  An isobaric yield ratio difference (IBD) method is proposed to study the
ratio of the difference between the chemical potential of neutron and proton to
temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$
determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of
the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the
isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are
found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni +
$^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with
a plateau in the small mass fragments plus an increasing part in the fragments
of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show
dependence on the $n/p$ ratio of the projectile. It is suggested that the
height of the plateau is decided by the difference between the neutron density
($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles,
and the width shows the overlapping volume of the projectiles in which $\rho_n$
and $\rho_p$ change very little. The difference between the IB- and
IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by
the many isotopes and isotones, while the IBD method only uses the yields of
two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than
the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys
the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the
density or the temperature, the density dependence is preferred since the low
density can result in low temperature in the peripheral reactions.
