Vacancy Concentration in Nickel through
Nanoindentation
Veronica Perez and David F. Bahr
RESULTS
BACKGROUND
f prob NiV5
Nist HT f-prob
Nanoindentation is the most common way to
Fig.2.a
B
fraction berk-HT
f prob NiV5
Yield point at 0.9 f-probability
600
NiV5 probability before and after (tmax)
test small volumes of materials for mechanical
500
1.2
Probability Before and after (tmax)
400
1.2
300
200
1
properties. This process consists of a sharp
1
100
0
0.8
diamond tip indenting the surface of the desired
-100
-20
0
20
40
60
0.8
80
displacement (nm)
B
0.6
material. Once the tip is removed it leaves an indent
0.6
Yield point at 0.2f-probability
600
500
0.4
0.4
400
300
from which hardness is calculated from, through
200
0.2
0.2
100
Fig.1
other software modulus, roughness, and other
0
0
-100
9
9
9
9
9
9
9
9
9
2.5 10 3 10 3.5 10 4 10 4.5 10 5 10 5.5 10 6 10 6.5 10 -20
0
20
40
60
0
9
1.5 10
80
2 10
9
2.5 10
9
3 10
9
3.5 10
9
4 10
displacement (nm)
Fig.2.b
tmax, pa
Fig.3
Tmax, Pa (HT)
mechanical properties can be determined.
Fig.1: yield point probability graph with the smaller tip before and after HT.
Fig2.A: graph of a high load yield point after HT. Fig2.B graph of a low load yield point
after HT. Fig.3: yield point probability graph with the larger tip before and after HT.
In the Positron Analysis, a beam of positrons
are injected into the sample. When annihilation
D
occurs the vacancy concentration can be determined
Fig.4 PM 7/6/2010
Data 16 12:57:05
Fig.5
f-prob instantaneous radius
f-prob average radius
0.00016
for the sample.
NiV5 Nist probability HT (individual indents)
1.2
0.00014
If once sample was to contain a higher vacancy
0.00012
1
0.0001
concentration it will appear in the spectra. The
8 10
0.8
-5
0.6
y = 4/3*(188*1e9)*((m0)^ 1.5...
effect of vacancy concentration in yield point data is
6 10
4 10
investigated in this project by the following steps.
2 10
-5
-5
Value
Error
m1
1163.7
2.4208
Chisq
1.3743e-8
NA
R
0.99677
NA
0.4
0.2
-5
0
0
0
1 10
-9
2 10
-9
3 10
-9
4 10
-9
5 10
-9
6 10
-9
7 10
-9
8 10
-9
0
5 10
9
1 10
10
1.5 10
10
2 10
10
2.5 10
10
tmax NiV5
Fig4. Curve fitting on elastic part of a yield point graph, calculates the tip
radius for the larger tip after HT. Fig5. Shows a τmax vs. f-probability graph
for the smaller tip with average and instantaneous radius tip.
4
Vacancy signal (1 == nearly vacancy free)
PROCEDURE
Preparation of Nickel Samples
Grinding, Polishing, Electro-polishing
First round of automations
Data collection, Roughness values and
Multiple curve analysis
Positron Analysis
Vacancy concentration
Calculations
Average and instantaneous tip radii
Calculating maximum pressure (p0),
maximum shear stress (τmax), and area
Encapsulation in vacuum
Heat treatment
Second round of automation
Data collection, New roughness values and
MC values
Calculations
Calculating new average and instantaneous
tip radii
Calculating p0, τmax, area
Ni samples
data fit sample
K. Lynn reference Ni(111)
#3 (on puck);
(off puck)
#4 (on puck)
#5 (on puck);
(off puck)
June 29 sample, annealed
1.25
1.20
9
In this research project, the objective was to determine
the effect that vacancy concentration has on the yield behavior
in nickel. By calculating the maximum sheer stress (τmax)
through an average radii and instantaneous radii it shows the
difference between the two τmax values. When calculating
τmax through the first method the elastic deformation section
of yield point graph was fitted to the Hertz equation, this
result in an average radius. When assuming instantaneous
radii the load and displacement at the yield point of each
indent was used in the second τmax formula. When τmax is
plotted vs. probability it can be observed that at low yield
loads the two τmax values are very close to each other;
however, at higher loads the instantaneous radii curve starts
deviating to higher τmax values while the average radii curve
maintains a steeper slope (fig.5).
It can be determined that after heat treatment the
probability with respect to τmax increases as shown in fig 1
and 3. In both figures a graph of τmax vs. f-probability is
displayed with two curves (before and after heat treatment).
With either tip, τmax increases considerably after heat
treatment.
It appears that by changing the vacancy concentration it
will also change the yield behavior and subsequently τmax.
The nickel sample was heat treated at 1023°C and slowly
cooled. In fig 6, it can be determined that before heat
treatment the vacancy concentration was around 1.15 at 2-3
µM. After heat treatment the vacancy concentration was
lowered to nearly 1.0 at the same depth, which is considered
as nearly vacancy free.
3
9
188 ∗ 10 ((𝑚0)
6𝐸 ∗2
𝑝𝑚 =
more
vacancies
1.15
1/3
𝜋 3𝑅2
𝑝
3/2
1/3
𝑡𝑚𝑎𝑥 = 0.31𝑝𝑚
𝑇𝑚𝑎𝑥 = 0.31
1.10
𝑎=
3𝑅𝑃 1/3
4𝐸 ∗
1
)(𝑚1 ∗ 10−9 )2; 𝑚1 = 3
8
𝐸 ∗2ʆ2
3𝜋
𝑝
𝑐2 = 𝑐1/𝑐𝑚𝑎𝑥(𝑐1)
Formulas
Hertz equation
Maximum pressure
τmax (average
radii)
τmax
(instantaneous)
Area under tip
CONCLUSION
By altering a nickel sample through heat treatment
the yield behavior was determined and compared to the
yield behavior before heat treatment. The results
concluded that after heat treatment the maximum sheer
stress increases considerably compared to the sample
before heat treatment. This complies with the results
from positron data, before the heat treatment the
vacancy concentration was much higher than after the
alteration. The slow cool after heat treatment resulted in
annealing vacancies out of the sample and resulting in
higher τmax values. Thus, heat treatment with a slow
quench will produce a higher τmax value for the yield
behavior.
1.05
References
1.00
0
Fig.
6
1
2
3
Gane. N and Bowden. F. P., Journal of Applied Physics, 1968
Bahr. F.D, Kramer. D.E and Gerberich W.W. Acta Materialia, 1997
Nanoindentation. “Introduction to Nanoindentation.”
www.Nanoindentation.cornell.edu
“Positron Analysis.” www.uwo.ca/isw/facilities/positron/index.html
4
Mean depth (m)
Fig. 6: Positron Analysis shows
that sample NiV5 (#5) before heat
treatment has a higher vacancy
concentration then after heat
treatment with a low quench,
suggesting the low quench annealed
vacancies out of the sample.
Fig.
7
Acknowledgements
Fig7. Roughness image of nickel
sample; note the height scale is
extremely exaggerated.
•Thanks for the support and funding of the WA NASA Space Grant and the
National Science Foundation under grant number DMR 0907378
•Thanks to Dr. Katerina Bellou, Marc Weber and Narendra S. Parmar for
their help using testing equipment and data analysis.