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

A branch of chemistry that deals with the behavior of matter and how chemical reactions work using a lens of theoretical physics and applied math. 

Calvin College

- Analytical Chemistry 
- Applied Chemistry (Chemical Engineering)
- Biochemistry
- Electrochemistry
- Geochemistry
- Inorganic Chemistry
- Organic Chemistry
- Physical Chemistry

Branches and Fields of Chemistry

American Chemical Society

Organic chemistry is the scientific discipline focused on carbon-based chemistry, which serves as the fundamental basis for studying biomolecules and the field of biochemistry.

Organic Chemistry

Biochemistry is the scientific discipline that studies the chemistry of life processes, with the primary objective of explaining biological form and function through chemical principles.

Biochemistry

A branch of chemistry that deals with information concerning the quantity and quality of matter.

Analytical Chemistry

A branch of engineering that uses a variety of disciplines, including but not limited to chemistry, math, physics, and biology to study or design chemical processes. This is done to refine or create new technologies and products that focus on improving quality of life.

Learn Before

Related

Learn After

Learn After

Related