1. Manganese oxide formation by heat treatment of MnCO3 in air.
<500 C Reaction 1
MnCO3 + ½ O2MnO2+CO2
>500 C Reaction 2
2 MnCO3 + ½ O2Mn2O3 + 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?

2. 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.
Neck
Pore
Neck
0.2 um
Why do the necks get larger and the pores get smaller as the heat treat time and or temperature increases?

3. Sintering of Nickel powder
Sintering of Nickel powder. The time lapse photography illustrates Neck formation and coarsening.

4. ΔP

5. P
σ=Patm + 2γ/r
P=Patm r
Flat surface
Curved surface
ΔP=2γ/r

6. ‘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.

7. Positive and Negative Curvature Corrugated Surface Example (2D)
vapor
ΔP=-γ/r
Negative Curvature
Atoms move from
high free energy to low.
solid
ΔP=γ/r
Positive Curvature

8. Two sphere model r2 r1 r
The neck has a negative curvature component (-1/ρ), acting to reduce the pressure relative to the spherical surface.