**6. Medium range order of alkali borate glasses**

In contrast to crystals with translational symmetry, glasses have disordered structure about local atomic arrangements. However, the structure of glasses has the medium range order (MRO) on a few nanometers' length scale [41, 42]. The MRO in liquid and glassy states is characterized by the first sharp diffraction peak (FSDP). The FSDP is observed by neutron and X-ray diffraction experiments in the static structure factor S(Q), where Q is the modulus of the wave vector [43]. The peak position Q1 and the peak width ΔQ of a FSDP correspond to a periodic ordering with a periodicity of 2π/Q1 and a static structure correlation length *L*fsdp given by

$$L\_{\rm fsdp} = 2\pi/\Delta\Omega\tag{19}$$

*Low Energy Excitations in Borate Glass DOI: http://dx.doi.org/10.5772/intechopen.106650*

**Figure 15.**

*Static structure factor S(Q) of alkali borate glasses observed by neutron diffraction. Q1 is the position of a FSDP.*

#### **Figure 16.**

*(a) Correlation between the static structure correlation length of FSDP and the ionic radius of alkali ions of alkali borate glasses, and (b) Correlation between the static structure correlation lengths of a FSDP and the dynamic correlation length of a boson peak.*

respectively. It was reported that the FSDP intensity and peak position can be quantified using the characteristic void distribution function, defined in terms of average void size, void distance, and void density [44].

The static structure factor S(Q) of alkali borate glasses determined by the neutron scattering is shown in **Figure 15** [38]. As the ionic radius of alkali ions decreases, the position Q1 of a FSDP increases. Using the peak width of a FSDP, the static structure correlation lengths *L*fsdp are determined. The correlation between the static structure correlation length and ionic radius of alkali ions is plotted in **Figure 16a**. It is found that as the ionic radius increases, the correlation length also increases. The MRO may be related to the local structure in the vicinity of an alkali ion in voids.

The correlation of various glasses between the boson peak frequency and the width of a FSDP was reported by Sokolov et al. [45]. Since the boson peak frequency is related to the dynamical correlation length *L*BP, the relation between the static structure correlation length and the dynamical correlation length is plotted in **Figure 16b**. The good correlation between the dynamical correlation length *L*BP and the static structure correlation length *L*fsdp indicates that the boson peak is the vibration related to the MRO defined by the width of a FSDP.
