The low-temperature specific heat of MWCNTs

The low-temperature specific heat of MWCNTs

The specific heat of multi-walled carbon nanotubes (MWCNTs) with a low defectiveness and with a low content of inorganic impurities has been measured in the temperature range from 1.8 to 275 K by the thermal relaxation method. The elemental composition and morphology of the MWCNTs were determined us...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2019
Hauptverfasser: Sumarokov, V.V., Jeżowski, A., Szewczyk, D., Bagatski, M.I., Barabashko, M.S., Ponomarev, A.N., Kuznetsov, V.L., Moseenkov, S.I.
Format: Artikel
Sprache:English
Veröffentlicht: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2019
Schriftenreihe:Физика низких температур
Schlagworte:
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/176086
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The low-temperature specific heat of MWCNTs / V.V. Sumarokov, A. Jeżowski, D. Szewczyk, M.I. Bagatski, M.S. Barabashko, A.N. Ponomarev, V.L. Kuznetsov, S.I. Moseenkov // Физика низких температур. — 2019. — Т. 45, № 3. — С. 395-403. — Бібліогр.: 55 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-176086
record_format dspace
spelling nasplib_isofts_kiev_ua-123456789-1760862025-02-09T16:28:21Z The low-temperature specific heat of MWCNTs Низькотемпературна питома теплоємність багатостінних вуглецевих нанотрубок Низкотемпературная удельная теплоемкость многостенных углеродных нанотрубок Sumarokov, V.V. Jeżowski, A. Szewczyk, D. Bagatski, M.I. Barabashko, M.S. Ponomarev, A.N. Kuznetsov, V.L. Moseenkov, S.I. Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) The specific heat of multi-walled carbon nanotubes (MWCNTs) with a low defectiveness and with a low content of inorganic impurities has been measured in the temperature range from 1.8 to 275 K by the thermal relaxation method. The elemental composition and morphology of the MWCNTs were determined using scanning electron microscopy analysis and energy dispersion x-ray spectroscopy. The MWCNTs were prepared by chemical catalytic vapor deposition and have mean diameters from 7 nm up to 18 nm and lengths in some tens of microns. MWCNTs purity is over 99.4 at.%. The mass of the samples ranged from 2–4 mg. It was found that the temperature dependence of the specific heat of the MWCNTs differs significantly from other carbon materials (graphene, bundles of SWCNTs, graphite, diamond) at low temperatures. The specific heat of MWCNTs systematically decreases with increasing diameter of the tubes at low temperatures. The character of the temperature dependence of the specific heat of the MWCNTs with different diameters demonstrates the manifestation of different dimensions from 1D to 3D, depending on the temperature regions. The crossover temperatures are about 6 and 40 K. In the vicinity of these temperatures, a hysteresis is observed. Питому теплоємність багатостінних вуглецевих нанотрубок (БСВНТ) з низькою дефектністю та низьким вмістом неорганічних домішок виміряно в діапазоні температур 1,8–275 К методом теплової релаксації. Зразки БСВНТ отримано хімічним каталітичним осадженням з парової фази. Елементний склад і морфологію БСВНТ визначено за допомогою скануючої електронної мікроскопії та енергодисперсійної рентгенівської спектроскопії. Нанотрубки мали середній діаметр від 7 до 18 нм і довжину в кілька десятків мікрон. Чистота БСВНТ була більш ніж 99,4 ат.%. Маса зразків становила від 2 до 4 мг. Виявлено, що температурна залежність питомої теплоємності БСВНТ значно відрізняється від теплоємності інших вуглецевих матеріалів (графена, в’язок ОСВНТ, графіту, алмазу) при низьких температурах. Теплоємність БСВНТ систематично зменшується зі збільшенням діаметра нанотрубок при низьких температурах. Температурні залежності питомої теплоємності БСВНТ з різними діаметрами демонструють притаманний низьковимірним системам характер від 1D до 3D в залежності від температурних областей. Температури кросовера складають близько 6 та 40 К. Поблизу цих температур спостерігається гістерезис. Удельная теплоемкость многостенных углеродных нанотрубок (МСУНТ) с низкой дефектностью и низким содержанием неорганических примесей измерена в диапазоне температур 1,8–275 К методом тепловой релаксации. Образцы МСУНТ получены химическим каталитическим осаждением из паровой фазы. Элементный состав и морфология МСУНТ определены с помощью сканирующей электронной микроскопии и энергодисперсионной рентгеновской спектроскопии. Нанотрубки имели средний диаметр от 7 до 18 нм и длину в несколько десятков микрон. Чистота МСУНТ более 99,4 ат.%. Масса образцов составляла от 2 до 4 мг. Обнаружено, что температурная зависимость удельной теплоемкости МСУНТ значительно отличается от теплоемкости других углеродных материалов (графена, связок ОСУНТ, графита, алмаза) при низких температурах. Теплоемкость МСУНТ систематически уменьшается с увеличением диаметра нанотрубок при низких температурах. Температурные зависимости удельной теплоемкости МСУНТ с разными диаметрами демонстрируют присущий низкоразмерным системам характер от 1D до 3D в зависимости от температурных областей. Температуры кроссовера составляют около 6 и 40 К. Вблизи этих температур наблюдается гистерезис. 2019 Article The low-temperature specific heat of MWCNTs / V.V. Sumarokov, A. Jeżowski, D. Szewczyk, M.I. Bagatski, M.S. Barabashko, A.N. Ponomarev, V.L. Kuznetsov, S.I. Moseenkov // Физика низких температур. — 2019. — Т. 45, № 3. — С. 395-403. — Бібліогр.: 55 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/176086 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
spellingShingle Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
Sumarokov, V.V.
Jeżowski, A.
Szewczyk, D.
Bagatski, M.I.
Barabashko, M.S.
Ponomarev, A.N.
Kuznetsov, V.L.
Moseenkov, S.I.
The low-temperature specific heat of MWCNTs
Физика низких температур
description The specific heat of multi-walled carbon nanotubes (MWCNTs) with a low defectiveness and with a low content of inorganic impurities has been measured in the temperature range from 1.8 to 275 K by the thermal relaxation method. The elemental composition and morphology of the MWCNTs were determined using scanning electron microscopy analysis and energy dispersion x-ray spectroscopy. The MWCNTs were prepared by chemical catalytic vapor deposition and have mean diameters from 7 nm up to 18 nm and lengths in some tens of microns. MWCNTs purity is over 99.4 at.%. The mass of the samples ranged from 2–4 mg. It was found that the temperature dependence of the specific heat of the MWCNTs differs significantly from other carbon materials (graphene, bundles of SWCNTs, graphite, diamond) at low temperatures. The specific heat of MWCNTs systematically decreases with increasing diameter of the tubes at low temperatures. The character of the temperature dependence of the specific heat of the MWCNTs with different diameters demonstrates the manifestation of different dimensions from 1D to 3D, depending on the temperature regions. The crossover temperatures are about 6 and 40 K. In the vicinity of these temperatures, a hysteresis is observed.
format Article
author Sumarokov, V.V.
Jeżowski, A.
Szewczyk, D.
Bagatski, M.I.
Barabashko, M.S.
Ponomarev, A.N.
Kuznetsov, V.L.
Moseenkov, S.I.
author_facet Sumarokov, V.V.
Jeżowski, A.
Szewczyk, D.
Bagatski, M.I.
Barabashko, M.S.
Ponomarev, A.N.
Kuznetsov, V.L.
Moseenkov, S.I.
author_sort Sumarokov, V.V.
title The low-temperature specific heat of MWCNTs
title_short The low-temperature specific heat of MWCNTs
title_full The low-temperature specific heat of MWCNTs
title_fullStr The low-temperature specific heat of MWCNTs
title_full_unstemmed The low-temperature specific heat of MWCNTs
title_sort low-temperature specific heat of mwcnts
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2019
topic_facet Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018)
url https://nasplib.isofts.kiev.ua/handle/123456789/176086
citation_txt The low-temperature specific heat of MWCNTs / V.V. Sumarokov, A. Jeżowski, D. Szewczyk, M.I. Bagatski, M.S. Barabashko, A.N. Ponomarev, V.L. Kuznetsov, S.I. Moseenkov // Физика низких температур. — 2019. — Т. 45, № 3. — С. 395-403. — Бібліогр.: 55 назв. — англ.
series Физика низких температур
work_keys_str_mv AT sumarokovvv thelowtemperaturespecificheatofmwcnts
AT jezowskia thelowtemperaturespecificheatofmwcnts
AT szewczykd thelowtemperaturespecificheatofmwcnts
AT bagatskimi thelowtemperaturespecificheatofmwcnts
AT barabashkoms thelowtemperaturespecificheatofmwcnts
AT ponomarevan thelowtemperaturespecificheatofmwcnts
AT kuznetsovvl thelowtemperaturespecificheatofmwcnts
AT moseenkovsi thelowtemperaturespecificheatofmwcnts
AT sumarokovvv nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT jezowskia nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT szewczykd nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT bagatskimi nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT barabashkoms nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT ponomarevan nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT kuznetsovvl nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT moseenkovsi nizʹkotemperaturnapitomateploêmnístʹbagatostínnihvuglecevihnanotrubok
AT sumarokovvv nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT jezowskia nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT szewczykd nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT bagatskimi nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT barabashkoms nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT ponomarevan nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT kuznetsovvl nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT moseenkovsi nizkotemperaturnaâudelʹnaâteploemkostʹmnogostennyhuglerodnyhnanotrubok
AT sumarokovvv lowtemperaturespecificheatofmwcnts
AT jezowskia lowtemperaturespecificheatofmwcnts
AT szewczykd lowtemperaturespecificheatofmwcnts
AT bagatskimi lowtemperaturespecificheatofmwcnts
AT barabashkoms lowtemperaturespecificheatofmwcnts
AT ponomarevan lowtemperaturespecificheatofmwcnts
AT kuznetsovvl lowtemperaturespecificheatofmwcnts
AT moseenkovsi lowtemperaturespecificheatofmwcnts
first_indexed 2025-11-27T22:53:59Z
last_indexed 2025-11-27T22:53:59Z
_version_ 1849985905654235136
fulltext Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3, pp. 395–403 The low-temperature specific heat of MWCNTs V.V. Sumarokov1, A. Jeżowski2, D. Szewczyk2, M.I. Bagatski1, M.S. Barabashko1,3, A.N. Ponomarev4, V.L. Kuznetsov5,6, and S.I. Moseenkov5 1B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine E-mail: sumarokov@ilt.kharkov.ua 2W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences P.O. Box 1410, Wroclaw 50–950, Poland 3National Research Tomsk Polytechnic University, 30 Lenin Ave., Tomsk 634050, Russia 4Institute of Strength Physics and Materials Science of SB RAS, 2/4 Academicheskii Ave., Tomsk 634055, Russia 5Boreskov Institute of Catalysis, 5 Lavrentiev Ave., Novosibirsk 630090, Russia 6National Research Tomsk State University, 36 Lenin Ave., Tomsk 634050, Russia Received December 17, 2018 The specific heat of multi-walled carbon nanotubes (MWCNTs) with a low defectiveness and with a low con- tent of inorganic impurities has been measured in the temperature range from 1.8 to 275 K by the thermal relaxa- tion method. The elemental composition and morphology of the MWCNTs were determined using scanning electron microscopy analysis and energy dispersion x-ray spectroscopy. The MWCNTs were prepared by chemi- cal catalytic vapor deposition and have mean diameters from 7 nm up to 18 nm and lengths in some tens of mi- crons. MWCNTs purity is over 99.4 at.%. The mass of the samples ranged from 2–4 mg. It was found that the temperature dependence of the specific heat of the MWCNTs differs significantly from other carbon materials (graphene, bundles of SWCNTs, graphite, diamond) at low temperatures. The specific heat of MWCNTs sys- tematically decreases with increasing diameter of the tubes at low temperatures. The character of the temperature dependence of the specific heat of the MWCNTs with different diameters demonstrates the manifestation of dif- ferent dimensions from 1D to 3D, depending on the temperature regions. The crossover temperatures are about 6 and 40 K. In the vicinity of these temperatures, a hysteresis is observed. Keywords: carbon nanotubes, MWCNTs, specific heat, low-dimensional systems. Introduction The discovery of carbon nanosystems (fullerenes, SWCNTs, MWCNTs, graphene) led to a great interest in both fundamental science and for applied purposes [1–9]. This is due to the peculiarities of their structures and unu- sual physico-chemical properties. In particular, MWCNTs are suitable objects for studying the physical properties of low-dimensional systems. Carbon nanotubes have also at- tracted great attention due to their potential technological applications (nanoelectronics, construction materials, phar- maceuticals, medicine, etc.) [10]. MWCNT is an isolated multi-layer roll of a graphene sheet or a set of coaxial SWCNTs in the form of a Russian nesting doll (Fig. 1). Between the layers, there is a weak van der Waals bond. The average diameter of MWCNTs is from a few to 100 nm. The distance between the atomic graphene layers is about 0.34 nm as in graphite [3]. The nanotube SWCNT is an elongated cylinder consisting of Fig. 1. Schematic sketch of the most common MWCNTs. Their multi-layered structure is a single-layer nanotube, “dressed” one by one according to the principle of Russian nesting dolls (a) or rolled up into a scroll of graphene sheet (b). © V.V. Sumarokov, A. Jeżowski, D. Szewczyk, M.I. Bagatski, M.S. Barabashko, A.N. Ponomarev, V.L. Kuznetsov, and S.I. Moseenkov, 2019 V.V. Sumarokov et al. equilateral hexagons with carbon atoms at their vertices. This is a graphene plane rolled into a tube. The physical properties of MWCNTs (in particular, thermal properties) depend on the methods and technology of tube preparation, their morphology, and the presence of impurities and defects. Usually, multi-walled carbon nano- tubes are prepared by CVD (chemical vapor deposition) or AD (arc discharge) method with different catalysts, using different technological procedures: temperature regimes, purification methods, etc. Studies of the specific heat of MWCNTs were carried out by both experimental and theoretical methods. Yi et al. [11] measured the specific heat and thermal conductivity of the small array like samples of highly aligned MWCNTs (1–2 mm long, with a cross-sectional diameter of 0.01–0.1 mm) by the self-heating 3ω method. The diameter of the MWCNTs was a few tens of nm, the walls of the nanotubes contained 10–30 layers. They found that the specific heat varies line- arly in the temperature range of 10–300 K. The authors note that because of the uncertainty of the number of MWCNTs in array-like samples, the absolute values of the thermal conductivity coefficient (and, hence, the heat capa- city determined with its help) suffer from uncertainty. Mizel et al. [12] used to study the specific heat of press- ed small cylindrical samples of MWCNTs (tubes were with outer diameters of order 10–20 nm and lengths exceed- ing 10 μm) weighing 10–20 mg with a diameter of 3.2 mm a thermal relaxation technique from 0.6 K up to 210 К. The analysis showed that the C(T)/T2 curves for MWCNTs and graphite coincide above 50 K. The curve C(T)/T2 for graphite has a maximum at 40 K. The C(T)/T2 dependence for the MWCNTs exceeds it for graphite below 40 K. And the maximum of the MWCNTs curve shifts toward helium temperatures. The similarity between C(T)/T2 for multi- walled tubes and for graphite indicates that the two materi- als are similar. Masarapu et al. [13] measured the specific heat of align- ed multi-walled carbon nanotubes (obtained by CVD me- thod with diameters in the range of 20–30 nm and consist- ing of 15–25 layers) in the temperature range from 1.8 to 250 K. They found that in the range of 40–250 K there is a linear dependence of the specific heat. Below 40 K, the specific heat gradually decreases, demonstrating a change in dimension from 1D to 3D behavior, indicated by differ- ent temperature dependences at low temperature. This be- havior of the heat capacity was attributed to a dimensional change in the density of states from 3D at low temperatures to a reduced dimension at higher temperatures. Below 5 K, the T–2 feature due to magnetic impurities was observed. In the works of Jorge et al. [14,15], the specific heat of MWCNTs was measured in the range of 10–120 K. Samples with diameters of 90, 48 and 30 nm were obtained by the CVD method. They have an aligned nanotube structure and an internal bamboo-like structure within each MWCNT. The authors found an anomalous peak at 60 K in these samples. The parameters of the peak (height and tempera- ture of the maximum) do not depend on the magnetic field and do not exhibit thermal hysteresis [15]. Authors [16] showed that taking into account the elec- tron contribution to the heat capacity depending on the dia- meter of the nanotubes, the concentration of impurities, and short-range order parameters (structural inhomogeneities) allowed them to describe the peculiarities of low-temperature behavior of the experimental specific heat of MWCNTs [15] with large diameters and an internal bamboo-like structure. However, according to Benedict et al. [17], the electron contribution to the heat capacity of pure carbon tubes is more than 100 times weaker than the phonon one. Muratov et al. [18] using the adiabatic calorimetry method carried out measurements of the heat capacity of MWCNTs with an average diameter of less than 30 nm in the temperature range from 60 to 300 K. They observed the anomaly in heat capacity at temperatures of 80–90 K. The authors believe that it is similar to that observed at about 60 K in [14]. The samples with a diameter of 25 nm [14] and 17 nm [15], which were synthesized by the catalytic decomposition of acetylene over iron nanoparticles, had a forest distribution. The internal bamboo-like structure was absent in these samples. The dimensional behavior crosso- ver (change from quasi-linear behavior to a higher dimen- sion) was observed at 33 K for samples with a larger diam- eter of tubes and a bamboo-like internal structure and at 55 K for samples with diameters of 17 and 25 nm without a bamboo-like internal structure. Popov [19] calculated the low-temperature specific heat of MWCNTs with different number n of layers within force- constant dynamical models. The specific heat curves of MWCNTs with n = 1–5 above 50–60 K coincide. At lower temperatures, the curves diverge. This discrepancy increases with decreasing temperature. At the same time, the degree of temperature dependence increases from 0.5 for n = 1 to 1 for n = 5. Brief information about the samples (morphology and methods of preparation), methods and temperature ranges of measurement of heat capacity in the reviewed papers are presented in the Table 1. The discrepancies between the experimental values of the specific heats of different works may be due to differ- ences in purity, in structure, in structural defects and heter- ogeneities, in the diameters and quantities of the layers in the MWCNTs samples and systematic errors. Systematic errors are mainly caused by the presence of carbonic and other impurities in the samples: gaseous helium (some- times used to cool the calorimetric cell), catalyst residues, atmospheric gases and other impurities. The authors [16,20–24] showed that electron scattering by impurities and structural inhomogeneities, such as non-uniformity of the short-range order, can lead to anomalous behavior of both the thermal, transport and electron properties of car- bon nanomaterials. 396 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 The low-temperature specific heat of MWCNTs In Hone’s study [25], it was found that the presence of helium in bundles of SWCNTs leads to an anomalous be- havior of the specific heat below 20 K (see Fig. 2 in Ref. 25). Adsorbed Xe, N2, and CH4 impurities lead to a significant increase in the specific heat of bundles of closed single-wall carbon nanotubes at low temperatures [26–30]. For example, the concentration of several admixture nitro- gen molecules per 1000 carbon atoms in bundles of single- walled carbon nanotubes leads to an increase in the specif- ic heat by a factor of 1.5 at ~ 2 K. Thus, thorough cleaning of samples from gas impurities is an integral part of obtain- ing precision data on the heat capacity of carbon nanoma- terials. In the reviewed papers, MWCNTs were obtained using different methods and technologies. The analysis of the discussed results is difficult due to the lack of complete in- formation in a number of papers on the purity of MWCNTs, measurement errors, etc. The results of meas- urements of the specific heat vary greatly; especially in the low-temperature region (see below Fig. 6). Despite inten- sive experimental studies, the specific heat at constant pressure of multilayer carbon nanotubes has not been com- prehensively studied at low temperatures. Also, interest in carbon nanotubes from the side of new applied problems requires more extensive studies of their properties depend- ing on their size, production technology, and so on. The present paper is devoted to studies of the low-tem- perature specific heat of multi-walled carbon nanotubes with a controlled level of defectiveness and with a low content of inorganic impurities in order to obtain infor- mation about the effects of dimensionality in the thermo- dynamics of MWCNTs with different diameters. We used the system set of MWCNTs, obtained using the same type of catalysts and defectiveness, which was characterized using TEM (transmission electron microscopy), Raman spectroscopy, XRF (x-ray fluorescence method), EDS (the energy dispersive x-ray spectroscopy), and temperature dependence of conductivity [31–37]. Experiment The calorimetric studies of MWCNTs have been made in the temperature range from 1.8 to 275 K. The specific heat was measured using the thermal relaxation method. The measurements were carried out on the physical proper- ty measurement system (PPMS) from Quantum Design Inc. operating in the heat capacity mode. A simplified draft of the set-up is shown in Fig. 2 [38]. Measuring system (the so-called puck) consist of a measuring platform on which a sample is anchored with an Apiezon grease. After mounting the sample on the puck, the chamber was sealed and cooled down to temperature 150 K. The measurements were carried out in high-vacuum conditions. Each time, two series of run were performed. During the first run measurements were performed from 150 K down to 2 K and from 2 K up to 275 K during the second one. The temperature of the sample was measured with the resistive thermometer Cernox (Lake Shore). The under consideration samples of MWCNTs were cut out from plates with thickness about 2–3 mm. The plates were obtained by compacting the MWCNTs powder under the pressure of 1.1 GPa as in Ref. 28. MWCNTs were prepared using the CVD method by de- composition of ethylene over the bimetallic Fe-Co/Al2O3 catalyst at 670°C Fe2Co as an active component [39,40]. This catalyst composition has been shown to provide MWCNTs of low defectiveness [31] and with low content Table 1. Brief information about the samples Ref. Synthesis technique Average diameter, nm (length) Temperature interval, K Measuring technique Sample mass [12] AD1 10–20 (10 µm) 1–200 Thermal relaxation technique 10–20 mg [11] CVD2 20–40 10–300 Self-heating 3ω method [15] CVD2 Sample A1 ∅903/∅584 6–120 Relaxation method 200 µg CVD2 Sample B ∅483/∅214 Sample C ∅173/∅54 [18] CVD2 below 30 56–300 Adiabatic technique [13] CVD2 20–30 (1–3 mm) 1.8–250 Relaxation technique 2.2 mg Notes: 1 arc discharge technique, 2 chemical vapor deposition, 3 outer diameter of MWCNTs, 4 inside diameter of MWCNTs. Fig. 2. Thermal connection scheme between a sample and the measuring platform in PPMS heat capacity puck. Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 397 V.V. Sumarokov et al. of inorganic impurities. Further refluxing of nanotubes with 15% HCl (followed by washing with distilled water until neutral pH and subsequent drying in air) allows de- creasing the content of catalyst traces to 0.3–0.5 wt%. Pu- rity of prepared MWCNTs powder is over 99.4 at.%. In- formation about the chemical composition of the samples is given in Table 2. In the experiment, 3 batches of MWCNTs powders differing in mean tube diameters were used: 7.2 nm (s1), 9.4 nm (s2) and 18 nm (s3). Information on the samples of the MWCNTs is given in Table 3. The mor- phology of MWCNTs with different diameters is visible in TEM images (Fig. 3). MWCNTs are not combined in bun- dles, unlike SWCNTs. Table 3. Information about the MWCNTs samples Sample Mean diameter, nm Length, nm Mass, mg s1 7.2 Up to 50000 2.35 s2 9.4 Up to 50000 2.37 s3 18 Up to 30000 4.3 Scanning electron microscopy (SEM) analysis was car- ried out on JEOL JSM-7500FA at 20 kV to evaluate sur- face morphology of the samples. Element composition and concentration were measured by the energy dispersive x-ray spectroscopy (EDS) [41]. The sample mass was specified with Sartorius CPA225D semi-microbalance. The mass of the samples was 2.35 mg (sample s1); 2.37 mg (sample s2) and 4.3 mg (sample s3) (see Table 3). During the experiment, the heat exchanging helium gas was not used for cooling of the calorimeter to the low temperatures. Measurement error did not exceed 2%. Other details of the experiment were described elsewhere in Refs. 42, 43. Results and discussion The specific heat of MWCNTs with mean diameter of 7.2 nm (sample s1), 9.4 nm (s2) and 18 nm (s3) was meas- ured in the temperature range from 2 to 275 K. The graphs of the temperature dependence of the specific heat of the studied samples are shown in Fig. 4. Figure 4 also displays the curves of the temperature dependence of the specific heat of graphene (theory) [25], bundles of SWCNTs (ex- periment) [26], graphite (experiment) [44–46] and dia- mond (experiment) [47,48]. It is noteworthy that the temperature dependences of the specific heat for all carbon materials discussed, with the exception of diamond, above 100 K are close: the dif- ference in the results of studies does not exceed 15–30%. The curves begin to diverge below 60–100 K. The behavior of the temperature dependence for dia- mond differs sharply from other carbon materials, which is apparently due to the fact that diamond has a sp3 bond, in contrast to the different forms of the sp2 bond for the re- maining carbon materials. In diamond, carbon atoms are strongly bonded with the nearest neighbors (sp3 hybridiza- Table 2. Chemical atomic composition of the MWCNTs samples Sample C at.% O at.% Si at.% Cl at.% Fe at.% Cr at.% Co at.% s1 99.49 0.24 0.07 0.01 0.17 0.02 0 s2 99.45 0.31 0 0.04 0.04 0 0.03 s3 99.72 0 0 0.01 0.17 0.01 0.09 Fig. 3. The TEM images of MWCNTs with mean diameter 7.2 nm (s1), 9.4 nm (s2) and 18 nm (s3). s1 s2 s3 398 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 The low-temperature specific heat of MWCNTs tion); there are very high frequencies of vibrational modes and a high Debye temperature of about 2000 K [48]. In the allotropic forms of carbon: graphite, MWCNTs, and bundles of SWCNTs, there are both strong (sp2 hyb- ridization in the plane or on the nanotube surface) and weak (van der Waals) interactions between the layers and the walls of the tubes in bundles. The contribution of low- frequency modes to the heat capacity of these allotropic forms of carbon increases with decreasing temperature below 300 K. As a result, below 300 K, the difference be- tween the temperature dependence curve of the heat capac- ity CP(T) of diamond and the curves of heat capacities CP(T) of graphite, graphene, MWCNTs, and SWCNT bundles increases with decreasing temperature. The character of the low-temperature dependences of graphite, MWCNTs, and SWCNTs bundles is qualitatively similar, and the dimensionality effect in the heat capacity of these materials is determined by the relative contribu- tion of low-frequency vibrations. In anisotropic layered graphite, carbon atoms form a hexagonal network and are connected by strong covalent “flat” bonds (sp2 hybridiza- tion) [49,50]. The Debye temperature due to vibrations of carbon atoms in the plane is about ≈ 2500 K (higher than in diamond [51]). Between the layers, the carbon atoms are bound by weak van der Waals forces. At low temperatures, the contribution to the heat capacity of graphite from low- frequency vibrational modes dominates. From the analysis of low-temperature data on the heat capacity of graphite, Ramos et al. [45] found, that the Debye temperature is ӨD ≈ 420 K, which is 5 times less than ӨD diamond. In graphene, there are both high-frequency (vibrations of car- bon atoms in the plane) and low-frequency (transverse vibrations) vibrational modes. In the SWCNTs bundles, there are high-frequency vi- brations of carbon atoms on the nanotube surface due to the strong interaction between carbon atoms (deformed sp2 hybridization) and low-frequency vibrational modes (trans- verse vibrations of atoms, elastic longitudinal and torsional vibrations of the tube as a whole). When the wavelength of the transverse oscillations is equal to or greater than the tube radius, the transverse radi- al modes are quantized [25]. Both in the SWCNTs and in multi-walled tubes, there is a weak interaction between the walls of the tubes due to the van der Waals forces. The low-energy part of the spectrum will change with an increase in the number of tubes in bundles of SWCNTs and the number of walls in MWCNTs. According to the theory [19], an increase in the number of as single-walled tubes in the SWCNT bundles as and layers in multi-walled tubes leads to an increase in the frequency and a decrease in the density of states in the low-energy part of the spec- trum. This reflects the trend observed in the experiments (present work and Refs. 12, 13). The theoretical heat capacity curve for graphene [25] (Fig. 4) demonstrates a linear dependence on temperature and lies above the other curves below 60 K. Above 6 K, the specific heat curves of MWCNTs (samples s1 and s2, diameters of tubes: 7.2 and 9.4 nm, respectively) and SWCNT bundles practically coincide. Below 6 K, the curves for MWCNTs (s1 and s2) diverge from the SWCNTs curve down towards graphite. Curves for MWCNTs sample s3 and for graphite noticeably diverge from curves of our samples s1 and s2 and graphene below 100 K. The curve for sample s3 with a tube diameter of 18 nm diverges from a graphite curve of about 30 K, below 30 K it lies higher than graphite curve, but below the curves s1 and s2. Fig. 4. (Color online) The temperature dependences of the specific heat of carbon materials. Theory: graphene [25] (1); Experiment: SWСNT bundles [26] (2); MWCNTs: the samples s1 (3); s2 (4); s3 (5) (present work); graphite: [44] (6), [45] (7); [46] (8); diamond [47] (9), [48] (10). (a) Entire temperature range; (b) Temperature range below 20 K. Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 399 V.V. Sumarokov et al. Comparison of the obtained results with the literature data showed that at temperatures below 6 K the specific heat of MWCNTs decreases monotonically with an in- crease in the average diameter of the tubes (see below Fig. 6). The heat capacity curve MWCNTs (diameter 15 nm) from Ref. 12 is located between our curves for samples s2 (∅9.4 nm) and s3 (∅18 nm), and the curve (∅25 nm) from Ref. 13 lies below ours curve s3 (∅18 nm). The results of Yi et al. [11], Jorge et al. [14,15] and Muratov et al. [18] are qualitatively close to each other. Below 60 K data of Yi et al. [11] and Jorge et al. [14,15] lie above both present results and the data from Refs. 12, 13. At 15 K, the data [11,14,15] exceed our results, the data from Ref. 12 (∅15 nm) and Ref. 13 (∅25 nm) more than 2 times. Note that the nature of such difference, apparently, is associated with a significant difference in the morpholo- gy of the tubes. The authors of [16] believe that this may be due to the manifestation of the electronic subsystem in the defective — “dirty” samples. For convenience of analysis, let us present the tempera- ture dependence of the MWCNTs specific heat of meas- ured samples s1 (∅7.2 nm), s2 (∅9.4 nm) and s3 (∅18 nm) in coordinates C/T2 vs T as are shown in Fig. 5. The nature of the temperature dependences of the heat capacity indi- cates the behavior with different dimensions in different temperature ranges. The curve s3 clearly shows how the behavior of C(T) changes with temperature, corresponding to a change in dimensionality from linear at high tempera- tures to cubic at low temperatures through the quadratic at intermediate temperatures. The nature of the temperature dependence of the specific heat of MWCNTs suggests that the manifestation of 1D–3D dimensionality is due to the competition between the con- tributions of low-frequency oscillations as in the tubes and between the walls of the tubes and high-frequency oscilla- tions on the surface of the tubes in the density of phonon states. The dominant contribution is made by low-frequency oscillations between the walls of the tubes, as can be seen in the example of sample s3, in which the number of layers is noticeably larger than in the tubes of samples s1 and s2. The change in the behavior of the temperature dependence of the specific heat with a quasi-1D dimension to a quasi- 2D is observed in the temperature range from about 40 to 200 K. The areas of crossovers are most brightly shown on sample s3 with a diameter of 18 nm: about 6 and about 40 K. Note that temperature hysteresis is observed in these areas. The quadratic temperature dependence of the specific heat is from 6 to 40 K. With the decrease of the diameter of the MWCNTs, the T2-temperature dependence is blurred and the absolute values of the heat capacity increase. At the same time, an analysis of the temperature depend- ences of the specific heats of literature data on graphite, SWCNT bundles, MWCNTs [12,13,26,44–46] shows that at the temperature close to 40 K a feature is observed — a crossover from quasi-1D to quasi-two-dimensional be- havior (see Fig. 6). Neutron studies [52–54] show that the curves of the density of states for SWCNTs and graphite exhibit anomalies at energies of 2.5–3.5 meV and 16 meV (see Figs. 17–19 in Ref. 54 and Fig. 5 in Ref. 52), which correspond to the temperatures of the anomalies in heat ca- pacity. Note that, as in the studies of heat capacity and ther- mal expansion [26], the temperature dependence of elec- trical conductivity [55] also exhibits a feature near 30 K. According to the authors of [55], this feature is due to Fig. 5. (Color online) The specific heat of the studied samples s1 (1), s2 (2) and s3 (3) in coordinates C/T2 vs T. Crossover tem- peratures are indicated by arrows. Fig. 6. (Color online) The specific heat in coordinates C/T2 vs T: bundles of SWCNTs [26] (1); the MWSNT sample s1 (∅7.2 nm) (2); the MWSNT sample s2 (∅9.4 nm) (3); MWSNTs (∅ ~ 15 nm) [12] (4); the MWSNT sample s3 (∅18 nm) (5); MWSNTs (∅ ~ 25 nm) [13] (6); graphite: [44] (7), [45] (8). 400 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 The low-temperature specific heat of MWCNTs the change in the mechanism of conductivity in a system oriented of SWCNTs from the state of the Luttinger liquid to the Mott dielectric phase in the temperature range 25–36 K. Also features in temperature dependences of conductivity (with diameters from 5.8 to 25 nm) and magnetoresistance (with diameters from 8.7 to 25 nm) MWCNTs (tubes simi- lar to ours) were observed at temperatures below 50 K (see Fig. 2 in Ref. 32). Conclusion The specific heats of systematic set of MWCNTs with variable external diameters and number of graphene walls have been measured from 2 to 275 K by the thermal re- laxation method. The elemental composition and morpho- logy of the MWCNTs were determined using scanning electron microscopy analysis and energy dispersion x-ray spectroscopy. The MWCNTs prepared by chemical cata- lytic vapor deposition contained over 99.4 at.%, which have mean diameters from 7 nm up to 18 nm and lengths in some tens of microns. It was found that the low-tempera- ture dependence of the specific heat of the MWCNTs of the studied samples differs significantly from other carbon materials (graphene, graphite, diamond) at low tempera- tures. It was also found that the specific heat of MWCNTs systematically decreases with increasing diameter of the tubes at low temperatures. The character of the temperature dependence of the specific heat of the MWCNTs samples with different diameters demonstrates the manifestation of different dimensionality from 1D to 3D, depending on the temperature regions. The crossover temperatures are about 6 and 40 K. In the vicinity of these temperatures, a temper- ature hysteresis is observed. Acknowledgments The authors thank Scientific and educational innovation center “Nanomaterials and nanotechnologies”, National Research Tomsk Polytechnic University for help in x-ray diffraction measurements and SEM-EDS analysis of the samples MWNCTs that were carried out within the frame- work of Tomsk Polytechnic University Competitiveness Enhancement Program. _______ 1. A.V. Eletskii, Usp. Phys. Nauk 167, 945 (1997) [Phys. Usp. 40, 899 (1997)]. 2. A.V. Eletskii, Usp. Phys. Nauk 179, 225 (1997) [Phys. Usp. 52, 209 (2009)]. 3. M.S. Dresselhaus, Carbon Nanotubes: Synthesis, Structure, Properties, and Applications, Springer-Verlag (2000). 4. Carbon Nanotubes: Science and Application, M. Meyyappan (ed.), CRC Press, Boca Raton, London, New York, Wa- shington D.C. (2005). 5. Carbon Nanotubes, A. Jorio, G. Dresselhaus, and M.S. Dresselhaus (eds.), Springer-Verlag, Berlin, Heidelberg, New York (2008). 6. A. Szabo, C. Perri, A. Csato, G. Giordano, D. Vuono, and J.B. Nagy, Materials 3, 3092 (2010). 7. S. Bellucci, Phys. Status Solidi C 2, 34 (2005). 8. M. Endo, M.S. Strano, and P.M. Ajayan, Potential Appli- cations of Carbon Nanotubes, in: Carbon Nanotubes. Topics in Applied Physics, A. Jorio, G. Dresselhaus, and M.S. Dresselhaus (eds.), Springer-Verlag, Berlin Heidelberg New York (2008). 9. M.F.L. De Volder, S.H. Tawfick, R.H. Baughman, and A.J. Hart, Science 339 (6119), 535 (2013). 10. Industrial Applications of Carbon Nanotubes, Huisheng Peng, Qingwen Li, and Tao Chen (eds.), Elsevier, Amsterdam, UK, US (2017). 11. W. Yi, L. Lu, Zhang Dian-lin, Z.W. Pan, and S.S. Xie, Phys. Rev. B 59, R9015 (1999). 12. A. Mizel, L.X.Benedict, M.L. Cohen, S.G. Louie, A. Zettl, N.K. Budraa, and W.P. Beyermann, Phys. Rev. B 60, 3264 (1999). 13. C. Masarapu, L.L. Henry, and B. Wei, Nanotechnology 16, 1490 (2005). 14. G.A. Jorge, V. Bekeris, C. Acha, M.M. Escobar, S. Goyanes, D. Zilli, and R.J. Candal, J. Phys.: Conf. Ser. 167, 012008 (2009). 15. G.A. Jorge, V. Bekeris, M.M. Escobar, S. Goyanes, D. Zilli, A.L. Cukierman, and R.J. Candal, Carbon 48, 525 (2010). 16. A.N. Ponomarev, V.E. Egorushkin, N.V. Melnikova, and N.G. Bobenko, Physica E 66, 13 (2015). 17. L.X. Benedict and S.G. Louie, and M.L. Cohen, Solid State Commun. 100, 177 (1996). 18. V.B. Muratov, O.O. Vasil’ev, L.M. Kulikov, V.V. Garbuz, Y.V. Nesterenko, and T.I. Duda, J. Superhard Materials 34(3), 173 (2012). 19. V.N. Popov, Phys. Rev. B 66, 153408 (2002). 20. N.G. Bobenko, V.E. Egorushkin, N.V. Melnikova, A.A. Belosludtseva, L.D. Barkalov, and A.N. Ponomarev, J. Struct. Chem. 59, 853 (2018). 21. N.G. Bobenko, V.E. Egorushkin, N.V. Melnikova, and A.N. Ponomarev, Physica E 60, 11 (2014). 22. V.E. Egorushkin, N.V. Melnikova, A.N. Ponomarev, and A.A. Reshetnyak, J. Phys.: Conf. Ser. 248, 012005 (2010). 23. M.S. Barabashko, A.E. Rezvanova, and A.N. Ponomarev, Fullerenes, Nanotubes and Carbon Nanostructures 25, 661 (2017). 24. V. Egorushkin, N. Melnikova, A. Ponomarev, and N. Bobenko, J. Mat. Sci. Eng. A 1, 161 (2011). 25. J. Hone, Science 289 (5485), 1730 (2000). 26. M.I. Bagatskii, M.S. Barabashko, A.V. Dolbin, V.V. Sumarokov, and B. Sundqvist, Fiz. Nizk. Temp. 38, 667 (2012) [Low Temp. Phys. 38, 523 (2012)]. 27. M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov, Fiz. Nizk. Temp. 39, 568 (2013) [Low Temp. Phys. 39, 441 (2013)]. 28. M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov, Pis’ma v Zh. Èksper. Teoret. Fiz. 99, 532 (2014) [JETP Lett. 99, 461 (2014)]. 29. M.I. Bagatskii, V.V. Sumarokov, and M.S. Barabashko, Fiz. Nizk. Temp. 42, 128 (2016) [Low Temp. Phys. 42, 94 (2016)]. Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 401 https://doi.org/10.1070/PU1997v040n09ABEH000282 https://doi.org/10.3367/UFNe.0179.200903a.0225 https://doi.org/10.3390/ma3053092 https://doi.org/10.1002/pssc.200460105 https://doi.org/10.1126/science.1222453 https://doi.org/10.1103/PhysRevB.59.R9015 https://doi.org/10.1103/PhysRevB.59.R9015 https://doi.org/10.1103/PhysRevB.60.3264 https://doi.org/10.1088/0957-4484/16/9/013 https://doi.org/10.1088/1742-6596/167/1/012008 https://doi.org/10.1016/j.carbon.2009.09.073 https://doi.org/10.1016/j.physe.2014.09.005 https://doi.org/10.1016/0038-1098(96)00386-9 https://doi.org/10.1016/0038-1098(96)00386-9 https://doi.org/10.3103/S1063457612030045 https://doi.org/10.1103/PhysRevB.66.153408 https://doi.org/10.1134/S0022476618040157 https://doi.org/10.1134/S0022476618040157 https://doi.org/10.1016/j.physe.2014.01.026 https://doi.org/10.1088/1742-6596/248/1/012005 https://doi.org/10.1080/1536383X.2017.1391225 https://doi.org/10.1126/science.289.5485.1730 https://doi.org/10.1063/1.4723677 https://doi.org/10.1063/1.4723677 https://doi.org/10.1063/1.4807048 https://doi.org/10.1134/S0021364014080049 https://doi.org/10.1063/1.4942395 V.V. Sumarokov et al. 30. M.I. Bagatskii, M.S. Barabashko, V.V.Sumarokov, A. Jeżowski, and P. Stachowiak, J. Low Temp. Phys. 187, 113 (2017). 31. V.L. Kuznetsov, S.N. Bokova-Sirosh, S.I. Moseenkov, A.V. Ishchenko, D.V. Krasnikov, M.A. Kazakova, and E.D. Obraztsova, Phys. Status Solidi B 251, 2444 (2014). 32. A.I. Romanenko, O.B. Anikeeva, T.I. Buryakov, E.N. Tkachev, K.R. Zhdanov, V.L.Kuznetsov, I.N. Mazov, and A.N. Usoltseva, Phys. Status Solidi B 246, 2641 (2009). 33. A.I. Romanenko, O.B. Anikeeva, T.I. Buryakov, E.N. Tkachev, K.R. Zhdanov, V.L. Kuznetsov I.N. Mazov, A.N. Usoltseva, and A.V. Ischenko, Diamond & Related Materials 19, 964 (2010). 34. K.V. Elumeeva, V.L. Kuznetsov, A.V. Ischenko, R. Smajda, M. Spina, L. Forro, and A. Magrez, AIP Adv. 3, 112101 (2013). 35. S.N. Bokova-Sirosh, V.L. Kuznetsov, A.I. Romanenko, M.A. Kazakova, D.V. Krasnikov, E.N. Tkachev, Y.I. Yuzyuk, and E.D. Obraztsova, J. Nanophotonics 10, 012526 (2016). 36. V.L. Kuznetsov, K.V. Elumeeva, A.V. Ishchenko, N.Yu. Beylina, A.A. Stepashkin, S.I. Moseenkov, L.M. Plyasova, I.Yu. Molina, A.I. Romanenko, O.B. Anikeeva, and E.N. Tkachev, Phys. Status Solidi B 247, 2695 (2010). 37. S.N. Bokova, E.D. Obraztsova, V.V. Grebenyukov, K.V. Elumeeva, A.V. Ishchenko, and V.L. Kuznetsov, Phys. Status Solidi B 247, 2827 (2010). 38. PPMS Manual–Heat Capacity Option User’s Manual, https://web.njit.edu/~tyson/PPMS_Documents/PPMS_Manu al/1085–150%20Heat%20Capacity.pdf 39. A. Usoltseva, V. Kuznetsov, N. Rudina, E. Moroz, M. Haluska, and S. Roth, Phys. Status Solidi B 244, 3920 (2007). 40. V.L. Kuznetsov, D.V. Krasnikov, A.N. Schmakov, and K.V. Elumeeva, Phys. Status Solidi B 249, 2390 (2012). 41. I.N. Mazov, I.A. Ilinykh, V.L. Kuznetsov, A.A. Stepashkin, K.S. Ergin, D.S. Muratov, and J.-P. Issi, J. Alloys Com- pounds 586, S440 (2014). 42. D. Szewczyk and A. Jeżowski, J. Edu. Tech. Sci. 2, 22 (2015). 43. D. Szewczyk, A. Jeżowski, A.I. Krivchikov, and J.L. Tamarit, Fiz. Nizk. Temp. 41, 598 (2015) [Low Temp. Phys. 41, 469 (2015)]. 44. T. Nihira and T. Iwata, Phys. Rev. B 68, 134305 (2003). 45. T. Pérez-Castañeda, J. Azpeitia, J. Hanko, A. Fente, H. Suderow, and M.A. Ramos, J. Low Temp. Phys. 173, 4 (2013). 46. M.G. Alexander, D.P. Goshorn, and D.G. Onn, Phys. Rev. B 22, 4535 (1980). 47. O.O. Vasil’ev, V.B. Muratov, and T.I. Duda, J. Super. Mat. 32, 375 (2010). 48. W. DeSorbo, J. Chem. Phys. 21, 876 (1953). 49. A.N. Obraztsov, E.A. Obraztsova, A.V. Tyurnina, and A.A. Zolotukhin, Carbon 45, 2017 (2007). 50. J.W. McClure, Phys. Rev. 108, 612 (1957). 51. I.A. Gospodarev, V.I. Grishaev, E.V. Manzhelii, E.S. Syrkin, S.B. Feodosyev, and K.A. Minakova, Fiz. Nizk. Temp. 43, 322 (2017) [Low Temp. Phys. 43, 264 (2017)]. 52. S. Rols, E. Anglare, J.L. Sauvajol, G. Coddens, and A.J. Dianoux, Appl. Phys. A 69, 591 (1999). 53. S. Rols, Z. Benes, E. Anglaret, J.L. Sauvajol, P. Papanek, J.E. Fisher, G. Goddens, H. Schober, and A.J. Dianoux, Phys. Rev. Lett. 85, 5222 (2000). 54. J.L. Sauvajol, E. Anglaret, S. Rols, and L. Alvarez, Carbon 40, 1697 (2002). 55. B.A. Danilchenko, L.I. Shpinar, N.A. Tripachko, E.A. Voitsihovska, S.E. Zelensky, and B. Sundqvist, Appl. Phys. Lett. 97, 072106 (2010). ___________________________ Низькотемпературна питома теплоємність багатостінних вуглецевих нанотрубок В.В. Сумароков, A. Jeżowski, D. Szewczyk, М.І. Багацький, М.С. Барабашко, А.Н. Пономарьов, В.Л. Кузнецов, С.І. Мосєєнков Питому теплоємність багатостінних вуглецевих нанотру- бок (БСВНТ) з низькою дефектністю та низьким вмістом не- органічних домішок виміряно в діапазоні температур 1,8–275 К методом теплової релаксації. Зразки БСВНТ отримано хіміч- ним каталітичним осадженням з парової фази. Елементний склад і морфологію БСВНТ визначено за допомогою скану- ючої електронної мікроскопії та енергодисперсійної рентге- нівської спектроскопії. Нанотрубки мали середній діаметр від 7 до 18 нм і довжину в кілька десятків мікрон. Чистота БСВНТ була більш ніж 99,4 ат.%. Маса зразків становила від 2 до 4 мг. Виявлено, що температурна залежність питомої теплоємності БСВНТ значно відрізняється від теплоємності інших вуглецевих матеріалів (графена, в’язок ОСВНТ, графі- ту, алмазу) при низьких температурах. Теплоємність БСВНТ систематично зменшується зі збільшенням діаметра нанот- рубок при низьких температурах. Температурні залежності питомої теплоємності БСВНТ з різними діаметрами демон- струють притаманний низьковимірним системам характер від 1D до 3D в залежності від температурних областей. Тем- ператури кросовера складають близько 6 та 40 К. Поблизу цих температур спостерігається гістерезис. Ключові слова: вуглецеві нанотрубки, БСВНТ, питома теп- лоємність, нізьковимірні системи. Низкотемпературная удельная теплоемкость многостенных углеродных нанотрубок В.В. Сумароков, A. Jeżowski, D. Szewczyk, М.И. Багацкий, М.С. Барабашко, А.Н. Пономарев, В.Л. Кузнецов, С.И. Мосеенков Удельная теплоемкость многостенных углеродных нано- трубок (МСУНТ) с низкой дефектностью и низким содер- жанием неорганических примесей измерена в диапазоне тем- ператур 1,8–275 К методом тепловой релаксации. Образцы МСУНТ получены химическим каталитическим осаждением 402 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 https://doi.org/10.1007/s10909-016-1737-z https://doi.org/10.1002/pssb.201451195 https://doi.org/10.1002/pssb.200982267 https://doi.org/10.1016/j.diamond.2010.02.035 https://doi.org/10.1063/1.4829272 https://doi.org/10.1117/1.JNP.10.012526 https://doi.org/10.1002/pssb.201000211 https://doi.org/10.1002/pssb.201000237 https://doi.org/10.1002/pssb.201000237 https://web.njit.edu/%7Etyson/PPMS_Documents/PPMS_Manual/1085-150%20Heat%20Capacity.pdf https://web.njit.edu/%7Etyson/PPMS_Documents/PPMS_Manual/1085-150%20Heat%20Capacity.pdf https://doi.org/10.1002/pssb.200776143 https://doi.org/10.1002/pssb.201200120 https://doi.org/10.1016/j.jallcom.2012.10.167 https://doi.org/10.1016/j.jallcom.2012.10.167 https://doi.org/10.1063/1.4922101 https://doi.org/10.1103/PhysRevB.68.134305 https://doi.org/10.1007/s10909-013-0884-8 https://doi.org/10.1103/PhysRevB.22.4535 https://doi.org/10.3103/S106345761006002X https://doi.org/10.1063/1.1699050 https://doi.org/10.1016/j.carbon.2007.05.028 https://doi.org/10.1103/PhysRev.108.612 https://doi.org/10.1063/1.4978291 https://doi.org/10.1007/s003390051037 https://doi.org/10.1103/PhysRevLett.85.5222 https://doi.org/10.1016/S0008-6223(02)00010-6 https://doi.org/10.1063/1.3467464 https://doi.org/10.1063/1.3467464 The low-temperature specific heat of MWCNTs из паровой фазы. Элементный состав и морфология МСУНТ определены с помощью сканирующей электронной микро- скопии и энергодисперсионной рентгеновской спектроско- пии. Нанотрубки имели средний диаметр от 7 до 18 нм и длину в несколько десятков микрон. Чистота МСУНТ более 99,4 ат.%. Масса образцов составляла от 2 до 4 мг. Обнаруже- но, что температурная зависимость удельной теплоемкости МСУНТ значительно отличается от теплоемкости других углеродных материалов (графена, связок ОСУНТ, графита, алмаза) при низких температурах. Теплоемкость МСУНТ систематически уменьшается с увеличением диаметра нанот- рубок при низких температурах. Температурные зависимости удельной теплоемкости МСУНТ с разными диаметрами де- монстрируют присущий низкоразмерным системам характер от 1D до 3D в зависимости от температурных областей. Тем- пературы кроссовера составляют около 6 и 40 К. Вблизи этих температур наблюдается гистерезис. Ключевые слова: углеродные нанотрубки, МСУНТ, удельная теплоемкость, низкоразмерные системы. Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 403 Introduction Experiment Results and discussion Conclusion Acknowledgments

Ähnliche Einträge