Microwave dielectric properties of Li3Mg2NbO6-based ceramics with (MxW1-x)5+(M = Li+, Mg2+, Al3+, Ti4+) substitutions at Nb5+sites
JOURNAL OF ALLOYS AND COMPOUNDS
Authors: Zhang, Ping; Hao, Manman; Xiao, Mi
Abstract
Li3Mg2Nb0.96 (MxW1-x)(0.04)O-6 (M = Li+, Mg2+, Al3+, Ti4+) ceramics were prepared by the solid-state reaction method. The sintering characteristics, microstructure, phase composition and microwave dielectric properties of Li3Mg2NbO6 ceramics with equivalent substitution ((Li1/5W4/5)(5+), (Mg1/4W3/4)(5+), (Al1/3W2/3)(5+) and (Ti1/2W1/2)(5+)) at the Nb-site were investigated firstly. After sintering at 1150 degrees C for 4 h, all samples were single-phase of orthogonal structure. Due to the difference in ion polarizability of the substituted ions, the dielectric constant changed. The substitution of (MxW1-x)(5+) in Li3Mg2Nb0.96 (MxW1-x)(0.04)O-6 ceramics significantly reduced dielectric loss. The quality factor showed a similar trend with the average bond valence. Moreover, the study found that the substitution of W-based composite ions has a small effect on the tau(f) values of Li3Mg2NbO6 ceramics. (C) 2020 Elsevier B.V. All rights reserved.
Stability for product groups and property (tau)
JOURNAL OF FUNCTIONAL ANALYSIS
Authors: Ioana, Adrian
Abstract
We study the notion of permutation stability (or P-stability) for countable groups. Our main result provides a wide class of non-amenable product groups which are not P-stable. This class includes the product group Sigma x Lambda, whenever Sigma admits a non-abelian free quotient and Lambda admits an infinite cyclic quotient. In particular, we obtain that the groups F-m x Z(d) and F-m x F-n are not P-stable, for any integers m, n >= 2 and d >= 1. This implies that P-stability is not closed under the direct product construction, which answers a question of Becker, Lubotzky and Thom. The proof of our main result relies on a construction of asymptotic homomorphisms from Sigma x Lambda to finite symmetric groups starting from sequences of finite index subgroups in Sigma and Lambda with and without property (tau). Our method is sufficiently robust to show that the groups covered are not even flexibly P-stable, thus giving the first such non-amenable residually finite examples. (C) 2020 Elsevier Inc. All rights reserved.
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