The structure of any compound is decided by inter-particle interaction represented basically by two body central potential between every pair of particles; here I presume that three body interactions if present are weak. The two body interaction has two component: (i) repulsive part and attractive part. The inter-particle distance (bond length) is decided by the equilibrium between repulsive and attractive forces. When we replace any atom substitutionally (as you have stated), it is natural that interaction energy of bonds with substituted atom is different than that with host atom that has been replaced. There are two possibilities: (a) the net cohesive energy of the doped system is lower than host or (b) it is higher. In the former case the doped system is more stable than host, while in the latter case it is less stable. In what follows your example corresponds to the former. While increase in bond length corresponds increase in the bond energy, yet the net change in cohesive energy could be negative if new bonds are stronger in their binding in comparison to old bonds in the host. So what is found to be in your example need not be true with every such case. However, if it is always true, it will be a useful information for my perusal.