Dielectric, electromechanical and elastic properties of   K$_{1-x}$(NH$_4$)$_x$H$_2$PO$_4$ compounds
  We present the results of the thermodynamic theory of piezoelectric ferroelectrics and of the phenomenological theory of thermodynamic characteristics of the KH$_{2}$PO$_{4}$ type ferroelectrics. Available experimental data for the dielectric, piezoelectric, and elastic characteristics of the KH$_{2}$PO$_{4}$ type ferroelectrics and NH$_4$H$_{2}$PO$_{4}$ type antiferroelectrics are described using the proposed microscopic theory of these crystals. Using the results of the thermodynamic theory and experimental data we calculate the dielectric, piezoelectric, and elastic characteristics of the K$_{1-x}$(NH$_4$)$_x$H$_2$PO$_4$ type systems. 
R.Levitskii, I.Zachek, L.Korotkov, D.Likhovaja, A.Vdovych, S.Sorokov,   Z.Trybula, Sz.Los
cond-mat.mtrl-sci