Table 1 Model parameters in Supplementary Eq. (S14) obtained by two fitting procedures (with and without resonant scattering in Callaway’s formula), for the thermal conductivity of anatase single-crystals

From: Tailoring thermal conduction in anatase TiO2

 

a C

a R

a U

θ D

T U

a p

ω 1

ω 2

α

TiO2

(106 s−1)

(s3)

(104 K−1s)

(K)

(K)

(108 s−1)

(K)

(K)

 

Black

11,400

616

5.01

1000

600

–

–

–

–

Brown

502

616

5.01

1000

600

–

–

–

–

Blackr

4.56

228

2.29

900

170

39.8

89.7

191

2.76

Brownr

4.56

228

2.29

900

170

3.63

89.7

191

2.76

Transp.

4.56

228

2.29

900

170

0

–

–

–

  1. aC, aR and aU are the parameters related to Casimir, Rayleigh and Umklapp scattering respectively, with TU a temperature characteristic of Umklapp processes. ΘD is the Debye temperature; ω1 and ω2 are two resonant frequencies and α an adjustment factor to account for the influence of ω1 with respect to ω2. When the resonant scattering is included (superscript r), only ap, the parameter proportional to the concentration of defects Nd, varies between the single crystals with different amount of oxygen vacancies.
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