Related Experiment Video
Updated: May 26, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Structural relationship between negative thermal expansion and quartic anharmonicity of cubic ScF3
Chen W Li1, Xiaoli Tang, J A Muñoz
1Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA. chenwli@gmail.com
Physical Review Letters
|December 21, 2011
Summary
Scandium trifluoride exhibits significant negative thermal expansion due to lattice dynamics. Quantum quartic oscillators in its structure explain this phenomenon and temperature-dependent stiffening of phonon modes.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Solid State Chemistry
Background:
- Cubic scandium trifluoride (ScF3) is known for its notable negative thermal expansion (NTE) over an extensive temperature range.
- Understanding the underlying mechanisms of NTE in ScF3 is crucial for its potential applications.
Purpose of the Study:
- To investigate the temperature dependence of lattice dynamics in ScF3.
- To elucidate the origins of the large negative thermal expansion in ScF3.
Main Methods:
- Inelastic neutron scattering experiments were conducted from 7 K to 750 K.
- First-principles phonon calculations and frozen phonon calculations were employed.
Main Results:
- Phonon density of states revealed substantial anharmonic contributions and thermal stiffening of modes around 25 meV.
- Identified specific phonon modes involving transverse fluorine atom motion behaving as quantum quartic oscillators.
- The quartic potential, arising from harmonic interatomic forces in the ScF3 DO9 structure, was found to be a key factor.
Conclusions:
- The quantum quartic oscillator behavior of certain phonon modes is responsible for the observed thermal stiffening and a significant portion of the negative thermal expansion in ScF3.
- Anharmonicity and specific lattice vibrational modes are critical to understanding the NTE properties of ScF3.
Related Concept Videos
01:22Thermal Expansion
The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an upward force on the hot air to, for example, make steam and smoke rise, and hot air balloons float. The same behavior happens in all liquids and gases,...
01:19Thermal Strain
Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
01:24Heat and Free Expansion
The work done by a thermodynamic system depends not only on the initial and final states but also on the intermediate states—that is, on the path. Like work, when heat is added to a thermodynamic system, it undergoes a change of state, and the state attained depends on the path from the initial state to the final state. Consider an ideal gas cylinder fitted with a piston. When the cylinder is heated at a constant temperature, the gas molecules absorb energy and expand slowly in a controlled...
01:16Thermal Sigmatropic Reactions: Overview
Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...