I have used M-H curve, and calculated the magnetic moment in term of Bohr magneton per formula unit. Now i want to compare the experimental values with the theoretical calculated values.
Co2+ is having magnetization of 3.87 BM, Mn2+ is 5.92 BM, Mn3+ is 4.90. But how to calculate for the LaCoO3, La0.95Sr0.05CoO3 and La0.95Sr0.05Co0.95Mn0.05O3 compound.
First, you must convert your Ms(emu/g) to ms(mB/formula) as follows :
ms(mB/formula) =Mole x Ms(emu/g) /5.585 (1)
Mole =molar mass of the compound (in g)
Ms is the saturation magnteization measured at very low temperature (emu/g)
-for the LaCoO3 and La0.95Sr0.05CoO3 : ms(mB/formula) =3.87 mB (2)
- for La0.95Sr0.05Co0.95Mn0.05O3 :
ms(mB/formula) =3.87 *0.95 mB +5.92*0.05 mB (3)
where I assume that only Mn2+ contributes to ms!
-If you have a mixture of Mn2+ and Mn3+, the second term of (3) becomes :
3.87*0.95 mB + 0.05*(x*5.92+y*4.9)mB (4)
where x and y design respectively the fraction of Mn2+ and Mn3+ in your compound
Thank you for your answer.
As you said that for LaCoO3 and La0.95Sr0.05CoO3 the values of magnetization is same but experimentally the value is different then how one can justify this.
I think (Perhaps) that , due to substitution (La, Sr) in the second compound, there may be a fraction of Co3+ which has 4.9 BM while Co2+ is 3.87 BM only!!
For LaCoO3, Ms=0.56 emu/g, La0.95Sr0.05CoO3, Ms=8.06 emu/g and for La0.95Sr0.05Co0.95Mn0.05O3 , Ms=9.15 emu/g
Does it fit to theoretical values?
First, eq (1) must e rewritten : ms(mB/formula) =Mole(kg)x Ms(emu/g) /5.585 (1)'
if Mole in kg
or ms(mB/formula) =Mole(g)x Ms(emu/g) /5585 (1)''
(if Mole in g)
Numerical applications
- LaCoO3, Mole = 246.84g Ms=0.56 emu/g , I find ms(mB/formula) =246.84*0.56 /5585 =0.0247BM
- La0.95Sr0.05CoO3 Mole =244.276g ;Ms=8.06 emu/g , I find ms(mB/formula) =244.276*8.06 /5585 =0.352BM
- La0.95Sr0.05Co0.95Mn0.05O3 ; Mole = 196.025g; Ms=9.15emu/g , I find ms(mB/formula) =196.0245*9.15 /5585 =0.321BM
All these numerical results are very far from the theoretical and ideal prediction. This may due to :
-either the sample is not stoichiometric (nano particles)
-or the saturation is not reached (insufficient applied field)
For example, in the case of LaCoO3, one can estimate the fraction c of Co2+ as follows: 0.0247 = c*3.87 ; c= 6.4 10-3 Co2+
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