GB2482595A

GB2482595A - Apparatus and method for determining damping coefficient

Info

Publication number: GB2482595A
Application number: GB201113240A
Authority: GB
Inventors: James Frank Smith
Original assignee: Micro Materials Ltd
Current assignee: Micro Materials Ltd
Priority date: 2010-08-02
Filing date: 2011-08-02
Publication date: 2012-02-08
Anticipated expiration: 2031-08-02
Also published as: GB201012895D0; GB201104962D0; GB201113240D0; GB2482595B

Abstract

Apparatus and a method for testing surface properties of a sample are disclosed. The apparatus comprises a sample holder 40 and a probe 26, with the apparatus operative, with a sample held in the sample holder to oscillate the sample holder with the probe in contact with the sample to cause the probe to oscillate, to measure the phase difference between the oscillations of the sample holder and the probe and the amplitude of the probe, and to determine the contact damping coefficient between the probe and the sample, and thereby calculate the instantaneous power transmitted between the sample and the probe. Alternatively, the probe may be oscillated and resultant oscillation of the contacting sample may be measured to determine the damping coefficient.

Description

Apparatus and method for testing materials This invention relates to an apparatus and a method for testing materials. In particular, it relates to testing surface frictional properties of materials on a scale down to that of nanometres.

The difficulty involved in measuring and understanding friction on a small scale is one of the main impediments to bringing nanomachines of various types to the marketplace. Friction testing typically involves applying a known normal force to a test probe and measuring the tangential force experienced by the probe as it moves over a surface of a sample under test.

The tangential force is usually measured by means of a strain gauge. Friction measurement on a very small scale is difficult, in part due to tangential force calibration and measurement uncertainties. In particular, force transducer misalignment can lead to large errors in low friction situations.

An alternative to direct measurement of frictional force would be to determine the damping which occurs as the probe moves on the surface of the sample. Such a method would not require tangential force calibration. Furthermore, energy dissipation of itself is of fundamental importance, particularly for film adhesion/cohesion characterisation. This is related to the damping coefficient. However, there are no general techniques available which can measure such energy dissipation directly. Indeed, recent work has shown that wear mechanisms can be elucidated in terms of frictional energy dissipation, although the approach taken stifi necessitated tangential force measurement.

An aim of this invention is to provide a method and apparatus for testing the frictional properties of a surface of a sample by measurement of the damping coefficient corresponding to energy dissipation between the probe and the sample, and thereby determining energy dissipated at the contact as a result of the sliding contact between the probe and the sample.

To this end, from a first aspect, this invention provides apparatus for assessing the interaction between a surface of a sample and a test probe, the apparatus comprising a sample holder, a S drive unit operative, on application of an oscillating electrical signal, to cause the sample holder to oscillate along a displacement axis, a probe, a position sensor operable to generate a signal indicative of the position of the probe, and comprising comparison means operable to determine the relative phase of oscillation of the sample and the probe by analysis of the signal which drives the drive unit and the output from the position sensor, the apparatus being operative, with a sample held in the sample holder: a. to apply a signal to the to cause the drive means to oscillate the sample holder with the probe in continuous contact with it to cause the probe to oscillate along a measurement axis, b. to use the position measurement means to measure a component of the displacement in the measurement axis of the probe and/or phase difference between the oscillations of the sample holder and the oscillations of the probe, and c. to operate the comparison means to determine the damping coefficient between the probe and the sample by analysis of the signal applied to the drive means and the signal and a signal derived from the position measurement means, and thereby calculate the instantaneous power transmitted between the sample and the probe.

The invention may also be embodied in an alternative configuration, in which the probe is driven and causes the sample to oscillate. Therefore, the invention further provides apparatus for assessing the interaction between a surface of a sample and a test probe, the apparatus comprising a sample holder, a probe, a drive unit operative, on application of an oscillating electrical signal, to cause the probe holder to oscillate along a displacement axis, a position sensor operable to generate a signal indicative of the position of the sample, and comprising comparison means operable to determine the relative phase of oscillation of the sample and the probe by analysis of the signal which drives the drive unit and the output from the position sensor, the apparatus being operative, with a sample held in the sample holder: a. to apply a signal to the drive means to cause the drive means to oscillate the probe to cause the probe to oscillate along a measurement axis, with the probe in continuous contact with the sample, b. to use the position measurement means to measure a component of the displacement in the measurement axis of the sample and/or phase difference between the oscillations of the sample and the oscillations of the probe, and c. to operate the comparison means to determine the damping coefficient between the probe and the sample by analysis of the signal applied to the drive means and a signal derived from the position measurement means, and thereby calculate the instantaneous power transmitted between the sample and the probe.

Typically, the measurement axis is parallel to or substantially parallel to the displacement axis.

Alternatively, the measurement axis may be normal to or substantially normal to the displacement axis. Most preferably, the sample holder can be rotated about an axis that is normal to the displacement axis. This allows a flat surface of the sample to be aligned parallel to or at a suitable angle with respect to the displacement axis as generally required for testing of a sample.

For example, the drive unit may include a piezoelectric stack.

The position sensor may advantageously include a capacitor that has plates which vary in separation with movement of the probe.

The comparison meais may include a lock-in amplifier.

The probe is preferably mounted such that it will naturally oscillate when displaced from a rest position. However, the probe support must also provide means for application of a force to press the probe onto the surface of a sample and means for continuously monitoring the displacement of the probe from a rest position. For example, it may be carried on a pendulum.

From a second aspect, this invention provides a method for assessing the interaction between a surface of a sample and a test probe, the method comprising: a. driving the sample in an oscillating movement along a displacement axis with a probe in continuous contact with the sample to cause the probe to oscillate, b. measuring the phase difference between a component of the oscillation of the sample along a measurement axis and the probe and the amplitude of the oscillation of the probe, and c. analysing the measurement made in step b. to determine the contact damping coefficient between the probe and the sample, and thereby calculating the instantaneous power transmitted between the sample and the probe.

In an alternative configuration, the invention provides a method for assessing the interaction between a surface of a sample and a test probe, the method comprising: a. driving the probe in an oscillating movement along a displacement axis with the probe in continuous contact with the sample to cause the sample to oscillate, b. measuring the phase difference between a component of the oscillation of the probe along a measurement axis and the sample and the amplitude of the oscillation of the sample, and c. analysing the measurement made in step b. to determine the contact damping coefficient between the probe and the sample, and thereby calculating the instantaneous power transmitted between the probe and the sample.

Typically, the measurement axis is parallel to or approximately parallel to the displacement axis. Alternatively, the measurement axis may be normal to or approximately normal to the displacement axis.

Most preferably, the sample has a generally flat surface against which the probe makes contact. During performance of the testing method the flat sample surface is usually aligned perpendicularly to probe axis. Thus, when the frictional drag between the probe and the sample is sufficient, movement of the flat surface can produce motion of the probe, at least a component of which is in the direction of the displacement axis. Measuring this displacement and the phase of the movement with respect to the movement of the sample and relating it to the driving signal allows the contact damping to be determined.

Methods embodying the invention may further comprise a calibration phase before testing is performed to determiie the oscillatory characteristics in the absence of frictional contact between the probe and the sample. The calibration phase may include determining the total effective mass of the oscillating system, including the probe with the probe holder and the pendulum at the probe position. The calibration phase may also include determining the phase relationship between a signal applied to drive the sample and a signal that indicates the position of the probe. The calibration phase may also include determining the damping of the pendulum itself which can be subtracted from the total system damping determined during sample testing.

The invention requires application of force to the probe via the probe assembly and displacement measurement via the probe assembly. Force and displacement calibrations are therefore necessary.

Embodiments of the invention will now be described in detail, by way of example, and with reference to the accompanying drawings, in which: Figure 1 is a schematic view of test apparatus being a first embodiment of the invention; Figures 2 and 3 are side and plan views of a sample holder of the embodiment of Figure 1; Figure 4 is a view of a probe in contact with a sample in the embodiment of Figure 1; Figure 5 is a block diagram of electronic components of the embodiment of Figure 1; Figure 6 illustrates the idealised mechanical equivalents of the components of the embodiment of Figure 1; Figure 7 is a schematic view of test apparatus being a second embodiment of the invention; Figure 8 is a plan views of a sample holder of the embodiment of Figure 7; Figure 9 is a view of a probe in contact with a sample in the embodiment of Figure 7; Figure 10 is a block diagram of electronic components of the embodiment of Figure 7; and Figure 11 illustrates the idealised mechanical equivalents of the components of the embodiment of Figure 7.

With reference to Figure 1, apparatus embodying the invention includes a pendulum assembly that is carried on a chassis (not shown). The pendulum assembly comprises an elongate, straight ceramic pendulum rod 10 that extends generally vertically within the apparatus when set up for use. The pendulum rod 10 is carried on a pivot 12, which allows the pendulum rod to pivot about a horizontal axis that passes through a point to balaice the coil and weight forces applied to the pendulum, which is, in this embodiment, its approximate midpoint.

A coil 14 is carried towards the upper end of the pendulum rod 10. The coil 14 is closely adjacent to a magnet 16. Energisation of the coil 14 can cause it to be attracted to or repelled from the magnet 16, thereby urging the pendulum rod 10 to rotate about the pivot 12. This pivoting movement is constrained by a limit stop 18, and damped by a damper 20 close to the lower end of the pendulum rod 10.

Below the pivot 12, a probe holder 24 is carried on the pendulum rod. A test probe 26 that carries an indenting tip extends along an axis generally horizontally from the probe holder 24 in a direction normal to the axis of rotation allowed by the pivot 12. During pivotal movement of the pendulum 10 about a small angular displacement, the probe 26 will move in an approximately straight line along its axis. The probe holder carries a metal plate 28 which, i in combination with a fixed plate 30, forms a capacitor that, as will be discussed below, provides a means by which a signal indicative of the position of the test probe can be derived.

The spacing between the plates, and therefore, the capacitance, varies as the pendulum rod 10 rotates about the pivot 12.

To ensure that the pendulum rod 10 remains vertical when no external force is applied to the sample, an adjustable balance weight 34 is carried on the pendulum rod 10.

The apparatus further includes a sample holding assembly shown in Figure 2 and 3. The sample holding assembly has a sample holder 40 upon which a sample to be tested 38 is carried. The sample holder 40 is supported by a supporting stage 42 and arranged such that it can rotate with respect to the supporting stage 42 about a vertical axis, and clamped in place by tightening a nut 44. The supporting stage 42 is connected by a clamp 48 to parallel leaf springs 46 that extend in a vertical plane.

The leaf springs 46 are received in a recess 50 within an oscillating bar 52. They are clamped within the recess 50 by a screw 56 that clamps the springs 46 to a spring clamp block 58 that is located between them. The distance between the sample holder 40 and the pendulum rod 10 can be adjusted by loosening the screw 56, sliding the springs 46 within the recess, and then tightening the screw 56.

The oscillating bar 52 is supported by a fixed bar 60 which is secured to the chassis by a mounting block 62. Close to its end remote from the sample, connection between the oscillating bar 52 and the fixed bar 60 is formed by a leaf spring 64. Close to its end adjacent to the sample, connection between the oscillating bar 52 and the fixed bar 60 is formed by a S piezoelectric stack 66. The piezoelectric stack 66 is clamped between the oscillating bar 52 and a loading screw 68 that is threaded within the oscillating bar 52.

With reference to Figure 5, the main electronic components of the system will now be described.

The system is controlled by a control computer 100. An electronic interface 102 can, under the control of the computer 100, can apply current to the coil 14 to cause the pendulum rod to deflect from the balanced vertical position. It can also receive signals from a capacitance bridge 104 to measure variations in the capacitance of the capacitor 104 formed by the plates 28, 30. The signal received from the capacitance bridge 104 is delivered to a lock-in amplifier 106. A signal generator 108 provides a reference signal to the lock-in amplifier 106 and to the control computer 100. The signal generator also provides a signal to a drive amplifier 110 for the piezoelectric stack 66.

Operation of the apparatus will now be described.

Prior to performing a test sequence, it is necessary to calibrate the apparatus. This is to allow the properties of the apparatus to be isolated from the properties of the sample. That is, in order to extract the properties of the contact point between the probe and a sample under test, it is essential to characterise and take into account the mechanical behaviour of the complete system by calibration. In particular, the pendulum experiences damping not only due to energy absorption at the contact, but also due to air damping and eddy current damping. The foliowing calibrations are required: The effective mass of the oscillating system A driving spring is connected between the probe holder 24 and a piezoelectric actuator that is able to move along the axis of the probe 26. The piezoelectric actuator applies an oscillating force to the pendulum 10 through the spring. The control computer 100 uses the capacitance bridge 104 to monitor the displacements that this oscillating force induces in the pendulum.

The frequency of oscillation of the applied force is varied until the frequency at which the maximum displacement of the pendulum 10 is found; this is the resonant frequency of the complete oscillating system. Signal amplitude data are then collected as the piezoelectric actuator is oscillated over a narrow frequency range on both sides of the resonant frequency.

Once the resonant frequency has been determined, provided that the stiffness of the drive spring is known, the effective mass of the oscillating system including the pendulum can be calculated.

The effective mass of oscillating sample assembly The supporting stage 42 is turned such that the sample holder 40 is normal to the axis of the test probe 26. Specifically, the complete assembly of Figure 3 is turned through 90 and the sample holder 40 is turned to make its side face perpendicular to the probe axis. A rigid pin then connects the sample holder 40 and the test probe 26 so the final oscifiation is not influenced by contact compliance. The tip of the test probe 26 is then brought into contact with the sample holder 40 under a relatively high static load in order to maintain them in contact with one another so as to prevent probe bouncing during oscillation. Then, in a similar manner to the above, signal amplitude data are collected as the piezoelectric actuator is oscillated over a narrow frequency range on either side of the frequency of maximum oscillation to determine the resonant frequency directly. This, together with the spring stiffness, allows the effective mass of all components oscillating on the leaf springs 46, including the sample 38, the sample holder 40, the supporting stage 42, the nut 44 and the clamp 48 to be calculated.

Phase difference within the electronic system With the supporting stage 42 oriented as described above, a rigid pin is connected between the sample holder 40 and the probe holder 24. The sample holder 40 and probe holder 24 are caused to oscillate at a particular frequency and amplitude combination. This allows the intrinsic system phase and amplitude to be recorded directly using the lock-in amplifier 106.

Pendulum damping The pendulum damping coefficient can be calculated from measured phase data when oscillated with a known spring installed together with phase data for the electronic system only, the pendulum effective mass, and the spring stiffness as derived in previous calibration steps. The value is calculated from standard forced harmonic motion analysis.

Spring stiffness Spring stiffnesses of the both pendulum 10, the probe 26, the sample 38 and their respective holders 24, 40 are found by direct measurement of applied force against displacement. That is, the spring is pressed by means of a known force ramp and the resulting displacement is recorded.

Track length This is found when the phase difference within the electronic system is measured, as described above. At a particular combination of frequency and amplitude, the oscillation moves the pendulum backwards and forwards without any influence from a slidiig probe contact. Again, the pendulum displacement is found by means of the a depth measurement facility, for example, similar to that disclosed in EP-A-1 095 254. The load applied by the pendulum fri this procedure is zero.

Once the apparatus has been calibrated, the steps for using it the invention can be summarised as follows: First, a nominally flat sample 38 is mounted on the sample holder 40, typically by bonding it in place with cyanoacrylate adhesive.

Align a flat surface of the sample 38 at a small angle to the normal of the axis of the probe 26.

Allow time for the apparatus and the sample to reach thermal equilibrium.

Apply a normal load to the test probe 26.

Cause the signal generator 108 to apply an alternating signal to the piezoelectric stack 66 to mechanically oscillate the sample holder 42 along an oscillation axis that is in a direction perpendicular to the axis of the test probe 26. This causes the test probe 26, when in contact with the angled surface of the specimen, to move backwards and forwards along its axis.

Use the lock-in amplifier 106 to determine the phase difference between the applied oscillatory motion and the resulting motion of the test probe 26. The lock-in amplifier 106 can compare the phases of the signal generated by the signal generator 108 and the signals derived from the capacitance bridge 104. The relative signal amplitudes of the sample holder 42 and the test probe 26 can also be determined by means of the lock-in amplifier 106. This data will typically be saved, and periodically averaged.

Through the well-known results of forced harmonic motion, use the averaged phase and signal values to obtain the damping coefficient of the contact between the probe 26 and the sample 38.

The contact damping coefficient together with knowledge of the acceleration of the test probe allows the instantaneous power to be calculated.

With reference to Figure 7, apparatus being a second embodiment of the invention includes a pendulum assembly that is carried on a chassis (not shown). The pendulum assembly comprises an elongate, straight ceramic pendulum rod 210 that extends generally vertically within the apparatus when set up for use. The pendulum rod 210 is carried on a spring pivot 212, which allows the pendulum rod 210 to pivot about a horizontal axis that passes through its balance point. The spring pivot is essentially frictionless and has spring stiffness that is generally negligible compared with the stiffnesses of other components of the system.

A coil 214 is carried towards the upper end of the pendulum rod 210. The coil 214 is closely adjacent to a magnet 216. Energisation of the coil 214 can cause it to be attracted to or repelled from the magnet 216, thereby urging the pendulum rod 210 to rotate about the pivot 212. This pivoting movement is constrained by a limit stop 218. A spring 220 chosen to produce optimum dynamic behaviour of the pendulum may be placed close to the lower end of the pendulum rod 210.

Below the pivot 212, a probe holder with extension 224 is carried on the pendulum rod. A test probe 226 that carries an indenting tip is carried at the top and towards the end of the probe holder such that the probe axis is approximately parallel to the pendulum rod 210.

During pivotal movement of the pendulum 210 about a small angular displacement, the probe will move on a circular trajectory with radius determined by its distance from the pivot 212.

The probe holder carries a metal plate 228 which, in combination with a fixed plate 230, forms a capacitor. The spacing between the plates, and therefore, the capacitance, varies as the pendulum rod 210 rotates about the pivot 212.

To ensure that the pendulum rod 210 remains vertical when no external force is applied to the sample, an adjustable balance weight 234 is carried on the pendulum rod 210 and a constant

background current is maintained in the coil 214.

The apparatus further includes a sample holding assembly shown in Figures 8 and 9. The sample holding assembly has a sample holder 240 upon which a sample to be tested 238 is carried. The sample holder 240 is attached to a piezoelectric stack 243 and the piezoelectric stack is attached to a mounting block 241, arranged such that it can rotate with respect to the supporting stage 262 about a horizontal axis, and clamped in place by tightening screws 244.

The supporting stage 262 is secured to the chassis.

With reference to Figure 10, the main electronic components of the system will now be described.

The system is controlled by a control computer 300. An electronic interface 302 can, under the control of the computer 300, apply current to the coil 214 to cause the pendulum rod 210 to deflect from the balanced vertical position. It can also receive signals from a capacitance bridge 304 to measure variations in the capacitance of the capacitor 304 formed by the plates 228, 230. The signal received from the capacitance bridge 2104 is delivered to a lock-in amplifier 306. A signal generator 308 provides a reference signal to the lock-in amplifier 306 and to the control computer 300. The signal generator also provides a signal to a drive amplifier 310 for the piezoelectric stack 266.

With reference to Figure 11, Cl and ki represent the damping and spring stiffness of the pendulum, m represents the effective mass of the oscillating system, and C2 and k2 represent the damping and stiffness of the contact. The piezoelectric stack 266 is shown at the right-hand side, and the components are constrained by rigid walls which represent the instrument chassis. For friction testing, k2 is usually taken as zero.

Operation of the apparatus will now be described.

Prior to performing a test sequence, it is necessary to calibrate the apparatus. This is to allow the properties of the apparatus to be isolated from the properties of the sample. That is, in order to extract the properties of the contact point between the probe and a sample under test, it is essential to characterise and take into account the mechanical behaviour of the complete system by calibration. In particular, the pendulum experiences damping not only due to energy absorption at the contact, but also due to air damping and eddy current damping. The following calibrations are required: The effective mass of oscillating system at the probe position A driving spring is connected between the probe holder 224 and a piezoelectric actuator that is able to move along the axis of the probe holder. The piezoelectric actuator applies an oscillating force to the pendulum 210 through the spring. The control computer 300 uses the capacitance bridge 304 to monitor the displacements that this oscillating force induces in the pendulum.

The frequency of oscillation of the applied force is varied until the frequency at which the maximum velocity of the pendulum 210 is found; this is the velocity resonant frequency of the complete oscillating system. Signal amplitude data are then collected as the piezoelectric actuator is oscillated over a narrow frequency range on both sides of the velocity resonant frequency. Once the resonant frequency has been determined, provided that the stiffness of the drive spring is known, the effective mass m of the oscillating system can be calculated for the test probe position from basic formula of forced harmonic motion: = V(slm) where is the angular frequency at resonance, s is the spring stiffness, and m is the effective mass.

Phase difference within the electronic system With the supporting stage 262 oriented as described above, a rigid pin is connected between the sample holder 240 and the probe holder 224. The sample holder 240 and probe holder 224 are caused to oscillate at a particular frequency and amplitude combination. This allows the intrinsic system phase and amplitude to be recorded directly using the lock-in amplifier 306. This information is required to calculate the pendulum damping. The amplitude of the pendulum motion is the same as that of the piezoelectric stack motion, but a phase difference between the motion of the piezoelectric stack 266 and that of the pendulum occurs due to electronic signal processing delays.

Pendulum damping The system damping coefficient can be calculated from measured phase data that is obtained when the system is oscillated with a known spring installed, together with phase data for the system only; the effective mass of the oscillating system including the pendulum, as derived in previous calibration steps; and the spring stiffness. The value is calculated from standard forced harmonic motion analysis: tan1(C1*co/(kl + k2 -maY) + g where: total phase difference kl pendulum spring stiffness k2 spring constant m effective oscillating system mass Cl system damping angular frequency g instrument contribution to measured phase Spring stiffness Spring stiffnesses of the pendulum 210 and any test spring are found by direct measurement of applied force against displacement. That is, the spring is pressed by means of a known force ramp applied to the loading coil 214 and the resulting displacement is recorded.

Once the apparatus has been calibrated, the steps for using it in the invention can be summarised as follows: First, an essentially flat sample 238 is mounted on the sample holder 240, typically by bonding it in place with cyanoacrylate adhesive.

A fiat surface of the sample 238 is aligned perpendicularly to the axis of the probe 226.

Time is allowed for the apparatus and the sample to reach thermal equilibrium.

A force is applied to the test probe 226.

The signal generator 108 is caused to apply an alternating signal to the piezoelectric stack 243 to mechanically oscillate the sample holder 240 in a direction perpendicular to the axis of the test probe 226. This causes the tip of the test probe 226, when in contact with the surface of the specimen, to move backwards and forwards parallel to the displacement axis. In general, operation at the resonant frequency of the oscillating system is avoided.

The lock-in amplifier 306 is used to determine the phase difference between the applied oscillatory motion and the resulting motion of the test probe 226. The lock-in amplifier 306 can compare the phases of the signal generated by the signal generator 308 and the signal derived from the capacitance bridge 304. The relative signal amplitudes of the sample holder 240 and the test probe 226 can also be determined by means of the lock-in amplifier 306. This data will typically be periodically averaged and saved. Typically, data would be acquired continuously for 15 seconds and would be averaged throughout this period, with multiple periods comprising a single test. Such a test results in a plot of average phase against time which can detect changes in contact frictional properties.

Through the well-known results of forced harmonic motion, the averaged phase values are used to obtain the damping coefficient of the contact between the tip of the test probe 226 and the sample 238: tanl((C1C2)*w/(k1 --k2 -mw2)) --taw'(C2*w/k2) g where: total phase difference kl pendulum spring stiffness k2 spring constant due to contact stiffness m effective oscillating system mass Cl system damping C2 contact damping angular frequency g instrument contribution to measured phase However, in normal use, the force due to k2 will essentially be constant (that is, k2 will not behave as a spring undergoing continuous compression or extension). In this situation, the phase value is given by the simpler expression: tan'(o(C1+C2) /(kl -moi2)) + g However, for very small oscillations, the value of k2 may not be negligible. For the case of a continuous variation in the spring force due to k2 (for example for small oscillation amplitudes) the excitation amplitude and the pendulum amplitude allow k2 to be obtained from the equation of motion and thus C2 to be determined. Averaged phase values are used to obtain the damping coefficient for the contact between the probe 226 and the sample 238.

The contact damping coefficient together with knowledge of the amplitude phase of the test probe allows the maximum instantaneous power to be calculated: Maximum instantaneous power C2*Vm2 C2*c02*xo2 where Vm is the maximum velocity of the probe and x0 is the maximum measured amplitude of the probe.

Claims

Claims 1. Apparatus arranged to assess the interaction between a surface of a sample and a test probe, the apparatus comprising a sample holder, a drive unit operative, on application of an oscillating electrical signal, to cause the sample holder to oscillate along a displacement axis, a probe, and a position sensor operable to generate a signal indicative of the position of the probe, comparison means operable to determine the relative phase of oscillation of the sample and the probe by analysis of the signal which drives the drive unit and the output from the position sensor, the apparatus being operable, with a sample held in the sample holder: a. to apply a signal to the drive means to oscillate the sample holder with the probe in continuous contact with the sample to cause the probe to oscillate along a measurement axis, b. to use the position sensor to measure a component of the displacement in the measurement axis of the probe and/or phase difference between the oscillations of the sample holder and the probe and the amplitude of the probe, and c. to operate the comparison means to determine the contact damping coefficient between the probe and the sample by analysis of the signal applied to the drive unit and the signal derived from the position measurement sensor, and thereby calculate the instantaneous power transmitted between the sample and the probe.
2. Apparatus for assessing the interaction between a surface of a sample and a test probe, the apparatus comprising a sample holder, a probe, a drive unit operative, on application of an oscillating electrical signal, to cause the probe holder to oscillate along a displacement axis, a position sensor operable to generate a signal indicative of the position of the sample, and comprising comparison means operable to determine the relative phase of oscillation of the sample and the probe by aialysis of the signal which drives the drive unit and the output from the position sensor, the apparatus being operative, with a sample held in the sample holder: a. to apply a signal to the drive means to cause the drive means to oscillate the probe to cause the probe to oscillate along a measurement axis, with the probe ii continuous contact with the sample, b. to use the position measurement means to measure a component of the displacement in the measurement axis of the sample and/or phase difference between the oscillations of the sample and the oscillations of the probe, and c. to operate the comparison means to determine the damping coefficient between the probe and the sample by analysis of the signal applied to the drive means and a signal derived from the position measurement means, and thereby calculate the instantaneous power transmitted between the sample and the probe.
3. Apparatus according to claim 1 or claim 2 in which the measurement axis is parallel to the displacement axis.
4. Apparatus according to claim 1 or claim 2 in which the measurement axis is normal to the displacement axis.
S. Apparatus according to any preceding claim in which the sample holder can be rotated about an axis that is normal to the displacement axis.
6. Apparatus accordlig to any preceding claim in which the drive unit includes a piezoelectric stack.
7. Apparatus according to any preceding claim in which the position sensor includes a capacitor that has plates which vary in separation with movement of the probe.
8. Apparatus according to any preceding claim in which comparison means includes a lock-in amplifier.
9. Apparatus according to any one of claims 3 to B as dependent from claim 1 in which the probe is mounted such that it will naturally oscillate when displaced from a rest position.
10. Apparatus according to claim 9 in which the probe is carried on a pendulum.
11. Apparatus according to any one of claims 3 to B as dependent from clalm 2 in which the sample holder is mounted such that it will naturally oscillate when displaced from a rest position.
12. Apparatus according to claim 11 in which the probe is carried on a pendulum.
13. Apparatus for testing surface properties of a sample substantially as herein described with reference to the accompanying drawings.
14. A method of assessing the interaction between a surface of a sample and a test probe, the method comprising: a. driving the sample in an oscillating movement along a displacement axis with a probe in continuous contact with the sample to cause the probe to oscillate, b. measuring the phase difference between a component of the oscillations of the sample in a measurement axis and the probe and the amplitude of oscillations of the probe, and c. analysing the measurement made in step b. to determine the contact damping coefficient between the probe and the sample, and thereby calculating the instantaneous power transmitted between the sample and the probe.
15. A method for assessing the interaction between a surface of a sample and a test probe, the method comprising: a. driving the probe in an oscillating movement along a displacement axis with the probe in continuous contact with the sample to cause the sample to oscillate, b. measuring the phase difference between a component of the oscillation of the probe along a measurement axis and the sample and the amplitude of the oscillation of the sample, and c. analysing the measurement made in step b. to determine the contact damping coefficient between the probe and the sample, and thereby calculating the instantaneous power transmitted between the probe and the sample.
16. A method according to claim 14 or claim 15 in which the measurement axis is substantially parallel to the displacement axis.
17. A method according to claim 14 or claim 15 in which the measurement axis is substantially normal to the displacement axis.
18. A method according to claim 16 or claim 17 in which sample has a generally flat surface against which the probe makes contact.
19. A method according to claim 18 in which the flat surface is aiigned at a small angle from normal to the displacement axis.
20. A method according to any one of claims 14 to 19 further comprising a calibration phase before testing is performed to determine the oscillatory characteristics in the absence of frictional contact between the probe and the sample.
21. A method according to claim 20 in which the calibration phase includes determining the effective mass and natural frequency of oscillation of the probe and or the sample.
22. A method according to claim 20 or claim 21 as dependent from claim 14 in which the calibration phase includes determining the phase relationship between a signal applied to the drive means and a position signal that indicates the position of the probe.
23. A method according to claim 20 or claim 21 as dependent from claim i in which the calibration phase includes determining the phase relationship between a signal applied to the drive means and a position signal that indicates the position of the sample.
24. A method for testing surface properties of a sample substantially as herein described with reference to the accompanying drawings.