Second half of June and into July was a bit of a write-off due to exams, travels, grant proposal writing and the like.

But now I am back to the work on Akermanite. My task is to fit simple models for the energies between pairs of atoms using the CASTEP calculations as my reference data. Specifically, we have energies and equilibrium structures for all pressures to use as data, and I plan to fit the values of the charges and the parameters in the functions of the form:

E(r) = B.exp(-r/rho) – C/r^6

where B, rho and C are parameters. I am doing this for all atom pairs, but aim to only fit C for O–O and Si–O, and use fitted values of rho (because of parameter correlations). 

I have tried using the variable pressure data, and then looking at a single pressure, but in short it is not working well. The problem can be seen by looking at the resultant structure:

{{file:173}} 

What is clear is that an oxygen atom wants to move down into the plane of Ca atoms, and the MgO4 tetrahedron becomes a square. The structure retains elements of its original topology, but is creating new bonds. This is of course allowed by the form of the potentials, which usually work much better. But we know that Akermanite has a slightly odd structure, so perhaps we need to use functions with somewhat better definition.

In this regard, I did try using harmonic bond-angle potentials for the O–Si–O and O–Mg–O bonds, but this didn't do too much for me. 

 

 

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The analysis of incommensurate structures in terms of full space group theory, and the application of the method to melilite

McConnell JDC

ZEITSCHRIFT FUR KRISTALLOGRAPHIE 214 (8): 457-464 1999 

Abstract: This paper deals with the application of full group theoretical methods to the elucidation of the symmetry and structure of an incommensurate phase. The analysis shows that the full symmetry sind structure of the incommensurate phase can be determined unequivocably where certain minimal symmetry data are available. The theory is compared with existing methods used in the study of incommensurate structures, and is applied to the elucidation of the incommensurate structure of melilite. The analysis demonstrates that there are two symmetrically distinct distortions of the Z tetrahedral site in melilite which, when it contains Fe, is responsible for two quite independent Mossbauer signatures.

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The nature of the incommensurate structure in akermanite, Ca2MgSi2O7, and the character of its transformation from the normal structure

McConnell JDC, McCammon CA, Angel RJ, Seifert F

ZEITSCHRIFT FUR KRISTALLOGRAPHIE 215 (11): 669-677 2000 

Abstract: Study of the Mossbauer effect over a range of both temperature and pressure on polycrystalline Fe-doped akermanite, and X-ray measurements of spontaneous strain on single crystals of akermanite under pressure, have been used to study the nature of the order parameters, and the characteristics for the transition of the normal to incommensurate structure in this compound. A recent study implies that the known atomic displacements in this: phase must satisfy the symmetry of a space group irreducible representation induced from the representations A(2) and B-1 of the group associated with the vector 000 of the space group P (4) over bar2(1)m, the high temperature space group of melilite. The Mossbauer effect deals with local order, and may be explained directly ill terms of the existence of two types of Fe-57(2+) containing Z tetrahedra, one of which is simply rotated on the basis of the A(2) representation (eta) and the other distorted on the basis of the diad symmetry of B-1, (xi). In contrast the single crystal strain effects observed by single crystal X-ray diffraction must be explained in terms of both local strains associated with the A(2) and B-1 distortions, and a macroscopic strain field which couples the local distortions under the full symmetry of the tetragonal phase. 

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Structure and phase transitions in Ca2CoSi2O7-Ca2ZnSi2O7 solid-solution crystals

Jia ZH (Jia, Z. H.), Schaper AK (Schaper, A. K.), Massa W (Massa, W.), Treutmann W (Treutmann, W.), Rager H (Rager, H.)

ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 62: 547-555 Part 4, AUG 2006

Abstract: While the incommensurability in melilites is well documented, the underlying atomic configurations and the composition-dependent phase behavior are not yet clear. We have studied the transition from the incommensurate phase to the high-temperature normal phase (IC-N), and to the low-temperature commensurate phase (IC-C) of selected members of the Ca2Co1-xZnxSi2O7 system using X-ray and single-crystal electron diffraction, as well as calorimetric measurements. The space group of the unmodulated normal phase and of the basic structure of the incommensurate phase is P (4) over bar2(1)m; the commensurate lock-in superstructure was refined as a pseudomerohedral twin in the orthorhombic space group P2(1)2(1)2. We found that the commensurate modulation is mainly connected with a sawtooth-like periodicity of rotations of the T-1 tetrahedra in the 3 x 3 superstructure. In this structure, the clustering of the low-coordinated Ca2+ ions is not complete so that only imperfect octagons were detected. Generally, the effect of increasing substitution of Co by Zn was a continuous reduction of the IC-N and IC-C transition temperatures. 

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Ab initio determination of the ground-state properties of Ca2MgSi2O7 akermanite

Razvan Caracas and Xavier Gonze

 

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My understanding is that Akermanite has an incommensurate phase transition due to the Ca being unable to fit in the gap in the structure. Because our models cannot include this phase transition (our atomic configuration is too small) it adjusts by expanding c slightly and increasing some of the Ca–O distances.

On this basis, we have an understanding of the effect we are seeing at around 4 GPa. What we are seeing below 4 GPa is clearly artificial, but it does tell us just how difficult it is for this structure to want to avoid doing something to solve its atomic mismatch problem.

One thing to do is to work out what is involved in this structure becoming stable. That will involve looking at the coordination in detail as a function of pressure.

Another thing we have discussed is to develop a decent empirical interatomic potential that we can use for larger samples.

I propose a dual approach

1. I will use the CASTEP data for all pressures to fit a potential. We have in this a range of interatomic distances and energies, as well as equilibrium structures and effectively the pressure-dependence
2. I will also use the experimental data in a separate study. Here we have a bit less in the way of data, but I can fix some of the parameters based on the CASTEP run. 

[More]

The analysis of incommensurate structures in terms of full space group theory, and the application of the method to melilite

McConnell JDC

ZEITSCHRIFT FUR KRISTALLOGRAPHIE 214 (8): 457-464 1999 

Abstract: This paper deals with the application of full group theoretical methods to the elucidation of the symmetry and structure of an incommensurate phase. The analysis shows that the full symmetry sind structure of the incommensurate phase can be determined unequivocably where certain minimal symmetry data are available. The theory is compared with existing methods used in the study of incommensurate structures, and is applied to the elucidation of the incommensurate structure of melilite. The analysis demonstrates that there are two symmetrically distinct distortions of the Z tetrahedral site in melilite which, when it contains Fe, is responsible for two quite independent Mossbauer signatures.

---

The nature of the incommensurate structure in akermanite, Ca2MgSi2O7, and the character of its transformation from the normal structure

McConnell JDC, McCammon CA, Angel RJ, Seifert F

ZEITSCHRIFT FUR KRISTALLOGRAPHIE 215 (11): 669-677 2000 

Abstract: Study of the Mossbauer effect over a range of both temperature and pressure on polycrystalline Fe-doped akermanite, and X-ray measurements of spontaneous strain on single crystals of akermanite under pressure, have been used to study the nature of the order parameters, and the characteristics for the transition of the normal to incommensurate structure in this compound. A recent study implies that the known atomic displacements in this: phase must satisfy the symmetry of a space group irreducible representation induced from the representations A(2) and B-1 of the group associated with the vector 000 of the space group P (4) over bar2(1)m, the high temperature space group of melilite. The Mossbauer effect deals with local order, and may be explained directly ill terms of the existence of two types of Fe-57(2+) containing Z tetrahedra, one of which is simply rotated on the basis of the A(2) representation (eta) and the other distorted on the basis of the diad symmetry of B-1, (xi). In contrast the single crystal strain effects observed by single crystal X-ray diffraction must be explained in terms of both local strains associated with the A(2) and B-1 distortions, and a macroscopic strain field which couples the local distortions under the full symmetry of the tetragonal phase. 

---

Structure and phase transitions in Ca2CoSi2O7-Ca2ZnSi2O7 solid-solution crystals

Jia ZH (Jia, Z. H.), Schaper AK (Schaper, A. K.), Massa W (Massa, W.), Treutmann W (Treutmann, W.), Rager H (Rager, H.)

ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 62: 547-555 Part 4, AUG 2006

Abstract: While the incommensurability in melilites is well documented, the underlying atomic configurations and the composition-dependent phase behavior are not yet clear. We have studied the transition from the incommensurate phase to the high-temperature normal phase (IC-N), and to the low-temperature commensurate phase (IC-C) of selected members of the Ca2Co1-xZnxSi2O7 system using X-ray and single-crystal electron diffraction, as well as calorimetric measurements. The space group of the unmodulated normal phase and of the basic structure of the incommensurate phase is P (4) over bar2(1)m; the commensurate lock-in superstructure was refined as a pseudomerohedral twin in the orthorhombic space group P2(1)2(1)2. We found that the commensurate modulation is mainly connected with a sawtooth-like periodicity of rotations of the T-1 tetrahedra in the 3 x 3 superstructure. In this structure, the clustering of the low-coordinated Ca2+ ions is not complete so that only imperfect octagons were detected. Generally, the effect of increasing substitution of Co by Zn was a continuous reduction of the IC-N and IC-C transition temperatures. 

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Here I plot the Ca-O distances from experiment:

{{file:106}}

(The tetrahedral distances are not sufficiently accurate compared to the small changes over the pressure range).

In comparison with the castep calculations, the main differences are that the experimental data reflects the trends of the calculation at higher pressure. We note that the shortest distance also represent two equal distances, as in the calculations.

Thus I re-iterate my suggestion of using the high-pressure structure and reducing the pressure in a set of calculations. 

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I have analysed the outputs from the simulation sweep. I would like to show two plots:

{{file:105}} Si-O and Mg-O distances normalised against the 0.5 GPa pressure value. The Mg-O value is the lowest value.

{{file:103}} Ca-O distances normalised against the 0.5 GPa pressure value. Ignore the colour codes (Castep does a distance sort in its printout and I couldn't be bothered to resort given that the behaviour is clear enough)

{{file:104}}  Enthalpy plot

The obvious interpretation is that there is a change in the structure around 4 GPa that is real. The smoothness of the enthalpy plot (enthalpy should be continuous through any change in phase) suggests we are seeing a real effect here.

The Si-O and Mg-O plots show some wiggles around the pressure of the anomoly, but these are not large.

The really important effect is on the Ca-O distances. There are 8 distances in the first shell of neighbours, but you can mostly see fewer than 8 curves because there are some groups of 2 identical distances. Let us look separately at the open and closed circles in the data (and disregard the way the colours switch from one trend to another).

Open circles.  Mostly you can see two sets of data; each set is mostly 2 distances (ie there are 4 open circle data sets, which you can see around 4.5 GPa when they separate). At low P the two independent distances differ by around 0.2 Å, but at pressures above the instability point they differ by only 0.02 Å.

Filled circles.  At higher pressure (where the colours are cleaner), the two curves with higher values are single distances, and the third curve is an overlap of 2 distances. If I interpret the trend right, one of the single distance curves starts as the lowest value at low pressure (red points), the distance increases on pressure (switching to red points), and then jumps to the largest distance in this group (green points). The other two curves follow a smoother trend (from low to high pressure, one curve goes from green to black, and the other goes from black to purple - sorry about the colours!).

In short, there appears to be a structural instability associated with the Ca coordination on increasing pressure. The experimental paper (when I get time I will plot their structural data, but it will be a bit of a chore) suggests that changes in the Ca coordination are associated with the incommensurate phase transition.

One thing you could do is to use the structure at around 7 GPa as the starting structure and run over some of the lower pressures just to have a look.

I should add that the structure at 20 GPa doesn't look very different from at low pressure. It isn't that there is a big change, more that there is probably a change in how the structure - particularly the local structure around Ca - can accommodate pressure. 

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Akermanite Ca-O distances from first pressure run

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I have looked at the experimental paper and plotted up the lattice parameter data.

a lattice parameter: {{file:83}}

c lattice parameter: {{file:84}}

c/a ratio: {{file:85}} 

Volume: {{file:86}}  

The c/a ratio in experiment shows a clear effect. The feature occurs because of the incommensurate phase transition. 

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Akermanite experimental volume

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Akermanite experimental c/a ration

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