  A singularly perturbed phase field model used to model lithium-ion batteries
including chemical and elastic effects is considered. The underlying energy is
given by $$I_\epsilon [u,c ] := \int_\Omega \left( \frac{1}{\epsilon} f(c) +
\epsilon\|\nabla c\|^2 + \frac{1}{\epsilon}\mathbb{C} (e(u)-ce_0) :
(e(u)-ce_0)\right) dx, $$ where $f$ is a double well potential, $\mathbb{C}$ is
a symmetric positive definite fourth order tensor, $c$ is the normalized
lithium-ion density, and $u$ is the material displacement. The integrand
contains elements close to those in energy functionals arising in both the
theory of fluid-fluid and solid-solid phase transitions. For a strictly
star-shaped, Lipschitz domain $\Omega \subset \mathbb{R}^2,$ it is proven that
$\Gamma - \lim_{\epsilon\to 0} I_\epsilon = I_0,$ where $I_0$ is finite only
for pairs $(u,c)$ such that $f(c) = 0$ and the symmetrized gradient $e(u) =
ce_0$ almost everywhere. Furthermore, $I_0$ is characterized as the integral of
an anisotropic interfacial energy density over sharp interfaces given by the
jumpset of $c.$
