Calcium aluminates are a range of minerals obtained by heating calcium oxide (CaO) and aluminium oxide (Al2O3) together at high temperatures. I want Elastic Constants Cij values for the following Calcium aluminates:
Monocalcium aluminate CaAl2O4 (CA) – Monoclinic (P21/n)
Monocalcium dialuminate CaAl4O7 (CA2) – Monoclinic (C2/c)
Monocalcium hexa-aluminate CaAl12O19 (CA6) – Hexagonal (P63/mmc)
If you have a look this Website (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.1292&rep=rep1&type=pdf) may help you
It strongly depends on tha shape of your minerals. However, I can suggest to measured them by Nanoindentation technique.
Emerson Coy Sir, I am doing Theoretical study, so It's not possible to measure values by Nanoindentation Technique. Do you have any book or related papers so that I can take values of Elastic constants for these Calcium Aluminates?
the elastic stiffness coefficientes are give by the derivative of the stress tensor vs strain ... If you obtain the stress-strain relation from ab-initio calculation, then Bijkl = sigma_ij/epsilon_kl
Aditi, The method I mentioned in my previous post where i suggest to use the deformation of the system to compute the elastic constant by means of the first derivative of the stress vs strain is considered a brute force method since you must apply 6 deformations (x,y,z,xy,xz,yz) to find all the elastic constants http://dft-blog.natanzon.eu/2008/03/how-to-calculate-elastic-constants-with.html . There are other methods that use the stress fluctuations to find it at a given temperature (google it)
Deformation of the preliminary relaxed crystal cell in the direction of interest (I would suggest deformations in both +/- directions and finding a mean value) is a pretty and simple, straightforward way of applying the Hooke's law.
Alternatively, you can use respond function calculation of second derivative of total energy within density-function perturbation theory http://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.035117.
This is more complicated approach, which enables you though to estimate other respond characteristics (piezoelectric tensor, Raman scattering efficiencies (non-resonant case), non-linear electronic susceptibility, electro-optic effect) as well.
Here is a tutorial of ABINIT package, which gives more insight on this technique: http://www.abinit.org/documentation/helpfiles/for-v7.10/tutorial/lesson_elastic.html
As my Colleague Andrij says that would it be the best option. However, for a quick reference this article might be useful.
Loof, J., Engqvist, H., Ahnfelt, N.-O., Lindqvist, K., Hermansson, L.
Mechanical properties of a permanent dental restorative material based on calcium aluminate
(2003) Journal of Materials Science: Materials in Medicine, 14 (12), pp. 1033-1037.
DOI: 10.1023/B:JMSM.0000003999.52349.0d
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