Pushing the limit of thermal conductivity of MAX borides and MABs

doi:10.1016/j.jmst.2021.05.006

Abstract

Abstract:

The emergence of MAX borides as well as MAB phases attracted great attention because of the renewable developments of ternary ceramics and offering great opportunities in potential applications. However, the number of borides remains limited, and further fundamental descriptions and detailed investigations on various properties are still lacking. In this report, we employ an integrated computational scheme that combines density functional theory with the evolutional algorithm to search for the favorable structures of P- and S-glued ternary borides terminated by Nb metal. We discover that the structures of 212-type, as e.g. Nb₂PB₂ and Nb₂SB₂, belong to the P6¯m2 space group, while those of 211-type, as e.g. Nb₂PB and Nb₂SB, prefer to crystallize in the P6₃/mmc space group, and the corresponding carbides Nb₂PC and Nb₂SC are also considered for the sake of completeness and comparative analsys. The predicted Nb₂PB₂, Nb₂PB, Nb₂SB, Nb₂PC and Nb₂SC are energetically stable, as revealed by the negative formation energies and by the proposed reaction paths with respect to the most competing phases, as well as dynamically stable, as suggested by the non-imaginary phonon spectra. The thermal conductivities of the six materials show unusual behaviors, particularly for the acoustic and optical contributions, and are accompanied by a strong anisotropy. Most importantly, Nb₂PB₂ is found to be an excellent thermal conductor with a total thermal conductivity of ~65 W/(m K), while Nb₂SC is found to be an ultra-low thermal conductor, with a total thermal conductivity of ~5 W/(m K). These values are clearly outside the currently reported range of thermal conductivities, which makes Nb₂PB₂ and Nb₂SC extremely interesting for fundamental research as well as prospective applications with the aid of artificial tunings on the almost independent MB block and the A layer. The discovery of these novel materials is expected to contribute substantially to the rapid development of ternary ceramics and to accelerate attempts in the applicability of MAX phases for heat conduction.

Key words: MAX and MAB phases, Density functional theory calculation, Structure searching, Thermal conductivity

Shaohan Li, Weiwei Sun, Yi Luo, Jin Yu, Litao Sun, Bao-Tian Wang, Ji-Xuan Liu, Guo-Jun Zhang, Igor Di Marco. Pushing the limit of thermal conductivity of MAX borides and MABs[J]. J. Mater. Sci. Technol., 2022, 97: 79-88.

Figures/Tables 6

Fig. 1. The energetics of the predicted structures of (a) Nb2PB2, (b) Nb2PB, (c) Nb2SB2, and (d) Nb2SB explored during the eight generations of the evolutionary process in USPEX. Crystal structures for the stable (e) Nb2AB2 and (f) Nb2AB structures from the side view (left) and top view (right) are characterized, where the blue, green and pink spheres represent for Nb, B and P/S atoms respectively. The unit cell is marked by the black dashed line. The angles with respect to Nb-A-A, B-Nb-B are marked by θ, η. The angle between B-B bond ζ is only characterized in Nb2AB2, as the B-B bond in Nb2AB cannot be formed (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Table 1 The calculated in-plane and out-of-plane lattice parameters a and c in Å, the formation energy ${{E}_{\text{form}}}$ in eV/f.u., and the reaction energy ΔEcomp with respect to the most competing phases in eV/f.u. of Nb2PB2, Nb2PB, Nb2SB2, Nb2SB, Nb2PC and Nb2SC.

Borides	a	c	E_form	ΔE_comp (The most competing phases)
Nb₂PB₂	3.21	6.68	-4.189	-1.290 (NbB₂, NbP)
Nb₂PB	3.35	11.76	-6.741	-0.972 (NbB, NbP)
Nb₂SB₂	3.22	6.69	-3.924	0.373 (Nb₂B₃, Nb₃B₄, Nb₃S₅)
Nb₂SB	3.38	11.65	-6.951	0.016 (NbB, Nb₃B₂, Nb₃S₄)
Nb₂PC	3.31	11.65	-3.051	-1.231 (Nb₆C₅, NbP, C)
Nb₂SC	3.32	11.72	-3.054	0.096 (Nb₂C, Nb₆C₅, Nb₃S₄)

Fig. 2. The phonon dispersion spectra (PDS) and the partial phonon density of states (PHDOS) are shown for (a) Nb2PB2, (b) Nb2PB, (c) Nb2SB2, (d) Nb2SB, (e) Nb2PC and (f) Nb2SC. Three acoustic modes (black) and optical band 4 (orange), 5 (violet), 6 (pink) are emphasized with bold lines. The partial PHDOS of Nb, X (B, C), A (P, S) are colored in red, cyan and blue respectively (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 3. Band structure (left panels) and Fermi surface (right panels) of (a) Nb2PB2, (b) Nb2PB, (c) Nb2SB2, (d) Nb2SB, (e) Nb2PC and (f) Nb2SC. The Fermi energy (EF) is set at 0 eV and visualized by a dotted line. The bands crossing the EF are highlighted and numbered by #17, #18 for Nb2PB2, #30, #31, #32 for Nb2PB, #17, #18, #19 for Nb2SB2, #30, #31, #32, #33 for Nb2SB, #30, #31, #32, #33 for Nb2PC, and #31, #32, #33, #34 for Nb2SC.

Table 2 $\;{{\kappa }_{\text{tot}}}$, ${{\kappa }_{\text{lat}}}$ and κele (W/(m K)) as well as the ratio of ${{\kappa }_{\text{ele}}}$over ${{\kappa }_{\text{lat}}}$ of the calculated materials, at RT.

MAX	A = P				A = S
MAX	${{\kappa }_{\text{tot}}}$	${{\kappa }_{\text{lat}}}$	${{\kappa }_{\text{ele}}}$	${{\kappa }_{\text{ele}}}$/${{\kappa }_{\text{lat}}}$	$\;{{\kappa }_{\text{tot}}}$	${{\kappa }_{\text{lat}}}$	${{\kappa }_{\text{ele}}}$	${{\kappa }_{\text{ele}}}$/${{\kappa }_{\text{lat}}}$
Nb₂AB₂	65.66	46.23	19.43	0.42	21.45	9.50	11.95	1.25
Nb₂AB	53.09	47.73	5.36	0.11	24.04	18.20	5.85	0.32
Nb₂AC	26.04	21.23	4.81	0.23	5.44	3.28	2.16	0.65

Fig. 4. Accumulated lattice thermal conductivity ${{\kappa }_{\text{lat}}}$ as a function of frequency at RT for (a) Nb2PB2, (b) Nb2PB, (c) Nb2SB2, (d) Nb2SB, (e) Nb2PC and (f) Nb2SC. ${{\kappa }_{\text{lat}}}$ along in- and out-of-plane directions are labeled by circle and triangle uniformly. The contribution from the overall acoustic modes and optical modes are distinguished with yellow and gray areas. The total contribution from the acoustic modes is indicated in percentage value. |${{\nu }_{i}}$| as a function of the wave vector for (g) Nb2PB2, (h) Nb2PB, (i) Nb2SB2, and (j) Nb2SB, (k) Nb2PC and (l) Nb2SC, including acoustic modes, and optical modes from bands 4, 5, 6. ${{\tau }_{i}}$ along the K-Γ path (in-plane) and Γ-A path (out-of-plane) at RT for (m) Nb2PB2, (n) Nb2PB, (o) Nb2SB2, (p) Nb2SB, (q) Nb2PC and (r) Nb2SC. The accumulation of acoustic modes is represented by black points, and the optical modes at bands 4-6 are symbolized as above. Temperature dependent $\kappa $ deduced from Slack's equation (diamond) as well as κmin from Clarke's model (dashed line) compared to DFT results: (s) Nb2PB2, (t) Nb2PB, (u) Nb2SB2, (v) Nb2SB, (w) Nb2PC and (x) Nb2SC. ${{\kappa }_{\text{tot}}}$ and ${{\kappa }_{\text{lat}}}$ from DFT are depicted with unfilled and hollow circles (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

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