Abstract

The piezoelectric photoacoustics application possibility for polycrystalline structure formation has been considered. The accent was on research and transient modeling with pulse laser irradiation. A mathematical model for the given setup with a single laser impulse was developed. The results of mathematical modeling were experimentally tested on cement samples.

© 2014 Optical Society of America

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References

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  1. F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed. (Edward Arnold, 1970).
  2. V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).
  3. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
  4. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
    [CrossRef]
  5. O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
    [CrossRef]
  6. O. V. Angelsky and P. P. Maksimyak, “Polarization-interference measurement of phase-inhomogeneous objects,” Appl. Opt. 31, 4417–4419 (1992).
    [CrossRef]
  7. O. V. Angelsky and P. P. Maksimyak, “Optical correlation measurements of the structure parameters of random and fractal objects,” Meas. Sci. Technol. 9, 1682–1693 (1998).
    [CrossRef]
  8. A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
    [CrossRef]
  9. O. V. Angelsky and P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993).
    [CrossRef]
  10. O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
    [CrossRef]
  11. Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
    [CrossRef]
  12. Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
    [CrossRef]
  13. W. Jackson and N. M. Amer, “Piezoelectric photoacoustic detection: theory and experiment,” J. Appl. Phys. 51, 3343–3353 (1980).
    [CrossRef]
  14. V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
    [CrossRef]
  15. D. A. Andrusenko and I. Ya. Kucherov, “Photothermal effect in solids with piezoelectric registration,” J. Tech. Phys. 69, 1–5 (1999) (in Russian).
  16. M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
    [CrossRef]
  17. A. A. Harkevich, “Theory of Electroacoustics Transducers,” (Moscow Science, 1973), in Russian.
  18. L. D. Landau and E. M. Liphitc, “Theory of Elasticity,” (Moscow Science, 1965), in Russian.
  19. A. V. Lykov, “Theory of Thermal Conductivity,” High School Moscow, 1967), in Russian.
  20. A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (Chapman & Hall/CRC, 2002).
  21. I. S. Grigoryeva and E. Z. Melihova, Physics Constants Handbook (Energoatomizdat, 1991), in Russian.
  22. , “Cements. Test methods. General provisions,” (in Russian).
  23. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
    [CrossRef]

2012 (2)

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
[CrossRef]

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

2011 (1)

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

2010 (1)

Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

2009 (1)

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

2006 (2)

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
[CrossRef]

1999 (2)

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

D. A. Andrusenko and I. Ya. Kucherov, “Photothermal effect in solids with piezoelectric registration,” J. Tech. Phys. 69, 1–5 (1999) (in Russian).

1998 (1)

O. V. Angelsky and P. P. Maksimyak, “Optical correlation measurements of the structure parameters of random and fractal objects,” Meas. Sci. Technol. 9, 1682–1693 (1998).
[CrossRef]

1996 (1)

V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
[CrossRef]

1994 (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

1993 (1)

O. V. Angelsky and P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993).
[CrossRef]

1992 (1)

1980 (1)

W. Jackson and N. M. Amer, “Piezoelectric photoacoustic detection: theory and experiment,” J. Appl. Phys. 51, 3343–3353 (1980).
[CrossRef]

Amer, N. M.

W. Jackson and N. M. Amer, “Piezoelectric photoacoustic detection: theory and experiment,” J. Appl. Phys. 51, 3343–3353 (1980).
[CrossRef]

Andrusenko, D. A.

D. A. Andrusenko and I. Ya. Kucherov, “Photothermal effect in solids with piezoelectric registration,” J. Tech. Phys. 69, 1–5 (1999) (in Russian).

Angelsky, O. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
[CrossRef]

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

O. V. Angelsky and P. P. Maksimyak, “Optical correlation measurements of the structure parameters of random and fractal objects,” Meas. Sci. Technol. 9, 1682–1693 (1998).
[CrossRef]

O. V. Angelsky and P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993).
[CrossRef]

O. V. Angelsky and P. P. Maksimyak, “Polarization-interference measurement of phase-inhomogeneous objects,” Appl. Opt. 31, 4417–4419 (1992).
[CrossRef]

Archelyuk, A. D.

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Baku, B. A.

Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Bekshaev, A. Y.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Blonskij, V.

V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
[CrossRef]

Burkovets, D. N.

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Ermolenko, S. B.

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Felde, C. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
[CrossRef]

Gorsky, M. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).

Grigoryeva, I. S.

I. S. Grigoryeva and E. Z. Melihova, Physics Constants Handbook (Energoatomizdat, 1991), in Russian.

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Hanson, S. G.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Harkevich, A. A.

A. A. Harkevich, “Theory of Electroacoustics Transducers,” (Moscow Science, 1973), in Russian.

Jackson, W.

W. Jackson and N. M. Amer, “Piezoelectric photoacoustic detection: theory and experiment,” J. Appl. Phys. 51, 3343–3353 (1980).
[CrossRef]

Kucherov, I. Ya.

D. A. Andrusenko and I. Ya. Kucherov, “Photothermal effect in solids with piezoelectric registration,” J. Tech. Phys. 69, 1–5 (1999) (in Russian).

Landau, L. D.

L. D. Landau and E. M. Liphitc, “Theory of Elasticity,” (Moscow Science, 1965), in Russian.

Lee, F. M.

F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed. (Edward Arnold, 1970).

Liphitc, E. M.

L. D. Landau and E. M. Liphitc, “Theory of Elasticity,” (Moscow Science, 1965), in Russian.

Lykov, A. V.

A. V. Lykov, “Theory of Thermal Conductivity,” High School Moscow, 1967), in Russian.

Maksimyak, A. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
[CrossRef]

Maksimyak, P. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).

O. V. Angelsky and P. P. Maksimyak, “Optical correlation measurements of the structure parameters of random and fractal objects,” Meas. Sci. Technol. 9, 1682–1693 (1998).
[CrossRef]

O. V. Angelsky and P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993).
[CrossRef]

O. V. Angelsky and P. P. Maksimyak, “Polarization-interference measurement of phase-inhomogeneous objects,” Appl. Opt. 31, 4417–4419 (1992).
[CrossRef]

Melihova, E. Z.

I. S. Grigoryeva and E. Z. Melihova, Physics Constants Handbook (Energoatomizdat, 1991), in Russian.

Peresunko, A. P.

Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Polyanin, A. D.

A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (Chapman & Hall/CRC, 2002).

Polyanskii, P. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
[CrossRef]

Ramachandran, V. S.

V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).

Schlesser, R.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Shendeleva, M. L.

V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
[CrossRef]

Tkhoryk, V. A.

V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
[CrossRef]

Ushenko, A. G.

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Ushenko, Y. A.

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Zenkova, C. Y.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Zgonik, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Adv. Opt. Technol. (1)

Y. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (2)

W. Jackson and N. M. Amer, “Piezoelectric photoacoustic detection: theory and experiment,” J. Appl. Phys. 51, 3343–3353 (1980).
[CrossRef]

V. Blonskij, V. A. Tkhoryk, and M. L. Shendeleva, “Thermal diffusivity of solids determination by photoacoustic piezoelectric technique,” J. Appl. Phys. 79, 3512–3516 (1996).
[CrossRef]

J. Biomed. Opt. (1)

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

J. Tech. Phys. (1)

D. A. Andrusenko and I. Ya. Kucherov, “Photothermal effect in solids with piezoelectric registration,” J. Tech. Phys. 69, 1–5 (1999) (in Russian).

Meas. Sci. Technol. (1)

O. V. Angelsky and P. P. Maksimyak, “Optical correlation measurements of the structure parameters of random and fractal objects,” Meas. Sci. Technol. 9, 1682–1693 (1998).
[CrossRef]

Opt. Eng. (1)

O. V. Angelsky and P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993).
[CrossRef]

Opt. Photon. News (1)

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photon. News 23, 25–29 (2012).
[CrossRef]

Phys. Rev. A (1)

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Phys. Rev. B (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, and P. Günter, “Dielectric, elastic, piezoelectric and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Proc. SPIE (2)

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E (2006).
[CrossRef]

Quantum Electron. (1)

O. V. Angelsky, A. G. Ushenko, A. D. Archelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Ukr. J. Phys. Opt. (1)

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

Other (8)

F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed. (Edward Arnold, 1970).

V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).

A. A. Harkevich, “Theory of Electroacoustics Transducers,” (Moscow Science, 1973), in Russian.

L. D. Landau and E. M. Liphitc, “Theory of Elasticity,” (Moscow Science, 1965), in Russian.

A. V. Lykov, “Theory of Thermal Conductivity,” High School Moscow, 1967), in Russian.

A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (Chapman & Hall/CRC, 2002).

I. S. Grigoryeva and E. Z. Melihova, Physics Constants Handbook (Energoatomizdat, 1991), in Russian.

, “Cements. Test methods. General provisions,” (in Russian).

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Figures (15)

Fig. 1.
Fig. 1.

PP-transient process: voltage dependence versus time.

Fig. 2.
Fig. 2.

Schematic representation of the piezoelement, consisting of layers: (1) BaTiO3, (2) metal plates, and (3) contacts.

Fig. 3.
Fig. 3.

Equivalent electrical circuit of the measuring device.

Fig. 4.
Fig. 4.

Dependence of the photoacoustic signal on time during the transient process.

Fig. 5.
Fig. 5.

Geometry of the model: (1) sample, (2) PZT ceramics, and (3) light spot.

Fig. 6.
Fig. 6.

Calculated temperature field on the surface of a square plate sapphire 20mm×20mm×1mm. Time: 1 s after the start of heating. Size of heat source: 2mm×2mm, q=δ(zl).

Fig. 7.
Fig. 7.

Calculated heat versus time.

Fig. 8.
Fig. 8.

Dependence of the maximum of (19) with=1 from k1 to αt, when k2=0.0005mm1, RC0=4.

Fig. 9.
Fig. 9.

Photoacoustic experimental setup: (1) sample in a sealed cell, (2) transparent substrate, (3) piezoelement, (4) divider, (5) laser, (6) photodiode, (7) amplifiers, (8) ADC, (9) PC, and (10) lens to change the diameter of the spot (optional).

Fig. 10.
Fig. 10.

Experimental dependence of Umax versus P0 for different sides of a silicon sample.

Fig. 11.
Fig. 11.

Changing of Umax during concrete hydration for different cement–water ratios.

Fig. 12.
Fig. 12.

Changing of tmax during concrete hydration for different cement–water ratios.

Fig. 13.
Fig. 13.

Scheme for measurement of backward scattering integral coefficient: (1) integral sphere, (2) chamber, (3) light detector, (4) He–Ne laser, (5) sample, and (6) optical window.

Fig. 14.
Fig. 14.

Experimental dependence of integral diffuse reflecting coefficient versus time during concrete hydration for different water-to-cement ratios.

Fig. 15.
Fig. 15.

Changing of (Umax/1γ) during concrete hydration for different cement–water ratios. Vertical lines illustrate beginning of hardening, registered by the Vicat needle. Solid line for cement–water ratio of 0.275; dashed line for a ratio of 0.3.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

I(t)=2P0π2a2er2/a2eβz(1+cos(ωt)).
T=T˜eiωt.
q=C0Ukεu.
U+RC0dUdt=Rkεdudt.
U(t)=kεC00tettRCu(t)dt.
u(t)=S(uxx+uyy)sampledAdt.
S(uxx+uyy)sampledA=2αSTsampledA.
I(t)={0,t<t0P0,tt0}.
TtatΔ3T=q.
2P0π2a2er2/a2eβz.
q=(1γ)P0δ(lz)s2Cρ|z=l.
T(0)=0.
Tz=k1T|z=l,
Tz=k2T|z=0.
Tx=0|x=0,x=A,
Ty=0|y=0,y=A.
T(x,y,z,t)=0tAs/2A+s/2As/2A+s20lqG(x,y,z,ξ,η,ζ,t)dξdηdζdtG(x,y,z,ξ,η,ζ,t)=G1(x,ξ,t)G2(y,η,t)G3(z,ζ,t),G1(x,ξ,t)=1A[1+2n=1cos(πnxA)cos(πnξA)exp(π2n2attA2)],G2(y,η,t)=1A[1+2n=1cos(πnyA)cos(πnηA)exp(π2n2attA2)],G3(z,ζ,t)=n=1ρn(z)ρn(ζ)ρn2exp(atνn2t),ρn(x)=cos(νnx)+k1νnsin(νnx),ρn2=k22νnνn2+k12νn2+k22+k52νn2+l2(1+k52νn2),
tan(νl)ν=k1+k2ν2k1k2.
0A0A(uxx+uyy)зpaзкadxdy=(1γ)P0s2Cρ0A0AT(x,y,z,t)dxdy|z=0.
T(x,y,z,t)=0tAs/2A+s/2As/2A+s20lδ(zl)G(x,y,z,ξ,η,ζ,t)dξdηdζdt.
T(x,y,z,t)=0tF(x,y,z,t)dtF(x,y,z,t)=As/2A+s/2As/2A+s20lδ(zl)G(x,y,z,ξ,η,ζ,t)dξdηdζ.
u(t)=ddt[(1γ)P0s2Cρ0A0A0tF(x,y,z,t)dtdxdy]|z=0=(1γ)P0s2Cρ0A0AF(x,y,z,t)dxdy|z=0.
U(t)=(1γ)P0s2CρkεC00tettRC0A0AF(x,y,z,t)dxdy|z=0dt.

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