Temperature-dependent atomic <i>B</i> factor: an <i>ab initio</i> calculation

Malica, Cristiano; Corso, Andrea Dal

doi:10.1107/s205327331900514x

Cited by 26 publications

(15 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Investigations of elastic constants are vital for applications related to the mechanical properties of solids. They provide information on stability, bonding, ductility, brittleness, anisotropy, compressibility, Vicker's hardness, and stiffness of solids 44,45 . For hexagonal crystals structures, five independent elastic constants ( C 11 , C 12 , C 13 ,C 33 , C 44 ) are required.…”

Section: Resultsmentioning

confidence: 99%

Ab initio study of the structure, elastic, and electronic properties of Ti3(Al1−nSin)C2 layered ternary compounds

Ahams

Shaari

Ahmed

et al. 2021

Sci Rep

View full text Add to dashboard Cite

The MAX phase materials such as layered ternary carbides that simultaneously exhibit characteristics of metallic and ceramic materials have received substantial interest in recent years. Here, we present a systematic investigation of the electronic, structural stabilities, and elastic properties of Ti3(Al1−nSin)C2 (n = 0,1) MAX phase materials using the ab initio method via a plane-wave pseudopotential approach within generalized-gradient-approximations. The computed electronic band structures and projected density of states show that both Ti3SiC2 and Ti3AlC2 are metallic materials with a high density of states at the Fermi level emanating mainly from Ti-3d. Using the calculated elastic constants, the mechanical stability of the compounds was confirmed following the Born stability criteria for hexagonal structures. The Cauchy pressure and the Pugh’s ratio values establish the brittle nature of the Ti3SiC2 and Ti3AlC2 MAX phase materials. Due to their intriguing physical properties, these materials are expected to be suitable for applications such as thermal shock refractories and electrical contact coatings.

show abstract

Section: Resultsmentioning

confidence: 99%

Ab initio study of the structure, elastic, and electronic properties of Ti3(Al1−nSin)C2 layered ternary compounds

Ahams

Shaari

Ahmed

et al. 2021

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Several other methods to account for the deviations of the Debye theory from empirical data are reviewed by Gopal (1966). Anharmonic perturbations of the oscillator potential and nonlinear phonon dispersion curves have been used by Merisalo & Larsen (1977, 1979), Field (1983, Malica & Dal Corso (2019), Ulian & Valdrè (2019). A discrete spectral component (Einstein terms) can be added to the Debye heat capacity at optical frequencies (cf.…”

Section: Discussionmentioning

confidence: 99%

“…e.g. Killean & Lisher, 1975;Martin & O'Connor, 1978a,b;Shepard et al, 1998;Malica & Dal Corso, 2019).…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited

Tomaschitz¹

2021

Acta Cryst Sect A

View full text Add to dashboard Cite

A phenomenological model of anisotropic lattice vibrations is proposed, using a temperature-dependent spectral cutoff and varying Debye temperatures for the vibrational normal components. The internal lattice energy, entropy and Debye–Waller B factors of non-cubic elemental crystals are derived. The formalism developed is non-perturbative, based on temperature-dependent linear dispersion relations for the normal modes. The Debye temperatures of the vibrational normal components differ in anisotropic crystals; their temperature dependence and the varying spectral cutoff can be inferred from the experimental lattice heat capacity and B factors by least-squares regression. The zero-point internal energy of the phonons is related to the low-temperature limits of the mean-squared vibrational amplitudes of the lattice measured by X-ray and γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal zinc lattice, including the temperature evolution of the B factors of zinc. In this case, the lattice vibrations are partitioned into axial and basal normal components, which admit largely differing B factors and Debye temperatures. The second-order B factors defining the non-Gaussian contribution to the Debye–Waller damping factors of zinc are obtained as well. Anharmonicity of the oscillator potential and deviations from the uniform phonon frequency distribution of the Debye theory are modeled effectively by the temperature dependence of the spectral cutoff and Debye temperatures.

show abstract

“…The atom displacement parameter (ADP; also called the temperature factor or B-factor) usually reflects the flexibility of the protein structure [44], which is related to the atomic thermal Debye-Waller factor in the lattice dynamics theory [45]. This critical crystallographic parameter is deemed to represent the atomic motion and static displacive disorder in protein structures [44,46].…”

Section: Atom Displacement Parameter Analysis Reveals a Different Flementioning

confidence: 99%

In Situ Proteolysis Condition-Induced Crystallization of the XcpVWX Complex in Different Lattices

Zhang

Wang

Jia

2020

IJMS

View full text Add to dashboard Cite

Although prevalent in the determination of protein structures; crystallography always has the bottleneck of obtaining high-quality protein crystals for characterizing a wide range of proteins; especially large protein complexes. Stable fragments or domains of proteins are more readily to crystallize; which prompts the use of in situ proteolysis to remove flexible or unstable structures for improving crystallization and crystal quality. In this work; we investigated the effects of in situ proteolysis by chymotrypsin on the crystallization of the XcpVWX complex from the Type II secretion system of Pseudomonas aeruginosa. Different proteolysis conditions were found to result in two distinct lattices in the same crystallization solution. With a shorter chymotrypsin digestion at a lower concentration; the crystals exhibited a P3 hexagonal lattice that accommodates three complex molecules in one asymmetric unit. By contrast; a longer digestion with chymotrypsin of a 10-fold higher concentration facilitated the formation of a compact P212121 orthorhombic lattice with only one complex molecule in each asymmetric unit. The molecules in the hexagonal lattice have shown high atomic displacement parameter values compared with the ones in the orthorhombic lattice. Taken together; our results clearly demonstrate that different proteolysis conditions can result in the generation of distinct lattices in the same crystallization solution; which can be exploited in order to obtain different crystal forms of a better quality

show abstract

Temperature-dependent atomic B factor: an ab initio calculation

Cited by 26 publications

References 43 publications

Ab initio study of the structure, elastic, and electronic properties of Ti3(Al1−nSin)C2 layered ternary compounds

Ab initio study of the structure, elastic, and electronic properties of Ti3(Al1−nSin)C2 layered ternary compounds

Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited

In Situ Proteolysis Condition-Induced Crystallization of the XcpVWX Complex in Different Lattices

Contact Info

Product

Resources

About