najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-5-530-538najo-289Research ArticlePHYSICSФИЗИКАComposite hydroxyapatite-multi-walled carbon nanotubes: study of porosity by terahertz time domain spectroscopyКомпозит гидроксиапатит-многостенные углеродные нанотрубки: Исследование пористости методом терагерцовой спектроскопии во временной областиhttps://orcid.org/0000-0002-7067-7979РезвановаА. Е.RezvanovaA. E.

Резванова Анастасия Евгеньевна 

Anastasiya E. Rezvanova

2/4 Akademicheskii ave., Tomsk, 634055

ranast@ispms.ruhttps://orcid.org/0009-0000-5133-4893КудряшовБ. С.KudryashovB. S.

Кудряшов Борис Сергеевич

Boris S. Kudryashov

2/4 Akademicheskii ave., Tomsk, 634055

bsk3@ispms.ruhttps://orcid.org/0000-0003-1524-7842ПономарёвА. Н.PonomarevA. N.

Пономарёв Александр Николаевич

Alexander N. Ponomarev

2/4 Akademicheskii ave., Tomsk, 634055

alex@ispms.ruhttps://orcid.org/0000-0002-1454-299XКнязьковаА. И.KnyazkovaA. I.

Князькова Анастасия Игоревна

Anastasiya I. Knyazkova

36 Lenin ave., Tomsk, 634050

a_knyazkova@bk.ruhttps://orcid.org/0000-0001-8189-0188НиколаевВ. В.NikolaevV. V.

Николаев Виктор Владимирович

Victor V. Nikolaev

36 Lenin ave., Tomsk, 634050

vik-nikol@bk.ruhttps://orcid.org/0000-0001-5760-1462КистенёвЮ. В.KistenevYu. V.

Кистенёв Юрий Владимирович 

Yuri .V. Kistenev

36 Lenin ave., Tomsk, 634050

yuk@iao.ruInstitute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of SciencesRussian FederationTomsk State UniversityRussian Federation202308062025145530538Copyright © Rezvanova A.E., Kudryashov B.S., Ponomarev A.N., Knyazkova A.I., Nikolaev V.V., Kistenev Y.V., 20252025Резванова А.Е., Кудряшов Б.С., Пономарёв А.Н., Князькова А.И., Николаев В.В., Кистенёв Ю.В.Rezvanova A.E., Kudryashov B.S., Ponomarev A.N., Knyazkova A.I., Nikolaev V.V., Kistenev Y.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/289

Optical properties of a ceramic biocomposite material based on hydroxyapatite (HA) with the additives up to 0.5 wt.% of multi-walled carbon nanotubes (MWCNTs) have been studied by terahertz timedomain spectroscopy in the frequency range 0.25 – 1.1 THz. It was found that the refractive index of the composite varies between 2.6 and 2.8 depending on the porosity of the material. The absorption coefficient decreases with increasing of MWCNTs concentration in the ceramic biocomposite. The values of the refractive index and the absorption coefficient of our ceramics close to those for cortical bone, dentine and enamel. The absorption curves show frequency peaks whose positions correspond to the macrocrystallite sizes. The size of macrocrystallites decreases with increasing concentration of MWCNTs, which leads to an increase in microhardness according to the Hall–Petch equation. The time delay of the terahertz signal through the sample increases for higher concentration of MWCNTs. This indicates that nanotubes embedded into the HA matrix fill the pores and decrease the area of the pore space, which increases the density of the ceramic composite and decreases its porosity.

Методом терагерцовой спектроскопии во временной области в диапазоне частот 0.25-1.1 ТГц изучены оптические свойства керамического биокомпозитного материала на основе гидроксиапатита (ГА) с добавками до 0.5 мас.% многостенных углеродных нанотрубок (МУНТ). Было обнаружено, что показатель преломления композита колеблется от 2.6 до 2.8 в зависимости от пористости материала. Коэффициент поглощения уменьшается с увеличением концентрации МУНТ в керамическом биокомпозите. Значения показателя преломления и коэффициента поглощения нашей керамики близки к таковым для кортикальной кости, дентина и эмали. Кривые поглощения показывают частотные пики, положение которых соответствует размерам макрокристаллитов. Размер макрокристаллитов уменьшается с увеличением концентрации МУНТ, что приводит к увеличению микротвердости в соответствии с уравнением Холла-Петча. Временная задержка прохождения терагерцового сигнала через образец увеличивается при более высокой концентрации МУНТ. Это указывает на то, что нанотрубки, внедренные в матрицу ГА, заполняют поры и уменьшают площадь порового пространства, что увеличивает плотность керамического композита и уменьшает его пористость.

керамический композитгидроксиапатитмногостенные углеродные нанотрубкитерагерцовая спектроскопияпористостьceramic compositehydroxyapatitemulti-walled carbon nanotubesterahertz spectroscopyporosityThe work by Rezvanova, Ponomarev, and Kudryashov was performed within the Government Statement of Work for the ISPMS SB RAS, project FWRW-2022-0002 and FWRW-2021-0007. The research by Knyazkova, Nikolaev, and Kistenev was supported by the grant under RF Government Decree No. 220 dated 09 April 2010 (Agreement No. 075-15-2021-615 of 04 June 2021). The authors are grateful to A. A. Neiman from the Nanotekh Regional Core Facility Centre of the Institute of Strength Physics and Materials Science SB RAS for his help with SEM images.ReferencesFiume E., Magnaterra G., Rahdar A., Vern´e E., Baino F. Hydroxyapatite for biomedical applications: A short overview. Ceramics, 2021, 4 (4), P. 542–563.Fiume E., Magnaterra G., Rahdar A., Vern´e E., Baino F. Hydroxyapatite for biomedical applications: A short overview. Ceramics, 2021, 4 (4), P. 542–563.Barabashko M.S., Tkachenko M.V., Neiman A.A., Ponomarev A.N., Rezvanova A.E. Variation of Vickers microhardness and compression strength of the bioceramics based on hydroxyapatite by adding the multi-walled carbon nanotubes. Appl. Nanosci., 2019, 10 (8), P. 2601–2608.Barabashko M.S., Tkachenko M.V., Neiman A.A., Ponomarev A.N., Rezvanova A.E. Variation of Vickers microhardness and compression strength of the bioceramics based on hydroxyapatite by adding the multi-walled carbon nanotubes. Appl. Nanosci., 2019, 10 (8), P. 2601–2608.Han Y., Wei Q., Chang P., Hu K., Okoro O.V., Shavandi A., Nie L. Three-dimensional printing of hydroxyapatite composites for biomedical application. Crystals, 2021, 11 (4), 353.Han Y., Wei Q., Chang P., Hu K., Okoro O.V., Shavandi A., Nie L. Three-dimensional printing of hydroxyapatite composites for biomedical application. Crystals, 2021, 11 (4), 353.Ebrahimi M. Porosity parameters in biomaterial science: Definition, impact, and challenges in tissue engineering. Front. Mater. Sci., 2021, 11 (4), 353.Ebrahimi M. Porosity parameters in biomaterial science: Definition, impact, and challenges in tissue engineering. Front. Mater. Sci., 2021, 11 (4), 353.Ponomarev A.N., Barabashko M.S., Rezvanova A.E., Evtushenko E.P. Influence of Porosity on Fracture Toughness of Hydroxyapatite/Multi- Walled Carbon Nanotubes Biocomposite Materials. Russ. Phys. J., 2021, 63 (11), P. 1885–1890.Ponomarev A.N., Barabashko M.S., Rezvanova A.E., Evtushenko E.P. Influence of Porosity on Fracture Toughness of Hydroxyapatite/Multi- Walled Carbon Nanotubes Biocomposite Materials. Russ. Phys. J., 2021, 63 (11), P. 1885–1890.Barabashko M.S., Tkachenko M.V., Rezvanova A.E., Ponomarev A.N. Analysis of temperature gradients in the hydroxyapatite ceramics with the additives of multi-walled carbon nanotubes. Russ. J. Phys. Chem., 2021, 95 (5), P. 1017–1022.Barabashko M.S., Tkachenko M.V., Rezvanova A.E., Ponomarev A.N. Analysis of temperature gradients in the hydroxyapatite ceramics with the additives of multi-walled carbon nanotubes. Russ. J. Phys. Chem., 2021, 95 (5), P. 1017–1022.Sreedhara S.S., Tata N.R. A novel method for measurement of porosity in nanofiber mat using pycnometer in filtration. J. Eng. Fiber. Fabr., 2013, 8 (4), 155892501300800.Sreedhara S.S., Tata N.R. A novel method for measurement of porosity in nanofiber mat using pycnometer in filtration. J. Eng. Fiber. Fabr., 2013, 8 (4), 155892501300800.Giesche H. Mercury porosimetry: A general (practical) overview. Part. Part. Syst. Charact., 2006, 23 (1), P. 9–19.Giesche H. Mercury porosimetry: A general (practical) overview. Part. Part. Syst. Charact., 2006, 23 (1), P. 9–19.Hollamby M.J. Practical applications of small-angle neutron scattering. Phys. Chem. Chem. Phys., 2013, 15 (26), P. 10566–10579.Hollamby M.J. Practical applications of small-angle neutron scattering. Phys. Chem. Chem. Phys., 2013, 15 (26), P. 10566–10579.Chalmers G.R., Bustin R.M., Power I.M. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units. Am. Assoc. Pet. Geol. Bull., 2012, 96 (6), P. 1099–1119.Chalmers G.R., Bustin R.M., Power I.M. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units. Am. Assoc. Pet. Geol. Bull., 2012, 96 (6), P. 1099–1119.Mitchell J., Webber J., Strange J. Nuclear magnetic resonance cryoporometry. Phys. Rep., 2008, 461 (1), P. 1–36.Mitchell J., Webber J., Strange J. Nuclear magnetic resonance cryoporometry. Phys. Rep., 2008, 461 (1), P. 1–36.Nikoghosyan A.S., Ting H., Shen J., Martirosyan R.M., Tunyan M.Y., Papikyan A.V., Papikyan A.A. Optical properties of human jawbone and human bone substitute Cerabone® in the terahertz range. J. Contemp. Phys., 2016, 51 (3), P. 256–264.Nikoghosyan A.S., Ting H., Shen J., Martirosyan R.M., Tunyan M.Y., Papikyan A.V., Papikyan A.A. Optical properties of human jawbone and human bone substitute Cerabone® in the terahertz range. J. Contemp. Phys., 2016, 51 (3), P. 256–264.Bawuah P., Markl D., Farrell D., Evans M., Portieri A., Anderson A., Goodwin D., Lucas R., Zeitler J.A. Terahertz-based porosity measurement of pharmaceutical tablets: A tutorial. J. Infrared, Millimeter, Terahertz Waves, 2020, 41 (4), P. 450–469.Bawuah P., Markl D., Farrell D., Evans M., Portieri A., Anderson A., Goodwin D., Lucas R., Zeitler J.A. Terahertz-based porosity measurement of pharmaceutical tablets: A tutorial. J. Infrared, Millimeter, Terahertz Waves, 2020, 41 (4), P. 450–469.Stringer M.R., Lund D.N., Foulds A.P., Uddin A., Berry E., Miles R.E., Davies A.G. The analysis of human cortical bone by terahertz time-domain spectroscopy. Phys. Med. Biol., 2005, 50 (14), P. 3211–3219.Stringer M.R., Lund D.N., Foulds A.P., Uddin A., Berry E., Miles R.E., Davies A.G. The analysis of human cortical bone by terahertz time-domain spectroscopy. Phys. Med. Biol., 2005, 50 (14), P. 3211–3219.Kistenev Y.V., Nikolaev V.V., Kurochkina O.S., Borisovb A.V., Sandykova E.A., Krivova N.A., Tuchina D.K., Timoshona P.A. Use of terahertz spectroscopy for in vivo studies of lymphedema development dynamics. Opt. Spectrosc., 2019, 126 (5), P. 523–529.Kistenev Y.V., Nikolaev V.V., Kurochkina O.S., Borisovb A.V., Sandykova E.A., Krivova N.A., Tuchina D.K., Timoshona P.A. Use of terahertz spectroscopy for in vivo studies of lymphedema development dynamics. Opt. Spectrosc., 2019, 126 (5), P. 523–529.Sudworth C.D., Fitzgerald A.J., Berry E., Zinov’ev N.N., Homer-Vanniasinkam S., Miles R.E., Chamberlain M., Smith M.A. The optical properties of human tissue at terahertz frequencies. European Conference on Biomedical Optics, 2003, 5143, P. 59–68.Sudworth C.D., Fitzgerald A.J., Berry E., Zinov’ev N.N., Homer-Vanniasinkam S., Miles R.E., Chamberlain M., Smith M.A. The optical properties of human tissue at terahertz frequencies. European Conference on Biomedical Optics, 2003, 5143, P. 59–68.Sim Y.C., Maeng I., Son J.-H. Frequency-dependent characteristics of terahertz radiation on the enamel and dentin of human tooth. Curr. Appl. Phys., 2009, 9 (5), P. 946–949.Sim Y.C., Maeng I., Son J.-H. Frequency-dependent characteristics of terahertz radiation on the enamel and dentin of human tooth. Curr. Appl. Phys., 2009, 9 (5), P. 946–949.Berry E., Fitzgerald A.J., Zinov’ev N.N., Walker G.C., Homer-Vanniasinkam S., Sudworth C.D., Miles R.E., Chamberlain J.M., Smith M.A. Optical properties of tissue measured using terahertz-pulsed imaging. Proceedings of SPIE, 2003, 5030, P. 459–470.Berry E., Fitzgerald A.J., Zinov’ev N.N., Walker G.C., Homer-Vanniasinkam S., Sudworth C.D., Miles R.E., Chamberlain J.M., Smith M.A. Optical properties of tissue measured using terahertz-pulsed imaging. Proceedings of SPIE, 2003, 5030, P. 459–470.Bessou M., Chassagne B., Caumes J.-P., Prad`ere C., Maire P., Tondusson M., Abraham E. Three-dimensional terahertz computed tomography of human bones. Appl. Opt., 2012, 51 (28), P. 6738–6744.Bessou M., Chassagne B., Caumes J.-P., Prad`ere C., Maire P., Tondusson M., Abraham E. Three-dimensional terahertz computed tomography of human bones. Appl. Opt., 2012, 51 (28), P. 6738–6744.Cai J., Guang M., Zhou J. et al. Dental caries diagnosis using terahertz spectroscopy and birefringence. Optics Express, 2022, 30 (8), P. 13134–13147.Cai J., Guang M., Zhou J. et al. Dental caries diagnosis using terahertz spectroscopy and birefringence. Optics Express, 2022, 30 (8), P. 13134–13147.Zyman Z., Ivanov I., Rochmistrov D., Glushko V., Tkachenko N., Kijko S. Sintering peculiarities for hydroxyapatite with different degrees of crystallinity. J. Biomed. Mater. Res., 2001, 54 (2), P. 256–263.Zyman Z., Ivanov I., Rochmistrov D., Glushko V., Tkachenko N., Kijko S. Sintering peculiarities for hydroxyapatite with different degrees of crystallinity. J. Biomed. Mater. Res., 2001, 54 (2), P. 256–263.Zyman Z.Z., Tkachenko M.V., Polevodin D.V. Preparation and characterization of biphasic calcium phosphate ceramics of desired composition. J. Mater. Sci. Mater. Med., 2008, 19 (8), P. 2819–2825.Zyman Z.Z., Tkachenko M.V., Polevodin D.V. Preparation and characterization of biphasic calcium phosphate ceramics of desired composition. J. Mater. Sci. Mater. Med., 2008, 19 (8), P. 2819–2825.Usoltseva A., Kuznetsov V., Rudina N., Moroz E., Haluska M., Roth S. Influence of catalysts’ activation on their activity and selectivity in carbon nanotubes synthesis. Phys. Stat. Sol., 2007, 244 (11), P. 3920–3924.Usoltseva A., Kuznetsov V., Rudina N., Moroz E., Haluska M., Roth S. Influence of catalysts’ activation on their activity and selectivity in carbon nanotubes synthesis. Phys. Stat. Sol., 2007, 244 (11), P. 3920–3924.Kuznetsov V.L., Krasnikov D.V., Schmakov A.N., Elumeeva K.V. In situ and ex situ time resolved study of multi-component Fe-Co oxide catalyst activation during MWNT synthesis. Phys. Stat. Sol., 2012, 249 (12), P. 2390–2394.Kuznetsov V.L., Krasnikov D.V., Schmakov A.N., Elumeeva K.V. In situ and ex situ time resolved study of multi-component Fe-Co oxide catalyst activation during MWNT synthesis. Phys. Stat. Sol., 2012, 249 (12), P. 2390–2394.Barabashko M.S., Drozd M., Szewczyk D., Je˙zowski A., Bagatskii M.I., Sumarokov V.V., Doblin A.V., Nesov S.N., Korusenko P.M., Ponomarev A.N., Geidarov V.G., Kuznetsov V.L., Moseenkov S.I., Sokolov D.V., Smirnov D.A. Calorimetric, NEXAFS and XPS studies of MWCNTs with low defectiveness. Fullerenes, Nanotubes Carbon Nanostruct., 2021, 29 (5), P. 331–336.Barabashko M.S., Drozd M., Szewczyk D., Je˙zowski A., Bagatskii M.I., Sumarokov V.V., Doblin A.V., Nesov S.N., Korusenko P.M., Ponomarev A.N., Geidarov V.G., Kuznetsov V.L., Moseenkov S.I., Sokolov D.V., Smirnov D.A. Calorimetric, NEXAFS and XPS studies of MWCNTs with low defectiveness. Fullerenes, Nanotubes Carbon Nanostruct., 2021, 29 (5), P. 331–336.Ponomarev A., Egorushkin V., Bobenko N., Barabashko M., Rezvanova A., Belosludtseva A. On the possible nature of armchair-zigzag structure formation and heat capacity decrease in MWCNTs. Materials, 2022, 15 (2), 518.Ponomarev A., Egorushkin V., Bobenko N., Barabashko M., Rezvanova A., Belosludtseva A. On the possible nature of armchair-zigzag structure formation and heat capacity decrease in MWCNTs. Materials, 2022, 15 (2), 518.Kudryashov B.S., Rezvanova A.E., Ponomarev A.N., Belosludtseva A.A., Barabashko M.S. Analysis of electron microscopic images of multiwalled carbon nanotubes: Determination of the average diameter. AIP Conference Proceedings, 2022, 2509 (1), 020118.Kudryashov B.S., Rezvanova A.E., Ponomarev A.N., Belosludtseva A.A., Barabashko M.S. Analysis of electron microscopic images of multiwalled carbon nanotubes: Determination of the average diameter. AIP Conference Proceedings, 2022, 2509 (1), 020118.Barabashko M., Ponomarev A., Rezvanova A., Kuznetsov V., Moseenkov S. Young’s modulus and vickers hardness of the hydroxyapatite bioceramics with a small amount of the multi-walled carbon nanotubes. Materials, 2022, 15 (15), 5304.Barabashko M., Ponomarev A., Rezvanova A., Kuznetsov V., Moseenkov S. Young’s modulus and vickers hardness of the hydroxyapatite bioceramics with a small amount of the multi-walled carbon nanotubes. Materials, 2022, 15 (15), 5304.TeraVil Ltd. URL: https://www.teravil.lt/t-spec.php. Accessed 27 July 2022.TeraVil Ltd. URL: https://www.teravil.lt/t-spec.php. Accessed 27 July 2022.Nishizawa S., Sakai K., Hangyo M., Nagashima T., Takeda M.W., Tominaga K., Oka A., Tanaka K., MorikawaO. Terahertz time-domain spectroscopy. Top. Appl. Phys., 2005, 97, P. 203–270.Nishizawa S., Sakai K., Hangyo M., Nagashima T., Takeda M.W., Tominaga K., Oka A., Tanaka K., MorikawaO. Terahertz time-domain spectroscopy. Top. Appl. Phys., 2005, 97, P. 203–270.Sakai K., Tani M. Introduction to Terahertz Pulses. Top. Appl. Phys., 2006, 97, P. 1–31.Sakai K., Tani M. Introduction to Terahertz Pulses. Top. Appl. Phys., 2006, 97, P. 1–31.Bawuah P., Ervasti T., Tan N., Zeitler J.A., Ketolainen J., Peiponen K.-E. Noninvasive porosity measurement of biconvex tablets using terahertz pulses. Int. J. Pharm., 2016, 509 (1–2), P. 439–443.Bawuah P., Ervasti T., Tan N., Zeitler J.A., Ketolainen J., Peiponen K.-E. Noninvasive porosity measurement of biconvex tablets using terahertz pulses. Int. J. Pharm., 2016, 509 (1–2), P. 439–443.Naftaly M., Tikhomirov I., Hou P., Markl D. Measuring open porosity of porous materials using THz-TDS and an index-matching medium. Sensors, 2020, 20 (11), 3120.Naftaly M., Tikhomirov I., Hou P., Markl D. Measuring open porosity of porous materials using THz-TDS and an index-matching medium. Sensors, 2020, 20 (11), 3120.Rungsawang R., Geethamma V. G., Parrott E.P.J., Ritchie D.A., Terentjev E.M. Terahertz spectroscopy of carbon nanotubes embedded in a deformable rubber. J. Appl. Phys., 2008, 103 (12).Rungsawang R., Geethamma V. G., Parrott E.P.J., Ritchie D.A., Terentjev E.M. Terahertz spectroscopy of carbon nanotubes embedded in a deformable rubber. J. Appl. Phys., 2008, 103 (12).Parrott E.P.J., Zeitler J.A., McGregor J., Oei Shu-Pei, Unalan H.E., Milne W.I., Tessonnier J.-P., Su Dang Sheng, Schlogl R., Gladden L.F. The use of terahertz spectroscopy as a sensitive probe in discriminating the electronic properties of structurally similar multi-walled carbon nanotubes. Advanced Materials, 2009, 21 (38–39), P. 3953–3957.Parrott E.P.J., Zeitler J.A., McGregor J., Oei Shu-Pei, Unalan H.E., Milne W.I., Tessonnier J.-P., Su Dang Sheng, Schlogl R., Gladden L.F. The use of terahertz spectroscopy as a sensitive probe in discriminating the electronic properties of structurally similar multi-walled carbon nanotubes. Advanced Materials, 2009, 21 (38–39), P. 3953–3957.Crawley D., Longbottom C., Wallace V.P., Cole B., Arnone D., Pepper M. Three-dimensional terahertz pulse imaging of dental tissue. J. Biomed. Opt., 2003, 8 (2), P. 303–307.Crawley D., Longbottom C., Wallace V.P., Cole B., Arnone D., Pepper M. Three-dimensional terahertz pulse imaging of dental tissue. J. Biomed. Opt., 2003, 8 (2), P. 303–307.Nazarov M.M., Shkurinov A.P., Kuleshov E.A., Tuchin V.V. Terahertz time-domain spectroscopy of biological tissues. Quantum Electron, 2008, 38 (7), P. 647–654.Nazarov M.M., Shkurinov A.P., Kuleshov E.A., Tuchin V.V. Terahertz time-domain spectroscopy of biological tissues. Quantum Electron, 2008, 38 (7), P. 647–654.Plazanet M., Tasseva J., Bartolini P., Taschin A., Torre R., Combes C., Rey C., Michele A.Di., Verezhak M., Gourrier A. Time-domain THz spectroscopy of the characteristics of hydroxyapatite provides a signature of heating in bone tissue. PLoS One, 2018, 13 (8), e0201745.Plazanet M., Tasseva J., Bartolini P., Taschin A., Torre R., Combes C., Rey C., Michele A.Di., Verezhak M., Gourrier A. Time-domain THz spectroscopy of the characteristics of hydroxyapatite provides a signature of heating in bone tissue. PLoS One, 2018, 13 (8), e0201745.Lee H.-J., Han J.-K., Janakiraman S., Ahn B., Kawasaki M., Langdon T.G. Significance of grain refinement on microstructure and mechanical properties of an Al-3% Mg alloy processed by high-pressure torsion. J. Alloys Compd., 2016, 686, P. 998–1007.Lee H.-J., Han J.-K., Janakiraman S., Ahn B., Kawasaki M., Langdon T.G. Significance of grain refinement on microstructure and mechanical properties of an Al-3% Mg alloy processed by high-pressure torsion. J. Alloys Compd., 2016, 686, P. 998–1007.Sotelo Martin L. E., Castro R. H. R. Al excess extends Hall-Petch relation in nanocrystalline zinc aluminate. J. Am. Ceram. Soc., 2022, 105 (2), P. 1417–1427.Sotelo Martin L. E., Castro R. H. R. Al excess extends Hall-Petch relation in nanocrystalline zinc aluminate. J. Am. Ceram. Soc., 2022, 105 (2), P. 1417–1427.Garet F., Hofman M., Meilhan J., Simoens F., Coutaz J.-L. Evidence of Mie scattering at terahertz frequencies in powder materials. Appl. Phys. Lett., 2014, 105 (3), 031106.Garet F., Hofman M., Meilhan J., Simoens F., Coutaz J.-L. Evidence of Mie scattering at terahertz frequencies in powder materials. Appl. Phys. Lett., 2014, 105 (3), 031106.

The authors declare that there are no conflicts of interest present.