Bhushan B. Nanotribology and Nanomechanics: An Introduction

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646 Adrian B. Mann

interfaces for coherency stresses. Combining the eﬀects of varying moduli and co-

herencystresses shows that the dependenceof strength on layerthickness has a peak

near the repeat period where coherency strains begin decreasing [131].

Another source of deviations in behavior at very small repeat periods is the

imperfect nature of interfaces. With the exception of atomically perfect epitaxial

ﬁlms, interfaces are generally not atomically ﬂat and there is some interdiﬀusion.

For the Cu/Ni ﬁlm of Table 12.1, the eﬀects of interdiﬀusion on hardness were

examined [124] by annealing the multilayers. The results were in agreement with

a model by Krzanowski [132] that predicted the variations in hardness would be

proportional to the amplitude of the composition modulation.

It is interesting to note that the explanations for enhanced mechanical proper-

ties in multilayered materials are all based on dislocation mechanisms. So it would

seem natural to assume that multilayered materials that do not contain dislocations

will show no enhanced hardness over their rule of mixtures values. This has been

veriﬁed by studies on amorphous metal multilayers [133], which shows that the

hardness of the multilayers, ﬁrstly, lies between that of the two individual materials

and, secondly, has almost no variation with repeat period.

12.6 Developing Areas

Overthe past 20 to30 years,the drivingforce forstudying nanomechanicalbehavior

of surfaces and thin ﬁlms has been largely, though not exclusively, the microelec-

tronics industry. The importance of electronics to the modern world is only likely

to grow in the foreseeable future, but other technological areas may overtake micro-

electronics as the driving force for research, including the broad ﬁelds of biomateri-

als and nanotechnology. In several places in this chapter, a number of developing

areas have been mentioned. These include nanoscale measurements of viscoelastic-

ity and the study of environmental eﬀects (temperature and surface chemistry) on

nanomechanical properties. Both of these topics will be vital in the study of biolog-

ical systems and, as a result, will be increasingly important from a research point of

view.

We still have a relatively rudimentary understanding of the nanomechanics of

complex biological systems such as bone cells (osteoblasts and osteoclasts) and

skin cells (ﬁbroblasts), or even, for that matter, simpler biological structures such

as dental enamel. For example, Fig. 12.30 shows how the mechanical properties of

dental enamel can vary within a single tooth [134]. But this is still a relatively large-

scale measure of mechanical behavior.The prismaticstructure of enamel means that

there are variations in mechanical properties on a range of scales from millimeters

down to nanometers.

In terms of data analysis, there remains much to be done. If an analysis method

can be developed that deals with the problems of pile-up and sink-in, the utility of

nanoindentation testing will be greatly enhanced.

12 Nanomechanical Properties of Solid Surfaces and Thin Films 647

Lingual

traverse

120

110

100

Surface Dentin

E (GPa)

Surface Dentin

E (GPa)

Surface Dentin

H (GPa)

Surface Dentin

H (GPa)

Surface Dentin

E (GPa)

Surface Dentin

H (GPa)

Center

traverse

Buccal

traverse

Pulp

Dentin

130

120

110

100

120

110

100

Fig. 12.30. Variations in E and H across human dental enamel. The sample is an upper 2nd

molar cut in cross section from the lingual to the buccal side. Nanoindentations are performed

across the surface to examine how the mechanical properties vary

References

1. G. Binnig, C.F. Quate, C. Gerber: Atomic force microscope, Phys. Rev. Lett. 56, 930–

933 (1986)

2. Microindentation Techniques in Materials Science and Engineering, ed. by P.J. Blau,

B.R. Lawn (ASTM, Pennsylvannia 1986)

3. J.N. Israelachvili: Intermolecular and Surface Forces (Academic, London 1992)

4. R.S. Bradley: The cohesive force between solid surfaces and the surface energy of

solids, Philos. Mag. 13, 853–862 (1932)

5. B.V. Derjaguin, V.M. Muller, Yu.P. Toporov: Eﬀect of contact deformations on the

adhesion of particles, J. Coll. Interface Sci. 53, 314–326 (1975)

6. V.M. Muller, V.S. Yuschenko, B.V. Derjaguin: On the inﬂuence of molecular forces on

the deformation of an elastic sphere and its sticking to a rigid plane, J. Coll. Interface

Sci. 77, 91–101 (1980)

7. V.M. Muller, B.V. Derjaguin, Yu.P. Toporov: On two methods of calculation of the

force of sticking of an elastic sphere to a rigid plane, Coll. Surf. 7, 251–259 (1983)

8. K.L. Johnson, K. Kendal, A.D. Roberts: Surface energy and the contact of elastic

solids, Proc. R. Soc. A 324, 301–320 (1971)

9. A.P. Ternovskii, V.P. Alekhin, M.Kh. Shorshorov, M.M. Khrushchov, V.N. Skvortsov:

Zavod Lab. 39, 1242 (1973)

10. S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii, G.D. Shnyrev: Deter-

mining Young’s modulus from the indentor penetration diagram, Zavod Lab. 41, 1137

(1975)

648 Adrian B. Mann

11. S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii: Mechanical prop-

erties of materials studied from kinetic diagrams of load versus depth of impression

during microimpression, Prob. Prochn. 9, 79 (1976)

12. S.I. Bulychev, V.P. Alekhin: Zavod Lab. 53, 76 (1987)

13. M.Kh. Shorshorov, S.I. Bulychev, V.P. Alekhin: Sov. Phys. Doklady 26, 769 (1982)

14. J.B. Pethica: Microhardness tests with penetration depths less than ion implanted layer

thickness. In: Ion Implantation into Metals, ed. by V. Ashworth, W. Grant, R. Procter

(Pergamon, Oxford 1982) p.147

15. D. Newey, M.A. Wilkens, H.M. Pollock: An ultra-low-load penetration hardness tester,

J. Phys. E: Sci. Instrum. 15, 119 (1982)

16. D. Kendall, D. Tabor: An ultrasonic study of the area of contact between stationary and

sliding surfaces, Proc. R. Soc. A 323, 321–340 (1971)

17. G.M. Pharr, W.C. Oliver, F.R. Brotzen: On the generality of the relationship among

contact stiﬀness, contact area and elastic-modulus during indentation, J. Mater. Res. 7,

613 (1992)

18. T.P. Weihs, C.W. Lawrence, B. Derby, C.B. Scruby, J.B. Pethica: Acoustic emissions

during indentation tests, MRS Symp. Proc. 239, 361–366 (1992)

19. D.F. Bahr, J.W. Hoehn, N.R. Moody, W.W. Gerberich: Adhesion and acoustic emis-

sion analysis of failures in nitride ﬁlms with 14 metal interlayer, Acta Mater. 45, 5163

(1997)

20. D.F. Bahr, W.W. Gerberich: Relationships between acoustic emission signals and phys-

ical phemomena during indentation, J. Mat. Res. 13, 1065 (1998)

21. A.B. Mann, D. van Heerden, J.B. Pethica, T.P. Weihs: Size-dependent phase transfor-

mations during point-loading of silicon, J. Mater. Res. 15, 1754 (2000)

22. A.B. Mann, D. van Heerden, J.B. Pethica, P. Bowes, T.P. Weihs: Contact resistance

and phase transformations during nanoindentation of silicon, Philos. Mag. A 82, 1921

(2002)

23. S. Jeﬀery, C.J. Soﬁeld, J.B. Pethica: Theinﬂuence of mechanical stress on the dielectric

breakdown ﬁeld strength of SiO

ﬁlms, Appl. Phys. Lett. 73, 172 (1998)

24. B.N. Lucas, W.C. Oliver: Indentation power-law creep of high-purity indium, Metall.

Trans. A 30, 601 (1999)

25. S.A. Syed Asif: Time dependent micro deformation of materials. Ph.D. Thesis (Oxford

Univ., Oxford 1997)

26. S.A. Syed Asif, R.J. Colton, K.J. Wahl: Nanoscale Surface Mechanical Property Meas-

urements: Force Modulation Techniques Applied to Nanoindentation. In: Interfacial

Properties on the Submicron Scale, ed. by J. Frommer, R. Overney (ACS Books,

Whashington 2000)

27. A.B. Mann, J.B. Pethica: Nanoindentation studies in a liquid environment, Langmuir

12, 4583 (1996)

28. J.W. Beams: Mechanical properties of thin ﬁlms of gold and silver. In: Structure and

Properties of Thin Films, ed. by C.A. Neugebauer, J.B. Newkirk, D.A. Vermilyea (Wi-

ley, New York 1959) pp.183–192

29. J.J. Vlassak, W.D. Nix: A new bulge test technique for the determination of Youngs

modulus and Poissons ratio of thin-ﬁlms, J. Mater. Res. 7, 3242 (1992)

30. W.M.C. Yang, T. Tsakalakos, J.E. Hilliard: Enhanced elastic modulus in composition

modulated gold-nickel and copper-palladium foils, J. Appl. Phys. 48, 876 (1977)

31. R.C. Cammarata: Mechanical properties of nanocomposite thin-ﬁlms, Thin Solid Films

240, 82 (1994)

32. G.A.D. Briggs: Acoustic Microscopy (Clarendon, Oxford 1992)

12 Nanomechanical Properties of Solid Surfaces and Thin Films 649

33. J. Kushibiki, N. Chubachi: Material characterization by line-focus-beam acoustic mi-

croscope, IEEE Trans. Sonics Ultrasonics 32, 189–212 (1985)

34. M.J. Bamber, K.E. Cooke, A.B. Mann, B. Derby: Accurate determination of Young’s

modulus and Poisson’s ratio of thin ﬁlms by a combination of acoustic microscopy and

nanoindentation, Thin Solid Films 398, 299–305 (2001)

35. S.E. Bobbin, R.C. Cammarata, J.W. Wagner: Determination of the ﬂexural modulus of

thin-ﬁlms from measurement of the 1st arrival of the symmetrical Lamb wave, Appl.

Phys. Lett. 59, 1544–1546 (1991)

36. R.B. King, C.M. Fortunko: Determination of inplane residual-stress state in plates us-

ing horizontally polarized shear waves, J. Appl. Phys. 54, 3027–3035 (1983)

37. R.F. Cook, G.M. Pharr: Direct observation and analysis of indentation cracking in

glasses and ceramics, J. Am. Ceram. Soc. 73, 787–817 (1990)

38. T.F. Page, W.C. Oliver, C.J. McHargue: The deformation-behavior of ceramic crystals

subjected to very low load (nano)indentations, J. Mater. Res. 7, 450–473 (1992)

39. G.M. Pharr, W.C. Oliver, D.S. Harding: New evidence for a pressure-induced phase-

transformation during the indentation of silicon, J. Mater. Res. 6, 1129–1130 (1991)

40. C.F. Robertson, M.C. Fivel: The study of submicron indent-induced plastic deforma-

tion, J. Mater. Res. 14, 2251–2258 (1999)

41. J.E. Bradby, J.S. Williams, J. Wong-Leung, M.V. Swain, P. Munroe: Transmission

electron microscopy observation of deformation microstructure under spherical inden-

tation in silicon, Appl. Phys. Lett. 77, 3749–3751 (2000)

42. Y.G. Gogotsi, V. Domnich, S.N. Dub, A. Kailer, K.G. Nickel: Cyclic nanoindenta-

tion and Raman microspectroscopy study of phase transformations in semiconductors,

J. Mater. Res. 15, 871–879 (2000)

43. H. Hertz: Über die Berührung fester elastischer Körper, J. reine angew. Math. 92, 156–

171 (1882)

44. J. Boussinesq: Application des potentiels à l’étude de l’équilibre et du mouvement des

solides élastiques (Blanchard, Paris 1885) Reprint (1996)

45. A.E.H. Love: The stress produced in a semi-inﬁnite solid by pressure on part of the

boundary, Philos. Trans. R. Soc. 228, 377–420 (1929)

46. A.E.H. Love: Boussinesq’s problem for a rigid cone, Quarter. J. Math. 10, 161 (1939)

47. I.N. Sneddon: The relationship between load and penetration in the axisymmetric

Boussinesq problem for a punch of arbitrary proﬁle, Int. J. Eng. Sci. 3, 47–57 (1965)

48. D. Tabor: Hardness of Metals (Oxford Univ. Press, Oxford 1951)

49. R. von Mises: Mechanik der festen Körper in plastisch deformablen Zustand, Goet-

tinger Nachr. Math.-Phys. K1, 582–592 (1913)

50. H. Tresca: Sur l’ecoulement des corps solids soumis s fortes pression, Compt. Rend.

59, 754 (1864)

51. A.B. Mann, J.B. Pethica: The role of atomic-size asperities in the mechanical defor-

mation of nanocontacts, Appl. Phys. Lett. 69, 907–909 (1996)

52. A.B. Mann, J.B. Pethica: The eﬀect of tip momentum on the contact stiﬀness and

yielding during nanoindentation testing, Philos. Mag. A 79, 577–592 (1999)

53. S.P. Jarvis: Atomic force microscopy and tip-surface interactions. Ph.D. Thesis (Oxford

Univ., Oxford 1993)

54. J.B. Pethica, D. Tabor: Contact of characterised metal surfaces at very low loads: De-

formation and adhesion, Surf. Sci. 89, 182 (1979)

55. J.S. Field, M.V. Swain: Determining the mechanical-properties of small volumes

of materials from submicrometer spherical indentations, J. Mater. Res. 10, 101–112

(1995)

650 Adrian B. Mann

56. W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic-

modulus using load and displacement sensing indentation experiments, J. Mater. Res.

7, 1564–1583 (1992)

57. S.V. Hainsworth, H.W. Chandler, T.F. Page: Analysis of nanoindentation load-

displacement loading curves, J. Mater. Res. 11, 1987–1995 (1996)

58. J.L. Loubet, J.M. Georges, O. Marchesini, G. Meille: Vickers indentation curves of

magnesium oxide (MgO), Mech. Eng. 105, 91–92 (1983)

59. J.L. Loubet, J.M. Georges, O. Marchesini, G. Meille: Vickers indentation curves of

magnesium oxide (MgO), J. Tribol. Trans. ASME 106, 43–48 (1984)

60. M.F. Doerner, W.D. Nix: A method for interpreting the data from depth sensing inden-

tation experiments, J. Mater. Res. 1, 601–609 (1986)

61. A. Bolshakov, W.C. Oliver, G.M. Pharr: Inﬂuences of stress on the measurement of

mechanical properties using nanoindentation. 2. Finite element simulations, J. Mater.

Res. 11, 760–768 (1996)

62. A. Bolshakov, G.M. Pharr: Inﬂuences of pileup on the measurement of mechanical

properties by load and depth sensing instruments, J. Mater. Res. 13, 1049–1058 (1998)

63. J.C. Hay, A. Bolshakov, G.M. Pharr: A critical examination of the fundamental rela-

tions used in the analysis of nanoindentation data, J. Mater. Res. 14, 2296–2305 (1999)

64. G.M. Pharr, T.Y. Tsui, A. Bolshakov, W.C. Oliver: Eﬀects of residual-stress on the

measurement of hardness and elastic-modulus using nanoindentation, MRS Symp.

Proc. 338, 127–134 (1994)

65. T.R. Simes, S.G. Mellor, D.A. Hills: A note on the inﬂuence of residual-stress on

measured hardness, J. Strain Anal. Eng. Des. 19, 135–137 (1984)

66. W.R. Lafontaine, B. Yost, C.Y. Li: Eﬀect of residual-stress and adhesion on the hard-

ness of copper-ﬁlms deposited on silicon, J. Mater. Res. 5, 776–783 (1990)

67. W.R. Lafontaine, C.A. Paszkiet, M.A. Korhonen, C.Y. Li: Residual stress measure-

ments of thin aluminum metallizations by continuous indentation and X-ray stress

measurement techniques, J. Mater. Res. 6, 2084–2090 (1991)

68. T.Y. Tsui, W.C. Oliver, G.M. Pharr: Inﬂuences of stress on the measurement of me-

chanical properties using nanoindentation. 1. Experimental studies in an aluminum al-

loy, J. Mater. Res. 11, 752–759 (1996)

69. T.Y. Tsui, J. Vlassak, W.D. Nix: Indentation plastic displacement ﬁeld: Part I. The case

of soft ﬁlms on hard substrates, J. Mater. Res. 14, 2196–2203 (1999)

70. T.Y. Tsui, J. Vlassak, W.D. Nix: Indentation plastic displacement ﬁeld: Part II. The

case of hard ﬁlms on soft substrates, J. Mater. Res. 14, 2204–2209 (1999)

71. D.L. Joslin, W.C. Oliver: A new method for analyzing data from continuous depth-

sensing microindentation tests, J. Mater. Res. 5, 123–126 (1990)

72. M.R. McGurk, T.F. Page: Using the P-delta(2) analysis to deconvolute the nanoinden-

tation response of hard-coated systems, J. Mater. Res. 14, 2283–2295 (1999)

73. Y.T. Cheng, C.M. Cheng: Relationships between hardness, elastic modulus, and the

work of indentation, Appl. Phys. Lett. 73, 614–616 (1998)

74. J.B. Pethica, W.C. Oliver: Mechanical properties of nanometer volumes of material:

Use of the elastic response of small area indentations, MRS Symp. Proc. 130, 13–23

(1989)

75. W.C. Oliver, J.B. Pethica: Method for continuous determination of the elastic stiﬀness

of contact between two bodies, United States Patent Number 4,848,141, (1989)

76. S.A.S. Asif, K.J. Wahl, R.J. Colton: Nanoindentation and contact stiﬀness measure-

ment using force modulation with a capacitive load-displacement transducer, Rev. Sci.

Instrum. 70, 2408–2413 (1999)

12 Nanomechanical Properties of Solid Surfaces and Thin Films 651

77. J.L. Loubet, W.C. Oliver, B.N. Lucas: Measurement of the loss tangent of low-density

polyethylene with a nanoindentation technique, J. Mater. Res. 15, 1195–1198 (2000)

78. W.W. Gerberich, J.C. Nelson, E.T. Lilleodden, P. Anderson, J.T. Wyrobek: Indenta-

tion induced dislocation nucleation: The initial yield point, Acta Mater. 44, 3585–3598

(1996)

79. J.D. Kiely, J.E. Houston: Nanomechanical properties of Au(111), (001), and (110)

surfaces, Phys. Rev. B 57, 12588–12594 (1998)

80. D.F. Bahr, D.E. Wilson, D.A. Crowson: Energy considerations regarding yield points

during indentation, J. Mater. Res. 14, 2269–2275 (1999)

81. D.E. Kramer, K.B. Yoder, W.W. Gerberich: Surface constrained plasticity: Oxide rup-

ture and the yield point process, Philos. Mag. A 81, 2033–2058 (2001)

82. S.G. Corcoran, R.J. Colton, E.T. Lilleodden, W.W. Gerberich: Anomalous plastic de-

formation at surfaces: Nanoindentation of gold single crystals, Phys. Rev. B 55, 16057–

16060 (1997)

83. E.B. Tadmor, R. Miller, R. Phillips, M. Ortiz: Nanoindentation and incipient plasticity,

J. Mater. Res. 14, 2233–2250 (1999)

84. J.A. Zimmerman, C.L. Kelchner, P.A. Klein, J.C. Hamilton, S.M. Foiles: Surface step

eﬀects on nanoindentation, Phys. Rev. Lett. 87, article 165507 (1–4) (2001)

85. J.D. Kiely, R.Q. Hwang, J.E. Houston: Eﬀect of surface steps on the plastic threshold

in nanoindentation, Phys. Rev. Lett. 81, 4424–4427 (1998)

86. A.B. Mann, P.C. Searson, J.B. Pethica, T.P. Weihs: The relationship between near-

surface mechanical properties, loading rate and surface chemistry, Mater. Res. Soc.

Symp. Proc. 505, 307–318 (1998)

87. R.C. Thomas, J.E. Houston, T.A. Michalske, R.M. Crooks: The mechanical response

of gold substrates passivated by self-assembling monolayer ﬁlms, Science 259, 1883–

1885 (1993)

88. W.D. Nix: Elastic and plastic properties of thin ﬁlms on substrates: Nanoindentation

techniques, Mater. Sci. Eng. A 234, 37–44 (1997)

89. J.J. Vlassak, W.D. Nix: Indentation modulus of elastically anisotropic half-spaces, Phi-

los. Mag. A 67, 1045–1056 (1993)

90. J.J. Vlassak, W.D. Nix: Measuring the elastic properties of anisotropic materials by

means of indentation experiments, J. Mech. Phys. Solids 42, 1223–1245 (1994)

91. B.R. Lawn: Fracture of Brittle Solids (Cambridge Univ. Press, Cambridge 1993)

92. G.M. Pharr: Measurement of mechanical properties by ultra-low load indentation,

Mater. Sci. Eng. A 253, 151–159 (1998)

93. D.B. Marshall, A.G. Evans:Measurement of adherence of residually stressed thin-ﬁlms

by indentation. 1. Mechanics of interface delamination, J. Appl. Phys. 56, 2632–2638

(1984)

94. C. Rossington, A.G. Evans, D.B. Marshall, B.T. Khuriyakub: Measurement of ad-

herence of residually stressed thin-ﬁlms by indentation. 2. Experiments with ZnO/Si,

J. Appl. Phys. 56, 2639–2644 (1984)

95. M.D. Kriese, W.W. Gerberich, N.R. Moody: Quantitative adhesion measures of multi-

layer ﬁlms: Part I. Indentation mechanics, J. Mater. Res. 14, 3007–3018 (1999)

96. M.D. Kriese, W.W. Gerberich, N.R. Moody: Quantitative adhesion measures of multi-

layer ﬁlms: Part II. Indentation of W/Cu, W/W, Cr/W, J. Mater. Res.

14,

3019–3026

(

1999)

97. M. Li, C.B. Carter, M.A. Hillmyer, W.W. Gerberich: Adhesion of polymer-inorganic

interfaces by nanoindentation, J. Mater. Res. 16, 3378–3388 (2001)

652 Adrian B. Mann

98. D.R. Clarke, M.C. Kroll, P.D. Kirchner, R.F. Cook, B.J. Hockey: Amorphization and

conductivity of silicon and germanium induced by indentation, Phys. Rev. Lett. 60,

2156–2159 (1988)

99. J.J. Gilman: Insulator-metal transitions at microindentation, J. Mater. Res. 7, 535–538

(1992)

100. G.M. Pharr, W.C. Oliver, R.F. Cook, P.D. Kirchner, M.C. Kroll, T.R. Dinger,

D.R. Clarke:Electrical-resistanceof metallic contacts on silicon and germanium during

indentation, J. Mater. Res. 7, 961–972 (1992)

101. A. Kailer, Y.G. Gogotsi, K.G. Nickel: Phase transformations of silicon caused by con-

tact loading, J. Appl. Phys. 81, 3057–3063 (1997)

102. J.E. Bradby, J.S. Williams, J. Wong-Leung, M.V. Swain, P. Munroe: Mechanical de-

formation in silicon by micro-indentation, J. Mater. Res. 16, 1500–1507 (2000)

103. G.S. Was, T. Foecke: Deformation and fracture in microlaminates, Thin Solid Films

286, 1–31 (1996)

104. A.J. Whitehead, T.F. Page: Nanoindentation studies of thin-ﬁlm coated systems, Thin

Solid Films 220, 277–283 (1992)

105. A.J. Whitehead, T.F. Page: Nanoindentation studies of thin-coated systems, NATO ASI

Ser. E 233, 481–488 (1993)

106. B.D. Fabes, W.C. Oliver, R.A. McKee, F.J. Walker:The determination ofﬁlm hardness

from the composite response of ﬁlm and substrate to nanometer scale indentations,

J. Mater. Res. 7, 3056–3064 (1992)

107. T.F. Page, S.V. Hainsworth: Using nanoindentation techniques for the characterization

of coated systems – a critique, Surface Coat. Technol. 61, 201–208 (1993)

108. X. Chen, J.J. Vlassak: Numerical study on the measurement of thin ﬁlm mechanical

properties by means of nanoindentation, J. Mater. Res. 16, 2974–2982 (2001)

109. P.J. Burnett, T.F. Page: Surface softening in silicon by ion-implantation, J. Mater. Sci.

19, 845–860 (1984)

110. P.J. Burnett, D.S. Rickerby: The mechanical-properties of wear resistant coatings.

1. Modeling of hardness behavior, Thin Solid Films 148, 41–50 (1987)

111. P.J. Burnett, D.S. Rickerby: The mechanical-properties of wear resistant coatings.

2. Experimental studies and interpretation of hardness, Thin Solid Films 148, 51–65

(1987)

112. P.M. Sargent: A better way to present results from a least-squares ﬁt to experimental-

data – an example from microhardness testing, J. Test. Eval. 14, 122–127 (1986)

113. S.J. Bull, D.S. Rickerby: Evaluation of coatings, Brit. Ceram. Trans. J. 88, 177–183

(1989)

114. B.R. Lawn, A.G. Evans, D.B. Marshall: Elastic/plastic indentation damage in ceram-

ics: The median/radial crack system, J. Am. Ceram. Soc. 63, 574–581 (1980)

115. R. Hill: The Mathematical Theory of Plasticity (Clarendon, Oxford 1950)

116. W.C. Oliver, C.J. McHargue, S.J. Zinkle: Thin-ﬁlm characterization using

a mechanical-properties microprobe, Thin Solid Films 153, 185–196 (1987)

117. N.G. Chechechin, J. Bottiger, J.P. Krog: Nanoindentation of amorphous aluminum ox-

ide ﬁlms. 1. Inﬂuence of the substrate on the plastic properties, Thin Solid Films 261,

219–227 (1995)

118. N.G. Chechechin, J. Bottiger, J.P. Krog: Nanoindentation of amorphous aluminum ox-

ide ﬁlms. 2. Critical parameters for the breakthrough and a membrane eﬀectin thin hard

ﬁlms on soft substrates, Thin Solid Films 261,

228–235 (1995)

119. D.E. Kramer, A.A. Volinsky, N.R. Moody, W.W. Gerberich: Substrate eﬀects on in-

dentation plastic zone development in thin soft ﬁlms, J. Mater. Res. 16, 3150–3157

(2001)

12 Nanomechanical Properties of Solid Surfaces and Thin Films 653

120. A.B. Mann: Nanomechanical measurements: Surface and environmental eﬀects. Ph.D.

Thesis (Oxford Univ., Oxford 1995)

121. A.B. Mann, J.B. Pethica, W.D. Nix, S. Tomiya: Nanoindentation of epitaxial ﬁlms:

A study of pop-in events, Mater. Res. Soc. Symp. Proc. 356, 271–276 (1995)

122. R. Saha, W.D. Nix: Eﬀects of the substrate on the determination of thin ﬁlm mechanical

properties by nanoindentation, Acta Mater. 50, 23–38 (2002)

123. S.A. Barnett: Deposition and mechanical properties of superlattice thin ﬁlms. In:

Physics of Thin Films, ed. by M.H. Francombe, J.L. Vossen (Academic, New York

1993)

124. R.R. Oberle, R.C. Cammarata: Dependence of hardness on modulation amplitude in

electrodeposited Cu-Ni compositionally modulated thin-ﬁlms, Scripta Metall. 32, 583–

588 (1995)

125. A. Madan, Y.Y. Wang, S.A. Barnett, C. Engstrom, H. Ljungcrantz, L. Hultman,

M. Grimsditch: Enhanced mechanical hardness in epitaxial nonisostructural Mo/NbN

and W/NbN superlattices, J. Appl. Phys. 84, 776–785 (1998)

126. R. Venkatraman, J.C. Bravman: Separation of ﬁlm thickness and grain-boundary

strengthening eﬀects in Al thin-ﬁlms on Si, J. Mater. Res. 7, 2040–2048 (1992)

127. J.D. Embury, J.P. Hirth: On dislocation storage and the mechanical response of ﬁne-

scale microstructures, Acta Mater. 42, 2051–2056 (1994)

128. D.J. Srolovitz, S.M. Yalisove, J.C. Bilello: Design of multiscalar metallic multilayer

composites for high-strength, high toughness, and low CTE mismatch, Metall. Trans. A

26, 1805–1813 (1995)

129. J.S. Koehler: Attempt to design a strong solid, Phys. Rev. B 2, 547–551 (1970)

130. S.V. Kamat, J.P. Hirth, B. Carnahan: Image forces on screw dislocations in multilayer

structures, Scripta Metall. 21, 1587–1592 (1987)

131. M. Shinn, L. Hultman, S.A. Barnett: Growth, structure, and microhardness of epitaxial

TiN/NbN superlattices, J. Mater. Res. 7, 901–911 (1992)

132. J.E. Krzanowski: The eﬀect of composition proﬁle on the strength of metallic multi-

layer structures, Scripta Metall. 25, 1465–1470 (1991)

133. J.B. Vella, R.C. Cammarata, T.P. Weihs, C.L. Chien, A.B. Mann, H. Kung: Nanoin-

dentation study of amorphous metal multilayered thin ﬁlms, MRS Symp. Proc. 594,

25–29 (2000)

134. J.L. Cuy, A.B. Mann, K.J. Livi, M.F. Teaford, T.P. Weihs: Nanoindentation mapping

of the mechanical properties of human molar tooth enamel, Arch. Oral Biol. 47, 281–

291 (2002)

Computer Simulations of Nanometer-Scale

Indentation and Friction

Susan B. Sinnott, Seong-Jun Heo, Donald W. Brenner, and Judith A. Harrison

Summary. Engines and other machines with moving parts are often limited in their design

and operational lifetime by friction and wear. This limitation has motivated the study of fun-

damental tribological processes with the ultimate aim of controlling and minimizing their

impact. The recent development of miniature apparatus, such as microelectromechanical sys-

tems (MEMS) and nanometer-scale devices, has increased interest in atomic-scale friction,

which has been found to, in some cases, be due to mechanisms that are distinct from the

mechanisms that dominate in macroscale friction.

Presented in this chapter is a review of computational studies of tribological processes at

the atomic and nanometer scale. In particular, a review of the ﬁndings of computational stud-

ies of nanometer-scale indentation, friction and lubrication is presented, along with a review

of the salient computational methods that are used in these studies, and the conditions under

which they are best applied.

13.1 Introduction

Engines and other machines with moving parts are often limited in their design and

operational lifetime by friction and wear. This limitation has motivated the study of

tribologicalprocesses withthe aim of controlling andminimizingthe impact ofthese

processes. There are numerous historical examples that illustrate the importance of

friction to the development of civilizations, includingthe ancient Egyptians who in-

ventedtechnologiestomovethestonesusedtobuildthepyramids[1];Coulomb,who

was motivated to study friction by the need to move ships easily and without wear

fromland to the water[1]; andJohnsonet al. [2], whodevelopedan improvedunder-

standing of contact mechanics and surface energies through the study of automobile

windshield wipers. At present, substantial research and developmentis aimed at mi-

croscale and nanoscale machines with moving parts that at times challenge our fun-

damentalunderstandingoffrictionand wear. Thishas motivatedthe studyofatomic-

scale friction and has, consequently, led to new discoveries such as self-lubricating

surfaces and wear-resistant materials. While there are similarities between friction

at the macroscale and the atomic scale, in many instances the mechanisms that lead

to friction at these two scales are quite diﬀerent. Thus, as devices such as magnetic

656 Susan B. Sinnott et al.

storage disks and microelectromechanical systems (MEMS) [3] continue to shrink

in size, it is expected that new phenomena associated with atomic-scale friction, ad-

hesion and wear will dominate the functioning of these devices.

The last two decades have seen considerable scientiﬁc eﬀort expended on the

study of atomic-scale friction[4–17]. This eﬀort has been facilitated by the develop-

ment of new advanced experimental tools to measure friction over nanometer-scale

distances at low loads, rapid improvements in computer power, and the matura-

tion of computational methodologies for the modeling of materials at the atomic

scale. For example, friction-force and atomic-force microscopes (FFM and AFM)

allow the frictional properties of solids to be characterized with atomic-scale reso-

lution under single-asperity indentation and sliding conditions [18–21]. In addition,

the surface force apparatus (SFA) provides data about the tribological and lubri-

cation responses of many liquid and solid systems with atomic resolution [22], and

the quartz crystal microbalance (QCM) providesinformation aboutthe atomic-scale

origins of friction [4,23]. Theseand related experimentalmethodsallow researchers

to study sliding surfaces at the atomic scale and relate the observed phenomena to

macroscopically observed friction, lubrication and wear.

Analytic models and computational simulations have played an important role

in characterizing and understanding friction. They can, for example, assist in the in-

terpretation of experimentaldata or providepredictionsthat subsequentexperiments

can conﬁrm or refute.Analytic modelshavelong been used to study friction, includ-

ing early studies by Tomlinson [24] and Frenkel and Kontorova [25]and more recent

studies by McClelland et al. [26], Sokoloﬀ [13, 27–33], Persson [34–37] and oth-

ers [38–44]. Most of these idealized models divide the complex motions that create

friction intomorefundamentalcomponentsdeﬁned byquantities such asspringcon-

stants, the curvatureand magnitude of potentialwells, and bulk phononfrequencies.

While these simpliﬁcations provide these approaches with some predictive capabi-

lities, many assumptions must be made in order to be able to apply these models to

study friction, which may lead to incorrect or incomplete results.

In atomic-scale molecular dynamics (MD) simulations, atom trajectories are

calculated by numerically integrating coupled classical equations of motion. Inter-

atomic forces that enter these equations are typically calculated either from total

energymethodsthat include electronicdegreesof freedom, orfrom simpliﬁedmath-

ematical expressions that give the potential energy as a function of interatomic dis-

placements. MD simulations can be considered numerical experiments that provide

a link between analytic models and experiments. The main strength of MD simu-

lations is that they can reveal unanticipated phenomena or unexpected mechanisms

for well-known observations. Weaknesses include a lack of quantum eﬀects in clas-

sical atomistic dynamics, and perhaps more importantly, the fact that meaningless

results can be obtained if the simulation conditions are chosen incorrectly. The next

section contains a review of MD simulations, including the approximations that are

inherent in their application to the study of friction, and the conditions under which

they should and should not be applied.