Manganese oxide formation by heat treatment of MnCO 3 in air. <500 C Reaction 1. MnCO 3 + ½ O 2 MnO 2 +CO 2. >500 C Reaction 2. 2 MnCO 3 + ½ O 2 Mn 2 O 3 + 2 CO 2. Note that in reaction 1, there is a net increase
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Manganese oxide formation by heat treatment of MnCO3 in air.
<500 C Reaction 1
MnCO3 + ½ O2MnO2+CO2
>500 C Reaction 2
2 MnCO3 + ½ O2Mn2O3 + 2 CO2
Note that in reaction 1, there is a net increase
Of ½ mole of gas for each mole of Mn, and for reaction 2 there is a net increase of ¾ of a mole of gas for each mole of Mn. What can you say about the entropy change in each reaction? How does this help explain the temperature dependence between the two reactions?
As the manganese oxide particles form from the carbonate salt, they begin to grow together, or ‘sinter’. The figure below is a TEM micrograph of neck formation during the sintering of Mn2O3 particles.
Why do the necks get larger and the pores get smaller as the heat treat time and or temperature increases?
Sintering of Nickel powder. The time lapse photography illustrates Neck formation and coarsening.
σ=Patm + 2γ/r
‘Master’ Equation of Thermodynamics
For an isothermal process with no change in composition
Divide both sides by the number of atoms in the system=N
ΔP=2γ/r for inside a spherical particle.
Positive and Negative Curvature
Corrugated Surface Example (2D)
Atoms move from
high free energy to low.
Two sphere model
The neck has a negative curvature component (-1/ρ), acting to reduce the pressure relative to the spherical surface.