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Lattice dynamics of LuPO4
Journal of Alloys and Compounds 250 (1997) 573–576
L
Lattice dynamics of LuPO 4 J.C. Nipko
a,b,
*, C.-K. Loong a , M. Loewenhaupt c , W. Reichardt d , M. Braden d , L.A. Boatner e a
Argonne National Laboratory, Argonne, IL 60439 -4814, USA b Colorado State University, Fort Collins, CO 80523, USA c ¨ Dresden, Dresden, Germany Technische Universitat d Forschungszentrum Karlsruhe, INFP, D-76021, Karlsruhe, Germany e Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Abstract Lutetium orthophosphate is an important nonmagnetic host material for rare-earth activated luminescence applications. We have measured the LuPO 4 phonon density of states and dispersion curves along the [ j 00], [ jj 0] and [00j ] symmetry directions by neutron spectroscopy using polycrystalline and single crystal samples. A quantitative analysis of the neutron results was carried out using a lattice dynamic shell model. Keywords: Phonons; Neutron spectroscopy; Rare-earth orthophosphate
1. Introduction The body-centered tetragonal unit cell of the zircon structure (space group D 19 4h (I4 1 / amd)) consists of four formula units of AMO 4 as shown in Fig. 1. A primitive cell can be chosen with only two formula units. This structure is common to a variety of optical materials, including natural minerals of zircon (ZrSiO 4 ) and xenotime (RPO 4 , R5Tb to Lu, Y and Sc), as well as rare-earth (RE) vanadates and arsenates. The Zr or R sites ¯ exhibit a unique point symmetry of D 2d (4m2) with a uniaxial direction along the c-axis. The high melting temperatures, structural and chemical stability, and longterm corrosion resistance of zircon and xenotime have
Fig. 1. The tetragonal zircon structure of LuPO 4 . *Corresponding author. 0925-8388 / 97 / $17.00 1997 Elsevier Science S.A. All rights reserved PII S0925-8388( 96 )02566-2
prompted the suggestion of their use as a nuclear waste storage media [1]. Information regarding the phonon properties is important to the understanding of the thermodynamic behavior of these materials under natural radiation damage and temperature–pressure conditions prevalent in the earth. Zircon-type crystalline hosts such as LuPO 4 in general show good optical quality (refractive index of 1.8–2.0, birefringence of 0.04–0.10, Mohrs hardness of 4–7.5), and phonons play a vital role in the luminescence properties of transition-metal doped crystals [2]. For example, charge-transfer type luminescence of Yb 31 and Sb 31 ions in RPO 4 (R5Sc, Lu and Y) indicates vibronic coupling involving phonons of energies about 275630 cm 21 (34.163.7 meV) [3]. The cooperative Jahn– Teller phase transitions in many stoichiometric RE phosphates and vanadates which involve coupling of the RE crystal-field-split states with acoustic or optic phonons have been investigated by Raman scattering and infrared absorption [4]. A group theoretical analysis of the vibrational modes of the zircon structure at the Brillouin zone center was given by Miller and coworkers [5] and by Dawson and coworkers [6] for the purpose of interpreting the optical data of YVO 4 and ZrSiO 4 , respectively. More recently, electronic-Raman scattering studies showed evidence of strong 4f-electron–phonon interactions in YbPO 4 [7]. Since information regarding the phonon dispersion relations in the zircon structure is incomplete, and experimental data of the phonon density of states of the RPO 4 compounds are not available, we have initiated a
574
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
systematic study of the phonon spectra and related thermodynamic properties by neutron-scattering techniques and lattice dynamical calculations. In the present work, we report the results of a study of the lattice dynamics of LuPO 4 using inelastic neutron scattering. LuPO 4 is chosen for this study since Lu 31 has a completely filled shell of f-electrons. Consequently, the atomic dynamics in LuPO 4 is not influenced by magnetic interactions with the f-electrons. The lattice dynamics in LuPO 4 thus provides an important base for any further analysis of f-electronic contributions to the thermodynamic properties and possible coupling to phonons in other isostructural rare-earth systems. We have measured the phonon density of states and dispersion curves along the [ j , 0, 0], [ j , j , 0], and [0, 0, j ] symmetry directions using polycrystalline and single-crystal samples. The data were analyzed in terms of a lattice-dynamic shell model, which is found to adequately describe the Lydanne–Sachs–Teller splittings, observed with infrared reflectivity [8] and neutron measurements, of the polar modes below 40 meV.
Fig. 2. Phonon dispersion curves of LuPO 4 along the [ j 00] symmetry direction. The symbols (x)5neutron, (d)5Infrared [8], (s)5Raman [10] indicate measured data, while the lines are calculations based on the model given in the text.
2. Experimental Polycrystalline powder and single-crystal samples of LuPO 4 were prepared by precipitation and flux techniques, respectively, described previously elsewhere [9]. Neutron inelastic scattering experiments on the polycrystalline sample were performed on the High-Resolution MediumEnergy Chopper Spectrometer (HRMECS) at the Intense Pulsed Neutron Source of Argonne National Laboratory. The HRMECS spectrometer has an energy resolution, DE in full-width-at-half-maximum that varies between 2 and 4% of the incident neutron energy (E0 ) over the neutron energy-loss region, E5E0 2E1 .0 (where E1 is the scattered-neutron energy). Measurements on the single crystal (with dimensions of approximately 0.531.031.5 cm 3 ) were performed on the 2T1 triple-axis spectrometer at the Laboratoire Leon Brillouin in Saclay, France. The measurements were performed with horizontally and vertically focusing pyrolytic graphite (PG) crystal arrays as monochromator and analyzer, set to scatter from the (002) planes, or with a copper crystal set to scatter from the (111) plane as monochromator and a PG crystal array set to scatter from the (002) planes as analyzer. The scans were conducted with fixed final energy of Ef 514.7 meV or Ef 530.5 in conjunction with the use of a PG filter in the scattered beam to avoid Bragg–Incoherent-Bragg contaminations.
Fig. 3. Phonon dispersion curves of LuPO 4 along the [ jj 0] symmetry direction. (See Fig. 2 for definitions of symbols and lines).
3. Results and discussion One-phonon excitations of LuPO 4 were measured at a temperature of 10 K along the [ j 00], [ jj 0] and [00j ] symmetry directions, shown in Figs. 2–4. The measured
Fig. 4. Phonon dispersion curves of LuPO 4 along the [00j ] symmetry direction. (See Fig. 2 for definitions of symbols and lines).
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
Fig. 5. Neutron weighted phonon density of states (NWPDOS) for LuPO 4 . The line represents the calculated NWPDOS based on the model and a convolution with the instrument resolution function.
phonon density of states was deduced from the inelastic neutron data on polycrystalline LuPO 4 at 10 K using the incoherent, one-phonon approximation. The result is given in Fig. 5, where the elastic region has been excluded which results in a low energy cut-off of 10 meV. The lattice-dynamic model employed here is a shell model with shell-core force constants and shell charges incorporated for the oxygen and lutetium ions only. The atom–atom interactions are assumed to be axially symmetric and the shell–core interactions are assumed to be isotropic. The model allows for nearest-neighbor P–O interactions and nearest and next-nearest-neighbor interactions for the Lu–O and O–O bonds. Third and fourth
575
nearest neighbor O–O interactions were also included to improve overall structural stability. Optimization of the model parameters are governed by criteria so as to: (i) minimize deviation of calculated phonon frequencies from those observed in the neutron and optical data [8,10]; (ii) minimize the internal pressure and forces acting on the atoms in their equilibrium positions to ensure the correct structure; (iii) enforce agreement between the calculated and measured elastic constants. Based on these criteria we obtained an optimized parameter set given in Table 1 from which phonon dispersion curves were calculated and shown in Figs. 2–4. The overall fit is good, in particular the measured dispersion curves below 40 meV are well reproduced by the model. The details of the model calculations will be given elsewhere. The calculations of the total and partial phonon densities of states (DOS) were carried out by sampling 3375 wave vectors within the irreducible Brillouin zone with an energy channel width of 1 meV. The calculated neutronweighted DOS obtained by summing the partial DOS for each element weighted by the corresponding neutron scattering cross section and inverse of mass, after convoluting with the instrumental resolution function, is given by the solid line in Fig. 5. The overall agreement between the measured and calculated spectra is good. The distinct frequency bands centered at 125, 85, 67, 40 and 25 meV are well reproduced by the model. There is some intensity in the region between 80 and 120 meV that is not accounted for by the model. Since neither the optical data nor the single crystal neutron data suggest one-phonon excitations in this region, the intensity is likely the result of multi-phonon processes and / or multiple scattering within the sample. The good agreement of model calculations with observed neutron data in the dispersion curves and DOS demonstrate that the lattice-dynamic model gives an accurate description of the phonon frequencies and eigen-
Table 1 Model parameters for the lattice dynamics of LuPO 4 . F(r) and G(r) refer to the longitudinal and transverse force constants, respectively Bond type
˚ Bond length (A)
F(r) (10 dynes cm ) G(r) (10 dynes cm )
` ` Born von Karman P–O Lu–O Lu–O O–O O–O O–O O–O
1.534 2.258 2.354 2.404 2.553 2.745 2.910
871.3 177.8 123.5 119.5 81.3 9.6 12.5
Shell-Core O Lu Charges O P Lu
3
2600 4100 Ionic 21.19 2.33 2.44
Shell 22.68 0 22.73
22
3
28.1 23.0 214.0 228.2 220.7 23.3 20.3
22
576
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
vectors throughout the Brillouin zone. Therefore, a combination of this lattice-dynamic model and an RE crystalfield formalism can provide a basis for further treatment of the interaction mechanisms between RE ions and the lattice throughout the isostructural RPO 4 series.
Acknowledgments Support for this work was provided by NATO Collaborative Research Grant No. CRG940096. Work performed at Argonne National Laboratory and Oak Ridge National Laboratory is supported by the U.S. DOE-BES under contracts No. W-31-109-ENG-38 and No. DE-AC0584OR21400, respectively. The neutron scattering experiments were performed at Laboratoire Leon Brillouin (CESaclay) and supported by HCM programme Access to Large Scale Facilities under contract ERB CHGECT 920001.
References [1] L.A. Boatner, G.W. Beall, M.M. Abraham, C.B. Finch, R.J. Floran, P.G. Huray and M. Rappaz, in Management of Alpha-Contaminated Wastes, IAEA-SM-246 / 73, IAEA, Vienna, 1981, p. 411.
[2] G. Blasse and A. Bril, J. Chem. Phys., 50 (1969) 2974; J.R. Thornton, Appl. Opt., 8 (1969) 1087. [3] A.J. Wojtowicz, A. Lempicki, D. Wisniewski and L.A. Boatner, MRS Sympos. Proceed., 348 (1994) 123. [4] R.T. Harley, in Spectroscopy of Solids Containing Rare Earth Ions, edited by A. Kapyanskii and R.M. Macfarlane, Elsevier, Amsterdam, 1987, p. 557; G.A. Gehring and K.A. Gehring, Rep. Prog. Phys., 38 (1975) 1. [5] S.A. Miller, H.H. Caspers and H.E. Rast, Phys. Rev., 168 (1967) 964. [6] P. Dawson, M.M. Hargreave and C.R. Wilkinson, J. Phys. C: Solid St. Phys., 4 (1971) 240. [7] P.C. Becker, N. Edelstein, G.M. Williams, J.J. Bucher, R.E. Russo, J.A. Koningstein, L.A. Boatner and M.M. Abraham, Phys. Rev. B, 31 (1985) 8102. [8] A. Armbruster, J. Phys. Chem. Solids, 37 (1976) 321. [9] M. Rappaz, L.A. Boatner and M.M. Abraham, J. Chem. Phys., 73 (1980) 1095. [10] P.C. Becker, Electronic Raman Scattering in Rare Earth Phosphate Crystals, Ph. D. Thesis, Lawrence Berkeley Laboratory, University of California, Berkeley (1986).
L
Lattice dynamics of LuPO 4 J.C. Nipko
a,b,
*, C.-K. Loong a , M. Loewenhaupt c , W. Reichardt d , M. Braden d , L.A. Boatner e a
Argonne National Laboratory, Argonne, IL 60439 -4814, USA b Colorado State University, Fort Collins, CO 80523, USA c ¨ Dresden, Dresden, Germany Technische Universitat d Forschungszentrum Karlsruhe, INFP, D-76021, Karlsruhe, Germany e Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Abstract Lutetium orthophosphate is an important nonmagnetic host material for rare-earth activated luminescence applications. We have measured the LuPO 4 phonon density of states and dispersion curves along the [ j 00], [ jj 0] and [00j ] symmetry directions by neutron spectroscopy using polycrystalline and single crystal samples. A quantitative analysis of the neutron results was carried out using a lattice dynamic shell model. Keywords: Phonons; Neutron spectroscopy; Rare-earth orthophosphate
1. Introduction The body-centered tetragonal unit cell of the zircon structure (space group D 19 4h (I4 1 / amd)) consists of four formula units of AMO 4 as shown in Fig. 1. A primitive cell can be chosen with only two formula units. This structure is common to a variety of optical materials, including natural minerals of zircon (ZrSiO 4 ) and xenotime (RPO 4 , R5Tb to Lu, Y and Sc), as well as rare-earth (RE) vanadates and arsenates. The Zr or R sites ¯ exhibit a unique point symmetry of D 2d (4m2) with a uniaxial direction along the c-axis. The high melting temperatures, structural and chemical stability, and longterm corrosion resistance of zircon and xenotime have
Fig. 1. The tetragonal zircon structure of LuPO 4 . *Corresponding author. 0925-8388 / 97 / $17.00 1997 Elsevier Science S.A. All rights reserved PII S0925-8388( 96 )02566-2
prompted the suggestion of their use as a nuclear waste storage media [1]. Information regarding the phonon properties is important to the understanding of the thermodynamic behavior of these materials under natural radiation damage and temperature–pressure conditions prevalent in the earth. Zircon-type crystalline hosts such as LuPO 4 in general show good optical quality (refractive index of 1.8–2.0, birefringence of 0.04–0.10, Mohrs hardness of 4–7.5), and phonons play a vital role in the luminescence properties of transition-metal doped crystals [2]. For example, charge-transfer type luminescence of Yb 31 and Sb 31 ions in RPO 4 (R5Sc, Lu and Y) indicates vibronic coupling involving phonons of energies about 275630 cm 21 (34.163.7 meV) [3]. The cooperative Jahn– Teller phase transitions in many stoichiometric RE phosphates and vanadates which involve coupling of the RE crystal-field-split states with acoustic or optic phonons have been investigated by Raman scattering and infrared absorption [4]. A group theoretical analysis of the vibrational modes of the zircon structure at the Brillouin zone center was given by Miller and coworkers [5] and by Dawson and coworkers [6] for the purpose of interpreting the optical data of YVO 4 and ZrSiO 4 , respectively. More recently, electronic-Raman scattering studies showed evidence of strong 4f-electron–phonon interactions in YbPO 4 [7]. Since information regarding the phonon dispersion relations in the zircon structure is incomplete, and experimental data of the phonon density of states of the RPO 4 compounds are not available, we have initiated a
574
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
systematic study of the phonon spectra and related thermodynamic properties by neutron-scattering techniques and lattice dynamical calculations. In the present work, we report the results of a study of the lattice dynamics of LuPO 4 using inelastic neutron scattering. LuPO 4 is chosen for this study since Lu 31 has a completely filled shell of f-electrons. Consequently, the atomic dynamics in LuPO 4 is not influenced by magnetic interactions with the f-electrons. The lattice dynamics in LuPO 4 thus provides an important base for any further analysis of f-electronic contributions to the thermodynamic properties and possible coupling to phonons in other isostructural rare-earth systems. We have measured the phonon density of states and dispersion curves along the [ j , 0, 0], [ j , j , 0], and [0, 0, j ] symmetry directions using polycrystalline and single-crystal samples. The data were analyzed in terms of a lattice-dynamic shell model, which is found to adequately describe the Lydanne–Sachs–Teller splittings, observed with infrared reflectivity [8] and neutron measurements, of the polar modes below 40 meV.
Fig. 2. Phonon dispersion curves of LuPO 4 along the [ j 00] symmetry direction. The symbols (x)5neutron, (d)5Infrared [8], (s)5Raman [10] indicate measured data, while the lines are calculations based on the model given in the text.
2. Experimental Polycrystalline powder and single-crystal samples of LuPO 4 were prepared by precipitation and flux techniques, respectively, described previously elsewhere [9]. Neutron inelastic scattering experiments on the polycrystalline sample were performed on the High-Resolution MediumEnergy Chopper Spectrometer (HRMECS) at the Intense Pulsed Neutron Source of Argonne National Laboratory. The HRMECS spectrometer has an energy resolution, DE in full-width-at-half-maximum that varies between 2 and 4% of the incident neutron energy (E0 ) over the neutron energy-loss region, E5E0 2E1 .0 (where E1 is the scattered-neutron energy). Measurements on the single crystal (with dimensions of approximately 0.531.031.5 cm 3 ) were performed on the 2T1 triple-axis spectrometer at the Laboratoire Leon Brillouin in Saclay, France. The measurements were performed with horizontally and vertically focusing pyrolytic graphite (PG) crystal arrays as monochromator and analyzer, set to scatter from the (002) planes, or with a copper crystal set to scatter from the (111) plane as monochromator and a PG crystal array set to scatter from the (002) planes as analyzer. The scans were conducted with fixed final energy of Ef 514.7 meV or Ef 530.5 in conjunction with the use of a PG filter in the scattered beam to avoid Bragg–Incoherent-Bragg contaminations.
Fig. 3. Phonon dispersion curves of LuPO 4 along the [ jj 0] symmetry direction. (See Fig. 2 for definitions of symbols and lines).
3. Results and discussion One-phonon excitations of LuPO 4 were measured at a temperature of 10 K along the [ j 00], [ jj 0] and [00j ] symmetry directions, shown in Figs. 2–4. The measured
Fig. 4. Phonon dispersion curves of LuPO 4 along the [00j ] symmetry direction. (See Fig. 2 for definitions of symbols and lines).
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
Fig. 5. Neutron weighted phonon density of states (NWPDOS) for LuPO 4 . The line represents the calculated NWPDOS based on the model and a convolution with the instrument resolution function.
phonon density of states was deduced from the inelastic neutron data on polycrystalline LuPO 4 at 10 K using the incoherent, one-phonon approximation. The result is given in Fig. 5, where the elastic region has been excluded which results in a low energy cut-off of 10 meV. The lattice-dynamic model employed here is a shell model with shell-core force constants and shell charges incorporated for the oxygen and lutetium ions only. The atom–atom interactions are assumed to be axially symmetric and the shell–core interactions are assumed to be isotropic. The model allows for nearest-neighbor P–O interactions and nearest and next-nearest-neighbor interactions for the Lu–O and O–O bonds. Third and fourth
575
nearest neighbor O–O interactions were also included to improve overall structural stability. Optimization of the model parameters are governed by criteria so as to: (i) minimize deviation of calculated phonon frequencies from those observed in the neutron and optical data [8,10]; (ii) minimize the internal pressure and forces acting on the atoms in their equilibrium positions to ensure the correct structure; (iii) enforce agreement between the calculated and measured elastic constants. Based on these criteria we obtained an optimized parameter set given in Table 1 from which phonon dispersion curves were calculated and shown in Figs. 2–4. The overall fit is good, in particular the measured dispersion curves below 40 meV are well reproduced by the model. The details of the model calculations will be given elsewhere. The calculations of the total and partial phonon densities of states (DOS) were carried out by sampling 3375 wave vectors within the irreducible Brillouin zone with an energy channel width of 1 meV. The calculated neutronweighted DOS obtained by summing the partial DOS for each element weighted by the corresponding neutron scattering cross section and inverse of mass, after convoluting with the instrumental resolution function, is given by the solid line in Fig. 5. The overall agreement between the measured and calculated spectra is good. The distinct frequency bands centered at 125, 85, 67, 40 and 25 meV are well reproduced by the model. There is some intensity in the region between 80 and 120 meV that is not accounted for by the model. Since neither the optical data nor the single crystal neutron data suggest one-phonon excitations in this region, the intensity is likely the result of multi-phonon processes and / or multiple scattering within the sample. The good agreement of model calculations with observed neutron data in the dispersion curves and DOS demonstrate that the lattice-dynamic model gives an accurate description of the phonon frequencies and eigen-
Table 1 Model parameters for the lattice dynamics of LuPO 4 . F(r) and G(r) refer to the longitudinal and transverse force constants, respectively Bond type
˚ Bond length (A)
F(r) (10 dynes cm ) G(r) (10 dynes cm )
` ` Born von Karman P–O Lu–O Lu–O O–O O–O O–O O–O
1.534 2.258 2.354 2.404 2.553 2.745 2.910
871.3 177.8 123.5 119.5 81.3 9.6 12.5
Shell-Core O Lu Charges O P Lu
3
2600 4100 Ionic 21.19 2.33 2.44
Shell 22.68 0 22.73
22
3
28.1 23.0 214.0 228.2 220.7 23.3 20.3
22
576
J.C. Nipko et al. / Journal of Alloys and Compounds 250 (1997) 573 – 576
vectors throughout the Brillouin zone. Therefore, a combination of this lattice-dynamic model and an RE crystalfield formalism can provide a basis for further treatment of the interaction mechanisms between RE ions and the lattice throughout the isostructural RPO 4 series.
Acknowledgments Support for this work was provided by NATO Collaborative Research Grant No. CRG940096. Work performed at Argonne National Laboratory and Oak Ridge National Laboratory is supported by the U.S. DOE-BES under contracts No. W-31-109-ENG-38 and No. DE-AC0584OR21400, respectively. The neutron scattering experiments were performed at Laboratoire Leon Brillouin (CESaclay) and supported by HCM programme Access to Large Scale Facilities under contract ERB CHGECT 920001.
References [1] L.A. Boatner, G.W. Beall, M.M. Abraham, C.B. Finch, R.J. Floran, P.G. Huray and M. Rappaz, in Management of Alpha-Contaminated Wastes, IAEA-SM-246 / 73, IAEA, Vienna, 1981, p. 411.
[2] G. Blasse and A. Bril, J. Chem. Phys., 50 (1969) 2974; J.R. Thornton, Appl. Opt., 8 (1969) 1087. [3] A.J. Wojtowicz, A. Lempicki, D. Wisniewski and L.A. Boatner, MRS Sympos. Proceed., 348 (1994) 123. [4] R.T. Harley, in Spectroscopy of Solids Containing Rare Earth Ions, edited by A. Kapyanskii and R.M. Macfarlane, Elsevier, Amsterdam, 1987, p. 557; G.A. Gehring and K.A. Gehring, Rep. Prog. Phys., 38 (1975) 1. [5] S.A. Miller, H.H. Caspers and H.E. Rast, Phys. Rev., 168 (1967) 964. [6] P. Dawson, M.M. Hargreave and C.R. Wilkinson, J. Phys. C: Solid St. Phys., 4 (1971) 240. [7] P.C. Becker, N. Edelstein, G.M. Williams, J.J. Bucher, R.E. Russo, J.A. Koningstein, L.A. Boatner and M.M. Abraham, Phys. Rev. B, 31 (1985) 8102. [8] A. Armbruster, J. Phys. Chem. Solids, 37 (1976) 321. [9] M. Rappaz, L.A. Boatner and M.M. Abraham, J. Chem. Phys., 73 (1980) 1095. [10] P.C. Becker, Electronic Raman Scattering in Rare Earth Phosphate Crystals, Ph. D. Thesis, Lawrence Berkeley Laboratory, University of California, Berkeley (1986).