A procedure for the determination of the angles α̃e(re,h;pe) and α̃i(ri,h;pi) which appear in the nonlinear system of differential equations describing the dynamics of the outer and inner radii of a tube grown by the edge-defined film-fed growth (EFG) tec

In this paper, a procedure for the determination of the angles α̃e(re,h;pe)(α̃i(ri,h;pi)) between the tangent line to the outer free surface (inner free surface) of the meniscus at the three-phase point, of coordinates (re,h)((ri,h))(re,h)((ri,h)) and the horizontal axis ‘Or’ is presented. These functions appear in the system of differential equations which describe the evolution of the outer radius rere (inner radius riri) of a tube grown from the melt by the edge-defined film-fed growth (EFG) technique. These angles can fluctuate during the growth. The deviation of the tangent to the crystal outer (inner) free surface at the triple point from the vertical is the difference α̃e(re,h;pe)−(π2−αg), (α̃i(ri,h;pi)−(π2−αg)), where αgαg is the growth angle. The deviation can also fluctuate, and the outer (inner) radius rere(ri)(ri) is constant when the deviation is constant equal to zero.The knowledge of α̃e(re,h;pe), α̃i(ri,h;pi) is necessary for the analysis of the nonlinear system of differential equations describing the dynamics of the tube growth and for the determination of the interface height hh and of the outer and the inner radii rere, riri, respectively, of the tube to be grown with a given pulling rate vv in specified thermal and pressure conditions pepe, pipi. These kinds of result are useful in experiment planning and manufacturing technology design. Numerical results are given for a silicon tube.