Editing Prussian blue (section)

===Crystal structure===
[[File:Iron-coordination-in-simplified-Prussian-blue-from-xtal-xray-3D-bs-17.png|thumb|left|200px|Fe [[coordination sphere]]s in idealized Prussian blue]]
[[File:Idealized, defect-free Prussian Blue.svg|thumb|right|200px|The [[unit cell]] of Prussian blue, with all sites occupied. Actually, one fourth of the {{chem2|Fe(CN)6}} groups shown will be missing, at random, giving on average only 18 cyanide ions (rather than the 24 shown) and three ferrous iron atoms.]]
[[File:Prussian Blue Powder XRD Profile, Simulated.jpg|thumb|left|200px|Simulated powder [[X-ray crystallography|x-ray diffraction]] profile for Prussian blue crystal, [[Miller index|crystallographic direction]] annotated. Image generated using CrystalMaker software.]]

The [[chemical formula]] of insoluble Prussian blue is {{chem2|Fe7(CN)18*''x''H2O}}, where ''x''&nbsp;=&nbsp;14–16. The structure was determined by using [[IR spectroscopy]], [[Mössbauer spectroscopy]], [[X-ray crystallography]], and [[neutron crystallography]]. Since X-ray diffraction cannot easily distinguish carbon from nitrogen in the presence of heavier elements such as iron, the location of these lighter elements is deduced by spectroscopic means, as well as by observing the distances from the iron atom centers. [[Neutron diffraction]] can easily distinguish N and C atoms, and it has been used to determine the detailed structure of Prussian blue and its analogs.<ref>Electrochemistry of polynuclear transition-metal cyanides – Prussian blue and its analogs. 1986. Accounts of Chemical Research. 19/162-168. {{doi|10.1021/ar00126a001}}.</ref><ref>Low Defect FeFe(CN)<sub>6</sub> Framework as Stable Host Material for High Performance Li-Ion Batteries. 2016. ACS Applied Materials and Interfaces. 8/23706-23712. {{doi|10.1021/acsami.6b06880}}.</ref><ref>Prussian blue analogues and their derived materials for electrochemical energy storage: Promises and Challenges. 2024. Materials Research Bulletin. 170/ {{doi|10.1016/j.materresbull.2023.112593}}.</ref><ref>Some performance characteristics of a Prussian blue battery. 1985. Journal of the Electrochemical Society. 132/1382-1384. {{doi|10.1149/1.2114121}}.</ref><ref>A neutron diffraction study of Prussian blue, Fe<sub>4</sub>[Fe<sub>4</sub>(CN)<sub>6</sub>]<sub>3</sub>. 14D<sub>2</sub>O. 1974. Zeitschrift fur Physikalische Chemie. 92/354-357. {{doi|10.1524/zpch.1974.92.4-6.354}}.</ref><ref>Valence Delocalization in Prussian Blue Fe(III)<sub>4</sub>[Fe(II)(CN)<sub>6</sub>]<sub>3</sub>·xD<sub>2</sub>O, by Polarized Neutron Diffraction. 1980. Helvetica Chimica Acta. 63/148-153. {{doi|10.1002/hlca.19800630115}}.</ref><ref>Neutron Diffraction Study of Prussian Blue, Fe<sub>4</sub>[Fe(CN)<sub>6</sub>]<sub>3</sub>·xH<sub>2</sub>O. Location of Water Molecules and Long-Range Magnetic Order. 1980. Inorganic Chemistry. 19/956-959. {{doi|10.1021/ic50206a032}}.</ref><ref>Neutron and X-ray diffraction studies on powders and single crystals of compounds structurally related to Prussian blue. 1999. Zeitschrift fur Naturforschung – Section B Journal of Chemical Sciences. 54/870-876. {{doi|10.1515/znb-1999-0708}}.</ref><ref>Crystalline, mixed-valence manganese analogue of Prussian blue: Magnetic, spectroscopic, X-ray and neutron diffraction studies. 2004. Journal of the American Chemical Society. 126/16472-16477. {{doi|10.1021/ja0465451}}.</ref><ref>Neutron diffraction and neutron vibrational spectroscopy studies of hydrogen adsorption in the Prussian blue analogue Cu<sub>3</sub>[Co(CN)<sub>6</sub>]<sub>2</sub>. 2006. Chemistry of Materials. 18/3221-3224. {{doi|10.1021/cm0608600}}.</ref><ref>Neutron diffraction study of molecular magnetic compound Ni<sub>1.125</sub>Co<sub>0.375</sub>[Fe(CN)<sub>6</sub>]·6.4H<sub>2</sub>O. 2006. Physica B: Condensed Matter. 385-386 I/444-446. {{doi|10.1016/j.physb.2006.05.147}}.</ref>

PB has a [[face centered cubic]] lattice structure, with four iron(III) ions per unit cell. "Soluble" PB crystals contain interstitial {{chem2|K(+)}} ions; insoluble PB has interstitial water, instead. In ideal insoluble PB crystals, the cubic framework is built from Fe(II)–C–N–Fe(III) sequences, with Fe(II)–carbon distances of 1.92 [[angstrom|Å]] and Fe(III)–nitrogen distances of 2.03 Å. One-fourth of the sites of {{chem2|Fe(CN)6}} subunits (supposedly at random) are vacant (empty), leaving three such groups on average per unit cell.<ref name='Herren'/> The empty nitrogen sites are filled with water molecules instead, which are coordinated to Fe(III).

[[File:Hydrated-Prussian-blue-unit-cell-a-centroids-all-OH-tilt-3D-bs-17.png|thumb|right|200px|The [[unit cell]] of Prussian blue determined by [[neutron diffraction]],<ref name='Herren' /> with [[crystallographic disorder|crystallographically disordered]] water molecules both in cyanide ion positions and in the void space of the framework. Again, one fourth of the {{chem2|Fe(CN)6}} groups shown will be missing. This illustration superimposes both possibilities at each site — water molecules or cyanide ions.]]

The Fe(II) centers, which are [[low spin]], are surrounded by six carbon [[ligand]]s in an [[octahedral]] configuration. The Fe(III) centers, which are [[high spin]], are octahedrally surrounded on average by 4.5 nitrogen atoms and 1.5 oxygen atoms (the oxygen from the six coordinated water molecules). Around eight (interstitial) water molecules are present in the unit cell, either as isolated molecules or [[hydrogen bond]]ed to the coordinated water. It is worth noting that in soluble [[hexacyanoferrate]]s Fe(II or III) is always coordinated to the carbon atom of a [[cyanide]], whereas in crystalline Prussian blue Fe ions are coordinated to both C and N.<ref>Prussian blue analogues and their derived materials for electrochemical energy storage: Promises and Challenges. 2024. Materials Research Bulletin. 170/. M. Fayaz, W. Lai, J. Li, W. Chen, X. Luo, Z. Wang, et al. {{doi|10.1016/j.materresbull.2023.112593}}</ref>

The composition is notoriously variable due to the presence of lattice defects, allowing it to be hydrated to various degrees as water molecules are incorporated into the structure to occupy [[cation]] vacancies. The variability of Prussian blue's composition is attributable to its low [[solubility]], which leads to its rapid [[precipitation (chemistry)|precipitation]] without the time to achieve full equilibrium between solid and liquid.<ref name='Herren'>{{cite journal|doi=10.1021/ic50206a032|title=Neutron diffraction study of Prussian blue, Fe<sub>4</sub>&#91;Fe(CN)<sub>6</sub>&#93;<sub>3</sub>·xH<sub>2</sub>O. Location of water molecules and long-range magnetic order|year=1980|last1=Herren|first1=F.|last2=Fischer|first2=P.|last3=Ludi|first3=A.|last4=Haelg|first4=W.|journal=Inorganic Chemistry|volume=19|issue=4|pages=956}}</ref><ref name='Lundgren'>{{cite journal|doi=10.1021/ic00278a036 |title=Observations on the composition of Prussian blue films and their electrochemistry|year=1988|last1=Lundgren|first1=C. A.|last2=Murray|first2=Royce W.|journal=Inorganic Chemistry|volume=27|issue=5|pages=933}}</ref>