The real crystal structure of a compound is defined by a deviation of the average structure caused by different types of defects. Extended defects, such as grain boundaries and dislocations influence the structure on a grand scale, without a variation on the level of individual unit cells. Small defects like single, isolated point defects, or correlated defects forming small defect-clusters, generally cause systematic variations of unit cells, which can be detected by diffraction methods. The method of average neutron-scattering length is an approach that gives a pos­sible solution of point defects. By this method it is possible to determine the cation distribution within the material for a wide range of structure types, and will be explained here using CuInSe2 and CuGaSe2 as examples.

The approach is based on the fact, that vacancies (VCu and VIn), as well as anti­site defects (InCu and CuIn), will change the neutron-scattering length of the cation sites 4a (copper site) and 4b (indium site) in the chalcopyrite-type structure sig­nificantly [15]. In a neutron diffraction experiment, the neutron interacts with the atomic nucleus and the neutron-scattering lengths of copper and indium are dif­ferent (bCu = 7.718 (4) fm, bIn = 4.065 (2) fm, bV = 0 [18]). Thus, the distribution of copper and indium on both cation sites of the structure can be revealed from the SOFs determined by Rietveld analysis of the neutron diffraction data.

If different species like Cu, In, and vacancies occupy the same structural site j, the average neutron-scattering length of this site is defined by:

bj = NCuj ■ bCu + Ninj ■ bIn + Nvj ■ bv (5.1)

Here, N is the fraction of the species on the corresponding site and b are the neutron-scattering lengths. As an additional requirement the full occupation of the site j has to be taken into account, which is achieved when ^2 Ni = 1 (i = Cu, In, V). In an example case the chalcopyrite-type crystal structure is used as basis model for the Rietveld refinement. Thereby, Cu occupies the 4a and In the 4b site. An experimental average neutron-scattering length for the two sites using the SOFs can be calculated by:

be4xap = SOF4a ■ bCu be4xap = SOF4b ■ bn (5.2)

where SOF4a and SOF4b are the cation site occupancy factors of the chalcopyrite — type crystal structure from the Rietveld analysis. The evaluation of the experimental average neutron-scattering length of a series of different Cu/In ratios, and therefore different degrees of off-stoichiometry, reveals a decrease of bff (see Fig. 5.6) with

decreasing Cu/In. Taking into account bV < bIn < bCu, a decrease of b4XT can only be caused by the presence of vacancies (VCu) or anti-site defects of type InCu. Since the decrease of b4XT becomes stronger with decreasing Cu/In, an increase of the par­ticular defect concentration can be assumed. Clearly, the value for b4b increases with decreasing Cu/In ratio. This can only be due to the presence of anti-site defects of type InCu (bCu > bIn).

The experimental average neutron-scattering lengths have to be compared with theoretical values. In a first step, these values are derived from a cation distribution model built on the basis of the known chemical composition of the material. The general formula for the calculation of the cation distribution is given by Eq. (5.1). A simultaneous comparison of bj with bjxp during variation of the cation-distribution model leads to the corresponding amounts of isolated point-defects.

Using this approach it was possible to determine the cationic point-defect con­centration for various chalcopyrite-type compounds. It was clearly shown that CuInSe2 tends, when being Cu-poor, to form VCu, InCu, and CuIn defects, resulting in a partially disordered chalcopyrite-type crystal structure. In contrast to CuInSe2, CuGaSe2 exhibits the same crystal structure, but due to the small ionic radii of Ga3+ [23] the material tends to form interstitial defects of type Gaj [24]. These differences sensitively influence the properties of a final solar device. The kind of point defects present in CuInSe2 allow a neutralization of isolated point-defects by clustering together forming a neutral defect complex of type (2VCu + InCu), which has a considerable binding-energy [16]. Such a neutralization of point defects cannot be assumed for CuGaSe2. This crucial difference is one reason why it is possible to design a thin-film solar cell with a very off-stoichiometric absorber and high defect — concentration, like CuInSe2, but maintain considerable efficiency. Tailoring high efficiency devices with a CuGaSe2 absorber layer is still a challenging task due to different problems. One aspect is the difference in the presence of intrinsic point — defects in Cu-poor CuGaSe2 discovered by neutron powder diffraction.

Inelastic neutron scattering (INS) is crucial in the study of hydrogen storage where the neutron can excite the quantum motion of the H2 molecule, and measure the transition energies directly (see Chap. 8). However, in the more general case INS amounts to “vibrational spectroscopy with neutrons” and in the present book is used to study local structure, vibrational dynamics, and the nature of hydrogen-bonding interac­tions. The main strength of the technique arises from the large neutron-scattering cross section of hydrogen, which causes vibrations involving hydrogen to dominate the spectra. This domination, particularly when combined with selective deuteration, is very powerful for providing assignment of the observed peaks to specific
vibrational-modes. In addition, it is now straightforward to calculate the INS directly from a molecular model which is not only an aid to assignment, but also a validation procedure for the model. The technique is comparable to infra-red and Raman spectroscopy, which have better resolution, but lack the hydrogen selectivity and simplicity of assignment. Incoherent INS has no selection rules and even modes that are silent in both infra-red (IR) and Raman can have significant INS intensity.

Clearly, the development of more efficient, cost-effective, and industrially-viable CO2 capture materials is essential for the deployment of large-scale CCS. Novel concepts for porous hosts used for CO2 capture and separation require a molecular level of control that can take advantage of differences in the chemical reactivity of gas molecules. A challenge in the capture of CO2 is tuning the selectivity of adsorbents, and coupled with this is the need to examine the adsorption selectivity at the molecular level. Neutron scattering has made important contributions in the understanding of the fundamental separation and storage mechanisms underpinning the functionality of porous materials used in CO2 capture processes. Great potential exists to develop porous hosts for this purpose using neutron scattering by probing adsorption sites, as well as guest orientation, dynamics, and diffusion in wide range of porous materials. Additionally, the characterization of the hosts themselves and their response to guest adsorption, both on a crystallographic and large-scale structure scale is important.

Postcombustion capture from power-plant flue streams provides one strategy towards reducing CO2 emissions to the atmosphere, however, there is an urgent need for new methods and materials that perform this separation. In contrast to the low pressure, predominantly CO2/N2 separation required for postcombustion capture, materials for precombustion (high pressure, predominantly CO2/H2) capture and natural-gas sweetening (predominantly CO2/CH4), have distinct requirements. Careful consideration must therefore be afforded to the working conditions of the material at which capture occurs in order to tailor the properties of that material. Commensurate with this requirement is the need for studying materials under rele­vant working conditions, with an emerging area of particular relevance being the understanding of gas transport in mixed gas and vapour streams. Such co-adsorption experiments, performed for CO2 and CH4 mixtures [88, 89], could be extended to study important ternary mixtures such as CO2/H2O/N2. This would allow derivation of important competitive gas-sorption mechanisms that are difficult to derive using other methods such as sorption analysis and diffuse-reflectance Fourier-transform infrared spectroscopy. This approach can be expanded further to include mixtures representative of separations that are industrially relevant, and for conversion and catalytic reactions.

In this section, an introductory study of molecular vibrations and, indirectly, relaxation dynamics, of single molecule HAT6 is made by extending previous ground-state computational work to excited states, while retaining the molecular tails [15, 16, 28, 29]. The model calculations are validated by IR and UV absorption measurements of HAT6 in solution at room temperature [30]. The goals are three-fold:

(i) To determine the electronic excitation with the largest oscillator strength in HAT6;

(ii) Modelling the molecular structure of the selected excited state;

(iii) Understanding effects of electron-phonon coupling by comparing the vibrations of the ground state (GS) and the selected excited state (ES1).

However, a thorough investigation of the vibronic and electronic aspects of the DLC-CT HAT6-TNF is presented in Sect. 6.3.1.5.

It has been found [30] that the HOMO-to-LUMO transition dominates the tar­geted ES1 with the largest oscillator strength (*1). The calculated excitation — energy using the time-dependent DFT matches perfectly the measured one at 3.76 eV. The most important feature is that ES1 can be approximated as simply a HOMO-to-LUMO excitation, the HOMO-to-LUMO contribution in ES1 being * 80 %. As far as changes in the PES in going from GS to ES1 are concerned, these can be explored directly by comparing the structural parameters of the two elec­tronic-states. Results of the structural analyses can be summarized as follows: the structural distortion of ES1, compared to GS, corresponds to geometrical changes mainly in the aromatic core of HAT6. The oxygen atoms are of central importance,

since they connect the aromatic core to the alkyl tails, and due to their electro­negativity, they could play an electronic role in the charge-transport process. Bond angles involving the oxygen atoms show changes that are comparable in amplitude to those within the aromatic core. The alkyl tails are, as expected, less sensitive to the ES1 structural distortion, but nevertheless, a change is found in the chain structure [30]. These changes reflect the different minima of the PES of GS and ES1, but gradients of the PES around local minima also change, and these are probed by the molecular vibrations. The HAT6 molecule with 144 atoms has 426 normal modes. The D3h symmetry of the molecule results in six irreducible rep­resentations (irreps) with the following distribution of modes; 42 (A’1), 41 (A’2), 166 (E’), 30(A”1), 29 (A”2), 118 (E”). The modes corresponding to E’ and E” are doubly degenerate. Modes with A”2 and E’ symmetry are IR active. Figure 6.14 compares the calculated IR spectrum with that measured. The agreement is very good allowing the excited state of the molecule and its vibrations to be studied with more confidence.

Figure 6.15 shows the calculated IR spectra for GS and ES1 over the whole spectral range (195 active modes) and, in more detail, in the restricted spectral range from 550 to 1,700 cm-1 (118 active modes). It is in this range that the most striking differences are observed between GS and ES1 and, indeed, differences occur throughout this part of the spectrum. However, we have selected bands with the strongest IR intensities (and high dipole strengths), these being denoted: I, II, III, and IV. Modes I—III are composed of single peaks (pairs of degenerate modes), whereas mode IV is composed of 5 peaks/frequencies. With the exception of II, the intensities of the modes are greater in ES1 than in GS. The frequency shifts in going from GS to ES1 are about 10 cm-1 for modes II-IV but for mode I the shift is 29 cm 1. The related atomic displacements for GS and ES1 modes in the four

frequency bands can be analysed. For mode I, which has the biggest frequency shift, the GS mode is an out-of-plane mode, whereas the ES1 mode is an in-plane mode. Accordingly, the displacements of the alkoxy tails are significantly different, being polarised in the planes perpendicular to the tail directions in GS and being polarised along the tails in ES1. For modes II-IV, the frequency shifts are smaller and the similarity of modes between GS and ES1 is stronger, with mode III being almost identical in the two electronic states. In these three bands, all modes show in-plane polarisation of the molecular cores. Mode II involves deformations of the aromatic cores and C-O stretches, with corresponding responses in the alkoxy tails, and the displacement patterns change between GS and ES1. For mode IV, the main difference between GS and ES1 involves the pattern of C-C stretches in the aro­matic core, but there is a notable difference in the chain displacements. It is evident from this investigation of GS and ES1 molecular vibrations that core and tail vibrations are coupled.

In the intermediate frequency range that has been considered, deformations of the aromatic core are accompanied by complex displacements of the alkoxy tails, and these are not simple rigid-body motions. Accordingly, the QENS study reported in Sect. 6.3.1.2, in which diffusive dynamics on the ps timescale were probed, proved in a consistent way, that motion of the alkyl tails is driven by the core dynamics. The alkyl chain (beyond the O atom) is also found to play a significant role in the molecular distortion and change in molecular vibrations upon electronic excitation. The vibrational spectrum in the excited electronic state, which has the strongest oscillator strength, is considerably different from that in the ground state, despite the size and overall flexibility of the system. This result, supported by the good agreement with measured IR and UV spectra, is encouraging for gaining insight into the technologically important relaxation processes within the conduction band that lead to serious efficiency losses in solar-cell applications. After all, most energy present in the incoming light is dissipated and converted to
heat due to fast relaxation from higher excitations towards the lower band edge. In this context Sect. 6.3.1.5 focuses also on some resonant Raman measurements which are related to the excited-state molecular structure via the vibrations that constitute the atomic shifts between the ground and excited electronic-state structures.