Mode-crystallography analysis of the crystal structures and the low- and high-temperature phase transitions in Na_0.5K_0.5NbO₃

Abstract

Na 0.5 K 0.5 NbO 3 has been synthesized by the conventional solid-state reaction process. The crystal structures and phase transitions, at low and high temperature, determined from the Rietveld refinements of X-ray and neutron powder diffraction data are reported. The structure evolution of Na 0.5 K 0.5 NbO 3 in the temperature range from 2 to 875 K shows the presence of three phase transitions. The first one, at $135 K, is discontinuous from the rhombohedral R3c (No. 161) space group to the room-temperature orthorhombic Amm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonal P4mm space group (No. 99) at $465 K, and the third is continuous from the tetragonal to the cubic Pm3m space group (No. 221) at $700 K. The obtained phase-transition sequence is R3c ! Amm2 ! P4mm ! Pm3m. No previous studies at low temperature have been carried out on the material with composition Na 0.5 K 0.5 NbO 3 . In the course of the determination of the three experimentally found phases, a novel method of refinement is presented. This is a step forward in the use of the symmetry-adapted modes as degrees of freedom in the refinement process: the parameterization of a direction in the internal space of the, in this case, sole irreducible representation, GM 4 À , responsible for the symmetry breaking from the parent cubic space group to the polar distorted low-symmetry phases. Eventually, this procedure enables the calculation of the spontaneous polarization.

Structure, dielectric, and piezoelectric properties of K0.5Na0.5NbO3-based lead-free ceramics

“…For x > 0.05, there is increased coalescing of peaks and a gradual weakening of (002) PC peak, indicating the formation of the pseudocubic phase. [49][50][51] The asymmetry in the (002) C peak (z45.4 ) in the XRD pattern for x ¼ 0.30 sample ( Fig. 1) is due to the Cu-K a2 radiation.…”

Suppression of abnormal grain growth in K0.5Na0.5NbO3: phase transitions and compatibility

“…3(a), black line). Although a reproduction of sample quality is difficult as has been mentioned before the calculated positions for potassium sodium niobate peaks (COD, #2300499 60 ) for K 0.5 Na 0.5 NbO 3 at room temperature could be verified for all tested KNN samples and a parameter range can be demonstrated within which potassium sodium niobate can be fabricated reliably without any second or multi niobate phases (Fig. 3(a)).…”

“…Often the reported results contradict each other in terms of applied crystallographic symmetries e.g. space group and crystallographic configuration at room temperature 60,61 . Yet, the application of the compatibility theory requires the accurate determination of lattice constants 63,64 .…”

“…In the end of the powder fabrication process, the material is most sensitive towards changes due to the fragile KNN equilibrium state, therefore the appearance of secondary phases after the third calcination is interpreted as transgression of the KNN equilibrium.

Figure 1Processing of KNN and KNN ex : powder batches and resulting diffractograms for KNN ex after each single processing step. ( a ) Comparison of KNN (indexed pattern 60 ) and KNN ex powder batches after the first milling (after 1 st mill.) and the first calcination (after 1 st calc.)

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“…Processing of KNN and KNN ex : powder batches and resulting diffractograms for KNN ex after each single processing step. ( a ) Comparison of KNN (indexed pattern 60 ) and KNN ex powder batches after the first milling (after 1 st mill.) and the first calcination (after 1 st calc.)…”