Bhushan B. Handbook of Micro/Nano Tribology, Second Edition

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optical ﬁber and the mirror is adjusted to a region with linearity by a micrometer (18). A bolt (19) is

loosened in this adjustment and is fastened after the adjustment to make the optical ﬁber move together

with the indenter. Measurement begins with increasing the voltage applied to the piezoelectric actuator.

After the indenter touches and penetrates the sample (loading process), the voltage applied to the

piezoelectric actuator is reduced (unloading process).

10.2.2.6 Ecole Central of Lyon Design

The surface force apparatus commonly used for molecular rheology of thin lubricant ﬁlms, was modiﬁed

by Loubet et al. (1993) to conduct nanoindentation studies. Figure 10.9 shows the schematic of their

nanoindenter design which uses piezoelectric crystal for indenter motion and two capacitance probes

for measurement of the load and the displacement. The indenter is ﬁxed to the piezoelectric crystal and

the specimen is supported by double-cantilever spring whose stiffness can be adjusted between 4

and 6

N/m. The double-cantilever spring prevents the surfaces from rolling and shearing during

loading. Two capacitance displacement probes are used. One of the capacitive sensor C

measures the

elastic deﬂection of the cantilever and thus the force transmitted to the sample. Another capacitive sensor

measures the relative displacement between the indenter and the sample (or indentation depth).

In an indentation experiment, for the coarse approach, the translation motion is obtained by a

differential micrometer. The desired displacement is controlled by a negative proportional integral (PI)

feedback loop acting on the piezoelectric crystal via a high-voltage ampliﬁer. The reference displacement

FIGURE 10.8

Schematic of a depth-sensing nanoindentation hardness apparatus by NEC Corp., Tokyo. (From

Yanagisawa, M. and Motomura, Y., 1987,

Lubr. Eng.

43, 52–56. With permission.)

signal consists of two ramp reference signal and a sinusoidal signal. Ramp reference signal allows the use

of a constant speed from 50 to 0.005 nm/s (typical speed of 0.5 nm/s). The sinusoidal motion designed

to determine the dynamic behavior of the solids is obtained using a two-phase lock-in analyzer. It is

generally set of about 0.26 nm rms in the frequency range of 0.01 to 500 Hz (typically 38 Hz). The

displacement resolution is 0.015 nm.

10.2.2.7 Cornell University Design

Hannula et al. (1986) developed the nanoindentation apparatus shown in Figure 10.10. It is used to

measure indenter penetration and load as a function of time during loading and unloading cycles. The

apparatus is constructed with two load trains such that both large (up to 50 mm) and small (up to 12 µm)

displacements can be applied accurately and independently to the same specimen. The large displacement

is produced by a moving crosshead. The small displacements are made possible by using a piezoelectric

translator. A load as small as 0.5 mN can be applied.

A specimen is attached to the (moving) crosshead and the diamond tip is attached to a part, which

also serves as a counter plate for two capacitance probes. These probes are used either for controlling

the position of the tip or for measuring the indentation depth. The load cell is placed between the part

and the piezoelectric translator and is used to measure the normal load. The specimen can be aligned

by using an

–

stage while observing the specimen directly with the microscope.

10.2.2.8 IBM Almaden Research Center Design

Wu et al. (1988, 1989) built a nanoindentation hardness apparatus based on the Cornell design. Their

apparatus uses a piezoelectric transducer (PZT) for indenter motion, capacitance probe for the displace-

ment, a servo-control circuitry for precise control of PZT motion, a multichannel data acquisition system,

and a closed-loop TV camera for viewing the interface between the indenter tip and sample surface.

(Also see Wu, 1991.) Figure 10.11a shows the block diagram of the apparatus which is composed of an

indenter assembly, a load cell assembly and a fully automated precision

–

stage. Figure 10.11b shows

schematically the indenter assembly and the load cell assembly. The indenter (5) is driven by a PZT

transducer stack (9) which is monitored by a servo system. The servo mechanism allows great ﬂexibility

FIGURE 10.9

Schematic of a depth-sensing nanoindentation hardness apparatus by Ecole Central of Lyon. (From

Loubet, J.L. et al., 1993, in

Mechanical Properties and Deformation of Materials Having Ultra-Fine Microstructures

(M. Nastasi et al., eds.), pp. 429–447. Kluwer Academic, Dordrecht. With permission.)

in controlling the motion of the indenter. The applied load can be calculated using the output voltage

of the load cell capacitance probe (1) and the calibrated load cell spring constant. The total depth

penetrated by the indenter with respect to the sample surface can be obtained either directly from the

sample capacitance gauge (6) or from the difference of the displacement measurements between indenter

gauge (7) and the load cell gauge (1). The load cell has loading ranges from a few tens of micronewtons

to 2 N with a resolution of about 30 µN. Indentations with a depth of as low as 20 nm with a depth

resolution of 1 nm can be made. For hardness measurements, the apparatus is operated in continuous

loading and unloading modes with indenting speeds of 2 to 20 nm s

–1

. A three-sided pyramidal diamond

indenter, known as the Berkovich indenter, is used for measurements.

The PZT stack is driven by a voltage ampliﬁer to follow a predetermined reference pattern and is

monitored by closed-loop servo-circuitry. Either the indenter displacement (IND) output (7) or the

normal load cell (LC) output (1) can be employed as a servo-input signal and in turn different testing

modes can be generated using an IND servo, constant indenter rate testing (typically used in the constant

loading and unloading tests), or constant indenter position (used in the load relaxation tests), or any

programmed displacement pattern for the indenter can be performed. But using an LC servo, constant

loading rate indentation (used in the continuous loading and unloading tests, or constant load inden-

tation (used in the indentation creep test), or cyclic loading (using sawtooth or sinusoidal references, in

the indentation fatigue tests) can be performed. Furthermore, under the LC servo mode, the microin-

denter can be used as an

in situ

proﬁler, which is used to measure the scratch track depth. Wu (1993)

modiﬁed the nanoindenter for continuous stiffness measurements using dynamic loading based on the

work by Oliver and Pethica (1989) and Pethica and Oliver (1989). The dynamic loading was accomplished

by superimposing a sinusoidal waveform with small amplitude to the linear ramping DC voltage. This

technique will be described in detail in a later section on nanoindenters.

The nanoindenter was modiﬁed to perform scratch tests, Figure 10.12a (Wu et al., 1989, 1990b; Wu,

1991). PZT-driven indenter assembly exhibits excellent rigidity and hence is mechanically stable in the

–

plane. This extremely rigid design along the horizontal plane is crucial to performing scratch tests.

FIGURE 10.10

Schematic of a depth-sensing nanoindentation hardness apparatus by Cornell University, Ithaca,

NY. (From Hannula, S.P. et al., 1986, in

The Use of Small-Scale Specimens for Testing Irradiated Materials

(W.R. Corwin

and G.E. Lucas, eds.) pp. 233–251, STP 888, ASTM, Philadelphia. With permission.)

FIGURE 10.11

(a) Block diagram of a depth-sensing nanoindentation hardness apparatus by IBM Almaden Research Center; (b) schematic

diagram of the indenter assembly and normal load cell assembly: (1) load cell capacitance probe, (2) sample post, (3) Be–Cu diaphragm springs;

(4) sample, (5) indenter, (6) sample capacitance probe, (7) indentation capacitance probe, (8) Be–Cu diaphragm, (9) PZT stack, (10) PZT preload

mechanism, (11) reference plane stage, (12) Z-stage. (From Wu, T.W. et al., 1988,

Thin Solid Films

166, 299–308. With permission.)

In their modiﬁed design, a tangential load cell (6, 9) as well as acoustic emission sensor (8) were added.

An additional capacitance probe (TG, 9) was placed to monitor the displacement of the indenter holder,

which is subsequently used to calculate the tangential force that the indenter applies on the sample

surface. The tangential load cell has a loading range of 750 mN with a resolution of about 15 µN. Another

capacitance probe (SD, 16) was added to measure scratch distance.

Figure 10.12b shows schematically the working principle of a nanoscratch test carried out by the

upgraded apparatus (Figure 10.12a). To perform a scratch test, the indenter is ﬁrst placed about 0.1 µm

away from the sample surface. This step allows a scratch to begin with a zero applied load. Next the

traveling range and speed of the X-translation stage are set usually at 150 µm and 1 µm/s, respectively;

then the motion is started. Finally, the PZT motor is activated to drive the indenter toward the sample

surface at the speed of about 15 nm/s. With this instrument, the following measurements can be made

simultaneously during a scratch test: applied load and tangential load along the scratch length (coefﬁcient

of friction); critical load, i.e., applied normal load corresponding to an event of coating failure during a

scratch process, total depth and plastic depth along the scratch length; the accumulated acoustic emission

(AE) counts vs. the scratch length. In addition to the mechanical data, scratch morphology analysis is

always available. Examples will be shown later in the chapter.

10.2.3 Commercial Depth-Sensing Nanoindentation Hardness

Apparatus and Its Modiﬁcations

10.2.3.1 General Description and Principle of Operation

Although the NEC Corp. design and Micro Materials design presented in the previous section are

commercially available, these are not popular. The most commonly used commercial depth-sensing

nanoindentation hardness apparatus is manufactured by MTS Nano Instruments Innovation Center,

1001 Larson Drive, Oak Ridge, TN 37830. Ongoing development of this apparatus have been described

by Pethica et al. (1983), Oliver et al. (1986), Oliver and Pethica (1989), Pharr and Oliver (1992), and

Oliver and Pharr (1992). This instrument is called the Nanoindenter. The most recent model is Nanoin-

denter II (Anonymous, 1991). The apparatus continuously monitors the load and the position of the

indenter relative to the surface of the specimen (depth of an indent) during the indentation process. The

area of the indent is then calculated from a knowledge of the geometry of the tip of the diamond indenter.

The load resolution is about ±75 nN and position of the indenter can be determined to ±0.1 nm.

Mechanical properties measurements can be made at a minimum penetration depth of about 20 nm (or

a plastic depth of about 15 nm) (Oliver et al., 1986). Speciﬁcations for the Nanoindenter are given in

Table 10.1. The description of the instrument that follows is based on Anonymous (1991).

The nanoindenter consists of three major components: the indenter head, an optical microscope, and

–

motorized precision table for positioning and transporting the sample between the optical

microscope and indenter, Figure 10.13a. The loading system used to apply the load to the indenter consists

of a magnet and coil in the indenter head and a high precision current source, Figure 10.13b. A coil is

attached to the top of the indenter (loading) column and is held in a magnetic ﬁeld. The passage of the

current through the coil is used to raise or lower the column and to apply the required force to make an

indent. The current from the source, after passing through the coil, passes through a precision resistor

across which the voltage is measured and is displayed. During measurement, voltage is controlled by a

computer. Two interchangeable indenter heads are available: the standard head, which features four load

ranges 0 to 4 mN, 0 to 20 mN, 0 to 120 mN, and 0 to 350 mN, and a high-load head, which has a load

range of 0 to 840 mN. The load resolution for the standard head in the most sensitive range is about

±75 nN, while the load resolution for the high load head is ±90 µN.

The displacement-sensing system consists of a special three-plate capacitive displacement sensor, used

to measure the position of the indenter. All three plates are circular disks approximately 1.5 mm thick.

The two outer plates have a diameter of 50 mm, and the inner, moving plate is half that size. The indenter

column is attached to the moving plate. This plate-and-indenter assembly is supported by two leaf springs

cut in such a fashion to have very low stiffness. The motion is damped by airﬂow around the central

plate of the capacitor, which is attached to the loading column. The load coil is used to raise or lower

the plate and the indenter assembly through its 100-µm travel between the outer plates of the capacitor.

Depth resolution of the systems is about ±0.04 nm. As seen in the plot at the right of Figure 10.13c, a

load voltage of 1.7 V will just lift the indenter off its bottom stop, and 1.8 V sufﬁce to bring it to the top

of its travel. It should be emphasized that only the motion of the indenter column as controlled by the

load coil is used in the actual making of an indent. The voltage output range of the displacement sensing

(capacitance) system is –2.5 to +2.5 V.

At the bottom of the indenter rod, a three-sided pyramidal diamond tip (Berkovich indenter, to be

discussed later) is generally attached.

The indenter head assembly is rigidly attached to the “U” beam below which the

–

table rides,

Figure 10.13a. The optical microscope is also attached to the beam. The position of an indent on a

specimen is selected using the microscope (maximum magniﬁcation of 1500

). The remote-operation

option provides a TV camera that is mounted atop the microscope, which permits the image of the

FIGURE 10.12

specimen to be viewed remotely. The specimens are held on an

–

table whose position relative to

the microscope or the indenter is controlled with a joystick. The spatial resolution of the position of the

table in the

–

plane is ±400 nm and its position is observed on the CRT. The specimen holder is a

rectangular metal plate (150

150

28.5 mm) with ten 31.8-mm-diameter holes for mounting of

standard metallographic samples. Samples can also be glued to special metal disks. The three components

just described are enclosed in a heavy wooden cabinet to ensure the thermal stability of the samples. The

apparatus should be housed in a laboratory in which the temperature is controlled to ±0.5°C. The entire

apparatus is placed on a vibration-isolation table. The operation of the apparatus is completely (IBM-

PC-compatible) computer controlled. Through an IEEE interface, the computer is connected to data

acquisition and control system.

The nanoindenter also comes with a continuous stiffness measurement device (Oliver and Pethica,

1989; Pethica and Oliver, 1989). This device makes possible the continuous measurement of the stiffness

of a sample, which allows the elastic modulus to be calculated as a continuous function of time (or

indentation depth). Useful data can be obtained from indents with depths as small as 20 nm. Because of

FIGURE 10.12

Schematic diagram of the upgraded nanoindentation hardness apparatus with the tangential load

cell assembly: IND, indenter probe; LC, normal load cell probe; TG, tangential load cell probe; SD, scratch distance

probe; and AE, acoustic emission detector, and (b) schematic illustration of the working principle of the nanoscratch

test. From Wu, T.W., 1991,

J. Mater. Res.

6, 407–426. With permission.)

the relatively small time constant of the measurements, the device is particularly useful in studies of time-

dependent properties of materials.

10.2.3.2 Calibration Procedures

Calibration of the loading system involves the accurate measurement of the voltage through the force

coil required to support a series of precalibrated hook weights so as to establish the change in force per

volt. The typical value for this constant is 26,876.5 µN/V.

Calibration of the displacement system is carried out by correlating the voltage output of the displace-

ment capacitor with the number of rings generated as the indenter tip is pressed against a lens-and-plate

system designed to produce newton rings. A mirror mounted at the bottom on the indenter tip is pressed

against a partially reﬂected lens and an He–Ne laser observed during the test on a video camera. The

relationship between displacement voltage and displacement is linear in the range of interest.

Other important calibrations include microscope-to-indenter distance and spring constant of indenter

support springs.

10.2.3.3 The Berkovich Indenter

The main requirements for the indenter are high elastic modulus, no plastic deformation, low friction,

smooth surface, and a well-deﬁned geometry that is capable of making a well-deﬁned indentation

impression. The ﬁrst four requirements are satisﬁed by choosing the diamond material for the tip. A

well-deﬁned perfect tip shape is difﬁcult to achieve. Berkovich is a three-sided pyramid and provides a

sharply pointed tip

compared with the Vickers or Knoop indenters, which are four-sided pyramids and

have a slight offset (0.5 to 1 µm) (Tabor, 1970; Bhushan, 1996). Because any three nonparallel planes

intersect at a single point, it is relatively easy to grind a sharp tip on an indenter if Berkovich geometry

is used. However, an indenter with a sharp tip suffers from a ﬁnite but an exceptionally difﬁcult-to-

measure tip bluntness. In addition, pointed indenters produce a virtually constant plastic strain impression

TABLE 10.1

Speciﬁcation of the Commercial Nanoindenter by Nano Instruments, Inc.

Load range

Standard head 0–4 mN

0–20 mN

0–120 mN

0–350 mN

High load head 0–840 mN

Load resolution

Standard head ±75 nN

High load head ±90 nN

Vertical displacement range 0–100 µm

Vertical displacement resolution ±0.1 nm

Typical approach rate 10 nm/s

Typical indentation load rate 10% of peak load/s

Typical indentation displacement rate 10% peak diplacement/s

Optical microscope magniﬁcation up to 1500

Spatial resolution of the

–

table ±400 nm in the

- and

-directions

Area examined in a single series of indentations 150

150 mm

Minimum penetration depth ~20 nm

Continuous stiffness option

Frequency range 10–150 Hz

Time constant 0.33 s

Smallest measurable distance 0.1 nm

Scratch and tangential force option

Scratch velocity max. 100 µm/s with 20 points/mm

Tangential displacement range 2 mm

Tangential displacement resolution 400 nm

Tangential load resolution 50 µN

Minimum measurable tangential load 0.5 mN

and there is the additional problem of assessing the elastic modulus from the continuously varying

unloading slope. Spherical indentation overcomes many of the problems associated with pointed indent-

ers. With a spherical indenter, one is able to follow the transition from elastic to plastic behavior and

thereby deﬁne the yield stress (Bell et al., 1992). However, a sharper tip is desirable, especially for extremely

thin ﬁlms requiring shallow indentation. Therefore, Berkovich indenter is most commonly used for

measurements of nanomechanical properties. Experimental procedures have been developed to correct

for the tip shape, to be described later.

In the construction of the Berkovich indenter, an octahedron piece of diamond with large dimension

mm, is directly brazed to a 304 stainless steel holder and the tip is ground to Berkovich

shape. The Berkovich indenter is a three-sided (triangular-based) pyramidal diamond, with a nominal

angle of 65.3° between the (side) face and the normal to the base at apex, an angle of 76.9° between edge

and normal, and with a radius of the tip less than 0.1 µm (Figure 10.14a and b) (Berkovich, 1951). The

typical indenter is shaped to be used for indentation (penetration) depths of 10 to 20 µm. The indents

appear as equilateral triangles (Figure 10.14c) and the height of triangular indent l

is related to the depth

(10.1a)

The relationship

) is dependent on the shape of the indenter. The height of the triangular indent l

related to the length of one side of the triangle

(10.1b)

and

(10.1c)

The projected contact area (

A) for the assumed geometry is given as

(10.2)

The exact shape of the indenter tip needs to be measured for determination of hardness and Young’s

modulus of elasticity. Since the indenter is quite blunt, direct imaging of indentations of small size in

the SEM is difﬁcult. Determination of tip area function will be discussed later.

10.2.3.4 Indentation Procedure

The indenter procedure in this section is based on Anonymous (1991). An indentation test involves

moving the indenter to the surface of the material and measuring the forces and displacements associated

during indentation. The surface is located for each indentation by lowering the indenter at a constant

loading rate against the suspending springs and detecting a change in velocity on contact with the surface.

In the testing mode, the load is incremented in order to maintain a constant loading rate or constant

displacement rate. The load and indentation depths are measured during indentation both in the loading

and unloading cycles. The force contribution of the suspending springs and the displacements associated

with the measured compliance of the instrument are removed.

Prior to indentation of test region on the sample surface, the scheme for the indentation pattern is

selected. Typical indentation experiment consists of combination of several segments e.g., approach, load,

hold, and unload, which can be programmed, Figure 10.15. Two typical examples are shown in Table 10.2

(Oliver and Pharr, 1992). A maximum of 12 segments can be programmed for an experiment. After













76 9

859

cot .

l = 0 866. a

7 407.

Aa h==0 433 23 76