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Comment on “Crystal growth and aggregation in suspensions of δ-MnO 2 nanoparticles: implications for
surface reactivity
Alain Manceau
To cite this version:
Alain Manceau. Comment on “Crystal growth and aggregation in suspensions of δ-MnO 2 nanopar- ticles: implications for surface reactivity. Environmental science .Nano, Royal Society of Chemistry, 2018, 5 (9), pp.2198-2200. �10.1039/C8EN00126J�. �hal-02314766�
1
Comment on "Crystal growth and aggregation in suspensions of δ-MnO2
1
nanoparticles: implications for surface reactivity" by Francesco F. Marafatto, Bruno
2
Lanson and Jasquelin Peña, Environ. Sci.: Nano, 2017, DOI: 10.1039/c7en00817a 3
4
Alain Manceau 5
6
Univ. Grenoble Alpes, CNRS, ISTerre, F-38000 Grenoble, France 7
8 9
Abstract. Here, it is shown that X-ray diffraction is sensitive to the lognormal distribution of the 10
-MnO2 crystallite size and to the strain gradient across the nanosheet. Rigorous modeling of the 11
two effects, which were overlooked by Marafatto et al. (Environ. Sci.: Nano, doi 12
10.1039/c7en00817a), is essential to understand the influence of non-uniform microstructures on 13
the physicochemical properties and surface reactivity of nanoparticulate -MnO2. 14
15 16
Marafatto et al.1 used laboratory powder X-ray diffraction (XRD) to determine layer and 17
interlayer structure, and lateral size of -MnO2 nanosheets synthesized at pH 6, 8 and 11. The 18
structure was obtained by fitting full XRD patterns in the 30° < 2(CuK) < 75° interval, which 19
includes the 20,11 and 02,31 hk scattering bands. The lateral size was estimated from the 20
diameter of the coherent scattering domains (CSDs) deduced from the modeling of the 20,11 21
band. The CSD values were observed to decrease from 7.2 ± 0.5 nm to 2.8 ± 0.5 nm when the 22
suspension pH was increased from 6 to 11. This trend was confirmed by measuring the full width 23
at half-maximum (FWHM) of the 02,31 band with a synchrotron X-ray source. However, the 24
variation of the crystallite size with pH was extremely different when obtained by calculation 25
from the fit of the 20,11 band and by experiment from the measurement of the 02,31 width. This 26
difference leads to the two questions:
27
1- Why are the results obtained from the analysis of the 20,11 and 02,31 reflections 28
inconsistent? It is proposed that the change with pH of the lognormal distribution of the 29
crystallite size2 was overlooked in the fit of the 20,11 profile.
30
2- How were the full XRD patterns fit without modeling the non-uniform strain of the -MnO2
31
crystallites resulting from the bending of the nanosheets2? A full-pattern fit could be obtained by 32
separately fitting and then joining the 20,11 and 02,31 reflection lines without considering the 33
non-uniform strain. However, non-uniform strain would have significant bearing on the 34
macroscopic physicochemical properties and surface reactivity of these -MnO2 crystallites, and 35
therefore must be considered.
36 37
1. Correlation between the arithmetic mean and standard deviation of the crystallite size 38
distribution 39
As shown in Fig. 1A, varying the CSD dimension modifies the width of both the 20,11 and 40
02,31 reflections.3 Thus, as a first approximation it should be possible to evaluate the same CSD 41
from either reflection. However, the authors obtained different power-laws for the same set of 42
samples between the crystallite size (CSD) and the particle size (RH) with each reflection: RH ∝ 43
CSDpH1.66 from the fit of the 20,11 reflection and RH ∝ CSDpH3.7 from the measurement of the 44
2 02,31 FWHM. As shown below, a main reason for this difference is the non-uniqueness of the 45
mathematical solution of the 20,11 fit.
46
The most common distribution of the crystallite size in a powder sample is by far the 47
lognormal distribution.4-6 Fig. 1B shows that the lognormal width () modifies the diffraction 48
line profile almost identically to the CSD value, defined here as the mean <D> of the ln(CSD) 49
distribution. The <D> and parameters are so tightly correlated that it is impossible to obtain 50
reliable structural parameters without enforcing some constraints from other knowledge, here the 51
experimental power-law RH ∝ CSDpH3.7. Thus, <D> and can be estimated iteratively from the 52
20,11 fit with the constraint that <D> matches RH ∝ [(<D>)pH]3.7 within errors. An example of 53
invariant XRD profile obtained with five sets of (<D>,) values is shown in Fig. 1C. In practice, 54
the 3.7 exponent can be approached by reducing the [2.8,7.2] nm CSD interval while refining 55
such that pH11 > pH8 > pH6. 56
Optimizing (<D>,) is supported because the distribution of crystallite size () in a powder 57
sample depends on crystal size (<D>), which itself depends on conditions of formation.5 The 2.8 58
nm size was interpreted mechanistically in terms of the rapid nucleation and aggregation of - 59
MnO2 crystallites at pH 11, and the 7.2 nm size as the growth of larger nanosheets at pH 3 60
through the oriented attachment of smaller -MnO2 crystallites. It seems physically realistic that 61
for smaller crystallites, the distribution of size relative to the mean would be larger (i.e., pH11 >
62
pH6).
63
The parameter is a dimensionless quantity which however gives an indication of the 64
dispersion in size of the crystallites. A mean CSD diameter <D> with a ln(CSD) width , 65
corresponds to a full-width at half maximum (FWHM) variation (1, 2) of : 66
1, 2 = exp[ln < > ± 2ln(2 ]
( ) D )
67
Taking <D>pH6 = 7.2 nm and = 0.5 gives 1 = 4.0 nm and 2 = 13.0 nm. The same width 68
applied to a <D>pH11 diameter of 2.8 nm corresponds to a FWHM variation from 1.5 nm to 5.1 69
nm. Fig. 2 shows that the sensitivity of the lognormal distribution to a heavy tail population of 70
crystallites is increasingly pronounced as the mean (<D>) and the dispersion (), and hence the 71
asymmetry, of the distribution increase.
72 73
2. Evidence for non-uniform microstrain deformation of the -MnO2 crystallites 74
Chemical and biogenic -MnO2 nanosheets are not flat but curled and occasionally kinked.2, 7- 75
13 The bending of the nanosheet causes the crystals to diffract at higher Bragg angle as if they 76
were smaller because the wavefunctions of the X-rays scattered by atoms at the edges of a crystal 77
go out-of-phase with those at the center. Thus, in principle, the true CSD value can only be 78
determined from the modeling of the 02,31 line with a physically meaningful function of the 79
form:
80
CSD[02,31] = CSD[20,11] x f() 81
A general analytical function is2 82
CSD[hkl]-2 = CSD[real]-2 [1 + (q/q0)2] 83
where CSD[real] is the actual size of the crystallite, is a dimensionless parameter describing 84
strain, q is the scattering vector q = (4/)sinand q0 corresponds to the first in-plane reflection.
85
Carrying out the calculation with = 0.4 gives CSD[02,31] / CSD[20,11] = 0.68. The strain- 86
broadening effect on the shape of the 02,31 reflection is shown in Fig. 1D. This calculation 87
3 demonstrates that strain caused the FWHM to broaden by ~65 %, and that the peak intensity 88
decreased by the same fraction because strain does not change the integral breadth of the peak.
89
Microstrain broadening was observed in all -MnO2 patterns which we have observed (Fig. 3 90
and Ref. 2), and should be general because -MnO2 nanosheets have limited interlayer cohesion 91
and can even be filamentous.9 Therefore, provision should be made for this factor in the 92
determination of (<D>,) if it is observed that the intensity ratio of the 20,11 and 02,31 93
reflections changes between pH 6 and 11.
94
Together, these considerations call into question how the fits of the full XRD patterns (30° <
95
2 < 75°) presented in Figure 2 of Marafatto et al.1 were obtained without considering 96
microstrain effects. An alternative way to match the relative intensities and widths of the 20,11 97
and 02,31 reflections would be to calculate them separately, assuming no microstrain, using 98
different CSD values and normalize arbitrarily their intensities to experiment, as shown in Fig.
99
S1. This procedure has no physical foundation. It may be necessary to reinvestigate other 100
chemical and biogenic -MnO2 samples10, 14-18 in light of the effects of non-uniform size 101
distribution and strain shown by Manceau et al.2 and the remarks presented here.
102 103
Notes and references 104
1. F. F. Marafatto, B. Lanson and J. Peña, Environ. Sci. Nano, 2018, DOI:
105
10.1039/c1037en00817a.
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2. A. Manceau, M. A. Marcus, S. Grangeon, M. Lanson, B. Lanson, A. C. Gaillot, S.
107
Skanthakumar and L. Soderholm, J. Appl. Crystallogr., 2013, 46, 193-209.
108
3. H. Yin, K. D. Kwon, J. Y. Lee, Y. Shen, H. Y. Zhao, X. M. Wang, F. Liu, J. Zhang and X.
109
H. Feng, Geochim. Cosmochim. Acta, 2017, 208, 268-284.
110
4. V. Drits, J. Srodon and D. D. Eberl, Clays Clay Miner., 1997, 45, 461-475.
111
5. J. I. Langford, D. Louër and P. Scardi, J. Appl. Cryst., 2000, 33, 964-974.
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6. R. B. Bergmann and A. Bill, J. Cryst. Growth, 2008, 310, 3135-3138.
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7. B. M. Tebo, J. R. Bargar, B. G. Clement, G. J. Dick, K. J. Murray, D. Parker, R. Verity and 114
S. M. Webb, Annu. Rev. Earth Planet.. Sci., 2004, 32, 287-328.
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8. B. Toner, S. Fakra, M. Villalobos, T. Warwick and G. Sposito, Appl. Environ. Microbiol., 116
2005, 71, 1300-1310.
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9. N. Miyata, Y. Tani, K. Maruo, H. Tsuno, M. Sakata and K. Iwahori, App. Environ.
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Microbiol., 2006, 72, 6467-6473.
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10. S. Grangeon, A. Manceau, J. Guilhermet, A. C. Gaillot, M. Lanson and L. Lanson, Geochim.
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Cosmochim. Acta, 2012, 85, 302-313.
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11. H. Yin, F. Liu, X. H. Feng, T. D. Hu, L. R. Zheng, G. H. Qiu, L. K. Koopal and W. F. Tan, 122
Geochim. Cosmochim. Acta, 2013, 117, 1-15.
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12. H. Yin, X. H. Feng, W. F. Tan, L. K. Koopal, T. D. Hu, M. Q. Zhu and F. Liu, J. Hazard.
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Mater., 2015, 288, 80-88.
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13. Z. J. Qin, Q. J. Xiang, F. Liu, J. Xiong, L. K. Koopal, L. R. Zheng, M. Ginder-Vogel, M. X.
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Wang, X. H. Feng, W. F. Tan and H. Yin, Chem. Geol., 2017, 466, 512-523.
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14. M. Villalobos, B. Lanson, A. Manceau, B. Toner and G. Sposito, Am. Mineral., 2006, 91, 128
489-502.
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15. B. Lanson, M. A. Marcus, S. Fakra, F. Panfili, N. Geoffroy and A. Manceau, Geochim.
130
Cosmochim. Acta, 2008, 72, 2478–2490.
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16. S. Grangeon, B. Lanson, M. Lanson and A. Manceau, Min. Mag., 2008, 72, 1197-1209.
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17. S. Grangeon, B. Lanson, N. Miyata, Y. Tani and A. Manceau, Am. Mineral., 2010, 95, 1608- 133
1616.
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18. S. Grangeon, B. Lanson and M. Lanson, Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng.
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Mater., 2014, 70, 828-838.
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4 19. A. Plançon, J. Appl. Cryst., 2002, 35, 377-.
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20. B. Lanson, http://isterre.fr/bruno-lanson, 2018.
138 139
Figure captions 140
141
Fig. 1. Effects of the -MnO2 microstructure on the hk diffraction line profiles. <D> = mean CSD 142
diameter in nm; = standard deviation of the lognormal distribution of diameters; = srain 143
parameter, A) Effect of the CSD dimension <D>. B) Effect of the lognormal width . C) 144
Correlation of <D> and . D) Effect of on the intensity and width of the 02,31 reflection.
145
Details on calculations can be found elsewhere.2 q is the scattering vection. q(Å-1) = 2/d(Å).
146 147
Fig. 2. Variation of the breadth of dispersion of the crystallite size, expressed as (FWHM) = , 148
with the lognormal mean (<D>) and the standard deviation ().
149 150
Fig. 3. Experimental and calculated whole-powder-patterns for -MnO2 samples showing the 151
contribution from non-uniform strain on the relative intensities of the 20,11 and 02,31 reflections 152
. A) Sample pattern distributed with the current version of the CALCIPOW19 programme (dated 153
April 2017) maintained by Bruno Lanson.20 Structural parameters are listed in Table S1. B) 154
MndBi3 XRD pattern and structural parameters (except and ) are from Grangeon et al..18 155
156 157
5 158
159
Figure 1
160 161 162
6 163
164
Figure 2
165 166 167
168
Figure 3
169
7
Supplementary Information
Comment on "Crystal growth and aggregation in suspensions of δ-MnO2
nanoparticles: implications for surface reactivity" by Francesco F. Marafatto, Bruno Lanson and Jasquelin Peña, Environ. Sci.: Nano, 2017, DOI: 10.1039/c7en00817a
Alain Manceau
Univ. Grenoble Alpes, CNRS, ISTerre, F-38000 Grenoble, France
Table S1. Atomic coordinates and site occupancies used to calculate the XRD profiles and to fit the -MnO2 sample pattern from Fig. 3A. Same conventions as in Table 3 from Ref. 18.
Coordinates
Atom x y z Occupancy
EMn (Mn1) 0 0 0 0.90
OMn1 0.333 0 0.14 2.0
TCMn (Mn2) 0 0 0.29 0.05
OMn2 -0.333 0 0.45 0.15
Interlayer Na -0.540 0 0.5 0.083
-0.230 0.310 0.5 0.083
-0.230 -0.310 0.5 0.083
Interlayer Water 0.120 0 0.5 0.083
-0.06 0.18 0.5 0.083
-0.06 -0.18 0.5 0.083
a = 4.919 Å; b = 2.84 Å; c = 7.20 Å, = = = 90°. Debye–Waller factors B (Å2) were fixed to 0.5 for Mn1, 1.0 for O1 and Mn2, and 2.0 for all other atoms
8 Fig. S1. Reconstruction of the -MnO2 pattern shown in Fig. 3A by adding the 20,11 and 02,31 line profiles calculated separately and without considering microstrain resulting from particle bending. In this way, the strain effect in the pattern apparently can be reproduced by (1) adjusting the calculated I(20,11) / I(02,31) ratio to I(20,11) / [0.65 x I(02,31)], and (2) increasing the width of the 02,31 line, i.e., changing the CSD dimension (not shown in the Figure).
