evolution mechanism of metallic dioxide mo from nanorods...

Research ArticleEvolution Mechanism of Metallic Dioxide MO2 (M = Mn Ti)from Nanorods to Bulk Crystal First-Principles Research

Pengsen Zhao1 Guifa Li 1 Bingtian Li1 Haizhong Zheng1 Shiqiang Lu1 and Ping Peng2

1Key Laboratory of Jiangxi Province for Persistent Pollutants Control and Resources Recycle Nanchang Hangkong UniversityJiangxi 330063 China2School of Material Science and Engineering Hunan University Hunan 410082 China

Correspondence should be addressed to Guifa Li lgf 918126com

Received 23 November 2017 Accepted 4 March 2018 Published 4 April 2018

Academic Editor Nageh K Allam

Copyright copy 2018 Pengsen Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Using first-principle calculations the surface energy cohesive energy and electronic properties of 120572-MnO2 and rutile TiO2nanorods and microfacets were investigated and clarified to in the first instance determine the evolution mechanism The resultsshow that the surface energies of 120572-MnO2 nanorods and microfacets conform to function 10401 Jmminus2 + N times 0608 Jmminus2 while thesurface energies of the rutile TiO2 nanorods and microfacets are governed by a 10102 times 11997 rule Their electronic propertiessuch as the Mulliken population and Mulliken charge can only be normalized by their surface areas to attain a linear functionMeanwhile the surface energy of 120572-MnO2 with the nanostructure closely conforms to the function for normalized Mullikenpopulation and Mulliken charge as 119891(119909) = 1029 times 119909 + 0101 with an 1198772 value of 0995 Thus our research into the evolutionmechanism affecting the surface effect of nanometer materials will be useful for investigating the intrinsic mechanism of thenanometer effect and doping process of metallic dioxide catalysts

1 Introduction

TiO2 which is a vital inorganic functional nanomaterial hasbeen widely used in down-flop pigments ultraviolet screen-ing photoelectric conversion photocatalysis and so on [1]MnO2 is a popular and cost-effectivematerial for the removalof pollutants in air water and industry [2] Both have beenwidely investigated and improved to enhance their catalyticperformance such as by doping with metallic elements [1 3]incorporation into carbon nanotubes [4] andmanufacturingwith a nanometer structure [5] Especially in the nanocrys-tallization process the TiO2 and MnO2 nanometer materialsexhibit additional surface and nanometer effects althoughthey have the same components and skeleton units as thebulk morphology Both have been successfully applied tocatalytic redox for some pollutants But they exhibit differentcatalytic capabilities for the same reactant in somewhere Toremove arsenite oxidation the arsenite (AsIII) is oxidized toAsV for more than 04 hours by manganese dioxide andthe Mn-As bond length is from 0271 nm to 034 nm [6]For the rutile TiO2 however it is found that the Ti-As

bond length is from0283 nm to 0405 nm and the adsorptionenergy of AsV on TiO2(110) is greater than that on MnO2[7] Regarding the decomposition of CO Chen et al [8]indicated that the CO adsorbed onto the anatase TiO2resulted in a moderate adsorption energy (about 03 eV)and a positive shift of the C-O stretching frequency (about+44 cmminus1) whereas the CO could no longer be adsorbedonto the MnO2 [9] Considering the adsorption of O2 ontoMnO2 the oxygen reduction reaction can occur either insolution [10] or in air [11] Meanwhile Petrik and Kimmel[12] stated that O2 could be adsorbed onto rutile TiO2 only atvery low temperaturesTheir different catalytic activities haveattracted the attention ofmany researchers Barnard et al [13]had modeled the electronic properties of TiO2 nanoparticlesand pointed out that the free energy of surface would keepconstant after the sizes of nanoparticles were larger than100 nm [14] After studying a series of low stoichiometricsurfaces they found the effects of edges and corners wereomitted when the nanoparticles were larger than sim2 nm andconstructed the morphology of rutile TiO2 only composedby 110Miller index [15] Nevertheless Deringer and Csanyi

HindawiJournal of NanomaterialsVolume 2018 Article ID 9890785 14 pageshttpsdoiorg10115520189890785

2 Journal of Nanomaterials

[16] andTompsett et al [17] discovered that nanorods of rutileTiO2 and 120572-MnO2 have the same equilibrium geometricmorphologies with a structure consisting mainly of 100and 110 Miller indexes Furthermore Hummer et al [18]pointed out that the surface energies of TiO2 were dependentwith edges and corners of nanocrystal at particle size le3 nmAt present former researches do not identify the intrinsicmechanism between bulk and nanorods although they havestudied the nanoscale morphology of rutile TiO2 and 120572-MnO2 for a long time But such an intrinsic mechanism playsa vital role in the design and optimization of metallic oxidenanomaterials In a previous paper [19] it have been statedthat there may be an optimal 120572-MnO2 nanorod which hasa surface energy suitable for promoting enhanced surfaceactivity together with an appropriate degree of cohesiveenergy for maintaining structural stability As an extension ofpreviouswork the present study further sets out to investigatethe evolutionmechanism of bulk and nanorods of MO2 (M =Mn Ti) metallic dioxide

2 Simulation Models and Method

To elucidate the nanometer effect of metallic dioxideMO2 (M = MnTi) with a nanostructure several modelsof MO2 (M = MnTi) in crystal bulk surface nanorodand microfacet topological configurations were constructedand studied systematically according to their stoichiomet-ric proportions Their corresponding simulated models areshown in Figures 1 and 2 Regarding the rutile TiO2 modelconstruction only two prominent and stable Miller indexplanes such as 100 and 110 are considered In the presentstudy the 120572-MnO2 and rutile TiO2 nanorod models wereconstructed based on the experimental results obtained byBarnard et al [13ndash15] and Deringer and Csanyi [16] All thesimulation models are shown in Figure 2 For the rutile TiO2(100) bulk surface there are triple units of 100 Miller indexslabs while for the 110 bulk surfaces there are double110 Miller index slabs as shown in Figures 2(b) and 2(c)respectively A microfacet rutile TiO2 [(100 times 110)] supercellstructure containing only double units of 100 and 110Miller index slabs which had been proven to exhibit a similarcatalysis performance as a nanostructure [19 22] was built asa bulk surface with nanometer morphologies only as shownin Figure 2(d) Regarding the nanorod (NR) models all ofthem were combined with only 110 and 100 Miller indexslabs as shown in Figures 2(e)ndash2(g) (In our future workfurther Miller index slabs will be considered to represent amore complicated situation)The smallest nanorod addressedin the present study that is (NR(1)) consisting of two110 and one 100 Miller index slab unit was built as aTi32O64 supercell as shown in Figure 2(e) The second rutileTiO2 nanorod (NR(2)) contains two units each of 100 and110 Miller index slabs to construct a Ti52O104 supercell(Figure 2(f)) The largest rutile TiO2 nanorod contains triple110 and double 100Miller index slab units named NR(3)which form a Ti88O176 supercell (Figure 2(g)) Similar wayof constructed configuration is forced to 120572-MnO2 nanorodsThe latter is the largest that can be handled in the calculationlimits of our computer cluster All these primitive nanorods

can be regarded as being free nanomaterials in morphologiesby using their periodic boundary conditions and transitionalsymmetryThe purpose of such constructions is to investigatethe surface effect of different Miller indices over severalmodels All the bulk surfacemodels were calculated assumingslabswith aminimum thickness of 14 A In all the bulk surfaceand nanorod models a separating vacuum distance of atleast 12 A was used to distance the slabs from their periodicimage For the first step all of themodels were not terminatedby hydrogenation as followed by Barnard et alrsquos report [13]The complicated surface models of metallic dioxide MO2(M = Mn Ti) will be studied in our further research Todistinguish the difference between 120572-MnO2 and rutile TiO2in similar configurations every simulated model was labeledldquoMrdquo or ldquoTrdquo to represent the 120572-MnO2 and rutile TiO2 seriesrespectively For example the (100) bulk surface for 120572-MnO2was labeled M(100) while T(100) represents the (100) bulksurface for rutile TiO2 This convention is used for everymodel shown in Figures 1 and 2

Based on the calculated sets of Deringer and Csanyi[16] all the above 120572-MnO2 and rutile TiO2 simulationmodels were relaxed by applying the following process afirst-principles pseudopotential plane-wave method basedon density functional theory was implemented in the Cam-bridge Sequential Total Energy Package (CASTEP) code [23]The electronic structure was calculated using the GeneralizedGradient Approximation (GGA) devised by Perdew et alwith a Tkatchenko-Scheffler approach (TS) being used forthe dispersion corrections [16] The PBE + U exchange-correlation function has been demonstrated to give a gooddescription of the defect properties in 120572-MnO2 [17] All cal-culations were performed in a ferromagnetic spin polarizedconfiguration while effects of more complexmagnetic orderswere left for future work due to their low energy scale Forthe rutile TiO2 however Deringer and Csanyi [16] pointedout that adding 119880 terms caused the results to steadily beworsened in much the same way as in [22 24] In the presentstudy therefore 119880 correction was not applied to any of therutile TiO2models All the subsequent calculations were per-formed based on the equilibrium lattice constants obtainedwithout cell relaxation using a cutoff of 500 eV which wasmore precise than previous papers [13ndash15 18] This includedthe recalculation of the energy for the bulk unit cell so thatall the comparative energies could be obtained A minimumof 8 times 1 times 1 119896-points were used in the Brillouin zone of theconventional cell and scaled appropriately for supercells Allthe atomic positions in these primitive cells were relaxed inspin polarized situation according to the total energy andforce using the BroydenndashFletcherndashGoldfarbndashShanno (BFGS)algorithm scheme [25] based on the cell optimization criteria(a root mean square (RMS) force of 003 eVA a stress of005GPa and a displacement of 0001 A) The convergencecriteria for the self-consistent field (SCF) and energy toleran-ces were set to 10 times 10minus6 and 50 times 10minus5 eVatom respectively

3 Results and Discussion

31 Test of Potential The value of the 119880 parameter for ourPBE + 119880 calculations is determined by ab initio calculations

Journal of Nanomaterials 3

OMn

(a)

OMn

(b)

OMn

(c)

OMn

(d)

OMn

(e)

OMn

(f)

OMn

(g)

Figure 1 Simulated severalmorphologies of HollanditeMnO2models where (a) 120572-MnO2 crystal (Mn8O16) (b) (100) bulk surface (Mn32O64M(100)) (c) (110) bulk surface (Mn16O32 M(110)) (d) [(100 times 110)]microfacet (Mn32O64 M[(100times 110)]) (e) nanorod(I) (Mn28O56 MNR(I))(f) nanorod(II) (Mn68O136 MNR(II)) and (g) nanorod(III) (Mn112O224 MNR(III))

Table 1 Predicted PBE + 119880 experimental and theoretical latticeparameters for 120572-MnO2

TiO2 119886 (A) 119887 (A) 119888 (A)This work 9922 9922 2904Ref [17] 9907 9907 2927Exp [20] 9750 9750 2861

Previous study [10] has demonstrated that a good descriptionof the structural stability band gaps and magnetic interac-tions can be obtained when PBE + 119880 is applied with the fullylocalized limit which is therefore also used in the presentstudy 119880 = 20 eV is employed for 120572-MnO2 Table 1 liststhe calculated lattice parameters for 120572-MnO2 obtained fromPBE + 119880 These results are within 18 of the theoretical[17] and experimental [20] parameters but the commontendency for PBE + 119880 to overestimate the unit cell volumeis evident Regarding the values listed for rutile TiO2 inTable 2 the results are also similar to those of theoretical [16]and experimental [21] reports on DFT + TS Therefore thecalculated sets are appropriate for investigating the surfaceeffects of MO2 (M = MnTi)

Table 2 Predicted DFT + TS experimental and theoretical latticeparameters for rutile TiO2


32 Evolution Character of Surface Energy In Tables 3 and4 the surface energy 119864surface for 120572-MnO2 and rutile TiO2obtained via PBE+119880 andDFT+TS calculations respectivelyis shown The surface energy is calculated by taking thedifference between the energy of a constructed slab and thesame number of 120572-MnO2 or rutile TiO2 formula units in thebulk [19]

119864surface = 119864total minus 119899119864b119878

(1)

where 119864total is the energy of a surface or nanorod modelcontaining 119899 formula crystal units 119864b is the total energy ofthe crystal and 119878 is the surface area of the simulated modelswhere the bulk surface and microfacet contain two surfaces


OTi

(a)

OTi

(b)

OTi

(c)

OTi

(d)

OTi

(e)

OTi

(f)

OTi

(g)

Figure 2 Simulated several morphologies of rutile TiO2 models where (a) TiO2 crystal supercell (Ti16O32) (b) (100) bulk surface (Ti27O54T(100)) (c) (110) bulk surface (Ti20O40 T(110)) (d) [(100 times 110)] microfacet (Ti34O68 T[(100 times 110)]) (e) nanorod(1) (Ti32O64 TNR(1)) (f)nanorod(2) (Ti52O104 TNR(2)) and (g) nanorod(3) (Ti88O176 TNR(3))

by their periodic boundary condition The results are shownin Figure 3 (as well as in Tables 3 and 4) In [19] it is shownthat the 119864surface values of the 120572-MnO2(100) and (110) bulksurfaces are equal to 06503 Jmminus2 and 06794 Jmminus2 respec-tively which are similar to the results reported by Tompsett etal (064 Jmminus2 and 075 Jmminus2 resp) [17] Regarding the rutileTiO2 the 119864surface value for the T(100) is equal to 12492 Jm

minus2which is a little larger than that (100 Jmminus2) obtained byDeringer and Csanyi [16] Furthermore the 119864surface valueof the T(110) is equal to 11503 Jmminus2 which is similar tothat (110 Jmminus2) obtained by Ramamoorthy et al [26] buta little larger than the 081 Jmminus2 obtained by Lindan et al[27] and the 080 Jmminus2 obtained by Deringer and Csanyi [16]However none of them influence the trend and the internallaw governing the surface energy in this manuscript

The results are shown in Figures 3 and 4 For 120572-MnO2it is found that the 119864surface value increases according to atrend of 119864surfaceM(100) lt 119864surfaceM(110) lt 119864surfaceMNR(I) lt119864surfaceMNR(II) lt 119864surfaceMNR(III) lt 119864surfaceM[(100 times 110)]as shown in Figure 3(a) (labeled byA) Given that the surfaceenergies of M(100) and M(110) are nearly equivalent theabscissa has no physical significance Therefore it assumesthat the abscissa value of M(100) and M(110) is 25 and

that of M[(100 times 110)] is 9 which is greater than that ofMNR(III) by 3 points as shown in Figure 3(a) (labeled byB)It is found that the surface energies of 120572-MnO2 of differentmorphologies fall in line with the relationship among themimplying the existence of an internal correlation Further-more the sequence of M[(100 times 110)] does not correspondto nanorod(III) because other nanorods may exist Uponclosely analyzing their geometric structure it is found that allthe 120572-MnO2 nanorods and microfacets are composed of twoMiller indexes for example the (110) and (100)microsurfacesThey differ only in the numbers of the (110) and (100) micro-surfaces If it is hypothesized that the average of the values of119864surfaceM(100) and 119864surfaceM(110) is one component elementof the surface energy for the nanorods and microfacets theirsurface energies exhibit some linear relationship This hasnot been observed previously Their formulized relationshipcan be explained as follows one constant parameter of thesurface energy 10401 Jmminus2 labeled 119860 and another constantparameter of the surface energy 06648 Jmminus2 labeled119861 whichis equal to the average of 119864surfaceM(100) and 119864surfaceM(110)that is (06593 Jmminus2 + 06974 Jmminus2)2 = 06648 Jmminus2 Thecorrelation function for the surface energy of the nanorodsand microfacets to the average value of the surface energy


Table3Surfa

ceenergy

(119864surface)andcohesiv

eenergy(119864

cohesiv

e)of

120572-MnO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119860 (A)

119861 (A)

119878 (A2)

119864 surface(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Mn 8O16

minus117

34896

0mdash

mdashmdash

mdashmdash

minus4722

3

Bulksurface

M(100)

minus469

34899

729040

19844

0576265

46843

06503

minus4673

5M(110)

minus234

66258

029040

1432

92416116

35340

06794

minus4648

7Microfacet

M[(100times110

)]minus1

1734

896

029040

242512

704255

444003

50437

minus4259

8

Nanorod

MNR(I)

minus410

29836

829040

683480

1984811

422991

1704

0minus4

218

8MNR(II)

minus996

51022

329040

1080360

3137342

955937

24376

minus4253

7MNR(III)

minus164

13772

6729040

1370

160

3978

914

1508172

30323

minus4273

5


Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)

Figure 3 Surface energy of 120572-MnO2 and rutile TiO2 in different morphologies

T[(100 times 110)]TNR(3)TNR(2)TNR(1)

MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999

Figure 4 Formulized treatment on surface energy of 120572-MnO2 andrutile TiO2 in different morphologies

for M(100) and M(110) is given as 119884 = 119860 + 119873 times 119861 where119873 is the quantization parameter for different nanorods andmicrofacetmodelsQuantization parameter119873plays two rolesin this paper firstly it implies that their surface energies havesome relationship between nanorods and corresponding bulksurface secondly it restricts the maximum value of surfaceenergy for nanorods And 119873 is defined as the additionalnumber of 110 or 100 Miller index slab units from min-imum nanorod MR(I) or NR(I) wherein the quantizationparameter119873 forMNR(I) or TNR(I) is equal to 1 respectivelyTheir quantization parameter 119873 is shown Figure 4 Their119873 values closely follow a linear relationship After fittingby linear regression the adjusted 119877 square (1198772) value isequal to 0999 as shown in Figure 4 We can thus derive afunction for the surface energy 119864surfaceMNR(I) = 10401 Jmminus2+ 1 times 06648 Jmminus2 119864surfaceMNR(II) = 10401 Jmminus2 + 21021times 06648 Jmminus2 119864surfaceMNR(III) = 10401 Jmminus2 + 29967 times06648 Jmminus2 and 119864surfaceM[(100 times 110)] = 10401 Jmminus2 +

60226 times 0608 Jmminus2 Thus it is clear why a previous adjust-ment of the abscissa in the surface energy of 120572-MnO2 wasa line correlation (Figure 3(a) labeled by B) This revealsthe evolution character of the surface energy for 120572-MnO2nanorods and microfacets

It is well known that the geometrical and chemicalperformances of rutile TiO2 are similar to those of 120572-MnO2From the results of analysis the surface energy of 120572-MnO2nanorods and microfacets has a quantization characterTherefore it is needed to determine whether there is the samefor rutile TiO2 To do so the surface energies of the rutileTiO2 are shown in Figure 3(b) and in Table 4 The trend inthe surface energy 119864surface for rutile TiO2 from bulk surfacerarr nanorodrarrmicrofacet was found to be different from thatof 120572-MnO2 Their surface energies were found to be similarto each other The difference between them is very smallas shown in Figure 3(b) For example the largest 119864surfaceis for T(100) which is equal to 12492 Jmminus2 The smallest isfor T(110) which is equal to 11503 Jmminus2 Their difference isonly 00989 Jmminus2 Furthermore the differences between themicrofacet and nanorods are obviously very smallThereforethe trend in the surface energy for the rutile TiO2 in a bulksurface and nanorods assumes a horizontal line as shownin Figure 3(b) In deep analysis the microfacet and nanorodmodels are also composed of twoMiller indexes for example(110) and (100) microsurfaces And it takes the average of119864surfaceT(100) (12492 Jmminus2) and 119864surfaceT(110) (11503 Jmminus2)as one constant 1198611015840 where 1198611015840 is equal to (12492 Jmminus2 +11503 Jmminus2)2 = 11997 Jmminus2 It is found that the relation-ship between the surface energy of microfacetsnanorodsand constant 1198611015840 can also be fitted by linear regression asshown in Figure 4 The surface energy function is givenby 119864surfaceTNR(1) = 10102 times 11997 Jmminus2 119864surfaceTNR(2) =10317 times 11997 Jmminus2 119864surfaceTNR(3) = 10347 times 11997 Jmminus2and 119864surfaceT[(100 times 110)] = 09879 times 11997 Jmminus2 Thisevolution character of the surface energy of rutile TiO2 isdifferent from that for 120572-MnO2 The quantization character


for 120572-MnO2 nanorods is a positive integer while that forrutile TiO2 is equal to 1 However they all have a quantizationphenomenon in their surface energies

33 Evolution Character of Cohesive Energy The cohesiveenergy represents the work that is required for a crystal to bedecomposed into atoms which in turn denotes the stability ofthe respective simulation model Here the 119864cohesive value forseveral 120572-MnO2 or rutile TiO2 models has been calculatedfrom the following equation [19]

119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)

where 119897 and119898 represent the number ofM (M=Ti orMn) andO atoms in the respective morphologies of rutile TiO2 or 120572-MnO2 119864

M119897O119898total denotes the total energy of the M119897O119898 models

and119864Mgas and119864O

gas are the energies of the gaseousM (M=Ti orMn) andOatoms respectively Before optimizing the gaseousatoms a 10 times 10 times 10 (A3) vacuum box is constructed and asingle atom is placed such as Ti Mn or O in the center ofthe box to be relaxed and thus to obtain its global minimumenergy The results are given as 119864Mn

gas = minus5881855 eV and119864Ogas = minus4322548 eV as given in Table 3 For rutile TiO2 the

results are 119864Tigas = minus15943577 eV and 119864O

gas = minus4319368 eVwherein the difference of energy for oxygen in 120572-MnO2 andrutile TiO2 was originated from their different calculatedsets in previous part of Simulation Models and MethodThe results are given in Table 4 A previous study [19] hasdiscussed the evolution of cohesive energy for 120572-MnO2 andfound that the structural stability of the nanorods andmicro-facet is lower than that of the crystal and bulk surfaces Thepresent study will examine the relationship between the bulksurface nanorods and microfacet If only the absolute valuesof the cohesive energy are considered it can only determinethat the structural stability of nanorods and microfacet islower than that of bulk surfaces and crystals as is alreadyknown Analyzing their geometric morphologies it is foundthat they are also composed by two Miller indexes forexample the (110) and (100)microsurfacesThis paper appliesthe same treatment to the average value of cohesive energy119864a-cohesive for M(110) andM(100) to establish a basic standardwhich is equal to minus46611 eVatom (where 119864cohesiveM(110) =minus46487 eVatom and 119864cohesiveM(100) = minus46735 eVatom) inFigure 5 Considering the ratio 1198991015840 of the cohesive energyfor microfacets and nanorods to 119864a-cohesive it is found thatevery instance of 119899 is nearly equal to 109 where 11989910158401 =119864a-cohesive119864cohesive MNR(I) = 11048 11989910158402 = 119864a-cohesive119864cohesiveMNR(II) = 10958 11989910158403 = 119864a-cohesive119864cohesive MNR(III) =10907 and 11989910158404 = 119864a-cohesive119864cohesive M[(100 times 110)] = 10942It is found that all the correlation constants are equal to109 as shown in Figure 6 This trend which presents asa horizontal line is different from the trend in the surfaceenergy Obviously a quantization phenomenon can be seenRegarding the cohesive energy of rutile TiO2 the differenceis found to be very small unlike the case of 120572-MnO2 Forexample the most stable structure is the rutile TiO2 crystalfor which the cohesive energy is equal to minus78669 eVatom

T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal

MNR(I)MNR(II) MNR(III)

M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2

Figure 5 Cohesive energy of 120572-MnO2 and rutile TiO2 in differentmorphologies

The least stable structure is TNR(1) for which the cohesiveenergy is equal to minus77255 eVatom The difference betweenthem is only equal to 01414 eVatom The second stablestructure is the bulk surface T(100) for which the cohesiveenergy is equal to minus77885 eVatom The cohesive energies ofthe bulk surface T(110) microfacets [(100times 110)] and TNR(3)are very similar being minus77750 eVatom minus77712 eVatomand minus77779 eVatom respectively The difference in theircohesive energies is only 00067 eVatom which may beregarded as being the calculation error so that they can allbe regarded as having the same structural stability Regardingthe trend in their cohesive energies shown in Figure 5they closely approximate to each other Applying the sametreatment to the cohesive energy of rutile TiO2 it canalso take the average value of cohesive energy 119864a-cohesive forT(110) and T(100) to be a basic standard which is equalto minus77817 eVatom (where 119864cohesiveT(110) = minus77750 eVatomand119864cohesiveT(100) =minus77885 eVatom) Considering the ratio11989910158401015840 of the cohesive energy for the nanorodsmicrofacets to119864a-cohesive it is found that every instance of 119899 is nearly equal to100 where 119899101584010158401 = 119864a-cohesive119864cohesiveTNR(1) = 10073 119899101584010158402 =119864a-cohesive119864cohesiveTNR(2) = 10037 119899101584010158403 = 119864a-cohesive119864cohesiveMNR(3) = 10049 and 119899101584010158404 = 119864a-cohesive119864cohesiveT[(100 times110)] = 10013 All the normalized parameters are nearlyequal to 100 as shown in Figure 6 Then the evolutioncharacter of the cohesive energy for 120572-MnO2 and rutile TiO2is abstracted absolutely In line with the evolution of thegeometric morphologies in the growth of nanorods the ratioof their cohesive energies divided by 119864a-cohesive is found to benearly equal to 1

34 Evolution Character of Electronic Structure From theabove analysis it is found that from the bulk surface tonanorods and even tomicrofacetwith a nanometer structurethe surface and cohesive energies of 120572-MnO2 and rutileTiO2 exhibit some quantization phenomena It is well knownthat the surface and cohesive energies are derived from the


Table 5 Normalizing variance of bond lengthsum(Δ119889)2s Mulliken populationsum(Δ119876A-B)2s andMulliken chargesum(Δ119876119860)2s of 120572-MnO2 bulk

surface nanorod and microfacet models

Models 119878 (A2) sum(Δ119889)2 sum(Δ119889)2s sum(Δ119876A-B)2 sum(Δ119876A-B)

2s sum(Δ119876A)2 sum(Δ119876A)

2sM(100) 576265 0114424 0001986 3138325 005446 02984 0005178M(110) 416116 0033487 0000805 1508575 0036254 01639 0003939MNR(I) 1984811 0114594 0000577 2611850 0013159 02932 0001477MNR(II) 3137342 0248664 0000793 6574800 0020957 06644 0002118MNR(III) 3978914 0332759 0000836 1075690 0027035 10484 0002635M[(100 times 110)] 444003 0095139 0001351 3009660 0042735 03248 0004612

MNR(I) MNR(II) MNR(III) M[(100 times 110)]

TNR(1) TNR(2) TNR(3) T[(100 times 110)]

09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2

Figure 6 Formulized treatment on cohesive energy of 120572-MnO2 andrutile TiO2 in different morphologies

geometric or electronic structures Therefore in the nextsection of this paper we study the evolution of the geometricand electronic structures by applying Mulliken analysis toreveal whether there is any quantization phenomenon cor-responding to those energies The Mulliken population 119876A-Bbetween atoms A and B and the Mulliken charge 119876A aredefined as follows [21]

119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)

where 119875120583V and 119878V120583 are the density and overlap matricesrespectively and 119908119896 is the weight associated with the calcu-lated 119896-points in the Brillouin zone Usually the magnitudeand sign of 119876(A) characterize the ionicity of atom A inthe supercell while 119876A-B can be used to approximate theaverage covalent bonding strength between atoms A and BIt is known that all the bulk surface nanorod and microfacetmodels originate from their crystal As a result the area ofthe crystal can be regarded as being infinite To determine

the intrinsic mechanism of the evolution character on thesurface and cohesive energies it sets a bond length 119889A-BMulliken population 119876A-B and Mulliken charge 119876A of thecrystal as the base values These base values are equal tothe average value of the bond length 119889A-B the Mullikenpopulation 119876A-B and the Mulliken charge 119876A in 120572-MnO2or rutile TiO2 crystal respectively Then the bond lengthvariance (Δ119889)2 is set equal to (119889A-B minus 119889A-B)

2 to elucidate theinfluence of the other geometric morphologies such as thebulk surface nanorods and microfacet by their growth TheMulliken population variance (Δ119876A-B)

2 is equal to (119876A-B minus119876A-B)2 However the Mulliken charge for 120572-MnO2 or rutile

TiO2 consists of two parts namely the lost charge of metallicelements Mn or Ti and the reception charge of the oxygenelements Therefore the Mulliken charge variance (Δ119876A)

2

is equal to the sum of (Δ119876M)2 and (Δ119876O)

2 In this case119889A-B 119876A-B 119876Mn and 119876O for 120572-MnO2 are equal to 1925503925 minus059 and 105 respectively For rutile TiO2 119889A-B119876A-B 119876Mn and 119876O are equal to 19714 05050 minus066 and131 respectively To identify the quantization phenomenonof the surface effect the summation of sum(Δ119889)2 sum(Δ119876A-B)

2andsum(Δ119876A)

2 by their surface area 119878 is normalized Althoughthe size and shape of nanocrystal have been set as a functionof its free energy [15] the surface area 119878 is the vital factor toaffect the chemical performance of nanomaterials Then thesurface area 119878 is chosen to be a normalized parameter in thispaper The detailed data is exhibited in Tables 5 and 6

The final results are shown in Figure 7 Figure 7 showsthat the normalized parameters sum(Δ119889)2s sum(Δ119876A-B)

2s andsum(Δ119876A)

2s for the bulk surface nanorod and microfacetmodels for 120572-MnO2 and rutile TiO2 fluctuate considerablyand exhibit irregularities Regarding the electronic propertiesof the bond strength and atomic charge the largest is forM(100) or T(110) to 120572-MnO2 or rutile TiO2 respectively asshown in Figures 7(a) and 7(d) whose the surface energy isthe smallest for eachmodel In the case of120572-MnO2 there is anintrinsic law conforming to the configuration evolution suchas the linear correlation between MNR(I) and MNR(III)shown in Figures 7(b) and 7(c) Upon plotting sum(Δ119876A-B)

2119904and sum(Δ119876A)

2s for MNR(I)-MNR(III) and M[(100 times 110)]along with the quantization number 119873 of the abscissavalue of 1 2 3 and 6 as shown in Figure 8 it is foundthat they exhibit a linear correlation with 1198772 of 0989 and0992 respectively It is well known that the value of thesurface energy sometimes reflects the catalytic performance


002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s

Figure 7 Normalizing bond length Mulliken population and Mulliken charge of 120572-MnO2 and rutile TiO2 in different morphologies


Table 6 Normalizing variance of bond length sum(Δ119889)2s Mulliken population sum(Δ119876A-B)2s and Mulliken charge sum(Δ119876A)

2s of rutile TiO2bulk surface nanorod and microfacet models


2s sum(Δ119876A)2 sum(Δ119876A)

2sT(100) 813473 0423012 00052 4611500 0056689 00252 000031T(110) 766949 0507518 0006617 5946150 007753 00582 0000759TNR(1) 1792087 1646453 0012502 6671700 0050661 01028 0000574TNR(2) 2301260 2358380 0010248 11433600 0049684 01240 0000539TNR(3) 3027520 2796938 0009238 20220300 0066788 01796 0000593T[(100 times 110)] 1316929 0899027 0006827 7728600 0058687 00837 0000636

2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s

Figure 8 Schematic curve of Normalizing Mulliken populationand Mulliken charge of 120572-MnO2 in different morphologies withnanostructure

of materials in which case the evolution in the normalizedMulliken population and the Mulliken charge of 120572-MnO2nanorods and microfacet are very similar to those of thesurface energy as shown in Figures 3 and 4 thus confirminghow the surface catalytic performance of nanomaterials ismainly controlled by the electronic structure Furthermorewe can assume that the surface energy (119864surface) is a functionof the normalized Mulliken population (sum(Δ119876A-B)2s) andnormalized Mulliken charge (sum(Δ119876A)2119904) Their summation(sum(Δ119876A-B)2119904 +sum(Δ119876A)2119904) is shown in Figure 9 It noted anabsolute linear relationship as shown in Figures 9(a) 9(b)and 9(c) where the function of 119864surface versus (sum(Δ119876A-B)

2s+sum(Δ119876A)

2s) is 119891(119909) = 1029 times 119909 + 0101 with an 1198772 value of0995 This indicates that the surface effect in nanomaterialsdiffers from that in bulk materials Regarding rutile TiO2a near-horizontal correlation between TNR(1) and TNR(3)is shown in Figures 7(e) and 7(f) Because all the nanorodsand microfacets are composed of 100 and 110 Millerindexes it can be assumed that their electronic structureoriginates from that of the (100) and (110) bulk surfacesThese were treated in the same way as their surface andcohesive energies If we hypothesize that the average value ofsum(Δ119876A-B)2119904 and sum(Δ119876A)

2s for M(100) and M(110) is onecomponent element contributing to the evolution characterof nanorods and microfacet their electronic structures canbe explored and some linear function can be found Firstwe abstracted the average value 119870 of sum(Δ119876A-B)


2s in M(100) and M(110) to be 119870M(119876A-B) = 004535and119870119872(119876A) = 0004559 respectively Second we abstractedthe quantization number by the quotient of the average valueof 119870 divided by the corresponding value of sum(Δ119876A-B)

2s and

sum(Δ119876A)2s for the nanorod andmicrofacet modelsThe same

treatment was applied to rutile TiO2 wherein the averagevalue1198701015840 ofsum(Δ119876A-B)

2s andsum(Δ119876A)2119904 in T(100) and T(110)

is found to be1198701015840M(119876A-B) = 006711 and1198701015840M(119876A) = 0000545respectively The results are shown in Figure 10 and in Tables5 and 6 Figure 10 shows that there is an obviously linearcorrelation in the evolution from nanorod to microfacet for120572-MnO2 regardless of theMulliken population andMullikencharge After linear fitting they obtain a function 119891(119897) =minus05921 lowast 119897 + 4011 for sum(Δ119876A-B)

2s and 119891(119898) = minus042 lowast119898+3461 forsum(Δ119876A)

2119904 respectively where the quantizationnumber 119897 or 119898 is a positive integer This evolution law isthe same as that of the surface energy shown in Figure 3For the rutile TiO2 regardless of the Mulliken populationand Mulliken charge there is another evolution law whichis different from that for 120572-MnO2 After linear fitting anear-horizontal line for sum(Δ119876A-B)

2119904 and sum(Δ119876A)2119904 in the

evolution from nanorod to microfacet for rutile TiO2 isobtained while the quantization number 119897 or 119898 is close to1 which is the same as the surface energy shown in Figure 3This abstracts the quantization phenomenon in an electronicstructure and its relationship with the surface energy

4 Discussion

It is well known that metallic oxides offer great potential forapplication to catalysts not only for clean energy applicationsbut also for pollution mitigation Typically applied dioxidesare 120572-MnO2 and rutile TiO2 Their nanometer structure isideal for attaining the greatest catalytic actionHowever thereare only a few valid theories that can be used to guide theirdesign The determination of the intrinsic mechanism ofthe surface effects and the correlation with the bulk surfaceor crystal has attracted the attention of many researchersDeringer and Csanyi [16] and Tompsett et al [17] determinedthe geometric configuration of 120572-MnO2 and rutile TiO2nanorods by applying the Wulff construction method theresults of which were corroborated by experiment Hummeret al [18] compared the discrepancy between the total calcu-lated nanoparticles surface energies and the summed energiesof the constituent faces for rutile TiO2 and inferred that theyuncorrelated with each other as the discrepancy was largeHowever they are not able to identify the contributors to thesurface effect In the present study the surface energies ofthe 120572-MnO2 nanorods exhibit a quantization phenomenonFollowing the growth of the nanorods the surface energies


Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)

sum((ΔQA-B)2s + sum(ΔQA-B)

2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)

Figure 9 Schematic curve of surface energy versus Normalizing Mulliken population or Mulliken charge of 120572-MnO2 in differentmorphologies with nanostructure

2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)

Mulliken chargeMulliken population

Y = minus0592 middot l + 4011

R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)

Figure 10 Formulized treatment onMulliken population andMul-liken charge of 120572-MnO2 and rutile TiO2 in different morphologies

of the nanorods are defined by the function 119864surface =10401 Jmminus2 +119873times0608 Jmminus2 where119873 is a positive integer andis a maximum value of 6 Then considering only the surfaceenergies of the 120572-MnO2 nanorods the optimal structureis identified Considering their stability they also obey thefollowing law119864a-cohesive119864cohesive MNRasymp 109The interactionbetween the surface energy and cohesive energy in thequantization phenomenon also conforms to the followingcommonly held view the growth of the surface energy ofnanometer materials will adversely affect their structuralstability This evolution character of the 120572-MnO2 nanorodsdiffers from that of rutile TiO2 It is found that the surfaceenergies of rutile TiO2 nanorod and microfacet conformto another function 119864surfaceTNR asymp 10102 times 11997 Jmminus2which means that the surface energy will remain nearlyconstant during the growth of rutile TiO2 nanomaterialsThis phenomenon indicates that the surface effect wouldhave a similar impact on a catalyst consisting of rutileTiO2 nanorods ignoring theirmorphologies Regarding their

structural stability it is found that their cohesive energyconforms to the following rule119864a-cohesive119864cohesiveTNRasymp 100This phenomenon indicates that the rutile TiO2 nanorodswill exhibit a better structural stability during the manufac-turing process relative to 120572-MnO2 nanorods With furtheranalysis their quantization phenomenon originates from theevolution character of the electronic structure in terms of thedifference in the bond strength and the atomic charge ratherthan the geometric configuration From the previous analysisthe surface energies of 120572-MnO2 nanorods and microfacetare increased straightly with the summation of sum(Δ119876A-B)

2sand sum(Δ119876A)

2s but they keep constant for rutile TiO2Mulliken population and charge are originated from thevalence electrons of component elements from their formulas[28] In other words if we enhance the valence electrons of120572-MnO2 catalysts by doping process their surface activitywould be improved because of the increased surface energySo it is not hard to understand why their doping elements forMnO2 catalysts are Pt [29] Pd [29] Ag [30] Nb [31] Fe [32]and so on which are translation metals with abundance ofvalence electrons instead of metalloid elements But for rutileTiO2 nanorods and microfacet their surface energies arefluctuating smoothlywith the summation ofsum(Δ119876A-B)


2s So if we dope the rutile TiO2 catalysts with trans-lation metals such as Fe V and Cr [33ndash35] their improvedeffect would be very limited because the catalytic perfor-mance of rutile TiO2 is sensitive to its change of energy gap[36] Then the doping processes for rutile TiO2 catalysts areused for themetalloid elements such as N [37] Sn [38] and S[39] which affects the internal bonding orbitals Conclusivelylimited by their surface energies of rutile TiO2 nanomaterialsthe optimized way to enhance the catalytic performance ofrutile TiO2 is that doping technology appending nanofabri-cation instead of single nanofabrication method Then our


investigation has a vital significance to understand and helpthe optimized processed of metallic oxides catalysts

Space limitations mean that within the scope of thispaper we have not been able to address other Miller indexesfor120572-MnO2 or rutile TiO2 nanorods such as 112 211 and111 for the 120572-MnO2 nanorods and 101 for the rutile TiO2nanorods as mentioned by Deringer and Csanyi [16] andTompsett et al [17] respectively although their proportionsare smaller than those of the (100) and (110) Miller indexesfor 120572-MnO2 or rutile TiO2 nanorods However we do notthink that this flaw influences the significance of this papergiven that we began by identifying the evolution mechanismof the metallic oxidation of MO2 (M = Mn Ti) nanorodsand microfacet which have a correlation with their bulksurfaces and structures The overall evolution character ofmetallic oxidation MO2 (M = Mn Ti) nanorods and theirother nanometer structures will be revealed and addressed inour future research Furthermore the evolution mechanismbetween a nanometer structure and bulk surfacewill be usefulfor investigating the intrinsic mechanisms of nanoeffects

5 Conclusion

The evolutionmechanism of metallic dioxideMO2 (M =MnTi) from nanorods to bulk crystal has been investigated byfirst-principles calculation The results of the investigationshow the following

(1) The surface energies of 120572-MnO2 and rutile TiO2nanorods and microfacets have a quantization phenomenonFor 120572-MnO2 it is found that the surface energy conformsto the function 119884 = 119860 + 119873 times 119861 where 119860 is equal to10401 Jmminus2 119861 is equal to 06648 Jmminus2 and 119873 is equal toa positive integer of no more than 6 For rutile TiO2 thesurface energy conforms to another function 119864surfaceTNR asymp10102 times 11997 Jmminus2 which remains constant regardless of thegeometric structure of the rutile TiO2 nanorods

(2) The cohesive energies of the 120572-MnO2 and rutileTiO2 microfacets and nanorods also have a quantizationphenomenon For 120572-MnO2 it is found that the cohe-sive energy conforms to the function 119864a-cohesive119864cohesiveMNR asymp 109 where 119864a-cohesive is equal to the average of119864cohesiveM(110) and119864cohesiveM(100) For rutile TiO2 the cohe-sive energy conforms to119864a-cohesive119864cohesive TNR asymp 100 where119864a-cohesive is equal to the average value of 119864cohesiveT(110) and119864cohesiveT(100)

(3) The electronic properties of 120572-MnO2 and rutileTiO2 nanorods and microfacet also exhibit a quantizationphenomenon After being normalized by their surface areathe Mulliken population and Mulliken charge variance of 120572-MnO2 exhibit a linear function as 119891(119899) = 05921 lowast 119897 + 4011for sum(Δ119876A-B)

2s and 119891(119899) = 042 lowast 119898 + 3461 However theMulliken population and Mulliken charge variance of rutileTiO2 exhibit a nearly horizontal line in the evolution fromnanorod to microfacet

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the projects of National NaturalScience Foundation of China (Grant no 51361026) Founda-tion of Jiangxi Educational Committee (GJJ160684) and KeyLaboratory of Jiangxi Province for Persistent Pollutants Con-trol and Resources Recycle (NanchangHangkongUniversity)(ST201522014)

References

[1] A El-Sayed N Atef A H Hegazy K R Mahmoud R MA Hameed and N K Allam ldquoDefect states determined theperformance of dopant-free anatase nanocrystals in solar fuelcellsrdquo Solar Energy vol 144 pp 445ndash452 2017

[2] J Luo C Hu X Meng J Crittenden J Qu and P Peng ldquoAnti-mony Removal from Aqueous Solution Using Novel 120572-MnO2Nanofibers Equilibrium Kinetic and Density Functional The-ory Studiesrdquo ACS Sustainable Chemistry amp Engineering vol 5no 3 pp 2255ndash2264 2017

[3] ZHuXXiao CChen et al ldquoAl-doped120572-MnO2 for highmass-loading pseudocapacitor with excellent cycling stabilityrdquo NanoEnergy vol 11 pp 226ndash234 2015

[4] K B Liew W R Wan Daud M Ghasemi et al ldquoManganeseoxidefunctionalised carbon nanotubes nanocomposite as cat-alyst for oxygen reduction reaction in microbial fuel cellrdquoInternational Journal of Hydrogen Energy vol 40 no 35 pp11625ndash11632 2015

[5] N K Allam K Shankar and C A Grimes ldquoA general methodfor the anodic formation of crystalline metal oxide nanotubearrays without the use of thermal annealingrdquo Advanced Materi-als vol 20 no 20 pp 3942ndash3946 2008

[6] J S Fischel M H Fischel and D L Sparks ldquoAdvances inunderstanding reactivity of manganese oxides with arsenic andchromium in environmental systemsrdquo ACS Symposium Seriesvol 1197 pp 1ndash27 2015

[7] L Yan S Hu J Duan and C Jing ldquoInsights from arsenateadsorption on rutile (110) Grazing-incidence X-ray absorptionfine structure spectroscopy and DFT+U studyrdquo The Journal ofPhysical Chemistry A vol 118 no 26 pp 4759ndash4765 2014

[8] H-Y T Chen S Tosoni and G Pacchioni ldquoA DFT study of theacidndashbase properties of anatase TiO2 and tetragonal ZrO2 byadsorption of CO and CO2 probe moleculesrdquo Surface Sciencevol 652 pp 163ndash171 2016

[9] Y Xi and J-C Ren ldquoDesign of a CO Oxidation Catalyst Basedon Two-DimensionalMnO2rdquoThe Journal of Physical ChemistryC vol 120 no 42 pp 24302ndash24306 2016

[10] Y Crespo and N Seriani ldquoA lithium peroxide precursor on the120572-MnO2 (100) surfacerdquo Journal of Materials Chemistry A vol 2no 39 pp 16538ndash16546 2014

[11] K Selvakumar S M Senthil Kumar R Thangamuthu et alldquoPhysiochemical investigation of shape-designedMnO2 nanos-tructures and their influence on oxygen reduction reactionactivity in alkaline solutionrdquo The Journal of Physical ChemistryC vol 119 no 12 pp 6604ndash6618 2015

[12] N G Petrik and G A Kimmel ldquoPhotoinduced dissociationof O2 on rutile TiO2(110)rdquo The Journal of Physical ChemistryLetters vol 1 no 12 pp 1758ndash1762 2010

[13] A S Barnard S Erdin Y Lin P Zapol and J W HalleyldquoModeling the structure and electronic properties of Ti O2nanoparticlesrdquo Physical Review B Condensed Matter and Mate-rials Physics vol 73 no 20 Article ID 205405 2006


[14] A S Barnard P Zapol and L A Curtiss ldquoModeling themorphology and phase stability of TiO2 nanocrystals in waterrdquoJournal of Chemical Theory and Computation vol 1 no 1 pp107ndash116 2005

[15] A S Barnard and P Zapol ldquoEffects of particle morphology andsurface hydrogenation on the phase stability of TiO2rdquo PhysicalReview B Condensed Matter and Materials Physics vol 70 no23 Article ID 235403 2004

[16] V L Deringer and G Csanyi ldquoMany-Body Dispersion Cor-rection Effects on Bulk and Surface Properties of Rutile andAnatase TiO2rdquoThe Journal of Physical Chemistry C vol 120 no38 pp 21552ndash21560 2016

[17] D A Tompsett S C Parker and M S Islam ldquoSurface prop-erties of 120572-MnO2 Relevance to catalytic and supercapacitorbehaviourrdquo Journal of Materials Chemistry A vol 2 no 37 pp15509ndash15518 2014

[18] D R Hummer J D Kubicki P R C Kent J E Post andP J Heaney ldquoOrigin of nanoscale phase stability reversals intitanium oxide polymorphsrdquoThe Journal of Physical ChemistryC vol 113 no 11 pp 4240ndash4245 2009

[19] Z Chen G Li H Zheng X Shu J Zou and P Peng ldquoMech-anism of surface effect and selective catalytic performance ofMnO2 nanorod DFT+U studyrdquo Applied Surface Science vol420 pp 205ndash213 2017

[20] C S JohnsonDWDeesM FMansuetto et al ldquoStructural andelectrochemical studies of 120572-manganese dioxide (120572-MnO2)rdquoJournal of Power Sources vol 68 no 2 pp 570ndash577 1997

[21] J K Burdett T Hughbanks G J Miller J W Richardson Jrand J V Smith ldquoStructural-electronic relationships in inorganicsolids Powder neutron diffraction studies of the rutile andanatase polymorphs of titanium dioxide at 15 and 295 KrdquoJournal of the American Chemical Society vol 109 no 12 pp3639ndash3646 1987

[22] T Kubo H Orita and H Nozoye ldquoSurface structures of rutileTiO2 (011)rdquo Journal of the American Chemical Society vol 129no 34 pp 10474ndash10478 2007

[23] M D Segall P J D LindanM J Probert et al ldquoFirst-principlessimulation ideas illustrations and the CASTEP coderdquo Journalof Physics CondensedMatter vol 14 no 11 pp 2717ndash2744 2002

[24] M E Arroyo-De Dompablo A Morales-Garca and M Tar-avillo ldquoDFTU calculations of crystal lattice electronic struc-ture and phase stability under pressure of TiO2 polymorphsrdquoThe Journal of Chemical Physics vol 135 no 5 Article ID054503 2011

[25] T H Fisher and J Almlof ldquoGeneral methods for geometry andwave function optimizationrdquoThe Journal of Physical ChemistryC vol 96 no 24 pp 9768ndash9774 1992

[26] M Ramamoorthy D Vanderbilt and R D King-Smith ldquoFirst-principles calculations of the energetics of stoichiometric TiO2surfacesrdquo Physical Review B Condensed Matter and MaterialsPhysics vol 49 no 23 pp 16721ndash16727 1994

[27] P J Lindan N M Harrison M J Gillan and J A WhiteldquoFirst-principles spin-polarized calculations on the reducedand reconstructedrdquo Physical Review B Condensed Matter andMaterials Physics vol 55 no 23 pp 15919ndash15927 1997

[28] M D Segall R Shah C J Pickard and M C Payne ldquoPopu-lation analysis of plane-wave electronic structure calculationsof bulk materialsrdquo Physical Review B Condensed Matter andMaterials Physics vol 54 no 23 pp 16317ndash16320 1996

[29] E Rezaei J Soltan N Chen and J Lin ldquoEffect of noble metalson activity of MnOx120574-alumina catalyst in catalytic ozonation

of toluenerdquo Chemical Engineering Journal vol 214 pp 219ndash2282013

[30] M Ozacar A S Poyraz H C Genuino C-H Kuo Y Mengand S L Suib ldquoInfluence of silver on the catalytic propertiesof the cryptomelane and Ag-hollandite types manganese oxidesOMS-2 in the low-temperatureCOoxidationrdquoApplied CatalysisA General vol 462-463 pp 64ndash74 2013

[31] Z Lian F Liu H He X Shi J Mo and Z Wu ldquoManganese-niobium mixed oxide catalyst for the selective catalytic reduc-tion of NO119909 with NH3 at low temperaturesrdquoChemical Engineer-ing Journal vol 250 pp 390ndash398 2014

[32] M Sun L Yu F Ye et al ldquoTransition metal dopedcryptomelane-type manganese oxide for low-temperaturecatalytic combustion of dimethyl etherrdquo Chemical EngineeringJournal vol 220 pp 320ndash327 2013

[33] K Nagaveni M S Hegde and G Madras ldquoStructure andphotocatalytic activity of Ti1minus119909M119909O2plusmn120575 (M = W V Ce ZrFe and Cu) synthesized by solution combustion methodrdquo TheJournal of Physical Chemistry B vol 108 no 52 pp 20204ndash20212 2004

[34] H Yamashita M Honda M Harada et al ldquoPreparation oftitanium oxide photocatalysts anchored on porous silica glassby a metal ion-implantation method and their photocatalyticreactivities for the degradation of 2-propanol diluted in waterrdquoThe Journal of Physical Chemistry B vol 102 no 52 pp 10707ndash10711 1998

[35] M Salmi N Tkachenko R-J Lamminmaki S Karvinen VVehmanen and H Lemmetyinen ldquoFemtosecond to nanosec-ond spectroscopy of transition metal-doped TiO2 particlesrdquoJournal of Photochemistry and Photobiology A Chemistry vol175 no 1 pp 8ndash14 2005

[36] L Yang M Liu Y Liu et al ldquoTheoretical analyses of organicacids assisted surface-catalyzed reduction of CrVI on TiO2nanowire arraysrdquo Applied Catalysis B Environmental vol 198pp 508ndash515 2016

[37] A Kadam R Dhabbe D-S Shin K Garadkar and J ParkldquoSunlight driven high photocatalytic activity of Sn dopedN-TiO2 nanoparticles synthesized by a microwave assistedmethodrdquo Ceramics International vol 43 no 6 pp 5164ndash51722017

[38] M Lubke I Johnson N M Makwana et al ldquoHigh powerTiO2 and high capacity Sn-doped TiO2 nanomaterial anodesfor lithium-ion batteriesrdquo Journal of Power Sources vol 294 pp94ndash102 2015

[39] K C Christoforidis S J A Figueroa andM Fernandez-GarcıaldquoIron-sulfur codoped TiO 2 anatase nano-materials UV andsunlight activity for toluene degradationrdquo Applied Catalysis BEnvironmental vol 117-118 pp 310ndash316 2012

CorrosionInternational Journal of

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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TribologyAdvances in



ChemistryAdvances in


Advances inPhysical Chemistry


BioMed Research InternationalMaterials

Journal of


Na

nom

ate

ria

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Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom


[16] andTompsett et al [17] discovered that nanorods of rutileTiO2 and 120572-MnO2 have the same equilibrium geometricmorphologies with a structure consisting mainly of 100and 110 Miller indexes Furthermore Hummer et al [18]pointed out that the surface energies of TiO2 were dependentwith edges and corners of nanocrystal at particle size le3 nmAt present former researches do not identify the intrinsicmechanism between bulk and nanorods although they havestudied the nanoscale morphology of rutile TiO2 and 120572-MnO2 for a long time But such an intrinsic mechanism playsa vital role in the design and optimization of metallic oxidenanomaterials In a previous paper [19] it have been statedthat there may be an optimal 120572-MnO2 nanorod which hasa surface energy suitable for promoting enhanced surfaceactivity together with an appropriate degree of cohesiveenergy for maintaining structural stability As an extension ofpreviouswork the present study further sets out to investigatethe evolutionmechanism of bulk and nanorods of MO2 (M =Mn Ti) metallic dioxide

2 Simulation Models and Method

To elucidate the nanometer effect of metallic dioxideMO2 (M = MnTi) with a nanostructure several modelsof MO2 (M = MnTi) in crystal bulk surface nanorodand microfacet topological configurations were constructedand studied systematically according to their stoichiomet-ric proportions Their corresponding simulated models areshown in Figures 1 and 2 Regarding the rutile TiO2 modelconstruction only two prominent and stable Miller indexplanes such as 100 and 110 are considered In the presentstudy the 120572-MnO2 and rutile TiO2 nanorod models wereconstructed based on the experimental results obtained byBarnard et al [13ndash15] and Deringer and Csanyi [16] All thesimulation models are shown in Figure 2 For the rutile TiO2(100) bulk surface there are triple units of 100 Miller indexslabs while for the 110 bulk surfaces there are double110 Miller index slabs as shown in Figures 2(b) and 2(c)respectively A microfacet rutile TiO2 [(100 times 110)] supercellstructure containing only double units of 100 and 110Miller index slabs which had been proven to exhibit a similarcatalysis performance as a nanostructure [19 22] was built asa bulk surface with nanometer morphologies only as shownin Figure 2(d) Regarding the nanorod (NR) models all ofthem were combined with only 110 and 100 Miller indexslabs as shown in Figures 2(e)ndash2(g) (In our future workfurther Miller index slabs will be considered to represent amore complicated situation)The smallest nanorod addressedin the present study that is (NR(1)) consisting of two110 and one 100 Miller index slab unit was built as aTi32O64 supercell as shown in Figure 2(e) The second rutileTiO2 nanorod (NR(2)) contains two units each of 100 and110 Miller index slabs to construct a Ti52O104 supercell(Figure 2(f)) The largest rutile TiO2 nanorod contains triple110 and double 100Miller index slab units named NR(3)which form a Ti88O176 supercell (Figure 2(g)) Similar wayof constructed configuration is forced to 120572-MnO2 nanorodsThe latter is the largest that can be handled in the calculationlimits of our computer cluster All these primitive nanorods

can be regarded as being free nanomaterials in morphologiesby using their periodic boundary conditions and transitionalsymmetryThe purpose of such constructions is to investigatethe surface effect of different Miller indices over severalmodels All the bulk surfacemodels were calculated assumingslabswith aminimum thickness of 14 A In all the bulk surfaceand nanorod models a separating vacuum distance of atleast 12 A was used to distance the slabs from their periodicimage For the first step all of themodels were not terminatedby hydrogenation as followed by Barnard et alrsquos report [13]The complicated surface models of metallic dioxide MO2(M = Mn Ti) will be studied in our further research Todistinguish the difference between 120572-MnO2 and rutile TiO2in similar configurations every simulated model was labeledldquoMrdquo or ldquoTrdquo to represent the 120572-MnO2 and rutile TiO2 seriesrespectively For example the (100) bulk surface for 120572-MnO2was labeled M(100) while T(100) represents the (100) bulksurface for rutile TiO2 This convention is used for everymodel shown in Figures 1 and 2

Based on the calculated sets of Deringer and Csanyi[16] all the above 120572-MnO2 and rutile TiO2 simulationmodels were relaxed by applying the following process afirst-principles pseudopotential plane-wave method basedon density functional theory was implemented in the Cam-bridge Sequential Total Energy Package (CASTEP) code [23]The electronic structure was calculated using the GeneralizedGradient Approximation (GGA) devised by Perdew et alwith a Tkatchenko-Scheffler approach (TS) being used forthe dispersion corrections [16] The PBE + U exchange-correlation function has been demonstrated to give a gooddescription of the defect properties in 120572-MnO2 [17] All cal-culations were performed in a ferromagnetic spin polarizedconfiguration while effects of more complexmagnetic orderswere left for future work due to their low energy scale Forthe rutile TiO2 however Deringer and Csanyi [16] pointedout that adding 119880 terms caused the results to steadily beworsened in much the same way as in [22 24] In the presentstudy therefore 119880 correction was not applied to any of therutile TiO2models All the subsequent calculations were per-formed based on the equilibrium lattice constants obtainedwithout cell relaxation using a cutoff of 500 eV which wasmore precise than previous papers [13ndash15 18] This includedthe recalculation of the energy for the bulk unit cell so thatall the comparative energies could be obtained A minimumof 8 times 1 times 1 119896-points were used in the Brillouin zone of theconventional cell and scaled appropriately for supercells Allthe atomic positions in these primitive cells were relaxed inspin polarized situation according to the total energy andforce using the BroydenndashFletcherndashGoldfarbndashShanno (BFGS)algorithm scheme [25] based on the cell optimization criteria(a root mean square (RMS) force of 003 eVA a stress of005GPa and a displacement of 0001 A) The convergencecriteria for the self-consistent field (SCF) and energy toleran-ces were set to 10 times 10minus6 and 50 times 10minus5 eVatom respectively

3 Results and Discussion

31 Test of Potential The value of the 119880 parameter for ourPBE + 119880 calculations is determined by ab initio calculations


OMn

(a)

OMn

(b)

OMn

(c)

OMn

(d)

OMn

(e)

OMn

(f)

OMn

(g)









(1)



OTi

(a)

OTi

(b)

OTi

(c)

OTi

(d)

OTi

(e)

OTi

(f)

OTi

(g)







Table3Surfa

ceenergy


eenergy(119864

cohesiv

e)of


lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119860 (A)

119861 (A)

119878 (A2)

119864 surface(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Mn 8O16

minus117

34896

0mdash

mdashmdash

mdashmdash

minus4722

3

Bulksurface

M(100)

minus469

34899

729040

19844

0576265

46843

06503

minus4673

5M(110)

minus234

66258

029040

1432

92416116

35340

06794

minus4648

7Microfacet

M[(100times110

)]minus1

1734

896

029040

242512

704255

444003

50437

minus4259

8

Nanorod

MNR(I)

minus410

29836

829040

683480

1984811

422991

1704

0minus4

218

8MNR(II)

minus996

51022

329040

1080360

3137342

955937

24376

minus4253

7MNR(III)

minus164

13772

6729040

1370

160

3978

914

1508172

30323

minus4273

5


Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





OMn

(a)

OMn

(b)

OMn

(c)

OMn

(d)

OMn

(e)

OMn

(f)

OMn

(g)









(1)



OTi

(a)

OTi

(b)

OTi

(c)

OTi

(d)

OTi

(e)

OTi

(f)

OTi

(g)







Table3Surfa

ceenergy


eenergy(119864

cohesiv

e)of


lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119860 (A)

119861 (A)

119878 (A2)

119864 surface(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Mn 8O16

minus117

34896

0mdash

mdashmdash

mdashmdash

minus4722

3

Bulksurface

M(100)

minus469

34899

729040

19844

0576265

46843

06503

minus4673

5M(110)

minus234

66258

029040

1432

92416116

35340

06794

minus4648

7Microfacet

M[(100times110

)]minus1

1734

896

029040

242512

704255

444003

50437

minus4259

8

Nanorod

MNR(I)

minus410

29836

829040

683480

1984811

422991

1704

0minus4

218

8MNR(II)

minus996

51022

329040

1080360

3137342

955937

24376

minus4253

7MNR(III)

minus164

13772

6729040

1370

160

3978

914

1508172

30323

minus4273

5


Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





OTi

(a)

OTi

(b)

OTi

(c)

OTi

(d)

OTi

(e)

OTi

(f)

OTi

(g)







Table3Surfa

ceenergy


eenergy(119864

cohesiv

e)of


lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119860 (A)

119861 (A)

119878 (A2)

119864 surface(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Mn 8O16

minus117

34896

0mdash

mdashmdash

mdashmdash

minus4722

3

Bulksurface

M(100)

minus469

34899

729040

19844

0576265

46843

06503

minus4673

5M(110)

minus234

66258

029040

1432

92416116

35340

06794

minus4648

7Microfacet

M[(100times110

)]minus1

1734

896

029040

242512

704255

444003

50437

minus4259

8

Nanorod

MNR(I)

minus410

29836

829040

683480

1984811

422991

1704

0minus4

218

8MNR(II)

minus996

51022

329040

1080360

3137342

955937

24376

minus4253

7MNR(III)

minus164

13772

6729040

1370

160

3978

914

1508172

30323

minus4273

5


Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Table3Surfa

ceenergy


eenergy(119864

cohesiv

e)of


lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119860 (A)

119861 (A)

119878 (A2)

119864 surface(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Mn 8O16

minus117

34896

0mdash

mdashmdash

mdashmdash

minus4722

3

Bulksurface

M(100)

minus469

34899

729040

19844

0576265

46843

06503

minus4673

5M(110)

minus234

66258

029040

1432

92416116

35340

06794

minus4648

7Microfacet

M[(100times110

)]minus1

1734

896

029040

242512

704255

444003

50437

minus4259

8

Nanorod

MNR(I)

minus410

29836

829040

683480

1984811

422991

1704

0minus4

218

8MNR(II)

minus996

51022

329040

1080360

3137342

955937

24376

minus4253

7MNR(III)

minus164

13772

6729040

1370

160

3978

914

1508172

30323

minus4273

5


Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Table4Surfa

ceenergy


eenergy(119864

cohesiv

e)of

rutileT

iO2crystalbu

lksurfa

ceand

nano

rodmod

els

Mod

els119864 t

otal

(eV)

119886 (A)

119861 (A)

119878 (A2)

119864 surface

(eV)

119864 surface

(Jmminus2)

119864 coh

esive

(eV)

Crystal

Ti2O4

minus248

183

19mdash

mdashmdash

mdashmdash

minus7866

9

Bulksurface

T(100)

minus670

03110

529528

137748

813473

63510

12492

minus7788

5T(110

)minus4

9631

124

529528

129870

766949

55137

11503

minus7775

0Microfacet

T[(100

times110

)]minus8

4372

529

829528

44600

01316

929

97551

11852

minus7771

2

Nanorod

TNR(

1)minus7

9405

046

729528

606920

1792

087

135744

12119

minus7725

5TN

R(2)

minus129

03745

7029528

779360

2301260

178022

12377

minus7752

8TN

R(3)

minus218

37772

2029528

1025320

3027520

234859

12412

minus7777

9


②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





②

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

M(110)M(100)

Crystal

①

2 4 6 8 100Model

0

2

4

6EＭＯ

Ｌ＝

(Ｇ

minus2)

(a)

TNR(3)TNR(2)TNR(1)

T[(100 times 110)]

T(100)T(110)

Crystal00

04

08

12

16

4 6 82Model

EＭＯ

Ｌ＝

(Ｇ

minus2)

(b)



MNR(I)

MNR(II)

MNR(III)

M[(100 times 110)]

0

1

2

3

4

5

6

Relat

ive p

aram

eter

s (n

)

1 2 3 4 5 60Model

Y = 0997 middot X + 0037

R2 = 0999








119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







119864cohesive = 1119897 + 119898

(119864M119897O119898total minus 119897119864M

gas minus 119898119864Ogas) (2)








T[(100 times 110)]

TNR(3)TNR(2)

TNR(1)

T(110)T(100)

T-Crystal

M(110)M(100)

M-Crystal


M[(100 times 110)]

2 3 4 5 6 71Models

minus48

minus46

minus44

minus42

minus40

Coh

esiv

e ene

rgy

(eV

)

minus80

minus79

minus78

minus77

minus76

minus75

Coh

esiv

e ene

rgy

(eV

)

－Ｈ2

４Ｃ2








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








2s sum(Δ119876A)2 sum(Δ119876A)




09

10

11

12

Relat

ive p

aram

eter

s (n

)

2 3 41Models

－Ｈ2

４Ｃ2



119876AB = sum119896

119908119896Asum120583

AsumV

2119875120583V (119896) 119878V120583 (119896)

119876 (A) = sum119896

119908119896Asum120583

AsumV

119875120583V (119896) 119878V120583 (119896)

(3)






2



2andsum(Δ119876A)





2119904and sum(Δ119876A)



002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





002

004

006

0000

0002

0004

0006N

orm

aliz

ing

para

met

ers

(c)

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

Nor

mal

izin

g pa

ram

eter

s

Models

(f)

sum(Δ

QA)2s

0000

0001

0002

0003sum(Δ

d)2s

sum(Δ

d)2s

sum(Δ

QA-

B)2 s

sum(Δ

QA-

B)2 s

－Ｈ2４Ｃ2

Models

00000

00002

00004

00006

00008

0000

0005

0010

0015

0020

000

002

004

006

008

010

Nor

mal

izin

g pa

ram

eter

sN

orm

aliz

ing

para

met

ers

(e)

４Ｃ2

Models

(d)

４Ｃ2

Models

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

T[(1

00 times

110

)]

TNR(

3)

TNR(

2)

TNR(

1)

T(11

0)

T(10

0)

(b)

Models－Ｈ2

(a)

Models

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

M[(

100 times

110

)]

MN

R(II

I)

MN

R(II

)

MN

R(I)

M(1

10)

M(1

00)

－Ｈ2

sum(Δ

QA)2s






2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








2s sum(Δ119876A)2 sum(Δ119876A)


2

Y = 000578 middot X + 000863

R2 = 0989

M[(100 times 110)]

Models

Y = 0000626 middot X + 0000833

R2 = 0992

001

002

003

004

005

006

3 4 5 6 70 1 2 3 4 5 6 7 80 10001

0002

0003

0004

0005

0006

MNR(III)

MNR(II)

MNR(I)

M[(100 times 110)]

MNR(III)

MNR(II)

MNR(I)

sum(Δ

QA)2s

sum(Δ

QA-

B)2 s



2s+sum(Δ119876A)





2s and







2119904 and sum(Δ119876A)2119904 in the


4 Discussion



Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Y = 1139 middot X + 0096

R2 = 0993

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA-B)2s

(a)

0

2

4

6

0002 0003 0004 00050001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1058 middot X + 0186

R2 = 0999

EＭＯ

Ｌ＝

(Ｇ

minus2)

sum(ΔQA)2s

(b)


2s

0

2

4

6

002 003 004 005001

M[(100 times 110)]

MNR(III)MNR(II)

MNR(I)

Y = 1029 middot X + 0101

R2 = 0995

EＭＯ

Ｌ＝

(Ｇ

minus2)

(c)


2

M[(100 times 110)]

T[(100 times 110)]

3 4 5 61 2 3 4 5 61

MNR(II)

MNR(I)

M[(100 times 110)]

T[(100 times 110)] TNR(2) TNR(3)

MNR(III)MNR(III)

MNR(II)

MNR(I)

TNR(1)TNR(2)

TNR(3)

TNR(1)



R2 = 0997Y = minus042 middot m + 3461

R2 = 0996

1

2

3

4

Relat

ive p

aram

eter

s (l)

1

2

3

4

Rela

tive p

aram

eter

s (m

)











5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







5 Conclusion








Acknowledgments


References












































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls


































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




evolution mechanism of metallic dioxide mo from nanorods...

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