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In my current work on Barium Fluoride calculations, I have endeavored to present additional information on this well known mineral. The aspects of mechanical properties of orthorhombic and hexagonal phases have been discussed to some extent. With my wealth of experience in teaching undergraduate and postgraduate students, I believe the work done in this book will prove valuable to computational research students of the two levels. I have added knowledge to understanding of properties of Barium Fluoride that I believe is helpful to both experimentalists and theorists. The knowledge in this book can be extended to other fluorides of any structure by any researcher. Some of the work we have done here can be done by the experimental work to verify the values for example of elastic constants of the orthorhombic and hexagonal phases of this material. The work done in generation of potentials for Barium Fluoride is at the initial stage and has been tested for the few properties of superionic properties of this material. The transition temperature can be verified to agree with other known works. I do believe the work done here will guide future research.