I am determining microstructural properties of aluminum. I need to know the elastic constants of aluminum in order to obtain the contrast factor of dislocations from the Ungár method, and then input this value in the modified Williamson-Hall method. Where do I obtain the elastic constants? Wich kind of aluminum crystal must be, single or polycrystal?
Hi, I am not the greatest expert of this specific method, but in general all this strain-stress methods in XRD need the knowledge of E_{hkl} that can only be defined for a mono-crystal.
Cheers
Probably you are using elastic theory of dislocation for isotropic solids. You need only the shear modulus for the screw dislocations and the shear modulus plus the Poisson's ration for the edge or mixed dislocations. mhu = 2.36 x1011dyne/cm2,, Poisson's = 0.347 for Aluminum.
See: Theory of Dislocations by John Hirth and Jens Lothe (App: 'Elastic Constant'. page: 774)
The most power mathematical technique to deal with the dislocations and point defects including their mutual strain field interactions is to employ the elastic Green's function and their discrete Fourier transform in anisotropic elastic crystals such as bbc Nb, alpha iron etc., where one has to consider the whole lattice structure including the symmetry, plus the complete set of elastic constant which are few in cubic systems. I have done this when I was dealing with the internal friction spectrum associated with the kinked dislocation/ heavy and light interstitial interactions that resulted what was called dislocation enhanced Snoek peak of Hydrogen (light) in Niobium. Normally isotropic defect such as Hydrogen, which occupies the tetrahedral sites in bcc shouldn't give any Snoek peak. But it was observed in cold-worked specimen!!! The Computer simulation using our analytic theory showed that there exist.
Internal Friction and Viscosity associated with mobile interstitial in the presence of a kink harmonically or uniformly moving in anisotropic bcc metals, J. Appl. Phys. 55 (8), (1984) pp. 2857-2866, and For the light interstitials such as Hydrogen in tetrahedral sites in bbc metals; See: J. Appl.Phys. 57(12) (1985).pp. 5127-5138.
Dear Henry,
I suppose that you need the elastic constans of Al single crystals at room temperature, so here they are from the clasical book T.H. Courtney, Mechanical Behaviour of Materials:
C11=108 GPa , C12=61 GPa , C44=29GPa , with this values the elastic Modulus are:
E=76 GPa , E=64 GPa
To silmulate the contrast of dislocations you need always use the elastic constants of single creystals, beacose basically your dislocation is always in a crystalline lattice, this means in a single crystal.
In case that you are doing your simulations at 0K you may go to the publication:
P.M. Sutton, Phys Rev B 112 (1958) 2139. where these elastic constantas are measured between 63 K and 773 K and extrapolated to 0K. Probably in more recent publications the elastic constants have been measured directly close to 0K.
I hope that this could help you.
- Badges
- Science method
- Similar topics
- Methodology
- Crystallography
- X-ray Diffraction