Adiabatic Cooling in Supersonic Beams

For molecules the line densities are much higher, and often the rotational structure can only be resolved by sub-Doppler spectroscopy. Limiting the collimation angle of the molecular beam below 2 x 10 rad, the residual Doppler width can be reduced to values below 500 kHz. Such high-resolution spectra with linewidths of less than 150 KHz could be, for instance, achieved in a molecular iodine beam since the residual Doppler width of the heavy I2 molecules, which is proportional to is already below this value for a 

More examples of sub-Doppler spectroscopy in atomic or molecular beams can be found in reviews on this field by Jacquinot [9.11], and Lange et al. [9.12], in the two-volume edition on molecular beams by Scoles [9.13], as well as in [9.14-9.17]. 

The total energy of a mole with mass M is the sum of the internal energy U = f/trans + rot + Uyib of a gas volume at rest in the reservoir, its potential energy / V, and the kinetic-flow energy of the gas expanding 

If the mass flow dM/dt through A is small compared to the total mass of the gas in the reservoir, we can assume thermal equilibrium inside the reservoir, which implies uq = 0. Since the gas expands into the vacuum chamber, the pressure after the expansion is small (p po). Therefore we may approx- 

This equation illustrates that a cold beam with small internal energy U is obtained, if most of the initial energy Uo po o is converted into kinetic-flow energy Mu. The flow velocity u may exceed the local velocity of sound c(/7, T), In this case a supersonic beam is produced. In the limiting case of total conversion we would expect U = 0, which means T = 0, We will later discuss several reasons why this ideal case cannot be reached in reality. 

For effusive beams discussed in the previous section, the pressure in the resevoir is so low that the mean-free path A of the molecules is large compared with the diameter a of the hole A. This implies that collisions during 

The decrease of the internal energy means also a decrease of the relative velocities of the molecules. In a microscopic model this may be understood as follows (Fig.9.8) During the expansion the faster molecules collide with slower ones flying ahead and transfer kinetic energy. 

The energy-transfer rate decreases with decreasing relative velocity and decreasing density and is therefore important only during the first stage of the expansion. Head-on collisions with impact parameter zero narrow the velocity distribution n(v ) of velocity components V = v parallel to the flow velocity u in the z-direction. This results in a modified Maxwellian distribution 

The energy transfer rate decreases with decreasing relative velocity and decreasing density and is therefore important only during the first stage of the expan- 

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Fig. 4.14 Energy transfer diagram for adiabatic cooling in supersonic molecular beams...

There are several aspects of laser spectroscopy performed with molecular beams that have contributed to the success of these combined techniques. First, the spectral resolution of absorption and fluorescence spectra can be increased by using collimated molecular beams with reduced transverse velocity components (Sect. 4.1). Second, the internal cooling of molecules during the adiabatic expansion of supersonic beams compresses their population distribution into the lowest vibrational-rotational levels. This greatly reduces the number of absorbing levels and results in a drastic simplification of the absorption spectrum (Sect. 4.2). 

In ICP-MS (Fig. 112) the ions formed in the ICP are extracted with the aid of a conical water-cooled sampler into the first vacuum stage where a pressure of a few mbar is maintained. A supersonic beam is formed and a number of collision processes take place as well as an adiabatic expansion. A fraction is sampled from this beam through the conical skimmer placed a few cm away from the sampler. Behind the skimmer, ion lenses focus the ion beam now entering a vacuum of 10-5. This was originally done with the aid of oil diffusion pumps or cryopumps, respectively, but very quickly all manufacturers switched to turbomolecular pumps backed by roughing pumps. 

As well as producing higher beam intensities, the supersonic nozzle sources have a further advantage. In the supersonic expansion through the Laval slit the gas is adiabatically cooled to very low temperatures of ca. 40°K [187] but increases its translational energy in the beam direction to the flow velocity of the gas, e.g. Mach number ca. 15 or peak velocity 70% higher than the most probable velocity of a 900°K oven [187]. Supersonic nozzles produce very narrow velocity distributions compared with the Maxwell—Boltzmann distribution obtainable from an effusive oven at the same temperature. 

An elegant technique for studying van der Waals complexes at low temperatures was developed by Toennies and coworkers [442]. A beam of large He clusters (lO -lO He atoms) passes through a region with a sufficient vapor pressure of atoms or molecules. The He droplets pick up a molecule which either sticks to the surface or diffuses into the central part of the droplet, where it is cooled down to a low temperature of 100 mK up to a few Kelvin (see Fig. 4.22). Since the interaction with the He atoms is very small, the spectrum of this trapped molecule does not differ much from that of a free cold molecule. However, unlike cooling during the adiabatic expansion of a supersonic jet, where Tyib > Trot > Ttrans in this case Trot = Tyib = Thc [443 45]. This implies that all molecules are at their lowest vibration-rotational levels and the absorption spectrum becomes considerably simplified. 

Techniques which are based on the supersonic expansion of a non condensable buffer gas do not suffer from this problem. They have been widely used in experimental science, for example in the first attempt to liquefy gases or, much more recently, as a source of cold molecules for spectroscopy (see the chapter by Davis et al.) or of molecular beams for collision dynamics studies. Cooling arises from conservation of energy which implies, that for a gas flow under adiabatic conditions, the sum of specific enthalpy and kinetic energy remains constant during the expansion. For a perfect gas with a constant specific heat capacity Cp and with a well defined temperature, the energy conversion is driven by the following equation ... 

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