A two dimensional (2D) electron backscatter diffraction (EBSD) analysis  reveals three of the necessary parameters, which describe the  lattice misorientation across the boundary. A three dimensional (3D) EBSD analysis is required to obtain the other two parameters that are used to describe the orientation of the grain boundary plane normal.Mg-calciumcarbonate or hydroxyapatite with different crystal habits and crystal orientations. The egg shell is a composite. Complete dissolution of the mineral phases leaves an organic ghost structure in which all architectural features can preserve. The orchestration of the release of these organic materials is controlled by the lining epithelia of the egg producing organ. EBSD is used to study cytomicrostructures  and orientations in egg shells in developing eggs of aves. However, to survey architectural variability and to determine the key materials involved using electron microscopy and mass spectrometry egg shells are selected from relevant species of many orders of birds (palaeo- and neognates) in orders. The organization of an egg shell is studied in rough and ion polished sections in 2D using scanning electron microscopy (SEM) and crystal orientation with electron back scatter diffraction (EBSD) mapping. In order to overcome the limitations of the 2D study of distribution of microscopic architectural features, samples of eggshells can be investigated in 3D with tomographic microscopy at the TOMCAT Xray tomographic microscopy facility at the Swiss light source.. In this way the microarchitecture is imaged first in three dimensions and the buildup can be studied in 2D using virtual sectioning before the sample is cut open using ion beams. Imaging SIMS in combination with proteases and suitable matrix crystals. It may display distribution of proteins and their post-translational modifications such as phosphate and sulphate groups over the various building block layers. These have  role in nucleation, propagation and termination of crystal growth. 

Two recent papers on application of EBSD to eggshell, with description of methods, are:

Moreno-Azanza M, Mariani E, Bauluz B, Canudo JI (2013) Growth mechanisms in dinosaur eggshells: an insight from electron backscatter diffraction. Journal of Vertebrate Paleontology 33: 121–130.

Trimby P, Grellet-Tinner G (2011) The hidden secrets of dinosaur eggs. Infocus Magazine 24: 4–21.  [This one includes EBSD on extant avian eggshell].

Thanks Daniel.