Lattice dynamical study of body-centred tetragonal indium

Ramamurthy, V.; Rajendraprasad, S.

doi:10.1007/bf02847377

Cited by 4 publications

(4 citation statements)

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“…indium are associated with four independent constants in the GTF model and the constant appearing in MD,, is in no way related to the other three. Consequently, the equivalence between the force constants of these models [33] imposes an arbitrary and unrealistic condition on the GTP constants. It should therefore be obvious from this discussion that the inconsistency among the matrix elements of the MAS model manifests itself as imaginary phonon frequencies along certain nonsymmetry directions and there are no means other than treating 01 appearing in (21) as an independent constant, t o eradicate this intrinsic deficiency.…”

Section: Resultsmentioning

confidence: 99%

“…As a consequence, the AS model becomes elastically inconsistent and the force constant expression for C,, obtained 18, 20 to 221 or by incorporating the electron-ion interactions [23 to 251. On the contrary, the unrealistic central force models which satisfy the Cauchy relations [32] as well as the Clark, Gazis, Wallis angular force (CGW) models which incorporate the three-body interactions and the mixed neighbour interactions [33] do not suffer from this deficiency. Besides, an internal inconsistency of the modified axially symmetric force (MAS) model which gives rise to imaginary phonon frequencies a t certain wave vectors [33] has not attracted any attention mainly because of the non-availability of experimental and theoretical dispersion curves along the nonsymmetry directions.…”

Section: Introductionmentioning

confidence: 99%

“…On the contrary, the unrealistic central force models which satisfy the Cauchy relations [32] as well as the Clark, Gazis, Wallis angular force (CGW) models which incorporate the three-body interactions and the mixed neighbour interactions [33] do not suffer from this deficiency. Besides, an internal inconsistency of the modified axially symmetric force (MAS) model which gives rise to imaginary phonon frequencies a t certain wave vectors [33] has not attracted any attention mainly because of the non-availability of experimental and theoretical dispersion curves along the nonsymmetry directions. These deficiencies invariably cast serious doubts on the validity of this model and its ability to reproduce the correct phonon frequencies of a tetragonal or hexagonal metal.…”

Section: Introductionmentioning

confidence: 99%

“…The former are expressed in terms of radial and tangential forces, while the latter are expressed in terms of an electron gas model based on the deformation potential approximation [37]. The equivalence between the force constants of different lattice dynamical models [33] as well as the available experimental data on the elastic constants [38] and phonon frequencies of indium [39] invariably prompted the present investigations. This paper describes the lattice dynamical study of f.c.t.…”

Section: Introductionmentioning

confidence: 99%

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On the Inconsistencies of Axially Symmetric Force Models for Noncubic Solids

Ramamurthy

1987

Physica Status Solidi (b)

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for noncubic solids and the circumstances under which its phonon frequencies become imaginary are analysed by making use of this model in the lattice dynamical study of face centred tetragonal indium. It is shown that the arbitrary differences in the tangential force constants along x and z directions destroy the compatibility between off-diagonal and diagonal matrix elements, relatively stronger off-diagonal elements give rise to imaginary frequencies at certain wave vectors along nonsymmetry directions while the failure of this model to comply with the rotational invariance conditions manifests itself as the elastic inconsistency. The distortions introduced by the deficiencies of this model into the phonon dispersion curves of f.c.t. indium, consequences of imposing additional invariance conditions on this model as well as its apparent equivalence with central and general tensor force models, are discussed.Der Ursprung der elastischen Inkonsistenz eines von Lehman, Wolfram und De Wames vorgeschlagenen, modifizierten axialsymmetrischen Kraftmodells fur nichtkubische Festkorper und die Umstiinde, unter denen die Phononenfrequenzen imaginar werden, werden analysiert, wobei das Model1 fur die Untersuchung der Gitterdynamik fur tetragonal fliichenzentriertes Indium benutzt wird. Es wird gezeigt, dal3 die statistischen Differenzen in den Konstanten der Tangentialkraft in x-und z-Richtung die Kompatibilitat zwischen nichtdiagonalen und diagonalen Matrixelementen zerstoren ; relativ stlirkere Nichtdiagonalelemente geben AnlaB zu imaginaren Frequenzen bei bestimmten Wellenvektoren in nichtsymmetrischen Richtungen, wahrend die Unfahigkeit dieses Modells, sich den Rotations-Invarianzbedingungen zu fugen, sich als elastische Inkonsistenz manifestiert. Die durch die Mangel dieses Modells eingefiihrten Verzerrungen der Phononendispersionskurven von t.f.z. Indium, die Folgen der auferlegten zusatzlichen Invarianzbedingungen fur dieses Modell und auch seine scheinbare Aquivalenz mit zentralen. und allgemeinen Tensorkraftmodellen werden diskutiert.

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Section: Resultsmentioning

confidence: 99%