Determining europium compositional fluctuations in partially stabilized zirconia nanopowders: a non-line-broadening-based method

A method is reported for assessing the compositional fluctuations in a ceramic sample, based only on the determination of the crystalline lattice parameters. Pure tetragonal phase partially stabilized zirconia powders are synthesized through the co-precipitation method by incorporating 4% Eu³⁺. The powder is subjected to compression cycles to promote the tetragonal-to-monoclinic transformation. The Rietveld analysis of the X-ray powder diffraction patterns, recorded after each compression cycle, gives information about the lattice parameters and monoclinic phase content. The determination of europium content in the residual tetragonal phase is accomplished considering the unit cell volume of t-ZrO₂ using Vegard's law. Using this information the compositional fluctuations over the sample were determined by considering two possible distributions of lanthanide ion content in the powders: a Gaussian and a Log-normal one. It was found that the Gaussian distribution better fits the experimental data. It was eventually demonstrated that these results are physically meaningful.

S1. Experimental

Sample prepared via alkaline coprecipitation from solution, followed by calcination at 1273 K for 6 h. The powder was subjected to cyclic compression stresses (and, at the end, ball milling) in order to promote martensitic transformation. After each compression cycle the powders were analyzed by means of X-ray diffraction.

S2. Refinement

The as synthesized powder was indexed as pure tetragonal zirconia, while, after the application of an external compression stress the monoclinic phase appears along with the tetragonal polymorph. With increasing cycles of stress the monoclinic content in the sample increases. The aplication of the stress along the same axes several times determines the appearance of a preferential orientation which was taken into account refining the March-Dollase parameter for the 111 direction of the tetragonal phase.

Computing details

Figures

(ZE0) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.6047 (2) Å	Particle morphology: plate-like
c = 5.1840 (4) Å	white
V = 67.36 (1) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Specimen mounting: adhesive tape	2θmin = 15°, 2θmax = 80°, 2θstep = 0.05°

Refinement

Rp = 0.050	Profile function: pseudo-Voigt
Rwp = 0.073	15 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 1.277	Preferred orientation correction: none
1301 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.961
Eu	0.75	0.25	0.25	?	.039
O	0.75	0.25	0.045 (1)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE1_tetr) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.6053 (1) Å	Particle morphology: plate-like
c = 5.1843 (2) Å	white
V = 67.39 (1) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.037	Profile function: pseudo-Voigt
Rwp = 0.052	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 1.769	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.958
Eu	0.75	0.25	0.25	?	.042
O	0.75	0.25	0.0442 (7)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE1_mono) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	V = 141.54 (8) Å^3
Mr = 125.33	Z = 4
Monoclinic, P21/c	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
a = 5.164 (1) Å	T = 293 K
b = 5.206 (1) Å	Particle morphology: plate-like
c = 5.325 (1) Å	white
β = 98.70 (1)°	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.037	Profile function: pseudo-Voigt
Rwp = 0.052	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 1.769	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.2729 (5)	0.0352 (5)	0.2121 (5)	?	.960
Eu	0.2729 (5)	0.0352 (5)	0.2121 (5)	?	.040
O1	0.094 (3)	0.335 (3)	0.361 (3)	?
O2	0.448 (4)	0.762 (3)	0.481 (4)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE2_tetr) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.6055 (1) Å	Particle morphology: plate-like
c = 5.1841 (3) Å	white
V = 67.39 (1) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.045	Profile function: pseudo-Voigt
Rwp = 0.060	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 2.341	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.958
Eu	0.75	0.25	0.25	?	.042
O	0.75	0.25	0.042 (1)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE2_mono) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	V = 141.41 (6) Å^3
Mr = 125.33	Z = 4
Monoclinic, P21/c	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
a = 5.1623 (7) Å	T = 293 K
b = 5.2052 (9) Å	Particle morphology: plate-like
c = 5.3229 (8) Å	white
β = 98.630 (8)°	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.045	Profile function: pseudo-Voigt
Rwp = 0.060	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 2.341	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.2736 (5)	0.0343 (4)	0.2129 (5)	?	.960
Eu	0.2736 (5)	0.0343 (4)	0.2129 (5)	?	.040
O1	0.088 (3)	0.332 (3)	0.340 (3)	?
O2	0.442 (3)	0.771 (3)	0.485 (3)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE3_tetr) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.6059 (2) Å	Particle morphology: plate-like
c = 5.1838 (4) Å	white
V = 67.40 (1) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.048	Profile function: pseudo-Voigt
Rwp = 0.066	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 2.856	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.957
Eu	0.75	0.25	0.25	?	.043
O	0.75	0.25	0.044 (4)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE3_mono) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	V = 141.31 (6) Å^3
Mr = 125.33	Z = 4
Monoclinic, P21/c	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
a = 5.1595 (7) Å	T = 293 K
b = 5.2069 (8) Å	Particle morphology: plate-like
c = 5.3223 (8) Å	white
β = 98.780 (7)°	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.048	Profile function: pseudo-Voigt
Rwp = 0.066	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 2.856	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.2747 (4)	0.0358 (4)	0.2125 (4)	?	.960
Eu	0.2747 (4)	0.0358 (4)	0.2125 (4)	?	.040
O1	0.101 (2)	0.330 (3)	0.351 (2)	?
O2	0.439 (2)	0.768 (2)	0.479 (3)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE4_tetr) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.6062 (3) Å	Particle morphology: plate-like
c = 5.1841 (6) Å	white
V = 67.42 (2) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.056	Profile function: pseudo-Voigt
Rwp = 0.075	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 3.610	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.956
Eu	0.75	0.25	0.25	?	.044
O	0.75	0.25	0.043 (2)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE4_mono) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	V = 141.29 (6) Å^3
Mr = 125.33	Z = 4
Monoclinic, P21/c	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
a = 5.1604 (7) Å	T = 293 K
b = 5.2072 (8) Å	Particle morphology: plate-like
c = 5.3208 (8) Å	white
β = 98.822 (7)°	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.056	Profile function: pseudo-Voigt
Rwp = 0.075	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 3.610	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.2748 (4)	0.0371 (4)	0.2120 (4)	?	.960
Eu	0.2748 (4)	0.0371 (4)	0.2120 (4)	?	.040
O1	0.099 (2)	0.331 (3)	0.346 (2)	?
O2	0.437 (2)	0.767 (2)	0.478 (3)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE5_tetr) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	Z = 2
Mr = 125.33	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
Tetragonal, P42/nmc	T = 293 K
a = 3.612 (1) Å	Particle morphology: plate-like
c = 5.172 (3) Å	white
V = 67.48 (8) Å^3	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 100°, 2θstep = 0.05°

Refinement

Rp = 0.049	Profile function: pseudo-Voigt
Rwp = 0.064	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 3.062	Preferred orientation correction: none
1701 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.75	0.25	0.25	?	.952
Eu	0.75	0.25	0.25	?	.048
O	0.75	0.25	0.048 (5)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

(ZE5_mono) zirconium dioxide

Crystal data

Zr0.96Eu0.04O1.98	V = 141.29 (6) Å^3
Mr = 125.33	Z = 4
Monoclinic, P21/c	Cu Kα1, Cu Kα2 radiation, λ = 1.540562 Å
a = 5.1603 (6) Å	T = 293 K
b = 5.2086 (7) Å	Particle morphology: plate-like
c = 5.3211 (7) Å	white
β = 98.912 (6)°	Specimen preparation: Prepared at 1273 K

Data collection

Philips PW 1319 diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Graphite monochromator	2θmin = 15°, 2θmax = 80°, 2θstep = 0.05°

Refinement

Rp = 0.049	Profile function: pseudo-Voigt
Rwp = 0.064	24 parameters
Rexp = ?	Background function: square polynomial
χ^2 = 3.062	Preferred orientation correction: none
1301 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0.2746 (3)	0.0373 (3)	0.2130 (3)	?	.960
Eu	0.2746 (3)	0.0373 (3)	0.2130 (3)	?	.040
O1	0.071 (2)	0.327 (2)	0.348 (2)	?
O2	0.450 (2)	0.754 (2)	0.481 (2)	?

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?