Semi-empirical model for axial segregation in metal-halide lamps

Abstract

Diffusive and convective processes in the metal-halide lamp cause an unwanted non-uniform distribution of the radiating metal additive (Dy in our case), which results in colour separation. The axial segregation has been described by Fischer (1976 J. Appl. Phys. 47 2954) for infinitely long lamps with a constant axis temperature. However, for our lamps this is not valid. We propose a semi-empirical extended model. The density inhomogeneity gives a measure for the non-uniformity of the Dy density distribution in the lamp. As an example, this parameter is calculated for some measurements obtained by imaging laser absorption spectroscopy.

Emission spectroscopy for characterizing metal-halide lamps

“…We use the axial inhomogeneity Figure 1. The Fischer curve shows the axial segregation as a function of the ratio between the convection and diffusion speeds [16][17][18]22]. In our case the amount of convection is changed by changing the gravitational acceleration.…”

“…We want to have a measure for the axial non-uniformity of the light output for different particles in the lamp. In [17] the inhomogeneity parameter α has been introduced. In most cases the square of the inhomogeneity (α 2 ) follows the same trend as the Fischer parameter, which describes the amount of axial segregation.…”

“…The intensity is affected by temperature stronger than the absolute number density, due to the temperature dependence of the highly excited states, causing a stronger temperature effect in the axial inhomogeneity parameter. For further explanation on the axial temperature gradient the reader is referred to literature [17].…”

“…For lamp Q4 (6 mg Hg) the maximum axial intensity inhomogeneity is around 2g. Lamp Q5 contains 12 mg Hg and has therefore a higher convection speed (v ∼ p Hg ) [17,13,37], increasing the ratio between convection and diffusion speeds. This explains that we are more at the right-hand side of the Fischer curve (figure 1) for this lamp Q5.…”

“…The Fischer model is valid for infinitely long lamps with a constant axial temperature profile only. This is not the case for our lamps and therefore a semi-empirical extended model has been proposed for our lamps [17]. The model takes the temperature gradient along the lamp axis into account and is valid for atomic Dy, whereas the Fischer model is valid for the elemental Dy density.…”