Ametal Katkılama ile Titanyum Dioksit Nanomalzemelerin Fotokatalitik Bozunmasının İyileştirilmesi
Yıl 2023,
, 874 - 882, 31.08.2023
Funda Ak Azem
,
Işıl Birlik
,
Özgür Yasin Keskin
,
Tülay Koç Delice
Öz
Yarı iletken fotokataliz, kimyasal reaksiyonları başlatmak için güneş ışığından yararlanan bir süreçtir. Yarı iletkenlerin fotokatalitik özelliklerinden faydalanmak ve daha iyi performans elde etmek için yapısal düzenlemeye gereksinim duyulmaktadır. Bu çalışmada, sol-jel yöntemi kullanılarak TiO2 nanoyapılarını değiştirmek için değişen miktarlarda nitrojen kullanılmıştır. Sentezlenen TiO2 nanoyapıların kristal yapıları X-ışını kırınımı (XRD) yöntemiyle incelenmiştir. Nanomalzemelerin elemental bileşimini analiz etmek için X-ışını fotoelektron spektroskopisi (XPS) yapılmıştır. XPS analizi, nitrojenin TiO2 kafesindeki varlığını doğrulamaktadır. Metilen mavisinin (MB) UV ışıması altında fotokatalitik bozunması, numunelerin fotokatalitik performansını değerlendirmek için kullanılmıştır. Bozulmayı değerlendirmek için, MB'nin 664 nm'de zaman içinde absorpsiyonu bir UV-Vis spektrofotometre kullanılarak ölçülmüştür. Sonuç olarak, katkılama işleminin TiO2’nin fotokatalitik performansını iyileştirdiği ve %0,2 N katkılı TiO2 nanoyapıların MB'nin fotokatalitik bozunmasında üstün fotokatalitik aktivite gösterdiği bulunmuştur.
Proje Numarası
2020.KB.FEN.026
Kaynakça
- Al-Shehri, B., Altass, H. M., Ashour, S. S., Shkir, M., Abd El Rahman, S. K. and Hamdy, M. S, 2020. Enhancement the photocatalytic performance of semiconductors through composite formation with Eu-TUD-1. Optik, 202, 163522.
- Andersson, M., Österlund, L., Ljungström, S. and Palmqvist, A., 2002. Preparation of nanosize anatase and rutile TiO2 by hydrothermal treatment of microemulsions and their activity for photocatalytic wet oxidation of phenol. The Journal of Physical Chemistry B, 106(41), 10674-10679.
- Asahi, R., Morikawa, T. Ohwaki, T., Aoki, K. and Taga, Y., 2001. Visible-light photocatalysis in nitrogen-doped titanium oxides. Science, 293(5528), 269-271.
- Bashiri, R., Mohamed, N. M. and Kait, C. F., 2017. Advancement of sol-gel-prepared TiO2 photocatalyst. Recent Applications in Sol-Gel Synthesis, Usha Chandra, Rijeka: InTech, 151-167.
- Chen, X. and Burda, C., 2004. Photoelectron spectroscopic investigation of nitrogen-doped titania nanoparticles. The Journal of Physical Chemistry B, 108(40), 15446-15449.
- Cheng, X., Yu, X., Xing, Z. and Wan, J., 2012. Enhanced photocatalytic activity of nitrogen doped TiO2 anatase nano-particle under simulated sunlight irradiation. Energy Procedia, 16, 598-605.
- Cong, Y., Zhang, J., Chen, F. and Anpo, M., 2007. Synthesis and characterization of nitrogen-doped TiO2 nanophotocatalyst with high visible light activity. The Journal of Physical Chemistry C, 111(19), 6976-6982.
- Corradi, A.B, Bondioli, F., Focher, B., Ferrari, A.M, Grippo, C., Mariani, E. and Villa, C., 2005. Conventional and Microwave‐Hydrothermal Synthesis of TiO2 Nanopowders. Journal of the American Ceramic Society, 88, 2639-2641.
- Dariani, R. S., Esmaeili, A., Mortezaali, A. and Dehghanpour, S., 2016. Photocatalytic reaction and degradation of methylene blue on TiO2 nano-sized particles. Optik, 127(18), 7143-7154.
- Dawson, M., Soares, G. B. and Ribeiro, C., 2014. Influence of calcination parameters on the synthesis of N-doped TiO2 by the polymeric precursors method. Journal of Solid State Chemistry, 215, 211-218.
- Di Valentin, C., Finazzi, E., Pacchioni, G., Selloni, A., Livraghi, S., Paganini, M.C., Giamello, E., 2007. N-doped TiO2: theory and experiment. Chemical Physics, 339, 44-56.
- Finazzi, E., Di Valentin, C. and Pacchioni, G., 2008. Boron-doped anatase TiO2: pure and hybrid DFT calculations. The Journal of Physical Chemistry C, 113, 220-228.
- Irie, H., Watanabe, Y. and Hashimoto, K.,2003. Carbon-doped anatase TiO2 powders as a visible-light sensitive photocatalyst. Chemistry Letters, 32(8), 772-773.
- Huang, D. G., Liao, S. J., Liu, J. M., Dang, Z. and Petrik, L., 2006. Preparation of visible-light responsive N–F-codoped TiO2 photocatalyst by a sol–gel-solvothermal method. Journal of Photochemistry and Photobiology A: Chemistry, 184(3), 282-288.
- Huang, J., Dou, L., Li, J., Zhong, J., Li, M. and Wang, T., 2021. Excellent visible light responsive photocatalytic behavior of N-doped TiO2 toward decontamination of organic pollutants. Journal of Hazardous Materials, 403, 123857.
- Ihara, T., Miyoshi, M., Iriyama, Y., Matsumoto, O. and Sugihara, S., 2003. Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping. Applied Catalysis B: Environmental, 42(4), 403-409.
- Jaiswal, R., Bharambe, J., Patel, N., Dashora, A., Kothari, D. C. and Miotello, A.,2015. Copper and Nitrogen co-doped TiO2 photocatalyst with enhanced optical absorption and catalytic activity. Applied Catalysis B: Environmental, 168, 333-341.
- Jaiswal, R., Patel, N., Kothari, D. C. and Miotello, A., 2012. Improved visible light photocatalytic activity of TiO2 co-doped with Vanadium and Nitrogen. Applied Catalysis B: Environmental, 126, 47-54.
- Keshmiri, M., Mohseni, M. and Troczynski, T., 2004. Development of novel TiO2 sol–gel-derived composite and its photocatalytic activities for trichloroethylene oxidation. Applied Catalysis B: Environmental, 53(4), 209-219.
- Lei, Y., Zhang, L. D. and Fan, J. C., 2001. Fabrication, characterization and Raman study of TiO2 nanowire arrays prepared by anodic oxidative hydrolysis of TiCl3. Chemical Physics Letters, 338(4-6), 231-236.
- Li, H., Hao, Y., Lu, H., Liang, L., Wang, Y., Qiu, J., ... and Yao, J., 2015. A systematic study on visible-light N-doped TiO2 photocatalyst obtained from ethylenediamine by sol-gel method. Applied Surface Science, 344, 112-118.
- Lu, C. M., Sharma, R. K., Lin, P. Y., Huang, Y. H., Chen, J. S., Lee, W. C. and Chen, C. Y., 2022. Characteristics of Doped TiO2 Nanoparticle Photocatalysts Prepared by the Rotten Egg White. Materials, 15(12), 4231.
- Macwan, D. P., Dave, P. N. and Chaturvedi, S., 2011. A review on nano-TiO2 sol-gel type syntheses and its applications. Journal of Materials Science, 46, 3669-3686.
Marschall, R. and Wang, L., 2014. Non-metal doping of transition metal oxides for visible-light photocatalysis. Catalysis Today, 225, 111-135.
- Mironyuk, I. F., Soltys, L. M., Tatarchuk, T. R. and Tsinurchyn, V. I., 2020. Ways to improve the efficiency of ТіО2-based photocatalysts. Physics and Chemistry of Solid State, 21(2), 300-311.
- Nithya, N., Bhoopathi, G., Magesh, G. and Kumar, C. D. N., 2018. Neodymium doped TiO2 nanoparticles by sol-gel method for antibacterial and photocatalytic activity. Materials Science in Semiconductor Processing, 83, 70-82.
- Diwald, O., Thompson, T. L., Goralski, E. G., Walck, S. D. and Yates, J. T., 2004. The effect of nitrogen ion implantation on the photoactivity of TiO2 rutile single crystals. The Journal of Physical Chemistry B, 108(1), 52-57.
Okato, T., Sakano, T. and Obara, M., 2005. Suppression of photocatalytic efficiency in highly N-doped anatase films. Physical Review B, 72(11), 115124.
- Pawar, M. J., Nimbalkar, V. B., Gaonar, M. D., Khajone, A. D. and Taywade, R. K., 2020. Effect of Nitrogen Doping on Photocatalytic Activity of TiO2. Journal of Nanoscience and Technology, 6(4), 918-923.
- Pradhan, S. K., Reucroft, P. J., Yang, F. and Dozier, A., 2003. Growth of TiO2 nanorods by metalorganic chemical vapor deposition. Journal of Crystal Growth, 256(1-2), 83-88.
- Tojo, S., Tachikawa, T., Fujitsuka, M. and Majima, T., 2008. Iodine-doped TiO2 photocatalysts: correlation between band structure and mechanism. The Journal of Physical Chemistry C, 112(38), 14948-14954.
- Sanchez-Martinez, A., Ceballos-Sanchez, O., Koop-Santa, C., López-Mena, E. R., Orozco-Guareño, E. and García-Guaderrama, M., 2018. N-doped TiO2 nanoparticles obtained by a facile coprecipitation method at low temperature. Ceramics International, 44(5), 5273-5283.
Senthilnathan, J. and Philip, L., 2010. Photocatalytic degradation of lindane under UV and visible light using N-doped TiO2. Chemical Engineering Journal, 161(1-2), 83-92.
- Soares, G. B., Bravin, B., Vaz, C. M. and Ribeiro, C., 2011. Facile synthesis of N-doped TiO2 nanoparticles by a modified polymeric precursor method and its photocatalytic properties. Applied Catalysis B: Environmental, 106(3-4), 287-294.
- Suwannaruang, T., Kamonsuangkasem, K., Kidkhunthod, P., Chirawatkul, P., Saiyasombat, C., Chanlek, N. and Wantala, K., 2018. Influence of nitrogen content levels on structural properties and photocatalytic activities of nanorice-like N-doped TiO2 with various calcination temperatures. Materials Research Bulletin, 105, 265-276.
- Ohno, T., Akiyoshi, M., Umebayashi, T., Asai, K., Mitsui, T. and Matsumura, M., 2004. Preparation of S-doped TiO2 photocatalysts and their photocatalytic activities under visible light. Applied Catalysis A: General, 265(1), 115-121.
- Umebayashi, T., Yamaki, T., Tanaka, S. and Asai, K., 2003. Visible light-induced degradation of methylene blue on S-doped TiO2. Chemistry Letters, 32(4), 330-331.
- Venkatachalam, N., Palanichamy, M. and Murugesan, V., 2007. Sol-gel preparation and characterization of nanosize TiO2: Its photocatalytic performance. Materials Chemistry and Physics, 104(2-3), 454-459.
- Xu, T., Wang, M. and Wang, T., 2019. Effects of N doping on the microstructures and optical properties of TiO2. Journal of Wuhan University of Technology-Mater. Sci. Ed., 34(1), 55-63.
- Yin, S., Aita, Y., Komatsu, M., Wang, J., Tang, Q. and Sato, T., 2005. Synthesis of excellent visible-light responsive TiO2-xNy photocatalyst by a homogeneous precipitation-solvothermal process. Journal of Materials Chemistry, 15(6), 674-682.
- Yu, J. C., Yu, J., Ho, W., Jiang, Z. and Zhang, L., 2002. Effects of F-doping on the photocatalytic activity and microstructures of nanocrystalline TiO2 powders. Chemistry of Materials, 14(9), 3808-3816.
- Zhang, Q., Gao, L. and Guo, J., (2000. Effects of calcination on the photocatalytic properties of nanosized TiO2 powders prepared by TiCl4 hydrolysis. Applied Catalysis B: Environmental, 26(3), 207-215.
- Zhao, Y., Qiu, X. and Burda, C., 2008. The effects of sintering on the photocatalytic activity of N-doped TiO2 nanoparticles. Chemistry of Materials, 20(8), 2629-2636.
- Zhao, Z. and Liu, Q., 2008. Effects of lanthanide doping on electronic structures and optical properties of anatase TiO2 from density functional theory calculations. Journal of Physics D: Applied Physics, 41, 085417.
Improvement of Photocatalytic Degradation of Titanium Dioxide Nanomaterials by Non-metal Doping
Yıl 2023,
, 874 - 882, 31.08.2023
Funda Ak Azem
,
Işıl Birlik
,
Özgür Yasin Keskin
,
Tülay Koç Delice
Öz
Semiconductor photocatalysis is a process that benefits from sunlight to start chemical reactions. In order to take advantage photocatalytic properties of semiconductors and to achieve better performance structural adjustment is needed. In this study, varying amounts of nitrogen were used to modify TiO2 nanostructures using the sol-gel method. The crystalline structure of the synthesized TiO2 nanostructures was studied using the X-ray diffraction (XRD) technique. X-ray photoelectron spectroscopy (XPS) was conducted to analyse the elemental composition of nanomaterials. XPS analyze confirms that nitrogen is introduced into the lattice of TiO2. The photocatalytic degradation of methylene blue (MB) under UV irradiation was employed to assess the photocatalytic performance of the samples. To evaluate degradation, the absorption of MB over time was measured using a UV-Vis spectrophotometer. As a result, the doping process has been found to improve the photocatalytic performance of TiO2, and 0.2% N doped TiO2 nanostructures demonstrated superior photocatalytic activity for photocatalytic degradation of MB.
Destekleyen Kurum
Dokuz Eylul University
Proje Numarası
2020.KB.FEN.026
Teşekkür
The financial support for this research was provided through Project No: 2020.KB.FEN.026 financed by Dokuz Eylul University Department of Scientific Research Projects. Additionally, the authors would like to thank Dogacan Dagdelen for his support.
Kaynakça
- Al-Shehri, B., Altass, H. M., Ashour, S. S., Shkir, M., Abd El Rahman, S. K. and Hamdy, M. S, 2020. Enhancement the photocatalytic performance of semiconductors through composite formation with Eu-TUD-1. Optik, 202, 163522.
- Andersson, M., Österlund, L., Ljungström, S. and Palmqvist, A., 2002. Preparation of nanosize anatase and rutile TiO2 by hydrothermal treatment of microemulsions and their activity for photocatalytic wet oxidation of phenol. The Journal of Physical Chemistry B, 106(41), 10674-10679.
- Asahi, R., Morikawa, T. Ohwaki, T., Aoki, K. and Taga, Y., 2001. Visible-light photocatalysis in nitrogen-doped titanium oxides. Science, 293(5528), 269-271.
- Bashiri, R., Mohamed, N. M. and Kait, C. F., 2017. Advancement of sol-gel-prepared TiO2 photocatalyst. Recent Applications in Sol-Gel Synthesis, Usha Chandra, Rijeka: InTech, 151-167.
- Chen, X. and Burda, C., 2004. Photoelectron spectroscopic investigation of nitrogen-doped titania nanoparticles. The Journal of Physical Chemistry B, 108(40), 15446-15449.
- Cheng, X., Yu, X., Xing, Z. and Wan, J., 2012. Enhanced photocatalytic activity of nitrogen doped TiO2 anatase nano-particle under simulated sunlight irradiation. Energy Procedia, 16, 598-605.
- Cong, Y., Zhang, J., Chen, F. and Anpo, M., 2007. Synthesis and characterization of nitrogen-doped TiO2 nanophotocatalyst with high visible light activity. The Journal of Physical Chemistry C, 111(19), 6976-6982.
- Corradi, A.B, Bondioli, F., Focher, B., Ferrari, A.M, Grippo, C., Mariani, E. and Villa, C., 2005. Conventional and Microwave‐Hydrothermal Synthesis of TiO2 Nanopowders. Journal of the American Ceramic Society, 88, 2639-2641.
- Dariani, R. S., Esmaeili, A., Mortezaali, A. and Dehghanpour, S., 2016. Photocatalytic reaction and degradation of methylene blue on TiO2 nano-sized particles. Optik, 127(18), 7143-7154.
- Dawson, M., Soares, G. B. and Ribeiro, C., 2014. Influence of calcination parameters on the synthesis of N-doped TiO2 by the polymeric precursors method. Journal of Solid State Chemistry, 215, 211-218.
- Di Valentin, C., Finazzi, E., Pacchioni, G., Selloni, A., Livraghi, S., Paganini, M.C., Giamello, E., 2007. N-doped TiO2: theory and experiment. Chemical Physics, 339, 44-56.
- Finazzi, E., Di Valentin, C. and Pacchioni, G., 2008. Boron-doped anatase TiO2: pure and hybrid DFT calculations. The Journal of Physical Chemistry C, 113, 220-228.
- Irie, H., Watanabe, Y. and Hashimoto, K.,2003. Carbon-doped anatase TiO2 powders as a visible-light sensitive photocatalyst. Chemistry Letters, 32(8), 772-773.
- Huang, D. G., Liao, S. J., Liu, J. M., Dang, Z. and Petrik, L., 2006. Preparation of visible-light responsive N–F-codoped TiO2 photocatalyst by a sol–gel-solvothermal method. Journal of Photochemistry and Photobiology A: Chemistry, 184(3), 282-288.
- Huang, J., Dou, L., Li, J., Zhong, J., Li, M. and Wang, T., 2021. Excellent visible light responsive photocatalytic behavior of N-doped TiO2 toward decontamination of organic pollutants. Journal of Hazardous Materials, 403, 123857.
- Ihara, T., Miyoshi, M., Iriyama, Y., Matsumoto, O. and Sugihara, S., 2003. Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping. Applied Catalysis B: Environmental, 42(4), 403-409.
- Jaiswal, R., Bharambe, J., Patel, N., Dashora, A., Kothari, D. C. and Miotello, A.,2015. Copper and Nitrogen co-doped TiO2 photocatalyst with enhanced optical absorption and catalytic activity. Applied Catalysis B: Environmental, 168, 333-341.
- Jaiswal, R., Patel, N., Kothari, D. C. and Miotello, A., 2012. Improved visible light photocatalytic activity of TiO2 co-doped with Vanadium and Nitrogen. Applied Catalysis B: Environmental, 126, 47-54.
- Keshmiri, M., Mohseni, M. and Troczynski, T., 2004. Development of novel TiO2 sol–gel-derived composite and its photocatalytic activities for trichloroethylene oxidation. Applied Catalysis B: Environmental, 53(4), 209-219.
- Lei, Y., Zhang, L. D. and Fan, J. C., 2001. Fabrication, characterization and Raman study of TiO2 nanowire arrays prepared by anodic oxidative hydrolysis of TiCl3. Chemical Physics Letters, 338(4-6), 231-236.
- Li, H., Hao, Y., Lu, H., Liang, L., Wang, Y., Qiu, J., ... and Yao, J., 2015. A systematic study on visible-light N-doped TiO2 photocatalyst obtained from ethylenediamine by sol-gel method. Applied Surface Science, 344, 112-118.
- Lu, C. M., Sharma, R. K., Lin, P. Y., Huang, Y. H., Chen, J. S., Lee, W. C. and Chen, C. Y., 2022. Characteristics of Doped TiO2 Nanoparticle Photocatalysts Prepared by the Rotten Egg White. Materials, 15(12), 4231.
- Macwan, D. P., Dave, P. N. and Chaturvedi, S., 2011. A review on nano-TiO2 sol-gel type syntheses and its applications. Journal of Materials Science, 46, 3669-3686.
Marschall, R. and Wang, L., 2014. Non-metal doping of transition metal oxides for visible-light photocatalysis. Catalysis Today, 225, 111-135.
- Mironyuk, I. F., Soltys, L. M., Tatarchuk, T. R. and Tsinurchyn, V. I., 2020. Ways to improve the efficiency of ТіО2-based photocatalysts. Physics and Chemistry of Solid State, 21(2), 300-311.
- Nithya, N., Bhoopathi, G., Magesh, G. and Kumar, C. D. N., 2018. Neodymium doped TiO2 nanoparticles by sol-gel method for antibacterial and photocatalytic activity. Materials Science in Semiconductor Processing, 83, 70-82.
- Diwald, O., Thompson, T. L., Goralski, E. G., Walck, S. D. and Yates, J. T., 2004. The effect of nitrogen ion implantation on the photoactivity of TiO2 rutile single crystals. The Journal of Physical Chemistry B, 108(1), 52-57.
Okato, T., Sakano, T. and Obara, M., 2005. Suppression of photocatalytic efficiency in highly N-doped anatase films. Physical Review B, 72(11), 115124.
- Pawar, M. J., Nimbalkar, V. B., Gaonar, M. D., Khajone, A. D. and Taywade, R. K., 2020. Effect of Nitrogen Doping on Photocatalytic Activity of TiO2. Journal of Nanoscience and Technology, 6(4), 918-923.
- Pradhan, S. K., Reucroft, P. J., Yang, F. and Dozier, A., 2003. Growth of TiO2 nanorods by metalorganic chemical vapor deposition. Journal of Crystal Growth, 256(1-2), 83-88.
- Tojo, S., Tachikawa, T., Fujitsuka, M. and Majima, T., 2008. Iodine-doped TiO2 photocatalysts: correlation between band structure and mechanism. The Journal of Physical Chemistry C, 112(38), 14948-14954.
- Sanchez-Martinez, A., Ceballos-Sanchez, O., Koop-Santa, C., López-Mena, E. R., Orozco-Guareño, E. and García-Guaderrama, M., 2018. N-doped TiO2 nanoparticles obtained by a facile coprecipitation method at low temperature. Ceramics International, 44(5), 5273-5283.
Senthilnathan, J. and Philip, L., 2010. Photocatalytic degradation of lindane under UV and visible light using N-doped TiO2. Chemical Engineering Journal, 161(1-2), 83-92.
- Soares, G. B., Bravin, B., Vaz, C. M. and Ribeiro, C., 2011. Facile synthesis of N-doped TiO2 nanoparticles by a modified polymeric precursor method and its photocatalytic properties. Applied Catalysis B: Environmental, 106(3-4), 287-294.
- Suwannaruang, T., Kamonsuangkasem, K., Kidkhunthod, P., Chirawatkul, P., Saiyasombat, C., Chanlek, N. and Wantala, K., 2018. Influence of nitrogen content levels on structural properties and photocatalytic activities of nanorice-like N-doped TiO2 with various calcination temperatures. Materials Research Bulletin, 105, 265-276.
- Ohno, T., Akiyoshi, M., Umebayashi, T., Asai, K., Mitsui, T. and Matsumura, M., 2004. Preparation of S-doped TiO2 photocatalysts and their photocatalytic activities under visible light. Applied Catalysis A: General, 265(1), 115-121.
- Umebayashi, T., Yamaki, T., Tanaka, S. and Asai, K., 2003. Visible light-induced degradation of methylene blue on S-doped TiO2. Chemistry Letters, 32(4), 330-331.
- Venkatachalam, N., Palanichamy, M. and Murugesan, V., 2007. Sol-gel preparation and characterization of nanosize TiO2: Its photocatalytic performance. Materials Chemistry and Physics, 104(2-3), 454-459.
- Xu, T., Wang, M. and Wang, T., 2019. Effects of N doping on the microstructures and optical properties of TiO2. Journal of Wuhan University of Technology-Mater. Sci. Ed., 34(1), 55-63.
- Yin, S., Aita, Y., Komatsu, M., Wang, J., Tang, Q. and Sato, T., 2005. Synthesis of excellent visible-light responsive TiO2-xNy photocatalyst by a homogeneous precipitation-solvothermal process. Journal of Materials Chemistry, 15(6), 674-682.
- Yu, J. C., Yu, J., Ho, W., Jiang, Z. and Zhang, L., 2002. Effects of F-doping on the photocatalytic activity and microstructures of nanocrystalline TiO2 powders. Chemistry of Materials, 14(9), 3808-3816.
- Zhang, Q., Gao, L. and Guo, J., (2000. Effects of calcination on the photocatalytic properties of nanosized TiO2 powders prepared by TiCl4 hydrolysis. Applied Catalysis B: Environmental, 26(3), 207-215.
- Zhao, Y., Qiu, X. and Burda, C., 2008. The effects of sintering on the photocatalytic activity of N-doped TiO2 nanoparticles. Chemistry of Materials, 20(8), 2629-2636.
- Zhao, Z. and Liu, Q., 2008. Effects of lanthanide doping on electronic structures and optical properties of anatase TiO2 from density functional theory calculations. Journal of Physics D: Applied Physics, 41, 085417.