Optical measurement of phase transition induced by friction

Optics Communications 436 (2019) 34–37

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Optical measurement of phase transition induced by friction Ryan Hogan a , Tran Vinh Son b , Alain Haché a ,∗ a b

Département de Physique et d’Astronomie, Université de Moncton, Canada E1A 3E9 Physics Department, Concordia University, 1455 Boulevard de Maisonneuve O, Montréal, Canada H3G 1M8

ARTICLE Keywords: Vanadium dioxide Phase transition Kinetic friction

INFO

ABSTRACT Optical effects are measured during the phase transition of vanadium dioxide (VO2 ) exposed to friction, thereby opening new possibilities for friction measurements and detection. Exposure to periodic cycles of kinetic friction yield measurable, repeatable and reversible changes in optical properties of the films. Changes in reflectance are detected with thermal flux intensities as low as 1 mW/cm2 . Characteristic response and recovery times are studied and modelled, as well as the effect of operating temperature, friction speed, pressure, friction coefficient and the thermal properties of the substrate.

1. Introduction Vanadium is a transition metal which can form several types of stable oxides, some of which exhibit insulator-to-metal phase transitions. A particularly interesting oxide is VO2 , whose phase transition occurs at the relatively low temperature of 68 ◦ C. As it transforms from an insulator to a metal, a sharp increase in electrical conductivity is observed, as well as important changes of refractive indices, which affect reflectance and transmittance in the near-infrared. Owing to these properties, VO2 has been used in a wide range of applications, including optical switching, optical filtering, optical sensing, infrared imaging, energy-saving windows, and tunable photonic devices [1–4]. The phase transition in VO2 is typically induced in one of four ways: (1) by heating with an external heat source [5,6], (2) by heating with an electric current passing through the material [7,8], (3) by optical excitation of free carriers [9,10], or (4) by mechanical strain [11,12]. In this paper, changes in optical properties are used to detect and study phase transitions in VO2 exposed to mechanical friction. The motivations for this research are twofold. First, it could extend applications of phase transition materials to include slippage sensing and provide a new method for friction measurement, for example by determining friction coefficients without measuring the friction force. Second, and at a more fundamental level, mechanical friction could provide a different approach to study these important materials and possibly correlate results to surface properties and morphology.

friction and use it as a heat source in the heat equation to find the surface temperature as a function of time. Considering two surfaces sliding against each other and characterized by a kinetic friction coefficient 𝜇𝑘 , an element of surface area 𝑑𝐴 with a normal force 𝑑𝑁 = 𝑝𝑑𝐴, with 𝑝 the local pressure, produces a kinetic frictional force 𝑑𝑓𝑘 = 𝜇𝑘 𝑑𝑁 = 𝜇𝑘 𝑝𝑑𝐴. With a sliding velocity 𝑣, the power dissipated per unit area is 𝑑𝑊 = 𝜇𝑘 𝑣𝑝. (1) 𝑑𝐴 This heat flux generated at the interface between media 1 and 2 propagates into each medium by an amount 𝐻1 and 𝐻2 , respectively, and by conservation of energy, we have

𝐻=

(2)

𝐻 = 𝐻1 + 𝐻2

By imposing continuity of temperature across the interface, the ratio 𝐻1 ∕𝐻2 is found to be

2. Theory

𝐻1 ∕𝐻2 = 𝑒1 ∕𝑒2 (3) √ where 𝑒 = 𝜅𝑐𝑣 is the thermal effusivity, with 𝜅 the thermal conductivity and 𝑐𝑣 the heat capacity per unit of volume. In this study, friction is applied in a controlled fashion using a rotating cylinder rubbing against a sample of VO2 . The cylinder of radius 𝑅 rotates at an angular velocity 𝜔 while pushing against the sample with a force 𝐹 . The local sliding velocity is a function of 𝜌, the distance to the centre of the cylinder, and is given by 𝑣 = 𝜌𝜔. With the average pressure given by 𝑃 = 𝐹 ∕(𝜋𝑅2 ), and putting this into Eq. (1), we obtain a heat flux with radial symmetry:

To determine the conditions under which a phase transition can occur in VO2 by friction, we first calculate the heat flux generated by

𝐻(𝜌) =

{

𝜇𝑘 𝑃 𝜔𝜌

0≤𝜌≤𝑅

0

𝜌>𝑅

∗ Corresponding author. E-mail address: [email protected] (A. Haché).

https://doi.org/10.1016/j.optcom.2018.11.072 Received 25 October 2018; Received in revised form 22 November 2018; Accepted 25 November 2018 Available online 4 December 2018 0030-4018/© 2018 Published by Elsevier B.V.

(4)

R. Hogan, T.V. Son and A. Haché

Optics Communications 436 (2019) 34–37

Fig. 2. Surface temperature at 𝜌 = 0 for periodic cycling of frictional heat applied by a rotating cylinder of radius 𝑅: with (A) a semi-infinite sample and (B) with sample of thickness 𝐿 = 𝑅∕3.

Fig. 1. Surface temperature profile with friction applied by a rotating cylinder of radius 𝑅. Time is given in units of 𝜏0 = 𝑅2 ∕𝐷 the characteristic time of heat diffusion across the source area.

Table 1 Specifications of samples used in this study.

This heat flux averaged over the contact area becomes 𝐻 = 2𝜇𝑘 𝜔𝑃 𝑅∕3. We can now solve the heat transfer equation ⃗ = −𝜅∇𝑇 (⃗𝑟). 𝐻

Sample

Substrate

Thermal diffusivity (m2 /s)

Thermal effusivity (J/𝑜 C s1∕2 m2 )

VO2 film thickness (nm)

A B C D

SiO2 SiO2 Al2 O3 Si

8.5 × 10−7 8.5 × 10−7 1.5 × 10−5 8.4 × 10−5

1450 1450 1.2 × 104 1.5 × 104

100 100 80 100

(5)

(6)

using a finite difference method and using Eq. (4) as boundary condition at the interface. Since the problem we consider has cylindrical symmetry, the problem is solved numerically on a 2D mesh grid for 𝜌 and 𝑧. Since thermal diffusion along the film is negligible compared to diffusion inside the substrate [13], the thermal properties of the film, which may depend on the substrate type, can be omitted. Fig. 1 shows examples of calculated surface temperature profiles at various times with a frictional heat source given by Eq. (4). Since the time evolution depends on the thermal diffusivity 𝐷 of the substrate, time is expressed in units of 𝜏0 = 𝑅2 ∕𝐷 the characteristic time for heat to diffuse over a length 𝑅, the size of the heat source. When expressed in units of 𝜏0 , the surface temperature profile and dynamics is the same for all substrates. Moreover, surface temperature converges to a steady profile when 𝑡 ≫ 𝜏0 . While the results of Fig. 1 assume a semi-infinite substrate, we find similar results with substrates with finite thickness, except with higher steady-state temperatures because of heat build-up. Fig. 2 shows surface temperature at the centre of the cylinder (𝜌 = 0) over time while periodic on/off cycles of friction are applied. Calculations are made for the case of a semi-infinite substrate (curve A) and a substrate with thickness 𝐿 = 𝑅∕3 (curve B). For both cases, the short time scale dynamics are similar and dictated by the time constant 𝜏0 . The main difference is that the thin substrate geometry takes longer to reach a steady-state. For all radius-to-thickness ratios, however, surface temperature eventually converges. In real situations involving finite-sized samples, long-term temperature stabilization will be influenced by 𝜏1 = 𝑆 2 ∕𝐷, the characteristic diffusion time to the nearest heat sink. This heat sink may be, for example, a sample holder, located at a distance 𝑆 from the cylinder. Characteristic diffusion times not only dictate temperature dynamics such as rise-times and cooling times, but the amplitude of it as well. The maximum amount of thermal energy per unit volume accumulated in the vicinity of the heat source goes as 𝐻𝜏. We should therefore expect a trade-off between signal speed and amplitude, whereby samples with faster response times (higher thermal diffusivity) produce smaller temperature amplitudes.

temperature in an oxygen-rich environment [16,17]. Vanadium was sputtered onto the substrate in a vacuum chamber with 1.5 mTorr of argon, and then annealed at 500 ◦ C for 1 h in the presence of 180 mTorr pressure of oxygen. This process oxidizes metallic vanadium and turns it into VO2 . Samples hereafter labelled A to D are VO2 films of 100 nm in thickness deposited on glass (samples A and B), sapphire (C), and silicon (D). Before use in friction experiments, the presence of a phase transition in VO2 films was verified by spectrophotometry. Film thickness and refractive indices were measured by transmission and reflection ellipsometry. A protective coating of SiO2 was applied to all samples [18]. Measuring 100 nm in thickness, this coating is not strictly necessary, as experiments with direct friction applied onto VO2 showed similar effects. However, direct exposure eventually wore off VO2 , whereas protected samples withstood repeated testing. The kinetic friction coefficient between SiO2 and the rubber cylinder used in this experiment was measured experimentally at 𝜇𝑘 = 0.53±0.01, with 0.67 for the static friction coefficient. Thermal effusivity of the rubber is 575 J/𝑜 Cs1∕2 m2 . Table 1 shows the characteristic thermal diffusion times of all samples. Phase transition in VO2 was monitored optically by measuring reflectance in real time. The experimental setup depicted in Fig. 3 shows the sample in a holder with a hole allowing for a laser beam at 1550 nm to reflect off the sample from the other side, through the substrate. Friction is applied with the rubber cylinder attached to a rotating arm controlled by a stepper motor. The arm is free to move on a sliding platform and held against the sample with a constant force produced by a hanging mass. A heater and thermocouple system keeps the sample at some constant ambient temperature 𝑇𝑜 . This set temperature is important, as it determines the minimum amount of frictional heat needed to induce a phase change. The closer 𝑇𝑜 is to the phase transition temperature of 68𝑜 C, the less frictional heating will be needed to induce effects. Ideally, in order to achieve maximum sensitivity, 𝑇𝑜 should be set to a value where reflectance changes the most with temperature, i.e. where the slope d𝑅∕d𝑇 is largest. As Fig. 4 shows, between 35 and 80 ◦ C, reflectance versus temperature shows negative and positive slopes, with

3. Experimental Metallic vanadium films were prepared on various substrate materials using magnetron sputtering [14,15], followed by oxidation at high 35

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Optics Communications 436 (2019) 34–37

Fig. 6. Reflectance change induced by friction on sample C (sapphire substrate). Here 𝑃 = 60 kPa, 𝜔=40.6 rad/s and 𝑇𝑜 =60 ◦ C.

Fig. 3. Side view of the experimental setup. Reflectance changes are measured from the sample’s back side.

Fig. 7. Reflectance change of sample D (silicon substrate) with friction at 𝑃 =150 kPa, 𝜔=31.4 rad/s and 𝑇𝑜 =60 ◦ C.

Fig. 4. Reflectance at 1550 nm by a 100 nm VO2 film as a function of temperature.

Fig. 8. Effect of angular speed at constant pressure (𝑃 = 59 kPa) on sample B (glass substrate) on reflectance modulation at 𝑇𝑜 = 70𝑜 C.

with a time constant of 0.2 s for recovery, in accordance with the diffusion time constant. On the other hand, the modulation amplitude drops to 𝛥𝑅∕𝑅 = 5% in spite of the higher generated thermal flux at 275 mW/cm2 . This confirms the theory that faster response times are obtained at the expense of smaller modulation amplitudes. This substrate is much more thermally conductive, and we estimate that 95% of heat dissipates into the sample. Results with silicon (sample D) are shown in Fig. 7. As a result of higher thermal diffusivity, the relative reflectance change drops to 0.1% even though the thermal flux is increased to 530 mW/cm2 . The characteristic time of relaxation in this sample is measured to 0.1 s. In this sample, we estimate frictional heat to be absorbed in the sample by more than 95%. The effect of angular speed is investigated in Fig. 8. Here all parameters are maintained at constant values except for the angular speed. Below some minimal angular speed, the thermal flux is insufficient to trigger measurable changes in VO2 . Above this threshold, reflectance modulation amplitude increases with speed. A similar effect is observed by varying pressure alone, as shown in Fig. 9. At a given angular speed, there is a minimum pressure required to observe phase transition, and above this threshold, modulation increases with pressure. These findings are consistent with Eq. (4). The effect of set temperature is shown in Fig. 10. As 𝑇𝑜 is varied from 50 ◦ C to 90 ◦ C, reflectance modulation takes negative, null or positive values, in accordance with the behaviour of reflectance with temperature shown in Fig. 4. Also, consistent with this behaviour is that the maximum amplitude is observed when 𝑇𝑜 is near 68 ◦ C. Since different samples can have different phase transition temperatures, this can be compensated for by adjusting the ambient temperature.

Fig. 5. Reflectance change on sample A with pressure 𝑃 = 42 kPa, angular speed 𝜔 = 14.7 rad/s and 𝑇𝑜 = 70 ◦ C.

the steepest parts near 65 ◦ C. Reflectance also shows hysteresis upon cooling: films return to their original properties but with at transition temperature that is lower. 4. Results and discussion Fig. 5 shows reflectance changes on sample A during on–off cycles of friction (10 s on and 60 s off) with ambient temperature value of 𝑇𝑜 = 70 𝑜 C. The force applied is 1.5 N, and with the cylinder radius 𝑅 = 3.25 mm, the corresponding average pressure is 45 kPa. From the ratio of effusivities between SiO2 and rubber, we estimate that 75% of frictional heat is directed towards the sample. Reflectance tends to increase initially but settles into a periodic and reproducible pattern during the on–off friction cycles. The recovery time is 15 s, as shown in the figure inset, a value comparable to 𝜏0 = 12s for SiO2 . The average thermal flux is 75 mW/cm2 , producing a maximum reflectance amplitude 𝛥𝑅∕𝑅 = 6%. With a signal-to-noise ratio of 5%, the estimated minimum detectable thermal flux is 3 mW/cm2 . In some tests, resolutions on the order of 1 mW/cm2 . VO2 on sapphire exhibits much faster modulation times when exposed to friction, as shown in Fig. 6. Periodic modulation is observed 36

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Optics Communications 436 (2019) 34–37

time of the signal and its amplitude. In some tests, we detected thermal flux changes of 1 mW/cm2 , and we think this could be improved in future studies. For example, higher modulation amplitudes could be attained by probing with longer wavelength, which experience larger reflectance changes, or by using different film thickness to exploit interference effects, or by using different polarizations states and angles of incidence. The possibility of detecting friction on VO2 opens new possibilities for applications in slippage sensing or for tribology devices capable of measuring friction coefficients without measuring shear and/or pressure forces. From a more fundamental point of view, friction could offer a new approach to study this important phase transition material. Directly exposing VO2 to kinetic friction by various materials could reveal surface properties, structural information and surface interactions.

Fig. 9. Effect of applied pressure on the reflectance of sample B (glass substrate) at constant friction velocity (𝜔 = 31.4 rads/s and 𝑇𝑜 = 70𝑜 C).

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Fig. 10. The effect of ambient temperature 𝑇𝑜 on reflectance changes at constant friction speed and pressure.

Fig. 11. Effect of friction coefficient on reflectance change.

The effect of friction coefficient is demonstrated in Fig. 11. While maintaining the same friction conditions, we added a drop of silicon oil between the rubber cylinder and the sample. As a result, reflectance modulation immediately dropped. Without oil, reflectance increases steeply and modulates with clear features related to diffusion times 𝜏0 and 𝜏1 , whereas with oil, the modulation is hard to distinguish from noise. Without sufficient friction force, the mechanism is no longer able to generate enough heat to induce significant reflectance change. Previous studies have showed the possibility of inducing a phase transition in VO2 by mechanical strain, an effect that could potentially be at play in this study. In this experiment, however, the pressures applied are much smaller than the strains necessary to induce phase transition, which is typically in the MPa, or GPa range [11,19,20] . Also, the time scales measured in this study are consistent with thermal effect, not strain effects which are almost instantaneous. 5. Conclusions We have investigated the phase transition in VO2 induced by kinetic friction. By exploiting reflectance changes during the phase transition, we optically monitored VO2 films during exposure to repeated cycles of friction, and determined the role of pressure, friction speed and ambient temperature. Reflectance measurements were found to be systematic and reproducible in several samples. One of the key parameters is the thermal diffusivity of the substrate material, which dictates the recovery 37