Study on order-disorder transition of ZrO alloys (O/Zr = 0−0.31) by heat capacity measurement

Low-temperature structural phase transition in deuterated and protonated lithium acetate dihydrate

“…Then, we would have DS = 0.5R ln 2 = 2.88 J Á mol À1 Á K À1 , in reasonable agreement with the experimentally determined value. This is also in agreement with the measured deuterium distribution function with 3 and 6 maxima at T = 14 K and T = 40 K, respectively [6] and consistent with other studies [14,15], where similar phase transitions were explained by an order-disorder mechanism and similar excess entropies were measured.…”

Thermophysical Properties of Laser-Sintered Zr-ZrB2 Cermets

“…As shown in Fig. 2, there are two heat capacity anomalies for ZrO x , which have been previously reported 28,29,46 for Zr–O alloys. These authors suggested that a heat capacity anomaly at lower temperature (400–600 K in Fig.…”

“…c p values of ZrB 2 , 25 Zr, and ZrO x 28,29 from the literature are also shown in the same figure for comparison. There were probably several forms of ordered and partially ordered structures of ZrO x 28,46–49 that coexisted in the cermets. This means that the c p estimation for ZrO x should consider for their respective contribution.…”

“…By applying the empirical Neumann–Kopp rule 27 with these values, the predicted heat capacities of the cermets are 0.332, 0.358, and 0.383 J·(g·K) −1 for 30Zr–ZrB 2 , 50Zr–ZrB 2 , and 70Zr–ZrB 2 , respectively. Specific heat capacity of Zr–O solid solution (represented as ZrO x in this paper for simplicity) has been reported to be 0.186–0.236 J·(g·K) −1 for x =0.10–0.31 at 350 K, which is smaller than the heat capacity of Zr 28,29 . The mean phonon velocity (ν ph ) is constant and approximately independent of temperature 24 .…”

“…The phonon constant volume heat capacity ( c v _ph ) reaches a maximum value (3 R , where R is the gas constant) as described by the Dulong–Petit law 24 at high temperatures ( T > T D , where T D is the Debye temperature). Reported T D is 910–965, 20,30 250–290, 28,31 and 322–383 K 28 for ZrB 2 , Zr, and ZrO x ( x =0.1–0.24), respectively. Because the phonon mean free path decreases as temperature increases, the phonon contribution to thermal conductivity ( k ph ) decreases with increasing temperature for most crystals at sufficiently high temperatures 24 .…”