Superlattices and Microstructures 90 (2016) 148e164

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Superlattices and Microstructures

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Nanocrystalline ordered vanadium carbide: Superlattice andnanostructure

A.S. Kurlov a, A.I. Gusev a, *, E. Yu. Gerasimov b, I.A. Bobrikov c, A.M. Balagurov c,A.A. Rempel a

a Institute of Solid State Chemistry, Ural Branch of the Russian Academy of Sciences, Ekaterinburg 620990, Russiab Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russiac Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, 141980, Moscow region, Russia

a r t i c l e i n f o

Article history:Received 2 November 2015Received in revised form 8 December 2015Accepted 10 December 2015Available online 13 December 2015

Keywords:SuperstructureNonstoichiometryNanoparticle sizeMicrostrainsMorphology

* Corresponding author.E-mail address: gusev@ihim.uran.ru (A.I. Gusev)

http://dx.doi.org/10.1016/j.spmi.2015.12.0060749-6036/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

The crystal structure, micro- and nanostructure of coarse- and nanocrystalline powders ofordered vanadium carbide V8C7 have been examined by X-ray and neutron diffraction andelectron microscopy methods. The synthesized coarse-crystalline powder of ordered va-nadium carbide has flower-like morphology. It was established that the real ordered phasehas the composition V8C7-d (d y 0.03) deviating from perfect stoichiometric compositionV8C7. The vanadium atoms forming the octahedral environment ,V6 of vacant sites inV8C7-d are displaced towards the vacancy ,. The presence of carbon onion-like structureswas found in the vanadium carbide powders with a small content of free (uncombined)carbon. The nanopowders of V8C7-d carbide with average particle size of 20e30 nm pro-duced by high-energy milling of coarse-crystalline powder retain the crystal structure ofthe initial powder, but differ in the lattice deformation distortion anisotropy.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Vanadium carbide is one of the most commonly used cubic carbides of transition metals. It is employed as a grain growthinhibitor in hardmetals and as an important structural component of alloyed steels widely applied in the production ofaircraft and automobile engines.

Disordered cubic vanadium carbide VCy with B1-type structure belongs to the group of strongly nonstoichiometriccompounds [1] and has wide homogeneity intervals: From VC0.72 to VC0.875 at 1500 K and from VC0.60 to VC0.88 at ~2450 K [2].CarbidesMC1.0 are the upper boundary of the homogeneity interval of nonstoichiometric cubic carbidesMCy except vanadiumcarbide. The cubic carbide VCy has the upper boundary of the homogeneity interval at the composition VC0.875, which is ratherfar from the stoichiometric composition MC1.0.

Under thermodynamic equilibrium, nonstoichiometric carbides can be in disordered or ordered state [1]. In non-stoichiometric cubic vanadium carbide VCy, ordered phases of the type V3C2, V6C5 and V8C7 can be formed [2]. The phase V8C7was found only in vanadium carbide VCy and it is not observed in carbides of other transition metals; its existence is con-nected with a specific position of the upper boundary of the homogeneity interval of vanadium monocarbide at VC0.875. Theordered phase V8C7 is formed rather easily during high-temperature sintering of vanadium and carbon or during reduction of

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vanadium oxide by carbon in the process of subsequent slow cooling of synthesized vanadium carbide from synthesistemperature to room temperature [1].

The V8C7 superlattice was first observed experimentally by X-ray diffraction (XRD) and nuclear magnetic reconancemethods [3e5]. The authors [3,4] showed that the phase V8C7 has cubic symmetry and belongs to the space group P4332. Theneutron diffraction investigations of the VC0.865 carbide at a temperature of 4.2 and 300 K [7] confirmed the existence of theV8C7 phase and its cubic symmetry. According to [6], the carbon atoms in the unit cell of V8C7 phase are not virtually displacedfrom the perfect lattice positions. However, the studies [5,7,8] of the V8C7 phase revealed large displacements of the V atomstowards the vacant site , of the nonmetal sublattice and even greater displacements of the C atoms. The estimates of theatomic displacement values made from the neutron diffraction results [6,9] and XRD data [8,10] differ considerably.

According to [11,12], alloying of cast iron and steels with vanadium carbide gives rise to nanosized disperse carbideparticles in the form of ordered phases V8C7 or V6C5. Vanadium carbide used as a grain growth inhibitor in hardmetals basedon tungsten carbide WC is formed as nanosized films or nanoparticles [13,14].

Methods for the production of substances in the nanostructured state have been developed in the latest decades. Thedisordered carbides MCywith cubic B1 type structure contain up to 30e50% structural vacancies, in the nonmetal sublattice[1,15]. Below 1300 K, the B1 structure becomes unstable and disorder-order phase transitions take place in nonstoichiometriccarbides resulting in the formation of ordered phases with complex superlattices [1,16,17]. Order-disorder and disorder-ordertransformations in carbides are first-order phase transitions with a discontinuous variation of volume at the disorder-ordertransformation temperature Ttrans [1,14,17]. The differences in the lattice parameters of the disordered and ordered phases inthe sample induce stresses leading to cracking of crystallites at the disordered-ordered phase interface. By controlling thesizes of the ordered phase domains, it is possible to produce nanostructured nonstoichiometric carbides [18,19].

The idea of formation of a nanostructure by atomic-vacancy ordering of nonstoichiometric compounds was implementedfor the first time on the example of nonstoichiometric vanadium carbide [20]. Vanadium carbide VC0.875 was the first carbide,in which nanostructure was created as a result of disorder-order transformation VC0.875 / V8C7 both in coarse-grainedpowder [20] and in bulk carbide [10].

Until recently, all the investigations of crystal structure of nanocrystalline nonstoichiometric substances available in theliterature were performed only by means of the XRD method. There is no mentioning of neutron diffraction analysis even inthe latest review [21] of diffraction analysis methods for nanocrystalline substances. Only lately, time-of-flight (TOF) neutrondiffraction analysis [22] was used for the first time to examine the peculiarities of microstructure of nanocrystalline non-stoichiometric niobium carbide NbC0.93 [23,24]. This is astonishing, as neutron TOF diffractometers operational on pulsedsources have a great potential for the characterization of the microstructure of fine-grained materials. Their resolutionfunction, in fact, is almost independent of scattering vector Qwithin a fairly wide range. This is certainly quite different fromthe conventional neutron diffractometers using a monochromatic beam where the resolution function R(Q) is usuallyparabolic with a rapid rise in the range of small Q values. In addition, the application of correlation Fourier technique onpulsed neutron source and the realization of the so-called геvегsе time-of-flight (RTOF) data acquisition method make itpossible to achieve very high resolution comparable with that of X-ray instrument while maintaining the short source-to-detector distance and, consequently, the high brightness. The resolution of RTOF diffractometer mostly depends оn themaximum rotation speed of the Fourier chopper, and can be turned for specific purposes. Diffraction peaks obtained on suchan instrument should be symmetric, without long “tails” observed on diffraction spectra from conventional TOF instruments,installed at spallation neutron sources. This fact greatly simplifies precise peak profile analysis [24].

Ordering in nonstoichiometric vanadium carbide is connected with redistribution of carbon atoms C and structural va-cancies , in the nonmetal sublattice sites. Although the crystal structure of the ordered phase V8C7 in coarse-grained bulksamples has been studied in sufficient detail, the information about atomic displacements is contradictory. Until now it is notknownwhether V8C7 has at least a narrow homogeneity interval or not at all. For nanocrystalline vanadium carbide, this is notknown either. Moreover, it is not clear even if the V8C7 superstructure is retained in nanocrystalline powders with medium-sized particles of 20e30 nm or less. This can be elucidated with the use of neutron diffraction analysis together with XRD andhigh-resolution transmission electron microscopy (HRTEM).

Among neutron tools, TOF diffractometers on pulse neutron sources [22] hold most promise for such studies. The use of acontinuous wavelength neutron spectrum makes it possible to cover a very wide interval of interplanar distances dhkl (from~0.05 up to ~1.5 nm and more). It is also important that the resolution of the TOF-diffractometer depends very weakly on dhklvalue.

In this work, X-ray diffraction, TOF-neutron diffraction analysis, high-resolution scanning and transmission electronmicroscopy were used for the first time to examine experimentally the crystal structure and microstructure of dispersednanocrystalline carbide V8C7 produced by high-energy ball milling of coarse-grained powder of the ordered phase V8C7. Thecoarse-grained powder of V8C7 was also studied for comparison.

2. Experimental details

The initial powder-like vanadium carbide VC0.875 was obtained by carbothermal reduction of the oxide V2O3 with carbonby the reaction V2O3 þmC/ 2VC0.875 þ 3CO in Ar atmosphere at 1570 K and then it was exposed to long-term aging at roomtemperature. The reduction of V2O3 by carbon in the amount ofm ¼ 4.75 corresponding to reaction stoichiometry resulted inthe formation of a two-phase product containing the cubic carbide VCywith an admixture of the lower hexagonal carbide V2C.

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That is why for synthesis of one-phase vanadium carbide, the oxide V2O3 was reduced under small excess of carbon(m ¼ 4.80e4.85). The synthesized powder of vanadium carbide VC0.875 was exposed to long-term (2 years) aging at roomtemperature in a closed vessel preventing penetration of water vapors from air.

The aged powder of nonstoichiometric vanadium carbide was milled in a PM-200 Retsch planetary ball mill (see details inSupplementary Material). The mass m of the initial powder, taken for milling, was 10 g. The duration of milling was 10 and15 h. The technique of high-energy ball milling is described in detail inworks [25,26]. The value of Emill at milling durations of10 and 15 h is 28.1 and 42.2 kJ [27,28]. The specific energy of milling Emol

sp�mill per 1 mol of carbide with molecular weightM s isEmolsp�mill ¼ Emill � (M/m). Taking this into account, energy Emol

sp�mill for V8C7 (VC0.875) vanadium carbide, which was milled for 10and 15 h, is equal to ~173 and ~259 kJ mol�1.

The content of adsorbed water in the vanadium carbide powders before and after milling was determined from the valueof mass loss after 1 h calcination of the powders at 570 K in vacuum. Chemical analysis of vanadium carbide nanopowders wascarried out on a МЕТАVАK CS-30 carbon/sulfur analyzer to estimate the total carbon content Сtotal and the content of free(uncombined) carbon Сfree. The content of impurity elements was determined using a Perkin Elmer ELAN 9000 massspectrometer.

The crystal structure and phase composition of nonstoichiometric vanadium carbide were studied using TOF neutrondiffraction and XRD.

X-ray measurements were performed on a Shimadzu XRD-7000 diffractometer using the Bragg-Brentano technique (seedetails in Supplementary Material). The XRD patterns were numerically analyzed with the use of the X'Pert Plus softwarepackage [29]. The average size D of coherent scattering regions (CSR) and the value of microstrains ε in milled vanadiumcarbide powders were found by the Williamson-Hall method from diffraction reflection broadening using the dependence ofthe reduced broadening b*(2q) ¼ [b(2q)cosq ]/l of the (hkl) reflections on the scattering vector s¼ (2sinq)/l [18,30e32]. In thefirst approximation, the size of CSR is considered as the average size of particles of a powder.

All the neutron diffraction spectra were obtained at 293 K on a HRFD high-resolution RTOF diffractometer [33] operatingon a pulsed reactor IBR-2 (JINR, Dubna). A continuouswavelength neutron spectrumwas used allowing a verywide interval ofinterplanar distances to be covered.

To avoid the possible systematic errors, the diffraction patterns weremeasured at different resolution levels with detectorsplaced at two scattering angles of 152� and 90�. As a result, the diffraction reflections from (110) to (10 10 2) in the interval ofdhkl interval from ~0.595 to ~0.058 nmwere registered. The resolution function of the neutron diffractometer was determinedfrom the peak width of the standard NAC and Al2O3 samples. The MRIA software package [34] was used for the analysis ofneutron diffraction patterns according to the Rietveld method.

The morphology and particle size of the vanadium carbide powders and also their elemental chemical composition wereexamined with a JEOL JSM 6390 LA scanning electron microscope coupled with a JED 2300 Energy Dispersive X-ray Analyzer.The microstructure of vanadium carbide powders was studied by the scanning electron microscopy (SEM) method on a ZeissSIGMAVPmicroscope also. In addition, the specific surface Ssp of the coarse-crystalline and nanocrystalline vanadium carbidepowders was measured on a Gemini VII 2390t Surface Area analyzer in order to estimate the particle size by the Bru-nauereEmmetteTeller (BET) method (see details in Supplementary Material).

The vanadium carbide nanoparticles were examined by high-resolution transmission electron microscopy (HRTEM)method. The HRTEM images were recorded on a JEOL JEM-2010 transmission electron microscope with 0.14 nm (1.4 Å) latticeresolution. The elemental chemical composition of nanoparticles was studied on the same microscope with the use of anPhoenix (EDAX) Energy Dispersive Spectrometer with a Si(Li) detector having energy resolution of 130 eV. For examination,the vanadium carbide nanoparticles were applied on a thin collodion support by which the copper grid has been covered.

The size distribution of particles in the initial and milled vanadium carbide powders was determined by the laserdiffraction method using a HORIBA LA-950V2 Laser Scattering Particle Size Distribution Analyzer.

3. Coarse-crystalline ordered V8C7 vanadium carbide

Aged powder of vanadium carbide is very hygroscopic. Right after removal from the closed vessel it contained not morethan 0.2 wt.% of physically adsorbed water, while after 3 month storage in air the content of water reached 2 wt.%. Note thatthe usual coarse-grained vanadium carbide powder does not possess such water absorbency.

According to chemical analysis data, the dried powder of aged vanadium carbide contains 18.5 ± 0.1 wt.% carbon including1.8 ± 0.1 wt.% free (uncombined) carbon, as well as ~0.5 wt.% impurity oxygen and has a composition of VC0.875±0.005 cor-responding to the upper boundary of the homogeneity interval of the cubic phase with B1 type structure. The data of gaschromatography show that the major part of impurity oxygen is in the chemisorbed form. The content of impurity metals ispresented in Table S1 (see Supplementary Material).

Preliminary X-ray structural certification of the vanadium carbide powders revealed that they contain the ordered cubic(space group P4332) V8C7 phase which formed as a result of ordering of the disordered basis phase VC0.875 having a B1structure as well as the disordered cubic (space group Fm3m) basis phase ~ VC0.875 (Fig. 1).

Fig. 1a displays an XRD pattern of aged vanadium carbide where along with the structural reflections of the cubic basisphase having B1 structure with lattice constant aB1 ¼ 0.41655 nm, additional weak reflections are observed. Refinementof the structure of the initial powder VC0.875 showed that all the additional reflections are superstructural and theirposition and intensity correspond to the cubic ordered V8C7 phase with space group P4332. The lattice constant of the

Fig. 1. The XRD patterns of the initial aged V8C7 powder (a) and nanocrystalline powders produced therefrom by 10 h (b) and 15 h (c) ball-milling. The long andshort marks correspond to diffraction reflections of disordered basic cubic (space group Fm3m) VC0.875 phase with B1 type structure and ordered cubic (spacegroup P4332) V8C7 phase. Vertical dashed lines show the positions of hexagonal WC reflections in the nanopowders. The insets for Fig. 1a show the increased partof XRD pattern with superstructure reflections, the doublet splitting of (400) ≡ (220)B1 reflection, and the unit cells of the V8C7 ordered phase with the indicatedunfilled octahedral interstices of metal sublattice. (C) V atoms, (B) C atoms. The XRD patterns are recorded in CuKa1,2 radiation.

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ordered phase is 0.8332 ± 0.0001 nm. The perfect cubic M8C7-type superstructure with space group P4332 has a doubled(as compared with the disordered basis phase) lattice constant [1,35]. Therefore the lattice constant of basis phase for theconsidered ordered vanadium carbide is aB1 ¼ 0.4166 nm, which is by ~0.00005 nm larger than for the disordered carbideVC0.875. According to [1], such a marked difference in the basis lattice constant for the ordered and disordered VC0.875carbides can be observed when the degree of ordering is close to maximum. The ratio of the intensities of structural andsuperstructure reflections also supports the view that the degree of long-range order in the ordered vanadium carbide isclose to maximum. The content of the ordered phase in the aged vanadium carbide powder is about 80 wt.%.

Table 1Effect of milling duration t and annealing temperature Tann on phase composition, content of free (uncombined) carbon Cfree, lattice constants a of orderedand disordered phases, specific surface. Ssp, average particle size D, and average microstrains εaver for V8C7 vanadium carbide powders.

t (h) Tann (K) Phasecomposition(wt.%)

Cfree content(wt.%)

*aV8C7

±0.00005 (nm)*aB1±0.00003 (nm)

Ssp±0.20 (m2 g�1) D±5 (nm) εaver±0.03(%)

V8C7 VC0.875 BET XRD Neutron XRD Neutron

0 e 79 ± 4 21 ± 3 1.2 0.83320 0.41655 1.11 1010 e e e e

10 e 59 ± 10 41 ± 10 1.3 0.83123 0.41556 28.23 40 24 19 0.53 0.6010 1070 64 ± 10 36 ± 10 0.3 0.83102 0.41541 13.01 83 40 e 0.20 e

10 1270 70 ± 10 30 ± 10 0.2 0.83013 0.41497 2.62 380 70 e 0.20 e

15 e 55 ± 10 45 ± 10 1.2 0.83114 0.41554 33.31 34 18 18 0.60 0.6215 1070 65 ± 10 35 ± 10 0.2 0.83109 0.41545 13.86 77 40 e 0.20 e

15 1270 70 ± 10 30 ± 10 0.2 0.83006 0.41491 2.21 450 80 e 0.20 e

*lattice constant from XRD data.

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According to the BET data, the average particle size in the initial coarse-grained V8C7 powder is ~1 mm (Table 1). The degreeof homogeneity of the initial V8C7 powder is rather high as evidenced by splitting of CuKa1,2 doublets. For the initial vanadiumcarbide, splitting is observed already for the reflection (220)B1 (Fig. 1a). Quantitative estimation of inhomogeneity Dy ofVСy±Dy (y¼ 0.875) from the (220)B1 reflection splitting [1,36] yielded the value Dy¼ 0.004. Thus, the composition of V8C7 wasdetermined with accuracy VC0.875±0.004.

Scanning electronmicroscopy (SEM) showed that the powder of ordered vanadium carbide consists of separate flower-likeparticles from 2 to 5 mm in size whose morphology resembles a tripped rosebud (Fig. 2). At high magnification, it is seen thatthese particles have a complex structure and are aggregations of a large amount of crystallites having a shape of twistedpetals. In the first approximation, the crystallites can be modeled by a disk with a diameter of 600e800 nm and thickness ofabout 20e40 nm. In spite of the nanometer thickness, the volume of each petal-crystallite is rather large owing to consid-erable linear dimensions and corresponds to a spherical particle with a diameter of ~150 nm. For this reason, the width of thestructural and superstructure diffraction reflections of the initial powder of ordered vanadium carbide is close to theinstrumental width (see Fig. 1a), and diffraction reflection broadening is absent.

The flower-likemicrostructure of nonstoichiometric vanadium carbidewas first detected experimentally and explained bythe authors [20]. They showed that the formation of the flower-like morphology is due to the disorder-order structural phasetransition VC0.875 / V8C7 that takes place during aging of nonstoichiometric carbide and is accompanied by a discontinuouschange in the crystal lattice constant aB1 of the disordered basis carbide. Because of the difference in the lattice parametersand specific volumes of the disordered and ordered phases, there appear tensions in the sample that lead to cracking ofcrystallites at the interfaces between disordered and ordered phases. The flower-like particles of the ordered carbide V8C7 arebrittle and can be easily broken down by minor mechanical action.

According to EDX-mapping results, the content of vanadium V and carbon C in the ordered vanadium carbide powder is79.2 ± 0.5 and 16.8 ± 0.4 wt.% (Fig. 3), which corresponds to VC0.83-0.89 carbide. The atomic ratio of V and C calculated from theintegrated EDX-peak intensities of V K and C K lines that registered in different parts of the flower-like particles ranges from0.84 to 0.91.

The neutron diffraction patterns of the coarse-crystalline powder of ordered vanadium carbide are shown in Fig. 4. All themeasured spectra of the coarse-crystalline powder ~ V8C7 exhibit weak superstructure reflections of the ordered phase V8C7(Fig. 4a,b). They are most easily observable in the region of large dhkl when the detector is positioned at the scattering angle2q ¼ 90� (Fig. 4b).

The profiles of some diffraction peaks have shoulders on the left and negative dips on the right (Fig. 5). The dips areconnectedwith the correlationmethod of data selection. The presence of shoulders is due to the occurrence of the disorderedcubic phase VC0.875 in the examined samples; this phase has B1 type structure with the lattice constantaB1 < aV8C7

=2. Thus,vanadium carbide powder contains the disordered phase along with the ordered phase. Therefore, the neutron diffractionspectra of vanadium carbide powders were processed by the Rietveld method using a two-phase model allowing for theordered phase V8C7 (F1) and disordered phase VC0.875 (F2). The decomposition of the experimental diffraction reflection (222)by the two-phase model is shown as an example in Fig. S1 (see Supplementary Material).

The reflection profile of the disordered phase was described by the Lorentz functions. The unit cell lattice constant aB1 ofthe disordered phase VC0.875 was determined by averaging of values obtained in the description of profiles of several intensivereflections. The inset (Fig. 5) displays the (222) reflection profile of the ordered phase V8C7 and the (111)B1 reflection profile ofthe disordered phase VC0.875. The peak of the disordered phase is almost 3 times broader than that of the ordered phase. Fromthe peak broadening of the ordered phase, it follows that this phase is represented by small-size (~50 nm) inclusions in thematrix of the ordered phase V8C7.

The coordinates of carbon atoms in the structure of coarse-crystalline ~ V8C7 powder were determined from the neutrondiffraction data. Further, using these coordinates, the coordinates of V atoms were found from the XRD data, and the occu-pancy of the carbon sublattice positions was refined. Then the neutron diffraction pattern of the coarse-crystalline ~ V8C7

Fig. 2. The SEM images of the initial aged powder of nonstoichiometric VC0.875 vanadium carbide at different magnifications. At a magnification of 5000 times, itis seen that each of the objects with a size of approximately 2e3 mm looks like an open rose bud. At a higher magnification, it is seen that observed crystallites-petals have the form of curved discs with a diameter from 600 to 800 nm and thickness approximately 20e40 nm. Joining, the crystallites-petals form a flower-like structure.

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powder was finally refined with the use of the deduced coordinates of C and V atoms and the occupancy of the carbonsublattice positions.

Fig. 3. EDX-analysis of the initial coarse-crystalline powder of ordered vanadium carbide.

Fig. 4. Normalized neutron diffraction patterns of the initial coarse-crystalline powder of ~V8C7 vanadium carbide measured by HRFD detectors placed at thescattering angles of (a) 152� and (b) 90� . Vertical marks indicate the positions of diffraction reflections of the cubic ordered V8C7 phase.

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The structure refinement of the vanadium carbide coarse-crystalline powder confirmed the presence of the ordered anddisordered phases (Fig. 5). The lattice constants of cubic unit cells of the V8C7 and VC0.875 phases is respectively 0.83291(1)and 0.41551(1) nm, i. e. aV8C7

>2aB1. Thus, the basis lattice constant of the ordered carbide is larger than that of the disorderedcarbide. This agrees with data [7,35,37] showing that at 300 K the basis lattice constant of the ordered carbide V8C7 is largerthan that of the disordered carbide VC0.875. The content of the disordered phase VC0.875 in the coarse-crystalline powder is21 ± 3 wt.%. An important feature of the real structure of the ordered phase is decreased occupancy of 4(a) positions withcarbon atoms, namely 0.97 (Table 2). This means that the ordered phase has a composition ~ V8C6.97 (~VC0.871) or V8C7-d,where dy 0.03. The coordinates of C3 and C4 carbon atoms in the lattice of the real ordered phase V8C7-d are close to those inthe perfect superlattice V8C7 (Table 2). The convergence factors achieved in structure refinement are equal to uRp ¼ 6.3% andRe ¼ 6.7%.

The derived crystal structure of the ordered phase V8C7-d (Table 2) features small displacements of V1 atoms, somewhatlarger displacements of V2 atoms and small displacement of C3 and C4 atoms from the perfect superlattice positions. The V2atoms forming the nearest octahedral environment ,V6 of the vacant sites in the carbon sublattice are shifted towards thevacancy ,. Earlier, appreciable displacements of atoms in the ordered V8C7-type phase towards the vacancy were found bythe authors [6]. All VeV distances in the perfect ordered V8C7 phase are equal to 0.2946 nm, whereas in the real super-structure they are from 0.2883 to 0.3058 nm. According to the neutron diffraction measurements, the displacements ofcarbon atoms C3 and C4 in V8C7 are very small. For example, in the (00z) plane with z z 0.625 the displacement Dl of the C4atom is ~0.0033(2) nm, while that of the C3 atom is close to zero. The displacements of the V1 and V2 atoms in the same plane(00z) are ~0.0053 and ~0.0055 nm, respectively. According to the XRD data [9], the displacement the C4 atom is almost 18times greater and is equal to ~0.058 nm, which is hardly probable. In work [10] the displacements of the C3 atoms are small,whereas the displacements of the C4 atoms are as large as in work [8]. Note that in works [8,10] the XRDmeasurements werecarried out on bulk samples of the ordered phase V8C7, but not on a powder as in our study.

The calculation [38], in which the V atoms in the V8C7 phase are displaced from the vacancy, completely contradicts theobtained experimental results. Our experiment and data [8,10] show that this is not so: the V2 atoms forming the octahedralenvironment,V6 of the vacant sites are shifted towards the vacancy ,. In the real ordered V8C7-d phase such displacementof V atoms will increase the electronic density of the vacancy positions 4(b), while the calculation [38] for the perfect V8C7phase gives zero electronic density in the vacancy positions 4(b) of the carbon sublattice. The conclusion that the vacancypositions in the ordered V8C7 phase have nonzero electronic density and traps positrons was experimentally confirmedearlier by the positron lifetime method [20].

According to the chemical analysis data, the aged vanadium carbide contains free (uncombined) carbon. It was noted thatthe atomic ratio of V and C determined by the EDXmethod in the SEM study of the ordered vanadium carbide (see Figs. 2 and3) in different parts of the flower-like particles is from 0.84 to 0.91. Since the relative carbon content in the cubic vanadiumcarbide VCy is within the interval 0.65 � y � 0.875, it is necessary to determine, in which form excessive carbon is present inthis compound. For this purpose, coarse-crystalline ordered vanadium carbide was examined by HRTEM method.

Fig. 5. Refinement of the neutron diffraction pattern of the initial coarse-crystalline vanadium carbide powder (measurements in the high-resolution mode bydetector placed at the scattering angle 2q ¼ 152�). In addition to the main ordered phase, the disordered phase with B1 type structure is present. Points show theexperimental spectrum, and solid lines show the theoretical spectrum and the contributions from ordered and disordered phases. The inset gives the profiles ofthe (222) reflection of the ordered V8C7-d phase and the (111)B1 reflection of the disordered VC0.875 phase. Short and long vertical marks indicate the positions ofreflections of the ordered V8C7-d (d y 0.03) phase and the disordered VC0.875 phase, respectively.

Table 2Refined crystal structure of ordered cubic (space group No 212 - P24332 (O6)) V8C7-d (d y 0.03).phase of nonstoichiometric vanadium carbide.

Atom Positionandmultiplicity

Atomic coordinates for coarse-crystalline ordered phase(a ¼ 0.83291(1) nm)

Atomic coordinates fornanocrystalline orderedphase(a ¼ 0.83268(3) nm)

Occupancy

x/a y/a z/a x/a y/a z/a

C1 (vacancy ,) 4(b) 0.6250 0.6250 0.6250 0.6250 0.6250 0.6250 0C2 4(a) 0.1250 0.1250 0.1250 0.1250 0.1250 0.1250 ~0.97C3 12(d) 0.1250 0.6248(2) 0.6252(2) 0.1250 0.6266(12) 0.6234(12) 1.0C4 12(d) 0.1250 0.3720(2) 0.8780(2) 0.1250 0.3686(12) 0.8814(12) 1.0V1 8(c) 0.3705 0.3705 0.3705 0.3705 0.3705 0.3705 1.0V2 24(e) 0.126 0.3815 0.128 0.126 0.3815 0.128 1.0

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Fig. 6 demonstrates a HRTEM image of the ordered cubic (space group P4332) carbide V8C7 nanoparticle. The observeddistances, 0.590 and 0.241 nm, coincide with the interplanar distances d(110) and d(222) of the ordered cubic V8C7 phase. Innanoparticle there takes place microtwinning. This is confirmed by the diffraction pattern obtained by Fast Fourier Trans-formation (FFT) of the HRTEM image from region 1. Indeed, the diffraction pattern contains reflection (1e10)*, which is a twinof reflection (110) in the twinning plane [100]. The inset in the lower left corner shows the EDX analysis of V8C7 nanoparticlefrom region 1. Besides, several regions with onion-like structure and interplanar distance of 0.335 nm are seen. This distancecoincides with spacing 0.335 nm between adjacent graphene layers, which is typical of spherical onion-like carbon structures[39e41]. Thus, free (uncombined) carbon contained in the initial coarse-crystalline ordered vanadium carbide is in the formof onion-like structures. A multilayer carbon onion-like shell formed around the particle of initial vanadium carbide isdepicted in Fig. 7 as an example.

4. Nanocrystalline ordered V8C7 vanadium carbide

As was noted, vanadium carbide VC0.875 is the first nonstoichiometric carbide, in which nanostructure was created inworks [10,20] as a result of disorder-order transformation VC0.875 / V8C7 [42].

The effect of milling on the variation of diffraction reflection profiles of vanadium carbide powders is shown in Fig. 1b, c.The vanadium carbide nanopowders contain the ordered cubic (space group P4332) V8C7 phase and the disordered cubic(space group Fm3m) phase ~ VC0.875 (Fig. 1). An increase in the duration t and energy Emill of milling is accompanied byappreciable broadening of all diffraction reflections.

Fig. 6. The HRTEM image of a particle of ordered cubic (space group P4332) V8C7 carbide. The inset at the top demonstrates a diffraction pattern obtained by FFTof the HRTEM image of region 1 (the zone axis [1e13]). The inset at the bottom shows EDX analysis of region 1 of a V8C7 carbide particle. There are also regionswith interplanar distance of 0.335 nm typical of carbon spherical onion-like structure.

Fig. 7. The HRTEM image of the carbon onion-like shell formed on the vanadium carbide core. The EDX analysis of region 1 confirming the presence of thecarbide core is shown in the inset.

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XRD of the nanocrystalline vanadium carbide powders produced by milling revealed that they contain an impurity phaseof hexagonal (space group P6m2) tungsten carbide WC in the amount of ~4.0e5.0 wt.% (Fig. 1b, c). The WC impurity appearsduring milling because of rubbing of the grinding balls and the lining of the bowls made of the hard alloy WC - 6 wt.% Co.

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The average size of the CSR in the vanadium carbide nanopowders after 10 and 15 h milling determined from the XRDreflection broadening is ~24 and ~18 nm, respectively. The average particle size of these powders estimated by the BETmethod from the specific surface value is equal to 40 and 34 nm (Table 1).

According to the SEM data, the V8C7 nanopowders produced by 10 and 15 h milling consist of nanoparticles 60e80 nm insize united into large loose agglomerates (Fig. 8).

The neutron diffraction patterns of the nanocrystalline vanadium carbide powder produced by 10 h milling of the initialcoarse-crystalline V8C7 powder are demonstrated in Fig. 9. Along with the disordered carbide reflections, the spectra containweaker superstructure reflections of the ordered phase V8C7 (Fig. 9a,b). In the spectrum recorded in the high-resolutionmode, the superstructure reflections in the region dhkl > 0.25 nm are poorly visible (Fig. 9a); however, in the low-resolution mode this dhkl region contains the superstructure reflections (211), (310) and (311) (Fig. 9b). The neutrondiffraction patterns of the nanopowder produced by 15 h milling are analogous. As compared with the coarse-crystallinepowder, the superstructure reflections in the spectra of V8C7 nanopowders are less clear because of considerable broadening.

Quantitative analysis of the neutron diffraction pattern (Fig. 10) showed that the vanadium carbide nanopowder containsordered and disordered phases, but as a result of milling the amount of the latter phase increased from 21 ± 3 to 41 ± 10 wt.%.The growth of the disordered phase concentration is due to a very highmilling energy Emol

sp�mill (from ~173 to ~259 kJ mol�1 for10 and 15 h milling), which exceeds the energy DHtr of the orderedisorder transformation V8C7 / VC0.875. According todifferent data, the energy DHtr of the V8C7 / VC0.875 transformation is 2.78 [43], 1.54 [44], 2.35 [7] and 3.0 kJ mol�1 [2,37].Most of the energy Emol

sp�mill is consumed for milling, while a small part of this energy induces the observed partial disordering.The lattice constants of cubic unit cells of the V8C7 and VC0.875 phases in the nanopowder are 0.83268(3) and 0.41466(4)

nm, which is somewhat smaller than in the coarse-crystalline powder. The experimental accuracy does not allow one todetermine reliably the deviations in the occupation of C atomic positions from the ideal values. It can be supposed that thenanocrystalline ordered phase has the same composition ~ V8C6.97 (V8C7-d, where d y 0.03) as the ordered phase in thecoarse-crystalline powder. The displacements of carbon atoms C3 and C4 in the lattice of the nanocrystalline ordered phaseV8C7-d are small, but still larger than those in the coarse-crystalline ordered phase (Table 2). This is due to noticeabledeformation distortion of the lattice during milling of the powder. For refined nanopowder structure uRp ¼ 2.8% andRe ¼ 3.9%.

The TEM results confirm the presence of ordered and disordered phases in nanocrystalline vanadium carbide. It is wellvisible that the sample contains inclusions of the disordered vanadium carbide VC0.875 with the size of ~8e10 nm in thematrix of the ordered phase V8C7 (Fig. 11a). According to the EDX data, the content of V and C in the ordered phase is~79.1 ± 0.8 and 16.5 ± 0.5 wt.%, which corresponds to carbide ~ VC0.87-0.88. The images of some nanoparticles have regionswith carbon onion-like structure (Fig. 11b), but the amount of such regions is much smaller than in the initial coarse-crystalline carbide V8C7.

The important features of the microstructure of nanocrystalline powders obtained by milling are a small particle size andthe presence of microstrains. Microstrains, like a small particle size, lead to diffraction reflection broadening. According to[28,31,32,36], in the case of nonstoichiometric compounds MCy±Dy, inhomogeneity Dy also leads to diffraction reflectionbroadening. In Section 3 it was shown that inhomogeneity of the initial vanadium carbide VC0.875±0.004 is very small(Dy ¼ 0.004) and in this case the contribution of inhomogeneity to reflection broadening can be neglected.

Size broadening bs(2q) is determined through the average size D of small particles as

Fig. 8. The SEM images of V8C7 nanopowders produced by (a) 10 h and (b) 15 h milling. The nanoparticles of size 60e80 nm are united into large looseagglomerates.

Fig. 9. Normalized neutron diffraction patterns of nanocrystalline ~ V8C7 powder produced by high-energy ball-milling of the initial coarse-crystalline powderduring 10 h. Measurements are performed by HRFD detectors placed at the scattering angles of (a) 152� and (b) 90� . Vertical marks indicate the positions ofdiffraction reflections of the cubic ordered V8C7 phase.

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bsð2qÞ ¼khkll

D$cos q¼ 2

khkldD

tanq; (1)

where khkly 1 is the Scherrer's constant, whose value depends on the particle form and diffraction reflection indices (hkl); l isthe emission wavelength; and d is the interplanar distance.

According to [45,46], the broadening bd(2q) induced by crystal lattice strain distortions is equal to

bd(2q) ¼ 4εhkltan(q), [rad] (2)

where εhkl ¼ s/Ehkl ¼ krC1=2hkl is the effective microstrain allowing for anisotropy of crystal deformation; s is the direction-

independent full width at half-maximum of the strain distribution function; Ehkl is the [hkl] direction-dependent Young'smodulus; and kr is the constant depending on the density of dislocations and the Burgers vector for a given sample, i. e. on thevariation of the interplanar distance and atomic displacements. In the elasticity theory, the anisotropic Young's modulus Ehklof cubic crystals is determined through the elastic constants c11, c12 and c44 or through elastic deformation tensor componentss11, s12 and s44 as

Ehkl ¼1

s11 � ð2s11 � 2s12 � s44ÞH; (3)

where H ¼ ðh2k2 þ k2l2 þ h2l2Þ=ðh2 þ k2 þ l2Þ2 is the anisotropy dislocation factor. The coefficient Chkl takes into account thepresence of edge and screw dislocations in the deformed crystal. According to [47], for cubic crystals the coefficient Chkl isequal to

Chkl ¼ fEChkl,E þ (1�fE)Chkl,S ¼ [fEAE þ (1�fE)AS] þ [fEBE þ (1�fE)BS]$H ¼ A þ BH, (4) (4)

where fE and fS ¼ (1 - fE) is the relative content of edge and screw dislocations, and A and B are the constants depending on thedensity of dislocations and their relative content for a given sample.

With allowance for εhkl ¼ krC1=2hkl and Eq. (4), expression (2) can be written as

bdð2qÞ ¼ 4krC1=2hkl tanq≡4krðAþ BHÞ1=2tanq: (5)

From Eqs. (4) and (5) it follows that anisotropy of microstrains is due to a greater extent to dislocations or dislocation-likedefects than to atomic displacements. The value of crystal volume averaged microstrains εaver is equal toεaver ¼ ðP εhklPhklÞ=

PPhkl, where Phkl is the multiplicity factor.

Fig. 10. Refinement of the neutron diffraction pattern of nanocrystalline vanadium carbide powder produced by milling of coarse-crystalline powder for 10 h(neutron diffraction pattern is measured in the high-resolution mode by detector placed at the scattering angle 2q ¼ 152�). Vanadium carbide nanopowdercontains ~41 wt.% of the disordered phase with B1 type structure along with the main ordered phase. Points show the experimental spectrum, and solid linesshow the theoretical spectrum and the contributions from ordered and disordered phases. Short and long vertical marks indicate the positions of reflections ofthe ordered V8C7-d (d y 0.03) phase and the disordered VC0.875 phase, respectively.

A.S. Kurlov et al. / Superlattices and Microstructures 90 (2016) 148e164 159

The quantitative analysis of the XRD reflection profile of the examined vanadium powders showed that they are describedby the pseudo-Voigt function with a large (up to 90% and more) contribution from the Lorentz function. According to [28], inthis case the physical reflection broadening, disregarding inhomogeneity, is a sum of size bs(2q) and strain bd(2q) broadeningsand is equal to

b(2q) ¼ bs(2q) þ bd(2q). (6)In XRD experiment, the dependence of reduced angular broadening b*(2q) ¼ [b(2q)cosq]/l on the scattering vector s ¼

(2sinq)/l is considered. Substitution of (1) and (5) into expression (6) and transformation to reduced broadening give

b*(2q) ¼ khkl/D þ 2kr(A þ BH)1/2s. (7)Separation of size and strain contributions to X-ray reflection broadening revealed that for any diffraction reflection the

contribution from strain broadening to the observed physical broadening is greater than 50%. It is clear that the considerationof microstrain anisotropy in analysis of XRD data is essential.

The superstructure reflections in nanocrystalline vanadium carbide powders are very weak, and the error in determiningtheir width is great. That is why for estimation of the nanoparticle size and the microstrain value we used structuraldiffraction reflections. For the calculation, the Scherrer's constant khklwas assumed equal to 1. The calculation showed that forV8C7 (VC0.875) nanopowders the least value of microstrains εhkl is observed in the [100]B1 direction and equivalent directions,while the largest value of microstrains εhkl is observed in the [111]B1 direction. Fig. 12 demonstrates the distribution ofmicrostrains εhkl in the nonequivalent directions [hkl] in V8C7 nanopowders produced during 10 and 15 h milling with energyEmill of ~28.1 and ~42.2 kJ, respectively. The radius of the spheres is proportional to the microstrain εaver averaged in all thecrystallographic directions, and the length of the vectors is proportional to the value of εhkl. As is seen, in both nanopowdersthe microstrains ε111, ε110, ε331 and ε211 in the directions [111]B1, [110]B1, [331]B1, and [211]B1 exceed the averaged microstrainεaver equal to 0.53% и 0.60% for milling energy of 28.1 and 42.2 kJ, respectively. Note that the directions [111]B1, [100]B1, [110]B1,[311]B1, [331]B1, [210]B1 and [211]B1 correspond to the diffraction reflections (111)B1, (200)B1, (220)B1, (311)B1, (331)B1, (420)B1and (422)B1 on the XRD patterns. The microstrain ε100 is smaller than εaver, whereas ε311 and ε210 almost coincide with theaveraged microstrain εaver. The numerical values of microstrains εhkl in different [hkl] crystallographic directions of V8C7nanopowders produced by 10 and 15 h milling are listed in Table S2 (see Supplementary Material).

In the neutron experiment, the diffraction reflection profiles of the examined vanadium carbide powders are described bythe pseudo-Voigt function with an appreciable contribution from the Gaussian function. In this case, the reflection broad-ening is determined disregarding inhomogeneity [22,23] as

b2ð2qÞ ¼ b2s ð2qÞ þ b2dð2qÞ: (8)

If the angular broadening is represented through the interplanar distance d in the form

b(2q) ¼ 2jDqj ¼ 2(Dd/d)tgq, (9)

Fig. 11. The HRTEM image of nanocrystalline vanadium carbide produced by 15 h milling. (a) The sample contains inclusions (1) and (2) of disordered vanadiumcarbide VC0.875 of size about 8e10 nm in the matrix of the ordered phase V8C7 (region (3) of the ordered V8C7 vanadium carbide is shown, the zone axis of thematrix region is [1-1-4]); the inset in the bottom shows the EDX analysis of region 3 of a nanoparticle of ordered V8C7 vanadium carbide. (b) A vanadium carbidenanoparticle, in which regions with carbon onion-like structure are observed.

A.S. Kurlov et al. / Superlattices and Microstructures 90 (2016) 148e164160

then after substitution of (1) and (5) into formula (8) we have

�Ddd

�2

¼�dD

�2

þ �2kr

�2Chkl: (10)

The dependence of the diffraction reflectionwidth Dd on the polycrystal interplanar distance d duringmeasurement on anHRFD TOF-diffractometer is described [22] as

Fig. 12. The distribution of microstrains εhkl in the non-equivalent directions [hkl]B1 in V8C7 (VC0.875) nanopowders produced by milling of the initial coarse-crystalline powder for (a) 10 and (b) 15 h, respectively. The radius of the sphere is proportional to the value of εaver, and the vector length in the directions[hkl]B1 is proportional to the value of εhkl.

Fig. 13. The squared width (Dd)2 of the structural diffraction reflections of vanadium carbide V8C7 (VC0.875) as a function of the squared interplanar distance d2:(a) coarse-crystalline powder (the resolution function of the HRFD diffractometer is indicated by a dotted line), (b) nanocrystalline powder obtained by 10 hmilling.

A.S. Kurlov et al. / Superlattices and Microstructures 90 (2016) 148e164 161

ðDdÞ2 ¼ C1 þ C2d2 þ C3d

2 þ C4d4; (11)

where the coefficients С1 and С2 are related to the resolution function and the TOF-diffractometer parameters (flight distance,scattering angle), С3 z (2ε)2 and C4 z (khkl/D)2. With allowance for microstrain anisotropy, expression (11) takes the form

Fig. 14. The HRTEM image of nanocrystalline vanadium carbide upon annealing at 1070 K. Only the ordered V8C7 phase is observed. The EDX analysis of region 1of vanadium carbide V8C7 nanoparticle and the diffraction pattern obtained by FFT of the HRTEM image of region 1 are shown in the insets.

A.S. Kurlov et al. / Superlattices and Microstructures 90 (2016) 148e164162

ðDdÞ2 ¼ C1 þ C2d2 þ C3ðAþ BHÞd2 þ C4d

4: (12)

When the effect of small size is lacking, dependences (11) and (12) as functions of d 2 will be linear, while at a small particlesize they will parabolic. For coarse-crystalline vanadium carbide V8C7 (VC0.875), the dependence Dd 2(d 2) (Fig. 13a) is linear,but the vanadium carbide reflections are somewhat broadened as compared with the resolution function, which is due to thepresence of small microstrains in the powder particles. The diffraction reflections of nanopowders are strongly broadened(see Fig. 1b, c), and the dependence Dd 2(d 2) for the nanopowder produced by 10 h milling is parabolic (Fig. 13b). The esti-mation of the nanopowder particle size and microstrains from dependence (11) gives D z 19 nm and ε z 0.60% (in thecalculation khkl was assumed to be 1). This agrees with the values Dz 24 nm and εaver z 0.53% (see Table 1) obtained from X-ray reflection broadening data.

Vanadium carbide nanopowders were annealed in vacuum at 1070 and 1270 K for 1 h. According to the chemical analysisdata, the annealing of the nanopowders led to the reduction of the total carbon content since free (uncombined) carbondisappeared almost completely. The diffraction reflections on the XRD patterns of the nanopowders (see Fig. S2 in Supple-mentary Material) narrow owing to the average particle size growth and a decrease in the microstrain value to 0.2%. As aresult of annealing at 1070 and 1270 K, the average particle size in the nanopowders increased up to 40 and 70e80 nm,respectively (see Table 1). XRD also showed that upon annealing of the vanadium carbide nanopowders, the relative contentof the ordered phase V8C7 in the nanopowders increased thanks to the disordereorder transformation. The data of XRD andchemical analysis are confirmed by the transmission electronmicroscopy results. The HRTEM images of the vanadium carbidenanopowders annealed at 1070 and 1270 K contain the ordered phase V8C7 with inclusions of a disordered phase, and thereare no even traces of carbon onion-like structures. Fig. 14 demonstrates as an example the vanadium carbide nanopowderobtained by 15 h milling and then annealed at 1070 K; it contains only the ordered phase V8C7.

5. Conclusion

The synthesized coarse-crystalline powder of ordered vanadium carbide has a flower-like microstructure. The formationof the flower-like microstructure is due to the structural disordereorder phase transition VC0.875 / V8C7, which takes placeduring aging of nonstoichiometric vanadium carbide.

By combining X-ray and time-of-flight neutron diffractionwe determined the real structure of the ordered cubic vanadiumcarbide and established that it has the composition V8C7-d differing from the perfect stoichiometric composition V8C7. Thevanadium atoms forming the octahedral environment ,V6 of vacant sites in V8C7-d are displaced towards the vacancy ,.

In the vanadium carbide powders with a small content of free (uncombined) carbon we found the presence of carbononion-like structures forming a shell on the vanadium carbide particles.

A.S. Kurlov et al. / Superlattices and Microstructures 90 (2016) 148e164 163

The nanopowders of V8C7-d carbide with the average particle size of 20e30 nm produced by high-energy ball milling ofcoarse-crystalline powder retain the crystal structure of the initial powder. Analysis of the structural data revealed anisotropicdistribution of microstrains in the nanopowders and allowed us to determine quantitatively the value of microstrains εhkl fordifferent [hkl] directions of the crystal lattice.

Vacuum annealing of the vanadium carbide nanopowders at temperatures to 1070 K is accompanied by a small variation ofthe composition, a weak growth of the average nanoparticle size and by reduction of microstrains with the nanostructureremaining the same.

Acknowledgments

This work is financially supported by the Russian Science Foundation (Grant 14-23-00025) through the Institute of SolidState Chemistry of the Ural Division of the RAS.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.spmi.2015.12.006.

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