Thermal stability of titanate nanorods and titania
nanowires formed from titanate nanotubes by heating
Tereza Brunatova1, Zdenek Matej1, Peter Oleynikov2,
Stanislav Danis1, Daniela Popelkova3, Xiaodong Zou2, Radomir Kuzel1
1Charles
University, Faculty of Mathematics and Physics, Dept.of Condensed Matter Physics, Prague, Czech
Republic
2Berzelii Center EXSELENT on Porous Materials,Stockholm University, Dept. of Materials and Environmental
Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
3Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic
Abstract:
The structure of titanate nanowires was studied by a combination of powder X-ray
diffraction (XRD) and 3D precession electron diffraction. Titania nanowires and
titanate nanorods were prepared by heating of titanate nanotubes. The structure of final
product depended on heating conditions. Titanium nanotubes heated in the air at
temperature 850 C decomposed into three phases - Na2Ti6O13 (nanorods) and two
phases of TiO2 - anatase and rutile. At higher temperatures the anatase form of TiO2
transforms into the rutile and the nanorods changes into rutile nanoparticles. By
contrast, in the vacuum only anatase phases of TiO2 were obtained by heating at 900
C. The anatase transformation into rutile began only after long time of heating at 1000
C. For the description of anisotropic XRD line broadening in the total powder pattern
fitting by the program MSTRUCT a model of nanorods with elliptical base was
included in the software. The model parameters – rod length, length of the major axis of
elliptical base, the ellipse flattening parameter and twist of the base could be refined.
Variation of particle shapes with temperature was found.
Key words: Titania nanowires, Titanate nanorods, X-ray diffraction, precession
electron diffraction
1.
Introduction
Titanium nanowires can be obtained from titanium nanotubes (Ti-NT) just by heating.
Since many potential applications of Ti-NT need some thermal treatment it is important
to study the changes of the structure of Ti-NT due to the temperature variations and also
the preparation process. Similarly to Ti-NT several phases of nanowires have been
reported. Two different thermal behavior of Ti-NT were reported which depends on
presence of sodium ions in the starting structure. The thermal behavior, if the starting
material contains sodium ions, was studied by Morgado et al [1]. They studied three
different samples which varied in amount of sodium ions. The sample with the highest
amount of sodium ions was a mixture of sodium hexatitanate (Na2Ti6O13) and the
sodium trititanate (Na2Ti3O7). The middle sample was a mixture of sodium hexatitanate
(Na2Ti6O13), rutile phase of TiO2 and anatase phase of TiO2. These two samples were
heated to 800 °C. The last sample with the least amount of sodium ions was heated only
to 550 °C and the final phases found were a combination of the anatase phase of TiO2
and the metastable phase -TiO2. Nicolic et al [2] observed that the structure of Ti-NT is
stable up to 500 C and then it transforms to sodium hexatitanate nanorods at 700 C. Yu
et al. [3] prepared nanotubes without sodium ions. During the heating at about 400 °C
the anatase structure started to appear which afterwards transformed to rutile at 700 °C
and the final transformation appeared at 900 °C. After calcination, aggregates of
particles with the diameter between 100 nm and 300 nm were found. Weng et al. [4]
reported that the effect of heating (800 °C) was decomposition of the tubular structure
to nanoparticles. Suzuki and Yoshikawa [5] obtained a combination of rutile TiO2 and
TiO2 (B) after heating at 800 °C.
This contribution was focused to study of structural changes of Ti-NT after heating at
850 °C, 900 C and 1000 C. A set of different samples were studied under various
conditions – time, temperature of heating and heating atmosphere (air or vacuum). The
studies were followed by investigations of final shape of particles obtained after
heating. They were found by the total powder diffraction pattern fitting.
2.
Experimental setup
For phase identification of titanium nanowires and nanorods two complementary
methods were applied: powder X-ray diffraction (PXRD) and 3D rotation electron
diffraction (PED). The phase transformation was observed in-situ in PXRD
diffractometer. For morphological studies scanning electron microscopy (SEM) was
applied and the energy dispersive X-ray spectroscopy (EDX) was used for the
determination of chemical composition.
The X-ray measurements were performed on PANanalytical MPD diffractometer
equipped with MRI high temperature chamber. As heating elements, platinum strip
with directing heating and radiant heater were used. The sample was mixed with a
solvent and spread directly on platinum strip heater. The sample was measured in the
Bragg–Brentano geometry with CuKα radiation, and the PIXcel detector, in the 2θ
range from 5° to 80°. Powder diffraction patterns were measured with the step size of
0.0263° 2θ; total integrating time for one step was 180 s. Incident beam was
conditioned by Soller slit (divergence 0.04 rad) and a beam mask of width 5 mm was
used. Automatic divergence slits were used both in primary and diffracted beam in
order to achieve constant irradiated area during measurement (5 × 8 mm2.) In front of
the PiXCel detector (in scanning mode), other Soller slits (0.04 rad divergence) and a
-filter (Ni) were placed.
ED patterns were collected on the single nanorod as well. As the interaction of electrons
with matter is ~104 times stronger than that for X-rays, dynamical effects should be
taken into account and the interpretation of ED patterns is more complicated than that
of XRD patterns. In order to overcome this problem, digital precession electron
diffraction (PED) [6] was used to collect ED data. In this method the electron
microscope is controlled by dedicated software only. The electron beam is rotated
along a circle at a certain angle (so-called precession angle; 2° in this work) around the
optical axis of the microscope. The beam rotation along the circle is sampled with a
fixed azimuthal step (3° in this work) which results in 120 individually beam-tilted ED
patterns. These patterns are combined into the final PED pattern by (1) aligning all
patterns against each other using cross-correlation and (2) summing up the aligned
patterns. The set of structure factors extracted from the final PED pattern is closer to
kinematical intensities. PED patterns were recorded on JEOL JEM 2100 LaB6 operated
at 200 kV accelerating voltage.
Nanorods were ultrasonically dispersed in ethanol and a drop of the sample was spread
on a holey carbon-coated microscope copper grid.
SEM experiments were performed on a Tescan Mira3 microscope. This microscope
had auto emission electron gun operated at 15 keV. Samples were ultrasonically
dispersed in ethanol and then a drop of the sample was spread on special microscope
holder.
EDX analyses were also performed on a Tescan Mira3 microscope. Samples were
placed on carbon adhesive tape to eliminate the signal from aluminium microscope
sample holder.
3.
Measurements
The nanowires and nanorods were obtained from Ti-NT by heating. Ti-NT were
prepared by hydrothermal method, the details of preparation could be found for
example in [7]. The structure of titananate nanotube was identificated as a
H2-xNaxTi2O5 H2O where x ~ 0.4. The structure of Ti-NT was determined with the aid
of combination of X-ray diffraction and electron microscopy (more details could be
found in our previous paper [8]). Here, seven different samples of titanate
nanowires/nanorods, which differed in heating conditions were studied. Three samples
were heated in the air and five samples were heated in vacuum.
The heating in the air was performed in the following way: at first, the sample was
heated at 850 C for 105 minutes. Then the sample was cooled down and PXRD
pattern, SEM images and EDX analysis were taken. In the next step the sample was
heated at 850 C for 1000 minutes and after the treatment, PXRD pattern, SEM images
and EDX analysis were taken again. The final heating of this sample was realized at
900 C for 1000 minutes. In order to investigate changes in morphology the SEM
images were captured like in the previous cases. The heating process in vacuum
(pressure 5.10-3 – 2.10-4 Pa) was a little different. The first sample was heated at 850 C
for 105 minutes, similar to the sample heated in the air. The second sample was heated
at 850 C for 3000 minutes and the third one was heated at 900 C for 3000 minutes.
Longer heating time was chosen because after 1000 minutes the observed differences in
diffraction patterns were almost invisible. The last sample was heated at 1000 C for
3000 minutes. After heating at 1000 C the sample was cooled down and the EDX and
SEM analyses as well as measurements of PXRD pattern were carried out. Finally, the
sample was heated back up to 1000 C. At this heating, the vacuum pump was shut
down to leave oxygen to interact with the sample.
4.
Result and discusion
The structure of the first sample heated in the air for 105 minutes was studied by the
combination of PED and PXRD. A single nanorod was studied by PED in order to
obtain the unit cell parameters. PED sugested the triclinic unit cell with the cell
parameters: a = 9.3 Å, b = 7.9 Å, c = 3.8 Å, α = 102.9 °, β = 91.9 °,  = 80.4 . By
comparison of these cell parameters with suggested structure it can be found that they
are similar to the reduced lattice cell of Na2Ti6O13 [9]. The structure determined from a
single nanorod by PED was in good agreement with published work Morgado et al. [1]
Nikolic et al. [2]. The analysis of PXRD pattern showed that in addition to Na2Ti6O13
two other phases of TiO2 - anatase and rutile were present.
4.1
Methods of evaluation of powder diffraction patterns
4.1.1 Qualitative PXRD analysis
For PXRD analysis a proper structural and microstructural models have to be chosen.
The samples compose of three crystalline fractions: the first two are common TiO2
phases (rutile and anatase) and the last one is assumed to be the monoclinic Na2Ti6O13
(space group C2/m, unique axis b). For peak position simulations as well as for the total
pattern fitting (TPF, a type of Rietveld refinement) applied later its structural model
was taken from PDF4 database [9]. It is evident in Figs. 1 and Fig. 2 that peak positions
of these three crystalline phases match all the diffraction maxima in the experimental
patterns. The strongest peaks from Na2Ti6O13, which is the phase of primary interest
here, are observed in the samples heated in the air at 850 °C. Their PXRD patterns are
depicted in Figs. 1. Changes in relative intensities as well as in widths of diffraction
maxima can be observed with increasing heating time (Fig. 1b). Beside this large
differences between diffraction line widths of individual Na2Ti6O13 reflections can also
be observed (compare 200 and -201 reflections in Fig. 1a and 020 reflection in Fig. 1c).
Time evolution of line widths during sample heating appears to be also different.
Whereas 200 and -201 reflections became narrower after longer heating time, the width
of 020 reflection increased. The PXRD broadening effects are clearly related to the fact
that the unique crystal axis-b is expected to be also the axis of Na2Ti6O13 nanorods. This
helps to understand the effect in a greater detail.
The line profile parameters (width, shape) were extracted from PXRD patterns of
samples heated in the air at 850 °C for some selected hkl reflections. The diffraction
peaks chosen were either only slightly overlapped with neighbouring peaks or formed
well defined multiplets, which can be decomposed with some restrictions on peak
positions. From the profile parameters the integral breadth (hkl) of individual hkl
reflections were determined and plotted as a function of the projection of diffracting
plane normal into the basal (cross-sectional) a-c plane of the rod (Fig. 3a). Integral
breadth in Fig. 3a does not depend monotonically on this projection, but a trend is
visible. If the diffraction vector is close to the rod axis the reflections are considerably
narrower than for the diffraction vector in the basal plane. In addition, a large scatter of
integral breadths of {h0l} reflections is visible in Fig. 3a. This is better shown in 3b,
where the breadths of {h0l} reflections are plotted with respect to their projection on
the crystal a-axis. The reflections close to the [100] direction are the most broadened,
which indicates that the crystallite is truncated in this direction. Integral breadths were
plotted for both samples in Fig. 3b and it is clear that the widths of the sample heated
for the longer time are systematically smaller. It can be concluded that the basal size of
rods was slightly growing with heating period.
In order to study the phenomena of anisotropic PXRD line broadening more
quantitatively a specific model of cylindrical crystals was introduced.
4.1.2 Diffraction line broadening from oval rods
There are several ways of description of anisotropic diffraction line broadening from
finite size of coherently scattering domains (crystallites). A phenomenological model
for crystals of arbitrary symmetry based on expansion in spherical harmonics was
proposed by Popa [10]. This model is available also in the Rietveld software – e.g. in
FullProf [11]. Different approach was used in the Debye-function study in [12]. In [13]
Scardi&Leoni introduced and in [14] further developed a physical model based on
calculation of common volume of polyhedral domains of general shape. With this
method both diffraction lines widths as well as their shape can be calculated. The
formalism [13, 14] was used here to derive Scherrer-like relation between nanorods
dimension (D) and integral breadth (hkl) of diffraction lines. The same theory also
gives an analytical formula for a Fourier transform of diffraction profiles – Fourier
coefficients (A), which can be used for modelling the whole diffraction patterns [15].
Details of the model can be found in Appendix A. Cylindrical shape of crystallites is
assumed (similar to that in Fig. A1). The rod axis parallel to some specific crystal
direction [h0k0l0] and the crystallites of length L are assumed. The crystal direction
[010] is the axis for the case of Na2Ti6O13. The base of the cylinder is generally
assumed to be of elliptic shape with the major axis equal to parameter D and the minor
axis (1 - f)∙D, where f is the flattening parameter of the ellipse. Also the elliptic base is
related to the crystal coordinate system. The second reference crystal direction [h1k1l1]
is chosen. The basal ellipse major axis is then parallel to [h1k1l1] projection into the
basal plane if the last model parameter (basal twist) D is equal to zero. Nonzero value
of the twist D is then the angle of anticlockwise rotation (around the rod axis) of the
basal major ellipse axis from the [h1k1l1] projection. In our case, the second reference
direction is [100].
The above model describes a mono disperse ensemble of particles. Actually, particles
of different sizes can occur, which is commonly described by a statistical distribution
[13, 15,16]. Model distributions usually include two parameters (e.g. mean and
variance). The rods here have three characteristic dimensions (D, (1 - f)∙D and L). It is
often implicitly assumed that one of them (length L) is significantly larger than the
other two (basal dimensions) and actually the diffraction line broadening due to finite
size of the larger dimension of the rod is negligible. Then corresponding size
distribution is not essential for the calculations and it can be related somehow to those
for other dimensions. It is also assumed that all the rods in the statistical ensemble are
of the same shape. This means an additional shape parameter
can be
defined as a constant for all the rods in the ensemble. The same is assumed also for
flattening parameter (f), which is an important simplification. The rod dimension –
major-axis (D) – can then be distributed according to the Gamma distribution p(D) with
mean  and variance ∙.
In Appendix A it is shown that within this model integral breadth (hkl) can directly
calculated as
𝛽ℎ𝑘𝑙 =
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙, 𝜓𝐷 , 𝑓, 𝑎𝐿 )
⁄⟨𝐷⟩
𝑉
and
𝛽ℎ𝑘𝑙 =
𝐾𝛽𝐿𝑉 (ℎ𝑘𝑙, 𝜓𝐷 , 𝑓, 𝑎𝐿 )
⁄⟨𝐿⟩
𝑉
(1)
where DV and LV are the volume weighted particle dimensions [16] and
and
are the shape dependent Scherrer constants (
). Volume
weighted particle dimension is directly related to the moments of the size distribution
function p(D). In our case, for the Gamma distribution, the volume weighted
dimensions are
⟨𝐷⟩𝑉 = 𝜇 + 3
and
⟨𝐿⟩𝑉 = 𝑎𝐿 · ⟨𝐷⟩𝑉 .
(2)
The Scherrer constants are not only functions of hkl indexes and the basal twist angle
(D) but they also depend on particle shape parameters – aL and flattening factor f.
Let (sx, sy, sz) be a unit vector parallel to the direction of the hkl diffraction vector
expressed in the orthonormal coordinate system of the crystal (z-axis parallel to the rod
axis [h0k0l0], x-axis parallel to [h1k1l1] basal projection). Its basal components (sx, sy)
can be simply transformed in the natural coordinate system of the basal ellipse as
𝑠𝑎
cos 𝜓𝐷
(𝑠 ) = (
−sin
𝜓𝐷
𝑏
sin 𝜓𝐷 𝑠𝑥
)( ) .
cos 𝜓𝐷 𝑠𝑦
(3)
Line broadening is then a function of sz and an effective diffraction direction projection
into the rod basal plane
𝑠∘ = √(𝑠𝑎 )2 + (𝑠𝑏 )2 ⁄(1 − 𝑓)2 .
(4)
Calculation is then divided into two cases in dependence on which of the two values
[s○, |sz|/aL] is greater.
For the case A) (sz ≤ aL∙s○ ) when the limiting dimension is perpendicular to the rod axis
15𝑎𝐿 𝜋𝑠∘2
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙) = 5𝑎
𝐿 (6𝑎1 +4𝑎2 +3𝑎3 +6𝜋)𝑠∘ −(20𝑎1 +15𝑎2 +12𝑎3 +15𝜋)𝑠𝑧
(5a)
and for the case the case B) (sz ≥ aL∙s○) when the limiting dimension is parallel to the
rod axis
15𝜋𝑠𝑧4
3
3
2
3
2
2
𝐿 (3𝑎3 𝑎𝐿 𝑠∘ +5𝑎2 𝑎𝐿 𝑠∘ 𝑠𝑧 +10𝑎1 𝑎𝐿 𝑠∘ 𝑠𝑧 +15𝜋𝑠𝑧 )
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙) = 𝑎
,
(5b)
where ai (i = 1,2,3) are numerical constants (their values can be found in Appendix A).
Hence, the Scherrer constants
are functions of model parameters (f and aL) and
in the analysis of experimental data it is necessary to optimize their values to improve
correlation of experimental data with the model
. The experimental breadths hkl
for samples heated in the air at 850 °C are plotted as a function of
in Fig. 3c. hkl
should be a linear function of
with the slope equal 1/DV. The correlation
between calculated and experimental values in Fig. 3c is not optimal but very strong
diffraction line broadening anisotropy is well accounted for by the model. It is again
confirmed that the rods heated for longer time period are larger in the basal direction.
Values of the model parameters are listed in Table 1 together with the values obtained
from the whole diffraction pattern modelling.
4.1.3 MSTRUCT modelling of the whole diffraction patterns
Theory in Appendix A gives also the Fourier coefficients of diffraction profiles. Hence,
the model can be easily included in the whole diffraction modelling method developed
by Scardi&Leoni [15]. Software package MSTRUCT [17,18] based on ObjCryst
library [19] was used.
In addition to the above model of size broadening, a phenomenological model of
microstrain broadening of Popa [20, 21] was included. Preferred orientation of
Na2Ti6O13 crystallites forming nanorods and nanowires could also be expected. This
can be most easily accounted for with the so-called “arbitrary texture model” known
from MAUD software [22]. This is the best option for diffraction line profile analysis
but it does not allow an accurate quantitative phase analysis. This problem was
bypassed by applying strong limitations on the texture model and critical comparison of
fitting results using model with and without the texture (discussed below). Anatase and
rutile also show strong PXRD line broadening due to small crystallite size (Fig. 1).
However, in this case a basic model of spherical crystallites (the same as e.g. in [23])
was sufficient. An example of the whole powder pattern fit is depicted in Fig. 4. The
refined parameters of the model of cylindrical rods for samples heated in the air at 850
°C are listed in Table 1. The results of quantitative phase analysis can be found in
Table 2.
Dimensions of sodium hexatitanate nanorods determined by the line profile analysis
(LPA) from integral breadths (hkl) of selected lines and those determined from the
whole pattern fitting by MSTRUCT in Table 1 are similar within the errors of
estimation. The uncertainties of the refined values are smaller for the whole pattern
fitting (MSTRUCT) method, which is more robust than LPA of a limited number of
selected diffraction lines. For the sample heated for 1000 min the latter method failed in
determination of the flattening parameter at all, whereas MSTRUCT refinement
converged to almost circular shape of rods. The values of the twist angle differ slightly
for the sample heated for 105 minutes. The shape of basal ellipses was depicted in Fig.
5. It illustrates that the basic rod shapes determined by different methods is similar and
nonzero miss-rotation (basal twist) of the LPA solution may be related to a limited
number of analysed reflections. Fig. 5 as well as values in Table 1 confirms a
qualitative observation discussed earlier, that with increasing heating time nanorods are
growing in their basal directions and are shortened along their axis. For the 105 min
sample results of the MSTRUCT refinements including and neglecting the microstrain
effect [20-21] are finally compared in Table 1. Actually they are very similar
confirming the domination of the size effect and weak influence of lattice defects.
We should give a few remarks to physical relevance of the model of an elliptic shape of
rods. The ellipse is the simplest extension of the circular model and it should represent
an ensemble average particle shape. It is more natural that sodium hexatitanate
nanorods and nanowires are delaminated by facets. A basic extension of the model
giving analytical formulae for a rod with rhomboid base can be found in Appendix A.
The methods were applied to the study of microstructural evolution of samples with
heating under different conditions.
4.2
Samples heated in the air
Three phases were observed in PXRD pattern of the sample heated in air at 850 C anatase and rutile forms of TiO2 and sodium hexatitanate. The same structures were
obtained by Morgado [1] and Yoshida [24]. For the sample heated for 105 minutes at
this temperature, the detailed study was performed. This sample was cooled down to
room temperature and low noise PXRD pattern was collected for longer time. A part of
the sample was studied by SEM and EDX. Whole profile fitting of PXRD pattern
confirmed the presence of three phases mentioned above, see Fig. 4. The weight
percentage of each phase was determined from the profile fitting. The phase
composition is summarized in Table 2. The SEM image (Fig. 6a) shows that the sample
cointained mixture of nanoparticles and nanorods. Because PED revealed the structure
of nanorods as sodium hexatitanate, from X-ray diffraction data we can conclude, that
the nanoparticles should have structures of TiO2 phases. The shape information from
SEM image (Fig. 6a) was utilized for fitting of PXRD pattern. The spherical
nanoparticles were used for phases of TiO2 in the model and different shapes (spherical
nanoparticles, spherical base nanorods and nanorods with elliptical base) for sodium
hexatitanate. The confirmation of the rod structure was obtained by the fitting
procedure where the goodness of fit was found to be the best for the model of elliptical
rods. However, all the three models for sodium hexatitanate gave the same phase
composition (Table 2).
After SEM investigations the sample was heated up to 850 C for 1000 minutes. During
the treatment a number of X-ray diffraction patterns have been collected. The time
evolution of PXRD pattern is shown in Fig. 2 where the transformation of anatase to
rutile can be clearly seen. However, still after 1000 minutes of annealing a small
amount of anatase was detected at PXRD pattern taken for the sample cooled down to
room temperature (Fig. 7a). The phase composition was determined from PXRD
pattern fitting (Table 2.) which confirmed the reduction of the amount of anatase.
In contrast to the sample heated in the air for 105 minutes, this sample lost almost 50%
of weight percentage of anatase (Table 2.) and a loss of sodium hexatitanate was
observed so that a part of nanorods transform to rutile. At the same time from SEM
image (Fig. 6b) it can be noticed that the concentration of nanorods decreased as well.
The last heating of this sample was at 900 C for 1000 minutes. PXRD pattern measured
after cooling down to the room temperature shows the dominant rutile TiO2 phase as it
is visible in Fig. 7b, contrary to Yoshida et al. [24] and Gajovic et al [25] where
Na2Ti6O13 and rutile were observed. In our samples only traces of sodium hexatitane
were observed as follows from the phase composition determination in Table 2 and also
from SEM image in Fig.6c where almost only nanoparticles were found. We can
conclude that during the long time heating the nanorods decomposed to rutile
nanoparticles. This is in agreement with the phase composition determined from PXRD
fitting (Table 2). The same behaviour was reported by Weng [4]. Breaking of nanorods
to nanoparticles was confirmed by fitting of PXRD patterns. The breaking of nanorods
can also be derived from Table 1 where the value of <L>V decreased by about 30 nm
from sample heated at 850°C for 105 minutes to that heated for 1000 minute. The
destroy of nanorods were also confirmed by EDX measurements. The sodium loss was
also detected in these samples heated in the air and almost no signal from sodium was
found in sample heated at 900 C for 1000 minutes.
4.3
Samples heated in vacuum
The temperature behaviour of the sample heated in the vacuum is completely different
from the sample heated in air. The first sample heated in the vacuum at 850 C for 105
minutes showed in PXRD pattern diffraction peaks identified as anatase TiO2. In the
SEM images (Figs. 8a,b) two kind of structures are clearly visible - nanoparticles and
nanowires. These nanowires looked like non-transformed nanotubes. During SEM
studies of this sample a lot of bandles of nanowires was observed. The nanoparticles
and nanorods were almost not found. During the heating the anatase phase was
incredibly stable. It was a major phase till final heating temperature - 1000 C for 3000
minutes. At this temperature and after some time a part of anatase started to transform
to rutile as it is visible Fig. 7d. Very weak signal of rutile, almost unrecognisable, was
observed at next heating at 900 C for 3000 minutes. On SEM image (Fig. 8c) of this
sample bundles of TiO2 unordered nanowires were observed. The chemical
composition of these bundles was recorded by EDX composition mapping. These
bundles did not contain any Na atoms. After heating at 850°C for 1000 minutes sodium
ions were detected by EDX and on PXRD pattern indication of sodium hexatitanate
was found. However, this phase just modify the background and anatase peak at ~ 25°
in 2θ as shown in Fig. 7c. After heating at 1000 C for 3000 minutes the vacuum pump
was shut down to give leave oxygen interact with sample. After 4 hours of swiching off
the vacum pump only small changes were detected on the PXRD pattern. After opening
the vacuum pipeline rutile phase started to grow. The transformation from anatase to
rutile was then completed.
5.
Conclusion
Phase composition, structure and microstructure of titanate/titania nanowires and
nanorods prepared by heating of titanate nanotubes were studied.
For the description of anisotropic XRD line broadening in the total powder pattern
fitting by the program MSTRUCT a model of nanorods with elliptical base was created
and included in the software. The model parameters – rod length, length of the major
axis of elliptical base, the ellipse flattening parameter and twist of the base could be
refined.
The sample heated in the air atmosphere at 850 C contained three different structures:
anatase and rutile phase of TiO2, Na2Ti6O13. The nanorods were enlogated particles
with the structure of Na2Ti6O13 while the structure of smaller and round-shape particles
was ascribed to the phases of TiO2. The structure of enlogated particles (Na2Ti6O13)
was confirmed by the precession electron diffraction (PED). PED was used for
calculation of the 3D unit cell parameters of single nanorod which were in good
agreement with the reduced lattice cell of Na2Ti6O13. During the annealing time the
anatase was transformed into to rutile. With longer heating time and higher heating
temperature the decomposition of nanorods to nanoparticles with rutile structure was
observed and confirmed by EDX. This decomposition of nanorods and phase
transformation from anatase to rutile were detected by PXRD pattern fitting. For PXRD
pattern fitting of sodium hexatitanate three diferent models were used – model of
spherical nanoparticles, spherical base nanorods and nanorods with eliptical base and
the best match was obtained for the model of elliptical base nanorods. This was also
confirmed by the line profile analysis. The transformations to sodium hexatitanate in
the sample heated in vacuum was not found as it was shown on PXRD patterns. With
increasing heating time, the formation of thermally stable unordered anatase nanowires
was detected. The transformation to stable phase of TiO2 - rutile was observed only
after long heating time at 1000 C. Thus the presence of oxygen is necessary to obtain
sodium hexatitane nanorod. By contrast, if the final product of heating should be
anatase nanowires then the inert atmosphere should be used.
Acknowledgement
The work is supported by the Grant agency of the Czech Republic no. P108/11/1539,
Grand agency of Charles University no. 470413, the Swedish Research Council (VR),
the Swedish Governmental Agency for Innovation Systems (VINNOVA) and Göran
Gustafsson Foundation for Natural Sciences and Medical Research. The EM facility
was supported by a grant from Knut and Alice Wallenberg Foundation. SEM
experiments were performed in MLTL (http://mltl.eu/), which is supported within the
program of Czech Research Infrastructures (project no. LM2011025).
References:
[1] Morgado E. jr, de Abreu M.A.S., Pravia O.R.C., Marinkovic B.A, Jardim P.M.,
Rizzo R. C., and Arajo A.S.:. A study on the structure and thermal stability of titanate
nanotubes as a function of sodium content, Solid State Science, 8, 2006.
[2] Nikolic L. M., Maletin M., Ferreira P., and Vilarinho P. M.:. Synthesis and
characterization of one-dimensional titanate structure. Processing and application of
ceramics, 2, 2008.
[3] Yu J. and Yu H. and Cheng B. and Trapalis C., Effects of calcination temperature on
the microstructures and photocatalytic activity of titanate nanotubes, Journal of
Molecular Catalysis A, 249, 2006
[4] Weng L.-Q. and Song S.-H. and Hodson S. and Baker A. and Yu J, Synthesis and
characterization of nanotubular titanates and titania, Journal of European Ceramic
Society, 26 ,2006
[5] Suzuki Y. and Yoshikawa S., Synthesis and thermal analysis of TiO2-derived
nanotubes prepared by the hydrothermal method, Journal of Materials Research, 19,
2004
[6] Zhang DL, Grüner D, Oleynikov P, Wan W, Hovmöller S, Zou XD. Precession
Electron Diffraction Using a Digital Sampling Method. Ultramicroscopy 2010;
111:47-55.
[7] Kralova D. and Pavlova E. and Slouf M. and Kuzel R., Preparation and structure of
titanate nanotubes, Materials Structure, 15, 2008, 1
[8] Brunatova T., Popelkova D., Wan W., Oleynikov P., Danis S., Zou X., Kuzel R.,
Study of titanate nanotubes by X-ray and electron diffraction and electron microscopy,
Materials Characterization, 87, 166–171, 2014
[9] ICDD PDF-4+ database, PDF card n. 04-009-3669.
[10] N. C. Popa. The (hkl) Dependence of Diffraction-Line Broadening Caused by
Strain and Size for all Laue Groups in Rietveld Refinement. Journal of Applied
Crystallography, 31(2): 176—180, 1998.
[11] M. Casas-Cabanas, J. Rodríguez-Carvajal, J. Canales-Vázquez, Y. Laligant, P.
Lacorre, M.R. Palacín. Microstructural characterisation of battery materials using
powder diffraction data: DIFFaX, FAULTS and SH-FullProf approaches. Journal of
Power Sources 174 (2007) 414–420.
[12] Giuseppe Cernuto, Norberto Masciocchi, Antonio Cervellino, Gian Maria
Colonna, Antonietta Guagliardi. Size and Shape Dependence of the Photocatalytic
Activity of TiO2 Nanocrystals: A Total Scattering Debye Function Study. Journal of
the American Chemical Society, 133(9):3114–3119, 201
[13] Scardi, P. and Leoni, M., Diffraction line profiles from polydisperse crystalline
systems, Acta Crystallogr., Sect. A: Found. Crystallogr. 57, 604-613, 2001.
[14] Leonardi, A., Leoni, M., Siboni, S. and Scardi, P.,Common volume functions and
diffraction line profiles of polyhedral domains, J. Appl. Crystallogr. 45, 1162-1172,
2012
[15] Scardi, P. and Leoni, M., Whole powder pattern modelling, Acta Crystallogr.,
Sect. A: Found. Crystallogr. 58, 190-200, 2002
[16] Langford, J. I., Louër, D., Scardi, P.,Effect of a crystallite size distribution on
X-ray diffraction line profiles and whole-powder-pattern fitting, J. Appl. Crystallogr.
33, 964-974, 2000.
[17] Z. Matěj, R. Kužel, L. Nichtová XRD total pattern fitting applied to study of
microstructure of TiO2 films, Powder Diffraction, v. 25 (2010) 125-131.
[18] http://www.xray.cz/mstruct/
[19] Vincent Favre-Nicolin and Radovan Černý. FOX, 'free objects fo crystallography':
a modular approach to ab initio structure determination from powder diffraction.
Journal of Applied Crystallography, 35(6):734—743, 2002
[20] N. C. Popa. The (hkl) Dependence of Diffraction-Line Broadening Caused by
Strain and Size for all Laue Groups in Rietveld Refinement. Journal of Applied
Crystallography, 31(2): 176—180, 1998.
[21] Václav Valeš, Lenka Matějová, Zdeněk Matěj, Tereza Brunátová, Václav Holý.
Crystallization kinetics study of cerium titanate CeTi2O6. Journal of Physics and
Chemistry of Solids 75 (2014), 265–270.
[22] L. Lutterotti, D. Chateigner, S. Ferrari, and J. Ricote. Texture, residual stress and
structural analysis of thin films using a combined x-ray analysis. Thin Solid Films, 450:
34—41, 2004
[23] Z. Matěj, L. Matějová, R. Kužel. XRD analysis of nanocrystalline anatase powders
prepared by various chemical routes: correlations between micro-structure and crystal
structure parameters. Powder Diffraction (28), Supplement S2, S161-S183.
[24] Yoshida R., Suzuki Y., and Yoshikawa S.:. Efects of synthestic conditions and
heat-treatment on the structure of partially ion-exchange titanate nanotube. Materials
chemistry and physics, 91, 2005.
[25] Gajovic A., Friscic I., Plodinec M., and Ivekovic D. :. High temperature Raman
specroscopy of titanate nanotubes. Journal of molecular structure, 924-926, 2009.
Table 1. Refined parameters of the model of Na2Ti6O13 cylindrical rods for samples
heated in the air at 850 °C - LV is the volume weighted crystallite length, DV is the
volume weighted major diameter of the nanorod elliptical base, f is its flattening
parameter and D is the base twist (see 4.1.2). LPA values were determined by direct
analysis of integral breadths (hkl) of selected diffraction lines. MSTRUCT values are
results from whole pattern fitting (including and neglecting effect of microstrain).
LPA
DV (nm)
LV (nm)
f
D (°)
29 ± 2
128 ± 30
0.5 ± 0.2
73 ± 10
105 min
MSTRUCT
no strain
with strain
27.7 ± 0.4
27.3 ± 0.4
122 ± 5
123 ± 5
0.25 ± 0.06 0.29 ± 0.07
90 ± 3
90 ± 2
1000 min
MSTRUCT
with strain
36 ± 2
36.9 ± 0.8
94 ± 15
92 ± 4
not det.
0.07 ± 0.07
88 ± 5
90 ± 16
LPA
Table 2. Phase composition in wt. % obtained from PXRD pattern fitting for different
fitting models.
model of sferical particles for
model of sferical rods for
Na2Ti6O13
Na2Ti6O13
anatase
rutile Na2Ti6O13 anatase
rutile
Na2Ti6O13
850C 105 min
850C 1000 min
900C 1000min
51 ± 6
42 ± 7
8±5
14 ± 3
6±1
0
35 ± 4
52 ± 5
92 ± 5
model of eliptical rods for Na2Ti6O13
Na2Ti6O13
anatase
rutile
33 ± 3
56 ± 5
92 ± 4
51 ± 5
41 ± 6
16 ± 2
7±2
33 ± 2
52 ± 4
51 ± 5
38 ± 7
15 ± 3
6±2
8 ±
0
92 ±4
8 ±
0
Appendix A - Diffraction line profiles from nanorods of elliptic and rhomboidal
cross section
Diffraction profile I(s) can be described also by its Fourier transform – so called Fourier
coefficients A(x)
𝐼(𝑠) ≈ ∫ 𝐴(𝑥) exp(2𝜋𝑖𝑠𝑥) 𝑑𝑥 ,
(A1)
where s = 1/d = 2sin()/ and x are the reciprocal and real space variables respectively.
In the case of line broadening due to finite size of scattering domains A(x) is equal to
common volume of the crystallite and its ‘ghost’ shifted a distance x in the direction
perpendicular to (hkl) reflecting planes (Fig. A1). For the case of rod shape crystallites
with circular base (Fig. A1) let call the projection of the reflecting planes normal into
the rod axis sz and sx let be its complement (𝑠𝑥 = √1 − 𝑠𝑧2 ). It is evident (Fig. A1) the
common volume Ac(x) is equal to the product of the rod length (L) reduced by the shift
(sz∙x) of the ‘ghost’ along the rod axis and the common area (Acirc) of two discs of
diameter D with centers separated by the distance sx∙x
𝐴𝑐 (𝑥) = 𝐿 (1 −
𝑠𝑧 𝑥
)∙
𝐿
𝐴𝑐𝑖𝑟𝑐 =
1
𝑠 𝑥
𝑠𝑥 𝑥
𝐿𝐷 2 (1 − 𝑧𝐿 ) ∙ 𝑓𝑐𝑖𝑟𝑐 ( 𝐷
)
2
,
𝑓𝑐𝑖𝑟𝑐 (𝑡) = 2 ∙ 𝐴𝑐𝑖𝑟𝑐 ⁄𝐷 2 = acos(𝑡) − 𝑡 √1 − 𝑡 2 .
(A2)
(A3)
To simplify further calculations the fcirc was approximated by a third order polynomial
𝜋
∗
(𝑡) = + 𝑎1 𝑡 + 𝑎2 𝑡 2 + 𝑎3 𝑡 3 .
𝑓𝑐𝑖𝑟𝑐 (𝑡) ≈ 𝑓𝑐𝑖𝑟𝑐
2
(A4)
Conditions fcirc(0) = /2, fcirc (1) = 0 and search for polynomial coefficients in the least
square sense gives
1
𝑎1 = 48 (−2816 + 867𝜋),
𝑎3 = −112 +
𝑎2 =
𝜋
−( 2
287𝜋
,
8
(A5)
+ 𝑎1 + 𝑎3 ) .
According to [13, 15] averaging over the distribution p(D) of particles diameters for the
Fourier coefficients can be written as
∞
𝐴(𝑥) = ∫𝑢(𝑥) 𝐴𝑐 (𝑥, 𝐷) 𝑝(𝐷)𝑑𝐷 .
(A6)
For the given real space length x only particles with some minimal diameter u(x) can
contribute to the integral in Eq. (A6). The following conditions must be satisfied: D >
u(x) = sx∙x and L > sz∙x. The second condition can be reformulated for D with the rod
shape ratio aL = L/D as D > u(x) = sz∙x/aL. Hence both conditions are satisfied if u(x) =
max[sx∙x, sz∙x/aL]. For the Gamma distribution of rod diameters (D) using
approximation in Eq. (A4) the integration (Eq. (A6)) gives
𝐴(𝑥) = [𝑎𝐿 𝜋 Γ(α + 3, u∗ ) + (2a1 aL sx − πsz ) x ∗ Γ(α + 2, u∗ )
+ 2(a2 aL sx − a1 sz ) sx x ∗ 2 Γ(α + 1, u∗ )
+ 2(a3 aL sx − a2 sz ) sx2 x ∗ 3 Γ(α, u∗ )
− 2a3 sz sx3 x ∗ 4 Γ(α − 1, u∗ )] ⁄[4 Γ(α)⁄3 ] ,
where = 𝜇/ , x ∗ = 𝑥/ and 𝑢∗ (𝑥) = max[|𝑠𝑥 |, |sz ⁄aL |] ∙ x ∗ . Γ() is the Euler
gamma function and Γ( z) is the incomplete gamma function.
From Fourier coefficients (Eq. (A7)) it is straightforward to calculate the integral
breadth of diffraction lines
(A7)
𝛽=
𝐴(0)
.
⁄ ∞
2 ∫0 𝐴(𝑥)𝑑𝑥
(A8)
For a rod with an elliptic cross section with two semi-axes a and b let define beside aL =
L/D two other parameters for basal anisotropy (aa, ab) connecting characteristic rod
basal size D with a and b parameters of the ellipse
𝑎 = 𝑎𝑎 𝐷⁄2 and
𝑏 = 𝑎𝑏 𝐷⁄2 .
(A9)
Let (sa, sb) be the components of a unit vector in the diffraction vector direction related
to the axes of the basal ellipse. The Fourier coefficients are now again proportional to
the common area of the ellipses shifted from each other by (sa, sb, sz)∙x.
Using simple transformation of coordinates
𝑥′ = 𝑥⁄𝑎 ,
𝑦
𝑦 ′ = ⁄𝑏
the problem is translated into the equivalent problem for the circle. Only the
transformation Jacobian and the rescaling of the shift vector has to be included
𝑠𝑎
𝑠 ⁄𝑎
Δ = (𝑠 ) ∙ 𝑥 → Δ′ = ( 𝑎 ) ∙ 𝑥 .
𝑠𝑏 ⁄𝑏
𝑏
This gives for the common area of ellipses
′
𝐴𝑒𝑙𝑙𝑖𝑝𝑠𝑒 (𝑥) = 2 ∙ 𝑎𝑏 ∙ 𝑓𝑐𝑖𝑟𝑐 (Δ ⁄2) .
Including D and asymmetry parameters aa, ab
𝐴𝑒𝑙𝑙𝑖𝑝𝑠𝑒 (𝑥) =
𝑎𝑎 𝑎𝑏 2
𝐷
2
2
𝑠
2
𝑠
𝑥
∙ 𝑓𝑐𝑖𝑟𝑐 (√(𝑎𝑎 ) + (𝑎𝑏 ) ∙ 𝐷) ,
𝑎
(A10)
𝑏
which has the same form as Eq.(A2). A crucial difference is in the substitution in the
argument of fcirc, which respects the asymmetrical dimensions of ellipse
2
2
𝑥
𝑥
𝑠
𝑠
𝑥
𝑠𝑥 ∙ 𝐷 → 𝑠∘ ∙ 𝐷 = √(𝑎𝑎 ) + (𝑎𝑏 ) ∙ 𝐷 .
𝑎
(A11)
𝑏
Hence the condition for u(x) in Eqs. (A6, A7) becomes
𝑠 2
𝑎𝑎
𝑠 2 s
𝑎𝑏
aL
𝑢∗ (𝑥) = max [√( 𝑎 ) + ( 𝑏 ) , z ] ∙ x ∗ .
(A12)
For Fourier coefficients of a rod with rhomboid cross-section defined by parameters
(D1= a1·D, D2 = a2·D, D, D) and depicted in Fig. A2 it hold
𝐴𝑐 (𝑥) = 𝐿 (1 −
𝑠𝑧 𝑥
)∙
𝐿
𝑠
𝑠
𝑠 𝑠
𝐷1 𝐷2 sin 𝛽 [1 − (𝐷1 + 𝐷2 ) 𝑥 + 𝐷1 𝐷2 𝑥 2 ] .
1
2
1
2
(A13)
If (sx, sy, sz) is a unit vector in diffraction vector direction the shift projections into
rhomboid basal edges are
𝑠1 = |[sx sin(𝜓𝐷 + 𝛽𝐷 ) − sy cos(𝜓𝐷 + 𝛽𝐷 )]⁄sin(𝛽𝐷 )| ,
𝑠2 = |[−sx sin(𝜓𝐷 ) + sy cos(𝜓𝐷 )]⁄sin(𝛽𝐷 )| .
(A14)
For Fourier coefficients including averaging over the Gamma distribution Eq. A6 gives
s1 s2 sz
𝐴(𝑥) = 𝑎𝐿 𝑎1 𝑎2 sin 𝛽𝐷 [ Γ(α + 3, u∗ ) − ( + + ) x ∗ Γ(α + 2, u∗ )
a1 a 2 a L
s1 s2 s1 sz s2 sz ∗ 2
+(
+
+
) x Γ(α + 1, u∗ )
a1 a 2 a1 a L a 2 a L
s1 s2 sz ∗ 3
−
x Γ(α, u∗ )] ⁄[ Γ(α)⁄3 ] ,
a1 a 2 a L
with characteristic limits
(A15)
s s2 sz
, ]
a1 a2 aL
𝑢∗ (𝑥) = max [ 1 ,
∙ x∗ .
Integration (Eq. 8) gives for Scherrer constant
A) u*(x) = s1/a1∙x*
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙) =
6𝑎2 𝑎𝐿 𝑠𝑎3
𝑎1 [2𝑎2 𝑠1 (3𝑎𝐿 𝑠1 −𝑎1 𝑠𝑧 )+𝑎1 𝑠2 (𝑎1 𝑠𝑧 −2𝑎𝐿 𝑠1 )]
,
(A16a)
6𝑎1 𝑎𝐿 𝑠𝑐3
2 [2𝑎1 𝑠2 (3𝑎𝐿 𝑠2 −𝑎2 𝑠𝑧 )+𝑎2 𝑠1 (𝑎2 𝑠𝑧 −2𝑎𝐿 𝑠2 )]
,
(A16b)
6𝑎1 𝑎2 𝑠𝑧3
[2𝑎
(3𝑎
𝑠
𝑠
−𝑎
𝐿
1 𝑧
2 𝑧
𝐿 𝑠2 )+𝑎𝐿 𝑠1 (𝑎𝐿 𝑠2 −2𝑎2 𝑠𝑧 )]
.
(A16c)
B) u*(x) = s2/a2∙ x*
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙) = 𝑎
C) u*(x) = sz/aL∙ x*
𝐾𝛽𝐷𝑉 (ℎ𝑘𝑙) = 𝑎
Figure Captions
Figure 1:
Parts of PXRD patterns of the sample heated in air at 850C: (a) close to low angle
Na2Ti6O13 reflections (bottom black hkl marks), (b) close to strong anatase (A) and
rutile (R) reflections, (c) close to the (020) Na2Ti6O13 reflection. Sample heated for
105 min – blue line, 1000 min – dot-dashed red line. Widths of selected lines are
marked. [010] direction is expected to be the Na2Ti6O13 rod axis.
Figure 2:
Time evolution of the diffraction pattern of the sample heated in air at 850C for 1000
minutes
Figure 3:
Integral breadths (hkl) of selected Na2Ti6O13 XRD lines for the sample heated in air at
850C for 105 min (blue ●) and 1000 min (red ×) plotted against: (a) size of projections
of (hkl) diffracting planes normals into crystal a-c plane, (b) size of projections of (h0l)
diffracting planes normals on crystal a-edge and (c) Scherrer constants (Khkl) of
cylindrical crystallites (see 4.1.1).
Figure 4:
Whole diffraction pattern fit of sample heated in air for 105 min. Measured points (blue
), fit (red line), hkl reflections marks: (bottom) Na2Ti6O13 – sodium hexatitanate,
(middle) A – anatase, (top) R – rutile. (Arbitrary texture model used.)
Figure 5:
Comparison of refined shape of Na2Ti6O13 rod elliptic base for sample heated at 850C
for 1000 min (delimitated by dashed line) and for 105 min (solid line for MSTRUCT fit
and dotted line for LPA). Face of the unit cell depicted is not in scale.
Figure 6:
SEM images of the sample heated in the air: a) sample heated at 850 C for 105
minutes, b) sample heated at 850 C for 10000 minutes, c) sample heated at 900 C for
1000 minutes.
Figure 7:
Low-angle parts of PXRD patterns fits of selected samples heated: (a) in air at 850C
for 1000 min, (b) in air at 900C for 1000 min, (c) in vacuum at 850C for 3000 min
and (d) in vacuum at 1000C for 3000 min. hkl reflections marks: (bottom) Na2Ti6O13 –
sodium hexatitanate, (middle) A – anatase, (top) R – rutile.
Figure 8:
SEM images of the sample heated in the vacuum: a) sample heated at 850 C for 105
minutes, b) sample heated at 850 C for 105 minutes, c) sample heated at 900 C for
3000 minutes.
Figure A1:
Rod-like cylindrical crystal (of diameter D and length L). Its Fourier coefficients are
equal to the common volume of the crystal and its ‘ghost’ shifted a distance x in the
direction (sx, 0, sz) perpendicular to (hkl) diffracting planes. The situation here satisfies
the condition sz < sx∙L/D.
Figure A2:
Base of a rod-like crystal with rhomboid cross-section. Fourier coefficients are
proportional to the common area Arhomb. Base dimensions (D1, D2, D) and its
orientation (D) can be generally independent of the crystal lattice unit cell. However in
nature, there is often some relation between them. E.g. the crystal is delimitated by
{100} and {10-1} facets as in the picture.