A silica glass arc tube was fabricated from a straight sil-

ica glass tube (GE quartz, GE214). The straight tube was heated by an oxygen-hydrogen burner and expanded by controlling the flow of N₂ gas inside of it, as shown in Figure 2.

Samples for the investigation of T_f and structural relaxation in the arc tube were prepared as follows. Samples for investigating the inner and outer surfaces were prepared by cutting 10 mm × 10 mm × 2 mm sections from the tubes (dark gray area in figure). Samples for investigating the inner bulk region were prepared by optical polishing of the cut surfaces to remove the hatched area shown in the figure. The final size of these samples was 10 mm × 10 mm × 0.5 mm. To investigate the depth profile of the OH concentration, 0.5 mm-thick rings were cut from the region of maximum tube diameter, and the cut surfaces were prepared by optical polishing. Samples for investigating the straight tube were also prepared by the same fabrication process. The samples for investigating the inner and outer surfaces were 10 mm × 10 mm × 3 mm in size; those of the inner bulk region were 10 mm × 10 mm × 0.5 mm in size, and those used to measure the depth profile of OH concentration were 0.5 mm thick.

The depth profile of the OH concentration was measured by a microscopic Fourier transform infrared spectrophotometer (mFT-IR) (PerkinElmer, Spectrum 2000) with a 100 μm × 100 μm aperture in transmission mode. The IR spot was scanned at intervals of 100 μm from the inner surface to the outer surface of each sample. The OH concentration was calculated from the peak intensity of the absorption peak at around 3667 cm⁻¹ using an absorption coefficient of 77.5 L/(mol∙cm).

T_f near the surface was determined by measuring the IR reflection peak at around 1120 cm⁻¹ for an area of 150 μm × 150 μm at a resolution of ±10^{−2 cm−1} [7]. The penetration depth of the IR spot was about 100 nm. T_f was calculated from the IR peak position using the following relation [7,8]:

In the inner bulk region, T_f can be measured using the IR absorption peak at around 2260 cm⁻¹ [6]. A measuring spot 5 mm in diameter was used. T_f was determined using [6,7]:

Structural relaxation in the samples was investigated in two ways. First, the arc tube was annealed for 2 h at temperatures ranging from 800˚C to 1300˚C in 50˚C steps. The annealed sample was then quenched in water, and the change in T_f was determined by the IR method described above. Second, the strict structural relaxation time was investigated by determining the change in T_f during thermal annealing [3]. Thermal annealing, quenching, and IR peak measurement were repeated at a fixed temperature between 800˚C and 1300˚C. Measurements continued until a change in T_f was observed [3]. To determine the activation energy of the inner surface and inner bulk region, the structural relaxation time was investigated by measuring the change in T_f during thermal annealing. The relaxation behavior can be represented by the stretched exponential function [5],

where T_a is the annealing temperature, t is the annealing time, τ is the structural relaxation time, and β is the stretched exponential factor. The relaxation time τ was derived by fitting the data according to Equation (3). The activation energy E_a of the structural relaxation was calculated by

where k_B is the Boltzmann constant [3].

Figure 3 shows the OH concentrations for the straight tube and the arc tube. Differences in the OH concentrations can be seen near the surfaces of both samples. OH contamination of the arc tube occurred mainly on the outer surface because the oxygen-hydrogen burner was in direct contact with this surface during fabrication [5]. Consequently, the OH concentration on this surface was quite high, ~100 ppm, and the OH contamination penetrated to ~500 µm below the surface. The OH concentration of the arc tube also increased on the inner surface, although this was not in direct contact with the burner. The OH concentration on this surface, around 15 ppm, was not as high as that on the outer surface but could enhance the structural relaxation around the inner surface area.

The measured T_f values for the straight tube and the arc tube are shown in Figure 4. These values were lower for the inner and outer surfaces than for the inner bulk region in both tubes.

Figure 5 shows T_f as a function of the annealing temperature of the arc tube. At temperatures below 900˚C, T_f