Science China Technological Sciences
, Volume 57, Issue 4, pp 692698
First online:
Densityfunctionaltheory formulation of classical and quantum Hooke’s law
 Hao HuAffiliated withDepartment of Materials Science and Engineering, University of Utah
 , Feng LiuAffiliated withDepartment of Materials Science and Engineering, University of Utah Email author
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A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress (σ ^{M}) originates from lattice strain (ɛ), following Hooke’s law: σ ^{M}=Cɛ, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress (σ ^{QE}) is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke’s law: σ ^{QE}=Ξ(Δn), where Ξ is the deformation potential of electronic states and Δn is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke’s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain (ɛ=0), and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.
Keywords
stress in the solid quantum electronic stress quantum Hooke’s law density functional theory Title
 Densityfunctionaltheory formulation of classical and quantum Hooke’s law
 Journal

Science China Technological Sciences
Volume 57, Issue 4 , pp 692698
 Cover Date
 201404
 DOI
 10.1007/s114310145500x
 Print ISSN
 16747321
 Online ISSN
 18691900
 Publisher
 Science China Press
 Additional Links
 Topics
 Keywords

 stress in the solid
 quantum electronic stress
 quantum Hooke’s law
 density functional theory
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