_{3−x}R

_{x}Mn

_{2}O

_{7}samples prepared by standard solid-state reaction, where R = Y or La and 0 ≤ x ≤ 0.33. Ab-initio calculations predict that Y-doping at Ca-sites should reduce the potential energy barrier for electron transport, as opposed to La-doping. We find that Y-doping prompts transformation from Ca

_{3}Mn

_{2}O

_{7}to Ca

_{2}MnO

_{4}, whereas La-doping is accompanied by no phase transformation. La-doping significantly hinders grain growth, for example, the average grain size decreases from 4.44 ± 0.24 to 1.20 ± 0.03 μm for x = 0 (undoped) and x = 0.33 upon La-doping, respectively. A. Azulay, T. Leibovitz, Y. Natanzon, Or Zabari, Y. Amouyal. J. Am. Ceram. Soc. (2022)

We observed unusual behavior, in which the Seebeck coefficient (S ) and electrical conductivity (σ) values increased simultaneously with temperature for Zn_{1–x–y}Al_{x}TiyO, originating from energy filtering of charge carriers due to both co-doping and the peculiar multiphase structure. High σ values were associated with the increase of electron concentration, while high S values were due to Fermi energy tuning and heavier effective masses initiated by Al and Ti co-doping. Besides increasing the PF, the multiphase structure played an essential role in reducing lattice thermal conductivity due to phonon scattering by the Umklapp, point defect, and second-phase mechanisms. Our approach yielded an increase of the TE figure of merit upon formation of a three-phase 2 wt % Ti-doped Zn_{0.98}Al_{0.02}O compound of ca. 10 times compared to the corresponding value attained for its two-phase ZnAl_{0.02}O counterpart. C. Gayner, Y. Natanzon, Y. Amouyal. ACS Appl. Mater. Interfaces (2022)

We found that the room-temperature values of electrical conductivity, Seebeck coefficient, and charge carrier mobility of the consolidated Bi_{2}Te_{3} samples increase with the reduction of the average grain size. This phenomenon was observed earlier for Bi_{2}Se_{3}, which is a well-known TI material. We also found that Nd-doping reduces the electrical conductivity, Seebeck coefficient, charge carrier mobility, and thermal conductivity near room temperature (310 K). Interestingly, Nd-doping reverses the dependence of mobility on grain size compared to undoped Bi_{2}Te_{3}, which is associated with its magnetic moment. G. Solomon, E. Song, C. Gayner, J. A. Martinez, Y. Amouyal. *ACS Appl. Nano Mater.* 4, 4419 (2021)

The diffusion coefficients of Ag in a PbTe matrix are evaluated utilizing first-principles calculations. Based on unique combination between calculations of point defect formation energies, electronic density of states (DOS), and electron localization function (ELF), we conclude that diffusion of Ag in PbTe in the interstitial mechanism is preferable compared to the vacancy or substitutional mechanism. We determine both the activation energy for diffusion and the pre-exponential diffusion coefficient for an interstitial mechanism, applying the transition state theory (TST), to be 1.08 × 10^{−5} cm^{2}·s^{−1} and 52.9 kJ·mole^{−1}, respectively. M. H. Dahan, A. Baranovskiy, Y. Natanzon, Y. Amouyal. *Acta Materialia* **202**, 243-254 (2020).

We apply the well-established phonon glass electron crystal (PGEC) concept in CaO(CaMnO3)m Ruddlesden–Popper layered perovskites by doping them with yttrium of lanthanum. This enables us to increase the transparency of CaO planes to electron transport at the same time while preserving their opacity to phonon transport. First-principles calculations indicate that the total local potential at CaO planes, where Y substitutes for Ca, is lower by ca. 50% compared to La substitution. Measurements of the electrical conductivity and Seebeck coefficients for Ca2–xRxMnO4 (R = La or Y; x = 0.01, 0.05, 0.1, and 0.15) bulk materials in the range of 300–1000 K confirm that compounds doped with Y exhibit higher electrical conductivity values than their La-doped counterparts. We attribute this to lower polaron hopping energy values (up to 23%) evaluated using the small polaron hopping model. A. Azulay, M. Wahabi, Y. Natanzon, Y. Amouyal. *ACS Appl. Mater. Interfaces* **12**, 49768–49776 (2020).

We review recent selected studies applying the density functional theory (DFT), and describe the merits and challenges in applying DFT for such calculations, highlighting the need to address both electronic and vibrational aspects. The vibrational component of the polaron is evaluated based on structural and total energy calculations, whereas the electronic component is derived from both total energy and electron density calculations. To address the most compelling challenge of calculating polaron properties using DFT, which is the issue of electron localization, we propose to employ calculations of selected vibrational properties, such as the sound velocity, shear modulus, and Grüneisen parameter, to represent the polaron hopping energy; all of which originate from the stiffness of inter-atomic bonds. Such methodology is expected to be more straightforward than the existing ones, however, demands standardization. Y. Natanzon, A. Azulay, Y. Amouyal. *Isr. J. Chem.* **60**, 768 (2020).

Various concepts and paradigms regarding energy filtering effect are reviewed. Ways to optimize thermoelectric transport via energy filtering are also discussed. The authors demonstrate the potential of energy filtering for thermoelectric energy conversion. Although this effect theoretically demonstrates improvement of the thermopower, applying it poses certain constraints, which demands further research. Predicated on data documented in literature, the unusual dependence of the thermopower and conductivity upon charge carrier concentrations can be altered through the energy filtering approach. Upon surmounting the physical constraints discussed in this article, thermoelectric materials research may gain a new direction to enhance the power factor and thermoelectric figure of merit. C. Gayner, Y. Amouyal. *Adv. Func. Mater.* **29**, 1901789 (2019)

The density functional theory is a powerful tool for thermal conductivity evaluation. This procedure requires consideration of both Grüneisen parameter and sound velocity. Doping of bismuth telluride with rare earth elements reduce thermal conductivity. Impurity phonon modes appear at frequencies up to 2 THz. The divalent impurities exhibit stronger effects compared to trivalent ones. A. Baranovskiy *et al.*, *Advanced Theory and Simulations* **1 (12)**, 1800162 (2019).

Vibrational properties of CaO(CaMnO_{3})_{m} (m = 1, 2, 3, and ∞) thermoelectric (TE) oxides for high-temperature energy conversion applications are studied both experimentally and computationally. It is found that thermal conductivity of CaO(CaMnO_{3})_{m} compounds is governed by phonon scattering on CaO/CaMnO_{3} boundaries for m = 1, 2, and 3 and by Umklapp processes for m = ∞. Thermal transport in this system is strongly dominated by acoustic phonon modes possessing much larger Grüneisen parameters (γ) compared to optical ones. A. Baranovskiy et al. *Nano Energy* **47** 451-462 (2018). DOI: 10.1016/j.nanoen.2018.02.054

Here, we correlate transmission Kikuchi diffraction and (scanning) transmission electron microscopy in conjunction with atom probe tomography to investigate the local structure and chemical composition of dislocations in a thermoelectric Ag-doped PbTe compound. Our investigations indicate that Ag atoms segregate to dislocations with a 10-fold excess of Ag compared with its average concentration in the matrix. Thermal conductivity is evaluated applying laser flash analysis, and is correlated with theoretical calculations based on the Debye–Callaway model, demonstrating that these Ag-decorated dislocations yield stronger phonon scatterings. These findings reduce the knowledge gap regarding the composition of dislocations needed for theoretical calculations of phonon scattering and pave the way for extending the concept of defect engineering to thermoelectric materials. Y. Yu et al.* ACS Applied Materials & Interfaces*,** 10 (4)**, 3609 (2018).

Significant enhancement of ZT for n-type PbTe-based compound due to controlled nucleation and growth of Ag-rich precipitates. T. Grossfeld, A. Sheskin, Y. Gelbstein, and Y. Amouyal, *Crystals* **7 (9)**, 281 (2017) http://www.mdpi.com/2073-4352/7/9/281

Effects of precipitation on the thermal conductivity of nickel-doped zinc oxide for thermoelectric applications. I. Koresh and Y. Amouyal, J. Eur. Ceram. Soc. **37** (11), 3541-3550 (2017)

A Practical Approach to Evaluate Lattice Thermal Conductivity in Two-Phase Thermoelectric Alloys for Energy Applications. Y. Amouyal, *Materials* **10** (4), 386 (2017).

Role of nanostructuring and microstructuring in silver antimony telluride compounds for thermoelectric applications. O. Cojocaru-Mirédin, L. Abdellaoui, M. Nagli, S. Zhang, Y. Yu, C. Scheu, D. Raabe, M. Wuttig, and Y. Amouyal, ACS Applied Materials & Interfaces **9**, 14779-14790 (2017).

**The longitudinal acoustic **

**Optical**

The longitudinal acoustic (top) and optical (second) modes of lattice vibrations in cubic Pm-3m CaMnO_{3}, simulated from density functional theory (DFT) calculations. The Ca, Mn, and O atoms are indicated by blue, aqua, and red spheres, respectively. It is observed that Ca-atoms mainly contribute to the acoustic modes, whereas the optical ones are dominated by oxygen.

A color-coded periodic table representing the lattice thermal conductivity calculated for 1.6 at. % X-doping at 700K for (a) Pb-site substitutions, XPb_{31}Te_{32} and (b) Te-site substitutions, XPb_{32}Te_{31}. The values in the diagram are expressed in Wm^{-1}K^{-1} , and are calculated based on an average phonon relaxation time of 10^{-11} s. E. Joseph and Y. Amouyal, *J. Appl. Phys.* **117 (17)**, 175102 (2015).

The temperature-dependent thermal conductivity measured for the Nb-doped compounds of different periodicities, having the structural form (CaMnO_{3})_{m}CaO ,using the laser flash analysis (LFA) technique: m=∞ (plus markers), m=1 (black), m=2 (red), m=3 (blue), m=4* (dark green), and m=5* (light green). A. Graff and Y. Amouyal, *Appl. Phys. Lett. ***105(18)**, 181906 (2014).

The calculated temperature dependent (a) lattice thermal conductivity based on the calculated sound velocity, and (b) total lattice thermal conductivity for La-doped PbTe of different concentrations. E. Joseph and Y. Amouyal, *J. Elect. Mater.* **44 (6)**, 1460 (2015).

The sound velocity averaged over the different modes calculated for a La-doped PbTe lattice, as a function of the doping level. A significant decrease of the sound velocity with increasing doping level is observed. E. Joseph and Y. Amouyal, *J. Elect. Mater.* **44 (6)**, 1460 (2015).

Temperature-dependent thermal conductivity, as measured by use of the LFA method, for a ternary alloy AgSbTe_{2}-based alloy (AST, squares) and a quaternary, La-doped, alloy (La-doped AST, circles). A notable difference between the thermal conductivity values is apparent along a wide temperature range Y. Amouyal, *J. Elect. Mater.* **43** (10), 3772 (2014).

The vibrational density of states (v-DOS) calculated, from first-principles, for the AgSbTe_{2} phase. The total v-DOS appears in black and the partial v-DOS associated with the Ag-sublattice vibrations is represented by the blue dashed curve. The noticeable overlap at approximately 2 THz implies that the primary vibrational peak in the AgSbTe_{2} v-DOS curve originates from the Ag sublattice. Attenuation of the v-DOS as a result of La-doping is observed for a La_{0.125}Ag_{0.875}SbTe_{2} lattice, denoted by the red line. Y. Amouyal, *J. Elect. Mater.* **43** (10), 3772 (2014).

The temperature-dependence of the C_{v}·v_{s}^{2}-products (Cv: heat capacity; vs: sound velocity) calculated for the AgSbTe_{2}– and La_{0.125}Ag_{0.875}SbTe_{2}-compounds from first-principles, marked with empty squares and circles, respectively. This product is a significant factor determining thermal conductivity; the marked difference between both plots evidently indicates the effects of La-doping on lowering thermal conductivity. Y. Amouyal, *Computational Materials Science* **78** (2013) 98.

The dispersion ω(k) – curves of the acoustic phonons calculated for both AgSbTe_{2} – and La_{0.125}Ag_{0.875}SbTe_{2}– compounds close to the Γ-point. It is indicated that the slopes of the one longitudinal (filled diamonds) and two transverse (filled circles and squares) acoustic modes of the AgSbTe_{2}-lattice are greater than those of the La_{0.125}Ag_{0.875}SbTe_{2}-lattice (empty diamonds, circles and squares, respectively). Y. Amouyal, *Computational Materials Science* **78** (2013) 98.

Temperature-dependent power factor (PF) values calculated for Nb-doped CaO(CaMnO_{3})_{m} compounds with different periodicities of m = ∞ (inf., cross markers), m = 1 (black squares), m = 2 (red circles), m = 3 (blue left-triangles), m = 4* (green diamonds), and m = 5* (purple right-triangles). A. Graff & Y. Amouyal *J. Electron. Mater.* **45** (3), 1508 (2016).

**The longitudinal acoustic**

**Optical**

**La _{0.125}Ag_{0.875}SbTe_{2}**

**AgSbTe _{2}**

The longitudinal acoustic modes of lattice vibrations in pure and lanthanum-doped 2x2x2 AgSbTe_{2}-based supercells, simulated from density functional theory (DFT) calculations. The La, Ag, Sb, and Te atoms are indicated by aqua, gray, yellow, and orange spheres, respectively. It is observed that La-substitution defects suppress lattice vibrations, thereby reducing lattice thermal conductivity. Y. Amouyal, *Computational Materials Science* **78** (2013) 98.

A high-resolution scanning electron microscope (SEM) micrograph of oriented Sb_{2}Te_{3}-precipitates in an Ag-Sb-Te-based matrix aged at 400 °C for 0.5 h.

A high-resolution scanning electron microscope (SEM) micrograph of a 4 at% Nb -doped CaMnO_{3}-based Ruddlesden-Popper compound produced by solid state reaction of powders and sintering at 1400 °C. A. Graff and Y. Amouyal, *Applied Physics Letters* **105** (18), 181906 (2014).