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Phonons in Rare‐Earth Aluminum Garnets and Their Relation to Lattice Vibration of AlO 4
Author(s) -
Papagelis K.,
Kanellis G.,
Arvanitidis J.,
Kourouklis G. A.,
Ves S.
Publication year - 1999
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/(sici)1521-3951(199909)215:1<193::aid-pssb193>3.0.co;2-g
Subject(s) - phonon , tetrahedron , symmetry group , symmetry operation , lattice (music) , symmetry (geometry) , group (periodic table) , normal mode , rare earth , vibration , molecular vibration , group theory , one dimensional symmetry group , crystal structure , primitive cell , rotational symmetry , molecular symmetry , physics , molecule , condensed matter physics , mathematics , chemistry , geometry , quantum mechanics , crystallography , mineralogy , acoustics
In this paper we present a theoretical attempt, based on symmetry arguments, to study the crystal dynamics of the rare‐earth aluminum garnets. The large number of atoms (80) in the primitive cell makes a detailed lattice dynamical calculation extremely difficult. So we propose an alternative method by examining the normal modes in groups according to their symmetry characters and associate these groups to certain modes related to molecular subunits. For the group of the three vibrational modes of A 1g symmetry of the garnet system we have calculated a new set of symmetry coordinates, close to the normal modes of the tetrahedral molecular subunit AlO 4 , using standard group theoretical techniques. We have checked the validity of this approach by studying the 3 × 3 block representing the A 1g symmetry in the dynamical matrix.