00:01
Hello students, in this question we are given a copper and gold from a regular solution with excess energy equals to gxs energy is equal to x of cu times x of silver.
00:19
So this gold is immobile while copper diffuses in gold lattice.
00:24
So because of a vacancy mechanism, we need to derive a one -dimensional diffusion model pertaining to the thin film of the copper diffusing into gold lattice in terms of lattice parameter, vibrational frequency and the concentration of vacancies and entropies and enthalpies of diffusion.
00:46
So suppose the thin gold film is laid down in a line, right? so at one point the fraction of xcu of copper atoms were present in the film.
00:58
So this is the film.
00:59
So you just line them up right gold film you line them up and it has to be diffused.
01:07
Right? so at some fraction of au of gold so that the total fraction of the atoms is 1.
01:21
So the composition will be xcu plus xau will be is equal to 1 right? that the composition concentration will be equal to 1 diffusion.
01:37
So the free energy of the system is given by the equation gxs is equal to xcu times xau as here.
01:47
So xau and xcu are the concentration of copper and gold respectively.
01:52
So we can assume that the gold atoms are immobile while copper atoms can diffuse in the gold lattice according to the vacancy mechanism.
02:00
So to derive the diffusion model, we will begin with the basic thermodynamic principle.
02:04
The first principle of thermodynamics states that the difference between enthalpy and entropy of the system is equal to the free energy.
02:11
So enthalpy enthalpy and entropy.
02:16
So h so enthalpy and a enthalpy and of the system, right? the first principle thermodynamics principle states that difference between enthalpy and entropy is equal to the free energy.
02:35
So the enthalpy of the system is defined as the amount of energy required to transfer one mole of atom from lattice side to another or move one mole of atoms from one temperature to another.
02:49
So the vibrational frequency omega will determine this right? vibrational frequency of gold lattice will determine whether it can move one mole of atom from one temperature to another.
03:04
Okay...