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Wadsley-Roth (W-R) phases, first studied by A. D. Wadsley and R. S. Roth in the 1960s,^[1][2][3] are a class of non-stoichiometric inorganic compounds defined by their complex crystallographic shear structures.^[4] These materials are a family of oxygen-deficient transition metal oxides formed via crystallographic shear (CS) planes derived from ReO₃-type structures.^[5] Owing to their block structure arrangements,^[6] they are also known as block structure oxides, and are currently studied as high-performance anode materials for fast-charging lithium-ion batteries.^{[7][8][unreliable source?]}

Wadsley-Roth phases are composed of corner-sharing metal-oxygen octahedra (MO₆ - where M is usually Nb, W, Mo or Ti), that form infinitely long (since there is no bound on z-axis) n ${\displaystyle \times }$m blocks joined by edge-sharing shear planes.^[4] In the parent ReO₃ structure, octahedra connection is through corners only whereas in W-R phases edge-sharing occurs. This structural shift, known as crystallographic shear, maintains the lattice structure with lower oxygen content preventing destabilizing point defects.^[5]

The integers, n and m represent the number of corner sharing octahedra along the x and y cartesian axes of the block cross-section. Based on the specific values of n and m, the material's stoichiometry (metal-to-oxygen ratio) and its lithium-diffusion pathways differ as well.^[4] This structural peculiarity, as established by Cava et al. (1983),^[9] prevents distortion during lithium insertion, proving it to be stable and useful during battery operation.

In transition metals, especially those with a d⁰ electronic configuration (such as Ti⁴⁺,Nb⁵⁺,W⁶⁺), the metal ions tend to experience second-order Jahn-Teller effect,^{[10][11][12][4][excessive citations]} due to which the metal ions shift off-center from the octahedra, which further causes significant bonding polarizations and structural distortions. This along with electrostatic repulsion between cations altogether allows Wadsley-Roth phases in maintaining its stability.

Wadsley-Roth phases are categorized into three types based on the junctions where the n ${\displaystyle \times }$m blocks join and it determines structural stability. Although the original naming scheme was introduced by Cava et al. (1983),^[9] more precise and descriptive additions^{[peacock prose]} were incorporated recently.^[13][14]

In Type E structures {E_iα[n × m], where subscript denotes the relative shift i in units of octahedral widths in α direction (α = x or y ); for square n × n blocks, the shift direction is irrelevant}, adjacent blocks are joined solely by sharing the edges of the MO₆ octahedra at the corners of the blocks. This is the simplest structural arrangement in the family.^[13] Also, it is often described to have A-B-A layer arrangement such that the stacking occurs in alternating pattern.^[15]

A common example is TiNb₂O₇ which is characterized as E₁[3 × 3] type, wherein the subscript specifies a one-octahedral-width shift between [3 × 3] blocks;^[16] Ti₂Nb₁₀O₂₉ is another example with [3 × 4] block size. It is 3 octahedra wide and 4 octahedra long in the a-c plane and extends infinitely along the b-axis (facilitates as Li ion channels).^[17][18]

In Type T structures, blocks of corner sharing octahedra are joined by tetrahedrally coordinated metal cations; the relative block shift leads to the formation of a void which is small for an octahedron but ideal for a square-shaped channels.^{[citation needed]}

Common example: MoNb₁₂O₃₃ is characterized as T[3 × 4] type.^[8]

In Type M structures, "mixed or hybrid" phases with both edge-sharing junctions and tetrahedral sites are present. Often it involves coherent intergrowth of blocks, thus permitting the growth of larger superstructures, offering diverse range of Li⁺ ions intercalation sites and hence advanced electrochemical profiles.^{[citation needed]}

Common example: H-Nb₂O₅ is the archetypal member of the Type M family;^[4] TiNb₂₄O₆₂ ^[19]

Wadsley-Roth phases are traditionally synthesized through high temperature solid-state reactions. Although this involves mixing stoichiometric quantities of precursor oxides, such as Nb₂O₅, TiO_{2 ,} and heating them in a furnace at very high temperatures ranging from 1000 °C to 1400 °C ^[4] for several days where precise control over the ramp rate and cooling rate is critical because of their metastable phases, lower temperature synthesis routes have been recently reported by Sturghill et al. using the Molybdenum-Niobium-Oxide (MNO) system, specifically MoNb₁₂0₃₃, developed at significantly lower temperatures, around 800 °C to 900 °C. This low-temperature route introduces "Wadsley defects" and cation disorder, enhancing Li⁺ ion diffusion and rate capability of anode materials made out of it.^{[8][unreliable source?]}

Sol-gel synthesis, hydrothermal synthesis and electrospinning techniques are also used to produce materials with desired properties like higher surface areas and shorter diffusion lengths for Li⁺ ions in a battery.^{[citation needed]}