# Cracking and Toughening Mechanisms in Nanoscale Metallic Multilayer Films: A Brief Review
## 2 Microstructure
### Dimensionally-Induced Structural Transformations  
#### 2.2.1 Phase Structure Transformation  
Phase structure transformation, which is difficulty for the bulks, can be directly detected in NMMFs since a great deal of interfaces can be the nucleation sites for phase transformation. Transformation of lattice structures often occurred when \(h\) is small [20; 21]. HRTEM images of (111) Cu/Co multilayers in Figure 3a shows that an fcc Co layer first formed on Cu, followed by an hcp Co layer. The orientation relationship between fcc and hcp Co is shown in Figure 3b. For Al/Ti multilayers [22], the interesting sequence of crystal structure transformation has also been reported. To account for polymorphic stability, three theories are proposed to understand the phase transformation in NMMFs, involving the influences of stacking fault energies [23] and coherency strains [24]. A thermodynamic approach [22; 25] considering the large excess energy associated with  
Figure 3: (**a**) HRTEM image of Cu/Co NMMFs with \(h\) = 5 nm reveals the coexistence of hcp and fcc Co.  
(**b**) The corresponding orientation relationship [20]. Figure 2: (**a**) HRTEM micrographs of the Cu/Nb interface in a PVD nanolayered composite; (**b**) Molecular simulation model of a Cu/Nb bi-layer. (**c**,**d**) are intrinsic defect structures (misfit dislocations) at the Cu/Nb interface [18]. thermally preferred interfaces is often believed to account for the phase transformation. The total energy of the bilayer was proposed to be at the minimum energy configuration. Following [PERSON] (1984), the specific free energy \(\Delta g\) could be described by Equation (1) for formation of a A/B bilayer:  
\[\Delta g=2\Delta\gamma+[\Delta G_{Al}f_{Al}+\Delta G_{Ti}f_{Ti}]\lambda \tag{1}\]  
where \(\Delta\gamma\) is the change in interfacial free energy, \(\Delta g\) figuratively denotes the free energy change of the constituent [PERSON] (1984). \(\lambda\) is bilayer thickness. As \(\lambda\) reduced from its maximum value, \(\Delta g\) should be 0 if both metals have their stable crystal structures as represented by the horizontal line shown in Figure 4. Driven by \(\Delta g<0\), the transformation of Ti from hcp to fcc structure is attributed to the slope of the line fcc/fcc is smaller than that of the line hcp/fcc when \(\lambda<\lambda^{*}_{fcc/fcc}\). As \(\lambda\) further reduced to or below \(\lambda^{*}_{hcp/hcp}\), the energy of the system can be reduced by transforming Al from fcc to hcp structure, resulting Al-hcp/Ti-hcp multilayers. Considering fcc and hcp are adapting the same closed packed structure, phase transformation appeared more easily. While this phenomenon can also been observed in bcc metal [21; 26]. For example, a metastable bcc Mg was reported [21] in Mg/Nb multilayers (Figure 5a); phase stability diagrams of Co/Cr, Zr/Nb and Ti/Nb multilayers are provided also [26]. When a transition occurs from fcc to bcc, the corresponding difference of the interfacial energies \(\Delta\gamma\) is as follows:  
\[\Delta\gamma=\gamma_{in}-\gamma_{c}=\frac{4\overline{\mu}\overline{S}_{vib} \overline{H}_{m}}{3\overline{V}_{m}R}-\frac{\mu_{A}\mu_{B}\overline{a}a_{B}}{2 \pi(\mu_{A}+\mu_{B})|a_{B}-a_{A}|(1+v)}\times(\ln(\frac{a_{B}}{2|a_{B}-a_{A}|} )+1) \tag{2}\]  
where \(\gamma_{in}\) and \(\gamma_{c}\) are the incoherent and coherent interface energy for fcc/bcc and fcc/fcc respectively; \(\mu\) and a are the shear modulus and atomic radiuses; \(R\) is the ideal gas constant, \(v\) is the Poisson ratio; \(\overline{a}\), \(\overline{H}_{m}\), \(\overline{S}_{vib}\), and \(\overline{V}_{m}\) are the mean values of the atomic diameter, the melting enthalpy, the vibration part of the overall melting entropy and the molar volumes of corresponding substances consisting of interfaces, respectively.