## 2 Materials and Methods  
The direct dry synthesis of NaAlH\({}_{4}\) has been explained in a previous publication [42]. NaAlD\({}_{4}\) was similarly prepared using NaD (Japan Metals & Chemicals Co., Ltd., 1-17-25, Shinkawa, Chuo-ku, Tokyo 104-8257, Japan) and AlD\({}_{3}\)[43] instead of NaH and AlH\({}_{3}\)[44], respectively. NaAlD\({}_{4}\) or NaAlH\({}_{4}\) (Merck KGaA, Darmstadt, Germany, 93% pure) and TiCl\({}_{3}\) (Merck KGaA, Darmstadt, Germany, 99.995+% pure) were mixed to obtain the composition of NaAlO(H)\({}_{4}\)-\(x\)TiCl\({}_{3}\) (\(x\) = 0-0.06). Each mixture (500 mg) and 20 steel balls with a diameter of 7 mm were placed in a steel vial with a volume of 30 cm\({}^{3}\) and mechanically milled in a planetary ball mill apparatus (Fritsch P7) at 400 rpm for 3 h at ambient temperature. The pressure-composition (\(p\)-\(c\)) isotherms of NaAlO\({}_{4}\)-0.02 TiCl\({}_{3}\) were measured at temperatures ranging from 398 to 408 K. The desorption measurement of the as-milled sample under 10 MPa D\({}_{2}\) at 403 K was started first, and then the sample vessel was evacuated before measuring every absorption up to 10 MPa D\({}_{2}\). The as-milled sample was heat-treated for 10 h at 9.5 MPa of deuterium or hydrogen at 403 K to obtain the neutron/X-ray diffraction patterns of the samples with larger crystallite sizes and fewer lattice strains. To minimize (hydro-)oxidation or nitrogenation, the samples were handled in a glove box filled with purified helium of less than 1 ppm oxygen and a dew point at a temperature below 183 K.  
The averaged structure of the samples (200 mg) in a V-Ni null scattering sample container with an outer diameter of 6.0 mm and a thickness of 0.1 mm were examined before and after the hydrogen desorption/absorption for an exposure time of 4 h at room temperature. This was done by ex-situ neutron diffraction on a neutron total scattering spectrometer (NOVA) (beamline BL21, with a decoupled liquid hydrogen moderator, an incident flight path of 15 m, and a scattered flight path of 1.0-1.4 m at the backscattering detector bank (0.06 \(\leq d\leq\) 5.2 A) connected to a 300 kW spallation neutron source at the Japan Proton Accelerator Research Complex (J-PARC). Scattering data were collected over a lattice spacing range of 0.1-5.2 A for neutron diffraction at room temperature. The consistency in the scattering data was confirmed using standard materials such as silicon powder (NIST SRM 640d). Synchrotron radiation X-ray diffraction measurements were carried out using a Rigaku R-AXIS V detector at the beamline BL22 XU at SPring-8. Scattering data were collected over a lattice spacing range of 0.3-6.5 A for X-ray diffraction with an incident energy of 70.21 keV (wavelength of 0.1766 A) at room temperature. The same samples were placed in a polyimide film tube with an inner diameter of 1 mm and a thickness of 0.05 mm and sealed with epoxy resin on both sides. The averaged crystal structure refinements over a lattice spacing range of 0.6-5.0 A for neutron diffraction at a backscattering detector bank and 0.8-5.0 A for X-ray diffraction, respectively, were performed by Rietveld refinement using the computer program \(Z\)-Rietveld [45; 46]. Anomalous X-ray scattering was performed with an ionization chamber monitor and an Ortec IGLT-16160 detector (Ge SSD) at BL7C at the Photon Factory, KEK. The gas path was equipped around the sample and between the monitor and the sample holder filled with He. The Ge SSD was placed immediately behind the sample through a solar slit. The incident energy was calibrated using a Cu film (8.9803 keV). The atomic scattering factor of the X-ray can be expressed as:  
\[f=f_{0}(Q)+f^{\prime}(E)+if^{\prime\prime}(E) \tag{5}\]  
where \(f_{0}\) is the Thomson scattering term, and \(f^{\prime}\) and \(f^{\prime\prime}\) are anomalous scattering factors [47]. \(f^{\prime\prime}\) is related to absorption.