Abstract

Neutron powder diffraction was applied to determine the deuteration level of K(H1−xDx)2PO4 (DKDP) crystals via the Rietveld refinement method. Micro-Raman spectroscopy was employed using the neutron results to investigate the relation between deuteration level and PO4 vibration peak of DKDP crystal. The relative variation [Δν1 = ν1(KDP)−ν1(DKDP)] of the PO4 vibration peak was linearly well dependent on the deuteration level. Attenuated Total Reflectance-Infrared (ATR-IR) spectroscopy was also used to study the total relative variation [β(DKDP)-β(KDP) + ν1(DKDP)−ν1(KDP)] of β(O-H/D) and ν1(PO4) absorption band with the deuteration level of DKDP crystals. The IR results illustrate that two linear relationships existed between the deuteration level and the relative variations of the spectra. The two spectroscopic techniques can be combined and used to measure the degree of deuteration in the crystals of DKDP grown from solutions with deuteration level of less than 92%. ATR-IR spectroscopy is more suitable for measuring highly deuterated DKDP crystals.

© 2016 Optical Society of America

1. Introduction

Potassium dihydrogen phosphate (KDP) with excellent frequency conversion and electro-optic effect is used in inertial laser fusion facilities [1–4]. Its isomorph, potassium dideuterium phosphate (DKDP), is widely used to suppress transverse stimulated Raman scattering [5,6]. Different degrees of substitution can alter the structural dimensions, bond lengths, and bond angles with the deuterium composition in crystals, although the difference between hydrogen and deuterium atoms is very little [7–9]. These chemical and physical properties are closely related with the deuteration level of DKDP crystals. Therefore, an accurate measurement of deuteration level is very important because of its applications.

Loiacono et al. [10] proposed the variation in ferroelectric transition temperature of DKDP crystal to determine its deuteration level. They reported that the ferroelectric transition temperature of the DKDP crystal was almost dependent linearly on its deuteration level. However, most experimental data are concentrated on the high deuteration level, whereas only few test data on mid-low deuteration range are available. Thus, this proposed method is much more accurate to measure the deuteration level of highly deuterated DKDP crystals. Yaksin et al. [11] suggested Raman shift to measure the deuteration level. Huser et al. [12] found that the relationship between the deuteration level and Raman shift of PO4 vibration peak is almost linear. Thus, micro-Raman spectroscopy is inferred to be suitable for measuring the deuteration level. However, this study would be more accurate if the relative variation would be used in the Raman shift of PO4vibration peak [13]. Thermal gravity analysis (TGA) was used in 2006 to measure the deuteration level depending on the thermo-decomposition of DKDP and KDP crystals [14].

Neutron diffraction is an effective technique to determine the deuteration level of DKDP crystals because of the sensitivity of the neutron to hydrogen and deuterium elements. Neutron diffraction was applied in 1988 to analyze the structural difference between DKDP and KDP crystals and determine the deuteration level in highly deuterated DKDP crystals [15]. Neutron diffraction is rarely used in studies, although this process is very useful in determining the deuteration level. Therefore, neutron diffraction can be used as a standard method to calibrate the deuteration level of DKDP crystals.

In the present work, the deuteration level of DKDP crystals was determined systematically by neutron diffraction. Micro-Raman and ATR-IR spectroscopies were applied using neutron diffraction results to investigate the dependence of deuteration level on the variation in Raman and IR spectra, respectively. These two spectral techniques can be used conveniently to determine the deuteration level of DKDP crystals. Both techniques can be used to measure the deuteration level of DKDP crystals grown from solutions with deuterium content of less than 92%. However, ATR-IR spectroscopy is more appropriate to measure more highly deuterated DKDP crystals.

2. Experimental section

2.1 Crystal growth and sample preparation

The DKDP crystals were grown from solutions with deuteration levels of 0%, 40%, 55%, 65%, 80%, 92%, 98%, and 99.5%. The deuteration level in the growth solution (Ds) is calculated as follows:

Ds=m(D)m(D)+m(H)
where m(D) and m(H) are the molar amounts of deuterium and hydrogen, respectively. Growth solution of less than 92% was prepared by dissolving the KDP salt in ionized water and deuterium water. The growth solution with deuteration level of more than 92% was prepared by dissolving pure DKDP salt in ionized water and deuterium water. Pure KD2PO4 salt was synthetized with the method illustrated in Refs [16] and [17]. The growth of all DKDP crystals was described in detail in Refs [18] and [19].

2.2 Neutron powder diffraction

Neutron powder diffraction experiments were performed using the high-pressure neutron powder diffractometer (HPNPD) at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics. The diffraction data were collected in the 2θ scan mode from 10° to 150° by the HPNPD with a monochromatic neutron beam with wavelength of 1.57639 Å generated from a Ge(115) monochromator. The neutron diffraction patterns obtained at room temperature were refined by Rietveld method using the FullProf.2k program [20].

2.3 Micro-Raman spectroscopic measurements

Raman spectral studies were conducted at room temperature using laser micro-Raman technique (LabRAM HR evolution) with an excitation wavelength of 532 nm. The spectral resolution in the experiments was approximately 0.7 cm−1. All Raman spectra were obtained by focusing the laser beam as deep as 40 μm into the bulk of the crystals to avoid contributions from the potentially influential layers by hydrogen in air. A single Si crystal was applied as a standard to calibrate the spectrograph before the spectra were obtained. The spectra were analyzed by fitting the PO4 Raman peak with a single lorentzian to determine the peak position. The error of these fitted peak positions is about 0.07 cm−1.

2.4 ATR-IR spectroscopic measurement

The spectral studies of powder specimens with size of approximately 1 μm were performed at room temperature using ATR-IR technique (Thermo Nexus5700) with an ATR cell. The internal reflection element (IRE) was a diamond crystal. FT-IR spectrometer was used to measure the absorption of all DKDP powder specimens in the spectral range of 4000–600 cm−1. The spectral resolution used in the experiments was approximately 1 cm−1. The spectra of all DKDP samples were displayed in the form of transmittance spectra.

3. Results and discussion

3.1 Determination of deuteration level of crystals via neutron diffraction

The deuteration level of grown DKDP crystals always differs from their mother solutions. Hydrogen and its isotope deuterium can be readily distinguished by neutrons. Hence, the degree of deuteration in crystals (Dc) can be actually obtained from the refined neutron diffraction data (Fig. 1). The Rietveld structural refinement method is used to refine the occupational ratio of hydrogen and deuterium to minimize the R factors. Table 1 shows the deuteration levels of the crystals grown from various deuterated level solutions and the refined R factors. The relatively small R-factors can well demonstrate the high quality of agreement between the observed and calculated profiles, which indicates that the determination of deuteration level is accurate.

 figure: Fig. 1

Fig. 1 Neutron diffraction patterns of potassium dideuterium phosphate (DKDP crystals) grown in solutions with different deuteration levels (Ds): (a) 0%, (b) 55%, (c) 40%, (d) 65%, (e) 80%, (f) 92%, (g) 98%, and (h) 99.5%

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Tables Icon

Table 1. Deuteration levels of crystals grown from various deutated growth solutions, bond lengths of (O-O) and (P-O), and the refined R factors.

Figure 1 shows that the intensity of the (200) reflection decreases with increasing deuteration level of the DKDP crystals. This result indicates that the substitution of D for H increases the separation between (200) lattice planes. Hydrogen or deuterium bond is vertical to (200) face as shown by the cell structure in Fig. 2. Table 1 shows that the (O-O) distance (Fig. 2(b)) is affected largely by the incorporation of deuterium in the crystals, the value of which increases with increasing deuteration level of the DKDP crystals. The change would affect the bond of hydrogen or deuterium and oxygen. Meanwhile, the bond length of (P-O) varies with the deuteration level of the DKDP crystals. These variations can cause spectroscopic change caused by the substitution of hydrogen by deuterium.

 figure: Fig. 2

Fig. 2 (a) Structure of DKDP crystal and (b) projection of the (001) plane.

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3.2 Raman spectrum

Neutron diffraction is very useful in determining the deuteration level in crystals, but this process is rarely performed. Thus, neutron diffraction should be used as a standard to determine the degree of deuteration of crystals. The position of the asymmetric P(OD)2 stretching vibration ν1 exhibits a linear dependency to H/D substitution. Hence, micro-Raman spectroscopy is frequently applied to conveniently determine the deuteration level of crystals according to the change in PO4 vibration peak [12]. The accuracy of the quantitative correlation between the degree of deuteration and Raman shift of the PO4 vibration peak is very critical to determine the deuteration level of crystals.

The observed main features are the Raman shifts of the PO4 vibration peak of the KDP crystal at 914.9 cm−1 and the shift toward shorter wavenumber of 878.8 cm−1 as deuteration levels of crystals increase to 99.1% (Fig. 3(a)). And, the intensity of the peak at about 960 cm−1, which presents in-plane bending mode of the hydrogen or deuterium bond [21], increases with increasing the deuteration level in DKDP crystals. Due to a Fermi resonance of a weak O-D bending mode [22], in KDP corresponding O-H bending is very weak, and its resonance with the 960 cm−1 line is practically zero, while in DKDP corresponding O-D bending become stronger with higher deuteration level. Investigating the dependence of relative Raman shift [Δν1 = ν1(KDP)−ν1(DKDP)] instead of the absolute Raman shift of crystals can be more useful to determine the deuteration level in this method to minimize errors from micro-Raman spectroscopy. Figure 3(b) shows that the dependence of the relative Raman shift for DKDP on the degree of deuteration Dc is almost perfectly linear, as follows:

Dc(%)=2.64×[ν1(KDP)ν1(DKDP)]
where ν1(KDP) and ν1(DKDP) represent the Raman shifts of the PO4 vibration peak (cm−1) of the KDP and DKDP crystals, respectively. The simulation result shows that one wavenumber change in the Raman shift could be attributed to a 2.64% variation in the deuteration level of the crystals.

 figure: Fig. 3

Fig. 3 Raman spectra of DKDP crystals (a), dependence of the variation in Raman shift [ν1(KDP)- ν1(DKDP)] of the totally symmetric PO4 vibration in DKDP on the degree of deuteration (b).

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The following three steps are performed using the results to measure the deuteration level via micro-Raman spectroscopy. First, the Raman equipment was calibrated using a single crystal Si. The Raman spectra of the KDP and DKDP crystals were then measured. Finally, Eq. (2) was used to calculate the deuteration level of the DKDP crystals.

Based on our experimental data the formula describing the dependentce of the relative Raman line width (W) of the PO4 vibration peak on deuteraion level can be fitted shown in Fig. 4 using lorentzian function:

w=10.4+21.9384×(DC0.559)2+0.855
Therefore, the relative Raman line width firstly increase and then decrease with increasing the deuterium content of DKDP crystals, witch can also be used to estimate deuteration level in crystals.

 figure: Fig. 4

Fig. 4 Dependence of the relative Raman line width of the totally symmetric PO4 vibration in DKDP on the degree of deuteration.

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3.3 IR spectrum

The neutron diffraction results show that the bond lengths of P-O and O-H/D varied with the different deuteration levels in the DKDP crystals. This change can make the β(O-H/D) (it presents stretching vibration of the O-H or O-D bond) and ν1(PO4) of their IR spectra shift toward larger wavenumber as the deuteration level of the crystals increased (Fig. 5(a)). The observed absorption wavenumber of β(O-H) of KDP was 1273.8 cm−1, and it shifted toward a larger wavenumber of 1300.5 cm−1 when deuteration level increased to 99.1% to become β(O-D). Similarly, the trend of ν1(PO4) was the same as that of β(O-H/D). The absorption wavenumber of ν1(PO4) is 828.7 cm−1 for KDP, whereas it become to 915.8 cm−1 for the 99.1% deuterated DKDP crystal. Therefore, we can measure the deuteration level of DKDP crystals depending on the relationship between the deuteration level and the variation in β(O-H/D) and ν1(PO4) of the IR spectra of DKDP crystals.

 figure: Fig. 5

Fig. 5 IR spectra of DKDP crystals (a), dependence of the variation in IR [β1(DKDP)-β1(KDP) + ν1(DKDP)- ν1(KDP)] of the total β(O-H/D)and ν1(PO4) vibration in DKDP on the degree of deuteration (b)

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Table 2 and Fig. 5(b) show that two kinds of linear relationship between the relative total change of β(O-H/D) and ν1(PO4) and deuteration level. When deuteration level is less than 73.8%, degree of deuteration Dc is almost perfectly linear with the toatal wavenumber variations of β(O-H/D) and ν1(PO4), as shown in the following Eq.:

Dc(%)=0.75×{[β(DKDP)β(KDP)]+[ν1(DKDP)ν1(KDP)]}
where β(DKDP) and β(KDP) are the β(O-H/D) absorption bands of DKDP and KDP crystals, respectively, and ν1(KDP) and ν1(DKDP) represent the absorption bands of PO4 (cm−1) of the KDP and DKDP crystals, respectively. The simulation results show that one IR wavenumber shift of both β(O-H/D) and ν1(PO4) could be attributed to a 0.75% deuteration level of DKDP crystals. This relationship becomes as follows when deuteration level is more than 73.8%:
Dc(%)=1.681×{[β(DKDP)β(KDP)]+[ν1(DKDP)ν1(KDP)]}91.5
This relationship indicates that one IR wavenumber shift of both β(O-H/D) and ν1(PO4) could be attributed to 1.68% deuteration level in DKDP crystals.

Tables Icon

Table 2. Absorption frequencies of IR bands of DKDP crystals.

The following two steps can be used to measure the deuteration level of DKDP crystals via IR spectroscopy. First, the IR spectra of the KDP and DKDP crystals were measured. Then, Eq. (4) and Eq. (5) were used to calculate the deuteration levels of the DKDP crystals.

3.4 Comparison the accuracies of micro-Raman and ATR-IR spectroscopy

Deuteration level can be determined by micro-Raman and ATR-IR spectroscopies depending on Eq. (2), Eq. (4) and Eq. (5). Table 3 shows that the deuteration level determined by micro-Raman spectroscopy and Eq. (2) is less than that measured by neutron diffraction except for Ds = 92%. The mix-difference appeared at lowly and highly deuterated level of DKDP crystals, which is approximately 4%. However, the deuteration level measured by ATR-IR spectroscopy based on Eq. (4) and Eq. (5) is more than that that measured by neutron diffraction except for Ds = 92%. The max-difference exists at low deuteration level. Consequently, both micro-Raman and ATR-IR spectroscopy can be combined and used to determine the deuteration level in DKDP crystals for measuring Ds≤ 92%. ATR-IR spectroscopy is better than micro-Raman spectroscopy for higher deuteration levels.

Tables Icon

Table 3. Deuteration level determined by neutron diffraction, micro-Raman, and IR spectroscopy

4. Conclusion

Neutron powder diffraction was applied to measure the deuteration of DKDP crystals. The deuteration level was obtained using the Rietveld method to refine the neutron diffraction data patterns. Micro-Raman spectroscopy of the bulk sample was applied at room temperature using the neutron results to investigate the relationship between the deuteration level and the relative wavenumber variation in the PO4vibration peak shift [Δν1 = ν1(KDP)−ν1(DKDP)]. One wavenumber variation in the Raman shift could be attributed to 2.64% deuteration. ATR-IR spectroscopy of the powder sample at room temperature was studied, and the results show two relationships between the deuteration level and the total relative variation in β(O-H/D) and ν1(PO4) absorption bands. This result indicates that a change of one wavenumber was caused by 0.748% deuteration when the deterioration level was less than 73.8%. By contrast, 1.681% deuteration could cause one wavenumber variation at deuteration level of more than 73.8%. Both micro-Raman and IR spectroscopy could be used to determine the deuteration level of DKDP crystals for crystals grown from solutions with deuteration level of less than 92%. However, IR spectroscopy presents more accurate results for highly deuterated DKDP crystal.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grants No. 51323002 and 51402173), the Ministry of Education (Grants No.625010360), the Project 2014BB07 from NPL, CAEP in China and the Fundamental Research Funds of Shandong University (Grants No.2015GN027).

References and links

1. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000). [CrossRef]  

2. E. I. Moses, “Ignition on the National Ignition Facility: a path towards inertial fusion energy,” Nucl. Fusion 49(10), 104022 (2009). [CrossRef]  

3. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002). [CrossRef]  

4. G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004). [CrossRef]  

5. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46(16), 3276–3303 (2007). [CrossRef]   [PubMed]  

6. J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

7. D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008). [CrossRef]  

8. S. G. Demos, P. DeMange, R. A. Negres, and M. D. Feit, “Investigation of the electronic and physical properties of defect structures responsible for laser-induced damage in DKDP crystals,” Opt. Express 18(13), 13788–13804 (2010). [CrossRef]   [PubMed]  

9. M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002). [CrossRef]  

10. G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974). [CrossRef]  

11. M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

12. T. Huser, C. W. Hollars, W. J. Siekhaus, J. J. De Yoreo, T. I. Suratwala, and T. A. Land, “Characterization of Proton Exchange Layer Profiles in KD2PO4 Crystals by Micro-Raman Spectroscopy,” Appl. Spectrosc. 58(3), 349–351 (2004). [CrossRef]   [PubMed]  

13. J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013). [CrossRef]  

14. G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006). [CrossRef]  

15. Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988). [CrossRef]  

16. S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003). [CrossRef]  

17. L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014). [CrossRef]  

18. F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015). [CrossRef]  

19. F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014). [CrossRef]   [PubMed]  

20. C. J. Rodriguez, PROGRAM FullProf.2k-version 3.20; Laboratoire Léon Brillouin (CEA-CNRS): Saclay, France, 2005.

21. B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013). [CrossRef]  

22. I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975). [CrossRef]  

References

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  • |

  1. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
    [Crossref]
  2. E. I. Moses, “Ignition on the National Ignition Facility: a path towards inertial fusion energy,” Nucl. Fusion 49(10), 104022 (2009).
    [Crossref]
  3. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
    [Crossref]
  4. G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
    [Crossref]
  5. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46(16), 3276–3303 (2007).
    [Crossref] [PubMed]
  6. J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).
  7. D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
    [Crossref]
  8. S. G. Demos, P. DeMange, R. A. Negres, and M. D. Feit, “Investigation of the electronic and physical properties of defect structures responsible for laser-induced damage in DKDP crystals,” Opt. Express 18(13), 13788–13804 (2010).
    [Crossref] [PubMed]
  9. M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
    [Crossref]
  10. G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
    [Crossref]
  11. M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).
  12. T. Huser, C. W. Hollars, W. J. Siekhaus, J. J. De Yoreo, T. I. Suratwala, and T. A. Land, “Characterization of Proton Exchange Layer Profiles in KD2PO4 Crystals by Micro-Raman Spectroscopy,” Appl. Spectrosc. 58(3), 349–351 (2004).
    [Crossref] [PubMed]
  13. J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
    [Crossref]
  14. G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
    [Crossref]
  15. Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
    [Crossref]
  16. S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
    [Crossref]
  17. L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
    [Crossref]
  18. F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
    [Crossref]
  19. F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
    [Crossref] [PubMed]
  20. C. J. Rodriguez, PROGRAM FullProf.2k-version 3.20; Laboratoire Léon Brillouin (CEA-CNRS): Saclay, France, 2005.
  21. B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
    [Crossref]
  22. I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975).
    [Crossref]

2015 (1)

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

2014 (2)

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

2013 (2)

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

2010 (1)

2009 (1)

E. I. Moses, “Ignition on the National Ignition Facility: a path towards inertial fusion energy,” Nucl. Fusion 49(10), 104022 (2009).
[Crossref]

2008 (1)

D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
[Crossref]

2007 (1)

2006 (1)

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

2004 (2)

2003 (1)

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

2002 (2)

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

2000 (1)

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

1997 (1)

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

1994 (1)

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

1988 (1)

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

1975 (1)

I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975).
[Crossref]

1974 (1)

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Atherton, L. J.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Auerbach, J. M.

Balascio, J. F.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Barker, C. E.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Bowers, M. W.

Broslavets, Y. Y.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Burnham, A. K.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

Campbell, J. H.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

De Yoreo, J. J.

Debray, J.

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

Deguchi, K.

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

DeMange, P.

Demos, S. G.

DeYoreo, J. J.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Dixit, S. N.

Duan, A. D.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Erbert, G. V.

Fang, C. S.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Feit, M. D.

Fu, D. W.

D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
[Crossref]

Fu, Y. J.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Fujita, H.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Gan, X. Y.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Gao, Z. S.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Goldstein, S.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Gu, Q. T.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Haynam, C. A.

He, Y.

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Hollars, C. W.

Huser, T.

Ibanez, A.

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

Ishimoto, T.

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

Jancaitis, K. S.

Ji, S. H.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Ji, S.-H.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Jitsuno, T.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Kasatani, H.

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

Kim, D. W.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Kim, Y. S.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Kozlowski, M. R.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Kuhs, W. F.

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

Land, T. A.

Laulicht, I.

I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975).
[Crossref]

Leroudier, J.

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

Li, G.

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Li, L.

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Li, Z.

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Liu, B.

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Liu, B. A.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Liu, F.

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

Liu, F. F.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Liu, F.-F.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Loiacono, G. M.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Manes, K. R.

Maney, R. T.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Marshall, C. D.

Mehta, N. C.

Menapace, J.

Miller, G. H.

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Montesanti, R. C.

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Moses, E.

Moses, E. I.

E. I. Moses, “Ignition on the National Ignition Facility: a path towards inertial fusion energy,” Nucl. Fusion 49(10), 104022 (2009).
[Crossref]

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Murray, J. R.

Nakatsuka, M.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Negres, R. A.

Nelmes, R. J.

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

Nostrand, M. C.

Ofek, R.

I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975).
[Crossref]

Orth, C. D.

Osborne, W.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Patterson, R.

Ren, H. K.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Sacks, R. A.

Sasaki, T.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Segonds, P.

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

Shaw, M. J.

Sidoryuk, O. E.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Siekhaus, W. J.

Spaeth, M.

Stansfield, R. F. D.

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

Su, G.

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Sun, X.

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Suratwala, T. I.

Sutton, S. B.

Tachikawa, M.

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

Tokiwa, H.

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

Tun, Z.

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

Van Wonterghem, B. M.

Wang, B.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Wang, S. L.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Wang, X. Q.

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

Wegner, P. J.

White, R. K.

Whitman, P. K.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

Widmayer, C. C.

Williams, W. H.

Wuest, C. R.

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Xiong, R. G.

D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
[Crossref]

Xu, M.

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

Xu, M. X.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Xu, M.-X.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Xu, X. G.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Xu, X.-G.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Yakshin, M. A.

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Yang, S. T.

Yoshida, H.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yoshida, K.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yoshimura, M.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yu, G.

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

Yu, G. W.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Zaccaro, J.

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

Zhang, L.

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

Zhang, L. S.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Zhang, L.-S.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Zhang, Q. H.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Zhang, W.

D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
[Crossref]

Zhou, H.

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

Zhou, H. L.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Zhu, L. L.

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Zhu, L.-L.

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Zhuang, X.

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Appl. Phys. Lett. (1)

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K (H1− xDx) 2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Appl. Spectrosc. (1)

Chin. Phys. Lett. (1)

B. Liu, H. L. Zhou, Q. H. Zhang, M.-X. Xu, S.-H. Ji, L.-L. Zhu, L.-S. Zhang, F.-F. Liu, X. Sun, and X.-G. Xu, “Raman spectra of deuterated potassium dihydrogen phosphate crystals with different degrees of deuteration,” Chin. Phys. Lett. 30(6), 067804 (2013).
[Crossref]

Cryst. Growth Des. (2)

J. Leroudier, J. Zaccaro, J. Debray, P. Segonds, and A. Ibanez, “Rapid Growth in Solution of a Solid Solution under Stationary Conditions,” Cryst. Growth Des. 13(8), 3613–3620 (2013).
[Crossref]

D. W. Fu, W. Zhang, and R. G. Xiong, “Isotope effect on SHG response and ferroelectric properties of a homochiral zinc coordination compound containing tetrazole ligand,” Cryst. Growth Des. 8(9), 3461–3464 (2008).
[Crossref]

Cryst. Res. Technol. (2)

S. L. Wang, Z. S. Gao, Y. J. Fu, A. D. Duan, X. Sun, C. S. Fang, and X. Q. Wang, “Study on rapid growth of highly-deuterated DKDP crystals,” Cryst. Res. Technol. 38(11), 941–945 (2003).
[Crossref]

F. Liu, L. Zhang, G. Yu, and X. Sun, “Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction,” Cryst. Res. Technol. 50(2), 164–170 (2015).
[Crossref]

Ferroelectrics (1)

M. Tachikawa, T. Ishimoto, H. Tokiwa, H. Kasatani, and K. Deguchi, “First-principle calculation on isotope effect in KH 2 PO 4 and KD 2 PO 4 of hydrogen-bonded dielectric materials,” Ferroelectrics 268(1), 3–9 (2002).
[Crossref]

ICF Quarterly Rep. (1)

J. H. Campbell, L. J. Atherton, J. J. DeYoreo, M. R. Kozlowski, R. T. Maney, R. C. Montesanti, and C. E. Barker, “Large-aperture, high-damage-threshold optics for beamlet,” ICF Quarterly Rep. 5(1), 52–61 (1994).

Int. Mater. Rev. (1)

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most power laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

J. Cryst. Growth (1)

L. Zhang, G. Yu, H. Zhou, L. Li, M. Xu, B. Liu, and X. Sun, “Study on rapid growth of 98% deuterated potassium dihydrogen phosphate (DKDP) crystals,” J. Cryst. Growth 401, 190–194 (2014).
[Crossref]

J. Phys. C Solid State Phys. (1)

Z. Tun, R. J. Nelmes, W. F. Kuhs, and R. F. D. Stansfield, “A high-resolution neutron-diffraction study of the effects of deuteration on the crystal structure of KH2PO4,” J. Phys. C Solid State Phys. 21(2), 245–258 (1988).
[Crossref]

J. Raman Spectrosc. (1)

I. Laulicht and R. Ofek, “Anomalous isotope effect on Raman linewidths in KH2AsO4 and KD2AsO4 crystals,” J. Raman Spectrosc. 4(1), 41–51 (1975).
[Crossref]

Laser Phys. (1)

M. A. Yakshin, D. W. Kim, Y. S. Kim, Y. Y. Broslavets, O. E. Sidoryuk, and S. Goldstein, “Determination of the deuteration degree of DKDP crystals by Raman spectroscopy technique,” Laser Phys. 7(4), 941–945 (1997).

Nucl. Fusion (1)

E. I. Moses, “Ignition on the National Ignition Facility: a path towards inertial fusion energy,” Nucl. Fusion 49(10), 104022 (2009).
[Crossref]

Opt. Eng. (1)

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Opt. Express (1)

Opt. Mater. (1)

G. Li, G. Su, X. Zhuang, Z. Li, and Y. He, “A new method to determine the deuterium content of DKDP crystal with thermo-gravimetric apparatus,” Opt. Mater. 29(2-3), 220–223 (2006).
[Crossref]

Sci. Rep. (1)

F. F. Liu, G. W. Yu, L. S. Zhang, L. Li, B. Wang, X. Y. Gan, H. K. Ren, H. L. Zhou, L. L. Zhu, S. H. Ji, M. X. Xu, B. A. Liu, X. G. Xu, Q. T. Gu, and X. Sun, “Effect of supersaturation on hillock of directional Growth of KDP crystals,” Sci. Rep. 4, 6886 (2014).
[Crossref] [PubMed]

Other (1)

C. J. Rodriguez, PROGRAM FullProf.2k-version 3.20; Laboratoire Léon Brillouin (CEA-CNRS): Saclay, France, 2005.

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Figures (5)

Fig. 1
Fig. 1 Neutron diffraction patterns of potassium dideuterium phosphate (DKDP crystals) grown in solutions with different deuteration levels (Ds): (a) 0%, (b) 55%, (c) 40%, (d) 65%, (e) 80%, (f) 92%, (g) 98%, and (h) 99.5%
Fig. 2
Fig. 2 (a) Structure of DKDP crystal and (b) projection of the (001) plane.
Fig. 3
Fig. 3 Raman spectra of DKDP crystals (a), dependence of the variation in Raman shift [ν1(KDP)- ν1(DKDP)] of the totally symmetric PO4 vibration in DKDP on the degree of deuteration (b).
Fig. 4
Fig. 4 Dependence of the relative Raman line width of the totally symmetric PO4 vibration in DKDP on the degree of deuteration.
Fig. 5
Fig. 5 IR spectra of DKDP crystals (a), dependence of the variation in IR [β1(DKDP)-β1(KDP) + ν1(DKDP)- ν1(KDP)] of the total β(O-H/D)and ν1(PO4) vibration in DKDP on the degree of deuteration (b)

Tables (3)

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Table 1 Deuteration levels of crystals grown from various deutated growth solutions, bond lengths of (O-O) and (P-O), and the refined R factors.

Tables Icon

Table 2 Absorption frequencies of IR bands of DKDP crystals.

Tables Icon

Table 3 Deuteration level determined by neutron diffraction, micro-Raman, and IR spectroscopy

Equations (5)

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D s = m ( D ) m ( D ) + m ( H )
D c ( % ) = 2.64 × [ ν 1 ( K D P ) ν 1 ( D K D P ) ]
w = 10.4 + 21.938 4 × ( D C 0 .559 ) 2 + 0.855
D c ( % ) = 0.75 × { [ β ( D K D P ) β ( K D P ) ] + [ ν 1 ( D K D P ) ν 1 ( K D P ) ] }
D c ( % ) = 1.681 × { [ β ( D K D P ) β ( K D P ) ] + [ ν 1 ( D K D P ) ν 1 ( K D P ) ] } 91.5

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