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 regularoctahedra positioned at the corners of the unit cell, whose center is occupied by the metal atom. All rare-earthmetals and moreover Ca, Sr, Ba, Tl and Pu form isostructural hexaborides (see [77E)]. Often these structures aredenoted as CaB6-type.
Alkali hexaborides are semiconductors. Hexaborides with divalent metals have been predicted to besemiconductors or insulators, while hexaborides with trivalent metals are assumed to be metallic. Sm ionsexhibit 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 54BNaxBa1−x B6 76NNaxTh1−x B6 76NNaB5C 98A
M+2B6
CaB6 4.1525 0.204 semiconductor 86I
SrB6 4.1897 −0.114 semiconductor 92C
BaB6 4.269 −0.077 semiconductor 77NEuB6 4.1849 0.195 semiconductor 95BYbB6 4.1479 0.268 semiconductor 95BLaB6 82BTbB6 82BGdB6 83SNdB6 83SPrB6 79P
Sm+2.6 B6 (intermediate valence)
SmB6 4.1332 0.513 gap at EF 93T
M+3B6
YB6 4.113 0.493 metal 77NLaB6 4.1466 0.419 metal 93OCeB6 4.1396 0.500 metal 89BPrB6 4.1319 0.492 metal 92CNdB6 4.1259 0.498 metal 94M,
95B
M+4B6
ThB6 4.1105 0.510 metal 77N
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. 3and 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 theobserved IR and Raman spectra).
Compound B – B
intraocta-hedral
Bond-bond
60°
Bond-bond
90°
Bond-bond
non ||
Bond-bond
||
M – B B – B
interocta-hedral
B – B – B
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
The magnitude of the 11B nuclear electric quadrupole interaction in divalent and trivalent-metal hexaborides andmixed-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 YbB6 CaB6 DyB6
Raman IR Raman IR Raman IR Raman IR Assignments1400 1450 1400 1480 1475 1430 1510 1470 ν5+tr (comb)
1300 1330 1340 1310 1500 1340 1400 1330
1225 1200 1258 s 1200 1270 s 1260 1314 s 1310ν1 A1g (s)
1190 1170...1090
1125...1095
1160...1100
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
960 800 m 935 w ν7 F2u (b)
845 w 860 w 792
730...685
740...685
770 s 760 s 775 s 773 m ν4 F2g (b)
752 sh 732 sh 762 sh 715 sh
730
685
470 w 480 510 w 520 526 w 520 500 w 480 ν3 F1g (r)
465 w 475 420 w 460 485 w 470 475
128 250 330 262 ν6 F1u (t)
150 250 180
TbB6 GdB6 NdB6 LaB6
Raman IR Raman IR Raman IR Raman IR Assignments1460 1410 1430 1430 1490 1480 1440 1430 ν5+tr (comb)
1380 1375 1350 1330 1395 1320 1330 1340
1298 1280 1290 s 1260 1285 s 1260 1242 1240ν1 A1g (s)
1155...1085
1160...1100
1165...1095
1170...1095
ν2 F1u (b)
1168 s 1156 w 1145 s 1152 s ν2 Eg (s)
1100 sh 1142 w 1136 sh 1112 sh
918 w 806 940 w 928 790 790 ν7 F2u (b)
845 w 790 842 w 790 778 690 700
680
715 sh 680 w 685 s 782 w ν4 F2g (b)
692 m 690 sh
670 m
490 523 560 w 500 500 w 533 ν3 F1g (r)
480 460 530 460
248 242 210 ν6 F1u (t)
185 175 170
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 0.93 0.86(3) 85GCeB6 1.06 1.00(5)NdB6 0.88 1.01(5)PrB6 0.84 0.82(8)
EuB6 0.03 ≤ 0.05GdB6 0.94 1.0(1)
YbB6 0.05 ≤ 0.05YB6 0.96 1.00(2)
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 hexaboridesin 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 REelement 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 stationaryplasma 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 Blum, P., Bertraut, F.: Acta Crystallogr. 7 (1954) 81.59S Samsonov, G.V., Shravlev, N.N., Paderno, Yu.B., Melik-Adamyai, V.R.: Kristallografiya 4 (1959)
538 (in Russian).65L L'vov, C.H., Nemtchenko, V.F., Paderno, Yu.B.: in: Vsokotemperaturnaye neorganicheskie
soednienia, Nauka Dumka ed., Kiev, 1965, p. 445 (in Russian).76N Naslain, P., Guette, A,, Hagenmuller, P.: J. Less-Common Met. 47 (1976) 1.77E Etourneau, J., Mercurio, J.P., Hagenmuller, P.: in: Boron and Refractory Borides, V.I Matkovich ed.,
Springer: Berlin, Heidelberg, New York, 1977, p. 115.77N Naslain, R., Etourneau, J., Hagenmuller, P.: in: Boron and Refractory Borides, V.I. Matkovich ed.,
Springer: Berlin, Heidelberg, New York, 1977, p. 262.79A Aono, M., Kawai, S.: J. Phys. Chem. Solids 40 (1979) 797.79P Paderno, V.N., Paderno, Yu.B., Pilyankevich, A.N., Lazorenko, V.I., Bulychev, S.I.: J. Less-Common
Met. 67 (1979) 431.80F Fujita, T., Suzuki, M., Isikawa, Y.: Solid State Commun. 33 (1980) 947.81K Korsukova, M.M., Stepanov, N.N., Gontcharova, E.V., Gurin, V.N., Nikanorov, S.P., Smirnov, I.A.:
J. Less-Common Met. 82 (1981) 211. (Proc. 7th Int. Symp. Boron, Borides and Rel. Compounds,Uppsala, Sweden, 1981).
81S Shelykh, A.I., Sidorin, K.K., Karin, M.G., Bobrikov, V.N., Korsukova, M.M., Gurin, V.N., Smirnov,I.A.: J. Less-Common Met. 82 (1981) 291.
82B Barantseva, I.G., Paderno, Yu.B.: Sov. Powder Metall. Met. Ceram. 21 (1982) 585.83G Gurin, V.N., Korsukova, M.M.: Prog. Cryst. Growth and Charact. 6 (1983) 59.83S Storms, E.K.: J. Appl. Phys. 54 (1983) 1076.85E Etourneau, J., Hagenmuller, P.: Philos. Mag. 52 (1985) 589.85G Grushko, Yu.S., Paderno, Yu.B., Mishin, K.Ya., Molkanov, L.I., Shadrina, G.A., Konovalova, E.S.,
Dudnik, E.M.: Phys. Status Solidi (b) 128 (1985) 591.86B 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. 142.86I Ito, T., Higashi, I.: Chem. Sci. 26 (1986) 479.86Y Yahia, Z., Turrell, S., Dhamlincourt, M.-C., Turrell, G.: in: Proc. 10th Int. Conf. Raman spectroscopy
86, Eugene, OR, USA,, Peticolas, W.L.; Hudson, B.; ed., Univ. Oregon: Eugene, OR, USA, 1986, p.11(abstract only).
86Z Zirngiebl, E., Blumenröder, S., Mock, R., Güntherodt, G.: J. Magn. Magn. Mater. 54-57 (1986) 359.87A 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.
87P 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.
87W 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.
88A 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).
88T Turrell, S., Yahia, Z., Huvenne, J.P., Lacroix, B., Turrell, G.: J. Mol. Struct. 174 (1988) 455.89B Blomberg, M.K., Merisalo, M.J., Korsukova, M.M., Gurin, V.N.: J. Less-Common Met. 146 (1989)
309.90Y Yahia, Z., Turrell, S., Turrell, G., Mercurio, J.P.: J. Mol. Struct. 224 (1990) 303.91A Alekseev, P.A., Ivanov, A.S., Kikoin, K.A., Mischenko, A.S., Lazukov, A.N., Rumyantsev, A.Yu.,
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 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).
92C Chernychev, V.V., Aslanov, L.A., Korsukova, M.M., Gurin, V.N.: (cited in 94K 11).93B Bat'ko, I., Flachbart, K., Mat'as, S., Paderno, Yu.B., Shicevalova, N.Yu.: J. Alloys Compounds 196
(1993) 133.93N Nagao, T., Kitamura, K., Iizuka, Y., Oshima, C., Otani, S.: Surf. Sci. 290 (1993) 436.93O Otani, S., Honma, S., Yajima, Y., Ishizawa, Y.: J. Cryst. Growth 126 (1993) 466.93T 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) 2479.93Y Yahia, Z., Turrel, S., Mercurio, J.P., Turrel, G.: J. Raman Spectroscopy 24 (1993) 207.94K 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. 15.94M 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.
95B Blomberg, M.K., Merisalo, M.J., Korsukova, M.M., Gurin, V.N.: J. Alloys Compounds 217 (1995)123.
97R 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).
97T Takahashi, K., Kunii, S.: J. Solid State Chem. 133 (1997) 198 (Proc. 12th Int. Symp. Boron, Borides andRel. Compounds, Baden, Austria, 1996).
98A Albert, B., Schmitt, K.: Chem. Commun. (1998) 2373.98E Emin, D.G., Evans, S.S., McCready, S.S.: Phys. Status Solidi (b) 205 (1998) 311.98P Paderno, V.N., Paderno, Yu.B., Filippov, V.B., Arkhipov, B.A.: J. Mater. Process. Manufact. Sci. 6
(1998) 311.99K2 Konovalova, E., Paderno, Yu.B.: J. Solid State Chem. (2000) (Proc. 13th Int. Symp. Boron, Borides
and Rel. Compounds, Dinard, France, Sept. 1999).99K1 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).99K2 Kunii, S., Takahashi, K., Iwashita, K.: J. Solid State Chem. (2000) (Proc. 13th Int. Symp. Boron,
Borides and Rel. Compounds, Dinard, France, Sept. 1999).99O Oku, T., Bovin, J.-O., Higashi, I., Tanaka, T., Ishizawa, Y.: J. Solid State Chem. (2000) (Proc. 13th
Int. Symp. Boron, Borides and Rel. Compounds, Dinard, France, Sept. 1999).99T Takahashi, Y., Ohshima, K., Okamura, F.P., Otani, S., Tanaka, T.: J. Phys. Soc. Jpn. 68 (1999) 2304.99W Werheit, H., Au, T., Schmechel, R., Paderno, Yu.B., Konovalova, E.S.: J. Solid State Chem. (2000)
(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 atomscompared with the atomic radii of the metal atoms (upper curve) [87P].
4.05
4.20
1.9
4.10
1.7
2.0
4.15
1.8
M = La Ce
58
Eu HoPr Nd
60
Tb TuSm
62
Gd
64Atomic number
Er
68
Yb
70
Dy
66
Lu
Latti
ce p
aram
eter
[Å]
a
M
MB6
Atom
ic ra
dius
[Å]
r
Fig. 3.
Metal hexaborides. Lattice parameters of metal hexaborides vs. atomic number; (a) boron coordinate XB; (b)lattice constant; (c) bond length between rare earth metal and boron atom; (d) intra-octahedral and inter-octrahedral bond lengths; (e) quantities of the temperature parameters for the mean square displacement ofatoms: circles at 295 K, Uiso for the rare earth metal atoms; down triangles, U22=33 for the boron atoms; uptriangle, U11 for the boron atoms [99T].
1.62
1.74
1.66
1.78
1.70
0.2
1.4
0.6
1.8
1.0
39 57 58 59 60 62 6361 64
Tem
p.fa
ctor
s,
,[1
0Å
]U
UU
iso11
22=
33–2
2
3.00
3.06
3.02
3.08
3.04
M-B
bon
d le
ngth
[Å]
e
c
0.198
0.201
0.199
0.202
0.200
Boro
n co
ordi
nate
X B
aB-
B bo
nd le
ngth
[Å]
d
4.10
4.16
4.12
4.18
4.14
Latti
ce p
aram
eter
[Å]
ab
39 57 58 59 60 62 6361 64Atomic number
0.203
intra B-B
inter B-B
M = Y La Ce Nd Sm Eu Gd
Uiso
U11
U22 = 33
MB6
M = Y La Ce Nd Sm Eu Gd
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].
1.60
Lattice parameter [Å]a4.10 4.12 4.14 4.16 4.18
MB6
1.64
1.68
1.72
1.76
1.80
M = Y
La
Ce
Nd
Sm3+
Eu2+
Gd
0.85
1.00
1.05
1.10
1.15
1.20
0.90
0.95
0.07
0.10
0.11
0.12
0.13
0.08
0.09
B-B
bond
leng
th [Å
]
Ioni
c rad
ius
[Å]
r
c
a b
Lattice parameter [Å]a4.10 4.12 4.14 4.16 4.18
Mea
n sq
uare
root
disp
lace
men
t[Å
]U iso
M = Y
LaCeNd Eu
GdSm
intra B-B
inter B-B
1/2
Eu2+
Sm
M = Y
LaCe
Nd
Gd
Lattice parameter [Å]a4.10 4.12 4.14 4.16 4.18
Eu
La
Ce
SmNd
Gd
M = Y
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
4.153
4.129
4.133 4.135
4.146
4.149
4.154
4.130
4.136
4.147
4.150
4.155
4.131
4.137
4.148
4.151
4.156
4.132
4.145 4.138
4.149 4.148
4.152
4.150
4.151
4.152
4.153
0 300Temperature [K]T
50 100 200150 250
Latti
ce p
aram
eter
[Å]
a
Latti
ce p
aram
eter
[Å]
a
CaB6
SmB6
Sm La B0.5 0.5 6
Sm Ca B0.4 0.6 6
Sm Ca B0.05 0.95 6
LaB6
Fig. 6.
Metal hexaborides. Correlation between B charge and VEC, the valence electron concentration (number ofvalence electrons per unit cell volume). The B charge is determined as the valence charge inside the boronsphere (with rB = 0.794 Å). Assuming localized 4f states for La and Ce or 4d states for Y makes these atomsdivalent [97R].
B-ch
arge
[]e
1.38
1.36
1.40
1.42
1.44
1.46
MB6
VEC [ /Å ]e 30.25 0.26 0.27 0.28 0.29 0.30 0.31
all valence electronsdivalent Y, La, Ce
Y
Ce
La
M = Ca
Sr
Ba
K
Fig. 7.
Metal hexaborides. The magnitude of the 11B nuclear electric quadrupole interaction (e2qQ) in divalent- andtrivalent-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 dottedcurves: theoretical calculations [79A].
1.00
0.95
1.05
1.10
1.00
0.95
1.15
1.05
1.25
1.151.20
1.35
1.30
1.40
1.45
1.10
1.20
1.30
1.25
1.35
eqQ
2[M
Hz]
eq[e
A]
–3
Lattice parameter [Å]a4.08 4.10 4.12 4.14 4.16 4.18 4.22 4.264.20 4.24
Gossard &Jaccarino [86B8]
M B63+
valence mixing SmB6
M B62+
M = DyHo
Tb Gd
Sm
Yb
Ca
EuNd
Pr
Ce La
Fig. 8.
Metal hexaborides. (a) Work function and (b) effective magnetic moment vs. atomic number [59S].
0
0
4
2
8
4
12
6
2
1
6
3
10
5
MB6
Eff.
mag
n.m
omen
t[r
el.u
nits
]p ef
fW
ork
func
tion
[eV]
φ
M = La Ce Pr Eu HoNd Pm Tb TuSm Gd Er YbDy Lu
b
a
5957 61 63 65Atomic number
69 7167
Fig. 9.
Metal hexaborides. Optical reflectivity spectra; R vs. photon energy. Long-dashed curve, LaB6, solid curve,SmB6, short-dashed curve, EuB6 [81S].
0 5 10 15 20 25 30 35 40
5
30
10
15
25
20
LaB6
SmB6
EuB6
(×10)
Refle
ctiv
ityR
[%]
Photon energy [eV]hν
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 indicatedat the spectra in the diagram. It is assumed that the phonon spectra occur in the spectra because symmetryselection rules are lifted in consequence of structural distortions [99W].
0 5 10 15 20 25 4030 4535 50
Refle
ctiv
ityR
0.56
0.60
0.72
0.64
0.80
0.76
0.68
0.84
0.92
0.88
0.96
1.00
Wavenumber [10 cm ]ν 2 –1
Sm B0.8 6 (shift – 0.16)
YB6 (shift – 0.2)
SmB6 (shift – 0.18)
TbB6 (shift – 0.08)
LaB6 (shift – 0.05)
CeB6
YB6 (shift – 0.2)
Fig. 11.
Metal hexaborides. IR diffuse reflectance spectra of representative MB6 compounds with two-valent Ca, Sr andYb, and three-valent Nd, Gd, La, Tb and Dy metal atoms [88T, 93Y].
a bWavenumber [cm ]ν –1 Wavenumber [cm ]ν –1
Inte
nsity
I
Inte
nsity
I
500 5001000 10001500 15002000 2000
M = Ca
M = Dy
Sr
Yb
Gd
Tb
Nd
La
MB6
Fig. 12.
Metal hexaborides. Raman spectra, relative intensity vs. Raman shift for hexaborides with twofold and threefoldionized metal atoms [88T, 93Y].
400
400
600
600
800
800
1000
1000
1200
1200
1400
1400
200
200
MB6
Ram
anin
tens
ityI R
Ram
anin
tens
ityI R
Wavenumber [cm ]ν –1
Wavenumber [cm ]ν –1
M = La3+
Gd3+
Dy3+
M =2+
Ca
Sr2+
Tb3+
Yb2+
Fig. 13.
Metal hexaborides. Wavenumbers of the phonon symmetry modes A1g, Eg, T2g and T1u vs. lattice parameter fordivalent 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 theexperimental data for EuB6.
140
1040
180
1080
1280
220
1120
1160
1320
620
700
12001200
1360
660
740
1240
1400
4.10 4.18Lattice parameter [Å]a0
4.12 4.14 4.16
Wav
enum
ber
[cm
]ν
–1
Wav
enum
ber
[cm
]ν
–1
mode symmetry MB6
M = Y
Gd Nd Sm
Ce La
Eu
A ( )1g 1Γ +
E ( )g 3Γ +
T ( )2g 5Γ +
T ( )1u 4Γ –
Fig. 14.
Metal hexaborides. Phonon frequencies obtained from the IR absorption spectra (calculated from the measuredreflectivity spectra in Fig. 10 by Kramers-Kronig transformation). Same symbols are used for phonons indifferent compounds, which can be probably attributed to one another. The dashed lines represent the Ramanfrequencies in Fig. 11. The full lines combine the plasmon polariton frequencies of the semiconductinghexaborides EuB6 and YbB6, and the arrows indicate the shift to the related resonance frequency in metallicLaB6 (softening of the high frequency F1u mode and hardening of the low frequency F1u mode) obviouslycaused by the high carrier concentration [99W].
4.10 4.12 4.14 4.16 4.18
0.2
1.0
0.4
1.2
0.6
1.4
0
0.8
1.6
Phon
onw
aven
umbe
r[1
0cm
]ν
3–1
Lattice parameter [Å]a0
EuB
C5.
90.
1
YB6
SmB 6
TbB 6
CeB 6
YbB 6
LaB 6
A1g
Eg
F2g
F1u(semicond)
F1u(met.)
F1u(semicond)
MB6
Fig. 15.
Metal hexaborides. Inverse molar magnetic susceptibility; χm−1 vs. T [97T]. χm in CGS-emu.
0 50 100 150 200 250 300
5
10
20
15
25
30
Temperature [K]T
Inv.
susc
eptib
ility
[mol
cm]
χ m–1–3
DyB6TbB6HoB6
Fig. 16.
Metal hexaborides. Pressure dependence of the electrical resistivity; ρ(p)/ρ(0) vs. hydrostatic pressure p. Fulllines, monocrystalline LaB6, EuB6 and YbB6 [91S], dashed lines, LaB6, SmB6 prepared from starting ratiosSm:B 1/7, 1/9, 1/12 (effect increases this way), YbB6, EuB6 [81K].
0 1 2 3 4 5 6 7 8
0.2
0.4
0.8
0.6
1.0
Rel.r
esist
ivity
ρ/ρ 0
Pressure [GPa]p
LaB6
SmB6
YbB6
YbB6
LaB6
EuB6
EuB6
(mono)
(mono)
(mono)
Fig. 17.
Metal hexaborides. Pressure dependence of the thermoelectric power S for LaB6, YbB6 and EuB6 [81K].
– 200
– 175
– 150
– 125
– 100
– 75
– 50
– 25
– 2.5
0
Ther
moe
lect
ric p
ower
[V
K]
Sµ
–1
0 2 4 86 10 12Pressure [GPa]p
LaB6
EuB6
YbB6
Fig. 18.
Metal hexaborides. Boron-boron bond lengths vs. lattice parameter a (full triangles, hypothetical equidistance)[94K].
B-B
bond
leng
th[Å
]
1.64
1.60
1.68
1.72
1.76
1.80MB6
4.100 4.125 4.150 4.2004.175 4.225 4.250 4.275
B-B intra
B-B inter
M = Th
Nd
Nd
Sm
Sm
Pr
Pr
Ce
Ce
La
La
Ca
Ca
Yb
Yb
Eu Sr
SrEu
Th
Ba
Ba
Lattice parameter [Å]a
Fig. 19.
Metal hexaborides. Characteristic Einstein temperatures of the Ln atoms vs. atomic number of the Ln element;full circles [94K]; triangles [99T].
100
90
110
120
130
140
150
56 59 62 65 68 71Ln atomic number
Eins
tein
tem
pera
ture
[]
EK
Ln = La
Ce Pr
Nd Sm
Eu
LnB6
YbGd
Fig. 20.
Metal hexaborides. Variation of the atomic equivalent temperature factors (normalized by a2) vs. the atomicnumber of the Ln element (full circles, Ln atom; open circles, B atom) [94K].
20
30
40
50
60
70
56 59 62 65 68 71Ln atomic number
LnB6
Ln = Yb
La
CePr
NdSm
Eu
U/ a
equi
v2
5[1
0]
B
Fig. 21.
Metal hexaborides. Entropy vs. T for LaB6, ferromagnetic EuB6, antiferromagnetic EuB6 [80F].
Entro
pyS/
R
0 20 40 60 80
1
3
2
4
5
ln 8
LaB6EuB6 (F)EuB6 (AF)
Temperature [K]T