the region around 28 GPa, consistent with other evidence for transition to a magnetically ordered state in that region. The NFS data (Fig. 9.16) provides evidence for
an additional high-spin to low-spin transition around 121 GPa.
10.6.3 Use of Multiple NRVS Centers: Thermoelectric
Materials
Thermoelectric materials can use a temperature gradient to generate electricity or
vice versa. A common figure of merit for such devices at temperature T is
ZT ¼ (σΣ
2 T)/κ, where σ is the electrical conductivity, S is the “Seebeck coefficient,”
and κ is the thermal conductivity. Since thermal conductivity is intimately related to
lattice vibrations, acoustic phonons, and the speed of sound, NRVS can play a
valuable role in characterizing these materials.
One promising class of thermoelectrics is skutterudites, compounds or minerals
with the composition LM 4 X 12 , where M is a transition metal, X is a group V
element, and L is often a lanthanide. These materials have a large unit cell with
voids that can accommodate a variety of L ions, and there is a wide range of
combinations which can be explored and tuned for desirable properties.
Skutterudites are interesting thermoelectric candidates in part because they can
operate at higher temperatures than conventional Bi–Te-based materials.
One particular skutterudite, SmFe 4 Sb 12 , is an ideal system for NRVS studies
because each of its constituent elements has an NRVS isotope:
149 Sm,
57 Fe, or
121 Sb
(Fig. 10.14). The sharp peak in the
149 Sm spectrum is assigned to a localized rare
earth “shake mode” that is decoupled from the lattice acoustic modes and presumably diminishes thermal conductivity.
10.6.4 Difficult Cases: Multi-Phonon Problems
and Anharmonic Samples
We have seen above that the probability of multi-phonon events rises as the LambMössbauer factor decreases (Fig. 10.6 and Eq. 10.10). We know from Eq. 9.10 that
f LM decreases as the Mössbauer resonance increases in energy (higher recoil) and as
the material gets softer (larger thermal motion). The NRVS of HgS (Fig. 10.6) is a
nice example of how bad things can get—this material has a relatively high-energy
resonance (26.3 keV) and a very low Debye temperature (~90 K), and the high
atomic weights of the HgS pair yield a number of optical modes at about 4 meV
[483]. Ishikawa estimated a Lamb-Mössbauer factor of ~0.005–0.01, which yields
an average number of phonons of about 5 [483]. Simulation of the spectrum thus
requires inclusion of contributions up to S
9 (E) (Fig. 10.6).
10.6 Applications and Interpretation
275
an additional high-spin to low-spin transition around 121 GPa.
10.6.3 Use of Multiple NRVS Centers: Thermoelectric
Materials
Thermoelectric materials can use a temperature gradient to generate electricity or
vice versa. A common figure of merit for such devices at temperature T is
ZT ¼ (σΣ
2 T)/κ, where σ is the electrical conductivity, S is the “Seebeck coefficient,”
and κ is the thermal conductivity. Since thermal conductivity is intimately related to
lattice vibrations, acoustic phonons, and the speed of sound, NRVS can play a
valuable role in characterizing these materials.
One promising class of thermoelectrics is skutterudites, compounds or minerals
with the composition LM 4 X 12 , where M is a transition metal, X is a group V
element, and L is often a lanthanide. These materials have a large unit cell with
voids that can accommodate a variety of L ions, and there is a wide range of
combinations which can be explored and tuned for desirable properties.
Skutterudites are interesting thermoelectric candidates in part because they can
operate at higher temperatures than conventional Bi–Te-based materials.
One particular skutterudite, SmFe 4 Sb 12 , is an ideal system for NRVS studies
because each of its constituent elements has an NRVS isotope:
149 Sm,
57 Fe, or
121 Sb
(Fig. 10.14). The sharp peak in the
149 Sm spectrum is assigned to a localized rare
earth “shake mode” that is decoupled from the lattice acoustic modes and presumably diminishes thermal conductivity.
10.6.4 Difficult Cases: Multi-Phonon Problems
and Anharmonic Samples
We have seen above that the probability of multi-phonon events rises as the LambMössbauer factor decreases (Fig. 10.6 and Eq. 10.10). We know from Eq. 9.10 that
f LM decreases as the Mössbauer resonance increases in energy (higher recoil) and as
the material gets softer (larger thermal motion). The NRVS of HgS (Fig. 10.6) is a
nice example of how bad things can get—this material has a relatively high-energy
resonance (26.3 keV) and a very low Debye temperature (~90 K), and the high
atomic weights of the HgS pair yield a number of optical modes at about 4 meV
[483]. Ishikawa estimated a Lamb-Mössbauer factor of ~0.005–0.01, which yields
an average number of phonons of about 5 [483]. Simulation of the spectrum thus
requires inclusion of contributions up to S
9 (E) (Fig. 10.6).
10.6 Applications and Interpretation
275