Rietveld refinements performed on mesoporous ceria layers at grazing incidence

Seven diffraction patterns were collected on a 100 nm Gd-doped ceria layer deposited on a silicon wafer under asymmetric reflection conditions. As the grazing-incidence angle decreases, large shifts (a few tens of degrees) and broadenings (two degrees below the critical angle) of hkl reflections are apparent in the diffraction patterns. The impact of these aberrations on the positions and profiles of the Bragg peaks is studied in detail in this work. On the basis of this analysis, diffraction patterns collected at different angles of incidence could then be refined using a unique structural model. From these refinements, the evolution of the coherent diffracting domains, the strain and the microstrain can clearly be traced as a function of depth.

Computing details

For both structures, data collection: no; cell refinement: yes; data reduction: no; program(s) used to solve structure: yes; program(s) used to refine structure: yes; molecular graphics: no; software used to prepare material for publication: no.

ceria (ce02-1)

Crystal data

Gd0.1Ce0.9O1.95	Cu Kαlpha 1 and 2 radiation
Cubic, FM3M	T = 295 K
a = 5.425475 Å	Particle morphology: mesoporous
V = 159.69 Å^3	black
Z = 4	rectangular, 60 × 70 mm

Data collection

No slits diffractometer	Data collection mode: reflection
Radiation source: focus line, Godel mirror	Scan method: step
Specimen mounting: thin film deposited on a Si(100) wafer	2θmin = 10°, 2θmax = 135°, 2θstep = 0.028°

Refinement

Least-squares matrix: full with fixed elements per cycle	Excluded region(s): no
Rp = 0.054	Profile function: pseudo voigt
Rwp = 0.041	11 parameters
Rexp = 0.015	Weighting scheme based on measured s.u.'s
RBragg = 0.037	Background function: rational function of sin(theta)
4395 data points	Preferred orientation correction: no

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Gd	0	0	0	0.832880	0.0020833
Ce	0	0	0	0.832880	0.01875
O	0.25	0.25	0.25	0.832880	0.0416667

ceria (ce02-02)

Crystal data

Gd0.1Ce0.9O1.95	Cu Kαlpha 1 and 2 radiation
Cubic, FM3M	T = 295 K
a = 5.412920 Å	Particle morphology: mesoporous
V = 158.59 Å^3	black
Z = 4	rectangular, 60 × 70 mm

Data collection

No slits diffractometer	Data collection mode: reflection
Radiation source: focus line, Godel mirror	Scan method: step
Specimen mounting: thin film deposited on a Si(100) wafer	2θmin = 10°, 2θmax = 133°, 2θstep = 0.056°

Refinement

Least-squares matrix: full with fixed elements per cycle	Excluded region(s): no
Rp = 0.052	Profile function: pseudo voigt
Rwp = 0.015	11 parameters
Rexp = 0.008	Weighting scheme based on measured s.u.'s
RBragg = 0.025	Background function: rational function of sin(theta)
2197 data points	Preferred orientation correction: no

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Gd	0	0	0	1.102761	0.0020833
Ce	0	0	0	1.102761	0.01875
O	0.25	0.25	0.25	1.102761	0.0416667