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

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Nanomechanical

Properties of Solid

Surfaces and Thin Films

Bharat Bhushan

10.1 Introduction

10.2 Nanoindentation Hardness Measurement

Apparatuses

Commercial Nanoindentation Hardness Apparatuses with

Imaging of Indents after Unloading • Prototype Depth-

Sensing Nanoindentation Hardness Apparatuses •

Commercial Depth-Sensing Nanoindentation Hardness

Apparatus and Its Modiﬁcations

10.3 Analysis of Indentation Data

Hardness • Modulus of Elasticity • Determination of Load

Frame Compliance and Indenter Area Function •

Hardness/Modulus

Parameter • Continuous Stiffness

Measurement • Modulus of Elasticity by Cantilever

Deﬂection Measurement • Determination of Hardness and

Modulus of Elasticity of Thin Films from the Composity

Response of Film and Substrate

10.4 Examples of Measured Mechanical Properties of

Engineering Materials

Load–Displacement Curves • Continuous Stiffness

Measurements • Hardness and Elastic Modulus

Measurements

10.5 Microscratch Resistance Measurement of Bulk

Materials Using Micro/Nanoscratch Technique

10.6 Nanoindentation and Microscratch Techniques

for Adhesion Measurements, Residual Stresses,

and Materials Characterization of Thin Films

Adhesion Strength and Durability Measurements Using

Nanoindentation • Adhesion Strength and Durability

Measurements Using Microscratch Technique • Residual

Stress Measurements Using Nanoindentation • Microwear

Measurements Using Modiﬁed Nanoindentation

10.7 Other Applications of Nanoindentation

Techniques

Time-Dependent Viscoelastic/Plastic Properties •

Nanofracture Toughness • Nanofatigue

10.8 Closure

References

10.1 Introduction

Mechanical properties of the solid surfaces and surface thin ﬁlms are of interest as the mechanical

properties affect the tribological performance of surfaces. Among the mechanical properties of interest,

one or more of which can be obtained using commercial and specialized hardness testers, are elastic–plas-

tic deformation behavior, hardness, Young’s modulus of elasticity, scratch resistance, ﬁlm-substrate adhe-

sion, residual stresses, time-dependent creep and relaxation properties, fracture toughness, and fatigue.

Hardness measurements can assess structural heterogeneities on and underneath the surface such as

diffusion gradients, precipitate, presence of buried layers, grain boundaries, and modiﬁcation of surface

composition.

Hardness implies the resistance to local deformation. For example, with materials that go through

plastic deformation, a hard indenter is pressed into the surface and the size of the permanent (or plastic)

indentation formed for a given load is a measure of hardness. With rubberlike materials (which do not

go through plastic deformation), an indenter is pressed into the material and how far it sinks under load

is measured. With brittle materials (which do not go through plastic deformation), hardness is measured

by scratching it by a harder material. Hardness signiﬁes different things to different people, for instance,

resistance to penetration to a metallurgist, resistance to scratching to a mineralogist, and resistance to

cutting to a machinist, but all are related to the plastic ﬂow stress of material.

Hardness measurements usually fall into three main categories: scratch hardness, rebound or dynamic

hardness, and static indentation hardness (Tabor, 1951). Scratch hardness is the oldest form of hardness

measurement. It depends on the ability of one material to scratch another or to be scratched by another

solid. The method was ﬁrst put on a semiquantitative basis by Friedrich Mohs in 1822, who selected ten

minerals as standards, beginning with talc and ending with diamond. The Mohs scale is widely used by

mineralogists and lapidaries (Tabor, 1951). Today, solid and thin-ﬁlm surfaces are scratched by a sharp

stylus made of hard material typically diamond, and either the loads required to scratch or fracture the

surface or delaminate the ﬁlm or the normal/tangential load–scratch size relationships are used as a

measure of scratch hardness and/or interfacial adhesion (Heavens, 1950; Tabor, 1951, 1970; Benjamin

and Weaver, 1960; Campbell, 1970; Ahn et al., 1978; Mittal, 1978; Perry, 1981, 1983; Jacobson et al., 1983;

Valli, 1986; Bhushan, 1987; Steinmann et al., 1987; Wu, 1991; Bhushan et al., 1995, 1996, 1997; Bhushan

and Gupta, 1995; Gupta and Bhushan, 1995a,b; Patton and Bhushan, 1996; Bhushan and Li, 1997; Li

and Bhushan, 1998b,c).

Another type of hardness measurement is rebound or dynamic hardness involving the dynamic

deformation or indentation of the surface. In this method, a diamond-tipped hammer (known as tup)

is dropped from a ﬁxed height onto the test surface and the hardness is expressed in terms of the energy

of impact and the size of the remaining indentation. For example, in the shore rebound scleroscope, the

hardness is expressed in terms of the height of rebound of the indenter.

The methods most widely used in determining the hardness of materials are

(quasi) static indentation

methods

. Indentation hardness is essentially a measure of their plastic deformation properties and only

to a secondary extent with their elastic properties. There is a large hydrostatic component of stress around

the indentation, and since this plays no part in plastic ﬂow the indentation pressure is appreciably higher

than the uniaxial ﬂow stress of the materials. For many materials, it is about three times as large, but if

the material shows appreciable elasticity, the yielding of the elastic hinderland imposes less constraint

on plastic ﬂow and the factor of proportionality may be considered less than 3. Indentation hardness

depends on the time of loading and on the temperature and other operating environmental conditions.

In the indentation methods, a spherical, conical, or pyramidal indenter is forced into the surface of the

material which forms a permanent (plastic) indentation in the surface of the material to be examined.

The hardness number (GPa or kg/mm

), equivalent to the average pressure under the indenter, is

calculated as the applied normal load divided by either the curved (surface) area (Brinell, Rockwell, and

Vickers hardness numbers) or the projected area (Knoop and Berkovich hardness numbers) of the contact

between the indenter and the material being tested, under load (Lysaght, 1949; Berkovich, 1951; Tabor,

1951, 1970; Mott, 1957; O’Neill, 1967; Westbrook and Conrad, 1973; Anonymous, 1979; Johnson, 1985;

Blau and Lawn, 1986; Bhushan and Gupta, 1997).

Macrohardness tests are widely used because of availability of inexpensive testers, simplicity of mea-

surement, portability, and direct correlation of the hardness with service performance. For applications

with ultrasmall loads (few mN to nN) being applied at the interface, nanomechanical properties of the

skin (as thin as a monolayer) of a solid surface or a surface ﬁlm are of interest. Furthermore, ultrathin

ﬁlms as thin as a monolayer are used for micromechanical applications and their mechanical properties

are of interest. Hardness tests can be performed on a small amount (few mg) of material and with the

state-of-the-art equipment it is possible to measure hardness of the few surface layers on the sample

surface.

In a conventional indentation hardness test, the contact area is determined by measuring the inden-

tation size by a microscope after the sample is unloaded. At least, for metals, there is a little change in

the size of the indentation on unloading so that the conventional hardness test is essentially a test of

hardness under load, although it is subject to some error due to varying elastic contraction of the

indentation (Stilwell and Tabor, 1961). More recently, in depth-sensing indentation hardness tests, the

contact area is determined by measuring the indentation depth during the loading/unloading cycle

(Pethica et al., 1983; Blau and Lawn, 1986; Wu et al., 1988; Bravman et al., 1989; Doerner et al., 1990;

Nix et al., 1992; Pharr and Oliver, 1992; Oliver and Pharr, 1992; Nastasi et al., 1993; Townsend et al.,

1993; Bhushan et al., 1995, 1996, 1997; Bhushan and Gupta, 1995; Gupta and Bhushan,1995a, b; Bhushan,

1996; Patton and Bhushan, 1996; Bhushan and Li, 1997; Li and Bhushan, 1998b,c). Depth measurements

have, however, a major weakness arising from “piling-up” and “sinking-in” of material around the

indentation. The measured indentation depth needs to be corrected for the depression (or the hump) of

the sample around the indentation, before it can be used for calculation of the hardness (Doerner and

Nix, 1986; Doerner et al., 1986; Wu et al., 1988; Nix, 1989; Oliver and Pharr, 1992; Fabes et al., 1992;

Pharr and Oliver, 1992). Young’s modulus of elasticity is the slope of the stress–strain curve in the elastic

regime. It can obtained from the slope of the unloading curve (Nix, 1989; Oliver and Pharr, 1992; Pharr

and Oliver, 1992). Hardness data can be obtained from depth-sensing instruments without imaging the

indentations with high reproducibility. This is particularly useful for small indents required for hardness

measurements of extremely thin ﬁlms.

In addition to measurements of hardness and Young’s modulus of elasticity, static indentation tests

have been used for measurements of a wide variety of material properties such as elastic–plastic defor-

mation behavior (Pethica et al., 1983; Doerner and Nix, 1986; Stone et al., 1988; Fabes et al., 1992; Oliver

and Pharr, 1992), ﬂow stress (Tabor, 1951), scratch resistance and ﬁlm–substrate adhesion (Heavens,

1950; Tabor, 1951; Benjamin and Weaver, 1960; Campbell, 1970; Ahn et al., 1978; Mittal, 1978; Perry,

1981, 1983; Jacobson et al., 1983; Valli, 1986; Bhushan, 1987; Steinmann et al., 1987; Stone et al., 1988;

Wu et al., 1989, 1990b; Wu, 1990, 1991; Bhushan et al., 1995, 1996, 1997; Bhushan and Gupta, 1995;

Gupta and Bhushan, 1995a, b; Patton and Bhushan, 1996; Bhushan and Li, 1997; Li and Bhushan, 1998b,

c), residual stresses (Swain et al., 1977; Marshall and Lawn, 1979; LaFontaine et al., 1991), creep (West-

brook, 1957; Mulhearn and Tabor, 1960/61; Atkins et al., 1966; Walker, 1973; Chu and Li, 1977; Hooper

and Brookes, 1984; Li et al., 1991), stress relaxation (Hart and Solomon, 1973; Chu and Li, 1980; Hannula

et al., 1985; Mayo et al., 1988a, 1990; LaFontaine et al., 1990a,b; Raman and Berriche, 1990, 1992; Wu,

1991; Nastasi et al., 1993), fracture toughness and brittleness (Palmquist, 1957; Lawn et al., 1980; Chan-

tikul et al., 1981; Mecholsky et al., 1992; Lawn, 1993; Pharr et al., 1993; Bhushan et al., 1996; Li et al.,

1997, 1998a), and fatigue (Li and Chu, 1979; Wu et al., 1991).

The extended load range of static indentation hardness testing is shown schematically in Figure 10.1.

We note that only the lower micro- and ultramicrohardness or nanohardness load range can be employed

successfully for measurements of extremely thin (submicron-thick) ﬁlms. The intrinsic hardness of

surface layers or thin ﬁlms becomes meaningful only if the inﬂuence of the substrate material can be

eliminated. It is therefore generally accepted that the depth of indentation should never exceed 30% of

the ﬁlm thickness (Anonymous, 1979). The minimum load for most commercial microindentation testers

available is about 10 mN. Loads on the order of 50 µN to 1 mN are desirable if the indentation depths

are to remain few tens of a nanometer. In this case, the indentation size sometimes reaches the resolution

limit of a light microscope, and it is almost impossible to ﬁnd such a small imprint if the measurement

is made with a microscope after the indentation load has been removed. Hence, either the indentation

apparatuses are placed

in situ

and a scanning electron microscope (SEM) or

in situ

indentation depth

measurements are made. The latter measurements, in addition, would offer the advantages to observe

the penetration process itself. In viscoelastic/visoplastic materials, since indentation size changes with

time,

in situ

measurements of the indentation size are particularly useful, which can, in addition, provide

more complete creep and relaxation data of the materials.

In this chapter, we will review various prototype and commercial nanoindentation hardness test

apparatuses and associated scratch capabilities for measurements of mechanical properties of surface

layers of bulk materials and extremely thin ﬁlms (submicron in thickness). A commercial depth-sensing

nanohardness test apparatus will be described in detail followed by data analysis and use of nanohardness

apparatuses for determination of various mechanical properties of interest.

10.2 Nanoindentation Hardness Measurement Apparatuses

In this section, we review nanoindentation hardness apparatuses in which the indent is imaged after the

load has been removed as well as the depth-sensing indentation apparatuses in which the load-indentation

depth is continuously monitored during the loading and unloading processes. Earlier work by Alekhin

et al. (1972), Ternovskii et al. (1973), and Bulychev et al. (1975, 1979) led to the development of depth-

sensing apparatuses. Both prototype and commercial apparatuses are reviewed. A commercial depth-

sensing nanoindentation hardness test apparatus manufactured by Nano Instruments, Inc., is extensively

used and is described in detail.

10.2.1 Commercial Nanoindentation Hardness Apparatuses

with Imaging of Indents after Unloading

For completeness, we ﬁrst describe a commercially available microindentation hardness apparatus (Model

No. Micro-Duromet 4000) that uses a built-in light optical microscope for imaging of indents after the

sample is unloaded. It is manufactured by C. Reichert Optische Werke AG, A-1171, Vienna, Box 95,

Austria, Figure 10.2 (Pulker and Salzmann, 1986). The case of the indenter is of the size of a microscope

objective mounted on the objective revolver. The load range for this design is from 0.5 mN to 2 N;

therefore, it is used for thicker ﬁlms.

A commercial nanoindentation hardness apparatus for use inside an SEM (Model No. UHMT-3) for

imaging the indents after the sample is unloaded, is manufactured by Anton Paar K.G., A-8054, Graz,

Austria. The apparatus is mounted on the goniometer stage of the SEM. In this setup, the indenter is

FIGURE 10.1

Extended load range of static indentation hardness testing.

mounted on a double-leaf spring cantilever and is moved against the sample by an electromagnetic system

to attain the required indentation load, which is measured by strain gauges mounted on the leaf springs,

Figure 10.3 (Bangert et al., 1981; Bangert and Wagendristel, 1986). Tilting the stage with respect to the

electron beam allows observation of the tip during the indentation process. The indentation cycle is fully

programmable and is controlled by the strain gauge signal. The motion of the indenter, perpendicular

to the surface, is performed by increasing the coil current until a signal from the strain gauges is detected.

Further, an increase of the current up to a certain gauge signal leads to the desired indentation force

ranging from 50 µN to 20 mN. After the required load has been reached and the dwell time has elapsed,

the sample is unloaded, and the indentation diagonal is measured by an SEM.

FIGURE 10.2

Schematic of the microindentation hardness

apparatus for use in a light optical microscope. (From Pulker,

H.K. and Salzmann, K., 1986,

SPIE Thin Film Technol.

652,

139–144. With permission.)

FIGURE 10.3

Schematic of the nanoindentation hardness apparatus for use in an SEM by Anton Parr K.G., Graz,

Austria. (From Bangert, H. et al., 1981,

Colloid Polym. Sci.

259, 238–242. With permission.)

10.2.2 Prototype Depth-Sensing Nanoindentation

Hardness Apparatuses

Of all the nanohardness apparatuses described in this section, the apparatus designs by IBM Almaden

Research Center and Nano Instruments, Inc., are the most modern apparatuses with the largest range of

test capabilities. However, the IBM Almaden apparatus is not commercially available. The apparatus built

by MTS Nano Instruments Innovation Center which is called the Nanoindenter, is commercially available

and is comparable to the IBM Almaden design with complete software. Nanoindenter is most commonly

used by the industrial and academic research laboratories. It will be described in some detail. The NEC

design is commercially available; however, this has limited capabilities and is not popular.

10.2.2.1 IBM T.J. Watson Research Center Microhardness Tester Design

The apparatus to be described here is a “microhardness apparatus” and is only included here for com-

pleteness. Pharr and Cook (1990) instrumented a conventional microhardness tester to measure inden-

tation load and penetration depth during the entire indentation process, Figure 10.4. This modiﬁed

machine has the advantage of being relatively inexpensive since many of its components are standard

equipment.

Pharr and Cook used a Buehler Micromet II machine with a load range of 0.1 to 10 N although other

commercially available units can be used. In their modiﬁcations, load was measured with a piezoelectric

load cell (Kistler model 9207) with a resolution of 0.5 mN and a maximum load of 50 N. The load cell

was conditioned by a Kistler model 5004 charge ampliﬁer with a frequency response of about 180 kHz.

Displacement was measured with two capacitec model HPC-75 capacitance gauges with matching ampli-

ﬁer and conditioner (model 3201). These gauges have high resolution of about 0.05 µm and frequency

response of 10 kHz. The sample stage was replaced with an assembly in which the load cell could be

rigidly supported. A mount for the displacement gauges was then connected directly to the top of the

FIGURE 10.4

Schematic of a modiﬁed commercial microhardness test apparatus for load-penetration depth mea-

surements. (From Pharr, G.M. and Cook, R.F., 1990,

J. Mater. Res.

5, 847–851. With permission.)

load cell. The specimen was attached to the center of this mount with the displacement gauges ﬂanking

it on either side. The gauges sensed the motion of a thin aluminum wing rigidly attached to the base of

the moving diamond and its mount. The outputs from the displacement gauges were averaged so as to

negate any displacements caused by bending in the system. The load and displacement outputs were

measured using a storage oscilloscope.

In a typical experiment, the load and displacement signals were recorded as a function of time, with

the load–displacement curve derived subsequently from these data. This modiﬁed apparatus can only be

used for loads as low as about 100 mN, making it useful for only microhardness measurements.

10.2.2.2 AERE Harwell/Micro Materials Design

Newey et al. (1982) developed an apparatus capable of continuously monitoring the penetration depth

as the load is applied, Figure 10.5. The test sample I is mounted on a piezoelectric barrel transducer J,

their horizontal position being controlled by a micrometer movement K. A high-voltage supply is

connected to the transducer J by means of a commutator arrangement. The indenter assembly C is made

from folded tantalum foil to give a light structure, and is ﬁtted with tungsten pivots seated in jeweled

bearings D, from which it is suspended. Force is applied electrostatically by increasing the potential on

the two plates B; force plate A is part of indenter assembly C and is kept at ground potential. The resulting

force causes A to move into B and indenter F to move toward the specimen. The indentation depth is

measured with a capacitor bridge arrangement. Plates G and H for measurement of indenter motion,

are concentric with the axis of the indenter holder and form part of a capacitor bridge arrangement

(plate G is insulated from C by mica sheet M). E is a piezoelectric bimorph transducer used to restrain

the indenter assembly C when the specimen is being moved toward the indenter. In the modiﬁed design

reported by Pollock et al. (1986), the specimen can be transferred between two locations (test and

microscopic observation). A particular area of interest may therefore be identiﬁed in the microscope and

then transferred to the test position.

This instrument is commercially available as Nano Test 550 from Micro Materials, Unit 3, The Byre,

Wrexham Technology Park, Wrexham, Clywd, U.K. In this apparatus, an indentation load up to 500 mN

with a resolution of 10 µN can be applied and the depth resolution measurement is better than 0.1 nm.

FIGURE 10.5

Schematic of a depth-sensing nanoindentation hardness apparatus by Newey et al. (From Newey, D.

et al., 1982,

J. Phys. E: Sci. Instrum.

15, 119–122. With permission.)

10.2.2.3 Philips Research Laboratory Design

Wierenga and Franken (1984) built a nanoindentation apparatus that measures

in situ

the indenter

penetration as a function of time (relaxation testing) or load with a resolution of 5 nm, Figure 10.6. The

indentation force can be varied from 10 µN to 5 mN. Indenter (1) is clamped to the holder (2) and can

easily be exchanged. The indenter holder (2) supported on an air bearing can be moved virtually

frictionlessly along a horizontal shaft (3). Two stops (4 and 5) attached to the shaft limit the movement

of the holder. The shaft is supported by a linear drive mechanism (6) making use of friction wheels and

guide rollers. The apparatus is equipped with two inductive displacement transducers (7 and 8) which

measure the displacement of the indenter with respect to the shaft and of the shaft with respect to the

surroundings, respectively. The signal from transducer 8 is automatically corrected for changes in the

ambient temperature during an experiment. This is done by the application of a temperature-sensing

element mounted on transducer 8. The indenter force is adjusted by means of an electromagnetic system.

A coil (9) is attached to the indenter holder and can move in the annular gap of an electromagnet (10),

which is mounted on the shaft. The sample holder (11) can be moved in two directions perpendicular

to the axis of the shaft (3). Samples are held by using an accessory (12) which is held by suction to the

sample holder. (Also see Wierenga and van der Linden, 1986.)

For an indentation experiment, the indenter is ﬁrst brought into contact with the sample. For this

purpose, transducer 7 is adjusted to give a zero signal when the stylus holder is somewhere between stops

4 and 5. By switching on the motor of the linear drive mechanism, the shaft and indenter are moved

toward the sample. After the indenter has touched the sample surface, movement of the shaft is auto-

matically halted when the signal from transducer 7 equals zero. The starting position for an indentation

experiment is achieved by moving the sample a short distance sideways at a minimum indenter force. If

the indenter force is increased, the signal from transducer 7 is kept to zero with the control system by

moving the shaft. Thus, the penetration depth can be determined with transducer 8, which measures the

displacement of the shaft with respect to the frame.

FIGURE 10.6

Schematic of a depth-sensing nanoindentation hardness apparatus by Philips Laboratory, Eindhoven,

The Netherlands: (1) indenter, (2) indenter holder, (3) central shaft, (4) and (5) stops, (6) linear drive mechanism,

(7) and (8) displacement transducers, (9) coil, (10) electromagnet, (11) sample holder, (12) accessory for holding

the sample (From Wierenga, P.E. and van der Linden, J. H. M., 1986, in

Tribology and Mechanics of Magnetic Storage

Systems,

Vol. 3 (B. Bhushan and N.S. Eiss, eds.), pp. 31–37, SP-21, ASLE, Park Ridge, IL. With permission.)

10.2.2.4 IBM Corporation/University of Arizona Tucson Design

Bhushan et al. (1985, 1988) and Williams et al. (1988) built a nanoindentation apparatus that can

independently control and measure indentation depths with a resolution of 0.2 nm and loads with a

resolution of 30 µN

in situ

, Figure 10.7. Samples and indenter positions are measured with a specially

designed polarization interferometer. A minimum load of about 0.5 mN can be applied. In the apparatus,

the test sample is clamped to the top of a mirror that is kinematically mounted to the moving stage of

a damped parallel spring guide. The spring guide ensures smooth, low-friction, vertical motion. A linear

actuator nested inside the parallel spring guide drives the moving stage vertically. The indenter is sus-

pended above the sample and screws into the bottom of the moving stage of another damped parallel

spring guide. Another mirror is kinematically mounted to the top of this stage. The indenter spring guide

is independently calibrated and checked for linearity so that the indenter load can be correctly inferred.

Both spring guides are damped to prevent oscillations and utilize auxiliary counterbalance springs to

keep the spring guides close to their neutral, unstressed position, where their motion is linear.

The vertical positions of the sample and indenter mirrors and thus the positions of the sample and

indenter are monitored independently by the polarization interferometer. Light from a helium–neon

laser enters the polarization interferometer where the light beam is separated by a diffraction grating

into seven separate beams, six equally spaced beams on a 12-mm-diameter circle and one in the center

of the circle, which serves as the reference (Williams et al., 1988). Leaving the interferometer, the beams

pass through a beam expander to enlarge the beam circle diameter. Three of the outer beams strike the

indenter mirror and the other three pass through holes in the indenter mirror and stage and strike the

sample mirror. Because of the large beam circle diameter, the beams avoid striking the central obstruc-

tions, the sample, and the indenter. The light reﬂected from both mirrors then returns to the interfer-

ometer. Thus, the positions of the sample and indenter mirrors are continuously monitored by comparing

the relative phases of the light beams returning from the mirrors to the central reference beam. The

computer subtracts the positions of the two mirrors to determine the resulting indentation depth and

multiplies the indenter mirror position and the spring constant of the indenter parallel spring guide to

determine the indentation load.

To initiate a test, the actuator slowly raises the sample toward the indenter until motion is registered

by the interferometer, implying that contact has been made between the sample and the indenter. The

control loop then takes over and performs the chosen test — it either keeps the load constant and

measures the penetration depth as a function of time or it keeps the depth constant and measures the

load as a function of time.

10.2.2.5 NEC, Kawasaki Design

Tsukamoto et al. (1987) and Yanagisawa and Motomura (1987, 1989) developed a nanoindentation

hardness apparatus. NEC Corp., Kawasaki 216, Japan is attempting to commercialize it, although it is

not popular, Figure 10.8. It consists of three parts: an indenter actuator, a load detector, and a displace-

ment sensor. Indenter (1) with a diamond tip is attached to stylus (2) which is clamped on holder (3).

The holder is attached to a piezoelectric actuator (4), which drives the holder up and down controlled

by a personal computer (5) through an ampliﬁer (6), a regulated power source (7), and an interface (8).

Indentation load is detected by a digital electrobalance (9) with a 1-µN resolution at loads of up to

300 mN. The output signal is fed to the

-axis of an

–

recorder (10). A sample (11) is placed on a

sample disk (12). Penetration depth is detected by a ﬁber-optic displacement instrument (13) with a

4-nm displacement resolution. Light from a tungsten lamp in the displacement instrument is irradiated

onto a mirror (15) through an optical ﬁber (14). The intensity of the reﬂected light from the mirror on

the sample disk is measured by a photodetector in the displacement instrument and reduced to a

displacement between the indenter and the sample. An output signal from the displacement instrument

is connected to the

-axis of the

–

recorder. The apparatus is surrounded by a metal box (20) to minimize

the inﬂuence of air currents and heat radiation. It is placed on a vibration-isolation air table (16).

For an indentation experiment, the indenter is ﬁrst brought into contact with the sample by a micro-

meter (17). When contact is detected with the sample by the electrobalance, the distance between the

FIGURE 10.7

Schematic of a depth-sensing nanoindentation hardness apparatus by IBM Corporation, Tucson, and University of Arizona, Tucson,

AZ. (From Bhushan, B. et al., 1988,

ASME J. Tribol.

110, 563–571. With permission.)