g. kaupp, m. r. naimi-jamal powerpoint presentation of the nanomech 5, hückelhoven, germany...

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

Iterative analysis of the Berkovich multiple unloads/reloads according to ISO 14577. fused quartz SrTiO3

unload # 1 2 3 4 1 2 3 4 Er (Gpa) 67,1 66,0 65,9 66,5 254,5 263,0 251,4 242,0 H (Gpa) 7,99 7,83 7,81 7,47 10,36 9,99 10,02 9,37 S (N/µm) 84,4 83,8 83,8 86,5 281,4 296,0 282,7 281,3 A (µm2) 1.242 1.267 1.270 1.329 0.9595 0.9945 0.922 1.061 B (constant) * 13,190 18,696 18,339 18,677 0,794 1,060 5,861 10,114 hf (nm) 127,97 136,55 136,47 142,66 119,14 126,03 135,76 145,59 m (exponent) * 1,314 1,255 1,258 1,261 2,173 2,140 1,794 1,686

*The exponent m and the constant B are iterated for the 20 to 95% FN range

Multiple unloadings/reloadings


Nanoindentation to glassy polymers


y = 97,419x-0,2487

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000

FN (µN)

Er

(GP

a)

Polycarbonate (PC): dependence of Er on the load

Strong exponential dependence

Er values according to the standard procedure!


hf

hmaxhchs

FN

surface profile after load removal

initial surface

surface profile under load

indenter

Common assumptions about the indentation geometry

This is certainly not valid for most materials, except the standards


Some different cube corner indents


(We will also clarify what happened under the surface)

Isotropic and far-reaching anisotropic indentation response

SrTiO3 (100)

SrTiO3 (110) SrTiO3 (111)

(rotation of the crystals)


The common standard formulas


The variation of the parameters B, hf, and m of S = Bm(h-hf)m-1 upon different

choices of the unloading range and their influence to the elastic and plastic properties

lower end(%)*

Er (GPa)

H (GPa)

S (µN/nm)

hc (nm)

A (nm2) B hf (nm)

m

5 327,0 12,9 102,4 45,0 76964,6 0,1 25,5 2,8 10 319,2 12,9 99,7 44,9 76569,4 0,3 27,4 2,5 15 305,4 13,1 94,9 44,6 75793,2 1,4 30,3 2,1 17 300,3 13,1 93,1 44,5 75468,5 2,3 31,4 2,0 20 293,6 13,2 90,8 44,3 75018,1 4,3 32,7 1,8 30 271,6 13,5 83,0 43,7 73251,8 22,8 36,5 1,4 40 283,4 13,3 87,2 44,1 74300,1 7,5 33,7 1,7 50 280,3 13,4 86,1 44,0 74036,3 10,9 34,7 1,6 52 279,4 13,4 85,8 44,0 73947,9 12,9 35,1 1,5 60 277,5 13,4 85,1 43,9 73759,1 18,4 36,1 1,4 70 285,4 13,3 87,9 44,1 74457,4 8,5 34,2 1,6 80 266,9 13,6 81,2 43,5 72646,9 70,9 40,0 1,0 90 230,8 14,6 67,9 41,9 67914,9 39,1 36,1 1,1

upper end: 95 %, FN = 989,3 µN, hmax = 52,7 nm

Exponent of the unloading curve ?


S2 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

An approach without use of projected areaNanoscopic FN – S2 plots for indents on fused silica

Furthermore, errors of stiffness are squared


FN = k h3/2 or FN2/3 = k2/3 h; k [µN/nm3/2]is termed indentation coefficient

Quantitative analysis of the loading curveThe 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


Further demonstration of the FN = k h3/2 relation


Au

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 thepressure induced phase tranformation


0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000

(norm. displ.)1.5 (nm1.5)

no

rmal

fo

rce (

µN

)

Quartz (10-10)

0

500

1000

1500

2000

2500

3000

0 250 500 750 1000(norm. displ.)1.5 (nm1.5)

no

rmal

fo

rce

(µN

)

SrTiO3 (110)

cubic SrTiO3(Pm-3m); tetragonal (I4/mcm) ?trigonal -quartzmonoclinic 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

-SiO2 and SrTiO3: linear plots with kinks indicating pressure induced phase transitions


0

50

100

150

200

250

0 500 1000 1500 2000

(norm. displ.)1.5

(nm)1.5

no

rmal

fo

rce

(µN

)

Ninhydrin

OH

OH

O

O

k1 = 0.169 [µN/nm3/2

Cube corner:

k2 = 0.0805 [µN/nm3/2

]

]

Phase transition with organic crystals


FN – h3/2 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 – h2 trial plot.


WN tot tgα = const FN3/2

Fused quartz at 700 µN load with pyramidal indenter tips.

Indenter

H (GPa)* Er(Gpa)* α tg α hmax (nm)

WNtot (µNµm)

WNtot tgα

60° pyramid 10.5 70.4 24.45° 0.4547 213 57.95 26.4 cube corner 10.2 69.9 42.28° 0.9093 143 37.79 34.4 Berkovich 9.1 69.8 70.30° 2.7928 66 17.34 48.4

* H and Er values refer to 1000 µN load

Crystalline α-quartz, cube corner, 5000 µN, 30/10/30 s. Strontium titanate, Berkovich, 3000 µN, 30/10/30 s.

Compd. Face hmax

(nm) Ha)

(Gpa) Er

a) (Gpa)

k1 (µNnm-3/2)

k2

(µNnm-3/2) Wp/We WNtot tgα

(µNµm) SiO2 (10-10) 201 15.3 109.0 1.956 1.590 1.07 420.8 SiO2 (01-10) 191 16.2 119.7 2.145 1.728 1.09 378.3 SiO2 (01-11) 179 17.4 133.6 2.730 1.844 1.26 379.1 SiO2 (10-11) 193 16.5 105.0 2.256 1.668 1.17 404.7 SiO2 (1-100) 193 16.6 109.4 2.303 1.656 1.05 395.6

SrTiO3 (100) 102 11.7 236 2.754 3.536 1.53 329.7 SrTiO3 (110) 103 12.0 254 2.462 3.390 2.04 331.1 SrTiO3 (111) 102 11.1 246 2.317 3.096 2.08 355.7

a) The generally recommended 20 – 95% fit to the unloading curve was used

WN tot = ∫ FN dh [µN.µm]

Useful parameter: total work of the indentation


Appearances of nanoscratches by AFM

ramp experiment constant normal force


Quantitative treatment of nanoscratching

FL = K FN3/2

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)

Lateral force proportional to (normal force)3/2


y = 0,1926x - 44,289

0

50

100

150

200

250

0 300 600 900 1200 1500

normal force (μN)

late

ral f

orce

(μN)

y = 0,0046x + 0,022

0

50

100

150

200

250

0 10000 20000 30000 40000 50000

normal force1.5 (μN1.5)

late

ral f

orce

(μN)

y = 0,0001x + 21,791

0

50

100

150

200

250

0 500000 1000000 1500000 2000000

normal force2 (μN2)

late

ral f

orce

(μN)

(a) (b) (c)normal force (µN) (normal force)1.5 (µN1.5) (normal force)2 (µN2)

FL = K·FN3/2 (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


exponent 1.5 (not 1 or 2)the steep line in (b) corresponds to phase transformed SrTiO3

We use our quantitative FL = K FN3/2 relation:

easy search for high pressure phase transitionsSrTiO3 (100), 0°, cube corner edge in front


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 parameteris 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)


Angular dependence of specific scratch work on (1-100) of -quartz and crystal packing

Angle µNµm (FN=1482 µN)

90° 206 45° 223 0° 225

spec WSc = FL.1 [µNµm] = work for 1 µm scratch length of the indented tip

c-direction (90): alternation of 0.5405nm Si-Si rows; the other directions are less distant and the skew (10-11) cleavage plane is cutting in c-direction


SrTiO3 (100) SrTiO3 (110) SrTiO3 (111)

Spec. scratch work (3 µm, 60 s, FN = 1190 µN ) Angle µNµm 0° 246.6 45° 270.1 90° 240.4



Angular and facial dependence of specific scratch work (WSc,spec = FL.1 [µNµm])

or residual scratch resistance (RSc,res = FLl/Vres[N/m2]) on strontium titanate(why should we use the latter parameter as the volume measurement is insecure?)


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 = FN / H = projected area at full load)

it follows RSc full = FL√3 / A = H FL√3 / FN (FN = normal force)

and with FL = const.FN

3/2 (our experimental relation)

RSc full = const3/2 H FL

1/3√3

2 convenient linear plots: FL = K RSc full3 ; FN = K’ RSc full

2


y = 225,24x + 2,1866

0

20

40

60

80

100

120

140

160

0 0,2 0,4 0,6 0,8

(RSc,full)3

F L

y = 376,62x + 12,893

0

50

100

150

200

250

300

350

0 0,2 0,4 0,6 0,8

(RSc,full)2

F N

ninhydrin

y = 7,3336x + 37,472

0

200

400

600

800

1000

0 50 100 150

(RSc,full)3

F L

y = 110,51x + 336,44

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30

(RSc,full)2

F N

quartz

Examples for linear FL = K RSc full3 and FN = K’ RSc full

2 plots

These lines cut close to the origin as required


y = 0,0054x + 0,7599

0

200

400

600

800

0 50000 100000 150000

(norm. displ.)2.25 (nm 2.25)

late

ral f

orc

e (μ

N)

y = 0,0202x - 5,2546

0

100

200

300

400

0 5000 10000 15000 20000

(norm. displ.)2.25 (nm 2.25)la

tera

l fo

rce

(μN

)

y = 0,0081x - 4,7136

0

50

100

150

200

250

300

0 10000 20000 30000 40000

(norm. displ.)2.25 (nm 2.25)

late

ral f

orc

e (μ

N)

y = 0,0001x + 4,512

0

20

40

60

80

100

0 200000 400000 600000 800000

(norm. displ.)2.25 (nm 2.25)

late

ral f

orc

e (

μN

) y = 0,0006x + 4,9997

0

20

40

60

80

0 40000 80000 120000

(norm. displ.)2.25 (nm 2.25)

late

ral f

orc

e (μ

N) y = 0,0001x + 4,512

0

20

40

60

80

100

0 200000 400000 600000 800000

(norm. displ.)2.25 (nm 2.25)

late

ral f

orc

e (μ

N)

(a) (b) (c)

(d) (e) (f)

(a) fused quartz, (b) SrTiO3, (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 powerpoint presentation of the nanomech 5, hückelhoven, germany...

Documents