Reglamento del Seguro General de Riesgos del Trabajo:

Efficient evaporation of the filament constituents reduces the measurement time and enhances the precision of the mobility measurements in consequence of pressure and temperature variations with time. The easiest way to achieve this goal is to increase the filament temperature, which possibly causes unwanted charge transfer reactions as mentioned before. Additionally, higher filament temperatures facilitate surface ioniza- tion [138, 139], which is usually very well described by the so-called Saha-Langmuir equation [140, 141]

n+

n0

= (g+/g0) exp [(eϕ−IP)/kBT], (7.5)

wheren+, n0 are the flux of ions and atoms, respectively, g+ and g0 are the statistical weights of the ionic and atomic states,eϕis the work function as discussed in Ref. [142],

IP is the first ionization potential of the atom (in eV) and T is the equilibrium tem- perature of the system, which may be set equal to the filament temperatureTF il. Since

the work functions of the lanthanide atoms [143] are smaller than their corresponding ionization potentials [144], the thermionic emission saturates at extremely high tem- peratures according to Eq. (7.5). Thermionic emission decreases the amount of neutral atoms within the ionization volume and leads to higher background in the ATDs, as can be inferred from Fig.7.3 (6) and (7). For instance, the first ionization potential of holmium is 6.02 eV [62, 144] and the work function of a hexagonal closed packed Ho- crystal may be taken equal to 4.37 eV [143]. The expected Ho+ _{flux is about 1.5·10}−7_% of the overall flux of evaporated Ho atoms atTF il = 1220 K assuming (g+/g0) = 1. The calculated ratio may appear negligibly small, during the mobility measurements of Gd or Tb, however, it may create a perturbing background in the time spectra due to the low vapor pressure of the latter elements compared with the one of holmium.

One should note that thermionic emission is not correlated with the laser pulsing, such that sample ions produced by surface ionization phenomena are randomly regis- tered during each measurement cycle. During the systematic mobility measurements, thermionic emission has been efficiently suppressed by manipulating suitable filament strips as described in Sect.7.1.2.

8 Ion mobility measurements in the

lanthanide region

In this chapter, the outcome of the experiments and the method used in this work to extract the ion mobility data for certain lanthanide elements is presented. The exper- imental results are then discussed on the basis of the mobilities calculated according to the rigid-sphere model, the polarization-limit model and the model involving the ion-atom interaction potentials presented in chapter2. Special emphasis will be placed on the influence of the electronic configuration of valence electrons on the mobility data.

8.1 Experimental results

Different multi-filaments have been used during the mobility experiments. Depending on the evaporation characteristics of the investigated lanthanides, the following element combinations have proven to be very well suited: (I) Ho in conjunction with Er, (II) Ho with Gd and Tb, (III) Ho together with Eu, Yb and Er and (IV) Ho with Gd. Dysprosium could not be investigated in the presence of Gd and has been omitted from the following mobility measurements.

All the results presented here are carried out using a laser beam of 1-3 mm diameter, depending on the vapor pressure of the constituents under consideration. The latter depends on the filament temperature, which has been varied in the range between 950◦_{C and 980}◦_{C for filaments containing gadolinium or terbium and between 800}◦_C

and 860 ◦_{C otherwise. The position of the ionization volume could not be reproduced}

exactly for the different multi-filaments such that only ATDs of the same multi-filament measured in one run may be directly compared to each other. Figure 8.1 shows the arrival time distributions of Gd+_{, Tb}+ _{and Ho}+ _{measured using a Gd-Tb-Ho multi-} filament. The time elapsed between the sequentially performed measurements is about 3 minutes, which is just sufficient to adjust the proper excitation wavelength provided by the dye laser. All elements are ionized via the two-step photoionization processes described in Sect. 3.2 using laser beams of different diameters (1-3 mm). Obviously, Gd+ _{ions need ca. 3 ms more time to get extracted from the drift cell compared with} Ho+ _{and Tb}+_{, which are detected almost at the same time. According to Fig. 8.1,} gadolinium definitely exhibits a larger collision integral Ω(1,1) _{than holmium and ter-} bium. Furthermore, it can be clearly discriminated in time from the other two elements using the IMS apparatus presented in this work.

As mentioned before, lanthanide molecules are much larger in size than their monoatomic ions. This means that their discrimination in time would not be a big challenge. Figure 8.2, for instance, shows the time spectra of Er+ _{and Ho}+ _{and their} corresponding oxide ions obtained while working with an Er-Ho multi-filament. Un- like the atoms, which are ionized via the element selective two-step photoionization process, the oxides are non-resonantly ionized using exclusively the UV light of the excimer laser. In this case the beam diameter amounts to 10 mm. This method is less efficient compared with the two-step photoionization process such that less events are registered in the oxide spectra. In case of low statistics, fit routines may fail to mimic the time spectra resulting in larger uncertainties of the ATD means. In general, increasing the measurement time would result in smaller uncertainties, but due to the pressure effects described in Sect. 6.3.2, broadened peaks will result for extended mea- surement periods. Nevertheless, in certain time spectra like the one shown in Fig. 8.2, good fits of the line shapes could be obtained using Gaussian fit functions. The time differences between the monoatomic ions and their oxides are about 5.6 ms and 6.2 ms for Er and Ho, respectively. This plot demonstrates the ability of the ion mobility

Figure 8.1: ATDs of Gd+_{(•), Tb}+₍

F) and Ho+(O) measured using a Gd-Tb-Ho multi-

filament at an argon pressure of 40.4 mbar (E/n = 1.8 Td) and a filament temperature ofTF il = 1220(20) K. The measurement time amounts to 300 s,

200 s and 40 s for Gd+_{, Tb}+_{and Ho}+_{, respectively, whereas all these spectra}

are measured within 15 minutes. The solid lines are Gaussian fits of the obtained spectra, which deliver the following ATD means: hta

¡ Gd+¢_{i =} (37.269 ±0.012) ms, hta ¡ Tb+¢i = (34.444 ±0.009) ms and hta ¡ Ho+¢_{i =} (34.310±0.019) ms.

Chapter 8: Ion mobility measurements in the lanthanide region 91

Figure 8.2: ATDs of Ho+ _{(◦), Er}+ _{(M), HoO}+ _{(2) and ErO}+ ₍

F) measured using an

Er-Ho multi-filament at an argon pressure of 40.6 mbar (E/n = 1.8 Td). In contrast to monoatomic ions, the oxides are ionized using exclusively the UV light of the excimer laser. The solid lines are Gaussian fits of the obtained spectra, which deliver the following ATD means: hta

¡ Ho+¢i = (35.291 ± 0.014) ms, hta ¡ Er+¢_{i = (35.229 ± 0.010) ms, ht} a ¡ HoO+¢_{i =} (41.488±0.027) ms and hta ¡ ErO+¢_{i= (40.782±0.017) ms.}

spectrometer to distinguish between the singly charged oxides of both elements, which actually implies the well-known bond length contraction [17] of lanthanides. The time difference between the two oxide peaks is about 706µs, which is quite significant and cannot be explained only by systematic errors, in particular because the measurements are performed in a sequential manner within 30 minutes at a constant buffer gas pres- sure. The tailing on the right hand side of the oxide peaks is probably caused by large and slow molecular ions that dissociate to give oxide ions within the supersonic gas jet inside the extraction chamber. The time difference between the holmium peaks in Fig. 8.1 and Fig. 8.2 is a consequence of modified experimental conditions, especially variations of the buffer gas pressure and of the position of the ionization volume with respect to the filament and to the electrode system of the drift cell.

According to Eq. 3.1, the mean drift time htdi is obtained by subtracting the mean

transit time htti = (182±12)µs (see Sect. 6.4) from the arrival time mean htai. Due

to the fact that the drift time is a linear function of the pressure as well as of the drift distance, one may normalize all means htd(X+)i of singly charged ions X+ to a

Figure 8.3: Normalized drift time means htdi∗ of some singly charged lanthanides. All

the means presented here correspond to an argon pressure of (Pref_cell = 40.97±

0.15) mbar (E/n= 1.8 Td), to a gas temperature of 300 K and to a starting position of (y, z) = (5 mm,5 mm) as shown in Fig. 6.10, which results in a drift distance of dref_d = (316±1) mm.

reference mean drift time of Ho+ _{according to}

htd(X+)i∗ =

htd(Ho+ref)i htd(Ho+)i

· htd(X+)i, (8.1)

where htd(Ho+_ref)i is the mean drift time of a reference time spectrum of holmium

measured at a certain buffer gas pressure Pref_cell and a certain drift distance dref_d . The value htd(X+)i and htd(Ho+)i is the mean drift time of the considered ion species

and of a corresponding holmium ion measured in one run under the same conditions, respectively. The normalized mean drift time of the sample ion is denoted byhtd(X+)i∗.

The result of such a normalization is shown in Fig. 8.3 and Fig. 8.4. The error bars shown in these figures result from the error propagation due to the normalization given by Eq. (8.1) and denote one sigma uncertainties of the htdi∗ _{values. The overlapping}

data markers in Fig. 8.3 imply the reproducibility of the mean values after normaliza- tion. The reproducibility of the results is within 0.3% even though slightly different conditions prevailed during the measurement runs. The mismatch of the data at erbium (Fig.8.3) could not be explained yet. The drift of the ions in the vicinity of the filament may introduce systematic errors due to e.g. field inhomogeneities prevailing there. Fur- thermore, the ion mobility depends also on the gas temperature T [2, 145, 146], such that variations of T near the filament may contribute to systematic errors, too. In

Chapter 8: Ion mobility measurements in the lanthanide region 93

Figure 8.4: Normalized drift time meanshtdi∗ of some singly charged lanthanide oxides

(same conditions as in Fig. 8.3). The means decrease as going to heavier monoxides, which nicely reflects the bond length contraction at the lan- thanides [17].

this work, the gas is assumed to be in a thermal equilibrium because a drastic increase of the gas temperature is expected only within the ionization volume and has been neglected so far. Also a dense vapor of the sample atoms may influence the mobility of the ions above the filament in a sense that ions do not drift in a pure buffer gas as required. Such an influence have not been considered in this work due to the fact that the ionization volume is located axially≈5 mm away from the tip of the filament, where the density of the vapor of sample atoms is drastically reduced, see Fig.6.10(a). If such systematic errors strongly influence the time spectra, then they are expected to produce similar variations in the normalized means, which is definitely not the case as can be seen in Fig. 8.3.

Noteworthy in this figure is that most investigated lanthanide ions show nearly equal drift time means. The only exception is Gd+_{with significantly largerhtdi}∗_{values, which}

actually indicate an increased collision cross section of the latter ion with respect to the other element ions. Also within the oxides, GdO+ _{exhibits a larger drift time} mean compared with that of TbO+ _{and ErO}+ _{as shown in Fig. 8.4, resulting in a} continuous decrease of htdi∗ as going to heavier monoxides. A detailed discussion of

the experimental results is provided in Sect. 8.3.

Table 8.1 summarizes the drift time texp_d of the investigated ion species, which is just an arithmetic mean of the corresponding htdi∗ _{values shown in Fig. 8.3 and Fig. 8.4.}

The errors indicated in this table are classified into systematic (sys) and statistical

(stat) errors, in order to emphasize the precision of the measurements. In the statistical

errors, both the propagation of the errors due to Eq. (8.1) as well as the deviation of the arithmetic means are considered. The systematic errors concern the accuracy of the

Table 8.1: Drift time of the investigated ions at an argon pressure of (Pref_cell = 40.97±

0.15) mbar (E/n= 1.8 Td,E = 17.9 V,dref_d = (316±1) mm). ion 151_Eu+ 156_Gd+

texp_d [ms] 33.84 (±0.03)stat(±0.13)sys 36.83 (±0.03)stat(±0.15)sys

ion 159_Tb+ 165_Ho+

texp_d [ms] 34.02 (±0.04)stat(±0.13)sys 33.91 (±0.02)stat(±0.13)sys

ion 168_Er+ 174_Yb+

texp_d [ms] 33.93 (±0.08)stat(±0.13)sys 33.95 (±0.03)stat(±0.13)sys

ion GdO+ _{(m= 172 u) HoO}+ _{(m = 181 u)}

texp_d [ms] 40.36 (±0.07)stat(±0.16)sys 39.90 (±0.04)stat(±0.16)sys

ion ErO+ _{(m = 184 u)}

texp_d [ms] 39.22 (±0.04)stat(±0.16)sys

results and are mainly determined by the uncertainty of the pressure values measured by the capacitance gauge. The variation in the operating temperature of the gauge is 1 ◦_{C at most, such that the relative error of the pressure is equal to 0.37% [147] at}

41 mbar argon. Moreover, the drift of the buffer gas pressure with time (see the left plot of Fig. 6.7) results in time differences between the ATD peaks of the sample ions within a single run lasting for about 10 min. Such tiny pressure variations remained unresolved during the experimental runs. They cause additional systematic errors in the order of 0.03% (see Sect. 6.3.2).