Among the intermetallics and alloys, YCu is an unusual material because it displays negative thermal expansion without spin ordering. The mechanism behind this behavior that is caused by the structural phase transition of YCu has yet to be fully understood. To gain insight into this mechanism, we experimentally examined the crystal structure of the low-temperature phase of YCu and discuss the origin of the phase transition with the aid of thermodynamics calculations. The result shows that the high-temperature (cubic CsCl-type) to low-temperature (orthorhombic FeB-type) structural phase transition is driven by the rearrangement of three covalent bonds, namely, Y-Cu, Y-Y, and Cu-Cu, which compete for the bonding energy and phonon entropy. At low temperatures, the mixing of Y and Cu does not take place easily because of the weak attractive force between these atoms expected from the small negative mixing enthalpy. This causes all three interactions to take part in the bonding, and Y and Cu are segregated to form an FeB-type structure, which is stabilized by internal energy. At higher temperatures, Cu ions are bound loosely with Y ions due to the large Y-Cu distance (3.01 angstrom), which results in large vibration entropy and stabilizes a CsCl-type crystal structure. In addition, the CsCl-type structure is reinforced by the Y-Y interaction between next-nearest neighbors, resulting in a smaller unit cell volume. The crystal structure has the simple cubic framework of Y containing Cu ions bound loosely at the cavity sites. The calculated frequency of the Y-like phonon modes is much higher than that of the Cu-like modes, indicating the presence of Y-Y covalent interactions in the CsCl-type phase.