Negative and zero thermal expansion in ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$

We show that a synergy of the covalency effect associated with the $A$-site and $B$-site cations in ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ (KBT) makes it unique among the Pb-free ferroelectrics by imparting a rare property of negative and zero thermal expansion (ZTE). We tuned this synergy in two different KBT alloys, ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-{\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ and ${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-\mathrm{Bi}\left({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$, and identified a common critical tetragonality below which the ZTE behavior disappears completely in both the systems.

Figure 1

Temperature dependence of tetragonal unit-cell volume: (a) $\mathrm{BaTi}{\mathrm{O}}_3$ and (b) $\mathrm{PbTi}{\mathrm{O}}_3$. $T_{\mathrm{C}}\to$ Curie point; PTE, ZTE, and NTE indicate positive, zero, and negative thermal expansions, respectively.

Figure 2

Temperature evolution of unit-cell volume of tetragonal $\left(P4mm\right)$ phase in (1−$x$)${\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-\left(x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3 \left[\right(1-x)\mathrm{KBT}-(x\left)\mathrm{NBT}\right]$: (a) $x=0.00$, (b) $x=0.58$, and (c) $x=0.60$; PTE, ZTE, and NTE indicate positive, zero, and negative thermal expansions, respectively. (d) Composition dependence of temperature range in which ZTE and NTE occur. Temperature ranges of ZTE and NTE suddenly collapse at $x=0.60$. Phase diagram of (e) KBT-($x$)NBT, which highlights temperature ranges for ZTE, NTE, and PTE. (f) Tetragonality and temperature range in which ZTE occurs as function of composition in KBT-($x$)NBT system.

Figure 3

[111]$\mathrm{pc}$ zone-axis electron-diffraction patterns of $(1-x)\mathrm{KBT}-\left(x\right)\mathrm{NBT}$ for (a) $x=0.50$ and (b) $x=0.60$. (c) Composition evolution of neutron powder-diffraction pattern of $(1-x)\mathrm{KBT}-\left(x\right)\mathrm{NBT}$ in two different limited 2θ ranges. Weak superlattice peaks are indicated by red arrows. (d) Schematic diagram of tetragonal unit cell. (e) Composition dependence of difference in lengths of $\mathrm{Ti}–{\mathrm{O}}_1$ and $\mathrm{Ti}–{\mathrm{O}}_3$ bonds at room temperature. This difference is treated as measure of intrinsic polarization. Intrinsic polarization drops abruptly for $x>0.58$, confirming weakening of polarization by onset of in-phase octahedral tilt.

Figure 4

(a), (b) Raman spectra of representative compositions in their ferroelectric state at room temperature. Arrows highlight abrupt change in nature of peak shift for $x>0.58$. (c) Composition dependence of frequencies of different modes at $30{}^{\circ }\mathrm{C}$. Frequencies of modes ${\omega }_1$ corresponding to Na/Bi/K-O vibration, ${\omega }_{2–3} \left(={\left[\left({\omega }_2^2+{\omega }_3^2\right)/2\right]}^{1/2}\right)$ related to coupling of off-centered Na/Bi/K and off-centered Ti cations, and ${\omega }_4, {\omega }_5, {\omega }_6$ corresponding to Ti-O vibrations decrease suddenly at $x=0.60$ at room temperature.

Figure 5

Temperature evolution of unit-cell volume of tetragonal $\left(P4mm\right)$ phase in $(1-y){\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-\left(y\right)\mathrm{Bi}\left({\mathrm{Mg}}_{0.5}{\mathrm{Ti}}_{0.5}\right)\mathrm{Ti}{\mathrm{O}}_3 \left[\right(1-y)\mathrm{KBT}-(y\left)\mathrm{BMT}\right]$: (a) $y=0.005$, (b) $y=0.06$, and (c) $y=0.065$. (d) Composition-temperature diagram highlighting temperature ranges for ZTE, NTE, and PTE. (e) Composition dependence of tetragonality and temperature range for ZTE. (f) Comparison of tetragonality dependence of temperature range of ZTE of KBT-($x$)NBT and KBT-($y$)BMT systems.