Ceramic Microstructure-Property Fractal-Diffractal Calculus : Static Synergetics Yield Optimization During Processing Via Real–Time Q.A.and Interactive Q.C

ABSTRACTCeramic microstructure-property relationships dominate any and all attempts at“better ceramics through chemistry”. Required is some universal calculus to allow analytic, universal, reversible scalable computation of one from the other. Static Synergetics universality-principle provides such a flexible versatile tool, heretofore not available. It is a reexpression of the very basic three laws of thermodynamics into r-,k-,and w-domainsthe equivalence of(symmetry-breaking/defect) Pattern-recognition(the “structure”) to signal-processing(the frequency-dependent FM) properties/ Functions. More basically, it is a manifestation of Noether's theoremthe basis of mechanics and orgin of the energy continuity equation that is the thermodynamic first law. Such an algorithm, the”software”of yield optimization(quality and quantity) real-time Q.A. and(in parallel with a specificity dominated process- model)interactive Q.C.requires as “hardware”produced input the small-angle-scattering(SAS)dominated diffraction-pattern/static structure factor SSAS(k) or Fourier transform r-domain Pattern/ photomicrograph-recognition imaging(of processing-introduced property-detrimental defects(heterogeneity heirarchy)). Output are universal FM:I/f flicker(voltage and/or current)noise power spectrum, signal-to-noise ratio over dynamic rangemulti-level system dominated anomalous low temperature/frequency thermalracoustic. properties, and 1/f relaxation response susceptibility polarization catastrophe derived dielectric, electrical, optical, noise, viscoelastic/mechanicalmagnetic,...property Functions. Input can be the ubiquitous,...universal Mandelbrot fractals,dominating ceramics;output(and internal)Functions are Berry-Nye-Jakeman wdomain diffractals,dominating all properties universally.How and Why it works are detailed exactly;universality, reversibility and scalability are analytically insured for self-similar(or selfaffine) fractal scaling-relation Pattern-recognition input;approximate. deviations from universal Functions output obtains from less than perfect mathematically ideal fractal scaling-relation Pattern-recognition input.Static Synergetics provides a new practical use for external radiation small-angle-scattering(SAS) diffraction-pattern/static structure factor measurements in ceramic material microstructure-property relationships during processing