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Published in David A. Cardwell, David C. Larbalestier, I. Braginski Aleksander, Handbook of Superconductivity, 2023
With increasing temperature, the amplitude of atomic vibration at the equilibrium position increases, leading to an increase in bond length and, thus, lattice expansion. The volume change with the lattice vibration will cause an increase in the total free energy of the lattice. Therefore, the temperature dependence of the thermal expansion coefficient is somewhat similar to that of the specific heat. At low temperatures, the thermal expansion coefficient increases rapidly with temperature and becomes almost constant above the Debye temperature ΘD on the assumption that the lattice simply expands. However, for most materials, it can increase even above ΘD through the formation of lattice defects such as vacancies and interstitials. Then the concentration of the defects is directly related to the thermal expansion.
Advanced Bonding Theories for Complexes
Published in Ashutosh Kumar Dubey, Amartya Mukhopadhyay, Bikramjit Basu, Interdisciplinary Engineering Sciences, 2020
Ashutosh Kumar Dubey, Amartya Mukhopadhyay, Bikramjit Basu
Numerically the “Bond Order” of a molecule is one half of the difference between the number of electrons present in the bonding molecular orbitals and the antibonding molecular orbitals in a given molecule (viz., BO = ½ [no. of electrons in BMO − no. of electrons in ABMO]). Here, a positive BO, meaning more number of electrons located in BMO, as compared to ABMO, signifies a stable molecule (w.r.t. the associated atoms) or the fact that the formation of the molecule is energetically favored. In contrast, both zero and negative values for the BO implies that the concerned molecule is not stable and is not likely to form from the concerned atoms. Additionally, a greater positive value of the bond order indicates greater bond dissociation energy and a shorter bond length.
Advanced Instruments: Characterization of Nanomaterials
Published in M. H. Fulekar, Bhawana Pathak, Environmental Nanotechnology, 2017
IR spectra look quite complex because the bond vibrations create absorption bands. The intensity of an absorption band depends on the change in the dipole moment of the bond and the number of the specific bonds present. The bond dipole results from two things: the bond length and the charge difference between the two atoms. When the molecule absorbs a photon, it stretches and the bond length changes. So, that only leaves the charge difference, which can be derived from the electronegativity values of the atoms involved. When there are two different atoms, there will be an electronegativity difference and a photon will be absorbed. In case there is no electronegativity difference, such as in an O2 or an N2 molecule, then a photon will not be absorbed, and the molecule will not be excited to a higher vibrational state. In principle, bigger the electronegativity difference, the more intense will be the absorption. Besides, the number of the specific bond also determines the intensity of a peak.
A comparative DFT study of structural, electronic, thermodynamic, optical, and magnetic properties of TM (Ir, Pt, and Au) doped in small Tin (Sn5 & Sn6) clusters
Published in Phase Transitions, 2022
Aoly Ur Rahman, Dewan Mohammad Saaduzzaman, Syed Mahedi Hasan, Md. Kabir Uddin Sikder
To study the various properties of transition metal-doped Sn, all the structures are optimized to reach the steady adsorption structure. In Figure 1(a), the optimized pristine structures of Sn5 and Sn6 are shown. The pristine clusters of Sn5 and Sn6 are doped with three transition metals: Gold (Au), Platinum (Pt), and Iridium (Ir) respectively in two different positions which are shown in Figure 1(b and c), where ‘M’ refers the middle position and ‘S’ refers the side position for doping with transition metals. The bond lengths of different atoms are directly related to the charge distribution and the stability of the system [47]. The bond length has an inverse relation with the stability of the clusters. The greater bond length indicates lower stability and vice versa [48]. The average bond length of both the Sn5 and Sn6 systems is dilapidated after doping Iridium (Ir), Platinum (Pt), and Gold (Au) which means that the stronger bonds are formed in the doped clusters which make those clusters more stable than the pristine clusters. The average bond length for all the structures in LanL2DZ basis set is demonstrated in Table 1 and the computed result of SDD basis set is provided in supplementary data ST 1. In Figure 1(d), the average bond length (Å) for the pristine and doped clusters in two different positions of doping are also illustrated.
Metal(II) chloride complexes containing a tridentate N-donor Schiff base ligand: syntheses, structures and antimicrobial activity
Published in Journal of Coordination Chemistry, 2021
Sadeka J. Munshi, Jaswinder Kaur Saini, Sanjay Ingle, Sujit Baran Kumar
The ORTEP diagram of 4 is shown in Figure 5. Complex 4 crystallizes in triclinic crystal system with space group P-1. The asymmetric unit of 4 (Figure 5a) consists of one cadmium(II) ion, two nitrogen atoms of the Schiff base ligand and four Cl atoms. This structure consists of polymeric chain of Cd atoms and two Cd centers are bonded by two bridging chloride ions as Cd-(Cl)2-Cd chain and produce a four-membered ring. Each Cd center has CdCl4N2 coordination environment with octahedral geometry and surrounded by two nitrogen atoms N2 and N3 of the Schiff base ligand L and four bridging Cl atoms. Two Cd-N bond distances of L are nearly equal (2.350 and 2.382 Å) but four Cd-Cl bonds (2.519, 2.566, 2.628 and 2.795 Å) are not equal, and they are much longer than Cd-N bond length of L. The distance between the two cadmium centers i.e. Cd-(Cl)2-Cd distance is 3.699 Å. Long and unequal bond lengths produce distortion in the molecule. The equatorial positions of the Cd atom occupied by Cl1, Cl2 of the bridging chloride, Cl2 of another bridged Cd atom and N2 of the ligand and the axial positions are occupied by N3 of L and Cl2 of the second bridged. L acts as a bidentate ligand in the molecule. The bridging nature of Cl atoms i.e. µ-Cl give a 1D polymeric zig-zag chain along the b-axis.
Highly efficient perovskite solar cells by tuning electronic structures of thienothiophene-based as hole transport materials
Published in Molecular Physics, 2020
Bingjie Han, Zhuo Li, Yuanzuo Li
The structures of original molecules (HTM1, HTM2) and four designed molecules were shown in Figure 1. HTM1 has the structure of 2,5-bis (5-(5-(5-hexylthiophen-2-yl) thiophen-2-yl)thiophen-2-yl)thiazolo [5,4-d]thiazole [20], in which the sulfur atoms locating at the position of X1 and X2 were substituted by nitrogen atoms, phosphorus atoms, silicon atoms and selenium atoms, corresponding to the four designed molecules respectively. Four designed molecules were obtained and designated as HTM3, HTM4, HTM5, HTM6 respectively. The parameters of bond lengths and dihedral angles were listed in Table 1, from optimising the original molecules and four designed molecules with DFT/B3LYP/6-31G (d) method. The bond length is related to the stability of the molecule, and shorter bond lengths are usually more conducive to structural stability. The data shows that the bond lengths of the six molecules have faintly changed in the same position, although the differences are not obvious. The differences in bond lengths of the six molecules at the same position are less than 0.01 Å. Atomic substitution has a certain impact on the dihedral angles, among which ∠C18-C19-C20-C21 has the largest variation. Table 1 also shows that substituting different atoms for sulfur atoms on both sides of the molecule will lead to the change of molecular structure, which indicates that atom substitution changes the molecular properties.