Abstract

Large single crystals of a nonlinear optical material LaxYyScz(BO3)4 have been obtained by High Temperature Top-Seeded Solution Growth (HTTSSG). This material is very interesting due to its easy growth procedure, its non hygroscopic properties, a suitable hardness to be reliably cut and polished, a large transparency wavelength range and also good nonlinear properties with potential for UV generation. However, the crystals show inhomogeneities and growth imperfections which can be observed by light scattering and by Schlieren photography method. Chemical etching is used to reveal defects. Observed striations can be related to the growth of rhombohedral facets.

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References

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  1. A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
    [Crossref]
  2. C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
    [Crossref]
  3. Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
    [Crossref]
  4. D. A. Keszler, “Borates for optical frequency conversion,” Curr. Opin. Solid State Mater. Sci. 1(2), 204–211 (1996).
    [Crossref]
  5. T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
    [Crossref]
  6. P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) 10(13), 979–992 (1998).
    [Crossref]
  7. C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
    [Crossref]
  8. N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
    [Crossref]
  9. N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
    [Crossref]
  10. D. A. Keszler, J. L. Stone-Sundberg, N. Ye, and M. A. Hruschka, “Borate crystals for optical frequency conversion,” United States Patent no. US 7,534,377 B2 (2009).
  11. V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
    [Crossref]
  12. A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
    [Crossref]
  13. C. Motzer and M. Reichling, “Morphological classification and quantitative analysis of etch pits,” J. Appl. Phys. 108(11), 113523 (2010).
    [Crossref]

2010 (1)

C. Motzer and M. Reichling, “Morphological classification and quantitative analysis of etch pits,” J. Appl. Phys. 108(11), 113523 (2010).
[Crossref]

2008 (1)

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

2007 (1)

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

2006 (1)

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

2005 (1)

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

2002 (1)

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

2000 (2)

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
[Crossref]

1998 (1)

P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) 10(13), 979–992 (1998).
[Crossref]

1996 (1)

D. A. Keszler, “Borates for optical frequency conversion,” Curr. Opin. Solid State Mater. Sci. 1(2), 204–211 (1996).
[Crossref]

1994 (1)

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

1990 (1)

C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
[Crossref]

Aka, G.

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

Aleksandrovsky, A. S.

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

Becker, P.

P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) 10(13), 979–992 (1998).
[Crossref]

Beregi, E.

A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
[Crossref]

Borsutzky, A.

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

Chen, C.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
[Crossref]

Chen, H.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Chen, W.

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

Hruschka, M. A.

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

Hu, X.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Jiang, H.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Kamimura, T.

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Keszler, D. A.

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

D. A. Keszler, “Borates for optical frequency conversion,” Curr. Opin. Solid State Mater. Sci. 1(2), 204–211 (1996).
[Crossref]

Kong, W.

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

L'Huillier, J. A.

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

Li, R.

C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
[Crossref]

Lin, S.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Liu, Y.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Lu, S.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Mao, H.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Mori, Y.

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Motzer, C.

C. Motzer and M. Reichling, “Morphological classification and quantitative analysis of etch pits,” J. Appl. Phys. 108(11), 113523 (2010).
[Crossref]

Ogawa, T.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Péter, A.

A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
[Crossref]

Polgar, K.

A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
[Crossref]

Reichling, M.

C. Motzer and M. Reichling, “Morphological classification and quantitative analysis of etch pits,” J. Appl. Phys. 108(11), 113523 (2010).
[Crossref]

Sasaki, T.

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Stone-Sundberg, J. L.

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

Tan, Q.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Tang, D.

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

Vasiliev, A. D.

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

Wallenstein, R.

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

Wang, J.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Wesemann, V.

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

Wu, Y.

C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
[Crossref]

Yap, Y. K.

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Ye, N.

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

Yoshimura, M.

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Zaitsev, A. I.

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

Zamkov, A. V.

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

Zhang, C.

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Zhang, Y.

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

Adv. Mater. (Deerfield Beach Fla.) (1)

P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) 10(13), 979–992 (1998).
[Crossref]

Appl. Phys. B (1)

V. Wesemann, A. Borsutzky, R. Wallenstein, and J. A. L'Huillier, “An improved Schlieren method for the sensitive and spatially resolved measurement of the quality of optical crystals with small apertures,” Appl. Phys. B 89(2-3), 377–383 (2007).
[Crossref]

Chem. Mater. (1)

N. Ye, J. L. Stone-Sundberg, M. A. Hruschka, G. Aka, W. Kong, and D. A. Keszler, “Nonlinear optical crystal YxLayScz(BO3)4 (x+y+z=4),” Chem. Mater. 17(10), 2687–2692 (2005).
[Crossref]

Curr. Opin. Solid State Mater. Sci. (1)

D. A. Keszler, “Borates for optical frequency conversion,” Curr. Opin. Solid State Mater. Sci. 1(2), 204–211 (1996).
[Crossref]

J. Appl. Phys. (1)

C. Motzer and M. Reichling, “Morphological classification and quantitative analysis of etch pits,” J. Appl. Phys. 108(11), 113523 (2010).
[Crossref]

J. Cryst. Growth (6)

A. Péter, K. Polgar, and E. Beregi, “Revealing growth defects in non-linear borate single crystals by chemical etching,” J. Cryst. Growth 209(1), 102–109 (2000).
[Crossref]

A. I. Zaitsev, A. S. Aleksandrovsky, A. D. Vasiliev, and A. V. Zamkov, “Domain structure in strontium tetraborate single crystal,” J. Cryst. Growth 310(1), 1–4 (2008).
[Crossref]

C. Zhang, J. Wang, X. Hu, H. Jiang, Y. Liu, and C. Chen, “Growth of large K2Al2B2O7,” J. Cryst. Growth 235(1-4), 1–4 (2002).
[Crossref]

Q. Tan, H. Mao, S. Lin, H. Chen, S. Lu, D. Tang, and T. Ogawa, “Defects in beta BaB2O4 (BBO) crystals observed by laser scanning tomography,” J. Cryst. Growth 141(3-4), 393–398 (1994).
[Crossref]

C. Chen, Y. Wu, and R. Li, “The development of new NLO crystals in borate series,” J. Cryst. Growth 99(1–4), 790–798 (1990).
[Crossref]

N. Ye, Y. Zhang, W. Chen, D. A. Keszler, and G. Aka, “Growth of nonlinear optical crystal Y0.57La0.72Sc2.71(BO3)4,” J. Cryst. Growth 292(2), 464–467 (2006).
[Crossref]

Mater. Sci. Eng. (1)

T. Sasaki, Y. Mori, M. Yoshimura, Y. K. Yap, and T. Kamimura, “Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light,” Mater. Sci. Eng. 30(1-2), 1–54 (2000).
[Crossref]

Other (1)

D. A. Keszler, J. L. Stone-Sundberg, N. Ye, and M. A. Hruschka, “Borate crystals for optical frequency conversion,” United States Patent no. US 7,534,377 B2 (2009).

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Figures (11)

Fig. 1
Fig. 1

As grown crystal from LCMCP 8.3g in crucible (diameter Ф = 40mm) and from Cristal Laser 93 g. in Ф = 80 mm crucible.

Fig. 2
Fig. 2

(a) Representation of rhombohedral and hexagonal structures, (b) rhombohedra cell viewed along X direction, Z axis is vertical, the angles measure the intersection of the YZ plane and edges of rhombohedral facets with respect to the Z axis ; (c) rhombohedral cell viewed along Y direction, Z axis is vertical ; dotted and full lines show the intersection of rhombohedral facets with the XZ plane ; (d) rhombohedral cell viewed along Z direction, the angle is defined by the intersection of the XY plane and the rhombohedral facets.

Fig. 3
Fig. 3

Experimental setup for Schlieren photography.

Fig. 4
Fig. 4

Crystal between crossed polarizers. (a): PA axis parallel to XZ axis; (b): axis slightly tilted. Sample size is 7x6mm

Fig. 5
Fig. 5

Schlieren pictures of the sample; (a) X cut face, (b) Z cut face.

Fig. 6
Fig. 6

Evolution of X cut face with time, X + facet: (a) chemical etching at 1h, and (b) at 5h. The whole surface is reconstructed with 9 microscope pictures.

Fig. 7
Fig. 7

Evolution with time of opposite sides for Y cut faces (Y + and Y- facets). First series of images corresponds to Y + facet: (a) chemical etching at 1h, (b) at 2h, (c) at 3h, (d) at 4h and (e) at 5h. Second series correspond to Y- facet: (f), (g), (h), (i) and (j) respectively for 1h, 2h, 3h, 4h and 5h. The high of each picture is 0.5 mm.

Fig. 8
Fig. 8

Evolution with time of opposite sides for Z cut faces (Z- upper and Z + bottom facets). First series of images corresponds to Z- facet: (a) chemical etching at 1h, (b) 2h, (c) 3h, (d) 4h and (e) 5h. The second series corresponds to Z + facet: (f), (g), (h), (i) and (j) respectively for 1h, 2h, 3h, 4h and 5h. The width of each picture is 0.5mm.

Fig. 9
Fig. 9

The sample is observed under microscope after chemical etching, X axis is perpendicular to the observation plane, Z axis being vertical. (a) after 1 hour a crossed lines structure is revealed. (b and c) after 3 hours clear stripes show etch pits and fine structures orientated in the other direction, (c) with higher magnification the shape of etch pits is observed.

Fig. 10
Fig. 10

(a) Y + face, magnification x200, after 1h numerous etch-pits with head of arrow shape; (b) Y- face, magnification x470, after 4h clear stripes oriented at ± 51.5° from z axis show a fine sub-structure.

Fig. 11
Fig. 11

(a) Numerous etch-pits are revealed after 4 hours, (b) the triangular etch-pit shape and the orientation of dislocations are due to the growth of (001), (010), and (001) faces of LYSB crystal.

Equations (1)

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sin α 2 = 3A 2 3 A 2 + C 2 α=103.23°.

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