Negative thermal expansion of a crystal does not imply that every local bond shortens. In a neutron total-scattering study of cubic scandium trifluoride, $\mathrm{ScF_3}$, Wendt et al. (2019) found that the nearest-neighbor Sc–F pair-distribution peak shifted to slightly larger separation on heating while the average crystal structure contracted. A separate neutron-scattering and reverse Monte Carlo study by Dove et al. (2020) also found positive thermal expansion of the mean Sc–F bond distance together with a decreasing lattice parameter.

These are different quantities: a **local interatomic separation** and the **periodic spacing of the average crystal structure**. Transverse fluorine motion in Sc–F–Sc linkages provides a qualitative tension-effect explanation for their opposite trends. The observation concerns cubic $\mathrm{ScF_3}$ in its negative-expansion temperature regime. The two studies disagree about the detailed motion model, so the bond/lattice distinction should be separated from any claim that the microscopic mechanism is settled.

Sources: [Wendt et al. (2019)](https://doi.org/10.1126/sciadv.aay2748); [Dove et al. (2020)](https://doi.org/10.1103/PhysRevB.102.094105).

Local Sc–F expansion and lattice contraction in cubic ScF3

Neutron total scattering with EPSR models examined choline chloride–urea (1:2 molar reline) at 1, 2, 5, 10, 15, 20 and 30 molar water equivalents. Some nanostructure persisted near 42 wt% water (10 equivalents); at the studied 51 wt% (15 equivalents), models supported an aqueous-solution interpretation despite residual component–component interactions. This is intermolecular restructuring, not observed classical phase separation or a universal exact cutoff: other formulations may transition at different hydration. [Hammond et al. (2017)](https://doi.org/10.1002/anie.201702486)

Source: https://onlinelibrary.wiley.com/doi/full/10.1002/anie.201702486

Composition-specific hydration restructuring in reline

For aA+bB⇌cC+dD, K_a=[(a_C^c a_D^d)/(a_A^a a_B^b)]_eq, with activities defined relative to specified standard states. Dimensionless activities make K_a dimensionless. A hypothetical ideal-gas reference gives a_i=f_i/f_i°; for an ideal gaseous mixture, a_i=x_iP/P°=p_i/P°. With matching activity standard states, the standard reaction Gibbs energy satisfies K_a=exp[-Δ_rG°/(RT)].

Sources:
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_%28Ellgen%29/15%3A_Chemical_Potential_Fugacity_Activity_and_Equilibrium/15.02%3A_The_Chemical_Potential_and_Activity_of_a_Gas
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_%28Ellgen%29/15%3A_Chemical_Potential_Fugacity_Activity_and_Equilibrium/15.07%3A_Chemical_Potential_Activity_and_Equilibrium

Equilibrium activity quotients and standard states

At a chosen temperature, use the lecture’s ideal gaseous mixture with p°=1 bar and positive partial pressures. Form Q from the current p_i/p° ratios, raising each to its stoichiometric power and dividing product factors by reactant factors. Q describes the current state; equilibrium gives Q_eq=K_p. The reaction Gibbs energy satisfies Δ_rG=Δ_rG°+RT ln Q, while Δ_rG°=-RT ln K_p. This pressure normalization makes both Q and K_p dimensionless.

Sources:
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_%28Ellgen%29/15%3A_Chemical_Potential_Fugacity_Activity_and_Equilibrium/15.07%3A_Chemical_Potential_Activity_and_Equilibrium
- https://ocw.mit.edu/courses/5-60-thermodynamics-kinetics-spring-2008/52946f97fcb18850c32e9d4b8f6bab6a_5_60_lecture15.pdf

Instantaneous Q and equilibrium K_p for ideal gases

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