The ferroelectric phase transition in $KH_2PO_4$ (KDP), $KDP_{1-x}ADP_x(K_{1-x}(NH_4)_xH_2PO_4)$ and $KDP_{1-x}KDA_x(KH_2P_{1-x}As_xO_4)$ crystals has been studied using dielectric measurements and Raman scattering for varing concentrations x of isomorphic impurities.
In the dielectric constant measurements we observed the linear dependence of the transition temperature $T_c$ on the impurity concentration x, characterized by $dT_c/dx\simeq -250K$ for $KDP_{1-x}ADP_x$ and $dT_c/dx\simeq -60K$ for $KDP_{1-x}KDA_x$ mixed crystals. Such a negative temperature shift is well understood in the virtual crystal approximation (VCA). The VCA solution for the transition temperature in the pseudo-spin model given by Lage and Stinchcombe was extended for out problems, and the numerical solutions giving the observed values were obtained as $\mu_{ADP}=0.36＼mu_{KDP}$ and $\mu_{KDP}$ and $\mu_{KDA} =0.88\mu_{KDP}$ with $\Omega_{KDP}=\Omega_{KDA}=\Omega_{ADP}=300K$. The physical significances of the approximations used and the resultant numerical values are critically discussed.
In the dielectric loss measurements we observed, for the domain freezing temperature $(T_f(x))$, $dT_f/dx\simeq -850K$ for $KDP_{1-x}ADP_x$ and $dT_f/dx\simeq -500K$ for $KDP_{1-x}KDA_x$ crystals. These results are also interpreted using the VCA solutions. The domain freezing phenomena of KDP type crystals was examined from the viewpoint of the roughening transition of the interfacial layer between domains and a qualitative explanation was given for more pronounced impurity effect on $T_f$ than $T_c$ using the roughening mechanism. In the high concentration regime of x≥0.05 for $KDP_{1-x}KDA_x$ crystals, we observed that the anomalous domain dynamics disappeared.
The polarization reversal current measurements using the step-function field E≤185 V in $KDP_{1-x}ADP_x$ crystals were also applied to observe the domain freezing. And the field dependence of the freezing temperature $T_f$ was observed to show $T_f$ significantly decreased with increasing field strength.
The coupled mode analysis was carried out for the $B_2$ symmetry soft-mode spectra using real, imaginary, and complex coupling. In pure KDP crystal the uncoupled soft mode frequency was observed to show the linear temperature dependence from $T_c$ to about 200 K for all the coupling schemes. The linearity from $T_c$ to room temperature was more apparent when fitted for the temperature-weighted ralaxation time $T/＼tau_1$. In $KDP_{1-x}ADP_x$ crystals we observed there were no significant changes in the soft mode spectrum in the low concentration limit x≤0.015. In $KDP_{1-x}KDA_x$ mixed crystals for x = 0.14 and 0.24 the frequency and the damping of the uncoupled soft mode were observed to increase slightly as compared with those of the pure KDP crystal. However, $w^2_1/\Gamma_1$ values are found nearly same for all crystals except in the low temperature region above $T_c$. And the uncoupled soft mode was found to attain a hard core frequency for the mixed crystals.
KDP,$KDP_{1-x}ADP_x$,$KDP_{1-x}KDA_x$ 결정들의 강유전성 상전이를 유전 상수 측정과 Raman 산란 실험을 통하여 연구하였다.
유전상수 측정에서 함량 X에 따른 상전이 온도 $T_c$의 변화는 $KDP_{1-x} ADP_x$ 결정의 경우 $dT_c/dX\simeq -250^\circ{k}$로 측정되었으며, $KDP_{1-x} KDA_x$ 결정의 경우는 $dT_c/dX\simeq -60^\circ{K}$로 측정이 되었다.
Pseudo-spin model의 VCA(virtual crystal approx.)해를 이 문제에 확장 시키면 $\mu_{ADP}=0.36\mu_{ADP}$ 와 $\mu_{KDA}=0.88\mu_{KDP}$의 수치해가 나오며, 이에 사용된 가정과 수치해의 물리적 의미에 대하여 논의하였다.
유전손실 측정에서 domain freezing 온도 $T_f$의 변화는 $KDP_{1-x} ADP_X$의 경우 $dT_{′}/dX\simeq -850^\circ{k}, $KDP_{1-x}KDA_x$의 경우는 $dT_{′}/dX\simeq -500^\circ{k}$로 측정이 되었다. 이것도 VCA 해를 사용하여 분석하였으며, 이와 같은 freezing 현상을 Roughening 전이의 개념으로서 설명하였다. $KDP_{1-x}KDA_x$의 경우 함량 X가 0.05 이상이면 비정상적 domain 운동이 사라짐이 관측되었다.
$B_2$ Raman 산란 spectrum의 soft mode를 여러가지 결합의 가정을 사용하여 분석하였다. 순수한 KDP 결정의 uncoupled soft mode에서 $\omega_1^2$는 $\sim 200^\circ{k}$ 아래에서 선형적 온도 의존도가 측정되었으며, 실온까지의 선형성은 T/λ에서 더욱 명백하게 나타났다. $KDP_{1-x} ADP_x$ 결정들은 $X\leg0.015$인 한계에서 순수한 KDP에 비해서 별다른 변화가 관측이 되지 않았다. $KDP_{1-x}KDA_x$ 결정들의 $X=0.14$와 $X=0.24$의 고농도 혼합 결정인 경우에는 uncoupled soft mode의 주파수와 감쇠상수는 KDP에 비해 증가하는 것이 관측되었으나 $\omega^2_1/\Gamma_c$ 은 $T_c$ 근처를 제외하고 모든 혼합 결정들에서 거의 같은 값을 가지는 것으로 관측 되었다. 아울러 uncoupled soft mode는 혼합 결정에서 hard core 주파수를 갖는 것이 판명되었다.
