Melting Point Depression and Fast Diffusion in Nanostructured Brazing Fillers Confined Between Barrier Nanolayers

Abstract

Successful brazing using Cu-based nanostructured brazing fillers at temperatures much below the bulk melting temperature of Cu was recently demonstrated (Lehmert et al. in, Mater Trans 56:1015–1018, 2015). The Cu-based nano-fillers are composed of alternating nanolayers of Cu and a permeable, non-wetted AlN barrier. In this study, a thermodynamic model is derived to estimate the melting point depression (MPD) in such Cu/AlN nano-multilayers (NMLs) as function of the Cu nanolayer thickness. Depending on the melting route, the model predicts a MPD range of 238-609 K for Cu_10nm/AlN_10nm NMLs, which suggests a heterogeneous pre-melting temperature range of 750-1147 K (476-874 °C), which is consistent with experimental observations. As suggested by basic kinetic considerations, the observed Cu outflow to the NML surface at the temperatures of 723-1023 K (450-750 °C) can also be partially rationalized by fast solid-state diffusion of Cu along internal interfaces, especially for the higher temperatures.

Appendix 1: Physico-Chemical Properties for the Cu/AlN NML System

The standard melting point and molar melting entropy of Cu are $T_{m}^{\text{o}}$ = 1357.77 K (Ref 23) and $\Delta_{m} S_{\text{mol}}^{\text{o}}$ = 9.51 J/mol K (Ref 23), respectively. The standard Gibbs energy change accompanying melting of pure Cu below its standard melting point (J/mol) is obtained from (Ref 23):

$$G_{{{m},{l}}}^{\text{o}} - G_{{{m},{s}}}^{\text{o}} = 12964.736 - 9.511904 \cdot T - 5.849 \times 10^{ - 21} \cdot T^{7} .$$

(8)

The T-dependence of the molar volume of solid Cu (cm³/mol) is obtained from (Ref 74-76):

$$V_{{{m},{s}}}^{\text{o}} = 7.042 + 3.159 \times 10^{ - 5} \cdot T^{1.355} .$$

(9)

The standard surface tension $\sigma_{l/g}^{\text{o}}$ (J/m²) and surface energy $\sigma_{s/g}^{\text{o}}$ (J/m²) of Cu equal (Ref 77, 78):

$$\sigma_{l/g}^{\text{o}} = 1.30 - 2.3 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right),$$

(10)

$$\sigma_{s/g}^{\text{o}} = 1.60 - 4.7 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right).$$

(11)

The liquid/barrier interfacial energy is written from the Young-Dupré equation as (Ref 79):

$$\sigma_{l/b}^{\text{o}} = \sigma_{l/g}^{\text{o}} + \sigma_{b/g}^{\text{o}} - W_{l/b}^{\text{o}} ,$$

(12)

where $\sigma_{b/g}^{\text{o}}$ (J/m²) is the surface energy of the barrier (AlN in our case), $W_{l/b}^{\text{o}}$ (J/m²) is the adhesion energy between the liquid metal and the barrier, which can be expressed as

$$W_{l/b}^{\text{o}} = \sigma_{l/g}^{\text{o}} \cdot \left( 1 + { \cos \varTheta } \right).$$

(13)

At the Cu melting point, $\sigma_{l/b}^{\text{o}}$ = 1.30 J/m² (see Eq 10). The surface energy of AlN is about (Ref 80) (J/m²):

$$\sigma_{b/g}^{\text{o}} = 2.53 - 3.5 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right)$$

(14)

The contact angle of liquid Cu on AlN, being a covalent and non-reactive ceramic, is about 150^° (Ref 79). Thus, as follows from Eq 13, the adhesion energy at the melting point of Cu is about $W_{l/b}^{\text{o}}$ = 0.17 J/m², which to a first approximation is taken T-independent. Thus, the T-dependence of $\sigma_{l/b}^{\text{o}}$ (J/m²) is obtained by combining Eq 10, 12, 14:

$$\sigma_{l/b}^{\text{o}} = 3.66 - 5.8 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right).$$

(15)

The interface between solid Cu and AlN is incoherent (Ref 15, 16). Neglecting lattice mismatch strain (Ref 69), the adhesion energy is similar to that of the liquid Cu, i.e., $W_{s/b}^{\text{o}}$ = 0.17 J/m². Then, the solid metal/barrier interfacial energy approximately equals (see Eq 11, 12, 14):

$$\sigma_{s/b}^{\text{o}} = 3.96 - 8.2 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right).$$

(16)

To a first approximation, the grain boundary energy of the barrier layer can be taken as 1/3 of its surface energy, $\sigma_{b/g}^{\text{o}}$ in Eq 14 (Ref 81), i.e.,

$$\sigma_{b/b}^{\text{o}} = 0.84 - 1.2 \times 10^{ - 4} \left( {T - T_{m}^{\text{o}} } \right).$$

(17)