EXAFS studies of the local atomic structure of the lead-free piezoelectric ceramics ${\mathrm{K}}_x{\mathrm{Na}}_{1-x}\mathrm{Nb}{\mathrm{O}}_3$ over the temperature range $10–1023\mathrm{K}$

We use the x-ray absorption fine structure spectroscopy at Nb $K$ edge to reveal the local atomic structure of ${\mathrm{K}}_x{\mathrm{Na}}_{1-x}\mathrm{Nb}{\mathrm{O}}_3$ (PSN) solid solutions. The study is performed over the temperature range $10–1023\mathrm{K}$ for six different $x$ values. We show that only the combined analysis of extended x-ray absorption fine structure and preedge fine structure provides complete and reliable information about the local structure of $\mathrm{Nb}{\mathrm{O}}_6$ octahedra. Such extensive treatment of the experimental data shows that the local structure of PSN could be described within the spherical model proposed earlier as a hypothesis for perovskite-type ferroelectric zirconates. We reveal that the Nb atoms are localized near their average positions on the sphere surfaces for all temperatures and $x$ values. With regard to previous results we point out the features of microscopic structure common for PSN and perovskite-type zirconates.

Figure 1

(Color online) Temperatures and concentrations employed in this investigation. The phase labels are as follows: FR—ferroelectric rhombohedral, FMON—ferroelectric monoclinic, FO—ferroelectric orthorhombic, AFO—antiferroelectric orthorhombic, FT—ferroelectric tetragonal, PC—paraelectric cubic, and m denotes a cell multiplication.

Figure 2

$k^3$-weighted normalized EXAFS functions for ${\mathrm{K}}_{0.5}{\mathrm{Na}}_{0.5}\mathrm{Nb}{\mathrm{O}}_3$ at 10 (a) and $1023\mathrm{K}$ (b).

Figure 3

(Color online) Preedge absorption fine structures for $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ (a) and ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}\mathrm{Nb}{\mathrm{O}}_3$ (b) at different temperatures. Temperatures are indicated in the figure.

Figure 4

(Color online) Preedge absorption fine structures for different concentrations $x$ at the room temperature. Concentrations are indicated in the figure.

Figure 5

(Color online) Reduced $R$ factor of fitting within the 8-site (blue filled circles) and 12-site (black filled squares) models for ${\mathrm{K}}_x{\mathrm{Na}}_{1-x}\mathrm{Nb}{\mathrm{O}}_3$ at $300\mathrm{K}$.

Figure 6

(Color online) Modulus of the $k^3$-weighted FT for different potassium concentrations $x$ at 10, 300, 553, and $1023\mathrm{K}$ (black solid lines—experiment; blue dashed lines—fitting results). The $x$ value grows from bottom to top within each panel.

Figure 7

(Color online) Modulus of the $k^3$-weighted FT at different temperatures for $x=0.00$, 0.40, 0.65 (black solid lines—experiment; blue dashed lines—fitting results). Temperatures and concentrations are indicated in the figure.

Figure 8

(Color online) The results of fitting performed for $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$: (a) FMON phase, (b) AO phase, and (c) PC phase. Left panels show the absolutes values of the Fourier transforms of the $k^3$-weighted $\chi \left(k\right)$ (black solid lines—experiment; blue dashed lines—fitting results); right panels show the first shell pair radial distribution functions (PRDFs). Fitting range is marked out by vertical red dashed lines.

Figure 9

(Color online) The results of fitting performed for ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}\mathrm{Nb}{\mathrm{O}}_3$: (a) FMON phase, (b) AO phase, (c) FT phase, and (d) PC phase. Left panels show the absolutes values of the Fourier transforms of the $k^3$-weighted $\chi \left(k\right)$ (black solid lines—experiment; blue dashed lines—fitting results); right panels show the first shell pair radial distribution functions (PRDFs). Fitting range is marked out by vertical red dashed lines.

Figure 10

(Color online) Absolute values (blue dashed lines) and imaginary parts (black solid lines) of the $k^3$-weighted FT of the Nb $K$-edge EXAFS signal for $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ measured at $10\mathrm{K}$ (on the top) and the differential FT. Temperatures are indicated in the figure.

Figure 11

(Color online) Absolute values (blue dashed lines) and imaginary parts (black solid lines) of the $k^3$-weighted FT of the Nb $K$-edge EXAFS signal for ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}\mathrm{Nb}{\mathrm{O}}_3$ measured at $10\mathrm{K}$ (on the top) and the differential FT. Temperatures are indicated in the figure.

Figure 12

(Color online) Absolute values (blue dashed lines) and imaginary parts (black solid lines) of the $k^3$-weighted FT of the Nb $K$-edge EXAFS signal measured for $x=0.65$ (on the top) and the differential FT at room temperature. Concentrations are indicated in the figure.

Figure 13

The first shell PRDFs obtained for the cubic phases of $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (a), $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$ (b), $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ (c), and ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}\mathrm{Nb}{\mathrm{O}}_3$ (d).