**4.2 Comparison of experimental and evaluated microstructures by phase field modeling**

In this section we have compared the experimental microstructure with numerical simulation microstructure based on the Cahn-Hilliard equation of phase separation and conjecture the experimental environments or synthesis parameter (**Figure 8**). **Figure 8(a)** shows the numerical simulated microstructure with the following parameters:

a.Initial composition b = 0.43 and c = 0.57

b.Cooling rate Δtmax = 300

#### **Figure 7.**

*Evolution of microstructure based on phase field modeling with different amounts of phase-separating domains from the homogenous matrix phase.*

**57**

*Phase Separation in Ce-Based Metallic Glasses DOI: http://dx.doi.org/10.5772/intechopen.88028*

agreement with the experimental findings.

**5. Conclusions**

**Figure 8.**

conclusions can be drawn:

*microstructure of Ce75Al21Ga4 alloy.*

Ga (0.01 at.%).

amorphous phases.

to Ce-4*f* 0

**Figure 8(b)** shows the phase-separated Ce75Al21Ga4 metallic glass. There are so many parameters which have also been calibrated like thermal mobility, gradient of energy coefficient, and noise string, which play an important role in numerical simulation. It can be seen that both microstructures are about the same features like spinodal decomposition phases. **Figure 8(b)** shows the experimental bright-field TEM microstructure of Ce75Al21Ga4 metallic glass. After comparing both images, one can notice that the evaluated microstructures are in good agreements with experimental results. It has been found that the numerical simulations are in good

*Comparison of experimental and theoretical phase field model of phase separation in spinodal decomposition* 

*(a) numerical simulated microstructure with 43% and 57% phase fraction and (b) experimental* 

Based on the results described and discussed in this chapter, the following

a.The substitution of Ga results in the formation of additional strong diffuse peak in XRD at the higher diffraction angle indicating the formation of two types of amorphous phases in Ce75Al25 − xGax alloys. The present investigation clearly demonstrates the formation of nanoamorphous domains in melt-spun ribbons of Ce75Al25 − xGax alloys even at very low concentration of

b.After Ga substitution, the phase separation in this case is related to change in the electronic state of Ce-4f electron. The study of Ce L3 edge XAS spectra of as-synthesized ribbons suggest that the Ga substitution partially given rise

of investigation, delineating issues related to the formation of two types of

c.The microstructure evaluated after solving the Cahn-Hilliard equation of phase separation using phase field modeling. It has been found that both droplet-like structure and interconnected structure appear in phase field modeling, when the phase fraction of the dispersed phase is increased from 30 to 45% and the size of each amorphous domain has increased with increasing cooling rate.

delocalized state. This study therefore opens up a new direction

**Figure 8.**

*Metallic Glasses*

**modeling**

following parameters:

b.Cooling rate Δtmax = 300

a.Initial composition b = 0.43 and c = 0.57

**4.1 Effect of initial composition**

**Figure 7** shows the phase separation patterns with different initial average concentrations during time steps 200, without considering the fluid flow. It has been suggested that there are two phases, namely, B and C, in the evaluated microstructures. In **Figure 7** the red region and blue region show the B-rich and C-rich phase, respectively. The volume fraction of the C phase has been shown in **Figure 7**. As we can see, when the volume fraction of the B and C phases is around 0.7 and 0.3, respectively, droplet-like structure has been formed (**Figure 7(a)**). When the volume fraction of the C phase increases from 0.3 to 0.4, an interconnected structure will form at the initial stage (**Figure 7(c)**). **Figure 7(e)** shows the equal volume fraction of both initial average concentrations with 0.5. It has been shown that at equal initial average concentration, spinodal- or interconnected-type microstructure has grown completely. **Figure 7(f–i)** shows the spinodal or interconnected to droplet-like microstructures, when it is subjected to increasing the initial average concentration of phase C from 0.5 to 0.7.

**4.2 Comparison of experimental and evaluated microstructures by phase field** 

cal simulation microstructure based on the Cahn-Hilliard equation of phase separation and conjecture the experimental environments or synthesis parameter (**Figure 8**). **Figure 8(a)** shows the numerical simulated microstructure with the

In this section we have compared the experimental microstructure with numeri-

*Evolution of microstructure based on phase field modeling with different amounts of phase-separating domains* 

**56**

**Figure 7.**

*from the homogenous matrix phase.*

*Comparison of experimental and theoretical phase field model of phase separation in spinodal decomposition (a) numerical simulated microstructure with 43% and 57% phase fraction and (b) experimental microstructure of Ce75Al21Ga4 alloy.*

**Figure 8(b)** shows the phase-separated Ce75Al21Ga4 metallic glass. There are so many parameters which have also been calibrated like thermal mobility, gradient of energy coefficient, and noise string, which play an important role in numerical simulation. It can be seen that both microstructures are about the same features like spinodal decomposition phases. **Figure 8(b)** shows the experimental bright-field TEM microstructure of Ce75Al21Ga4 metallic glass. After comparing both images, one can notice that the evaluated microstructures are in good agreements with experimental results. It has been found that the numerical simulations are in good agreement with the experimental findings.
