Exploration of the correlation between weak absorption and thermal-stress for KDP and 70%-DKDP crystals

Journal of Alloys and Compounds 790 (2019) 212e220

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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Exploration of the correlation between weak absorption and thermalstress for KDP and 70%-DKDP crystals Duanliang Wang a, *, Chuanying Shen a, **, Jiejie Lan a, Pingping Huang b, c, Zixiao Cui a, Tiantian Kang a, Yan Niu a, Shenglai Wang b, c, ***, Jiyang Wang b, Robert I. Boughton d a Shandong Province Key Laboratory of Laser Polarization and Information Technology, School of Physics and Physical Engineering, Qufu Normal University, Qufu, Shandong, 273165, China b State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan, Shandong, 250100, China c Key Laboratory of Functional Crystal Materials and Device (Shandong University), Ministry of Education, Jinan, 250100, China d Department of Physics and Astronomy, Bowling Green State University, Bowling Green, OH, 43403, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 December 2018 Received in revised form 5 March 2019 Accepted 10 March 2019 Available online 12 March 2019

For KDP and 70%-DKDP crystals, knowledge of thermal-stress distribution induced by weak absorption effect is crucial for their applications, especially in high-power laser systems. Based on photo-thermal common-path interferometry (PCI) technique, the correlations of weak absorption effect with different crystal orientations were systematically evaluated at 1064 nm. An obviously anisotropic property is demonstrated, and a similar pattern of z > x > I > II is also represented for KDP and 70%-DKDP crystals. More importantly, crystal uniformity could be reflected by the weak absorption results, indicating that PCI method could be considered as a novel way to identify the crystal quality. Meanwhile, Thermal parameters including thermal expansion and thermal conductivity were obtained. Using the finiteelement method (FEM), the temperature gradients and thermal-stresses along z and x-cut samples were distinctly explored, implying that the corresponding distributions are mainly attributed to crystal orientations. Importantly, another fundamental factor is confirmed that the variation of deuterium content could influence the behaviors of temperature gradients and thermal-stresses distributions. Thus, taking advantage of PCI and FEM as a new approach is more conducive to better understanding the mechanism of laser-matter interactions. © 2019 Elsevier B.V. All rights reserved.

Keywords: KDP and DKDP Weak absorption Thermal parameter Temperature gradient Thermal-stress

1. Introduction As a kind of excellent nonlinear optical materials, tetragonal potassium dihydrogen phosphate (KDP) and potassium dideuterium phosphate (DKDP) crystals have aroused extensive attention and been widely applied in piezoelectric transducer, sonar device, electro-optical switch, frequency conversion fields [1e4]. In particular, KDP and DKDP crystals are still the only materials suiting to inertial confinement fusion (ICF) [5,6]. Therefore, crystal quality, optical and nonlinear optical properties have attracted scientists interested to explore [7e9]. However, the crystal damage has

* Corresponding author. ** Corresponding author. *** Corresponding author. State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan, Shandong, 250100, China. E-mail addresses: [email protected] (D. Wang), [email protected] (C. Shen), [email protected] (S. Wang). https://doi.org/10.1016/j.jallcom.2019.03.167 0925-8388/© 2019 Elsevier B.V. All rights reserved.

seriously affected the applications and operation life. Due to the laser-crystal interaction, the generation of optic absorption is inevitable [10e12]. With the accumulation of absorption, thermal problems could raise the crystal temperature [13e15], create thermal stress related with thermal expansion, and even induce the variation of microstructure. Furthermore, above phenomena could affect laser propagation, induce phase mismatch, decrease second harmonic generation (SHG) efficiency, and further result in crystal damage [16,17]. Nevertheless, weak absorption effect of KDP and DKDP crystals is relatively less investigated up to now. Better understanding weak absorption induced by intense laser is necessary to acquire the generating mechanism of damage. In particularly, thermal stability and stress caused temperature non-uniformity, which are determined by thermal expansion and thermal conductivity, can be altered by optical absorption. Hence, further exploring their relevancies between thermal stress and weak absorption effect should be beneficial to crystal utilization. For this reason, weak absorption properties of KDP and DKDP

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with 70%-deuterium content crystals, as grown by conventional method, were firstly investigated by photo-thermal common-path interferometer (PCI) at 1064 nm [18,19]. Specially, the dependences of weak absorption on crystallographic orientation were completely presented, and identified that a larger weak absorption effect along z-cut could be induced. The corresponding thermal performances including thermal expansion and thermal conductivity, which are intimately associated with weak absorption effect and thermal-stress, were fully explored, respectively. Further, the characteristics of thermal-stress involving weak absorption are obtained through a comprehensive calculation by the finiteelement method (FEM) in this paper. 2. Experimental 2.1. Crystal growth In experiment, traditional temperature cooling technique was applied to acquire KDP and DKDP (70%-deuterium content) crystals. The growth solution was synthesized through high purity KH2PO4, deionized water and heavy water, and then filtered using a 0.22 mm membrane. Besides, formula (1) as follows could provide ideas for calculating deuteration level in solution [20].

uðDÞ ¼

nðDÞ  100% nðDÞ þ nðHÞ

(1)

where nðDÞ and nðHÞ represent molar amounts of deuterium and hydrogen atoms, respectively. After that, crystal growth along z-cut were controlled by a shimada controller named FP21 with an accuracy of ±0.1  C, and the colorless transparent crystals grown were described in Fig. 1 (a). 2.2. Weak absorption and thermal properties Considering the crystal structure characteristics and experimental requirements of weak absorption measurement, samples with different orientations were cut from the middle parts of asgrown crystals according to Fig. 1 (b), and the specified dimension was about 10  10  5 (length along the incident light beam) mm3. To further understand the interconnections between weak absorption and crystal quality, samples along z-direction cutting from the upper, middle and lower regions as shown in Fig. 1 (a) were chosen for the measurements. Weak absorption were

213

performed by photo-thermal common-path interferometer (PCI) [21], and a succinct schematic diagram was mainly presented in Fig. 2 (a). In experimenting, the laser intensity at focus was greater than that of the surrounding areas for samples. This implied that irradiation area directly would absorb more energy, leading to the internal radial temperature gradient. A tiny variation of refractive index could be induced, and the sample could be deemed to an optical element as laser beams through the inner regions, which was analogous to a lens as shown in Fig. 2 (b). Then the corresponding relationships between sample position and optical signal were recorded in real-time on computer. In our experiments, the weak absorption properties of KDP and 70%-DKDP specimens with different directions were explored using PCI technique. The laser calorimeter that the sensitivity is approximately 108 (0.01 ppm) was manufactured by Stanford PhotoThermal Solutions, and the wavelengths of pump beam and probe laser were 1064 nm and 633 nm, respectively. Compared to the laser power of probe laser (about 5 mW), the power values of pump beam could range from 0 to 10 w, while a laser power of 3.2 w was applied in experiments. Thermal properties including thermal expansion and thermal conductivity play a critical role in the applications of KDP and DKDP crystals, especially high-power laser systems. Thereby, samples along z-cut, x-cut, I and II-type were used for the thermal expansion measurements with a thermal-mechanical analyzer (Diamond TMA: TMS-2, Perkin-Elmer), while the corresponding thermal conductivities were explored using a laser flash apparatus (NETZSCH LFA457) over the range of 293e423 K for KDP and 70%DKDP crystals.

2.3. Numerical simulation of thermal and stress induced by weak absorption 2.3.1. Thermal analysis As is known that the existence of weak absorption for crystalline material may lead to an inhomogeneous temperature distribution under laser irritation. Better understanding the thermal field distribution caused by weak absorption, the FEM based on AnsysWorkbench Fluent software, as a wonderful platform, was applied to calculate the variation of temperature [22]. In optical transmission system, partial laser energy absorbed by anisotropic crystals is normally converted into thermal energy, and further cause crystal temperature to increase. This phenomenon is identified as a transient heat-transfer process, meaning that the crystal

Fig. 1. (a) As-grown of high-quality KDP and DKDP crystals (b) Cutting schematic diagram of samples with different orientations.

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Fig. 2. (a) The schematic diagram of photo-thermal common-path interferometer (b) Principle of photo-thermal lens effect.

temperature and heat-boundary conditions change over time. To compromise computational accuracy and convenience, some relevant parameters, such as density, thermal conductivity and specific heat, are considered to be constant, and the absorbed energy is completely transferred to temperature increment of crystalline material. According to the Fourier's law without internal heat source in system, the temperature equilibrium and stability equation during in the cooling process can be expressed via equation (2) [22,23].

. . . vT l ¼ v2 T vx2 þ v2 T vy2 þ v2 T vz2 vt rc

! (2)

where T is crystal temperature, and t is temperature falling time, while l, r and c represent the thermal conductivity, density and specific heat capacity of crystal, respectively. Furthermore, considering the generation of convection heat transfer between crystalline surfaces and air, the third boundary condition is adopted in process of lowing the temperature and described as formula (3) [22].

    l vT=vn ¼ h Tw  Tf

(3)

w

In equation, l is thermal conductivity of the direction that is perpendicular to the corresponding face, n is the normal direction of crystal face, Tw and Tf respectively denote surface temperature of crystal and ambient temperature. Moreover, the convective heattransfer coefficient h blends natural convection and radiation heat transfer in a way.

2

C11 6 C12 6 6 C13 C¼6 6 0 6 4 0 0

C12 C11 C13

C13 C13 C33

0 0 0 0 0 0

0 0 0

0 0 0 C44 0 0

0 0 0 0 0 C44 0 0 C66

3 7 7 7 7 7 7 5

(5)

where C11 ¼ 71.2, C12 ¼ 5, C13 ¼ 14.1, C33 ¼ 56.8, C44 ¼ 12.6, and C66 ¼ 6.22 (in units of GPa) for KDP crystal. With regard to 70%DKDP crystal, the values of C11, C12, C13, C33, C44 and C66 are 36.92, 13.84, 11.75, 57.64, 12.31 and 5.88, respectively. On the basis of displacement field, the geometric equation of the stain ε shows the relationship between strain and distortion as mentioned blow [22,23].

8 vu > > > < εx ¼ vx > vn vu > > : gxy ¼ þ vx vy

εy ¼

gxz ¼

vn vy

vw vu þ vx vz

εz ¼

gyz ¼

vw vz

9 > > > =

vu vv > > > þ ; vy vz

(6)

where εx, εy, εz, gxy, gyz, and gzx are the strains with different orientations distinguishing from the following table. Meanwhile, u, v and w signify the corresponding displacements (or distortions) in x, y and z directions, respectively. In the process of calculation, the related basic parameters of KDP and 70%-DKDP crystals were also presented in Table 1 [24,25]. In brief, the distributional characteristics of temperature field and thermal stress caused by weak absorption effect could be obtained through theoretical analysis.

3. Results and discussion 2.3.2. Thermo-elastic stress analysis Based on the thermal field analysis as the laser interacts with sample, the computations of thermal stress were conducted through the finite-element method in ANSYS Mechanical. For a thermo-elastic anisotropic material, the relationship between stress and strain can be described by the expression (4) of Lambropoulos [22].

h



s ¼ C ε  a T  Tref

i

(4)

where s, ε, and a are the stress, strain, and thermal expansion coefficient, while T and Tref represent the crystal temperature and the reference temperature considered as the initial temperature in our simulations, respectively. In addition, C is the elastic constant matrix, which can be indicated as follows [22,23].

3.1. Weak absorption effect Under certain conditions including laser wavelength and energy, the absorption degree of crystals can be reflected from the

Table 1 The related basic parameters of KDP and 70%-DKDP crystals. Parameters

KDP

70%-DKDP

Density (kg*m3) Specific Heat (kJ*kg1* K1) Heat Conductivity (W*m1*K1)

2338 [22] 857 [22] 1.35kc 1.67⊥c 40.7 kc 25.1⊥c

2355 [24] 828 [24] 1.25kc 1.70⊥c 43.1kc 24.7⊥c

Thermal Expansion Coefficient (K1*106)

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corresponding weak absorption value, which is an important parameter associated with “photo-thermal lens effect”. For KDP single crystal, the weak absorption curves along x-cut, I-type, IItype and z-cut were measured in detail by the PCI technique [11], and the corresponding absorption values a at 1064 nm are clearly shown in Fig. 3, respectively. According to the results, it is reasonable to deduce the degree of weak absorption effect from the remarkable absorption peak, and the detailed parameters corresponding to crystal orientations are shown in Table 2. The peak values along x, I, II and z-direction derived from middle region are approximate 3900 ppm/cm, 3500 ppm/cm, 3400 ppm/cm and 5800 ppm/cm, respectively. This means that weak absorption effect along z-direction is larger than other samples, and the order of accumulating capacity is z > x > I > II, illustrating its anisotropic characteristic. Thus, such a considerable difference may be mainly attributed to anisotropy of KDP structure, and can be interpreted by the following reason. In comparison with other directions, a larger interatomic distance in (001) face is formed during the process of growth, signifying more vacant spaces exist in crystal construction along z-direction. Meanwhile, the larger interstitial areas are inclined to be expanded in contrast to II-type with the lower interstice. In addition, taking the sample of z-cut as sample, the weak absorption effect dependence on growth regions including bottom and top areas were also demonstrated in Fig. 3(e and f). The absorption value of top area is about 4600 ppm/cm, and smaller than bottom region with a value of 6000 ppm/cm that is almost equivalent to the middle region. Such differentials further declare that

215

Table 2 Bulk weak absorption values a (ppm/cm) of DKDP and KDP specimens with different directions. Crystals

KDP 70%-DKDP

Middle

Top

x-cut

I-type

II-type

z-cut

z-cut

3900 4500

3500 3000

3400 2300

5800 5700

4600 5500

Bottom

6000 5600

weak absorption effect of KDP crystal is closely related to crystalline quality [26,27]. During the process of growth, the scattering centers including cluster and dislocation are easier to be formed in bottom region with poor quality [10]. More importantly, from the absorption curves we can see that the absorption region is not always smooth, especially the curves of Fig. 3(e and f), and present a larger undulatory property illustrating the inhomogeneity of crystal quality. Fig. 4 illustrates the weak absorption curves of DKDP crystal with different directions at 1064 nm. From the figure, it can be seen that DKDP crystal has distinct weak absorption characteristics with a clear difference among these samples. The corresponding weak absorption values are presented in Table 2, which are about 4500 ppm/cm, 3000 ppm/cm, 2300 ppm/cm and 2700 ppm/cm for x-cut, I-type, II-type and z-cut deriving from middle region, respectively. The results to be gained are clear that optical absorptivity of z direction is significantly greater than the samples along x-cut, I-type and II-type, whereas the absorption values along

Fig. 3. Bulk weak absorption curves of KDP specimens at 1064 nm: (aed) x-cut, I-type, II-type and z-cut in middle region (e) z-cut in top region (f) z-cut in bottom region.

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Fig. 4. Bulk weak absorption curves of DKDP specimens at 1064 nm: (AeD) x-cut, I-type, II-type and z-cut in middle-region (E) z-cut in top-region (F) z-cut in bottom-region.

I-type is approximately equal to II-type. Thus, for DKDP crystal, the anisotropy of weak absorption effect is an essential characteristic similar to KDP, and the usual order of sequence is also z > x > I > II. The reason we conclude that crystal structure has a slight variation with isotope effect during the process of hydrogen (H) atoms replaced by deuterium (D) atoms. Furthermore, the dependence of weak absorption effect on crystal quality was also explored through contrasting the results of different parts. In top area, the specific value along z-cut is about 5500 ppm/cm, while it equals to 5600 ppm/cm in bottom region. Combining on the result of middle part, 70%-DKDP crystal with good homogeneity [28], meaning that a crystal with better quality can be created, has been formed in different growth period. According to the above results, the weak absorption values of KDP and 70%-DKDP crystals are distinctly associated with crystal configuration. For both crystals, weak absorption effects along variable axis exhibit characteristic distribution trends, and z-cut possesses a larger absorbability in comparison with other test specimens. In particularly, a peculiar characteristic is that for 70%DKDP crystals weak absorption effects with different orientations have a fluctuation with variation of deuterium content with respect to KDP. The main reason may be due to the changes of lattice parameters caused by the substitution of deuterium atoms [26,29]. Moreover, the numerical values of weak absorption can be a reflection of crystal uniformity in different growth phases. Informed by that, we can deduce that the variation curves of weak absorption by PCI method provide a promising way to distinguish

crystal quality or homogeneity. 3.2. Thermal properties Fig. 5 shows the thermal expansion and thermal conductivity curves of KDP and 70%-DKDP crystals versus temperature. As a determining factor that greatly influence optical damage in highpower laser system, the thermal expansion coefficient is widely used to calculate the gained laser energy, especially the condition of thermal fracture. From the curves in Fig. 5, it can be seen that thermal expansion curves along x-cut, I-type, II-type and z-cut are significant increased linearly with increasing temperature for KDP and 70%-DKDP crystals, demonstrating that thermal expansion with no thermal contraction occurs in the course of heating. After calculating, we can see the average thermal expansion coefficients of KDP are 2.51  105 K1, 3.43  105 K1, 2.85  105 K1, and 4.07  105 K1 along x-cut, I-type, II-type and z-cut when the temperature is below 385 K, and the corresponding values are about 2.47  105 K1, 3.56  105 K1, 3.02  105 K1, and 4.31  105 K1 for 70%-DKDP crystal, respectively. From the above results, it is evident that the relation of thermal expansion capacity is x < II < I < z, which means that z-cut is particularly sensitive to temperature. Furthermore, the distinct anisotropic characteristics implies that a slow cooling rate is necessary to avoid the initiation and propagation of cracks. By comparison, the thermal expansion coefficient of DKDP crystal is slightly larger than that of KDP, mainly due to the replacements of hydrogen bonds by deuterium bonds in

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217

Fig. 5. Thermal expansion and thermal conductivity versus temperature curves of KDP and 70%-DKDP crystals.

the crystal growth process. As is known, larger local thermal gradient could be caused by poor thermal conductivity, thus evaluation of thermal conductivity is essential for a crystal device of frequency doubling [30,31]. For thermal conductivity measurements of KDP and 70%-DKDP crystals in Fig. 5, it is clear that, with the different orientations along x-cut, I-type, II-type and z-cut, thermal conductivity exhibits a common tendency to firstly increase slowly in the temperature range of 298e323 K and then decrease with the increase temperature above 323 K. By a comparison of results, one common feature is that the thermal conductivity with four orientations is x > II > I > z in both crystals. Furthermore, the thermal conductivities of KDP along x, I, II and z-directions at room temperature are about 1.67 W m1 $ K1, 1.47 W m1 $ K1, 1.58 W m1 $ K1 and 1.35 W m1 $ K1, while the corresponding values of 70%-DKDP equal to 1.70 W m1 $ K1, 1.48 W m1 $ K1, 1.54 W m1 $ K1 and 1.25 W m1 $ K1, respectively. In further these parameters will contribute to numerical simulation of thermal stress resulted in weak absorption effect. From above results, a slight difference between KDP and 70%-DKDP crystals is displayed, and this behavior may be likely due to the variation of crystal structure induced by embedded deuterium atoms. 3.3. Simulation analysis of thermal field and stresses According to the above research results and analysis, a wonderful weak absorption effect could be generated directly in high-power laser system for KDP and 70%-DKDP crystals. Thus, this indicates that the temperature grads and thermal stress, which is associated with the formation of refractive index gradient in actual application, could be further induced by energy absorption. This phenomenon's not in favor of realizing phase matching and lead to the decrement of conversion efficiency. Hence, it is essential to

better understand the distributional characteristics of temperature grads and thermal stress (s) caused by weak absorption. In accordance with the above weak absorption characteristics and influence factors including thermal expansion and thermal conductivity, temperature grads and thermal stress along z and x-cut were further explored by finite volume method based on AnsysWorkbench Fluent software as follows. For KDP crystal along z-cut and x-cut samples, temperature grads and thermal stress distribution caused by weak absorption effect are presented in Fig. 6. Firstly, the temperature profile of (001) and (100) faces are clearly rendered in Fig. 6 (a) and (b), respectively. A marked disparity in (001) and (100) faces are displayed, mainly due to different thermal conductivities for y-direction (or x-direction) and z-direction. Moreover, the maximum temperature difference (DT) between core and periphery is obtained, and the values of (001) and (100) faces are 1.25  C and 0.79  C respectively. Thus, thermal gradient in (100) face is smaller than (001) face, mainly due to a relatively larger thermal conductivity along x axis. Further, the corresponding thermal stresses in (001) face and along [001] direction are shown in Fig. 6 (c), while Fig. 6 (d) illustrates the stress distributions of (100) face and [100] direction. Sees from the chart, a compressive stress at irradiation area by laser is demonstrated in (001) and (100) faces, whereas tensile stresses in a symmetrical distribution are generated at the periphery region. The phenomenon is largely attributed to temperature gradient and thermal expansion effect of brittle materials [22]. As the temperature rising at central areas, the variation of high-temperature region is compressed, and the lower-temperature zone on the periphery is exposed to tensile forces. According to the calculated results, the maximum compressive stress and tensile stress values in (001) face are - 0.24  105 Pa and 3.78  105 Pa, and the corresponding values in (100) face are - 0.12  105 Pa and 2.97  105 Pa,

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Fig. 6. Temperature grads and thermal stress distributions of z-cut and x-cut samples for KDP crystal.

respectively. This proves that a larger thermal stress has been caused for z-cut sample, which is well in agreement with that the results of thermal gradient. Meanwhile, for all samples the tensile stress is far greater than thermal compressive stress in the corresponding cross section, meaning that the cracking phenomenon is more prone to be caused available to marginal areas. In addition, thermal stress distributions along z and x cuts show a gradual decline, and the variation tendency along x-cut become more gentle than z-cut. Fig. 7 shows the temperature grads and thermal stress distribution of z-cut and x-cut samples for 70%-DKDP crystal. In Fig. 7(A) and (B), thermal gradients in (001) and (100) crystallographic planes are on display, while the corresponding values of DT are 1.26  C and 0.92  C, respectively. This characteristic of z-cut > x-cut is consistent with KDP, however DT of 70%-DKDP is larger than KDP for x-cut mainly because of the lower thermal conductivity. Comparing to (001) face, the asymmetrical distribution of temperature gradient in (100) face is clearly demonstrated, confirming that the heat transfer capability along y-axis (or x-axis) is stronger

than z-axis owing to crystalline anisotropy of DKDP. Better understanding the impact of temperature, we further explored the stress distributions of (001) and (100) faces as shown in Fig. 7(C) and (D). From the figure, it can be shown that. As known from the simulation results, the maximum tensile stresses of (001) and (100) faces are 2.13  105 Pa and 2.74  105 Pa, while the corresponding compressive stresses are - 0.25  105 Pa and 0.07  105 Pa, respectively. Thus, the tensile stress of (001) face with a larger DT is smaller than (100) face, this may be primarily due to different elastic constants. For z-cut sample, the generation of stress depends largely on C33 that is larger than C11, which have a greater influence on x-cut. In contrast, another noticeable feature is that a corresponding greater compressive stress in (001) face is attributed to low thermal-conductivity. Moreover, similarly to KDP crystal with tetragonal system, in contrast to (001) face, an asymmetrical distribution in (100) face is on exhibition. Further, the changing trends along x and z directions are also explored and displayed clearly in Fig. 7(C) and (D). Based on the above results of KDP and 70%-DKDP crystals, all

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219

Fig. 7. Temperature grads and thermal stress distributions of z-cut and x-cut samples for 70%-DKDP crystal.

these demonstrate that temperature grads and thermal-stress distribution are mainly associated with crystal orientation. In general, a common behavior of DT is that the value with z-cut sample is significantly greater than x-cut under the same laser irradiation. Another characteristic is that thermal-stresses including the maximum tensile and compressive stresses have a decreasing trend for 70%-DKDP, implying that the variation of deuterium content play an indispensable role in crystal performance. Importantly, the stress of KDP in (001) face show a greater value than (100) face, while an opposite result in (001) face is obtained for the tensile stress of 70%-DKDP crystal. The proposed reason for this behavior may be principally associated with the existence of deuterium atoms. In the construction of crystal  structure, H2PO 4 groups have been gradually replaced by D2PO4 groups [20,32], which further lead to the variation of relative physical parameters, especially elastic constant matrix. Comparing with the analysis of weak absorption results, we can see clearly that heat accumulation induced by the interactions between crystal and

laser beam would cause the generation of temperature gradients, differential thermal expansion, and inhomogeneous distribution of thermal-stresses in the three-dimensional space. The common effect of temperature gradients and thermal-stresses would result in the variations of refractive index, laser-beam distortion [33,34], and thus decrease the efficiency of frequency conversion [35,36]. Hence, better understanding the correlation between weak absorption effect and thermal-stress is essential to improve the utilization of crystals. This also implies that taking advantage of PCI and finite element method is an effective approach to master information induce by high-power laser systems. 4. Conclusions In summary, for KDP and 70%-DKDP crystals as grown by conventional growth method, weak absorption effects at 1064 nm were in detail explored based on PCI technique. A notable feature is that the spatial distributions of weak absorption effect have the

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certain relevance with crystal orientations, and a greater effect is exhibited for z-cut specimen. More importantly, Crystal uniformity could be identified by PCI method as a novel way to determine crystal quality. For thermal parameters, slight deviations between KDP and 70%-DKDP crystals are mainly due to the D substitution on the crystal structure. Based on the researches of weak absorption and thermal performances, the temperature non-uniformity and stress are analyzed using FEM. Interestingly, FEM calculations imply that the temperature grads and thermal stresses are closely related to crystal orientations and deuterium content. More importantly, the method of combining PCI and FEM techniques may provide a versatile strategy to better understand the mechanism of thermalstress distributions induced by weak absorption effect for KDPfamily, especially in high-power laser environment. Acknowledgements This work has been supported by National Natural Science Foundation of China (Grant Nos. 51602174, 51321062 and 11847079) and the Natural Science Foundation of Shandong Province (Grant Nos. ZR2018BEM008 and ZR2016EMQ04).

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