Thermal diffusivity, conductivity and expansion of

Yb3xY3(12x)Al5O12 (x ¼ 0:05; 0.1 and 0.25) single crystals

Xiaodong Xu*, Zhiwei Zhao, Jun Xu, Peizhen Deng

Crystal Center, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800,

People’s Republic of China

Received 8 February 2004; accepted 4 March 2004 by P. Wachter

Abstract

Yb:YAG single crystals were grown by the Czochralski method. Thermal properties like thermal diffusivity, conductivity

and expansion of various Yb3þ concentration are studied from 50 to 500 8C. The effects of temperature and Yb3þ concentration

on the thermal properties of Yb:YAG crystals are discussed. The deterioration of thermal properties of highly doped Yb:YAG is

possibly due to the structural distortion caused by the Yb3þ ions.

q 2004 Elsevier Ltd. All rights reserved.

PACS: 42.70.Hj; 67.80.Gb

Keywords: B. Crystal growth; D. Heat capacity; D. Heat conduction; D. Thermal expansion

1. Introduction

Yttrium aluminum garnet (YAG) is an excellent host

material and possesses many qualities that are desirable for

high-average-power laser applications because of its high

thermal conductivity and excellent physical and chemical

properties [1–4]. As a rare-earth ion with the simplest

energy-level construction, Yb3þ has some important

advantages, such as few quantum defects (8.6%) between

the pump and the laser photons, which result in low thermal

loading (fractional heating of less than 11%); a long

radiative lifetime of the upper laser level (1.3 ms); and no

excited-state absorption or upconversion loss compared

with other rare-earth ions [5–7]. Because of its strong and

broad absorption band near 941 nm, which is matched by

the emission wavelength of InGaAs laser diodes Yb3þ-

doped YAG used as gain for high efficiency, high power

diode-pumped solid-state lasers has attracted great attention

following the development of highly efficient InGaAs laser

diodes [8]. Previously, pulsed, cw, Q-switched, passively

model-locked femtosecond and multiwatt laser action was

achieved in laser-diode-pumped Yb:YAG systems. The

highest cw output power was 2.65 kW, with an optical-to-

optical efficiency of 28% in a sidepumped rod Yb:YAG

scheme [9].

The thermal diffusivity, conductivity and expansion are

three important parameters for the assessment of a laser

crystal. Knowledge of the thermal properties of Yb:YAG

crystals with different concentration at different temperature

is essential to selection of the proper material for the use in

laser systems. In this paper we report experimental

measurements of the thermal properties for several Yb3þ

concentration of Yb:YAG over a temperature range from 50

to 500 8C. The effect of Yb3þ concentration and temperature

on these parameters is discussed.

2. Experiments

Yb:YAG crystals with dopant concentration of 5, 10, and

25 at.% Yb3þ were grown by the Czochralski method. The

99.999%-pure raw materials were appropriately predried

and weighed according to a specific molar ratio. After the

compounds were ground and mixed, they were pressed into

0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ssc.2004.03.007

Solid State Communications 130 (2004) 529–532

www.elsevier.com/locate/ssc

* Corresponding author. Tel.: þ86-21-699-18482; fax: þ86-21-

599-28755.

E-mail address: zzw8006@sina.com.cn (Z. Zhao).

pieces and put into an aluminum crucible. The pieces were

heated to 1350 8C for 24 h. The charge was then loaded into

an iridium crucible for crystal growth. During the growth the

pulling rate was 1 mm/h, the rotation rate was 10–20 rpm,

and the growth atmosphere was nitrogen. The initial growth

boundary in solid melt was convex toward the melt, so

dislocations and impurities were reduced or eliminated from

the crystal. After that, the growth boundary became flat. To

prevent the crystal from cracking, we cooled it slowly to

room temperature after growth. All crystals had a blue–

green coloration, which could be removed by annealing of

the samples in air at 1600 8C for 36 h.

The samples for thermal measurements were cut form

the air-annealed crystals. Thermal diffusivity was measured

by pulsed laser technique with a Xe lamp pumped Nd:Glass

laser, The sample dimensions were F 10.3 £ 2 mm3. The

specific heat was measured by the method of differential

scanning calorimeter (DSC) equipment (Model

DSC404/6/F). We used a thermal-expansion analyzer

(Model DIL 402PC) to measure the thermal expansion of

the Yb:YAG crystals. The samples for thermal-expansion

measurement were oriented wafers and their dimensions

were 50 mm £ 5 mm £ 5 mm. We measured the densities of

these crystals by using a drainage method.

3. Results and discussion

The variations in temperature of the thermal diffusivity

of Yb:YAG crystals are reported in Fig. 1. The thermal

diffusivity decreases as the temperature increases, and its

reduction occurs more slowly at high temperature. The

thermal diffusivity for 5 at.% Yb:YAG at 50 8C is

1.72 £ 1026 m2/s, and it is reduced as much as 38% to

1.06 £ 1026 m2/s at 500 8C. From Fig. 1 we can also see the

apparent influence of the Yb3þ doping concentration on the

thermal diffusivity. The thermal diffusivity decreases with

increasing Yb3þ concentration, and values of thermal

diffusivity at 50 8C are 1.72 £ 1026, 1.62 £ 1026, and

1.54 £ 1026 m2/s for single crystals with doping level 5,

10, and 25 at.%, respectively.

Fig. 2 presents the dependence of the specific heat of

Yb:YAG crystals on the temperature. From the figure we

can see that the specific heat increases as the temperature

increases in the measuring range. The Yb3þ doping

concentration leads to a change of specific heat within the

experiment temperature. The specific heat of Yb:YAG

crystal decreases with the increase of Yb3þ concentration in

the range from 50 to 300 8C. When the temperature exceeds

300 8C, the specific heat of highly doped Yb:YAG crystal is

higher than that of Yb:YAG crystal with low doping level; at

the same time, the specific heat of highly doped Yb:YAG

crystal increases more quickly than that of Yb:YAG crystal

with low doping level in the measuring range temperature

from 50 to 500 8C. The results show that the variety of

temperature has great influence on highly doped Yb:YAG

crystals.

The thermal conductivity was calculated according to:

K ¼ arCp ð1Þ

where a is the thermal diffusivity, r is the density and Cp is

the specific heat capacity. Fig. 3 shows the density of

Yb:YAG crystals as a function of Yb3þ concentration. The

density increases with the increase of Yb3þ concentration,

and the density is a linear function of Yb3þ concentration.

The thermal conductivity of Yb:YAG crystals at different

temperature calculated using Eq. (1) are displayed in Fig. 4,

and we can see the apparent influence of Yb3þ doping

concentration on the thermal conductivity. At 50 8C while

the doping concentration of Yb3þ ions increases from 5 to

25 at.%, the thermal conductivity decreases by as much as

11%, from 5.23 to 4.64 W/m k. From Fig. 4, we can also see

that with the increase of temperature thermal conductivity

decreases. In Yb:YAG crystals, the main mechanism of heat

Fig. 1. Thermal diffusivity of Yb:YAG crystals as a function of

temperature for several Yb3þ doping concentrations.

Fig. 2. Specific heat of Yb:YAG crystals as a function of

temperature for several Yb3þ doping concentrations.

X. Xu et al. / Solid State Communications 130 (2004) 529–532530

transfer is the heat transfer by phonon. Yb3þ doping into

YAG crystals inevitably induces structural distortion in

crystals. The defects in crystals remarkably reduce phonon

mean free path and the thermal conductivity decreases as

Yb3þ doping concentration increases. The deterioration of

thermal properties of highly doped Yb:YAG will more

easily lead to thermooptic aberrations, lensing and birefrin-

gence. Therefore, in order to acquire high-beam quality and

stable laser output from highly doped Yb:YAG media,

efficient cooling system must be adopted.

For an isotropic cubical crystal Yb:YAG, there is only

one independent principal thermal expansion component. It

can be obtained by measurement of the thermal expansion of

the k111l oriented samples. The experimental data we got

were the thermal expansion length with the increase of

temperature from room temperature. Fig. 5 shows the linear

thermal expansion coefficients calculated from room

temperature to several other temperatures. The coefficients

increase more quickly before 300 8C, whereas they change

slowly at the range from 300 to 500 8C, which causes the

crystals to crack more easily at low temperature when the

crystals are cooled to room temperature after growth. From

Fig. 5, we can also see that the apparent influence of the

Yb3þ doping concentration on the thermal expansion. The

thermal expansion coefficient of Yb:YAG increases with the

increase of Yb3þ concentration, and the coefficients from

room temperature to 500 8C are 8.06 £ 1026, 8.18 £ 1026

and 8.31 £ 1026 K21 for single crystals with doping level 5,

10 and 25 at.%. This increase is possibly due to the

structural distortion caused by the Yb3þ ions.

4. Conclusion

Yb3xY3(12x)Al5O12 (x ¼ 0:05; 0.1 and 0.25) single

crystals were grown by the Czochralski method. Thermal

diffusivity, thermal conductivity and thermal expansion of

various Yb3þ concentration are studied from 50 to 500 8C.

Thermal diffusivity and thermal conductivity decrease with

the increase of temperature and Yb3þ doping concentration,

and thermal expansion coefficient increases with the

increase of temperature and Yb3þ doping concentration.

The deterioration of thermal properties of highly doped

Yb:YAG is possibly due to the structural distortion caused

by the Yb3þ ions.

Acknowledgements

This work is supported by the High Technology and

Development Project of the People’s Republic of China

(Grant No. 2002AA311030)

Fig. 3. Density of Yb:YAG crystals as a function of Yb3þ

concentration.

Fig. 4. Thermal conductivity of Yb:YAG crystals as a function of

temperature for several Yb3þ doping concentrations.

Fig. 5. Thermal expansion coefficient of Yb:YAG crystals as a

function of temperature for several Yb3þ doping concentrations.

X. Xu et al. / Solid State Communications 130 (2004) 529–532 531

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