An ordered array of colloidal building blocks whose optical-scale periodicity gives Bragg reflection and photonic stop bands. Particle size and refractive-index contrast control the response; defects and stacking disorder can broaden it.

The frequencies ${\omega }_n(\mathbf{k})$ of electromagnetic Bloch modes form allowed bands in a periodic dielectric. Their gaps and curvature determine forbidden propagation, confinement and group velocity.

At fixed temperature, a photon gas has constant energy density $u$ and radiation pressure $p=u/3$. An increase $\Delta V$ in volume requires both $\Delta U=u\Delta V$ and expansion work $p\Delta V$, giving absorbed heat $4u\Delta V/3$.

A cavity with two transverse photon polarizations and standing-wave spacing $\pi /L$ has energy density of states $2L/(\pi \hslash c)$. In the continuum regime, integrating the Bose occupation at zero chemical potential gives $U=bL{T}^2$, where $b=\pi k_B^2/(3\hslash c)$. The thermal quantities are $C_L=S=2bLT$, Helmholtz free energy $A=-bL{T}^2$ and generalized pressure $P=b{T}^2=U/L$. The last quantity has units of force. These thermal formulas exclude a separate boundary-dependent vacuum energy and require temperature above the mode-spacing scale.

In a direct-beam model with an effective ozone cross section $\sigma$, removal of an overlying column $\Delta N$ multiplies the transmitted photodissociation flux by $e^{\sigma \Delta N}$. A real photodissociation coefficient integrates wavelength-dependent cross section, quantum yield and actinic flux, including scattering and the local radiation field.

A molecular allotrope consisting of tetrahedral ${\mathrm{P}}_4$ molecules. Every vertex has three P–P bonds and one lone pair; its $60^{\circ }$ P–P–P angles produce substantial angle strain.

A phosphonate with an adjacent ester-bearing carbon that can supply the carbon nucleophile in a Horner–Wadsworth–Emmons olefination.

A lysophospholipid is a phospholipid derivative missing an acyl chain relative to its corresponding diacyl form. The changed headgroup-to-tail geometry can alter curvature preference and bilayer stability.

A phosphoinositide is a phosphorylated derivative of phosphatidylinositol. Phosphate position changes the recognition surface of the headgroup, allowing distinct species to recruit different membrane-associated proteins.

phosphatidylinositol is a glycerophospholipid with an inositol headgroup. phosphorylation of that headgroup produces distinct phosphoinositides.

The phosphine oxide $\mathrm{M}{\mathrm{e}}_3\mathrm{PO}$, with three P–C bonds and one terminal P–O bond.

The Tolman electronic parameter compares ligand electronic influence using the symmetric CO stretching band of a matched metal-carbonyl probe, classically $\mathrm{Ni}(\mathrm{CO}{)}_3\mathrm{L}$. Lower frequency commonly indicates greater net electron release into the remaining CO ligands. It combines donation and acceptance and is not a direct measurement of octahedral splitting.

1,2-Bis(dimethylphosphino)ethane has the connectivity $\mathrm{M}{\mathrm{e}}_2\mathrm{PC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{PM}{\mathrm{e}}_2$. Chelation through both phosphorus donors contributes four electrons in ionic electron counting.

The diphosphine $\mathrm{P}{\mathrm{h}}_2\mathrm{PC}{\mathrm{H}}_2\mathrm{PP}{\mathrm{h}}_2$. Chelation to one metal makes a four-membered metal–P–C–P ring.

The diphosphine $\mathrm{P}{\mathrm{h}}_2\mathrm{PC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{PP}{\mathrm{h}}_2$. Chelation to one metal makes a five-membered ring.

The diphosphine $\mathrm{P}{\mathrm{h}}_2\mathrm{P}(\mathrm{C}{\mathrm{H}}_2{)}_3\mathrm{PP}{\mathrm{h}}_2$. Chelation to one metal makes a six-membered ring.

A cyclotriphosphazene contains an alternating six-membered ${\mathrm{P}}_3{\mathrm{N}}_3$ ring. Substitution at its phosphorus atoms can generate geminal, non-geminal and spiro derivatives.

A polymer with an alternating phosphorus–nitrogen backbone and typically two substituents at phosphorus. Polar bonding and negative hyperconjugation differ from a continuously conducting conjugated carbon backbone.