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Thermal neutron cross-section libraries for aromatic hydrocarbons
Nuclear Instruments and Methods in Physics Research B 268 (2010) 2487–2491
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Thermal neutron cross-section libraries for aromatic hydrocarbons F. Cantargi a,b,*, J.R. Granada a,b,c a
Centro Atómico Bariloche (CNEA), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina Instituto Balseiro (CNEA/UnCuyo), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina c Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina b
a r t i c l e
i n f o
Article history: Received 29 March 2010 Available online 6 May 2010 Keywords: Thermal cross-section libraries Cryogenic moderator materials Cold neutron sources
a b s t r a c t Solid phases of aromatic hydrocarbons, such as benzene, toluene, mesitylene and a 3:2 mixture by volume of mesitylene and toluene, were studied as potential moderator materials for a cold neutron source. Existing information on the (lattice) translational and rotational modes of the different molecular species was used to produce generalized frequency spectra; the latter included the internal vibrational modes which in turn involved the analysis of the weights of the different modes. Cross-section libraries were generated in ENDF and ACE formats for hydrogen bounded in those materials at several temperatures, and were used in Monte Carlo calculations to analyze their neutron production compared with standard cryogenic materials like liquid hydrogen and solid methane, the best moderators in terms of cold neutron production. In particular, cross-section libraries were generated at 20 K, which is a typical operating temperature for the majority of the existing cold neutron sources. It was found that those aromatic hydrocarbons produce neutron spectra which are slightly warmer than that of solid methane while presenting a high resistance to radiation, conforming in this way a new and advantageous alternative to traditional moderator materials. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since subthermal energy neutrons are increasingly required in neutron scattering experiments, a large effort was devoted to the development of new cold neutron sources, based on cryogenic materials that can efficiently produce very low-energy neutrons and that are capable to withstand strong radiation fields. To fulfill the first condition, the candidate materials must possess low-frequency modes that can be excited in the interaction with neutrons, giving rise to a significant downscattering probability even at low neutron energies. In this context, the quasi-spherical methane molecule is the most efficient unit [4], but its poor resistance to radiolysis practically prevents its use as a cold moderator material in modern intense neutron sources [2]. With the aim of producing cross-section libraries which could be subsequently used in a cold neutron source design, here we describe and analyze the most important properties of a group of aromatic hydrogenous compounds: benzene and methyl derivatives of it. Specifically, the last ones involve solid toluene, mesitylene and a 3:2 (by volume) mixture of mesitylene and toluene, at several temperatures, in particular at 20 K which is the operating tem* Corresponding author at: Centro Atómico Bariloche (CNEA), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina. Tel.: +54 2944 445216; fax: +54 2944 445299. E-mail address: [email protected] (F. Cantargi). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.04.030
perature of the majority of the existing cold neutron sources. Some of those materials have already been proposed as cold moderators some time ago [15,5]. At room temperature benzene (C6H6) is a colorless, very volatile liquid. The molecule is non-polar, flat, with a regular hexagonal shape. Although it is an unsaturated hydrocarbon, it does not usually undergo addition reactions but substitutional ones. One of the most common reaction is the substitution of one hydrogen by a methyl radical in the benzene ring, thus forming methylbenzene (C7H8), material commonly known as toluene. If the substitution involves three methyl groups instead of one starting from the benzene molecule, different molecular conformations can be obtained, one of them is the symmetric 1–3–5 trimethylbenzene (C9H12), usually known as mesitylene.
2. Dynamical properties The structural and dynamical properties of a given system determine the characteristics of its interaction with slow-neutrons. The probability for the occurrence of a scattering process with the exchange of certain amount of energy and momentum between the neutron and the scatterer is controlled by those properties, in turn contained in the scattering law S(Q,x) of the system. In the frame of the Gaussian approximation the dynamics of the material is enclosed in its generalized frequency spectrum, and this is in fact
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the important piece of information needed to predict scattering probabilities in the case of hydrogenous materials, where interference effects are negligible. In the frequency spectrum of a molecular solid, each mode is related to a certain kind of motion of the target system, either vibrations or rotations of the individual molecule or collective movements associated to the solid. The lattice modes also possess low energies excitations that are associated to collective oscillations of the molecules. The vibrational degrees of freedom of the individual molecule appear at higher energies while the modes associated to molecular rotations typically appear at intermediate energies. Generally, except for very particular materials, the frequency spectrum is not available and it is necessary to find an appropriate representation of it. In this work, frequency spectra for a set of aromatic hydrocarbons were constructed by combining a ‘‘continuous part” taken from experimental data [11] and synthetic contributions [7] which are discrete oscillators related to specific vibrational modes of the individual molecules. In addition, in the construction of this spectra, we considered an adjustable parameter related to the weight of the translational and librational modes, and a normalization condition for the sum of weights associated to the different dynamical modes. 2.1. Benzene The benzene molecule has two types of vibrational modes: inplane and out-of-plane. In Fig. 1 we present the continuous part of the frequency spectrum proposed for this material. The low-energy part of this spectrum, up to 0.05 eV, was taken from the measured curve [11]. It represents the lattice modes of phase I, which is the solid phase at normal pressure [16]. The broad pseudo Gaussian centered at 0.12 eV condenses all the out-of-plane vibrational modes and some in-plane modes such as the ring breathing mode. The in-plane modes not taken into account are the C–H stretching modes, which were represented by a discrete oscillator at 0.38 eV with a weight of 0.35 (not shown in the figure).
Fig. 2. Continuous part of the frequency spectra for the two solid phases of toluene. The curve corresponding to the crystal phase has been shifted up.
modes associated to librational motion of the methyl unit shows up in this spectrum. Toluene solidifies in two different phases [14], glassy and crystalline, depending on the cooling rate and thermal treatment. The glassy phase has an enhanced intensity of low-energy modes as compared to the parabolic dependence with wave-number characteristic of the crystalline phase, and this of course is convenient to increase the slowing down power at cold neutrons energies. Frequency spectra for the two solid phases of toluene were built using experimental data [11] for the low-energy part (see Fig. 2) and, taking into account what is known for benzene and methane [1], three discrete oscillators at 0.12, 0.17 and 0.37 eV were included. The first one is associated to the ring breathing mode, the second to the C–H stretching of the methyl group and the last one to the C–H stretching in the ring. 2.3. Mesitylene
2.2. Toluene The toluene molecule involves a single methyl group substituting one hydrogen in the benzene one. As a result, and besides the intra-radical vibrational modes, a significant amount of low-energy
The 1–3–5 trimethylbenzene molecule has three methyl groups placed symmetrically around the benzenic ring, presumably the configuration with richest density of rotational states at low energies. On the contrary, if we observe frequency spectra of those mol-
Fig. 1. Continuous part of the frequency spectrum proposed for phase I of solid benzene.
Fig. 3. Continuous part of the frequency spectra for the three solid phases of mesitylene. The curves corresponding to phases II and III have been shifted up.
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Fig. 4. Continuous part of the frequency spectrum for mesitylene:toluene 3:2 by volume.
Fig. 5. Total cross-section of mesitylene at 32 K measured at our laboratory compared with the calculated curve from our new libraries.
ecules having two methyl groups side by side such as o-xylene, pseudocumene, durene or mellitene, that richness does not show up [11]. According to the cooling rate, solid mesitylene may exist in three different phases [11] which are displayed in Fig. 3. Phase II, showing the typical behavior of a disordered one, is the most interesting as an efficient cryogenic moderator material. Frequency spectra for each solid phase were built using the experimental data for low energies together with the three oscillators already used in the toluene spectra [1]. 2.4. Mesitylene:toluene 3:2 by volume Mixtures of mesitylene with other aromatic molecules are able to produce glassy solids irrespective of the cooling rate or thermal treatment [11]. That is the case of the mixture of mesitylene with toluene, in the fraction 3:2 by volume. The frequency spectrum for this new material was built by combining the experimental data shown in Fig. 4 together with the same oscillators used in the toluene and mesitylene spectra [1]. 3. Cross-section libraries All the frequency spectra shown in the previous section were used for feeding the LEAPR module of the NJOY Nuclear Data Processing System [9], to produce the cross-section libraries for hydrogen bounded in each material at different temperatures. It is necessary to emphasize that in a frequency spectrum not only is important the energy associated to a mode, but also its weight. For all the studied materials an initial set of weights for the different modes was proposed. Bearing in mind the structural complexity of the molecular systems considered, the actual assignement of weights within each frequency spectrum required the employment of experimental information to validate them. A set of total cross-section measurements on those solid aromatics at different temperatures was performed employing the 25 MeV electron LINAC based pulsed neutron source at Centro Atómico Bariloche [13,12]. For each material a comparison between cross-sections measured at our laboratory and calculated with the NJOY system was done. These comparisons were used to refine the weights corresponding to the contribution of different modes to the frequency spectra [1]. In Figs. 5 and 6 we show, as examples, calculated and
Fig. 6. Total cross-section of the mixture mesitylene and toluene 3:2 by volume at 32 K measured at our laboratory compared with the calculated curve from our new libraries.
measured cross-sections for mesitylene and the mixture at 32 K respectively, which was the lowest temperature attainable with our experimental set-up. In all the cases the agreement attained between experimental and calculated cross-sections is very satisfactory. With these spectra with refined weights, cross-section libraries were calculated for the remaining experimental temperatures finding again a very good agreement between calculated and experimental cross-sections. This fact enabled the validation of our libraries and the criteria used for building the frequency spectra. For each material we were able to find a unique frequency spec-
Table 1 Weights associated to each part of the frequency spectra. Material
Lattice modes
Ring breathing mode
hm < 0:10 eV hm1 ¼ 0:12 eV Toluene 0.130 Mesitylene 0.188 M:T 3:2 0.167
0.300 0.170 0.217
C–H stretching in CH3 hm2 ¼ 0:17 eV
C–H stretching in the ring hm3 ¼ 0:37 eV
0.230 0.310 0.281
0.340 0.332 0.335
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p-hydrogen at 20 K [6], as well as the one due to clathrate [3]. Indeed, methane and clathrate are the best hydrogenous materials for producing cold neutrons at that temperature, but both of them can hardly stand strong radiation fields as the aromatic hydrocarbons do. From the neutron spectra calculation performed for the mentioned TMR configuration, the effective neutron temperature was calculated for each material at different temperatures. In Fig. 8 these temperatures are shown as a function of the physical temperature of the materials. It can be seen that the solid aromatic hydrocarbons produce neutron spectra slightly warmer than the solid methane in the whole temperature range. 4. Conclusions
Fig. 7. Normalized neutron spectra produced with our libraries and a standard TMR configuration.
trum which characterizes each phase and which can be used in a calculation with NJOY at any temperature within that phase. In Table 1 we show the energies of the different modes and the assigned weights for the spectra used for producing the cross-section libraries for the set of aromatic materials studied. With these frequency spectra, cross-section libraries for hydrogen bounded in these materials were generated at 20 K, which is the operating temperature of the majority of the existing cold neutron sources. Once the new cross-section libraries were validated, neutron spectra calculations were performed using the MCNP code [10], on a standard target-moderator-reflector configuration used at the Hokkaido LINAC [8]. The normalized neutron spectra thus produced are shown in Fig. 7 for a temperature of 20 K, where it is evident that the methyl group containing molecules produce a more intense and cooler spectrum than that due to benzene. In addition, the best of the group in that sense is mesitylene in phase II, closely followed by the mixture of mesitylene and toluene. In this figure we also compare these moderators with traditional cold hydrogenous moderator materials, like solid methane at 22 K and liquid
Fig. 8. Effective temperature as a function of the physical temperature for each studied material compared to methane.
Cross-section libraries for a group of solid hydrogeneous aromatic were generated in ENDF and ACE formats using the NJOY processing system. For this purpose, the dynamics of those materials was reviewed, and making use of existing experimental information on the density of states for translational and rotational (librational) motions, synthetic frequency spectra were developed for them. They were validated by comparing with experimental data and were used to predict neutron spectra emerging from a typical TMR configuration, by using the MNCP code for the evaluation of the energy distribution of neutrons coming out from the cold moderator. Although solid methane is the best moderator in terms of cold neutron production, it has very poor radiation resistance, causing spontaneous burping even at fairly low doses. Such effect is considerably reduced in the aromatic hydrocarbons. On the other hand, all of them show a similar and significant neutron production, with the exception of benzene. Even though those aromatic materials are very easy to handle, the solid phases that produce an enhanced flux of cold neutrons correspond to amorphous structures rich in low-energy excitations, and they can be created through lengthy cooling processes requiring in many cases additional annealing stages. The 3:2 mesitylene–toluene mixture, that forms in a simple and direct manner the appropriate disordered structure, constitutes an excellent cryogenic moderator material, as it is able to produce an intense flux of cold neutrons while presenting high resistance to radiation, thus conforming a new and advantageous alternative to traditional moderator materials. References [1] F. Cantargi, Neutronic properties of aromatic hydrocarbons as cryogenic moderators, Ph.D Thesis, Instituto Balseiro, 2007. [2] E. Shabalin, E. Kulagin, S. Kulikov, V. Melikhov, Radiat. Phys. Chem. 67 (2003) 315. [3] F. Cantargi, J.R. Granada, S. Petriw, M.M. Sbaffoni, Neutron cross-section libraries for aromatic molecular systems of interest as cold neutron moderators, in: Proceedings of the 18th Meeting of the International Collaboration on Advanced Neutron Sources, ICANS-XVIII, Dongguan, China, 2007. [4] J.M. Carpenter, Nucl. Instrum. Methods 234 (1985) 542. [5] L. Cser, P. Vertés, J. Neutron Res. 6 (1997) 185. [6] J.R. Granada, V.H. Gillette, M.E. Pepe, M.M. Sbaffoni, J. Neutron Res. 11 (2003) 25. [7] J.R. Granada, V.H. Gillette, M.M. Sbaffoni, F. Cantargi, S. Petriw, M.E. Pepe, Neutron cross sections of cryogenic materials: a synthetic kernel for molecular solids, in: Proceedings of the Sixth Meeting of the International Collaboration on Advanced Cold Moderators, Julich, Germany, 2002. [8] Y. Kiyanagi, Application of hokkaido linac, in: Proceedings of the Workshop on Neutron Science using Accelerator based Small Neutron Source, Sapporo, Japan, 2006. [9] R.E. MacFarlane, D.W. Muir, NJOY Nuclear Data Processing System, Los Alamos National Laboratory, 1994. [10] MCNP, Monte Carlo Neutron and Photon Transport Code System, C00730MNYCP00, RSIC, 2006. [11] I. Natkaniec, K. Holderna-Natkaniec, J. Kalus, I. Majerz, Vibrational spectra of selected methyl derivatives of benzene and their solutions as potential materials for cold moderators, in: Proceedings of the 16 Meeting of the
F. Cantargi, J.R. Granada / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2487–2491 Intenational Collaboration on Advanced Neutron Sources, ICANS XVI, Dsseldorf-Neuss, Alemania, 2003. [12] L.R. Palomino, F. Cantargi, J.J. Blostein, J. Dawidowski, J.R. Granada, Nucl. Instrrum. Methods B 267 (2009) 175–177. [13] L. Torres, J.R. Granada, J.J. Blostein, Nucl. Instrum. Methods Phys. Res. B 251 (2006) 304–305.
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[14] I. Tsukushi, O. Yamamuro, K. Yamamoto, K. Takeda, T. Kanaya, T. Matsuo, J. Phys. Chem. Sol. 60 (1999) 1541–1543. [15] K. Unlu, C. Rios-Martinez, B.W. Wehring, J. Radioanal. Nucl. Chem. 193 (1995) 145–154. [16] Y. Yonetani, K. Yokoi, Mol. Phys. 99 (2001) 1743–1750.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Thermal neutron cross-section libraries for aromatic hydrocarbons F. Cantargi a,b,*, J.R. Granada a,b,c a
Centro Atómico Bariloche (CNEA), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina Instituto Balseiro (CNEA/UnCuyo), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina c Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina b
a r t i c l e
i n f o
Article history: Received 29 March 2010 Available online 6 May 2010 Keywords: Thermal cross-section libraries Cryogenic moderator materials Cold neutron sources
a b s t r a c t Solid phases of aromatic hydrocarbons, such as benzene, toluene, mesitylene and a 3:2 mixture by volume of mesitylene and toluene, were studied as potential moderator materials for a cold neutron source. Existing information on the (lattice) translational and rotational modes of the different molecular species was used to produce generalized frequency spectra; the latter included the internal vibrational modes which in turn involved the analysis of the weights of the different modes. Cross-section libraries were generated in ENDF and ACE formats for hydrogen bounded in those materials at several temperatures, and were used in Monte Carlo calculations to analyze their neutron production compared with standard cryogenic materials like liquid hydrogen and solid methane, the best moderators in terms of cold neutron production. In particular, cross-section libraries were generated at 20 K, which is a typical operating temperature for the majority of the existing cold neutron sources. It was found that those aromatic hydrocarbons produce neutron spectra which are slightly warmer than that of solid methane while presenting a high resistance to radiation, conforming in this way a new and advantageous alternative to traditional moderator materials. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since subthermal energy neutrons are increasingly required in neutron scattering experiments, a large effort was devoted to the development of new cold neutron sources, based on cryogenic materials that can efficiently produce very low-energy neutrons and that are capable to withstand strong radiation fields. To fulfill the first condition, the candidate materials must possess low-frequency modes that can be excited in the interaction with neutrons, giving rise to a significant downscattering probability even at low neutron energies. In this context, the quasi-spherical methane molecule is the most efficient unit [4], but its poor resistance to radiolysis practically prevents its use as a cold moderator material in modern intense neutron sources [2]. With the aim of producing cross-section libraries which could be subsequently used in a cold neutron source design, here we describe and analyze the most important properties of a group of aromatic hydrogenous compounds: benzene and methyl derivatives of it. Specifically, the last ones involve solid toluene, mesitylene and a 3:2 (by volume) mixture of mesitylene and toluene, at several temperatures, in particular at 20 K which is the operating tem* Corresponding author at: Centro Atómico Bariloche (CNEA), Av. Bustillo 9500, R8402AGP Bariloche, Río Negro, Argentina. Tel.: +54 2944 445216; fax: +54 2944 445299. E-mail address: [email protected] (F. Cantargi). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.04.030
perature of the majority of the existing cold neutron sources. Some of those materials have already been proposed as cold moderators some time ago [15,5]. At room temperature benzene (C6H6) is a colorless, very volatile liquid. The molecule is non-polar, flat, with a regular hexagonal shape. Although it is an unsaturated hydrocarbon, it does not usually undergo addition reactions but substitutional ones. One of the most common reaction is the substitution of one hydrogen by a methyl radical in the benzene ring, thus forming methylbenzene (C7H8), material commonly known as toluene. If the substitution involves three methyl groups instead of one starting from the benzene molecule, different molecular conformations can be obtained, one of them is the symmetric 1–3–5 trimethylbenzene (C9H12), usually known as mesitylene.
2. Dynamical properties The structural and dynamical properties of a given system determine the characteristics of its interaction with slow-neutrons. The probability for the occurrence of a scattering process with the exchange of certain amount of energy and momentum between the neutron and the scatterer is controlled by those properties, in turn contained in the scattering law S(Q,x) of the system. In the frame of the Gaussian approximation the dynamics of the material is enclosed in its generalized frequency spectrum, and this is in fact
2488
F. Cantargi, J.R. Granada / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2487–2491
the important piece of information needed to predict scattering probabilities in the case of hydrogenous materials, where interference effects are negligible. In the frequency spectrum of a molecular solid, each mode is related to a certain kind of motion of the target system, either vibrations or rotations of the individual molecule or collective movements associated to the solid. The lattice modes also possess low energies excitations that are associated to collective oscillations of the molecules. The vibrational degrees of freedom of the individual molecule appear at higher energies while the modes associated to molecular rotations typically appear at intermediate energies. Generally, except for very particular materials, the frequency spectrum is not available and it is necessary to find an appropriate representation of it. In this work, frequency spectra for a set of aromatic hydrocarbons were constructed by combining a ‘‘continuous part” taken from experimental data [11] and synthetic contributions [7] which are discrete oscillators related to specific vibrational modes of the individual molecules. In addition, in the construction of this spectra, we considered an adjustable parameter related to the weight of the translational and librational modes, and a normalization condition for the sum of weights associated to the different dynamical modes. 2.1. Benzene The benzene molecule has two types of vibrational modes: inplane and out-of-plane. In Fig. 1 we present the continuous part of the frequency spectrum proposed for this material. The low-energy part of this spectrum, up to 0.05 eV, was taken from the measured curve [11]. It represents the lattice modes of phase I, which is the solid phase at normal pressure [16]. The broad pseudo Gaussian centered at 0.12 eV condenses all the out-of-plane vibrational modes and some in-plane modes such as the ring breathing mode. The in-plane modes not taken into account are the C–H stretching modes, which were represented by a discrete oscillator at 0.38 eV with a weight of 0.35 (not shown in the figure).
Fig. 2. Continuous part of the frequency spectra for the two solid phases of toluene. The curve corresponding to the crystal phase has been shifted up.
modes associated to librational motion of the methyl unit shows up in this spectrum. Toluene solidifies in two different phases [14], glassy and crystalline, depending on the cooling rate and thermal treatment. The glassy phase has an enhanced intensity of low-energy modes as compared to the parabolic dependence with wave-number characteristic of the crystalline phase, and this of course is convenient to increase the slowing down power at cold neutrons energies. Frequency spectra for the two solid phases of toluene were built using experimental data [11] for the low-energy part (see Fig. 2) and, taking into account what is known for benzene and methane [1], three discrete oscillators at 0.12, 0.17 and 0.37 eV were included. The first one is associated to the ring breathing mode, the second to the C–H stretching of the methyl group and the last one to the C–H stretching in the ring. 2.3. Mesitylene
2.2. Toluene The toluene molecule involves a single methyl group substituting one hydrogen in the benzene one. As a result, and besides the intra-radical vibrational modes, a significant amount of low-energy
The 1–3–5 trimethylbenzene molecule has three methyl groups placed symmetrically around the benzenic ring, presumably the configuration with richest density of rotational states at low energies. On the contrary, if we observe frequency spectra of those mol-
Fig. 1. Continuous part of the frequency spectrum proposed for phase I of solid benzene.
Fig. 3. Continuous part of the frequency spectra for the three solid phases of mesitylene. The curves corresponding to phases II and III have been shifted up.
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Fig. 4. Continuous part of the frequency spectrum for mesitylene:toluene 3:2 by volume.
Fig. 5. Total cross-section of mesitylene at 32 K measured at our laboratory compared with the calculated curve from our new libraries.
ecules having two methyl groups side by side such as o-xylene, pseudocumene, durene or mellitene, that richness does not show up [11]. According to the cooling rate, solid mesitylene may exist in three different phases [11] which are displayed in Fig. 3. Phase II, showing the typical behavior of a disordered one, is the most interesting as an efficient cryogenic moderator material. Frequency spectra for each solid phase were built using the experimental data for low energies together with the three oscillators already used in the toluene spectra [1]. 2.4. Mesitylene:toluene 3:2 by volume Mixtures of mesitylene with other aromatic molecules are able to produce glassy solids irrespective of the cooling rate or thermal treatment [11]. That is the case of the mixture of mesitylene with toluene, in the fraction 3:2 by volume. The frequency spectrum for this new material was built by combining the experimental data shown in Fig. 4 together with the same oscillators used in the toluene and mesitylene spectra [1]. 3. Cross-section libraries All the frequency spectra shown in the previous section were used for feeding the LEAPR module of the NJOY Nuclear Data Processing System [9], to produce the cross-section libraries for hydrogen bounded in each material at different temperatures. It is necessary to emphasize that in a frequency spectrum not only is important the energy associated to a mode, but also its weight. For all the studied materials an initial set of weights for the different modes was proposed. Bearing in mind the structural complexity of the molecular systems considered, the actual assignement of weights within each frequency spectrum required the employment of experimental information to validate them. A set of total cross-section measurements on those solid aromatics at different temperatures was performed employing the 25 MeV electron LINAC based pulsed neutron source at Centro Atómico Bariloche [13,12]. For each material a comparison between cross-sections measured at our laboratory and calculated with the NJOY system was done. These comparisons were used to refine the weights corresponding to the contribution of different modes to the frequency spectra [1]. In Figs. 5 and 6 we show, as examples, calculated and
Fig. 6. Total cross-section of the mixture mesitylene and toluene 3:2 by volume at 32 K measured at our laboratory compared with the calculated curve from our new libraries.
measured cross-sections for mesitylene and the mixture at 32 K respectively, which was the lowest temperature attainable with our experimental set-up. In all the cases the agreement attained between experimental and calculated cross-sections is very satisfactory. With these spectra with refined weights, cross-section libraries were calculated for the remaining experimental temperatures finding again a very good agreement between calculated and experimental cross-sections. This fact enabled the validation of our libraries and the criteria used for building the frequency spectra. For each material we were able to find a unique frequency spec-
Table 1 Weights associated to each part of the frequency spectra. Material
Lattice modes
Ring breathing mode
hm < 0:10 eV hm1 ¼ 0:12 eV Toluene 0.130 Mesitylene 0.188 M:T 3:2 0.167
0.300 0.170 0.217
C–H stretching in CH3 hm2 ¼ 0:17 eV
C–H stretching in the ring hm3 ¼ 0:37 eV
0.230 0.310 0.281
0.340 0.332 0.335
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p-hydrogen at 20 K [6], as well as the one due to clathrate [3]. Indeed, methane and clathrate are the best hydrogenous materials for producing cold neutrons at that temperature, but both of them can hardly stand strong radiation fields as the aromatic hydrocarbons do. From the neutron spectra calculation performed for the mentioned TMR configuration, the effective neutron temperature was calculated for each material at different temperatures. In Fig. 8 these temperatures are shown as a function of the physical temperature of the materials. It can be seen that the solid aromatic hydrocarbons produce neutron spectra slightly warmer than the solid methane in the whole temperature range. 4. Conclusions
Fig. 7. Normalized neutron spectra produced with our libraries and a standard TMR configuration.
trum which characterizes each phase and which can be used in a calculation with NJOY at any temperature within that phase. In Table 1 we show the energies of the different modes and the assigned weights for the spectra used for producing the cross-section libraries for the set of aromatic materials studied. With these frequency spectra, cross-section libraries for hydrogen bounded in these materials were generated at 20 K, which is the operating temperature of the majority of the existing cold neutron sources. Once the new cross-section libraries were validated, neutron spectra calculations were performed using the MCNP code [10], on a standard target-moderator-reflector configuration used at the Hokkaido LINAC [8]. The normalized neutron spectra thus produced are shown in Fig. 7 for a temperature of 20 K, where it is evident that the methyl group containing molecules produce a more intense and cooler spectrum than that due to benzene. In addition, the best of the group in that sense is mesitylene in phase II, closely followed by the mixture of mesitylene and toluene. In this figure we also compare these moderators with traditional cold hydrogenous moderator materials, like solid methane at 22 K and liquid
Fig. 8. Effective temperature as a function of the physical temperature for each studied material compared to methane.
Cross-section libraries for a group of solid hydrogeneous aromatic were generated in ENDF and ACE formats using the NJOY processing system. For this purpose, the dynamics of those materials was reviewed, and making use of existing experimental information on the density of states for translational and rotational (librational) motions, synthetic frequency spectra were developed for them. They were validated by comparing with experimental data and were used to predict neutron spectra emerging from a typical TMR configuration, by using the MNCP code for the evaluation of the energy distribution of neutrons coming out from the cold moderator. Although solid methane is the best moderator in terms of cold neutron production, it has very poor radiation resistance, causing spontaneous burping even at fairly low doses. Such effect is considerably reduced in the aromatic hydrocarbons. On the other hand, all of them show a similar and significant neutron production, with the exception of benzene. Even though those aromatic materials are very easy to handle, the solid phases that produce an enhanced flux of cold neutrons correspond to amorphous structures rich in low-energy excitations, and they can be created through lengthy cooling processes requiring in many cases additional annealing stages. The 3:2 mesitylene–toluene mixture, that forms in a simple and direct manner the appropriate disordered structure, constitutes an excellent cryogenic moderator material, as it is able to produce an intense flux of cold neutrons while presenting high resistance to radiation, thus conforming a new and advantageous alternative to traditional moderator materials. References [1] F. Cantargi, Neutronic properties of aromatic hydrocarbons as cryogenic moderators, Ph.D Thesis, Instituto Balseiro, 2007. [2] E. Shabalin, E. Kulagin, S. Kulikov, V. Melikhov, Radiat. Phys. Chem. 67 (2003) 315. [3] F. Cantargi, J.R. Granada, S. Petriw, M.M. Sbaffoni, Neutron cross-section libraries for aromatic molecular systems of interest as cold neutron moderators, in: Proceedings of the 18th Meeting of the International Collaboration on Advanced Neutron Sources, ICANS-XVIII, Dongguan, China, 2007. [4] J.M. Carpenter, Nucl. Instrum. Methods 234 (1985) 542. [5] L. Cser, P. Vertés, J. Neutron Res. 6 (1997) 185. [6] J.R. Granada, V.H. Gillette, M.E. Pepe, M.M. Sbaffoni, J. Neutron Res. 11 (2003) 25. [7] J.R. Granada, V.H. Gillette, M.M. Sbaffoni, F. Cantargi, S. Petriw, M.E. Pepe, Neutron cross sections of cryogenic materials: a synthetic kernel for molecular solids, in: Proceedings of the Sixth Meeting of the International Collaboration on Advanced Cold Moderators, Julich, Germany, 2002. [8] Y. Kiyanagi, Application of hokkaido linac, in: Proceedings of the Workshop on Neutron Science using Accelerator based Small Neutron Source, Sapporo, Japan, 2006. [9] R.E. MacFarlane, D.W. Muir, NJOY Nuclear Data Processing System, Los Alamos National Laboratory, 1994. [10] MCNP, Monte Carlo Neutron and Photon Transport Code System, C00730MNYCP00, RSIC, 2006. [11] I. Natkaniec, K. Holderna-Natkaniec, J. Kalus, I. Majerz, Vibrational spectra of selected methyl derivatives of benzene and their solutions as potential materials for cold moderators, in: Proceedings of the 16 Meeting of the
F. Cantargi, J.R. Granada / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2487–2491 Intenational Collaboration on Advanced Neutron Sources, ICANS XVI, Dsseldorf-Neuss, Alemania, 2003. [12] L.R. Palomino, F. Cantargi, J.J. Blostein, J. Dawidowski, J.R. Granada, Nucl. Instrrum. Methods B 267 (2009) 175–177. [13] L. Torres, J.R. Granada, J.J. Blostein, Nucl. Instrum. Methods Phys. Res. B 251 (2006) 304–305.
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[14] I. Tsukushi, O. Yamamuro, K. Yamamoto, K. Takeda, T. Kanaya, T. Matsuo, J. Phys. Chem. Sol. 60 (1999) 1541–1543. [15] K. Unlu, C. Rios-Martinez, B.W. Wehring, J. Radioanal. Nucl. Chem. 193 (1995) 145–154. [16] Y. Yonetani, K. Yokoi, Mol. Phys. 99 (2001) 1743–1750.