Elastic behavior associated with phase transitions in incommensurate ${\text{Ba}}_2{\text{NaNb}}_5{\text{O}}_{15}$

The elastic behavior of barium sodium niobate $\left({\text{Ba}}_2{\text{NaNb}}_5{\text{O}}_{15}\right)$ has been investigated by resonant ultrasound spectroscopy through six different structural phases, with emphasis on the five incommensurate phase transitions near 40, 110, 547, 565, and 582 K. Data near 40 K are at least consistent with the existence of a lock-in transition to $P4nm$ at that temperature [Filipic et al., J. Phys.: Condens. Matter 19, 236206 (2007)], which has been controversial. A relaxation process occurs around the transition near 110 K and is assigned to a process involving movement of domain walls of the phase. Unusual behavior is observed through the high-temperature incommensurate transitions with large variations in frequency in the ultrasonic resonances, and a broad peak in the dissipation. No clear signature of the $1q\text{−}2q$ incommensurate-incommensurate transition at 565 K is observed. This is compatible with a model in which incommensurate-incommensurate transitions are not expected to manifest elastic anomalies.

Figure 1

(Color online) Schematic phase diagram of barium sodium niobate after Refs. 9, 23, 24, 25, 32, 34.

Figure 2

(Color online) RUS spectra for single crystal BNN for frequencies in the region 400–1200 kHz. Above room temperature, spectra were recorded at intervals during cooling from 920 K to room temperature from the first data collection. Below room temperature, spectra were recorded at intervals during heating from 10 K to room temperature. The $y$ axis is amplitude, with spectra displaced in proportion to their temperature. The amplitude of the low temperature spectra has been scaled down by a factor of 0.05 for ease of comparison. Spectra collected at temperatures close to the six different structural phases are shown in blue. Labels A, B, C, and D correspond to the resonances described in the text.

Figure 3

(Color online) Low temperature variation in the frequency (top) and $Q^{-1}$ (bottom) with temperature for resonances A (black squares), B (red circles), and C (green triangles). The frequency for each resonance has been divided by the value at 10 K for a better comparison.

Figure 4

(Color online) Variation in frequency (top) and $Q^{-1}$ (bottom) with temperature in the vicinity of the high temperature incommensurate transition, for resonances A (black squares), D (blue diamonds), as well as the values for resonance A obtained from a second measurement (open squares).

Figure 5

(Color online) Variation in frequency with temperature in the vicinity of the high-temperature incommensurate transition, for resonances E (open squares), F (open circles) in a second BNN sample for both the heating and cooling runs.

Figure 6

(Color online) Variation in frequency (top) and $Q^{-1}$ (bottom) with temperature in the vicinity of the ferroelectric transition, for resonances A (black squares) and B (red circles).

Figure 7

(Color online) Overview of the elastic constant and dissipation behavior of BNN from the present study. Values of $C_{33}$ and $C_{44}$ have been estimated on the basis of room temperature elastic constant data of Denda and Mansukh (Ref. 31) and assumed assignments of resonances A and B. They have been labeled as $C^{\prime }{}_{33}$ and $C^{\prime }{}_{44}$ to signify that their variations are estimated from resonances which do not depend exclusively on $C_{33}$ and $C_{44}$, respectively.