G Kaupp M R NaimiJamal Powerpoint Presentation of

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, 7. -9. September 2004

Multiple unloadings/reloadings G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Nanoindentation to glassy polymers G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Polycarbonate (PC): dependence of Er on the load Strong exponential dependence Er values according to the standard procedure! G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. 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, 7. -9. September 2004

Some different cube corner indents G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Isotropic and far-reaching anisotropic indentation response Sr. Ti. O 3 (100) (rotation of the crystals) (We will also clarify what happened under the surface) Sr. Ti. O 3 (110) Sr. Ti. O 3 (111) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

The common standard formulas G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Exponent of the unloading curve ? G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

An approach without use of projected area Nanoscopic FN – S 2 plots for indents on fused silica S 2 FN -1 = 4 π-1(Er)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 Furthermore, errors of stiffness are squared G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Quantitative analysis of the loading curve The relation of lateral force and normal displacement FN = k h 3/2 or FN 2/3 = k 2/3 h; k [µN/nm 3/2]is termed indentation coefficient 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, 7. -9. September 2004

Further demonstration of the FN = k h 3/2 relation G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Gold exhibits phase transition; square plots are invalid Au Au Linearity up to 10 m. N 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, 7. -9. September 2004

a-Si. O 2 and Sr. Ti. O 3: linear plots with kinks indicating pressure induced phase transitions trigonal a-quartz monoclinic coesite (>2. 2 GPa) tetragonal stishovite (>8. 2 GPa) cubic Sr. Ti. O 3(Pm-3 m); tetragonal (I 4/mcm) ? 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 G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Phase transition with organic crystals G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

FN – 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 FN – h 2 trial plot. G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Useful parameter: total work of the indentation WN tot = ∫ FN dh [µN. µm] G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Appearances of nanoscratches by AFM ramp experiment constant normal force G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Quantitative treatment of nanoscratching Lateral force proportional to (normal force)3/2 FL = K FN 3/2 K [N-1/2] is the new scratch coefficient What then about the „friction coefficient“ FL/FN? not correct in nanoscratching! Our quantitative relation is valid for all types of materials (we published on that) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

The relation of lateral force and (fixed) normal force FL = K·FN 3/2 (K = scratch coefficient [N-1/2]) Fused quartz and cube corner indentation tip, edge in front (a) normal force (µN) (b) (normal force) 1. 5 (µN 1. 5) (c) (normal force) 2 (µN 2) Linear plot through the origin only with exponent 1. 5 (not 1 or 2) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

We use our quantitative FL = K FN 3/2 relation: easy search for high pressure phase transitions Sr. Ti. O 3 (100), 0°, cube corner edge in front exponent 1. 5 (not 1 or 2) the steep line in (b) corresponds to phase transformed Sr. Ti. O 3 G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Instead of inapplicable friction coefficient (FL / FN) 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 WSc = FL. 1 [µNµm] (We just multiply the lateral force value with 1 µm) G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Angular dependence of specific scratch work on (1 -100) of a-quartz and crystal packing spec WSc = FL. 1 [µNµm] = work for 1 µm scratch length of the indented tip Angle µNµm (FN=1482 µN) 90° 206 45° 223 0° 225 c-direction (90): alternation of 0. 5405 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, 7. -9. September 2004

Angular and facial dependence of specific scratch work (WSc, spec = FL. 1 [µNµm]) or residual scratch resistance (RSc, res = FLl/Vres[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, 7. -9. September 2004

New Parameter: Full Scratch Resistance (RSc full) Definition RSc = FL l / V [Gpa] (FL = lateral force; l = length) RSc full = FL l / Vfull = FL/Q (Q = indenter cross section) for ideal cube corner Q = A / √ 3 (A = F N / H = projected area at full load) it follows RSc full = FL√ 3 / A = H FL√ 3 / FN (FN = normal force) and with F L = const. FN 3/2 (our experimental relation) RSc full = const 3/2 H FL 1/3√ 3 2 convenient linear plots: FL = K RSc full 3 ; FN = K’ RSc full 2 G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Examples for linear FL = K RSc full 3 and FN = K’ RSc full 2 plots quartz ninhydrin These lines cut close to the origin as required G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004

Consistency of our quantitative laws (normal force) ~ (normal displacement)3/2 and (lateral force) ~ (normal force)3/2 imply the relation (lateral force) ~ (normal displacement)9/4 (a) (b) (c) (d) (e) (f) (a) fused quartz, (b) Sr. Ti. O 3, (c) Si, (d) thiohydantoin, (e) ninhydrin and (f) tetraphenylethylene G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7. -9. September 2004