 (1993) 207.
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August 22 - 26, 1993, Jpn. J. Appl. Phys. Series 10 (1994), p. 15.
Malyshev, A., Chernyshov, D., Trounov, V., Gurin, V.N., Korsukova, M.M.: Proc. 11th Int. Symp.
Boron, Borides and Rel. Compounds, Tsukuba, Japan, August 22 - 26, 1993, Jpn. J. Appl. Phys.
Series 10 (1994), p. 19.
Blomberg, M.K., Merisalo, M.J., Korsukova, M.M., Gurin, V.N.: J. Alloys Compounds 217 (1995)
123.
Ripplinger, H., Schwarz, K., Blaha, P.: J. Solid State Chem. 133 (1997) 51 (Proc. 12th Int. Symp.
Boron, Borides and Rel. Compounds, Baden, Austria, 1996).
Takahashi, K., Kunii, S.: J. Solid State Chem. 133 (1997) 198 (Proc. 12th Int. Symp. Boron, Borides and
Rel. Compounds, Baden, Austria, 1996).
Albert, B., Schmitt, K.: Chem. Commun. (1998) 2373.
Emin, D.G., Evans, S.S., McCready, S.S.: Phys. Status Solidi (b) 205 (1998) 311.
Paderno, V.N., Paderno, Yu.B., Filippov, V.B., Arkhipov, B.A.: J. Mater. Process. Manufact. Sci. 6
(1998) 311.
Konovalova, E., Paderno, Yu.B.: J. Solid State Chem. (2000) (Proc. 13th Int. Symp. Boron, Borides
and Rel. Compounds, Dinard, France, Sept. 1999).
Korsukova, M.M., Gurin, V.N., Vegas, A., Gonzalez-Calbert, J.M., Otani, S.: J. Solid State Chem.
(2000) (Proc. 13th Int. Symp. Boron, Borides and Rel. Compounds, Dinard, France, Sept. 1999).
Kunii, S., Takahashi, K., Iwashita, K.: J. Solid State Chem. (2000) (Proc. 13th Int. Symp. Boron,
Borides and Rel. Compounds, Dinard, France, Sept. 1999).
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Int. Symp. Boron, Borides and Rel. Compounds, Dinard, France, Sept. 1999).
Takahashi, Y., Ohshima, K., Okamura, F.P., Otani, S., Tanaka, T.: J. Phys. Soc. Jpn. 68 (1999) 2304.
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(Proc. 13th Int. Symp. Boron, Borides and Rel. Compounds, Dinard, France, Sept. 1999).
Fig. 1.
Metal hexaborides. Unit cell with B6 octahedra at the corners and the metal (M) atom in the center.
MB6
M
B
Fig. 2.
Metal hexaborides. Lattice parameters of metal hexaborides (lower curve) vs. atomic number of the metal atoms
compared with the atomic radii of the metal atoms (upper curve) [87P].
Atomic radius r [Å]
2.0
58
60
Atomic number
62
64
66
M
68
70
1.9
1.8
1.7
Lattice parameter a [Å]
4.20
4.15
4.10
4.05
M = La Ce Pr Nd
MB6
Sm Eu Gd Tb Dy Ho Er Tu Yb Lu
Fig. 3.
Metal hexaborides. Lattice parameters of metal
lattice constant; (c) bond length between rare
octrahedral bond lengths; (e) quantities of the
atoms: circles at 295 K, Uiso for the rare earth
triangle, U11 for the boron atoms [99T].
La
M=Y
0.203
Ce
Sm
Nd
Eu
hexaborides vs. atomic number; (a) boron coordinate XB; (b)
earth metal and boron atom; (d) intra-octahedral and intertemperature parameters for the mean square displacement of
metal atoms; down triangles, U22=33 for the boron atoms; up
Gd
Boron coordinate XB
a
4.10
1.78
Gd
3.06
62
63
64
b
intra B-B
1.74
B-B bond length [Å]
M-B bond length [Å]
–2 2
Eu
4.12
0.199
Temp. factors Uiso , U11 , U22 = 33 [10 Å ]
Sm
4.14
0.200
3.04
1.70
3.02
3.00
1.8
Nd
4.16
0.201
0.198
3.08
Ce
Lattice parameter a [Å]
MB6
0.202
La
M=Y
4.18
1.66
c
1.62
39
1.4
1.0
Uiso
U22 = 33
0.6
0.2 e
39
U11
57
58
59
60
61
Atomic number
62
63
64
inter B-B
d
57
58
59
60
61
Atomic number
Fig. 4.
Metal hexaborides. (a) Ionic radius of the RE ions; (b) intra-octahedral and inter-octrahedral bond lengths and
(c) square root for Uiso for the rare earth metal atoms vs. lattice parameter [99T].
1.20
1.80
MB6
1.15
Eu
2+
La
1.05
Ce
Nd
1.00
0.95
Sm
4.12
4.14
4.16
Lattice parameter a [Å]
1.68
b
M=Y
Gd
0.09
Nd
0.08
Sm
Eu
Ce
4.12
2+
La
4.14
4.16
Lattice parameter a [Å]
1.60
4.10
4.18
0.10
0.07
4.10
Eu
Nd
La
Sm
Eu
inter B-B
Ce
Gd
0.12
0.11
intra B-B
1.72
M=Y
a
0.13
La
Sm
M=Y
1.64 M = Y
0.85
4.10
1/2
Mean square root displacement Uiso
[Å]
3+
Gd
0.90
c
B-B bond length [Å]
Ionic radius r [Å]
1.10
Nd
Gd
1.76
Ce
4.18
4.12
4.14
4.16
Lattice parameter a [Å]
4.18
Fig. 5.
Metal hexaborides. Temperature dependence of the lattice parameters of CaB6, Sm0.05Ca0.95B6, Sm0.4Ca0.6B6,
SmB6, Sm0.5La0.5B6, LaB6 determined by neutron scattering in [88A, 91A].
4.152
CaB6
4.151
4.150
4.149
4.149
4.148
Sm0.05Ca0.95B6
4.148
4.147
4.146
4.145
4.138
4.137
4.136
4.133
4.135
SmB6
4.132
4.131
4.130
4.129
4.153
Sm0.5La0.5B6
4.152
4.151
4.156
4.150
LaB6
4.155
4.154
4.153
4.152
0
50
100 150
200
Temperature T [K]
250
300
Lattice parameter a [Å]
Lattice parameter a [Å]
Sm0.4Ca0.6B6
Fig. 6.
Metal hexaborides. Correlation between B charge and VEC, the valence electron concentration (number of
valence electrons per unit cell volume). The B charge is determined as the valence charge inside the boron
sphere (with rB = 0.794 Å). Assuming localized 4f states for La and Ce or 4d states for Y makes these atoms
divalent [97R].
1.46
MB6
Y
1.44
M = Ca
B-charge [e]
1.42
Ce
La
Sr
1.40
1.38
1.36 K
0.25
all valence electrons
divalent Y, La, Ce
Ba
0.26
0.27
0.28
0.29
VEC [e/Å3]
0.30
0.31
Fig. 7.
Metal hexaborides. The magnitude of the 11B nuclear electric quadrupole interaction (e2qQ) in divalent- and
trivalent-metal hexaborides and mixed-valent SmB6 vs. lattice parameter [86B]. The right ordinate |eq| shows
the magnitude of the electric field gradient at the boron nucleus converted from |e2qQ|. Broken and dotted
curves: theoretical calculations [79A].
1.45
Gossard &
Jaccarino [86B8]
1.40
1.35
1.35
3+
M B6
valence mixing SmB6
2+
M B6
1.25
1.30
M = Dy
1.20
1.20
Yb
Gd
Ca
Sm
–3
Tb
1.15
1.15
Eu
Nd
1.10
Pr
1.10
1.05
Ce
1.05
La
1.00
1.00
0.95
4.08
e q [eA ]
Ho
2
e qQ [MHz]
1.25
1.30
0.95
4.10
4.12
4.14
4.16 4.18 4.20
Lattice parameter a [Å]
4.22
4.24
4.26
Fig. 8.
Metal hexaborides. (a) Work function and (b) effective magnetic moment vs. atomic number [59S].
57
6
59
61
Atomic number
63
65
67
69
71
MB6
Work function φ [eV]
5
4
3
2
1
Eff. magn. moment peff [rel. units]
0
12
a
10
8
6
4
2
b
0
M = La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tu Yb Lu
Fig. 9.
Metal hexaborides. Optical reflectivity spectra; R vs. photon energy. Long-dashed curve, LaB6, solid curve,
SmB6, short-dashed curve, EuB6 [81S].
30
Reflectivity R [%]
25
20
15
10
(×10)
LaB6
5
0
EuB6
5
10
15
SmB6
20
25
30
Photon energy hν [eV]
35
40
Fig. 10.
Metal-hexaborides (metallic). IR reflectivity spectra of single-crystal pure YB6, LaB6, CeB6, SmB6, Sm0.8B6
and TbB6.. Some of the spectra are vertically shifted to avoid superposition. The amount of the shift is indicated
at the spectra in the diagram. It is assumed that the phonon spectra occur in the spectra because symmetry
selection rules are lifted in consequence of structural distortions [99W].
1.00
0.96
CeB6
0.92
LaB6 (shift – 0.05)
0.88
Reflectivity R
0.84
0.80
TbB6 (shift – 0.08)
0.76
0.72
0.68
Sm0.8B6 (shift – 0.16)
0.64
YB6 (shift – 0.2)
0.60
0.56
YB6 (shift – 0.2)
0
5
10
15
SmB6 (shift – 0.18)
20
25
30
35
2
–1
Wavenumber ν [10 cm ]
40
45
50
Fig. 11.
Metal hexaborides. IR diffuse reflectance spectra of representative MB6 compounds with two-valent Ca, Sr and
Yb, and three-valent Nd, Gd, La, Tb and Dy metal atoms [88T, 93Y].
MB6
M = Dy
M = Ca
Gd
Tb
Sr
500
a
1000
1500
–1
Wavenumber ν [cm ]
Intensity I
Intensity I
Yb
2000
500
b
Nd
La
1000
1500
–1
Wavenumber ν [cm ]
2000
Fig. 12.
Metal hexaborides. Raman spectra, relative intensity vs. Raman shift for hexaborides with twofold and threefold
ionized metal atoms [88T, 93Y].
MB6
M = La
3+
Raman intensity IR
Gd
Dy
Sr
400
Raman intensity IR
Tb
400
2+
600
M = Ca
200
3+
2+
Yb
200
3+
800
1000
–1
Wavenumber ν [cm ]
1200
1400
800
1000
–1
Wavenumber ν [cm ]
1200
1400
2+
3+
600
Fig. 13.
Metal hexaborides. Wavenumbers of the phonon symmetry modes A1g, Eg, T2g and T1u vs. lattice parameter for
divalent EuB6, intermediate valent SmB6 and trivalent YB6, GdB6, NdB6, CeB6 and LaB6 [86Z]. Circles,
experimental data; solid lines, averaged and extrapolated; dashed lines, assumed variation based on the
experimental data for EuB6.
1400
MB6
mode symmetry
1360
M=Y
1320
Gd
Nd Sm
A1g(Γ1 )
1280
+
Ce
La
Eu
1200
–1
Wavenumber ν [cm ]
–1
Wavenumber ν [cm ]
1200
1160
1240
Eg(Γ3+ )
1120
1080
1040
740
700
T2g(Γ5+ )
660
620
220
180
140
4.10
T1u(Γ4– )
4.12
4.14
4.16
Lattice parameter a0 [Å]
4.18
Fig. 14.
EuB5.9C0.1
LaB6
YbB6
CeB6
SmB6
YB6
1.6
TbB6
Metal hexaborides. Phonon frequencies obtained from the IR absorption spectra (calculated from the measured
reflectivity spectra in Fig. 10 by Kramers-Kronig transformation). Same symbols are used for phonons in
different compounds, which can be probably attributed to one another. The dashed lines represent the Raman
frequencies in Fig. 11. The full lines combine the plasmon polariton frequencies of the semiconducting
hexaborides EuB6 and YbB6, and the arrows indicate the shift to the related resonance frequency in metallic
LaB6 (softening of the high frequency F1u mode and hardening of the low frequency F1u mode) obviously
caused by the high carrier concentration [99W].
MB6
1.4
A1g
Eg
3
–1
Phonon wavenumber ν [10 cm ]
1.2
1.0
F1u(semicond)
0.8
F2g
0.6
0.4
F1u(met.)
0.2
F1u(semicond)
0
4.10
4.12
4.14
4.16
Lattice parameter a0 [Å]
4.18
Fig. 15.
Metal hexaborides. Inverse molar magnetic susceptibility; χm−1 vs. T [97T]. χm in CGS-emu.
–3
Inv. susceptibility χm–1 [mol cm ]
30
25
20
15
DyB6
TbB6
HoB6
10
5
0
50
100
150
Temperature T [K]
200
250
300
Fig. 16.
Metal hexaborides. Pressure dependence of the electrical resistivity; ρ(p)/ρ(0) vs. hydrostatic pressure p. Full
lines, monocrystalline LaB6, EuB6 and YbB6 [91S], dashed lines, LaB6, SmB6 prepared from starting ratios
Sm:B 1/7, 1/9, 1/12 (effect increases this way), YbB6, EuB6 [81K].
LaB6
1.0
Rel.resistivity ρ/ρ0
0.8
SmB6
LaB6 (mono)
YbB6
0.6
EuB6
0.4
EuB6 (mono)
0.2
0
YbB6 (mono)
1
2
3
4
5
Pressure p [GPa]
6
7
8
Fig. 17.
Metal hexaborides. Pressure dependence of the thermoelectric power S for LaB6, YbB6 and EuB6 [81K].
0
LaB6
– 2.5
–1
Thermoelectric power S [µV K ]
– 25
– 50
EuB6
– 75
– 100
– 125
YbB6
– 150
– 175
– 200
0
2
4
6
8
Pressure p [GPa]
10
12
Fig. 18.
Metal hexaborides. Boron-boron bond lengths vs. lattice parameter a (full triangles, hypothetical equidistance)
[94K].
1.80
MB6
B-B bond length [Å]
M = Th Pr Ce
La
1.76
Nd
Sm Ca Yb
B-B intra
Eu Sr
1.72
Eu
1.68
Ca
Sm Ce
1.64
Sr
Ba
Ba
B-B inter
Yb
La
Nd Pr
Th
1.60
4.100 4.125 4.150 4.175 4.200 4.225 4.250 4.275
Lattice parameter a [Å]
Fig. 19.
Metal hexaborides. Characteristic Einstein temperatures of the Ln atoms vs. atomic number of the Ln element;
full circles [94K]; triangles [99T].
150
LnB6
Ln = La
Einstein temperature
E [K]
140
130
120
Ce
Pr
Nd
Eu
Sm
110
100
90
56
59
Gd
62
65
Ln atomic number
Yb
68
71
Fig. 20.
Metal hexaborides. Variation of the atomic equivalent temperature factors (normalized by a2) vs. the atomic
number of the Ln element (full circles, Ln atom; open circles, B atom) [94K].
70
LnB6
Ln = Yb
Uequiv / a2 [105]
60
50
Nd
40
Ce
La
Pr
Sm
Eu
30
B
20
56
59
62
65
Ln atomic number
68
71
Fig. 21.
Metal hexaborides. Entropy vs. T for LaB6, ferromagnetic EuB6, antiferromagnetic EuB6 [80F].
5
Entropy S/R
4
LaB6
EuB6 (F)
EuB6 (AF)
3
ln 8
2
1
0
20
40
Temperature T [K]
60
80