Batteries are an important aspect of sustainable energy technologies, as they can be used either for the storage of electric energy for the grid or for the electrification of the transport fleet, making these sectors less reliant on fossil fuels (chapter 1). The Li-ion battery has revolutionized the world in many ways, enabling portable electric devices as honored by the Nobel prize in 2019 to John B. Goodenough, M. Stanley Whittingham and Akira Yoshino. As the Li-ion battery is quite a mature technology by now, large gains in performance parameters (especially energy density) will need alternative battery concepts and new chemistries. There are many possibilities, and one of them is a switch from liquid to solid electrolytes (chapter 2). The work presented in this thesis investigates the structure-to-property relationship of halide solid-electrolytes Li₃M(III)X₆. For solid electrolytes to replace liquid electrolytes, the material needs a combination of properties. An important property is the ionic conductivity, which should be high enough for room-temperature operation of the battery and determines, among other design parameters, the rate-capability (or power density) of the battery. Another property that is important is the electrochemical stability window, which determines the electrochemical stability of the electrolyte in contact with the electrodes of the material. Both of these properties are strongly related to the crystal structure and chemistry of the solid electrolyte (chapter 2). Therefore, both the structure and properties are investigated using a variety of techniques, mostly x-ray and neutron diffraction, AC-impedance and solid-state NMR relaxometry (chapter 3). The work is presented in four data containing chapters: • Chapter 4: The materials investigated show very complex behavior relating to diffusion on short time scales, as investigated by NMR T₁-relaxometry. The first chapter therefore provides an in-depth introduction to solid-state NMR relaxometry and spectral density fitting. Using two examples, namely Li₆PS₅X, a sulfide solid-electrolyte class previously studied in the research group, and halide Li₃YCl₃Br₃, it is illustrated how multiple jump processes can present in the curve of the relaxation rates vs. inverse temperature. • Chapter 5: In this chapter, aliovalent substitution in Li₃InCl₆ with Zr(IV) is explored. The Zr(IV) replaces the In(III) and introduces an additional Li-vacancy. The substitution can also affect the crystal structure of the material, affecting ionic diffusion in other ways than changing the charge carrier concentration. Using combined x-ray and neutron diffraction, it is found that the ordering of the In(III) and Zr(IV) is affected by the substitution. This affects also the diffusion on short timescales, as can be observed with NMR relaxometry as well as from the solid-state NMR lineshape. The combination of the structure solution and the puzzle pieces provided by solidstate NMR suggest, that the structural change induced by the substituent leads to more three-dimensional conduction. • Chapter 6: While chlorides have higher electrochemical stability, bromide anions are more polarizable and may have lower association energy with Li, which can lead to higher Li-ion conductivity. This chapter investigates the trade-off between ionic conductivity and electrochemical stability in materials Li₃YClBrₓCl₆₋ₓ. It is found that 75% Br is most beneficial for ionic conductivity rendering a very conductive material (~5 mS/cm at room temperature), higher concentration of bromine indeed lower the electrochemical stability window. The introduction of 25% Br, however, also leads to an increase in ionic conductivity while preserving the electrochemical stability. This suggests that Br-substitution can be a viable method to increase the ionic conductivity of Li-ion conducting chlorides while preserving the electrochemical stability. • Chapter 7: The Li₃M(III)Cl₆ (M(III)= Ho, Y, Dy, Tm) usually are reported to crystallize in a trigonal crystal structure. This paper shows that synthesizing these materials by co-melting with some LiCl deficiency stabilizes an orthorhombic phase of the material. Both of these structures are based on quasi hexagonally close-packed Cl atoms, with the M(III) and Lithium on octahedral sites. The different crystal symmetry is caused by a change in the arrangement of the cations. The orthorhombic phase has ~8 times higher ionic conductivity compared to the trigonal phase. Ab initio molecular dynamic simulations revealed that this is due to a fast conduction pathway along the c-direction of the crystal structure. This path corresponds to jumps between face-sharing octahedra. Therefore, it is likely that the cation arrangement in the orthorhombic structure is favorable for that diffusion path, leading to an increase in ionic conductivity. It is interesting to compare the effect of the different material design strategies aliovalent substitution (Chapter 5), halogen alloying (chapter 6) and tuning of the crystal structure (Chapter 7) on the properties of interest for Li₃M(III)X₆ solid electrolytes. The electrochemical stability window is indeed higher for chlorides than for bromides, but it is found that 25% Br substitution preserves the stability of the chloride in Li₃YCl₆. For ionic conductivity, the largest increase is observed for halogen alloying (factor ~40 increase in ionic conductivity when substituting 25% of the chlorine with bromine atoms), followed by the trigonal to orthorhombic phase transition (factor ~8 improvements) and, lastly, aliovalent substitution (factor ~1.6 improvement). Regarding the measurement methods, two notable findings were found. Firstly, this thesis showed that x-ray diffraction data is important in this system to reach reliable occupancies in the crystal structure solution (chapter 5), as neutrons scattered on lithium and most of the M(III) have a 180°phase shift and therefore cancel their signal when occupying the same site. Lastly, it is shown that the complex shapes of the NMR T₁ relaxation rates can be explained using a superposition of individual, BPP-type jump processes. Fitting such a model is complex, and data measured at multiple larmor frequencies should be used to increase the reliability of the fit. To perform such a fit, a programm was developed in the scope of this thesis to simultaneously fit such measurements and analyze the error associated with the parameter by sampling the posterior probability distribution of the parameter using a Markov chain Monte Carlo sampler.