  A new method for preparation of single crystals of the superconducting
intermetallic MgB2 compound from a Mg-Cu-B melt flux is presented. The high
vapour pressure of Mg at elevated temperature is a serious challenge of the
preparation process. The approximate thermodynamic calculations of the ternary
Mg-Cu-B phase diagram show a beneficial effect of Cu, which extends the range
of formation of MgB2 to lower temperatures. Within the as-solidified Mg-Cu-B
melt flux the MgB2 compound forms plate-like single crystals up to a size of
0.2 x 0.2 x 0.05 mm3 or alternatively rims peritectically grown around MgB4
particles. AC-susceptibility measurements were conducted with specimen selected
from different parts of the as-solidified flux containing MgB2 particles.
Peritectically formed MgB2-particles display the highest transition temperature
of Tc = 39.2 K and a relatively narrow transition width of DTc = 1.3 K. Other
sections of the sample exhibit various superconducting transitions from Tc = 39
K to 7.2 K. This variation of Tc is attributed to a finite homogeneity range of
the MgB2 compound whereas significant Cu solid solubility in MgB2 can be
excluded.
