Accordion-like graphites prepared by exfoliation of a low temperature graphite fluoride were fluorinated using F2 gas at various temperatures. The fluorinated exfoliated graphite exhibits unusual dual CF bonding, i.e. weakened covalent and covalent. This bonding allows the discharge potential at the beginning of the electrochemical processes to be increased. Moreover, the accordion-like texture avoids partial exfoliation and loss of the electrical contact for some parts of the electrode, and allows the growth of LiF particles in the opened macro-porosity.