From thermal conductive to thermal insulating: Effect of carbon vacancy content on lattice thermal conductivity of ZrCx

doi:10.1016/j.jmst.2020.11.068

Abstract

Abstract:

Lattice thermal conductivities of zirconium carbide (ZrC_x, x = 1, 0.75 and 0.5) ceramics with different carbon vacancy concentrations were calculated using a combination of first-principles calculations and the Debye-Callaway model. The Grüneisen parameters, Debye temperatures, and phonon group velocities were deduced from phonon dispersions of ZrC_x determined using first-principles calculations. In addition, the effects of average atomic mass, grain size, average atomic volume and Zr isotopes on the lattice thermal conductivities of ZrC_x were analyzed using phonon scattering models. The lattice thermal conductivity decreased as temperature increased for ZrC, ZrC_0.75 and ZrC_0.5 (Zr₂C), and decreased as carbon vacancy concentration increased. Intriguingly, ZrC_x can be tailored from a thermal conducting material for ZrC with high lattice thermal conductivity to a thermal insulating material for ZrC_0.5 with low lattice thermal conductivity. Thus, it opens a window to tune the thermal properties of ZrC_x by controlling the carbon vacancy content.

Key words: Zirconium carbide, Lattice thermal conductivity, Theoretical study, First-principle calculations

Yue Zhou, William G. Fahrenholtz, Joseph Graham, Gregory E. Hilmas. From thermal conductive to thermal insulating: Effect of carbon vacancy content on lattice thermal conductivity of ZrC_x[J]. J. Mater. Sci. Technol., 2021, 82: 105-113.

Figures/Tables 11

Fig. 1. Thermal conductivities of zirconium carbide measured in previous studies [[15], [16], [17], [18], [19]].

Table 1 Densification methods and sample characteristics of ZrCx from previous studies sorted by highest to lowest thermal conductivity.

Ref.	Densification method	Composition	Relative density	Average grain size	Impurity Content	Thermal conductivity (W m^-1 K^-1)
[13]	HP	ZrC_0.98	95%	50 μm	<0.2 wt.%	32.2, 600 ℃
[16]	HP	ZrC_0.98	95%	50 μm	<0.2 wt.%	38.5, 1300 ℃
[15]	SPS	ZrC	93.3 %	∼10 μm	N/A	31.3, 200 ℃
[17]	HP	ZrC	91.5 %	N/A	>0.165 wt.%	26.7, 1325 ℃
[14]	HP	ZrC	91.9 %	3.7 μm	N/A	17.7, 300 ℃

Fig. 2. Crystal structures of (a) ZrC, (b) ZrC0.75 and (c) Zr2C (ZrC0.5).

Table 2 Calculated lattice parameters (a), elastic constants (c11, c44, c12), shear modulus (G), bulk modulus (B), elastic modulus (E), Poisson’s ratio (v), and microhardness (HV) of ZrC, ZrC0.75 and Zr2C (ZrC0.5) in the present and (previously reported) calculations.

Composition	Lattice constant a (Å)	c₁₁ (Gpa)	c₄₄ (GPa)	c₁₂ (GPa)	G (GPa)	B (GPa)	E (GPa)	v	H_V (GPa)
ZrC	4.706, (4.705) [63]	451.6, (451.6) [63]	155.4, (155.3) [63]	106.9, (106.9) [63]	162.2, (162.1) [63]	221.8, (221.8) [63]	391.2, (390.7) [63]	0.21, (0.206) [61]	24.2, (23.4) [22], (24.3) [22]
ZrC_0.75	4.692	369.2	108.9	98.4	119.5	188.6	295.9	0.24	16.2
Zr₂C (ZrC_0.5)	9.369 [22]	205.3	101.6	100.0	82.1, (71) [22]	135.1, (137) [22]	204.7	0.25	11.7, (8.4) [22], (10.8) [23]

Fig. 3. Phonon dispersion (a) and mode Grüneisen parameters (b) of ZrC.

Table 3 Grüneisen parameters, Debye temperatures, and group velocities of ZrC, ZrC0.75 and Zr2C (ZrC0.5) compared with a highly thermal conductive (ZrB2) [37] and thermal insulating rare-earth pyrochlores [64].

Composition	γTA1	γTA2	γLA	θTA1	θTA2	θLA	vTA1	vTA2	vLA
Composition	N/A			(K)			(km s^-1)
ZrC	1.79	1.51	1.65	340	340	467	4.2	4.2	8.0
ZrC_0.75	0.92	1.28	1.52	242	242	242	2.4	2.4	3.2
Zr₂C	10.05	9.12	4.32	167	172	220	4.0	4.8	7.1
ZrB₂	1.50	1.22	1.43	380	355	422	6.5	6.5	9.2
Nd₂Zr₂O₇	6.23	10.10	2.75	138	138	260	3.13	3.13	5.91
Sm₂Zr₂O₇	7.40	11.98	2.81	137	137	256	3.09	3.09	5.78
Gd₂Zr₂O₇	7.19	11.57	2.75	137	137	252	3.06	3.06	5.63

Fig. 4. Phonon dispersion (a) and mode Grüneisen parameters (b) of ZrC0.75.

Fig. 5. Phonon dispersion (a) and mode Grüneisen parameters (b) of Zr2C (ZrC0.5).

Fig. 6. Lattice thermal conductivities of (a) ZrC, (b) ZrC0.75 and (c) Zr2C (ZrC0.5) based on theoretical prediction. (κUI: isotope effect; κUA: isotope and grain boundary effects; κN: isotope, grain boundary, U, and N effects.).

Fig. 7. Lattice thermal conductivities of (a) ZrC, (b) ZrC0.75 and (c) Zr2C (ZrC0.5) with different grain sizes.

Fig. 8. Isotopopically pure and natural abundance isotope lattice thermal conductivities of (a) ZrC, (b) ZrC0.75 and (c) Zr2C (ZrC0.5).

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