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Properties of potential eco-friendly gas replacements for particle detectors in high-energy physics

Modern gas detectors for detection of particles require F-based gases for optimal performance. Recent regulations demand the use of environmentally unfriendly F-based gases to be limited or banned. This review studies properties of potential eco-friendly gas candidate replacements.


Introduction
Many currently used refrigerant gases have a great impact on the environment since they either contribute largely to the greenhouse gas effect, or because they tear the ozone layer, or both. In an attempt to protect the environment, regulations preventing the production and use of certain refrigerant gases have been implemented [1].
Gas detectors are widespread for detection, tracking and triggering of charged particles such as muons in Nuclear and High Energy Physics (HEP). They are characterized by simple and reliable use, but utmost care must be taken to issues such as properties of gas interaction with materials, gas purification, gas mixture contaminants, etc.
A large part of gas muon detectors used in HEP operates with mixtures containing the regulated refrigerants as quenching medium in applications where excellent time resolution and avalanche operation are necessary. Therefore, actions towards finding new mixtures must be undertaken. Gas Electron Multiplier (GEM) [9] detectors operate in experiments such as CMS (Compact Muon Solenoid) at the LHC (Large Hadron Collider) with an argon/CO 2 mixture [11]. However, for high time resolution applications an argon/CO 2 /CF 4 mixture is used [12], where CF 4 has a Global-Warming Potential (GWP) of 7390 [13]. Resistive Plate Counters (RPC) [10] currently operate with a F-based R134a/Isobutane/SF 6 gas mixture, with typical GWP of 1430. Investigations into new gas mixtures has to be performed in order to keep the mixture properties while complying with the regulations. A few industrial refrigerant industrial replacements were proposed [14] as alternatives to R134a. A study of transport properties of currently used gas mixtures in HEP, and evaluation of transport properties of freon-less gas mixtures, was recently published [15] [16].
The aim of this paper is to discuss some of the important properties of gases for particle gas detectors, to list and summarize basic properties of eco-friendly refrigerants from the literature, to discuss their properties for materials compatibility and safe use, and make a prediction on selected parameters crucial for the performance of gas detectors considered. While this study is aimed to GEM and RPC detectors, its findings can be considered for selection of ecogas replacement for other gas detectors.

Gas properties
For a gas mixture to be appropriate in a gas detector, first of all it has to comply with the regulations. Furthermore, its properties must also be appropriate for the specific type of detectors. For example, a gas that is suitable for the RPC detectors may not be fully optimized for the GEM detectors. To better find the appropriate gas for a detector, an understanding of the influence of different parameters is required. This section aims to clarify the most essential parameters for gases.

Global-warming potential and Ozone depletion potential
In order to estimate the impact of a refrigerant on the environment, the effects have to be quantified. Two important effects are the contribution to the greenhouse effect and the depletion of the ozone layer. The first mentioned effect is measured in Global-Warming Potential (GWP), and is normalized to the effect of CO 2 (GWP = 1), while the effect on the ozone layer is measured in Ozone Depletion Potential (ODP), normalized to the effect of CCl 3 F (ODP = 1). The effects of selected refrigerant candidates are listed in table 1.

Stopping power
When a particle passes through a medium, energy is transferred from the particle to the surroundings. The energy lost is typically defined as the stopping power expressed as 1 ρ dE dx , where ρ denotes the density of the medium, E denotes energy, and x is length. This expression is itself dependent on the momentum p of the particle. In the next section it will be shown the particle will experience a minimum energy loss at around p/M c ≈ 3, where M is the particle mass, and c is the speed of light. By knowing the average minimum energy loss, we also know the minimum energy the particle loses by passing through a detector. The minimum mean ionization energies for the refrigerants under consideration are summarized in table 2.

Radiation length
The radiation length X 0 is a characteristic length of a medium. It describes both the mean distance required for a high energy electron to lose all but e −1 of its energy due to bremsstrahlung, and 7 / 9 of the mean free path of a e + e − pair produced by a high-energy photon [18]. These quantities are also estimated and summarized in table 2.

Ion pair production
When an incoming particle passes through a medium, it will eventually interact with the medium and transfer some of its energy to ionize atoms. In this process, a pair con-sisting of an ionized atom and a free electron is produced. The number of ionizations produced by an incoming particle per unit length is denoted by N P , in units of cm −1 .
Each produced ion pair will have an initial kinetic energy and can itself produce an ion pair, called secondary ion pair production. The sum of the primary and secondary ion pairs production per unit length is denoted N T , and will be mainly depending on the material and the incoming particle energy and mass. This parameter is relevant in particle gas detectors as it determines both the number and the size of avalanches produced by a single incoming particle when the gas is under an amplifying electric field.

Drift velocity
In the absence of electric field, electrons move randomly in all direction having an average thermal energy 3/2KT . In presence of an electric field, the electrons start to drift along the field direction with mean drift velocity v d (the average distance covered by the drift electron per unit time). The drift velocity depends on the pressure, temperature and could be affected by the presence of pollutants like water or oxygen. Electric field lines are, in addition, deformed by any magnetic field applied to the gas volume.
Finally, electronegative pollutants deplete the gas of electrons. Computer codes such as Magboltz [17] computes the drift velocity using montecarlo techniques, by tracing electrons at the microscopic level through numerous collisions with gas molecules.

Diffusion
Electrons and ions in a gas are subject only to an electric field and move on average along the electric field, but individual electrons deviate from the average due to scattering on the atoms of the gas. Scattering leads to variations in velocity, called longitudinal diffusion, and to lateral displacements, called transverse diffusion. The scattering process in each direction can, to a good approximation, be considered gaussian on a microscopic scale. In cold gases like carbon-dioxide for example, the diffusion is small, while the drift velocity is low and unsaturated for values of electric fields common in gas detectors; this implies a non linear space time relation. Warm gases, like argon for instance, have a higher diffusion; when mixed with polyatomic/organic gases having vibrational thresholds between 0.1 and 0.5 eV, diffusion is reduced in most cases, while the drift velocity is increased.

Townsend coefficients
The average distance an electron travels between ionizing collisions is called mean free path and its inverse is the number of ionizing collision per centimeter α (the first Townsend coefficient). This parameter determines the gas gain of the gas. If n 0 is the number of primary electron without amplification in uniform electric field, and n is the number of electrons after distance x under avalanche condition, then n is given by n = n 0 e αx and the gas gain G is given by G ≡ n 0 /n = e αx . The first Townsend

Hazards and flammability
Many refrigerants may constitute danger for the user and its environment. The greatest dangers involved are the flammability and toxicity. We have used two standards in categorizing the refrigerants in table 3 and 4. The Ashrae standard [19] gives each refrigerant a number denoting flammability from 1 (not flammable) to 3 (highly flamable), as well as a letter A (non-toxic) or B (Toxic). The Health Material Hazardous Material Information System (HMIS), rates Health/ Flammability/ and Physical hazards from 0 (low) to 4 (high).

Compatibility with materials
Some refrigerants are incompatible with certain materials, and can either react violently, or have long term effect. Some refrigerants may even produce toxic decomposition and/or polymerization. Known incompatibilities and toxic byproducts are summarized in Table 3 and 4.

Aging and longevity
Aging is defined (following [20]) the general deterioration of the detectors during their operation. The aging phenomenon is very complex and depends on several parameters. The commonly used variables include the cross-sections, electron/photon energies, electrostatic forces, dipole moments, chemical reactivity of atoms and molecules, etc. For a comprehensive (although non recent) collection see [21][22] [23]. A more recent review of ageing effects in GEM detectors can be found in [24].

Stopping power
Quantities such as the minimum ionization energy can be found if the stopping power is known. An approximate expression for moderately relativistic particles in the momentum region 0.1 ≤ βγ = p/M c ≤ 1000 can be found using the Bethe-Bloch equation, given by [30] 1 where − dE dx is the mean energy loss per length, ρ is the density of the medium, I is the mean excitation energy, and δ(βγ) is the density effect correction function to ionization energy loss. K is a constant given by 4πN A r 2 e m e c 2 , and T max is the maximum energy transfer in a single collision, given by where M is the mass of the incoming particle.
The mean excitation energy I for a composite medium can be approximated from the composite atoms by the relation [51].
Not compatible with aluminium, alloys containing more than 2% magnesium, alkali metals in powdered form and carbon dioxide above 1000 • C.
If involved in a fire, production under thermal decompose into pyrolysis products containing hydrogen fluorid and carbonyl fluoride. Under normal condition, hazardous decomposition and/or polymerization products should not be produced. If exposed to fire, hazardous products may be produced.   where w j , Z j , A j and I j is the fraction by weight, atomic number, atomic weight and mean ionization energy, respectively, of the j'th constituent. The shape of the δ(γδ) function for non-conducting materials can be approximated by where X = log 10 (γδ). For finding an approximate expression for the parametersC, X 0 and X 1 based on experimental fits, we refer to [52]. For gases with momenta below βγ, the density effect correlation function can be neglected. A plot of the calculated energy loss for different refrigerants is show in figure 1.

Radiation length
The radiation length of an atom can be found by [18] X 0 = 716.405(cm −2 mol)A/ Z 2 (L rad − f (z)) + ZL rad (6) where L 1 and L 2 is given by table 3.2, f (z) is the one-photon exchange approximation, and z = αZ, α being the fine-structure constant and Z is the atomic number.  Table 6: L 1 and L 2 expressions for various atom numbers.
This formula, however, only holds for free atoms. When one wants to find the stopping power for a molecule, one has to take into account the influence from molecular bindings, crystal structures and polarization of the medium. By neglecting these effects, however, one can find an approximate expression by weighting the radiation length of the single atoms where j reffers to the j'th atom's constituent.

Estimation of ionization pair production
In order to model the number of primary ionization caused by a single particle, the cross section for all the particle-atom interaction should be calculated. The number of primary electrons per unit length would then be the integral over energy across all the energy transfer cross sections. This is tedious work since all electron orbital transfers have to be considered. An easier, but approximate correlation between primary ionization and atom number has been found based on experimental data by [53] which holds for normal pressure and temperature (NPT) (1 atm, 20 • C). For different pressure and temperature, the number scales with the density. This value should only be taken as a rough estimation though. This formula has proven to work best for hydrocarbons and worst for molecules consisting mainly of fluorine, differing as much as 30% from the experimental value for CF 4 .
The total number of ionization has proven to be more difficult to estimate. Whereas no general formula has been derived, the most straightforward method will be to use the cross sections used to calculate the primary ionization electrons, and use Monte Carlo simulations to track the production of secondary electrons from primary electrons. The total number of pair ionization turns out to be dependent on the incoming particle energy and mass, and a general expression can therefore be difficult to find. For an incoming particle, W = ∆E N defines the average energy cost to produce an ion pair.
Luckily, this turns out to be a function slowly varying with particle energy [27], and can therefore be taken to be a constant in an energy interval. The total ionization per unit length can then be found by If the W values for specific gases are know, the average W value for a gas mixture can be found by [53] W where n m denotes the index of the molecule, and f (n m ) denotes the relative number of molecules of the given sort in the mixture.
The value of W is difficult to predict, and there is not a direct way to give a proper estimate based on experimental data alone. A montecarlo simulation is in preparation which uses the photoabsorption ionization and relaxation (PAIR) model [53] and it will be the subject of a forthcoming paper.

Quantum chemistry calculations
In this section of the paper we describe the calculation of gas properties using the quantum chemistry calculation tool NWCHEM . The ionization energies, electron affinities and the absorption spectrums are calculated for several kinds of potential Eco-friendly gas replacements. The results are validated and compared with different methods or calculation schemes. In the last part, the problems related to the computation of the Townsend parameter and prop sects for future works are discussed.
Developments of quantum chemistry in the past few decades have improved the calculation to be accurate enough to be compared with real experiments. These calculations enable us to study gas properties from atom level, where the underlying theory is believed to be more fundamental and may therefore provide us more general descriptions of the chemical properties.
In the paper, we used the NWCHEM software [54] for computation, and the PY-MOL [55] tool for visualization. The calculation determines the electronic structure of the molecule system and can provide basic information of the system like ground state energy, dipole momentum, charged density and molecular orbit. To obtain properties more suitable to be compared to experimental data, the software also provides frameworks to compute the absorption spectrum and the ionization energy.
Here we first show the basic geometrical information for interested molecules.
Then we describe the procedure to calculate the absorption spectrum and in the following we present the methods to calculate the ionization energy and the electron affinity.
In the end, we discussed the possibility to estimate the Townsend parameter under some certain environment of particle detectors.

Molecules and their optimized geometries
The freon gases we have been interested in are R134a (CH 2 F CF 3 ), R152a (C 2 H 4 F 2 ), HFO1234ze (CF HCHCF 3 ), HFO1234yf (CH 2 CF CF 3 ), CF 3 I and HFO1233zd (CHClCF CF 3 ). Meanwhile we choose R12(CCl 2 F 2 ) to be the standard freon gas model. CH 4 and CF 4 are the molecules we were used to make a comparison between the NWCHEM calculated results and experimental results, in order to check the reliability of NWCHEM . Fig.(2) shows the optimized ground state geometries of gas molecules, where the green balls stand for carbon atoms, the grey balls stand for hydrogen atoms, the indigo balls stand for fluorine atoms, the brown balls stand for chlorine atoms, and purple ball for iodine. Fig.(3) shows the highest occupied molecular orbitals (HOMO) of gas molecules.

Calculation of absorption spectrum
The excitation energy of a molecule is one of the fundamental properties of molecular interactions one can get from experiment. To study these properties, we used the framework introduced in Ref. [56] to simulate the time-dependent response of molecules under external fields using quantum chemical calculations. The framework implemented is the Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) [57] method within the NWCHEM , making it capable of doing the simulation beyond small perturbation from the ground state.
In our case, we are mostly interested in low excitations of small molecules. We therefore adopt the procedure as described in section 3 of the reference [56]. The choice of external field is δ-function-like electric field "kick" where t 0 is the center of pulse, w is the pulse width, which has dimensions of time, d =x,ŷ,ẑ is the polarization of the pulse, and κ is the maximum field strength.
(a) CH 4 Figure 2: Optimized ground state geometries of gas molecules.
The system is then evolved in time, and the dipole moment can be calculated with respect to the added dipole coupling term where D is the transition dipole tensor of the system. Then we Fourier transform the dipole signals to construct the complex polarizability tensor α i,j (ω), and finally the dipole absorption spectrum is We first validate our calculation by repeating the calculation of CH 4 lowest excitation energy in Table (7) of the paper [56]. With the same basis set (6-311G) and functional (B3LYP), our calculation gives 11.16 eV excitation energy, which is consistent with the 11.13 eV in the paper. The small difference can come from other minor uncertainty sources like the choice of time separation in the simulation.
We further checked the dependence of wave function basis sets as well as density functional of our results. The dependence of basis sets is found to be much smaller than the functional one. Fig.(4) and Fig.(5) compares the results using two different functionals. As shown in the figures, although the strength varies large between the two functionals, the excitation energies are similar, especially the lowest one, which is also the same story as in the reference [56].
The same calculation is performed to gas molecules of our interest. The optical absorption spectrums are compiled in Fig.(6).
In the Fig.(7) we put together all spectra of interesting molecules. Comparing to the R12, which is one of the Freon gas spectrum, we found the similarity between molecules are in good agreement with their structures. In other words, the absorption spectrum is closer to that of R12 if the candidate molecule is similar to the R12 molecular structure.
6 Calculation of the vertical ionization energy and the electron affinity   Table.(8).
The Fig.(8) compares the HOMO (in blue) and LUMO (in green) of R12 on the left plot and the HOMO for neutral R12 molecule (in blue) and charged one R12 ion (in red) on the right plot. Similar plot for HFO1234ze is shown in Fig.(9). As can be seen from the HOMO plot, the molecular orbit between the neutral molecule and charged molecule are similar, especially for the R12, which has less atoms in the molecule.
Since the Koopman's theorem will be exact when the molecular orbit for the neutral molecule and charged molecule are the same, we calculated the atom number averaged difference between our two methods, which reflect the difference of the molecular orbitals. The results are shown in Table.(8) As the lowest excitation energy can be estimated from the energy gap between the HOMO and LUMO, we also make a comparison of these results to those obtained in the previous section. From the comparison in Table.(8), we see that, although the absolute values of the excitation energy have relatively large differences between the two approaches, the difference of the excitation energies among the molecules considered is only marginal.    Table 8: Results of electron affinity calculation and the lowest excitation. The lowest excitation energy from the absorption for all molecules except for the CH 4 , which is directly read out from the calculation, are obtained from the mean value of a Gaussian fit to the lowest peak in the spectrum.

Estimation of the first Townsend parameter
Following Ref. [60], we express the dependance of the first Townsend parameter α as a function of the reduced electric field E/p where A and B are parameters depending on the gas type and electric field range, and p the gas pressure.
The reference [60] shows that the first Townsend coefficient at high reduced electric field depends almost entirely on the mean free path of the electrons. The mean free path, which is defined as where n is the number of atoms per unit volume and σ is the total cross section for electron collision with atoms, can be calculated if the environment of gas molecule is provided. Firstly, the n is dependent on the gas pressure and can be put by hand. Secondly, the σ(v), which is a function of electron velocity v, can be calculated from the NIST website [61]. Then, noting that at high reduced electric field, the first Townsend coefficient can be expressed as a combination of two components: where E m is the electric field that drifting an electron over λ m and reach the ionization energy (I 0 ) of the gas. Therefore, we can estimate with two free parameters A, B, which need to be determined from experiments.
For real gases, we cannot take the free path lengths as a constant and the ionization cross section is only a fraction of the total cross section. In that case the estimation needs to be modified and use the following equation: Numerous measurements of the Townsend coefficients are available for standard gas mixtures, such as those reviewed in [62].

Conclusions
Currently used F-based gases today used in HEP gas detectors are being phased out by industry and replaced by eco-friendly substitute gases. This study has reported on a general survey of industrially available replacements for HEP gases, discussed their physical properties, materials compatibility and safety issues. Parameters of interest for their use in HEP detectors have been computed following different approaches ranging from parametrizations to quantum chemical calculations: ionization energy, electronegativity, number of primary pairs. Statistical methods to compute amplification parameters of the ionization shower production such as the Townsend coefficients were investigated and preliminary results reported. Promising candidates with lower GWP are identified for further studies.