I am calculating the bulk modulus for a certain perovskite and I get different values of B at different pressures.... I presume my structure is porous.....Is there a relationship between porosity and B??
Dear James,
Indeed, you may find a relationship between the bulk modulus (often addressed as "K") and porosity. Note further that, in the rock physics community, we often make a difference between the different geometries of pore structures. Often, rocks are found to be constituted of equant pores and penny-shaped micro-cracks. The dependence of K to the confining pressure mainly originates from the closure of the second pore familly: the penny-shaped microcracks.
In order to better understand this relationship, and the different effects of pores geometries, I would advise to read "The rock physics handbook" (Mavko & Dvorkin) and "Introduction to the physics of rocks" (Guéguen & Palciauskas).
I am not sure I understood your question, but here are the links from googlescholar for the two books:
- Introduction to the physics of rocks (https://books.google.fr/books?hl=fr&lr=lang_en|lang_es|lang_fr&id=fCP5qyRyX-oC&oi=fnd&pg=PP7&dq=introduction+to+the+physics+of+rocks&ots=NZ5Cd9ZsK_&sig=L2HFv0QIW_r9qps-BE_rmm7aRWA#v=onepage&q=introduction%20to%20the%20physics%20of%20rocks&f=false)
-The rock Physics handbook (https://books.google.fr/books?hl=fr&lr=lang_en|lang_es|lang_fr&id=2yzcyUqEqskC&oi=fnd&pg=PR1&dq=the+rock+physics+handbook&ots=PDPJHLMLhD&sig=e6SfdWR9AWV8MEOA_duOxDEdMho#v=onepage&q=the%20rock%20physics%20handbook&f=false)
This would constitute a good starting point.
Hello James, I hope my answer is not too late. In general, bulk modulus B does not only depend on porosity, but also pore shape (as already said above) and topology (isolated pores or interconnected network). Therefore, the bulk modulus as a function of porosity may vary between bounds, so-called Hashin-Shtrikman bounds. The lower bound is zero (or very low in practise) for porous bodies. The upper bound is Bu=B(1-f)/(1+cf), where B is the bulk modulus of the pore-free matrix, f ist the volume fraction of pores (porosity) and
c=0.5(1+v)/(1-2v), where v is the Poisson ratio of the matrix. For small isolated pores, the actual bulk modulus is expected to be close to the upper bound, so that the equation might be useful for you. If you do not know the Poisson ratio of the matrix, you might try to reduce the above equation to Bu=B(1-2f) as a rough estimation. Frank
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