Effect of Amorphous-Crystalline Phase Transition on Superlubric Sliding

Ebru Cihan, Dirk Dietzel, Benedykt R. Jany, and André Schirmeisen

Phys. Rev. Lett. 130, 126205 – Published 24 March 2023

Abstract

Structural superlubricity describes the state of greatly reduced friction between incommensurate atomically flat surfaces. Theory predicts that, in the superlubric state, the remaining friction sensitively depends on the exact structural configuration. In particular the friction of amorphous and crystalline structures for, otherwise, identical interfaces should be markedly different. Here, we measure friction of antimony nanoparticles on graphite as a function of temperature between 300 and 750 K. We observe a characteristic change of friction when passing the amorphous-crystalline phase transition above 420 K, which shows irreversibility upon cooling. The friction data is modeled with a combination of an area scaling law and a Prandtl-Tomlinson type temperature activation. We find that the characteristic scaling factor $γ$ , which is a fingerprint of the structural state of the interface, is reduced by 20% when passing the phase transition. This validates the concept that structural superlubricity is determined by the effectiveness of atomic force canceling processes.

Received 23 May 2022
Accepted 26 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.126205

Physics Subject Headings (PhySH)

Friction

Nanoparticles

Atomic force microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ebru Cihan ^1,2, Dirk Dietzel ^1,3,*, Benedykt R. Jany ⁴, and André Schirmeisen ^1,3

¹Institute of Applied Physics, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany
²Institute for Materials Science and Max Bergmann Center for Biomaterials, TU Dresden, 01069 Dresden, Germany
³Center for Materials Research, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany
⁴Marian Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30348 Krakow, Poland

^*dirk.dietzel@ap.physik.uni-giessen.de

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Issue

Vol. 130, Iss. 12 — 24 March 2023

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Images

Figure 1
Lateral manipulation of an antimony nanoparticle on graphite. (a) Top: AFM topography image before manipulation. Bottom: Topography image after manipulation. (b) Lateral force signal along the path of manipulation. The AFM tip reaches the nanoparticle at about $x = 150 nm$ and the lateral force signal increases to $Δ F_{l, static}$ before $Δ F_{l, sliding}$ then corresponds to the sliding friction of the nanoparticle.
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Figure 2
(a)–(c) Temperature dependence of sliding friction measured for three different nanoparticles for continuously increasing temperatures between 300 and 750 K (blue symbols). The red data point in (a) was recorded after cooling particle 1 from 750 back to 300 K. For increasing temperatures below 700 K the temperature dependence can be divided into two regimes as indicated by the theoretical curves based on thermally activated stick slip (continuous lines). The transition corresponds to the typical temperature range for structural phase transitions of nanoscale antimony as indicated by the grey background color. In addition, a high temperature regime with increased friction emerges once the sample temperature exceeds $400 ° C$ .
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Figure 3
Friction forces measured during manipulation of nanoparticle 1 [ $A = 59 700 {nm}^{2}$ , Fig. 2] at 300 K before and after heating. A significant reduction in friction by a factor of 1.76 is found. In addition, the AFM-topography images (top) verify that particle size and shape have not changed during exposure to high temperatures. In particular, no significant evaporation of antimony occurred.
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Figure 4
SEM and EBSD analysis of Sb particles on HOPG. (a),(b) SEM surface morphology of the unheated sample (a) and the sample heated to 513 K (b). (c),(d) SEM EBSD IQ maps of the unheated sample (c) and the sample heated to 513 K (d). (e),(f) EBSD inverse pole figure maps ( $Z$ out of plane) for HOPG (e) and the heated Sb particles (f). The orientation of hexagonal unit cells is shown for selected points.
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Figure 5
Irreversible friction changes for Sb nanoparticles after heating to 500 K. The friction values were obtained at three different temperatures from nanomanipulation experiments for three different groups of nanoparticles of similar size. Left: friction measurements at 300 K, Middle: friction measurements after heating the sample to 500 K, Right: friction measurements at 300 K after the sample was cooled down again. After heating, the nanoparticle friction is reduced by a factor of approximately 2.
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Figure 6
Normalized sliding friction as a function of the number of antimony atoms at the interface measured for 2 ensembles of nanoparticles at 300 K before (green hexagons) and after (red circles) heating the sample to 500 K. The straight lines represent the scaling of friction vs the atom number for the two cases. The friction data has been normalized by the single atom friction of antimony on HOPG which, in turn, was derived from fitting $F_{l, sliding} = F_{0} N^{0.5}$ to the dataset analyzed before heating. From the dotted lines, the error of $γ^{'}$ can be estimated.
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