  Over 1500 DBZ or DZ white dwarfs (WDs) have been observed so far, and
polluted atmospheres with metal elements have been found among these WDs. The
surface heavy element abundances of known DBZ or DZ WDs show an evolutionary
sequence. By using Modules for Experiments in Stellar Evolution, we create DB
WDs, and simulate the element diffusion due to high gravitational fields and
the metal-rich material accretion coming from the planet disrupted by the WD.
In our models, the input parameters ($\alpha_{\rm MLT}$, $\alpha_{\rm th}$ and
$Z$) have very weak effect on DB WD structures including interior temperatures,
chemical profiles and convective zones.The mass-accretion rate and the
effective temperature of DB WDs determine the abundances of heavy elements. The
evolutionary sequence of Ca element for about 1500 observed DB or DBZ WDs
cannot be explained by the model with a constant mass-accretion rate, but is
consistent well with the model in which the mass-accretion rate decreases by
one power law when $T_{\rm eff}>10$ kK and slightly increases by another power
law when $T_{\rm eff}<10$ kK. The observed DB WD evolutionary sequence of heavy
element abundances originates from WD cooling and the change of mass-accretion
rate.

Solar and Stellar Astrophysics