Properties of Lanthanum-Doped Bismuth Sodium Titanate (Bi0.5Na0.5TiO3) Prepared by Soft Combustion Technique

In this work, soft combustion technique was used to study the effect of lanthanum (La) doping on the properties of Bi0.5Na0.5TiO3 (BNT). The amount of La dopant investigated for (Bi0.5Na0.5)(1-1.5x)LaxTiO3 (BNLT) pellets were x = 0, 0.01, 0.02, 0.05 and 0.10 (0, 1, 2, 5 and 10 mol% La). The addition of La dopant into the BNT structure caused lattice distortion and altered the crystal symmetry of the BNT from hexagonal to tetragonal symmetry for BNLT. BNT and BNLT pellets were sintered at 1100°C for 3 hours and pure perovskite phase BNT was obtained with the addition of La up to 5 mol%. A secondary phase of Bi2(Ti2O7) appeared when the pellet was doped with 10 mol% of La dopant. Increasing of La dopant in the pellet resulted in the increasing of dielectric constant and decreasing of dielectric loss. An optimum property was obtained by 5 mol% BNLT with dielectric constant of 753 and dielectric loss of 0.0377. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

SMEM Algorithm Is Not Fully Compatible with Maximum-Likelihood Framework

The expectation-maximization (EM) algorithm with split-and-merge operations (SMEM algorithm) proposed by Ueda, Nakano, Ghahramani, and Hinton (2000) is a nonlocal searching method, applicable to mixture models, for relaxing the local optimum property of the EM algorithm. In this article, we point out that the SMEM algorithm uses the acceptance-rejection evaluation method, which may pick up a distribution with smaller likelihood, and demonstrate that an increase in likelihood can then be guaranteed only by comparing log likelihoods.