Anisotropic thermal properties of Yb:YCOB crystal influenced by doping concentrations

Qiannan Fang; Dazhi Lu; Haohai Yu; Huaijin Zhang; Jiyang Wang

doi:10.1364/OME.9.001501

1. Introduction

The Yb³⁺ ion doped YCa₄O(BO₃)₃ (Yb:YCOB) crystal, which possesses excellent optical and thermal properties [1–4], is a promising laser material. According to previous reports, the Yb³⁺ ion has a very simple energy level scheme, and the splitting of the ground state manifold (²F_7/2) is approximately 1000 cm⁻¹ [3]. This feature is desirable for efficient laser operation. In a recent study, a 17 W continuous-wave (CW) laser with a slope efficiency of 78% was achieved pumped by a laser diode based on a Y-cut Yb:YCOB crystal [5], and a CW output power of 101 W with a Z-cut Yb:YCOB thin disk crystal was achieved, having a slope efficiency of 53% [6]. The relatively long upper state level lifetime of Yb:YCOB (2.6 ms) [7] is suitable for energy storage in Q-switching, and the 5-ns pulsed lasers with an average pulse energy as high as 1.28 mJ and a repetition rate of 3.23 kHz were realized based on the X-cut Yb:YCOB crystal [5]. In addition, the Yb:YCOB crystal has a broad emission spectrum [1,3], which is beneficial for generating shorter pulses. The mode-locking laser of Yb:YCOB was reported with a pulse duration of 35 fs [8]. Furthermore, the non-centrosymmetric YCOB crystal exhibits excellent nonlinear properties [9]. Hence, this YCOB crystal doped with the Yb³⁺ ion possesses both laser and nonlinear optical properties, which is referred to as the self-frequency-doubling (SFD) crystal. Nowadays, the SFD green and yellow lasers using Yb:YCOB crystals were obtained, with the output power of 330 mW and 1.08 W, respectively [10,11]. Moreover, the Yb:YCOB crystal has a good chemical stability, high laser damage threshold, high quantum efficiency, and low excitation state absorption, which is more advantageous for the efficient laser output.

The thermal properties such as the thermal expansion, thermal diffusion, specific heat and thermal conductivity have a significant influence on both the crystal growth and the laser output efficiency [12,13]. If a crystal possesses a large anisotropic thermal expansion, low specific heat and low thermal conductivity, it may be cracked easily during its growth process. Meanwhile, this kind of crystal may also generate a large temperature gradient during the laser experiment, leading to the thermal lensing, that will degrade the output efficiency, reduce the resonator stability and even crack the crystal. Therefore, the thermal properties are vital parameters and should be evaluated carefully before applying for a particular crystal. What’s more, the thermal properties can be affected by the doping concentration of the rare earth ions [13,14]. For Yb³⁺ doped crystals, high doping concentration is required for efficient lasing since the relatively small absorption and emission cross-sections (about 10⁻²¹ cm²) [1,15,16]. However, the high doping concentration will induce the decreasing of the phonon free path and consequently a lower thermal conductivity [17,18]. It may also decrease the thermal fracture limit and increase the thermal focal lens [19], which will reduce the laser output power and efficiency. And a low doping concentration may bring down the ability to absorb the pump light. Meanwhile, different doping concentrations may affect the directions of the principal axes in the thermal frame [20]. It is therefore necessary to analyze the influence of the doping concentrations on the thermal properties, to ensure the orientations of principal axes of the thermal properties, and to achieve an efficient laser output.

Several studies were conducted on the thermal properties of the Yb:YCOB crystal [2,21,22], however, no report was found on the effect of the doping concentrations on the thermal properties of the Yb:YCOB crystals. In this study, the influence of the doping concentrations on the values along the principal axes in the thermal frame and the angles between the principal axes of the thermal frame and reference coordinate were evaluated in detail. It is concluded that the doping concentrations have a slight influence on the thermal properties. Consequently, the YCOB crystal can be doped with a high concentration to enhance its ability to absorb the pump light without severe thermal effects, thus improving the conversion efficiency in the laser process.

2. Analysis of the crystal structure and composition

The different doping concentration Yb:YCOB crystals used in the experimental measured were grown by the Czochralski method. To determine the lattice structure of different doping concentration crystals, the X-ray powder diffraction (XRD) was applied and the results revealed that the diffraction indices matched well with every diffraction peak marked on the standard diffraction card of YCOB (ICSD No. 50-0403). The unit cell parameters were then analyzed, and the results are presented in Table 1. It can be seen that the values of the cell parameters are similar to those in the previous report [9]. Moreover, the cell parameters slightly decrease as the doping concentration increases, given that the ionic radius of Yb³⁺ is slightly less than that of Y³⁺ [23]. The composition of the crystals was then measured using the X-ray fluorescence spectrometer (XRF), and the effective segregation coefficients (K_eff) were presented in Table 2. It can be seen that the K_eff values of the Yb³⁺, Y³⁺ and Ca²⁺ ions in Yb:YCOB crystals with different doping concentrations are close to 1, which indicates that the distribution of the elements is homogeneous and uniform during the crystal growth process. The analysis of the crystal structure and composition reveals that the Yb:YCOB crystals prepared for the measurement of the thermal properties exhibit good crystallization and homogeneity.

Table 1. Crystallographic data of the Yb_xY_1-xCa₄O (BO₃)₃ crystals (results of XRD analysis). Note: x represents the doping concentration

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Table 2. Effective segregation coefficients of Yb³⁺, Y³⁺ and Ca²⁺ ions in the Yb_xY_1-xCa₄O (BO₃)₃ crystals

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3. Thermal properties of the Yb:YCOB crystal

3.1 Symmetrical second-rank tensor measurement for the monoclinic crystal and the required crystal orientations for the measurement of thermal properties

For the Yb:YCOB crystal, which belongs to a monoclinic system with the space group Cm and point group m, the thermal expansion and thermal conductivity are symmetrical second-rank tensors with four independent components referred to conventional coordinates [24,25]. The principal values of the thermal expansion and conductivity in the thermal frame were calculated along five directions, and the relationship between the five directions was illustrated in Fig. 1. Here, it can be seen that the a and c axes are perpendicular to the c^# and a^# axes, respectively. The angle α between the a and a^# axes or the c and c^# axes is 11.19°, given that the angle between the a and c axes of Yb: YCOB crystal is 101.19° [26]. The orthogonal axes (X₁, X₂, X₃) are the reference axes. To obtain the four independent components in the thermal tensor matrix, the Yb: YCOB crystals were cut along the a, b, c, a^#, c^# orientations, respectively.

Fig. 1 The relationship of the crystal cutting directions for the measurement of the thermal properties.

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In the Yb:YCOB crystal with monoclinic system, the crystallographic b axis is one of the principal axes of the symmetric second-rank tensor $[T_{i j}]$ (i,j = 1, 2, 3). Thus, in the reference coordinate system (X₁, X₂, X₃), $[T_{i j}]$ can be represented as [27,28]:

[\begin{matrix} T_{11} & 0 & T_{31} \\ 0 & T_{22} & 0 \\ T_{31} & 0 & T_{33} \end{matrix}]

The diagonal components T₁₁, T₂₂ and T₃₃ can be measured directly along the a, b and c^# directions. The T₃₁ component can be calculated by means of the Mohr circle construction. In Fig. 1, a new coordinate system (X₁’, X₂, X₃’) was presented as the X₁ and X₃ axes rotated anticlockwise around the X₂ axis through an angle α, thus forming the X₁’ and X₃’ axes. The transformation matrix is expressed as follows [29]:

(\begin{matrix} \cos α & 0 & - \sin α \\ 0 & 1 & 0 \\ \sin α & 0 & \cos α \end{matrix})

For the new coordinate system (X₁’, X₂, X₃’), the symmetric second-rank tensor $[T_{i j}^{'}]$ (i,j = 1, 2, 3) can be presented as:

[\begin{matrix} T_{11}' & 0 & T_{31}' \\ 0 & T_{22} & 0 \\ T_{31}' & 0 & T_{33}' \end{matrix}]

The diagonal components T₁₁’, T₂₂ and T₃₃’ can be measured directly along the a^#, b and c directions. Moreover, according to the transformation law for second-rank tensors, the symmetric second-rank tensors $[T_{i j}^{'}]$ and $[T_{i j}]$ are related using the following equation [24]:

\begin{array}{l} [\begin{matrix} T_{11}' & 0 & T_{31}' \\ 0 & T_{22} & 0 \\ T_{31}' & 0 & T_{33}' \end{matrix}] = (\begin{matrix} \cos α & 0 & - \sin α \\ 0 & 1 & 0 \\ \sin α & 0 & \cos α \end{matrix}) \times [\begin{matrix} T_{11} & 0 & T_{31} \\ 0 & T_{22} & 0 \\ T_{31} & 0 & T_{33} \end{matrix}] \times (\begin{matrix} \cos α & 0 & \sin α \\ 0 & 1 & 0 \\ - \sin α & 0 & \cos α \end{matrix}) \\ = [\begin{matrix} (\begin{array}{l} T_{11} \cos^{2} α + T_{33} \sin^{2} α \\ - T_{31} \sin 2 α \end{array}) & 0 & [\begin{array}{l} (T_{11} - T_{33}) \sin 2 α / 2 \\ + T_{31} \cos 2 α \end{array}] \\ 0 & T_{22} & 0 \\ [\begin{array}{l} (T_{11} - T_{33}) \sin 2 α / 2 \\ + T_{31} \cos 2 α \end{array}] & 0 & (\begin{array}{l} T_{11} \sin^{2} α + T_{33} \cos^{2} α \\ + T_{31} \sin 2 α \end{array}) \end{matrix}] \end{array}

As a result, the following equations are obtained:

T_{11}^{'} = T_{11} \cos^{2} α + T_{33} \sin^{2} α - T_{31} \sin 2 α

T_{33}^{'} = T_{11} \sin^{2} α + T_{33} \cos^{2} α + T_{31} \sin 2 α

T_{31}^{'} = (T_{11} - T_{33}) \sin 2 α / 2 + T_{31} \cos 2 α

T_{31} = \frac{(T_{11} - T_{33}) \cos 2 α - (T_{11}^{'} - T_{33}^{'})}{2 \sin 2 α}

It can be seen that the T₃₁ component in the reference coordinate (X₁, X₂, X₃) can be calculated with Eqs. (5) and (6). It is therefore necessary to determine the orientation of the principal axes (X_I, X_II, X_III), and the values of the principal components of the symmetric second-rank tensor $[T_{i j}]$ can be represented as:

[\begin{matrix} T_{I} & 0 & 0 \\ 0 & T_{I I} & 0 \\ 0 & 0 & T_{I I I} \end{matrix}]

From a comparison of the symmetric second-rank tensors (3) and (9), it can be assumed that if T₃₁’ is equal to zero, the coordinate system (X₁’, X₂, X₃’) will become to the principal axes (X_I, X_II, X_III). The orientation angle of the principal axes (X_I, X_II, X_III) with respect to the reference axes (X₁, X₂, X₃) can be determined by setting the right-hand side of Eq. (7) equal to zero, which yields:

α = \frac{1}{2} arc \tan (\frac{2 T_{31}}{T_{33} - T_{11}})

The principal values T_I and T_III can be calculated based on Eq. (5) and (6), and the component T_II is equal to the value along b axis [24]. A positive number represents an anticlockwise rotation with respect to the b axis, and a negative number represents a clockwise rotation. In order to reduce the experimental error, we measured three samples at each temperature and orientation in the all thermal property tests, and then computed the average values to calculate the thermal property values along the principal axes. Besides, the least-squares method was used to correct the results [30]. Because there are four measured data in the ac plane, we introduce the following matrix:

Θ = (\begin{matrix} \sin^{2} θ_{1} & \sin 2 θ_{1} & \cos^{2} θ_{1} \\ \sin^{2} θ_{2} & \sin 2 θ_{2} & \cos^{2} θ_{2} \\ \sin^{2} θ_{3} & \sin 2 θ_{3} & \cos^{2} θ_{3} \\ \sin^{2} θ_{4} & \sin 2 θ_{4} & \cos^{2} θ_{4} \end{matrix})

where the angle θ_i (i = 1, 2, 3, 4) represents the angle rotation of these four measured c^#, a, c, a^# directions counterclockwise from c axis. Then the transformation matrix can be written as:

R = {(Θ_{T} Θ)}^{- 1} Θ_{T}

where Θ_T is the transpose of Θ. Then the revised components T₁₁, T₃₁ and T₃₃ can be obtained from the equation:

(\begin{matrix} T_{11} \\ T_{31} \\ T_{33} \end{matrix}) = R (\begin{matrix} c^{#} \\ a \\ c \\ a^{#} \end{matrix})

The revised values of T₁₁, T₃₁ and T₃₃ instead of the original measured elements to calculate the symmetric second-rank tensor with only minor errors.

3.2 Thermal expansion coefficient of Yb:YCOB crystal with different doping concentrations

The thermal expansion coefficient is a symmetric second-rank tensor and different orientations possess different values. Two cuboid crystal samples were therefore cut from the Yb:YCOB crystal with dimensions of 6 mm × 5 mm × 4 mm (a × c^# × b, and a^# × c × b, respectively). It is evident that the thermal expansion ratio is almost linear over the measured temperature range from 303.15 to 873.15 K [2,24]. The average linear thermal expansion coefficient for the a, c^#, b, a^# and c directions can be calculated according to the following formula:

\bar{α} (T_{0} \to T) = \frac{Δ L}{L_{0}} \frac{1}{Δ T}

where

\bar{α} (T_{0} \to T)

is the average linear thermal expansion coefficient from the temperature T₀ to T; T is the measured temperature; T₀ is the room temperature;

Δ T = T - T_{0}

is the change in temperature; L₀ is the sample length at the temperature T₀;

Δ L

is the change in sample length from T₀ to T. Based on the measured thermal expansion coefficients with the thermal mechanical analyzer (TMA) (Pyris Diamond, Perkin Elmer Inc.) in the directions of a, c^#, b, a^# and c axes, using Yb:YCOB crystals with different doping concentrations, and the revised values of T₁₁, T₃₁ and T₃₃, the thermal expansion coefficients along the principal axes at room temperature were calculated, as presented in Table 3. The symmetric second-rank tensor of the thermal expansion coefficients in the directions of the three principal axes, taking 5 at.% doped crystal for example, can be calculated as:

Table 3. Thermal expansion coefficients along the principal axes of the Yb_xY_1-xCa₄O (BO₃)₃ crystals.

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(\begin{matrix} 4.45 & 0 & 0 \\ 0 & 3.62 & 0 \\ 0 & 0 & 12.3 \end{matrix}) \times 10^{- 6} K^{- 1}

The curve of the thermal expansion coefficients along principal axes varying with doping concentrations was plotted, as shown in Fig. 2. Based on Eq. (10), the angles between the principal axes in the thermal expansion coefficient frame and the reference coordinate (X₁, X₂, X₃) are provided in Table 4. From Fig. 2 and Table 3, it was concluded that the thermal expansion coefficients in the three directions of the principal axes are apparently anisotropic, and the variations in the directions of the three principal axes are different. However, the changes in the values of the principal axes due to the doping concentrations were very small. As shown in Table 4, it can be seen that the rotation angle increases with ascending the doping concentration. However, the change is less than 0.5°. Thus, the doping concentration has a slight effect on the values and rotation angles of the principal axes in the thermal expansion coefficient frame. This is because that the ionic radius of the Yb³⁺ ion is close to that of the Y³⁺ and Ca²⁺ ions, and the distortion of the ligand structure is minimal when the Yb³⁺ ions substitute the Y³⁺ or Ca²⁺ ions [26,31,32]. The weak anisotropic thermal expansion coefficients influenced by the doping concentrations indicate that the Yb:YCOB crystal is suitable for laser applications and crystal processing without thermal strain.

Fig. 2 The curve of thermal expansion coefficients with respect to doping concentrations with Yb:YCOB crystals.

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Table 4. The angles between the principal axes in the thermal expansion coefficient frame and reference coordinate of the Yb_xY_1-xCa₄O (BO₃)₃ crystals

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3.3 Thermal diffusion, density, specific heat and thermal conductivity of Yb:YCOB crystal with different doping concentrations

Thermal diffusion plays an important role in the process of thermal conduction. Five crystal samples with dimensions of 6 mm × 6 mm × 2 mm along the a, c^#, b, a^# and c axes were prepared, and the experimental results measured with the flash method (NETZSCHLFA 447 Nanoflash equipment), which were shown in the Fig. 3, reveal that the thermal diffusivity coefficients decrease slightly as the temperature increases. These differences are due to the small doping concentrations. This can be attributed to the decrease of the phonon free path with the enhancement of the molecular thermal dynamics [33]. The density of the Yb:YCOB crystal was then measured by the buoyancy method at 303.15 K, which is expressed as:

ρ = \frac{m_{1}}{m_{1} - m_{2}} ρ_{w}

where

ρ

and

ρ_{w}

represent the densities of the measured crystal and water, respectively; m₁ is the crystal mass in the air; and

m_{1} - m_{2}

is the crystal mass in water. The theoretical density was then calculated based on the following equation:

ρ = \frac{M Z}{N_{A} V}

where M is the molar mass of the crystal; Z is the number of molecules per unit cell; V is the volume of the unit cell; and N_A is the Avogadro constant. The measured and theoretical densities of Yb:YCOB crystals with different doping concentrations are shown in Table 5, and it can be seen that the measured density is consistent with the theoretical value. The density increases as ascending the doping concentration, because that the atomic mass of Yb³⁺ is larger than that of Y³⁺ and Ca²⁺ ions. The specific heat is a critical factor that affects the damage threshold of crystals. In the pulse laser operation, the higher specific heat is, the higher damage threshold of the crystal is. Figure 4 presents the specific heat curves with respect to the temperature of the Yb:YCOB crystals with different doping concentrations, measured by differential scanning calorimetry (DSC). It can be seen that the specific heat increases as the temperature increases, and the doping concentration of the Yb³⁺ ions has a slight influence on the specific heat when the temperature is less than 450 K. At the same temperature, the crystal with a high doping concentration exhibits a lower specific heat, given that the specific heat is inversely proportional to the atomic mass of the crystal [18] and the atomic mass of Yb³⁺ is larger than that of Y³⁺ and Ca²⁺. With the measured density, thermal diffusion coefficients and specific heat, the thermal conductivity can be calculated using the following equation:

k = d ρ C_{p}

where k, d, $ρ$ and C_p denote the thermal conductivity, thermal diffusion coefficient, density and specific heat of the crystal, respectively. The calculated thermal conductivity based on the least-squares method along principal axes at the room temperature are presented in Table 6, and the angles between the principal axes in the thermal conductivity frame and the reference coordinate (X₁, X₂, X₃) are provided in Table 7. The symmetric second-rank tensor of the thermal conductivity in the directions of three principal axes, taking the 5 at.% doped crystal for example, can be calculated as:

Fig. 3 Thermal diffusion versus temperature with different doping concentration Yb: YCOB crystals.

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Table 5. The density of the Yb_xY_1-xCa₄O (BO₃)₃ crystals

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Fig. 4 Specific heat curves versus temperature of Yb:YCOB crystals with different doping concentrations.

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Table 6. The thermal conductivity along principal axes of the Yb_xY_1-xCa₄O (BO₃)₃ crystals

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Table 7. The angles between principal axes in the thermal conductivity frame and reference coordinate of the Yb_xY_1-xCa₄O (BO₃)₃ crystals

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(\begin{matrix} 2.04 & 0 & 0 \\ 0 & 2.06 & 0 \\ 0 & 0 & 2.09 \end{matrix}) W m^{- 1} K^{- 1}

Figure 5 presents the changes in the thermal conductivity due to the doping concentrations. It can be seen that the values of the principal axes first increase and then decrease with an increase of the doping concentration in the three directions of the principal axes. Moreover, the rotation angles slightly increase when ascending the doping concentration. The increasing thermal conductivity is due to the optical-acoustic resonance scattering [34,35]. When Yb³⁺ ions doping in the YCOB crystal, it can substitute both Y³⁺ and Ca²⁺ ions [31]. The substitution of Ca²⁺ ions by Yb³⁺ ions will cause vacancy defects, which make the acoustic phonons be responsible for heat transport. The scattering of the optical-acoustic phonons coupling contributes to the increasing thermal conductivity. However, the higher doping concentration gives rise to a more disordered structure, which will reduce the mean free path of the phonons and decrease the thermal conductivity. When the doping concentration is lower than 20%, the influence of acoustic phonons is in dominance. And the disordered structure has the advantage as the doping concentration is higher than 20%, leading to the thermal conductivity peak in Fig. 5. But slight changes in the values and rotation angles of the principal axes are observed in accordance with an increase in the doping concentration, owing to the similar ionic radii of Yb³⁺, Y³⁺ and Ca²⁺ ions [26]. Furthermore, the Yb:YCOB crystal exhibits a weakly anisotropic thermal conductivity, which indicates that the Yb:YCOB crystal has a higher laser damage threshold [36]. In conclusion, the doping concentration has a slight effect on the anisotropic thermal properties of the Yb:YCOB crystal, which is beneficial for the realization of an efficient laser output.

Fig. 5 Thermal conductivity with respect to the doping concentrations of Yb:YCOB crystals.

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4. Conclusions

In summary, the thermal properties, which include the thermal expansion, thermal diffusion, specific heat, and thermal conductivity were investigated using Yb:YCOB crystals with different doping concentrations, which exhibit good crystallization and homogeneity, as characterized by of XRD and XRF measurements. The values and rotation angles of the principal axes between the thermal property frame and reference coordinate were then calculated at room temperature. According to the calculated results, it is concluded that the doping concentrations have a slight influence on the values and rotation angles of the principal axes in the thermal property frame. The YCOB crystal can be doped with a high concentration to enhance its ability to absorb the pump light without severe thermal effects, thus improving the conversion efficiency in the laser process. In addition, the thermal survey indicates that the Yb:YCOB crystal exhibits weak anisotropic thermal properties, which can protect the crystal from cracking during crystal growth, processing, and laser applications. Hence, the minimal influence of the doping concentrations on the anisotropic thermal characteristics aids in the realization of a stable, durable and efficient laser system with Yb:YCOB crystals.

Funding.

National Natural Science Foundation of China (NSFC) (51632004, 51772173); National Key Research and Development Program of China (Grant Nos. 2016YFB0402103, 2016YFB0701002, 2016YFB1102301); Provincial Key Research and Development Program of Shandong (Grant No. 2017CXGC0414); Institute of Chemical Materials, China Academy of Engineering Physics (CAEP) (32203).

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	Cell parameters
x	a (Å)	b (Å)	c (Å)	β (˚)
0.05	8.0709	16.0087	3.5272	101.16(6)
0.10	8.0654	16.0012	3.5201	101.15(3)
0.15	8.0541	15.9542	3.5164	101.14(2)
0.20	8.0445	15.9432	3.5124	101.13(5)
0.25	8.0369	15.9321	3.5103	101.12(6)
0.30	8.0274	15.9223	3.5068	101.11(5)

x	0.05			0.10			0.15
Element	Yb	Y	Ca	Yb	Y	Ca	Yb	Y	Ca
K_eff	0.954	1.002	0.984	1.019	0.998	0.944	0.940	1.011	0.982
x	0.20			0.25			0.30
Element	Yb	Y	Ca	Yb	Y	Ca	Yb	Y	Ca
K_eff	0.981	1.005	0.961	1.024	0.992	0.978	1.063	0.973	1.022

x	X_I (10⁻⁶ K⁻¹)	X_II (10⁻⁶ K⁻¹)	X_III (10⁻⁵ K⁻¹)
0.05	4.45	3.62	1.23
0.10	5.56	3.01	1.27
0.15	5.16	4.14	1.19
0.20	5.89	4.19	1.31
0.25	5.32	3.45	1.26
0.30	4.29	3.12	1.22

x	0.05	0.10	0.15	0.20	0.25	0.30
Theoretical density (g/cm³)	3.341	3.373	3.404	3.436	3.467	3.499
Experimental density (g/cm³)	3.339	3.387	3.398	3.446	3.475	3.508

X	X_I (W m⁻¹ K⁻¹)	X_II (W m⁻¹ K⁻¹)	X_III (W m⁻¹ K⁻¹)
0.05	2.04	2.06	2.09
0.10	2.06	2.09	2.11
0.15	2.08	2.11	2.14
0.20	2.11	2.13	2.16
0.25	2.08	2.10	2.13
0.30	2.05	2.07	2.10

Anisotropic thermal properties of Yb:YCOB crystal influenced by doping concentrations

Abstract

1. Introduction

2. Analysis of the crystal structure and composition

3. Thermal properties of the Yb:YCOB crystal

3.1 Symmetrical second-rank tensor measurement for the monoclinic crystal and the required crystal orientations for the measurement of thermal properties

3.2 Thermal expansion coefficient of Yb:YCOB crystal with different doping concentrations

3.3 Thermal diffusion, density, specific heat and thermal conductivity of Yb:YCOB crystal with different doping concentrations

4. Conclusions

Funding.

References

Cited By

Figures (5)

Tables (7)

Equations (19)

Optical Materials Express