Specific Heat and Debye-Waller (Lamb-Mössbauer) Factor for a Finite One-Dimensional Lattice

Khatri, D.S.; Kothari, L. S.

doi:10.1119/1.1986129

American Journal of Physics

1971

DOI: 10.1119/1.1986129

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Specific Heat and Debye-Waller (Lamb-Mössbauer) Factor for a Finite One-Dimensional Lattice

D.S. Khatri

L. S. Kothari

Abstract: It is shown that the Debye-Waller factor (or Lamb-Mössbauer factor) for a finite one-dimensional lattice is nonzero (it is zero for an infinite one-dimensional lattice) and experimental situations can exist when elastic neutron scattering or recoilless emission or absorption of γ rays may be observed in polymers. Specific heat of finite linear lattices is also worked out. It is found that the conditions under which one may replace the sum over lattice modes by an integration without introducing much error in t… Show more

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1976

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Anharmonic Vibrations of a Small Linear Chain

Mazumdar

Kothari

1976

Physica Status Solidi (b)

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The anharmonic vibrations are investigated of a small linear chain under fixed end points and periodic boundary conditions. Numerical results as well as perturbat,ive solution of the problem are given. It is observed that even in cases where one should expect a large effect of anharmonic terms, the numerical results are very close to the harmonic motion. The perturbative solution developed here gives a change in frequency in second order without having to take recourse to the "tucking-in-technique".Die anharmonischen Schwingungen einer kleinen Kette mit festen Endpunkten und periodischen Randbedingungen werden untersucht. Sowohl numerische Ergebnisse als auch eine Storungsbehandlung des Problems werden angegeben. Es zeigt sich, daB auch in Fallen, bei denen man einen groBen EinfluB von anharmonischen Gliedern erwartet, die numerischen Ergebnisse ganz in der NIhe der harmonischen Bewegung liegen. Die hier entwickelte Storungsbehandlung gibt eine Schwingungszahlanderung zweiter Ordnung ohne Ruckgriff auf die ,,Technik der Einbettung".

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Anharmonic Vibrations of a Small Linear Chain

Mazumdar

Kothari

1976

Physica Status Solidi (b)

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Surface and Size Effects in the Specific Heat of Linear Chains

S.¹,

Alldredge²,

Wette³

1976

Physica Status Solidi (b)

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The size and surface effects in the specific heat of the monatomic linear chain are investigated for a small to intermediate number of atoms and for temperatures from OK u p t o B0, the zero-Debye temperature. It is shown that the surface-excess heat capacity, 6C, can reliably be extracted for chains of as few as ten atoms, although size effects are still quite appreciable for 50 to 100 atoms. The low-temperature limiting value of + k~ for 6C is reached for T & 0.076,. The freezing out of the lowest non-zero frequency in 6C becomes appreciable only for T & 0.058,, in the ten-atom chain and, more generally, for T & 9 , / N in the N-atom chain.GroBen-und Oberflacheneffekte der spezifischen Wbrme der monoatomaren. linearen Kette werden fur kleine his mittlere Atomnummern und fur Temperaturen von 0 K bis Oo (Null-Debye-Temperatur) untersucht. E s wird gezeigt, daJ3 die zusatzliche Oberflachenwarmekapazitlt 6C selbst fur Ketten mit nur etwa 10 Atomen zuverlassig bestimmt werden kann, obwohl der GroBeneffekt fur 50 his 100 Atome noch betrachtlich ist. Der Tieftemperatur-Grenzwert von a k B fur SC wird fur T 5 0.076, erreicht. Das Einfrieren der niedrigsten von null verschiedenen Frequenz von 6C ist in der

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Specific Heat and Debye-Waller (Lamb-Mössbauer) Factor for a Finite One-Dimensional Lattice

Cited by 2 publications

References 0 publications

Anharmonic Vibrations of a Small Linear Chain

Anharmonic Vibrations of a Small Linear Chain

Surface and Size Effects in the Specific Heat of Linear Chains

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