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The First Law of Thermodynamics
Published in Kathleen E. Murphy, Thermodynamics Problem Solving in Physical Chemistry, 2020
Ionic compounds have an additional stability due to the lattice energy between the ions in the solid structure, which adds to the energy of bond formation. The lattice energy is defined as the energy required to separate an ionic solid into its component monatomic gaseous ions, which cannot be directly measured. But lattice energies can be estimated using cyclic diagrams (called Born–Haber cycles), which use bond energies and other known ∆H values to produce the chemical change needed from the formation equation for the compound. Construct a cycle, using only known ∆H values, that will let you determine the lattice energy of KF(s) from its heat of formation.Use the cycle to estimate the lattice energy for KF(s) and compare it to the tabled values that are between 801 and 822 kJ per mole.
Inorganic Chemistry
Published in Steven L. Hoenig, Basic Chemical Concepts and Tables, 2019
An important property of an ionic crystal is the energy required to break the crystal apart into individual ions, this is the crystal lattice energy. It can be measured by a thermodynamic cycle, called the Born-Habercycle.
Solid State Background
Published in P.J. Gellings, H.J.M. Bouwmeester, Electrochemistry, 2019
Isaac Abrahams, Peter G. Bruce
The lattice energy of an ionic crystal is derived from a balance of attractive and repulsive forces within the crystal. The strength of attraction and repulsion between ions are represented by potential functions. The simplest of these is based on Coulomb’s law which essentially states that like charges repel and unlike charges attract. So for two ions A and B at an internuclear separation r, the coulombic force of attraction for unlike ions and repulsion for like ions is given by: () F = ZAeZBer2
Dependence of local atomic structure on piezoelectric properties of PbZr1−xTixO3 materials
Published in Journal of Asian Ceramic Societies, 2022
Il-Gok Hong, Jong-Ho Kim, Ho-Yong Shin, Chan-Yeup Chung, Un-Gyu Paik, Jong-in Im
To explain this large discrepancy between the calculated and the experimental data, several reasons can be taken into account. First and foremost, experimentally, in the MPB region, the tetragonal and the rhombohedral phases coexist, while DFPT calculations were carried out using only in the rhombohedral structure for practical reasons. Second, the rhombohedral phase has a higher lattice energy barrier then tetragonal [26]. Therefore, the change induced on the lattice by Sr doping is smaller than in the tetragonal phase, and the spontaneous polarization is less pronounced, accordingly. In addition, in the actual experiment, the movement of atoms and the domain wall movement becomes easier because of the PbO loss in incomplete sintering and A-site voids due to Sr doping. As a result, Ec decreases and the piezoelectric constant increases. Therefore, we can assume that the calculated value of the piezoelectric constant is lower than the experimental value because of the discrepancies in the microstructural features that are necessarily oversimplified in the computational model with respect to the actual phenomenon. Despite these quantitative differences, the experimental and the computational results definitely follow the same qualitative trend and provide useful insights to the understanding of the microscopic piezoelectric properties of PZT.
Ultra-low temperature sintering and microwave dielectric properties of Mg-substituted SrCoV2O7 ceramics
Published in Journal of Asian Ceramic Societies, 2022
Yu-Ting Huang, Ching-Cheng Huang, Tsung-Hsien Hsu, Cheng-Liang Huang
where I is the ionic strength, ni represents the number of ions with integer charge Zi, the molecular volume and unit-cell volume is denoted as Vm and Vcell, respectively. Z is the number of formula units per unit cell. The results of lattice energy vs. sintering temperature of SCVO specimen are given in Figure 5. The lattice energy is inversely proportional to the unit cell volume and reveals a maximum of 44,350 kJ/mol at 660°C suggesting that the structural stability is predictable through the thermal process and the most stable structure of the specimen can be achieved at 660°C. In addition, the variation of Q × f is consistent with that of the lattice energy since a high lattice energy results in a high structural stability leading to a low dielectric loss in the oxides.
Predicting cation ordering in MgAl2O4 using genetic algorithms and density functional theory
Published in Materials and Manufacturing Processes, 2018
The total lattice energy is calculated using both classical potentials and DFT. In the former, the interatomic forces are based on a Born-model where long-range (Coulombic) interactions are calculated using an Ewald sum [1] and where the short-range forces are modeled using a Buckingham pair potential of the form: as implemented in GULP [1]. Here r is the interatomic distance, and the parameters A, ρ, and C are fixed for a given pair of species with values taken from the popular Bush et al. [27] or the Lewis and Catlow compilations [28] as a part of the GULP library.