Supplementary Information

Cryogenic nanoindentation size effect in [0 0 1]-oriented face-center and body-

center 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-free-

high 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 No tip cooling (nm/s) Tip cooling (nm/s)28 mN 50±10.9 1.89±0.3520 mN 31.8±4.05 1.28±0.1612 mN 12.8±4.19 0.99±0.27

W

Max Force No tip cooling (nm/s) Tip cooling (nm/s)28 mN 23.06±2.11 1.10±1.020 mN 19.99±1.54 0.88±1.1212 mN 13.05±0.93 0.71±0.38

FS

Max Force No tip cooling (nm/s) Tip cooling (nm/s)28 mN 1.39±0.32 0.37±0.3620 mN 0.97±0.25 0.00±0.57312 mN 0.57±0.26 0.62±0.87

Al

Max Force Tip cooling (nm/s)28 mN 4.235±0.38720 mN 3.763 ±0.57312 mN 2.807±0.87

Au

Max Force Tip cooling (nm/s)28 mN 1.785±0.97820 mN 1.280±0.31112 mN 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