Determining internal porosity in Prussian blue analogue cathode materials using positron annihilation lifetime spectroscopy

Prussian blue analogues (PBAs), $${{A}_x{M}[{M'}({\text {CN}})_{6}]_{1-{{y}}}\cdot {z} {\text {H}}_{2}{\text {O}}}$$A x M [ M ′ ( CN ) 6 ] 1 - y · z H 2 O , are a highly functional class of materials with use in a broad range of applications, such as energy storage, due to their porous structure and tunable composition. The porosity is particularly important for the properties and is deeply coupled to the cation, water, and $${[{M'}({\text {CN}})_{6}]^{{{n}}-}}$$[ M ′ ( CN ) 6 ] n - vacancy content. Determining internal porosity is especially challenging because the three compositional parameters are dependent on each other. In this work, we apply a new method, positron annihilation lifetime spectroscopy (PALS), which can be employed for the characterization of defects and structural changes in crystalline materials. Four samples were prepared to evaluate the method’s ability to detect changes in internal porosity as a function of the cation, water, and $${[{M'}({\text {CN}})_{6}]^{{{n}}-}}$$[ M ′ ( CN ) 6 ] n - vacancy content. Three of the samples have identical $${[{M'}({\text {CN}})_{6}]^{{{n}}-}}$$[ M ′ ( CN ) 6 ] n - vacancy content and gradually decreasing sodium and water content, while one sample has no sodium and 25% $${[{M'}({\text {CN}})_{6}]^{{n}-}}$$[ M ′ ( CN ) 6 ] n - vacancies. The samples were thoroughly characterized using inductively coupled plasma-optical emission spectroscopy (ICP-OES), thermogravimetric analysis (TGA), X-ray diffraction (XRD), and Mössbauer spectroscopy as well as applying the PALS method. Mössbauer spectroscopy, XRD, and TGA analysis revealed the sample compositions $${{\text {Na}}_{1.8(2)}{\text {Fe}}^{2+}_{0.64(6)}{\text {Fe}}^{2.6+}_{0.36(10)} [{\text {Fe}}^{2+}({\text {CN}})_{6}]}\cdot 2.09(2){{\text {H}}_{2}{\text {O}}},$$Na 1.8 ( 2 ) Fe 0.64 ( 6 ) 2 + Fe 0.36 ( 10 ) 2.6 + [ Fe 2 + ( CN ) 6 ] · 2.09 ( 2 ) H 2 O , $${{\text {Na}}_{1.1(2)}{\text {Fe}}^{2+}_{0.24(6)}{\text {Fe}}^{2.8+}_{0.76(6)} [{\text {Fe}}^{2.3+}({\text {CN}})_{6}]}\cdot 1.57(1){{\text {H}}_{2}{\text {O}}}$$Na 1.1 ( 2 ) Fe 0.24 ( 6 ) 2 + Fe 0.76 ( 6 ) 2.8 + [ Fe 2.3 + ( CN ) 6 ] · 1.57 ( 1 ) H 2 O , $${{\text {Fe}}[{\text {Fe}}({\text {CN}})_{6}]}\cdot$$Fe [ Fe ( CN ) 6 ] · 0.807(9) $${\text {H}}_{2}{\text {O}}$$H 2 O , and $${{\text {Fe}}[{\text {Fe}}({\text {CN}})_{6}]_{0.75}}\cdot$$Fe [ Fe ( CN ) 6 ] 0.75 · 1.5 $${{\text {H}}_{2}{\text {O}}}$$H 2 O , confirming the absence of vacancies in the three main samples. It was shown that the final composition of PBAs could only be unambiguously confirmed through the combination of ICP, XRD, TGA, and Mössbauer spectroscopy. Two positron lifetimes of 205 and 405 ps were observed with the 205 ps lifetime being independent of the sodium, water, and/or $${[{\text {Fe}}({\text {CN}})_{6}]^{{{n}}-}}$$[ Fe ( CN ) 6 ] n - vacancy content, while the lifetime around 405 ps changes with varying sodium and water content. However, the origin and nature of the 405 ps lifetime yet remains unclear. The method shows promise for characterizing changes in the internal porosity in PBAs as a function of the composition and further development work needs to be carried out to ensure the applicability to PBAs generally. Graphical