In calculating the lithium diffusion coefficient using DLi=1/2 (RT/(n2ACσw F2))2
How do you calculate the C or bulk concentration of Li (mol cm-3)?
There are two ways that make sense to me, but with those i still cannot have any closer value to the published ones.
1. From tap density (g/cm3) -- then we know how many mole of electrode molecule per cm3 (mol/cm3) -- from here we can multiply it with the number of Li per mol --- to obtain C value. But this is not the way i prefer.
2. From the molecular volume (A3)-- we know the number of Li per formula and also number of formula (Z) per unit cell --- then we can have how many Li atom in 1 molecular volume -- by changing the Angstrom to cm and converting the number of Li atom to mol (dividing it by 6.023 x 1023) -- then we can have how many mol of Li per cm3 -- or C value. This is what i think is correct.
However, either one of them cannot give me a matched value to the reported C.
Have i made any mistake or had misunderstanding on the C?
Any suggestion please?
I assume that you are trying to calculate the diffusion coefficient from impedance data.
Method 2. is the right way to calculate C if you want to measure the solid-state diffusion coefficient, but then your electrode should be a single crystal af the electrode material and A the exposed area of the crystal.
If you are doing impedances an a real porous electrode, then the measured diffusion coefficient is a property of the composite - mainly governed by the electrolyte diffusion coefficient, the porosity and the tortuosity of the electrode. In that case, you may use method 1., but remember that the number you get is a characteristic property of the electrode in question and NOT of the electrode material itself. Only if you go to very low frequencies you may observe a transition to kinetics determined by the electrode material. In that case you are better off using the transition to finite diffusion and a characteristic dimension of your electrode particles.
I assume that you are trying to calculate the diffusion coefficient from impedance data.
Method 2. is the right way to calculate C if you want to measure the solid-state diffusion coefficient, but then your electrode should be a single crystal af the electrode material and A the exposed area of the crystal.
If you are doing impedances an a real porous electrode, then the measured diffusion coefficient is a property of the composite - mainly governed by the electrolyte diffusion coefficient, the porosity and the tortuosity of the electrode. In that case, you may use method 1., but remember that the number you get is a characteristic property of the electrode in question and NOT of the electrode material itself. Only if you go to very low frequencies you may observe a transition to kinetics determined by the electrode material. In that case you are better off using the transition to finite diffusion and a characteristic dimension of your electrode particles.
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