TMT4155 Heterogeneous equilibria and phase diagrams, fall 2010 ...
TMT4155 Heterogeneous equilibria and phase diagrams, fall 2010 ...
TMT4155 Heterogeneous equilibria and phase diagrams, fall 2010 ...
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Institutt for materialteknologi<br />
Norges teknisk-naturvitenskapelige universitet<br />
<strong>TMT4155</strong> <strong>Heterogeneous</strong> <strong>equilibria</strong> <strong>and</strong> <strong>phase</strong> <strong>diagrams</strong>, <strong>fall</strong> <strong>2010</strong><br />
Exercise 10 - solution<br />
i) (Note that the three binaries found from this ternary diagram are not in accordance with the<br />
latest version of the <strong>phase</strong> diagram of these three systems)
Institutt for materialteknologi<br />
Norges teknisk-naturvitenskapelige universitet<br />
ii) In the figure below 9 different Alkemade triangles are identified (they are labelled with a<br />
number from 1 to 9)<br />
The ternary system is divided into 9 Alkemade triangles, each of these is accompanied by one<br />
specific invariant reaction. Note that due to solid solution in three of the solid <strong>phase</strong>s quasibinary<br />
systems (green lines) are found in between some of the Alkemade triangles. The green<br />
lines illustrate vertical sections of the ternary system, which can be looked upon as a binary<br />
system with only two components.<br />
1. Corundum-Spinel-Mullite<br />
Invariant reaction <strong>and</strong> temperature: Corundum + liquid → Spinel + Mullite 1578°C<br />
2. Spinel-Mullite-Sapphirine<br />
Invariant reaction <strong>and</strong> temperature: Mullite + Spinel + liquid → Sapphirine 1482°C<br />
3. Spinel-Sapphirine-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: Sapphirine + liquid → Spinel + Cordierite 1453°C<br />
4. Spinel-Forsterite-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: liquid + spinel → Forsterite + Cordierite 1370°C
Institutt for materialteknologi<br />
Norges teknisk-naturvitenskapelige universitet<br />
5. Mullite-Sapphirine-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: Mullite + liquid → Sapphirine + Cordierite 1460°C<br />
6. Silica-Mullite-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: Mullite + liquid → Tridymite + Cordierite 1440°C<br />
7. SiO2-Protoenstatite-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: liquid → Tridymite + Protoen. + Cordierite 1355°C<br />
8. Protoenstatite-Forsterite-Cordierite<br />
Invariant reaction <strong>and</strong> temperature: liquid → Forsterite + Protoen. + Cordierite 1365°C<br />
9. Periclase-Spinel-Forsterite-<br />
Invariant reaction <strong>and</strong> temperature: liquid → Periclase + Spinel + Forsterite 1710°C<br />
iv)<br />
Composition Liquidus temperature Solidus temperature<br />
A ~1510ºC 1355ºC<br />
B ~1525ºC 1365ºC<br />
C (quasi-binary system) ~1440ºC ~1360ºC<br />
Composition C is in the quasi-binary system SiO2 - 2MgO·2Al2O3·5SiO2. Due to the solid<br />
solution of cordierite the solidus temperature in the quasi-binary system will depend on the<br />
composition of the quasi-binary (depend on the Mg:Al ratio). The possible upper <strong>and</strong> lower<br />
limits for the solidus temperature can be found by the solidis temperature of the two ternary<br />
systems enclosing the quasi-binary system: 1355ºC (SiO2-Protoenstatite-Cordierite) <strong>and</strong><br />
1440ºC (Silica-Mullite-Cordierite). In our case the composition is more close to the ternary<br />
system SiO2-Protoenstatite-Cordierite <strong>and</strong> the solidus temperature is estimated to be ~1360ºC.<br />
D (binary system) ~1850ºC 1557ºC<br />
E (binary system) ~1640ºC 1543ºC<br />
F (binary system) ~1800ºC 1590ºC
iii) Isothermal sections at 1600 <strong>and</strong> 1800°C:<br />
Institutt for materialteknologi<br />
Norges teknisk-naturvitenskapelige universitet
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