Elastic neutron scattering in Biophysics Carmen Abia Sanz Physics Oviedo University November 6, 2017 By investigating water dynamics of biological samples at different temperatures, a better understanding of biological mechanisms determining our state of health can be gained. With this purpose, an elastic incoherent neutron scattering experiment was performed at the IN13, a backscattering spectrometer of the Institut Laue-Langevin (ILL), in Grenoble, France. The aim of this document is to show the learning, work and results accomplished during a four week internship at the ILL, as a student of the 2017 Summer School Programme. 1 Motivation 2 Theoretical background Neutron scattering techniques use neutron beams as a probe to investigate macromolecules and wa- ter molecules dynamics. Due to their electri- Water is a key component of most physical sys- cal neutrality, neutrons are non-destructive and tems of our planet; it plays an important role in can penetrate deeply into matter which makes biological systems. Therefore, the study of the them an ideal probe for studying biological sam- properties of water is necessary for the under- ples. standing of the structural stability, the dynamics and the functions of biological molecules. This Since neutrons appear to behave either as parti- type of studies has an impact in areas such as cles, as waves or as microscopic magnetic dipoles, medicine, where understanding biological mecha- all these specific properties enable them to yield nisms determining our state of health can improve information which is often impossible to obtain us- life expectancy, as well as the quality of life. In ing other techniques. Focusing on thermal neutron wavelengths and energies ( ∼ 1 . 8 ˚ this experiment in particular, neutron scattering A and 0 . 025 eV), technology is used to study water properties of it is remarkable that they are comparable to the several tumoral systems and, by comparing them interatomic distances and to thermal energy of ex- with regular biological systems, relevant informa- citations. Consequently, these particles are sensi- tion will be obtained. tive to the amplitudes and frequencies of molecu- 1
lar motions simultaneously, making neutron scat- incoherent. tering an outstanding technique to provide infor- S ( Q , ω ) ∝ σ coh + σ inc mation about both dynamics and structure of bi- ologycal systems. The coherent contribution provides information In an scattering event, see (Figure 1), there is about the correlation between two particles, in two different positions at two different times (crystals). an incoming neutron beam, with an initial energy While the incoherent contribution provides infor- E i and an initial wave vector k i , it interacts with mation about the autocorrelation (correlation over the atomic nuclei of a sample and neutrons with final energies E f and final wave vectors, k f , are the same particle) at two differen times, which obtained. There are two kinds of scattering pro- gives directly access to molecular motions. cess: elastic and inelastic. In the elastic case, The table (Table 1) compares the coherent and which is the one studied, there is not energy trans- incoherent cross section of some elements. Since fer, E i = E f , only momentum transfer. As it is hydrogen has one of the largest incoherent cross shown in (Figure 1), the k f is pointing to the cir- section of all nuclei, neutron scattering from a non- cunference so that the modules of both k i and k f crystalline biological sample is dominated by inco- herent scattering of this element. It is important are the same, but their direction can experiment to consider that when a neutron measurement is a change. The momentum transfer is defined by done both contributions are acquired, they are not the scattering vector Q = k f − k i ; it is linked to ditinguishable. However, neutron scattering sig- the inicial wavelength and the scattering angle by 4 π sin θ nals from hydrogenous compounds are essencially Q = 2 . λ i incoherent. Inelastic Element σ coh (barns) σ inc (barns) scattering k f E f > E i H 1 . 76 79 . 91 Elastic scattering k f E f = E i O 4 . 23 0 . 01 Inelastic scattering Q C 5 . 55 0 . 00 E f < E i N 11 . 01 0 . 49 k f Table 1: Incoherent and coherent cross sections θ θ 2 The elastic incoherent scattering function, Incoming neutrons bean k i S inc ( Q ), can be written within the Gaussian ap- proximation, in which it is supposed that the Figure 1: Scattering event hidrogen atoms (in this case) have small fluctu- ations around their equilibrium positions. Math- ematically, when � u 2 � Q 2 ≪ 1: During the scattering event, a neutron interacts with a nucleus. The probability of this event is S inc ( Q ) ∝ e − 1 6 � u 2 � Q 2 (1) proportional to the expose surface of the nucleus. Such surface is so-called cross section , σ , and is where � u 2 � are the atomic mean square displace- specific for each element in nature; the bigger the ments (MSD), which is a measure of the devia- cross section is, the scattering event is more likely tion time between the position of a particle and to happen. the equilibrium position. In this particular ex- What the instruments are able to measure is the periment, thermal elastic neutron scattering gives scattering function , S ( Q , ω ), which is proportional directly access to the vibrations of hidrogen atoms to the cross section. In a scattering function, two and how they change as the temperature is modi- contributions can be distiguished: coherent and fied. 2
3 Material and methods in a cryofurnace and orientated in (422) direction to obtain the wavelength 2 . 23 ˚ A and an energy of Backscattering spectrometer: IN13 16 . 4 meV. The IN13 instrument at the ILL is a thermal neu- tron backscattering spectrometer mainly devoted The neutrons are diffused with a small angle of to life sciences. Due to its high energy resolution 1 . 8 ◦ . It is not possible to fulfill the backscattering and high momentum transfer, this spectrometer is condition, which would improved the energy res- useful for the microscopic study of single particle olution, since it is not possible to backscatter the motions which are observed by incoherent neutron particles into the guide. scattering. The expression of the energy resolution can be deduced by differentiating Bragg’s law The graphite deflector, composed by pyrolytic graphite crystals, serves to focus the beam on the λ = 2 d sin θ (2) sample position, following the lambda variations the following expression is obtained induced by the change of lattice parameters of ∆ E = 2 ∆ λ = 2 cot θ ∆ θ + 2 ∆ d the heated monochromator crystal. Before hit- (3) E λ d ting the sample, the energy-selected neutrons pass The distintive high energy resolution of IN13, through a chopper and a monitor. The chopper only 8 µ eV, is achieved by working with the (with a speed of 6756 rpm) is used to suppress the largest possible Bragg angle at the monochroma- neutrons scattered directly from the sample into tor and the analyser crystals (ideally θ = 90 ◦ so the detectors and to suppress higher orders of the that cot( θ ) = 0); which is approached with the reflection of the monochromator CaF 2 crystals, backscattering geometry . The second term in (3) since the incident neutron beams are imperfectly is only dependent on the crystal quality. monochromatic due to instrument characteristics. Regarding the high momentum transfer (be- The monitor is a detector which measures the in- tween 0 . 5 and 4 . 9 ˚ A − 1 ) it is relevant to mention coming neutron flux intensity. that a small wavelenght has to be used in order to achieve it. For that reason, the spectrometer is Once the neutron beam is scattered by the sam- installed at the termal guide H24. ple, they are analysed in momentum and energy Thermal guide H24 transfers by a set of nine CaF 2 crystal analysers. 16 . 45 meV E i FWHM 8 µ eV 2 . 23 ˚ These are also glued in a 422 orientation on the A λ i 8 ◦ < θ M < 89 ◦ surface of spherically curved concave aluminium Angular range 0 . 5 − 4 . 9 ˚ plates (Figure 2); in this way, the elastic scatter- A − 1 Q-range ∆ Q < 0 . 1˚ ing geometry can be reached selecting the neu- A − 1 Q-resolution trons with the right energy ( E i = E f ). Dynamics time observed ∼ 80 ps Monochromator CaF 2 (422) Analyser CaF 2 (422) This selected neutrons will go to the detectors of the instrument. Specifically, they are counted Table 2: IN13 Characteristics by individual 3 He detectors and a cylindrical mul- tidetector consisting of several 3 He detector tubes. In an IN13 experiment, the neutron beam comes 3 He gas produc- from the thermal moderator passing through the The neutrons can ionize the thermal guide H24 and arrives to the monochro- ing electrons, so an electric current is measured mator crystals, which are CaF 2 crystals mounted through an electric potential difference. 3
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