Basic lengths in SNSs
length scales
- inter-atomic distance is ainter−atomic≃2.4A
The nearest neighbor distance is 0.235 nm which is about 5x of Bohr radius. And the diameter of a silicon atom is 2.35A (lattice size of Si is 5.4A)
- medium-range order is ξ=Λ(ℏc3sρ)1/2≃1.6∗10∗10−12erg(13∗10−10)1/2≃44 ˙A,
where Λ=10eV=1.6∗10−11erg
by matching energy scales of phonon and dipole interaction energy ℏcsξ≃Λ2c2sρξ3
- fundamental glasson length agl=2Λ2mglℏ2ρc2t
by matching energy scales of localised kinetic energy and dipole interaction energy ℏ22mglξ2≃Λ2c2sρξ3
taking mgl=5∗10−26g, we get
agl≃2(1.6∗10−11erg)25∗10−26g(10−26erg∗s)2(2g/cm3)(4∗105)2≃80˙A
we get the mass scale mgl=5∗10−26g without any particular model