[Paper Review] Incommensurately modulated twin structure of nyerereite Na1.64K0.36Ca(CO3)2

Н. Б. Болотина, Pavel N. Gavryushkin+7 more|arXiv (Cornell University)|Jan 9, 2017

X-ray Diffraction in Crystallography4 citations

TL;DR

This study reports the first determination of an incommensurately modulated twin structure in nyerereite (Na1.64K0.36Ca(CO3)2) using (3+1)D superspace crystallography in the Cmcm(α00)00s symmetry group with a modulation vector q = 0.383a*. The structure features complex modulation of cation and anion sites via crenel functions and x-harmonics, revealing a three-component twin related by threefold rotation about [001], and provides a comparative analysis with K-free Na2Ca(CO3)2 and γ-Na2CO3.

ABSTRACT

Incommensurately modulated twin structure of nyerereite Na1.64K0.36Ca(CO3)2 has been first determined in the (3+1)D symmetry group Cmcm({\\alpha}00)00s with modulation vector q = 0.383a*. Unit-cell values are a = 5.062(1), b = 8.790(1), c = 12.744(1) {\\AA}. Three orthorhombic components are related by threefold rotation about [001]. Discontinuous crenel functions are used to describe occupation modulation of Ca and some CO3 groups. Strong displacive modulation of the oxygen atoms in vertexes of such CO3 groups is described using x-harmonics in crenel intervals. The Na, K atoms occupy mixed sites whose occupation modulation is described by two ways using either complementary harmonic functions or crenels. The nyerereite structure has been compared both with commensurately modulated structure of K-free Na2Ca(CO3)2 and with widely known incommensurately modulated structure of {\\gamma}-Na2CO3.

Motivation & Objective

• To determine the crystal structure of nyerereite Na1.64K0.36Ca(CO3)2 with incommensurate modulation.
• To resolve the complex twin structure involving three orthorhombic components related by threefold rotation about [001].
• To model the occupation and displacement modulations of Ca, CO3, Na, and K sites using advanced superspace formalism.
• To compare the modulated nyerereite structure with commensurately modulated K-free Na2Ca(CO3)2 and the well-known incommensurate γ-Na2CO3 structure.

Proposed method

• Employed (3+1)D superspace crystallography in the Cmcm(α00)00s symmetry group to describe the incommensurate modulation.
• Used discontinuous crenel functions to model occupation modulation of Ca and selected CO3 groups.
• Applied x-harmonics within crenel intervals to describe strong displacive modulation of oxygen atoms in CO3 groups.
• Modelled mixed-site occupation of Na and K using either complementary harmonic functions or crenel functions.
• Determined unit-cell parameters: a = 5.062(1), b = 8.790(1), c = 12.744(1) Å.
• Performed structural comparison with K-free Na2Ca(CO3)2 and incommensurate γ-Na2CO3 to assess structural trends.

Experimental results

Research questions

• RQ1 What is the true superspace symmetry and modulation vector of the incommensurately modulated nyerereite structure?
• RQ2 How are the cation (Na, K, Ca) and anion (CO3) sites occupied and displaced in the modulated structure?
• RQ3 What is the nature of the twin relationship among the three orthorhombic components in nyerereite?
• RQ4 How does the modulated nyerereite structure compare structurally to K-free Na2Ca(CO3)2 and γ-Na2CO3?
• RQ5 What is the role of crenel functions and x-harmonics in accurately describing the complex modulation?

Key findings

• The nyerereite structure was refined in the (3+1)D superspace group Cmcm(α00)00s with a modulation vector q = 0.383a*.
• Three orthorhombic components form a twin structure related by a threefold rotation about the [001] direction.
• Occupation modulation of Ca and selected CO3 groups is described using discontinuous crenel functions.
• Displacive modulation of oxygen atoms in CO3 groups is modeled using x-harmonics within crenel intervals.
• Na and K atoms on mixed sites are described using either complementary harmonic functions or crenel functions.
• The structure is compared to K-free Na2Ca(CO3)2 and γ-Na2CO3, revealing distinct modulation patterns and structural relationships.