J. Am. Ceram. Soc., 97 [4] 1143–1150 (2014)
DOI: 10.1111/jace.12757
© 2013 The American Ceramic Society
Journal
Optical Properties and van der Waals–London Dispersion Interactions in
Berlinite Aluminum Phosphate from Vacuum Ultraviolet Spectroscopy
Daniel M. Dryden,‡ Guolong L. Tan,§ and Roger H. French‡,†
‡
Department of Materials Science and Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland, Ohio 44118
§
Wuhan University of Technology, 122 Luoshi Road, Wuhan, Hubei 430070, China
close structural similarities between AlPO4 and SiO2 at ambient pressure, a close correspondence in interband transition
optical behavior may be expected.
Inorganic phosphates are usually large band gap materials which have been previously investigated as hosts for
phosphors.26–28 The large band gap is thought to be associated with the large energy gap between the bonding and
antibonding states of the phosphate groups; that is, excitations across the band gap involve electronic states most
closely associated with the PO3
groups. A number of
4
phosphate phosphors with the form RPO4:R′3+ (R = Y, La,
Gd, and Lu; R′ = Eu, Gd, and Sm) were studied, and the
host sensitization bands and absorption band edges lay in a
narrow energy range of 7.75 and 8.61 eV in spite of differing R ions and crystal structures,27 suggesting that the
absorption edge arises from optical transitions associated
with the phosphate groups common to all these materials,
with the crystal structure and choice of cation causing only
minor variation.26,28
Theoretical studies of the electronic and structural properties of AlPO4, using either semiempirical29 and first-principles30,31 methods, are somewhat sparse in the literature. The
energy bands of berlinite calculated from the first-principles
method30,31 are similar to a-quartz.32
Phosphate complex anions are present in a wide range
of critical biological materials, including the phosphatesugar backbone of DNA,19,33 hydroxyapatite and other
related apatites,18 adenosine triphosphate,34,35 phospholipids,20 and DNA-CNT hybrid organic–inorganic systems.36
There is, however, a paucity of research on the electronic
stucture, optical properties, and long-range vdW–Ld interactions in spite of the enormous body of work concerning
their biological functions. Given the importance of phosphate ions in determining the electronic structure of inorganic phosphates, it is plausible that phosphate groups
play a similarly significant role in the electronic structure
of the biological materials and systems in which they are
present.
Optical spectra of berlinite AlPO4 in the visible, ultraviolet, and vacuum ultraviolet (VUV) as well as the resulting
complex optical properties n and k, e′ and e″, and interband
transition strength Jcv are the focus of this study. These
results are used to calculate the van der Waals–London
dispersion contribution to long-range interactions, elucidating the role of phosphate anions in nano- and mesoscale
science.
The interband optical properties of single-crystal berlinite
AlPO4 have been investigated in the vacuum ultraviolet (VUV)
range using VUV spectroscopy and spectroscopic ellipsometry.
The complex optical properties were directly determined from
0.8 to 45 eV. Band gap energies, index of refraction and complex dielectric functions, oscillator index sum rule, and energy
loss functions were calculated through Kramers–Kronig transformation. Direct and indirect band gap energies of AlPO4
over the absorption coefficient range of 33–11 000 cm – 1 are
8.06 and 7.89 eV, respectively. The index of refraction at
2 eV, nvis, is 1.51. The interband transition features at 10.4,
11.4, 14.2, 16.2, 17.3, 21, 22.5, 24.5, and 31 eV were indexed
and correlated with the electronic structure of AlPO4. Strong
similarities were observed between AlPO4 and its structural
isomorph SiO2 in the exciton and interband transitions, resulting from the similarity of their constituent tetrahedra and the
strong electron localization therein. The London dispersion
spectrum for AlPO4 was calculated, and the Hamaker
coefficients for AlPO4 with various interlayers were calculated
using the Lifshitz method. These results elucidate the role
of phosphate complex anions on the electronic structure and
van der Waals forces in important organic and inorganic
systems.
I.
U
Introduction
the behavior and design of nano- and
mesoscale systems requires a detailed knowledge of
long-range interactions, including electrostatic, polar, and
van der Waals–London dispersion (vdW–Ld) forces. Of
these, only vdW–Ld interactions are universally present, and
they are intimately linked to the material’s electronic structure and optical properties.1,2 In our previous work, vdW–Ld
forces were investigated in a range of materials.2–8 There is
interest in the interband optical properties of and vdW–Ld
forces in AlPO4 due to its structural and optical similarity to
SiO2,9 its application in battery10,11 and LED12 cathodes, as
a mesoporous glass13,14 for molecular sieves15 and laser
dyes,16,17 and because of the important role the phosphate
complex ion plays in biological materials.18–20
Several oxides with the composition ABO4 form structures
isomorphic to SiO2 allotropes quartz, tridymite, and cristobalite,21
including BPO4, AlPO4, FePO4, GaPO4, BaSO4, and
AlAsO4. The AlPO4 allotrope berlinite is isomorphic to
a-quartz(D43 ) and undergoes the same temperature-induced
a–b transition as quartz near 850 K.22–25 In light of these
NDERSTANDING
II.
Experimental Methods
(1) Sample Preparation
The basal plane single-crystal sample of AlPO4, obtained
from Shannon,37–42 was analyzed using X-ray diffractometry
(SMART Diffractometer; Bruker AXS, Karlsruhe, Germany)
and the widely accepted unit cell parameters were confirmed.21 The surface was mechanically polished on both
W.-Y. Ching—contributing editor
Manuscript No. 33732. Received August 30, 2013; approved November 3, 2013.
†
Author to whom correspondence should be addressed. e-mail: roger.french@case.edu
1143
1144
faces with 0.25-lm diamond polish, and subsequently chemically polished to remove surface damage.43
(2) Spectroscopic Ellipsometry
Spectroscopic ellipsometry (VUV-VASE; J.A. Woollam Co.,
Lincoln, NE) was performed over a spectral range of
0.69–8.55 eV, with a spot diameter at the sample of 2 mm at
normal incidence. Measurements were conducted using light
incident on the front surface of the sample at an incident
angle of 60°, 70°, and 80° relative to the surface normal.
Measurements of sample transmission were also used to
reduce the influence of surface roughness and increase the
overall accuracy of the modeling. These parameters were
analyzed using the Fresnel equations,44 which are 1D solutions to the Maxwell equations, using a linear least-squares
fit to determine the material’s optical constants.
(3) VUV-LPLS Spectroscopy
Vacuum ultraviolet reflectance spectroscopy3,4 for electronic
structure studies of materials has the advantage of covering
the complete energy range of the valence interband transitions.45 The VUV-LPLS reflectometer used here includes an
unpolarized laser plasma light source, monochromator, and
filters; the details of its construction are discussed elsewhere.8,46 The energy range of the instrument is from 1.7 to
44 eV (700–28 nm), which extends far beyond the air cutoff
of 6 eV and the window cutoff of 10 eV. The energy resolution of the instrument is from 16 meV at 10 eV to 200 meV
at 35 eV. The reflectance spectra are then scaled using leastsquares fitting to the reflectance results determined from
ellipsometric modeling.
(4) Kramers–Kronig Analysis of VUV Reflectance
The Kramers–Kronig transform was used to recover the
reflected phase from the reflectance data, according to:
hðEÞ ¼
2E
P
p
Z
0
1
ln qðE 0 Þ
dE 0
E0 2 E2
(1)
where P is the Cauchy principal value and q(E) is the
reflected amplitude (not to be confused with the measured
reflectance, given by |q(E)|2).3,47 The complex reflectance is
given by:
n 1 ik
~
RðEÞ ¼ qðEÞeihðEÞ ¼
n þ 1 ik
(2)
Because the integral in the Kramers–Kronig transform spans
energies from 0 to ∞, the reflectance spectrum must be augmented by extending the reflectance data outside the VUV
experimental range by fitting low- and high-energy wings.3
Once the complex reflectance has been determined, the
complex index of refraction ð^
n ¼ n þ ikÞ is then calculated
algebraically from Eq. (2). The dielectric function is related
by the expression e′ + i e″ = (n + ik)2.
The complex interband transition strength Jcv was calculated according to:
Jcv ¼ i
Vol. 97, No. 4
Journal of the American Ceramic Society—Dryden et al.
E2 0
ðe þ ie 00 Þ
8p2
The analysis of the spectra was performed using electronic
structure tools (EST).† The effective number of electrons per
cubic centimeter, neff, contributing to interband transitions
up to energy E is calculated using the oscillator strength, or
f-sum, rule,50 evaluated for Jcv as:
neff ðEÞ ¼
4
m0
Z
E
0
J 0 cv ðE 0 Þ 0
m0
dE ¼
E0
2p2 h2 e2
Z
E
E 0 e 00 ðE 0 ÞdE 0
0
(4)
The reported results for f-sum rule calculations are converted
to electrons per AlPO4 formula unit, using a formula unit
volume of 0.078 nm3.
(5) Determination of van der Waals–London Dispersion
Interactions and Hamaker Coefficients
Once optical properties and electronic structure of bulk crystalline AlPO4 were determined, the full spectral Hamaker
coefficient51 of the vdW–Ld interaction was calculated using
the Lifshitz quantum electrodynamic method, described in
detail elsewhere.1,52,53 This requires a Kramers–Kronig transform to recover the London dispersion spectrum e(iξ):
eðinÞ ¼ 1 þ
2
p
Z
0
1
xe00 ðxÞ
dðxÞ
x2 þ n2
(5)
whereas e(x) describes the material’s response to an externally applied electromagnetic oscillation, e(iξ) through the
fluctuation-dissipation theorem describes the response of the
material to spontaneous, intrinsic fluctuations at a frequency
ξ which according to the Lifshitz theory determine the vdW–
Ld behavior of the material.1 For the case of two semiinfinite
half-spaces of material 1 which are separated from each
other by one unique intervening material 2 of thickness l (cf.
Fig. 1)—referred to as the three-layer (121) configuration—
the Hamaker coefficient, A121, determines the magnitude of
the van der Waals force between the two half-spaces. In a
three-layer (121) system, the center material shields the
attraction of the two half-spaces of material 1. The Hamaker
coefficient is at a maximum for a vacuum interlayer, and is
zero when material 2 is identical to material 1. In a (123)
system, wherein the semiinfinite half-spaces consist of different
materials, the value of the Hamaker coefficient may be interpreted as the favorability of wetting of the interlayer on the
surface of material 1. A negative Hamaker coefficient implies
good wetting, whereas a positive Hamaker coefficient suggests that wetting is unfavorable. In our previous work, this
model has been generalized to 99 layers.48,54 Hamaker coefficients may also be calculated for anisotropic cylinders such
as carbon nanotubes55 and other geometries5 using the
Gecko hamaker56 open-source software program, which
includes a database of optical spectra.
(3)
which corresponds to the joint density of states, and is
proportional to the optical transition probability.
The bulk energy loss function (ELF) is given by ℑ[1/e
(E)], whereas the surface ELF is ℑ[1/(e(E) + 1)]. The bulk
ELF is identical to the ELF recovered through electron
energy loss spectroscopy, another commonly used technique
for electronic structure analysis of ceramics.48,49
Fig. 1. Schematic drawing of a three-layer (123) configuration of
semiinfinite half-spaces with an interlayer film.
†
EST consists of a number of programs for the quantitative analysis of optical,
VUV, and electron energy loss spectroscopy (EELS) spectra. It has been developed
under Grams, a PC-based spectroscopy environment. EST is available from Deconvolution and Entropy Consulting, Ithaca, NY, or www.deconvolution.com.
April 2014
1145
Optical Properties and vdW-Ld in AlPO4
III.
Results
Calculated values of n and k from spectroscopic ellipsometry
are shown in Fig. 2. The reflectance spectrum of berlinite
AlPO4 is shown in Fig. 3, with results calculated from ellipsometry overlaid in gray. Figure 4 shows the calculated spectra for n and k, and Fig. 5 shows the complex dielectric
function. The real part of the interband transition strength
J0cv is shown in red in Fig. 6; spectra for quartz and amorphous SiO2 are shown for comparison. Table I reports the
energies of the main interband transition features for all
three spectra in Fig. 6, along with the initial and final energy
bands responsible for each respective feature. Figure 7 shows
the bulk and surface ELFs, indicating a strong plasmon resonance at 23.7 eV.
The effective number of electrons per formula unit participating in interband transitions at energies less than or equal
to the photon energy E, based on the oscillator sum rule
given in Eq. (4), is displayed in Fig. 8 which shows the oscillator strength sum rule for AlPO4 in units of electrons per
formula unit, and Fig. 9 shows the London dispersion spectrum e(iξ) for AlPO4. Table II gives the Hamaker coefficients
for different three-layer (121) and (123) configurations of
berlinite AlPO4 with other materials, along with similar
configurations involving SiO2 for comparison.
Fig. 2. Complex index of refraction n^ ¼ n þ ik of AlPO4 modeled
from spectroscopic ellipsometry results.
Fig. 4. Complex index of refraction n^ ¼ n þ ik of AlPO4 from
VUV-LPLS spectroscopy, via Kramers–Kronig transform, where n is
shown in gray and k in black. Results calculated from spectroscopic
ellipsometry are overlaid in gray.
Fig. 5. Complex dielectric constant ^e ¼ e0 þ ie00 of berlinite AlPO4,
where the real part of the dielectric constant e′ is shown in black and
the imaginary part e″ is shown in gray. Results from spectroscopic
ellipsometry are overlaid in gray.
IV.
Discussion
(1) Optical Properties of Berlinite AlPO4
Berlinite AlPO4 belongs to a class of isostructural compounds which crystallize, at room temperature, in the trigonal phase (space group P3221), adopting structures made up
of tetrahedra. It is the SiO4 and PO4 tetrahedral units that
compose the similar structural units for SiO2 and AlPO4
respectively, and which determine their respective electronic
structures and optical properties.57
The complex index of refraction, n + ik, is shown in
Fig. 4. The visible range (2 eV) index of refraction, nvis, of
berlinite was determined to be 1.51, compared to 1.53 for
quartz SiO2 and 1.45 for amorphous SiO2, in good agreement with literature values.38 Both berlinite AlPO4 and
quartz SiO2 have similar theoretical densities (2.62 and 2.66
g/cm3, respectively),58 and as expected, the denser of the two
materials exhibits a higher nvis.
Fig. 3. Reflectance of berlinite AlPO4 from VUV-LPLS
spectroscopy. Calculated reflectance from spectroscopic ellipsometry
is overlaid in gray.
(2) Band Gap Energies
Direct and indirect band gap energies were determined using
linear fits in the region of the absorption edge to plots of
1146
Vol. 97, No. 4
Journal of the American Ceramic Society—Dryden et al.
Fig. 6. Real part of the interband transition strength ℜ[JCV] of
berlinite AlPO4, z-cut quartz SiO2, and Suprasil amorphous SiO2, as
determined from Kramers–Kronig analysis of VUV reflectance data.
AlPO4 is shown in red, quartz SiO2 is shown in blue, and
amorphous SiO2 is shown in navy.
a2E2 and a1/2, respectively, where a is the absorption coefficient in units of cm1.6 The values of the direct and indirect
band gaps in berlinite AlPO4 were determined to be, within
an optical absorption coefficient range of 33–11 000 cm1,
8.06 and 7.89 eV, respectively. For comparison, quartz SiO2
fitted by this same method had a larger direct gap energy of
8.3 eV.6
(3) Origin of Interband Transition Features
The reflectance spectrum shown in Fig. 3 is a directly measurable property that can be used to calculate all related
optical properties via Kramers–Kronig transform, but the
features in the interband transition strength (Jcv) spectrum
(Fig. 6) correspond directly to the energies of allowed excitations among the energy bands of the material (whereas the
reflectance peaks are shifted from these transition energies
due to the dispersion indicated by the index n). The critical
point features in the Jcv spectra of berlinite AlPO4, quartz
SiO2, and amorphous SiO2, as well as their correlations, are
reported in Table I. Many of the peaks for AlPO4 line up
perfectly with those reported in both quartz and amorphous
SiO2,6 and vary only in intensity. The features at 10.3, 11.4,
14.2, and 17.3 eV are similar across all three phases, and
agree qualitatively with other reported optical transitions for
silica.57,59 Quartz and berlinite also share the same electronic
structure and have very similar band diagrams.26,29,30,60
Table I.
Fig. 7. Bulk energy loss function (ELF), ℑ[1/e(E)], of berlinite
AlPO4, showing a strong plasmon resonance at 23.7 eV. The surface
ELF is also shown.
Tight-binding band structure calculations have given similar
density of states (DOS) for AlPO4 and SiO2 crystals as
well,29,30 which are consistent with X-ray photoemission
valence band spectra.29 These similarities in DOS and band
structure carry-over directly to the optical properties, most
clearly in evidence in the optically excited interband transitions.27 Therefore, each interband transition peak in the
VUV spectrum of berlinite AlPO4 could be indexed and
referenced to that of SiO2, and subsequently explained in a
similar way as that used in SiO2.29,57,59,61–70
Many of the features in these spectra may also be seen in
amorphous SiO2,6 most notably those at 10.4, 11.6, 14.03,
and 17.3 eV, suggesting that these features are not dependent
solely on the long-range crystalline structure of the material,
but instead on the similarity in the tetrahedral units that
make up the solid. Although amorphous SiO2 is a networked
solid that lacks this long-range order, the O–Si–O and Si–O–
Si bond angles within the tetrahedra do not differ strongly,
on average, from those seen in quartz SiO2.57,71 The orbital
overlaps are essentially unaffected, resulting in an electronic
structure and subsequently VUV optical properties that are
almost identical to that of quartz; only the minor differences
seen, such as peak broadening or missing features at high
energies, can be ascribed to local variations in bond angles
and the lack of long-range order.6 By virtue of berlinite
AlPO4 sharing many of these same interband transitions, the
long-range order in berlinite AlPO4 can only play a limited
role in the behavior of the material. The PO4 tetrahedral
units must themselves be responsible for these features,
regardless of the long-range crystalline structure of the
material.
Interband Transition Strength ℜ(JCV) Features for Berlinite ALPO4, z-cut Quartz SiO2, and Amorphous SiO2
ℜ(JCV) feature energies [eV]
AlPO4
10.3
11.4
14.2
–
17.3
–
20.9
22.5
24.4
28
32
a-SiO2
10.4
11.6
14.03
16.2
17.3
20.1
21.3
22.6
–
27.5
32
a-SiO2
10.4
11.6
14.03
–
17.3
–
21.3
21.5
–
–
–
Bands involved
59,61–64
Exciton state
Valence band at 12.9 eV to conduction band edge57,65–67
Valence band to exciton57,65,66,68
–
Valence band to exciton57,65,66,68
–
Valence band to exciton68
Valence band to exciton67,68
O 2s, P 3s to exciton69,70
O 2s to exciton68
O 2s to conduction band68
April 2014
Optical Properties and vdW-Ld in AlPO4
1147
at energies at or below 44 eV. It is expected that the remaining interband oscillator strength has been spread to interband transition energies above 44 eV, as seen in many other
materials,3,4,6,49,54,72 and the curve would rise further until it
saturates at the expected value of 32 electrons.50
Fig. 8.
Fig. 9.
Oscillator strength sum rule of AlPO4.
London dispersion spectrum e(iξ) for AlPO4.
(4) Oscillator Strength Sum Rule
The expected value of the oscillator strength sum rule for
AlPO4 is 32 electrons per formula unit, consisting of 2 Al 3s
electrons, 1 Al 3p electron, 16 O 2p electrons, 8 O 2s electrons, 2 P 3s electrons, and 3 P 3p electrons. The oscillator
strength sum rule for AlPO4, as calculated from its interband
transition strength spectrum, is shown in Fig. 8, indicating
that 19 electrons per formula unit participate in transitions
(5) van der Waals–London Dispersion Forces with AlPO4
The physical geometry considered for these Hamaker coefficient calculations consists of two semiinfinite half-spaces separated by an interlayer medium. Both half-spaces and the
interlayer medium may consist of any material, or vacuum.
Fully retarded Hamaker coefficients are calculated as a function of the separation of the two semiinfinite half-spaces—or,
equivalently, as the thickness of the interlayer medium—and
take into account retardation effects that result from the
finite speed of light.1 For any structure where the interlayer
has different physical properties and electronic structure from
the surrounding materials, the Hamaker coefficient can
become appreciable.
Table II shows the Hamaker coefficients A121 and A123 of
different physical configurations with berlinite AlPO4 and
quartz SiO2 (c-SiO2) as their main components, evaluated at
interlayer spacing of 0.2 nm, that is, on the order of an interatomic bond length.
The Hamaker coefficients for (AlPO4–vacuum–AlPO4) and
(c-SiO2–vacuum–c-SiO2) are 87.5 and 93.9 zJ, respectively;
this difference of 7.3% is notable, given that the visible range
index of refraction nvis of AlPO4 is only marginally lower
than that of SiO2. (1.51 and 1.52, respectively, or only
0.7%). However, the optical mismatch between the halfspaces and interlayer that determines the magnitude of the
Hamaker coefficient must be evaluated not only in the visible
range, but at all allowed Matsubara frequencies in the materials: the apparent discrepancy is eliminated when the properties of the materials at higher energies are taken into
account. Figure 6 shows that the JCV for crystalline SiO2 is
significantly greater than that of AlPO4 at energies above
15 eV, and this additional oscillator strength contributes to
greater optical mismatch at higher energy Matsubara
frequencies, leading to the notable difference in Hamaker
coefficients. These results underscore the importance of considering a wide range of energies at which to evaluate optical
properties when considering vdW–Ld interactions.
Although the optical mismatch between AlPO4 and c-SiO2
becomes greater at high energies, it is still relatively small;
when a structure of (AlPO4–c-SiO2–AlPO4) is considered, the
Hamaker coefficient almost vanishes. Switching the interlayer
and half-space media does not change the Hamaker coefficient, as the optical mismatch at each interface remains
unchanged. The lower density of amorphous SiO2 (a-SiO2)
compared to AlPO4 or c-SiO2 results in larger Hamaker coefficients of 0.99 and 1.84 zJ, respectively, for the geometries
NR
Table II. Hamaker Coefficients ANR
121 or A123 For Three-Layer (121) and (123) Systems with SiO2 or AlPO4. Low-and HighEnergy Power-Law Wings were Attached to Spectra with Powers of a = 2 and b = 3, Respectively, with a Low-Energy Cutoff of
8.75 eV for Al2O3, and 0 eV for all Other Materials. Spectra for Crystalline SiO2 are from Z-cut Quartz
Physical geometry
A121 (zJ)
A121 (zJ)
Physical geometry
87.50
0.13
0.99
15.57
22.85
14.59
93.90
0.13
1.84
12.90
19.83
17.47
(c-SiO2|vacuum|c-SiO2)
(c-SiO2|AlPO4|c-SiO2)
(c-SiO2|a-SiO2|c-SiO2)
(c-SiO2|Al2O3|c-SiO2)
(c-SiO2|Si3N4|c-SiO2)
(c-SiO2|water|c-SiO2)
Physical geometry
A123 (zJ)
A123 (zJ)
Physical geometry
(AlPO4|Al2O3|vacuum)
(Al2O3|AlPO4|vacuum)
50.55
36.41
45.96
34.30
(c-SiO2|Al2O3|vacuum)
(Al2O3|c-SiO2|vacuum)
(AlPO4|vacuum|AlPO4)
(AlPO4|c-SiO2|AlPO4)
(AlPO4|a-SiO2|AlPO4)
(AlPO4|Al2O3|AlPO4)
(AlPO4|Si3N4|AlPO4)
(AlPO4|water|AlPO4)
1148
Vol. 97, No. 4
Journal of the American Ceramic Society—Dryden et al.
(AlPO4–a-SiO2–AlPO4) and (c-SiO2–a-SiO2–c-SiO2). Considering an interlayer with an electronic structure and optical
properties that differ considerably from those of AlPO4 or
c-SiO2 results in a considerably higher Hamaker coefficient,
as demonstrated when interlayers of Al2O3, Si3N4, or water
are considered. For these materials, values of A121 range
from 12.9 zJ for (c-SiO2–Al2O3–c-SiO2) to 22.85 zJ for
(AlPO4–Si3N4–AlPO4). Even the smallest of these values is
two orders of magnitude larger than the Hamaker coefficient
for (AlPO4–c-SiO2–AlPO4) of 0.13 zJ.
A useful application for (123) configurations is to model
the wetting of one material on the surface on another; that
is, to have one half-space consist of air, thus resulting in a
system consisting of a thin film of one material on the surface of a bulk substrate. This may result in the wetting condition where the Hamaker coefficient becomes negative,
corresponding to a net repulsion between the air and the substrate, or equivalently the favorability of wetting of the film
on the substrate (as eliminating the large optical mismatch of
the substrate–air interface reduces the system’s free energy).
In general, negative Hamaker coefficients are seen in stepwise
increasing
or
decreasing
index
systems
wherein
nsubstrate > nfilm > nair. This is seen in the systems (Al2O3–cSiO2–air) and (Al2O3–AlPO4–air), which give A123 values of
34.3 and 36.4 zJ, respectively. Both AlPO4 and c-SiO2
have an nvis between that of Al2O3 (nvis = 1.75) and air
(nvis = 1), and as expected, this stepwise index system gives
negative Hamaker coefficients, indicating that the vdW–Ld
forces in the system will contribute toward good wetting.
When the materials of the substrate and film are switched,
large positive Hamaker coefficients are seen: (AlPO4–Al2O3–
air) gives 50.55 zJ and (c-SiO2–Al2O3–air) gives 45.96 zJ,
indicating that neither AlPO4 nor SiO2 have vdW–Ld forces
that favor wetting on Al2O3 substrates, although c-SiO2 is
slightly less averse to wetting than AlPO4.
(6) Implications for PO4 Anions in Biological Materials
Mishra et al. observed, over a wide range of metal phosphates, that the phosphate group was more influential in
the electronic structure than the respective cations.26,28 Electrons are highly localized within the PO4 group, and the
molecular orbitals resulting from O–P bonds dominate the
density of states in both the valence and conduction band,
as confirmed by first-principles calculations.31 This large
electron localization and large availability of allowed
transitions leads to this marked influence of the phosphate
group on interband optical properties, regardless of the surrounding environment. For this reason, it is likely that the
phosphate groups present in organic molecules like DNA,
phospholipids, or hydroxyapatite would play a strong role
in the electronic structure and optical properties of these
systems, and therefore be highly influential in the van der
Waals forces present as well. Unfortunately, little work has
been done to directly determine the wide-range optical or
electronic properties of these systems. Rulis et al.18 reported
ab initio electronic structure and optical properties for a
range of apatites X2Ca10(PO4)6, where X = (OH, F, Cl,
Br). Much like AlPO4, the density of states around the
band gap was dominated by the phosphate group, and
the complex dielectric permittivity was almost invariant with
the selection of cation. The apatites also showed a characteristic density of transitions within the 10–15 eV range,
which could be ascribed to the influence of the PO4 group,
as in AlPO4.
The electronic structure of DNA is a subject of much
interest for applications in nanostructures and electronics,5,73–81 but full spectral optical properties and van der
Waals calculations are not available. Gervasio et al.19 noted the
importance of the phosphate groups in the backbone in their
interactions with the water molecules surrounding a strand
of Z-DNA. Furthermore, ab initio calculations indicated that
phosphate groups were responsible, along with Na+ counterions, for the states defining the bottom of the conduction
band in the modeled z-(GC)6 oligonucleotide. More recently,
Shapir et al.33 used scanning tunnelling spectroscopy to
directly determine the Density of States of a single doublehelix strand of DNA, and compared these results with a
DFT calculation. The calculated and experimental results
were in good agreement with each other, although the
authors suggested that a midband peak due to the Na+
should also be expected. Shapir’s results showed a larger
band gap than Gervasio’s, but otherwise showed similar
trends in the origin of the density of states, with the valence
band edge defined by the base pairs, and the conduction
band edge defined by the Na+ counterions. Shapir did not
specifically discuss the influence of the phosphate backbone
on the reported results, but the data reported were nonetheless in good agreement with Gervasio. Further research is
clearly needed to elucidate the role of the phosphate ion in
DNA, and to differentiate between phosphate and counterion
effects.
Even fewer results are reported on influence of the phosphate ions in the structure of phospholipids. Mashaghi
et al.20 confirmed that charge density in a phospholipid was
concentrated at the phosphate end, but did not report any
other features of the electronic structure, density of states, or
optical properties. The role of van der Waals forces is known
to be critical in the alignment of the phospholipid tails, and
these forces have been measured experimentally.82,83 Full
spectral optical properties and van der Waals calculations for
these systems would prove invaluable in verifying experimental results, but are not currently available.
V.
Conclusion
Kramers–Kronig dispersion analysis of reflectance data is
critical in accurately determining the VUV optical properties
of a material. By combining spectroscopic ellipsometry and
VUV-LPLS reflectometry, highly accurate quantitative optical properties over a wide range of energies have been determined for berlinite AlPO4 from 0.8 to 45 eV. Besides the
VUV reflectance and dielectric constants, the complex index
of refraction, interband transition strength, oscillator
strength sum rule, ELF, and London dispersion spectrum
have also been reported. Berlinite AlPO4 shares most common interband transition peaks with quartz SiO2 as previously reported at 10.4, 11.6, 14.03, and 17.10 eV. The
similarity in optical properties arises from their similar structural units—PO4 and SiO4 tetrahedra, respectively—which
form the similar crystal structure and energy band structure.
Three special interband transition peaks were discovered for
AlPO4 at 21.52, 24.5, and 32 eV, which are not observed in
the quartz SiO2 spectrum. The London dispersion spectrum
and Hamaker coefficients for multiple layered configurations
involving AlPO4 have also been reported, and the results
compared to similar systems involving quartz SiO2. The
Hamaker coefficient for (AlPO4|vacuum|AlPO4) was smaller
than that of (SiO2|vacuum|SiO2), but by less than visible
range optical properties alone would suggest. Various configurations of A123 were also examined to determine the wetting
effects in systems involving AlPO4. The bulk plasma peak in
the ELF spectra derived from the VUV optical spectra is
observed at 25.3 eV for AlPO4, which is at the same position
as in SiO2. The differences in the berlinite AlPO4 and quartz
SiO2 spectra above 20 eV can be explained by the doubling
of the unit cell length for AlPO4 and the difference in orbital
overlap due to the differences in elements and their bond
lengths. The dominance of the phosphate complex ion in
determining electronic structure points to its possible influence in the electronic and optical behavior of organic and
biological phosphates, as demonstrated clearly in a range of
apatites, and consistent with findings for DNA and phospholipids.
April 2014
Optical Properties and vdW-Ld in AlPO4
Acknowledgments
We are grateful to Dr. L. K. Denoyer for software development and M. K.
Yang for help with the spectroscopy. This work was funded by DOE-BESDMSE-BMM under award DE-SC0008068.
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