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Groot, I. M. N. (2009, December 10). The fight for a reactive site. Retrieved from https://hdl.handle.net/1887/14503
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Chapter 2
Experimental set-up and techniques
2.1 Ultra-high vacuum set-up
The study of surface science processes requires very well-defined conditions which can be achieved using an ultra-high vacuum (UHV) set-up. The experiments described in this thesis were carried out on such a system. The set-up connects a series of five chambers, which are individually pumped by turbomolecular pumps [1, 2]. A schematic picture is given in Figure 2.1. The system is equipped with an angle-integrating quadrupole mass spectrometer (QMS) in the main chamber, a differentially pumped QMS, a low-energy electron diffraction (LEED) apparatus, a sputter gun and a supersonic molecular beam. The main ultra-high vacuum chamber has a base pressure < 1×10−10mbar and contains the single crystal surface.
This sample is mounted on a manipulator allowing for rotational (360◦) and translational (x, y, z) movement. Cooling with liquid nitrogen and resistively heating the sample allows for temperature control between 80 and 1500 K.
The sample consists of a 10 mm diameter 3 mm (Ru(0001)) or 2 mm (Pt) thick single crystal, cut and polished within 0.1◦ of the desired plane (Surface Preparation Laboratory, Zaandam, the Netherlands). It is cleaned by repeated cycles of Ar+bombardment, annealing in O2 at 1200 K (Ru(0001)) or 900 K (Pt), followed by annealing at 1500 K (Ru(0001)) or 1200 K (Pt) to remove oxygen and restore surface order. Long range surface order is checked by LEED. The cleanliness of the surface is deduced from temperature programmed desorption (TPD) spectroscopy of H2, CO, NO and O2. TPD features are known to be very sensitive to impurities and cleanliness of steps [3–12].
A well-defined supersonic molecular beam is created by expansion of hydrogen from∼1- 4 atm through a 43 or 60 μm nozzle and subsequent collimation by a series of orifices and skimmers, into the ultra-high vacuum chamber. Details about the molecular beam line are given in Ref. [2]. The energy of the beam is controlled by the variable temperature of the nozzle (room temperature to 1700 K) and by seeding techniques. Deuterium molecules are accelerated by seeding them in H2 gas, while H2 and D2 can be decelerated by seeding in argon, nitrogen or helium (H2). The kinetic energy of H2 and D2 is determined for all expansion conditions by time-of-flight spectrometry (see Section 2.4). The initial reaction probability, S0, of H2 and D2 is determined using the King and Wells technique [13] (see Section 2.4).
31
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9
? @A
" 5 5
# 9
" 55
#
D EG
HIJK K NO P #R
S 5#
TUV
W XZ[ \]^__X`
abc
HIJK K NO
d ef
: 9
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j k
Figure 2.1: Schematic of the experimental set-up.
2.2 Molecular beam techniques 33
2.2 Molecular beam techniques
A molecular beam is a collimated source of gas molecules with a well-defined spatial distri- bution, particle flux and energy distribution among the internal degrees of freedom (trans- lational, vibrational, rotational and electronic). For a very extensive overview on molecular beams, see Refs. [14, 15]. In the experiments described in this thesis a supersonic molecular beam is used. In a supersonic molecular beam gas is expanded at high pressure (several atmospheres) through a small orifice (below 100 μm) into a low-pressure ambient back- ground [16]. Hence, a gas jet is formed in which the molecular velocity exceeds the speed of sound. The Maxwell-Boltzmann velocity distribution becomes strongly peaked and has a low temperature due to the cooling experienced by the gas upon expansion. The veloc- ity distribution can be described by a shifted Maxwell-Boltzmann distribution [17, 18] for a density sensitive detector:
S(v)∼ v2e−(v−v0α )2, (2.1)
where v0 is the flow velocity and α is a measure for the velocity spread. In an ideal supersonic molecular beam the electronic, vibrational and rotational degrees of freedom are all in the ground state. In reality, the hydrogen molecules used in our experiments are in the electronic ground state, but have a vibrational temperature equal to the nozzle temperature and a rotational temperature equal to ∼ 0.8Tn [19–21]. The fact that rotational cooling is poor in hydrogen beams causes the population of several excited rotational states, especially at higher nozzle temperatures. For an overview of the rotational and vibrational states populated in our beam, as obtained from calculated Boltzmann fractions, see Tables 2.1 and 2.2 in the appendix of this chapter.
In the supersonic molecular beam the accelerating flow can be approximated as an isen- tropic flow, with negligible viscous and heat conduction effects. The gas flow starts from a negligibly small velocity, called the stagnation state (P0, T0), and it accelerates, with an imposed pressure difference (P0− Pb) towards the nozzle exit. Here P0 is the initial pressure and Pb is the background pressure. The gas flow may reach sonic speed at the exit, provided the pressure ratio P0/Pb exceeds a critical value given by:
G≡ ((γ + 1)/2)γ−1γ . (2.2)
Here γ is the ratio between Cp and Cv, the heat capacities by constant pressure and volume.
This value G is <2.1 for all gases. For a gas that shows (near)ideal behavior as He or Ar, Cp ∼ 52R. For gases as H2, D2 or N2 these values are larger, i.e. ∼ 72R.
A supersonic flow is interesting because of two characteristics. First, unlike subsonic flow, a supersonic one increases velocity or Mach number M as the flow area increases, so that M > 1 beyond the nozzle exit. Second, a supersonic gas cannot ’sense’ downstream boundary conditions. This is caused by the fact that information propagates at the speed of sound, whereas the gas moves faster (M > 1). Hence, the gas does not ’know’ about the boundary conditions, but it must adjust. The resulting dilemma is solved by the occurrence of shock waves: very thin non-isentropic regions of large density, pressure, temperature and velocity gradients. The core of the expansion is isentropic and the properties are independent
of Pb because the supersonic flow in this region is not aware of any external condition. From this region, the so-called zone-of-silence, the molecular beam is extracted.
The expanded gas is considered to be ideal and viscous and heat conduction effects are neglected. The energy equation (first law of thermodynamics) for such a flow is given by:
h + v02
2 = h0, (2.3)
where h is the enthalpy, h0 is a constant referred to as the total or stagnation enthalpy per unit mass, and v0 is the flow velocity. If the gas is cooled substantially in the expansion, and its temperature is much smaller than its initial temperature, measured in the frame that moves with the flow velocity, we obtain for the maximum or terminal velocity:
V∞ =
2R/W ∗ (γ(γ − 1)) ∗ T0, (2.4)
where W is the molar weight of the expanded molecules, and R is the gas constant. For an isentropic, ideal gas expansion, where γ is constant, we obtain:
P P0 = T
T0
γ/(γ−1)
= (1 + γ− 1
2 M2)−γ/(γ−1), (2.5)
ρ ρ0 = n
n0 = T T0
1/(γ−1)
= (1 + γ− 1
2 M2)−1/(γ−1). (2.6)
Hence, once M is known, all thermodynamic variables in the supersonic expansion can be computed.
2.3 Surface science techniques
2.3.1 Temperature programmed desorption spectroscopy
Temperature programmed desorption (TPD) belongs to a class of techniques in which a reaction is monitored while increasing the temperature linearly. Adsorption of gas on a metal surface only occurs in a certain temperature range. When the temperature is raised above this threshold, the molecules desorb and return to the gas phase. The temperature at which desorption occurs depends on the strength of the adsorbate-surface interaction, and on the coverage θ, e.g. due to adsorbate-adsorbate interactions.
Our TPD experiments were done in the following way. First, the surface is exposed to the desired adsorbate at low surface temperature (e.g. for H2 around 100 K). Subsequently, the surface is heated, usually with a rate of 1 K s−1. The desorbing molecules that return to the gas phase are monitored with a mass spectrometer. At our set-up, two types of desorption experiments can be done: angle-integrated and angle-resolved measurements. In the angle-integrated measurements all molecules in the gas phase are monitored with the angle-integrating QMS. In the angle-resolved measurements the crystal is positioned at a
2.3 Surface science techniques 35
certain angle with respect to the differentially pumped QMS and only molecules desorbing at that particular angle are detected.
To describe the desorption process, the Polanyi-Wigner equation can be used [22]:
r(θ) =−dθ
dt = ν(θ)θne−Ed(θ)/RT
T = T0 + βt, (2.7)
where r is the rate of desorption, θ the surface coverage, t is the time, ν is the pre-exponential Arrhenius factor, n the order of desorption, Edthe activation energy of desorption, R the gas constant, T the surface temperature, and β the heating rate, equal to dT /dt. A frequently used approximation, only valid for first order desorption processes (n = 1), is the Redhead equation [23]:
Ed= RTmax
lnνdTmax
β − 3.46
. (2.8)
This equation can be used to estimate the activation energy of desorption using the temper- ature at which the desorption maximum is observed (Tmax) and the heating rate β that has been applied. For more complicated desorption processes different methods are necessary which are described in Refs. [24, 25].
2.3.2 Low energy electron diffraction
Single crystal surfaces as used in the experiments described in this thesis have very well- defined structures. The atoms are arranged in an ordered lattice. This ordered lattice is reflected in a diffraction pattern when low energy electrons (< 100 eV) are elastically scat- tered from the surface in a process called low energy electron diffraction (LEED). Detailed information about LEED can be found in Ref. [26].
In a LEED system, the elastically back-scattered electrons are spatially analyzed after traveling through a field-free region. This is achieved by passing the scattered electrons through two hemispherical grids. A retarding voltage is applied to the second grid, to eliminate inelastic electrons. The diffracted beams are then accelerated into a hemispherical phosphor screen. The LEED pattern displayed is the reciprocal lattice of the real surface.
In real space, the electron diffraction takes place according to Bragg’s law:
2dsinθ = nλ. (2.9)
Here θ is the angle between the scattered beam and the surface, d is the distance between the lattice planes, n is an integer and λ is the wavelength of the electrons. In reciprocal K-space the diffraction takes place according to the so-called Laue equation:
K − K0 = Ghkl. (2.10)
Here h, k and l are the indices of the parallel lattice planes.
When adsorbates interact with the surface, its structure and thus the LEED picture can be influenced. Adsorbates can form ordered structures on the surface and extra spots will appear in the diffraction pattern.
With LEED the average terrace width of stepped surfaces can be determined [27, 28].
The spots in the LEED pattern are split due to the presence of steps on the surface. The following formula is valid:
Δϕ =
λ
N a+g if ϕ = 0
λ
(Na+g)cosϕ−dsinϕ if ϕ= 0. (2.11)
Here ϕ is the angle at which the spot is present, Δϕ is the angle between the doublet (split) spots, λ is the wavelength, N is the number of atoms, a is the lattice constant, d is the distance between the lattice planes, and g is the distance between two atoms on the corner of the step.
The width of the terrace can be determined from:
ΔK/K = a/D. (2.12)
Here ΔK is the distance between the doublet spots, K is the distance between the normal spots, a is the lattice constant, and D is the terrace width. The terrace widths we determine from the LEED patterns are consistent with the expected values of 3 (Pt(211)), 4 (Pt(533)) and 6 atoms (Pt(755)).
2.4 Experimental procedures
2.4.1 Time-of-flight spectrometry
To determine the kinetic energy of the hydrogen molecules expanded in the molecular beam, we use time-of-flight (TOF) spectrometry [29]. For this purpose, the beam has to be chopped into pulses by a chopper wheel with a short duty cycle, since the measured TOF distributions are convoluted with the chopper gating function. The larger the duty cycle the more the chopper gating function dominates the TOF spectrum. The chopper gating function is described by:
f (t) = 2∗
2R
0
√R2− x2dx, (2.13)
with R the radius of the molecular beam and x the displacement of the slit in the chopper wheel. The duty cycle of the chopper wheel used for the TOF experiments is 0.5%. The chopper wheel is spun at a frequency of∼230 Hz. To the chopper wheel a photodiode sensor is attached, which starts the TOF measurement. Since the sensor is attached next to the slit, there is a time difference between the start of the measurement and the first molecules flying through the slit. This time difference we call Δttrig. In addition, we have to correct for the fact that we trigger at the edge of the slit, instead of in the middle of the gas pulse. This time difference we call Δtcorr. This correction is calculated by the ratio of half the slit width and the circumference of the chopper wheel divided by the frequency, i.e. 0.5/(130π)∗ 1/f.
2.4 Experimental procedures 37
The molecules in the expansion are detected by the differentially pumped QMS, which is placed in line-of-sight with the molecular beam. This QMS can be extracted over a length of 20 cm, so the flight path of the molecules can be varied between 0.3 and 0.5 m. In addition to the offset caused by the time difference between sensor signal and actual molecules, we also have to take into account the following: The arrival point of the flight distance of the molecules is the ionizer of the QMS, and not the multiplier. Therefore, the total mean flight time ttotal of the molecules is given by:
ttotal = tT OF + Δttrig+ Δtcorr+ ΔtQM S+ Δtelec, (2.14) where tT OF is the mean flight time we are interested in. Δtelecis added for accuracy. Here we include all offsets that might be caused by electronic delays in the photodiode sensor or the multichannel scaler (MCS) that is used to record the TOF spectra. A detailed explanation of how to determine the different contributions to the total flight time is given in Ref. [2].
With these methods we determined a trigger delay of 0.06± 0.0008 ∗ τ/2 ms, a correction of 0.001∗ τ, an electronic delay of zero, and a delay in the QMS of 0.011 ± 0.0006 ms for H2. This delay is dependent on the extraction potential of the ionizer. We use an extraction potential of 250 V. Here τ is the time it takes the chopper wheel to complete 1 cycle.
For a gas pulse that is approximated by a delta-function, the velocity distribution can be described with Eq. 2.1 in Section 2.2. We convert this function to the time-domain:
f (v)dv =
g(t)dt. (2.15)
Using v = L/t and dv∼ t−2 the function can be rewritten as:
g(t)∼ (L
t)5∗ exp
−
L t −tL0
α
2
. (2.16)
Here α is the half width at 1/e or α =
2kT /m. However, since we use a density sensitive detector, the response of the QMS is given by [29]:
gdens(t)∼ g(t) v ∼ (L
t)4∗ exp
−
L t − tL0
α
2
. (2.17)
The time t in this equation is the actual flight time for the molecule as a neutral, and has therefore to be corrected for the delays described above. In addition, since we do not detect a delta-function-like gas pulse, we add 12 of these gdens(t) functions, each separated by 2 μs and scaled with the appropriate amplitude as a model for the convolution with the gating function.
To calculate the kinetic energy of the hydrogen molecules we convert the velocity distri- bution to the energy domain by:
g(E) = 1
m
2E/mf (v), (2.18)
where E = 0.5mv2. The energy of the molecules is then taken from the peak position of the energy distribution (the most probable kinetic energy). The width in energy (the error bars in the horizontal direction) is taken from the 68% confidence interval of the velocity distribution. Since the energy spread within the molecular beam is not symmetrical, this results in different error bars in the + and - direction. Since the results in the kinetic energy domain are not deconvoluted from the finite width in time of the gating function of the chopper wheel, the width in the energy distribution is overestimated, especially at high kinetic energies.
To obtain the wide range in kinetic energy as used for the stepped platinum, Pt(S), surfaces, we apply the technique of (anti)seeding. When mixing the desired gas with a gas that is heavier (antiseeding) the kinetic energy of both gases will decrease. When mixing the desired gas with a lighter carrier gas (seeding) the kinetic energy will increase. For H2 only antiseeding techniques can be applied, since H2 is the lightest gas that is present on Earth.
Deuterium can be seeded in H2 to increase its kinetic energy. The theoretical value of the mean energy of a(n) (anti)seeded beam can be computed assuming ideal behavior [14]:
Etheor = 5 2
mH2
xH2mH2 + xseedmseed
kTn. (2.19)
Here m is the atomic/molecular mass, x is the mole fraction, k is the Boltzmann constant and Tn is the nozzle temperature. The ’real’ measured value will always differ slightly from the theoretical value. This is caused by the so-called velocity slip. In the ideal case, both the desired gas and the carrier gas will have the same mean velocity. However, in reality the heavier molecules will move slower due to non-ideal behavior of the expansion mixture [14].
This accounts for a change in measured kinetic energy compared to the theoretical value.
When using nitrogen as a carrier gas, we notice that more hydrogen molecules are removed from the axis of the molecular beam, causing a larger deviation from ideal behavior then when (anti)seeding in noble gases as helium and argon. When using helium and argon as carrier gases the deviation from ideal behavior is at most 9%. For nitrogen this is at most 20%.
2.4.2 King and Wells technique
The reaction probability of hydrogen on the flat Ru(0001) and the stepped Pt(S) surfaces is determined by the adsorption reflection technique of King and Wells [13], which determines the pumping speed of the surface, using a reference surface where adsorption is zero (the second shutter). The measurement consists of the following steps:
• The molecular beam of hydrogen is blocked at three different places (first beam shutter, valve and second beam shutter, see Fig. 2.1), and thus hydrogen gas is prevented from entering the main chamber, where the metal surface is present. The background pressure of H2 (D2) gas is measured in the main chamber with the angle-integrating QMS.
• First, the valve located between the buffer and main chamber is opened. An effusive beam of hydrogen enters the main chamber and a pressure rise is noted. The hydrogen beam is prevented from hitting the sample.
2.4 Experimental procedures 39
QMS signal
Time
Pdrop
P
Figure 2.2: Example of a King & Wells measurement. ΔP corresponds to an increase in the hydrogen partial pressure when the direct beam enters the main chamber. Pdrop corresponds to the drop in partial pressure when hydrogen dissociates at the metal surface.
• Second, the shutter in front of the chopper wheel is opened, and the direct hydrogen beam enters the main chamber, but does not hit the sample yet. A second pressure rise is observed.
• Finally, the last shutter, that is located directly in front of the sample, is opened. The direct beam impinges on the metal surface and hydrogen is able to dissociate. This dissociation of hydrogen is accompanied by a drop in pressure.
• The reaction probability (S0) of hydrogen can be calculated by:
S0 = Pdrop
ΔP , (2.20)
where Pdrop is the decrease in pressure of the direct beam when it impinges on the surface, and ΔP is the increase in pressure when the direct hydrogen beam enters the main chamber (see Figure 2.2). A plot is made of reaction probability versus kinetic energy of the hydrogen molecule.
In determining the reaction probability a complication arises from the effusive hydrogen load on the main chamber. Since the crystal temperature is well below the onset of associative desorption for small hydrogen coverages, the effusive load from the expansion chamber leads to hydrogen adsorption prior to letting the molecular beam impinge onto the crystal. We have quantified H2 adsorption prior to the actual measurement of S0 using integrated TPD
features with a full monolayer as reference. For all data presented in this thesis, the initial hydrogen coverage was < 0.04 ML (Ru and Pt).
A well known, second issue is that accurate determination of high reaction probabilities is complicated by convolution of the time-dependent drop in partial pressure when exposing the clean crystal to the molecular beam with the vacuum time constant. Therefore, we have verified the accurateness of our measurements on Ru(0001) using two independent means.
First, for high fluxes, which yield excellent signal-to-noise ratios, we apply a fitting proce- dure to the King and Wells pressure trace. The fitted function consists of an exponential and a linear part, which was previously found to accurately describe coverage-dependent adsorption [30]. Extrapolating the fitted function back to the exact time when the beam im- pinged onto the clean surface corrects to a large extent for the convolution mentioned above.
Second, for the same range of probed kinetic energies, we have systematically decreased the flux by employing chopper wheels with lower duty cycles and/or dropping the expansion pressure. We reduce the flux until we find no more increase in reactivity. These two tech- niques yield consistent values for S0 in the low energy range. At high energy, the fitting and extrapolation procedure still underestimates S0 and we only report values determined by lowering the flux.
2.4 Experimental procedures 41
Appendix
Table 2.1: Rovibrational population of the supersonic molecular beam for different nozzle temper- atures for D2. Calculated Boltzmann fractions less than 1% are not shown.
Tn / K v fraction v J fraction J
300 0 1.0 0 0.11
1 0.47
2 0.19
3 0.18
4 0.03
5 0.01
500 0 1.0 0 0.07
1 0.33
2 0.18
3 0.27
4 0.07
5 0.06
6 0.01
900 0 0.99 0 0.04
1 0.21
2 0.14
3 0.27
4 0.11
5 0.14
6 0.04
7 0.04
1300 0 0.96 0 0.03
1 0.15
2 0.11
3 0.23
4 0.11
5 0.17
6 0.06
7 0.08
8 0.02
9 0.02
1700 0 0.92 0 0.02
1 0.12
2 0.09
3 0.20
4 0.10
5 0.18
6 0.07
7 0.10
8 0.04
9 0.05
10 0.01
11 0.01
Table 2.2: Rovibrational population of the supersonic molecular beam for different nozzle temper- atures for H2. Calculated Boltzmann fractions less than 1% are not shown.
Tn / K v fraction v J fraction J
300 0 1.0 0 0.16
1 0.70
2 0.09
3 0.05
500 0 1.0 0 0.10
1 0.58
2 0.14
3 0.16
4 0.01
700 0 1.0 0 0.07
1 0.48
2 0.15
3 0.24
4 0.03
5 0.02
900 0 1.0 0 0.06
1 0.40
2 0.14
3 0.29
4 0.05
5 0.05
1100 0 1.0 0 0.05
1 0.35
2 0.13
3 0.31
4 0.06
5 0.08
6 0.01
1300 0 0.99 0 0.04
1 0.30
2 0.12
3 0.31
4 0.07
5 0.11
6 0.02
7 0.02
1500 0 0.98 0 0.03
1 0.27
2 0.11
3 0.31
4 0.08
5 0.14
6 0.02
7 0.03
1700 0 0.97 0 0.03
1 0.24
2 0.11
3 0.30
4 0.08
5 0.15
6 0.03
7 0.04
2.4 Experimental procedures 43
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