Vibrational Spectroscopy of Binary Titanium Borides: First ...downloads.hindawi.com/journals/acmp/2017/4207301.pdf · ResearchArticle Vibrational Spectroscopy of Binary Titanium Borides:

Research ArticleVibrational Spectroscopy of Binary TitaniumBorides First-Principles and Experimental Studies

Urszula D Wdowik1 Agnieszka Twardowska1 and BogusBaw Rajchel2

1 Institute of Technology Pedagogical University Podchorazych 2 30-084 Krakow Poland2Institute of Nuclear Physics Polish Academy of Sciences Radzikowskiego 152 31-342 Krakow Poland

Correspondence should be addressed to Urszula D Wdowik sfwdowikcyf-kredupl

Received 30 August 2016 Accepted 1 December 2016 Published 3 January 2017

Academic Editor Da-Ren Hang

Copyright copy 2017 Urszula D Wdowik et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Vibrational dynamics of binary titanium borides is studied from first-principles Polarized and unpolarized Raman spectra of TiBTiB2 andTi3B4 are reported alongwith the experimental spectra of commercial powder and bulk TiB2 containing less than 1 wt ofimpurity phasesTheX-ray diffraction spectroscopy applied for phase composition examination of both bulk and powdermaterialsidentifies only the TiB2 phase The simulated Raman spectra together with literature data support interpretation and refinementof experimental spectra which reveal components arising from titanium dioxide (TiO2) and amorphous boron carbide (B4C)impurity phases as well as graphitic carbon These contaminations are the by-products of synthesis consolidation and sinteringaids employed to fabricate powder and bulk titanium diboride

1 Introduction

Generally the TindashB system comprises three compoundsnamely TiB TiB2 and Ti3B4 [1]These borides have attractedmuch experimental and theoretical research because of theirunique properties such as high melting point high hardnesshigh elastic modulus good thermal and electrical conductiv-ity excellent oxidation resistance and considerable chemicalstability [2] The combination of these properties makestitanium borides promising materials for multifunctionalapplications for example electrode materials cutting toolswear-resistant parts protecting coatings and all kinds ofhigh-temperature structural components [3]

Themost extensively studiedTiB2 compoundhas recentlygained renewed experimental interest due to its applicationfor deposition of thin TindashB films [4ndash6]We note that chemicalcomposition of TindashB film varies with applied conditions ofdeposition and hence the phase composition of depositedmaterial differs from that desired and expected An analysisof the phase composition of thin and frequently amorphous(or partially amorphous) TindashB films by the X-ray diffraction(XRD) method remains uncertain due to the content of lightboron element Therefore for characterization of deposited

thin TindashB films some complementary methods such as theRaman spectroscopy have to be applied On the other handreference Raman spectra are usually based on measurementscarried out on samples prepared in different conditionsand thus the resulting Raman spectra show differences inposition intensities and even the number of peaks amongthe spectra recorded for the same phase and analyzed invery similar experimental conditions In order to resolvethese ambiguities one may calculate positions and intensitiesof the Raman-active modes for a given system using thecurrently available theoretical tools such as those based onstate-of-the-art density functional theory (DFT) Results ofnumerical simulations can then be used for interpretationand refinement of respective experimental spectra

So far a number of theoretical and experimental workshave been done to investigate the structural electronicand elastic properties of titanium borides [7ndash11] leavingtheir dynamical properties highly unexplored [12 13] Thisresearch extends and supplements the present knowledge ontitanium borides by providing information on their vibra-tional properties In particular the positions and intensities ofthe Raman-active phonons of TiB TiB2 and Ti3B4 are deter-mined form first-principles calculations by using the DFT

HindawiAdvances in Condensed Matter PhysicsVolume 2017 Article ID 4207301 9 pageshttpsdoiorg10115520174207301

2 Advances in Condensed Matter Physics

theory and the direct methodWe also provide interpretationof the Raman spectra measured for commercially availablepowder and bulk samples of titanium diboride Results ofthese studies are hoped to stimulate further experimental andtheoretical progress in the field of TindashB system

2 Methodology

21 Experimental Experimentswere performed for commer-cial TiB2 powder (H C Starck Germany) and bulk (targetGoodfellow UK) samplesThe grain size of TiB2 powder withpurity of about 99wt was in the range 25ndash35 120583mThe tar-get sample of 30mm in diameter and 4mm in thickness wasmechanically polished on one side using diamond grinding(9 6 and 3 120583m) and finally polished in 1 120583m suspensionAt each polishing step the surface was degreased by 2-Propanol and then ultrasonically cleaned in acetone bathfor 5 minutes After drying (in air) the target was mountedin a vacuum chamber to perform ion cleaning at roomtemperature and pressure of 10minus2 Pa The iron cleaning wasdone by a beam of Ar+ ions of energy of 10 keV directedat sample at an angle of 65∘ (measured to the normal oftarget surface) Such preparation procedure is required for theRamanmeasurements as the spectrometer used in our studiesis equipped with the confocal (light) microscope Moreoverthe target is further used for deposition of TiB2 thin films bythe PVDmethod (results not discussed in the present paper)

Phase identification was performed by the X-ray diffrac-tion (XRD) method using PANalytical Empyrean diffrac-tometer The CuK120572 radiation (intended 120582 = 15406 Aintensity ratio CuK120572

1

CuK1205722

= 2 119880 = 40 kV I = 30mA) inthe Bragg-Brentano configuration was used for this purposeThe XRD patterns were collected in 2Θ geometry over thescattering angles ranging from 20∘ to 82∘ with a step sizeof 002∘ Analysis was performed according to the ICSDdatabase and the Rietveld method which took into accountthe ratio CuK120572

1

CuK1205722

= 2The Raman spectroscopy was applied to refine the phase

composition of both powder and bulk (target) samples Toexcite Raman spectra the NdYAG laser beam with wave-length of 532 nm and a power of 625mW was used Unpo-larized Raman spectra in backscattering geometry were col-lected at room temperature using theThermo-Nicolet RamanALMEGA XR dispersive confocal spectrometer operating inthe micro-Raman mode Raman spectra were recorded withnormal (4 cmminus1) and high-spectral (2 cmminus1) resolutions

22 Theoretical Calculations were carried out within theDFT method implemented in the VASP code [14 15]Electron-ion interaction was represented by the projectoraugmented wave (PAW) method The generalized gradientapproximation with parametrization of Perdew Burke andErnzerhof (GGA-PBE) [16 17] was applied for the exchangeand correlation potential The wavefunctions were expandedin a plane-wave basis set with a cutoff energy of 420 eVReference configurations for valence electrons were (3d34s1)for Ti and (2s22p1) for B Lattice constants and internalatomic positions of TiB TiB2 and Ti3B4 unit cells were

fully optimized with convergence criteria for the residualHellman-Feynmann (HF) forces and the systemrsquos total energyof 10minus5 eV Aminus1 and 10minus7 eV respectively The Brillouin zonesof TiB TiB2 and Ti3B4 were sampled using respectively54 96 and 50 irreducible k-points generated accordingto the Monkhorst-Pack scheme Phonon calculations wereperformed within the direct method approach [18 19] andharmonic approximation The HF forces were obtained bydisplacing the symmetry nonequivalent Ti and B atomsfrom their equilibrium positions by plusmn002 A in the supercellscontaining 64 atoms (TiB) 92 atoms (TiB2) and 112 atoms(Ti3B4) The HF forces were calculated with reduced numberof k-points The total number of calculated displacementsamounted to 12 for TiB 6 for TiB2 and 24 for Ti3B4 Peakintensities of the nonresonant Raman spectrum (in Stokesprocess) were calculated from the well-known expression[20] 119868 prop |esRei|2120596minus1(119899 + 1) where (119899 + 1) is the populationfactor for Stokes scattering with 119899 = [exp(ℏ120596119896119861119879) minus 1]

minus1

denoting the Bose-Einstein thermal factor ei (es) is thepolarization of the incident (scattered) radiation and R isthe Raman susceptibility tensorThe components of R tensor(120572119894119895) were determined from derivatives of the electric polar-izability tensor over the atomic displacements [19 21 22]The electric polarizabilities were calculated within the linear-response method [23] and for each symmetry nonequivalentatomwas displaced from its equilibrium position by plusmn001 ADetails of calculations can also be found elsewhere [24 25]We also note that anharmonic effects leading to changes inphonon frequencies and reflected by shifts of the Ramanpeaksrsquo positions have been neglected This is mainly becauseour measurements are performed at room temperaturewhere the effects related to the thermal expansion of com-pounds from the TindashB system are negligible Also the effectof anharmonicity on the widths of Raman peaks is notconsidered in the present work Thus the Raman peaks aresimulated by Lorentzian functions with artificial FWHMscorresponding to energy resolution of the Raman spectrom-eter used in our studies

3 Results and Discussion

31 Structural Properties Titanium monoboride (TiB) crys-tallizes in the orthorhombic FeB structure with the spacegroup 119875119899119898119886 (no 62) [26] where both Ti and B atomsoccupy (4119888) lattice sites Its primitive unit cell consists of 8atoms (4 formula units)Themain building block of TiB is thetrigonal prism with the B atom at the center and the Ti atomsin corners The transverse stacking of the trigonal prisms incolumnar arrays leads to a zig-zag chain of B atoms alongthe [010] direction as schematically shown in Figure 1

Titanium diboride (TiB2) has hexagonal layered struc-ture of AlB2-type (space group 1198756119898119898119898 no 191) with Tiand B atoms located respectively at (1119886) and (2119889) Wyckoffpositions [27] The primitive unit cell of TiB2 consists of 3atoms (1 formula unit)TheTiB2 crystal structure is presentedin Figure 2 Each Ti atom is surrounded by 12 equidistant Batoms whereas each B atom has 3 B atoms at a short distanceand 6 Ti atoms at a much longer distance The B-sublattice

Advances in Condensed Matter Physics 3

a a

cb

c

b

Figure 1 The 2 times 2 times 1 supercells of TiB Blue and green balls denote Ti and B atoms respectively Dashed box represents the unit cell of TiBcrystal

a

c

b ac

b

Figure 2 The 2 times 2 times 2 supercell of TiB2 Blue and green balls denote Ti and B atoms respectively Dashed box represents the unit cell ofTiB2 crystal

resembles that of graphitic carbonThe Ti-sublattice is nestedin the interstices provided by the B-sublattice

Typical X-ray diffraction spectra of commercial powderand bulk samples of TiB2 are shown in Figure 3 The XRDpatterns of powder and target TiB2 are very similar to eachother and the Rietveld analysis confirms that the samplescontain titanium diboride as a majority phase with the latticeconstants 119886powder = 30178 A 119888powder = 32160 A 119886target =30324 A and 119888target = 32345 A which correspond to otherexperimental studies [27] (119886 = 30292 A and 119888 = 32284 A)

The crystal structure of Ti3B4 is orthorhombic (spacegroup 119868119898119898119898 no 71) and isomorphous with that of Ta3B4[28]There are 2 nonequivalent B atoms at (4119894) and (4119895) latticesites Also Ti atoms reside in 2 different Wyckoff positionsnamely (2119889) and (4119894) Thus the primitive unit cell of Ti3B4contains 14 atoms The crystal structure of Ti3B4 is displayedin Figure 4

Parameters of the TiB TiB2 and Ti3B4 structures deter-mined at the ground state are summarized in Table 1 alongwith the available experimental data for comparison Ingeneral the calculated structural parameters of the TindashBcompounds remain in very good agreement with results ofthe previous experiments [26ndash28] Therefore our theoreticalbond lengths between boron atoms (BndashB) titanium andboron atoms (TindashB) and between titanium atoms (TindashTi)which are collected in Table 2 closely correspond to thoseobserved in experimental studies In all considered titaniumborides the shortest bond lengths (sim18 A) are found betweenB atoms The TindashB bonds are much longer (sim24 A) as

compared to BndashB bonds but shorter than the TindashTi bonds(sim29 A) The values of interatomic distances reflect thenature of bonding in titanium borides This has already beendiscussed in numerous theoretical studies considering theelectronic structure of these compounds [7ndash11] Results ofthe present research confirm that the chemical bonding inTiB TiB2 and Ti3B4 is a mixture between covalent ionicand metallic bonding Strong covalent bonds exist betweenB atoms while mixed metallic-covalent bonds are betweenTi atoms There is also a mixed ionic-covalent interactionbetween Ti and B atoms

32 Zone-Center Phonon Modes The optically active zone-center phonon modes in TiB TiB2 and Ti3B4 are eitherRaman-active (gerade) or infrared- (IR-) active (ungerade)due to the presence of inversion symmetry in these systemsThe Γ-point phonon modes in TiB can be decomposed intothe irreducible representations of the point group 119863162ℎ asfollows 4119860119892oplus2119860119906oplus21198611119892 oplus41198611119906oplus41198612119892 oplus21198612119906oplus21198613119892 oplus41198613119906Among them 3modes (1198611119906oplus1198612119906oplus1198613119906) are lattice translationalmodes and 119860119906 ones are silent (optically inactive) The modeswith symmetries 119860119892 1198611119892 1198612119892 and 1198613119892 are Raman-activewhereas modes 1198611119906 1198612119906 and 1198613119906 are IR-active Both Tiand B atoms occupying the (4119888) lattice positions contributeto the Raman and IR-active modes The optical IR modesof 1198611119906 and 1198613119906 symmetries correspond to the oscillationsof the dipole moment within the crystal ac-plane whereasthose of 1198612119906 symmetry to the oscillations parallel the crys-tal b-axis The 119860119892 and 1198612119892 phonons involve vibrations of


(201

)

(200

)(111

)(1

02)

(110

)(0

02)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Powder TiB2

2Θ (deg)

(a)

(201

)

(200

)(1

11)

(102

)

(110

)

(002

)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Target TiB2

2Θ (deg)

(b)

Figure 3 X-ray diffraction spectra of (a) powder (H C Starck Germany) and (b) bulk (target Goodfellow UK) samples of titanium diboride(TiB2) Experimental data and the Rietveld refinement are represented by symbols and curves respectively Small vertical lines indicatepositions of the Bragg peaks corresponding to the TiB2 phase The XRD peaks are indexed according to the reference 04-010-8469 [27]

a

a ccb

b

Figure 4 The 1 times 2 times 1 supercell of Ti3B4 Blue and green balls denote Ti and B atoms respectively Dashed box represents the unit cell ofTi3B4 crystal

Table 1 Structural parameters of TiB TiB2 and Ti3B4 determinedat the ground state and from experiments [26ndash28]

Parameter Present ExperimentTiB (119875119899119898119886 no 62) [26]

a (A) 61105 612b (A) 30504 306c (A) 45623 456Ti (4119888) (01772 14 01214) (0177 14 0123)B (4119888) (00298 14 05985) (0029 14 0603)

TiB2 (1198756119898119898119898 no 191) [27]a (A) 30336 30292c (A) 32261 32284Ti (1119886) (00 00 00) (00 00 00)B (2119889) (13 23 12) (13 23 12)

Ti3B4 (119868119898119898119898 no 71) [28]a (A) 32596 3259b (A) 137374 13737c (A) 30389 3036Ti1 (2119889) (12 12 00) (12 12 00)Ti2 (4119894) (00 01858 00) (00 018 00)B1 (4119894) (00 03684 00) (00 037 00)B2 (4119895) (00 04356 12) (00 044 12)

the Ti- and B-sublattices within the ac-plane while the1198611119892 and 1198613119892 phonons arise from atomic vibrations alongthe b-axis The frequencies of the Raman and IR-active

Table 2 Interatomic distances (in A) for titanium borides

Compound BndashB TindashB TindashTiTiB 181 235 287TiB2 175 238 303

Ti3B4

177 (B2ndashB2) 233 (Ti2ndashB2) 284 (Ti2ndashTi2)178 (B1ndashB1) 235 (Ti2ndashB1) 297 (Ti1ndashTi2)304 (B1ndashB2) 240 (Ti1ndashB2) 304 (Ti1ndashTi1)

243 (Ti1ndashB1)

phonon modes predicted by our calculations for TiB arelisted in Table 3 The silent 119860119906 modes are found at 2802and 4531 cmminus1 The IR modes gather into 2 bands withlower-frequency band located at sim250 cmminus1 and the higher-frequency band extending from about 470 to 560 cmminus1Similarly the Raman modes are also concentrated within 2bands The lower-frequency band ranges from about 260 to350 cmminus1 and the higher-frequency one from570 to 780 cmminus1

Phonons at the Brillouin zone center of the TiB2 structurecan be classified according to the irreducible representationsof the point group 11986316ℎ as follows 1198602119906 oplus 1198611119892 oplus 2119864

(2)2119892 oplus 2119864

(2)1119906

The modes with 1198602119906 and 1198641119906 symmetries are IR-active themodes of 1198642119892 symmetry are Raman-active and the 1198611119892 modeis silent Modes 1198642119892 and 1198641119906 remain doubly degenerate The1198602119906 oplus 119864

(2)1119906 phonons constitute lattice translational modes

The IR-active 1198602119906 and 1198641119906 modes are related to the dipolemoment oscillations perpendicular and parallel to the crystalhexagonal plane respectively In theRaman-active1198642119892modes


Table 3 Frequencies of the Raman and IR-active phonon modes inTiB Units cmminus1

Mode symmetry Raman Infrared1198611119906 2451198613119906 255119860119892 2591198613119892 2721198612119892 2931198611119892 299119860119892 3051198612119892 3471198613119906 4681198611119906 4941198612119906 4991198613119906 5421198611119906 564119860119892 5701198612119892 6071198612119892 634119860119892 6391198611119892 7601198613119892 780

the Ti atoms are at rest and hence these modes are onlyassociated with the B atoms vibrating within the hexagonalplane The 1198642119892 Raman phonon appears at 8831 cmminus1 and theinfrared 1198641119906 and1198602119906 phonons have frequencies of 5151 cm

minus1

and 5215 cmminus1 respectively The calculated frequency of thesilent 1198611119892 amounts to 5579 cmminus1 The frequencies of theRaman and infrared modes in TiB2 crystal determined in thepresent DFT studies closely correlated with those obtainedpreviously [12 13]

The Γ-point phonon modes in Ti3B4 can be decomposedinto the irreducible representations of the point group 119863252ℎ inthe following way 3119860119892 oplus 31198611119892 oplus 31198613119892 oplus 41198611119906 oplus 41198612119906 oplus41198613119906 where the Raman modes have symmetries of 119860119892 1198612119892and 1198613119892 The 1198611119906 1198612119906 and 1198613119906 modes are infrared-activeThere are 3 acoustic modes constituted by the IR phonons(Γacoustic = 1198611119906 oplus 1198612119906 oplus 1198613119906) The IR-active 1198611119906 1198612119906and 1198613119906 are associated with the oscillations of the dipolemoment along the crystallographic c b and a axes respec-tivelyTheTi1 atoms residing in (2119889) sites do not contribute tothe Raman modes Therefore the 119860119892 1198612119892 and 1198613119892 phononsresults from the displacements of Ti2 B1 and B2 atoms alongthe c a and b axes of the Ti3B4 crystal Respective frequenciesof the Raman and IR modes are collected in Table 4

33 Raman Spectra The Raman tensors of the 119860119892 1198611119892 1198612119892and 1198613119892 phonon modes in TiB have the following nonzerocomponents

119860119892 120572119909119909 = 119886

120572119910119910 = 119887

120572119911119911 = 119888

Table 4 Frequencies of the Raman and IR-active phonon modes inTi3B4 Units cm

minus1

Mode symmetry Raman Infrared1198613119892 2491198611119892 2631198611119906 2771198613119906 2871198612119906 313119860119892 3231198612119906 4831198611119906 4881198613119892 4991198611119892 5041198613119906 528119860119892 5501198613119906 5561198611119892 5741198612119906 7151198611119906 8041198613119892 829119860119892 835

1198611119892 120572119909119910 = 120572119910119909 = 119889

1198612119892 120572119909119911 = 120572119911119909 = 119890

1198613119892 120572119910119911 = 120572119911119910 = 119891

(1)

and the polarization selection rules [29] for the pointgroup 11986316ℎ allow the polarized Raman scattering experi-ments to determine phonons having particular symmetriesIn the backscattering geometry where the wave vector ofincident (ki) and scattered (ks) radiations remain antiparallelthe modes of 119860119892 symmetry can be measured for exampleat 119885(119883119883)119885 scattering configuration (in Portorsquos notation)In order to observe the 1198611119892 1198612119892 and 1198613119892 modes one needsto apply the 119885(119883119884)119885 119884(119883119885)119884 and 119883(119884119885)119883 scatteringgeometries respectivelyThepolarized backscatteringRamanspectra at scattering configurations outlined above are shownin Figure 5 One notes that not all Raman-activemodes of TiBare intense enough to be experimentally observed

The Raman spectrum of TiB2 single crystal is charac-terized by a single peak due to the mode of 1198642119892 symmetrywhich can be detected at 119885(119883119884)119885 scattering geometry Thecorresponding Raman tensor of the doubly degenerate 1198642119892phonon mode has the following form

119864(1)2119892 120572119909119909 = 119889

120572119910119910 = minus119889

119864(2)2119892 120572119909119910 = 120572119910119909 = minus119889

(2)

The Raman tensors of the 119860119892 1198611119892 and 1198613119892 modes inTi3B4 crystal are defined in the same manner as for the TiB


Inte

nsity

200 300 400 500 600 700 800Raman shift (cmminus1)

AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)

Figure 5 Backscattering Raman spectra of TiB crystal calculated at scattering geometries (a) 119885(119883119883)119885 (b) 119885(119883119884)119885 (c) 119884(119885119883)119884 and(d) 119883(119884119885)119883 Spectra are simulated at 300K and with laser excitation wavelength of 532 nm Peaks are represented by Lorentzian functionswith artificial FWHMs of 2 cmminus1

Inte

nsity

(arb

uni

ts)

200 300 400 500 600 700 800 900Raman shift (cmminus1)

Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)

Figure 6 Backscattering Raman spectra of Ti3B4 crystal calculated at scattering geometries (a) 119885(119883119883)119885 (b) 119885(119883119884)119885 and (c) 119883(119884119885)119883Spectra are simulated at 300K and with laser excitation wavelength of 532 nm Peaks are represented by Lorentzian functions with artificialFWHMs of 2 cmminus1

crystal (see (1)) Therefore one determines the 119860119892 1198611119892 and1198613119892 phonons in Ti3B4 by using the same scattering geometriesas those given for orthorhombic TiB crystal The resultingRaman spectra are presented in Figure 6

In majority of cases experimental characterization of theTindashB material by using the Raman spectroscopy is basedon measurements performed on powder samples and hencethe resulting spectra of polycrystalline materials may differfrom those for single crystals Indeed the simulated unpo-larized Raman spectra in backscattering geometry of TiBTiB2 and Ti3B4 polycrystals which are shown in Figure 7remain quite distinct from the polarized spectra of therespective single crystals given in Figures 5 and 6 First of all

not all Raman-active modes are observed due to their weakintensities The peaks of TiB and Ti3B4 polycrystals originatefrom phonons of the 119860119892 symmetry Therefore the unpo-larized Raman spectrum of multiphase TindashB system mayconsist of three bands The low-frequency (240ndash360 cmminus1)andmiddle-frequency (520ndash680 cmminus1) bands are expected tobe dominated by themodes of TiB and Ti3B4 phases whereasthe high-frequency band (800ndash900 cmminus1) is expected to bedominated by the modes of TiB2 and Ti3B4 phases

According to the group symmetry analysis the TiB2compound exhibits a single doubly degenerate Raman-activemode of 1198642119892 symmetry which should be revealed by theRaman spectra of either a single crystal or polycrystalline


Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4


Figure 7 Unpolarized Raman spectra of TiB TiB2 and Ti3B4 poly-crystals calculated at backscattering geometries Spectra are simu-lated at 300K and with laser excitation wavelength of 532 nm Peaksare represented by Lorentzian functions with artificial FWHMs of2 cmminus1

Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)

Figure 8 Experimental Raman spectrum of commercial TiB2powder (H C Starck Germany) measured at room temperaturewith laser excitation wavelength of 532 nm

samples However a typical Raman spectrum of TiB2commercial powder sample shows more rich experimentalpattern than that predicted theoretically Such spectrumis presented in Figure 8 It shows a small intensity peakat 143 cmminus1 and broad high-intensity peaks at 260 420and 610 cmminus1 These peaks are characteristic for rutile tita-nium dioxide (TiO2) phase whose vibrational spectrumhas 4 vibrational bands centered around 145 cmminus1 (1198611119892)445 cmminus1 (119864119892) 610 cm

minus1 (1198601119892) and 240 cmminus1 for second-order scattering effect (SOE) [30 31] We note that similarspectrum was also obtained for commercial powder TiB2although with slightly different positions of the Ramanpeaks (260 409 and 598 cmminus1) and it was assigned to theanatase phase of TiO2 [32] Our spectrum is unlikely torepresent powder anatase TiO2 as such spectrum usuallyshows 5 Raman modes centered around 144 cmminus1 (119864119892)

1089

1000

827

728

Target sample

532

480

318

271

200 400 600 800 1000 1200Raman shift (cmminus1)

Inte

nsity

(arb

uni

ts)

881

(TiB

2)

Figure 9 Experimental Raman spectrum of commercial TiB2target (Goodfellow UK) measured at room temperature with laserexcitation wavelength of 532 nm

196 cmminus1(119864119892) 394 cmminus1 (1198611119892) 516 cm

minus1 (1198611119892 + 1198601119892) and638 cmminus1 (119864119892) [30 33 34] Moreover the characteristicfeature of anatase spectrum is the high-intensity peak at144 cmminus1 which dominates over the remaining peaks hav-ing comparably smaller intensities In addition the high-frequency range of our spectrum reveals two quite intensepeaks at about 1360 and 1570 cmminus1 indicating the presence ofgraphitic carbon with 1199041199012 and 1199041199013 bonds [35] Neverthelesswe confirm that even a small amount of contaminating phasesuch as TiO2 and unreacted carbon being by-products of thecarbothermal reduction process employed to fabricate TiB2powder according to the following reaction [36]

TiO2 + B2O3 + 5C 997888rarr TiB2 + 5CO uarr (3)

can prevail in the Raman spectrum of commercial TiB2powder

TiB2 can also be prepared by reduction of TiO2 by boroncarbide (B4C) and carbon as follows [37]

2TiO2 + B4C + 3C 997888rarr 2TiB2 + 4CO uarr (4)

The above procedure is frequently applied to produce com-mercial targets of TiB2 Thus the Raman spectrum of suchtarget usually shows a dominant contribution from the by-products of synthesis and consolidation reactions as shownin Figure 9 Here the main peaks appearing at 271 318 480532 728 827 1000 and 1089 cmminus1 are associated with theamorphous B4C phase which displays characteristic Ramanbands at 270 320 481 531 728 830 1000 and 1088 cmminus1[38ndash40] Additionally one detects a weak feature at about970 cmminus1 which is also visible in the previously measuredspectra of crystalline and amorphous boron carbide [39 40]Besides our Raman spectrum of target sample reveals apeak at 881 cmminus1 being an evidence of the presence of TiB2phase for which a Raman peak was predicted by our DFTcalculations at 883 cmminus1


4 Summary and Conclusions

The present work reports on experimental Raman spectraof commercially available powder and bulk samples of tita-nium diboride It is shown that micro-Raman spectroscopyenables identification of impurity phases contained in thesamples even though their concentration remains below1wt Detailed analysis uncover contamination of commer-cial TiB2 powder and bulk samples by TiO2 and B4C phasesrespectively which are the by-products of chemical reac-tions applied to produce samples Additionally the graphiticcarbon is identified as a fingerprint of sintering aids usedin production process of bulk TiB2 Vibrational propertiesof titanium borides (TiB TiB2 and Ti3B4) in particularpositions and intensities of the Raman-active phonons weregained from theoretical approach based on the DFTmethodTheoretical Raman spectra were simulated at conditions closeto those encountered in experiments and for ideal crystalsnamely free of defects and residual stresses which are alwayspresent in real samples due to their preparation procedureThus our ab initio results can serve not only as a guide forinterpretation of experimental Raman spectra or symmetrymode assignment in particular titanium borides but also forestimation of effects connected with macrostresses and theirinfluence on positions and intensities of themeasured Ramanpeaks

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

Interdisciplinary Center for Mathematical and Compu-tational Modeling (ICM) Warsaw University Poland isacknowledged for providing the computer facilities underGrant no G28-12

References

[1] J L Murray P K Liao and K E Spear ldquoThe B-Ti (Boron-Titanium) systemrdquo Bulletin of Alloy Phase Diagrams vol 7 no6 pp 550ndash555 1986

[2] V I Matkovich Boron and Refractory Borides Springer BerlinGermany 1977

[3] R GMunro ldquoMaterial properties of titaniumdiboriderdquo Journalof Research of the National Institute of Standards and Technologyvol 105 no 5 pp 709ndash720 2000

[4] M Gu C Huang B Zou and B Liu ldquoEffect of (Ni Mo) andTiN on the microstructure and mechanical properties of TiB2ceramic tool materialsrdquo Materials Science and Engineering Avol 433 no 1-2 pp 39ndash44 2006

[5] P H Mayrhofer C Mitterer L Hultman and H ClemensldquoMicrostructural design of hard coatingsrdquo Progress in MaterialsScience vol 51 no 8 pp 1032ndash1114 2006

[6] A Twardowska ldquoOn mechanical and friction-wear propertiesof TiBx coated alumina sintersrdquoMechanik no 5-6 pp 492ndash4932016

[7] D-C Tian and X-B Wang ldquoElectronic structure and equationof state of TiB2rdquo Journal of Physics CondensedMatter vol 4 no45 pp 8765ndash8772 1992

[8] P Vajeeston P Ravindran C Ravi and R Asokamani ldquoElec-tronic structure bonding and ground-state properties of AlB2-type transition-metal diboridesrdquo Physical Review B vol 63 no4 Article ID 045115 12 pages 2001

[9] K B Panda and K S R Chandran ldquoFirst principles determi-nation of elastic constants and chemical bonding of titaniumboride (TiB) on the basis of density functional theoryrdquo ActaMaterialia vol 54 no 6 pp 1641ndash1657 2006

[10] L Sun Y Gao B Xiao Y Li and G Wang ldquoAnisotropic elasticand thermal properties of titanium borides by first-principlescalculationsrdquo Journal of Alloys and Compounds vol 579 pp457ndash467 2013

[11] G Wang Y Li Y Gao Y Cheng and S Ma ldquoTheoretical studyof structural mechanical thermal and electronic properties ofTi3B4 withTa3B4 structure under high pressurerdquoComputationalMaterials Science vol 104 pp 29ndash34 2015

[12] R Heid B Renker H Schober P Adelmann D Ernst and K-P Bohnen ldquoLattice dynamics and electron-phonon coupling intransition-metal diboridesrdquo Physical Review B vol 67 no 18Article ID 180510 pp 1ndash4 2003

[13] E Deligoz K Colakoglu and Y Ciftci ldquoLattice dynamicalproperties of SCB2 TiB2 and VB2 compoundsrdquo Solid StateCommunications vol 149 no 41-42 pp 1843ndash1848 2009

[14] G Kresse and J Furthmuller ldquoEfficient iterative schemes forab initio total-energy calculations using a plane-wave basis setrdquoPhysical Review B vol 54 no 16 pp 11169ndash11186 1996

[15] G Kresse and J Furthmuller ldquoEfficiency of ab-initio totalenergy calculations for metals and semiconductors using aplane-wave basis setrdquo Computational Materials Science vol 6no 1 pp 15ndash50 1996

[16] J P Perdew K Burke andM Ernzerhof ldquoGeneralized gradientapproximation made simplerdquo Physical Review Letters vol 77no 18 pp 3865ndash3868 1996

[17] J P Perdew K Burke andM Ernzerhof ldquoGeneralized gradientapproximation made simple [Phys Rev Lett 77 3865 (1996)]rdquoPhysical Review Letters vol 78 no 7 p 1396 1997

[18] K Parlinski Z Q Li andY Kawazoe ldquoFirst-principles determi-nation of the soft mode in cubic ZrO2rdquo Physical Review Lettersvol 78 no 21 article 4063 1997

[19] K Parlinski Software PHONONver 615 Cracow Poland 2015[20] M Cardona Ed Light Scattering in Solids I vol 8 of Topics in

Applied Physics Springer Berlin Germany 1983[21] P Umari A Pasquarello and A Dal Corso ldquoRaman scattering

intensities in 120572-quartz a first-principles investigationrdquo PhysicalReview B vol 63 no 9 Article ID 094305 2001

[22] P Umari X Gonze andA Pasquarello ldquoConcentration of smallring structures in vitreous silica from a first-principles analysisof the Raman spectrumrdquo Physical Review Letters vol 90 no 2Article ID 027401 2003

[23] M Gajdos K Hummer G Kresse J Furthmuller and F Bech-stedt ldquoLinear optical properties in the projector-augmentedwave methodologyrdquo Physical Review B vol 73 no 4 Article ID045112 2006

[24] U D Wdowik A Twardowska and M Medala-Wasik ldquoLatticedynamics of binary and ternary phases in Ti-Si-C system acombined Raman spectroscopy and density functional theorystudyrdquo Materials Chemistry and Physics vol 168 pp 58ndash652015


[25] U D Wdowik M Wasik and A Twardowska ldquoInfluence ofcarbon dopants on the structure elasticity and lattice dynamicsof Ti5Si3C119909 Nowotny phasesrdquo Modelling and Simulation inMaterials Science and Engineering vol 24 Article ID 0250012016

[26] B F Decker and J S Kasper ldquoThe crystal structure of TiBrdquoActaCrystallographica vol 7 no 1 pp 77ndash80 1954

[27] S Mohr H Muller-Buschbaum Y Grim and H G vonSchnering ldquoHndashTiO oder TiB2-eine Korrekturrdquo Zeitschrift furAnorganische und Allgemeine Chemie vol 622 no 2 pp 1035ndash1037 1996

[28] K E Spear P Mcdowell and F Mcmahon ldquoExperimentalevidence for the existence of the Ti3B4 phaserdquo Journal of theAmerican Ceramic Society vol 69 no 1 pp C-4ndashC-5 1986

[29] R Loudon ldquoThe Raman effect in crystalsrdquo Advances in Physicsvol 50 no 7 pp 813ndash864 2001

[30] O Frank M Zukalova B Laskova J Kurti J Koltai and LKavan ldquoRaman spectra of titanium dioxide (anatase rutile)with identified oxygen isotopes (16 17 18)rdquo Physical ChemistryChemical Physics vol 14 no 42 pp 14567ndash14572 2012

[31] Y Zhang C X Harris P Wallenmeyer J Murowchick andX Chen ldquoAsymmetric lattice vibrational characteristics ofrutile TiO2 as revealed by laser power dependent ramanspectroscopyrdquo Journal of Physical Chemistry C vol 117 no 45pp 24015ndash24022 2013

[32] Lrsquo Baca and N Stelzer ldquoAdapting of solndashgel process for prepa-ration of TiB2 powder from low-cost precursorsrdquo Journal of theEuropean Ceramic Society vol 28 no 5 pp 907ndash911 2008

[33] V Swamy A Kuznetsov L S Dubrovinsky R A Caruso D GShchukin and B CMuddle ldquoFinite-size and pressure effects onthe Raman spectrum of nanocrystalline anatase TiO2rdquo PhysicalReview B - Condensed Matter and Materials Physics vol 71 no18 Article ID 184302 2005

[34] X Chen and S S Mao ldquoTitanium dioxide nanomaterials syn-thesis properties modifications and applicationsrdquo ChemicalReviews vol 107 no 7 pp 2891ndash2959 2007

[35] F Tuinstra and J L Koenig ldquoRaman spectrum of graphiterdquoTheJournal of Chemical Physics vol 53 no 3 pp 1126ndash1130 1970

[36] R V Krishnarao and J Subrahmanyam ldquoStudies on the for-mation of TiB2 through carbothermal reduction of TiO2 andB2O3rdquoMaterials Science and Engineering A vol 362 no 1-2 pp145ndash151 2003

[37] C Subramanian T S R C Murthy and A K Suri ldquoSynthesisand consolidation of titanium diboriderdquo International Journalof Refractory Metals and Hard Materials vol 25 no 4 pp 345ndash350 2007

[38] X Q Yan W J Li T Goto and M W Chen ldquoRaman spec-troscopy of pressure-induced amorphous boron carbiderdquoApplied Physics Letters vol 88 no 13 Article ID 131905 2006

[39] J Guo L Zhang T Fujita T Goto and M Chen ldquoPressure-induced depolarization and resonance in Raman scattering ofsingle-crystalline boron carbiderdquo Physical Review B vol 81 no6 Article ID 060102 2010

[40] K M Reddy P Liu A Hirata T Fujita and M W ChenldquoAtomic structure of amorphous shear bands in boron carbiderdquoNature Communications vol 4 article 2483 2013

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


theory and the direct methodWe also provide interpretationof the Raman spectra measured for commercially availablepowder and bulk samples of titanium diboride Results ofthese studies are hoped to stimulate further experimental andtheoretical progress in the field of TindashB system

2 Methodology

21 Experimental Experimentswere performed for commer-cial TiB2 powder (H C Starck Germany) and bulk (targetGoodfellow UK) samplesThe grain size of TiB2 powder withpurity of about 99wt was in the range 25ndash35 120583mThe tar-get sample of 30mm in diameter and 4mm in thickness wasmechanically polished on one side using diamond grinding(9 6 and 3 120583m) and finally polished in 1 120583m suspensionAt each polishing step the surface was degreased by 2-Propanol and then ultrasonically cleaned in acetone bathfor 5 minutes After drying (in air) the target was mountedin a vacuum chamber to perform ion cleaning at roomtemperature and pressure of 10minus2 Pa The iron cleaning wasdone by a beam of Ar+ ions of energy of 10 keV directedat sample at an angle of 65∘ (measured to the normal oftarget surface) Such preparation procedure is required for theRamanmeasurements as the spectrometer used in our studiesis equipped with the confocal (light) microscope Moreoverthe target is further used for deposition of TiB2 thin films bythe PVDmethod (results not discussed in the present paper)

Phase identification was performed by the X-ray diffrac-tion (XRD) method using PANalytical Empyrean diffrac-tometer The CuK120572 radiation (intended 120582 = 15406 Aintensity ratio CuK120572

1

CuK1205722

= 2 119880 = 40 kV I = 30mA) inthe Bragg-Brentano configuration was used for this purposeThe XRD patterns were collected in 2Θ geometry over thescattering angles ranging from 20∘ to 82∘ with a step sizeof 002∘ Analysis was performed according to the ICSDdatabase and the Rietveld method which took into accountthe ratio CuK120572

1

CuK1205722

= 2The Raman spectroscopy was applied to refine the phase

composition of both powder and bulk (target) samples Toexcite Raman spectra the NdYAG laser beam with wave-length of 532 nm and a power of 625mW was used Unpo-larized Raman spectra in backscattering geometry were col-lected at room temperature using theThermo-Nicolet RamanALMEGA XR dispersive confocal spectrometer operating inthe micro-Raman mode Raman spectra were recorded withnormal (4 cmminus1) and high-spectral (2 cmminus1) resolutions

22 Theoretical Calculations were carried out within theDFT method implemented in the VASP code [14 15]Electron-ion interaction was represented by the projectoraugmented wave (PAW) method The generalized gradientapproximation with parametrization of Perdew Burke andErnzerhof (GGA-PBE) [16 17] was applied for the exchangeand correlation potential The wavefunctions were expandedin a plane-wave basis set with a cutoff energy of 420 eVReference configurations for valence electrons were (3d34s1)for Ti and (2s22p1) for B Lattice constants and internalatomic positions of TiB TiB2 and Ti3B4 unit cells were

fully optimized with convergence criteria for the residualHellman-Feynmann (HF) forces and the systemrsquos total energyof 10minus5 eV Aminus1 and 10minus7 eV respectively The Brillouin zonesof TiB TiB2 and Ti3B4 were sampled using respectively54 96 and 50 irreducible k-points generated accordingto the Monkhorst-Pack scheme Phonon calculations wereperformed within the direct method approach [18 19] andharmonic approximation The HF forces were obtained bydisplacing the symmetry nonequivalent Ti and B atomsfrom their equilibrium positions by plusmn002 A in the supercellscontaining 64 atoms (TiB) 92 atoms (TiB2) and 112 atoms(Ti3B4) The HF forces were calculated with reduced numberof k-points The total number of calculated displacementsamounted to 12 for TiB 6 for TiB2 and 24 for Ti3B4 Peakintensities of the nonresonant Raman spectrum (in Stokesprocess) were calculated from the well-known expression[20] 119868 prop |esRei|2120596minus1(119899 + 1) where (119899 + 1) is the populationfactor for Stokes scattering with 119899 = [exp(ℏ120596119896119861119879) minus 1]

minus1

denoting the Bose-Einstein thermal factor ei (es) is thepolarization of the incident (scattered) radiation and R isthe Raman susceptibility tensorThe components of R tensor(120572119894119895) were determined from derivatives of the electric polar-izability tensor over the atomic displacements [19 21 22]The electric polarizabilities were calculated within the linear-response method [23] and for each symmetry nonequivalentatomwas displaced from its equilibrium position by plusmn001 ADetails of calculations can also be found elsewhere [24 25]We also note that anharmonic effects leading to changes inphonon frequencies and reflected by shifts of the Ramanpeaksrsquo positions have been neglected This is mainly becauseour measurements are performed at room temperaturewhere the effects related to the thermal expansion of com-pounds from the TindashB system are negligible Also the effectof anharmonicity on the widths of Raman peaks is notconsidered in the present work Thus the Raman peaks aresimulated by Lorentzian functions with artificial FWHMscorresponding to energy resolution of the Raman spectrom-eter used in our studies

3 Results and Discussion

31 Structural Properties Titanium monoboride (TiB) crys-tallizes in the orthorhombic FeB structure with the spacegroup 119875119899119898119886 (no 62) [26] where both Ti and B atomsoccupy (4119888) lattice sites Its primitive unit cell consists of 8atoms (4 formula units)Themain building block of TiB is thetrigonal prism with the B atom at the center and the Ti atomsin corners The transverse stacking of the trigonal prisms incolumnar arrays leads to a zig-zag chain of B atoms alongthe [010] direction as schematically shown in Figure 1

Titanium diboride (TiB2) has hexagonal layered struc-ture of AlB2-type (space group 1198756119898119898119898 no 191) with Tiand B atoms located respectively at (1119886) and (2119889) Wyckoffpositions [27] The primitive unit cell of TiB2 consists of 3atoms (1 formula unit)TheTiB2 crystal structure is presentedin Figure 2 Each Ti atom is surrounded by 12 equidistant Batoms whereas each B atom has 3 B atoms at a short distanceand 6 Ti atoms at a much longer distance The B-sublattice


a a

cb

c

b


a

c

b ac

b









(201

)

(200

)(111

)(1

02)

(110

)(0

02)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Powder TiB2

2Θ (deg)

(a)

(201

)

(200

)(1

11)

(102

)

(110

)

(002

)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Target TiB2

2Θ (deg)

(b)


a

a ccb

b




a (A) 61105 612b (A) 30504 306c (A) 45623 456Ti (4119888) (01772 14 01214) (0177 14 0123)B (4119888) (00298 14 05985) (0029 14 0603)

TiB2 (1198756119898119898119898 no 191) [27]a (A) 30336 30292c (A) 32261 32284Ti (1119886) (00 00 00) (00 00 00)B (2119889) (13 23 12) (13 23 12)





Ti3B4


243 (Ti1ndashB1)



(2)2119892 oplus 2119864

(2)1119906








minus1




119860119892 120572119909119909 = 119886

120572119910119910 = 119887

120572119911119911 = 119888


minus1


1198611119892 120572119909119910 = 120572119910119909 = 119889

1198612119892 120572119909119911 = 120572119911119909 = 119890

1198613119892 120572119910119911 = 120572119911119910 = 119891

(1)



119864(1)2119892 120572119909119909 = 119889

120572119910119910 = minus119889

119864(2)2119892 120572119909119910 = 120572119910119909 = minus119889

(2)



Inte

nsity


AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)


Inte

nsity

(arb

uni

ts)


Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)







Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




a a

cb

c

b


a

c

b ac

b









(201

)

(200

)(111

)(1

02)

(110

)(0

02)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Powder TiB2

2Θ (deg)

(a)

(201

)

(200

)(1

11)

(102

)

(110

)

(002

)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Target TiB2

2Θ (deg)

(b)


a

a ccb

b




a (A) 61105 612b (A) 30504 306c (A) 45623 456Ti (4119888) (01772 14 01214) (0177 14 0123)B (4119888) (00298 14 05985) (0029 14 0603)

TiB2 (1198756119898119898119898 no 191) [27]a (A) 30336 30292c (A) 32261 32284Ti (1119886) (00 00 00) (00 00 00)B (2119889) (13 23 12) (13 23 12)





Ti3B4


243 (Ti1ndashB1)



(2)2119892 oplus 2119864

(2)1119906








minus1




119860119892 120572119909119909 = 119886

120572119910119910 = 119887

120572119911119911 = 119888


minus1


1198611119892 120572119909119910 = 120572119910119909 = 119889

1198612119892 120572119909119911 = 120572119911119909 = 119890

1198613119892 120572119910119911 = 120572119911119910 = 119891

(1)



119864(1)2119892 120572119909119909 = 119889

120572119910119910 = minus119889

119864(2)2119892 120572119909119910 = 120572119910119909 = minus119889

(2)



Inte

nsity


AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)


Inte

nsity

(arb

uni

ts)


Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)







Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




(201

)

(200

)(111

)(1

02)

(110

)(0

02)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Powder TiB2

2Θ (deg)

(a)

(201

)

(200

)(1

11)

(102

)

(110

)

(002

)

(101

)

(100

)

(001

)

Inte

nsity

(arb

uni

ts)

20 25 30 35 40 45 50 55 60 65 70 75 80

Target TiB2

2Θ (deg)

(b)


a

a ccb

b




a (A) 61105 612b (A) 30504 306c (A) 45623 456Ti (4119888) (01772 14 01214) (0177 14 0123)B (4119888) (00298 14 05985) (0029 14 0603)

TiB2 (1198756119898119898119898 no 191) [27]a (A) 30336 30292c (A) 32261 32284Ti (1119886) (00 00 00) (00 00 00)B (2119889) (13 23 12) (13 23 12)





Ti3B4


243 (Ti1ndashB1)



(2)2119892 oplus 2119864

(2)1119906








minus1




119860119892 120572119909119909 = 119886

120572119910119910 = 119887

120572119911119911 = 119888


minus1


1198611119892 120572119909119910 = 120572119910119909 = 119889

1198612119892 120572119909119911 = 120572119911119909 = 119890

1198613119892 120572119910119911 = 120572119911119910 = 119891

(1)



119864(1)2119892 120572119909119909 = 119889

120572119910119910 = minus119889

119864(2)2119892 120572119909119910 = 120572119910119909 = minus119889

(2)



Inte

nsity


AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)


Inte

nsity

(arb

uni

ts)


Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)







Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







minus1




119860119892 120572119909119909 = 119886

120572119910119910 = 119887

120572119911119911 = 119888


minus1


1198611119892 120572119909119910 = 120572119910119909 = 119889

1198612119892 120572119909119911 = 120572119911119909 = 119890

1198613119892 120572119910119911 = 120572119911119910 = 119891

(1)



119864(1)2119892 120572119909119909 = 119889

120572119910119910 = minus119889

119864(2)2119892 120572119909119910 = 120572119910119909 = minus119889

(2)



Inte

nsity


AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)


Inte

nsity

(arb

uni

ts)


Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)







Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Inte

nsity


AgZ(XX)Z

(arb

uni

ts)

(a)


B1g Z(XY)Z

Inte

nsity

(arb

uni

ts)

(b)


B2g Y(XZ)Y

Inte

nsity

(arb

uni

ts)

(c)


B3g X(YZ)X

Inte

nsity

(arb

uni

ts)

(d)


Inte

nsity

(arb

uni

ts)


Ag Z(XX)Z

(a)

Inte

nsity

(arb

uni

ts)


B1g Z(XY)Z

(b)

Inte

nsity

(arb

uni

ts)


B3g X(YZ)X

(c)







Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Inte

nsity

(arb

uni

ts)

TiBTiB2

Ti3B4



Powder sample

610

420

260 (SOE)

143


Inte

nsity

(arb

uni

ts)




1089

1000

827

728

Target sample

532

480

318

271


Inte

nsity

(arb

uni

ts)

881

(TiB

2)












Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






Competing Interests


Acknowledgments


References















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics

























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Documents

Vibrational Spectroscopy of Binary Titanium Borides: First ...downloads.hindawi.com/journals/acmp/2017/4207301.pdf · ResearchArticle Vibrational Spectroscopy of Binary Titanium Borides: