Bond volumes in crystals and glasses and a study of the germanate anomaly

The unit cell of a crystal is decomposed into partial volumes V-b of its bonds. V-b is described in terms of the bond length d and the coordination number N by V-b = V-0 + alpha*(d(3)/N). On the basis of structural data of about 170 binary and ternary compounds, including berates, silicates and germanates, it is demonstrated that V-0 = 0 and alpha(comp)* = 12.25 define compact structures. V-0 not equal 0 is a signature of structures containing free volumes or voids. The universal character of alpha(comp)* permits the determination of the free volume V-0 in alkali-germanate glasses and thereby a quantitative test of the idea that a change of the germanium coordination is the origin of the germanate anomaly. The test shows that the idea does not work since the pure transition from N-Ge = 4 to N-Ge = 6 changes the volume of the glass only by a marginal amount. It is suggested that a redistribution of void sizes which is accompanied by a negative deformation of the network is the leading mechanism which is responsible for the anomaly. (C) 1999 Elsevier Science B.V. All rights reserved.