  We present a computational study of the compound
Y(Co$_{1-x-y}$Fe$_x$Cu$_y$)$_5$ for 0 $\leq x,y \leq 0.2$. This compound was
chosen as a prototype for investigating the cell boundary phase believed to
play a key role in establishing the high coercivity of commercial Sm-Co 2:17
magnets. Using density-functional theory, we have calculated the magnetization
and magnetocrystalline anisotropy at zero temperature for a range of
compositions, modeling the doped compounds within the coherent potential
approximation. We have also performed finite temperature calculations for
YCo$_5$, Y(Co$_{0.838}$Cu$_{0.162}$)$_5$ and
Y(Co$_{0.838}$Fe$_{0.081}$Cu$_{0.081}$)$_5$ within the disordered local moment
picture. Our calculations find that substituting Co with small amounts of
either Fe or Cu boosts the magnetocrystalline anisotropy $K$, but the change in
$K$ depends strongly on the location of the dopants. Furthermore, the
calculations do not show a particularly large difference between the magnetic
properties of Cu-rich Y(Co$_{0.838}$Cu$_{0.162}$)$_5$ and equal Fe-Cu
Y(Co$_{0.838}$Fe$_{0.081}$Cu$_{0.081}$)$_5$, despite these two compositions
showing different coercivity behavior when found in the cell boundary phase of
2:17 magnets. Our study lays the groundwork for studying the rare earth
contribution to the anisotropy of Sm(Co$_{1-x-y}$Fe$_x$Cu$_y$)$_5$, and also
shows how a small amount of transition metal substitution can boost the
anisotropy field of YCo$_5$.
