Christopher J. Davies
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Christopher J. Davies has a total of 134 co-authors. Here are the top co-authors by number of shared publications:
- Andrew M. Walker
Department of Earth Sciences University of Oxford Oxford UK
15 shared publications - Jon E. Mound
University of Leeds
15 shared publications - Alfred Wilson
School of Earth and Environment, University of Leeds, Leeds, UK
13 shared publications - Dario Alfè
Department of Earth Sciences and London Centre for Nanotechnology, University College London, London, UK
13 shared publications - Andrew John Biggin
University of Liverpool (Liverpool, United Kingdom)
8 shared publications - David Gubbins
School of Earth and Environment University of Leeds Leeds UK
7 shared publications
Latest Publications
- Open Access
- 24 October 2026
- Published by Elsevier in Earth and Planetary Science Letters
- Vol. 697
Observational signatures of core-mantle interactions inferred from top-heavy thermochemical geodynamo simulations
- 24 October 2026
- Published by Elsevier in Earth and Planetary Science Letters
- Vol. 697
Open AccessObservational signatures of core-mantle interactions inferred from top-heavy thermochemical geodynamo simulations
- Open Access
- 3 July 2026
- Published by Springer Nature in Research Square
Geomagnetic reversals are modulated by the motion of basal mantle structures
The Earth cools over time via convection. In the mantle, solid-state convection over millions of years changes heat and mass distribution and causes adjustments of Earth’s inertia axis with respect to the spin axis. In the outer core, convection of a liquid iron alloy drives dynamo action and generates a magnetic field that episodically changes polarity. Periods without any polarity reversals for tens of million years, called superchrons, have long been thought to be related to changes in core-mantle boundary (CMB) heat flux. However, a quantitative link between CMB heat flux and geomagnetic reversals has remained elusive. Here, we identify a strong correlation between changes in the amplitude of inertia-corrected equatorial CMB heat flux heterogeneities and geomagnetic reversal frequencies from 170 million years ago. This correlation is due to changes in the equatorial extent of hot basal mantle structures that increased during the Jurassic reversal hyperactivity period and decreased during the Cretaceous Normal Superchron. The direct relationship between CMB heat flux predicted by our models and reversal frequencies is driven by changes at shorter wavelengths than previously considered, opening new avenues to investigate the links between CMB heat flux heterogeneities, outer core stratification, and reversal frequencies.
- 3 July 2026
- Published by Springer Nature in Research Square
Open AccessGeomagnetic reversals are modulated by the motion of basal mantle structures
The Earth cools over time via convection. In the mantle, solid-state convection over millions of years changes heat and mass distribution and causes adjustments of Earth’s inertia axis with respect to the spin axis. In the outer core, convection of a liquid iron alloy drives dynamo action and generates a magnetic field that episodically changes polarity. Periods without any polarity reversals for tens of million years, called superchrons, have long been thought to be related to changes in core-mantle boundary (CMB) heat flux. However, a quantitative link between CMB heat flux and geomagnetic reversals has remained elusive. Here, we identify a strong correlation between changes in the amplitude of inertia-corrected equatorial CMB heat flux heterogeneities and geomagnetic reversal frequencies from 170 million years ago. This correlation is due to changes in the equatorial extent of hot basal mantle structures that increased during the Jurassic reversal hyperactivity period and decreased during the Cretaceous Normal Superchron. The direct relationship between CMB heat flux predicted by our models and reversal frequencies is driven by changes at shorter wavelengths than previously considered, opening new avenues to investigate the links between CMB heat flux heterogeneities, outer core stratification, and reversal frequencies.
- Open Access
- 15 May 2026
- Published by Centre pour la Communication Scientifique Directe (CCSD) in Journal of Studies of Earth’s Deep Interior
- Vol. ume 2
Thermochemical models of outer core convection with heterogeneous core-mantle boundary heat flux
Convection in Earth's outer core is driven by the release of heat and light elements at the inner core boundary. A key question is whether these buoyancy sources drive convection throughout the core, or whether a stable layer exists just below the core-mantle boundary (CMB). Recent simulations incorporating CMB heat flux heterogeneities propose locally stable ``regional inversion lenses'' (RILs) rather than a global layer, allowing stable and unstable regions to coexist. However, these simulations combine thermal and compositional anomalies, ignoring differences in diffusivities and boundary conditions. Here we simulate thermal, chemical, and thermochemical convection at Ekman number $E=10^{-5}$, with thermal and chemical flux Rayleigh numbers $\widetilde{Ra}_T=30-4000$ and $\widetilde{Ra}_ξ=30-100000$, and Prandtl numbers $Pr_T=1$ and $Pr_ξ=10$. Purely chemical simulations accumulate light elements below the CMB, forming locally stable regions near the poles or global layers, depending on $\widetilde{Ra}_ξ$. These chemically stratified regions persist in thermochemical simulations even when thermal forcing is destabilising. Introducing heterogeneous CMB heat flux produces thermally stratified RILs even with strongly destabilising compositional buoyancy. Our simulations reveal a diverse range of locations, properties, and morphologies of stable regions depending on $\widetilde{Ra}_T$ and $\widetilde{Ra}_ξ$, they can have a seismically detectable thickness and strength and might also have a signature in geomagnetic observations. Submitted to Journal of Studies of Earths Deep Interior- 15 May 2026
- Published by Centre pour la Communication Scientifique Directe (CCSD) in Journal of Studies of Earth’s Deep Interior
- Vol. ume 2
Open AccessThermochemical models of outer core convection with heterogeneous core-mantle boundary heat flux
Convection in Earth's outer core is driven by the release of heat and light elements at the inner core boundary. A key question is whether these buoyancy sources drive convection throughout the core, or whether a stable layer exists just below the core-mantle boundary (CMB). Recent simulations incorporating CMB heat flux heterogeneities propose locally stable ``regional inversion lenses'' (RILs) rather than a global layer, allowing stable and unstable regions to coexist. However, these simulations combine thermal and compositional anomalies, ignoring differences in diffusivities and boundary conditions. Here we simulate thermal, chemical, and thermochemical convection at Ekman number $E=10^{-5}$, with thermal and chemical flux Rayleigh numbers $\widetilde{Ra}_T=30-4000$ and $\widetilde{Ra}_ξ=30-100000$, and Prandtl numbers $Pr_T=1$ and $Pr_ξ=10$. Purely chemical simulations accumulate light elements below the CMB, forming locally stable regions near the poles or global layers, depending on $\widetilde{Ra}_ξ$. These chemically stratified regions persist in thermochemical simulations even when thermal forcing is destabilising. Introducing heterogeneous CMB heat flux produces thermally stratified RILs even with strongly destabilising compositional buoyancy. Our simulations reveal a diverse range of locations, properties, and morphologies of stable regions depending on $\widetilde{Ra}_T$ and $\widetilde{Ra}_ξ$, they can have a seismically detectable thickness and strength and might also have a signature in geomagnetic observations. Submitted to Journal of Studies of Earths Deep Interior - Open Access
- 6 March 2026
- Published by Oxford University Press (OUP) in Geophysical Journal International
- Vol. 246 (1)
Accessing the dipole–multipole transition in rapidly rotating spherical shell dynamos
SUMMARY: Earth’s magnetic field has exhibited erratic polarity reversals over much of its history; however, the processes that cause polarity transitions are still poorly understood. Dipole reversals have been found in many numerical dynamo simulations and often occur close to the transition between dipole-dominated and multipolar dynamo regimes. However, the physical conditions used in reversing simulations are necessarily far from those in Earth’s liquid iron core because of the long runtimes needed to capture polarity transitions and because a systematic exploration of parameter space is needed to find the dipole-multipole transition. Here, we use the theory of distinguished limits in an attempt to simplify the search for the dipole-multipole transition at increasingly realistic physical conditions. We consider three limits that are all built from the requirements of a constant magnetic Reynolds number $\mathrm {Rm}$; one limit further attempts to impose balance between Magnetic, Coriolis, and Archimedean forces (a Quasi Geostrophic Magneto-Archimedian-Coriolis balance) while the other two seek to constrain solutions to an inertia-MAC, or Quasi Geostrophic Inertia-MAC, balance. The presence of inertia, although not geophysically realistic, allows us to build limits that more closely follow the conditions where simulated reversals have been found to date. Numerical simulations along paths in parameter space defined by these limits show some consistencies with the assumed dynamical balances within the accessible parameter space, but also important discrepancies from predicted behaviour for certain diagnostic quantities, particularly the magnetic field strength and the magnetic/kinetic energy ratio. Furthermore, the paths do not follow the dipole-multipole transition; starting from reversing conditions, simulations move into the dipolar non-reversing regime as they are advanced along the path. By increasing the Rayleigh number, a measure of the buoyancy driving convection, above the values predicted by the distinguished limit, we are able to bound the dipole-multipole transition down to an Ekman number $\mathit {E}\sim 10^{-6}$, comparable to the most extreme conditions reported to date. Our results, therefore, demonstrate that using distinguished limits is an efficient method for seeking the dipole-multipole transition in rapidly rotating dynamos. However, the conditions under which we bound the dipole-multipole transition become increasingly hard to access numerically and also increasingly unrealistic because $\mathrm {Rm}$ rises beyond plausible bounds inferred from geophysical observations. Future work combining the theory of distinguished limits with variations in the core buoyancy distribution, as suggested by recent studies, appears a promising approach to accessing the dipole-multiple transition at extreme physical conditions.- 6 March 2026
- Published by Oxford University Press (OUP) in Geophysical Journal International
- Vol. 246 (1)
Open AccessAccessing the dipole–multipole transition in rapidly rotating spherical shell dynamos
SUMMARY: Earth’s magnetic field has exhibited erratic polarity reversals over much of its history; however, the processes that cause polarity transitions are still poorly understood. Dipole reversals have been found in many numerical dynamo simulations and often occur close to the transition between dipole-dominated and multipolar dynamo regimes. However, the physical conditions used in reversing simulations are necessarily far from those in Earth’s liquid iron core because of the long runtimes needed to capture polarity transitions and because a systematic exploration of parameter space is needed to find the dipole-multipole transition. Here, we use the theory of distinguished limits in an attempt to simplify the search for the dipole-multipole transition at increasingly realistic physical conditions. We consider three limits that are all built from the requirements of a constant magnetic Reynolds number $\mathrm {Rm}$; one limit further attempts to impose balance between Magnetic, Coriolis, and Archimedean forces (a Quasi Geostrophic Magneto-Archimedian-Coriolis balance) while the other two seek to constrain solutions to an inertia-MAC, or Quasi Geostrophic Inertia-MAC, balance. The presence of inertia, although not geophysically realistic, allows us to build limits that more closely follow the conditions where simulated reversals have been found to date. Numerical simulations along paths in parameter space defined by these limits show some consistencies with the assumed dynamical balances within the accessible parameter space, but also important discrepancies from predicted behaviour for certain diagnostic quantities, particularly the magnetic field strength and the magnetic/kinetic energy ratio. Furthermore, the paths do not follow the dipole-multipole transition; starting from reversing conditions, simulations move into the dipolar non-reversing regime as they are advanced along the path. By increasing the Rayleigh number, a measure of the buoyancy driving convection, above the values predicted by the distinguished limit, we are able to bound the dipole-multipole transition down to an Ekman number $\mathit {E}\sim 10^{-6}$, comparable to the most extreme conditions reported to date. Our results, therefore, demonstrate that using distinguished limits is an efficient method for seeking the dipole-multipole transition in rapidly rotating dynamos. However, the conditions under which we bound the dipole-multipole transition become increasingly hard to access numerically and also increasingly unrealistic because $\mathrm {Rm}$ rises beyond plausible bounds inferred from geophysical observations. Future work combining the theory of distinguished limits with variations in the core buoyancy distribution, as suggested by recent studies, appears a promising approach to accessing the dipole-multiple transition at extreme physical conditions. - Open Access
- 3 February 2026
- Published by Springer Nature in Nature Geoscience
- Vol. 19 (3) , 345-352
Mantle heterogeneity influenced Earth’s ancient magnetic field
Heat flowing from the core to the mantle drives the geodynamo that produces Earth’s global magnetic field. Palaeomagnetic measurements record the behaviour of this field through time and have the potential to inform us about deep Earth structures and dynamics on either side of the core–mantle boundary. In practise, insights have proved difficult to obtain because of the limited spatiotemporal resolution of palaeomagnetic records and uncertainties in how to interpret them. Here we use palaeomagnetic datasets and models alongside numerical simulations of the geodynamo to show that certain observed characteristics of ancient magnetic field behaviour are uniquely or preferentially reproduced in the presence of strong lateral variability in core–mantle heat flux. Our findings suggest that strong contrasts in the spatial pattern of the temperature gradients and/or thermal conductivity of the lowermost mantle that are linked, today, to seismologically observed structures, have influenced the geodynamo for at least the last few hundred million years. The identified palaeomagnetic signatures provide a new means to constrain the properties and time evolution of the core–mantle boundary. Furthermore, our insights into how thermal heterogeneity at the base of the mantle can break the axial symmetry of the time-averaged magnetic field may help resolve longstanding palaeogeographic controversies.
- 3 February 2026
- Published by Springer Nature in Nature Geoscience
- Vol. 19 (3) , 345-352
Open AccessMantle heterogeneity influenced Earth’s ancient magnetic field
Heat flowing from the core to the mantle drives the geodynamo that produces Earth’s global magnetic field. Palaeomagnetic measurements record the behaviour of this field through time and have the potential to inform us about deep Earth structures and dynamics on either side of the core–mantle boundary. In practise, insights have proved difficult to obtain because of the limited spatiotemporal resolution of palaeomagnetic records and uncertainties in how to interpret them. Here we use palaeomagnetic datasets and models alongside numerical simulations of the geodynamo to show that certain observed characteristics of ancient magnetic field behaviour are uniquely or preferentially reproduced in the presence of strong lateral variability in core–mantle heat flux. Our findings suggest that strong contrasts in the spatial pattern of the temperature gradients and/or thermal conductivity of the lowermost mantle that are linked, today, to seismologically observed structures, have influenced the geodynamo for at least the last few hundred million years. The identified palaeomagnetic signatures provide a new means to constrain the properties and time evolution of the core–mantle boundary. Furthermore, our insights into how thermal heterogeneity at the base of the mantle can break the axial symmetry of the time-averaged magnetic field may help resolve longstanding palaeogeographic controversies.
- Open Access
- 8 January 2026
- Published by American Physical Society (APS) in Physical Review Fluids
- Vol. 11 (1)
Effect of hyperdiffusion on rotating Rayleigh-Bénard convection
We analyze the effect of a scale-dependent horizontal hyperdiffusivity in rotating Rayleigh-Bénard convection. The hyperdiffusion (HD) is parametrized by a cutoff wave number k 0 and a growth rate q to limit its effects to the smaller scales, enabling simulations to be conducted at more rapid rotation rates and buoyancy forcing (as measured by the Ekman number Ek and Rayleigh number Ra, respectively) than in conventional direct numerical simulations (DNSs). We have performed 107 simulations spanning the ranges E = 10 − 4 -- 10 − 7 and Ra = 10 6 -- 7 × 10 10 and directly compared HD and DNS heat transfer (measured by the Nusselt number Nu), flow speeds (quantified by the Péclet number Pe), force balances, and boundary layer thicknesses. We identify two different effects of HD that are particularly clear when k 0 is below the dominant scale of the flow k ⊥ : At low supercriticality Ra ̃ , Nu, and Pe are increased compared to DNS due to a weakening of the rotational constraint; at high Ra ̃ , Nu and Pe are decreased compared to DNS owing to suppression of energy at scales greater than k ⊥ . The thermal boundary layer thickness changes in proportion to Nu, while the mechanical boundary layer thickness is marginally affected because it is determined by a vertical balance, whereas HD is applied horizontally. Heat transfer diagnostics are more strongly affected by HD than flow diagnostics, while changing k 0 has a greater impact on solution behavior than changing q over the range of values studied. For all HD simulations with k 0 ≥ 3 k ⊥ , all diagnostics remain within the standard deviation of the DNS.
- 8 January 2026
- Published by American Physical Society (APS) in Physical Review Fluids
- Vol. 11 (1)
Open AccessEffect of hyperdiffusion on rotating Rayleigh-Bénard convection
We analyze the effect of a scale-dependent horizontal hyperdiffusivity in rotating Rayleigh-Bénard convection. The hyperdiffusion (HD) is parametrized by a cutoff wave number k 0 and a growth rate q to limit its effects to the smaller scales, enabling simulations to be conducted at more rapid rotation rates and buoyancy forcing (as measured by the Ekman number Ek and Rayleigh number Ra, respectively) than in conventional direct numerical simulations (DNSs). We have performed 107 simulations spanning the ranges E = 10 − 4 -- 10 − 7 and Ra = 10 6 -- 7 × 10 10 and directly compared HD and DNS heat transfer (measured by the Nusselt number Nu), flow speeds (quantified by the Péclet number Pe), force balances, and boundary layer thicknesses. We identify two different effects of HD that are particularly clear when k 0 is below the dominant scale of the flow k ⊥ : At low supercriticality Ra ̃ , Nu, and Pe are increased compared to DNS due to a weakening of the rotational constraint; at high Ra ̃ , Nu and Pe are decreased compared to DNS owing to suppression of energy at scales greater than k ⊥ . The thermal boundary layer thickness changes in proportion to Nu, while the mechanical boundary layer thickness is marginally affected because it is determined by a vertical balance, whereas HD is applied horizontally. Heat transfer diagnostics are more strongly affected by HD than flow diagnostics, while changing k 0 has a greater impact on solution behavior than changing q over the range of values studied. For all HD simulations with k 0 ≥ 3 k ⊥ , all diagnostics remain within the standard deviation of the DNS.
- Open Access
- 24 November 2025
- Published by Springer Nature in Nature Communications
- Vol. 16 (1) , 10318
Author Correction: Constraining Earth’s core composition from inner core nucleation
- 24 November 2025
- Published by Springer Nature in Nature Communications
- Vol. 16 (1) , 10318
Open AccessAuthor Correction: Constraining Earth’s core composition from inner core nucleation
- Open Access
- 4 September 2025
- Published by Springer Nature in Nature Communications
- Vol. 16 (1) , 1-10
Constraining Earth’s core composition from inner core nucleation
The composition of Earth’s core is a fundamental property of the Earth’s deep interior, defining its present structure and long term thermal and magnetic evolution. However, the composition of the core is not well understood, with several combinations of light elements being able to satisfy the traditional constraints from cosmochemistry, core formation and seismology. The classic view of inner core formation does not include the necessity for liquids to be supercooled to below their melting point before freezing. Attempts to calculate the magnitude of this supercooling have found that several binary core compositions are incompatible with inner core nucleation. Here we show, through molecular dynamics simulations, that nucleation from an Fe 1− x C x =0.1-0.15 composition is compatible with a range of geophysical constraints. Whilst not a complete description of core chemistry, our results demonstrate that inner core nucleation places a strong constraint on the composition of Earth’s core that may allow discrimination between previously identified potential compositions.
- 4 September 2025
- Published by Springer Nature in Nature Communications
- Vol. 16 (1) , 1-10
Open AccessConstraining Earth’s core composition from inner core nucleation
The composition of Earth’s core is a fundamental property of the Earth’s deep interior, defining its present structure and long term thermal and magnetic evolution. However, the composition of the core is not well understood, with several combinations of light elements being able to satisfy the traditional constraints from cosmochemistry, core formation and seismology. The classic view of inner core formation does not include the necessity for liquids to be supercooled to below their melting point before freezing. Attempts to calculate the magnitude of this supercooling have found that several binary core compositions are incompatible with inner core nucleation. Here we show, through molecular dynamics simulations, that nucleation from an Fe 1− x C x =0.1-0.15 composition is compatible with a range of geophysical constraints. Whilst not a complete description of core chemistry, our results demonstrate that inner core nucleation places a strong constraint on the composition of Earth’s core that may allow discrimination between previously identified potential compositions.
- Open Access
- 2 May 2025
- Published by Springer Nature in Research Square
Heterogeneity in core-mantle heat flow influenced the ancient geodynamo
Studies of the behaviour of the geodynamo through time, preserved in palaeomagnetic records, have a unique potential to inform us about the time-varying thermal structure of Earth’s core-mantle boundary region. In practise, however, such insights have proved difficult to obtain because of the limited spatiotemporal resolution of palaeomagnetic records and uncertainties in how to interpret them. Here we show that certain key characteristics of the palaeomagnetic field observed over the last 23 Myr can only be reproduced by numerical simulations of the geodynamo that have heterogeneous heat flux conditions imposed on their outer boundaries. We further demonstrate that a signal of azimuthal asymmetry in field behaviour, characteristic of such heterogeneity, is evident in the variance of records of palaeosecular variation recovered from low latitudes, that are up to 265 Myr old. Finally, we show that imposing strong heterogeneity in the heat flow boundary conditions significantly increases the parameter range over which simulations can reproduce aspects of palaeosecular variation that have been observed to be stable through much of geological time. In conjunction, these findings provide compelling new evidence that significant thermal heterogeneity at the core-mantle boundary has influenced the geodynamo for at least the last few hundred million years. The identified palaeomagnetic signatures of thermal heterogeneity at the core-mantle boundary provide a new means to constrain the properties and time-evolution of this region of Earth’s interior. Furthermore, our insights into how thermal heterogeneity at the base of the mantle can break the axial symmetry of the time-averaged magnetic field may provide an important step towards resolving longstanding palaeogeographic controversies.
- 2 May 2025
- Published by Springer Nature in Research Square
Open AccessHeterogeneity in core-mantle heat flow influenced the ancient geodynamo
Studies of the behaviour of the geodynamo through time, preserved in palaeomagnetic records, have a unique potential to inform us about the time-varying thermal structure of Earth’s core-mantle boundary region. In practise, however, such insights have proved difficult to obtain because of the limited spatiotemporal resolution of palaeomagnetic records and uncertainties in how to interpret them. Here we show that certain key characteristics of the palaeomagnetic field observed over the last 23 Myr can only be reproduced by numerical simulations of the geodynamo that have heterogeneous heat flux conditions imposed on their outer boundaries. We further demonstrate that a signal of azimuthal asymmetry in field behaviour, characteristic of such heterogeneity, is evident in the variance of records of palaeosecular variation recovered from low latitudes, that are up to 265 Myr old. Finally, we show that imposing strong heterogeneity in the heat flow boundary conditions significantly increases the parameter range over which simulations can reproduce aspects of palaeosecular variation that have been observed to be stable through much of geological time. In conjunction, these findings provide compelling new evidence that significant thermal heterogeneity at the core-mantle boundary has influenced the geodynamo for at least the last few hundred million years. The identified palaeomagnetic signatures of thermal heterogeneity at the core-mantle boundary provide a new means to constrain the properties and time-evolution of this region of Earth’s interior. Furthermore, our insights into how thermal heterogeneity at the base of the mantle can break the axial symmetry of the time-averaged magnetic field may provide an important step towards resolving longstanding palaeogeographic controversies.
- Open Access
- 2 April 2025
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 481 (2311)
A non-equilibrium slurry model for planetary cores with application to Earth’s F-layer
Slurry regions may exist in the cores of several terrestrial bodies and are expected to influence the dynamics of deep planetary interiors and the viability of maintaining global magnetic fields. Here, we develop a two-component slurry model of the lowermost outer core of the Earth (the F-layer). In contrast to most previous models of slurries in planetary cores, we explicitly model the physics controlling the nucleation, growth and sinking of individual iron crystals and do not assume that the layer is in phase equilibrium. We assume that falling crystals do not interact and that the temperature and the overall composition are imposed, which allows us to solve for the volume fraction of solid in the layer and the size distribution of crystals. Models that produce a plausible heat budget and density excess compared with the bulk core yield a solid fraction that is far below that predicted by phase equilibrium and have a crystal size distribution dominated by the smallest particles with a maximum particle radii of 3 cm. The model can be used to understand the role of non-equilibrium effects in other planetary cores.
- 2 April 2025
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 481 (2311)
Open AccessA non-equilibrium slurry model for planetary cores with application to Earth’s F-layer
Slurry regions may exist in the cores of several terrestrial bodies and are expected to influence the dynamics of deep planetary interiors and the viability of maintaining global magnetic fields. Here, we develop a two-component slurry model of the lowermost outer core of the Earth (the F-layer). In contrast to most previous models of slurries in planetary cores, we explicitly model the physics controlling the nucleation, growth and sinking of individual iron crystals and do not assume that the layer is in phase equilibrium. We assume that falling crystals do not interact and that the temperature and the overall composition are imposed, which allows us to solve for the volume fraction of solid in the layer and the size distribution of crystals. Models that produce a plausible heat budget and density excess compared with the bulk core yield a solid fraction that is far below that predicted by phase equilibrium and have a crystal size distribution dominated by the smallest particles with a maximum particle radii of 3 cm. The model can be used to understand the role of non-equilibrium effects in other planetary cores.