2. Consider the free energy functional of an inhomogeneous system that depends on a non-conserved order...
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2. Consider the free energy functional of an inhomogeneous system that depends on a non-conserved order parameter 7 and temperature T, written in one-dimension as: ∞ θη T [G₂- G = Go+ a(T-Tc)n² + Cn³ + Bn¹ + D ()] dx. əx Te is the critical temperature. (a) Write an expression for the equilibrium value of the order parameter, 7, as a function of temperature and the coefficients B, C, a, etc., for a homogeneous system. Is the nature of the transformation different for cases of constant C 0 and for vanishing Cas T passes through the critical temperature? (b) Explain how and why the diffraction patterns (intensity vs. angle) change as a material alloy in going from ordered to disordered state or vice versa. 2. Consider the free energy functional of an inhomogeneous system that depends on a non-conserved order parameter 7 and temperature T, written in one-dimension as: ∞ θη T [G₂- G = Go+ a(T-Tc)n² + Cn³ + Bn¹ + D ()] dx. əx Te is the critical temperature. (a) Write an expression for the equilibrium value of the order parameter, 7, as a function of temperature and the coefficients B, C, a, etc., for a homogeneous system. Is the nature of the transformation different for cases of constant C 0 and for vanishing Cas T passes through the critical temperature? (b) Explain how and why the diffraction patterns (intensity vs. angle) change as a material alloy in going from ordered to disordered state or vice versa.
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