The nature of negative linear expansion in layer crystals C, Bn, GaS, GaSe and InSe

Negative thermal expansion of HTSC-type structures: low temperature structure measurements on Eu1+x(Ba1−yRy)2−xCu3O7−d compounds and theoretical treatment

“…The values of the temperatures of the maxima obtained in [6,7] for the quantities ( ) D T have shown good agreement with the temperatures of the minima on the measured dependences of the LTEC ( ) a || T of strongly anisotropic layered crystals [5].…”

“…Later, negative values of the LTEC have been found (see, for example, [5]) for strongly anisotropic layered crystals containing modes with characteristic «quasi-bending» curvature in a long-wave length region of the vibration spectrum (for example, graphite), and for compounds (such as GaSe, GaS, InSe) in which the phonon spectra exibit either a weaker corresponding curvature or the latter is not revealed at all. Recently, similar features were observed on advantageous superconductors like MgB 2 .…”

“…At once we should notice, that in [5][6][7] crystal structures were considered in which the strong anisotropy of interatomic interaction remains in the long-range order and manifests itself, in particular, in anisotropy of the elastic constants. In crystals such as 1-2-3 HTSC the anisotropy of the elastic constants is insignificant and, moreover, has the other sign, as the sound velocity along the layers is higher than in the direction normal to the layers [10].…”

Negative thermal expansion in the layered semiconductor TlGaSe2

“…Figure 1 shows our data on the temperature dependences of the LECs of single crystals of TlGaSe 2 in the plane of the layers (α || ) and perpendicular to them (α ⊥ ). It is seen that large positive values of α ⊥ (T) are observed, as is characteristic for practically all layered crystals in the direction of weak coupling [10]. The α ⊥ (T) curve shows pronounced anomalies in the form of three peaks at temperatures T = 102, 110 and 120 K. The α || (T) curve is much different.…”

“…Recent measurements of C 13 in graphite [16] have shown that the value of C 13 in [14] and in many other papers is several times larger than the correct value measured in [16], C 13 = 1.5 × 10 11 dyn/cm 2 . We have shown previously [10] that in view of the smallness of C 13 in graphite, it is the first term in relation (1) that is responsible for the negative values of α || (T), i.e. the negativity of α || (T) is due to the negative values of γ || .…”