We have measured the temperature dependence of the nuclear quadrupole
resonance (NQR) frequency, nu(Q), and the spin-lattice relaxation time
of Ba-135 and Ba-137 in the superconductor YBa2Cu4O8 (T-c = 81 K). Th
e temperature dependence of nu(Q)(T) is given by nu(Q)(T) = nu(Q)(0)(1
- AT(alpha)). The relaxation is of quadrupolar origin and can be desc
ribed perfectly by a two-phonon Raman process with a Debye temperature
of 185 K.