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Zaulychnyy Ya V, Solonin Yu M, Foya O O, Khyzhun O Yu, [VASYLKIV Oleg](https://orcid.org/0000-0002-5041-6130)

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[Energy redistribution of the valence electrons due to nanodispersion of materials and its evidence as determined by the ultrasoft X-ray emission spectra](https://mdr.nims.go.jp/datasets/e42d9c0e-e191-4c0b-985b-7a8c6085e5d2)

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Microsoft Word - ZAULICHNYI.doc169 ЭЛЕКТРОННЫЕ СТРУКТУРА И СВОЙСТВА PACS numbers: 71.20.-b, 71.28.+d, 73.22.-f, 78.70.En, 79.60.-i, 82.80.Ej, 82.80.Pv Energy Redistribution of the Valence Electrons Due to Nanodispersion of Materials and Its Evidence as Determined by the Ultrasoft X-Ray Emission Spectra Ya. V. Zaulychnyy, Yu. M. Solonin, O. O. Foya, O. Yu. Khyzhun,  and O. Vasylkiv* I. M. Frantsevych Institute for Problems of Materials Science, N.A.S.U., 3 Krzhyzhanov’sky Str., UA-03680 Kyyiv-142, Ukraine *ICYS, National Institute for Materials Science,  1-1 Namiki, Tsukuba,  305-0044 Ibaraki, Japan An investigation under equal experimental conditions of the ultrasoft x-ray emission bands of coarse-grained and nanosize powders of different materials reveals the narrowing of the spectra and changes of their shapes when de-creasing powder size. As shown, this is a consequence of the energy redistri-bution of valence-electron states after the breaking of interatomic bonds un-der dispersion of the materials into nanosizes, when a number of surface at-oms with broken bonds become commensurable with the number of atoms within the nanoparticles. The energy redistribution of electrons occupying mainly the π-bonding states is changed significantly due to the increasing curvature of the surfaces of carbon nanomaterials with the decrease of their sizes. As revealed, the specific narrowing of the x-ray emission bands repre-senting electron states of some symmetry is proportional to occupancy of these states. Дослідження в однакових експериментальних умовах ультрам’яких рен-тґенівських емісійних смуг крупних та нанорозмірних порошків ріжних матеріялів свідчить про звуження спектрів та зміну їх форми при змен-шенні розміру порошків. Показано, що це є наслідком енергетичного пе-рерозподілу валентних електронів в результаті розриву міжатомового зв’язку при дисперґуванні матеріялів до нанорозмірів, коли число повер-хневих атомів із розірваними зв’язками стає порівнянним з числом ато-мів в об’ємі наночастинок. Енергетичний перерозподіл електронів, що заповнюють переважно π-зв’язуючі стани, суттєво змінюється при збіль-шенні кривини поверхні вуглецевих наноматеріялів в результаті змен-шення їх розмірів. Встановлено, що питомі звуження рентґенівських емі-сійних смуг, котрі відображають енергетичний розподіл електронних Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol. 2008, т. 30, № 2, сс. 169—187  Оттиски доступны непосредственно от издателя  Фотокопирование разрешено только  в соответствии с лицензией © 2008 ИМФ (Институт металлофизики им. Г. В. Курдюмова НАН Украины)Напечатано в Украине.170 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. станів певної симетрії у сполуці, є пропорційними заселености цих станів. Исследования в одинаковых экспериментальных условиях ультрамягких рентгеновских эмиссионных полос крупных и наноразмерных порошков различных материалов свидетельствуют о сужении спектров и изменении их формы при уменьшении размера порошков. Показано, что это являет-ся следствием энергетического перераспределения валентных электронов в результате разрыва межатомных связей при диспергировании материа-лов до наноразмеров, когда число поверхностных атомов с разорванными связями становится сравнимым с числом атомов в объеме наночастиц. Энергетическое перераспределение электронов, которые заполняют пре-имущественно π-связующие состояния, существенно изменяется при уве-личении кривизны поверхности углеродных наноматериалов в результате уменьшения их размеров. Установлено, что удельные сужения рентгенов-ских эмиссионных полос, отображающих энергетическое распределение электронных состояний определенной симметрии в соединении, пропор-циональны заселенности этих состояний. Key words: ultrasoft x-ray emission spectroscopy, electronic structure, chemical bonding, nanodispersion. (Received July 16, 2007)   1. INTRODUCTION The energy state and unique properties of nanosystems are determined mainly by a considerable contribution of an interatomic interaction of the surface and near-surface atoms. Therefore, a study of the energy distribution of the valence electrons (EDVE) directly involved in in-teratomic interactions in nanoparticles is of current importance. Be-cause the number of atoms in nanoparticles with sizes of 10—100 nm is several times greater than in clusters with several hundreds of atoms, the theoretical calculations employing Xα-methods [1—5] do not repre-sent the electronic structure of the nanoparticles adequately. Theo-retical methods developed recently for calculations of the electronic structure of nanoparticles involving 103—106 atoms are rather compli-cated [6—8]. Admixtures chemisorbed on the surfaces of nanoparticles make great contributions to the parameters of the interactions of sur-face atoms when investigating the EDVE of nanoparticles by means of optical [9—11], x-ray photoelectron spectroscopy (XPS) [12—18] and x-ray absorption spectroscopy (XAS) [19—22] methods. Recrystallization and agglomeration of nanoparticles prevent purification of their sur-face by heating-up [23]. Ion etching essentially breaks the morphology of nanoparticles and removes a substantial part of them from the sub-strates. The adhesive contact of discontinuous thin films with the sub-strates affects their electronic structure.   Therefore, it is necessary to study the EDVE of nanoparticles in the  ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 171 absence of chemical and adhesive interactions and at sufficiently low temperatures. It is possible using the mechanical adhesion of nanopar-ticles on cooled substrates (i.e., under rubbing of the metals possessing high thermal conductivity, e.g., Cu or Au) and employing excitation of the spectra reflecting the EDVE by the electron beam that purifies the nanoparticle surfaces from chemisorbed admixtures and does not heat-up the nanoparticles.  The x-ray ultrasoft emission spectroscopy (XRUSES) method satisfies all these conditions under the excitation of radiation by electrons with energies of 2.0 to 9.0 keV. Under such conditions, the depth of photon emission giving the main contribution to the spectra intensity does not exceed 10 atomic layers in the nanoparticles. The x-ray emission bands reflect the partial density of electronic states of different symmetries of all kinds of atoms of a compound under investigation.   Changes of the shapes of the x-ray emission С2p-like bands due to their narrowing at І = 2Іmax/3 (I is the intensity) were observed when studying the electronic structure of high-pressure phases particularly of nanodiamonds (with coherent scattering areas (CSA) of 2.0, 3.0 and 5.0 nm) obtained from a highly nonequilibrium carbonic plasma as a result of explosive detonation [24]. This narrowing magnitude in-creases with a decrease in the CSA. The above narrowing effect was confirmed rather recently on nanodiamonds [25]. An even greater ef-fect of the narrowing and the changing shapes of the x-ray emission NKα and ВKα bands reflecting the EDVE of the р-symmetry of nitrogen and boron, respectively, was revealed in investigations of blended BN nanopowders. The effect of NKα narrowing exceeds by three times that for the ВKα band, and the value increases with decreasing nanoparticle sizes [26].  Subsequent XRUSES studies of the nanopowders of other com-pounds with different atomic-crystalline structures and chemical bonding types have revealed that the nanosize narrowing of the spectra was observed in all nanomaterials investigated by us because the con-tributions of the localized levels of the electronic states to the valence bands after the interatomic bond breaking become commensurable with the contributions of states involved into unbroken bonds.   Because the fine structure of the x-ray emission bands depends upon many crystal-chemical characteristics and its nanosize change becomes apparent in the different energy intervals of the valence bands, the aim of the present paper is (1) to show that the effect of narrowing and changes of the shapes of the ultrasoft x-ray emission bands (USXREB) reflecting the energy redistribution of the valence electrons is a com-mon electronic-structural characteristic of a transition of materials from the bulk to a nanosize state and (2) to elucidate also the depend-ence of the above effect upon the type of chemical bonding and atomic-crystal structure. 172 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al.  Therefore, it is necessary to study and analyze the parameters of the USXREB obtained from the bulk and nanomaterials, among which there are following powders:  1) covalent-ionic graphite-like (h-BN) and blended-like (c-BN) crys-tal modifications of boron nitride;  2) metal-covalent isostructural crystal TiC and TiN compounds with different ionicity degrees of the interatomic bonds;  3) ionic-covalent ТiО2 and ВаТiО3 with rutile- and perovskite-like structures, respectively;  4) carbon nanomaterials with a high contribution of closed bonds in their total quantity (fullerenes, low-imperfect nanotubes) and of opened bonds (onions, high-imperfect nanotubes and nanofibres). 2. EXPERIMENTAL All the mentioned at the end of the introduction section materials un-der consideration were well characterized in Refs. [27, 28]. The above characterizations employing x-ray diffraction analysis have revealed that all the samples under study are single-phase materials.  The ultrasoft x-ray emission CKα, NKα, OKα, BKα (K → LII,III transi-tion) and TiLα (LIII → MIV,V transition) bands reflecting the energy dis-tribution of the C2p-, N2p-, O2p- and B2p- and valence Tisd-like states, respectively, in the studied materials were obtained using two RSM-500 spectrometers. The x-ray emission CKα, NKα, OKα and TiLα bands were derived using the RSM-500 spectrometer with a diffraction grat-ing possessing 600 lines/mm and a radius of curvature of R ≈ 6 m. In the RSM-500 spectrometer used for studies of the BKα band, the disper-sion element was a diffraction grating with 600 lines/mm and a radius of curvature of R ≈ 2 m. In the both spectrometers, the detectors were secondary electron multipliers VEU-6 with CsI photocathodes.  Operating conditions of x-ray tubes in the present experiments were the following: accelerating voltage Ua = 4 kV and anode current Ia = 10 mA when studying the BKα bands and Ua = 5 kV and Ia = 5 mA when measuring the CKα, NKα, OKα and TiLα bands. The spectrometer en-ergy resolutions were 0.2 eV in the case of measuring the BKα band and about 0.3 eV in the energy regions corresponding to the positions of the CKα, NKα, OKα and TiLα bands. Comparisons of the x-ray emission bands on a common energy scale were fulfilled taking into account data of XPS measurements of binding energies of the B1s, C1s, N1s, O1s and Ti2p core-level electrons.  The measurements were made in an ion-pumped chamber of an ES-2401 spectrometer having a base pressure less than 5⋅10−8 Pa. In the mentioned spectrometer, the MgKα radiation (E = 1253.6 eV) was used as a source of spectra excitation. The binding energy of (84.00±0.05) eV of the XPS Au4f7/2 core-level spectrum was used as a reference.   ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 173 3. RESULTS AND DISCUSSION 3.1. Dependence of Nanosize Narrowing and Changes of the Shapes of the USXREB Due to the Transition of Covalent-Ionic BN from the Bulk to a Nanostate upon the Crystal-Chemical Characteristics of Its Modifications Analysis of the comparison of the СKα and superimposed on a common energy scale the NKα and ВKα emission bands [24, 26] with band-structure calculations of diamond and blended BN has shown that the nanosize narrowing is observed in the energy region where the sp3-hybride states involved in the С−С- and B−N-bonds of bulk crystals are located.  Essential distinctions in nanosize narrowings and changes of the shapes of the x-ray emission СKα, NKα and ВKα bands in crystal-analogues, diamond and blended BN, are obviously accounted for by only the ionic component [29] of the B−N-interaction. In Ref. [26], a detailed analysis of the influence of chemical bonding ionicity on the nanosize ef-fect of the band’s narrowing was not carried out and a transfer of the elec-tronic density from one atom to another one reflects substantially on the intensities of the corresponding spectra; therefore, it is of great impor-tance to elucidate the specific contribution to the mentioned effect of the population of the nitrogen and boron energy levels localized after bond breaking. Taking into account the fact that the widths of the NKα and ВKα bands of the bulk blended c-BN are different (Fig. 1, a), it is neces-sary to introduce the parameter of the specific narrowing of these bands in one or another part of the spectra. In this case, we chose the spectra width at Іmax/2. The specific narrowing is then η = (ΔЕ 1/2c − ΔЕ 1/2n )/ΔЕ1/2c , where ΔЕ 1/2c is the energy width of the x-ray emission bands at the half-maximum intensity in a coarse powder and ΔЕ 1/2c is that in a nanopowder. The dependencies calculated in the present work for the ηNKα and ηВKα spe-cific narrowing of the x-ray emission NKα and ВKα bands upon the aver-age sizes (d ) of c-BN powders (Fig. 1, b) were found to be linear with dif-ferent coefficients kNKα and kBKα. Their ratios ηNKα/ηВKα ≈ 2.1±0.1 were approximately equal for all fractions of the c-BN nanopowders.  The ratios were found to be close to the ratio QNVp /Q BVp  = 2.0, where QNVp  is the number of valence р-electrons located near one nitrogen atom and Q BVp  is that near the boron atom, calculated in Ref. [29]. This indicates that the bigger the population of the levels of the atom emitting x-ray quanta the bigger is their contribution to the narrowing of the emission bands due to level’s localization as a consequence of the disappearance of their split-ting when the B−N-bonds break.  Because the EDVE [29] and the shapes of the x-ray emission NKα and ВKα bands of h-BN and c-BN are different [30], the energy redistribu-tion of the valence electrons should therefore be different on going 174 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. from coarse-grained h-BN to turbostratic h-BN (the average size of the latter particles is _d  = 5 nm). Therefore, in the present paper for the first time, the NKα and ВKα spectra of coarse-grained and turbostratic h-BN were investigated under the same conditions.  The number of the valence electrons and charge states of the atoms do not change as a result of ultradispersion (the binding energies of the core-level В1s and N1s electrons are invariable [27]); therefore, the ВKα bands, as well as the NKα spectra, obtained from the coarse-grained and nanopowder BN were reduced to equal squares. From a comparison of these spectra on a common energy scale (Fig. 1, c), it is obvious that the ВKα bandwidth of turbostratic h-BN is smaller by  Fig. 1. Comparison of the x-ray emission NKα and BKα bands of c-BN powders with fraction sizes of 2.0 μm (dash-dotted curves 1), 0.3 μm (dashed curve 2), 0.2 μm (dotted curve 3), 0.1 μm (solid curves 4) (a) and the dependence of the specific narrowing of the bands upon the average size of c-BN particles (b); comparison of the x-ray emission NKα and BKα bands of coarse 5.0 μm (solid curves) and turbostratic 5.0 nm h-BN (dashed curves) powders (c): the dotted curves are the spectra of turbostratic h-BN (5.0 nm) heated by an electronic beam up to yellow-and-white luminescence of the particles (T > 1500 K evalu-ated by a pyrometer).  ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 175 0.2—1.0 eV as compared with that of coarse h-BN in its high-energy part. In the energy region where the sp2-hybrid states providing the B−Nσ-bonds are reflected, the intensity of the peculiarity с of the NKα band decreases.  This is a result of the disappearance of splitting of Вр- and Nр-energy levels due to the dehybridization of a part of the sp2-states after the breaking of B−N-bonds due to the nanodispersion of h-BN. The Np-dehybridizated states in turbostratic h-BN shift to the top of the valence band. This fact is reflected in the shift of the short-wave contour at the peak d of the NKα band towards higher energies. From a comparison of the bandwidth reduction of c-BN (Fig. 1, a) and h-BN (Fig. 1, c), it is ap-parent that the ВKα bandwidth is reduced more in h-BN but the NKα bandwidth is reduced more in c-BN.  This is explained obviously by the fact that in coarse c-BN all elec-trons, including those transferred to nitrogen, occupied the splitting levels of the sp3-hybrid states whereas in h-BN the main part of the electrons occupies the weakly bonding Nрz-states reflected in the nar-row peak d of the NKα band [31]. The Nрz-states split weakly due to the low degree of π-overlapping with low-populated Врz-orbitals.  Therefore, in h-BN a smaller number of electrons are involved in splitting the sp2-states as compared with that in c-BN. This fact is re-flected in a smaller contribution to the emission of the NKα band of the electrons involved in the dehybridized states. Thus from the above analysis, it is obvious that, during ultradispersion, the nearest sur-roundings essentially affect both the narrowing value and the changes of the shape of the USXREB representing the energy redistribution of the valence electrons.  3.2. Peculiarities of Nanosize Narrowing of the USXREB Obtained for Isostructural Metal-Covalent Titanium Carbides and Nitrides with a Face-Centred Cubic Lattice In order to study a dependence of the effect of the nanosize narrowing of the USXREB upon the presence of the metallic component of the chemical bonding, we have analyzed the x-ray emission СKα, NKα and TiLα bands obtained for three nanosize fractions and coarse powders of metal-covalent ТіС and TiN [32, 33] with the face-centred cubic struc-ture of the NaCl type. The Fm3m space symmetry group of these com-pounds is close to those of diamond (Fd3m) and c-BN (F43m), but the quantity of the nearest neighbours and the geometry of the neighbour-hoods are different. The measuring of widths of the СKα, NKα and TiLα bands at Іmax/2 of coarse and nanopowders with specific surface areas Ssp = 9.4, 16.8, 24.2 m2/g for TiC [32] and Ssp = 10, 20, 50 m2/g for TiN [33] and calculations of the specific narrowing of these bands have re-176 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. vealed that the narrowing increases with decreasing fraction sizes. The specific narrowing of the СKα and NKα bands is greater than that of the TiLα band, and their ratios are ηCKα/ηTiLα ≈ 1.3 for ТіС and ηNKα/ηTiLα ≈ ≈ 1.45 for TiN; whereas the ratios of the number of valence electrons near the constituent atoms calculated in Ref. [34] are Q CVp /Q TiVsd  ≈ 1.39 (ТіС) and Q NVp /Q TiVsd  ≈ 1.64 (TiN). These facts confirm the conclusion stated in section 3.1.  In metal-covalent TiN, in addition to the presence of the ionic com-ponent of the chemical bonding, the Fermi level passes through the high density of the metal-bonding band, where a significant part of the occupied anti-bonding states is also present [35]. In ТіС, the number of valence electrons and the transfer of the electrons from titanium to carbon are smaller in comparison with those in TiN; therefore, the anti-bonding (Tisd + Ср)*-states are unoccupied and the Fermi level passes only through the minimum density of the metal-bonding states.  The analysis of a comparison of the x-ray emission СKα, NKα and TiLα bands with data of theoretical calculations of the electronic struc-ture of ТіС and TiN [34] carried out in Refs. [32, 33] has shown that the band’s narrowing occurs in the energy regions where hybrid-bonding Tisd + Xр-states (X = C, N) are located. In the energy range where the non-bonding states are mainly located, the widths of the both emission bands are not reduced, i.e. the contours of the bands of coarse-grained and nanopowder materials coincide. The TiLα band nar-rows in low-energy and in high-energy regions due to the breaking of the covalent and metallic components of the bonds. The breaking of the metallic bonds leads to narrowing the TiLα and СKα bands in the near-Fermi region in TiC owing to the localization of levels of high-energy Tisd + Ср states delocalized in the lattice. These states provide the me-tallic component of the Ті−С interaction in TiC.  Because the electrons of the localized energy levels have to increase their energy after the bond breaking, their levels have to shift to the high-energy side and can locate in the energy region corresponding to the non-bonding states in a coarse powder. This can also be due to the fact that the high-energy contours of the СKα band (Fig. 2, а) of coarse-grained and nanopowders of ТіС coincide in the ΔE2 energy range. In our opinion, the above effect is not visible in the case of TiN due to the superposition of the NKα band and the TiLl-line in this compound.  On the other hand, the short-wave contour at the main maximum d of the TiLα band obtained from TiN (Fig. 2, b), due to the concentration in the energy region −(5.0—3.5) eV of the energy localized levels even shifted somewhat to the high-energy side after breaking the Ti−Ti- and Ti−N-bonds. Part of the hybrid K4 (Срx−y, Tiy), Δ5 (Cpy,z, Ti2g), ∑3 (Cpz, Tidz(x+y)) states is located in the above mentioned energy region in the bulk crystal according to the calculations [35]. Their splitting should also disappear during the bond breaking. The energy redistribution of  ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 177 the metal-bonding Tisd-states, which splitting disappeared after the bond breaking during the ultradispersion of TiN, is reflected by the smaller width and the intensity of the peak e of the TiLα band. The redis-tribution shifts by 0.2—1.5 eV towards high energies the short-wave con-tour of the TiLα band at I < 0.4Imax.  It is worth mentioning that a high-energy shift by 0.4 eV of the whole short-wave contour of the x-ray emission NKα band obtained  Fig. 2. Comparison of the x-ray emission TiLα, CKα and NKα bands of coarse powders (dash-dotted curves), nanopowders (solid curves) and mate-rials consolidated from the nanopowders at high-pressure and room tem-perature (dashed curves) of TiC (a) and TiN (b).178 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. from the finest powder of c-BN as compared with that of the band of coarse c-BN was caused by a significant increase in the contributions of the occupied Np-like states corresponding to the broken bonds of atoms belonging to the large specific surface of c-BN nanopowders into the energy region corresponding to the top of the valence band. This fact shows that energy redistributions of the valence electrons as a result of the increasing energy of states involved in the broken bonds have some differences because of the ultradispersion of crystals with covalent and metallic bonds. The differences are the consequence of the different distributions and localizations of metal- and covalent-binding states within the valence bands as well as the different magnitudes of changes in energy states when the splitting of their energy levels dis-appears after braking the metallic and covalent bonds.   After the nanopowders’ consolidation, crystallization and other processes, as a result of recombination of broken chemical bonds on the surface of the nanoparticles, the splitting of energy levels of the above-mentioned electronic states should take place, and due to this fact, the USXREB should broaden.  Indeed, the x-ray emission СKα, NKα and TiLα bands obtained from the nanopowders of solid ТіС and TiN (Fig. 2) consolidated at 7 GPа and at room temperature (Т = 293 K) were found to be broadened in the same energy regions where they were narrowed in the spectra of the nanopowders. This is a result of the energy levels splitting as a conse-quence of their orbital superimposition when drawing together surface atoms of contacting nanoparticles under the high-pressure contraction of the nanopowders. 3.3. Estimation of Band-Energy Changes as a Result of ТіО2 and ВаТіО3 Ultradispersion Using the Data for the Narrowing and Transformation of Shapes of the X-Ray Emission TiLα and ОKα Bands The elucidation of the dependence of the nanosize narrowing of the USXREB and energy redistributions of the valence electrons on the types of chemical bonding would be incomplete without a study of these effects in an ionic ТіО2 crystal with a rutile structure (r-ТіО2). In this crystal, the greater part of the occupied Op-states has to be non-bonding due to the big contribution to the cohesion energy of the Cou-lomb interaction between the titanium and oxygen ions. Therefore, in the present paper for the first time, the effect of nanosize narrowing of the x-ray emission TiLα and ОKα bands was studied during the transi-tion from a coarse powder to two fractions of nanopowders with aver-age sizes of d  = 107 and 10 nm (Fig. 3, a). Also for the first time, the broadening of the ОKα band (Fig. 3, b) of r-ТіО2 nanopowder (d  = 10 nm) due to its recrystallization under heating (as a result of the rise from 8 to 45 W of the power of the electron beam exiting the spectra)  ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 179 was investigated.  The valence band of coarse-grained r-ТіО2 contains mainly the Ор-states. The bonding hybrid (Tid(eg) + Ор) states and the Ор-states in-volved into the О−О-bonds contribute to the low-energy part, but the non-bonding Ор-states are the main contributors to the high-energy part of the valence band [36−39]. The first contributions are repre-sented by the wide feature а of the x-ray emission ОKα band and the second contributions by the peak b.  Comparison of the x-ray emission ОKα and TiLα bands obtained from  Fig. 3. Comparison on a common energy scale of calculated Tid- and Op-like densities of states and of the x-ray emission TiLα and OKα bands of coarse (dashed curves) and nanosize (solid and dotted curves) powders of TiO2 (a) and BaTiO3 (c): the solid curves are the spectra corresponding to the finest nanopowders with average sizes of 10 nm (TiO2) and 24 nm (BaTiO3) and the dotted curves are the spectra of TiO2 nanopowder with size of 107 nm; the x-ray emission OKα bands of r-TiO2 nanopowders measured at increasing power of the exciting electron beam (b). 180 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. coarse ТіО2 and the nanopowders (Fig. 3, a) has revealed that the ОKα band narrows by 0.2—0.5 eV on going from coarse ТіО2 to the nanopow-der with average nanoparticle sizes of d  = 107 nm and by 0.2—1.1 eV when going to the fraction with d  = 10 nm.  This narrowing is observed in the low-energy part of the ОKα band formed by contributions of the Op-bonding states (the feature а of the band). The difference square of the ОKα band of coarse TiO2 and the nanopowder with d  = 10 nm is many times larger than that of the coarse-grained and nanopowder with the size of d  = 107 nm. At the same time, the TiLα band narrowing in the energy region −(6—4) eV is only 0.2—0.3 eV. The ratio of the calculated specific narrowing of the x-ray emission ОKα and TiLα bands at the intensities corresponding to their maximum narrowing equals to ηОKα/ηTiLα = 0.25/0.07 = 3.60±0.30, whereas the ratio of the population of the Ор- and Tid-like states [40] equals to QОр/QTid = 5.33/1.46 = 3.7 (this result is in accordance with those described above for c-BN, TiC, TiN).  From a comparison of the ОKα bands presented in Fig. 3, a, one can see that, like during ultradispersion of covalent-ionic c-BN, in a nanopowder of ionic-covalent r-ТіО2 the Ор-states corresponding to the broken bonds of surface atoms concentrate near the top of the valence band, increasing in this energy region the density of the non-bonding Ор-states. Taking into account the fact that chemical content and the number of the valence electrons in all three powders are exactly the same, the ОKα bands were normalized so that their squares are equal (the method of normalization is similar to that employed in Ref. [41] for XPS spectra). The energy redistribution of the О2р-states when going from the coarse-grained to nanopowder TiO2 should result in significant changes of the band energy of electrons and its contribution to the in-ternal energy of nanopowders. The calculated ratios of the integrals 0 0( ) ( )F Fc nE EE EI E EdE I E EdE⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠∫ ∫ , where I(E) is proportional to P(E)N(E) in the approximation that P(E) depends weakly upon Е and it is similar or equal for these powders, have revealed the increasing of band energy by 3 and 17% when going from coarse TiO2 to the nanopowders with d  = 107 and d  = 10 nm, cor-respondingly. Consequently, one can assume that significant changes or the appearance of new properties of r-ТіО2 are possible when the change in internal energy is sufficient due to changes in band energy be-cause of nanocrystallinity of this material.   The charge states of titanium and oxygen atoms are similar in ionic-covalent perovskite-like ВаТіО3 (p-BaTiO3) and r-ТіО2 compounds, tak- ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 181 ing into account XPS measurements of the binding energies of Ti2p3/2 and O1s core-level electrons (see Ref. [42]).  However, due to the different geometry of the octahedral surround-ing of Ті atoms by oxygen, all the О−О-distances in p-ВаТіО3 (0.28327 nm) are greater than the doubled ionic radius of oxygen (2rО2−). In con-trast, in r-ТіО2 the distances are О−О = 0.25327 nm < 2rО2− = 0.270 nm [43, 44]. Therefore, in r-ТіО2, the О−О-bonds exist, and in p-ВаТіО3, they are absent.  From a comparison on a common energy scale of the x-ray emission ОKα and TiLα bands obtained from the coarse and nanosize powders (Ssp = 40 m2/g) with d  = 24 nm of p-ВаТіО3 (Fig. 3, c), it is obvious that the band narrowing occurs in the sequence ‘coarse→nanopowder’, mainly due to redistribution of the Op- and Tid-states, localized as a re-sult of the Ti−O-bands breaking, towards the higher energies. The Op- and Tid-states in the coarse powder were hybridized [42, 45]. The x-ray emission ОKα band of the coarse ВаТіО3 powder does not contain the low-energy subband а, due to the absence of the Op-bonding states in-volved in the О−О-bonds in this compound. Because of this fact, the ОKα band of the barium titanate coarse powder is symmetric, and its half-width equals to 3.4 eV (the half-width is smaller by 1.0 eV as compared with that of r-ТіО2). The ОKα band of the barium titanate nanopowder is asymmetric, narrowed by 0.2—0.5 eV, and its high-energy contour is shifted by 0.5—0.9 eV as compared with that of coarse-grained BaTiO3. This is due to the fact that, in the ВаТіО3 nanopowder after breaking the Ті−О-bonds, the dehybridized Ор-states concentrate near the top of the valence band, where according to the calculations [46], the non-hybridized ‘pure’ non-bonding Ор-states are located. The same effect was also observed in the case of ultradispersion of the above-described covalent-ionic c-BN and ionic-covalent r-ТіО2.  However, the main difference in the redistribution of the valence electronic states due to ultradispersion of ТіО2 and ВаТіО3 is the fact that, in spite of the resemblance of the shapes of the TiLα-bands in these compounds, the TiLα-band of the barium titanate nanopowder narrows by 0.2—1.0 eV in the low-energy region and broadens by 0.3—0.5 eV in the energy region −(5.0—7.0) eV corresponding to the position of the high-energy contour at the main peak b of the band. This is a re-sult of the fact that the population of the Tid + Ор-hybrid states in ВаТіО3 is significantly higher as compared with that in r-ТіО2 [47].   The calculated integrals ratio 0 0( ) ( )F Fc nE EE EI E EdE I E EdE⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠∫ ∫  for ВаТіО3 has revealed that the band energy changes by 11% when going from the coarse powder to the powder with d  = 24 nm, which is smaller 182 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. than that in r-ТіО2 as mentioned above. Therefore, from the above facts, it is obvious that the redistribution of valence electronic states, due to the great contribution of broken bonds in the nanopowders, depends on the character of the chemical bonding and the atomic-crystal structure of ma-terials.  3.4. Dependences of the Cp-State Energy Distribution and of the Shapes of the X-Ray Emission СKα Band on the Sizes of Carbon Materials In contrast to crystalline nanopowders, ideal fullerene does not possess broken bonds, and in ideal onions and carbon nanotubes, they exist only on the ends of the nanotubes; the contribution of the broken bonds to the total value of bonds is insignificant in the above materials. At the same time, in nanosize graphene layers which form carbon nanofibres, quanti-ties of the broken and closed bonds are commensurable. Figure 4 presents the x-ray emission СKα spectra of graphite, onions, nanotubes and nano-fibres studied under similar conditions. Figure 4 shows also the СKα bands of С60 and С70 investigated in Ref. [48] and obtained in the present work for C60 with smaller apparatus distortions (ΔEap ≤ 0.2 eV in the pre-sent work and ΔEap = 0.4 eV in Ref. [48]).  The spectra were compared to elucidate whether the effects of nar-rowing and changes in the shape of the СKα bands with decreasing sizes of the carbon materials become apparent and in what way. From the comparison of curves 1 and 2 (Fig. 4), it is obvious that a divided sub-band of the СKα band of С60 is narrower at I > Imax/2 (by 0.2—0.5 eV) as compared with that of С70 in the region of photon energies hν = 274.5—276.0 eV, and also in the energy region corresponding to contributions of the π-states. The minimum of the СKα band dividing the pure π-bands (features e and f) and those mixed with the σ-states in С60 is deeper than that in С70, where there is no separation into π1 (f) and π2 (е) sub-bands [49].  The π1 and π2 sub-bands are typical for С60 due to the difference in the degree of π-overlapping of orbitals above the spherical surface of С60 be-tween atoms at the distances of 0.144 and 0.139 nm. The high intensity, symmetry and undivided shape of the π-sub-band in С70 are the result of the presence of 8 groups of interatomic distances (0.137 to 0.147 nm), be-cause the degree of π-overlapping of the Срz-orbitals in C70 does not differ so noticeably as in С60. Such a dispersion of the lengths of σ-bonds leads obviously to a greater width of the sub-band of the СKα band correspond-ing to the π + σ-mixed states in С70.  Figure 4, b shows a comparison of the СKα bands of onions (curve 5), the sizes of which are about 5 nm, and graphite (curve 6). From the above fig-ure, it is obvious that the СKα band of the onions is narrower at I > Imax/2 in comparison with that of graphite, mainly in the energy region where the π and π + σ-bonding states are reflected.  ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 183  In the energy region hν = 273.0—275.0 eV, corresponding to the sp2-hybride states of the σ-bonds, the differences are minor. The narrowing of the spectra in the low-energy region is due to the presence of a noticeable quantity of broken bonds due to the fact that spherical sp2-bonding layers consist of broken, torn or bowed graphene fragments [50]. The greater nar-rowing in the high-energy part of the СKα band is a result of breaking the π-bonds between the fragments and decreasing π-overlapping of the Ср-orbitals above the bowed surface of the fragments.  Fig. 4. Comparison of the x-ray emission CKα bands of carbon nanomaterials: the spectra of C60 and C70 fullerenes (curve 1 is the spectrum of C60 obtained in the pre-sent paper, curves 2 and 3 are the spectra of C60 and curve 4 is the spectrum of C70 obtained in Ref. [48]) (a); the spectra of onions (curve 5) and thermally exfoliated graphite (curve 6) (b); the spectra of nanotubes: double-walled with a diameter 4 nm (curve 7) and 200-walled with a diameter of 140 nm (curve 8) obtained in arc dis-charge by ‘MER-corporation’ (c); the spectra of catalytic nanotubes with diameters of 70 nm (curve 9) and 20 nm (curve10) (d). 184 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al.  From the comparison of the СKα bands (Fig. 4, c, curves 7 and 8) of 200-walled nanotubes with a diameter of 140 nm and double-walled nanotubes with a diameter of 4 nm obtained in arc discharge without catalysts by ‘MER-corporation’, it is evident that the low-energy con-tours of the band reveal coincidence.  However, in the high-energy part of the СKα band where the π- and π + σ-binding states are positioned, the features с, с′ and d, е reflecting mixed ррσ + ррπ and pure ррπ [51] interactions in the radial planes and along the axis of the nanotubes, respectively, become apparent.  However, the bandwidth of СKα of double-walled carbon nanotubes  Fig. 5. The x-ray emission CKα bands of carbon fibres, in orientation I: fibres with a diameter of 30 nm (curve 1) and 18 μm (2), in orientation II: fibres with a diameter of 30 nm (curve 3) and 18 μm (curve 4). Note: orientation I: the angle between the direction of x-ray emission and the main direction of the Cpz-orbitals is in the range of 0—180°; orientation II: the angle between the direction of x-ray emission and the main direction of the Cpz-orbitals is 90°; e are direc-tions of the electron beams; c are directions of the axis corresponding to gra-phene layers; hν directions of x-ray emission. ENERGY REDISTRIBUTION OF THE VALENCE ELECTRONS 185 is reduced in comparison with that of the 200-walled nanotubes only near the top of the band (at I > 0.75Imax).  This is the result of a decrease of the π + σ-overlapping in the radial plane inside the 200-walled nanotubes with an increase in diameter of every following wall (as a consequence, states involved in such bonds shift towards higher energies).  The comparison of the СKα spectra of nanotubes with diameters of 70 and 20 nm (Fig. 4, curves 9 and 10; the latter nanotubes contain many broken bonds after purification from a Co catalyst) reveals that the spectrum width of imperfect nanotubes is reduced in the low-energy and high-energy parts of the СKα band.   All axes of the рz-orbitals will be perpendicular to the selection direc-tion of the x-ray, when filaments of the carbon fibres are parallel to it (Fig. 5, orientation II). Therefore, the contribution of the π-bonding рz-orbitals into the СKα band intensity is maximum in orientation II, whereas it will be much smaller in orientation I [52]. The comparison of the СKα spectra of thick (18 μm) and nanosize (30 nm) fibres, obtained for the І- (Fig. 5, curves 1 and 2) and ІІ-orientations (Fig. 5, curves 3 and 4), has allowed us to determine qualitatively the ratio of contributions of the broken π- and σ-bonds to the narrowing of the СKα band when go-ing from thick fibres to nanofibres.  The specific narrowing calculations at І = 0.86Imax (where the nar-rowings are the greatest at the І- and ІІ-orientations) have shown that ηІ ≈ ηІІ ≈ 0.24±0.01. This would be expected because the ratio of the number of broken and closed π-bonds does not depend on the fibre ori-entation. The greater contribution of the σ-states to the emission of the СKα band at the ІІ-orientation becomes apparent in the narrowing of the band in the low-energy region reflecting the sp2-hybride σ-bonding states, when going from the thick fibre to the nanofibre. This is the result of the increasing contribution of localized energy levels dehybridized due to sp2-state bonds breaking.  4. CONCLUSIONS  The effect of the narrowing and changes of the shapes of the x-ray emission bands reflecting the energy distribution of the valence elec-trons of atoms forming compounds was revealed due to the excitation of x-ray spectra by electron bombardment, which allows refining the nanomaterial surfaces from chemisorbents, when going from bulk to nanomaterials that prove to be common for objects under investiga-tion. This occurs due to the disappearance of splitting of the energy levels of states after the breaking of chemical bonds of the surface at-oms, which quantity in nanoparticles is commensurable with the quan-tity of atoms in their volume.  It was established that the greater population of energy levels of 186 Ya. V. ZAULYCHNYY, Yu. M. SOLONIN, O. O. FOYA et al. anions in crystalline compounds causes a greater specific narrowing of the ultrasoft x-ray emission bands radiated by cations and anions. The specific narrowing ratios are close to the ratios of density of electrons concentrated near anions and cations. It was revealed that the energy levels of the states participating in the broken bonds in ionic-covalent crystals are located near the top of the valence bands, increasing their energy and causing an increase in crystal band energy.  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