Integral scaling behavior of different morphologies of 3D xenon crystals

Three-dimensional crystals have been observed in situ during the growth from supercooled melt. Depending on growth conditions three crystal morphologies were formed: dendrites, doublons and seaweed. Fractal dimensions of contour and area have been determined using correlation and box dimension techniques. Algorithms have been developed on the basis of fractal geometry to extract quantities from contour and area of projections of a crystal to characterise the crystal morphology. A method is presented to find hidden length scales in apparently scale invariant physical systems. We show that intrinsic length scales found by this method can be used to characterise morphologies of xenon crystals. It is shown that scaling relations by conventional tools of fractal geometry omit important intrinsical behavior and provide only averaged quantities.