Molecular dynamics simulation of the friction between talc (001) surfaces

surf~e ELSEVIER

science

Applied Surface Science 119 (1997) 335-340

Molecular dynamics simulation of the friction between talc (001) surfaces Hiroyuki Tamura, Kazuya Tsujimichi, Hideo Yamano, Kazuomi Shiota, Momoji Kubo, Adil Fahmi, Akira Miyamoto * Department of Molecular Chemistry.and Engineering, FacMty of Engineering, Tohoku Universi~, Aoba-ku, Sendal 980-77, Japan Received 22 November 1996; accepted 29 March 1997

Abstract

Molecular dynamics simulation is applied to study the friction between two talc (001) surfaces. The friction is large for commensurate contact (misfit angle of 0°) and small for incommensurate contact (misfit angle of 30°). © 1997 Elsevier Science B.V. Keywords: Friction; Talc surfaces; Molecular dynamic calculations

I. I n t r o d u c t i o n

When two solids slide against each other, the frictional phenomenon occurs. Despite the numerous experimental and theoretical [1-19] studies devoted to this subject, very little is known about the atomistic origin of the frictional forces. New experimental techniques such as friction force microscopy (FFM) [3-7], quartz crystal microbalance (QCM) [1,8,9] and surface force apparatus (SFA) [10,11] are used. Computer simulations mainly based on molecular dynamics (MD), where the friction is described by interatomic interactions between atoms of sliding surfaces, start to emerge [2,12-19]. Friction phenomena are too complex to be understood simply and clearly in realistic situations. It is useful to study simple friction phenomena via com-

* Corresponding author. Tel.: +81-22-2177233; fax: +81-222177235; e-mail: [email protected].

puter simulations. We apply MD simulation to understand the atomistic origin of the friction between talc (001) surfaces. Talc has a layered structure and interlayer interactions are very weak, whereas the cohesive energy of each layer is strong. Therefore, talc is easily cleaved at (001) planes. This surface is flat and its lattice arrangement was observed clearly by atomic force microscopy (AFM) [20]. Therefore, it is suitable for the study of the atomistic friction without wear. Previous friction experiments on muscovite mica [10] have shown that friction forces are maximum for commensurate contact and minimum for incommensurate contact. Talc and muscovite mica have similar atomic arrangements, except for the presence of potassium ions between muscovite layers which make interlayer forces stronger. Therefore, their (001) surfaces are expected to present similar behavior. We performed our MD simulations on the friction between talc (001) surfaces at commensurate and

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H. Tamura et al. /Applied Surface Science 119 (1997) 335-340

336

incommensurate contacts to investigate the relationship between the interface interaction and the behavior of surface atoms in sliding conditions.

'

2. Method of calculation

Uij = ZiZje2//rij + fo( bi + bj) × exp{( a i + a j - rij ) / ( b i + bj)}

+ Dij { e x p [ - 2bij ( r i j - ri; )] ( r i j - ri; )] }.

ox

Fig. 1. Side view of the slab model for talc (001) surface, it contains 7 layers and a total of 570 atoms.

MD calculation was performed using a modified version of MXDORTO program developed by Kawamura et al. [21]. The interaction potential has the following form:

- 2exp[-bij

OH gO H

z

(1)

The first term is the Coulomb potential, the second is the exchange-repulsion potential and the third term is the Morse potential. The cut-off distance for exchange-repulsion and Morse potentials is 13 A. Z is the nuclear charge, e the elementary electric charge, r the interatomic distance and f0 = 6.9511 × 10 - l l is a constant for units adaptation. The parameters a and b represent the size and the stiffness of the atoms, respectively. The pressure was controlled by scaling the cell size and the temperature was controlled by scaling atomic velocities. The Verlet algorithm [22] was used to calculate atomic velocities, while the Ewald method [23] was applied to calculate electrostatic interactions.

3. Results and discussion

are relaxed with no constraint. The interaction between the two slabs is rather weak. Therefore, at the final step of the simulation, they present similar structures and they are separated by a distance of 4 ,~. Next, we isolate a single relaxed slab and perform a static calculation to obtain the potential Pslab within a single slab. In order to calculate the change of the friction with the misfit angle and the interface distance, we freeze the structures of the two slabs (rigid model) at their equilibrium geometries. Next we fix the bottom slab and move the top one. We select the interface distance and misfit angle and we move the top slab in the (x, y) plane. This movement makes the top slab scanning the (x, y) plane in a way similar to the constant height mode in AFM simulation [24]. The interaction between atom pairs are summed up at each scan-point. The interval between two points is 0.5 A and the scanned area is 2 0 × 2 0 A. We calculate the interaction potential between the two s l a b s , Pinterf.... for selected values of the misfit angle and the interface distance (distance between oxygen atoms from the top layer of the bottom slab with those from the bottom layer of the top slab). The interaction potential, Pinterf .... is defined as the difference between the potential of the whole system, Ptotal, and potentials of the two free slabs in their equilibrium geometry:

3.1. Dependence of the friction on the misfit angle: rigid model

Pinterface = e t o t a l - 2 Pslab"

The model used in this calculation consists of two talc (001) slabs arranged along the z axis. Each slab is built up from seven layers and includes one Mg layer between two Si layers (Fig. 1); the total number of atoms is 570. The system is periodic along x and y directions. First we performed MD at 300 K on the two slab system to obtain equilibrium geometries. Both slabs

Besides, we also calculated the lateral forces by summing up interatomic forces acting between atoms in the two slabs. The choices of the misfit angle values of 0 ° and 30 ° (Fig. 2) are dictated by friction experiments on muscovite mica [10], where the 0 ° value corresponds to the maximum friction (commensurate contact) and the value of 30 ° corresponds to the minimum friction (incommensurate contact). On the other hand, we

(2)

H. Tamura et al. // Applied Surface Science 119 (1997) 335-340

(a)

[kJ/tool] (b)

I F

Y

v (~

=x

'

(a)

_'r

B

~ x[A]

10.5

[kJ/mol]

" 6

5 x[A]

12.3

Interface distance 3 A

: 3eX

&

337

1

(c)

[kJ/mol]

(d)

[kJ/mol]

"V"

~X

(b)

(c)

Fig. 2. (a) Top view of the talc (001) surface. The intersection between triangles correspond to oxygen atoms. (b) Two slabs in commensurate contact (misfit angle of 0°): line triangle corresponds to the top slab and dashed triangle corresponds to the bottom slab. (c) Two slabs in contact with a misfit angle q.

choose two interface distances: 4 ,~ which is the equilibrium distance and a smaller value of 3 .~. We will see below that frictional forces increase with the decrease of the interface distance. The results are presented as contour maps of the interface potential as shown in Fig. 3. The x and y axes give the scanned area, whereas the fluctuation in the potential is given by the change in the color of the pattern. White and dark spots correspond to positions of high and low potentials, respectively. A third axis which correlates the brightness of the pattern with the magnitude of the potential (kJ/mol) is added to the contour maps. Since the scanned area is very small, the obtained patterns do not have an ordered structure such as moir6 fringes. We notice that the calculated potential is repulsive (positive values). At the interface distance of 3 A, the fluctuation of the potential is larger for the misfit angle 0 °, between 10.5 and 19.3 kJ/mol (Fig. 3a), than the case of the misfit angle of 30°, between 12.3 and 12.8 kJ/mol (Fig. 3b). In Fig. 3a, we distinguish two spots: spot A (high repulsion), spot B (medium repulsion). Spot A corresponds to the arrangement where oxygen atoms of the top slab eclipse those from the bottom slab (Fig. 4a), then six oxygen

.

- 0

•

S

xIA]

m m

3.~

.

" 0

m m

~i

x[A]

3,o

Interface distance 4 A

Fig. 3. Contour maps of the interface potential as a function of the gravity center displacement in the (x, y) plane at selected misfit angle q and interface distance h: (a) q = 0 °, h = 3 A; (b) q = 30 °, h = 3 A;(c) q = 0 °, h = 4 A ; ( d ) q = 3 0 °, h = 4 . , ~ .

(a)

(b)

Fig. 4, Arrangements of oxygen atoms corresponding to spot A (a) and B (b) positions of Fig. 3. In (a) oxygens from the top slab eclipse those from the bottom slab. In (b) some of bottom slab oxygens (dark balls) are not eclipsed, which leads to weaker repulsion.

H. Tamura et al. / Applied Surface Science 119 (1997) 335-340

338

(a)

[dyn]

•

- 0

I'

e

5

x[A]

F

-15.4

(b)

[dyn]

3.2. M D s i m u l a t i o n " 0

~

x[A]

-0.6

Interface distance 3 A (c)

[dyn] (d)

[dyn] I

- 0

5

xlAl

-1.1

distance (from 3 to 4 A) leads to the decrease of lateral forces because of the increase in oxygenoxygen repulsion. These forces are larger where the lattice misfit angle is 0 °.

i

[i~

. . . .

-~-

Interface distance

~

x[A]

L

We use the same system as before, except that we assume a three-dimensional periodic boundary conditions (the periodicity along the z direction is included). The initial state of the system, obtained by MD calculation, corresponds to the relaxed slabs at a pressure of 1 atm and a temperature of 300 K. Next, the Mg atoms from the bottom slab are not allowed to move along the x axis which is the sliding direction, and MD was performed at a fixed pressure

-0.I

4A

2

(a)

Fig. 5. Contour maps of the lateral forces as a function of the gravity center displacement in the (x, y) plane at selected misfit angle ~ and interface distance h: (a) q = 0 °, h = 3 A; (b) q = 30 °, h = 3 A ; ( c ) q = O °, h = 4 A ; ( d ) q = 3 0 °, h = 4 A .

0=30 °

x o

g

0 0=0 °

atoms from each slab coincide. Spot B corresponds to the arrangement where six oxygens from the top slab eclipse only four oxygens from the bottom slab, which leads to weaker repulsion. At the equilibrium distance of 4 ~, (Fig. 3b-c) the fluctuation of the potential is smaller (3.5-4.4 k J / m o l at 0 ° and 3.94.0 kJ/mol at 30°). We notice that, regardless of the interface distance, the fluctuation of the potential is large when the misfit angle is 0 °. This is in agreement with experiments on muscovite where the friction is large at the commensurate contact. Similar to the interface-potential patterns, Fig. 5 shows contour maps for the projection of lateral forces along the x axis. The strength and the direction of the force were indicated by the brightness (bright and dark correspond to forces of positive and negative values, respectively). The fluctuation of the force is larger for the commensurate contact, between - 15.4 and 17.2 dyn (Fig. 5a). We indicate the positions of spots A and B defined previously. Comparing Fig. 5a ( q = 0 °, h = 3 A) and 5c ( q = O °, h = 4 A), we see that the increase in the interface

._~

0

D

2 Time (ps)

4

0.12

Cb)

0.08 >,

0.04 E

0=0

0

8

== E3

0=30

-0,04 0

°

°

4

2 Time(ps)

(c) := ~5 ~J

-0.04

o E

-0.08

~.j/0= t5

0"

-0.12 0

2 Time (ps)

4

Fig. 6. Displacement of the gravity center of the top slab along x (a) and y (b) and z (c) axis after an initial velocity of 50 m / s .

H. Tamura et al. / Applied Surface Science 119 (1997) 335-340

of 1. atm (the temperature was not controlled during this simulation). The calculations were performed for the following two approaches: 3.2.1. Initial velocities of 50 m / s were given to all atoms of the top slab Fig. 6 shows the displacement and the velocity of the gravity center of the top slab. At the commensurate contact (q = 0°), the velocity decreases since the top slab cannot cross the first peak of the potential. After the initial velocity was given, the top slab oscillates along y and z directions without appreciable translation (Fig. 6b-c). However, the internal energy of each slab did not increase after 10 ps of

(a) × ~,

~

lO

e~ 30°

A ,,

g o X

N

-10

= 0°

o

8 u.

o

10

5

339

simulation. At the incommensurate contact (q = 30°), where the potential is fiat, the velocity remains constant ( x ( t ) is a linear function, Fig. 6a). In this case the oscillation of the sliding slab is very small along y and z directions (Fig. 6b-c) and the internal energy of each slab did not increase. Therefore, the strength of the frictional forces at the commensurate contact is large enough to prevent translational movement. 3.2.2. Mg atoms from the top slab are moved along the x axis with a constant velocity of 50 m / s The projection of the frictional forces along the x axis is shown in Fig. 6a. They fluctuate with the displacement of the top layer and are larger for the commensurate contact. The displacement of the gravity center of the top layer along the z axis (Fig. 7b) shows a vertical oscillatory behavior. Therefore, frictional forces induce oscillations of the sliding slab but no slab-distortion was observed. The lateral displacement along y axis (Fig. 7c) shows a large deviation from the initial position in case of the commensurate contact, probably to avoid a position of high repulsion.

Time (ps)

(b)

".~

0.2 -

'

4. Conclusion

J 0.1

0

o

(c)

.y

•

o

5 Time (ps)

10

...................

~

\

-

O= 30 °

\ \

i:5

The present study shows the dependence of the friction on the misfit angle and interface distance. The scan of the sliding plane shows positions of high and low potentials. The friction is large for the commensurate contact, misfit angle of 0 ° and small for the incommensurate contact, misfit angle of 30 ° , in agreement with the previous experiments on muscovite. With the decrease of the interface distance, frictional forces increase following the increase in oxygen-oxygen repulsion. MD simulation shows that the frictional forces are due to the fluctuations in the interface potential. These forces induce oscillations of the sliding slab, but no structural distortion was observed.

5 Tlrne (ps)

Fig. 7. Frictional forces along the x axis (a) and displacement of the gravity center of the top slab along the z (b) and y (c) axes, when the top slab is moved along the x axis with a constant velocity of 50 m / s .

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H. Tamura et al./ Applied Surface Science 119 (1997) 335-340

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