TITLE: The generalized reference lever: A simple, reliable and traceable calibration method for

arbitrary normal and friction forces

ABSTRACT BODY:

No reliable calibration method has yet been developed for scanning probe friction measurements. As a

result, the tribology basic science literature sits on a foundation of uncalibrated measurements that may or

may not be comparable across studies. This paper aims to resolve this critical problem. Essentially, we

adapt a mature and widely accepted technology, the pre-calibrated reference lever, as a means to store forces

from a traceable calibration standard of fixed range (e.g. microbalance) and scale them to accommodate the

load ranges (normal and lateral) of an arbitrary scanning probe. This paper presents the theory, demonstrates

a simple prototype device and method of use, and validates the approach along several independent lines

of analysis. As the results demonstrate, the generalized reference lever method is simple, reliable, and

traceable. The concept, approach, and validation will be especially easy to grasp and implement by those

who are practiced with the reference lever method of normal force calibration.

THE GENERALIZED REFERENCE LEVER: A SIMPLE, RELIABLE AND TRACEABLE CALIBRATION METHOD FOR ARBITRARY NORMAL AND FRICTION FORCESA. Bhattacharjee, Christopher L. Evan, N.T. Garabedian, D.L. Burris email: dlburris@udel.edu

Late

ral F

orce

(mN

)

0 0.2 0.60.4 0.8 1.21.0 1.4 1.81.60

0.5

1.0

1.5

2.0

2.5

Voltage (V)

Pos 1 : 1.478 mN/VPos 2 : 1.48 mN/VPos 3 : 1.601 mN/V

Pos 4 : 1.799 mN/V

0 2 4 6 8 10

0.4

0.8

1.2

1.6

1.8

0

Posi�on (mm)

Calib

ra�o

n Co

nsta

nt (m

N\V

)

Predicted result: 1.39 ± 0.05 mN/V

Calib

ra�o

n Co

nsta

nt (μ

N\V

)

Set Point Voltage (V)1 2 3 4 6 8

0

2

4

6

8

10

12

14

Set Point Voltage (V)0 1 2 3 4 5 6 7 8

Calib

ra�o

n Co

nsta

nt (μ

N\V

)

0

5

10

15

20

25

What is the weight ?Weight Balance: 5 lb

FN

FL

What is the applied force ?Sensor: .... Voltage

Calibration is required to know the applied force

CALIBRATION

Microbalance is the standard as a reference for calibration of normal force.

How do we calibrate lateral force at the tip of a probe?

Reference lever method is widely used and accepted means of applying pre calibrated standard to calibrate normal force.

Can we apply the reference lever method for lateral calibration ?

REFERENCE LEVER

δ

δx

Rigid Reference

Kref

KC

Refe

renc

e le

ver

ProbeRigid Surface

KC= Stiffness of a probe & Kref = Stiffness of reference lever

Calibration constant of a probe,

SComposite & Srigid are sensitivity for composite (probe and reference lever) and rigid surface respectively

KC Kref

1/KT = 1/KC +1/Kref

CC= Kref (1/Scomposite -1/Srigid )

Displacement(mm)0.01 0.1 1 10

Nor

mal

For

ce (m

N)

100

10

1

0.1

0.01

Kref = 2.7035 ± 0.01 N/m

Microbalance

Trib

omet

er

CALIBRATION OF OUR REFERENCE LEVER

Post on Microbalancetray for indentation

Microbalance and tribom-eter are in conjuction for the calibration of reference lever. Reference lever is ba-sically a cantilever beam which is calibrated with the help of microbalance. Once calibrated, refer-ence lever will act like a

microbalance.

The reference lever on ourprototype device was axi-symmetric and exhibited a linear relationship be-tween force and de�ection throughout microbalance calibration (20 µN to 20 mN). This calibrated refer-ence lever will store force information now and we can utilize this information to calibrate a scanning probe at an arbitary forces.

Sample calculation (Probe 1): Srigid = 480.64 V/mm, Scomposite= 2.24 V/mm, & Kref = 2.7035 N/m Calibration constant of probe 1: CC= Kref(1/Scomposite -1/Srigid ) = 1.2 mN/V

CALIBRATION OF A PROBE(LATERAL DIRECTION)

APPLICATION TO AFM

Fric

�on

Forc

e (μ

N) 4

0

2

6

-2

-4

-6

20 40 60 80 1000

Posi�on (nm)

Fric

�on

Forc

e (μ

N) 4

0

2

6

-2

-4

-6

5 10 15 20 250

Posi�on (μm)

AFM Friction mea-surement on MoS2 Normal force during the experiment were 114.7 μN (blue) & 223.8 μN (orange)

Friction measure-ment on MoS2 in Mi-crotribometry.Applied normal force during the experi-ment were 105.4 μN (blue) & 223.8 μN (orange)

AFM probe: Steel colloid of 50 μm mounted on regular AFM beam. AFM probe is then calibrated with the help of reference lever for nomal and lateral direction Normal Direction Lateral Direction

Average normal calibration constant: 22.4 μN/V

Average lateralcalibration constant: 12.2 μN/V

Reference lever: 1.24 mN/V

Friction force is derived from the middle 30% of the whole track. Friction force from two di�erent instruments at similar normal force and same material system is almost same. We could not keep the same track length for the above two experi-ments as we did not have tilting stage in our AFM setup.

9

Posi�on

Probe 1Probe 2Probe 3AFM

2

10

Fric

�on

Forc

e (μ

N)

4

6

8

0300

Normal Force (μN)350 400250200150100500

BRIDGING THE GAP BETWEEN MICRTRIBOMETRY & AFM

Friction experiment on MoS2 from microtribometry and AFM align with each other. This validates our calibration technique working successfully to calibrate AFM beam irrespective of normal and lateral direction

6310

Direct calibration technique can not calibrate lateral force right at the tip. Calibration con-stant changes based on the contact point. Therefore, friction force is the best way to cali-brate lateral force.

Volta

ge (V

)

Displacement (μm)

0

1

2

3

4

5

0 2 4 6 8 10

Srigid = 480.64 ± 0.7 V/mm

Reference lever

Lateral Stage

Prob

e

0 50 100 150 200 250 300 350

0.2

0.4

0.6

0.8

Displacement(μm)

Volta

ge (V

)

S = 2.24 ± 0.02 V/mm

0

Calibration of a probe with reference lever device Sensitivity of probe: indentation on rigid surface Sensitivity of composite: indentation onreference lever

Reference lever

Pre-calibrated reference lever can potentially resolve the long-standing chal-lenge of developing a simple, reliable, widely used lateral force calibration tech-nique for the nanotribology community. Pre-calibrated reference lever enables conversion of direct displacement mea-surements into traceable force measurements.

Normal calibration constants with reference lever are within 2.5% of direct micro-balance calibration which is the gold standard for calibration.

Friction forces from reference lever calibrated microtribometry and AFM mea-surements with steel colloids against MoS2 has been statistically indistinguish-able demonstrating that lateral force calibration is not any less reliable than normal force calibration.

0

0.5

1.0

1.5

2.0

2.5

0.4 0.8 1.2 1.6 2.0 Voltage (V)

Nor

mal

For

ce (m

N) CC = 1.173 ± 0.005 mN/V

0Probe 1 Probe 2 Probe 3

00.20.40.60.81.01.21.41.61.8

Calib

ra�o

n Co

nsta

nt (m

N\V

)

Dire

ct C

alib

ra�o

n

Refe

renc

e Le

verD

e�ec

tion

sens

or

Prob

eMicrobalance

Direct calibration of a probe with microbalanceTr

ibom

eter

15 µm

15 µm

2.2 µm

-2.7 µm

all-free-download.comFundamentalsof scanning probe microscopy, V. L. Mironov

Reference lever device is mounted on top of the lateral stage of tribometer. Easy installation, cali-bratation procedure is quite simple and fast.

Five independent indentation measurements are performed to get the average sensitivity and standard deviation of the measurements.

Mocrobalance provides force information and de�ection sensor (cap probe) presents de�ec-tion in terms of voltage changes.

Calibration constant of a probe through direct calibration method

Validation and comparision between reference lever and direct calibration method.

2.3%

0.3%

0.38%

Error:

Topography of 50 μm steel colloid, mounted at the �p of microtri-bometry probes

MoS2 (material system) for friction measurements. Image shows multiple basal planes.

Reference lever device

50 µm

1.

2.

3.

4.

CLOSING REMARKS

VALIDATION: REFERENCE LEVER VS DIRECT CALIBRATION