Specific Heat of Amorphous and Crystalline PbTiO₃ at Low Temperatures

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Specific heat data are reported, 1.7–30 K, on four samples of PbTiO₃: amorphous ribbon (∼20 vm thick); crystallized ribbon (∼1 μm grain size); crystalline powder (∼1 μm grain size); and ceramic pellet (∼2 μm grain size). Both the amorphous and crystallized ribbon samples display strong Schottky behavior below 4 K with nearly identical (two level) energy separations ≅78 mK. PbO loss from the thin ribbons is postulated to explain these effects. Below 3 K, the powder and pellet samples display a glasslike linear term in the specific heat, and the coefficients of these terms (1.4×10⁻⁵ J cm⁻³K⁻²) are the same magnitude as those found in glasses. All crystalline forms of PbTiO₃ display maxima in C⁄T³ at 15 K, and these maxima are accurately represented by single Einstein terms with frequencies 47–52 cm⁻¹. Amorphous PbTiO₃ displays a C⁄T³ maximum at 10 K, as does vitreous SiO₂. A Debye temperature for crystalline PbTiO₃ of 337 K is reported; the effective Debye temperature for amorphous PbTiO₃ is found to be 256 K.