|Analysis of scale-invariant properties in experimentally grown morphologies of diffusion limited growth in 3 dimensions|
|Donnerstag 27 Mai 2004 , 09h00|
We investigate in our in situ experiments three-dimensional xenon crystals during free growth into pure supercooled melt. Supercooling is the only control parameter of the system and determines the morphology of the crystal. Dendritic, seaweed and doublon morphologies have been observed. Characteristic parameters of dendrites and doublons were deduced from experimental data and compared with theoretical predictions and simulations of 2D and 3D phase field models. We present a morphology diagram based on our simulations and our experimental results. Fractal dimensions (contour and area) have been determined by correlation method and an optimized box-counting algorithm. We present a technique to detect integral hidden length scales in experimental structures and find these length scales to depend on morphology. We present a method of reconstructing the three-dimensional shape of an experimentally grown xenon dendrite based on a hybrid approach of sophisticated image processing and measured parameters of dendrites. The reconstruction is quantitative and reveals more details as conventional techniques. A quantitative investigation of the dendrite surface and volume shows in both cases a power law dependence on distance from the tip and temporal evolution. Three-dimensional doublons are studied experimentally and are reconstructed. A hyperbolic dependence of the width of the growth channel on supercooling is found. The temporal evolution of doublons and the relaxtion to dendritic growth is analyzed and quantitatively reconstructed.