First-Principles Determination of Chain-Structure Instability in   KNbO$_3$
  A complete mapping in the Brillouin zone of the structural instability associated with the ferroelectric phase transitions of KNbO$_3$ has been obtained by first-principles calculations using an LAPW linear response approach. The wavevector dependence of the instability reveals pronounced two-dimensional character, which corresponds to chains oriented along $\left<100\right>$\ directions of displaced Nb atoms. The results are discussed in relation to models of the ferroelectric phase transitions. 
Rici Yu, Henry Krakauer (College of William and Mary)