General nanomoulding with bulk metallic glasses

A critical requirement for any moldable material is that its intrinsic length scale is small compared to the size of the mold's features. Polymers are ultimately limited by their chain lengths and crystalline materials are limited by their grain sizes. Bulk metallic glasses (BMGs) lack intrinsic size limitation on the nanoscale [1–5]. In addition to this crucial attribute, BMGs are hard and tough compared to other materials used for nanomoulding, yet they can be softened into a state in which they can be readily molded [2]. These properties are often combined with favorable chemistry for biocompatibility, electrochemical activity, antibacterial behavior, and biodegradability.

Despite their attractiveness, until recently, BMGs could not be molded into features below 100 nm. Kumar et al [1] was first to mold Pt_57.5Cu_14.7Ni_5.3P_22.5 into pores of 10–100 nm in diameter and lengths that correspond to an aspect ratio of over 20. The ability to mold BMGs in a controllable manner has triggered broad research in exploring applications, such as electrochemical catalysts [6–9], micro fuel cell [10], MEMS/NEMS [5, 11, 12], programmable biomaterials [13–15] and wastewater treatment materials [16, 17]. Besides these applications, molded BMG nanostructures have also enabled the scientific community to study size and confinement effects on mechanical properties [18–25], deformation modes [26–29], crystallization [30, 31] and flow behaviors [23]. However, Kumar's findings and all following BMG nanomoulding has been limited to very few, noble-metals-based alloys such as Pt_57.5Cu_14.7Ni_5.3P_22.5 [1] and Pd₄₃Ni₁₀Cu₂₇P₂₀ [32–34] with a high resistance to oxide formation. Enabling the broad potential applications of BMG nanomoulding requires the development of nanomoulding strategies for more economic BMGs. Most BMGs, however, readily oxidize, particularly when heated into the supercooled liquid region (SCLR) like during thermoplastic forming (TPF) [35]. Such oxidizing results in the formation of a rigid oxide layer which dramatically affects and ultimately prohibits the TPF filling of nanosized pores for the vast majority of BMGs. We show here a general description for quantitative prediction of molding of BMGs into nanoscale features, which accounts for possible oxide formation. Our model includes a threshold pressure and a capillary contribution, which are required to break the oxide film and overcome the capillary force to enter into a nanopore, respectively. In addition, a viscous term, which when compared to the strength of the mold, defines the possible moldable aspect ratios. Based on this quantitative model which we use to construct a nanomoulding processing map for Zr₃₅Ti₃₀Cu_8.25Be_26.75, we introduce a strategy to reduce the capillary effect, which allows us to fabricate nanorods in air from highly reactive, non-noble based BMGs such as Zr₃₅Ti₃₀Cu_8.25Be_26.75, Zr₄₄Ti₁₁Cu₁₀Ni₁₀Be₂₅ and Mg₆₅Cu₂₅Y₁₀.

The nanomoulding experiments are operated in air with a heating-cell equipped Instron 5569 machine (50 kN maximum load capacity). The processing temperature for Zr₃₅Ti₃₀Cu_8.25Be_26.75, Zr₄₄Ti₁₁Cu₁₀Ni₁₀Be₂₅ and Mg₆₅Cu₂₅Y₁₀ with/without oils is 435 °C and 175 °C, respectively. The total processing time for all of the samples is ∼2 min and the maximum loading force is 50 KN. Demoulding of Zr₃₅Ti₃₀Cu_8.25Be_26.75 and Zr₄₄Ti₁₁Cu₁₀Ni₁₀Be₂₅ nanorods is achieved through etching Al₂O₃ templates with KOH solution (3 mol L⁻¹, temperature of 85 °C). For Mg₆₅Cu₂₅Y₁₀, we use H₃PO₄ solution (concentration of ∼85%, temperature of 85 °C) due to the high reactivity of the alloy with both alkaline and acidic solutions.

To demonstrate the use of BMGs as molds and moldable materials, we choose as an example Pt_57.5Cu_14.7Ni_5.3P_22.5 as a moldable material and Pd₄₃Ni₁₀Cu₂₇P₂₀ as a mold material. Firstly, a Pd₄₃Ni₁₀Cu₂₇P₂₀ BMG disc is thermoplastically formed into a nanoporous Al₂O₃ template at 360 °C. The maximum loading force and processing time are 5 KN and 2 min, respectively. Pd₄₃Ni₁₀Cu₂₇P₂₀ nanorods arrays to be used subsequently as a mold are exposed by etching the Al₂O₃ template. We then place a Pt_57.5Cu_14.7Ni_5.3P_22.5 disc which is covered by a thin layer of high temperature oil on the Pd₄₃Ni₁₀Cu₂₇P₂₀ nanorods array mold and thermoplastically form the mold-replicate combination at 270 °C. Demoulding is realized by a small mechanical force applied at room temperature.

Thermoplastic compression molding, a process in which moldable material is heated to flow into micro/nanopore under an applied pressure, has been widely used in surface patterning for polymers [36–39] and BMGs [3, 12, 40–45] due to its simplicity and scalability. Typically for a cylindrical pore with diameter, d, the required pressure to drive a liquid into a pore, p, can be calculated from Hagen–Poiseuille law

$$\begin{eqnarray}&&p=4\eta {{\dot{\varepsilon }}_{{\rm max} }}\frac{L}{d},\end{eqnarray} \tag{ 1 }$$

where η is the liquid's viscosity and ${{\dot{\varepsilon }}_{{\rm max} }}$ is the maximum shear strain rate. ${{\dot{\varepsilon }}_{{\rm max} }}$ is located at the liquid-mold interface when assuming a parabolic velocity distribution. This flow resistance linearly scales with the viscosity of the liquid (figure 1(a)). Typically for creep flow of BMGs in their SCLRs, ${{\dot{\varepsilon }}_{{\rm max} }}\tilde{\ }1\;{{{\rm s}}^{-1}},$ and their minimum accessible viscosity can vary significantly among BMG formers ranging 10⁵–10⁹ Pa s [46]. For η > 10⁹ Pa s, the molding pressure of 10 GPa is prohibitively high to fill an aspect ratio of three. Figure 1(a) and equation (1) also suggest that the viscous resistance of BMG liquids is size independent, which has been experimentally confirmed for molds larger than approximately one micron [47]. However, for nanosized molds, <100 nm, experiments revealed a size dependent forming pressure [1]. Kumar et al introduced a capillary effect to the viscous term into equation (1) to account for the size dependence [1]. The total pressure is then

$$\begin{eqnarray}&&p=4\eta {{\dot{\varepsilon }}_{{\rm max} }}\frac{L}{d}-\frac{4\gamma \;{\rm cos} \;\theta }{d}.\end{eqnarray} \tag{ 2 }$$

Here θ is the contact angle between BMG liquid and mold, and γ is the surface energy of BMG liquids. The capillary term (second term in equation (2)) is independent of L and inversely proportional to the diameter (figure 1(b)). Hence, the capillary term is independent of the aspect ratio and therefore sets the lower boundary for hydrophobic molds. For an applied pressure below p = −4γ*cos θ/d, nanorods cannot be molded.

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However, equation (2) does not consider that most BMG surfaces, in their supercooled state, are covered with an oxide layer, especially when molded in air [35]. The formation and thickness of such a rigid oxide layer increases with the reactivity of the BMG alloys. In order to mold the BMG into nanosized pores, this rigid oxide layer must break to allow BMG liquid to flow into the pores. Up to now, reactive BMGs like Zr-based BMGs have never been molded into pores below 1 μm, suggesting that the molding barrier from the oxide layer may be dominant on the nanoscale. In order to quantify this effect we modeled the surface oxide film by the Karman's nonlinear equations (in cylindrical coordinate system)

$$\begin{eqnarray}&&r\frac{{\rm d}}{{\rm d}r}\left( \frac{1}{r}\frac{{\rm d}}{{\rm d}r}\left( {{r}^{2}}{{N}_{r}} \right) \right)+\frac{Eh}{2}{{\left( \frac{{\rm d}w}{{\rm d}r} \right)}^{2}}=0,\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&D\frac{{\rm d}}{{\rm d}r}\left( \frac{1}{r}\frac{{\rm d}}{{\rm d}r}\left( r\;\frac{{\rm d}w}{{\rm d}r} \right) \right)={{N}_{r}}\frac{{\rm d}w}{{\rm d}r}+\frac{pr}{2},\end{eqnarray} \tag{ 4 }$$

where E is the elastic modulus, $D=\frac{E{{h}^{3}}}{12\left( 1-{{v}^{2}} \right)}$ is flexural rigidity and v is Poisson ratio, w is the normal displacement, N_r is the total membrane stress, and p is the uniform pressure exerted by the supercooled BMG liquid. Based on a dimensionless analysis, the pressure (p₀) to break this surface oxide layer should be of the form of

$$\begin{eqnarray}&&\frac{{{p}_{0}}}{E}=f\left( \frac{{{\sigma }_{{\rm c}}}}{E},\;v,\;\frac{h}{d} \right),\end{eqnarray} \tag{ 5 }$$

where σ_c is the strength of the oxide layer, and h the thickness of the oxide layer. From linear theory of small deflection and von-Mises yielding criterion, equation (5) can be written as

$$\begin{eqnarray}&&{{p}_{0}}=\frac{16}{3}\frac{{{\sigma }_{{\rm c}}}}{\sqrt{1-v+{{v}^{2}}}}{{\left( \frac{h}{d} \right)}^{2}},\end{eqnarray} \tag{ 6 }$$

which defines the pressure to break the oxide layer. This pressure barrier scales with (1/d)² and is more dramatic than the linear-scaling entering barrier from surface dewetting (second term in equation (2)). This scaling behavior reveals that the oxide layer barrier is indeed dominating the filling requirements of small pores. Considering the nonlinear effect, the more accurate pressure to break the oxide layer (p₀/E) is related to the maximum deflection value (w_m/h) when first yielding at clamped edges [48]

$$\begin{eqnarray}&&\begin{array}{lllllllllllllll} \frac{1-{{v}^{2}}}{\sqrt{1-v+{{v}^{2}}}}\frac{{{\sigma }_{{\rm c}}}}{E}{{\left( \frac{a}{h} \right)}^{2}}=\frac{{{w}_{{\rm m}}}}{h}\left( 4+\frac{1}{90}\left( 1+v \right)\left( 113-13v \right) \right. \\ \quad \times \left. {{\left( \frac{{{w}_{{\rm m}}}}{h} \right)}^{2}}+\frac{1}{1890}{{\left( 1+v \right)}^{2}}\left( 40-26v \right){{\left( \frac{{{w}_{{\rm m}}}}{h} \right)}^{3}} \right), \\ \end{array}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\frac{{{p}_{0}}}{E}=\frac{16}{3}\frac{1}{1-{{v}^{2}}}{{\left( \frac{h}{a} \right)}^{4}}\left( \frac{{{w}_{{\rm m}}}}{h}+\alpha {{\left( \frac{{{w}_{{\rm m}}}}{h} \right)}^{3}} \right),\end{eqnarray} \tag{ 8 }$$

where $\alpha =\frac{1}{360}\left( 1+v \right)\left( 173-73v \right).$ By substituting the mechanical properties of the oxide layer (E ∼ 200 GPa, σ_c ∼ 1 GPa, and v ∼ 0.3) and the oxide thickness (1 and 10 nm) into equation (7), the maximum deflection value (w_m/h) at yielding is calculated. Then substituting this value into equation (8), the critic pressure p₀ to rupture the oxide layer is finally obtained (figure 1(c)). It is obvious that when molding into small pores, the surface oxide layer becomes increasingly important. However, this is only the case for reactive alloys such as Zr-BMGs. For alloys with high corrosion resistance such as Pt-BMGs, the contribution of an oxide layer can be neglected.

The maximum aspect ratio that can be achieved in molding nanorods is ultimately limited by the strength of the mold (σ₀), which defines the upper bound for the applied pressure. As a consequence, the maximum aspect ratio that can be realized is given by

$$\begin{eqnarray}&&{{\left( \frac{L}{d} \right)}_{{\rm max} }}=\frac{1}{4\eta {{{\dot{\varepsilon }}}_{{\rm max} }}}\left( {{\sigma }_{0}}+\frac{4\gamma \;{\rm cos} \;\theta }{d} \right).\end{eqnarray} \tag{ 9 }$$

Equations (2), (7), (8) and (9) describe the general nanomoulding of supercooled BMGs (figures 1(a)–(c)). This description can be used to construct a BMG's processing map, which reveals the dominating effect of nanomoulding at different pore diameters. Taking Zr₃₅Ti₃₀Cu_8.25Be_26.75 for example, parameters are ${{\dot{\varepsilon }}_{{\rm max} }}\tilde{\ }1\;{{{\rm s}}^{-1}},$ η = 10⁷ Pa s, θ = 150°, γ = 1 J m⁻². Furthermore, we assume a maximum strength of σ₀ = 300 MPa for Al₂O₃ template (with 200 nm diameter pores) from a 0.2% elastic limit [49]. Combining equations (2), (3), and (5), the processing map can be constructed (figure 1(d)), where the oxide thickness is set as h = 10 nm, the upper bound in our experiments. We measure such a thickness of the oxide layer by oxidizing Zr₃₅Ti₃₀Cu_8.25Be_26.75 thin plate at 435 °C for 4 min in air. Subsequently, the plate is stretched to break the surface oxide layer and the thickness is determined using SEM (figure 5).

4.1. Nanomoulding non-noble BMGs by adding a wetting layer

The processing map (figure 1(d)) reveals the dominating effects controlling molding into different size pores. Prior to this work, Zr-BMGs have not been molded into features smaller than 1 μm. For this size region, the processing map reveals that the dominating barrier originates from either the capillary effect or surface oxide. To reduce these barriers, and hence enable nanomoulding with non-noble BMGs, we propose a simple strategy through introducing a wetting layer to the Al₂O₃ template surface (figure 2(a)). Specifically, we immerse Al₂O₃ templates and/or BMGs into high temperature oil prior to the molding operation. Oils typically wet ceramics and metals. We choose DuPont Kryto oil which wets Al₂O₃ template and Zr₃₅Ti₃₀Cu_8.25Be_26.75 well (contact angle θ < 45°, figure 6). By reducing the surface energy through the surface wetting oil, we successfully mold Zr₃₅Ti₃₀Cu_8.25Be_26.75 and Zr₄₄Ti₁₁Cu₁₀Ni₁₀Be₂₅ into 100 nm nanopores. One of the results for 200 nm nanorods with aspect ratio over five is shown in figure 2(d). In contrast, molding under the same processing conditions but without oil does not result in any filling of the 200 nm pores (figure 2(c)).

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We attribute the successful nanomoulding of Zr-BMG when using an oil layer to the reduced surface energy of BMG liquids which decreases the capillary (second term in equation (2)). When forming supercooled Zr₃₅Ti₃₀Cu_8.25Be_26.75 into a nanopore wetted with oil, the capillary term in equation (2) changes to $4\left( {{\gamma }_{{\rm oil}-{\rm BMG}}}-{{\gamma }_{{\rm oil}}} \right)/d,$ and the interfacial tension between oil and supercooled BMG can be estimated by ${{\gamma }_{{\rm oil}-{\rm BMG}}}={{\gamma }_{{\rm oil}}}+{{\gamma }_{{\rm BMG}}}-\sqrt{{{\gamma }_{{\rm oil}}}\cdot {{\gamma }_{{\rm BMG}}}}$ [50]. The capillary term thus becomes $4{{\gamma }_{{\rm BMG}}}\left( 1-\sqrt{{{\gamma }_{{\rm oil}}}/{{\gamma }_{{\rm BMG}}}} \right)/d,$ which suggests that the capillary effect can be reduced by using oil. In addition, the changing of sticky boundary to lubrication boundary may help to reduce the flowing resistance and thus enable the fabrication of nanorods with larger aspect ratio, which is still under investigation.

To demonstrate the general applicability of this strategy, we also mold Zr₄₄Ti₁₁Cu₁₀Ni₁₀Be₂₅ and Mg₆₅Cu₂₅Y₁₀ into pores of 200 nm in diameter (figure 3). When applying an oil film, both alloys can be nanomolded. The appearance of the Mg₆₅Cu₂₅Y₁₀ nanorods is affected by the subsequent H₃PO₄ etching to remove the Al₂O₃ template.

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4.2. BMGs used as molds and moldable materials

Besides using BMGs as ideal moldable materials, BMGs' drastic temperature dependent strength can also be utilized as a means to use them as molds. For example the softening temperatures of thermoplastics are usually below 200 °C, which is lower than the glass transition temperatures (T_g) for most BMGs. Hence, BMGs are high strength at these temperatures, hence can be used as molds for thermoplastic polymers. Due to the large range of glass transition temperatures among BMGs, nanomoulding one BMG with another BMG mold is also possible. The selection of the appropriate BMGs depends on their relative glass transition temperatures. This attribute and requirement are schematically shown in figure 4(a), where the viscosity (or flow stress) of BMGs can decrease by several orders of magnitude when the temperature approaches T_g. Compared with other mold materials such as silicon and Al₂O₃ molds, BMG nanomolds are advantageous due to their high elasticity, strength, and toughness. These attributes warrant long mold life, ability to demould, and precise and inexpensive fabrication of the mold.

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To demonstrate this concept, Pd₄₃Ni₁₀Cu₂₇P₂₀ nanorod arrays of 200 nm in diameter are fabricated by replicating Al₂O₃ mold at 360 °C. Subsequently, these nanorod arrays act as a mold and are replicated at 270 °C with oil-wetted Pt_57.5Cu_14.7Ni_5.3P_22.5. Demoulding at room temperature can be readily achieved by small mechanical forces. This method, in contrast to all previous BMG nanomoulding methods, allows the reuse of the mold. As such it represents a step towards commercial usage of BMG nanostructures since it drastically reduces fabrication costs which in the past included the disposable Al₂O₃ template.

We identified the governing contributions for most general BMG nanomoulding. These are viscous, capillary, and surface oxide layer fracture. The viscous contribution dominates for supercooled BMGs with large viscosity, when filled into high aspect ratios. The capillary term scales with the characteristic dimension of the nanopore and is determined by interface wetting properties (surface energy/contact angle). The surface oxide layer controls the filling barrier at smaller scales since it scales with the square of the diameter of the nanopore. Our general description allows for quantitative predictions, which can be used to create a processing map for BMG nanomoulding.

The processing map reveals the limiting factors, which have prevented nanomoulding for the majority of BMG alloys in the past. We used this knowledge to develop a molding strategy using a wetting layer to reduce the entering barriers. Using this method, reactive BMGs based on Zr and Mg can be nanomolded under practical conditions. Furthermore, the wetting layer also dramatically reduces interfacial forces, which suggest the possibility for a non-disposable mold method for BMG nanomoulding.

This work was primarily supported by the National Science Foundation under MRSEC DMR-1119826. Facilities use was supported by YINQE. We thank Dr Sungwoo for help casting Mg-BMG.

A.1. Oxidation rates

We oxidized Zr₃₅Ti₃₀Cu_8.25Be_26.75 in air at 435 °C and subsequently stretched the BMG to break its surface oxide layer. The total processing time is ∼4 min. The ruptured surface oxide layer is clearly revealed under an optical microscope (figure 5(a)). Using SEM (figures 5(b)–(c), the sample stage is tilted 30°), the oxide thickness is measured to ∼156 nm, which corresponds to a 0.65 nm s⁻¹ oxidation rate if assuming a linear oxidation. During the TPF-based molding, we usually consume ∼15 s to reach the processing temperature, which defines the upper bound thickness of the oxide layer to ∼10 nm (0.65*15 nm).

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A.2. Wetting properties of high temperature oil with templates and BMGs

The contact angles of oil drops on surfaces of Al₂O₃ and polished Zr₃₅Ti₃₀Cu_8.25Be_26.75 are smaller than 45° (figure 6), which suggests the high temperature oil (DuPont Kryto) used in our experiments wet both of them well.

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