[Paper Review] Stability of ferroelectric ice

Toshiaki Iitaka|arXiv (Cornell University)|Jul 11, 2010

Freezing and Crystallization Processes1 references3 citations

TL;DR

This paper proposes that the ferroelectric ice phase with the $Cmc2_1$ structure is only stable in the presence of a specific dopant concentration, which screens the depolarizing field that otherwise destabilizes the polar phase in pure ice. Using first-principles calculations and a model of polar crystallites, the study shows that pure ice Ih cannot sustain this ferroelectric phase at low temperatures, and instead, a non-polar proton-ordered phase (specifically Structure 14, space group $P2_1$) is the likely true ground state of pure ice.

ABSTRACT

We theoretically study the stability conditions of the ferroelectric ice of the Cmc21 structure, which has been considered, for decades, one of the most promising candidates of the low temperature proton-ordered phase of pure ice Ih. It turned out that the Cmc21 structure is stable only with a certain amount of dopant and the true proton-ordered phase of pure ice Ih remains to be found at lower temperature. Implication for spin ice is mentioned.

Motivation & Objective

• To re-evaluate the thermodynamic stability of the $Cmc2_1$ ferroelectric ice phase, long considered a candidate for the true proton-ordered phase of pure ice Ih.
• To investigate the role of dopants in stabilizing the $Cmc2_1$ structure, challenging the traditional view that dopants act only as catalysts.
• To assess the impact of macroscopic electrostatic fields (depolarization fields) on polar ice crystallites and their effect on phase stability.
• To identify the true low-temperature proton-ordered phase of pure ice Ih by comparing energies and electrostatic contributions across 16 distinct proton-ordered configurations.
• To explore implications for spin ice and astronomical observations of ice in space, particularly regarding long-range electric fields.

Proposed method

• First-principles electronic structure calculations using ABINIT with plane-wave basis, norm-conserving pseudopotentials, and the PBE-GGA functional.
• Calculation of Kohn-Sham total energy $E_{KS}$, permanent polarization $\vec{P}_0$, and dielectric constant $\epsilon$ for 16 distinct proton-ordered configurations of ice Ih in an orthorhombic unit cell.
• Application of Berry phase theory to compute the macroscopic polarization $\vec{P}_0$.
• Use of density functional linear response theory to compute the dielectric constant $\epsilon$.
• Development of a model crystallite with surface charges due to polarization and dopants, incorporating the depolarization field $\vec{\cal E} = -(4\pi/\epsilon)\vec{P}_0$.
• Incorporation of electrostatic energy $ (2\pi P_0^2 / \epsilon)\Omega $ into the total energy to assess stability under open-circuit conditions.

Experimental results

Research questions

• RQ1 Is the $Cmc2_1$ ferroelectric ice structure thermodynamically stable in pure ice without dopants?
• RQ2 What is the role of dopants in stabilizing the $Cmc2_1$ phase—solely catalytic or also electrostatically stabilizing?
• RQ3 How do depolarization fields from surface polarization charges affect the stability of polar ice crystallites?
• RQ4 What is the true low-temperature proton-ordered phase of pure ice Ih, and which of the 16 configurations is most stable?
• RQ5 Can the autoionization of water (producing $H_3O^+$ and $OH^-$) provide sufficient charge to stabilize the $Cmc2_1$ phase in ultra-pure ice?

Key findings

• The $Cmc2_1$ structure (ferroelectric) is the most stable among the 16 proton-ordered configurations, with a Kohn-Sham energy of 0 Hartree (Table 1, Structure 1).
• The depolarization field in a pure $Cmc2_1$ crystallite generates a macroscopic electrostatic energy of $ (2\pi P_0^2 / \epsilon)\Omega = 0.0720 $ Hartree, which destabilizes the phase.
• Dopants stabilize the $Cmc2_1$ phase by screening the surface polarization charge, eliminating the destabilizing electrostatic term.
• The minimum crystallite size $L_{\text{min}}$ required for stabilization by autoionization is estimated at 1 cm, making spontaneous nucleation unlikely.
• Structure 14 (space group $P2_1$) is identified as a promising candidate for the true proton-ordered phase of pure ice, with a Kohn-Sham energy 100 K higher than $Cmc2_1$ but without the electrostatic penalty.
• The phase transition temperature for pure ice is estimated at ~36 K, significantly lower than the 72 K observed in doped ice, due to the absence of random hydrogen bond networks in the pure case.