The discovery and synthesis of new polymorphs of solids is one of the most attractive tasks for chemists in the development of new materials. To transfer the current synthesis means from empirically random search to rational design based on theoretic prediction has become one of the most desired goals in material science. To achieve this requires a systematic study of the free energy of the interesting materials. The present work here will report a transmission electron microscopy study in structure evolution from amorphous to polycrystalline phases of alkaline earth fluorides, by which the energy landscape of the fluoride materials are experimentally explored. Structural disorder and distortion play a significant role in structure evolution, especially when amorphous phases are involved. An experimentally precise characterization of the disordered structure is crucial for a correct understanding of the phase transformation. An important quantity in such characterization is the so-called pair-distribution function (PDF), which represents the distribution of atomic pair distances in the investigated material and can therefore also provide insight into the structural distortions in crystalline materials. PDF measurements currently gains increasing application in various fields of material science, especially in neutron and X-ray diffraction. In comparison, electron diffraction can be performed in standard transmission electron microscopes and is thus easily accessible. It also offers the possibility of obtaining data from small material volumes which may be crucial in hetero-structured specimens. However, the PDF technique based on electron diffraction is still not a routine as in X-ray synchrotron and neutron radiation measurements due to the difficulties caused by strong dynamic scattering of electrons, inelastic scattering contribution, and difficult large-angle acquisition. This work carefully studied the electron diffraction based PDF technique. Modifications of the technique were focused on the large-angle data acquisition in energy-filtered diffraction experiments and data processing as well as multiple scattering correction, by which the reliability of the experimental PDF was remarkably improved. In this work, the modified PDF technique based on in-situ electron diffraction was used to investigate the structure evolution in the phase transformation processes of alkaline earth fluorides. By combination of molecular dynamic simulations the experimental PDFs were clearly interpreted. The structure evolution was further comprehended and finally interpreted within the energy landscape concept. High-resolution transmission electron microscopy, electron energy-loss spectroscopy, and energy-filtered transmission electron microscopy were also involved in the studies for investigation of crystalline structures. In addition to the experiments, structural modelling based on reversed Monte-Carlo method was studied. An approach based on a modified reverse Monte-Carlo method for overcoming the difficulty caused by the dynamic scattering was reported.