Abstract

Three crystals used in solid-state lasers, namely, yttrium aluminum garnet (YAG), yttrium orthovanadate (YVO4), and gadolinium calcium oxoborate (GdCOB), were investigated to determine the influence of dopants on their thermal diffusivity. The thermal diffusivity was measured by thermal wave method with a signal detection based on mirage effect. The YAG crystals were doped with Yb or V, the YVO4 with Nd or Ca and Tm, and the GdCOB crystals contained Nd or Yb. In all cases, the doping caused a decrease in thermal diffusivity. The analysis of complementary measurements of ultrasound velocity changes caused by dopants leads to the conclusion that impurities create phonon scattering centers. This additional scattering reduces the phonon mean free path and accordingly results in the decrease of the thermal diffusivity of the crystal. The influence of doping on lattice parameters was investigated, additionally.

© 2008 Optical Society of America

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    [CrossRef]
  3. G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).
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    [CrossRef]
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2008

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

2006

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

2005

J. Kucytowski and K. Wokulska, “Lattice parameter measurements of boron-doped Si single crystals,” Cryst. Res. Technol . 40, 424-428 (2005).
[CrossRef]

2004

X. Xu, Z. Zhao, P. Song, J. Xu, and P. Deng, “Growth of high-quality single crystals of 50 at. % Yb:YAG and its spectral properties,” J. Alloys Compd. 364, 311-314 (2004).
[CrossRef]

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12(x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529-532 (2004).
[CrossRef]

2002

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

2001

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

1999

1998

F. Mougel, A. Kahn-Harari, G. Aka, and D. Pelenc, “Structural and thermal stability of Czochralski grown GdCOB oxoborate single crystals,” J. Mater. Chem. 8, 1619-1623 (1998).
[CrossRef]

1997

1992

W. F. Banholzer and T. R. Anthony, “Diamond properties as a function of isotopic compositions”, Thin Solid Films 212, 1-10 (1992).
[CrossRef]

1976

R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,”Acta Cryst. A 32, 751-767 (1976).
[CrossRef]

1964

J. E. Geusic, H. M. Marcos, and L. G. Van Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets,” Appl. Phys. Lett. 4, 182-184(1964).
[CrossRef]

1960

W. L. Bond, “Precision lattice constant determination,“ Acta Cryst. 13, 814-818 (1960).
[CrossRef]

Aka, G.

Anthony, T. R.

W. F. Banholzer and T. R. Anthony, “Diamond properties as a function of isotopic compositions”, Thin Solid Films 212, 1-10 (1992).
[CrossRef]

Balembois, F.

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

Banholzer, W. F.

W. F. Banholzer and T. R. Anthony, “Diamond properties as a function of isotopic compositions”, Thin Solid Films 212, 1-10 (1992).
[CrossRef]

Bodzenta, J.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

Bond, W. L.

W. L. Bond, “Precision lattice constant determination,“ Acta Cryst. 13, 814-818 (1960).
[CrossRef]

Ch. Wang,

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Chen, W.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

Chenais, S.

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

Chow, Y. T.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Colin, P.

Coquelin, P.

Damlet, J. P.

Dardenne, K.

Deng, P.

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12(x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529-532 (2004).
[CrossRef]

X. Xu, Z. Zhao, P. Song, J. Xu, and P. Deng, “Growth of high-quality single crystals of 50 at. % Yb:YAG and its spectral properties,” J. Alloys Compd. 364, 311-314 (2004).
[CrossRef]

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

Dong, J.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

Duron, F.

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

Equall, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Forget, S.

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

Georges, P.

S. Chenais, F. Duron, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: The case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89-153(2006).
[CrossRef]

Geusic, J. E.

J. E. Geusic, H. M. Marcos, and L. G. Van Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets,” Appl. Phys. Lett. 4, 182-184(1964).
[CrossRef]

Graf, M.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Harder, C.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Hofman, B.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

Honea, E. C.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Hu, X.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Huber, G.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Hutcheson, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Jiang, H.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Kahn-Harari, A.

Kazmierczak-Balata, A.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

Keller, U.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Kucytowski, J.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

J. Kucytowski and K. Wokulska, “Lattice parameter measurements of boron-doped Si single crystals,” Cryst. Res. Technol . 40, 424-428 (2005).
[CrossRef]

Kullberg, M. P.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Liu, J.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Lukasiewicz, T.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

Marcos, H. M.

J. E. Geusic, H. M. Marcos, and L. G. Van Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets,” Appl. Phys. Lett. 4, 182-184(1964).
[CrossRef]

Meng, X.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Mix, E.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Moguel, F.

Moser, M.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Mougel, F.

F. Mougel, K. Dardenne, G. Aka, A. Kahn-Harari, and D. Vivien, “Ytterbium-doped Ca4GdO(BO3)3: an efficient infrared laser and self-frequency doubling crystal,” J. Opt. Soc. Am. B 16, 164-172 (1999).
[CrossRef]

F. Mougel, A. Kahn-Harari, G. Aka, and D. Pelenc, “Structural and thermal stability of Czochralski grown GdCOB oxoborate single crystals,” J. Mater. Chem. 8, 1619-1623 (1998).
[CrossRef]

Paschotta, R.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Patel, F. D.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Payne, S. A.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Pelenc, D.

Qiu, H.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

Rao, S. Srinivas

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

Ravinder, D.

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

Reddy, B. Ravinder

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

Reddy, D. Linga

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

Salin, F.

Sato, Y.

Shannon, R. D.

R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,”Acta Cryst. A 32, 751-767 (1976).
[CrossRef]

Shao, Z.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Shekhar Reddy, A. Chandra

S. Srinivas Rao, A. Chandra Shekhar Reddy, D. Ravinder, B. Ravinder Reddy, and D. Linga Reddy, “Ultrasonic investigation on mixed manganese-zinc ferrite,” Mater. Lett. 56, 175-177 (2002).
[CrossRef]

Song, P.

X. Xu, Z. Zhao, P. Song, J. Xu, and P. Deng, “Growth of high-quality single crystals of 50 at. % Yb:YAG and its spectral properties,” J. Alloys Compd. 364, 311-314 (2004).
[CrossRef]

Speth, J.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and material properties of highly doped Yb:YAG”, IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Spühler, G. J.

G. J. Spühler, R. Paschotta, M. P. Kullberg, M. Graf, M. Moser, E. Mix, G. Huber, C. Harder, and U. Keller, “A passively Q-switched Yb:YAG microchip laser,” Appl. Phys. B 72, 285-287 (2001).

Szperlich, P.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

Taira, T.

Van Uitert, L. G.

J. E. Geusic, H. M. Marcos, and L. G. Van Uitert, “Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets,” Appl. Phys. Lett. 4, 182-184(1964).
[CrossRef]

Vivien, D.

Wang, J.

H. Zhang, J. Liu, J. Wang, Ch. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, Y. T. Chow, and H. Jiang, “Laser properties of different Nd-doped concentration Nd:YVO4 laser crystals,” Opt. Lasers Eng. 38, 527-536 (2002).
[CrossRef]

Wokulska, K.

J. Bodzenta, A. Kaźmierczak-Bałata, K. Wokulska, J. Kucytowski, P. Szperlich, T. Łukasiewicz, and B. Hofman, “Analysis of influence of Yb concentration on thermal, elastic, optical and lattice parameters in YAG single crystal,” J. Alloys Compd. doi:10.1016/j.jallcom.2008.05.041 (2008), .
[CrossRef]

J. Kucytowski and K. Wokulska, “Lattice parameter measurements of boron-doped Si single crystals,” Cryst. Res. Technol . 40, 424-428 (2005).
[CrossRef]

Xu, J.

X. Xu, Z. Zhao, P. Song, J. Xu, and P. Deng, “Growth of high-quality single crystals of 50 at. % Yb:YAG and its spectral properties,” J. Alloys Compd. 364, 311-314 (2004).
[CrossRef]

X. Xu, Z. Zhao, J. Xu, and P. Deng, “Thermal diffusivity, conductivity and expansion of Yb3xY3(1−x)Al5O12(x=0.05, 0.1 and 0.25) single crystals,” Solid State Commun. 130, 529-532 (2004).
[CrossRef]

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1-7 (2002).
[CrossRef]

Xu, X.

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Figures (12)

Fig. 1
Fig. 1

Geometry of the thermal wave measurement.

Fig. 2
Fig. 2

Phase of the thermal wave as the function of the distance from heated and cooled sample surface. Measurement was carried out for pure YVO 4 single crystal (sample #9) in the [100] direction at 0.4 Hz . Experimental points are fitted with the straight line.

Fig. 3
Fig. 3

Time of arrival of consecutive echoes determined in pulse-echo method for pure YVO 4 single crystal (sample #9) in the [100] direction. Experimental points are fitted with the straight line.

Fig. 4
Fig. 4

Thermal diffusivity of pure and doped YAG single crystals.

Fig. 5
Fig. 5

Longitudinal sound velocity in pure and doped YAG single crystals.

Fig. 6
Fig. 6

Lattice parameter of pure and doped YAG single crystals.

Fig. 7
Fig. 7

Thermal diffusivity of pure and doped YVO 4 single crystals measured in directions c and c .

Fig. 8
Fig. 8

Fig. 8. Longitudinal sound velocity in pure and doped YVO 4 single crystals measured in directions c and c .

Fig. 9
Fig. 9

Changes in lattice parameters of YVO 4 single crystals caused by doping. The lattice parameters of pure crystal are a = 7.120390 ( 9 ) Å and c = 6.290196 ( 9 ) Å .

Fig. 10
Fig. 10

Thermal diffusivity of pure and doped GdCOB single crystals measured in directions X, Y, and Z of the axes of the optical indicatrix.

Fig. 11
Fig. 11

Longitudinal sound velocity in pure and doped GdCOB single crystals measured in directions X, Y, and Z of the axes of the optical indicatrix

Fig. 12
Fig. 12

Changes in lattice parameters of GdCOB single crystals caused by doping. The lattice parameters of pure crystal are a = 8.102251 ( 31 ) Å , b = 16.01833 ( 28 )     Å , c = 3.561736 ( 24 ) Å .

Tables (4)

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Table 1 Basic Information About the Samples

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Table 2 Thermal Diffusivity α, Thermal Conductivity κ, Longitudinal Ultrasound Velocity v, and Lattice Parameter a of Pure and Doped YAG Single Crystals

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Table 3 Thermal Diffusivity α, Thermal Conductivity κ, Longitudinal Ultrasound Velocity v in the Directions c and c , and Lattice Parameters a and c of Pure and Doped YVO 4 Single Crystals

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Table 4 Thermal Diffusivity α, Thermal Conductivity κ, Longitudinal Ultrasound Velocity v in the Directions of the X, Y, and Z Axes of the Optical Indicatrix, and the Lattice Parameters a, b, andc of Pure and Doped GdCOB Single Crystals

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

κ i j = | κ 0 0 0 κ 0 0 0 κ | .
κ ij = | κ 11 0 0 0 κ 11 0 0 0 κ 33 | ,
κ ij = | κ 11 0 κ 13 0 κ 22 0 κ 13 0 κ 33 | .
κ ij = | κ 11 0 0 0 κ 22 0 0 0 κ 33 | = | κ X 0 0 0 κ Y 0 0 0 κ Z | .
κ ij = ρ c α ij ,
Δ T ( x , t ) = Δ T 0 exp ( π f α x ) cos ( 2 π f t π f α x + φ 0 ) ,
Δ φ ( x ) = π f α x + φ 0 .
t n = ( 2 n 1 ) d v ,
κ = 1 3 C u λ ,
α = 1 3 u λ .

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