G. Kaupp, M. R. Naimi-Jamal Powerpoint Presentation of the Nanomech 5, Hückelhoven, Germany September 5-7, 2004

Nanoindentations Why do we need the new quantitative treatment? G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Multiple unloadings/reloadings G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Nanoindentation to glassy polymers G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Polycarbonate (PC): dependence of E r on the load Strong exponential dependence E r values according to the standard procedure! G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Common assumptions about the indentation geometry This is certainly not valid for most materials, except the standards G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Some different cube corner indents G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

(We will also clarify what happened under the surface) Isotropic and far-reaching anisotropic indentation response SrTiO 3 (100) SrTiO 3 (110)SrTiO 3 (111) (rotation of the crystals) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

The common standard formulas G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Exponent of the unloading curve ? G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

S 2 F N -1 = 4 π -1 (E r ) 2 H -1 (a) cube corner, (a’) defective cube corner, (b) Berkovich, (c) 60° pyramidal indenter tip; 95%- 20% of the unloading curves were iterated An approach without use of projected area Nanoscopic F N – S 2 plots for indents on fused silica Furthermore, errors of stiffness are squared G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

F N = k h 3/2 or F N 2/3 = k 2/3 h; k [µN/nm 3/2 ]is termed indentation coefficient Quantitative analysis of the loading curve The relation of lateral force and normal displacement Fused quartz: a-d: sharp cube corner (trial plots a and c invalid), e: sharp 60° pyramid, f: conosphere (R = 1 µm) Valid for all types of materials in nanoindentations On the basis of Hertzian theory this exponent would be the arithmetric mean of the flat and the conical punch‘s G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Further demonstration of the F N = k h 3/2 relation G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Au Gold exhibits phase transition; square plots are invalid Linearity up to 10 mN load and 370 nm depth. Faulty square plots or microindentations do not detect the pressure induced phase tranformation G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

cubic SrTiO 3 (Pm-3m); tetragonal (I4/mcm) ? trigonal  -quartz monoclinic coesite (>2.2 GPa) tetragonal stishovite (>8.2 GPa) Also fused quartz gives a phase transition (amorphous to amorphous). This has been complicating the quantitative analysis of its loading curve! The kinks are smeared out in faulty square plots and in microindentations  -SiO 2 and SrTiO 3 : linear plots with kinks indicating pressure induced phase transitions G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Phase transition with organic crystals G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

F N – h 3/2 plot of the cyclic loading curve of a cube corner nanoindentation on PC showing two straight lines and a kink in the loading curve that is not seen in the F N – h 2 trial plot. G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

W N tot = ∫ F N dh [µN.µm] Useful parameter: total work of the indentation G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Appearances of nanoscratches by AFM ramp experiment constant normal force G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Quantitative treatment of nanoscratching F L = K F N 3/2 K [N -1/2 ] is the new scratch coefficient What then about the „friction coefficient“ F L /F N ? not correct in nanoscratching! Our quantitative relation is valid for all types of materials (we published on that) Lateral force proportional to (normal force) 3/2 G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

(a)(b)(c) normal force (µN)(normal force) 1.5 (µN 1.5 )(normal force) 2 (µN 2 ) F L = K·F N 3/2 (K = scratch coefficient [N -1/2 ]) Linear plot through the origin only with exponent 1.5 (not 1 or 2) The relation of lateral force and (fixed) normal force Fused quartz and cube corner indentation tip, edge in front G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

exponent 1.5 (not 1 or 2) the steep line in (b) corresponds to phase transformed SrTiO 3 We use our quantitative F L = K F N 3/2 relation: easy search for high pressure phase transitions SrTiO 3 (100), 0°, cube corner edge in front G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Instead of inapplicable friction coefficient (F L / F N ) or residual scratch resistance (which lacks precision of the residual volume measurement) an easily and unambiguously obtained new parameter is defined: The specific scratch work (the work for 1 µm scratch length following indentation with a specified normal force) spec W Sc = F L. 1 [µNµm] (We just multiply the lateral force value with 1 µm) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Angular dependence of specific scratch work on (1-100) of  -quartz and crystal packing Angle µNµm (F N =1482 µN) 90° ° 223 0° 225 spec W Sc = F L. 1 [µNµm] = work for 1 µm scratch length of the indented tip c-direction (90): alternation of nm Si-Si rows; the other directions are less distant and the skew (10-11) cleavage plane is cutting in c-direction G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

Angular and facial dependence of specific scratch work (W Sc,spec = F L. 1 [µNµm]) or residual scratch resistance (R Sc,res = F L l/V res [N/m 2 ]) on strontium titanate (why should we use the latter parameter as the volume measurement is insecure?) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

New Parameter: Full Scratch Resistance (R Sc full ) Definition R Sc = F L l / V [Gpa] (F L = lateral force; l = length) R Sc full = F L l / V full = F L /Q (Q = indenter cross section) for ideal cube corner Q = A / √3 (A = F N / H = projected area at full load) it follows R Sc full = F L √3 / A = H F L √3 / F N (F N = normal force) and with F L = const.F N 3/2 (our experimental relation) R Sc full = const 3/2 H F L 1/3 √3 2 convenient linear plots: F L = K R Sc full 3 ; F N = K’ R Sc full 2 G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

ninhydrin quartz Examples for linear F L = K R Sc full 3 and F N = K’ R Sc full 2 plots These lines cut close to the origin as required G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004

(a)(b) (c) (d) (e) (f) (a) fused quartz, (b) SrTiO 3, (c) Si, (d) thiohydantoin, (e) ninhydrin and (f) tetraphenylethylene (normal force) ~ (normal displacement) 3/2 and (lateral force) ~ (normal force) 3/2 imply the relation (lateral force) ~ (normal displacement) 9/4 Consistency of our quantitative laws G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, September 2004