Dear Hussam,

For a cubic crystal, there are general relationships for the modulus E(hkl) in an arbitrary crystallographic direction [hkl]. And this relationship is not dependent on the particular Space Group.

You will need the values of the three elastic constants C11, C12 and C44. Or alternatively you should know the Young modulus E on two directions, E and E. Then:

1/E[hkl] =1/E - 3(1/E-1/E)x(a2b2+a2c2+b2c2)

Where a, b and c (sorry, they should be greek letters) are the direction cosines of the [hkl] direction respect the three directions [100], [010] and [001] respectively.

I recommend a couple of books:

Physical properties of Crystals, J.F. Nye, Oxford University Press, 1992.

Mechanical behavior of materials, T.H. Courtney, Mc Graw Hill, 1990.

I hope that this could be useful for you,

Best regards,

Prof. J. San Juan

Thank you very much Prof. J. San Juan for yours contribution

HI every one

Firstly , Thanks for Prof, Jose San Juan.

I have some steps to solve me issue

but i don't have the values of

The elastic stiffness constant C11, C12 C44 of cubic spinal Co3O4