Lattice vacancies responsible for the linear dependence of the low-temperature heat capacity of insulating materials

Abstract

The linear dependence on temperature (γT) of the heat capacity at low temperatures (T < 15 K) is traditionally attributed to conduction electrons in metals; however, many insulators also exhibit a linear dependence that has been attributed to a variety of other physical properties. The property most commonly used to justify the presence of this linear dependence is lattice vacancies, but a correlation between these two properties has never been shown. We have devised a theory that justifies a linear heat capacity as a result of lattice vacancies, and we provide measured values and data from the literature to support our arguments. We postulate that many small Schottky anomalies are produced by a puckering of the lattice around these vacancies, and variations in the lattice caused by position or proximity to some form of structure result in a distribution of Schottky anomalies with different energies. We present a mathematical model to describe these anomalies and their distribution based on literature data that ultimately results in a linear heat capacity. From these calculations, a quantitative relationship between the linear term and the concentration of lattice vacancies is identified, and we verify these calculations using values of γ and vacancy concentrations for several materials. We have compiled many values of γ and vacancy concentrations from the literature which show several significant trends that provide further evidence for our theory.

A thermodynamic investigation of the cellulose allomorphs: Cellulose(am), cellulose Iβ(cr), cellulose II(cr), and cellulose III(cr)

“…In the above equation the T term represents lattice or oxygen vacancies, the T 3 and T 5 terms represent lattice vibrations, and the T 3=2 e Àd=T term possibly represents low frequency modes associated with amorphous materials [51][52][53]. The fitting parameters are given in T < 10 K and 0.01ÁC p;w for 10 K < T< 302 K).…”

Heat capacities, standard entropies and Gibbs energies of Sr-, Rb- and Cs-substituted barium aluminotitanate hollandites

“…vacancies) in insulating materials [26], and the B 3 , B 5 , B 7 , and B 9 terms represent the harmonic-lattice expression [27]. We note that these samples also exhibit a slight contribution from low-energy modes with a gap in the density of states, but these fits and their interpretation have been published elsewhere [28].…”

Origin of the Spin-Orbital Liquid State in a NearlyJ=0IridateBa3ZnIr2O9

“…4(b), which shows only a broad peak around ∼15 K followed by a decay around 30 K. A fit of the magnetic heat capacity (C m ¼ γT þ βT 2 ) at a comparatively higher temperature range (3-9 K) roughly gives a strong T-linear contribution of γ ¼ 25.9 mJ=mol K 2 , unusual for insulating systems. Also, the finite γ value does not change with application of external magnetic field as high as 90 kOe, suggesting its origin to be gapless excitations from spinon density of the QSOL state or minor lattice oxygen vacancies, but not any paramagnetic impurity [27][28][29][30][31], as seen in other spin liquid systems too [32][33][34][35]. The magnetic entropy obtained by integrating C m =T with T is shown in Fig.…”