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1 Journal J. Am. Ceram. Soc., 97 [4] (2014) DOI: /jace 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, Euclid Ave., Cleveland, Ohio Wuhan University of Technology, 122 Luoshi Road, Wuhan, Hubei , China The interband optical properties of single-crystal berlinite AlPO 4 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 AlPO 4 over the absorption coefficient range of cm 1 are 8.06 and 7.89 ev, respectively. The index of refraction at 2 ev, n vis, is 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 AlPO 4. Strong similarities were observed between AlPO 4 and its structural isomorph SiO 2 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 AlPO 4 was calculated, and the Hamaker coefficients for AlPO 4 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. Introduction UNDERSTANDING 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 AlPO 4 due to its structural and optical similarity to SiO 2, 9 its application in battery 10,11 and LED 12 cathodes, as a mesoporous glass 13,14 for molecular sieves 15 and laser dyes, 16,17 and because of the important role the phosphate complex ion plays in biological materials Several oxides with the composition ABO 4 form structures isomorphic to SiO 2 allotropes quartz, tridymite, and cristobalite, 21 including BPO 4, AlPO 4, FePO 4, GaPO 4, BaSO 4, and AlAsO 4. The AlPO 4 allotrope berlinite is isomorphic to a-quartz(d 4 3 ) and undergoes the same temperature-induced a b transition as quartz near 850 K In light of these W.-Y. Ching contributing editor Manuscript No Received August 30, 2013; approved November 3, Author to whom correspondence should be addressed. roger.french@case.edu close structural similarities between AlPO 4 and SiO 2 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 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 PO 3 4 groups. A number of phosphate phosphors with the form RPO 4 :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 AlPO 4, using either semiempirical 29 and first-principles 30,31 methods, are somewhat sparse in the literature. The energy bands of berlinite calculated from the first-principles method 30,31 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 AlPO 4 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 J cv 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. II. Experimental Methods (1) Sample Preparation The basal plane single-crystal sample of AlPO 4, obtained from Shannon, 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 1143

2 1144 Journal of the American Ceramic Society Dryden et al. Vol. 97, No. 4 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 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 spectroscopy 3,4 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 ( 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 Z 1 p P ln qðe 0 Þ E 02 E de 0 (1) 2 0 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: R~ðEÞ ¼qðEÞe ihðeþ ¼ n 1 ik n þ 1 ik 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 J cv was calculated according to: (2) The analysis of the spectra was performed using electronic structure tools (EST). The effective number of electrons per cubic centimeter, n eff, contributing to interband transitions up to energy E is calculated using the oscillator strength, or f-sum, rule, 50 evaluated for J cv as: n eff ðeþ ¼ 4 m 0 Z E 0 J 0 cvðe 0 Þ E 0 de 0 ¼ m 0 2p 2 h 2 e 2 Z E 0 E 0 e 00 ðe 0 ÞdE 0 The reported results for f-sum rule calculations are converted to electrons per AlPO 4 formula unit, using a formula unit volume of nm 3. (5) Determination of van der Waals London Dispersion Interactions and Hamaker Coefficients Once optical properties and electronic structure of bulk crystalline AlPO 4 were determined, the full spectral Hamaker coefficient 51 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 ¼1 þ 2 p Z 1 0 (4) xe 00 ðxþ x 2 þ n 2 dðxþ (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, A 121, 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 nanotubes 55 and other geometries 5 using the Gecko hamaker 56 open-source software program, which includes a database of optical spectra. J cv ¼ i E2 8p 2 ðe0 þ ie 00 Þ (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

3 April 2014 Optical Properties and vdw-ld in AlPO III. Results Calculated values of n and k from spectroscopic ellipsometry are shown in Fig. 2. The reflectance spectrum of berlinite AlPO 4 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 J 0 cv is shown in red in Fig. 6; spectra for quartz and amorphous SiO 2 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 AlPO 4 in units of electrons per formula unit, and Fig. 9 shows the London dispersion spectrum e(iξ) for AlPO 4. Table II gives the Hamaker coefficients for different three-layer (121) and (123) configurations of berlinite AlPO 4 with other materials, along with similar configurations involving SiO 2 for comparison. Fig. 4. Complex index of refraction ^n ¼ n þ ik of AlPO 4 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. 2. Complex index of refraction ^n ¼ n þ ik of AlPO 4 modeled from spectroscopic ellipsometry results. Fig. 5. Complex dielectric constant ^e ¼ e 0 þ ie 00 of berlinite AlPO 4, 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 AlPO 4 Berlinite AlPO 4 belongs to a class of isostructural compounds which crystallize, at room temperature, in the trigonal phase (space group P3 2 21), adopting structures made up of tetrahedra. It is the SiO 4 and PO 4 tetrahedral units that compose the similar structural units for SiO 2 and AlPO 4 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, n vis,of berlinite was determined to be 1.51, compared to 1.53 for quartz SiO 2 and 1.45 for amorphous SiO 2, in good agreement with literature values. 38 Both berlinite AlPO 4 and quartz SiO 2 have similar theoretical densities (2.62 and 2.66 g/cm 3, respectively), 58 and as expected, the denser of the two materials exhibits a higher n vis. Fig. 3. Reflectance of berlinite AlPO 4 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

4 1146 Journal of the American Ceramic Society Dryden et al. Vol. 97, No. 4 Fig. 6. Real part of the interband transition strength R[J CV ] of berlinite AlPO 4, z-cut quartz SiO 2, and Suprasil amorphous SiO 2,as determined from Kramers Kronig analysis of VUV reflectance data. AlPO 4 is shown in red, quartz SiO 2 is shown in blue, and amorphous SiO 2 is shown in navy. a 2 E 2 and a 1/2, respectively, where a is the absorption coefficient in units of cm 1. 6 The values of the direct and indirect band gaps in berlinite AlPO 4 were determined to be, within an optical absorption coefficient range of cm 1, 8.06 and 7.89 ev, respectively. For comparison, quartz SiO 2 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 (J cv ) 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 J cv spectra of berlinite AlPO 4, quartz SiO 2, and amorphous SiO 2, as well as their correlations, are reported in Table I. Many of the peaks for AlPO 4 line up perfectly with those reported in both quartz and amorphous SiO 2, 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 Fig. 7. Bulk energy loss function (ELF), I[ 1/e(E)], of berlinite AlPO 4, 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 AlPO 4 and SiO 2 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 AlPO 4 could be indexed and referenced to that of SiO 2, and subsequently explained in a similar way as that used in SiO 2. 29,57,59,61 70 Many of the features in these spectra may also be seen in amorphous SiO 2, 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 SiO 2 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 SiO 2. 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 AlPO 4 sharing many of these same interband transitions, the long-range order in berlinite AlPO 4 can only play a limited role in the behavior of the material. The PO 4 tetrahedral units must themselves be responsible for these features, regardless of the long-range crystalline structure of the material. Table I. Interband Transition Strength R(J CV ) Features for Berlinite ALPO 4, z-cut Quartz SiO 2, and Amorphous SiO 2 R(J CV ) feature energies [ev] AlPO 4 a-sio 2 a-sio 2 Bands involved Exciton state 59, Valence band at 12.9 ev to conduction band edge 57, Valence band to exciton 57,65,66, Valence band to exciton 57,65,66, Valence band to exciton Valence band to exciton 67, O2s, P3s to exciton 69, O2s to exciton O2s to conduction band 68

5 April 2014 Optical Properties and vdw-ld in AlPO 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. Oscillator strength sum rule of AlPO 4. Fig. 9. London dispersion spectrum e(iξ) for AlPO 4. (4) Oscillator Strength Sum Rule The expected value of the oscillator strength sum rule for AlPO 4 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 AlPO 4, 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 AlPO 4 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 A 121 and A 123 of different physical configurations with berlinite AlPO 4 and quartz SiO 2 (c-sio 2 ) 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 (AlPO 4 vacuum AlPO 4 ) and (c-sio 2 vacuum c-sio 2 ) are 87.5 and 93.9 zj, respectively; this difference of 7.3% is notable, given that the visible range index of refraction n vis of AlPO 4 is only marginally lower than that of SiO 2. (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 J CV for crystalline SiO 2 is significantly greater than that of AlPO 4 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 AlPO 4 and c-sio 2 becomes greater at high energies, it is still relatively small; when a structure of (AlPO 4 c-sio 2 AlPO 4 ) 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 SiO 2 (a-sio 2 ) compared to AlPO 4 or c-sio 2 results in larger Hamaker coefficients of 0.99 and 1.84 zj, respectively, for the geometries Table II. Hamaker Coefficients A NR 121 or ANR 123 For Three-Layer (121) and (123) Systems with SiO 2 or AlPO 4. 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 Al 2 O 3, and 0 ev for all Other Materials. Spectra for Crystalline SiO 2 are from Z-cut Quartz Physical geometry A 121 (zj) A 121 (zj) Physical geometry (AlPO 4 vacuum AlPO 4 ) (c-sio 2 vacuum c-sio 2 ) (AlPO 4 c-sio 2 AlPO 4 ) (c-sio 2 AlPO 4 c-sio 2 ) (AlPO 4 a-sio 2 AlPO 4 ) (c-sio 2 a-sio 2 c-sio 2 ) (AlPO 4 Al 2 O 3 AlPO 4 ) (c-sio 2 Al 2 O 3 c-sio 2 ) (AlPO 4 Si 3 N 4 AlPO 4 ) (c-sio 2 Si 3 N 4 c-sio 2 ) (AlPO 4 water AlPO 4 ) (c-sio 2 water c-sio 2 ) Physical geometry A 123 (zj) A 123 (zj) Physical geometry (AlPO 4 Al 2 O 3 vacuum) (c-sio 2 Al 2 O 3 vacuum) (Al 2 O 3 AlPO 4 vacuum) (Al 2 O 3 c-sio 2 vacuum)

6 1148 Journal of the American Ceramic Society Dryden et al. Vol. 97, No. 4 (AlPO 4 a-sio 2 AlPO 4 ) and (c-sio 2 a-sio 2 c-sio 2 ). Considering an interlayer with an electronic structure and optical properties that differ considerably from those of AlPO 4 or c-sio 2 results in a considerably higher Hamaker coefficient, as demonstrated when interlayers of Al 2 O 3,Si 3 N 4, or water are considered. For these materials, values of A 121 range from 12.9 zj for (c-sio 2 Al 2 O 3 c-sio 2 ) to zj for (AlPO 4 Si 3 N 4 AlPO 4 ). Even the smallest of these values is two orders of magnitude larger than the Hamaker coefficient for (AlPO 4 c-sio 2 AlPO 4 ) 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 n substrate > n film > n air. This is seen in the systems (Al 2 O 3 c- SiO 2 air) and (Al 2 O 3 AlPO 4 air), which give A 123 values of 34.3 and 36.4 zj, respectively. Both AlPO 4 and c-sio 2 have an n vis between that of Al 2 O 3 (n vis = 1.75) and air (n vis = 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: (AlPO 4 Al 2 O 3 air) gives zj and (c-sio 2 Al 2 O 3 air) gives zj, indicating that neither AlPO 4 nor SiO 2 have vdw Ld forces that favor wetting on Al 2 O 3 substrates, although c-sio 2 is slightly less averse to wetting than AlPO 4. (6) Implications for PO 4 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 PO 4 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 X 2 Ca 10 (PO 4 ) 6, where X = (OH,F,Cl, Br ). Much like AlPO 4, 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 ev range, which could be ascribed to the influence of the PO 4 group, as in AlPO 4. 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 AlPO 4 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 AlPO 4 shares most common interband transition peaks with quartz SiO 2 as previously reported at 10.4, 11.6, 14.03, and ev. The similarity in optical properties arises from their similar structural units PO 4 and SiO 4 tetrahedra, respectively which form the similar crystal structure and energy band structure. Three special interband transition peaks were discovered for AlPO 4 at 21.52, 24.5, and 32 ev, which are not observed in the quartz SiO 2 spectrum. The London dispersion spectrum and Hamaker coefficients for multiple layered configurations involving AlPO 4 have also been reported, and the results compared to similar systems involving quartz SiO 2. The Hamaker coefficient for (AlPO 4 vacuum AlPO 4 ) was smaller than that of (SiO 2 vacuum SiO 2 ), but by less than visible range optical properties alone would suggest. Various configurations of A 123 were also examined to determine the wetting effects in systems involving AlPO 4. The bulk plasma peak in the ELF spectra derived from the VUV optical spectra is observed at 25.3 ev for AlPO 4, which is at the same position as in SiO 2. The differences in the berlinite AlPO 4 and quartz SiO 2 spectra above 20 ev can be explained by the doubling of the unit cell length for AlPO 4 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.

7 April 2014 Optical Properties and vdw-ld in AlPO 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-BES- DMSE-BMM under award DE-SC References 1 V. A. Parsegian, Van Der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists. Cambridge University Press, New York, NY, R. H. French, Origins and Applications of London Dispersion Forces and Hamaker Constants in Ceramics, J. Am. Ceram. Soc., 83 [9] (2000). 3 D. J. Jones, R. H. French, H. M ullejans, S. Loughin, A. D. Dorneich, and P. F. Carcia, Optical Properties of AlN Determined by Vacuum Ultraviolet Spectroscopy and Spectroscopic Ellipsometry Data, J. Mater. Res., 14 [11] (1999). 4 R. H. French, Electronic Band Structure of Al 2 O 3, With Comparison to AlON and AlN, J. Am. Ceram. Soc., 73 [3] (1990). 5 R. H. French, V. A. Parsegian, R. Podgornik, R. F. Rajter, A. Jagota, J. Luo, D. Asthagiri, M. K. 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