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