Sintering constrained

Constrained sintering can be well described macroscopically by using continuum mechanics. If a powder compact is elastically isotropic and linearly viscous, the constitutive equations are written as 

In the case of thin film sintering the lateral constraint imposed by a rigid substrate allows a shrinkage only in the direction (z-direction) perpendicular to the film. The imposed constraint induces an in-plane tensile stress and the stress accelerates the shrinkage in the z-direction. From the lateral constraint Ex = Sy = 0, cr = 0, and cTx = cry = cr, and the expressions of the uniaxial strain rates in Eq. (5.33), the densification rate in the z-direction is expressed as 

This equation correlates the densification rate of a constrained film, Sz, with the densification rate of a free sintered body, e/, via the viscous Poisson s ratio, Vp. As the grain size is comparable to the thickness of a thin film, however, 

With a decreased particle size, what sintering mechanisms become relatively more important Why  

Consider two glass spheres in contact just below their melting point. Draw schematically their shape change and describe its kinetics with annealing time. No gravity effect is assumed. 

---

R.K. Bordia and A. Jagota, Crack growth and damage in constrained sintering films. J. Am. Ceram. Soc., 76 (1993) 2475-2485. 

Green DJ, Guillon O, Roedel J (2008) Constrained sintering a delicate balance of scales. 

Although assumptions of ideal material properties such as linear elasticity and isotropy were considered during simulations of the 3D reconstructed microstructures, the isotropy of the actual microstructures remained questioned. One of the factors responsible for the fact that the microstructures of the films could not possibly be ideally isotropic was that the films experienced constrained sintering which induced greater lateral shrinkage/densification across the direction normal to the surface than that in the other two directions which might result in non-identical... 

Fig. 11 A case of heavily constrained sintering, the porous powder compact is placed between the two rigid bodies which are fixed in space and can not deform. Perfect bounding at the interfaces and the plane strain condition are assumed.

Every system is constrained to some extent. For example, the sintering of a pure single-phase powder is constrained by inhomogeneities (such as agglomerates) present in the powder compact. However, the term constrained sintering is commonly taken to describe sintering in which the constraint is deliberately imposed and is a necessary feature of the system. An identical system in which the con-... 

Figure 11.13 Examples of constrained sintering (a) a composite in which inclusions prevent the powder matrix form sintering freely (b) an adherent thin film for which sintering in the plane of the film is inhibited by the substrate (c) a multilayer in which the layers sinter at different rates.

CONSTRAINED SINTERING II ADHERENT THIN FILMS AND MULTILAYERS... 

Crack Growth and Damage in Constrained Sintering of Films... 

Reactive hot pressing of a mixture of powdCTS has been used successfully to produce composites (69,70). Densification is more readily achieved in this case when compared to the reaction sintering process described in Chapto 11, and this is due to the enhanced driving force for densification as well as the ability of the applied pressure to break down unfavorable microstructural features produced by the reaction, such as particle-particle bridges that constrain sintering. 

Needes, C.R., Wang, C.B., Barker, M.F., Ollivier, P.T., Hang, K.W., Yong, C., and Souders, K.E., Constrained sintered LTCC materials systems for interconnects and packages, IMAPS Conference and Exhibition on Ceramic Interconnect Technology The Next Generation, Denver, CO, April 7-9, 2003. 

---