Kinetic Modeling of LTCC Shrinkage: Effect of Alumina Content

Abstract

We studied sintering of LTCC-type glass matrix composites (GMCs) consisting of small glass and alumina particles of equal size. Primarily, crystals act as rigid inclusions, decelerating the densification rate. In later stages, they also dissolve, partially increasing the viscosity. Release of alumina finally induces crystallization of alumosilicates, which enables post-firing stability. To study both effects, two model GMCs were prepared: an α-Al2O3 + barium alumoborosilicate glass (BABS)–GMC, which shows neither significant dissolution nor crystallization, and an α-Al2O3 + calcium alumoborosilicate glass (CABS)–GMC, which dissolves readily and promotes crystallization. The kinetics of shrinkage for both GMC were modeled by utilizing Frenkel theory for the early stage and Mackenzie–Shuttleworth theory for the late stage, assuming that sintering is superimposed by the weighted contributions of triparticle glass–crystal clusters, their random occurrence (ideal mixing), and a shrinkage rate controlled by the GMC effective viscosity. In agreement with modeling, the experimental results showed that the shrinkage rate of BABS–GMC decreases progressively for crystal volume fractions Φ > 0.15. The attainable shrinkage is reduced by up to 8% for Φ = 0.45. For the CABS–GMC with Φ = 0.25, a reduction of Φ to 0.20 was evident due to partial α-Al2O3 dissolution. This effect was found able to increase the sintering temperature by ~50–60 K.