# Janus ScYCBr 2 MXene as a Promising Thermoelectric Material

Mounir Ould-Mohamed, Tarik Ouahrani, Reda Boufatah, Ángel

Morales-García, Ruth Franco, Michael Badawi, Daniel Errandonea

► To cite this version:

Mounir Ould-Mohamed, Tarik Ouahrani, Reda Boufatah, Ángel Morales-García, Ruth Franco, et al. Janus ScYCBr 2 MXene as a Promising Thermoelectric Material. ACS Applied Energy Materials, 2024, 7 (15), pp.6598-6611. 10.1021/acsaem.4c01221. hal-04897211

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https://hal.univ-lorraine.fr/hal-04897211v1

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# Janus ScYCBr₂ MXene as a Promising Thermoelectric Material

Mounir Ould-Mohamed,* Tarik Ouahrani,* Reda Boufatah, Ángel Morales-García, Ruth Franco, Michael Badawi, and Daniel Errandonea*

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Cite This: ACS Appl. Energy Mater. 2024, 7, 6598–6611

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## ACCESS

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Supporting Information

**ABSTRACT:** Finding green energy resources that contribute to the battle against global warming and the pollution of our planet is an urgent challenge. Thermoelectric electricity production is a clean and efficient method of producing energy; consequently, scientists are currently researching and creating thermoelectric materials to increase the efficiency of thermoelectric electricity production and expand the potential of the thermoelectric effect for clean energy production. This work focuses on a comprehensive study of the thermoelectric properties of two-dimensional ScYCBr₂. We report here a computational analysis of this Janus-like MXene, which is predicted to exhibit outstanding thermoelectric properties. The study uses density-functional theory to provide evidence of the important role played by symmetry breaking to promote low-thermal transport by favoring certain phonon scattering channels. Compared to its symmetric parent compounds, the asymmetric Janus-type ScYCBr₂ displays additional phonon scattering channels reducing the thermal conductivity. An exhaustive investigation of the dynamical stability for both zero-temperature and high-temperature conditions was also performed to support the stability of ScYCBr₂. Our analysis shows that thanks to its asymmetric structure, the ScYCBr₂ MXene has thermoelectric properties that largely surpass those of its parent symmetric counterpart Sc₂CBr₂, being a material with a remarkable thermoelectric high figure of merit. Another advantage of ScYCBr₂ is its high carrier mobility. This work not only demonstrates that this material is a promising thermoelectric material but also shows that ScYCBr₂ can operate efficiently at high temperatures up to 1200 K.

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**KEYWORDS:** Thermoelectric, Ab initio calculations, Seebeck effect, Thermal conductivity, Green energy

## INTRODUCTION

Thermoelectric materials (TEM) offer a green and sustainable way to produce electricity which could be beneficial for the planet compared to hydrocarbons and other contaminant sources of energy. Thermoelectric devices do not produce contaminant emissions, not contributing thus to global warming.¹ TEM are ideal for constructing thermoelectric generators that allow heat to be directly transformed into electricity based on the Seebeck effect.² Thermoelectric devices could be used in power plants and factories to convert waste heat into electrical power and in cars to increase fuel efficiency. One of the most important challenges for developing competitive thermoelectric technologies is creating highly efficient TEM, which would be very helpful for a variety of environmental applications. The performance of TEM materials is currently characterized by the dimensionless figure of merit (ZT) defined as $ZT = \frac{S^2\sigma}{\kappa_e + \kappa_l}T$,³ where S stands for the Seebeck coefficient, σ for the electrical conductivity, T for the absolute temperature, and κe and κl for electronic and lattice thermal conductivity, respectively.

Two-dimensional (2D) materials have shown to be very promising for developing highly efficient TEM due to their high thermoelectric figures of merit.⁴,⁵ Thanks to this characteristic and their excellent mechanical properties they might be utilized to create flexible and ultrathin thermoelectric devices, which would satisfy the requirements of the

developing nanoelectronics market.⁶ In addition, 2D materials have a large surface area-to-volume ratio, which gives them unique characteristics, including adjustable chemical functionality, and an electrical conductivity that in some cases is greater than that of their bulk counterparts.⁷,⁸ They are also appropriate for thermoelectric devices due to their reduced thermal conductivity and improved charge carrier mobility.⁷,⁸ Thanks to these characteristics, over recent years, 2D materials have gained large interest as high-performance TEM for efficient conversion of energy in small-packed power generators and cooling devices.⁹ The 2D materials explored for improving thermoelectric devices include graphene, transition metal dichalcogenides, and recently MXene compounds (MXenes).¹⁰

The emergence of 2D MXene structures in 2011¹¹ has sparked significant research interest, making them a captivating area of study ever since. The basic configuration of 2D MXene compounds is described by the chemical formula $M_{n+1}X_nT_x$¹² (where n ranges from 1 to 3), where M represents an early

Received: May 13, 2024

Revised: July 8, 2024

Accepted: July 9, 2024

Published: July 22, 2024

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transition metal, X denotes carbon and/or nitrogen, and T corresponds to surface terminations such as oxygen or fluorine. The MXene family has unique properties, including high mechanical strength, high electrical conductivity, and hydrophilicity. MXene materials also exhibit remarkable electrochemical properties, making them promising candidates for energy storage applications,<sup>13,14</sup> such as batteries and supercapacitors. Additionally, MXenes have potential applications in catalysis,<sup>15,16</sup> water purification,<sup>17</sup> and electromagnetic interference shielding.<sup>18</sup>

Experiments reported by Zha et al.<sup>19</sup> showed that the Ti<sub>2</sub>CO<sub>2</sub> MXene exhibits promising characteristics for thermoelectric applications. More recently, while investigating the Pt<sub>2</sub>CO<sub>2</sub> Mxene monolayer, Wei et al.<sup>20</sup> measured a large ZT with a value approaching 1.05 at 1000 K, which supports the potential use of Pt<sub>2</sub>CO<sub>2</sub> as a thermoelectric material. Moreover, using the Boltzmann theory, Kumar et al.<sup>21</sup> have predicted remarkably high Seebeck coefficients for the MXene compounds Sc<sub>2</sub>CO<sub>2</sub> and Sc<sub>2</sub>CF<sub>2</sub>, being their Seebeck coefficients as high as 1022 and 1036 µV/K at room temperature, respectively. Significantly, the Y<sub>2</sub>CF<sub>2</sub> MXene exhibits a figure of merit of 1.38 at 900 K, which was attributed to its low thermal conductivity. This implies its potential application as a medium-temperature TEM.<sup>22</sup> In summary, the growing family of 2D MXene materials offered exciting opportunities for developing clean sources of energy.

It is well-known that the structural characteristics of 2D materials lead to localization effects which favor an increased phonon scattering and a decreased thermal conductivity.<sup>23</sup> Increasing the complexity of the crystal structure is an efficient way to increase the phonon scattering channels by breaking the degeneracy of phonon modes, therefore helping to effectively reduce the thermal conductivity. It has been conjectured that an asymmetric 2D structure derived from the MXene structure (for instance a Janus-type structure) might inherit the primary characteristics of the phonon dispersion of the MXene parent compounds. Nevertheless, the specific features of the phonon dispersion of the Janus structure, due to the broken symmetry, might reduce the lattice thermal conductivity of the asymmetric 2D structure. Derivation of Janus compounds from M<sub>2</sub>XT<sub>2</sub> MXenes can be done in different ways as heterogeneity in the surfaces is possible through manipulation of the M as well as the T elements.<sup>24</sup> Studies with complex structures employing Janus-like derived MXenes showed that the electric dipole in these structures is exceptionally high and perpendicular to the 2D plane, enhancing the phonon scattering rates,<sup>25</sup> reducing the thermal conductivity, and consequently improving the thermoelectric response. Due to the fact that charge redistribution influences the electrical conductivity of materials, breaking the symmetry of the crystal structure can also enhance the electrical conductivity by introducing additional charge carriers (electrons and/or holes), which are critical for the efficiency of thermoelectric materials. So the introduction of an asymmetry in the crystal structure could enhance the transport properties. The asymmetric structure also gives rise to an intrinsic dipole moment, leading to a band edge realignment.<sup>26</sup> This can result in preferential scattering directions or modified carrier mobilities, impacting in the electrical and thermal conductivity. The anisotropy of the material also influences carrier scattering mechanisms and promotes the formation of energy-dependent scattering mechanisms which enhance the Seebeck coefficient (S).<sup>27</sup> This effect arises from the asymmetry-induced modifications in

the electronic density of states near the Fermi level, affecting the thermoelectric power generation capacity and modifying selection rules that determine allowed and forbidden scattering channels in a given material.<sup>28</sup> Additionally, the dipole moments can introduce additional scattering mechanisms for phonons. When phonons encounter polar molecules or ions with dipole moments, they experience an interaction that can scatter phonons, reducing their mean free path and thus lowering the thermal conductivity.

To understand the influence of asymmetry on thermoelectric properties, we examine here the asymmetric Janus-type ScYCBr<sub>2</sub> MXene, evaluating its thermoelectric characteristics in relation to its parent symmetric compound Sc<sub>2</sub>CBr<sub>2</sub>. Y<sub>2</sub>CBr<sub>2</sub> was also studied but it was found to be dynamically unstable being therefore excluded from the discussion of the results. We will show that the effects of the asymmetry induced by the presence of different atoms in the surfaces (Sc or Y, see Figure S1 in the Supporting Information) mainly affect the high-order phonon scattering, which allows for the regulation of thermal conductivity via anharmonic interactions. In particular, we have found noticeably differences in the behavior of the three low-frequency flexural acoustic phonons, which highly influence the behavior of the thermal conductivity.<sup>29</sup> In addition, we will present results on the structural stability, and the phonon transport and electronic transport properties of the studied compound.

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## COMPUTATIONAL METHODOLOGY

In the present work, spin-polarized first-principles calculations have been conducted using the density-functional theory (DFT).<sup>30</sup> The computer simulations have been carried out using the Quantum Espresso (QE) package.<sup>31</sup> The gradient-corrected exchange-correlation functional of the Perdew-Burke-Ernzerhof for solids (PBEsol) form has been adopted to describe the exchange-correlation energy within the general-gradient approximation (GGA).<sup>32</sup> The DFT-D2 approach elaborated by Grimme<sup>33</sup> has been employed to treat the dispersion interactions. We have used an 8 × 8 × 1 grid of Monkhorst-Pack k-points<sup>34</sup> for sampling the Brillouin zone. The kinetic-energy cutoff for the wave function and charge density have been respectively taken to be equal to 45 and 360 Ry. The electronic convergence criteria have been set to 10<sup>-10</sup> Ry. Also, a Marzari-Vanderbilt scheme has been used with a 0.01 Ry width. The atomic positions in the unit cell and the lattice parameters have been relaxed by using the variable-cell command of the QE package based on the Broyden-Fletcher-Goldfarb-Shanno procedure<sup>35</sup> until the forces on each atom were converged and the force on each atom reached less than 7.49 × 10<sup>-6</sup> Ry/a.u. Due to the two-dimensional nature of the studied structure, a vacuum space of 25 Å along the z-direction has been applied. This permits us to eliminate interactions between neighboring slabs. Additionally, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional<sup>36</sup> has been used to calculate the electronic properties. This approach allows a more accurate calculation of the electronic band structure and carrier mobility overcoming the limitations of the traditional PBEsol functional. The phonon dispersion curves, the corresponding phonon density of state, phonon group velocities, and harmonic force constants have been calculated with a supercell of 2 × 2 × 1 using the finite displacement method. Long-range electrostatic interactions (nonanalytical correction) are included by using the Born effective charges. These calculations have been performed by using both
<figure><img src="image_11.png" /><figcaption>**Figure 1.** Schematic representation of the Janus ScYCBr₂ MXene. Gray, dark yellow, black, and metallic green spheres represent Br, Sc, C, and Y atoms, respectively.</figcaption></figure>

<table><caption>**Table 1.** Optimized Lattice Constant (a (Å)), Thickness of the 2D Layer (Δh (Å)), and Bond Distances (d (Å)) of ScYCBr₂ and Sc₂CBr₂ 2D Structures Compared to Previous Results on Compounds of the Same Family<sup>a</sup></caption><thead><tr><th></th><th>a</th><th>Δh</th><th>d<sub>Sc-Y</sub></th><th>d<sub>Sc-C</sub></th><th>d<sub>Sc-Br</sub></th><th>d<sub>Y-Br</sub></th><th>d<sub>Y-C</sub></th></tr></thead><tbody><tr><td>ScYCBr<sub>2</sub><sup>a</sup></td><td>3.565(1)</td><td>6.273(1)</td><td>3.2674(1)</td><td>2.381(1)</td><td>2.715(1)</td><td>2.845(1)</td><td>2.456(1)</td></tr><tr><td>Sc<sub>2</sub>C Br<sub>2</sub><sup>a</sup></td><td>3.452(1)</td><td>6.038(1)</td><td>-</td><td>2.329(1)</td><td>2.694(1)</td><td>-</td><td>-</td></tr><tr><td>ScYCBr<sub>2</sub><sup>45</sup></td><td>3.650(1)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Sc<sub>2</sub>CBr<sub>2</sub><sup>46</sup></td><td>3.507(1)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Sc<sub>2</sub>CCl<sub>3</sub><sup>47</sup></td><td>3.470(1)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Y<sub>2</sub>CCl<sub>2</sub><sup>47</sup></td><td>3.520(1)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<sup>a</sup>The symbol * identifies the present results.

Phonopy<sup>37</sup> and Alamode<sup>38</sup> packages interfaced with the Quantum Espresso code. The linearized phonon Boltzmann equation (BTE) has been employed to compute the lattice thermal conductivity (κ<sub>L</sub>). This calculations has been carried out employing the single-mode relaxation time approximation (RTA) as incorporated in the Phono3py package interfaced with the QE code, In both codes, the expression for κ<sub>L</sub> is formulated as follows:

$$ \kappa_L = \frac{1}{NV_0} \sum_{\lambda} C_{\lambda} \nu_{\lambda} \otimes \nu_{\lambda} \tau_{\lambda} \quad (1) $$

where N, V₀, and λ are the total number of q points used for sampling the Brillouin Zone, the volume of the unit cell, and the phonon mode respectively, while C<sub>λ</sub>, ν<sub>λ</sub>, and τ<sub>λ</sub> refer to specific heat, phonon group velocity, and phonon lifetime, respectively. In these calculations, the finite-displacement method has been employed to calculate the second-order force constants (harmonic contribution). Such calculations have been carried out on a 2 × 2 × 1 supercell sampled with a dense 8 × 8 × 1 k-point mesh. The third-order and four-order anharmonic interatomic force constants (IFCs) were calculated using the finite displacement method with the same supercell (convergence tests are displayed in Figure S2 of the Supporting Information). For the computation of the lattice thermal conductivity, the reciprocal space of the primitive cell has been sampled by a 50 × 50 × 1 k-point meshes. The lattice thermal conductivity of 2D materials is influenced by the unit-cell length along the z-direction. Normalization is then essential. It can be achieved by multiplying these values by the ratio L<sub>z</sub>/d,<sup>39</sup> where L<sub>z</sub> represents the unit-cell length along

the z-direction and d is the effective thickness (this magnitude is obtained as the sum of the atomic layer thickness and the van der Waals radius of the atoms of the surfaces of the MXene structure<sup>41</sup>). To compute the anharmonic phonon dispersion as a function of temperature, the fourth-order force constants using the harmonic eigenvectors should be computed. This calculation is not implemented in Phonopy but is implemented in the Alamode code<sup>38</sup> which has been used to calculate the harmonic and anharmonic interatomic force constants in order to evaluate the anharmonic phonon dispersion (for more details see the Supporting Information). Finally, the electronic transport properties of the Janus-type ScYCBr₂ MXene, including the Seebeck coefficient and electrical and thermal conductivity, have been computed using the BoltzTrap2 code<sup>42</sup> interfaced with the QE software.

## ■ RESULTS AND DISCUSSIONS

2D Sc₂CBr₂ has a noncentrosymmetric trigonal layered crystal structure described by the space group P3m1 (No. 164) and has a point group symmetry D₃d (-3m). 2D ScYCBr₂ has an asymmetrically ordered Janus-type structure<sup>43,44</sup> described by space group P3m1 (No. 156) and has a point group C₃v (3m). It is formed by five atomic layers arranged in the sequence Br-Sc-C-Y-Br. In contrast Sc₂CBr₂ is a symmetric MXene structure. The asymmetry of ScYCBr₂ allows its two surfaces to have different physical properties. The atomic arrangement of ScYCBr₂ is shown in Figure 1 where we show a perspective view of the 2D structure. In terms of structural characteristics as well as the cluster expansion (CE) method,<sup>24</sup> the Br atomic layers of ScYCBr₂ MXenes can occupy either the hcp-hcp, hcp-hcp-
$hcp-hcp$ or $fcc-fcc$ hollow sites (See the four configurations in Figure S3 of the Supporting Information). However, after structural optimization, we have found that the $hcp-hcp$ occupation gives the most stable configuration. The total energy per atom of the four configurations are respectively, $E(hcp-hcp) = -8.24$ eV/atom, $E(hcp-fcc) = -8.18$ eV/atom, $E(fcc-hcp) = -8.14$ eV/atom and $E(fcc-fcc) = -8.08$ eV/atom. Thus, the functional groups prefer to occupy hollow sites that are associated with the Sc/Y sites stabilizing them in an $hcp-hcp$ configuration. The optimized lattice constants, bond distances, and thickness of the more stable $hcp-hcp$ configuration are summarized in Table 1. The table includes the lattice parameters previously reported for ScYCBr$_2$ and Sc$_2$CBr$_2$ and related compounds.<sup>45–47</sup> In contrast to the parent structures, in the Janus-type structure, the bond lengths of Sc–Br and Y–Br are different. According to the calculated thickness, we can expect that the investigated compound has pronounced quantum-confinement (QC) effects.<sup>48</sup> Due to the dimension of the thickness, phonons will play a major role in thermal transport. However, because of the strong temperature dependence, the role of phonons declines gradually in the presence of a temperature gradient, which is mainly induced by the suppression of the phonon lifetime.

To assess the dynamical stability of the investigated 2D structures, we have calculated the phonon dispersion for each compound. From them, we have obtained the phonon density of states (PHDOS). The phonon dispersion and PHDOS of ScYCBr$_2$ are shown in Figure 2a and 2b. These calculations were carried out independently using the Phonopy and Almode codes, see Figure S4 in the Supporting Information. The agreement between the two methods suggests that both codes give similar results for the phonons of the investigated compounds. The phonon dispersion and PHDOS of Sc$_2$CBr$_2$ are shown in Figure 2c and 2d. Considering that the primitive cells of the studied compounds have five atoms, 15 phonon modes are expected, as illustrated in Figure 2. No imaginary phonon frequencies are observed for the two compounds, supporting their dynamical stability. We would like to add here that mechanical stability is also fulfilled (see Supporting Information and Table S1). The modes at the $\Gamma$ point of the Brillouin zone can be labeled by irreducible representations as follows: for Sc$_2$CBr$_2$, $M = 2A_{1g} + 3A_{2u} + 3E_u + 2E_g$ where $\Gamma_{acoustic} = A_{2u} + E_u$ and $\Gamma_{optic} = 2A_{1g}(R) + 2A_{2u}(IR) + 2E_u(IR) + 2E_g(R)$. For ScYCBr$_2$, $M = 5A_1 + 5E$, where $\Gamma_{acoustic} = A_1 + E$ and $\Gamma_{optic} = 4A_1(R/IR) + 4E(R/IR)$. Where the letters R and IR in the parentheses indicate whether the mode is Raman or infrared active, respectively. The parent structure possesses a higher symmetry than the Janus one. The break of the mirror symmetry<sup>49</sup> leads to additional phonon branches in the Janus structure. This difference in crystal symmetry will be the cause of some restrictions on possible phonon scattering channels.<sup>50</sup> This fact indirectly affects phonon scattering through energy and momentum conservation conditions.<sup>51</sup> Thus, the broken in-plane crystal symmetry will impact the thermal conductivity.

We additionally studied the thermal stability of both compounds through *ab initio* molecular-dynamics (AIMD) calculations at a finite temperature to understand their response to thermal fluctuations. Figure S5 in the Supporting Information provides information to understand the response of the studied materials to thermal vibrations at ambient and high temperatures. The ScYCBr$_2$ and Sc$_2$CBr$_2$ MXenes show periodic temperature fluctuations as well as a negative stable

<figure><img src="image_12.png" /><figcaption>**Figure 2.** (a) Phonon dispersion and (b) density of states calculated at 0 K for ScYCBr$_2$. (c) Phonon dispersion and (d) density of states calculated at 0 K for Sc$_2$CBr$_2$. The acoustic branches are shown in red (ZA mode), blue (TA mode), and green (LA mode).</figcaption></figure>

periodic total energy as a function of the AIMD time simulation.

From the phonon dispersions represented in Figure 2, it can be seen that, for both compounds, near the $\Gamma$ point the dispersion relation of the transverse acoustic (TA) and longitudinal acoustic (LA) branches is linear. On the other hand, the out-of-plane flexural acoustic (ZA) branch exhibits a quadratic dispersion, which is a known characteristic of 2D materials. The nonlinearity is more pronounced in the case of the Janus-like ScYCBr$_2$ MXene due to the asymmetric nature of the structure and the lack of mirror symmetry. Thus, the ZA mode is not a completely out-of-plane vibration as in Sc$_2$CBr$_2$, but one with an in-plane component, which causes the ZA mode to get involved in more scattering processes. Contrary to conventional symmetric chalcogenide monolayers, in MXenes there is a splitting between the optical LO and TO modes at the $\Gamma$ point<sup>52</sup> in the phonon spectra which is caused by the dipole moment induced by the large electronegativity of Br. Regarding atomic contributions to vibrations, the carbon atoms mostly contribute to the optical branches in the high-frequency area; in contrast, the contributions of Sc and Y atoms dominate the intermediate frequency range and the
contribution of Br atoms is dominant in the low-frequency region. The separation between vibrations associated with Y and Sc atoms in ScYCBr₂ opens additional ways to control thermal conductivity by modifying the harmonic/anharmonic phonon characteristics due to the decoupling of their atomic vibrations and the unequal contribution of the different phonons to thermal transport at different frequencies.²⁹ It is also important to note that according to the anharmonic phonon dispersions, here calculated at various temperatures (see Figure 3a, 3b, 3c, and 3d), both ScYCBr₂ and Sc₂CBr₂ are

<figure><img src="image_13.png" /><figcaption>**Figure 3.** Anharmonic phonon dispersion curves as a function of temperature of (a) Janus-like ScYCBr₂. In (b) we represent a zoom of the highlight region in the Γ − M direction. (c) and (d) show the same results for the ScCBr₂ MXene.</figcaption></figure>

stable not only at 0 K but also at high temperatures from 300 to 1200 K. This fact indicates that ScYCBr₂ and Sc₂CBr₂ deserve to be investigated as candidate materials to achieve high thermoelectric efficiency since often practical applications involve high temperatures.

The phonon group velocity of each mode is given by
$v_k = \frac{\partial w_k}{\partial q}$, where $w, k,$ and $q$ represent the vibrational frequency,
the vibrational mode index, and the wave vector, respectively.
The group velocities of the three acoustic branches ZA, TA,
and LA of ScYCBr₂ near the Γ point are 2.82, 3.43, and 5.67
km/s, respectively (see Figure 4a). The group velocities are
ordered following the sequence LA > TA > ZA. The ZA mode
has a lower group velocity than the TA and LA modes, which

<figure><img src="image_14.png" /><figcaption>**Figure 4.** Calculated phonon group velocity of the (a) Janus-like ScYCBr₂ MXene and (b) ScCBr₂ MXene.</figcaption></figure>

is due to the nonlinear dispersion of the ZA branch near the Γ
point. Consequently, the LA mode is responsible for the
majority of the thermal transport. Analogous findings have
been found in other 2D materials, including XTeI (X = Sb,
Bi),⁴⁰ SnY₂ (Y = S,Se),⁵³ and PbTe.⁵⁴

It is noteworthy that the maximum of phonon group velocity
plots is between 2.50 and 8.00 Km/s, which is typical in
thermoelectric materials.⁵⁵ The maximum phonon group
velocity in ScYCBr₂ is slightly smaller than 6 km/s, which is
similar to the maximum phonon group velocity of several 2D
materials, such as ZrOSe (6.1 km/s),⁵⁶ PtAs₂ (6 km/s)⁵⁷ and
TiS₃ (6.5 km/s).⁵⁸ Despite the differences between the crystal
structures, ScYCBr₂ and Sc₂CBr₂ have a similar group velocity
for the ZA modes. Consequently, the specific heat (C_v) curves
are similar (see Figure S6 in the Supporting Information). The
values of the specific heat of both compounds are low, of the
order of 190 J/K, which fulfills a prerequisite for high-
performance TE materials. According to the dynamical theory,
the thermal conductivity is κ_L = 1/3 C_v v_g. Then a reduced group
velocity and reduced C_v favor a low lattice thermal
conductivity. Noticeably, compared to state-of-the-art thermo-
electric asymmetric monolayers like SnSSe and PbSSe,⁵⁹ whose
acoustic mode occupies a wavenumber range of 0–3.5 THz,
the acoustic phonon frequencies range of the Janus-like
ScYCBr₂ extends only up to 2.9 THz. In contrast, in ScCBr₂
the range covered by the frequencies of the acoustic phonon
modes is above 4 THz (see Figure 4b). This characteristic
implies that the overall rate of the thermal energy transport in
the Janus-like ScYCBr₂ MXene is smaller than in the other
materials of the same family. As a consequence of it, the heat
conduction decreases, improving the ability of ScYCBr₂ to
convert temperature gradients into electrical power.

To gain a deeper insight into the anharmonic properties of
the phonons of ScYCBr₂ and Sc₂CBr₂, we have also calculated
the phonon lifetimes. Their values at room temperature are
represented in Figures 5a and 5b. The lifetimes of the optical
phonons of ScYCBr₂ are considerably shorter than the
<figure><img src="image_15.png" /><figcaption>Figure 5. Phonon lifetime distribution vs frequency in (a) Janus-like ScYCBr₂ MXene and (b) Sc₂CBr₂ MXene.</figcaption></figure>

lifetimes of the acoustic modes, going from 0.5 to 5 ps, and are shorter compared to the lifetime of the optical modes of SnSe,⁶⁰ indicating that the optical modes have little contribution to the lattice thermal conductivity in ScYCBr₂ (see Figure 5). More significantly, as shown in Figure 5a and 5b, the lifetime range determined for the Janus-like material is smaller than that of its parent Sc₂CBr₂ MXene. To further explore the phonon modes responsible for the flow of heat within the material (heat carriers) on the two studied structures, we have investigated the contribution of different modes to $κ_L$. Figure 6 shows the thermal conductivity of the two MXenes. It can be seen that ScYCBr₂ has a lower thermal conductivity than its parent symmetric MXene and other MXenes. Notice that the inverse T dependence of $κ_L$ suggests that to effectively address the phonon scattering, the Umklapp process needs to be taken into account.⁶¹ Additionally, the decrease of $κ_L$ with increasing temperature is primarily attributed to the enhancement of phonon-phonon scattering with increasing temperature.

<figure><img src="image_16.png" /><figcaption>Figure 6. Calculated lattice thermal-conductivity $κ_L$ of ScYCBr₂ and Sc₂CBr₂. The plot also shows results from TiHfCO₂ and Ti₂CO₂ taken from the work by Murari et al.⁶⁴</figcaption></figure>

According to our calculations, the room-temperature thermal conductivity of ScYCBr₂ is 5.24 Wm⁻¹K⁻¹ and it decreases to 1.27 Wm⁻¹K⁻¹ at 1200 K. On the other hand, in Sc₂CBr₂ $κ_L$ is 8.44 W m⁻¹ K⁻¹ at ambient temperature. These values are significantly lower than the thermal conductivity of graphene (2200 Wm⁻¹K⁻¹), WS₂ (72 Wm⁻¹K⁻¹),⁶² and WSe₂ (53.0 Wm⁻¹K⁻¹),⁶³ and much lower than the thermal conductivity of similar structures like TifCO₂ and Ti₂CO₂ which are reported in the study performed by Murari et al.⁶⁴ To understand the atomic contribution to $κ_L$, we have analyzed it using the cumulative lattice thermal conductivity as a function of the phonon frequency. This analysis gives the primary causes of such low $κ_L$. As can be seen in Figure S7 in the Supporting Information, in ScYCBr₂ the modes below 3 THz account for 70% of the lattice thermal conductivity. According to the PHDOS, the main contribution to heat transport comes from the vibrations of Br atoms (see Figure 2).

The interactions between phonons and defects, impurities, and other phonons determine the transport characteristics of phonons in materials, including the thermal conductivity. In particular, the thermal conductivity depends on the balance between phonon scattering mechanisms and phonon transport, Strong scattering processes (e.g., due to high defect concentrations or rough interfaces) result in a low thermal conductivity, whereas materials with few scattering centers exhibit a high thermal conductivity. So, we will analyze these processes in the two studied materials.

Combining the linearized phonon BTE and the law of Fourier, the lattice thermal conductivity ($κ_l$) can also be expressed as⁶⁵

$$κ_l = \sum_{\lambda} c_{\nu,\lambda} v_{\lambda,\alpha} v_{\lambda,\beta} \tau_{\lambda} = \frac{1}{V} \sum_{\lambda} \hbar \omega_{\lambda} \frac{\partial n_{\lambda}}{\partial T} v_{\lambda,\alpha} v_{\lambda,\beta} \tau_{\lambda} \quad (2)$$

where $α$ and $β$ are the Cartesian coordinates, $λ = (q, v)$ denotes the phonon mode with wave vector **q** and phonon polarization **v**, $c_{ν,λ}$ is the phonon specific heat capacity, $v_λ$ is the phonon group velocity, and $τ_λ$ is the phonon relaxation time. **V** is the volume of the primitive cell, $ħ$ is the reduced Planck constant, $ω_λ$ is the phonon frequency, and $n_λ$ is the Bose-Einstein distribution at temperature **T**. Getting $τ_λ$, which is connected to multiple scattering processes, is a crucial in the
described calculations. To avoid the boundary scattering effects, in our calculations, we have used the relation $1/τ_λ = 1/τ_λ^{anhar} + 1/τ_λ^{iso} + 1/τ_λ^{4ph}$, which assesses the total relaxation time in RTA and it is obtained from the isotopic and anharmonic three-phonon scattering processes. Figure S8 in the Supporting Information presents the anharmonic three-phonon (3ph), four-phonon (4ph), isotopic, and also the sum of the 3 ph and 4ph contributions. According to our results, the 3ph-phonon mechanism is the major contribution to the heat conduction in ScYCBr₂ and Sc₂CBr₂ being the role of other mechanisms negligible. This conclusion is compatible with results reported in other MXenes.⁶⁶ Therefore, for the rest of the discussion, we will focus only on the three phonon scattering processes.

The scattering rates at 300 K for the anharmonic three-phonon scattering interactions are displayed in Figure 7. In

<figure><img src="image_17.png" /><figcaption>**Figure 7.** Anharmonic three-phonon scattering rates of the (a) Janus-like ScYCBr₂ and (b) symmetric Sc₂CBr₂ MXene. The phonon-phonon scattering rates are calculated on a 100 × 100 × 1 q-grid mesh. The plot also shows the contribution of each phonon mode.</figcaption></figure>

both compounds, ScYCBr₂ and Sc₂CBr₂, the relaxation time of the acoustic modes is shorter than those of the optical modes. In addition, the relaxation time of the acoustic modes is the shortest in ScYCBr₂. The acoustic phonon relaxation time is concentrated between $10^{-1}$ ps and $10^°$ ps, while the optical phonon relaxation time falls within the range of $10^{-1}$ ps and $10^{+1}$ ps. The longer phonon relaxation time of the acoustic modes is in accordance with their dominant contribution of the acoustic branches to $κ_L$ (see Figure S9 in the Supporting Information). Moreover, further comparison indicates that most of the acoustic LA, and optical ZO and LO modes have a much stronger phonon scattering in the asymmetric MXene than in the symmetric one. It is also noted that for the Janus structure, we have higher phonon scattering rates, which implies that more modes are active at a given temperature. Thus, based on the lattice thermal conductivity eq 2, the value of the lattice thermal conductivity is mainly determined by the sum of the anharmonic three-phonon scattering and isotopic scattering rates (see Figure S8 in the Supporting Information),

and the group velocity of phonons. This explains why the lattice thermal conductivity is slightly lower in the Janus-like ScYCBr₂ than in the symmetric Sc₂CBr₂ MXene.

To understand how phonon transport works at its fundamental level in Sc₂CBr₂ and ScYCBr₂, we have calculated the contributions of various phonon branches to the lattice thermal conductivity (See Figures 8a and 8b). Certain

<figure><img src="image_18.png" /><figcaption>**Figure 8.** Temperature dependence of the thermal conductivity of each phonon mode channel in $κ_L$ of (a) symmetric Sc₂CBr₂ and (b) Janus-like ScYCBr₂ MXene. Percentage contribution of each phonon mode to $κ_L$ for (c) symmetric Sc₂CBr₂ and (d) Janus-like ScYCBr₂ MXene.</figcaption></figure>

differences are evident for both materials. The contribution of the TA, LA, and ZA modes in the Janus-type structure is respectively around 29%, 22%, and 1% at temperatures ranging from 100 to 400 K and diminished by only 1% from 400 to 1200 K, see Figure 8(c). In contrast, in the asymmetric MXene material, the most involved channels are ZA, TA, and then LA, with a percentage of, respectively, 35%, 28%, and 20%, see Figure 8(d). Furthermore, we have observed that a channel from the optical branches somewhat contributes to the conductivity of the Janus-type structure. This is a consequence of the symmetry breaking in ScYCBr₂. Figures 8a and 8b also illustrate how $κ_L$ changes with temperature for each mode. These figures also show the evolution of $κ_L$ with temperature. It is possible to attribute the difference in contribution between the asymmetric and symmetric structures to the different symmetry and, consequently, to the different selection rules and eigenvectors of the phonon modes.

Once the most favorable material for thermoelectric applications and the most favorable scattering phonon channels are identified, it is necessary to check other TE properties. The thermoelectric efficiency is primarily associated with the value of the figure-of-merit ($ZT = S^2\sigma T/(\kappa_L + \kappa_c)$), which depends also on the electronic thermal conductivity ($\kappa_e$) and the conductivity ($\sigma$), being this proportional to the carrier mobility ($\mu$). Indeed, because the mobility affects the capacity of electrons and holes to transport heat and electricity, the
<figure><img src="image_19.png" /><figcaption>**Figure 9.** Carrier mobility $\mu$ of ScYCBr$_2$ and Sc$_2$CBr$_2$. (a) gives the mobility of electrons and (b) the mobility of holes. The evolution of the electronic thermal conductivity ($\kappa_e/\tau$) as a function of temperature for (c) electrons and (d) holes, for different carrier charge concentrations of the Janus-type ScYCBr$_2$ MXene. The evolution of the electronic thermal conductivity ($\kappa_e/\tau$) as a function of temperature for (e) electrons and (f) holes, for different carrier charge concentrations of the symmetric Sc$_2$CBr$_2$ MXene.</figcaption></figure>

carrier mobility is also a crucial factor in the study of thermoelectric materials. In Figure 9, we present results of the carrier mobility for ScYCBr$_2$ and Sc$_2$CBr$_2$. They have been calculated for both types of charge carriers using the deformation potential theory.⁶⁷ This theory has been shown to be a reliable method for predicting the carrier mobility of 2D semiconductors, including MoS$_2$. A detailed description of the methodology is given in the **Supporting Information**.

The values of the electron and hole mobilities at room temperature are given in Table S2 of the **Supporting Information**. The values have been extracted from the applications of strains on the band structure plots. See Figures S10, S11, and S12 in the **Supporting Information**. As the mobility of the charge carriers is related to the scattering rate and dispersion of bands in the band structures, we have taken care to use the band structures calculated using the HSE06 functional,³⁶ one of the most accurate descriptions for such calculations. According to our results, the electron mobility is larger than the hole mobility. This is a consequence of the fact that near the Fermi level, the valence band (see Figure S13 in

the **Supporting Information**) is less dispersive than the conduction band. The flat valence band leads to a large effective mass for the holes and consequently to a low mobility for them. At high temperatures, $\mu$ decreases for both types of carriers (see Figures 9(a) and 9(b)). We have also found that the electron and hole mobilities are different in the x and y transport directions, indicating that the carrier mobilities are anisotropic. Comparing the values of the mobility reported in the literature for similar structures, the anisotropy of the mobility in the studied compound is moderate.

In order to further study the electronic transport properties, we have used the Boltztrap2 code⁴² and we have considered a temperature-dependent relaxation times approximation as proposed by Casu et al.⁶⁸ (see in the **Supporting Information**, the results in Figure S14, the global relaxation time values in Table S3, and the explanation of the method utilized to determine the relaxation time as a function of temperature). As mentioned before, the high performance of Janus-type ScYCBr$_2$ MXene could be achieved thanks to its mechanical properties, its high electrical conductivity, its low thermal
<figure><img src="image_20.png" /><figcaption>**Figure 10.** From the top to the bottom we present the evolution of the Seebeck coefficient, the electrical conductivity, the electronic thermal conductivity, and the panel power factor, as a function of n-type (left) and p-type (right) carrier concentration of ScYCBr₂. The TE properties decrease with an increase in temperature because τ increases with it, see Table S3 in the Supporting Information.</figcaption></figure>

conductivity, and the potential of the material to generate electric power at a given temperature. Figure 9c–f illustrate how the electronic thermal conductivity increases drastically with temperature. This increase is clearly due to the change of the charge carrier concentration from 10¹⁸ cm⁻³ to 10²¹ cm⁻³ as well as to the enhancement of the electron group velocity at high temperatures. The plots also show that n-type carriers (i.e., electrons in the conduction band) are largely responsible for the electronic transport. In this case, the electronic thermal conductivity (κₑ) is nearly four times larger in the case of electrons than in the case of holes. Such a characteristic made ScYCBr₂ quite efficient for thermoelectric devices utilizing high-mobility carriers. Interestingly κₑ increases with temperature to attain 8 × 10⁴ W/(mK) at 1200 K. We have also found that κₑ is similar for BrSc₂CBr₂ and ScYCBr₂. However, there are some differences, in the dependence of this magnitude on the hole charge carrier concentration (see for comparison Figure 9(c)–(f)). Nonetheless, compared to metallic Au, Ag, and Cu,⁶⁹ the magnitude of the electronic thermal conductivity magnitude is still relatively moderate in the two studied materials. This is mostly due to the semiconducting nature of the studied material and the strong

electron–phonon interaction in them, which produces comparatively short electron relaxation times.

In order to gain a more thorough comprehension of our findings we have also studied the thermoelectric coefficients as a function of carrier concentration at 300, 600, 900, and 1200 K. Figures 10 and 11 display the electrical conductivity, σ, power factor, PF = S²σ, the absolute value of the Seebeck coefficient |S|, and the electronic thermal conductivity, κₑ. To understand the behavior of these properties from Figures 10 and 11, we should remember that in our approximation the relaxation is a function of temperature.⁶⁸ The S value of n-type carriers is close to the S value of p-type carrier. Comparing the two compounds ScYCBr₂ is the material with the highest S. In spite of this, both structures can achieve S = 300 µVK⁻¹ at 1200 K for both types of carriers at a moderate carrier concentration (10²⁰ cm⁻³). On the other band, the low S-coefficient (brown dashed lines) found for both charge types at 1200 K with the carrier concentration beyond ×10²¹ cm⁻³ can be attributed to a bipolar conduction effect. This is a common effect for narrow gap semiconductors, like the materials here studied with band gap energies ~1.5 eV. This effect makes the
<figure><img src="image_21.png" /><figcaption>**Figure 11.** From the top to the bottom we present the evolution of the Seebeck coefficient, the electrical conductivity, the electronic thermal conductivity, and the panel power factor, as a function of **n**-type (left) and **p**-type (right) carrier concentration of Sc₂CBr₃. The TE properties decrease with an increase in temperature because τ increases with it, see Table S3 in the Supporting Information.</figcaption></figure>

absolute value of the Seebeck coefficient to increase initially and then decrease at high temperatures.⁷⁰

As it can be also discerned from Figures 10 and 11, our computed electrical transport coefficient and σ follow the expected trend for both types of carrier concentrations. Here, because there are more charge carriers, the electrical conductivity rises with carrier concentration following the Mott equation. The more dispersive character of the bands in the conduction region may be the reason for the higher electrical conductivity values observed for **n**-type carrier concentrations. When the concentration of **n**-type carriers is equal to 10²¹ cm⁻³, we obtain higher power factor values at 300 K of ~8 × 10²¹ Wm⁻¹K⁻²s⁻¹ (for a time relaxation τ = 1.13 × 10⁻¹⁴s), even though the values of **p**-type carriers are nearly two times smaller. This high value can be attributed to the unusually high electrical conductivity. In terms of electronic thermal conductivity, it follows the same pattern as the electrical conductivity. For high temperatures, we can see that the electrical conductivity rises to reach a value of 4 × 10²¹ Wm⁻¹K⁻²s⁻¹. In the case of Sc₂CBr₃, σ reaches relatively smaller values: ~8 × 10²¹ Wm⁻¹K⁻²s⁻¹ for the **n**-type and ~2 × 10²¹ Wm⁻¹K⁻²s⁻¹ for the **p**-type charges.

The power factor is a relevant parameter for characterizing the electronic transport properties. It is dependent on both S and σ. S and it is inversely proportional to the carrier concentration, whereas σ increases as the carrier concentration rises. Because of the larger electrical conductivity, for **n**-type carriers the PF in both materials is always higher than the PF for **p**-type carriers. In addition, due to the inverse relationship between the electrical conductivity and temperature, the PF value falls with increasing temperature. More significantly, we can observe multiple peaks, with the most important occurring at a concentration of 10²¹ cm⁻³. These results suggest that heat can be efficiently converted into electrical power using the Janus structure.

Finally, we will examine the thermoelectric performance of both ScYCBr₂ and Sc₂CBr₂ by evaluating the figure of merit (ZT). We start by outlining the functional relationship between ZT for different carriers and the carrier concentration vs various temperatures. The results are shown in the 2D maps of Figures 12, and 13. It is clear that at high temperatures, the optimal ZT is achieved for **n**-type carrier concentrations of ~10²⁰ cm⁻³ for both materials. However, the **p**-type carriers maximize the electrical transport but only at a large carrier
<figure><img src="image_22.png" /><figcaption>**Figure 12.** Figure of merit (ZT) map as a function of temperature and carrier charge concentration for both **n**-type and **p**-type carriers for ScYCBr~2~.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 13.** Figure of merit (ZT) map as a function of temperature and carrier charge concentration for both **n**-type and **p**-type carriers for Sc~2~CBr~2~.</figcaption></figure>

concentration of 10²¹ cm⁻³. Such higher carrier concentration could be associated with an increased thermal conductivity, which can be detrimental to thermoelectric performance. We note that electrons are the main transport carriers for the investigated MXenes. Thus, with this behavior combined with the low thermal conductivity and the dynamical and thermal stability of the structures, we can conclude that Janus-like ScYCBr~2~ MXene meets the requirements for being a high-efficiency thermoelectric material. The ZT value reached respective values of 1.2 and 0.7 for the **n**-type ScYCBr~2~ and Sc~2~CBr~2~, and 0.73 and 0.41 for the **p**-type materials. Such results are rather similar to those found by Murari et al. for similar structures.⁶⁴

## CONCLUSIONS

Along this contribution, we have provided conclusive evidence that the asymmetric Janus-type ScYCBr~2~ MXene has very promising thermoelectric properties. We have achieved this conclusion from computational simulations of both phonon and electronic transport properties. The study is based on the density-functional theory, and it is complemented by calculations applying the phonon Boltzmann transport theory. We have found that 2D ScYCBr~2~ is dynamically and thermally stable from 0 K to high temperatures. Results have also shown that there is a significant degeneracy between the ZA and LA modes near the Γ – M point. The acoustic branches show a robust coupling between them, resulting in an important anharmonicity and low-mean-free paths of phonons. The properties of the related symmetric Sc~2~CBr~2~, MXene have also been studied and compared to the asymmetric ScYCBr~2~. Our findings suggest that, compared to Sc~2~CBr~2~, in ScYCBr~2~, the phonon anharmonicity is less relevant. We have also shown that the symmetry breaking in ScYCBr~2~ enhances the phonon scattering channels by making additional scattering centers for phonons and, consequently, reduces thermal transport. We have also found that the behavior of the lattice thermal conductivity κ~L~ is correlated with the phonon group velocity and phonon lifetime. Additionally, by assuming that the compounds could be doped with **n**-type and **p**-type impurities,¹⁰ we have demonstrated that the Janus-like ScYCBr~2~ MXene exhibits excellent **n**-type transport properties and high thermoelectric properties at both ambient temperature and 1200 K. In summary, this work has allowed us to understand the potential of ScYCBr~2~ as an excellent thermoelectric material. We think that the synthesis of this material for high-performance thermoelectric applications would be encouraged by our study.

## ASSOCIATED CONTENT

### Data Availability Statement

All relevant data are available from the corresponding author upon reasonable request.

### Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsaem.4c01221.

Structural model of the studied materials, the methods used to estimate the carrier mobility, the anharmonic phonon dispersion plots, the lattice thermal conductivity, and the temperature-dependent relaxation time; several figures showing the third-order force constant interaction cutoff convergence tests, the molecular-dynamic simulation of temperature and total energy as a function of the time step, the specific heat capacity of both structures, the cumulative lattice thermal conductivity at 300 K, the three-phonon, four-phonon, and isotopic scattering rate as a function of frequency, and finally the band structure and relaxation time (PDF)

## AUTHOR INFORMATION

### Corresponding Authors

Mounir Ould-Mohamed – LPTHIRM, Département de Physique, Faculté des Sciences, Université Saâd Dahlab-Blida 1, Blida 09000, Algeria; Email: ouldmohamed_mounir@univ-blida.dz

Tarik Ouahrani – Ecole Supérieure en Sciences Appliquées, ESSA-Tlemcen, BB 165 RP Bel Horizon, Tlemcen 13000,
Algeria; Laboratoire de Physique Théorique, Université de Tlemcen, Tlemcen 13000, Algeria; Université de Lorraine, Laboratoire Lorrain de Chimie Moléculaire CNRS, Metz F-57000, France; Email: tarik.ouahrani@univ-tlemcen.dz

**Daniel Errandonea** – Departamento de Física Aplicada – Instituto de Ciencia de Materiales, Matter at High Pressure (MALTA) Consolider Team, Universidad de Valencia, Valencia 46100, Spain; ● orcid.org/0000-0003-0189-4221; Email: daniel.errandonea@uv.es

## Authors

**Reda Boufatah** – Laboratoire de Physique Théorique, Université de Tlemcen, Tlemcen 13000, Algeria

**Ángel Morales-García** – Departament de Ciència de Materials i Química Física and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Barcelona 08028, Spain; ● orcid.org/0000-0003-0491-1234

**Ruth Franco** – MALTA Consolider Team and Departamento de Química Física y Analítica, Universidad de Oviedo, Oviedo E-33006, Spain

**Michael Badawi** – Université de Lorraine, Laboratoire Lorrain de Chimie Moléculaire CNRS, Metz F-57000, France; ● orcid.org/0000-0002-3504-4180

Complete contact information is available at:
https://pubs.acs.org/10.1021/acsaem.4c01221

## Author Contributions

Mounir Ould Mohamed: Investigation, Writing - original draft-DFT calculations; Tarik Ouahrani: Conceptualization, DFT calculations, Analysis, Writing-review and editing. Reda Boufatah: DFT and python calculations; Ángel Morales-García: review and editing; Ruth Franco: Writing-review and editing; Michael Badawi: review and editing; Daniel Errandonea: Analysis and discussion, Writing-review and editing.

## Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

T.O. thanks the financial support obtained from Université de Tlemce through project PRFU B00L02EP130220230001. D.E. thanks the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades, MCIU (10.13039/501100011033) under grants RED2022-134388-T and PID2022-138076NB-C41, D. E. also thanks the financial support of Generalitat Valenciana. through grants PROM-ETEO CIPROM/2021/075-GREENMAT and MFA/2022/007. This study forms part of the Advanced Materials program and is supported by MCIU with funding from the European Union Next Generation EU (PRTR-C17.11) and by the Generalitat Valenciana. R.F. acknowledges the Financial support from Spanish MCIU under project MCIU-22-PID2021-122585NB-C21. We thank the MALTA-Consolider supercomputing center for awarding us access to computer facilities. The authors would like to thank Dr. Robin Turnbull for constructive criticism of the manuscript and English editing.

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