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Abstract
The interaction between light and matter is a fundamental issue in nature, accompanied by the transfer of different kinds of energy and phase transitions. The discovery of the thermodynamic transition processes under strong irradiations could trigger novel phenomena and inspire the understanding of the interaction process, but it is still a challenge to observe in-situ. In this work, with the deuterated potassium dihydrogen phosphate (DKDP) crystal as a representative, the structural thermodynamic transition processes are originally investigated by introducing the in-situ neutron diffraction technique. The chemical bond fracture and breaking are found to be anisotropic, but suppressing, the destruction is not synchronous, which firstly presents the cumulative effect of energy in the structure and clarifies the relationship of the microcosmic chemical bonds and macroscopical destructions. Our results not only have important reference significance for understanding the research and development of materials under strong fields but also play an important role in understanding the physical processes of the interaction between light and matter.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Strong fields, such as light, electric and magnetic fields, have important effects on the behavior of materials, and the interacted matter could response nonlinearly, but always accompanied by the phase transitions and even damages of the matter [1–7]. The transition processes driven by the strong fields determines the upper limit and resulted application effect of materials. Discovery of the phase transition and energy transfer processes under different scales is a fundamental and essential issue in nature. For the light-matter interaction, the phase transition may not be driven by the light directly but also always by the other forms of energy transferred from the light. For instance, the laser-induced damage is more likely to be related to temperature rise by the thermal absorption by the nonlinear absorption of electrons or carriers with the laser pulse length region from 10−8 s to continuous wave for the transparent optical solid materials [1,8,9], and in contrast, the femtosecond lasers could print of semiconductor quantum dots by photoexcitation-induced chemical bonding down to nanometer scale [10–12]. Therefore, what would happen in the structure of matters under strong light fields would be key for understanding the phase transitions and energy transfer processes, which would be helpful for the study of nonlinear optics, photochemistry, photocatalysis and even optoelectronics [12–17].
For understanding the light driving phase transition process, plenty of models have been proposed based on the demonstration of mater under the irradiations., including the Drude Mie thermal [18,19], absorption distribution [20,21], defect induced damage models [22,23], etc. Normally, under the long pulse irradiations, a part of the light energy is absorbed by matter in the form of heat as a laser beam irradiates on the surface of a material. The absorption of energy can cause the temperature to rise, which will lead to thermal expansion, strain, movement of internal defects, and irreversible damage (e.g., cracking, melting and vaporization) [1,24,25]. Compared to the surrounding host materials, the temperature of inclusions or surface regions of inclusions increases during phase transition and damage. These high temperatures will generate stresses near the inclusions, which may exceed the theoretical strength of host materials and then lead to damage [23,26]. This laid the theoretical foundation of the thermal absorption mechanism. However, the observation in-situ of light driving phase-transition is still a challenge, which blocks the understanding of thermodynamic process for the interaction between light and transparent materials. New scientific techniques and perspectives need to be introduced to study this process.
Neutron diffraction is an important non-destructive testing method with the advantages of deep penetrability (centimeter-level) through the surface to the internal without damaging the sample, high signal-to-noise ratio of diffraction peak, in-situ measurement to the change of residual stress in crystals by loading the environmental device and so on [27–30]. The development of neutron diffraction could inspire us to study the light driving phase transition process in-situ under high light fields.
In this paper, we propose a strategy to study the structural thermodynamic transition processes by the in-situ neutron diffraction technique, taking the deuterated potassium dihydrogen phosphate (DKDP) crystal as an example, which are currently used as frequency conversion crystals in the inertial confinement fusion (ICF) due to their unique excellent performances [31–36]. The cumulative effect of energy in the structure and the relationship of the microcosmic chemical bonds and macroscopical destructions are investigated as temperature rise in DKDP crystals. This work may deepen the understanding for the thermodynamic process of the interaction between light and matter under strong fields.
2. Experimental section
2.1 Crystal growth
Deuterated potassium dihydrogen phosphate (DKDP) crystal is grown from aqueous solution by the “point-seed” rapid growth technique in a standard glass 5000 mL crystallizer [34]. The DKDP growth solution is prepared by dissolving high purity KDP salt in de-ionized water and deuteroxide. The deuterium content of growth solution is around 80%, which can obtain DKDP crystal with the deuterium content of 70% [37]. Crystallization is performed in a temperature range of 56.2 °C - 45.5 °C and the crystal rotates in the mode of “forward-stop-backward” with a speed of 77 rpm. The details of the growth process are described in Ref. [38]. The samples are cut from the prism sector of the as-grown crystal along X and Z axis directions, which are corresponding to the crystallographic axes a and c, respectively.
2.2 Structure measurements
Lattice parameters are measured by X-ray powder diffraction (D8 Advance), which is used to characterize the effect of temperature on structure of DKDP crystal with deuterium content of 70%. DKDP crystals are ground to powders with particle size of about 1 µm, which are put into the temperature-controlling device matching with the XRD instrument. XRD spectrum are collected with temperature of every 10 °C increasing in the range of 25 °C - 165 °C.
Thermal expansion measurements are carried out by thermal dilatometer (NETZSCH-DIL402C) for the two single crystal samples with the length of 10 mm, which are cut from the DKDP crystal along Z-direction and X-direction, respectively. The temperature ranges of the measurements are 20 °C - 160 °C and 20 °C - 200 °C, respectively. The heating rate is 2 °C/min.
2.3 Neutron diffraction measurements
The variation of residual stress along X and Z-directions with temperature in DKDP single crystal are measured on the residual stress neutron diffractometer (RSND) at Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics (CAEP). It is equipped with an additional temperature controlling device on the sample stage, which is used to heat the sample with the accuracy of ±1 °C. The maximum loading of sample stage is 500 kg. The samples are heated at 2 °C/min and keep at the temperature for half an hour to stabilize the temperature field and then the neutron diffraction peak of the crystal at this temperature is measured. The diffraction information of the two single crystal samples with the length of 10 mm are obtained when the neutron fluxes (4.7 × 106 n/cm2/s) with the wavelength (λ) of 1.587 Å focus on the sample center. The wavelength range of RSND diffractometer is 0.12∼0.28 nm and the spectrometer resolution is 1.91 × 10−3 (λ=0.231 nm) [39]. The other specifications of RSND diffractometer are illustrated in detail with Ref. [39,40]. The measurement accuracies of RSND diffractometer are 0.001°∼ 0.005° for diffraction peak position (2θ) and 10−5 for the strain, respectively.
The Bragg positions and full-width at half-maximum (FWHM) are obtained by fitting the diffraction peaks with Gaussian function. According to the peak position, the strain (ε(hkl)) perpendicular to crystal plane is calculated by Eq. (1).
Where d(hkl) is the spacing of crystal face (h k l) that is calculated by Bragg's law $2d\sin \theta = n\lambda $, d0 is the interplanar spacing of stress-free crystal, which can be obtained from X-ray powder diffraction. The residual stress (σij) in crystallographic coordinate is calculated by Hooke’s law as follows. Where Cijmn represents the elastic stiffness constant of crystals.3. Results and discussion
3.1 X-ray powder diffraction
Part of the XRD spectrums for the DKDP crystals is shown in Fig. 1(a). The positions of each diffraction peak shift to lower angles with the increase of temperature, which indicates that the spacing of crystal face increases in the heating process. The lattice parameters of DKDP crystal are obtained by refining the diffraction data, as shown in Fig. 1(b). The lattice parameters a and c increase linearly with temperature variation. The lattice parameter a gradually increases from 7.4593 Å at 25 °C to 7.4828 Å at 165 °C, while lattice parameter c gradually increases from 6.9726 Å at 25 °C to 7.0134 Å at 165 °C. As seen in Fig. 1(b), the thermal expansion rate along the X-direction is smaller than that along the Z-direction. This is because the structure along the X-direction is relatively loose in DKDP crystal, which can absorb part of the thermal expansion.
Fig. 1. (a) Part of XRD patterns of DKDP crystal at different temperatures and (b) lattice parameters of DKDP crystal at different temperatures which are obtained by refining the diffraction data from (a).
3.2 Thermal expansion of DKDP crystal
The crystal samples along X-direction and Z-direction (Fig. 2(a) and (d)) are heated from 20 °C to 160 °C at a heating rate of 2 °C/min, and then slowly cool to room temperature. The heated samples are again heated from 20 °C to 200 °C at the same heating rate, and then the temperature is slowly lowered to room temperature. Figure 2(g) shows thermal expansion curves of DKDP crystals along X-direction and Z-direction with the temperature range of 20 °C - 160 °C and 20 °C - 200 °C, respectively. When the temperature rises from 20 °C to 160 °C, the thermal expansions of crystals basically change linearly, with the value of $4.74 \times {10^{ - 5}}$ °C for Z- direction and $2.95 \times {10^{ - 5}}$ °C for X-direction. The heated samples are transparent without cracking or phase transformation, as shown in Fig. 2(b) and (e). The results show that phase transition temperatures of 70% DKDP crystals are higher than 160 °C.
Fig. 2. DKDP crystals before and after thermal expansion at room temperature, 160 °C, and 200 °C for Z-direction (a)-(c) and X-direction (d)-(f) samples, respectively, and (g) the thermal expansion ration of DKDP along X and Z with temperature variation.
When the heated samples are again heating from 20 °C to 200 °C, the changes of thermal expansions for DKDP crystal appear different. For Z-direction crystal, the thermal expansion changes greatly in a short time when the temperature rises to 173 °C - 180 °C, while it remains almost unchanged between 180 °C and 200 °C. It indicates that when the crystal is heated to 173 °C, a very large thermal stress is generated and then causes the crystal to crack. This is confirmed by Fig. 2(c), which shows that the crystal has cracks and turned white. Therefore, the chemical bonds along the Z-direction are broken at 160 °C - 200 °C, and the crystal occurs cracking between 173 °C and 180 °C. For X-direction crystal, when the temperature rises to 180 °C, the thermal expansion of the crystal increases by nearly 10 times within a few seconds, indicating that the X-direction crystal has endured a significant thermal stress at 180 °C and has reached the critical cracking value. The crystal as shown in Fig. 2(f) turns white and appears many cracks, which indicates that the chemical bonds of the crystal along the X-direction have been broken with the temperature range of 160 °C - 200 °C.
3.3 Residual stress along Z-direction vs temperature
The neutron diffraction peaks of DKDP crystal along Z-direction at different temperatures are shown in Fig. 3(a). The diffraction peak position of the (004) crystal face gradually decreases with the increase of temperature, from 54.222° at room temperature (RT) to 53.767° at 165 °C. When the temperature rises to 170 °C continually, the diffraction peak disappears. It indicates that the chemical bonds of the crystal along the Z-direction have been broken. Combined with the experimental results of thermal expansion, it can be known that the chemical bonds along the Z-direction for 70% DKDP crystal are first broken before the crystal occurs crack at 173 °C.
Fig. 3. (a) The neutron diffraction peaks of (004) face in DKDP crystal with temperature variation from RT to 170°C, (b) the stress and strain along Z-direction at different temperatures, and (c) The height and FWHM of the diffraction peaks at different temperatures obtained from (a).
According to Bragg's law $2\textrm{d}\sin \theta = n\lambda $, the spacing of the (004) crystal face increases continuously with the increase of temperature, which means that the increase in temperature causes the crystal to expand. The sample with powder state is stress-free, and in this case the 2 θ angle of (004) crystal face is 54.16°. Therefore, the sample has compressive stress along the Z-direction at RT, as seen in Fig. 3(a). Figure 3(b) shows the stress and strain along Z-direction at different temperatures. When the temperature is close to 60 °C, the macroscopic compressive stress in the lattice is completely released. As the temperature rising gradually, the lattice continues to expand and produce tensile stress along the Z-direction. The generated tensile stress and the strain are 272 MPa and 0.0067 at 165 °C, respectively. The diffraction peak disappears at 170 °C, which means the crystal has undergone phase transition. The results show that the thermal stress of 70% DKDP crystal along the Z-direction is 272 MPa.
In addition to the shift of neutron diffraction peak positions, the intensity and full-width at half-maximum (FWHM) of diffraction peaks also vary to a certain extent with the increase of temperature, as shown in Fig. 3(c). The intensity of diffraction peaks first increases and then decreases at different temperatures. It can be seen that the diffraction peak intensity gradually increases when the temperature increases from RT to 90 °C. This indicates that the atoms deviating from the lattice equilibrium position in the Z-direction are gradually repaired. The increase in temperature provides sufficient energy for dislocated atoms to reach the equilibrium position in the Z-direction. As the temperature rises from 90 °C to 165 °C, the diffraction peak intensity gradually decreases and meanwhile atoms gain more energy, which result in a greater vibration amplitude along the equilibrium position, and thus lead to the decrease of the peak intensity.
The FWHM of diffraction peak can be widened by the dislocations in crystal, so the magnitude of dislocation density can be evaluated based on FWHM. The relationship of dislocation density D, FWHM and Burger vector b can be expressed as follows [41].
The FWHM of crystal gradually increases with heated from RT to 60 °C, as shown in Fig. 3(c). According to the formula (3), dislocation density of (004) crystal face increases during this heating process. This is because the dislocation atoms acquire certain energy and start to move towards the lowest energy state, which increases the overall dislocation rate of the crystal during the movement process. In Fig. 3(c), the variation of peak intensity with the increase of temperature indicates that the Berger vector b of dislocation decreases in this temperature interval, thus the increase of temperature leads to the increase of dislocation density in crystal. While the crystal is heated from 60 °C to 90 °C, the FWHM decreases to the same level as RT, which indicates that some of the dislocated atoms have been located in the lattice with the lowest energy. The increase of temperature in the range of RT - 90 °C provides energy for all the dislocation atoms, while the atoms with less dislocation degree enter the lattice with the lowest energy state after obtaining energy, and then some dislocation defects are repaired. However, the splitting peak shape of the diffraction peak always exists in this temperature range (Fig. 3(a)), which indicates that there are small angle grain boundaries on the (004) crystal face of DKDP crystal. When the temperature rises to 90 °C, the small angle grain boundaries cannot be completely restored, while the splitting degree of the diffraction peak is weakened. This shows that the size of planar defects in the crystal decreases with increasing temperature.
When the temperature increases from 90 °C to 165 °C, the neutron diffraction peak of the crystal changes from the splitting state to a single peak, which shows that the displaced atoms have obtained enough energy to repair the small angle grain boundary, and then the quality of the crystal is improved due to the better mosaic degree of the crystal. However, the FWHM increases gradually when the crystal is heated from 90 °C to 120 °C, which means the dislocation density of crystal increases. This may be due to the gradual evolution of small angle grain boundaries into dislocations, thus increasing the dislocation density. The FWHM reaches the minimum at 140 °C, which indicates that the unrepaired displaced atoms have been repaired with enough energy. It also means that the optimization of the crystal quality by thermal annealing has reached the limit. The FWHM increases rapidly with temperature rising from 155 °C to 165 °C. This indicates that the atoms in the crystal acquire very large energy, which lead to the atom amplitudes along the Z-direction becoming larger. When the temperature rises from 165 °C to 170 °C, the atoms in the crystal gain enough energy to break the chemical bonds.
3.4 Residual stress along X-direction vs temperature
The neutron diffraction peaks of (200) face in DKDP crystal at various temperature are shown in Fig. 4(a). The 2θ angles of diffraction peak gradually increase from 24.660° at RT to 24.842° at 91 °C. With the temperature increases continually, the position of diffraction peak decreases, which is reduced to 24.312° at 190 °C. The diffraction peak disappears at 195 °C. These results indicate that the chemical bonds along X-direction for 70% DKDP crystal have been broken at temperature range of 190 °C - 195 °C. Combined with the results of thermal expansion experiments, DKDP crystal occurs cracking along X-direction at 180 °C, and the chemical bonds break at range of 190 °C - 195 °C. It can be seen that the temperatures of chemical bond fracture along different crystallographic orientations are anisotropy.
Fig. 4. (a) The neutron diffraction peaks of (200) face in DKDP crystal with temperature variation from RT to 195°C, (b) the stress and strain along X-direction at different temperatures, and (c) The height and FWHM of the diffraction peaks at different temperatures obtained from (a).
The strain and stress along X-direction at different temperatures have been calculated with the position of neutron diffraction peaks, which are shown in Fig. 4(b). It is shown that there exists a tensile stress of about 400 MPa along X-direction for the crystal at RT. The tensile stress release gradually when the temperature increases from RT to 64 °C. When the temperature increases to 180 °C, the value of thermal strain reaches 0.02 and thermal stress reaches 1163 MPa, which results in the cracking along X-direction for the crystal. The thermal expansion ration is only 0.0046 at 180 °C, which is far smaller than the lattice strain at this temperature. This difference can be explained from the crystal structure. The atomic spacing along X-direction are large compared with Z-direction. Although the spacing of (200) crystal face increases with temperature increasing, the loose structure along X-direction could tolerate the expansion of (200) crystal face. Therefore, the macro expansion of DKDP crystal is smaller than the lattice expansion.
The intensity and FWHM of diffraction peaks also change with temperature variation, as shown in Fig. 4(c). The diffraction peak intensity decreases gradually from RT to 64 °C, which indicates that the increase of temperature causes atoms in crystal to move in the X-direction. The atoms that are misaligned in the X-direction migrate to the equilibrium position with temperature increasing. However, the energy provided at this temperature cannot completely enable atoms to cross the energy barrier, resulting in a higher dislocation degree of all atoms in the X-direction. It will lead to the weaken of diffraction peak intensity. As the temperature continues to rise to 141 °C, the peak intensity gradually increases to the highest. It indicates that atoms in the X-direction gain enough energy to jump over the energy barrier and return to the equilibrium position with temperature rise. When the temperature rises from 141 °C to 150 °C, the diffraction peak intensity gradually weakens, which indicates that the defect with larger binding energy starts to activate and results in a greater dislocation degree of atoms along the X-direction. The peak intensity basically remains unchanged in the range of 150 °C - 165 °C, and then gradually increased as the temperature rising to 190 °C.
The FWHM of (200) crystal face increases when the temperature rises from RT to 64 °C. According to formula (3), it can be seen that the increase of temperature increases the dislocation density of the crystal face. The increase in temperature activates the atoms in the dislocation and makes them tend back to the lattice with the lowest energy. The mismatch degrees of atoms are increased in this process. The FWHM of diffraction peak gradually decreases when the temperature rises to 141 °C, which means that dislocation density of (200) crystal face gradually decreases. This is mainly due to two aspects: on the one hand, some dislocations disappear after obtaining enough energy; on the other hand, the Berger vector along the X-direction decreases with increasing temperature. The FWHM gradually increases from 141 °C to 150 °C, indicating that the temperature increase reactivates the dislocation atoms and increases the dislocation density in crystal. When the temperature rises to 177 °C continually, the dislocation atoms have jumped the potential barrier and the dislocation density reaches the minimum. As the temperature continues to increase, the FWHM remains little change.
4. Conclusion
The structural thermodynamic transition processes of DKDP crystal are originally investigated by introducing the in-situ neutron diffraction technique. The results show that the chemical bond fracture of 70% DKDP crystals is anisotropic with the range from 165 °C to 170 °C along the Z-direction and from 190 °C to 195 °C along the X-direction. The chemical bond breaking of the Z-direction crystal occurs before cracking, while it shows opposite behavior in the X- direction. In addition, the maximum thermal stresses of crystal are obtained, which is 272 MPa along the Z-direction and 1163 MPa along the X-direction, respectively. The dislocation variation in the crystal during heating process is revealed by the intensity, FWHM and peak shape of neutron diffraction peak. Atoms with a small degree of dislocation get enough energy to return to the lattice of periodic arrangement in the early heating process, and those with a larger degree of dislocation are repaired while continuing to increase the temperature. However, the dislocation density of crystals will increase in this process. The experimental results indicate that there are two key temperatures at 90 °C and 140 °C in the thermal annealing process of 70% DKDP crystal. If the crystal could keep for a period of time at these two temperatures, some defects could be repaired and then the crystal quality would be improved. Our results will have important implications for understanding DKDP crystals used as frequency conversion optical components in the ICF. Meanwhile, it will also play an important role in understanding the physical processes of the interaction between light and matter.
Funding
Young Scholars Program of Shandong University (Grant No. 2018WLJH65).
Disclosures
The authors declare no competing financial interest.
Data availability
Data underlying the results presented in this review are not publicly available at this time but may be obtained from the authors upon reasonable request.
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