Phase field modelling, a robust computational approach for modelling, predicting microstructure evolution and to speculate mesoscale morphological in various materials. In this study, we have discretized the time variable using semi-implicit instead of explicit scheme, semi-implicit scheme is known to allow a larger time step size than explicit schemes. Meanwhile, the discretization of the space variable is carried out using a Fourier spectral method, having a convergence rate that is exponential when compared to the second order Finite-difference method. Meanwhile, numerical implementation of Cahn-Hilliard equation via semi-implicit Fourier spectral algorithm for conserved quantities was also demonstrated for binary alloy simulation. However, Isothermal conditions are considered and Non-dimmensionalisation is done. Lastly, we implemented a MATLAB code to solve the phase field equation and visualize our model.