The formation of solid solutions between the non-isotype compounds ZnC and CuBIIIC2 (B-Al, Ga, In; C-S, Se) enables the band-gap energy to be changed from the large value of the binary wide-gap semiconductor ZnC to the band gap of the chalcopyrite-type end member CuInC2 [37]. The possible application of 2(ZnS)- CuInS2 mixed crystals as absorbers in thin-film solar cells was introduced by Bente et al. [38]. However, these solid-solution series are characterized by a relatively — large miscibility gap, where a tetragonal and a cubic phase coexists [37, 39-41], thus the applicable range is limited.

For tetragonal Zn2x(CuB)1-xC2 mixed crystals, the question of the distribution of the three cations Zn[2]+, Cu+ and B3+ on the two cation positions of the chalcopyrite — type structure arises. Like in CIGSe, the cation distribution influences the opto­electronic properties of the solid-solution compounds. The Cu-Zn differentiation problem existing in X-ray diffraction due to a nearly-equal atomic form-factor f for Cu+ and Zn2+, can be solved by neutron diffraction because of the different neutron scattering cross-sections for Cu and Zn, which are based on the different neutron scattering lengths (bZn = 5.68 fm, bCu = 7.718 fm [18]).

The most detailed analysis was performed for chalcopyrite-type Zn2x(CuIn)1-xS2 mixed crystals [42]. It should be noted that the study was performed using powder samples with stoichiometric composition (the chemical composition was determined by wavelength-dispersive X-ray spectroscopy using an electron microprobe system). For the interpretation of the average neutron-scattering lengths of the cation sites 4a and 4b (b^f and Zgb), derived from the cation SOFs determined by Rietveld analysis of neutron powder diffraction data, the principle of the conservation of tetrahedral bonds (CTB) for ternary ABC2 chalcopyrites [43] was applied. In the chalcopyrite-type structure a displacement of the anion from its ideal position (У, i. e. the middle of the cation tetrahedron) by u — У (u is the anion x-coordinate) can be observed. Hence different bond lengths RAC ф RBC result, which in turn cause different-sized anion tetrahedra AC4 and BC4, resulting in a tetragonal deformation П = c/2a parallel to the crystallographic c-axis. The bond lengths are [43]

The parameters n and u are considered as the degrees of freedom of the chal­copyrite-type structure [Jaffe, Zunger 84]. The Abrahams-Bernstein relation [44]

1 c2 1

u = 2 — 32? -16 (5J)

correlates the tetragonal distortion u with the lattice parameters a and c. However, there is a limitation: only one of the anion tetrahedra is assumed to be deformed, whereas the other is taken as regular.

According to the CTB, the degrees of freedom (n and u) would attain values that simultaneously minimize the difference between the bond lengths RAC and RBC and the sums of the elemental radii as

RAC(a, g, u) — га — rc= 0 and RBC(a, g, u) — Гв — rC = 0 (5.8)

By applying Eqs. (5.6) and (5.7) the solutions for Eq. (5.8) can be written as о 12a2

a

2p + a — (2p + a)2-18a2

g2 = 8(P — a)

g = 3a2

Here a is the bond-mismatch parameter and P the mean-square-bond

a = rax _ RBx = (rA + rX)2-(rB + rX)2 ^5 11^

P = RAX + RBx = (rA + rX)2-(rB + rX)2

The CTB model can be extended to quaternary chalcopyrite-type compounds, assuming the covalent radii in the equations above as the average radius of the cations on the two cation positions, according to

rA = ZnArZn2+ + CuArCu+ + InArIn3+ and (5 12)

rB = ZnBrZn2+ + CuBrCu+ + InBrIn3+

Here ZnA, CuA, and InA are the mole fractions of the cations on the Wyckoff position 4a (A) and 4b (B) according to the cation-distribution model. These fractions corre­spond to the total amount ofZn, Cu, and In in (2ZnS)x(CuInS2)1-x (i. e. ZnA + ZnB = 2x). Thus the average cation-radii are influenced by the cation distribution.

For the calculation of the average neutron-scattering lengths of the cation sites 4a and 4b (b^ and b4a1c), a certain cation distribution has to be assumed. A first comparison with the experimentally-determined average neutron-scattering lengths show, that Zn is not statistically distributed on the sites 4a and 4b. Thus three different aspects have to be taken into account for modelling the cation distribution:

(i) Zn is non-statistically distributed

(ii) If Zn prefers the 4a position a CuIn anti-site is enforced and if Zn prefers the 4b position an InCu anti site is enforced (enforced anti-sites)

(iii) Independent of the Zn distribution, CuIn and InCu anti-sites may exist (spontaneous anti-sites)

The evaluation criteria for the cation distribution in tetragonal (2ZnS)x(CuInS2)1-x mixed crystal were formulated as:

(1) u(exp) = u(calc) (u(exp) is determined by Rietveld analysis of the powder diffraction data, u(calc) applying the CTB rule)

(2) bZ = b4f and b4bP = fo4f

Applying both criteria, and taking into account the aspects (i)-(iii), the cation distribution was evaluated in two steps. First, the possible cation distributions fulfilling criterion (1) were derived. As can be seen from Fig. 5.11, a variety of different cation distributions are possible.

In the second step criterion (2) is also taken into account. The graphical solution is shown in Fig. 5.12. It becomes clear, that Zn occupies the 4b site preferentially, enforcing *1.8-4.5 % InCu. Moreover, there is a small fraction of spontaneous Cu-In anti-sites (i. e. CuIn and InCu).

Taking into account the experimental error of the average neutron-scattering lengths Ь^ and bb it can be deduced, that 27.5 % of the Zn occupies the 4a site,

whereas the rest of the Zn occupies the 4b site. This leads to 3.6 % enforced InCu anti-site. These results are in a good agreement with the cation distribution eval­uated from X-ray powder diffraction data ((Zn + Cu)Cu = 0.91(3); InCu = 0.09(3); (Zn + Cu)In = 0.14 and InIn = 0.86(3)), but here Cu and Zn could not be

distinguished. The cation distribution in Zn2x(CuIn)1-xS2 mixed crystal is sum­marized in Table 5.3.

The CTB rule was only applied for the sulfide mixed-crystals due to the rela — tively-well known cation radii in sulfides [23]. For the selenide and telluride Zn2x(CuIn)1-xC2 mixed crystals the differences between bff and bc4fc as well as beJf and b>4afc, assuming a statistical Zn distribution in the calculation of the average neutron-scattering lengths, were considered [42, 45]. Here, a non-statistical distri­bution of Zn on the both cation sites was also found. With increasing ZnX-content in Cu0.5In0.5X there is a propensity for a more statistical distribution of the cations, indicating a tendency for disorder in the cation substructure.

It can be assumed that the non-statistical distribution of Zn and the associated Cu-In anti-sites are related to the limited solubility of ZnX in Cu0.5B0.5X. This fact can be discussed within the framework of formation energies of intrinsic point — defects in copper chalcopyrites. The Cu-In anti-site occupancy, resulting in CuIn and InCu, are the defects with the lowest formation energies (in CuInSe2: 1.3 eV for CuIn and 1.4 eV for InCu [46]). Thus, these defects can be formed relatively easily. Nevertheless, the formation energies of ZnCu or ZnIn are not known. If one of the occupancies were energetically unfavourable, the solubility would be affected.

Using the approach of the average neutron-scattering length and the CTB rule it was possible to determine the cation distribution for various stoichiometric chal- copyrite-type Zn2x(CuB)1-xC2 compounds. It was clearly shown that Zn tends to occupy the 4b site preferentially, resulting in the formation of InCu and CuIn defects, resulting in a partially disordered chalcopyrite-type crystal structure.

Whilst the difficulties of realising sustainable energy are decreasing, the difficulties of fossil-fuel based energy are increasing and the point will inevitably arrive when sustainable energy is not only socially and environmentally more favourable, but also makes economic sense in its own right. Sustainable-energy materials will develop over the long run, and the role of neutron-scattering techniques in the understanding of these is almost certain to develop in parallel. Generic improve­ment in neutron sources and instrumentation will enable smaller samples to be measured in shorter times, and this is part of the wider scientific agenda. However, there are also specific improvements that will benefit the study of energy materials.

In situ and operando experiments are crucial for “close to market” studies, and whilst these are not simple with neutrons, they are generally more straightforward than with other methods. Perhaps ironically, it is now possible to construct real lithium batteries that are optimised for operando neutron-diffraction measurements, where the optimisation may affect cost, but has little or no effect on the actual operation. Often the modification for operando neutron scattering amounts to deuteration of materials and neutron-scattering centres are increasingly housing specialised deuteration facilities, capable of deuterating complex molecules.

The complex systems that characterise the development of energy materials give complex neutron-scattering signals, from which it can be difficult to deconvolve unambiguous information. However, the rapid increase in computer hardware and software is enabling the experiment, data treatment, theory, and modelling to be brought together to provide consistent interpretation of the neutron-scattering data. Although at present this is the domain of specialists, considerable efforts are being made throughout the neutron-scattering community to bring this type of approach within the reach of non-specialist users. Although previously the multiprocessor computer hardware required for this type of work was only available at central­computing establishments, it is now becoming ubiquitous in universities and neutron­scattering centres where there is generally good local support.

The experimental programme at neutron-scattering centres has to strike a balance between scientific, societal, commercial, and national interests, the details of which depend on the strategy and “terms of reference” of the centre. Sustainable-energy materials are almost equally important in all aspects of this balance, which provides a unique opportunity for communication and collaboration across these aspects and between neutron-scattering centres. Although this type of initiative has yet to occur, there have been a large number of conferences and workshops at the purely scientific level that have been funded from a diverse range of sources. Larger gatherings, specifically highlighting neutron scattering, would provide an over­arching description of problems, bottle-necks, and resources, from industry, strat­egists, and through to experimentalists.

References

1. I. S. Anderson, A. J. Hurd, R. McGreevy (eds.), Neutron Scattering Applications and Techniques, (Springer, Berlin)

2. L. Liang, R. Rinaldi, H. Schober. (eds.), Neutron Applications in Earth, Energy and Environmental Sciences (Springer, Berlin, 2009)

3. http://www. springer. com/series/8141. Accessed 4 March 2014

4. H. Jobic, D. N. Theodorou, Microporous Mesoporous Mater 102, 21 (2007)

Part I

Residual stresses are those that remain in a component after external forces are removed; they are self-equilibrating in nature and are often caused by deformation or uneven heating during manufacture; particularly casting, forging, forming, or welding operations. Residual stresses are significant in the failure of components as they contribute to fracture, fatigue, stress corrosion cracking (SCC), hydrogen — assisted cold cracking, hydride formation, or lead to unacceptable deformation during manufacture. An understanding of residual stress is essential in developing new components, materials, and joining techniques for nuclear-energy systems.

As most metal-forming operations involve heating and or deformation, residual stresses are almost always present due to differential thermal-strains, phase trans­formations, or plastic mismatch. These mismatches cause elastic strains, which result in residual stresses. The structural issues that arise from residual stresses are of two types, those that are conventional structural-integrity issues (fracture, fatigue, stress corrosion cracking susceptibility, creep crack growth, hydride formation, and dis­tortion) and issues that come about due to the interaction of residual stress and radiation with service exposure (stress relaxation, creep, and swelling; all induced by radiation).

Structural integrity assessments of nuclear components rely on accurate values of the residual stresses; in the absence of better information these must be con­servatively assumed to be equal to the yield strength, leading to small critical-defect sizes and loads. The regular use of residual stress measurements by neutron dif­fraction has been able to safely reduce the conservatism of these estimates by providing accurate, validated measurements. Stresses cannot be measured directly, only the elastic strains locked into the material. Broadly speaking, there are two methods of measuring residual stresses; compliance methods and methods that measure lattice strains in crystalline materials (typically metals) [1—3]. Compliance methods assess deformations that occur during cutting or other methods of material removal. Lattice strains are typically measured by diffraction and comparing lattice spacings in the strained and unstrained condition, this can be done by X-ray (including synchrotron) and neutron diffraction. Neutron diffraction has many advantages over other methods of measuring residual stresses due to its good penetrating power and spatial resolution within the bulk of the component.

A difficulty with diffraction measurements is that a stress-free sample is often required for reference. Furthermore, the compositional strain-variation that may occur across welds leads to unavoidable sources of error due to so-called chemical strains. There may be significant variation in the weld position and composition between the stress-free sample and the measured component. Where one stress component is known to be near zero measurement at a range of angles normal to the surface using the sin20 technique [3] can obviate the need for a stress-free sample.

Energy storage is a key enabling technology to the larger area of sustainable energy. For transport applications, the storage needs to mirror the energy density of petrol and diesel, and because sustainable energy-sources such as solar and wind are variable in nature, the buffering capacity of storage is also of importance. The main energy-storage technologies are batteries, capacitors, pumped storage, hydrogen, flywheels, and compressed (or liquefied) gasses. Each has its technological and logistical challenges, with Chaps. 7 and 8 examining the two major areas of lithium — ion batteries and hydrogen storage, respectively.

The central theme in both battery and hydrogen-storage materials is increasing energy density gravimetrically and volumetrically, in a way that enables the energy to be stored and retrieved in a time and energy-efficient way. It is difficult for either battery or hydrogen storage materials to compete with the energy density of petrol and diesel. Neutron techniques of analysis here are used to understand the inter­actions that hold the energy-carrier in place, but can then release it when it is required for use. In these chapters the role of in situ studies is particularly important and this is an area in which the penetration of neutrons excels. It is sufficiently important that neutron-scattering centres provide custom made gas-handling and potentiostat/galvanostat equipment that can be used by several different groups.

Chapter 7 shows a large volume of study has been undertaken to determine the crystal structure of electrode materials to determine the position and environment of lithium in complex and multiphase electrode materials, even as the battery is charged and discharged. However, disordered and amorphous materials often have the desired materials properties, and it is illustrated that neutron scattering is also relevant to these by using the total scattering technique and spectroscopy. Although lithium is better suited to study by neutron scattering than many other techniques, it is nevertheless challenging, particularly when compared to hydrogen (Chap. 8). First, the absorption cross-section of one of the naturally-occurring lithium isotopes is high, and whilst this can be overcome, and even exploited by isotopic selectivity, this is expensive. Secondly, not only would we like fast diffusion for better bat­teries, but it would make the study of diffusion by neutron scattering easier. Current

neutron instrumentation can access lithium diffusion when used at high resolution, but this limits the neutron counting-rate, making the experiments more difficult, and in some cases impractical. Fortunately, in some examples it is reasonably straightforward to derive the dynamics of the lithium by studying the response (or driving dynamics) of the environment, in this case it is the environment that has a strong neutron signal.

Hydrogen storage (Chap. 8) has probably been the most important area of sustainable-energy research for neutron scattering due to the special interaction between neutron and hydrogen and its isotope deuterium. In common with battery materials, there has been a large volume of work using diffraction to determine the position and environment to be derived of the H-atoms (or molecules), much of which existed prior to hydrogen-storage applications. The interplay between atomistic modelling and neutron scattering pervades sustainable-energy research, but is particularly important in hydrogen storage due to the ease with which the dynamics of the model can be compared with neutron-spectroscopy results. This enables very detailed information about how hydrogen interacts with all the com­ponents of its environment, and whilst this is also possible for the battery materials above, the experimental difficulties associated with lithium make it much more challenging. Hydrogen is a light element and quantum effects in its dynamics are pronounced. Because of the way in which the neutron spin interacts with the nuclear spin of hydrogen, neutrons provide a very sensitive measure of these quantum dynamics, which is in turn very sensitive to its environment. These dynamics are not only of interest for tuning the interaction of hydrogen with its storage material, but are also of fundamental interest in their own right and much of the theory for understanding the measured neutron-scattering spectra had already been established because of this. There is a considerable body of analogous work for methane, which whilst of considerable technological importance, is not covered in this book. The analogy is strongest for storage in metal-organic framework and clathrate materials, and in most cases the extension of the work presented here for hydrogen to the methane case is straightforward.

MIL-53(Cr), and its isostructural form MIL-47(V), are built up from infinite chains of corner-sharing Cr3+O4(OH)2 or V4+O6 octahedra interconnected by 1,4-ben — zenedicarboxylate groups (Fig. 2.5). These three dimensional MOFs contain one-dimensional diamond-shaped channels with pores of nm dimensions. One may note that MIL-53(Cr) exhibits hydroxyl groups located at the metal-oxygen-metal links (u2-OH groups) which open up the possibility of additional preferential adsorption sites and thus different adsorption or diffusion mechanisms to that of MIL-47(V) where these specific groups are absent.

The self-diffusion of H2 in these two structures was studied by QENS combined with molecular dynamics (MD) simulations [2, 22]. For the QENS measurements, the frameworks and the ^2-OH groups in MIL-53(Cr) were deuterated to reduce the signal from the MOF. To illustrate the possibility to obtain information on diffusion anisotropy, one and three dimensional diffusion models are compared with exper­imental spectra in Figs. 2.6 and 2.7. When the diffusion is isotropic (three­dimensional), the theoretical dynamic structure-factor, S(Q, rn), corresponding to a translational motion has a Lorentzian profile in energy, but the line shape is more elongated in the case of diffusion in one-dimensional channels, because a powder average has to be made [22].

In MIL-53(Cr), profiles corresponding to three-dimensional diffusion and con­voluted with the instrumental resolution do not fit perfectly through the experi­mental points (Fig. 2.6a and Ref. [22] for spectra obtained at other Q values). A normal one-dimensional diffusion model, with a more waisted shape, fits better the experimental data (Fig. 2.6b and Ref. [22]). This is due to the interaction between H2 and the ^2-OD groups, leading to a one-dimensional diffusion along the tunnels via a jump sequence involving these hydroxyl groups. Normal one­dimensional diffusion means that the molecules can cross each other in the tunnels of MIL-53. When the molecules cannot pass each other, the diffusion is called single file [23].

In MIL-47(V), the reverse is found: The three-dimensional diffusion model reproduces better the QENS spectra than one-dimensional diffusion (Fig. 2.7 and Ref. [22]). The motions of H2 in this MOF are random because there are no specific adsorption sites for hydrogen.

The Ds values of H2 in both solids are reported in Fig. 2.8 as a function of loading. Contrary to the concentration dependence obtained in NaX (Fig. 2.4), Ds decreases in both MILs when the H2 loading increases, this is due to steric reasons in these one-dimensional systems, and to the absence of strong adsorption sites. Experiment and simulation find higher diffusivities in MIL-47(V) than in MIL-53 (Cr), whatever the loading. This can be explained by the presence of the ^2-OD groups in MIL-53(Cr) which act as attractive sites and steric barriers for H2, leading thus to a slower diffusion process. Further, a high H2 mobility is observed in both MILs, at low loading, the Ds values are about two orders of magnitude higher than in zeolites (Fig. 2.4 and Ref. [15]). Extrapolating Ds to zero loading in Fig. 2.8 leads to a value of the order of 10-6 m2s-1 in MIL-47(V). This is comparable to the supermobility predicted in single-walled carbon nanotubes [24].

Fig. 2.8 Self-diffusivities of H2 at 77 K as a function of loading in MIL-47(V) (rounds) and MIL-53(Cr) (squares): QENS (full symbols) and MD (empty symbols), where u. c. = unit cell

As hydrogen is such a strong scatterer, the presence of hydrogen, water, and hydrides are easily detected in neutron radiography and tomography [61]. Coolant behaviour in the fuel bundle of a boiling-water reactor (BWR) was examined by Zboray et al. [62] with neutron tomography (Fig. 4.13), allowing the coolant flow and channels to be optimized.

In the next sections we will outline the basics of the neutron techniques of analysis that underpin the chapters that follow. Neutrons have the same principle attributes as photons for the study of a wide range of materials. Neutrons can be diffracted giving information about atomic position, scattered inelastically giving information about atomic (or molecular) motion, and neutrons can be absorbed giving spatial information concerning material composition through radiography and tomography. The instrumentation for photons is well known, but for neutrons there is an almost analogous group of techniques that together cover length scales from fractions of an

A to microns (and up to many centimetres for radiography) and timescales that cover from femtoseconds to hundreds of nanoseconds. The generic properties of neutrons lead to the recurrent use of particular neutron scattering and neutron-based analysis throughout this book, and this section explains the rudiments of these.

Large-scale structure analysis methods such as small and ultra-small angle neutron scattering (SANS and USANS, respectively), yield unique, pore-size-specific insights into the kinetics of CO2 sorption in a wide range of pores (nano to meso). These methods also provide data that may be used to determine the density of adsorbed CO2
through the evolution of microstructure and adsorption capacity. This approach has been applied to the analysis of CO2 in geological samples, including coal. By studying coal exposed to CO2 at subsurface-like temperature and pressure the phase behaviour of the confined CO2, particularly the densification occurring on changing from the gaseous to the liquid phase, was found to have significant operational and reservoir capacity ramifications when assessing the suitability of unmineable coal seams for use as CO2 sequestration reservoirs [51]. The results show that the sorption capacity of coal is sample-dependent and strongly affected by the phase state of the injected fluid (subcritical or supercritical). Subcritical CO2 densifies in the coal matrix, with details of CO2 sorption differing greatly between different coals and dependent on the amount of mineral matter dispersed in the coal. A purely organic matrix was found to absorb more CO2 per unit volume than one containing mineral matter, although the mineral matter markedly accelerated the sorption kinetics [52].

Figure 3.6 shows SANS and USANS data for coal from Seelyville (Indiana, USA) exposed to several pressures of CO2, which could be described using a power law for the scattered intensity with an exponent of -3, indicating the fractal character of the scattering. The scattering intensity shows Q-dependency as a result of the CO2 in the pores. After completion of the pressure cycling, the neutron­scattering curves returned to their original shapes within 1 %, implying that the microstructure was not permanently affected by exposure to CO2 over a period of days. This result indicated that the phenomenon of coal plasticization upon expo­sure to CO2 may be less widespread than thought previously. The work also found that the small pores within coal are filled preferentially over larger void-spaces by the invading CO2, a result echoed by MOFs [32]. Apparent diffusion coefficients for CO2 in coal are thought to vary in the range 5 x 10 7 to more than 10 4 cm2min 1 according to the CO2 pressure and location. At higher pressures CO2 is shown to

diffuse immediately into the coal matrix, swelling the coal and changing its mac­romolecular structure, where it is postulated to create microporosity through the extraction of volatile components [53]. Injection of CO2 into model subsurface geologic formations has been identified as a key strategy for CO2 storage. Key to the success of such a strategy is the prevention of leakage from the host by an effective cap with low porosity and permeability characteristics. Shales comprise the majority of caps encountered in subsurface injection sites with pore sizes typ­ically less than 100 nm and whose surface chemistries are dominated by quartz and clays. Analysis of simple, well-characterized fluid-substrate systems can provide details on the thermodynamic, structural, and dynamic properties of CO2 under conditions relevant to sequestration. In particular, the behaviour of CO2 interacting with model silica substrates can act as proxies for more complex mineralogical systems. SANS data for CO2-silica aerogel (95 % porosity; *7 nm pores) indicates the presence of fluid depletion for conditions above the critical density [54].

Substitution of indium by zinc and tin in CuIn(S, Se)2 leads to the quaternary compound semiconductor Cu2ZnSn(S, Se)4 (CZTSSe). The record efficiency of thin-film solar cells using a CZTSSe absorber layer is above 10 % [47].

Both compounds, CZTS and CZTSe, belong to the family of tetrahedrally — coordinated adamantine semiconductors [48]. Here each anion is tetrahedrally coordinated by four cations (two copper, one zinc and one tin), whereas each cation is coordinated by four anions (sulfur or selenium). Thus, the structure is charac­terized by a well-defined framework of tetrahedral bond arragnements, which is advantageous for the properties of the material.

For the quaternary a2BiiCivXJi chalcogenides with A-Cu; B-Zn; C-Si, Ge, Sn and X-S, Se, different crystal structures are discussed in literature: the kesterite — type structure (space group I4), the stannite-type structure (space group I42m), as well as the wurtz-stannite (space group Pmn21) and the wurtz-kesterite type structure (space group Pc). The same tetrahedral metal-coordination (2Cu, one II — and one IV-element surrounding each S-atom) is possible in all four space groups. A clear decision can only be made by a detailed structure analysis for each compound.

At room temperature CZTS adopts the space group /4. The structure can be described as a cubic close-packed array of sulfur atoms, with metal atoms occu­pying one half of the tetrahedral voids. CZTSe was reported to crystallize in the space group 142m in a topologically-identical structure, but different cation distri­bution of A1 and B11 among the positions (0, 0, 0), (0, XA, ^), and (0, XA, %) [49]. Both structures are represented in Fig. 5.13.

Neutron powder diffraction and the method of the average neutron-scattering length were used to clarify possible differences of the cation distribution in CZTS and CZTSe, especially with respect to the electronically-similar elements copper and zinc [50, 51].

According to the general formula for the calculation of the average neutron­scattering length (see also Sect. 5.3.2)

bj = Aj • bA + Bj • bB + Vj (5.13)

where A and B are two different cations, V represent possible vacancies and j stands for the Wyckoff position, the following equations were derived for the calculation of the experimental average neutron-scattering lengths 4bjexp

exp

b2a occ2a ‘ bCu

b2xp = OCC2c ‘ bZn b2dp = occ2d • bCu

b2x/ = Occ2a • bZn

b4d^ = occ4d • bCu

The cation site-occupancy values occ, resulted from the Rietveld analysis of the neutron diffraction data. Because the study was performed using stoichiometric powder samples (the chemical composition of the samples was determined by wavelength-dispersive X-ray spectroscopy), vacancies were not taken into account.

The Rietveld analysis of the neutron diffraction data was performed by applying different cation-distribution models within both structure types as the starting model for the crystal structure (see Table 5.4). The cation site occupancies were taken as free parameters in the refinement. It was found that the refined cation site-occu­pancy values differ from their nominal values (Table 5.4), with the exception of the tin. Thus, one can conclude that the site is not only occupied by the initially — supposed model cation, but also by a mixture of different elements. For example, a decrease of the average neutron-scattering length of the 2d site in the kesterite-type structure can be attributed to a partial Zn occupation due to bCu > bZn.

The refined cation site occupancies were used to calculate the experimental average neutron-scattering lengths (see Fig. 5.14). The first result obtained was a confirmation of the occupancy of the 2b site by tin in both compounds. Con­cerning the sites 2a, 2c and 2d for the space group /4 as well as 2a and 4d for the space group /42m, a similar picture for both compounds appears. Irrespective of the structure model used in the Rietveld analysis, the average neutron-scattering length of the 2a position indicates that this position is occupied by copper only. The average neutron-scattering lengths of the sites 2c and 2d indicate a mixed occu­pancy of these both sites by copper and zinc. Approximately 50 % of the zinc site 2c is occupied by copper and vice versa concerning the copper site 2d, forming

CuZn and ZnCu anti-sites. Nevertheless, this disorder is limited to the positions 2c and 2d and hence to the lattice planes at z = 1/4 and 3/4. The 2a site is always occupied by copper only, and there are no indications of zinc occupying that site.

These facts bring us to the conclusion that both compounds, CZTS and CZTSe, adopt the kesterite-type structure, but exhibit Cu-Zn disorder in the (00l) lattice planes at z = 1/4 and 1/3. This disorder creates CuZn and ZnCu anti-site defects. These results are supported by ab initio calculations carried out on these systems [52, 53]. The authors report that the CuZn anti-site acceptor can be predicted as the most probable defect and thus can be easily formed. Moreover, the kesterite-type structure was indicated as the ground-state structure for both CZTS and CZTSe, though the stannite-type structure has only a slightly-lower binding energy (CZTS: 2.9 meV/atom [52], 1.3 meV/atom [53], CZTSe: 3.8 meV/atom [52], 3.3 meV/atom [53]).

Using the approach of the average neutron-scattering length, and applying dif­ferent structural models with different cation distributions in the structural description in the Rietveld refinement procedure, the crystal structure of CZTS and CZTSe was determined and intrinsic point-defects were identified experimentally. In contradiction with earlier X-ray diffraction studies, the kesterite-type structure was also proved for CZTSe.

Energy generation is not only important for meeting the requirements of consumers and industry, but is crucial for national security and economic competitiveness. Environmental sustainability is a global issue that needs to respond to existing damage from direct emissions as well as unplanned future events such as spills and leakages. Neutron techniques of analysis play some role in progressing all tech­nologies for renewable-energy generation, although this may be limited to structural materials for wind, marine and hydro energy generation, whilst neutron scattering in earth sciences plays a significant role in geothermal energy. Chapters in Part 1 concentrate on those aspects of energy generation that are mainstream for neutron — based methods, but are nevertheless relevant to the more general sustainable-energy technologies in energy generation.

Catalysis (Chap. 2) not only plays a central role in sustainable-energy generation where renewable feedstocks are used, but also plays a more general role in increasing efficiency, reducing energy consumption, and producing cleaner targeted products from fossil-based sources such as oil, natural gas, and coal. Active sites in catalysis are often present in only trace quantities, and characterizing these with neutrons is usually limited to model compounds. However, almost the whole range of neutron techniques of analysis have been used to help in the design, characterisation and optimisation of catalysts by measuring the structure of the catalysts themselves, and following the dynamics of the reactants and products. The hydrogen economy requires an efficient means of generating, storing, and using hydrogen, all of which involve some catalysis. However, because the most important role of catalysis is in energy generation, we gather all aspects of the topic in Chap. 2.

Although global CO2 emissions threaten today’s way of life, cost-effective methods to separate, capture, store, or use CO2 from fossil fuels represent a major challenge. As existing technologies use solvents that impose a heavy energy-pen­alty (about 30 % of the energy generated by the plant), a key scientific challenge is the development of materials that can interact with flue-gas streams to capture and concentrate CO2 with lower energy requirements. Porous materials such as

coordination polymers offer a new way to address this in that they not only possess the highest surface area of any known materials, but they can be engineered to be selective for CO2. Therefore, solid porous hosts represent one of the most prom­ising technologies for separating and storing gases of importance in the generation and use of energy. Studying the uptake of CO2 in such materials at the fundamental level is required to progress these towards commercialisation, with such studies allowing direct feedback into the synthesis of materials with enhanced CO2 uptake, selectivity, and chemical stability. Neutron scattering is essential in this research with in situ studies involving pressure and/or temperature being of particular importance. Both structural and dynamical information is important in this area in order to establish the gas-host interaction, and forms the basis of Chap. 3.

Structural materials are important to all forms of sustainable-energy production and neutron scattering is increasingly being used to characterize and understand fatigue and failure, and in this context we concentrate on materials for nuclear — energy applications in Chap. 4. Nuclear materials are particularly demanding because they must meet the mechanical demands not only under pressure, tem­perature, and chemical environment, but also under the effects of irradiation. Neutron-based characterisation of such materials mainly takes the form of neutron diffraction to understand how the microstructure and crystal structure characterize bulk material-properties. Superficially, this is a straightforward measurement, but in practice we need to understand how crystal structure, microstructure, chemical composition, and orientation are all coupled, and how these can be controlled to obtain (or avoid) particular properties. Major neutron-scattering centres now have at least one instrument that is conceived specially to do these types of experiment.

One of the greatest contributions neutron scattering has made in the study of sustainable energy-materials is in solar cells, which are divided into inorganic and organic in Chaps. 5 and 6, respectively. Photovoltaics (PV) is required for each of them, and is the direct conversion of light into electrical energy, the first PV device having been built by Edmond Becquerel who discovered [R. Williams, J. Chem. Phys. 32,1505 (1960)] thePV effect in 1839. The operating principles of this effect are based on a sequence of light-matter interactions that can be summarized as follows:

(i) Absorption of photons with a given energy matching the semiconducting properties of the device (band gap and intrinsic coefficients);

(ii) Free charge-carrier generation in inorganic semiconductors and bound exciton (pair of electron-hole) creation in the case of the organic analogous and exciton [E. A. Silinsh, V. Capek Organic Molecular Crystals — Interac­tion, Localization and Transport Phenomena (American Institute of Physics, New York, 1994)] dissociation;

(iii) Charge transport via relevant pathways;

(iv) Charge collection at dedicated electrodes and photocurrent generation.

PV solar cells convert solar energy into electricity via the PV effect in a variety of strategies that can be classified as (Fig. 1): Multijunction, single-junction GaAs, crystalline Si, thin-film, as well as organic and emerging (including hybrids).

Sustained development has been achieved for each of the PV strategies over the past decades (Fig. 1). It is important to notice that step changes in efficiency mainly arise with the discovery of a new strategy, but that this is not always upwards. This is because many factors contribute to the cost per Watt, and low efficiency may be counterbalanced by overall cost, which is composed of:

(i) Energy pay-back time;

(ii) Stability and lifetime;

(iii) Environmentally friendly materials and production;

(iv) Cost and supply of materials;

(v) Adaptability of shape/form;

(vi) Size/weight.

For PV materials there is a convenient separation of the materials in the broader classification of inorganic and organic. More attention has been devoted to inor­ganics, which have been known for well over a century and promise very high efficiency. In contrast, the first organic PV (OPV) was crystalline anthracene [H. Kallmann, M. Pope, J. Chem. Phys. 30, 585 (1959)], this having been first observed in 1959. OPVs have only been only attracting significant attention in the past decade (Fig. 2), at least in part as a result of robust concepts and principles for organic semiconductors set up around 1970 by Alan J. Heeger, Alan G. MacDiarmid, and Hideki Shirakawa, who were awarded the Nobel Prize in 2000 for this contribution. This paved the way for the use of organic materials as PV devices, inducing and stimulating a tremendous interest in research on OPVs for both fundamental and technical purposes.

In inorganic (thin film, Chap. 5) and organic (Chap. 6) solar cells we focus our attention on case studies of model systems with the aim of showing how neutron techniques of analysis in combination with other techniques contribute to our understanding and resolution of specific challenges in PV materials. The failure of one of the earliest cells, Cu2S-CdS, due to Cu+ to Cu2+ conversion, illustrates the importance of understanding functional properties of PV materials at a number of levels. PV materials cover a vast range, from soft, almost liquid materials through to hard crystalline materials, with local and large-scale structure, interfaces, and dynamics over a wide range of timescales also being important. The challenge for diffraction is that the required semi-conductors are usually not only non-stoichi­ometric (due to doping), but also composed of elements with similar atomic numbers. The non-stoichiometry can lead to structural defects that affect the material and electronic properties so it is essential to have a method for identifying and characterising these differences. Chapter 5 shows how the neutron scattering cross-sections enable not only neighbouring elements to be distinguished, but also the study of defect non-stoichiometric structures. Chapter 6 concerns investigating the comparatively weak forces holding the organic and polymeric molecules together, these being both advantageous and disadvantageous for PV applications. Hence, whilst for inorganic PV materials the atoms can be regarded as localized, for organic PV materials molecular dynamics plays at least an equally important role as time-average atomic position. Dynamics on different timescales is responsible for recombination, charge-transfer, processing, and ultimately ageing, all of which are important to the PV’s function.

Chapter 6 shows not only the use of neutron diffraction, but also how different neutron spectroscopies can be used to unravel the dynamics that helps or hinders different aspects of the PV process.