  This research is a theoretical study that simulates the volume expansion of a
prelithiated silicon nanowire during lithium ion insertion and the application
of an electric current. Utilizing density functional theory (DFT) the ground
state energy E_g (x) of prelithiated silicon (Li_xSi) is define as a function
of the lithium ion (Li+) concentration (x). As the Li+ are increased, E_g (x)
becomes increasingly stable from x=1.00 through x=2.415 and decreases in
stability as the lithium ion concentration becomes x >2.415 until full
lithiation of the silicon nanowire is reached at x=3.75. After the
determination of the lithiated silicon ground state energies an electric
current is applied to the lithiated silicon nanowire at varies Li+
concentrations x. It was discovered that the volume expansion began at
approximately x=3.25 and increased to over 300% of the original volume of a
pristine silicon nanowire at x=3.75 which at this point was full lithiation.
This is in sharp contrast to prior research studies where the ground state
energy was not considered. In previous studies the computation of the volume
expansion starts approximately at x=0.75 and produces a continuous nonlinear
volume expansion until the process was terminated at full lithiation.
