Volume of a dislocation network

We derive a simple analytical line integral expression for the relaxation volume tensor of an arbitrary interconnected dislocation network. This quantity determines magnitude contribution to dimensional changes and volumetric swelling material, highlights fundamental dual role dislocations as sources internal strain well carriers plastic deformation. To illustrate applications method, we compute stacking fault tetrahedron, defect commonly occurring in fcc metals; unusual tetrahedral configuration formed by $(a/2)\ensuremath{\langle}111\ensuremath{\rangle}$ $a\ensuremath{\langle}001\ensuremath{\rangle}$ bcc metal; estimate relative extended heavily irradiated tungsten.