Theoretical prediction of mechanics, transport, and thermoelectric properties of full Heusler compounds ${\mathrm{Na}}_2\mathrm{KSb}$ and $X_2\mathrm{CsSb} (X=\mathrm{K},\mathrm{Rb})$

Full Heusler compounds have become a research hotspot in the thermoelectric (TE) field, because they have the remarkable electronic properties and high-TE power factor. Nevertheless, the inherent high thermal conductivity ${\kappa }_L$ hinders their further application as TE device. Hence, we investigate the mechanical, transport, and thermoelectric properties in ${\mathrm{Na}}_2\mathrm{KSb}$ and ${\mathrm{X}}_2\mathrm{CsSb}$ (X = K, Rb) with eight valence electrons per formula unit (f.u.) by using the first-principles calculations combined with self-consistent phonon (SCP) theory, compressive sensing (CS) techniques, and Boltzmann transport equation (BTE). Due to the strong three phonon scattering combined with small phonon group velocity, we obtain the ultralow lattice thermal conductivities. An evaluation of their mechanical properties reveals that they are all brittle compounds, and ${\mathrm{Rb}}_2\mathrm{CsSb}$ has the strongest elastic anisotropy. To capture rational electron transport properties, we include the effects of the acoustic deformation potential (ADP) scattering, polar optical phonon (POP) scattering, and ionized impurity (IMP) scattering on the electron relaxation time. Finally, a high p-type $\mathit{ZT}$ values of 2.74 (2.48) at 600 (900) K are captured in the cubic ${\mathrm{K}}_2\mathrm{CsSb}$ $\left({\mathrm{Na}}_2\mathrm{KSb}\right)$. These findings not only help us to comprehensively understand the physical properties of full Heusler compounds with eight valence electrons per f.u., but also support them as potential candidates for thermal management and thermoelectric applications.

Figure 1

(a) Crystal structure of ${\mathrm{X}}_2\mathrm{YSb}$ (X = Na, K, Rb; Y= K, Cs) was visualized using VESTA [59]. The calculated phonon dispersions and corresponding phonon density of states (PDOS) at different temperatures for (b) ${\mathrm{Na}}_2\mathrm{KSb}$, (c) ${\mathrm{K}}_2\mathrm{CsSb}$, and (d) ${\mathrm{Rb}}_2\mathrm{CsSb}$, where the result of HA represents the 0 K.

Figure 2

Temperature-dependent ${\kappa }_L$ of the three FH compounds calculated using $\mathrm{SCP}+\mathrm{BTE}$. For ${\mathrm{Na}}_2\mathrm{KSb}$, the result of $\mathrm{HP}+\mathrm{BTE}$ is also shown for comparison. The 1-mm grain boundary scattering is also considered.

Figure 3

Lattice thermal conductivity spectrum ${\kappa }_L$ ($\omega$) and relevant cumulative ${\kappa }_L$ for the three FH compounds ${\mathrm{Na}}_2\mathrm{KSb}, {\mathrm{K}}_2\mathrm{CsSb}$, and ${\mathrm{Rb}}_2\mathrm{CsSb}$.

Figure 4

(a) The projected electron localization function (ELF) in (001) plane for ${\mathrm{Na}}_2\mathrm{KSb}$ visualized using VESTA [59]. The distances from the origin are $\frac{\mathit{a}}{4}$ (left) and $\frac{\mathit{a}}{2}$ (right), respectively. The values of the ELF range from 0.0 to 1.0, in which 1.0 signify that electrons localized completely. The electron band structure and relevant electron density of states for (b) ${\mathrm{Na}}_2\mathrm{KSb}$, (c) ${\mathrm{K}}_2\mathrm{CsSb}$, (d) ${\mathrm{Rb}}_2\mathrm{CsSb}$.

Figure 5

The calculated carrier mobility (${\mu }_e$ and ${\mu }_h$) as a function of temperature for ${\mathrm{Na}}_2\mathrm{KSb}, {\mathrm{K}}_2\mathrm{CsSb}$, and ${\mathrm{Rb}}_2\mathrm{CsSb}$.

Figure 6

The calculated (a) electrical conductivity $\sigma$, (b) Seebeck coefficient S, (c) electrical thermal conductivity ${\kappa }_e$, and (d) TE power factor $\sigma {\mathrm{S}}^2$ for ${\mathrm{K}}_2\mathrm{CsSb}$.

Figure 7

The calculated TE figure of merit for (a) n-type ${\mathrm{Na}}_2\mathrm{KSb}$, (b) p-type ${\mathrm{Na}}_2\mathrm{KSb}$, (c) ${\mathrm{K}}_2\mathrm{CsSb}$, and (d) ${\mathrm{Rb}}_2\mathrm{CsSb}$.