Dunbar P. Birnie

Crystallization kinetics and the JMAK equation

Abstract In the present work the application of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory for the calculation of the volume fraction crystallized is discussed for several particular cases of isothermal transformations. In particular, the following three situations, for which the JMAK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and (3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle formation, finite size effects and non-uniform nucleation lead to a reduction of the crystallization rate. Furthermore, transformations which produce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK t4 law arising from time dependent nucleation must include size-dependent growth effects to obtain a logically consistent result.

Rational solvent selection strategies to combat striation formation during spin coating of thin films

Striation defects in spin-coated thin films are a result of unfavorable capillary forces that develop due to the physical processes commonly involved in the spin-coating technique. Solvent evaporation during spinning causes depletion at the surface of the more volatile solution components while simultaneous viscous out-flow occurs providing the main source of solution thickness reduction during any typical spinning run. The composition changes in the surface layer can either stabilize or destabilize the surface with respect to convective motions within the coating solution. Destabilization (and therefore possible striation formation) happens when the surface composition changes so that a larger surface tension will develop. Thus, a careful cross-referencing of solvent volatility with surface tension effects can help establish solution conditions that will prevent this instability from arising. A plot of solvent vapor pressure ( P v ) versus solvent surface tension (σ) is introduced and utilized to help discuss the impact of solvent choice when making coatings via spin coating. One important result is that when desiring to deposit a coating having a surface tension of σ solid , then it is favorable to use a fully miscible solvent that has a higher surface tension (i.e., σ liquid > σ solid ). More complicated solution mixtures were also examined, including dual-solvent systems and water-containing systems.

Combined flow and evaporation of fluid on a spinning disk

Fluid flow and fluid evaporation both contribute to the overall rate of thinning during spinning of a fluid on a disk. Laser interferometry of solvent thinning behavior on spinning silicon wafers was performed to yield plots of solvent thickness evolution. These plots of thickness versus time were then analyzed to understand the respective contributions of viscous flow and evaporation to the thinning. A technique is described for extracting both the viscosity and the evaporation rate from the interference data. Well understood solvent systems are examined as test cases for this deconvolution. It is also demonstrated that nonevaporating fluids can be analyzed, even though their thickness evolution has no easily referenced endpoint to the thinning, in contrast to the volatile solvents which are rapidly spun dry.

Kinetics of transformation for anisotropic particles including shielding effects

A derivation is presented for X(t), the transformed fraction as a function of time, in a phase transformation process which produces randomly oriented anisotropic particles. The key novel element in the development and results is the inclusion of blocking (shielding) effects. The derivation is performed for a 2D system in which symmetrical particles of arbitrary shape are formed. In addition, approximate calculations are performed for X(t) for the case of elliptical particles in order to estimate the influence of growth rate anisotropy upon the magnitude of the blocking effects.

Total-dose radiation effects on sol-gel derived PZT thin films

Sol-gel derived PZT (lead zirconate-titanate) thin films were irradiated to a total-dose of 1 Mrad(Si) or 86 krad(PZT) under open-circuit bias. An asymmetric distortion in the hysteresis curves was observed. The distortion depends on the polarization state of the capacitor before irradiation. Postirradiation electrical cycling makes the hysteresis loops symmetric initially, but results in fatigue effects. The leakage and switching current behavior after irradiation and post-rad cycling were studied using a static current versus voltage measurement. Retention and fatigue properties are not worsened after irradiation except for the polarization reduction. The radiation effects are consistent with the sheet charge model. The fatigue effects due to post-rad cycling are consistent with an increase in the space-charge regions near the electrodes or oxygen-deficient dendrite growth. >

Avrami exponents for transformations producing anisotropic particles

Abstract The behavior of Avrami exponents (AE) for systems which produce anisotropic particles (for which shielding effects and phantoms occur) is examined. Probabilistic arguments used in previous studies are applied to derive expressions for the AE as a function of time or the extent of transformation. Numerical calculations for the one dimensional (ID) cases of site saturation and continuous nucleation show that blocking effects produce a minimum in plots of AE versus extent of transformation. The influence of growth rate anisotropy upon the magnitude of the reduction in the AE is also examined and certain features of the behavior of the AE for 2D and 3D systems are discussed.

Domain switching and spatial dependence of permittivity in ferroelectric thin films

A domain model consistent with the measured capacitance–voltage (CV) characteristics of lead zirconate titanate (PZT) capacitors is proposed. Two variants of this model are presented and compared with experimentally measured CV data. The basic model is developed adopting a macroscopic electric field that is spatially uniform through the depth of the film. Then, this model is generalized to allow a variation of the electric field with depth and to include a physically reasonable, position-dependent domain structure. Specifically, the spatial variation of the electric field is related to dopant–ion charges. As a result of the interaction between the domain properties and the electrical doping, a position dependent permittivity is induced, and the electrical properties of the capacitors are affected. Finally, computer simulations to fit the measured CV characteristics are performed to help understand the extent of the coupling between the domain properties and the electrical doping. It is found that there is...

STRUCTURAL INVESTIGATION OF BA6-3XLN8+2XTI18O54 (X = 0.27, LN = SM) BY SINGLE CRYSTAL X-RAY DIFFRACTION IN SPACE GROUP PNMA (NO. 62)

Single crystals of barium samarium titanium oxide Ba 6−3 x Sm 8+2 x Ti 18 O 54 ( x = 0.27) have been synthesized and studied using x-ray diffraction. Superstructure reflections, which cause a doubling of the cell along the short axis, were taken into account and the refinement was conducted in the orthorhombic space group Pnma . Unit cell parameters from single crystal x-ray diffraction were a = 22.289(1), b = 7.642(1), and c = 12.133(1) A. Refinement on F resulted in R1 = 5.37% for 1410 F o > 4σ with the thermal parameters of the Sm and Ba atoms refined anisotropically and the thermal parameters of the Ti and O atoms refined isotropically. The structure is made up of a network of corner sharing TiO 6 −2 octahedra creating rhombic (perovskite-like) and pentagonal channels. The two pentagonal channels are fully occupied by Ba atoms. The refinement suggests that one rhombic channel is fully occupied by Sm atoms (Sm3/Sm4), one rhombic channel is partially occupied by Sm atoms (100% Sm1/86.25% Sm5), and one rhombic channel is shared by BaySm atoms (59.25% Ba3/40.75% Sm2), resulting in a formula of Ba 10.38 Sm 17.08 Ti 36 O 108 with Z = 1. The above site occupancies differ from the site occupancies previously reported in the literature for refinements conducted with the short axis approximately equal to 3.8 A.

Effect of solvent evaporation rate on skin formation during spin coating of complex solutions

Spin coating can often be used to create highly uniform coating son flat substrates using sol-gels and other precursor solutions. Typically, fluid flow considerations dominate the early part of spinning while solvent evaporation controls the behavior at later stages. However, even though evaporation does not control the early stage, it is still occurring throughout the entire process and evaporation-related issues can arise during the flow- dominated stage that may ultimately become coating thickness non-uniformities in the final product. Striation defect formation is a good example of this. During the spin coating process the evaporation of solvent takes place at the top surface of the flowing fluid, thus a concentration profile for the solute specs will exist within the flowing solution. Since the solute species in sol-gel solutions are often prone to condensation or cross-linking reactions, it is possible for this top surface to experience a rapid increase in viscosity and potentially to act as a barrier to further evaporation. This top layer could be equivalent to the skin layer on drying paint.

Esterification kinetics in titanium isopropoxide-acetic acid solutions

FTIR observation has been used to analyze the reaction between titanium isopropoxide and acetic acid under a variety of conditions. Isopropyl acetate ester forms in these mixtures and serves as an indicator of the extent of condensation between the titanium precursors. Condensation occurs to a gradually increasing extent to form a broad spectrum of titanium oxo-acetate polymers. The temperature dependence of the time to reach observable precipitation in these solutions has also been mapped out. The activation energy for this process was found to be 0.7 eV. The precipitation times have a direct bearing on how these solutions can be used when making a wide variety of titanium containing sol-gel solutions.