Tribo-Induced Melting Transition at a Sliding Asperity Contact

PRL 103, 205502 (2009) PHYSICAL REVIEW LETTERS
week ending
13 NOVEMBER 2009
T ¼ qa k ; (1)
where k ¼ 81:6 W=ðm KÞ is the thermal conductivity of
indium.
To calculate the heat flux supplied to the interface, we
approximate the energy dissipation when the tip comes
into contact with the QCM. We calculate the kinetic energy
of the quartz/electrode system using the measured oscillation
amplitude with a previously measured QCM amplitude
distribution [30]. The dominant term of the kinetic
energy (by 3 orders of magnitude) comes from the quartz
crystal itself, taking the form:
KE quartz ¼ 2R2 d½A$ cosð$tÞŠ 2 ð1 e 2b Þ
; (2)
16b
with R the electrode radius, d the thickness of the crystal,
(half of a wavelength when operated in the fundamental
mode), the density of quartz, ! the angular frequency, A 0
the maximum amplitude of oscillation at the center of the
electrode, t time, and b a constant of the amplitude distribution
which we assume to be 3 [30]. Using the changes in
amplitude from Fig. 1, we can find the change in energy per
cycle, which when multiplied by the frequency yields the
power dissipated. Figure 4 shows the results of these
calculations along with the calculated maximum temperature
rise assuming that half of the dissipated power went
into the indium as heat flux (with the other half going into
the tungsten tip) at a contact radius of 200 nm. The results
show that ample energy dissipation is present to melt the
indium.
We have reported here our observation of a velocity
dependent transition from solid to liquidlike behavior for
an STM tip in sliding contact with an indium electrode of a
QCM, the first such observation for a sliding asperity
contact. The velocity dependent nature of the frequency
shift implies a change in the mechanisms of frictional
dissipation; e.g., the contact region changes from solid to
liquid. An analysis of the change in kinetic energy of the
QCM when the tip comes in contact with the substrate
shows that ample energy is dissipated to melt the indium,
with temperature studies indicating that the onset of this
transition is close to indium’s surface melting temperature.
The results suggest that the surface, rather than bulk,
melting point temperature is the more relevant quantity
for tribological considerations.
This work has been supported by the Extreme Friction
MURI program, AFOSR No. FA9550-04-1-0381, and by
NSF DMR0320743 and DMR0805204. D. B. Brenner and
D. Irving are gratefully acknowledged for many useful
discussions.
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