Manganese oxide formation by heat treatment of MnCO 3 in air.

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Manganese oxide formation by heat treatment of MnCO 3 in air.

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Manganese oxide formation by heat treatment of MnCO 3 in air.

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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.

Neck

Pore

0.2 um

Neck

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.

ΔP

P

σ=Patm + 2γ/r

P=Patm

r

Flat surface

Curved surface

ΔP=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)

vapor

ΔP=-γ/r

Negative Curvature

Atoms move from

high free energy to low.

solid

ΔP=γ/r

Positive Curvature

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.