## X ray

Emil Bøje Lind Pedersen

### General X-ray introduction

X-rays are electro-magnetic waves with wavelength in the interval 0.01 – 10 nm. They were first discovered by Wilhelm Röntgen in 1895. The first application of X-ray imaging was the now famous absorption images of Anna Röntgen’s hand (see figure 1). For material science crystallography was one of the early adopters of X-rays. In 1912 Max von Laue did the first X-ray diffraction on copper sulphateFriedrich, W., Knipping, P. & von Laue, M. Interferenz-Erscheinungen bei Röntgenstrahlen, von W. Friedrich, P. Knipping und M. Lane. Interf. bei Röntgenstrahlen, von W. Friedrich, P. Knipping und M. Lane (München: Verlag der Königlich-Bayerischen Akademie der Wissenschaften., 1912).. Next year Bragg for the first time solved the atomic crystal structure of NaClBragg. The Structure of Some Crystals as Indicated by their Diffraction of X-rays. Proc. R. Soc. Lond. A89, 248–277 (1913). Since then crystallography has been routinely used to map atomic structures of vide range of crystalline materials even soft materials like proteinsDOI:10.1038/80754.

Figure 1: X-ray absorption image of Anne Röntgens hand. Early X-ray imaging that demonstrates absorption contrast between light elements (carbon, oxygen and hydrogen in organic tissue) and heavier elements (Ca in Bone).

The electro-magnetic properties of X-rays mean they interact primarily with the electron clouds surrounding the molecules and not the atom cores themselves. In general, X-rays interact stronger with heavier elements since they are surrounded by more electrons, which for instance give rise to contrast in medical images with more absorption in bones (calcium) and less absorption in organic tissue (carbon, oxygen and hydrogen). The density of the material also plays a role to X-ray interaction. With knowledge of elements and material density one can calculate the electron density which often is proportional to X-ray interaction.

### X-ray techniques and application in OPV research

Compared to optical light, the energy of the X-rays is much higher, which allow them to penetrate through solid materials. Some of the X-rays will not penetrate due to interaction with the material and give rise to absorption contrast. This depends on the electron density of the material but also which electron energy levels are available. Just like optical light can excite electrons from LUMO to HOMO levels, low energy X-rays can excite core electrons to HOMO levels or higher. Since these states are molecules specific the absorption profile for X-rays can be used to make compositional maps of thin films with OPV materials and even determine degradation stateDOI:10.1039/C4TC00028E. Besides absorption X-rays can also interact with electrons by scattering. Constructive interference from multiple scattering signals becomes diffraction described by Braggs law. $$2d \sin\theta = n\lambda$$ Where d is the distance between repeating structures (crystal planes), θ is the X-ray scattering angles, n is an integer number and λ is the wavelength. The distance is roughly inverse proportional to scattering angle. In essence this means small repeating distances will diffract to large angles so small distances is easier to detect. This allows X-ray diffraction to accurately determine the distances between ordered molecules – distances often in the 10-10 m scale.

Many OPV materials are not entirely crystalline but semi-crystalline. This means only a fraction of the molecules will pack in a regular pattern depending on how they are processed. The packing distances are speculated to affect charge transport and thereby device performance. X-ray diffraction thus allows a view into the orientation and ordering at the molecular level. X-ray diffraction can even be combined with roll to roll processing for systematic characterization of processing conditions.DOI:10.1039/c2jm34596j

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