Hexagonal Close-Packed 
                $$^4\hbox {He}$$
                
                    
                                    
                        
                            
                                
                                4
                            
                            He
                        
                    
                
             as Crystalline Multilayered Polytype: An Alternative for ‘Supersolid’ or ‘Glassy-Like’ Phase

Chishko, K. A.; Antsygina, T. N.; Poltavskaya, M. I.

doi:10.1007/s10909-016-1726-2

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…It is shown in [34] that hcp polytype can be treated as anisotropic elastic continuum with specific dispersion law in direction of disordered c axis. Previously, this model was applied [35] to interpret the discovered experimentally in Ref. [1,3], but at approximately similar temperatures (of order  0.1 K).…”

Section: Discussionmentioning

confidence: 96%

“…As a result, it means the passage to long-wave approximation, and such a procedure is quite natural as to the solid helium where the Debye temperature is of order higher as the melting temperature of the crystal. Finally, the phononic free energy of the 4 He polytype can be written in the form [34,35] (V is the volume of the system, a is the interatomic distance and c is the period of ideal hcp lattice, = / ) c a γ…”

Section: T βmentioning

confidence: 99%

“…After all these simplifications the spectrum of the problem [34,35] at the ideal ratio = = 1.63 8/3 γ can be written as where ( ) U r is the energy of interatomic interaction on interatomic distance r, and m is the atomic mass. In fact, for high-symmetric close-packed helium lattice with twelve neighbors in the first and second coordination spheres the non-central part of interatomic interaction is small, and / 1 a D Ω  .…”

Section: T βmentioning

confidence: 99%

“…As alternative to ordinary dislocation concept and glassy approach we propose [34,35] the model of hcp polytype [36][37][38] which made us possible to explain successfully the anomalies in temperature dependences of pressure reported in Refs. 1, 2.…”

Section: Introductionmentioning

confidence: 99%

“…The 1D packing order in the polytype stack changes with temperature, so that the corresponding (non-phononic) degrees of freedom contribute to the total free energy of the system. At low temperature both phononic ph ( C T has the local maximum, and, respectively, ( ) P T is locally non-monotonic (inflection point on the curve ( ) P T [35]) in the vicinity of 0.1-0.2 K. The paper is built as follows. Section 2 gives the statement of the problem.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of dilute 3He–4He solid solutions with hcp structure

Chishko

2018

Low Temperature Physics

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To interpret the anomalies in heat capacity C V (T) and temperature-dependent pressure P(T) of solid hexagonal close-packed (hcp)4He we exploit the model of hcp crystalline polytype with specific lattice degrees of freedom and describe the thermodynamics of impurity-free 4 He solid as superposition of phononic and polytypic contributions. The hcp-based polytype is a stack of 2D basal atomic monolayers on triangular lattice packed with arbitrary long (up to infinity) spatial period along the hexagonal c axis perpendicular to the basal planes. It is a crystal with perfect ordering along the layers, but without microscopic translational symmetry in perpendicular direction (which remains, nevertheless, the rotational crystallographic axis of third order, so that the polytype can be considered as semidisordered system). Each atom of the hcp polytype has twelve crystallographic neighbors in both first and second coordination spheres at any arbitrary packing order. It is shown that the crystal of such structure behaves as anisotropic elastic medium with specific dispersion law of phonon excitations along c axis. The free energy and the heat capacity consist of two terms: one of them is a normal contribution (with C V (T)  T 3 ) from phonon excitations in an anisotropic lattice of hexagonal symmetry, and another term (an "excessive" heat) is a contribution resulted by packing entropy from quasi-one-dimensional system of 2D basal planes on triangular lattice stacked randomly along c axis without braking the closest pack between neighboring atomic layers. The excessive part of the free energy has been treated within 1D quasi-Ising (lattice gas) model using the transfer matrix approach. This model makes us possible to interpret successfully the thermodynamic anomaly (heat capacity peak in hcp 4 He) observed experimentally.

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Section: Discussionmentioning

confidence: 96%

Section: T βmentioning

confidence: 99%

Section: T βmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of dilute 3He–4He solid solutions with hcp structure

Chishko

2018

Low Temperature Physics

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Interatomic Interaction and Structural Ordering in He II Phase

Chishko

2019

J Low Temp Phys

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Low-energy excitations in helium-like dimer within an exact diagonalization approach

Chishko

2018

Low Temperature Physics

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The non-relativistic quantum-mechanical problem on bound states of four interacting spinless electrons moving in the Coulomb field of two attractive point centers with  0 = 2 spaced at fixed distance R 0 (4 He 2 dimer within Born-Oppenheimer-Heitler-London approximation) has been solved rigorously through exact diagonalization (expansion on truncated orthonormalized basis) method. The four-spin-conditioned relativistic corrections (of order ~1/c 2) to the ground state level of the dimer have been calculated with exact diagonalization on spin cluster, the spectrum and eigenvectors of the spin problem have been obtained. It is shown that pair spin coupling is antiferromagnetic with exchange constant of 12 K (it provides antisymmetry of the spin-singlet ground-state wave function for isolated 4 He atom with two fermions coupled within the unitary spatially symmetric shell), but within four-electron shell of 4 He 2 dimer this fact yields the quintet ground state of the four-spin cluster totally antisymmetric relative to pair permutations. The exchange within the interatomic bond depends on the interatomic distance, so that there is a coupling between spin and phonon degrees of freedom which leads to renormalization of phonon spectrum in condensed phase as compared to the corresponding spinless medium. This effect can be interpreted as a direct analog of translation-rotation interaction in molecular cryocrystals.

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Hexagonal Close-Packed $$^4\hbox {He}$$ 4 He as Crystalline Multilayered Polytype: An Alternative for ‘Supersolid’ or ‘Glassy-Like’ Phase

Cited by 6 publications

References 15 publications

Thermodynamics of dilute 3He–4He solid solutions with hcp structure

Thermodynamics of dilute 3He–4He solid solutions with hcp structure

Interatomic Interaction and Structural Ordering in He II Phase

Low-energy excitations in helium-like dimer within an exact diagonalization approach

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