Challenge a lattice hypothesis with an independent spacing

Use a wavelength-spacing model

For the supplied first-order Bragg relation, λ=2d sinθ. The angleθ is the angle used in this reflection construction; a reported scattering angle2θ must be halved before substitution. With λ=.154 nm andθ=20°, d≈.22513 nm. This is an inferred plane spacing under the stated model, not automatically a unit-cell edge.

Make the reflection assignment explicit

For cubic cells, d=a/√(h²+k²+l²). The workbench compares allowed monatomic reflections SC(100), BCC(110) and FCC(111). The same d therefore gives a=d,√2d or√3d respectively. Each inference is conditional on its indexing and structural hypothesis; the instrument’s single coordinate does not independently supply that choice.

Cross-check with a second observable

Using the same fictional40.0 g/mol mass and full-occupancy counts1,2,4, each hypothesis predicts a density from its inferred edge. Compare those predictions with an independent density packet rather than selecting whichever label seems familiar. Additional peak positions and systematic absences can further constrain indexing and structure; they are not supplied by one peak alone.

Work a changed angle

Atθ=30°, sinθ=.5, so d=.154 nm. An FCC(111) hypothesis then gives edge about.26674 nm. Using the full60° scattering angle by mistake would produce a different spacing and an incorrect cubic volume, magnifying the error in density. Units and angle definitions are part of the inference, not formatting details.

Preserve model alternatives

A discrepancy could reflect wrong indexing, composition, defects, calibration or an inadequate structural model. Full agreement with one spacing and a density would still not prove that every defect or phase impurity is absent. The activity supplies virtual diffraction evidence and no X-ray source, exposure or instrument-operation procedure. Retain the hypothesis, independent check and unresolved alternatives rather than report a unique identity unsupported by the observations.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Lattice and diffraction evidence. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.