Energy crossovers in nanocrystalline zirconia

Article abstract of DOI:10.1111/j.1551-2916.2004.00031.x

The synthesis of nanocrystalline powders of zirconia often produces the tetragonal phase, which for coarse-grained powders is stable only at high temperatures and transforms into the monoclinic form on cooling. This stability reversal has been suggested to be due to differences in the surface energies of the monoelinic and tetragonal polymorphs. In the present study, we have used high-temperature oxide melt solution calorimetry to test this hypothesis directly. We measured the excess enthalpies of nanocrystalline tetragonal, monoclinic, and amorphous zirconia. Monoelinic ZrO₂ was found to have the largest surface enthalpy and amorphous zirconia the smallest. Stability crossovers with increasing surface area between monoclinic, tetragonal, and amorphous zirconia were confirmed. The surface enthalpy of amorphous zirconia was estimated to be 0.5 J/m². The linear fit of excess enthalpies for nanocrystalline zirconia, as a function of area from nitrogen adsorption (BET) gave apparent surface enthalpies of 6.4 and 2.1 J/m₂, for the monoclinic and tetragonal polymorphs, respectively. Due to aggregation, the surface areas calculated from crystallite size are larger than those measured by BET. The fit of enthalpy versus calculated total interface/surface area gave surface enthalpies of 4.2 J/m² for the monoclinic form and 0.9 J/m² for the tetragonal polymorph. From solution calorimetry, the enthalpy of the monoclinic to tetragonal phase transition for ZrO₂ was estimated to be 10±1 kJ/mol and amorphization enthalpy to be 34±2 kJ/mol.

Full text of DOI:10.1111/j.1551-2916.2004.00031.x

J. Am. Ceram. Soc., 88 [1] 160–167 (2005)
DOI: 10.1111/j.1551-2916.2004.00031.x
ournal
J
Energy Crossovers in Nanocrystalline Zirconia
w
z
Michael W. Pitcher, Sergey V. Ushakov, and Alexandra Navrotsky
Thermochemistry Facility and NEAT ORU, University of California at Davis, California 95616
Brian F. Woodfield, Guangshe Li, and Juliana Boerio-Goates
Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602
Brian M. Tissue
Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
The synthesis of nanocrystalline powders of zirconia often pro-
duces the tetragonal phase, which for coarse-grained powders is
stable only at high temperatures and transforms into the mono-
clinic form on cooling. This stability reversal has been suggested
to be due to differences in the surface energies of the monoclinic
and tetragonal polymorphs. In the present study, we have used
high-temperature oxide melt solution calorimetry to test this
hypothesis directly. We measured the excess enthalpies of nano-
crystalline tetragonal, monoclinic, and amorphous zirconia.
Several explanations have been proposed for this occurrence
of tetragonal zirconia: differences in surface energy between the
5
–8
polymorphs, the influence of anionic impurities, the influence
of lattice strain, structural similarities between the precursor
materials and tetragonal zirconia, and the influence of lattice
9
defects and/or water vapor. There has been debate as to which
mechanism is dominant in the stabilization of nanoscale te-
tragonal zirconia. Recent elegant experiments by Wu et al.
10
give strong evidence that nanocrystalline tetragonal zirconia is
not just kinetically metastable but can be truly thermodynam-
ically more stable than monoclinic zirconia in air below 12001C
as long as coarsening is precluded.
Monoclinic ZrO was found to have the largest surface enth-
2
alpy and amorphous zirconia the smallest. Stability crossovers
with increasing surface area between monoclinic, tetragonal,
and amorphous zirconia were confirmed. The surface enthalpy
Reversal in phase stability at the nanoscale has been seen in
other oxides, most notably Al O and TiO . In previous studies
using high temperature oxide melt calorimetry for nanocrystal-
2
of amorphous zirconia was estimated to be 0.5 J/m . The linear
2
3
2
fit of excess enthalpies for nanocrystalline zirconia, as a function
of area from nitrogen adsorption (BET) gave apparent surface
enthalpies of 6.4 and 2.1 J/m , for the monoclinic and tetragonal
1
1,12
13
line alumina
and titania, it was shown that direct meas-
2
urement of the enthalpy difference between the nanocrystalline
polymorphs can separate the contributions of the surface energy
and of the enthalpy of phase transition. The goal of the present
work is to gather calorimetric evidence concerning the phase
stability reversal seen in nanocrystalline zirconia.
polymorphs, respectively. Due to aggregation, the surface areas
calculated from crystallite size are larger than those measured
by BET. The fit of enthalpy versus calculated total interface/
2
surface area gave surface enthalpies of 4.2 J/m for the mono-
clinic form and 0.9 J/m for the tetragonal polymorph. From
2
solution calorimetry, the enthalpy of the monoclinic to tetrago-
nal phase transition for ZrO was estimated to be 1071 kJ/mol
II. Experimental Procedure
2
and amorphization enthalpy to be 3472 kJ/mol.
(1) Synthesis
Phase-pure samples of the amorphous, tetragonal, and mono-
clinic forms of zirconia were synthesized by modifying a pro-
I. Introduction
1
4
cedure developed by Ciuparu et al. A 10% wt/v aqueous
solution (B0.43M) of zirconyl nitrate (ZrO(NO ) ) was add-
ed dropwise to a 150% excess of hydrazine hydrate
IRCONIA (ZrO
2
) has attracted considerable attention over the
last two decades because of its important applications. Be-
sides being used as a ceramic and refractory material, it has also
3
2
Z
(NH NH ꢀ H O) at 1001C with stirring. The pH was moni-
2
2
2
1
2
3
found use as a catalyst, in oxygen sensors, and in fuel cells
tored to ensure that it was greater than 8.5. The milky white
suspension was digested at 1001C for 6 days. The precipitate
was then washed and centrifuged until the supernatant was
neutral and free of nitrate ion. The white powder was dried
overnight at 1201C and then calcined at 5501C for 6 h to give
amorphous zirconia. Further calcination produced tetragonal
and monoclinic zirconia samples of varying crystallite size and
surface area (see Table I). Bulk monoclinic zirconia (Alfa-
Aesar, Ward Hill, MA, Puratronics, 99.978% (metals basis))
was dried at 12001C (Table I).
4
and is being considered as a gate dielectric. Zirconia exists in
three distinct polymorphs. The room-temperature stable form is
monoclinic (m), which undergoes reversible phase transforma-
tions, to the tetragonal (t) form near 11701C and the cubic (c)
phase near 23701C. However, syntheses of fine-grained powders
of zirconia by precipitation from aqueous solution (and other
5
methods) often yields the tetragonal polymorph.
I-Wei Chen—contributing editor
Table I shows that high surface area nanocrystalline mono-
clinic zirconia has not been synthesized using the method above.
Upon conversion to the monoclinic phase the surface area
drops off rapidly. This effect has also been reported by Chuah
Manuscript No. 10617. Received October 22, 2003; approved July 26, 2004.
Supported by the National Science Foundation, Grant number EAR-123998; NIRT:
Surface Reactivity of Nanocrystalline Oxides and Oxyhydroxides. One of the authors (S. V.
U.) acknowledges financial support from Motorola and the University of California
through the UC-Discovery Grant program. High-resolution TEM imaging was performed
at the National Center for Electron Microscopy, Lawrence Berkeley National Laboratory.
1
5
et al. Attempts at producing high surface area phase pure
monoclinic nanocrystals using a two-step sintering method,
1
6
17
18
hydrothermal synthesis, and laser vaporization were also
unrewarding.
w
Current address: Department of Chemistry, Shasta College, 11555 Old Oregon Trail,
Redding, P.O. Box 496006, California 96049-6006.
Author to whom correspondence should be addressed. e-mail: anavrotsky@uc.
z
Several mixed monoclinic/tetragonal samples with high sur-
face area were prepared by modifying a hydrothermal synthesis
davis.edu
1
60

January 2005
Energy Crossovers in Nanocrystalline Zirconia
161
Table I. Sample Characterization and Thermochemical Data of Phase Pure Zirconia Samples
Surface area
Crystallite
size XRD XRD SA
measured by BET
z
Calcination
w
H
2
O
DH (wrt coarse mon.)
(kJ/mol)
2
(m /g)
2
m /g
2
m /mol
DHds (kJ/mol)y
z
Sample ID
T (1C)
Phase
(wt%)
(nm)
DHds (J/g)
Aesar
1200
1200
1200
1100
1100
1000
1000
875
Mon. o0.0001
45.5
39.0
18.0
10.6
16.3
16.1
9.0
4.9
5.1
5.1
4.4
23
26
57
97
63
62
112
206
198
198
230
1.5
4.0
5.5
5.6
8.5
5.7
38.0
48.5
74.8
185 581.772.4(6) 71.6870.29(6)
493 615.074.4(6) 69.8170.54(6)
—
1.8770.61
036F
008F
008E
036E
008D
036D
008C
008B
036C
036B
w
Mon.
Mon.
Mon.
Mon.
1.4829
1.8729
0.6350
1.8348
678 572716(6)
690 537710(6)
62.872.0(6)
63.671.3(6)
8.9072.0
8.171.3
12.171.0
1047 544.977.8(6) 59.5870.96(6)
702 499.475.7(6) 61.5370.70(6)
4682 471.475.2(6) 44.5570.64(6)
5976 463.776.4(6) 50.2570.79(6)
9217 470.875.2(6) 44.6270.65(6)
Tetr. o0.0001
10.1570.76
27.1370.70
21.4370.84
27.0670.71
34.1070.54
47.5870.63
Tetr.
Tetr.
Tetr.
Tetr.
Tetr.
3.1678
1.6329
3.1355
2.7035
2.5347
750
875
750
104.4 12864 400.373.7(6) 37.5870.46(6)
132.2 16290 287.774.5(6) 24.1070.56(6)
z
3
Calcination time was 6 h at 7501–11001C and 2 h at 12001C. Calculated from crystallite size assuming spherical particle shape (S 5 6 ꢁ 10 /Dr where S is the surface area
2
3
y
in m /g, D is the diameter of a spherical particle in nm, and r is the density in g/cm , taken as 5.82 m-ZrO
number of experiments given in parentheses. Error is two standard deviations of the mean. One extra decimal place is retained to avoid extra errors. zFor reaction ZrO
monoclinic, coarse)-ZrO (polymorph, nano).
BET, Brunauer–Emmett–Teller.
2 2
, and 5.94 for t-ZrO ). Corrected for water. Value is the mean of the
2
(
2
1
developed by Yoshimura and S o¯ miya. Amorphous hydrous
7
(2) Characterization Techniques
zirconia was precipitated from zirconium (IV) chloride solution
with ammonium hydroxide (NH OH). It was then washed and
4
X-ray diffraction (XRD) patterns were collected using an INEL-
CPS120 diffractometer (INEL, France) operated at 30 kV and
centrifuged until the supernatant tested free of chloride and was
neutral. Drying at 1201C for 48 h was then carried out. Ap-
proximately 0.5 g of the dried powder was then placed in a 23-
mL Parr pressure vessel and filled with approximately 10 mL of
a mineralizer solution (8% w/v aqueous potassium fluoride
3
0 mA. Collection time was approximately 1 h. The phase percent-
ages and apparent crystallite sizes of the samples were determined
by Rietveld refinement/whole profile fitting (WPF) using Jade 6
19
software. Atomic positions and strain were not refined. The
standard deviation of the crystallite size obtained from the refine-
ment was 0.1–1.0 nm. However, because the accuracy of this tech-
nique is problematic for crystallite sizes smaller than 10 nm, and
since the particles’ shape and strain contribution to broadening
were not considered, we assign an uncertainty of 71 nm in the
estimated absolute crystallite size, for values reported in Tables I
and Table II. Transmission electron microscopy (TEM) observa-
tions (e.g. Fig. 2) agreed with this estimate of average particle size.
The specific surface area was measured using the Brunauer–
Emmett–Teller (BET) technique with a Gemini 2360 instrument
(
2
KF)). The vessel was then placed in an oven at 2001C for
4 h. On cooling, the precipitate was washed and centrifuged
until the supernatant tested free of fluoride. It was then dried
overnight at 1001C. Some of the mixed monoclinic/tetragonal
samples obtained were calcined at 5001 or 7501C to produce
a set of samples with varying crystallite size and surface area (see
Table II).
A final mixed monoclinic/tetragonal zirconia sample with ex-
tremely high surface area (see Table II) was prepared using a
1
8
gas-phase condensation technique. A cw-CO
5 W was used to evaporate a zirconia target obtained com-
mercially from Cerac, Inc. (Milwaukee, WI) (purity 99.7%). The
2
laser operated at
(
Micromeritics, Norcross, GA). Water contents were deter-
4
mined by weight loss measurements. Zirconia samples, accu-
rately weighed inside a glove box, were heated overnight at or
above 11001C in air. The products were white, implying negli-
gible oxygen deficiency. The difference between the final weight
and initial weight was taken to be water content. Raman spectra
of the samples were measured using a Chromex Raman 2000
Spectrometer (Chromex, Billerica, MA). The light source was a
diode laser operating at 785 nm. Scattered light at the laser
wavelength (Rayleigh line) was suppressed using a long-pass
cut-off filter. The excitation light was directed at the sample and
the back-scattered Raman radiation was collected. A Tylenol
1
8
apparatus has been described in detail elsewhere. Prior to dep-
osition, the synthesis chamber was evacuated to 2.5 Torr using
an oil-free diaphragm pump. The target surface was heated to
27001C (monitored with an optical pyrometer) for 5 min with an
unfocused beam. The chamber was then filled with oxygen to a
pressure of 10 Torr. The beam was focused (B2 mm spot size)
on the target and the target rotated at B0.15 rpm throughout
vaporization (2 h). A stainless steel plate, located about 50 mm
from the target collected the particles. The sample was then
transferred to an argon-filled glove box using a glove bag. This
sample was extremely hygroscopic.
(Acetaminophen) tablet was used for calibrating the Raman
shifts. Scanning electron microscopy (SEM) studies were
Table II. Sample Characterization and Thermochemical Data for Mixed Phase (m-/t-) Zirconia Samples
Crystallite size
XRD (nm)
Surface area
measured by (BET)
Calcination Mon. phase
H
2
O
DH (wrt coarse mon.)
(kJ/mol)
2
m /g
2
m /mol
DHds (kJ/mol)w
z
Sample ID
T (1C)
(wt%)
(wt%)
m
t
DHds (J/g)
0
0
0
0
0
0
0
82
94
94
96A
96B
96C
99 y
120
120
750
120
500
750
120
—
62
53
89
53
56
92
51
54
5.4606 26.0
7.3954 23.5
5.7724 30.1
7.9172 24.5
6.9056 22.9
6.4410 31.3
7.4042 26.3
18.2
20.1
26.4
19.1
18.4
24.8
20.6
4.0
57.1
71.3
20.4
60.7
43.0
20.6
61.1
175.2
y
7036
8786
2514
7479
5298
2538
7529
21 588
469712(16)
517.179.5(6)
478718(4)
53378.5(6)
513713(6)
531713(6)
523715(6)
100736(2)
33.871.5(16)
31.171.2(6)
33.5972.3(4)
30.871.0(6)
33.071.6(6)
37.571.6(6)
31.871.8(6)
ꢂ16.374.5(2)
43.5971.54
49.6871.22
40.7772.29
52.2571.09
51.1671.64
35.6771.65
51.0871.84
112.1774.51
GZ1
5.8800
4.8
w
z
Corrected for water. Corrected for tetragonal phase, see text for details. Sample prepared by condensation from vapor, product extremely hygroscopic.
BET, Brunauer–Emmett–Teller.

1
62
Journal of the American Ceramic Society—Pitcher et al.
Vol. 88, No. 1
conducted using a FEI XL30-SFEG high-resolution SEM (FEI,
Hillsboro, OR). TEM was performed on Philips CM12 (Philips,
6
Hillsboro, OR) (LaB filament) and CM200 FEG instruments.
(
3) Calorimetry
High-temperature drop solution calorimetry in lead borate sol-
vent was performed in a custom-built Calvet twin microcalo-
Oxygen gas was flushed
20,21
rimeter described previously.
through the glassware at B35 mL/min and bubbled through
the solvent at B5 mL/min. This maintains oxidizing conditions,
helps remove water evolved from the sample, and agitates the
solvent to aid dissolution. All the samples were handled in an
argon-filled glove box (O
2
and H
2
O o1 ppm). The samples were
pressed into pellets (B5 mg) inside the glove box, weighed, and
stored in a glass vial. When a stable calorimeter baseline was
obtained, the pellet from the glass vial was dropped into the
calorimeter. The total time the pellet was exposed to air was
less than 2 s. The resultant heat effect, referred to further as
Fig. 1. Raman spectrum of a nanocrystalline sample of tetragonal zir-
conia (36C in Table I). This sample does not contain any monoclinic
phase by X-ray diffraction.
‘
‘the drop solution enthalpy,’’ consists of the heat content of the
sample from room temperature to the calorimeter temperature,
the heat of sample dehydration, and the heat of solution. Cal-
orimeter calibration was performed using the heat content of
corundum pellets of similar weight.
There have been several literature claims for the synthesis of
These syntheses employ var-
2
5–29
the nanophase cubic zirconia.
ious strategies including the utilization of the sol–gel reaction
and precipitation in the presence of various polymers. Our at-
tempts at repeating these syntheses have yielded only the te-
tragonal and monoclinic polymorphs, as confirmed by Rietveld
refinement of their XRD patterns. We suspect that the mate-
rial identified as cubic in earlier studies may well have been
tetragonal.
Thermogravimetric measurements were made with a Netzsch
49 apparatus (Netzsch, Selb, Germany). Samples were heated
4
from room temperature to 10001C under an argon flow (40 mL/
min) at 101C/min.
III. Results
Surface areas measured by BET and crystallite size deter-
mined from Rietveld refinement of XRD patterns are shown in
Tables I and II. The total surface/interface area calculated by
assuming single-crystal spherical particles is significantly higher
than that accessible for nitrogen adsorption. This indicates sig-
nificant aggregation in the samples. This is confirmed by SEM
and TEM imaging (e.g., Fig. 2).
(1) Structural Characterization and Surface/Interface
Areas Estimation
Rietveld analyses on the powder XRD patterns was performed
for all samples. The crystallite sizes were refined for all samples
and the amounts of the tetragonal and monoclinic forms in the
two-phase mixtures were also determined (see Tables II and III).
We detected the presence of trace amounts of the monoclinic
phase in some of the tetragonal samples with a larger crystallite
size listed in Table I, but the percentage was not quantifiable and
any small correction for this effect in calorimetry was neglected.
(
2) Calorimetry
Tables I and III list the enthalpies of drop solution. The enth-
alpy difference between a nanocrystalline sample and bulk
monoclinic zirconia arises from polymorphism, surface energy,
and the presence of water. The latter has to be accounted for in
the thermochemical cycle. For the purposes of the current in-
vestigation we used the same assumption as in our previous
0
Initial intensity (I/I ) analysis of the X-ray powder patterns of
2
the higher surface area tetragonal samples (440 m /g) led us to
suspect that we had synthesized the cubic form of zirconia.
However, Rietveld refinement suggested that the tetragonal po-
lymorph had been formed. Raman data for one of these samples
is in excellent agreement with previous Raman studies on zir-
conia, lending further evidence to our samples being te-
tragonal rather than cubic. Cubic zirconia is expected to have a
single Raman band centered around 490 cm , whereas tetrago-
nal zirconia should exhibit six Raman bands, with frequencies at
about 148, 263, 325, 472, 608, and 640 cm . A Raman spec-
30,31
13
studies of amorphous zirconia
and nanocrystalline titania
that the water present in all nanocrystalline zirconia samples is
energetically equivalent to bulk liquid water. This will be dis-
cussed in detail below. Therefore, the excess enthalpy of the
nanocrystalline polymorphs (n) with respect to the most stable
phase, namely coarse monoclinic zirconia (m), can be calculated
using the following thermochemical cycle:
2
2–24
ꢂ1
ꢂ1
trum for a sample identified as tetragonal (with no monoclinic
detectable) by Rietveld refinement is shown in Fig. 1. It confirms
that this sample is indeed tetragonal.
ZrO (n, 251C)ꢀ xH O (l, 251C)
DHds (n)
2
2
-(dilute solution, 7001C)1xH O (g, 7001C)m
2
Table III. Summary of Thermochemical Data for Amorphous Zirconia
Calcination
SA BET,
2
(m /mol)
zz
Sample ID
T (1C)
2
H O (wt%)
DHds (J/g)
DHds (kJ/mol)
DHtrans (kJ/mol)
Method, reference
BZ01w
z
140
600
550
300
—
10.55
o0.01
1183
20 000
30 694
33 031
42 000
305.379.5(7)
354.076.7(6)
358.275.9(6)
669719(7)
—
ꢂ13.671.2
41.7070.89
21.4072.6
20.272.7
33.372.2
43.071.5
50.372.6
58.673.3
50.174.9
3Na O ꢀ 4MoO at 7001C
J
2
3
ww
ZS91bc
2PbOꢀ B O at 8001C
2
3
036A
BZM
5.0457
2PbOꢀ B O at 7001C
2 3
y
13.0
2–4
2PbOꢀ B O at 8001C
2 3
2 3
z
ZrO /An
w
ꢂ30.474.6
3Na O ꢀ 4MoO at 7001C
2
z
Precipitated from ZrOCl
2
ꢀ 8H
2
O with NH OH. Sol–gel synthesis with 10 at% SiO
4
2
quenched in DSC before crystallization, surface area estimated from crystallite size
y
OH surface area calculated from particle size (3.8 nm) from TEM.30 zExtrapolated from anatase-amorphous
after crystallization. Precipitated from ZrOCl
ZrO
drop solution calorimetry. JDHds ZrO
DHds ZrO
2
ꢀ 8H
2
O with NH
4
2
2
2
(coarse, mon. lead borate, 8001C) 5 84.6971.17(8) kJ/mol; DHds SiO glass in lead borate at 8001C 5 38.7270.75 kJ/mol.
ww
31 zz
Corrected for water. Value is the mean of the number of experiments indicated in parentheses.
2
(coarse, mon in sod. moly, 7001C)5 19.771.8(9) kJ/mol.
Error is 2 SD of the mean.
BET, Brunauer–Emmett–Teller.

January 2005
Energy Crossovers in Nanocrystalline Zirconia
163
Fig. 2. Sample of nanocrystalline zirconia from laser evaporation
GZ1). Top: high-resolution transmission electron microscopy micro-
graph, typical crystal habit for naturally occurring monoclinic ZrO
baddelyte) shown on inset. Bottom: XRD pattern and difference for
Rietveld fit for the same sample, m, monoclinic; t, tetragonal reflections.
(
2
(
ZrO (m, 251C)-(dilute solution, 7001C)
DHds (m)
2
H O (l, 251C)-H O (g, 7001C)
DH (water)
2
2
The enthalpy for the reaction
Fig. 3. Enthalpy of nanocrystalline zirconia polymorphs with respect
to bulk monoclinic zirconia. Data points shown for BET surface area
(SA). Thin lines represent 95% confidence limits for data fit. Dashed
lines represent the fit if surface areas calculated from XRD are used and
are considered less accurate, see text.
ꢃ
ꢃ
ZrO2ðm; 25 CÞ ¼ ZrO2ðn; 25 CÞ
can be obtained as
DHðm ! nÞ ¼ DHdsðmÞ ꢂ DHdsðnÞ þ DHðwaterÞ
(
3) Amorphous Zirconia
Table III presents the calorimetric data for amorphous zirconia
from this work and other drop solution experiments conducted in
Besides pure amorphous zirconia samples syn-
The excess enthalpy of nanocrystalline polymorphs with respect
to coarse monoclinic zirconia can be thought of as the sum of
the enthalpy due to polymorphism and that due to increased
surface area. The latter is thought of as a surface enthalpy but,
as particles get smaller, the distinction between relaxation/re-
structuring at the surface and in the bulk becomes less clear. The
excess enthalpy can be written as follows, using nanophase te-
tragonal zirconia (n,t) as an example:
30,31
our laboratory.
thesized by precipitation, we have included data for high surface
area amorphous zirconia obtained from a series of samples sup-
3
1
ported on TiO
2
(anatase) with varying Zr/Ti ratio, and data from
32
ZrO with 10 mol% SiO . All data points form a close to linear
2
2
trend versus surface area (Fig. 3). This suggests that the difference
between the surface energy of the pure hydrated amorphous zir-
conia and its interface energy in the nanocomposites with anatase
and silica is too small to be distinguished in these experiments.
From solution calorimetry data, the surface enthalpy of
DHðm ! n; tÞ ¼ A gðtÞ þ DHtransðm ! tÞ
ðtÞ
where g is the surface enthalpy and A is the surface area. We
know the surface area of the samples from BET measurements.
Thus, by plotting enthalpy versus surface area for the different
polymorphs, we can obtain the surface and transition enthalpies.
Since we were not able to synthesize pure monoclinic zirconia
2
amorphous zirconia is 0.570.1 J/m and the estimated am-
orphization enthalpy of bulk monoclinic zirconia is 34.372.2
kJ/mol. The difference in enthalpy between amorphous and te-
tragonal zirconia, extrapolated to zero surface area, 22.672.2
kJ/mol, is in excellent agreement with the amorphization enth-
alpy (negative of crystallization enthalpy) measured by dif-
ferential scanning calorimetry (DSC) for low surface area
2
with BET surface areas larger than 10 m /g, the excess enthalpy
for nanoscale monoclinic zirconia was derived from the mixed
monoclinic/tetragonal zirconia samples, as shown in Table II.
The contribution to the excess enthalpy from the tetragonal
phase in the samples was calculated using the linear fit for pure
tetragonal zirconia (Fig. 3, DH (kJ/mol) 5 0.0021A110.61) and
its crystallite size and weight percent as determined by refine-
ment of the XRD data.
3
3
amorphous zirconia, 22.471.2 kJ/mol.
(
4) Tetragonal Zirconia
Figure 3 shows the excess enthalpies (relative to the coarse
monoclinic phase) of nanocrystalline tetragonal zirconia

1
64
Journal of the American Ceramic Society—Pitcher et al.
Vol. 88, No. 1
2
samples (kJ/mol) versus surface area (m /mol) as measured by
BET. A linear fit (with 95% confidence envelope) yields both
the surface enthalpy (slope) and bulk phase transformation
with an aqueous solutions of sodium hydroxide, reported that
the formation enthalpy of hydrous ZrO
different from that of monoclinic ZrO and concluded that the
water in hydrous ZrO ‘‘must be only loosely held by physical
2
is less than 5 kJ/mol
2
enthalpy (intercept). From the graph, the surface enthalpy is
2
2
2
38
.170.05 J/m and the transformation enthalpy of bulk mono-
trapping in the micelles of the solid.’’ The fact that some water
is still found in nanocrystalline zirconia heated to 4001C suggests
that not all the water is loosely held. The structural heteroge-
neity of oxide surfaces supports the observation that the heat of
adsorption usually becomes less exothermic with increasing
clinic to bulk tetragonal is 10.6170.57 kJ/mol.
(
5) Monoclinic Zirconia
Figure 3 shows the enthalpy of nanoscale monoclinic samples
compared with bulk monoclinic zirconia. For monoclinic zir-
conia DH(m-n) 5 Ag. A linear fit (with 95% confidence inter-
vals) is therefore forced through the origin. The surface enthalpy
obtained for monoclinic zirconia is significantly larger than that
for tetragonal. Using BET data for surface area, the surface
39
coverage. Since in hydrous zirconia the bulk of the weight
loss (observed by thermogravimetry) occurs below 4001C, the
‘‘loosely held’’ water assumption probably is reasonable. Nev-
ertheless, we stress that our data most probably relate to hy-
droxylated surfaces. No calorimetric studies on atomically clean
surfaces have been reported to date.
2
enthalpy of nanocrystalline monoclinic zirconia is 6.470.2 J/m .
The linear fit for the monoclinic data is not as good as that for
the tetragonal polymorph. Several samples with a relatively low
BET surface area have higher excess enthalpy than would be
expected from the linear trend. These correspond to samples
with more than 5 wt% water that were synthesized by refluxing
under hydrothermal conditions and dried at 1201C. It is entirely
possible that, due to these synthesis conditions, some of the re-
maining water in these samples may be structural rather than
physisorbed. Our water correction does not take this scenario
into account.
(
2) Aggregation in Powders and Interface Energies
Assuming that the surface area, as measured by BET, is the only
source of excess enthalpy relative to a bulk phase of the same
structure, our data yield surface energies for monoclinic and te-
2
tragonal zirconia polymorphs of 6.470.2 and 2.170.05 J/m ,
respectively. The errors reported are derived from how well the
2
linear trend fits the experimental data (R value) and from prop-
agated errors in the measured drop solution enthalpy and the
BET surface areas for individual samples. However, we know
from the crystallite size, as determined by XRD and by TEM
imaging, that our samples are aggregated, thus not all the sur-
face is accessible for measurement by BET. This ‘‘internal’’ sur-
face (and/or interface) contribution is neglected when the BET
surface area is used for calculations. The total surface/interface
area can be estimated from crystallite size measured by XRD,
assuming spherical particles. A linear fit of the excess enthalpies
versus surface areas, calculated in this way, yields surface ent-
halpies for the monoclinic and tetragonal polymorphs of 4.2 and
IV. Discussion
3
4
Wilson gave an excellent definition for the process of inter-
preting calorimetric data: ‘‘Calorimeters faithfully record all the
changes that occur in a sample. A temptation is to mould the
resulting calorimetric signal into a pre-conceived idea, but al-
though getting a result from a calorimeter is easy, to get a cor-
rect result takes a lot of time, effort and cogitation.’’ This is
especially true when one is dealing with nanophase materials,
since the number of variables increases and so increase the
spread in the data and error sources. At the same time, charac-
terization techniques are often less accurate or too local. Keep-
ing this in mind, let us first consider what would be the ideal
samples for calorimetric measurements of surface energy and
then discuss what deviations from ideality we have and how they
might affect the interpretation of our data.
2
2
0
.9 J/m . However, the R of the linear fit using XRD-derived
surface areas is much worse than for the fit for BET surface ar-
eas (see Fig. 3). This might be due to several factors: (i) the larger
errors in surface/interface areas calculated from XRD crystallite
size; (ii) specific interfacial energies depend on the degree of in-
terface coherence, thus their values may differ in samples pre-
pared under different conditions; and (iii) our samples have
different degrees of aggregation and the contribution of inter-
facial areas to total surface area is not constant, thus excess
enthalpies may not depend linearly on surface areas calculated
from XRD crystallite size. We are not able to separate the con-
tribution of interfacial enthalpy to the total excess enthalpy.
Additional experiments are needed on samples with the same
crystallite size, but with different degrees of aggregation. Such
samples are not easy to make. For the present study, considering
all sources of error, the quality of fit, and consistency with pre-
Obviously, for measuring the surface energy of zirconia po-
lymorphs, it is necessary to have samples of the different poly-
morphs with varying surface area. Ideally, every nanoparticle in
the powder would be a single crystal with an equilibrium crystal
shape and of the same size. The crystal faces of our nanocrystals
should be atomically clean, with no adsorbed water or carbon-
ates. In this case, BET measurements would give all the surface
area that contributes to excess enthalpy and the differences in
surface energies between different crystal planes could be de-
rived from the crystal shape. These ideal conditions can never be
realized, though. Our samples contain water and the crystallites
not only form aggregates but also are not of equilibrium shape.
We discuss these effects below.
1
3
1,12
13
,
vious studies on Al
enthalpies derived from the BET areas as more reliable.
2
O
and TiO
2
we consider the surface
(
3) Phase Transition Enthalpies and Stability Crossovers
The monoclinic to tetragonal transformation enthalpy (at 251C),
which we have obtained from extrapolation of the oxide melt
calorimetry data, is 10.61 70.57 kJ/mol. Our estimate lies be-
tween the values of Mitsuhashi et al. (12.5 kJ/mol) and Cough-
lin and King (5.94 kJ/mol). Those studies did not consider
surface area or water content as possible variables.
Figure 4 summarizes the enthalpy of nanocrystalline zirconia
using the BET surface area. The darker line segments show the
phases of lowest enthalpy as a function of surface area. Cross-
overs in the phase of lowest enthalpy are seen for ZrO , as have
2
been seen for A1
brookite, and anatase). As in those systems, the more metast-
able the coarse phase (higher intercept in Fig. 4), the lower its
surface enthalpy (slope in Fig. 4). These crossovers suggest that
for ZrO , as for the Al O and TiO , polymorphs metastable
as coarse phases may become thermodynamically stable at the
nanoscale.
7
(
1) Correction for Water and Hydration Enthalpy
4
0
We have attributed all weight loss in our samples to the presence
of water and assumed a zero adsorption enthalpy relative to
liquid water. Reported experimental data on the hydration enth-
alpy of zirconia are scarce. The formation enthalpy for amor-
phous ZrO
2
ꢀ 5H
2
O was reported as ꢂ2616.3 kJ/mol in a NBS
3
circular in a table dated 1949. Using formation enthalpies for
5
3
6
11,12
monoclinic ZrO
calculate the hydration enthalpy to be about –98 kJ per mole of
ZrO
or approximately ꢂ20 kJ per mole of bound water. How-
ever, the source for these data has not been found. Latimer
2
(ꢂ1100.6 kJ/mol) and liquid water, one can
O
2 3
(corundum and spinel)
and TiO (rutile
2
1
3
2
3
7
casts doubt on this value, pointing to its large difference from
the reported hydration enthalpy of TiO . Turnbull, when con-
ducting calorimetric studies of the reactions of zirconium halides
2
2
3
2
2

January 2005
Energy Crossovers in Nanocrystalline Zirconia
165
room temperature this will result in DG (of tetragonal zirconia
with respect to bulk monoclinic zirconia) being approximately 2
kJ/mol less endothermic than DH. Since the tetragonal phase is
higher in entropy than the monoclinic, and the amorphous is
presumably higher still, the effect of TDS will be to shift the
crossovers to somewhat lower surface area (larger particle size).
Whether the monoclinic–tetragonal transition in zirconia at
small particle sizes is largely controlled by thermodynamics or
by kinetic factors has been disputed for at least 20 years. Gar-
5
,6
vie presented a thermodynamic argument in terms of stability
crossovers at the nanoscale that appears to be supported by our
3
3,43,44
calorimetric data. Others
have argued that small tetrago-
nal crystals are metastable and their rate of transformation is
controlled by martensitic nucleation kinetics. We note that the
situation may be fairly different in relatively dense anhydrous
ceramics at high temperature than in hydrated nanoparticles.
Our observed crossovers in energetics suggest that, at least for
the latter case, a thermodynamic stability field of tetragonal (and
amorphous) zirconia at the nanoscale exists. Such materials are,
of course, metastable with respect to coarsening and subsequent
transformation to the monoclinic phase.
Fig. 4. Phase stability crossover of nanocrystalline zirconia. The darker
line segments indicate the energetically stable phases.
The formation of nanoparticles of a given size and phase dis-
tribution from an aqueous solution is almost certainly control-
led by the processing route and generally does not represent
thermodynamic equilibrium. However, their subsequent coars-
ening and phase transformation must reflect the observed ther-
modynamics, inasmuch as phase transformation must occur
with a decrease in free energy. Because the rates of grain growth
and phase transformation generally follow different kinetic and
mechanistic pathways, many transformation scenarios (and dis-
tribution of products) can be consistent with the crossovers in
enthalpy and free energy.
(
4) Entropy and Gibbs Free Energy of Phases
Phase stability in a thermodynamic sense, of course, is governed
by the Gibbs free energy (DG 5 DHꢂTDS) rather than the enth-
alpy alone. There are two effects that must be considered. The
first is any change in entropy arising from differences in surface
area. For CoO nanoparticles, recent measurement of heat ca-
pacity by adiabatic calorimetry confirms that the entropy dif-
ference between 7-nm nanoparticles and coarse material is small.
2
It is probably reasonable to presume similar behavior for ZrO .
4
0
The second factor is differences in entropy arising from poly-
morphism. Low-temperature heat capacity and entropy data,
measured by adiabatic calorimetry, are available for monoclinic
(5) Previously Reported Values of Surface Enthalpies/
Energies
4
1,42
and yttria-stabilized cubic zirconia
but not for tetragonal
The literature values for the surface enthalpies of the different
polymorphs of zirconia, reported to date, are summarized in
Table IV, along with the values obtained in this work. The
measurements previously conducted on amorphous zirconia in
zirconia. We can obtain an estimate of the entropy difference
between monoclinic and tetragonal zirconia from our value of
the phase transformation enthalpy of monoclinic to tetragonal
zirconia. Since, for a phase transition, DG 5 0 5 DHꢂTDS, then
substituting DH 5 10.6 kJ/mol and T 5 1443 K for the transi-
3
0–32
our laboratory
Mitsuhashi et al. also used high-temperature oxide melt solu-
are consistent with our new data (Table III).
7
ꢂ1
tion, one gets DS 5 7.3 J (mol ꢀ K) , i.e., tetragonal zirconia is
tion calorimetry to deduce the surface energies of monoclinic
and tetragonal zirconia to be 1.2 and 1.1 J/m , respectively. They
ꢂ1
2
7
.3 J (molꢀ K) higher in entropy than monoclinic zirconia. At
Table IV. Reported Transformation and Surface Enthalpies for Zirconia Polymorphs
2
DHtrans (kJ/mol)w
g (J/m )
Method, reference
3
0
g am.
0.7
Approx. from oxide melt calorimetry, Molodetsky et al.
Oxide melt calorimetry, this work
0.570.1
4
6
g tetr.
0.59
At 18501C for Ca-stabilized ZrO , based on interfacial angles
2
30
1
1
2
.970.5
.11
.170.05
Based on critical crystallite size, Molodetsky et al.
7
Oxide melt calorimetry, Mitsuhashi et al.
This work, using surface area from BET
This work, using total surface/interface area from XRD
z
B0.9
1
5
.13
Based on crystallite size effect, Garvie
6
Based on crystallite size effect, Garvie
7
g mon.
1.46
1.23
Oxide melt calorimetry, Mitsuhashi et al.
6
.470.2
This work, using surface area from BET
This work, using total surface/interface area from XRD
z
B4.5
DHtrans (kJ/mol)
4
0
DH
5.9470.4
12.5
Drop calorimetry, Coughlin and King
Oxide melt calorimetry, Mitsuhashi et al.
Oxide melt calorimetry, this work
trans
7
m-t
10.6170.57
3
2
DH
ꢂ22.471.2
At 4501C, differential scanning calorimetry, Ushakov et al.
Oxide melt calorimetry, this work
trans
a-t
ꢂ22.672.2
DH
ꢂ34.372.2
Oxide melt calorimetry, this work
trans
a-m
w
z
Transformation (DHtrans) and surface (g) enthalpies values are given for room temperature, unless otherwise noted. Considered less accurate than from BET.
BET, Brunauer–Emmett–Teller; XRD, X-ray diffraction.

1
66
Journal of the American Ceramic Society—Pitcher et al.
Vol. 88, No. 1
10
N. -L. Wu, T. -F. Wu, and I. A. Rusakova, ‘‘Thermodynamic Stability of
Tetragonal Zirconia Nanocrystallites,’’ J. Mater. Res., 16 [3] 666–9 (2001).
reported the monoclinic to tetragonal transition enthalpy as 12.5
kJ/mol. We believe that this discrepancy may arise because they
did not apply any correction for the water content in nanophase
zirconia, which is probably substantial for their samples from
hydrothermal synthesis.
11
J. M. McHale, A. Auroux, A. J. Perrota, and A. Navrotsky, ‘‘Surface Energies
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788–91 (1997).
12
J. M. McHale, A. Navrotsky, and A. J. Perrota, ‘‘Effects of Increased Surface
Area and Chemisorbed H O on the Relative Stability of Nanocrystalline g-Al
and a-Al ,’’ J. Phys. Chem. B., 101, 603–13 (1997).
M. R. Ranade, A. Navrotsky, H. Z. Zhang, J. F. Banfield, S. H. Elder, A.
Zaban, P. H. Borse, S. K. Kulkarni, G. S. Doran, and H. J. Whitfield, ‘‘Energetics
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D. Ciuparu, A. Ensuque, G. Shafeev, and F. Bozon-Verduraz, ‘‘Synthesis and
5
,6
2
2 3
O
Garvie first suggested in 1965 that stabilization of tetrago-
nal zirconia in fine-grained powders is due to its lower surface
energy compared with monoclinic zirconia. By using a critical
2 3
O
13
2
particle size of 30 nm (from XRD), a value of 0.77 J/m for the
2
14
surface energy for tetragonal zirconia and a value of 5.94 kJ/mol
for the monoclinic to tetragonal transition enthalpy, Garvie cal-
culated the surface energy of monoclinic zirconia as 1.13 J/m . If
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G. K. Chuah, S. Jaenicke, S. A. Cheong, and K. S. Chan, ‘‘The Influence of
15
2
Preparation Conditions on the Surface Area of Zirconia,’’ Appl. Catal. A: Gen.,
1
45, 267–84 (1996).
16
I. -W. Chen and X. -H. Wang, ‘‘Sintering Dense Nanocrystalline Ceramics
we use data from our work, namely a monoclinic to tetragonal
transition enthalpy of B10 kJ/mol and a surface enthalpy of
Without Final-stage Grain Growth,’’ Nature, 404, 168–71 (2000).
M. Yoshimura and S. S o¯ miya, ‘‘Hydrothermal Synthesis of Crystallized nano-
2
tetragonal zirconia of B2 J/m , then to get a crossover from
tetragonal to monoclinic zirconia at a particle size of 30 nm re-
17
particles of Rare Earth-doped Zirconia and Hafnia,’’ Mater. Chem. Phys., 61, 1–8
(1999).
quires the surface energy of monoclinic zirconia to be approx-
imately 4.5 J/m . This is reasonably close to the value we
18
2
H. Eilers and B. M. Tissue, ‘‘Synthesis of Nanophase ZnO, Eu
by Gas-phase Condensation with CW-CO Laser Heating,’’ Mater. Lett., 24,
61–5 (1995).
2 3 2
O and ZrO
3
measured. Molodetsky et al. observed the critical size for the
0
2
2
1
9
amorphous to tetragonal transition at 3.5 nm and calculated the
surface energy for the tetragonal phase as 1.9 J/m , which is in
very good agreement with the data in this study.
JADE, Materials Data Inc., Livermore, CA (2002).
20
A. Navrotsky, ‘‘Progress and New Directions in High Temperature Calorime-
2
try Revisited,’’ Phys. Chem. Min., 2, 89–104 (1977).
A. Navrotsky, ‘‘Progress and New Directions in High Temperature Calorime-
21
Recently, the surfaces of zirconia polymorphs were studied by
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D. Simeone, J. L. Bechade, D. Gosset, A. Chevarier, P. Daniel, H. Pilliaire,
22
4
5
and G. Baldinozzi, ‘‘Investigation on the Zirconia Phase Transition Under Irra-
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A. A. M. Ali and M. I. Zaki, ‘‘HT-XRD, IR and Raman Characterization of
face energy of the most stable monoclinic (ꢂ111) and tetragonal
23
(
111) relaxed surfaces are equal within the calculational accura-
Metastable Phases Emerging in the Thermal Genesis Course of Monoclinic Zir-
conia Via Amorphous Zirconium Hydroxide: Impacts of Sulfate and Phosphate
Additives,’’ Thermochim. Acta, 387, 29–38 (2002).
2
cy (1.246 vs 1.239 J/m at T 5 0 K) and proposed that surface
energy anisotropy is the key for understanding the stabilization
of tetragonal zirconia in nanocrystals. This emphasizes the im-
portance of experimentally established benchmarks in the en-
ergetics of zirconia surfaces.
2
4
P. E. Quintard, P. Barberis, A. P. Mirgorodsky, and T. Merle-Mejean,
‘Comparative Lattice-Dynamical Study of the Raman Spectra of Monoclinic
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´
´
‘
(2002).
25
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V. Summary and Conclusions
26
2
bility of Cubic Phase in Nanocrystalline ZrO ,’’ J. Mater. Res., 9 [2] 263–5 (1994).
By high-temperature oxide melt solution calorimetry we have
measured the excess enthalpies in the monoclinic, tetragonal,
and amorphous zirconia polymorphs of varying surface area.
This yields a stability map for nanocrystalline and amorphous
zirconia and gives an independent estimate of phase transition
and amorphization enthalpies in bulk phases. All nanocrystal-
line phases are thermodynamically metastable with respect to
coarse monoclinic zirconia but with increasing surface/interface
area, monoclinic zirconia gains excess enthalpy faster than te-
tragonal zirconia. Amorphous zirconia has the lowest surface
energy and becomes energetically favorable over crystalline
phases at high surface areas.
27
J. C. Ray, R. K. Pati, and P. Pramanik, ‘‘Chemical Synthesis and Structural
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28
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29
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2
9, 3743–8 (1994).
30
I. Molodetsky, A. Navrotsky, M. J. Paskowitz, V. J. Leppert, and S. H. Ris-
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31
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2
2
2
3
1
32
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Acknowledgments
33
I. -W. Chen and Y. -H. Chiao, ‘‘Martensitic Nucleation in ZrO
2
,’’ Acta Me-
We thank Juraj Majzlan, John M. Neil, and Hongwu Xu for assistance and
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Energy Crossovers in Nanocrystalline Zirconia
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