Thermomechanical Behavior of Molded Metallic Glass Nanowires

Metallic glasses are disordered materials that offer the unique ability to perform thermoplastic forming operations at low thermal budget while preserving excellent mechanical properties such as high strength, large elastic strain limits, and wear resistance owing to the metallic nature of bonding and lack of internal defects. Interest in molding micro- and nanoscale metallic glass objects is driven by the promise of robust and high performance micro- and nanoelectromechanical systems and miniature energy conversion devices. Yet accurate and efficient processing of these materials hinges on a robust understanding of their thermomechanical behavior. Here, we combine large-scale thermoplastic tensile deformation of collections of Pt-based amorphous nanowires with quantitative thermomechanical studies of individual nanowires in creep-like conditions to demonstrate that superplastic-like flow persists to small length scales. Systematic studies as a function of temperature, strain-rate, and applied stress reveal the transition from Newtonian to non-Newtonian flow to be ubiquitous across the investigated length scales. However, we provide evidence that nanoscale specimens sustain greater free volume generation at elevated temperatures resulting in a flow transition at higher strain-rates than their bulk counterparts. Our results provide guidance for the design of thermoplastic processing methods and methods for verifying the flow response at the nanoscale.


S2
(PID) control. Over the course of a test the power dissipation and/or load were progressively increased while periodically capturing images in the SEM. When programming the PID controller, the feedback was intentionally slowed down in an effort to prevent mechanical or thermal instabilities. However such instabilities were still prevalent and often resulted in thermal run away and melting of the nanowire as shown in Figure S1a. After melting, the glass rapidly cools and can be found supported by a carbon sheath produced by imaging contamination or on the grips in the form of quenched spheres of metallic glass.
Strain was then calculated by tracking the positions of Pt-based EBID fiducial markers using digital image correlation techniques. After taking a sub image containing a single fiducial marker, a Gaussian to the average x and y profile as shown in Figure S1b. The marker coordinate is then determined as the peak position of the x and y profile fits. Tracking was accomplished by using the fit to the marker profile from the previous frame as the initial condition for fitting the marker profile in the current frame. The tracking resulted in a trajectory for each marker in both the x and y directions.
The trajectories were used to calculate the displacement of each marker and the average displacement of the two grips. The trajectories also allowed the potential in plane misalignment angle to be calculated for each frame. The true force along the nanowire axis was determined based on the resolved force and the potential in plane misalignment angle. In this way in plane angles were explicitly accounted for. However it is important to note that generally the angles were small and after accounting for the angle did not greatly affect the measurement. Critically, potential out of plane angles and displacements could not be accounted for and are a source of error.

S3
Engineering strains were then calculated as the change in nanowire length and accounted for displacement of the grips along the load train and laterally due to thermal drift. The very first image of the testing sequence was used as the unstrained reference. Engineering stress was calculated by measuring the nanowire diameter before deformation and assuming a circular cross-section. Subsequently true stress and strain were calculated by assuming uniform deformation and constant volume during plastic deformation.

Scaling of Viscosity with Power Dissipation:
The viscosities determined from nine thermomechanical tests (each symbol type is a distinct nanowire) are shown in Figure S1 as a function of power dissipated times length squared (µW-µm 2 ), which normalizes to T-T heat sink from the solution to the heat equation for steady state heat generation and conduction 3 . The inset shows the measured viscosity as log-viscosity versus power dissipated times length squared. From Figure S1 it is observed that the measured viscosity varied from 2×10 14 -8×10 11 Pa-s, which further indicates temperatures approaching T g .
Additionally, the shape of the viscosity-normalized power relation appears to be exponential. In glassy solids many relaxation processes vary exponentially with temperature, as often described by the Vogel-Fulcher-Tammann (VFT) relationship 4 . The VFT relation, which was derived from a reaction rate theory, describes the viscosity dependence on temperature by the fragility parameter. A low fragility, or strong glass, indicates a near-Arrhenius-like relationship between viscosity and temperature, whereas a high fragility (weak glass) indicates a strong deviation from Arrhenius dependence of viscosity on temperature. Thus the apparent exponential dependence of viscosity on normalized power indicates that the nanowire temperature is dependent on power dissipation, consistent with Joule heating. However, while the VFT parameters for the Pt-based S4 glass studied here can be estimated, the large scatter in the viscosity data precludes an accurate fit and a true conversion of dissipated power to nanowire temperature 5 .
It is important to consider sources of scatter in the power dissipated. In particular the Ptbased electron beam induced deposition (EBID) material used as both mechanical grips and electrical contacts likely produces a large amount of scatter. Generally, the electrical properties of EBID are variable with a strong dependence on the deposition conditions 6 . However even at consistent deposition conditions larger scatter in resistivity is often observed [6][7][8] . Thus the large variability in the power dissipation and the corresponding material response is likely influenced by the EBID electrical contacts.

Preservation of Amorphous Structure
When assessing the flow behavior of a metallic glass it is critical to ensure that the response is not influence by nucleation and growth of crystalline domains. The bright field transmission electron micrograph in Figure 5d from the main text provides evidence that the nanowires remain fully amorphous. Here we provide additional evidence in through a selected area electron diffraction (SAED) pattern and additional bright field micrographs and calculations of expected crystallization times in Figure S2. The calculations of crystallization time were made following the results from Legg et al. 5 These calculations indicate that the nanowires could be held at temperatures near T g for more than 10 hours before crystallization would become a concern. This calculation, in concert with the post-mortem TEM observations, provides significant confidence that crystallization is not an important factor when determining the flow response.

S5
To estimate the strain-rate sensitivity = log log a polynomial function was first fitted to log versus log for each nanowire specimen subject to load jump tests. The strain-rate sensitivity was then estimated by the derivative of the polynomial function evaluated at the measured strain-rate. The same process was employed to estimate the strain-rate sensitivity for all bulk data. This procedure is illustrated in Figure S3 using a subset of the data from Figure 4b.
The transition from Newtonian to non-Newtonian flow is determined using the estimated strain-rate sensitivities. When the strain-rate sensitivity is greater than 0.7 the flow is considered Newtonian; a strain-rate sensitivity less than 0.7 is described as non-Newtonian. Overall the location of the transition is insensitive to the chosen threshold. Choosing a different threshold will shift the boundary slightly. However since the same threshold was used for both the nanowire and bulk data the trends should be consistent regardless of the threshold value.

Estimation of Experimental Error
In this study several sources of error have been identified. The primary sources of measurement error originate from the measurement of MG nanowire diameter and cross-sectional area, noise in the load sensor, and the strain measurement by digital image correlation.
In this study, we have approximated the nanowire cross-section to be circular with a diameter, d. The diameter is taken as the average diameter measured at many locations over the length of the specimen. The typical variation in diameter is typically less than 10 nm, which is taken as an upper bound. We have not accounted for any evolution in cross-sectional shape; our conservative estimate on diameter may compensate for this uncertainty.
When performing digital image correlation the accuracy is determined by the pixel resolution of the SEM, the signal to noise ratio of the image, and the fitting of the fiducial marker S6 profiles. Here the strain noise floor is measured to be at 40,000x magnification.
The measured noise in the force measurement during feedback control was (200 Hz sampling rate). The error in strain-rate was determined as the root mean squared error determined during fitting of slope in strain versus time data within the steady state creep segments.
Finally for calculated quantities (i.e. stress and viscosity) we used the standard expressions for error propagation to estimate the experimental error 9 . Assuming all uncertainties are random and independent the uncertainty in a quantity, q, is described as  Figure S2: Using the measured strain-rates and stress the viscosity of the all thermoplastically deforming nanowires was determined. When plotted against power-length 2 , the normalization for ΔT derived from the heat equation for conduction in 1 dimension, the viscosity shows an apparent exponential dependence. The inset shows the viscosity data as log-viscosity vs. powerlength 2 to further show the apparent exponential relationship between viscosity and powerlength 2 .  Figure S3: Post mortem TEM imaging provides evidence that the nanowires remain fully amorphous. a) SAED patterns taken on from a melted nanowire show no signs of crystal diffraction spots. Bright field images in b) and c) show uniform contrast and no lattice fringes within the nanowire failure surface. In d) the estimated time until the onset of crystallization as a function of temperature is calculated using parameters from 5 . S11 Figure S4: Strain-rate sensitivities are found by fitting load jump data with a polynomial function. By evaluating the derivative of the polynomial function at each data point the strainrate sensitivity is estimated. The procedure is illustrated here a subset of the data from Figure 4b. The black dashed lines are the polynomial fit while the green triangles indicate the slope at each data point. Each triangle is labeled with its respective slope.