Transcript Document 7653707

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
Iterative analysis of the Berkovich multiple unloads/reloads according to ISO 14577.
fused quartz
SrTiO3
unload #
1
2
3
4
1
2
Er (Gpa)
67,1
66,0
65,9
66,5
254,5
263,0
H (Gpa)
7,99
7,83
7,81
7,47
10,36
9,99
S (N/µm)
84,4
83,8
83,8
86,5
281,4
296,0
2
A (µm )
1.242
1.267
1.270
1.329
0.9595
0.9945
B (constant) * 13,190 18,696 18,339
18,677
0,794
1,060
hf (nm)
127,97 136,55 136,47
142,66
119,14
126,03
m (exponent) *
1,314
1,255
1,258
1,261
2,173
2,140
*The exponent m and the constant B are iterated for the 20 to 95% FN range
3
251,4
10,02
282,7
0.922
5,861
135,76
1,794
4
242,0
9,37
281,3
1.061
10,114
145,59
1,686
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
30
y = 97,419x-0,2487
25
Er (GPa)
20
15
10
5
0
0
1000
2000
3000
4000
5000
FN (µN)
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
FN
surface profile after
load removal
initial surface
indenter
hf
hmax
hs
hc
surface profile
under load
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
SrTiO3 (100)
(rotation of the crystals)
(We will also clarify
what happened under
the surface)
SrTiO3 (110)
SrTiO3 (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 ?
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
Er
H
S
hc
end(%)* (GPa) (GPa) (µN/nm) (nm)
5
327,0 12,9
102,4
45,0
10
319,2 12,9
99,7
44,9
15
305,4 13,1
94,9
44,6
17
300,3 13,1
93,1
44,5
20
293,6 13,2
90,8
44,3
30
271,6 13,5
83,0
43,7
40
283,4 13,3
87,2
44,1
50
280,3 13,4
86,1
44,0
52
279,4 13,4
85,8
44,0
60
277,5 13,4
85,1
43,9
70
285,4 13,3
87,9
44,1
80
266,9 13,6
81,2
43,5
90
230,8 14,6
67,9
41,9
upper end: 95 %, FN = 989,3 µN, hmax = 52,7 nm
A (nm2)
B
76964,6
76569,4
75793,2
75468,5
75018,1
73251,8
74300,1
74036,3
73947,9
73759,1
74457,4
72646,9
67914,9
0,1
0,3
1,4
2,3
4,3
22,8
7,5
10,9
12,9
18,4
8,5
70,9
39,1
hf
(nm)
25,5
27,4
30,3
31,4
32,7
36,5
33,7
34,7
35,1
36,1
34,2
40,0
36,1
m
2,8
2,5
2,1
2,0
1,8
1,4
1,7
1,6
1,5
1,4
1,6
1,0
1,1
G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7.-9. September 2004
An approach without use of projected area
Nanoscopic FN – S2 plots for indents on fused silica
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
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 h3/2 or FN2/3 = k2/3 h; k [µN/nm3/2]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 h3/2 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 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, 7.-9. September 2004
a-SiO2 and SrTiO3: linear plots with kinks indicating pressure
induced phase transitions
3000
6000
SrTiO3 (110)
5000
normal force (µN)
normal force(µN)
Quartz (10-10)
4000
3000
2000
1000
0
2500
2000
1500
1000
500
0
0
1000
2000
1.5
(norm. displ.) (nm1.5)
3000
trigonal a-quartz
monoclinic coesite (>2.2 GPa)
tetragonal stishovite (>8.2 GPa)
0
250
500
750
1.5
1.5
(norm. displ.) (nm )
1000
cubic SrTiO3(Pm-3m); tetragonal (I4/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
250
normal force (µN)
Ninhydrin
Cube corner:
200
k1 = 0.169 [µN/nm3/2 ]
150
k2 = 0.0805 [µN/nm3/2 ]
100
O
50
OH
0
0
500
1000
1500
(norm. displ.)1.5 (nm)1.5
OH
2000
O
G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7.-9. September 2004
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.
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]
WN tot tgα = const FN3/2
Fused quartz at 700 µN load with pyramidal indenter tips.
Indenter
H (GPa)*
Er(Gpa)*
60° pyramid
10.5
70.4
cube corner
10.2
69.9
Berkovich
9.1
69.8
* H and Er values refer to 1000 µN load
α
tg α
24.45°
42.28°
70.30°
0.4547
0.9093
2.7928
hmax
(nm)
213
143
66
WNtot
(µNµm)
57.95
37.79
17.34
WNtot tgα
26.4
34.4
48.4
Crystalline α-quartz, cube corner, 5000 µN, 30/10/30 s.
Strontium titanate, Berkovich, 3000 µN, 30/10/30 s.
hmax
Ha)
Era)
k1
k2
Wp/We WNtot tgα
-3/2
-3/2
(nm) (Gpa) (Gpa) (µNnm ) (µNnm )
(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
Compd.
Face
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 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)
G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7.-9. September 2004
The relation of lateral force and (fixed) normal force
FL = K·FN3/2
(K = scratch coefficient [N-1/2])
Fused quartz and cube corner indentation tip, edge in front
150
100
50
200
150
100
50
0
0
0
300
600
900 1200 1500
normal force (µN)
normal force (μN)
200
150
100
50
0
0
(b)
y = 0,0001x + 21,791
lateral force (μN)
200
y = 0,0046x + 0,022
lateral force (μN)
lateral force (μN)
y = 0,1926x - 44,289
(a)
250
250
250
10000 20000 30000 40000 50000
(normal force)1.5 (µN1.5)
normal force 1.5 (μN1.5)
0
(c)
500000 1000000 1500000 2000000
(normal force)2 (µN2)
normal force 2 (μN2)
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 FN3/2 relation:
easy search for high pressure phase transitions
SrTiO3 (100), 0°, cube corner edge in front
exponent 1.5 (not 1 or 2)
the steep line in (b) corresponds to phase transformed SrTiO3
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
90°
45°
0°
µNµm (FN=1482 µN)
206
223
225
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
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/m2]) on strontium titanate
(why should we use the latter parameter as the volume measurement is insecure?)
SrTiO3 (100)
Spec. scratch work (3 µm, 60 s,
FN = 1190 µN )
SrTiO3 (110)
Spec. scratch work (3 µm, 60 s,
FN = 1190 µN )
SrTiO3 (111)
Spec. scratch work (3 µm, 60 s,
FN = 1190 µN )
Angle
µNµm
Angle
µNµm
Angle
µNµm
0°
45°
90°
246.6
270.1
240.4
0°
45°
90°
244.3
253.0
206.8
0°
45°
90°
326.2
239.5
241.9
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
it follows
Q = A / √3
RSc full = FL√3 / A = H FL√3 / FN
FL = const.FN3/2
and with
(A = FN / H = projected area at full load)
(FN = normal force)
(our experimental relation)
RSc full = const3/2 H FL1/3√3
2 convenient linear plots:
FL = K RSc full3 ; FN = K’ RSc full2
G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7.-9. September 2004
Examples for linear FL = K RSc full3 and FN = K’ RSc full2 plots
3500
1000
3000
y = 7,3336x + 37,472
800
y = 110,51x + 336,44
2500
FL
FN
600
2000
1500
400
1000
200
quartz
500
0
0
0
50
100
(RSc,full)
150
0
20
(RSc,full)
160
30
2
350
y = 225,24x + 2,1866
140
120
y = 376,62x + 12,893
300
ninhydrin
250
FN
100
FL
10
3
80
200
150
60
100
40
50
20
0
0
0
0,2
0,4
(RSc,full)3
0,6
0,8
0
0,2
0,4
(RSc,full)
0,6
0,8
2
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
400
400
200
300
200
100
0
(a)
50000
(norm . displ.)
100000
2.25
(nm
150000
2.25
)
(b)
100
0
5000
10000
15000
20000
200
150
100
50
(norm . displ.) 2.25 (nm 2.25)
0
(c)
40
20
y = 0,0006x + 4,9997
60
0
40
20
(norm . displ.)
2.25
(nm
2.25
)
(e)
2.25
30000
(nm
2.25
40000
)
y = 0,0001x + 4,512
60
40
20
0
0
200000 400000 600000 800000
20000
(norm . displ.)
80
0
0
10000
100
lateral force (μN)
60
y = 0,0081x - 4,7136
0
80
y = 0,0001x + 4,512
lateral force (μN)
lateral force (μN)
250
0
0
(d)
lateral force (μN)
600
80
300
y = 0,0202x - 5,2546
y = 0,0054x + 0,7599
lateral force (μN)
lateral force (μN)
800
40000
(norm . displ.)
80000
2.25
(nm
120000
2.25
)
0
(f)
200000 400000 600000 800000
(norm . displ.) 2.25 (nm 2.25)
(a) fused quartz, (b) SrTiO3, (c) Si, (d) thiohydantoin, (e) ninhydrin and (f) tetraphenylethylene
G. Kaupp, M. R. Naimi-Jamal, Nanomech 5, 7.-9. September 2004