Optical Properties and Van Der Waals-London Dispersion

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J. Am. Ceram. Soc., 97 [4] 1143–1150 (2014) DOI: 10.1111/jace.12757 © Journal 2013 The American Ceramic Society 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

The interband optical properties of single-crystal berlinite close structural similarities between AlPO4 and SiO2 at ambi- AlPO4 have been investigated in the vacuum ultraviolet (VUV) ent pressure, a close correspondence in interband transition range using VUV spectroscopy and spectroscopic ellipsometry. optical behavior may be expected. The complex optical properties were directly determined from Inorganic phosphates are usually large band gap materi- 0.8 to 45 eV. Band gap energies, index of refraction and com- als which have been previously investigated as hosts for plex dielectric functions, oscillator index sum rule, and energy phosphors.26–28 The large band gap is thought to be associ- loss functions were calculated through Kramers–Kronig trans- ated with the large energy gap between the bonding and formation. Direct and indirect band gap energies of AlPO4 antibonding states of the phosphate groups; that is, excita- over the absorption coefficient range of 33–11 000 cm – 1 are tions across the band gap involve electronic states most 3 8.06 and 7.89 eV, respectively. The index of refraction at closely associated with the PO4 groups. A number of 3+ 2 eV, nvis, is 1.51. The interband transition features at 10.4, phosphate phosphors with the form RPO4:R′ (R = Y, La, 11.4, 14.2, 16.2, 17.3, 21, 22.5, 24.5, and 31 eV were indexed Gd, and Lu; R′ = Eu, Gd, and Sm) were studied, and the and correlated with the electronic structure of AlPO4. Strong host sensitization bands and absorption band edges lay in a similarities were observed between AlPO4 and its structural narrow energy range of 7.75 and 8.61 eV in spite of differ- 27 isomorph SiO2 in the exciton and interband transitions, resulting R ions and crystal structures, suggesting that the ing from the similarity of their constituent tetrahedra and the absorption edge arises from optical transitions associated strong electron localization therein. The London dispersion with the phosphate groups common to all these materials, spectrum for AlPO4 was calculated, and the Hamaker with the crystal structure and choice of cation causing only 26,28 coefficients for AlPO4 with various interlayers were calculated minor variation. using the Lifshitz method. These results elucidate the role Theoretical studies of the electronic and structural proper- 29 of phosphate complex anions on the electronic structure and ties of AlPO4, using either semiempirical and first-princi- van der Waals forces in important organic and inorganic ples30,31 methods, are somewhat sparse in the literature. The systems. 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 phosphate- 19,33 I. Introduction sugar backbone of DNA, hydroxyapatite and other related apatites,18 adenosine triphosphate,34,35 phospholip- NDERSTANDING the behavior and design of nano- and ids,20 and DNA-CNT hybrid organic–inorganic systems.36 U mesoscale systems requires a detailed knowledge of There is, however, a paucity of research on the electronic long-range interactions, including electrostatic, polar, and stucture, optical properties, and long-range vdW–Ld inter- van der Waals–London dispersion (vdW–Ld) forces. Of – actions in spite of the enormous body of work concerning these, only vdW Ld interactions are universally present, and their biological functions. Given the importance of phos- they are intimately linked to the material’s electronic struc- phate ions in determining the electronic structure of inor- 1,2 – ture and optical properties. In our previous work, vdW Ld ganic phosphates, it is plausible that phosphate groups forces were investigated in a range of materials.2–8 There is – play a similarly significant role in the electronic structure interest in the interband optical properties of and vdW Ld of the biological materials and systems in which they are forces in AlPO4 due to its structural and optical similarity to 9 10,11 12 present. SiO2, its application in battery and LED cathodes, as Optical spectra of berlinite AlPO in the visible, ultravio- a mesoporous glass13,14 for molecular sieves15 and laser 4 16,17 let, and vacuum ultraviolet (VUV) as well as the resulting dyes, and because of the important role the phosphate complex optical properties n and k, e′ and e″, and interband complex ion plays in biological materials.18–20 transition strength Jcv are the focus of this study. These Several oxides with the composition ABO4 form structures – 21 results are used to calculate the van der Waals London isomorphic to SiO2 allotropes quartz, tridymite, and cristobalite, dispersion contribution to long-range interactions, elucidat- including BPO4, AlPO4, FePO4, GaPO4, BaSO4, and ing the role of phosphate anions in nano- and mesoscale AlAsO4. The AlPO4 allotrope berlinite is isomorphic to science. a 4 -quartz(D3) and undergoes the same temperature-induced a–b transition as quartz near 850 K.22–25 In light of these II. Experimental Methods (1) Sample Preparation W.-Y. Ching—contributing editor 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 con- Manuscript No. 33732. Received August 30, 2013; approved November 3, 2013. 21 †Author to whom correspondence should be addressed. e-mail: [email protected] firmed. The surface was mechanically polished on both 1143 1144 Journal of the American Ceramic Society—Dryden et al. Vol. 97, No. 4 faces with 0.25-lm diamond polish, and subsequently chemi- The analysis of the spectra was performed using electronic cally polished to remove surface damage.43 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 50 (2) Spectroscopic Ellipsometry f-sum, rule, evaluated for Jcv as: Spectroscopic ellipsometry (VUV-VASE; J.A. Woollam Co., Z Z Lincoln, NE) was performed over a spectral range of E 0 0 E 4 J cvðE Þ 0 m0 0 00 0 0 0.69–8.55 eV, with a spot diameter at the sample of 2 mm at neffðEÞ¼ dE ¼ E e ðE ÞdE m E0 p22 2 normal incidence. Measurements were conducted using light 0 0 2 h e 0 incident on the front surface of the sample at an incident (4) angle of 60°,70°, and 80° relative to the surface normal. Measurements of sample transmission were also used to The reported results for f-sum rule calculations are converted reduce the influence of surface roughness and increase the to electrons per AlPO4 formula unit, using a formula unit overall accuracy of the modeling. These parameters were volume of 0.078 nm3. analyzed using the Fresnel equations,44 which are 1D solu- tions to the Maxwell equations, using a linear least-squares fit to determine the material’s optical constants. (5) Determination of van der Waals–London Dispersion Interactions and Hamaker Coefficients Once optical properties and electronic structure of bulk crys- (3) VUV-LPLS Spectroscopy talline AlPO4 were determined, the full spectral Hamaker Vacuum ultraviolet reflectance spectroscopy3,4 for electronic coefficient51 of the vdW–Ld interaction was calculated using structure studies of materials has the advantage of covering the Lifshitz quantum electrodynamic method, described in the complete energy range of the valence interband transi- detail elsewhere.1,52,53 This requires a Kramers–Kronig trans- tions.45 The VUV-LPLS reflectometer used here includes an form to recover the London dispersion spectrum e(iξ): unpolarized laser plasma light source, monochromator, and Z filters; the details of its construction are discussed else- 2 1 xe00ðxÞ where.8,46 The energy range of the instrument is from 1.7 to eðinÞ¼1 þ dðÞx (5) p x2 þ n2 44 eV (700–28 nm), which extends far beyond the air cutoff 0 of 6 eV and the window cutoff of 10 eV. The energy resolu- tion of the instrument is from 16 meV at 10 eV to 200 meV whereas e(x) describes the material’s response to an exter- at 35 eV. The reflectance spectra are then scaled using least- nally applied electromagnetic oscillation, e(iξ) through the squares fitting to the reflectance results determined from fluctuation-dissipation theorem describes the response of the ellipsometric modeling. 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 (4) Kramers–Kronig Analysis of VUV Reflectance half-spaces of material 1 which are separated from each The Kramers–Kronig transform was used to recover the other by one unique intervening material 2 of thickness l (cf. reflected phase from the reflectance data, according to: Fig. 1)—referred to as the three-layer (121) configuration— the Hamaker coefficient, A121, determines the magnitude of Z 1 0 2E ln qðE Þ 0 the van der Waals force between the two half-spaces. In a hðEÞ¼ P dE (1) three-layer (121) system, the center material shields the p E02 E2 0 attraction of the two half-spaces of material 1. The Hamaker coefficient is at a maximum for a vacuum interlayer, and is where P is the Cauchy principal value and q(E) is the zero when material 2 is identical to material 1. In a (123) reflected amplitude (not to be confused with the measured system, wherein the semiinfinite half-spaces consist of different reflectance, given by |q(E)|2).3,47 The complex reflectance is materials, the value of the Hamaker coefficient may be inter- given by: preted as the favorability of wetting of the interlayer on the surface of material 1. A negative Hamaker coefficient implies n 1 ik ~RðEÞ¼qðEÞeihðEÞ ¼ (2) good wetting, whereas a positive Hamaker coefficient sug- n þ 1 ik gests that wetting is unfavorable. In our previous work, this model has been generalized to 99 layers.48,54 Hamaker coeffi- – Because the integral in the Kramers Kronig transform spans cients may also be calculated for anisotropic cylinders such ∞ 55 5 energies from 0 to , the reflectance spectrum must be aug- as carbon nanotubes and other geometries using the mented by extending the reflectance data outside the VUV 56 3 Gecko hamaker open-source software program, which experimental range by fitting low- and high-energy wings. includes a database of optical spectra. Once the complex reflectance has been determined, the complex index of refraction ðn^ 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:

E2 J ¼ i ðe0 þ ie 00Þ (3) cv 8p2 which corresponds to the joint density of states, and is Fig. 1. Schematic drawing of a three-layer (123) configuration of proportional to the optical transition probability. semiinfinite half-spaces with an interlayer film. 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 †EST consists of a number of programs for the quantitative analysis of optical, energy loss spectroscopy, another commonly used technique VUV, and electron energy loss spectroscopy (EELS) spectra. It has been developed 48,49 under Grams, a PC-based spectroscopy environment. EST is available from Deconvolu- for electronic structure analysis of ceramics. tion and Entropy Consulting, Ithaca, NY, or www.deconvolution.com. April 2014 Optical Properties and vdW-Ld in AlPO4 1145

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 0 Jcv 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 partici- pating 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 Fig. 4. Complex index of refraction n^ ¼ n þ ik of AlPO4 from formula unit, and Fig. 9 shows the London dispersion spec- VUV-LPLS spectroscopy, via Kramers–Kronig transform, where n is e ξ trum (i ) for AlPO4. Table II gives the Hamaker coefficients shown in gray and k in black. Results calculated from spectroscopic for different three-layer (121) and (123) configurations of ellipsometry are overlaid in gray. berlinite AlPO4 with other materials, along with similar configurations involving SiO2 for comparison.

^ 0 00 Fig. 5. Complex dielectric constant e ¼ e þ ie 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 ^ ¼ þ Fig. 2. Complex index of refraction n n ik of AlPO4 modeled ellipsometry are overlaid in gray. from spectroscopic ellipsometry results.

IV. Discussion

(1) Optical Properties of Berlinite AlPO4 Berlinite AlPO4 belongs to a class of isostructural com- pounds which crystallize, at room temperature, in the trigo- nal 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 agree- 38 ment with literature values. 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 (2) Band Gap Energies spectroscopy. Calculated reflectance from spectroscopic ellipsometry Direct and indirect band gap energies were determined using is overlaid in gray. linear fits in the region of the absorption edge to plots of 1146 Journal of the American Ceramic Society—Dryden et al. Vol. 97, No. 4

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 Fig. 6. Real part of the interband transition strength ℜ[JCV]of ELF is also shown. 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 Tight-binding band structure calculations have given similar amorphous SiO2 is shown in navy. 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 a2E2 and a1/2, respectively, where a is the absorption coeffi- structure carry-over directly to the optical properties, most cient in units of cm 1.6 The values of the direct and indirect clearly in evidence in the optically excited interband transi- 27 band gaps in berlinite AlPO4 were determined to be, within tions. Therefore, each interband transition peak in the – 1 an optical absorption coefficient range of 33 11 000 cm , VUV spectrum of berlinite AlPO4 could be indexed and 8.06 and 7.89 eV, respectively. For comparison, quartz SiO2 referenced to that of SiO2, and subsequently explained in a 29,57,59,61–70 fitted by this same method had a larger direct gap energy of similar way as that used in SiO2. 8.3 eV.6 Many of the features in these spectra may also be seen in 6 amorphous SiO2, most notably those at 10.4, 11.6, 14.03, and 17.3 eV, suggesting that these features are not dependent (3) Origin of Interband Transition Features solely on the long-range crystalline structure of the material, The reflectance spectrum shown in Fig. 3 is a directly mea- but instead on the similarity in the tetrahedral units that surable property that can be used to calculate all related make up the solid. Although amorphous SiO2 is a networked optical properties via Kramers–Kronig transform, but the solid that lacks this long-range order, the O–Si–O and Si–O– features in the interband transition strength (Jcv) spectrum Si bond angles within the tetrahedra do not differ strongly, 57,71 (Fig. 6) correspond directly to the energies of allowed excita- on average, from those seen in quartz SiO2. The orbital tions among the energy bands of the material (whereas the overlaps are essentially unaffected, resulting in an electronic reflectance peaks are shifted from these transition energies structure and subsequently VUV optical properties that are due to the dispersion indicated by the index n). The critical almost identical to that of quartz; only the minor differences point features in the Jcv spectra of berlinite AlPO4, quartz seen, such as peak broadening or missing features at high SiO2, and amorphous SiO2, as well as their correlations, are energies, can be ascribed to local variations in bond angles 6 reported in Table I. Many of the peaks for AlPO4 line up and the lack of long-range order. By virtue of berlinite perfectly with those reported in both quartz and amorphous AlPO4 sharing many of these same interband transitions, the 6 SiO2, and vary only in intensity. The features at 10.3, 11.4, long-range order in berlinite AlPO4 can only play a limited 14.2, and 17.3 eV are similar across all three phases, and role in the behavior of the material. The PO4 tetrahedral agree qualitatively with other reported optical transitions for units must themselves be responsible for these features, silica.57,59 Quartz and berlinite also share the same electronic regardless of the long-range crystalline structure of the structure and have very similar band diagrams.26,29,30,60 material.

Table I. Interband Transition Strength ℜ(JCV) Features for Berlinite ALPO4, z-cut Quartz SiO2, and Amorphous SiO2

ℜ(JCV) feature energies [eV]

AlPO4 a-SiO2 a-SiO2 Bands involved 10.3 10.4 10.4 Exciton state59,61–64 11.4 11.6 11.6 Valence band at 12.9 eV to conduction band edge57,65–67 14.2 14.03 14.03 Valence band to exciton57,65,66,68 – 16.2 –– 17.3 17.3 17.3 Valence band to exciton57,65,66,68 – 20.1 –– 20.9 21.3 21.3 Valence band to exciton68 22.5 22.6 21.5 Valence band to exciton67,68 24.4 ––O2s,P3s to exciton69,70 28 27.5 – O2s to exciton68 32 32 – O2s 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 remain- ing 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

(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 Fig. 8. Oscillator strength sum rule of AlPO4. 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 half- spaces 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 Fig. 9. London dispersion spectrum e(iξ) for AlPO . coefficients. These results underscore the importance of con- 4 sidering 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 (4) Oscillator Strength Sum Rule becomes greater at high energies, it is still relatively small; The expected value of the oscillator strength sum rule for when a structure of (AlPO4–c-SiO2–AlPO4) is considered, the AlPO4 is 32 electrons per formula unit, consisting of 2 Al 3s Hamaker coefficient almost vanishes. Switching the interlayer electrons, 1 Al 3p electron, 16 O 2p electrons, 8 O 2s elec- and half-space media does not change the Hamaker coeffi- trons, 2 P 3s electrons, and 3 P 3p electrons. The oscillator cient, as the optical mismatch at each interface remains strength sum rule for AlPO , as calculated from its interband 4 unchanged. The lower density of amorphous SiO2 (a-SiO2) transition strength spectrum, is shown in Fig. 8, indicating compared to AlPO4 or c-SiO2 results in larger Hamaker coef- that 19 electrons per formula unit participate in transitions ficients of 0.99 and 1.84 zJ, respectively, for the geometries

NR NR Table II. Hamaker Coeﬃcients A121 or A123 For Three-Layer (121) and (123) Systems with SiO2 or AlPO4. Low-and High- Energy 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

Physical geometry A123 (zJ) A123 (zJ) Physical geometry

+ (AlPO4–a-SiO2–AlPO4) and (c-SiO2–a-SiO2–c-SiO2). Consid- phosphate groups were responsible, along with Na counte- ering an interlayer with an electronic structure and optical rions, for the states defining the bottom of the conduction properties that differ considerably from those of AlPO4 or band in the modeled z-(GC)6 oligonucleotide. More recently, 33 c-SiO2 results in a considerably higher Hamaker coefficient, Shapir et al. used scanning tunnelling spectroscopy to as demonstrated when interlayers of Al2O3,Si3N4, or water directly determine the Density of States of a single double- are considered. For these materials, values of A121 range helix strand of DNA, and compared these results with a from 12.9 zJ for (c-SiO2–Al2O3–c-SiO2) to 22.85 zJ for DFT calculation. The calculated and experimental results (AlPO4–Si3N4–AlPO4). Even the smallest of these values is were in good agreement with each other, although the two orders of magnitude larger than the Hamaker coefficient authors suggested that a midband peak due to the Na+ for (AlPO4–c-SiO2–AlPO4) of 0.13 zJ. should also be expected. Shapir’s results showed a larger A useful application for (123) configurations is to model band gap than Gervasio’s, but otherwise showed similar the wetting of one material on the surface on another; that trends in the origin of the density of states, with the valence is, to have one half-space consist of air, thus resulting in a band edge defined by the base pairs, and the conduction system consisting of a thin film of one material on the sur- band edge defined by the Na+ counterions. Shapir did not face of a bulk substrate. This may result in the wetting con- specifically discuss the influence of the phosphate backbone dition where the Hamaker coefficient becomes negative, on the reported results, but the data reported were nonethe- corresponding to a net repulsion between the air and the sub- less in good agreement with Gervasio. Further research is strate, or equivalently the favorability of wetting of the film clearly needed to elucidate the role of the phosphate ion in on the substrate (as eliminating the large optical mismatch of DNA, and to differentiate between phosphate and counterion the substrate–air interface reduces the system’s free energy). effects. In general, negative Hamaker coefficients are seen in stepwise Even fewer results are reported on influence of the phos- increasing or decreasing index systems wherein phate ions in the structure of phospholipids. Mashaghi 20 nsubstrate > nfilm > nair. This is seen in the systems (Al2O3–c- et al. confirmed that charge density in a phospholipid was SiO2–air) and (Al2O3–AlPO4–air), which give A123 values of concentrated at the phosphate end, but did not report any 34.3 and 36.4 zJ, respectively. Both AlPO4 and c-SiO2 other features of the electronic structure, density of states, or have an nvis between that of Al2O3 (nvis = 1.75) and air optical properties. The role of van der Waals forces is known (nvis = 1), and as expected, this stepwise index system gives to be critical in the alignment of the phospholipid tails, and negative Hamaker coefficients, indicating that the vdW–Ld these forces have been measured experimentally.82,83 Full forces in the system will contribute toward good wetting. spectral optical properties and van der Waals calculations for When the materials of the substrate and film are switched, these systems would prove invaluable in verifying experimen- large positive Hamaker coefficients are seen: (AlPO4–Al2O3– tal results, but are not currently available. air) gives 50.55 zJ and (c-SiO2–Al2O3–air) gives 45.96 zJ, indicating that neither AlPO nor SiO have vdW–Ld forces 4 2 V. Conclusion that favor wetting on Al2O3 substrates, although c-SiO2 is slightly less averse to wetting than AlPO4. Kramers–Kronig dispersion analysis of reflectance data is critical in accurately determining the VUV optical properties of a material. By combining spectroscopic ellipsometry and (6) Implications for PO4 Anions in Biological Materials VUV-LPLS reflectometry, highly accurate quantitative opti- Mishra et al. observed, over a wide range of metal phos- cal properties over a wide range of energies have been deter- phates, that the phosphate group was more influential in mined for berlinite AlPO4 from 0.8 to 45 eV. Besides the the electronic structure than the respective cations.26,28 Elec- VUV reflectance and dielectric constants, the complex index trons are highly localized within the PO4 group, and the of refraction, interband transition strength, oscillator molecular orbitals resulting from O–P bonds dominate the strength sum rule, ELF, and London dispersion spectrum density of states in both the valence and conduction band, have also been reported. Berlinite AlPO4 shares most com- 31 as confirmed by first-principles calculations. This large mon interband transition peaks with quartz SiO2 as previ- electron localization and large availability of allowed ously reported at 10.4, 11.6, 14.03, and 17.10 eV. The transitions leads to this marked influence of the phosphate similarity in optical properties arises from their similar struc- group on interband optical properties, regardless of the sur- tural units—PO4 and SiO4 tetrahedra, respectively—which rounding environment. For this reason, it is likely that the form the similar crystal structure and energy band structure. phosphate groups present in organic molecules like DNA, Three special interband transition peaks were discovered for phospholipids, or hydroxyapatite would play a strong role AlPO4 at 21.52, 24.5, and 32 eV, which are not observed in in the electronic structure and optical properties of these the quartz SiO2 spectrum. The London dispersion spectrum systems, and therefore be highly influential in the van der and Hamaker coefficients for multiple layered configurations Waals forces present as well. Unfortunately, little work has involving AlPO4 have also been reported, and the results been done to directly determine the wide-range optical or compared to similar systems involving quartz SiO2. The 18 electronic properties of these systems. Rulis et al. reported Hamaker coefficient for (AlPO4|vacuum|AlPO4) was smaller ab initio electronic structure and optical properties for a than that of (SiO2|vacuum|SiO2), but by less than visible range of apatites X2Ca10(PO4)6, where X = (OH ,F,Cl, range optical properties alone would suggest. Various config- Br ). Much like AlPO4, the density of states around the urations of A123 were also examined to determine the wetting band gap was dominated by the phosphate group, and effects in systems involving AlPO4. The bulk plasma peak in the complex dielectric permittivity was almost invariant with the ELF spectra derived from the VUV optical spectra is the selection of cation. The apatites also showed a charac- observed at 25.3 eV for AlPO4, which is at the same position teristic density of transitions within the 10–15 eV range, as in SiO2. The differences in the berlinite AlPO4 and quartz which could be ascribed to the influence of the PO4 group, SiO2 spectra above 20 eV can be explained by the doubling as in AlPO4. of the unit cell length for AlPO4 and the difference in orbital The electronic structure of DNA is a subject of much overlap due to the differences in elements and their bond interest for applications in nanostructures and electron- lengths. The dominance of the phosphate complex ion in ics,5,73–81 but full spectral optical properties and van der determining electronic structure points to its possible influ- Waals calculations are not available. Gervasio et al.19 noted the ence in the electronic and optical behavior of organic and importance of the phosphate groups in the backbone in their biological phosphates, as demonstrated clearly in a range of interactions with the water molecules surrounding a strand apatites, and consistent with findings for DNA and phospho- of Z-DNA. Furthermore, ab initio calculations indicated that lipids. April 2014 Optical Properties and vdW-Ld in AlPO4 1149

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