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The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method

Yoichi Sato and Takunori Taira

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Abstract

We have measured thermal conductivity of GdVO4, YVO4, and Y3Al5O12. In order to avoid the miss leading from three-dimensional (3D) thermal diffusion, we developed the quasi-one-dimensional (q1D) flash method. By taking in account the heat radiation effect in transparent materials for this measurement, YVO4 was found to have larger thermal conductivity than GdVO4. The measured thermal conductivities were 12.1, 10.5, 10.1, 8.9, and 8.5 W/mK for c-cut YVO4, c-cut GdVO4, YAG, a-cut YVO4, and a-cut GdVO4, respectively. The dependence of Nd-conductivity coefficient (dκ/dC Nd) for convenient evaluation of the doping effect in thermal conductivity is also discussed.

©2006 Optical Society of America

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Figures (9)
Fig. 1.
Fig. 1. Detected rise in temperature of YAG with 1-mm thickness under flash method. Blue line is measured temperature and red-line is the fitting by Cape-Lehman model in ref. 12 (a) and radiation model in ref. 14(b).

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Fig. 2.
Fig. 2. Sample preparation for flash method by coating. For heat loading and temperature detection, sample should be coated by ca. 10-μm carbon (a). By inserting the 280-nm Au-coating layer the leaked flash and infra-red radiation can be reduced (b).

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Fig. 3.
Fig. 3. Concept of q1D flash method. Temperature measured by heat radiation from the back surface of the sample in ideal case (a). There is anisotropic heat dissipation into the sample holder (b). When the aperture inserted, the heat radiation affected by 3D thermal diffusion cannot be contributed to detect temperature (c).

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Fig. 4.
Fig. 4. Dependence of aperture size on the measured thermal conductivity. Thermal conductivity was measured 5 times at each conditions of aperture at 25 °C.

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Fig. 5.
Fig. 5. Heat capacities of 1.0 at.% Nd3+-doped GdVO4, YVO4, and YAG fabricated by Scientific Materials, Shandong Newphotonics, and ITI Electro-Optics, respectively.

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Fig. 6.
Fig. 6. Dependence of thermal conductivity in a-cut GdVO4 (a) and c-cut GdVO4 (b) synthesized by different suppliers. The differences between suppliers are 1.3% (a) and 2.1% (b).

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Fig. 7.
Fig. 7. Dependence of thermal conductivity in a-cut YVO4 (a) and c-cut YVO4 (b) synthesized by different suppliers. The differences between suppliers are 2.7 % (a) and 1.2% (b).

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Fig. 8.
Fig. 8. The simultaneously evaluated thermal conductivity in YAG, a-cut GdVO4 and YVO4, and c-cut GdVO4 and YVO4.

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Fig. 9.
Fig. 9. Dependence of thermal conductivity in GdVO4, YVO4, and YAG on Nd3+-doping concentration. Solid-lines are the fitting by Eq. (3), and dotted lines are extrapolated line.

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Tables (2)

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Table 1. Problems of the measured thermal conductivity in transparent materials by the flash method.

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Table 2. Thermal conductivity of GdVO4, YVO4, and YAG at 25C°.

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Equations (6)

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ρ C p ∂ T ∂ t − κ ∂ 2 T ∂ x 2 = 0 ,
∂ T ( 0 , t ) ∂ x = 4 σεT ( 0,0 ) 3 λ T ( 0 , t ) + η 4 σεT ( 0.0 ) 3 λ [ T ( 0 , t ) − T ( d , t ) ] ,
∂ T ( d , t ) ∂ x = 4 σεT ( d , 0 ) 3 λ T ( d , t ) + η 4 σεT ( 0.0 ) 3 λ [ T ( d , t ) − T ( 0 , t ) ] ,
κ = 1 π a 0 2 k B v κ 0 δ Tan − 1 ( π a 0 δ κ 0 2 k B v ) ,
δ = ∑ i c i ( M i − M M ) 2 ,
V N = 4 π 3 ( a 0 2 ) 3 .

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