  In the present study, the calculations of two-body decays B^{0}_{s}
\rightarrow \ TT [ T denotes tensor mesons, a_{2}(1320), K^{*}_{2}(1430),
f_{2}(1270), f^{'}_{2}(1525)] in the perturbative QCD approach are presented.
The ensuing predictions encompass branching ratios, polarization fractions, and
direct CP violations, all elucidated in comprehensive detail. It is discerned
that (1) for pure annihilation decay, the longitudinal polarization is around
90.0\%, whereas the transverse polarizations manifest comparatively diminutive
magnitudes. (2) The direct CP asymmetry is directly proportional to the
interference between the tree and penguin contributions. For most of the decays
investigated within this discourse, the direct CP asymmetry remains modest in
magnitude. (3) There are precisely six distinct categories of Feynman diagrams
for B^{0}_{s} \rightarrow \ TT , because the tensor mesons cannot be produced
through the (V \pm A) currents or (S \pm P) density, thereby prohibiting
factorizable emission diagrams. The nonfactorizable and annihilation
contributions are ascertained to be pivotal in these decay modes. The
calculated branching ratios of our calculation for B^{0}_{s} \rightarrow \ TT
are at the order of 10^{-6} and 10^{-7}, which can be tested in the LHCb and
Belle II experiments. (4) Mixing exists for the f_{2}(1270) and
f^{'}_{2}(1525), just as the \eta and \eta^{'} mixing, the branching ratios
about the mixing angle \theta are given in this work. However, it is different
from f_{1}(1285)-f_{1}(1420), the mixing angle is notably small, thereby
resulting in only marginal alterations in the decay branching ratios.
