Problem Set #3

 

1. You may wish to consult the table of units provided.  Given the following experimental measurements at room conditions

                                                                                                                       

Phase               G (kJ mol-1)                 V (cm3 mol-1)               S (J mol-1 K-1)

                                                                                                                       

Andalusite       -1.376                          51.530                         93.22

Sillimanite       +0.935                        49.900                         96.11

Kyanite            -2.760                          44.090                         83.76

                                                                                                                       

 

where G is the Gibbs free energy of formation from the oxides, V is the molar volume, and S is the molar entropy [Source: Robie, Hemingway, and Fisher, USGS Bulletin 1452, USGS, 1979]:

 

a) Calculate the phase diagram for the aluminosilicate polymorphs.  Ignore the effects of pressure and temperature on the volume and entropy differences.

 

b) Confirm the Clapeyron equation by calculating the slope of the each phase transition from the volume and entropy of transition and comparing this to your graph.

 

c) Compare your phase diagram with that determined by:

 

Bohlen, S. R., A. Montana, and D. M. Kerrick, Precise determinations of the equilibria kyanite-reversible-sillimanite and kyanite-reversible-andalusite and a revised triple point for Al2SiO5 polymorphs, American Mineralogist, 76, 677-680, 1991.

 

Discuss similarities and differences and possible reasons for any disagreement.

 

d) If you find a rock that contains both kyanite and sillimanite, what is the least pressure from which it might originate?  To what depth does this correspond?  By what process(es) might such a rock be brought to the surface?  In what tectonic environment might you expect to find such a rock?

 

 2. The gray-scale image below is a two-dimensional projection onto the a-b plane of the structure of kaolinite.  The bases of the Si-tetrahedra are seen as white and light gray triangles; the Al-octahedra are seen beneath in darker gray.  Such projections, viewed as two-dimensional patterns, are useful for analyzing the symmetry of crystals.

a) Identify the lattice by drawing lattice points on the image.

 

b) Identify the unit cell by drawing on the image.  Hint: for this mineral, g is very close to 90û.

 

c) An analysis of the full three-dimensional symmetry shows that a­b­c.  To what crystal system does this structure belong?