Order and disorder among the layered double hydroxides: combined Rietveld and DIFFaX approach

A combined approach using the Rietveld technique of structure refinement and DIFFaX simulations of the powder patterns enables us to not only arrive at the complete structure of the layered double hydroxides (LDHs), but also classify and quantify the nature of structural disorder. Hydrolysis of urea dissolved in mixed-metal salt solutions containing a divalent metal (Mg²⁺, Co²⁺) with Al³⁺ results in the homogeneous precipitation of the corresponding LDH. The products obtained are highly crystalline enabling a complete structure determination including subsequent refinement by the Rietveld method. In contrast, the LDH of Ni²⁺ with Al³⁺ crystallizes with the incorporation of stacking faults. A combined Rietveld-DIFFaX approach shows that even `crystalline' samples of this LDH incorporate up to 9% of stacking faults, which are not eliminated even at elevated temperatures (473 K). These studies have implications for the order, disorder and `crystallinity' of layered phases in general and metal hydroxides in particular.

S1. Experimental

Solid urea was added to 40 ml of a 0.5 M mixed metal [M(II) +Al(III)] nitrate solution maintaining the urea/[M(II) + Al(III)] molar ratio at 3.3. The clear solution obtained was heated at different temperatures between 353 K and 473 K for 24 h. Heating above the boiling point of water was carried out in a teflon lined autoclave under autogenous pressure. The solids were recovered by filtration, copiously washed to constant pH and then dried at 353 K.

S2. Refinement

The Rietveld refinement technique was used for structure determination (FULLPROF. 2k code, version 3.3 June 2005-LLB JRC). In all the refinements, the modified pseudo-voigt line shape function with five variables (U, V, W, X and ?) is used to fit the experimental profiles. Refinements were also carried out with profiles incorporating the Pearson VII correction for comparing the effect of profile function on the quality of the fit and the difference profile. The background adjustment in the calculated patterns was made using a twelve polynomial function. The crystal structure of mineral hydrotalcite, was chosen as the model (ICSD No. 6296, Space group: R-3 m, a = 3.054 Å; c = 22.81 Å) for the Rietveld refinement of the structures of the M—Al—CO32- LDHs (M = Ni2+, Co2+). For M = Mg2+, a more recent model structure (CC-81963, Space group: R-3 m, a = 3.046 Å; c = 22.772 Å) was used (Bellotto et al., 1996).

Computing details

For both compounds, program(s) used to refine structure: FULLPROF.

Figures

Figure 4 Results of the Rietveld refinement of the structure of the Mg—Al—CO32- LDH using the X-ray powder diffraction pattern given in Figure 3(b). The impurity peaks have been excluded in the profile fitting procedure. Figure 5 Results of the Rietveld refinement of the structure of the Co—Al—CO32- LDH.

(Mg0.667Al0.33OH2CO30.1666.0.56H2O)

Crystal data

?	γ = 120°
Mr = ?	V = 181.68 (4) Å^3
Rhombohedral, R3M	Z = ?
Hall symbol: -R 3 2"	Cu Kα radiation, λ = 1.540530 Å
a = 3.04245 (2) Å	T = 298 K
c = 22.664143 (1) Å	?, ? × ? × ? mm
α = 90°

Data collection

X'pert Pro Philips diffractometer	Data collection mode: reflection
Radiation source: rotating-anode X-ray tube	Scan method: continuous
Graphite monochromator	2θmin = 5.043°, 2θmax = 70.023°, 2θstep = 0.020°

Refinement

Rp = 22.558	3250 data points
Rwp = 32.313	19 parameters
Rexp = 16.708	0 restraints
RBragg = 10.291
χ^2 = NOT FOUND

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Mg	0.00000	0.00000	0.00000	0.00000*	0.66667
Al	0.00000	0.00000	0.00000	0.00000*	0.33333
O1	0.00000	0.00000	0.3747 (4)	0.00000*
O2	0.125 (3)	−0.125 (3)	0.50000	0.00000*	0.176 (4)
C	0.33333	0.66667	0.50000	0.00000*	0.08329

(Co.681Al0.311OH2CO30.1557.0.53H2O)

Crystal data

?	γ = 120°
Mr = ?	V = 183.93 (2) Å^3
Rhombohedral, R3M	Z = ?
Hall symbol: -R 3 2"	Cu Kα radiation, λ = 1.540530 Å
a = 3.066045 (19) Å	T = 298 K
c = 22.593113 (1) Å	?, ? × ? × ? mm
α = 90°

Data collection

Radiation source: rotating-anode X-ray tube

2θmin = 4.988°, 2θmax = 69.968°, 2θstep = 0.020°

Refinement

Rp = 19.866	3250 data points
Rwp = 27.538	16 parameters
Rexp = 22.252	0 restraints
RBragg = 9.063
χ^2 = NOT FOUND

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Co	0.00000	0.00000	0.00000	0.00921*	0.68157
Al	0.00000	0.00000	0.00000	0.00921*	0.31147
O1	0.00000	0.00000	0.3747 (4)	0.00000*
O2	0.11386	−0.11386	0.50000	0.00000*	0.16627
C	0.00000	0.00000	0.16700	0.00000*	0.07787