research article molecular dynamics study on lubrication...

Research ArticleMolecular Dynamics Study on Lubrication Mechanism inCrystalline Structure between Copper and Sulfur

Ken-ichi Saitoh1 Tomohiro Sato1 Masanori Takuma1

Yoshimasa Takahashi1 and Ryuketsu Chin2

1Department of Mechanical Engineering Faculty of Engineering Kansai University 3-3-35 Yamate-cho Suita Osaka 564-8680 Japan2Kobe Steel Ltd 2-3-1 Shinhama Arai-cho Takasago Hyogo 676-8670 Japan

Correspondence should be addressed to Ken-ichi Saitoh saitoukansai-uacjp

Received 11 August 2015 Revised 24 September 2015 Accepted 29 September 2015

Academic Editor Te-Hua Fang

Copyright copy 2015 Ken-ichi Saitoh et alThis 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

To clarify the nanosized mechanism of good lubrication in copper disulfide (Cu2S) crystal which is used as a sliding material

atomistic modeling of Cu2S is conducted and molecular dynamics (MD) simulations are performed in this paper The interatomic

interaction between atoms and crystalline structure in the phase of hexagonal crystal of Cu2S are carefully estimated by first-

principle calculations Then approximating these interactions we originally construct a conventional interatomic potentialfunction of Cu

2S crystal in its hexagonal phase By using this potential function we performMD simulation of Cu

2S crystal which

is subjected to shear loading parallel to the basal plane We compare results obtained by different conditions of sliding directionsUnlike ordinary hexagonalmetallic crystals it is found that the easy-glide direction does not always show small shear stress for Cu

2S

crystal Besides it is found that shearing velocity affects largely the magnitude of averaged shear stress Generally speaking highervelocity results in higher resistance against shear deformation As a result it is understood that Cu

2S crystal exhibits somewhat

liquid-like (amorphous) behavior in sliding condition and shear resistance increases with increase of sliding speed

1 Introduction

In recent years using lead (Pb) in metallic material is strictlyprohibited due to risk to human health That is why lead-free alloy is now being sought for mechanical materialsIt has been recognized that bronze which is composed ofcopper (Cu) and tin (Sn) atoms forms a material withgood performance of lubrication by the addition of Pbatoms Therefore Cu-Sn alloys are widely used for slidingmechanical elements such as brake frictionmaterials (brake-pads) ormechanical bearingmaterials Broadly speaking it isunderstood that Pb solids basically have low melting pointand they easily tend to be fluidic under high temperatureand high pressure condition as in the environment insidethe sliding equipment One example of substitution of Pbis bismuth (Bi) but it is regarded as one of rare metalsand it is hard to obtain much Therefore it requires us toclear the hurdle concerning both cost and safety Recentlyit is reported that bronze with the addition of sulfur (S)

atoms shows very good performance of lubrication in slidingmaterial and it has already been patented and been actuallydeveloped as an engineering material for industrial use [1]Historically it has been well known that S atoms provide anice machinability (in cutting) of copper alloy because theywork as ldquotip-breakerrdquo in cutting process [2] Besides S atom iswell accepted as a component of solid lubricant like Pb atomFor example molybdenum disulfide MoS

2 including many

S atoms exhibits high performance as the solid lubricantTherefore alloys made of Cu and S may provide good slidingand friction performance In those alloys S atom will play arole of the long-standing Pb atom instead Nevertheless thelubricating mechanism in Cu-S system has not been clarifiedyet and we should uncover it by studying further

Hirai et al have succeeded in developing a bronze madewith microscopic dispersion of copper sulfide (Cu

2S) and

they are now proceeding to its industrial use [3] Akamatsuet al are also exploring the fabricating method of Cu

2S alloy

by the motivation of avoiding the risk to human health [4]

Hindawi Publishing CorporationJournal of MaterialsVolume 2015 Article ID 963257 13 pageshttpdxdoiorg1011552015963257

2 Journal of Materials

In the field of mineralogy Cu2S crystal is well known as a

mineral called chalcocite Recently since the Cu2S structure

has a unique electronic behavior as for ionic conductivity itis planned to be used for switching device applications suchas a solar power plant material [5] and a superconductivitymaterial [6 7] In the context of unique sliding and frictionbehavior of Cu

2S crystal already found experimentally the

present authors have studied it by atomistic modeling One ofstable stoichiometries of copper and sulfide system is foundat Cu

2S (Cu S = 2 1) Interestingly this Cu

2S compound

exhibits very complicated solid phase transition behavior[8 9] Around the standard temperature the unit structureof Cu

2S is orthorhombic but it transforms into hexagonal

symmetry above 105∘C (degrees Celsius)Moreover in highertemperature above 460∘C it is transformed into cubic crys-tal

When copper alloys are used for sliding and frictionmaterials they are generally placed in a severe condition ofhigh temperature beyond several hundred ∘C and thereforethe behavior of hexagonal crystal (HC) would be worthstudying extensively In Cu

2S crystal consequently one S

atom has two neighbor Cu atoms So they tend to organizea triangular conformation and keep their firm interatomicbonding when they are stabilized The same mechanismconcerning S atom is also suggested in MoS

2system which

is famous as good solid lubricant where the S atom makesfirm bonding with metal atoms [10]

Other than chalcocite (Cu2S) there are some well-known

natural minerals based on copper alloy [11 12] such asbornite (Cu

5FeS4) chalcopyrite (CuFeS

2) covellite (CuS)

and digenite (Cu9S5) All of these alloys are interesting as

for interrelationship in their fabrication and all of them maybe applied to new functional material in the future Amongthem however Cu

2S crystal is still a main compound so it

should be focused on particularlyThus in this paper we willstudy the atomistic structure of Cu

2S in HC and discuss its

atomistic behavior in sliding and friction processIn the present study aiming at unempirical approach

the first-principle (ab initio) calculation is utilized to identifythe crystal structure of Cu

2S So far there have been some

studies of copper sulfides by ab initio method which aremainly employing density functional theory (DFT) [5 13 14]The electronic structure has been reproduced but unfortu-nately there still remains ambiguity about atomic positionof coppers in the unit crystal and so further modelingand discussion will be required Therefore in this studyby using conventional DFT software package Wien2k [15]the optimization of the unit structure of the Cu

2S in HC

is carried out based on Kashida et alrsquos structural model[13] As a result we obtain its energetically stable structureand we determine its basic crystalline information that islattice constants as for lengths 119886 and 119888 assuming the HCconfiguration

In order to understand the dynamics of sliding or fric-tion occurring in Cu

2S crystal molecular dynamics (MD)

simulation is suitable Lattice constants 119886 and 119888 and ground-state energies which are obtained by ab initio calculations areused in the determination of interatomic potential for MDsimulation In the MD simulation an existing interatomic

potential function of MoS2[10] is referred to for its function

or functional form This seems reasonable because thosetwo crystals of metal sulfide (Cu

2S and MoS

2) have many

common features as described aboveThus we simulate atomistically the sliding of Cu

2S crystal

by using MD method with an original and nonempiricalinteratomic potential The computation model is built bystacking layers on slip plane (basal plane) of HC lattice and itis at the first place compressed and then shear deformation isapplied Here the compression is crucial since in the actualsituation the friction behavior in sliding is to take placeunder severe contact condition with large compressive stress(pressure on the contacting surface) We will focus on thedependence on crystalline direction of sliding or on slidingvelocity in such severe condition

This paper is organized as follows Following the Intro-duction we describe the basic information of crystal struc-ture of Cu

2S and show some theories needed for the

modeling and the calculation Then the essence of the abinitio calculation is shown and the procedure to implementthe interatomic potential is briefly presented Thereafterthe MD model used in sliding simulation is explainedThe summary of results in ab initio calculation and MDresults of sliding simulation are shown and their discus-sion is made Finally the conclusion of this paper will bemade

2 Theory and Method

21 Atomic Structure of Cu2S Crystal As pure compounds

of copper sulfide there are covellite (CuS) and chalcocite(Cu2S) and the latter is focused on now For Cu

2S

orthorhombic crystal is obtained in room temperature butbeyond 105∘C it transforms into hexagonal crystal (HC)Furthermore in higher temperature than 460∘C it changes tocubic crystal [8] Copper alloys are often subject to very highpressure and relatively high temperature during operationsuch as in the surface layer of mechanical bearing Thusthe present simulation should focus on the temperaturerange around several hundred kelvins Accordingly the Cu

2S

material here is assumed to be in HC HC is also taken inMoS2and carbon allotrope (graphite or nanometer-thickness

graphene) and both of them are well-known solid lubricantsAmong conventional metals however HC metal such asmagnesium (Mg) is relatively inferior in deformation dueto the lack of crystalline slip systems when compared withface-centered cubic (fcc) crystals such as aluminum (Al) andCu Only the basal slip of hexagonal crystal is always wellactivated in Mg crystal and so its slip is highly directiondependent It is guessed that sliding motion in HC structurewill prefer such direction-dependent featureThis leads to thefact that compounds with HC structure such as Cu

2S and

MoS2 will be good at lubrication

22 First-Principle Calculation Cu atoms are metal andinclude metallic bonds but on the other hand S atomsare nonmetal and show large electronegativity Accordinglybond between atoms inside Cu

2S seems very complicated

Journal of Materials 3

Possibly ionic bond and metallic bond would be nonlinearlyinterrelated In considering the structure and bonding stateof solid crystal it is helpful to reproduce and observe thedetailed electron density distribution Besides those resultscan be taken into account in the construction of accurateinteratomic potential for MD simulations First-principle(FP) calculation (in Latin words ab initio calculation)refers to all quantum-mechanical computational chemistrymethods and is sometimes called ldquoband calculationrdquo Itobtains electron density around atomic nuclei based on theperiodic crystal structure of constituent atoms Nowadaysa number of software packages of FP method are availablein many researches Among those software packages ourchoice is WIEN2k package [15] which is based on densityfunctional theory (DFT) The characteristic of WIEN2k isthat it uses full-potential formulation instead of muffin-tinapproximation and that it uses the linearized augmentedplane wave basis set with local orbitals (LAPW + lo) As forcorrelation exchange term it can apply either local densityapproximation (LDA) or generalized gradient approximation(GGA)The detailed theory and usage are not the main focusof this study and should be omitted here

While all the S atoms in Cu2S are simply located at the

lattice point of HC it is suggested that Cu atoms seem tohave large mobility inside the unit cell especially in hightemperature keeping their symmetric atomic configurationSince actual position ofCu atoms inCu

2S is quite complicated

and is in fact giving controversy the present study employsexisting crystal model used in previous computation ofKashida et al [13] It is confirmed that the model agrees withexperimental fact as well as theoretical one Initial atomicposition of Cu

2S in HC is shown in Table 1 Figure 1 shows

initial position of atoms in Cu2S crystal unit

In order to obtain the minimum (ground-state) energythe atomic configuration is adjusted via the function ofoptimization in the software Lattice constants for angle(120572 120573 120574) are fixed so that the HC lattice should bemaintainedOn the other hand lattice constants for lengths (119886 119888) arechanged as follows Keeping a certain ratio of 119888119886 the lengths(119886 119888) are varied from compressive state to tensile one Thedeviation of 119888119886 from the initial value is +4sim+10 Thevolumetric change by the change of (119886 119888) ranges withinminus2sim+6 The exchange correlation energy of PBE-GGA isemployed Judgement of the energy convergence is done at00001 Ry where 1 Ry = 2180 times 10

minus18 J = 1360 eV Table 2summarizes calculation conditions and parameters used inthe present study The number of 119896-points is varied andapproximately above 20000 we may say that the total energywill be converged and shows sufficient accuracy Thereforewe recognize that 46 times 46 times 22 = 46552 119896-points arelarge enough and this will be used through the presentstudy

23 The Potential Function of Cu2S for MD As mentioned

above copper disulfide Cu2S has a variety of crystalline

structures depending on the temperature The structure isorthorhombic in standard temperature HC above 105∘C andcubic further above 460∘C Here as HC is assumed and

Table 1 Cu2S atomic coordinates and crystal data

(a)

Element Coordinate (relative to unit cell)119909 119910 119911

S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578

(b)

Property Unit ValueLattice constant(1) 119886 nm 0389Lattice constant(2) 119888 nm 0688Lattice constant(3) 120572 deg 900Lattice constant(4) 120573 deg 900Lattice constant(5) 120574 deg 1200Atoms per unit cell mdash 3Space group mdash P6

3

120572 120573120574

c

a

Cu

Cu

CuCu

Cu

Cu

CuCu

CuCu

S

S

Figure 1 Crystal structure of Cu2S (hexagonal crystal unit 13 of

conventional hexagonal prism)

the composition ratio is Cu S = 2 1 one S atom shouldcorrespond to two Cu atoms Therefore those three atomscompose a structural unit and the three-body bond is formedas a function of their angle By the way MoS

2has HC

structure as well The structural feature common to thoseHC lattices is that their slip plane is only limited to thebasal plane (0001) This is completely different from fcc orbcc which is accompanying many slip systems In fact theslip of HC lattice takes place only when a certain conditionhas been fulfilled Thus the potential function which wasproposed for MoS

2[10] can be utilized as the reference to

construct the function needed in the present study for Cu2S

Though MoS2and Cu

2S have the contrary ratio as to S

atom a lot of common features are likely to be found inthese two crystals For example angular-dependent three-body interaction is crucial for stabilization of both crystalsTo begin with we apply the potential forms used in theMoS2study and then our results obtained by first-principle

calculation are properly fitted to a new potential functionfor Cu

2S We insist that since the fitting data is obtained

theoretically only by DFT calculations the new potentialfunction will be an unempirical (ab initio) one


Table 2 Calculation condition for structural optimization of Cu2S

crystal

Exchange correlation potential mdash PBE-GGAEnergy to separate core from valence states Rylowast minus60Energy convergence criteria Rylowast 00001

Change of 119888119886 ratioRate of change +4sim+10Increment of rate (for 119888119886) +2

Volume changeRate of change minus2sim+6Increment of rate (for 119888119886) +1lowastEnergy unit 1 Ry = 2180 times 10minus18 J = 1360 eV

The detail of the new potential function for Cu2S is as fol-

lows The potential function is a summation of three distinctpotential functions as shown in (1) Ionic and metallic bondsare represented by Born-Mayer-Huggins (BMH) potential120601BMH and Morse potential 120601Morse as expressed in (2) and(3) respectively Angular-dependent potential for the bond ofCu-S interaction 120601angle is represented as (4) which is three-body potential Parameters for those potential functions aresummarized in Table 3

120601 = 120601BMH + 120601Morse + 120601angle (1)

120601BMH =

1199111198941199111198951198902

119903

+ 1198910(119887119894+ 119887119895) exp(

119886119894+ 119886119895minus 119903

119887119894+ 119887119895

) +

119888119894119888119895

1199036 (2)

120601Morse = 119863119894119895[exp minus2120573

119894119895(119903119894119895minus 1199030)

minus 2 exp minus120573119894119895(119903119894119895minus 1199030)]

(3)

120601angle = 119867120579(120579 minus 120579

0)2

(4)

In those equations 119911119894or 119911119895is electronic charge of each atom

and the values 119911S = minus20 and 119911Cu = +10 are employed for Sand Cu atoms respectively 119891

0= 1 [kcalA] = 4186 [kJA] is

the parameter which determines the stiffness of each ionicsphere and is transferred from the study of MoS

2 In the

Morse potential the equilibrium distance 1199030and bond energy

119863119894119895are fitted to those in the optimized structure which is

obtained in our ab initio calculation In the angular potentialequilibrium three-body angle 120579

0is also determined by our

ab initio calculation But it is difficult to derive the springconstant 119867

120579just from our ab initio calculation so the same

value as in MoS2is applied here Of course the value of 119867

120579

influences rigidity But its function form is basically harmonicand we found that the effect of spring constant on sliding isnot so crucial

24 Molecular Dynamics Model for Cu2S Sliding Figure 2

shows theMDmodel for sliding simulation In the first placethe optimized atomic configuration obtained by ab initiocalculation is prepared and then is thermally equilibratedat a finite temperature Then the structure is compressed

Table 3 Interatomic potential parameters for Cu2S crystal

(a) B-M-H potential

Atoms 119886119894

119887119894

119888119894

Unit [A] [A] [kJ05sdotA3mol05]Cu 0696 0085 0000S 1831 0085 70000

(b) Morse potential

Application 119863119894119895

120573119894119895

1199030

Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532

(c) Angular potential

Application 119867120579

1205790

Unit [kJmol] [deg]Cu-S-Cu 196648 98943S-Cu-S 196648 98943

in 119911 direction as shown in Figure 2 After that the atomicvelocity in the 119909 direction of two special regions (shownwith yellow color in the figure) is constrained so that sheardeformation is applied to the whole region in the directionparallel to the slip plane These processes are supposedto mimic a Cu

2S crystal in sliding condition This kind

of dynamic sliding simulation has been often studied fortribology-system as found in literatures so far [16] and itsadvantage is that we can observe directly the sliding behaviorof atomic system

It is supposed that crystalline slip plane of Cu2S plays

an important role in the slip deformation As stated aboveCu2S crystal unit has the HC conformation and the pri-

mary slip plane should be (0001) in Millerrsquos indices Theprimary slip direction should be the shortest interatomicdistance existing on the (0001) plane that is ⟨21 10⟩ Wewill call it (b)-direction hereafter The second easiest slipdirection should be ⟨0110⟩ which we call (a)-direction here-after In the present study we configure these two possibleslip directions for sliding simulation and compare theseresults

Other factors affecting sliding behavior of Cu2S would be

velocity and temperature Sliding velocities are varied so thatcorresponding shear velocities are 01 10 and 50ms Thereader should feel that these velocities seem quite higher thanused in actual slidingmachine or equipment However in theMD simulation time increment has to be very short such as1 fs (femtosecond) or less so such large deformation rate isinevitable

25 Analyzing MD Results In the present study the MDresults are mainly analyzed by radial distribution function(RDF) and atomic shear stress Strict formalization of stresstensor with regard to three-body term would require furtherdiscussion at this stage [17] so we use here an approximateand practial treatment These analyzing methods for MDresults are explained below


A model sliding in (b)-direction

z

yAtoms

A model sliding in (a)-direction

z

x

Cu

S

Fixed

Parallel to basal plane

Basal plane(0001)

(a)-direction

(b)-direction(slip direction of hexagonal crystal)

The model for researching dependence on direction or velocity

⟨0110⟩

110⟩⟨2

Figure 2 Abstract of MD sliding model of Cu2S crystal

251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu

2S crystal used in the present study exhibits HC

structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed

252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of

continuum Accordingly we need to formulate atomic stresstogether with some approximation

Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as

120590 (119894) =

1

2Ω (119894)

sum

119895

120597120601 (119894 119895)

120597119903 (119894 119895)

r (119894 119895) otimes r (119894 119895)119903 (119894 119895)

(5)

where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be


straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression

120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)

where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential

function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]

3 Results and Discussion

31 Optimization of Lattice Constant of Cu2S Crystal by

First-Principle Calculation The relation between volume andenergy of Cu

2S crystal unit is obtained as in Figure 3 by first-

principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice

constants are used as values to configure atomic positions inthe specimen of Cu

2S crystal

32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally

Minimum

Change of volume ()

Difference from initial structure

+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)

6543210minus1minus2minus001

009

01

008

007

006

005

004

003

002

001

0

Figure 3 Volume-energy relation of Cu2S crystal structure

Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)

Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)

strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903

0 120573119894119895and the energy parameter 119863

119894119895needed

in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4

The optimized crystalline structure of Cu2S which has

been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and


21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg

Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal

Table 4 Potential parameters fitted by FP calculations

(a) Morse potential (Cu-S)

Kind of pair 119863119894119895

120573119894119895

1199030

Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)

(b) Angular potential (S-Cu-S Cu-S-Cu)

Combination 1205790

Unit degS-Cu-S 98966Cu-S-Cu 98966

(c) B-M-H ionic potential (Cu-S)

Kind of pair 1199031015840

0119886Cu 119886S

Unit nm nm nm25319 070052 18314lowast

119886Slowast has been already obtained for MoS2 potential [10]

octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579

0and pairwise

distance 1199031015840

0 Finally they are 120579

0= 98966

∘ and 1199031015840

0= 2532 nm

respectivelyAdditionally the BMH term requires ionic radii 119886Cu and

119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903

0in Morse potential

above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS

2[10]

Thus MD potential parameters to reproduce the HCstructure of Cu

2S are obtained by mostly FP calculation and

they are summarized in Table 4

33 Sliding and Friction Behavior of Cu2S

331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu

2S

is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful

The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding

Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity

Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the


Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu

(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)

(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2

Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)

absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be

120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)

This stress deviation 120591119886reflects a sudden increase of friction

due to roughness of slide planes The time transition of 120591119886

is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591

119886 120591119886is

averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction

The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the

(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591

119886is changed as shown in Figures 9(B)

and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps

We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding


(a)

(a)-direction(b)-direction

(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(A) Shear length = 02nm (B) 04nm

(C) 06nm (D) 08nm

Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)

is carried out sufficiently the crystalline structure of Cu2S

has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding

332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591

119886

It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591

119886linearly increases with the same gradientThis fact

means that the material deforms in elastic manner for smallsliding and deformation However after that 120591

119886decreases

suddenly The larger the sliding velocity is the larger theaveraged value of 120591

119886is obtained It is reasonable that time rate

of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the

largest level of 120591119886 For (b)-direction Figure 10(B) shows that

the value of 120591119886increases with increase of sliding velocity It

is concluded that shear stress of this material depends largelyon sliding velocity

The relation between 120591119886and sliding velocity V is sum-

marized in Table 5 120591ave time average of 120591119886 is also shown

at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is

not by usual crystalline slip (glide) mechanism of ordinarymetals

On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such


(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms

Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding

Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V

Sliding velocityVms

Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding

05 193 22810 214 25450 264 283Average 224 255

amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the

present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591

0= 20sim25GPa These ideal shear

stresses at V = 0 correspond to static friction of materials Italso means that 120591

0are at least required for layered atoms to

exhibit a material flow

4 Conclusion

In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu

2S) under the sliding


0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)

= 05ms (a)-dir = 05ms (b)-dir

minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms

Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction

motion The MD simulation includes a new implementationof potential energy function for Cu

2S crystal where some

first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion

(1) First-principle calculations are performed for thehexagonal unit structure of Cu

2S crystal From the

optimized structure original lattice parameters 119886

and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability

for the hexagonal crystal structure of Cu2S in MD

simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-

erally found for usual hexagonal crystals is not thedirection with small resistance to sliding

(3) Cu2S crystal shows partially liquid-like structure and

behavior in which the shear stress occurring in thematerial depends on the sliding velocity

In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu

2S It is supposed that they are made

possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu

2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20

= 50ms (a)-dir = 10ms (a)-dir

= 05ms (a)-dir

0 01 02 03 04 05Shear distance (nm)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

Stress increase by velocity

minus20

= 50ms (b)-dir = 10ms (b)-dir

= 05ms (b)-dir

(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩

Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities

0

5

10

15

20

25

30

0 1 2 3 4 5


Linear fit ((a)-dir)Linear fit ((b)-dir)

(ms)

120591 a(G

Pa)

Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support

References

[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013

[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009

[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009

[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)

[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid

phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012

[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012

[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012

[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu

2Srdquo Science vol 141 no 3577 pp 276ndash277 1963

[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu

2Srdquo Mineralogical Society of America Special

Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting

[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009

[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu

5FeS4)rdquo

American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005


[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu

2S nanorodrdquo

Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence

band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003

[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007

[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml

[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014

[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004

[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989

[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov

[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012

[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


In the field of mineralogy Cu2S crystal is well known as a

mineral called chalcocite Recently since the Cu2S structure

has a unique electronic behavior as for ionic conductivity itis planned to be used for switching device applications suchas a solar power plant material [5] and a superconductivitymaterial [6 7] In the context of unique sliding and frictionbehavior of Cu

2S crystal already found experimentally the

present authors have studied it by atomistic modeling One ofstable stoichiometries of copper and sulfide system is foundat Cu

2S (Cu S = 2 1) Interestingly this Cu

2S compound

exhibits very complicated solid phase transition behavior[8 9] Around the standard temperature the unit structureof Cu

2S is orthorhombic but it transforms into hexagonal

symmetry above 105∘C (degrees Celsius)Moreover in highertemperature above 460∘C it is transformed into cubic crys-tal

When copper alloys are used for sliding and frictionmaterials they are generally placed in a severe condition ofhigh temperature beyond several hundred ∘C and thereforethe behavior of hexagonal crystal (HC) would be worthstudying extensively In Cu

2S crystal consequently one S

atom has two neighbor Cu atoms So they tend to organizea triangular conformation and keep their firm interatomicbonding when they are stabilized The same mechanismconcerning S atom is also suggested in MoS

2system which

is famous as good solid lubricant where the S atom makesfirm bonding with metal atoms [10]

Other than chalcocite (Cu2S) there are some well-known

natural minerals based on copper alloy [11 12] such asbornite (Cu

5FeS4) chalcopyrite (CuFeS

2) covellite (CuS)

and digenite (Cu9S5) All of these alloys are interesting as

for interrelationship in their fabrication and all of them maybe applied to new functional material in the future Amongthem however Cu

2S crystal is still a main compound so it

should be focused on particularlyThus in this paper we willstudy the atomistic structure of Cu

2S in HC and discuss its

atomistic behavior in sliding and friction processIn the present study aiming at unempirical approach

the first-principle (ab initio) calculation is utilized to identifythe crystal structure of Cu

2S So far there have been some

studies of copper sulfides by ab initio method which aremainly employing density functional theory (DFT) [5 13 14]The electronic structure has been reproduced but unfortu-nately there still remains ambiguity about atomic positionof coppers in the unit crystal and so further modelingand discussion will be required Therefore in this studyby using conventional DFT software package Wien2k [15]the optimization of the unit structure of the Cu

2S in HC

is carried out based on Kashida et alrsquos structural model[13] As a result we obtain its energetically stable structureand we determine its basic crystalline information that islattice constants as for lengths 119886 and 119888 assuming the HCconfiguration

In order to understand the dynamics of sliding or fric-tion occurring in Cu

2S crystal molecular dynamics (MD)

simulation is suitable Lattice constants 119886 and 119888 and ground-state energies which are obtained by ab initio calculations areused in the determination of interatomic potential for MDsimulation In the MD simulation an existing interatomic

potential function of MoS2[10] is referred to for its function

or functional form This seems reasonable because thosetwo crystals of metal sulfide (Cu

2S and MoS

2) have many

common features as described aboveThus we simulate atomistically the sliding of Cu

2S crystal

by using MD method with an original and nonempiricalinteratomic potential The computation model is built bystacking layers on slip plane (basal plane) of HC lattice and itis at the first place compressed and then shear deformation isapplied Here the compression is crucial since in the actualsituation the friction behavior in sliding is to take placeunder severe contact condition with large compressive stress(pressure on the contacting surface) We will focus on thedependence on crystalline direction of sliding or on slidingvelocity in such severe condition

This paper is organized as follows Following the Intro-duction we describe the basic information of crystal struc-ture of Cu

2S and show some theories needed for the

modeling and the calculation Then the essence of the abinitio calculation is shown and the procedure to implementthe interatomic potential is briefly presented Thereafterthe MD model used in sliding simulation is explainedThe summary of results in ab initio calculation and MDresults of sliding simulation are shown and their discus-sion is made Finally the conclusion of this paper will bemade

2 Theory and Method

21 Atomic Structure of Cu2S Crystal As pure compounds

of copper sulfide there are covellite (CuS) and chalcocite(Cu2S) and the latter is focused on now For Cu

2S

orthorhombic crystal is obtained in room temperature butbeyond 105∘C it transforms into hexagonal crystal (HC)Furthermore in higher temperature than 460∘C it changes tocubic crystal [8] Copper alloys are often subject to very highpressure and relatively high temperature during operationsuch as in the surface layer of mechanical bearing Thusthe present simulation should focus on the temperaturerange around several hundred kelvins Accordingly the Cu

2S

material here is assumed to be in HC HC is also taken inMoS2and carbon allotrope (graphite or nanometer-thickness

graphene) and both of them are well-known solid lubricantsAmong conventional metals however HC metal such asmagnesium (Mg) is relatively inferior in deformation dueto the lack of crystalline slip systems when compared withface-centered cubic (fcc) crystals such as aluminum (Al) andCu Only the basal slip of hexagonal crystal is always wellactivated in Mg crystal and so its slip is highly directiondependent It is guessed that sliding motion in HC structurewill prefer such direction-dependent featureThis leads to thefact that compounds with HC structure such as Cu

2S and

MoS2 will be good at lubrication

22 First-Principle Calculation Cu atoms are metal andinclude metallic bonds but on the other hand S atomsare nonmetal and show large electronegativity Accordinglybond between atoms inside Cu

2S seems very complicated















(a)


S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578

(b)


3

120572 120573120574

c

a

Cu

Cu

CuCu

Cu

Cu

CuCu

CuCu

S

S




2has HC




Though MoS2and Cu








crystal






120601 = 120601BMH + 120601Morse + 120601angle (1)

120601BMH =

1199111198941199111198951198902

119903

+ 1198910(119887119894+ 119887119895) exp(

119886119894+ 119886119895minus 119903

119887119894+ 119887119895

) +

119888119894119888119895

1199036 (2)

120601Morse = 119863119894119895[exp minus2120573

119894119895(119903119894119895minus 1199030)


(3)

120601angle = 119867120579(120579 minus 120579

0)2

(4)



0= 1 [kcalA] = 4186 [kJA] is


2 In the








120579





(a) B-M-H potential

Atoms 119886119894

119887119894

119888119894


(b) Morse potential

Application 119863119894119895

120573119894119895

1199030

Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532



1205790













z

yAtoms


z

x

Cu

S

Fixed


Basal plane(0001)

(a)-direction



⟨0110⟩

110⟩⟨2








120590 (119894) =

1

2Ω (119894)

sum

119895

120597120601 (119894 119895)

120597119903 (119894 119895)

r (119894 119895) otimes r (119894 119895)119903 (119894 119895)

(5)




120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)









2S crystal


Minimum

Change of volume ()


+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)


009

01

008

007

006

005

004

003

002

001

0


Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)




119894119895needed





21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials

















(a)


S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578

(b)


3

120572 120573120574

c

a

Cu

Cu

CuCu

Cu

Cu

CuCu

CuCu

S

S




2has HC




Though MoS2and Cu








crystal






120601 = 120601BMH + 120601Morse + 120601angle (1)

120601BMH =

1199111198941199111198951198902

119903

+ 1198910(119887119894+ 119887119895) exp(

119886119894+ 119886119895minus 119903

119887119894+ 119887119895

) +

119888119894119888119895

1199036 (2)

120601Morse = 119863119894119895[exp minus2120573

119894119895(119903119894119895minus 1199030)


(3)

120601angle = 119867120579(120579 minus 120579

0)2

(4)



0= 1 [kcalA] = 4186 [kJA] is


2 In the








120579





(a) B-M-H potential

Atoms 119886119894

119887119894

119888119894


(b) Morse potential

Application 119863119894119895

120573119894119895

1199030

Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532



1205790













z

yAtoms


z

x

Cu

S

Fixed


Basal plane(0001)

(a)-direction



⟨0110⟩

110⟩⟨2








120590 (119894) =

1

2Ω (119894)

sum

119895

120597120601 (119894 119895)

120597119903 (119894 119895)

r (119894 119895) otimes r (119894 119895)119903 (119894 119895)

(5)




120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)









2S crystal


Minimum

Change of volume ()


+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)


009

01

008

007

006

005

004

003

002

001

0


Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)




119894119895needed





21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





crystal






120601 = 120601BMH + 120601Morse + 120601angle (1)

120601BMH =

1199111198941199111198951198902

119903

+ 1198910(119887119894+ 119887119895) exp(

119886119894+ 119886119895minus 119903

119887119894+ 119887119895

) +

119888119894119888119895

1199036 (2)

120601Morse = 119863119894119895[exp minus2120573

119894119895(119903119894119895minus 1199030)


(3)

120601angle = 119867120579(120579 minus 120579

0)2

(4)



0= 1 [kcalA] = 4186 [kJA] is


2 In the








120579





(a) B-M-H potential

Atoms 119886119894

119887119894

119888119894


(b) Morse potential

Application 119863119894119895

120573119894119895

1199030

Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532



1205790













z

yAtoms


z

x

Cu

S

Fixed


Basal plane(0001)

(a)-direction



⟨0110⟩

110⟩⟨2








120590 (119894) =

1

2Ω (119894)

sum

119895

120597120601 (119894 119895)

120597119903 (119894 119895)

r (119894 119895) otimes r (119894 119895)119903 (119894 119895)

(5)




120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)









2S crystal


Minimum

Change of volume ()


+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)


009

01

008

007

006

005

004

003

002

001

0


Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)




119894119895needed





21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





z

yAtoms


z

x

Cu

S

Fixed


Basal plane(0001)

(a)-direction



⟨0110⟩

110⟩⟨2








120590 (119894) =

1

2Ω (119894)

sum

119895

120597120601 (119894 119895)

120597119903 (119894 119895)

r (119894 119895) otimes r (119894 119895)119903 (119894 119895)

(5)




120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)









2S crystal


Minimum

Change of volume ()


+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)


009

01

008

007

006

005

004

003

002

001

0


Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)




119894119895needed





21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





120590120572120573

(119894) =

1

2Ω (119894)

sum

119895

120597120601pair (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

1

3Ω (119894)

sum

119895119896

(

120597120601angle (119894 119895)

120597119903 (119894 119895)

119903120572(119894 119895) 119903

120573(119894 119895)

119903 (119894 119895)

+

120597120601angle (119895 119896)

120597119903 (119895 119896)

119903120572(119895 119896) 119903

120573(119895 119896)

119903 (119895 119896)

+

120597120601angle (119896 119894)

120597119903 (119896 119894)

119903120572(119896 119894) 119903

120573(119896 119894)

119903 (119896 119894)

)

(6)









2S crystal


Minimum

Change of volume ()


+10+8

+6+4

Ener

gy d

iffer

ence

(eV

)


009

01

008

007

006

005

004

003

002

001

0


Distance r (nm)090807060504030201

minus8

minus6

minus4

minus2

0

2

4

6

8

Mo-S bondCu-S bond

FP calculation

times10minus19En

ergy

EminusE0

(J)




119894119895needed





21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




21564Aring

26712Aring

23926Aring

35219Aring

Cu

S

S

S S S S S

Cu

SS S

124125 deg

91599deg106333deg

65876deg




Kind of pair 119863119894119895

120573119894119895

1199030



Combination 1205790



Kind of pair 1199031015840

0119886Cu 119886S




0and pairwise

distance 1199031015840


0= 98966

∘ and 1199031015840

0= 2532 nm



0in Morse potential


2[10]






2S






Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Disordered

Ordered layer

CuCu

CuCu

SS

S

To front

To back

To right

To left

Disordered

Ordered layer

CuCuCu

S

S

S Cu





120591119886=

1003816100381610038161003816120591tot minus 120591tot (0)

1003816100381610038161003816 (7)




119886 120591119886is








(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a)


(a)

(b)16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)


(b)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501

(a)(b)


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(b)

(b)

(a)

(a)

16

14

12

1

08

06

04

02

0

g(r)

r (nm)04504035030250201501


(C) 06nm (D) 08nm





119886




119886decreases













(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a)

(a)

(b)

(b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

r (nm)04504035030250201501

12

1

08

06

04

0

02

g(r)


(a) (b)

r (nm)04504035030250201501

14

12

1

08

06

04

02

0

g(r)


(a) (b)

(a) (b)

(B) = 10ms

(C) = 50ms

(A) Velocity = 05ms



Sliding velocityVms


05 193 22810 214 25450 264 283Average 224 255







4 Conclusion




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

20

40

60

80

0 200 400 600 800 1000

Shea

r stre

ss (G

Pa)

Time (ps)

(b)

(a)


minus20

0

20

40

60

80

0 100 200 300 400 500 600

Shea

r stre

ss (G

Pa)

Time (ps)

(a)(b)

minus20


(a)

(b)

0

20

40

60

80

Shea

r stre

ss (G

Pa)

minus20

Time (ps)


200150100500

(A) = 05ms (B) = 10ms

(C) = 50ms






2S crystal From the











2S crystal


0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

20

40

60

80

0 01 02 03 04 05

Shea

r stre

ss (G

Pa)

Shear distance (nm)

Slow decrease

Fast decrease

minus20


= 05ms (a)-dir


0

20

40

60

80

Shea

r stre

ss (G

Pa)


minus20


= 05ms (b)-dir



0

5

10

15

20

25

30

0 1 2 3 4 5



(ms)

120591 a(G

Pa)




Acknowledgments


References
















5FeS4)rdquo




2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





2S nanorodrdquo


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article molecular dynamics study on lubrication...

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