Índice de coherencia energética en los cristales de nieve

Project Description
This project introduces a dimensionless energetic coherence index (K*) intended to organize measurable energy-density contributions governing snow crystal growth. The framework integrates lattice cohesion energy, surface free energy, thermal energy, dipolar interactions, environmental perturbations, and vapor flux.
The objective is to explore whether morphological transitions (plates, columns, dendrites) correlate with structured energetic regimes without modifying established crystallographic or surface-kinetic models.
The approach is quantitatively structured, dimensionally consistent, and experimentally testable. Laboratory replication protocols and statistical validation criteria are provided. Experimental confirmation remains pending.

Energetic Coherence Interpretation of Snow Crystal Morphology

The Energetic Coherence Interpretation of Snow Crystal Morphology is a conceptual framework proposed by C.J. Pérez Pulido (2026) within the ISHEA Institute research program. It presents an interpretive layer for understanding transitions in snow crystal morphology as mapped in the Nakaya diagram.

The framework does not replace established crystallographic or surface-kinetics models but proposes an integrative parameter intended to organize energetic contributions influencing crystal growth.

Background

Snow crystal morphology has been systematically studied since the work of Ukichiro Nakaya (1954), who mapped crystal habit as a function of temperature and water vapor supersaturation. Subsequent theoretical advances, particularly by Kenneth G. Libbrecht, explained morphological transitions using surface attachment kinetics and diffusion-limited growth theory.

Ice in its most common atmospheric form (Ice Ih) exhibits hexagonal symmetry due to the tetrahedral hydrogen-bond network of water molecules. Under varying thermodynamic conditions, crystals form plates, columns, needles, or dendritic structures.

Conceptual Framework

The coherence interpretation introduces a qualitative parameter K intended to integrate multiple energetic contributions:

Molecular cohesion energy of the hydrogen-bond lattice

Surface free energy

Thermal energy

Environmental perturbations

Dipolar interactions

Directional vapor flux associated with supersaturation

The parameter is dimensionless when normalized as energy densities and is proposed as an organizational index rather than an independent predictive model.

Interpretation of Morphological Transitions

Within this framework:

High K regimes correspond to stable dendritic growth

Intermediate K regimes correspond to plate or column formation

Low K regimes correspond to irregular or unstable growth

The persistence of sixfold symmetry is interpreted as reflecting a high-coherence configuration of the hydrogen-bond network in Ice Ih.

The model is presented as consistent with diffusion-limited aggregation theory and classical thermodynamics.

Relationship to Established Models

The coherence framework is explicitly described as complementary to:

Nakaya’s morphology diagram

Surface-kinetics models of crystal growth

Classical crystallography of ice Ih

Thermodynamic nucleation theory

It does not modify established physical laws but attempts to provide an integrative interpretive layer across scales.

Proposed Quantitative Development

The framework suggests that formalization would require:

Measurable lattice cohesion energy per unit volume

Surface free energy values for basal and prism faces

Boltzmann thermal energy scaling

Supersaturation gradient quantification

Environmental perturbation indexing

Experimental validation would involve controlled laboratory crystal growth with correlation between calculated coherence index values and observed morphology.

See Also

Snow crystal

Nakaya diagram

Ice Ih

Diffusion-limited aggregation

Fractal geometry

Surface kinetics

References

Nakaya, U. (1954). Snow Crystals: Natural and Artificial.
Libbrecht, K. G. (2005, 2017). Surface kinetics and snow crystal growth.
Petrenko & Whitworth (1999). Physics of Ice.
Debenedetti (1996). Metastable Liquids.
Mandelbrot (1983). The Fractal Geometry of Nature.