Quadrupole Ordering and Rattling Motion of Clathrate Compound Pr sub( 3)Pd sub( 20)Ge sub( 6)

We have investigated the quadrupole ordering of 4f-electrons and the rattling motion of guest rare-earth ions in the clathrate compound Pr ... Pd ... Ge ... using ultrasonic measurements. The elastic constants ( C ... - C ... )/2 and C ... exhibit considerable softening at low temperatures. A minimum of ( C ... - C ... )/2 at T ... = 0.25 K indicates antiferroquadrupole ordering associated with a Gamma ... doublet of a crystal-field ground state at the 8c site, while a minimum of C ... at T ... = 60 mK indicates the indicates the ferroquadrupole ordering of a Gamma ... triplet of a crystal-field ground state at the 4a site. The antiferroquadrupole phase depending on magnetic field direction shows a highly anisotropic behavior. The field-induced ordered phase due to the level crossing of the CEF ground state at the 8c site in magnetic fields along the [001] direction has been found. Furthermore, for the elastic constant C ... and the attenuation coefficient a ... we found a frequency dependence at two different temperatures of 15 and 25 K, which we describe in terms of the Debye-type dispersion with an Arrhenius-type relaxation time t= t ... exp ( E / k ... T ) for two different activation energies of E ... = 102 K and E ... = 198 K. These ultrasonic dispersions are caused by the thermally activated rattling motions of guest rare-earth Pr ... ions at the 4a site of Pr ... Pd ... Ge ... (ProQuest: ... denotes formulae/symbols omitted.)