Supplementary Information
Cryogenic nanoindentation size effect in [0 0 1]-oriented face-center and bodycenter cubic single crystals
Seok-Woo Lee*, Lucas Meza, Julia R. Greer
Division of Engineering and Applied Science, California Institute of Technology, 1200E.
California Blvd, Pasadena, CA 91125, USA
1. Cryogenic Set up
The InSEMTM (Nanomechanics, Inc), one-of-a-kind in-situ nanomechanical
measurement apparatus was originally developed for the nanomechanical tests at room
temperature such as nanopillar compression/tension and nanoindentation (For more
information, please see http://jrgreer.caltech.edu). Recently, we installed the temperature
control system to study the nanomechanical behavior at cryogenic temperatures. Fig. S1
shows a photograph of our newly developed cryogenic system connected to the
InSEMTM. Liquid nitrogen or liquid helium can be transferred through the vacuum
shielded transfer line, and can drop the temperature of the cold finger down to the boiling
temperature of cooling liquids. The schematic diagram in Fig. S2 shows that both the
sample and the indenter tip are simultaneously cooled with the use of two oxygen-freehigh thermal-conductivity (OFHC) copper lines. This simultaneous cooling is very
important to avoid the thermal drift during mechanical tests, which could cause the
significant error in displacement measurement. The more details will be discussed in the
next section.
We also have the temperature sensors, the heaters, and the temperature controller.
The temperature controller reads the temperatures at the cold finger and at the sample
stage in real-time, and keep the desired temperatures at those two places by using PID
(proportional-integral-derivative) feedback loop. We use the bi-polar heater to control the
sample temperature. Electric currents in bi-polar heaters move along two opposite
directions at the same time, and the magnetic field from each uni-polar heater is cancelled
out. Then, the electron beam is not disturbed by the magnetic field from the heater.
However, the distance between cold finger and electron beam is relatively distant, so the
uni-polar heater is used to control the temperature of cold finger.
2. Thermal Drift Measurements
As discussed in the previous section, the simultaneous cooling of both sample and
indenter tip is very important to minimize the thermal drift. The thermal drift is, by
definition, the displacement change rate at a constant load, and its unit is usually nm/s. In
principle, if there is no change in temperature, the thermal drift must be zero, but the
temperature change in the testing environment causes the thermal expansion/contraction
of both a sample and the indenter tip, and produces the unintentional change in
displacement. Currently, in our system, there is no temperature sensor at the indenter tip.
Because the indenter tip is an extremely delicate part of the system, it is not easy to install
the temperature sensor and heater. However, it is possible to control the temperature at
the tip by monitoring the thermal drift. If the temperature on the sample is different from
that of the tip, the thermal expansion/contraction of both sample and the tip alters the
applied load immediately after thermal contact. In order to avoid unintentional load
change, the machine applies the displacement change to keep a prescribed load. Thus, the
magnitude of thermal drift is an indirect measure of temperature difference between the
sample and indenter tip. Thus, by adjusting the width of OHFC copper line between the
tip cooling assembly and the indenter tip, it is possible to find the optimum thickness of
copper line to provide the minimum thermal drift, which is comparable with the thermal
drift at room temperature.
We measured the thermal drifts in two cases, without tip cooling and with tip
cooling for Nb, W and fused-silica at 160 K, and with tip cooling for Al and Au at 160 K.
We applied the loading rate of 4 mN/s and the maximum load 12, 20 and 28 mN. The
thermal drift is measured after unloading at 20% of the maximum load for 10 seconds. As
seen in the table S1, in the case of Nb, which is a highly thermal-conductive metal, the
thermal drift without tip cooling is about 50 nm/s, which is very high. This implies that
there is an additional 100 nm displacement for 2 seconds. If we perform nanoindentation
for the 200 nm indentation depth, we would get the total displacement of ~300 nm, and
the measurement error would be significant since the thermal drift exhibit only the drift
only after unloading. Thermal drift during loading would be also huge, and different from
the measured thermal drift during unloading, leading to the significant error in the
displacement measurement.
With the tip cooling, it was possible to obtain the small thermal drift, which is
comparable with the room temperature value. This ensures the small displacement error
in our displacement measurements. Note that the thermal drift is highly dependent of the
thermal conductivity of materials. In the case of a fused-silica, the thermal drift is not
high even without tip cooling. There is almost no thermal transport between the tip and
fused-silica, not causing the thermal expansion/contraction of the sample and the tip.
However, in the case of metals, the thermal drift should be managed carefully since a
large thermal conduction causes the high thermal drift value. Thus, it is very important to
keep the temperature the same at both the tip and sample, especially for metallic samples.
Furthermore, the thermal drift is also dependent of the contact area. The thermal
drift is generally higher for the high maximum load (equivalently the large contact area).
For the higher maximum load, the indentation testing time is higher for the constant
loading rate, and the contact area is also larger. Thus, the thermal flow is much larger,
leading to the higher thermal drift. Thus, in general, the rapid loading rate would be
desired to reduce the testing time.
We measured indentation moduli of four metallic materials at 160, 230 and 298 K,
and also those of fused silica, which is a standard calibration material, at 160 K and 298
K to see the effect of temperature on the machine compliance. From the deep indentation
on Al, we measured the machine stiffness of our system as 74,074 N/m at room
temperature. With the same machine compliance, we found that indentation moduli of
four metals and fused silica appear to be relatively constant within the studied
temperature range of 160~298 K, and the average value shows the slight increasing trend
as the temperature decreases. Typically, the elastic constant of most metals from 298 K to
160 K increases only less than 5 %.1 Thus, our measurement is consistent with the
literature, and indentation are not so affected by our testing condition, indicating that that
the machine stiffness is not sensitive to our testing condition, too.
3. Minimum Temperature
Since the sample stage is not directly located at the cold finger, the temperature of
the sample is higher than that of the cold finger. The cold finger temperature is very close
to the boiling temperature of cooling liquid. In our case, we observed the temperature of
the cold finger is nearly 78 K without any heating (the boiling temperature of liquid
nitrogen is 77 K). However, we have had ~ 130K as the minimum possible temperature
of the sample stage. After about 10 hours cooling, the temperature stays near ~130 K
under the steady-state. The major reason for the rise of the temperature is the thermal
conduction from the sample stage. Currently, we insulated the sample stage using
alumina block, but it is still not easy to avoid the thermal conduction through the sample
stage. Currently, we are using the same wire set up for both the sample and the indenter
tip cooling. It would be necessary to use the thicker line for the sample cooling since the
thermal loss is more significant from the sample stage.
4. References
1. C. Kittel, Introduction to Solid State Physics, 8th ed. John Wiley & Sons, Inc, (2005),
p. 84.
2. M.A Meyers, K.K. Chawla, Mechanical behavior of Materials, Prentice Hall, 1999
p.91.
3. W.C. Oliver and G.M. Pharr, J. Mater. Res. 7 1564-1583 (1992).
4. H. Li, N.X. Randall, and J.J. Vlassak, J. Mater. Res. 25 729-734 (2010).
Figure S1. (a) A photograph and (b) schematic diagram of the current in-situ cryogenic
nanomechanical tester
Figure S2. (a) The schematic diagram of tip cooling assembly and (b) a photograph of
the tip cooling assembly inside the chamber of scanning electron microscope.
Nb
Max Force
28 mN
20 mN
12 mN
No tip cooling (nm/s)
50±10.9
31.8±4.05
12.8±4.19
Tip cooling (nm/s)
1.89±0.35
1.28±0.16
0.99±0.27
W
Max Force
28 mN
20 mN
12 mN
No tip cooling (nm/s)
23.06±2.11
19.99±1.54
13.05±0.93
Tip cooling (nm/s)
1.10±1.0
0.88±1.12
0.71±0.38
FS
Max Force
28 mN
20 mN
12 mN
No tip cooling (nm/s)
1.39±0.32
0.97±0.25
0.57±0.26
Tip cooling (nm/s)
0.37±0.36
0.00±0.573
0.62±0.87
Al
Max Force
28 mN
20 mN
12 mN
Tip cooling (nm/s)
4.235±0.387
3.763 ±0.573
2.807±0.87
Au
Max Force
28 mN
20 mN
12 mN
Tip cooling (nm/s)
1.785±0.978
1.280±0.311
0.842±0.366
Table S1. The thermal drift measurements for Nb, W and fused-silica (FS) without and
with tip cooling at 160 K. Also, thermal drift measurements for Au and Al with tip
cooling are available.
T (K)
Al (GPa)
Au (GPa)
W (GPa)
Nb (GPa)
Fused Silica
160
76.97 ±
5.56
93.27 ±
5.75
422.85 ±
39.78
138.77 ±
18.33
63.92 ±
4.79
230
79.53 ±
5.17
81.59 ±
4.21
443.52 ±
56.4
134.19 ±
47.36
N/A
298
73.44 ±
3.83
84.68 ±
2.61
401.38 ±
23.91
132.33 ±
4.53
65.58 ±
9.10
298
63.862
42.272
388.832
144.932
723
Table S1. The indentation moduli of five different materials at 160, 230, and 298 K. The
values in the lowest bottom are Young’s modulus of [0 0 1]-oriented crystals in
literatures. The superscripts in the bottom row indicate the references. Note that the large
difference between indentation and Young’s moduli of Au would be due to the strong
elastic anisotropy of Au.4