  A consistent and unified picture for critical phenomena of charged AdS black
holes in $f(R)$ gravity is drawn in this paper. Firstly, we investigate the
phase transition in canonical ensemble. We derive the explicit solutions
corresponding to the divergence of $C_Q$. The two solutions merge into one when
the condition $Q_c=\sqrt{\frac{-1}{3R_0}}$ is satisfied. The curve of specific
heat for $Q<Q_c$ has two divergent points and can be divided into three
regions. Both the large radius region and the small radius region are
thermodynamically stable with positive specific heat while the medium radius
region is unstable with negative specific heat. However, when $Q>Q_c$, the
specific heat is always positive, implying the black holes are locally stable
and no phase transition will take place. Secondly, both the $T-r_+$ curve and
$T-S$ curve $f(R)$ AdS black holes are investigated and they exhibit Van der
Vaals like behavior as the $P-v$ curve in the former research. Critical
physical quantities are obtained and they are consistent with those derived
from the specific heat analysis. We carry out numerical check of Maxwell equal
area law for the cases $Q=0.2Q_c, 0.4Q_c, 0.6Q_c, 0.8Q_c$. The relative errors
are amazingly small and can be negligible. So the Maxwell equal area law holds
for $T-S$ curve of $f(R)$ black holes. Thirdly, we establish
geometrothermodynamics for $f(R)$ AdS black hole to examine the phase
structure. It is shown that the Legendre invariant scalar curvature
$\mathfrak{R}$ would diverge exactly where the specific heat diverges. To
summarize, the above three perspectives are consistent with each other, thus
providing a unified picture which deepens the understanding of critical
phenomena of $f(R)$ AdS black holes.
