Correction: A new computational strategy to calculate the edge energy of a relaxed step. Calcite (CaCO₃) as a case study

Abstract

Correction for ‘A new computational strategy to calculate the edge energy of a relaxed step. Calcite (CaCO₃) as a case study’ by M. Bruno et al., CrystEngComm, 2021, 23, 7340–7347, https://doi.org/10.1039/D1CE01119G.

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The authors regret an error in the calculation of the values of the edge energies listed in Table 2: the calculations were performed without considering the factor of 2 in eqn (1). The correct Table 2 is shown below.

Table 2 Edge energy, ρ, of the [4̄41], [42̄1] and [010] steps running on the (10.4) face of calcite. Labels Ca and CO₃ indicate the termination of the step ledge

Step edges	ρ (J m^−1)
Acute-[4̄41]	8.10 × 10^−11
Obtuse-[4̄41]	1.38 × 10^−10
[42̄1]Ca	1.34 × 10^−10
[42̄1]CO3(A)	3.22 × 10^−10
[42̄1]CO3(B)	1.26 × 10^−10
Acute-[010]Ca	1.34 × 10^−10
Obtuse-[010]Ca	1.48 × 10^−10
Acute-[010]CO3	1.65 × 10^−10
Obtuse-[010]CO3	1.25 × 10^−10

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Accordingly, the relaxed 2D equilibrium shape (ES) of the nucleus on the (10.4) face calculated with the edge energies in Table 2 and reported in Fig. 5 of the original paper is wrong. The correct Fig. 5 is shown below.

Fig. 5 (a) Unrelaxed and (b) relaxed 2D equilibrium shapes (ESs) of the nucleus on the (10.4) face. The arrows indicate the directions of the steps. Labels ac and ob represent the acute and obtuse steps, respectively, while Ca and CO₃ indicate the atomic step terminations. The quantitative comparison of the unrelaxed and relaxed ESs clearly shows the different sizes of the 2D nuclei and that, when relaxed, all the step energies are closer to each other. Owing to this property, the shape of the 2D nuclei should become more sensitive to the foreign adsorption (solvent, impurities) on the step ledges.

This mistake also led to a misinterpretation of the literature data reported in several parts of the manuscript:

1. In the Abstract, the sentence “We calculated, as the most stable step, the acute [4̄41] edge (ρ = 5.04 × 10⁻¹⁰ J m⁻¹), followed by the Ca-terminated acute-[010] (5.39 × 10⁻¹⁰ J m⁻¹) and Ca-terminated [42̄1] (9.77 × 10⁻¹⁰ J m⁻¹)” must be replaced by “We calculated, as the most stable step, the acute [4̄41] ledge (ρ = 8.10 × 10⁻¹¹ J m⁻¹), followed by the CO₃-terminated obtuse-[010] (1.25 × 10⁻¹⁰ J m⁻¹) and CO₃-terminated [42̄1] (1.26 × 10⁻¹⁰ J m⁻¹)”.

2. In section “3.1. Acute and obtuse [4̄41] steps on the (10.4) face”, the sentences “The edge energies of the acute-[4̄41] and obtuse-[4̄41] edges are 5.04 × 10⁻¹⁰ and 6.19 × 10⁻¹⁰ J m⁻¹, respectively (Table 2). Kristensen et al.³ estimated the ρ values for acute-[4̄41] and obtuse-[4̄41] edges of 2.37 × 10⁻¹⁰ and 1.26 × 10⁻¹⁰, respectively, which are noteworthily lower than ours. And on top of that, according to their calculations, the obtuse-[4̄41] edge is more stable than the acute-[4̄41] one, which is the opposite of that we obtained with our simulations. Nygren et al.¹⁵ calculated an average edge energy for the acute and obtuse steps of 2.5 × 10⁻¹⁰ J m⁻¹, a value lower than our averaged step energy, 5.62 × 10⁻¹⁰ J m⁻¹, and slightly higher with respect to that by Kristensen et al.,³ 1.82 × 10⁻¹⁰ J m⁻¹” must be replaced by “The edge energies of the acute-[4̄41] and obtuse-[4̄41] edges are 8.10 × 10⁻¹¹ and 1.38 × 10⁻¹⁰ J m⁻¹, respectively (Table 2). Kristensen et al.³ estimated the ρ values for acute-[4̄41] and obtuse-[4̄41] edges of 2.37 × 10⁻¹⁰ and 1.26 × 10⁻¹⁰, respectively. According to their calculations, the obtuse-[4̄41] edge is more stable than the acute-[4̄41] one, which is the opposite of that we obtained with our simulations. Nygren et al.¹⁵ calculated an average edge energy for the acute and obtuse steps of 2.5 × 10⁻¹⁰ J m⁻¹, a value higher than our averaged step energy, 1.09 × 10⁻¹⁰ J m⁻¹, and slightly higher with respect to that by Kristensen et al.,³ 1.82 × 10⁻¹⁰ J m⁻¹”.

3. The discussion in points 1 and 2 on page 7345 (left column, rows 22–42) should be disregarded.

4. In section “3.2. [42̄1] steps on the (10.4) face”, the sentences “We only show in Fig. 3b the relaxed structure of the [42̄1]_Ca edge, since it has the lowest edge energy (Table 2), 9.77 × 10⁻¹⁰ J m⁻¹. Nevertheless, this value is almost twice with respect to that of the acute-[4̄41] edge. The ρ values of the [42̄1]_CO3(A) and [42̄1]_CO3(B) edges are 1.30 × 10⁻⁹ and 2.57 × 10⁻⁹, respectively. To the best of our knowledge, no experimental values exist to compare with our theoretical ones. There is only an unrelaxed average value calculated at the empirical level by Massaro et al.,²⁰ 15.80 × 10⁻¹⁰ J m⁻¹, by using the same strategy described by Aquilano et al.;⁶ such a value is slightly lower than our averaged relaxed one, 16.16 × 10⁻¹⁰ J m⁻¹” must be replaced by “We only show in Fig. 3b the relaxed structure of the [42̄1]_Ca edge, which has an edge energy of 1.34 × 10⁻¹⁰ J m⁻¹ (Table 2). The ρ values of the [42̄1]_CO3(A) and [42̄1]_CO3(B) edges are 3.22 × 10⁻¹⁰ and 1.26 × 10⁻¹⁰ J m⁻¹, respectively. To the best of our knowledge, no experimental values exist to compare with our theoretical ones. There is only an unrelaxed average value calculated at the empirical level by Massaro et al.,²⁰ 15.80 × 10⁻¹⁰ J m⁻¹, by using the same strategy described by Aquilano et al.;⁶ such a value is higher than our averaged relaxed one, 1.94 × 10⁻¹⁰ J m⁻¹”.

5. In section “3.3. Acute and obtuse [010] steps on the (10.4) face”, the sentences “According to the calculated edge energies (Table 2), the following stability order of the steps is obtained: acute-[010]_Ca < acute-[010]_CO3 < obtuse-[010]_Ca < obtuse-[010]_CO3. The edge energy of the acute-[010]_Ca step is 5.39 × 10⁻¹⁰ J m⁻¹, slightly higher than that of the most stable acute-[4̄41] step. Interestingly, the acute-[010] steps (both Ca and CO₃-terminated) have edge energies lower than the obtuse ones, just like for the [4̄41] step. Also in this case, no experimental values of ρ exist to compare with our theoretical ones. There is only an unrelaxed average value calculated at the empirical level by Massaro et al.,²⁰ 11.43 × 10⁻¹⁰ J m⁻¹, which is similar to the ρ value we obtained for the obtuse-[010]_CO3 edge (Table 2)” must be replaced by “According to the calculated edge energies (Table 2), the following stability order of the steps is obtained: obtuse-[010]_CO3 < acute-[010]_Ca < obtuse-[010]_Ca < acute-[010]_CO3. The edge energy of the obtuse-[010]_CO3 step is 1.25 × 10⁻¹⁰ J m⁻¹, slightly higher than that of the most stable acute-[4̄41] step. Also in this case, no experimental values of ρ exist to compare with our theoretical ones. There is only an unrelaxed average value calculated at the empirical level by Massaro et al.,²⁰ 11.43 × 10⁻¹⁰ J m⁻¹”.

6. In section “4. Conclusions”, the sentence “In particular, we observed that the most stable is the acute-[4̄41] step with ρ = 5.04 × 10⁻¹⁰ J m⁻¹, followed by the Ca-terminated acute-[010] step (5.39 × 10⁻¹⁰ J m⁻¹) and Ca-terminated [42̄1] step (9.77 × 10⁻¹⁰ J m⁻¹)” must be replaced by “In particular, we observed that the most stable is the acute-[4̄41] step with ρ = 8.10 × 10⁻¹¹ J m⁻¹, followed by the CO₃-terminated obtuse-[010] (1.25 × 10⁻¹⁰ J m⁻¹) and CO₃-terminated [42̄1] (1.26 × 10⁻¹⁰ J m⁻¹)”.

In section “4. Conclusions”, the sentences “2. The calculations in this work deeply change the situation: the acute-[010]_Ca step cuts the two <4̄41> steps linked by the glide symmetry plane, whereas this does not happen for the obtuse-[010]_Ca step (Fig. 5b). Both the acute- and obtuse-[010] steps with CO₃ termination never became a part of the ES. 3. The <42̄1> step with Ca termination does not (for very little) become a part of the ES, but it is highly probable that the adsorption of the solution on the step (certainly reducing the value of the edge energy) can bring this edge into play as well” must be replaced by “2. The calculations in this work deeply change the situation: the obtuse-[010]_CO3 step cuts the two <4̄41> steps linked by the glide symmetry plane, whereas this does not happen for the acute-[010]_CO3 step (Fig. 5b). Both the acute- and obtuse-[010] steps with Ca termination never become part of the ES. 3. The <42̄1> step with CO₃ termination becomes part of the ES”.

These errors do not affect the overall conclusions of the paper.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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