## 3 Verification of the Main Starting Hypotheses of the Interstitialcy Theory
### Relation between the Shear Modulus and Heat Effects  
A simple analysis of Equations (1) and (2) shows that the IT implies an intrinsic relation between shear modulus changes and heat effects in MGs. Indeed, integration of Equation (1) taking account of Equation (2) leads to an expression for the enthalpy increment \(\Delta H\) upon insertion of interstitial-type defects, which can be expressed through the shear moduli of glass and maternal crystal, \(\Delta H\approx(\mu-G)/\beta\rho\), where \(\beta\) is the shear susceptibility and \(\rho\) is the density. Then, one can arrive at an expression relating the heat flow with the change of the shear modulus,  
\[W=\frac{\dot{T}}{\rho\beta}\left(\frac{G}{\mu}\frac{\partial\mu}{\partial T}- \frac{\partial G}{\partial T}\right)\,, \tag{4}\]  
where \(\dot{T}\) is the rate of temperature change. This relationship was repeatedly tested and found to give an excellent description of the heat flow on the basis on shear modulus relaxation data not only upon structural relaxation below the glass transition temperature \(T_{g}\) and in the supercooled liquid state but upon crystallization as well [45; 46]. The latter fact is really surprising and actually suggests that the whole excess internal energy \(\Delta U\) (with respect to the crystalline maternal state) is mostly related to the interstitial-type defect system frozen-in upon glass production. An analysis gives a simple expression for this quantity [47],  
\[\Delta U\approx\Delta H\approx\frac{\mu}{\beta\rho}\left(1-\frac{G}{\mu} \right). \tag{5}\]  
It is seen that the excess internal energy is simply controlled by the shear moduli of glass and maternal crystal. Upon crystallization, the defect system disappears and this energy is released as heat, i.e., \(\Delta U\approx Q_{cryst}\), where \(Q_{cryst}\) is the heat of crystallization. A specially designed experiment confirmed this idea [48]. From a physical viewpoint, this result means that the whole heat content of glass (i.e., the excess enthalpy with respect to the crystalline maternal state) is mostly determined by the interstitial-type defect system frozen-in upon glass production.  
On the other hand, considering the initial and relaxed states of MGs and calculating the corresponding differences for the heat flow and shear modulus, \(\Delta W=W_{rel}-W\) and \(\Delta G=G_{rel}-G\), Equation (4) after simplification can be rewritten as [49]  
\[\Delta W=-\frac{\dot{T}}{\rho\beta}\frac{\partial\Delta G}{\partial T}. \tag{6}\]  
This relationship shows that the quantities \(\Delta W\) and \(\partial\Delta G/\partial T\) should be proportional to each other. Figure 4 shows these quantities derived from calorimetric and shear modulus data for bulk glassy \(Zr_{65}Al_{10}Ni_{10}Cu_{15}\). It is clearly seen that they are indeed proportional. This allows determination of proportionality constant and calculation of the shear susceptibility \(\beta\). Table 1 shows \(\beta\)-values thus derived for a few MGs. It is seen that these values belong to a relatively narrow range \(15\leq\beta\leq 22\) that, in general, agrees with the IT. Other methods used for the determination of \(\beta\) give close results [49]. Since the shear susceptibility determines the shear softening effect (via Equation (2)), the heat effects (according to Equations (4) and (5)) and also related to the anharmonicity of the interatomic potential, it appears to be a major integral parameter of the glassy structure.