Upload
musonly
View
216
Download
0
Embed Size (px)
Citation preview
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
1/7
R E S E A R C H P A P E R
Nano-powders of Na0.5K0.5NbO3 made by a solgel method
Anirban Chowdhury Jonathan Bould
Yifan Zhang Craig James Steven J. Milne
Received: 30 September 2008 / Accepted: 21 January 2009 / Published online: 14 February 2009
Springer Science+Business Media B.V. 2009
Abstract Sodium potassium niobate (NKN) nano-
particle powders were synthesised through the thermal
decomposition of a solgel NKN precursor. Powders
and gels were characterised by X-ray diffraction
(XRD), Fourier transform infrared spectroscopy
(FTIR), thermogravimetric analysis (TGA) and trans-
mission electron microscopy (TEM). Hydrated
carbonate phases formed as a result of reaction with
evolved vapours during organic decomposition, and by
reaction of NKN powders with H2O and CO2 on
exposure to air. The primary particle size of thepowders increased from\50 to\250 nm as decom-
position temperatures were raised from 500 to 950 C.
Keywords Nano-powders Solgel
Sodium potassium niobate X-ray diffraction
Fourier transform infrared spectroscopy
Transmission electron microscopy
Synthesis method
Introduction
Over the past few years, environmental concerns
have stimulated interest in developing lead-free
ferroelectric and piezoelectric ceramic compositions
as replacements for lead zirconate titanate. One of the
most promising candidates in this category is a solid
solution series based on sodium potassium niobate
(NKN), Nax
K1-xNbO3, modified by lithium and
tantalum ions (Saito et al. 2004; Guo et al. 2005).For the Na
xK1-xNbO3 system (NKN), composi-
tions around x = 0.5, Na0.5K0.5NbO3, lie in the
vicinity of one of the systems morphotropic phase
boundaries and show the most favourable ferroelec-
tric and piezoelectric parameters (Shirane et al. 1954;Haertling 1967; Egerton and Dillon 1959; Jaeger and
Egerton 1962; Tennery and Hang 1968). Given the
technological potential of NKN-based piezoceramics,
it is important to develop appropriate ceramic fabri-
cation techniques. Bulk ceramics are prepared
traditionally using powders obtained from milling
and calcining mixtures of oxides or compounds such
as carbonates that decompose into oxides at high
temperatures. These calcined powders are then com-
pacted and sintered to form high-density ceramics.
However, in the case of NKN, it is difficult to achievehigh densities using conventional powder processing
methods. There are also problems in avoiding loss of
volatile Na2O and K2O vapours during both calcina-
tion and sintering.
Over recent years, a number of solution-based
powder synthesis routes have been developed as
alternatives to the mixed-oxide route, including co-
precipitation and solgel methods (Smart and Moore
1996). These soft chemistry methods can result in
A. Chowdhury (&) J. Bould Y. Zhang
C. James S. J. Milne
Institute for Materials Research, Houldsworth Building,
University of Leeds, Leeds LS2 9JT, UK
e-mail: [email protected]
123
J Nanopart Res (2010) 12:209215
DOI 10.1007/s11051-009-9595-0
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
2/7
smaller particle sizes and improved chemical unifor-
mity compared to mixed-oxide routes. When applied
to NKN, they could offer reductions in processing
temperatures which would be expected to reduce the
tendency for loss of alkali metal oxides, and to
produce smaller particle size thereby enhancing
densification kinetics.Sodium niobate, NaNbO3, nanopowders have been
reported from the reaction of hydrogen peroxide
solution with sodium and niobium ethoxides (Cheng
et al. 2006). Transmission electron micrographs of
the powder heat treated at 500 C for 1 h revealed
primary particles around 1530 nm in size. Lithium
modified NaNbO3 has been made using Na2CO3 and
Li2CO3 precursors along with ammonium niobium
oxalate, NH4H2[NbO(C2O4)3] 3H2O (Franco et al.
1999). The powders were of a high surface area,
*10 m2 g-1, with equivalent spherical diameters of*130 nm. Powders of NaNbO3 (Nobre et al. 1996)
have also been reported using methods based on a
Pechini-type reaction route, involving citric acid and
ethylene glycol reagents, giving high crystallinity and
high surface area *28 m2 g-1, with equivalent
spherical diameters of*46 nm.
In the present study, we report the synthesis and
properties of Na0.5K0.5NbO3 (NKN) nanopowders
produced via a solgel method involving ethoxides of
sodium, potassium and niobium as precursors, and 2-
methoxyethanol as solvent.
Experimental
Precursor solutions were prepared from commercially
available ethoxides of sodium [CH3CH2ONa], potas-
sium [CH3CH2OK] and niobium [(CH3CH2O)5Nb]
(Aldrich). The ethoxides were stored and handled
under a dry N2 atmosphere in a re-circulating glove
box (Saffron, UK). Chemicals were weighed and
mixed in 2-methoxyethanol [CH3OCH2CH2OH](Aldrich), followed by stirring for 2 h to give a
yellow-coloured solution, referred to as the stock
solution, with a concentration of 0.34 M (in terms of
Nb content).
The stock solution was maintained at 6070 C,
with slow stirring for 4 h. The sample was exposed to
atmospheric moisture, but no deliberate addition of
water was carried out. A sticky resinous gel formed
after standing for a further 3 h at room temperature.
The gel was transferred to an oven and dried at
120 C for a period of 24 h to form a yellow powder.
For each batch, *0.5 g of dried gel powder was
produced; this was ground into a finer powder using
an agate mortar and pestle. The powder was calcined
at different temperatures in order to study phase
development using XRD (Philips APD 1700, Almelo,The Netherlands) with CuK
aradiation. Fourier
transform infrared spectroscopy (FTIR) was carried
out on samples of the NKN powder after calcination
at different temperatures for dwell times of 30 min
(Perkin Elmer Spectrum One FTIR spectrometer).
Spectra were recorded over the wavenumber range
4,0001,000 cm-1. The particle size and morphology
were evaluated using transmission electron micros-
copy (TEM, Philips CM 200 FEGTEM, Eindhoven,
the Netherlands) with an accelerating voltage of
200 kV. Unit cell parameters were calculated using aleast squares refinement programme. For TEM
investigations, powders were suspended in isopropa-
nol, and a drop of this suspension was deposited on a
holey carbon-coated film supported on a 400 mesh
copper grid. Thermogravimetric analysis (TGA) was
conducted in air (Stanton & Redcroft TGA 1000,
London, England). The gel for this purpose was
obtained by drying the sol at 60 C for 4 h. The TGA
furnace was run at 20 C min-1 until 950 C. This
was the maximum working temperature deemed to
avoid significant levels of alkali metal evaporationand consequent damage to the apparatus; the TGA
sample was held at 950 C for 20 min. Surface area
measurements were performed using a 3-point BET
technique (Quantachrome Instruments, Florida,
USA).
Results and discussion
A standard TGA plot of the NKN gel powder shows
decomposition and mass loss to occur in five discretestages, up to a temperature of 750 C, Fig. 1. The
approximate temperature ranges of these decomposi-
tion steps were as follows (the percentage mass loss
for each stage is shown in parenthesis): \130 C
(5.4%); 130350 C (2.0%), 350470 C (1.3%),
470560 C (1.7%) and 560750 C (0.8%). The
total mass loss up to 750 C was therefore around
11% of the original dried gel starting sample. A
small, gradual loss of a further 1 mass % occurred
210 J Nanopart Res (2010) 12:209215
123
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
3/7
from *750 C up to the maximum temperature
studied, 950 C, Fig. 1.
The TGA loss at \130 C is consistent with
evaporation of: ethanol (boiling point = 79 C)
derived from the metal ethoxides; methoxyethanol
solvent (boiling point = 124 C); and water present
in the precursors, or absorbed from the atmosphere.
In order to investigate the thermal decomposition
sequence in more detail, FTIR analysis of the gel
residue after different heat treatments was carried out.Peaks were assigned with reference to standard texts
(Socrates 2001; Williams and Fleming 1990). Helpful
background information on this specific NKN system
was obtained by running FTIR spectra of Na2CO3,
K2CO3 powders (both Aldrich) and a Nb2O5 nano-
sized powder formed from the thermal decomposition
of Nb(OC2H5)5 at 600 C. These are presented in
Fig. 2; the spectra indicate that each of the three
compounds shows a hydrated phase to be present. InNb2O5, this is indicated by FTIR peaks at 3,480 cm
-1
(broad) and 1,630 cm-1, Fig. 2. For NKN-based
ceramics made by conventional mixed-oxide pro-
cessing, it is normal practice to dehydrate the alkali
metal carbonate powders prior to use as they are
known to absorb H2O from the atmosphere (Fig. 2),
but this result demonstrates that it is also advisable to
dehydrate the starting Nb2O5 reagent for the purpose
of attaining accurate control of product composition.
The FTIR spectra of the NKN gel samples after
heating at progressively higher temperatures areshown in Fig. 3. Wavenumbers of key peaks are
listed in Table 1. The FTIR spectrum from the gel
sample dried at 250 C indicates weak, broad peaks
centred *3,300, 1,610, 1,430 and 1,310 cm-1. The
broad absorbance around 3,300 cm-1 is typical of O
H stretch from H2O. Based on the knowledge of other
metal-alkoxy solgel systems (Chowdhury et al.
2008), the TGA steps up to 470 C, are probably,
associated with the thermal decomposition of organic
residues (cleavage of covalent organic bonds). Hence,
organic groups are likely to be present in the 250 Csample. Any CC stretch would overlap with the
lower wavenumber range of the broad OH band. The
Fig. 1 A TGA plot for the dried sodium potassium niobate
(NKN) gel-powders (heated in air). The percentage values in
bracket show the mass change during the respective temper-
ature zones
4000 3500 3000 2500 2000 1500 1000
1775
1550 - 12002965
2855
1500 - 1200
2595
3480
1630
Transmitta
nce
Wavenumber (cm-1)
2488
2448
1775
1063
K2CO
3
Nb2O
5
Na2CO
3
Fig. 2 FTIR plots of (a)
Na2CO3 (Aldrich), (b)K2CO3 (Aldrich) and (c)
Nb2O5 (obtained by drying
the Niobium ethoxide
(Aldrich) precursor at
600 C)
J Nanopart Res (2010) 12:209215 211
123
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
4/7
peaks at 1,430 and 1,310 cm-1 could arise from
combinations of absorbances due to organic func-
tional groups, e.g. asymmetric bending of CH3 groups
(around 1,430 cm-1) and symmetric CH3 bending (at
1,310 cm-1), but could also signify that inorganic
carbonates, or bicarbonates (HCO3-) are present in
the gel (Rojac et al. 2006; Busca and Lorenzelli
1982). Indeed, there is a very strong absorbance in
the range *1,5001,200 cm-1 in the Na2CO3 and
K2CO3 spectra in this region (Fig. 2). A very weakpeak at 1,770 cm-1 is consistent with C=O stretch, of
for example inorganic ester, Fig. 3, but alternatively,
both Na2CO3 and K2CO3 show strong absorptions in
this region (Fig. 2), suggesting the peak could arise
from an inorganic carbonate group.
The small 1,770 cm-1 peak also existed in the
350 C sample, Fig. 3; the other peaks were similar
to those of the 250 C sample. However, the
1,770 cm-1 peak was absent in the 450 C sample.
It is assumed that all organics had decomposed by
*450 C.
At 650 C there were several changes. The1,365 cm-1 peak disappeared and there was a peak
at 1,654 cm-1 as opposed to 1,630 cm-1 at lower
temperatures, Table 1. At 750 C, peaks at 1,520 and
1,215 cm-1 are developed. On increasing the decom-
position temperature to 850 C, the peak at
*1,630 cm-1 could not be distinguished, but 1,430
and 1,215 cm-1 peaks remained, together with OH
stretch at high wavenumbers, indicating a hydrated
phase. The 950 C sample showed no evidence of
secondary carbonated/hydrated phases.
The 1% mass change highlighted by TGA above750 C is most probably due to the final residual
carbonate phase decomposing, but the FTIR spectra
showed hydrated carbonate phases persisted in a
NKN powder sample even after decomposition at
850 C. It is probable that some of the hydrated
carbonates detected in the high temperature FTIR
samples are a consequence of a reaction between the
NKN powders, after thermal decomposition, with
moisture and carbon dioxide in the air during sample
storage, prior to recording the FTIR spectra. The
absence of peaks in FTIR patterns in the 950 Csample may therefore be due to its larger particle
size, as described below, and consequent lower
surface area available to react with atmospheric
vapours.
The peak changes described above are considered
to mark a change from a system containing a mixture
of organic residues and co-existing hydrated carbon-
ates, \450 C, to one where NKN co-exists with
hydrated carbonate phases (450850 C), and finally
single-phase NKN is present (950 C). Variations in
peak positions at temperatures above 550 C signifyslight changes in the composition of the constituent
carbonate species are taking place.
X-ray diffraction (XRD) plots of the calcined
NKN powders are shown in Fig. 4. There was no
evidence of crystallisation in the 350 C powder.
However, a sample heated at 450 C (for 30 min)
was crystalline, exhibiting a pseodocubic XRD
pattern (the broad hump in the background intensity
is due the glass sample holder). Close inspection
4000 3500 3000 2500 2000 1500 1000
1520
13101610
1430
1450
3300
250C
350C
450C
550 C
650C
750 C
850C
950C
1770
1430 1120
1070
1770 1630 1310
1070
1630 1365
1070
1630 1365
1070
1654
1430
1070
16541430
1215
1430
1215
Transm
ittance
Wavenumber (cm-1)
Fig. 3 The Fourier transform infrared spectra of sodium
potassium niobate (NKN) gel-powders heated at various
temperatures
Table 1 Wavenumbers of key peaks of the NKN gel samples
after heating at progressively higher temperatures
Temp (C) Wavenumbers of the key peaks (cm-1)
250 *3,300 (very broad), 1,770, 1,610, 1,430,1,310, 1,120, 1,070
350 *3,300 (very broad), 1,770, 1,630, 1,450,
1,310, 1,070
450 *3,300 (very broad), 1,630, 1,365, 1,070
550 *3,300 (very broad), 1,630, 1,365, 1,070
650 *3,300 (very broad), 1,654, 1,430, 1,070
750 *3,300 (very broad), 1,654, 1,520, 1,430, 1,215
850 *3,300 (faint), 1,430, 1,215
950 *3,300 (faint)
212 J Nanopart Res (2010) 12:209215
123
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
5/7
reveals faint extra peaks at 10.6, 27.5 and 48.2 2h,
in addition to the NKN peaks. In combination with
FTIR results (Fig. 3), the extra XRD peaks most
likely originate from hydrated carbonate phase(s),
although no matches could be found with any metal
carbonate or hydrated phases listed in standard XRD
data files. For samples heated at C550 C, no extra
XRD peaks were detected. Hence the hydrated
carbonate phase(s), indicated in the FTIR patterns,
were present at a level below the XRD detection limit(a few wt%), or present in an amorphous form.
The XRD pattern of the 650950 C samples
showed splitting of some peaks, e.g. the pair of
closely spaced peaks at *22 2h and also the peaks
at *46 2h. The Na0.5K0.5NbO3 phase is known to
be orthorhombic at room temperature (Tennery and
Hang 1968). Initial crystallisation occurred at 450 C,
but peaks in this sample, and the 550 C sample,
were broad and no clear peak splitting was observed.
The patterns for the 650950 C samples in Fig. 4
exhibited peak splitting, although continued peakbroadening made it difficult to resolve closely spaced
peaks.
A variation in the relative intensity of certain
peaks was observed in the temperature range 650
950 C. For alkali niobates, the relative intensity of
pairs of peaks at*22 2h and*45 2h (Fig. 4) can
be indicative of variations in the proportions of
orthorhombic and tetragonal phases. For single-phase
orthorhombic samples, the peak intensity ratio a may
be expressed as a = (I110/I001 ? I220/I002)/2, with a
value ofa = 1.8, whilst for a tetragonal NKN-based
composition, a * 0.5 (Skidmore and Milne 2007).
The a values for the 850 and 950 C samples were
only slightly lower than the expected value for an
orthorhombic phase (Skidmore and Milne 2007), with
experimental values of 1.5 and 1.4 for the 850 and
950 C samples, respectively. Therefore, crystallisa-
tion to predominantly orthorhombic NKN phase is
indicated to occur on heating the precursor gels toC850 C. However, the peak ratio displayed by the
650 and 750 C samples, a * 1, suggests that a
significant amount of tetragonal phase may co-exist
with the orthorhombic phase at intermediate temper-
atures. The tetragonal phase of NKN is
thermodynamically stable above *200 C. Its pres-
ence in a metastable form in the 650 and 750 C
samples could be due to particle size effects.
Compositional non-uniformities in the samples may
also affect peak intensities at intermediate decompo-
sition temperatures.Estimated values of unit cell lattice parameters
were obtained using a least squares refinement
programme, giving values of: a = 5.660 A, b =
5.655 A and c = 3.946 A (calculated for a sample
decomposed at 850 C) with standard deviations of
B0.001 A. These values compare to a = 5.695 A,
b = 5.721 A and c = 3.974 A for a standard ortho-
rhombic NKN pattern (JCPDS, Joint Committee for
Powder Diffraction file number 32-0822).
10 20 30 40 50 60
(022)/(202)
(112)
(131)/(311)
(130)/(221)
(220)
(020)/(200)/(111)(002)
(001)
***
Intensity
(arb.units)
2 (degree)
9500C
8500C
7500C
6500C
5500C
4500C
3500C
(110)
(001
)
(110) (020)/(200)/(111) (2
2
0)
(002)
(130)/
(221)
(1
12)
(131)/(311)
(022)/(202)
Fig. 4 X-ray diffraction
plots for sodium potassium
niobate (NKN) powders
heated at various
temperatures; the *
symbol depicts the extra
phases in the 450 C
sample. The 850 and
950 C patterns are indexed
on the basis of an
orthorhombic system (Joint
Committee for Powder
Diffraction File no. 32-
0822)
J Nanopart Res (2010) 12:209215 213
123
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
6/7
Figure 5 shows TEM images of the NKN pow-ders after heat treatments at 500950 C. As
expected, the particles are much smaller than those
produced by conventional mixed-oxide processing
(Bomlai et al. 2007). The 500 C micrograph
(Fig. 5a) shows most of the primary particles to be
\50 nm in size, but many of the individual primary
particles were clustered into agglomerates. Similar
particle sizes occurred in the 625 C sample,
Fig. 5b. Raising the temperature to 700 C produced
a large increment in size, with particle sizes
increasing to B170 nm, Fig. 5c. Particles up to*250 nm in size were present in the 950 C sample
(Fig. 5d). BET measurements indicated a surface
area of*11.5 m2/g for a powder decomposed at
550 C, decreasing to *2.4 m2/g for a 950 C
sample. Due at least in part to agglomeration
effects, the equivalent spherical diameters calculated
from these values of measured surface areas were
approximately twice the size of the primary particles
observed directly using TEM.
Conclusions
Thermal analysis and FTIR studies indicated that
Na0.5K0.5NbO3 (NKN) precursor gels made from an
ethoxide-based solgel route decomposed to produce
a NKN hydrated carbonate phase at process temper-
atures up to 850 C. There was also some evidence
that hydrated carbonate phases secondary phases
were produced by reaction of the NKN powders with
atmospheric moisture and carbon dioxide. The NKN
particle sizes varied from \50 nm in samples
decomposed at 500 C, to\250 nm for the highesttemperature studied, 950 C. The absence of second-
ary phases formed on exposure to air in powders
produced at 950 C is consistent with their increased
particle size and lower surface area.
References
Bomlai P, Wichianrat P, Muensit S, Milne SJ (2007) Effect of
calcination conditions and excess alkali carbonate on the
Fig. 5 TEM micrographs
of the sodium potassium
niobate (NKN) powders
obtained by heating the
precursor gel at a 500 C,
b 625 C, c 700 C and
d 950 C
214 J Nanopart Res (2010) 12:209215
123
7/30/2019 Nano-powders of Na0.5K0.5NbO3 made by a solgel method
7/7
phase formation and particle morphology of
Na0.5K0.5NbO3 powders. J Am Ceram Soc 90:16501655.
doi:10.1111/j.1551-2916.2007.01629.x
Busca G, Lorenzelli V (1982) Infrared spectroscopic identifi-
cation of species arising from reactive adsorption of
carbon oxides on metal oxide surfaces. Mater Chem 7:89
126. doi:10.1016/0390-6035(82)90059-1
Cheng Z, Ozawa K, Osada M, Miyazaki A, Kimura H (2006)
Low-temperature synthesis of NaNbO3 nanopowders and
their thin films from a novel carbon-free precursor. J Am
Ceram Soc 89:11881192. doi:10.1111/j.1551-2916.2005.
00857.x
Chowdhury A, Thompson PR, Milne SJ (2008) TGA-FTIR
study of a lead zirconate titanate gel made from a triol-
based solgel system. Thermochim Acta 475:5964.
doi:10.1016/j.tca.2008.06.009
Egerton L, Dillon DM (1959) Piezoelectric and dielectric
properties of ceramics in the system of potassium-sodium
niobate. J Am Ceram Soc 42:438442. doi:10.1111/
j.1151-2916.1959.tb12971.x
Franco RCR, Camargo ER, Nobre MAL, Leite ER, Longo E,
Varela JA (1999) Dielectric properties of Na1-xLixNbO3ceramics from powders obtained by chemical synthesis.
Ceram Int 25:455460. doi:10.1016/S0272-8842(98)
00054-6
Guo Y, Kakimoto K-I, Ohsato H (2005) (Na0.5K0.5)NbO3-Li-
TaO3 lead-free piezoelectric ceramics. Mater Lett 59:241.
doi:10.1016/j.matlet.2004.07.057
Haertling GH (1967) Properties of hot-pressed ferroelectric
alkali niobate ceramics. J Am Ceram Soc 50:329330.doi:10.1111/j.1151-2916.1967.tb15121.x
Jaeger RE, Egerton L (1962) Hot pressing of potassium sodium
niobates. J Am Ceram Soc 45:209213. doi:10.1111/
j.1151-2916.1962.tb11127.x
Nobre MAL, Longo E, Leite ER, Varela JA (1996) Synthesis
and sintering of ultrafine NaNbO3 powder by use of
polymeric precursors. Mater Lett 28:215220.
doi:10.1016/0167-577X(96)00062-6
Rojac T, Kosec M, Segedin P, Malic B, Holc J (2006) The
formation of a carbonato complex during the mechano-
chemical treatment of a Na2CO3-Nb2O5 mixture. Solid
State Ion 177:29872995. doi:10.1016/j.ssi.2006.08.001
Saito Y, Takao H, Tani T, Nonoyama T, Takatori K, Homma
T, Nagaya T, Nakamura M (2004) Lead-free piezoce-
ramics. Nature 432:8487. doi:10.1038/nature03028
Shirane G, Newnham R, Pepinsky R (1954) Dielectric prop-
erties and phase transitions of NaNbO3 and (Na, K)NbO3.
Phys Rev 96:581588. doi:10.1103/PhysRev.96.581
Skidmore TA, Milne SJ (2007) Phase development during
mixed-oxide processing of a [Na0.5K0.5NbO3]1-x-[Li-
TaO3]x powder. J Mater Res 22:22652272. doi:10.1557/
jmr.2007.0281
Smart L, Moore E (1996) Solid state chemistry: an introduc-tion, 2nd edn. Chapman and Hall, London
Socrates G (2001) Infrared and Raman characteristic group
frequencies: tables and charts. Wiley, Chichester
Tennery VJ, Hang KW (1968) Thermal and X-ray diffraction
studies of the sodium niobate(V)-potassium niobate(V)
system. J Appl Phys 39:47494753. doi:10.1063/
1.1655833
Williams DH, Fleming I (1990) Spectroscopic methods inorganic chemistry. McGraw-Hill, London
J Nanopart Res (2010) 12:209215 215
123
http://dx.doi.org/10.1111/j.1551-2916.2007.01629.xhttp://dx.doi.org/10.1016/0390-6035(82)90059-1http://dx.doi.org/10.1111/j.1551-2916.2005.00857.xhttp://dx.doi.org/10.1111/j.1551-2916.2005.00857.xhttp://dx.doi.org/10.1016/j.tca.2008.06.009http://dx.doi.org/10.1111/j.1151-2916.1959.tb12971.xhttp://dx.doi.org/10.1111/j.1151-2916.1959.tb12971.xhttp://dx.doi.org/10.1016/S0272-8842(98)00054-6http://dx.doi.org/10.1016/S0272-8842(98)00054-6http://dx.doi.org/10.1016/j.matlet.2004.07.057http://dx.doi.org/10.1111/j.1151-2916.1967.tb15121.xhttp://dx.doi.org/10.1111/j.1151-2916.1962.tb11127.xhttp://dx.doi.org/10.1111/j.1151-2916.1962.tb11127.xhttp://dx.doi.org/10.1016/0167-577X(96)00062-6http://dx.doi.org/10.1016/j.ssi.2006.08.001http://dx.doi.org/10.1038/nature03028http://dx.doi.org/10.1103/PhysRev.96.581http://dx.doi.org/10.1557/jmr.2007.0281http://dx.doi.org/10.1557/jmr.2007.0281http://dx.doi.org/10.1063/1.1655833http://dx.doi.org/10.1063/1.1655833http://dx.doi.org/10.1063/1.1655833http://dx.doi.org/10.1063/1.1655833http://dx.doi.org/10.1557/jmr.2007.0281http://dx.doi.org/10.1557/jmr.2007.0281http://dx.doi.org/10.1103/PhysRev.96.581http://dx.doi.org/10.1038/nature03028http://dx.doi.org/10.1016/j.ssi.2006.08.001http://dx.doi.org/10.1016/0167-577X(96)00062-6http://dx.doi.org/10.1111/j.1151-2916.1962.tb11127.xhttp://dx.doi.org/10.1111/j.1151-2916.1962.tb11127.xhttp://dx.doi.org/10.1111/j.1151-2916.1967.tb15121.xhttp://dx.doi.org/10.1016/j.matlet.2004.07.057http://dx.doi.org/10.1016/S0272-8842(98)00054-6http://dx.doi.org/10.1016/S0272-8842(98)00054-6http://dx.doi.org/10.1111/j.1151-2916.1959.tb12971.xhttp://dx.doi.org/10.1111/j.1151-2916.1959.tb12971.xhttp://dx.doi.org/10.1016/j.tca.2008.06.009http://dx.doi.org/10.1111/j.1551-2916.2005.00857.xhttp://dx.doi.org/10.1111/j.1551-2916.2005.00857.xhttp://dx.doi.org/10.1016/0390-6035(82)90059-1http://dx.doi.org/10.1111/j.1551-2916.2007.01629.x