Free Evaporation
The vapor pressure which corresponds to each temperature from 600 to 1200 °C was derived from [9, 10]
As discussed in the above, the maximum evaporation rate under the perfect vacuum condition is defined by the Langmuir Eq. (1).
For the initial 100 g of Ga in the crucible, the radius of circular liquid surface calculated from the taper of the crucible shown in Fig. 1 is 0.948 cm and surface area of the Ga melt is 2.82 cm^{2}. As the crucible is tilted to 26° vertically in the MBE, the surface area of Ga melts increases to 3.14 cm^{2}. Using these values, the evaporation rate of Ga from 800 to 1400 K is shown in Fig. 2. The amount of Ga evaporated can be obtained from Langmuir equation by multiplying surface area of Ga melt that faces with the vapor phase and evaporation time (16 h for distillation and 400 h for growth). These are listed in Table 1 for the distillation and growth steps.
As shown in Table 1, a total of 67.9 g of Ga was lost with the majority being during the distillation step. This is because Ga saturation vapor pressure in distillation is two orders higher than that in growth. Clearly, free evaporation using the Langmuir equation overestimates the Ga loss.
Fig. 2 Maximum evaporation rate of Ga as a function of temperature
Table 1 Maximum evaporation rate and evaporated amount of Ga for distillation and growth
Time (h) 
Temperature (K) 
Ga saturation vapor pressure (atm) 
Evaporation rate (kg/m^{2} • h) 
Evaporated Ga amount (g) 

Distillation 
16 
1360 
4.50E05 
9.12E02 
45.8 
Growth 
400 
1160 
2.52E07 
1.76E03 
22.1 