**2. Borate glass and alkali metal modification**

Borate glass is the most contemporary glass and optical material for technological and environmental applications. Pure borate glass undergoes a glass transition at *T*<sup>g</sup> = 260°C. The melting temperature is *T*<sup>m</sup> = 450°C [11]. The character of the temperature dependence of thermal expansibility, surface tension, and viscosity, in the range up to 1400°C, proves that, in the crystalline state and in the vitreous state below about 300°C, boron oxide consists of units held together by "weak" forces and that with increasing temperature this structure changes gradually toward a "strong" one [10]. The borate glass is strong with a fragility index of *m* = 30. Boron oxide glass has a random threedimensional network of BO3-triangles with a comparatively high fraction of sixmembered rings (boroxol rings). Krogh-Moe discussed structure models for boron oxide glass and molten boron oxide with reference to spectroscopic data, diffraction data, and other physical properties for boron oxide [12]. Borate glasses for scientific and industrial applications were reviewed by Bengisu [13].

Borate glass is modified by alkali metals and physical properties remarkably change by the appearance of various structural units and structural groups. In this chapter, we discuss the dynamical properties of binary alkali metal borate glasses, *x*M2O(1*x*)B2O3 (M = Li, Na, K, Rb, Cs), i.e., lithium borate (LiB), sodium borate (NaB), potassium borate (KB), rubidium borate (RbB), and cesium borate (CsB) glasses. In alkali borate glasses, the physical properties are of special interest, because their alkali content dependences often show maxima and minima termed "borate anomaly" [14]. Their dependence also shows the difference among the kind of alkali metal ions. The dependences of density against the alkali content are classified to two groups. In LiB, NaB, and KB glasses, density shows a moderate increase as the alkali content increases, and they have the nature of covalent packing. While in RbB and CsB glasses, density remarkably increases against the alkali content increases, and they have the nature of ionic packing [15].

Since the physical properties are related to the structure, the variation has been discussed in terms of three kinds of structural units, BØ3, BØ4 �, and BOØ2 �, for the alkali content below *x* = 0.50 as shown in **Figure 3** [15, 16]. Here, O and Ø denote the nonbridging and bridging oxygens, respectively. In pure borate glass, the coordination number of boron is three, and units BØ3 are dominant. When borate glass is modified by alkali ions, the units BØ4 � and BOØ2 � are formed by the chemical reactions of Eqs. (3) and (4). The two units coexist by the disproportion reactions of Eq. (5). As the ionic radius of alkali ions increases, the number of nonbridging oxygen increases and the average coordination number of boron decreases. Consequently, the number of BØ4 � decreases, while that of BOØ2 � increases.

$$\text{M}\_2\text{O} + 2\text{B}\mathfrak{O}\_3 \to 2\text{M}^+ + \text{B}\mathfrak{O}\_4 \tag{3}$$

$$\text{M}\_2\text{O} + 2\text{B}\mathfrak{O}\_3 \rightarrow 2\text{M}^+ + \text{BO}\mathfrak{O}\_2^- \tag{4}$$

$$\text{B}\mathfrak{O}\_4^- \hookrightarrow \text{BO}\mathfrak{O}\_2^- \tag{5}$$

For the detailed discussion on the variation of structure, several kinds of superstructural units or structural groups such as boroxol ring, pentaborate, and diborate groups were considered [17].

For the analysis on the variation of physical properties, we introduce the quantity *V*m(B) and *V*<sup>m</sup> (O), which denote the volume of glass containing one a mole of boron and oxygen, respectively.

$$V\_m(B) = \frac{M[\varkappa M\_2O(1-\varkappa)B\_2O\_3]}{2\rho(1-\varkappa)}\tag{6}$$

$$V\_m(O) = \frac{M[\infty M\_2O(1-\varkappa)B\_2O\_3]}{\rho(3-2\varkappa)}\tag{7}$$

Where ρ is density, *M xM*½ � <sup>2</sup>*O*ð Þ 1 � *x B*2*O*<sup>3</sup> is the molar mass of the entity *xM*2*O*ð Þ 1 � *x B*2*O*3. **Figure 4** shows alkali content dependences of volumes of glass containing one mole of (a) boron and (b) oxygen atoms [15].

**Figure 3.** *Structural units of alkali borate glasses.*

**Figure 5.**

*Alkali content dependences of the derivatives of the molar volumes (a)* κV*m(B), and (b)* κV*m(O) of alkali borate glasses [15].*

Both *V*m(B) and *V*m(O) increase with respect to alkali content in LiB, NaB, and KB glasses, while they decrease in RbB and CsB glasses. At a given alkali content, the packing of boron and oxygen in the glass structure becomes more compact as the ionic radius of alkali ion increases. The boron atoms are packed most compactly at *x* = 0.20 for LiB, *x* = 0.08 for NaB, *x* = 0.02 for KB, *x* = 0.01 for RbB, and none for CsB glasses.

The remarkable changes occur in the response to the stress such as their pressure derivatives. We discuss the derivatives of the molar volumes *V*m(B) and *V*<sup>m</sup> (O) with respect to pressure.

$$-\frac{d}{dp}V\_m(B) = -\frac{1}{V}\frac{dV}{dP}V\_m(B) = \kappa V\_m(B),\tag{8}$$

$$-\frac{d}{dp}V\_m(\mathcal{O}) = -\frac{1}{V}\frac{dV}{dP}V\_m(\mathcal{O}) = \kappa V\_m(\mathcal{O}),\tag{9}$$

*where <sup>κ</sup>* ¼ � <sup>1</sup> *V dV dP* , is the compressibility. The *κV*m(B) represents the effect of boron atoms on the elasticity, and the *κV*m(O) represents the effect of oxygen atoms on the elasticity. **Figure 5** shows the alkali content dependences of *κV*m(B) and *κV*m(O) [15]. Both *κV*m(B) and *κV*<sup>m</sup> (O) at a given alkali content decrease as the ionic radius of alkali ions increases. In LiB and NaB glasses with covalent packing, *κV*m(B) and *κV*m(O) monotonically decrease. However, in KB, RbB, and CsB glasses with ionic packing, the concave and convex shapes appear. We discuss these dependences by the division into following three alkali content ranges.

