Abstract

A Monte Carlo ray tracing procedure is proposed to simulate thermal optical processes in heterogeneous materials. It operates within a detailed 3D image of the material, and it can therefore be used to investigate the relationship between the microstructure, the constituent optical properties, and the macroscopic radiative behavior. The program is applied to porous silica glass. A sample was first characterized by 3D x-ray tomography; then, its normal spectral emittance was calculated and compared with the experimental spectrum measured independently by high-temperature infrared emittance spectroscopy. We conclude with a discussion of the light-scattering mechanisms occurring in the sample.

© 2007 Optical Society of America

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  1. R. Siegel and M. Spuckler, "Analysis of thermal radiation effects on temperatures in turbine engine thermal barrier coatings," Mater. Sci. Engl. A 245, 150-159 (1998).
    [CrossRef]
  2. D. Damm and A. Fedorov, "Radiative heat transfer in SOFC materials and components," J. Power Sources 143, 158-165 (2004).
    [CrossRef]
  3. R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
    [CrossRef]
  4. D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
    [CrossRef]
  5. B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).
  6. D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
    [CrossRef]
  7. O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
    [CrossRef]
  8. M. Tancrez and J. Taine, "Direct identification of absorption and scattering coefficient and phase function of a porous medium by a Monte Carlo technique," Int. J. Heat Mass Transfer 47, 373-383 (2004).
    [CrossRef]
  9. R. Coquard and D. Baillis, "Radiative characteristics of opaque spherical particles beds: a new method of prediction," J. Thermophys. Heat Transfer 18, 178-186 (2004).
    [CrossRef]
  10. R. Coquard and D. Baillis, "Radiative characteristics of beds of spheres containing an absorbing and scattering medium," J. Thermophys. Heat Transfer 19, 226-234 (2005).
    [CrossRef]
  11. A. G. Fedorov and R. Viskanta, "Radiative transfer in semitransparent glass foam blancket," Phys. Chem. Glasses 41, 2769-2776 (2000).
  12. L. Dombrovsky, J. Randrianalisoa, D. Baillis, and L. Pilon, "Use of the Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles," Appl. Opt. 44, 7021-7031 (2005).
    [CrossRef] [PubMed]
  13. J. Randrianalisoa, D. Baillis, and L. Pilon, "Modeling radiation characteristics of semitransparent media containing bubbles or particles," J. Opt. Soc. Am. A 23, 1645-1656 (2006).
    [CrossRef]
  14. B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
    [CrossRef]
  15. O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
    [CrossRef]
  16. B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
    [CrossRef]
  17. R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, 2002), pp. 923-966.
  18. D. De Sousa Meneses, J. F. Brun, P. Echegut, and P. Simon, "Contribution of semiquantum dielectric function models to the analysis of infrared spectra," Appl. Spectrosc. 58, 969-974 (2004).
    [CrossRef]
  19. B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
    [CrossRef]
  20. V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
    [CrossRef]
  21. M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
    [CrossRef]
  22. J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
    [CrossRef]
  23. P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
    [CrossRef] [PubMed]
  24. S. Torquato, Random Heterogeneous Material, Microstructure, and Macroscopic Properties (Springer-Verlag, 2002).
  25. B. P. Singh and M. Kaviany, "Independent theory versus direct simulation of radiation heat transfer in packed beds," Int. J. Heat Mass Transfer 34, 2869-2882 (1991).
    [CrossRef]
  26. B. P. Singh and M. Kaviany, "Modeling radiative heat transfer in packed beds," Int. J. Heat Mass Transfer 35, 1397-1405 (1992).
    [CrossRef]
  27. C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," Int. J. Heat Mass Transfer 39, 3175-3180 (1996).
    [CrossRef]
  28. B. T. Wong and M. P. Menguc, "Depolarization of radiation by non-absorbing foams," J. Quant. Spectrosc. Radiat. Transfer 73, 273-284 (2002).
    [CrossRef]
  29. K. Kamiuto, "Study of the scattering regime diagrams," J. Thermophys Heat Transfer 4, 432-443 (1990).
    [CrossRef]
  30. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

2007 (1)

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

2006 (3)

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
[CrossRef]

J. Randrianalisoa, D. Baillis, and L. Pilon, "Modeling radiation characteristics of semitransparent media containing bubbles or particles," J. Opt. Soc. Am. A 23, 1645-1656 (2006).
[CrossRef]

2005 (6)

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

L. Dombrovsky, J. Randrianalisoa, D. Baillis, and L. Pilon, "Use of the Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles," Appl. Opt. 44, 7021-7031 (2005).
[CrossRef] [PubMed]

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of beds of spheres containing an absorbing and scattering medium," J. Thermophys. Heat Transfer 19, 226-234 (2005).
[CrossRef]

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

2004 (4)

D. Damm and A. Fedorov, "Radiative heat transfer in SOFC materials and components," J. Power Sources 143, 158-165 (2004).
[CrossRef]

M. Tancrez and J. Taine, "Direct identification of absorption and scattering coefficient and phase function of a porous medium by a Monte Carlo technique," Int. J. Heat Mass Transfer 47, 373-383 (2004).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of opaque spherical particles beds: a new method of prediction," J. Thermophys. Heat Transfer 18, 178-186 (2004).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, P. Echegut, and P. Simon, "Contribution of semiquantum dielectric function models to the analysis of infrared spectra," Appl. Spectrosc. 58, 969-974 (2004).
[CrossRef]

2002 (1)

B. T. Wong and M. P. Menguc, "Depolarization of radiation by non-absorbing foams," J. Quant. Spectrosc. Radiat. Transfer 73, 273-284 (2002).
[CrossRef]

2001 (1)

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

2000 (3)

A. G. Fedorov and R. Viskanta, "Radiative transfer in semitransparent glass foam blancket," Phys. Chem. Glasses 41, 2769-2776 (2000).

V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

1999 (1)

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

1998 (1)

R. Siegel and M. Spuckler, "Analysis of thermal radiation effects on temperatures in turbine engine thermal barrier coatings," Mater. Sci. Engl. A 245, 150-159 (1998).
[CrossRef]

1996 (2)

C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," Int. J. Heat Mass Transfer 39, 3175-3180 (1996).
[CrossRef]

R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
[CrossRef]

1994 (1)

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

1992 (1)

B. P. Singh and M. Kaviany, "Modeling radiative heat transfer in packed beds," Int. J. Heat Mass Transfer 35, 1397-1405 (1992).
[CrossRef]

1991 (1)

B. P. Singh and M. Kaviany, "Independent theory versus direct simulation of radiation heat transfer in packed beds," Int. J. Heat Mass Transfer 34, 2869-2882 (1991).
[CrossRef]

1990 (1)

K. Kamiuto, "Study of the scattering regime diagrams," J. Thermophys Heat Transfer 4, 432-443 (1990).
[CrossRef]

Adler, P. M.

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Argento, C.

C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," Int. J. Heat Mass Transfer 39, 3175-3180 (1996).
[CrossRef]

Auger, Y.

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

Baillis, D.

J. Randrianalisoa, D. Baillis, and L. Pilon, "Modeling radiation characteristics of semitransparent media containing bubbles or particles," J. Opt. Soc. Am. A 23, 1645-1656 (2006).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of beds of spheres containing an absorbing and scattering medium," J. Thermophys. Heat Transfer 19, 226-234 (2005).
[CrossRef]

L. Dombrovsky, J. Randrianalisoa, D. Baillis, and L. Pilon, "Use of the Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles," Appl. Opt. 44, 7021-7031 (2005).
[CrossRef] [PubMed]

R. Coquard and D. Baillis, "Radiative characteristics of opaque spherical particles beds: a new method of prediction," J. Thermophys. Heat Transfer 18, 178-186 (2004).
[CrossRef]

Blin, A.

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Bouvard, D.

C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," Int. J. Heat Mass Transfer 39, 3175-3180 (1996).
[CrossRef]

Brun, J. F.

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, P. Echegut, and P. Simon, "Contribution of semiquantum dielectric function models to the analysis of infrared spectra," Appl. Spectrosc. 58, 969-974 (2004).
[CrossRef]

Buslaps, T.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Canizares, A.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

Chabin, M.

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Chermanne, S.

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

Coquard, R.

R. Coquard and D. Baillis, "Radiative characteristics of beds of spheres containing an absorbing and scattering medium," J. Thermophys. Heat Transfer 19, 226-234 (2005).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of opaque spherical particles beds: a new method of prediction," J. Thermophys. Heat Transfer 18, 178-186 (2004).
[CrossRef]

Damm, D.

D. Damm and A. Fedorov, "Radiative heat transfer in SOFC materials and components," J. Power Sources 143, 158-165 (2004).
[CrossRef]

De Sousa Meneses, D.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, P. Echegut, and P. Simon, "Contribution of semiquantum dielectric function models to the analysis of infrared spectra," Appl. Spectrosc. 58, 969-974 (2004).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

Di Michiel, M.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Dinaov, E. M.

V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

Dombrovsky, L.

Echegut, P.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, P. Echegut, and P. Simon, "Contribution of semiquantum dielectric function models to the analysis of infrared spectra," Appl. Spectrosc. 58, 969-974 (2004).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

Falus, P.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Fedorov, A.

D. Damm and A. Fedorov, "Radiative heat transfer in SOFC materials and components," J. Power Sources 143, 158-165 (2004).
[CrossRef]

Fedorov, A. G.

A. G. Fedorov and R. Viskanta, "Radiative transfer in semitransparent glass foam blancket," Phys. Chem. Glasses 41, 2769-2776 (2000).

Fernandez-Carreiras, D.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Gervais, F.

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Gore, J. P.

R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
[CrossRef]

Gruener, G.

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

Honkimäki, V.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Howell, J. R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, 2002), pp. 923-966.

Iaconna, E.

B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
[CrossRef]

Jacquin, C. G.

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

Jacquin, C. J.

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Jones, K. W.

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Kamiuto, K.

K. Kamiuto, "Study of the scattering regime diagrams," J. Thermophys Heat Transfer 4, 432-443 (1990).
[CrossRef]

Kaviany, M.

B. P. Singh and M. Kaviany, "Modeling radiative heat transfer in packed beds," Int. J. Heat Mass Transfer 35, 1397-1405 (1992).
[CrossRef]

B. P. Singh and M. Kaviany, "Independent theory versus direct simulation of radiation heat transfer in packed beds," Int. J. Heat Mass Transfer 34, 2869-2882 (1991).
[CrossRef]

Levitz, P.

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

Lindquist, W. B.

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Malki, M.

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

Martins, T.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Meneses, Sousa

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Menguc, M. P.

B. T. Wong and M. P. Menguc, "Depolarization of radiation by non-absorbing foams," J. Quant. Spectrosc. Radiat. Transfer 73, 273-284 (2002).
[CrossRef]

Merino, J. Manuel

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Mital, R.

R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
[CrossRef]

Odier, P.

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Pilon, L.

Plotnichenko, V. G.

V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

Randrianalisoa, J.

Rousseau, B.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

Rozenbaum, O.

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

Siegel, R.

R. Siegel and M. Spuckler, "Analysis of thermal radiation effects on temperatures in turbine engine thermal barrier coatings," Mater. Sci. Engl. A 245, 150-159 (1998).
[CrossRef]

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, 2002), pp. 923-966.

Simon, P.

Singh, B. P.

B. P. Singh and M. Kaviany, "Modeling radiative heat transfer in packed beds," Int. J. Heat Mass Transfer 35, 1397-1405 (1992).
[CrossRef]

B. P. Singh and M. Kaviany, "Independent theory versus direct simulation of radiation heat transfer in packed beds," Int. J. Heat Mass Transfer 34, 2869-2882 (1991).
[CrossRef]

Sokolov, V. O.

V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

Spanne, P.

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Spuckler, M.

R. Siegel and M. Spuckler, "Analysis of thermal radiation effects on temperatures in turbine engine thermal barrier coatings," Mater. Sci. Engl. A 245, 150-159 (1998).
[CrossRef]

Svensson, O.

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Taine, J.

B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
[CrossRef]

M. Tancrez and J. Taine, "Direct identification of absorption and scattering coefficient and phase function of a porous medium by a Monte Carlo technique," Int. J. Heat Mass Transfer 47, 373-383 (2004).
[CrossRef]

Tancrez, M.

M. Tancrez and J. Taine, "Direct identification of absorption and scattering coefficient and phase function of a porous medium by a Monte Carlo technique," Int. J. Heat Mass Transfer 47, 373-383 (2004).
[CrossRef]

Thovert, J. F.

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Thovert, J.-F.

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

Torquato, S.

S. Torquato, Random Heterogeneous Material, Microstructure, and Macroscopic Properties (Springer-Verlag, 2002).

Viskanta, R.

A. G. Fedorov and R. Viskanta, "Radiative transfer in semitransparent glass foam blancket," Phys. Chem. Glasses 41, 2769-2776 (2000).

R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Wong, B. T.

B. T. Wong and M. P. Menguc, "Depolarization of radiation by non-absorbing foams," J. Quant. Spectrosc. Radiat. Transfer 73, 273-284 (2002).
[CrossRef]

Yousefian, F.

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

Zeghondy, B.

B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Spectrosc. (1)

High Temp.--High Pressures (1)

O. Rozenbaum, D. De Sousa Meneses, P. Echegut, and P. Levitz, "Influence of the texture on the radiative properties of semitransparent materials. Comparison between model and experiment," High Temp.--High Pressures 32, 61-66 (2000).
[CrossRef]

Int. J. Heat Mass Transfer (5)

M. Tancrez and J. Taine, "Direct identification of absorption and scattering coefficient and phase function of a porous medium by a Monte Carlo technique," Int. J. Heat Mass Transfer 47, 373-383 (2004).
[CrossRef]

B. P. Singh and M. Kaviany, "Independent theory versus direct simulation of radiation heat transfer in packed beds," Int. J. Heat Mass Transfer 34, 2869-2882 (1991).
[CrossRef]

B. P. Singh and M. Kaviany, "Modeling radiative heat transfer in packed beds," Int. J. Heat Mass Transfer 35, 1397-1405 (1992).
[CrossRef]

C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," Int. J. Heat Mass Transfer 39, 3175-3180 (1996).
[CrossRef]

B. Zeghondy, E. Iaconna, and J. Taine, "Experimental and RDFI calculated radiative properties of a mullite foam," Int. J. Heat Mass Transfer 49, 3702-3707 (2006).
[CrossRef]

Int. J. Thermophys. (1)

B. Rousseau, J. F. Brun, D. De Sousa Meneses, and P. Echegut, "Temperature measurement: Christiansen wavelength and blackbody reference," Int. J. Thermophys. 26, 1277-1286 (2005).
[CrossRef]

J. Non-Cryst. Solids (2)

D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

V. G. Plotnichenko, V. O. Sokolov, and E. M. Dinaov, "Hydroxyls groups in high-purity glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Condens. Matter (1)

D. De Sousa Meneses, J. F. Brun, B. Rousseau, and P. Echegut, "Polar lattice dynamics of the MgAl2O4 spinel up to the liquid state," J. Phys. Condens. Matter 18, 5669-5686 (2006).
[CrossRef]

J. Power Sources (1)

D. Damm and A. Fedorov, "Radiative heat transfer in SOFC materials and components," J. Power Sources 143, 158-165 (2004).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

B. T. Wong and M. P. Menguc, "Depolarization of radiation by non-absorbing foams," J. Quant. Spectrosc. Radiat. Transfer 73, 273-284 (2002).
[CrossRef]

B. Rousseau, M. Di Michiel, A. Canizares, D. De Sousa Meneses, P. Echegut, and J.-F. Thovert, "Temperature effect (300-1500 K) on the infrared photon transport inside an x-ray microtomographic reconstructed porous silica glass," J. Quant. Spectrosc. Radiat. Transfer 104, 257-265 (2007).
[CrossRef]

J. Thermophys Heat Transfer (1)

K. Kamiuto, "Study of the scattering regime diagrams," J. Thermophys Heat Transfer 4, 432-443 (1990).
[CrossRef]

J. Thermophys. Heat Transfer (3)

R. Mital, J. P. Gore, and R. Viskanta, "Measurements of radiative properties of cellular ceramics at high temperature," J. Thermophys. Heat Transfer 10, 33-38 (1996).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of opaque spherical particles beds: a new method of prediction," J. Thermophys. Heat Transfer 18, 178-186 (2004).
[CrossRef]

R. Coquard and D. Baillis, "Radiative characteristics of beds of spheres containing an absorbing and scattering medium," J. Thermophys. Heat Transfer 19, 226-234 (2005).
[CrossRef]

Mater. Sci. Engl. A (1)

R. Siegel and M. Spuckler, "Analysis of thermal radiation effects on temperatures in turbine engine thermal barrier coatings," Mater. Sci. Engl. A 245, 150-159 (1998).
[CrossRef]

Phys. Chem. Glasses (1)

A. G. Fedorov and R. Viskanta, "Radiative transfer in semitransparent glass foam blancket," Phys. Chem. Glasses 41, 2769-2776 (2000).

Phys. Rev. B (1)

B. Rousseau, D. De Sousa Meneses, A. Blin, M. Chabin, P. Echegut, P. Odier, and F. Gervais, "High-temperature behavior of infrared conductivity of a Pr2NiO4+δ single crystal," Phys. Rev. B 72, 104114 (2005).

Phys. Rev. E (1)

J.-F. Thovert, F. Yousefian, P. Spanne, C. G. Jacquin, and P. M. Adler, "Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone," Phys. Rev. E 63, 061307 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

P. Spanne, J. F. Thovert, C. J. Jacquin, W. B. Lindquist, K. W. Jones, and P. M. Adler, "Synchrotron computed microtomography of porous media: topology and transports," Phys. Rev. Lett. 73, 2001-2004 (1994).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

O. Rozenbaum, D. De Sousa Meneses, Y. Auger, S. Chermanne, and P. Echegut, "A spectroscopic method to measure the spectral emissiviy of semi-transparent materials up to high temperature," Rev. Sci. Instrum. 70, 4020-4025 (1999).
[CrossRef]

M. Di Michiel, J. Manuel Merino, D. Fernandez-Carreiras, T. Buslaps, V. Honkimäki, P. Falus, T. Martins, and O. Svensson, "Fast microtomography using high-energy synchrotron radiation," Rev. Sci. Instrum. 76, 043702 (2005).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

S. Torquato, Random Heterogeneous Material, Microstructure, and Macroscopic Properties (Springer-Verlag, 2002).

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, 2002), pp. 923-966.

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Figures (10)

Fig. 1
Fig. 1

Refractive index n S i O 2 and absorption coefficient K SiO 2 of a silica glass of high purity at 300 K (solid curve) and at 1300 K (dashed curve). The symbols correspond to the data of Randrianalisoa et al. at T = 300 K in [13].

Fig. 2
Fig. 2

EDX analysis of S2. An ESEM image of S2 is shown in inset.

Fig. 3
Fig. 3

Example of an x-ray reconstructed image extracted from S1 normal to the z direction: (a) Gray levels image at z = 75, (b) same image after binarization.

Fig. 4
Fig. 4

Mid-cross-section images normal to the (a) x and to the (b) y axes ( 150 × 480 pixels).

Fig. 5
Fig. 5

(a) Spatial correlation functions R Z x , R Z y , and R Z z , with the lag u set along the x, y, and z directions through the parallelepipedic domain V (of 480 × 480 × 150 voxels), obtained by the x-ray microtomographic analysis of S1. (b) Enlarged view of the same data.

Fig. 6
Fig. 6

Volume-weighted radius distribution for various subdomains cut from V. The subdomains are obtained by the removal of a peripheral layer of thickness Δ ( Δ = 1 , 8 , 16 , and 32 p x ).

Fig. 7
Fig. 7

Cumulated distribution function of the gaps measured in the domain V.

Fig. 8
Fig. 8

Normal hemispherical spectral reflectance calculated at T = 1300 K for the reconstructed porous fused silica glass with d = 1 mm and ζ = 0.129 ( ) . Normal hemispherical spectral transmittance calculated at T = 1300 K for the reconstructed fused silica glass ( ) . The dashed curves depict the normal spectral transmittance, and the solid curves depict the normal spectral reflectance of a fictitious fused silica glass slab, at T = 1300 K.

Fig. 9
Fig. 9

Mean path length l ¯ matrix of the rays having traveled within the reconstructed porous sample.

Fig. 10
Fig. 10

Normal spectral emittance of the reconstructed porous sample (10 mm × 10 mm × 1 mm) at T = 1300 K, for a spectral range going from 400 cm 1 to 5000   cm 1 (■) calculated according to the Monte Carlo ray tracing procedure. The dashed curve represents the experimental spectrum measured on S2. The solid curve depicts the normal spectral emittance of a fictitious homogeneous slab of fused silica glass ( 10   mm × 10   mm × 1   mm ) . Note that the absorption band observed in the experimental spectrum in the 3000 4000 cm 1 wavenumber range is attributable to the presence of OH groups.

Equations (7)

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K SiO 2 ( σ , T ) = 4 × π × k SiO 2 ( σ , T ) × σ .
ζ = Z ( x ) ,
R Z ( u ) = [ Z ( x ) Z ] [ Z ( x + u ) Z ] ζ ( 1 ζ ) ,
E ( σ , T ) = 1 R ( σ , T ) T r ( σ , T ) .
n ˜ 1 ( σ , T ) sin θ i = n ˜ 2 ( σ , T ) sin θ ˜ t ( σ , T ) ,
θ i = θ r ,
ρ ( σ , θ i , T ) = 1 2 [ | cos θ i / cos θ ˜ t ( σ , T ) n ˜ 1 ( σ , T ) / n ˜ 2 ( σ , T ) cos θ i / cos θ ˜ t ( σ , T ) + n ˜ 1 ( σ , T ) / n ˜ 2 ( σ , T ) | 2 + | cos θ ˜ t ( σ , T ) / cos θ i n ˜ 1 ( σ , T ) / n ˜ 2 ( σ , T ) cos θ ˜ t ( σ , T ) / cos θ i + n ˜ 1 ( σ , T ) / n ˜ 2 ( σ , T ) | 2 ] .

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