Correct Enumeration of Vibration Frequencies in the Brillouin Zone

1960 ◽  
Vol 76 (5) ◽  
pp. 777-779 ◽  
Author(s):  
B Dayal ◽  
S P Singh
2020 ◽  
Vol 22 (3) ◽  
pp. 1381-1391
Author(s):  
Jin-Wen Yang ◽  
Li An

No imaginary vibration frequencies can be observed along any high symmetry directions of the Brillouin zone (BZ), confirming that the UGe3 intermetallic compound is dynamically stable.


2015 ◽  
Vol 11 (3) ◽  
pp. 3224-3228
Author(s):  
Tarek El-Ashram

In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;𝑽𝑭𝑽𝑩= 𝒏𝑽𝑬𝑪𝟐for all crystalline systems (wheren is the number of atoms per lattice point).


2001 ◽  
Vol 711 ◽  
Author(s):  
Octavio Gomez-Martinez ◽  
Daniel H. Aguilar ◽  
Patricia Quintana ◽  
Juan J. Alvarado-Gil ◽  
Dalila Aldana ◽  
...  

ABSTRACTFourier Transform infrared spectroscopy has been employed to study the shells of two kind of mollusks, American oysters (Crassostrea virginica) and mussels (Ischadium recurvum). It is shown that it is possible to distinguish the different calcium carbonate lattice vibrations in each case, mussel shells present aragonite vibration frequencies, and the oyster shells present those corresponding to calcite. The superposition, shift and broadening of the infrared bands are discussed. Changes in the vibration modes due to successive thermal treatments are also reported.


ACS Nano ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 1833-1840
Author(s):  
Kuai Yu ◽  
Yang Yang ◽  
Junzhong Wang ◽  
Gregory V. Hartland ◽  
Guo Ping Wang

1983 ◽  
Vol 26 (5) ◽  
pp. 488-491
Author(s):  
M. L. Zolotarev ◽  
A. S. Poplavnoi

1994 ◽  
Vol 49 (6) ◽  
pp. 695-702 ◽  
Author(s):  
B. Thimme Gowda ◽  
Alarich Weiss

Abstract Chlorine bound to nitrogen is an interesting oxidizing agent in aqueous, partial aqueous and non-aqueous media. One can assume that the oxidizing action of the chlorine depends on the polarization of the Cl atom in the bond N -Cl which will depend on the electron distribution in the ligands R and R″ of the configuration R -NCl -CO -R″. 17 compounds were synthesized with R = substituted phenyl radical C6H5-y Xy, X = Cl, NO2, R″ = CH2Cl. The 35Cl NQR frequencies are observed in the range 52 to 54 MHz (T = 77 K) for the Cl(N) 34 to 37 MHz for the phenyl chlorines and the CH2Cl group. Their temperature dependence was followed up to 300 K. Therefrom the assignment of the resonance to certain Cl-atoms in the molecules is possible. Generally, the substitution of a negative substituent X (Cl, NO2) in the phenyl ring raises the resonance frequencies; the influence of the CH2Cl group on the N -Cl bond is weak. Strong is the influence of the carbonyl group on the N -C l bond. The IR group frequencies ν(C = O) are found in the range 1680 ≤ ν (C = O)/ cm−1≤ 1717, shifted up by ≤ 20 cm−1 compared to the corresponding acetamide R ⎯ NH ⎯CO ⎯ R″. Influence of the phenyl ring substitution on ν (C = O) does not follow a simple law of inductive effect. Also a correlation between the vibration frequencies of the N ⎯ Cl group and the phenyl group substitution is not found.


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