Interferometric Tomography Measurement of the Temperature Field in the Vicinity of a Dendritic Crystal Growing from a Supercooled Melt

The shape of a crystal growing from a supercooled pure melt is influenced by the temperature-dependent kinetics of the nucleation on the interface. In the course of this growth, heat is released from the interface, thus feeding back on the temperature field. In this intrinsically nonlinear process, the three-dimensional temperature field in the fluid is a vital dynamic parameter which has not been previously measured. This can be done with the aid of multi-directional interferometry, using the temperature dependence of the refractive index of the melt. If the growth regime lies in the path of one of the interferometer beams, a phase shift, proportional to the integrated refractive index change, is observed. To measure the three-dimensional field of the refractive index requires some form of tomographic reconstruction. We built an apparatus that includes a crystal growing cell which is viewed by four Mach-Zehnder interferometers. The interferograms are analyzed by Fourier fringe analysis, and the field is reconstructed by the algebraic reconstruction technique (ART), an algorithm which has been shown by Verhoeven to be suitable for limited data tomography. Measured temperature fields around growing crystals of heavy ice (D2O) and succinonitrile are presented. Internal self-consistency of the field magnitudes is demonstrated, without the need for adjustable parameters. 1,2,34,5,6,7