2.3.2. Doping Influence on BNC Heteronanotubes

Ternary boron carbonitride nanotubes have recently been in the focus of theoretical and experimental activities because of their excellent mechanical, electrical, and non-linear optical properties which could be controlled by varying their chemical composition [133–135]. Hence, BNC heteronanotubes may play an important role as new generation of thermoelectric materials, and are also of grea<sup>t</sup> interest in environmentally relevant issues such as waste heat recovery and solid-state cooling [9,136]. In Ref. [120], we studied the influence of doping on the thermal transport properties of (6,6)-BNC heteronatubes, by considering three different BN doping distribution patterns of a carbon nanotube: helical, horizontal, and random. For this, a (6,6)-CNT of length 43.3 Å was the reference structure (supercell composed by 432 C atoms). Helical BN strips, BN chains (parallel to the transport direction, which corresponds to the z-axis), and BN rings (one ring containing 3B and 3N atoms) were introduced in an otherwise perfect (6,6)-CNT to represent helical, horizontal, and random impurity distributions (see Figure 4a). For a helical distribution, the BN concentration was varied from *c* = 11% to *c* = 89%, while for other cases concentrations ranging from *c* = 16% to *c* = 84% were studied. The limits of 0% and 100% correspond to pure carbon and hexagonal boron–nitride nanotubes, respectively.

The geometry of the BNC heteronanotubes (BNC-HNT) was optimized with the DFTB method [137,138] with periodic boundary conditions along the z-axis. C-C and B-N bond lengths amount to 1.43 Å and 1.48 Å, respectively. The optimized helical BNC-HNT presented a wave-like profile along the axial direction resulting from the difference between bond lengths at the interfaces (see, e.g., [80,139,140]). Since the doping distribution can be introduced in different ways, the phonon transmission for random and horizontal distributions were averaged over five and three different atomic configurations, respectively. For the transport calculations, the baths are composed of twice the optimized supercell, and the central region includes only one supercell. To have a better understanding of the influence of doping on the transport properties, we introduce the quantity *RDOS* = *ηX*(*ω*)/*ηTotal*(*ω*), where *ηTotal*(*ω*) is the total DOS given by Equation (17), and *ηX*(*ω*) can be either the LDOS of C or BN domains.

**Figure 4.** (**a**) Atomistic view of BNC heteronanotubes with helical, horizontal, and random distribution of BN domains. Carbon atoms (cyan), boron atoms (pink), and nitrogen atoms (blue) are shown. (**b**) Variation of the phonon transmission function, *<sup>τ</sup>ph*, of helical BNC heteronanotubes after increasing the BN concentration, *c*. (**c**) Comparison of *<sup>τ</sup>p<sup>h</sup>* for different doping distribution patterns with *c* = 50%. Variation of *RDOS* for carbon domains as a function of the vibrational frequency (**d**) for helical BNC heteronanotubes at three different doping concentrations and (**e**) for helical, horizontal, and random BNC heteronanotubes at *c* = 50%. Reproduced from Ref. [120] with permission from the PCCP Owner Societies.

In Figure 4b, the influence of helical BN stripes on the phonon transmission of a (6,6)-CNT is shown. The high frequency modes ( *ω* > 1400 cm<sup>−</sup>1) are strongly affected by increasing the BN concentration. These modes correspond to local vibrations related to carbon atoms; this is seen in *RDOS* after increasing the doping concentration (see Figure 4d). On the contrary, the transmission of low-frequency vibrations below 200 cm<sup>−</sup><sup>1</sup> is not changed much when varying the disorder concentration. Figure 4c shows the phonon transmission of BNC-HNT with fixed concentration *c* = 50% and different BN spatial arrangements. As expected, a random distribution of B and N atoms blocks the transmission over almost the whole frequency spectrum; only low-frequency modes experience less scattering at the localized impurities, so that their transmission is much less affected. Helical and horizontal disorder in BNC-HNT leads to a stronger blocking of the transmission at high frequencies ( *ω* > 1400 cm<sup>−</sup>1) due to the absence of B-N-C local vibrations in that range (see Figure 4e).

Figure 5 shows the concentration dependence of the phonon thermal conductances, *<sup>κ</sup>ph*, for each doping distribution pattern at *T* = 300 K. Horizontal BNC-HNT shows the highest thermal conductance, while the lowest *<sup>κ</sup>p<sup>h</sup>* is obtained for (6,6)-CNT with BN domains randomly distributed. The thermal conductance of helical BNC-HNT remains nearly constant ( ∼2.5 nW/K) for concentrations between 30% and 80%, and then increases until it reaches the value corresponding to a pristine BNNT, ∼3.0 nW/K. An additional case was studied with a helical BNC-HNT connected to CNT leads and, as a consequence of the new contact-device interface, the thermal conductance is continuously suppressed with increasing concentration. Notice that the dominant contribution to the thermal conductance at 300 K mostly derives from long wavelength modes with frequencies ≤ 200 cm<sup>−</sup><sup>1</sup> [120].

**Figure 5.** Phonon thermal conductance as a function of the BN concentration for helical, horizontal, and random pattern distributions. Results for helical BNC heteronanotubes connected to two CNT leads are also shown. Reproduced from Ref. [120] with permission from the PCCP Owner Societies.
