The 2013 discovery that the archetypal ionic system Na–Cl forms stoichiometry-violating compounds under pressure — NaCl₃, Na₃Cl, Na₂Cl, Na₃Cl₂, NaCl₇ — raised a cluster of unresolved questions. Follow-up work has confirmed and extended the phenomenon (KCl₃ synthesized; unpredicted Na₂Cl₃ and Na₄Cl₅ discovered in 2023; unconventional Na–Cl stoichiometries realized at ambient conditions in two dimensions and confinement), yet: cubic NaCl₇, predicted thermodynamically stable above ≈142 GPa, has never been synthesized; the computed phase diagram is demonstrably incomplete (the unpredicted Na₂Cl₃ and Na₄Cl₅ were missed by exhaustive variable-composition searches) and at least one measured stabilization pressure disagrees with the calculations, a discrepancy attributed to limitations of the density-functional treatment; the proposed pseudogap-driven stabilization mechanism remains qualitative; and no bulk exotic chloride has been recovered to ambient pressure — Pnma-NaCl₃ and Na₃Cl decompose at ≈18–20 GPa on decompression. The problem is to complete the experimental and quantitative determination of the Na–Cl pressure–composition phase diagram — verification of the unconfirmed stability fields, a quantitative stabilization mechanism, and determination of ambient recoverability — as one interlinked scientific objective.

Background

At ambient conditions sodium chloride is the archetype of ionic bonding: the large electronegativity difference between Na and Cl fixes nominal charges of +1 and −1, so charge balance admits only the 1:1 stoichiometry, adopted in the B1 (rocksalt) crystal structure. A 2013 study by Zhang, Oganov, and co-workers overturned this textbook picture under compression. Combining variable-composition evolutionary crystal-structure prediction (the USPEX method, which explores both composition and atomic arrangement using density-functional-theory (DFT) total energies computed with the PBE exchange–correlation functional, a compound being judged thermodynamically stable when it lies on the convex hull of formation enthalpy versus composition at a given pressure) with diamond-anvil-cell experiments — samples compressed between two diamond anvils to pressures of tens to hundreds of gigapascals and laser-heated to ≈2000 K to overcome kinetic barriers — they predicted a suite of stable 'forbidden' compounds: NaCl₃ (stable above 20 GPa), NaCl₇ (above 142 GPa), Na₂Cl (above ≈100 GPa), Na₃Cl₂ (above ≈120 GPa), and Na₃Cl (above ≈77 GPa). In laser-heating experiments on NaCl with excess chlorine or excess sodium at 55–80 GPa they synthesized two of them, cubic NaCl₃ and tetragonal Na₃Cl, verified by synchrotron X-ray diffraction and Raman spectroscopy.

The predicted structures violate ambient chemical intuition in instructive ways. Between 20 and 48 GPa, NaCl₃ is an orthorhombic (Pnma) semiconductor built of Na⁺ cations and nearly linear [Cl₃]⁻ polyhalide anions — chlorine analogues of the familiar trihalide ions I₃⁻ and Br₃⁻. Above 48 GPa it transforms into a metallic cubic phase with the A15 (Cr₃Si-type) structure (space group Pm-3n) — the same structure type as classic type-II superconductors such as Nb₃Sn — in which short Cl–Cl contacts form extended monatomic chlorine chains running along three perpendicular directions. NaCl₇, predicted stable only above 142 GPa, is obtained from this structure by substituting the central Na atom inside the Cl₁₂ icosahedron with Cl. Na₃Cl is a layered tetragonal (P4/mmm) metal with excess sodium. Most of the new phases are poor metals with pronounced pseudogaps — deep minima in the electronic density of states at the Fermi level — which the authors proposed as the electronic driving force of stabilization, without quantifying the connection. Because Na and Cl become nearly the same size near 200 GPa, Na/Cl site interchange (non-stoichiometry and disorder) was also flagged as probable in the dense phases.

The experimental metastability limits define the recovery problem: on decompression the synthesized phases persist only to ≈18 GPa (Pnma-NaCl₃, which then decomposes to NaCl plus Cl₂) and ≈20 GPa (Na₃Cl, which decomposes to NaCl plus Na). A Peierls-type argument — a one-dimensional, partially filled chlorine-chain band is unstable toward bond alternation once pressure no longer enforces uniform short Cl–Cl distances — led the authors to conclude that the A15-type phases (Pm-3n-NaCl₃ and Pm-3-NaCl₇) cannot be quenched to atmospheric pressure at all. The 2013 paper left open what it could not settle: the unverified high-pressure stability fields (above all NaCl₇), unexplained characterization anomalies (Raman peaks in cubic NaCl₃ forbidden by the Pm-3n selection rules, suggesting disorder or variable stoichiometry; absence of superconductivity in A15-NaCl₃ despite its superconductor-associated structure type), the unquantified pseudogap mechanism, and whether any exotic stoichiometry can be quenched or chemically stabilized at ambient conditions. On the accuracy of the computed diagram the paper reported a check rather than an open question: including zero-point vibrational energies shifts the Na₃Cl boundary from 77 to 82 GPa, and the authors concluded that the stability fields are only slightly affected. Later work has resolved part of this list (the K-Cl generalization was carried out by the same group) while leaving the remainder — verification, mechanism, and recovery — open.

Problem Statement

Complete the experimental and quantitative determination of the pressure–composition phase diagram of the Na–Cl binary system at high pressure, as opened by the 2013 discovery of stoichiometry-violating sodium chlorides. The problem has three interlinked components:

(1) Experimental verification of the predicted but unconfirmed stability fields. Above all, determine by high-pressure synthesis (laser-heated diamond-anvil-cell or equivalent methods) and in situ structure determination whether cubic NaCl₇ (space group Pm-3), predicted by the 2013 study (ref. 1) to become thermodynamically stable above ≈142 GPa, actually exists in its predicted stability field; likewise for the sodium-rich compounds Na₃Cl₂ (predicted stable above ≈120 GPa) and Na₂Cl (above ≈100 GPa). Confirming, refining, or refuting these predicted phase boundaries is part of the deliverable. Because the 2013 study stresses that the newly predicted compounds form only at high temperature and with excess Na or Cl, mere non-observation in an experiment that does not overcome the kinetic barriers does not by itself refute a predicted stability field.

(2) A quantitative account of the stabilization mechanism. Establish, as three jointly required parts, the relationship between the pseudogap in the electronic density of states and the formation enthalpies of the exotic chlorides, the role of electron–phonon coupling, and the accuracy of the predicted phase boundaries with respect to exchange–correlation treatment; the zero-point-vibrational-energy sensitivity, already checked by the 2013 study, is a consistency re-check of the computed boundaries rather than a separate deliverable.

(3) Ambient recoverability. Determine whether any of the exotic sodium chlorides — bulk NaCl₃, Na₃Cl, Na₂Cl₃, Na₄Cl₅, or their chemical derivatives — can be recovered to ambient pressure as a bulk phase, or stabilized there by a route (thermal quenching, chemical modification, encapsulation, or confinement) that preserves the high-pressure compound, given the observed decomposition of Pnma-NaCl₃ at ≈18 GPa and Na₃Cl at ≈20 GPa on decompression and the Peierls-type argument against quenchability of the A15-type phases. The unconventional Na–Cl stoichiometries already realized at ambient conditions in two dimensions, as nanoclusters, or in confinement are not bulk high-pressure phases recovered or preserved from pressure, and do not by themselves settle this component.

These components jointly support one objective: a verified, mechanistically grounded account of the Na–Cl system's pressure-stabilized unconventional stoichiometries and their ambient stabilizability. The mechanism is what explains which compounds the phase diagram contains, and recovery is the zero-pressure limit of the metastability landscape that the phase diagram defines, so the three parts are mutually constraining rather than independent. Two secondary characterization questions attached to the same system — the selection-rule-violating Raman peaks in cubic NaCl₃ (disorder or variable stoichiometry versus phase mixtures) and the absence of superconductivity in A15-NaCl₃ despite its type-II-superconductor structure type — fall within a complete account but are not independent deliverables.

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