Quantitative Analysis of the Morphology of {101} and {001} Faceted Anatase TiO2 Nanocrystals and Its Implication on Photocatalytic Activity

Article abstract of DOI:10.1021/acs.chemmater.7b01172

The atomistic structure and morphology (shape and size) of nanomaterials have strong influences on their physical and chemical properties. However, many characterization techniques focus exclusively on one length-scale regime or another when developing quantitative morphology/structural models. In this article, we demonstrate that powder X-ray diffraction and neutron pair distribution function (PDF) can be used to obtain accurate average morphology and atomistic structure of {001} and {101} faceted anatase TiO₂ nanocrystals based on differential evolution refinements using Debye scattering equation calculations. It is also demonstrated that the morphology polydispersity of TiO₂ nanocrystals can be effectively obtained from the diffraction data via a numerical refinement routine. The morphology refinement results are in good agreement with those from transmission electron microscopy and the modeling of small angle neutron scattering data. This method is successfully used to quantify the facet-specified photocatalytic hydrogen evolution activity of anatase TiO₂ nanocrystals with different {001} to {101} ratios. It is found that the sample with an intermediate amount of both {001} and {101} facets shows the best photocatalytic hydrogen evolution reaction (HER) activity. It is expected that the simultaneous structure and morphology refinement technique can be generally used to study the relationship between morphology and functionality of nanomaterials.

Full text of DOI:10.1021/acs.chemmater.7b01172

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Article
Quantitative analysis of the morphology of {101} and {001} faceted
2
anatase TiO nanocrystals and its implication on photocatalytic activity
Jue Liu, Daniel Olds, Rui Peng, Lei Yu, Guo Shiou Foo, Shuo
Qian, Jong Keum, Beth S. Guiton, Zili Wu, and Katharine Page
Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b01172 • Publication Date (Web): 14 Jun 2017
Downloaded from http://pubs.acs.org on June 16, 2017
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Chemistry of Materials
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Quantitative analysis of the morphology of {101} and {001} faceted
anatase TiO2 nanocrystals and its implication on photocatalytic ac-
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Jue Liu†,*, Daniel Olds†, Rui Peng‡, Lei Yu§, Guo Shiou Foo‡, Shuo Qian#, Jong Keum‡, Beth S. Guiꢀ
ton§, Zili Wu‡, Katharine Page†,*
†Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
§ Department of Chemistry, University of Kentucky, Lexington, KY 40506, United States
‡Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
#Biology and Soft Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
ABSTRACT: The atomistic structure and morphology (shape and size) of nanomaterials have strong influences on their physical
and chemical properties. However, many characterization techniques focus exclusively on one lengthꢀscale regime or another when
developing quantitative morphology/structural models. In this article, we demonstrate that powder Xꢀray diffraction and neutron
pair distribution function (PDF) can be used to obtain accurate average morphology and atomistic structure of {001} and {101}
faceted anatase TiO2 nanocrystals based on differential evolution refinements using Debye scattering equation calculations. It is
also demonstrated that the morphology polydispersity of TiO2 nanocrystals can be effectively obtained from the diffraction data via
a numerical refinement routine. The morphology refinement results are in good agreement with those from transmission electron
microscopy and the modeling of small angle neutron scattering data. This method is successfully used to quantify the facetꢀ
specified photocatalytic hydrogen evolution activity of anatase TiO2 nanocrystals with different {001} to {101} ratios. It is found
that the sample with an intermediate amount of both {001} and {101} facets shows the best photocatalytic hydrogen evolution reacꢀ
tion (HER) activity. It is expected that the simultaneous structure and morphology refinement technique can be generally used to
study the relationship between morphology and functionality of nanomaterials.
Introduction
materials. On the other hand, the composition and atomic
structure also play a very important role for specific functionꢀ
alities of nanomaterials. For example, the water splitting perꢀ
formance of (ZnO)x(GaN)1ꢀx nanoparticles is strongly correlatꢀ
ed to its composition (x value),20 and the enhanced correlation
of internal dipoles of BaTiO3 nanocubes have been hypotheꢀ
sized to stabilize nanoscale ferroelectricity.21 Therefore, to
better understand the relationship between the functionality
and structure of nanomaterials, it would be highly desirable to
characterize the morphology and internal atomistic structure
simultaneously.
Nanomaterials have emerged as very important candidates for
energy storage, catalysis and semiconductor applications.1ꢀ5 It
has also been recognized for a long time that the morphology
(particle shape and size) of nanomaterials can strongly affect
their physical and chemical properties.6ꢀ9 It is for this reason
that nanomaterials with specific morphologies, such as nanoꢀ
spheres, ꢀcubes, ꢀoctahedra, ꢀplates and ꢀneedles etc., are highꢀ
ly sought for a variety of applications.10ꢀ14 Electron microscoꢀ
py techniques, i.e. scanning electron microscopy (SEM) and
transmission electron microscopy (TEM), as well as small
angle Xꢀray/neutron scattering (SANS/SAXS) have been
widely used to investigate the morphologies of nanomaterials.
However, it is worth noting that TEM and SEM images can
only provide selected local morphology information, often
conveying questionable representative results of the whole
sample.15ꢀ16 In addition, these approaches become problematic
when nanoparticles are agglomerated,17 and samples can be
damaged by high energy electron beams.18ꢀ19 Therefore, it is
imperative to develop an average (bulk) morphology evaluaꢀ
tion tool to assist traditional electron microscopy investigaꢀ
tions to gain more reliable morphology information of nanoꢀ
Xꢀray or neutron Bragg diffraction has been widely used to
gain accurate atomistic structures of crystalline materials.22ꢀ24
This approach correlates the measured diffraction intensity
with crystal structure by mathematical functions, notably the
three Laue equations.25ꢀ26 For large crystals, the translational
periodicities along three crystallographic axis direction (a, b
and c) are large enough that each of these equations only difꢀ
fers from zero when Bragg diffraction conditions (2dsinθ =
nλ) are strictly satisfied, and hence the Bragg diffraction peaks
are very intense and sharp. In contrast, for small nanocrystals,
the translational periodicities are limited or even eliminated
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and thus the nonꢀzero areas broaden for the three Laue equaꢀ techniques such as TEM or small angle Xꢀray/neutron scatterꢀ
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tions, resulting in much broader Bragg diffraction peaks: a
phenomenon that is often termed as size broadening.27ꢀ28
Therefore, measurement of the widths of Bragg diffraction
peaks provides the simplest method to estimate the crystallite
size of polycrystalline samples (depending on the instrumental
resolution, sensitivity is typically available up to 100 nm in
particle dimensions). Several wellꢀadapted methods, such as
Scherrer equation,27 StokesꢀWilson method29 and Warrenꢀ
Averbach method,30 can be used to treat the size broadening
effects from powder diffraction data. However, it should be
noted that the coꢀexistence of strain, dislocations, or defects
(e.g. stacking faults) may bring other isotropic or anisotropic
broadening effects into the diffraction profiles. Theoretically,
quantitative information about the atomistic structure and size
of nanoparticles can be extracted from corresponding Bragg
diffraction profiles if all of these broadening effects can be
effectively deconvoluted.31 However, in reality, Bragg diffracꢀ
tion peaks of small nanocrystals are often found to be so broad
ing. More recently, our group developed a new approach for
this “shapeꢀcorrection” that can be used during structure reꢀ
finement utilizing the calculated complete PDF G*(r) from an
atomistic model with known Qmin from measurements.43 This
approach provides an efficient route to quantitative analysis of
the atomistic structure of nanomaterials using PDF data. This
becomes even more critical in terms of irregular particle
shapes where the calculation of accurate mathematical expresꢀ
sions for the shape function is exceptionally challenging.
9
ꢊ
ꢋꢌꢍ
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2
ꢄ
ꢁ ꢃ
ꢀ ꢂ =
ꢇ ꢁ ꢃ
ꢉ
ꢁ
ꢃ
ꢅ
ꢆ ꢈ ꢆ − 1 sin ꢆꢂ dꢆ
ꢊ
ꢋꢎꢏ
ꢁ ꢃ
ꢁ ꢃ
= 4ꢄꢂꢐ ꢂ − 4ꢄꢂꢐꢑꢒꢑ ꢂ
∗ꢁ ꢃ
ꢁ ꢃ
= ꢀ ꢂ − 4ꢄꢂꢐꢑꢒꢑ ꢂ
(1)
In this article, we demonstrate that DSE analysis of Bragg
diffraction and PDF can be used as a powerful tool to obtain
accurate atomistic structure and morphology (shape, average
particle size and particle size distribution) information for
{001} and {101} faceted anatase TiO2 nanocrystals. Anatase
TiO2 nanocrystals have attracted tremendous attention in reꢀ
cent years because of their excellent catalytic, especially phoꢀ
tocatalytic, activity.5, 44 In particular, TiO2 nanocrystals with
dominant {001} facets are highly desired because they are
theoretically predicted to possess more active sites (fiveꢀ
coordinated Ti) and higher surface energy relative to other
energetically more favorable facets such as {101} or {100}
etc., and are thus believed to show better heterogeneous cataꢀ
lytic performance.45ꢀ46 This assessment has been well adopted
in the community for many years though very limited direct
experimental evidence can be found, presumably due to the
lack of high quality anatase TiO2 samples with dominant
{001} facets.47 The tailored synthesis of {001} dominant
nanocrystals had been found to be exceptionally challenging
because the highly energetic {001} facets diminish quickly in
that they overlap significantly or even smear into the backꢀ
32
ground, resulting in difficult profile deconvolution.16,
In
addition, the existence of anisotropic particle shapes for many
nanocrystals (e.g. nanoꢀdisks, ꢀrods, ꢀtetrapods) brings further
complexity into the conventional Rietveldꢀtype analysis. In
contrast to the traditional treatment of powder diffraction data
(in reciprocal space), the Debye scattering equation (DSE)33
calculation operates in real space and takes no preꢀassumption
of any translational periodicity. Thus, it can be equally applied
to materials with longꢀrange order as well as materials with
intermediate/shortꢀrange order or even amorphous materials
and liquids.34 Historically, the major limitation of using DSE
for structure analysis is the requirement of tremendous
amounts of computational power, as the summation of DSE
runs over all atoms and thus the computational time is proporꢀ
tional to the square of the number of atoms in the particle
(~N2). However, as computational power continues to grow,
the calculation of scattering profiles of nanoparticles with diꢀ
mensions of tens of nanometers is now achievable within a
reasonable amount of time (hours) even on personal computꢀ
ers. For example, several groups have successfully used the
Debye scattering equation to study the morphology and atomꢀ
istic structure of oxide nanoparticles15ꢀ16, 35 and lead chalcoꢀ
genide quantum dots36 with powder Xꢀray diffraction data.
48ꢀ49
equilibrium or nearꢀequilibrium synthetic conditions.46,
Fortunately, Yang et al. discovered that {001} facets can be
stabilized by using fluorine as a surface stabilizer under hydroꢀ
thermal conditions.7 Though the initial demonstration was to
synthesize micronꢀsized TiO2 single crystals with a high ratio
of {001} facets, this method was immediately adopted and
modified to synthesize nanocrystals with larger surface areas
for catalytic and energy storage related applications.50ꢀ51 With
tremendous successes in synthesizing anatase TiO2 nanocrysꢀ
tals with different {001} ratios in recent years, more and more
controversial experimental results about the ranking of the
catalytic reactivity of different facets have been reported.35, 52
This controversy, in large part, is caused by the difficulty in
separating the catalytic contribution from distinct facets and
the lack of an effective method to accurately quantify the surꢀ
face area of each facet.35, 53 This motivates us to carry out the
current comprehensive morphology study of anatase TiO2
nanocrystals with different amounts of {001} and {101} facꢀ
ets. By accurately determining the shape, size and polydisperꢀ
sity of the synthesized nanocrystals, the relationship between
the surfaceꢀnormalized photocatalytic HER reactivity and the
morphology of nanocrystals is successfully unraveled. This
study also paves the way for quantitatively investigating the
relationship between the functionality and the morphology of
Pair distribution function (PDF) analysis has emerged as anꢀ
other powerful tool to study the particle shape, size and atomꢀ
istic structure of nanomaterials or materials with appreciable
amount of disorder.34, 37ꢀ40 The realꢀspaceꢀbased PDF analysis
utilizes both Bragg scattering and diffuse scattering inforꢀ
mation, and thus is very sensitive to shortꢀrange ordering
(SRO) in disordered materials or intermediateꢀrange structure
in nanoscale materials. Despite its great advantages in studyꢀ
ing the structure of nanomaterials, it is worth noting that the
detailed morphology (size and shape) information is often
absent from the experimental PDF (G(r)) data due to the lack
of lowꢀQ scattering data at dedicated PDF instruments (typical
Qmin ~0.1 Å or higher), as can be seen in equation (1). This
problem is overcome in modeling by implementing a characꢀ
teristic shape function γ0(r), or the soꢀcalled envelope funcꢀ
tion, into the PDF analysis process.41ꢀ42 However, this apꢀ
proach is effective only if a priori knowledge of the morpholꢀ
ogy (shape and size) of nanoparticles is obtained from other
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Chemistry of Materials
other technologically important nanomaterials based on the Neutron total scattering data were collected at the NOMAD
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developed methods.
beamline at the Spallation Neutron Source (SNS) at Oak
Ridge National Laboratory. NOMAD is a high flux, intermeꢀ
diate resolution neutron powder diffractometer that is specifiꢀ
cally designed for high quality neutron total scattering (both
Bragg scattering and diffuse scattering). For the current experꢀ
iment, about 0.2ꢀ0.3 g powder samples were loaded into 3 mm
quartz capillaries. Two 30 min scans were collected for each
powder sample and then summed together to improve the staꢀ
tistics. The detectors were calibrated using scattering from a
diamond powder standard prior to the measurements. Neutron
powder diffraction data were normalized against a vanadium
rod, the background was subtracted, and the total scattering
structure factor S(Q) data were transformed to pair distribution
function data G(r) using the specific IDL codes developed for
the NOMAD instrument.57 Small box (unitꢀcell based) refineꢀ
ments were carried out in the TOPAS software suite (version
6).58 Further particle morphology simulations/refinements
were carried out in the DISCUS/KUPLOT/DIFFEV software
package.48
Experimental Details
1. Synthesis of anatase TiO2 nanoꢀoctahedra and nanoꢀplates
Aqueous TiCl4 solution was prepared by adding 6.6 mL of
TiCl4 to 50 mL of aqueous HCl solution (0.43 mol/L) drop by
drop under vigorous stirring in an ice bath. TiCl4 solution was
added to 5 wt.% NH3.H2O aqueous solution drop by drop unꢀ
der vigorous stirring. After a light blue Ti(OH)4 (precursor)
precipitate was formed, 10 mL of 4 wt.% aqueous NH3.H2O
solution was added to adjust the pH between 6 and 7. The
suspension was centrifuged after ageing for 2 h at room temꢀ
perature. The precipitate was washed two times with water and
one time with ethanol. To prepare TiO2 nanoꢀoctahedra 2 g
fresh Ti(OH)4 precursor was dispersed in 30 mL of 50 vol.%
water/isopropanol. The suspension was transferred to a 50 mL
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o
Teflonꢀlined autoclave, and heated to 180 C for 24 h. The
product was centrifuged after the reaction and washed with
deionized water three times and ethanol one time. TiO2 nanoꢀ
plates were prepared using Ti(OC4H9)4 as precursor.
Ti(OC4H9)4 (5 mL) was added to 20 mL distilled water drop
by drop under stirring. 0.5 mL of 47 wt.% aqueous HF was
added slowly after stirring for 15 min. The suspension was
stirred for 30 min before being transferred to a 50 mL Teflonꢀ
lined autoclave and heated to 180 oC for 24 h. The product was
centrifuged after the reaction and then extensively washed
with NaOH solution to remove the surface F ligands.35, 54 The
final product was then washed with ethanol three times before
recovering. Both nanoꢀoctahedra and nanoꢀplate samples were
calcined at 300 °C for 4h. To study the change in photocatalytꢀ
ic activity, another thicker nanoꢀplate sample was synthesized
by calcining the pristine nanoꢀplates at 500 °C for 4h. This is
enabled by the nature of oriented attachment growth of these
nanoꢀplates in the cꢀaxis direction at elevated temperatures
(Figure S1,3).55
4. Small angle neutron scattering
Small angle neutron scattering (SANS) data were collected at
the BioꢀSANS beamline at the High Flux Isotope Reactor
(HFIR) at Oak Ridge National Laboratory.59 BioꢀSANS is a
moderate resolution, broad Qꢀrange small angle instrument
optimized for the study of complex and hierarchical structures
across multiple lengthꢀscales. The neutron wavelength was 6
Å with wavelength spread ~ 13.2%. Two position sensitive
detectors covering lowꢀQ and highꢀQ respectively were conꢀ
figured to provide a Q coverage of 0.007 – 0.9 Åꢀ1 for the
measurement. A powder sample of TiO2 nanoꢀplates held in 3
mm quartz capillaries was measured at room temperature. The
SANS data were reduced and azimuthally averaged using
standard procedures to correct for detector sensitivity, instruꢀ
ment dark current, sample transmission and quartz capillary
background with facilityꢀprovided data reduction software
Mantid.60 Data were fit using the size distribution module of
the Irena macros for Igor Pro,61 modeling the structure as a
disc with thickness 9.7 nm. Using Moore’s indirect Fourier
transform method,62 the pairꢀdistance distribution function was
calculated from the data, corresponding to the total scattering
G(r). Small angle scattering profiles were calculated for the
atomistic models63 fit within the DISCUS/KUPLOT/DIFFEV
refinements, which were then weighted and combined using
polydispersity profiles derived from the diffraction fits. Addiꢀ
tionally, the product of two derived polydispersity profiles
(varying both width and height) was computed.
BrunauerꢀEmmettꢀTeller (BET) surface areas of the TiO2
nanocrystals were measured via nitrogen adsorption at ꢀ196 °C
using a Micrometrics Gemini 275 system. For the samples
calcined at 300 °C, TiO2 nanoꢀplates and nanoꢀoctahedra have
surface areas of 58 and 101 m2/g, respectively. The thicker
TiO2 nanoꢀplates calcined at 500 °C have a surface area of 36
m2/g.
2. Xꢀray diffraction
Powder diffraction patterns were collected on a PANalytical
X’Pert MPD Pro Xꢀray powder diffractometer with Cu Kα
radiation (λ = 1.54187 Å) equipped with an Anton Paar XRKꢀ
90 linear detector. The diffraction experiments were carried
out with a step size of 0.016711° and at a scan rate of 80 seꢀ
conds/step in BraggꢀBrentano configuration. The primary and
secondary radius was set to 240 mm. Le Bail and Rietveld
analyses were carried out in the TOPAS software suite (verꢀ
sion 6). Simulations of corresponding powder diffraction patꢀ
terns using the Debye scattering equation were conducted in
the DISCUS/KUPLOT/DIFFEV program suite.56 The instruꢀ
mental function is modeled with a symmetrical PseudoꢀVoigt
function obtained from fitting the diffraction profile of a
standard CeO2 powder specimen.
5. Transmission Electron Microscopy (TEM)
TEM imaging was performed on a Hitachi HFꢀ3300 at 300
kV. TEM samples were prepared by sonication of the asꢀ
synthesized anatase TiO2 nanoꢀplates and nanoꢀoctahedra in
isopropanol, followed by dropcasting onto the lacey carbon
coated copper TEM grids and then drying at 60 °C for 1 h.
Manual counting was used to analyze the width and thickness
dispersion of nanoꢀplates from TEM images in ImageJ.64
6. Hydrogen evolution reaction (HER) activity
Photocatalytic hydrogen evolution reaction over the TiO2
samples was carried out in a quartz reactor. In a typical photoꢀ
catalytic experiment, 40 mg of TiO2 was dispersed via soniꢀ
3. Neutron pair distribution function
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cation in 40 mL of water/methanol (3:1 volume ratio) solution. Powder Xꢀray (Cu Kα) diffraction patterns of these two samꢀ
1
Prior to the photocatalytic reaction, the quartz cell was deaerꢀ
ated by a continuous flush with ultrahigh pure Argon gas for
30 minutes. The light input is provided by a 200ꢀW Hg lamp
equipped with a band pass filter to allow the pass of UV light
with wavelength in the range of 325ꢀ385 nm. The suspension
was stirred vigorously during the entire photocatalytic reaction
and the temperature of the system was held at 25ºC by the
cooling water circulating around the entire quartz cell. The
hydrogen gas yield was determined and quantified by using
gas chromatography compiled with a hydrogen calibration
plot, with model BUCK 910 (molecular sieve column, TCD
detector, and Argon as carrier gas). To calculate the apparent
quantum yield (AQY), we used the average 355 nm for the
UV light source. The energy of photon is Eph = hν = hc/λ,
where h is the Planck's constant, ν is the frequency, c is the
speed of light, and λ is the wavelength of the light source.
Therefore, the energy of photon for solar simulated light
source is determined to be 5.6 × 10ꢀ19 J. The number of the
photons irradiating per second on the reactor can be calculated
by equation Nph=Φ/Eph, where Φ is the intensity of the light
source hitting on quartz reactor (it was measured to be 8.8 W
by a Newport 843ꢀR power meter). The number of electrons
that are effectively participated in the photocatalytic reaction
can be determined from the hydrogen yield and are determined
by equation Ne = ꢁhydrogen yield per hour) × 2 × (Avogadro's
number), where hydrogen yield per hour is calculated by usꢀ
ing the hydrogen yield divided by the corresponding number
of hours. Taking everything together, the AQY is determined
as (Ne/Nph/3600) × 100%.
ples (300 °C nanoꢀplates and nanoꢀoctahedra) are remarkably
different, as can be seen in Figure S4. The diffraction pattern
of the truncated nanoꢀoctahedra sample shows no obvious
anisotropic peak broadening, indicating the near isotropic
morphology (slightly truncated octahedra) of this sample. In
clear contrast, the diffraction pattern of the nanoꢀplate sample
shows strong anisotropic peak broadening with much weaker
and broader 004, 105 and 116 reflections relative to reflections
associated with abꢀplane dimensions such as 020 (or 200) and
220. This feature indicates that the asꢀprepared nanocrystals
are highly anisotropic with much larger coherence length withꢀ
in abꢀplane dimensions and very limited coherence length
along the cꢀaxis direction. These observations suggest that two
parameters, the plate width (w) and thickness (h), are required
to describe the morphology of the asꢀprepared anatase TiO2
nanocrystals. It is worthwhile to note that strain/dislocation
may also contribute to the broadening of Bragg diffraction
peaks, yet the FWHM (full width at half maximum) of the
diffraction peaks associated with the cꢀaxis direction or abꢀ
plane dimension are nearly proportional to 1/cosθ and thus
indicate that size broadening is the dominant effect for peak
broadening (Figure S5).66 Therefore, no strain or dislocation
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(a)
Results and discussion
1. Qualitative morphology analysis
According to the theoretical calculation of Barnard et al,65
anatase TiO2 nanocrystals with slightly truncated octahedral
(or tetragonal bipyramid) shape (those with dominant {101}
facets) are predicted to possess the lowest surface energy unꢀ
der hydrogenated or hydroxyl conditions. This is fully conꢀ
sistent with experimental observations of the morphology of
synthetic and natural anatase TiO2.47 To synthesize nanocrysꢀ
tals with dominant highly energetic {001} facets, it is necesꢀ
sary to modify the relative surface energy between (001) and
(101) faces. One effective method is to partially replace the
surface oxygen or hydroxyl by capping ligands with stronger
electronegativity, such as fluorine, during the synthetic proꢀ
cess.7 In the current study, anatase TiO2 nanocrystals with two
different morphologies were successfully synthesized using
hydrothermal reaction with and without hydrofluoric acid
(HF) agent. TEM images (Figure S1 and S2) confirm that the
sample synthesized without HF is dominated by slightly trunꢀ
cated nanoꢀoctahedra with dominant {101} facets while the
one synthesized with HF contains a majority of thin nanoꢀ
plates with a high percentage of {001} facets. A third sample
of thicker nanoplates with an intermediate amount of {001}
and {101} facets was synthesized by calcining the {001} domꢀ
inant nanoꢀplates at 500 °C for 4 h (Figure S3). It is worth
noting that these hydrothermally synthesized samples are
highly agglomerated, making accurate morphology analysis
difficult using automatic TEM counting or small angle scatterꢀ
ing approaches.
(b)
Figure 1. Simulated Xꢀray (λ = 1.54187 Å) diffraction patterns of
truncated anatase TiO2 nanocrystals with (a) fixed abꢀplane width
(12.5 nm) as a function of thickness along the cꢀaxis direction and
(b) fixed thickness (10 nm) as a function of abꢀplane width. Note
a limited 2θꢀrange is shown. The red colored hkl indices are the
reflections associated with abꢀplane dimensions while the black
indices are the reflections with major contributions from the cꢀ
axis direction.
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induced effects will be considered in the current report. In
addition, since Xꢀrays are not sensitive to light atoms and H
mainly contributes to the incoherent scattering in the neutron
scattering data, the intensity contributions from residual surꢀ
face ligands, such as ꢀOH or ꢀH will also be ignored for the
current study.
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We first carried out sensitivity tests to prove that Debye scatꢀ
tering equation (DSE) calculation of powder Xꢀray diffraction
data can be used as an effective tool to probe the average morꢀ
phology of {101} and {001} faceted nanocrystals. For the
sensitivity test of thickness (h), a series of truncated anatase
TiO2 nanoꢀoctahera with fixed abꢀplane width (12.5 nm) but
variable thickness (from 2 nm to 24 nm with a step size of 1
nm) were created using DISCUS software.56 The TiO2 anatase
unit cell was expanded to a 40 × 40 × 30 supercell and then
truncated into the desired morphology with specific boundary
conditions. The simulated XRD patterns using DSE calculaꢀ
tion are shown in Figure 1a, clearly showing that the relative
peak intensity of 004, 105, and 116 reflections increases as the
thickness increases. In addition, the Bragg diffraction peaks
become sharper and more symmetric as the thickness increasꢀ
es. These simulations indicate that powder XRD is indeed
highly sensitive to the variation of the thickness of nanoꢀplates
up to approximately 20 nm thickness, beyond which patterns
become difficult to distinguish. Sensitivity tests of the abꢀ
plane (w) dimensions were carried out in a similar manner:
the thicknesses of truncated nanoꢀoctahedra were fixed to 10
nm while the plate widths were varied from 10 to 60 nm with
a step size of 2.5 nm. The simulated XRD patterns (Figure 1b)
reveal that the reflections associated with in abꢀplane scatterꢀ
ing such as 020 and 220 become sharper and more intense as
the plate width increases, up to approximately 50 nm, above
which the patterns appear very similar. In contrast, 004, 105
and 116 reflections remain relatively broad with only subtle
intensity increases. Overall, the powder XRD is likely to be
very sensitive to the average morphology (h and w) of {101}
and {001} faceted anatase TiO2 nanocrystals in this size reꢀ
gime.
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Figure 2. (a) Simulated Xꢀray diffraction (λ = 1.54187 Å) pattern
(blue) of TiO2 nanoꢀoctahedra with a dimension of 12.5 nm (w)
by 9 nm (h). For comparison, experimental Xꢀray (Cu Kα) diffracꢀ
tion data with background subtraction is shown in red. (b) Simuꢀ
lated Xꢀray diffraction (λ = 1.54187 Å) pattern (blue) of TiO2
nanoꢀplate with a dimension of 10 nm (abꢀplane width) by 35 nm
(thickness), shown with experimental diffraction data in red.
function calculation was carried out in a similar fashion as that
for the powder Xꢀray diffraction. However, it is worth noting
that the reduced pair distribution function is computed from
the Fourier transformation of the normalized scattering intenꢀ
sity (equation 1), thus, the theoretical reduced pair distribution
function G*(r) can be obtained only if the full Qꢀrange of scatꢀ
tering data is available, which is experimentally unachievable.
The lack of lowꢀQ data gives rise to a characteristic difference
between the experimental G(r) and the theoretical G*(r) perꢀ
taining to long lengthꢀscale structural features, often referred
to as the particle shape function. In the current study, an emꢀ
pirical method was used to extract the shape function out of
the theoretical G*(r) through an inverse deconvolution routine,
details about the methodology can be found in the report by
These results inspired us to further estimate the morphology of
these two different faceted nanocrystals by visually comparing
the DSE simulated Xꢀray diffraction data to the experimental
data. By varying the width (w) and thickness (h) of the trunꢀ
cated nanoꢀoctahedra, a reasonable agreement between simuꢀ
lated patterns (blue curves) and background corrected experiꢀ
mental data (red curves) have been achieved for both samples,
as can be seen in Figure 2. The TiO2 nanocrystals synthesized
without HF are found to be slightly truncated nanoꢀoctahedra
with an estimated w of 12.5 nm and h of 18 nm, while the ones
synthesized with HF agent are more heavily truncated with
larger plate width w of 35 nm and much thinner h of 10 nm.
This result is in good agreement with previous theoretical calꢀ
culations and experimental observations,7, 50 and also matches
our TEM observations (Figure S1 and S2). However, it is
worth noting that the relative intensity of some diffraction
peaks, such as the 101 reflection, of simulated diffraction patꢀ
terns are much stronger than the experimental data, indicating
that quantitative refinement of both atomistic structure and
morphology is needed.
Olds et al.43 Moreover, instrumental resolution, which is often
ꢗ
ꢕ
ꢖ
ꢘꢌꢋꢙ
ꢚ
expressed as the dampening effect (ꢓꢔ ꢁ
ꢖ), strongly afꢀ
ꢃ
fects the sensitivity of PDF data at long pairꢀpair distances (r).
For a moderate or high resolution PDF instrument such as
NOMAD (with Qdamp between 0.01 and 0.02 Å), the G(r) inꢀ
tensity will smear out at pairꢀpair distance larger than 200 Å,
making it difficult to gain reliable morphology information of
nanomaterials with an average particle size larger than 20 nm.
To demonstrate the sensitivity of using neutron PDF to deterꢀ
mine nanoꢀplate thickness (h), a series of theoretical G*(r)
were calculated from truncated anatase TiO2 nanoꢀoctahedra
with variable thickness but fixed width (w = 12.5 nm) in
Morphology sensitivity analysis using neutron pair distribution
DISCUS 56
, the dampening effect (Qdamp = 0.0180 Å) was fixed
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(d)
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Figure 3. Simulated shape functions for truncated TiO2 nanocrystals with (a) variable thickness (2 nm to 26 nm) but fixed width (12.5 nm),
and (b) with variable width (10 nm to 60 nm) but fixed thickness (10 nm). Corresponding shapeꢀcorrected neutron PDF data (40 Å to 60
Å) are shown in (c) and (d) separately. Note that shape functions and PDF data have been calculated taking the instrument resolution efꢀ
fects expected at the NOMAD instrument into account.
to the value obtained from refinement of a standard Si sample
measured on NOMAD. Shapeꢀcorrected G(r) data were then
calculated using Dshaper.43 The extracted shape functions and
a selected region of shapeꢀcorrected PDF data (40 Å to 60 Å)
are shown in Figure 3a and 3b. It clearly shows that the simuꢀ
lated PDFs and shape functions are indeed very sensitive to
the thickness variation up to about 14 nm. The intensity
change becomes subtle above this value. Similar calculations
were carried out to test the sensitivity of plate width (w). Corꢀ
responding shape function and corrected PDF data are shown
in Figure 3c and 3d. It can be seen that with fixed thickness
(10 nm), the calculated patterns are sensitive to the width variꢀ
ation up to about 30 nm. It is also worth noting that the simuꢀ
lated PDF data in the range of several unit cells (Figure S6a
and S7a, 0 ꢀ 20 Å) are essentially the same for nanocrystals
with either different thickness or different width in this size
regime (particle sizes over 10 nm); the differences in G(r)
becomes observable only at atomic pairꢀpair distances larger
than 20 Å. Thus, collecting high resolution experimental G(r)
mental data has been achieved. However, intensity mismatch
for the 101 (2θ around 25º) and 200 (2θ around 48º) reflecꢀ
tions can be observed in the difference curve, which is very
likely caused by the slightly anisotropic particle shape. In adꢀ
dition, the refined atomic displacement parameters for Ti and
O are negative; indicating that thermal vibration induced inꢀ
tensity dampening tends to compensate for the anisotropic
morphology induced intensity variation. This result indicates
that quantitative morphology modeling is critical for accurate
atomistic structure refinement of the asꢀprepared TiO2 nanoꢀ
crystals.
One of the greatest advantages of DSE refinement is that, theꢀ
oretically, atomistic structure and morphology information can
be simultaneously refined from the same data set (e.g. Bragg
diffraction data or PDF). Unfortunately, the conventional
leastꢀsquare minimization algorithm, which is computationally
effective, cannot be directly used for the DSE refinement beꢀ
cause of the discrete functional dependence between refineꢀ
ment criteria (R values or χ2) and morphologyꢀdependent variꢀ
ables (w and h here). Therefore, most reported DSE analyses
are limited to qualitative simulations.68 More recently, global
minimization techniques, such as simulated annealing16 and
differential evolution algorithms,15 have been successfully
implemented into the DSE refinement. However, these reꢀ
finement algorithms are much slower relative to the gradient
leastꢀsquare minimization, further slowing the already compuꢀ
tationally expensive DSE calculation. In a differential evoluꢀ
tion refinement, a model progresses with a population of canꢀ
didate structures. The characteristics (parameters) of the popuꢀ
lation members are evaluated against data and ranked before
with small dampening effect is crucial for the accurate deterꢀ
mination of the morphology of these anatase TiO2 nanocrysꢀ
tals.
2. Quantitative morphology refinement for nanoꢀoctahedra
with a monodisperse morphology model
Regular Rietveld refinement with powder XRD was carried
out for TiO2 nanoꢀoctahedra using the fundamental parameter
approach67 with isotropic (spherical) particle shape. The reꢀ
finement result is shown in Figure 4a and Table S1. A reasonꢀ
able agreement between the calculated pattern and experiꢀ
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Chemistry of Materials
generating parameters for the next generation of candidate
fit has been achieved with Rwp = 4.59% and χ2 = 1.81. The
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models. Since there is a whole population of structures to
evaluate, it is highly desirable to limit the number of free paꢀ
rameters used for the global optimization. In the current study,
only the structure and morphology related parameters, namely
lattice parameter a and c, atomic displacements of Ti and O, zꢀ
axis coordinate of O, the size in the abꢀplane (w) and the size
along cꢀaxis direction (h), are refined via the evolution algoꢀ
rithm (a brief introduction of the differential evolution algoꢀ
rithm can be found in the supporting information and related
references69), while other parameters such as a scale factor and
background functions are refined using leastꢀsquare minimizaꢀ
tion. A detailed refinement scheme is shown in Figure S8. The
structure of bulk anatase TiO2 was used as an initial model
with an estimated starting w of 12.5 nm and h of 18 nm. Deꢀ
tailed refinement routines and boundary conditions of strucꢀ
tural parameters can be found in the supporting information.
evolution of refined parameters can be found in Figure 5 and
Figure S10. The final refined structure and morphology inforꢀ
mation are shown in Table 1. The average width in the abꢀ
plane was refined to be 13.4(5) nm and the thickness was reꢀ
fined to be 16.4(8) nm. These values differ dramatically from
the qualitative estimation where width is estimated to be 12.5
nm and thickness is estimated to be 18.0 nm. This result sugꢀ
gests that simultaneous atomistic structure and morphology
refinement is critical for accurate morphology quantification.
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Figure 5. Evolution of width (a) and thickness (b) parameters in
the population set as a function of refinement generation using
differential evolution refinement with XRD data. It can be seen
that the width of the plate converges to around 13.4 nm while the
thickness converges to about 16.4 nm.
Figure 4. (a) Rietveld refinement of TiO2 nanoꢀoctahedra against
powder Xꢀray diffraction data (Cu Kα radiation) using a TiO2
bulk structure model with isotropic size broadening. (b) Structure
and morphology refinement using combined differential evolution
and leastꢀsquare refinement with Debye scattering equation calcuꢀ
lation. Experimental data are shown in black dots, calculated patꢀ
tern in red, tick marks indicating Bragg reflections in blue, and
difference curve in green. The refined average morphologies are
inserted.
Table 1. Atomistic structure and morphology of {101}
dominant nano-octahedra refined from powder XRD data
using the combined differential evolution and least-square
minimization with the monodisperse model
Remarkably good agreement (Rwp ~ 4.50%) between the simuꢀ
lated and experimental data was reached after 350 refinement
generations. However, a careful inspection of the Rwp values
for all 60 members (the population used for differential evoluꢀ
tion refinement) reveals that the refinement did not converge
after 350 generations. Instead, it splits into two different
groups, as can be seen in Figure S9. This result is highly inꢀ
formative, which indicates that strong correlation exists among
some of the refined parameters. Indeed, the atomic displaceꢀ
ment of Ti (BTi) and O (BO) are found to be strongly correlated
with the morphology parameters (h and w). Therefore, the
atomic displacement parameters of Ti and O were fixed to the
values (BTi = 0.45 Å2 and BO = 0.85 Å2) obtained from refineꢀ
ment of PDF data (details can be found in the next paragraph).
The final refinement result is shown in Figure 4b, an excellent
width (w) = 13.4 (5) nm thickness (h) = 16.4 (8)nm
S.G. I 41/amd a = 3.7866 (1) Å c = 9.4990 (1) Å
Atom Wyck.
x
y
z
Occ. Biso (Å2)
Ti
O
2a
4f
0.00 0.25
0.375
1.0
0.45
0.85
0.00 0.25 0.1688(4) 1.0
A similar strategy was used for the structure and morphology
refinement using neutron PDF data. Noticeable improvement
was achieved for the fit with differential evolution refinement
relative to that of the conventional leastꢀsquare refinement, as
can be seen in Figure 6. The refined structure and morphology
information are listed in Table S2 and the evolution of strucꢀ
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tural parameters during refinement is shown in Figure S11. ogy related parameters (w and h) and lattice parameters (a and
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Results are consistent, though far more quantitative, than obꢀ
servations from TEM images in Figure S2. In contrast to the
refinement using XRD data, no obvious correlation between
BTi and BO is observed, reflecting the importance of incorpoꢀ
rating neutron total scattering into the structural analysis. In
both the XRD and neutron PDF cases, data is better fit and
models are more reasonable with refinement strategies incorꢀ
porating particle shape. Interestingly, refined h and w parameꢀ
ters were found equivalent within error in the XRD and neuꢀ
tron PDF analyses, though the atomic displacement parameters
had to be fixed in the XRD data to neutron PDF determined
values. In general, it is expected that the PDF will be more
sensitive to smaller nanoparticles (< 20 nm dimensions) while
diffraction data will be more sensitive to larger nanoparticles
(with an upper limit of sensitivity that depends on the instruꢀ
ment resolution).
c) were refined via the differential evolution method, while the
zꢀaxis coordinate of O (z = 0.1688) and the atomic displaceꢀ
ments were fixed to the values from the previous refinement of
nanoꢀoctahedra (BTi =0.45 Å2 and BO = 0.85 Å2). It can be seen
from Figure 7 that remarkable improvements have been
achieved from the differential evolution refinement relative to
that from the Rietveld refinement. The weighted refinement
residual drops from 9.99% (Rietveld refinement) to 5.05%
(differential evolution refinement) after 50 generations.
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Figure 7. Rietveld refinement (a) versus differential evolution
refinement (b) against XRD data (fixed Biso values and atomic
positions) for TiO2 nanoplates. Experimental data are shown in
black dots, calculated pattern in red, tick marks indicating Bragg
reflections in blue, and difference curve in green. The refined
morphologies are inserted.
The evolution of parameters during refinement is shown in
Figure S12. The average width is refined to be 33.1(8) nm and
thickness is refined to be 9.7(3) nm. These quantitatively deꢀ
termined values from the entire powder sample are consistent
with TEM images in Figure S1. Due to the large size of the
nanoꢀplates, DSE refinement was not run against the neutron
PDF data. Similar strategies have been applied to the DSE
refinement of the morphology of the 500 °C calcined nanoꢀ
plate sample. The average width is refined to be 38.4(8) nm
and thickness is refined to be 17.9(5) nm. The refinement reꢀ
sults are shown in Figure S13 and Table S4.
Figure 6. The result of leastꢀsquare refinement (a) versus differenꢀ
tial evolution (b) using neutron pair distribution function. Data
are shown as black circles, model fits as red lines, and difference
curves as green lines offset below data and model fit.
2.2 Quantitative morphology refinement for TiO2 nanoꢀplates
(300 ºC) with a monodisperse morphology model
Rietveld refinement with bulk anatase TiO2 structure using
XRD data of nanoꢀplates was performed in a similar manner
as that for the nanoꢀoctahedra. The results are shown in Figure
7a and Table S3. The fit is significantly worse than that of the
Rietveld refinement of the nanoꢀoctahedra sample due to the
more anisotropic particle shape of these heavily truncated thin
nanoꢀplates. It is also worth noting that the atomic displaceꢀ
ments of Ti and O refine to negative values, indicating that the
atomic structure parameters cannot be accurately determined
without quantifying the particle morphology. This inspires us
to carry out the simultaneous atomistic structure and morpholꢀ
ogy refinement using the global minimization algorithm.
However, since the particle size of these nanoꢀplates is large
enough (~ 35 × 35 nm in the abꢀplane) to prevent fast DSE
calculation,16 it is prohibitive to refine all structure and morꢀ
phology parameters at the same time. In order to confine the
refinement to a reasonably achievable time, only the morpholꢀ
Table 2. Atomistic structure and morphology of {001}
dominant anatase TiO2 nano-plates refined from powder
XRD data using the combined differential evolution and
least-square refinement with monodisperse model
width (w) = 33.1 (11) nm thickness (h) = 9.7 (3) nm
S.G. I 41/amd (2) a= 3.7918 (4) Å c = 9.5019 (15) Å
Atom Wyck.
x
y
z
Occ. Beq (Å2)
Ti
O
2a
4f
0.00 0.25 0.375
0.00 0.25 0.1688
1.0
1.0
0.45
0.85
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(c)
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(f)
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Figure 8. Thickness (a) and width (b) distribution of TiO2 nanoꢀplates (300 °C annealed) obtained from counting of TEM images. Blue
curves are the lognormal fits of the observed distributions. Refined thickness (c) and width (d) distribution (numberꢀbased) of anatase TiO2
nanoꢀplate with XRD data (a population of 30 was chosen for the differential evolution refinement). Refinement results with thickness (e)
and width (f) lognormal distribution. The calculated XRD patterns are shown in red, experimental data in black dots and difference curves
in green.
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3. The influence of polydispersity on the morphology analysis
of {001} dominant anatase TiO2 nanoꢀplates
to the discrete nature of DSE calculation/refinement. This
discrete nature means that only a numerical solution (not an
analytical solution) can be used to extract the morphology
distribution. For powder samples that contain large amounts of
nanoparticles, it can be expected that the morphology varies
nearly continuously from the smallest particle to the largest
ones. Theoretically, the relationship between volumetricꢀbased
scattering power and the total scattering intensity (I(Q)) can be
resolved if the morphology distribution function is known.
This approach has been widely adapted for morphology analyꢀ
sis of small angle scattering data.17, 77 However, this method
cannot provide any information about the atomistic structure
Though tremendous efforts have been spent on pursuing monꢀ
odispersed anatase TiO2 nanocrystals in the last few decades,6,
14, 53 an effective synthetic method has not been fully achieved
yet, especially for nanocrystals with dominant highly energetic
{001} facets.49 Therefore, polydispersity should be taken into
consideration for accurate morphology evaluation. While the
Fourier analysis of Bragg diffraction profiles have been widely
used to extract the polydispersity information out of powder
diffraction data,31, 70ꢀ71 very few previous reports on polydisꢀ
persity analysis using DSE can be found,72ꢀ76 presumably due
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because it utilizes a volumetric particle scattering factor inꢀ monodisperse model (Rwp = 5.05%). These results demonstrate
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stead of atomic scattering factors in calculating the total scatꢀ
tering intensity. Thus, the only method available to directly
correlate both atomistic structure and morphology distribution
to the total scattering intensity is the DSE calculation.
the importance of incorporating polydispersity for accurate
morphology analysis, and highlight challenges in computaꢀ
tional power required to do so. A similar strategy was applied
to investigate the morphology polydispersity of the nanoꢀ
octahedra and 500 °C calcined nanoꢀplates, and the refined
results are shown in Figure S15 and Figure S16. In contrast to
the 300 °C calcined nanoꢀplates sample, where the thickness
polydispersity plays the major role, the width polydispersity
was found to be the dominant effect for morphology polydisꢀ
persity of these two samples.
To numerically resolve the morphology distribution using
DSE calculation, it is necessary to calculate Xꢀray diffraction
patterns from a series of truncated anatase TiO2 nanoꢀ
octahedra with either fixed width (w) but variable thickness
(h) or vice versa (grid points). After assigning a weighting
scheme (numberꢀbased) to each calculated diffraction pattern
(or grid), the morphology distribution can then be obtained by
optimizing the weight of each calculated pattern using global
minimization (preferred) or leastꢀsquare refinement until an
acceptable agreement between the calculated pattern and exꢀ
perimental data is achieved. Theoretically, it is possible to
resolve both width and thickness distribution simultaneously.
However, it is computationally too expensive to apply this to
relatively large nanocrystals at this time. For example, if an
interval of 1 nm is chosen for nanocrystals with thickness
range of 25 nm and width range of 80 nm, a total of 2000 inꢀ
dividual diffraction patterns have to be calculated. This is not
practical for particles as large as tens of nanometers. In addiꢀ
tion, no evidence of strong correlation between the plate
thickness and width is observed from the TEM images (Figure
S1 to S3). Therefore, thickness and width distributions are
refined separately (with either fixed width or fixed thickness).
For width distribution refinement, the plate thickness was
fixed to the average value of 9.7 nm while the width was alꢀ
lowed to vary from 5 nm to 80 nm with an interval of 1 nm;
while for the thickness distribution refinement, the width was
fixed to 33.1 nm while the thickness was varied from 1 nm to
26 nm with an interval of 0.5 nm. Both the width and thickꢀ
ness are assumed to follow a lognormal distribution, which is
found to be the most common polydispersity distribution for
synthetic and natural nanoparticles.78 It is also in general
agreement with the TEM observations. The refinement results
are shown in Figures 8c to 8f, and weighted refinement residꢀ
uals are shown as a function of refinement generation in Figꢀ
ure S12. It can be seen that the mean thickness (8.6 nm) reꢀ
fined with the polydisperse model is much smaller relative to
that refined from the monodisperse model (9.7 nm). The
thickness of the prepared nanoꢀplates are found to span a
broad range with large standard deviation, a result that is fully
consistent with the distribution obtained from the counting of
TEM images (Figure 8a). In contrast to the wide and asymꢀ
metrical distribution of the plate thickness, the refined plate
width distribution behaves more symmetric (close to Gaussian
distribution) with smaller relative standard deviation. It is also
worth noting that though the mean width (33.3 nm) obtained
from TEM counting is similar to the refinement result, the
distribution from TEM spans a slightly wider region relative to
that obtained from the refinement. This can be understood by
the fact that the average width of these nanoꢀplates are large
enough (over 30 nm) that the sensitivity from XRD is relativeꢀ
ly low, as can be seen from the sensitivity test in Figure 1b.
This is also reflected in the refinement result (Figures 8e and
8f), where the refinement of the thickness polydispersity imꢀ
proves the fits dramatically (Rwp = 4.48%) while the refineꢀ
ment of the width polydispersity has only subtle improvements
(Rwp = 4.84%) relative to that of the refinement using the
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were benchmarked against SANS analysis utilizing a disc
model for the nanoꢀplate samples and a sphere model for the
nanoꢀoctahedra sample. Fits and solved polydispersity profiles
of the disc and sphere diameters are shown in Figure S17.
Direct modeling of the polydisperse nanoꢀplate models were
found most accurate when using the fixed thickness, varying
width models. The resultant fits do not precisely correlate with
the results of the DSE derived analysis and TEM counting,
which suggests the average disc/sphere sizes are slightly
smaller than the corresponding atomistic/counting models.
The modeling of the nanoꢀplates/octahedra as discs/sphere
underestimates their surface area to volume ratio as compared
to the true truncated octahedral nanoꢀstructures. In addition,
while SANS is perhaps the most sensitive diffraction probe for
particle size distributions, it cannot distinguish average partiꢀ
cle size from average aggregate size. Models that are more
sophisticated can be used to extrapolate more accurate morꢀ
phology distribution profiles, which falls out of the scope of
the current study and will be presented elsewhere.
4. Quantitative analysis of the facet dependent photocatalytic
hydrogen evolution reactivity of anatase TiO2 nanocrystals
The anatase TiO2 {001} facet with more undercoordinated Ti5c
(five coordinated Ti) is generally believed to be more catalytiꢀ
cally active relative to the energetically more stable {101}
facet.45 However, a number of controversial results have been
reported in recent years where samples with higher percentꢀ
ages of {001} facets are found to be photocatalytically less
active.35, 52 Several new theoretical models, such as the faceꢀ
preferred surface charge carrier transfer79 or the surface hetꢀ
erojunction,80 are thus proposed to address the controversial
observations. Nevertheless, a conclusive agreement has not
been achieved, in large part, due to the difficulty to fully sepaꢀ
rate and quantify the catalytic contributions from different
facets, especially for nanocrystals with large surface areas for
both facets. As has been discovered by Gordon et al,35 the
measured BET surface of {001} dominant nanoꢀplates is subꢀ
stantially smaller than the theoretical surface area calculated
from morphology simulation due to significant particle stackꢀ
ing of nanoꢀplates, as can be seen in Figure S1. This plate
stacking significantly reduces the effective {001} surface but
has negligible influence on the {101} surface. Therefore,
simply normalizing the catalytic reaction rate to the BET surꢀ
face often results in two possible mistakes: first, if the catalytꢀ
ic reaction is carried out using well dispersed sample in liquids
where much higher surface area is exposed (e.g. photoꢀ
hydrogenation using the methanolꢀwater mixture) relative to
the BET surface, it would result in the overestimation of the
catalytic performance of the {001} dominant sample; second,
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Figure 9. (a) Mass and (b) surface normalized photocatalytic HER of three anatase TiO2 nanocrystals with different {001} to {101} facet
ratios. Photocatalysis was conducted under UV irradiation (325ꢀ385 nm) with methanol as the sacrificial reagent. The apparent quantum
yields (AQY) are 0.2% for nanoꢀplate1 (300 °C), 1.7% for nanoꢀplate2 (500 °C) and 2.1% for nanoꢀoctahedra.
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if the catalytic reaction is carried out in powder form (such as
CO2 reduction), it would lead to the underestimation of the
catalytic activity of {001} facets because of the serious plate
stacking which heavily reduces the effective {001} surface
area. Thus, in either case, it is highly desirable to calculate the
accurate facetꢀspecified surface areas to better understand the
relationship between the catalytic performance and the morꢀ
phology of anatase TiO2 nanocrystals.
has been observed for the 500 °C calcined nanoꢀplate sample,
as can be seen in Table S5.
With the effective facetꢀspecified surface area accurately deꢀ
termined, it is now possible to quantify the surface normalized
photocatalytic hydrogen evolution reaction (HER) rate of anaꢀ
tase TiO2 nanocrytals with different {001} to {101} ratios.
After ultrasonic and under the vigorous photocatalysis stirring
condition, it is expected that the stacking of TiO2 nanocrystals
is minimal so that the contact surface area should be close to
the calculated theoretical surface area. The massꢀnormalized
photocatalytic HER activity of the three anatase TiO2 nanoꢀ
crystals are shown in Figure 9 and Figure S20, which shows
the HER activity rates in the order of nanoꢀoctahedraꢀ300°C >
nanoꢀplateꢀ500 °C > nanoꢀplateꢀ300 °C. However, Figure 9
shows that the surface normalized HER rates follows the order
of nanoꢀplateꢀ500 °C > nanoꢀoctahedraꢀ300°C >> nanoꢀplateꢀ
300 °C. (The percentage of {001} facets follows the order of
nanoꢀplateꢀ300 °C > nanoꢀplateꢀ500 °C >> nanoꢀoctahedra,
contradicting previous assessments about the relative photoꢀ
catalytic HER reactivity of {001} and {101} facets, where
{001} facets are often simply reported to be either more or
less35, 52 active relative to the {101} facets. Our observation
clearly indicates that a high percentage of {001} facet (nanoꢀ
plateꢀ300 °C) does not guarantee better photocatalytic HER
performance. Similarly, samples with a high percentage of
{101} facet (nanoꢀoctahedra) show slower photocatalytic HER
rate than the nanoꢀplates with an intermediate fraction of both
facets (nanoꢀplateꢀ500 °C), indicating that a high percentage
of {101} facets alone also does not guarantee better photocataꢀ
lytic HER performance. In fact, the nanocrystals with an inꢀ
termediate percentage of both {001} and {101} facets shows
the best surface normalized photocatalytic HER reactivity.
This result suggests that synergistic effect may exist between
{001} and {101} facets of anatase TiO2, a phenomenon that
has been recently observed by several groups though based on
a less quantitative analysis.80ꢀ83 Therefore, our quantitative
surface normalized activity analysis provides further evidence
to support some of these assessments. It is also worth noting
that the BET surface normalized HER activities are much
higher relative to the theoretical surface normalized activities,
reflecting the importance of accurate surface area calculation
in avoiding overestimation of the hydrogen evolution rate
This inspired us to carry out the facetꢀspecified surface area
calculation for three nanocrystals with different {001} to
{101} ratios: the {101} dominant nanoꢀoctahedra and {001}
dominant nanoꢀplates as described in the previous section, and
a third sample with intermediate {001} to {101} ratio. The
detailed calculation procedure for particle surface area is deꢀ
scribed in Figure S18. The calculation results using monodisꢀ
perse, thickness (h) and width (w) polydispersity models are
shown in Figure S19 and Table S5. The theoretical surface
area of the {001} dominant 300 °C annealed nanoꢀplate is
substantially higher than the corresponding BET surface. The
{001} surface area calculated from thickness polydispersity
(67.9 m2/g) is significantly larger relative to the result obtained
from the monodisperse model (46.7 m2/g), indicating the imꢀ
portance of considering polydispersity for accurate surface
area quantification. Interestingly, the surface areas calculated
from width polydispersity are very similar to those obtained
from the calculation of monodisperse models, which can be
understood by the fact that the width distribution for the synꢀ
thesized TiO2 nanoꢀplates is relatively narrow and symmetric
(close to Gaussian distribution), as can be seen in Figure 8d.
Similarly, the theoretical surface area of {101} dominant
nanoꢀoctahedra calculated from a monodisperse model is also
larger relative to the BET surface. However, this difference is
very likely to arise from random particle aggregation instead
of oriented stacking, as can be seen in corresponding TEM
images in Figure S1. Moreover, it is found that the width polꢀ
ydispersity (instead of thickness polydispersity) becomes the
principal effect for the {101} dominant sample: the {101}
surface area calculated from width polydispersity (137.8 m2/g)
is substantially larger relative to that obtained from the monoꢀ
disperse model (106.2 m2/g) while the {001} surface area only
varies slightly from the monodisperse model. Similar character
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Department of Energy (DOE) Office of Science User Facility
from faceted anatase TiO2 nanocrystals. Moreover, according
to the previous report,35,53 the residual surface Fꢀ can slightly
increase (not decrease) the photocatalytic HER performance of
nanoplate anatase TiO2. Thus, the higher residual Fꢀ concentraꢀ
tion in the 300 ºC annealed nanoplate sample (relative to the
other two samples, XPS in Figure S23) is unlikely to affect the
current conclusion. Finally, it is worth noting that other facꢀ
tors, such as the population of point defects, the absolute partiꢀ
cle size, the surface structure and the capability to scatꢀ
ter/absorb light of different nanocrystals may also affect the
photocatalytic activity.35, 84ꢀ86 Nevertheless, the current method
to accurately determine the surface area normalized activity
rate should still be applied to better underpin and understand
these complex effects.
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8
operated for the DOE Office of Science by Argonne National
Laboratory under Contract No. DEꢀAC02ꢀ06CH11357. Photocaꢀ
talysis work was conducted at the Center for Nanophase Materials
Sciences, which is a DOE Office of Science User Facility. Partial
salary support (L.Y.) was provided by the National Science Founꢀ
dation under OIA 1355438. Materials synthesis and laboratory
characterization were supported by the U.S. Department of Enerꢀ
gy, Office of Science, Basic Energy Sciences, Chemical Sciences,
Geosciences, and Biosciences Division. This manuscript has been
authored by UTꢀBattelle, LLC under Contract No. DEꢀAC05ꢀ
00OR22725 with the U.S. Department of Energy. The United
States Government retains and the publisher, by accepting the
article for publication, acknowledges that the United States Govꢀ
ernment retains a nonꢀexclusive, paidꢀup, irrevocable, worldwide
license to publish or reproduce the published form of this manuꢀ
script, or allow others to do so, for United States Government
purposes. The Department of Energy will provide public access to
these results of federally sponsored research in accordance with
the DOE Public Access Plan (http://energy.gov/downloads/doeꢀ
publicꢀaccessꢀplan).
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Conclusion
Powder Xꢀray diffraction and neutron pair distribution funcꢀ
tion are demonstrated to be powerful tools to obtain both accuꢀ
rate average atomistic structure and morphology information
of {001} and {101} faceted anatase TiO2 nanocrystals. It is
also demonstrated that the morphology (shape and size) distriꢀ
bution of anatase TiO2 nanocrystals can be accurately deterꢀ
mined through numerical analysis of powder diffraction data
using the Debye scattering equation calculation. This method
has been successfully used to quantify the facetꢀspecified phoꢀ
tocatalytic hydrogen evolution activity of anatase TiO2 nanoꢀ
crystals with different {001} to {101} ratios. It is found that
the sample with an intermediate amount of both {001} and
{101} facets shows the best photocatalytic HER activity. This
result suggests that a synergistic effect may exist between
{001} and {101} facets of anatase TiO2 nanocrystals. It is
expected that this morphology quantification technique could
be generally adopted to study the relationship between morꢀ
phology and functionality of other technological important
nanomaterials.
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AUTHOR INFORMATION
Corresponding Author
* pagekl@ornl.gov
liuj1@ornl.gov
ACKNOWLEDGMENT
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of Energy, Office of Science, Office of Basic Energy Sciences,
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