Critical behavior of debye waller factor and thermal expansion coefficient at ferroelectric phase transition of first and second order

The thermal expansion of a ceramic material in general leads to a positive thermal expansion coefficient (α). In the last decennium, several families of materials which exhibit negative thermal expansion, arising from a specific geometrical effect in their so-called open framework structures, have been discovered. Usually, this negative thermal expansion coefficient is small, anisotropic and the phenomena occur in a very small temperature interval. ZrW2O8 is an exception because of its large and isotropic negative thermal expansion coefficient (NTE) in a temperature range from 0.5K to 1050K. A cubic symmetry is found over the entire stability range with a phase transition from α-ZrW2O8 to β-ZrW2O8 near 430K. This phase transition is noticed by a change in α. The aqueous citrate-gel method is a suitable synthesis route for negative thermal expansion ceramics and will give a fine, pure and homogenous oxide mixture, well suitable for the preparation of ZrW2O8. The expansion coefficient of α–ZrW2O8 is -11 μm/m K whereas for the β- ZrW2O8 a value of -3 is obtained.

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Coupling between acoustic and soft transverse optical phonons leads to negative thermal expansion of GeTe near the ferroelectric phase transition

Physical Review B ◽

10.1103/physrevb.97.224106 ◽

2018 ◽

Vol 97 (22) ◽

Cited By ~ 8

Author(s):

Đorđe Dangić ◽

Aoife R. Murphy ◽

Éamonn D. Murray ◽

Stephen Fahy ◽

Ivana Savić

Keyword(s):

Phase Transition ◽

Thermal Expansion ◽

Ferroelectric Phase Transition ◽

Ferroelectric Phase ◽

Negative Thermal Expansion ◽

Transverse Optical ◽

Optical Phonons

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Modeling of High-Signal Electrostriction. II

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-9-1007 ◽

1990 ◽

Vol 45 (9-10) ◽

pp. 1095-1101

Author(s):

J von Cieminski

Keyword(s):

Phase Transition ◽

Temperature Dependence ◽

Strain Field ◽

Ferroelectric Phase Transition ◽

Ferroelectric Phase ◽

Second Order ◽

Experimental Results ◽

High Signal ◽

Qualitative And Quantitative

Abstract The predictions obtained with a thermodynamical method are compared with experimental results. Several materials which pass a ferroelectric phase transition of first or second order are investigated. The predictions correspond well with the experimentaly determined qualitative and quantitative features as to the field and temperature dependence. Finally, extraordinary strain-field curves are predicted and proved.

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Influence of phase transition from order to disorder and Philip's ionicity on the thermal expansion coefficient of pyrochlore type compositions with a multivalent environment

New Journal of Chemistry ◽

10.1039/c6nj02482c ◽

2017 ◽

Vol 41 (1) ◽

pp. 245-255 ◽

Cited By ~ 3

Author(s):

Ushakumari A. Renju ◽

Padala Prabhakar Rao ◽

Divakaran S. Vaisakhan Thampi

Keyword(s):

Phase Transition ◽

Thermal Expansion ◽

Ionic Conductivity ◽

Thermal Expansion Coefficient ◽

Expansion Coefficient ◽

Pyrochlore Type

The pyrochlore to fluorite transition in the RE2Y2/3Zr2/3Nb2/3O7 system allows us to understand the interrelationships among ionicity, thermal expansion and ionic conductivity.

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Defect induced forbidden X-ray reflections in RbH2PO4.

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314084708 ◽

2014 ◽

Vol 70 (a1) ◽

pp. C1529-C1529

Author(s):

Carsten Richter ◽

Dmitri Novikov ◽

Enver Mukhamedzhanov ◽

Michail Borisov ◽

Elena Ovchinnikova ◽

...

Keyword(s):

Phase Transition ◽

Ferroelectric Phase Transition ◽

Ferroelectric Phase ◽

Incident Radiation ◽

Waller Factor ◽

Energy Spectra ◽

Dihydrogen Phosphate ◽

Additional Contribution ◽

X Ray ◽

Hydrogen Position

Resonant X-ray diffraction was used to study the proton jumps in hydrogen-bonded rubidium dihydrogen phosphate (RDP) crystals. In the paraelectric RDP phase, hydrogen is delocalized between two crystallographically equivalent positions. At lower temperatures, this symmetry can be broken, which defines the processes that lead to the para- to ferroelectric phase transition. We have measured the energy spectra of the forbidden reflections 006 and 550 at incident radiation energies close to the Rb K-edge in a wide temperature range, down to the temperature of the ferroelectric phase transition. In the paraelectric phase we observed a growth of integrated intensity for both forbidden reflections with temperature. This behavior is opposite to conventional non-resonant Bragg reflections, where the intensity decreases in accordance with the Debye-Waller factor. The developed theoretical model explains this effect with the thermal motion induced (TMI) scattering mechanism and also confirms the adiabatic approximation stating that electrons instantly follow the nuclei movements. In the 550 energy spectra, we have observed an additional contribution to the resonant structure factor which could be associated with the presence of transient Slater-type proton configurations (PC) in the half-filled hydrogen position.

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