DOI: 10.1021/cg1004962
ScVO4: Explorations of Novel Crystalline Inorganic Optical Materials in Rare-Earth Orthovanadate Systems
2010, Vol. 10 4389–4400
Hengjiang Cong,† Huaijin Zhang,*,† Bin Yao,† Wentao Yu,† Xian Zhao,† Jiyang Wang,† and Guangcai Zhang‡ †
State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan 250100, China, and ‡National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China Received April 14, 2010; Revised Manuscript Received July 24, 2010
ABSTRACT: Novel tetragonal scandium orthovanadate crystals doped with neodymium ions (Nd:ScVO4) have been successfully grown with the floating zone (FZ) method for applications in photonic devices. High-temperature stability studies and X-ray structural studies show that thermally induced vanadium oxide vaporization triggers a series of topological transitions from the rutile lattice to the defect fluorite lattice when crystallization begins in the ScVO4 melt. Besides zircon-type ScVO4 and bixbyite-type Sc2O3, a third form with metallic properties called tetragonal Sc2VO5 was thus obtained. Ab initio calculations further reveal that such structural transitions at high-temperature are directly driven by increasing covalency in the scandiumoxygen bonds and are energetically favored. In addition, the anisotropic mechanical and optical properties of ScVO4, such as elastic stiffness, Young’s modulus, dielectric constants, and refractive index, were calculated using density functional theory and evaluated for future applications. The calculated results tend to support the experimental data.
*To whom correspondence should be addressed. E-mail: hjzhang@ icm.sdu.edu.cn.
macroscale, such as top-seeded flux growth (TSSG),23 floating zone (FZ),24 and Czochralski (CZ) method,25 while the combustion method,26 wet-chemical synthesis,27,28 sol-gel method,21,29 and hydrothermal method30,31 are employed on the nanoscale. Despite both the great scientific and vast technological importance that has been attached to zircon-type orthovanadate systems, the properties of crystalline ScVO4, the first member of this family, have still remained nearly unknown for quite a long time since the initial discovery.32 The first polycrystalline samples of Nd:ScVO4 were prepared by sintering scandium oxide and vanadium pentoxide in 1973. A comparison was then made among various vanadate crystals, showing that ScVO4 has the broadest and most intense bands, making it the most promising host matrix for Nd3þ ions.33 Later, unusual thermal expansion behavior was found in ScVO4 at elevated temperatures from 300 to 634 K.34 The result was followed by a systematic study of the structure-property relationships in the thermal expansion of zircon-type RVO4 in 1989.35 Recently, another systematic theoretical investigation of thermal and mechanical properties has been conducted empirically on the RVO4 family, showing that ScVO4 has the largest bulk modulus and lattice energy density.36 The magnetic properties of the various oxygen defect structures of ScVO4 have also been studied.37 More recently, it was reported that laser output at 1068 nm has been achieved in 0.5 atom % Nd doped ScVO4 crystals38 and tuning the YVO4 lattice with ScVO4 to form a disordered structure has been used in an attempt to obtain highly efficient ultrashort pulsed lasers,39 indicating that ScVO4 has great potential in practical optical applications. Compared with other zircon-type vanadates, however, greater difficulty has been encountered in the growth of bulk ScVO4 crystals, and accordingly the reported laser performance is severely degraded by the poor quality of the crystals. This can be ascribed to the fact that many chemical and physical properties of scandium-containing compounds are not well characterized, partly due to their rarity and
r 2010 American Chemical Society
Published on Web 08/27/2010
I. Introduction The quest for novel crystalline inorganic optical materials is of wide interest and great importance in a variety of applications associated with the rapid growth of photonic technologies. Currently, one of the most important classes of materials in this area is the rare-earth orthovanadate family with the chemical formula RVO4 (R = Sc, Y, La-Lu), where two polymorphs are present at ambient pressure. With a decrease in the ionic radius of the R3þ cation, the orthovanadates crystallize from a monoclinic monazite-type structure with space group P21/n to a tetragonal zircon-type structure with space group I41/amd.1 It is also known that the zircon-type structure results in a more asymmetric crystal field around the R3þ ions, which is advantageous for luminescence, increasing the radiative rate constant, thus showing much better performance than the monazite structure.2 In the last few decades, numerous investigations have been carried out on tetragonal RVO4 crystals, which have been widely utilized as catalysts,3-5 polarizers,6,7 phosphors,8-10 scintillators,11 multiphoton-induced fluorescence materials,12 χ(3) nonlinear optical materials,13,14 and laser host matrices,15,16 many of which are now commercially available. Among these crystals, YVO4, with a relatively small ionic radius, is one of the best-known and most widely used optical materials: Nd:YVO4 crystals have a low pump threshold and a large absorption coefficient at 808 nm (the standard wavelength of currently available laser diodes), which is five times the threshold in Nd:YAG.17,18 Eu:YVO4 crystals have a high photoluminescent (PL) quantum yield of about 70% for f-f transition and are thus capable of emitting a variety of colors.19-21 Up to now, the most efficient Nd doped vanadate self-Raman laser has been realized with Nd:YVO4 with a conversion rate of 13.9%.22 Various methods have been employed to prepare the crystalline materials on the
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difficulty of separation and thus high cost,40 and partly due to the great difficulty in obtaining sufficiently large single-crystal samples for further measurements. All these problems have formed a serious impediment to the potential applications of ScVO4. To this end, we report that ScVO4 crystals with a relatively high Nd doping content have been successfully prepared. The high-temperature stability of ScVO4 and its phase evolution upon heating were observed by using ex-situ and in situ thermal analysis, combined with the techniques of powder X-ray diffraction and atomic emission spectrometry. From X-ray single-crystal structure analysis, the underlying topological relationships associated with the various thermal transitions were studied. On the basis of ab initio electronic band structure calculations, the origin of the relative stability of the scandium-containing compounds was investigated in detail. In addition, important mechanical and optical anisotropic properties of the tetragonal ScVO4 crystals in practical applications are predicted and compared with those of its nearest relative YVO4. II. Experimental and Computational Procedures Synthesis of Polycrystalline Samples and Crystal Growth of Nd: ScVO4. Polycrystalline ScVO4 and NdVO4 were prepared via a three-step liquid phase coprecipitation synthesis process. V2O5 with a purity of 99.99% was dissolved in hot high-purity ammonia (>99.9%) then reacted with ammonia to yield NH4VO3. Δ
V2 O5 þ 2NH3 3 H2 O f 2NH4 VO3 þ H2 O
ð1Þ
99.99% pure oxides Nd2O3 and Sc2O3 were dissolved in hot highpurity nitric acid (>99%), yielding Nd(NO3)3 and Sc(NO3)3, respectively. Δ
Ln2 O3 þ 6HNO3 f 2LnðNO3 Þ3 þ 3H2 O
ð2Þ
NdVO4 and ScVO4 polycrystalline materials then were synthesized by mixing the solutions of Nd(NO3)3 and NH4VO3 or Sc(NO3)3 and NH4VO3, respectively. LnðNO3 Þ3 þ NH4 VO3 þ 2NH3 3 H2 O f LnVO4 þ 3NH4 NO3 þ H2 O
ð3Þ
Starting materials consisting of NdVO4 and ScVO4 powder of chemical composition Nd0.01Sc0.99VO4 were ground and loaded into a rubber membrane to fabricate the seed and the feed rod. They were then hydrostatically pressed into round rods at about 68 KN. The molded specimens were sintered at 1473.15 K for 4 h in air. The growth apparatus used was an image furnace with a four ellipsoidal mirrors (Crystal Systems Inc., FZ-T-12000-X-I-S-SU) with four 3 kW xenon lamps equipped as the heat source. The crystal was grown at a rate of 5-8 mm/h in a pure oxygen (>99.9%) atmosphere. The feed rod and the seed rod were rotated at 30 rpm in opposite directions. Thermal Stability Characterization. ScVO4 polycrystalline powders weighing 40 g was loaded into an iridium (Ir) crucible with a diameter of 66 mm and a height of 40 mm, before radio frequency (RF) heating in an atmosphere of N2 þ O2 (2% by volume) using a 2 kHz intermediate frequency furnace. The temperature was measured using a Pt/Pt-Rh thermocouple and controlled by a EUROTHERM 818 controller/programmer with a precision of 0.5 K. The heating rate was set to about 10 K min-1 until it was observed that all the powder in the crucible was completely melted. The temperature was then maintained fixed for nearly 20 h. After that, the melt was slowly cooled down to room temperature for further phase characterization. In order to obtain in situ detection of any possible thermal behavior of the ScVO4 during growth, simultaneous thermogravimetric and differential thermal analysis (TG/DTA) experiments were performed in the air atmosphere using a NETZSCH STA 449
F1 Jupiter simultaneous thermal analyzer. Polycrystalline ScVO4 powder weighing 36.97 mg was heated from 308.15 to 1823.15 K and then cooled down to room temperature at a linear rate of 10 K min-1 throughout. Phase Characterization. Four samples collected from as-grown crystals, volatiles, upper layer, and lower layer of the annealed melts from ex-situ thermal analysis were all dissolved in 10 mL of hot hydrochloric acid (36-38%) and subsequently diluted with demineralized water in a 100 mL standard flask. The amount of elemental Sc, V, and Nd was determined by the external standard method using a Thermo Electron IRIS Intrepid II XSP atomic emission spectrometer with inductively coupled plasma (ICP-AES). High resolution X-ray powder diffraction (XPRD) was also performed using a Bruker D8 ADVANCE X-ray diffractometer with four-bounce Ge (220)-monochromated Cu KR1 radiation (λ = 1.54056 A˚) for the following samples: ScVO4 raw materials, asgrown crystals, lower layer, and upper layer of the annealed melts. The data were collected at room temperature with 2θ ranging from 20 to 80°. Single-Crystal Structural Characterization. Small but well-shaped single crystal pellets were selected from the as-grown crystal and annealed melts by using polarized optical microscopy in order to minimize absorption and defects that are easily introduced in the material by cutting and polishing. Single crystal X-ray diffraction structural analysis was performed from the data collected at room temperature by using a Bruker SMART APEXII CCD area-detector diffractometer with a normal 3KW sealed tube, a crystal-to-detector distance of 4.99 cm, 512 512 pixels/frame, φ/ω scan with a step of 0.30°, exposure/frame of 20.0 s/frame and SAINT integration. After an absorption correction was applied, the crystal structures were solved by Patterson methods and refined by full-matrix least-squares methods. All the calculations were performed using the SHELXTL program.41 General Computational Methodology. The crystallographic data on Sc2O3, Sc2VO5, ScVO4, and YVO4 (ICSD42 File No. 78074) determined by X-ray diffraction (XRD) were used as input files for ab initio calculations. The determination of the electronic band structure was performed by using CASTEP, a plane-wave pseudopotential total energy package,43,44 based on density functional theory (DFT) with Vanderbilt-type ultrasoft pseudopotentials.45 The exchange-correlation energy was treated with a generalized gradient approximation using Perdew-Burke-Ernzerhof functionals (GGA-PBE).46 A k-point mesh with a spacing of 0.04 A˚-1 generated by the Monkhorst-Pack scheme47 was chosen in the numerical integration over the Brillouin zone, and a plane-wave cutoff energy of 380 eV was adopted throughout the calculations. The valence states of O (2s2sp4) and the shallow-core and valence states of Sc (3s23p63d14s2), V (3s23p63d34s2), and Y (4s24p64d15s2) were explicitly treated in the pseudopotentials to avoid applying a nonlinear core correction. The self-consistent total energies were minimized using the Pulay method for the density mixing scheme48 in connection with the conjugate gradient (CG) technique.49 The quasi-Newton method with the Broyden-Fletcher-GoldfarbShanno (BFGS) scheme50 used for geometric structures optimization ensures a robust and efficient search of energy minimum of the electronic ground state. The tolerances of the geometric optimization were selected as follows: difference in total energy within 5 10-6 eV/atom, maximum ionic Hellmann-Feynman (HF) force within 0.01 eV/A˚, maximum ionic displacement within 5 10-4 A˚ and maximum stress within 0.02 GPa. The technique for the projection of plane-wave states onto a linear combination of atomic orbitals (LCAO) basis set was used to perform Mulliken population analysis.51,52
III. Results and Discussion Crystal Growth, Thermal Stability, and Materials Characterization. The effective ionic radii of Sc3þ and Nd3þ are 0.870 and 1.109 nm at a coordination number of eight (CN = 8), respectively.53 This inherently large discrepancy in ionic radius (∼27%) obviously violates the Hume-Rothery rules, which state that for substitutional solid solutions the maximum difference between the atomic radii of the solute and solvent atoms should be no more than 15%. Whether a
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Figure 1. (a) Morphology of as-grown crystal rod, cracking fragments and polished ScVO4 single crystal; (b) a cross-sectional view of the annealed melts of the ex-situ thermal analysis experiment (white bar indicates the borderline between two distinct layers).
relatively high amount of Nd3þ ions can be successfully doped into ScVO4 is the first problem we are interested in. As Figure 1a shows, a single crystal of ScVO4 doped with nominally 1 atom % Nd has been successfully grown by the FZ method. After mechanical polishing, a 3 3 1 mm colorless and transparent ScVO4 single crystal cube without macrodefects was obtained. However, the as-grown ScVO4 rod is very easy to crack, and inside the cracked fragments, as shown in the upper left of Figure 1a, there is a change in color homogeneity with some dark spots along the side. Moreover, it is worth noting that in the coated region outside the asgrown crystal rod there are new phases being formed during growth, dark brown in some places and pure white in other places, obviously different from the yellow-brown ScVO4 on the inner. The process of growth of RVO4 single crystals from the melt frequently encounters a serious problem regarding volatility. The main volatile components are generally acknowledged to be the vanadium oxides compounds. Although the liquid
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coprecipitation method has been proven to be a successful way to suppress such volatility in the growth process, compared with other rare-earth orthovanadates stronger evaporation components still have been observed in FZ growth of ScVO4. This condition induces the melt to substantially deviate from stoichiometry and thus to severely affect the crystallization of ScVO4. Thus, examining the high-temperature thermal behavior behind the growth process is especially important. In light of this, we first conducted an ex-situ thermal experiment to examine the change in the thermal stability that accompanies the smaller size of the Sc3þ ions. Noticeably, after cooling, vertical stratification was found in the melt retained in the crucible, as shown in Figure 1b. Three layers with distinct colors were formed: a thin layer on top, mainly containing orange-yellow flecks characteristic of V2O5; a layer of dark black color in the upper region; and a layer of dark green color at the bottom. Many spontaneously formed crystalline grains can be also found inside. The total mass loss in the samples is estimated to be about 10.55% after a 20 h period in the molten state to ensure complete decomposition. A more accurate in situ measurement of the high-temperature thermal transition of ScVO4 followed. Figure 2a,b shows the TG/DTA data of ScVO4 during the heating and cooling cycle, respectively. When heated, the TG data indicate that only a slight mass change occurs below 1523.15 K, corresponding to the hygroscopic properties of ScVO4. Then the sample begins to lose its weight continuously, indicating the emergence of decomposition. It is estimated that up to 1809.15 K the total weight loss is 3.348%, and the evaporation rate is about 0.1298% min-1, which is significantly larger than that of other vanadates.54 Figure 2a indicates that the melting of ScVO4 undergoes a three-step endothermic process, located at 1663.15, 1714.95, and 1755.25 K. The incongruent melting point of ScVO4 is equal to 1663.15 K, which is the lowest in the rare-earth orthovanadate family.55 Accordingly, there are three exothermic process during crystallization presented in Figure 2b: one sharp peak located at 1358.55 K and two weak broad peaks located around 1493.65 and 1588.95 K, respectively. The temperature difference between the melting and crystallization processes indicates a large amount of supercooling in the growth of ScVO4. The enthalpy of fusion is 293.6 J g-1 (42.25 kJ mol-1), which is higher than other common rare-earth oxide crystals.56,57 We further measured the elemental contents and phase purity of the samples collected from both experiments. From Table 1, the effective segregation coefficient of Nd3þ ions in FZ grown Nd:ScVO4 is roughly estimated to be 0.94 on average, a value that is higher than those for FZ grown Nd: LuVO4 (0.50),58 Nd:YVO4 (0.82),59 and Nd:GdVO4 (0.90).60 Comparing the lattice parameters of ScVO4 with those of NdVO4 (ICSD File No. 78074), it is seen that the largest difference lies along the [100] or [010] crystal direction, both of which expand by nearly 8%. A similar expansion can also be detected in Nd:ScVO4 by X-ray powder diffraction (XRPD), as shown in Figure 3, where the strongest peak of Nd:ScVO4 (200) moves toward the low angle region by an amount of 0.0812° relative to that of pure ScVO4 powders. This result indicates that the nearly 1 atom % Nd doping induces a maximum lattice expansion of 0.3% in the [100] direction. All these results show that the Nd3þ ions have been successfully doped into the crystal and a more disordered structure will be formed with an increase in the Nd content.
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Figure 2. (a, b) TG/DTA data. Table 1. Elemental Content of the Samples
Sc (wt %) V (wt %) Nd (wt %) n(Sc)/n(V) Sc þ V þ Nd (wt %)
as-grown crystal
lower layer
upper layer
24.28 29.03 0.73 0.9477 54.04
21.65 35.84
29.97 24.36
0.015 28.91
0.6845 57.49
1.394 54.33
5.88 10-4 28.925
volatiles
Therefore, tetragonal ScVO4 is a very promising host material to produce a highly efficient ultrashort pulsed laser. Although the two elements are very close neighbors, Table 1 also indicates that the volatiles in the ex-situ thermal experiment primarily belong to vanadium compounds so that the evaporation of scandium is negligible. In addition, it shows that incongruent vanadium oxide vaporization brings about a more serious change in Sc-V stoichiometry in the ScVO4 melt, where the upper layer of the annealed melt was found to be a scandium excess region (also an anion-deficient one) and
the lower layer a vanadium excess region. Figure 3 further shows that, corresponding to the three exothermic processes shown in Figure 2b, three scandium-containing compounds have been formed: tetragonal ScVO4, Sc2VO5, and cubic Sc2O3. The crystallization of zircon-type ScVO4 primarily occurs near the vanadium excess region, while a novel tetragonal phase Sc2VO5, comes to dominate the scandium excess region. From Figure 3, we also see that there is another cubic phase ScVO3, formed in crystalline ScVO4 during the FZ growth. Combining these results, it can be inferred that when the temperature is raised, vanadium tends to aggregate on top of the melt with the decomposition of ScVO4, and thus forms a vanadium enriched layer. Under the action of natural convection due to the hot crucible walls, the accumulated vanadium is brought back to the bottom, and thus three distinct layers with different vanadium content are formed. We cannot therefore grow ScVO4 crystals using the Czochralski method, a conclusion that is consistent
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with experimental observations.38,39 It is due to the higher growth rate and steeper temperature gradient in the FZ method that crystalline ScVO4 can be obtained. It can also be concluded that the thermally induced evaporation of the vanadium oxide has triggered two structural transitions in zircon-type ScVO4 when crystallization begins in the melt: one is from the tetragonal phase to the cubic phase and the other is from one tetragonal phase to another tetragonal phase. Crystal Structure Analysis. To date, there have been only four distinct stoichiometric scandium-containing compounds, namely, ScVO4, Sc2VO5, ScVO3 (ICSD File No. 54877), Sc2O3, found in the Sc-V-O phase diagram. To further investigate the structure-property relationships in the thermal transitions of ScVO4, the crystal structures have been studied by X-ray diffraction. Details of the crystal data,
Figure 3. XPRD patterns of the samples.
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structural refinements, and some physical parameters are summarized in Table 2. Selected important bond lengths and bond angles for Sc2O3, ScVO4, and Sc2VO5 are listed in Tables 1 and 2 of Supporting Information, respectively. In the RVO4 zircon-type lattice, each of the cations is surrounded by two nearest-neighbor cations of the other kind (along the [001] direction) plus eight (4 like þ 4 unlike) cations at a 21.4% greater distance, forming a body-centered tetragonal sublattice. This cation arrangement is characteristic of the rutile structure (ICSD File No. 51940). The zircon-type structure can be envisioned as being derived from the latter by alternatively substituting large R and small V cations in the chains formed by the edge sharing TiO6 octahedra in the rutile structure to form a 21/2 21/2 2 superlattice. However, as Figure 4 shows, in contrast to rutile, in the zircon-type RVO4 the larger R cations form a bisdisphenoid with a higher CN of 8, while the smaller V cations form a tetrahedron with a lower CN of 4. Notice that the RO8 bisdisphenoids form a porous structure by sharing edges with each other and the small VO4 tetrahedrons are dispersed inside the six-member ring interstices, both occupying an equivalent Wyckoff 4a and 4b position. It can also be seen that merely by conforming to an approximately diamond-like packing the RO8 bisdisphenoids stabilize the whole structure of zircon-type RVO4. Therefore, it is expected that zircon-type RVO4 will be unstable whenever the R cation is either too big or too small to afford the exact eight ligands in a bisdisphenoid structure. For ScVO4, although Sc has a similarly small ionic radius to Zr (rSc = 0.870, rZr = 0.840, CN = 8), because its lower positive charge and a weaker electron negativity of V it cannot account for a large portion of negative charge from the anions surrounding Sc and thus raises the repulsion forces between the neighboring ligands. The Sc cations cannot hold the bisdisphenoidal coordination up to normal melting and accordingly the mismatch between the zircon-type structure and the decreasing cation size is the origin of the high-temperature instability of ScVO4. Crystal structures of cubic Sc2O3 and tetragonal Sc2VO5 are shown in Figure 5, panels a and b, respectively. The disordered structure of cubic ScVO3 is very similar to that of Sc2O3, by replacing Sc atoms with V atoms in some of the corresponding sites of the Sc2O3 structure. From Table 2, it is seen that the difference in the lattice constants between Sc2O3 and ScVO3 is only 2.25%. Therefore, we propose that Sc2O3 is the ultimate decomposition product of ScVO4 ,while ScVO3 is only an intermediate phase formed by V evaporation.
Table 2. Crystal Data, Structure Refinements and Physical Parameters for ScVO4, Sc2VO5, ScVO3, and Sc2O3 at Room Temperature formula fw cryst syst space group color a, A˚ b, A˚ c, A˚ V, A˚3 Z Dcalc g cm-3 λ, A˚ μ, mm-1 GOF on F2 R1, wR2 (all data) melting point, °C a
From ref 61. b From ref 62.
ScVO4 159.90 tetragonal I41/amd (No. 141) yellow brown 6.7885(3) 6.7885(3) 6.1392(6) 282.92(3) 4 3.754 Mo KR, 0.71073 5.50 1.12 0.021, 0.059 1397.0
Sc2VO5 220.86 tetragonal I4 (No. 82) dark brown 7.7897(3) 7.7897(3) 14.6052(9) 886.24 (7) 10 4.138 Mo KR, 0.71073 6.19 0.87 0.024, 0.059
Sc0.912V1.088O3a 144.42 cubic Ia3 (No. 206) dark brown 9.6182(1) 9.6182(1) 9.6182(1) 889.78 16 4.31 Neutron 1.60 0.0402, 0.0507
Sc2O3 137.92 cubic Ia3 (No. 206) white 9.83490(10) 9.83490(10) 9.83490(10) 951.283(17) 16 3.852 Mo KR, 0.71073 5.41 1.36 0.015, 0.044 2489b
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Figure 4. Polyhedral and topological structure of ScVO4 projected along [111].
Figure 5. Crystal structure of (a) Sc2O3 and (b) Sc2VO5 (The longer bonds to Sc (>2.8 A˚) are dashed).
All three of the structures take on the anion-deficient fluorite structure, where a cubic close packing of cations is formed. For Sc2O3, the six-coordinated Sc atoms are of two types: instead of eight oxygen neighbors at the vertices of a cube, two are missing, as the right side of Figure 5a shows. For onequarter of the Sc atoms, these two vacant slots are at the end of a body-diagonal (Sc1), and for the remainder at the ends of a face-diagonal (Sc2). Things get more complicated for the structural environment of cations in Sc2VO5, as Figure 5b shows. The V atoms are of two distinct types: one is 4-foldcoordinated to form a tetrahedron, while the other is 6-foldcoordinated to form an octahedron. In addition, the Sc atoms can be categorized into three types: the 6-fold-coordinated Sc cations that form an octahedron by omitting two Sc-O long bonds of 2.8492 (37) A˚, where a pair of oxygens lie on a face-diagonal of a cube (Sc1), and two 7-foldcoordinated Sc cations, one that forms a pentagonal dipyramid (Sc2), while the other forms a capped octahedron (Sc3).
The furthest oxygen anions in the first coordination neighborhood are at distances of 2.325 (5), 2.5929 (33), and 2.4551 (36) A˚, respectively. The variation in the stoichiometric relation between Sc and V will inevitably induce a change in the number of O atoms. Both Sc2O3 and ScVO3 take on the C-M2O3 bixbyite structure by removing one-quarter of the anions from the fluorite structure. In Sc2VO5 5 5 3 fluorite (24.6332 (14) 24.6332 (14) 14.6052 (14) A˚) are assembled to form a superlattice, where the number of oxygen atoms in the fluorite subcell differs from 6 to 8: 1/15 with no oxygen defects; 8/15 with a one-eighth oxygen defect; 6/15 with a one-quarter oxygen defect. The subcells without oxygen defects are isolated from each other by an enclosure of six subcells with a one-quarter oxygen defect. We can also compare the distortion of the cation coordination polyhedra for the scandium containing compounds with that of YVO4 by using the distortion parameters
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Δd=(1/n)Σn{[d(M-O)n-]/}2 and Δa = (1/n)Σn{[a(O-M-O)n - a(O-M-O)>]/}2.63 From Table 3, it is observed that in all cases Sc2O3 has the most evenly distributed Sc-O coordination polyhedra while with decreasing cation radius from Y to Sc the coordination polyhedra centered at Sc and V are somewhat more irregularly distorted. Moreover, in Sc2VO5 the less distorted polyhedra are always found to have a low coordination number. (The relatively large distortion of the Sc-O coordination polyhedra in Sc2VO5 indicates a system of mixed bonding type for scandium, which will be addressed in the next section.) To sum up, with the incongruent vaporization of vanadium oxide, two thermal transitions from a rutile-type structure to a fluorite-type structure are triggered in the nonstoichiometric melt, which can be rationalized in terms of structural similarities during topotactic processes, as well as major lattice reconstructions for the nontopotactic steps due to poorly mismatched ionic radii. The schematic diagram is shown in Figure 6. In the first case when crystallization begins, Sc and V atoms compete to fill the sites in the face center of a cube, forming a fluorite structure. With ongoing evaporation of V atoms near the surface, more and more Sc atoms are assembled topotactically into the structure, followed by a large contraction of the whole lattice (for [100]/[010] 27.6% and for [001] 19.9%). Only a distorted anion deficient fluorite structure, namely, bixbyite Sc2O3, can survive (transformation of 44 f 44). In the latter case when in the molten state, the Table 3. Distortion of Bond Lengths Δd and Bond Angles Δa in Sc2O3, Sc2VO5, ScVO4, and YVO4 Sc2O3 Sc
CN = 6 CN = 7
V
CN = 8 CN = 4 CN = 6
Sc2VO5
Δd
Δa
Δd
Δa
0 2.79
106.1 219.3
32.0
281.8
58.8 34.1
205.7 345.2
0 45.7
0.241 52.8
ScVO4
YVO4
Δd
Δa
Δd
Δa
27.8 0
131.6 37.9
8.1 0
132.8 36.5
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ScO8 bisdisphenoids collapse resulting in a low coordination number, and thus more anions are allocated to the V cations, breaking the junction between ScO8 bisdisphenoids and VO4 tetrahedra. Thus, three distinct types of V ions can been categorized: 1/8 keeping regular tetrahedral coordination, 3/8 with a distorted octahedral coordination, and one-half escaped. The activated V ions can work their way out by interchanging with nearest-neighbor Sc ions interfacially or intrafacially. For convenience, the analysis of this complex process can be rationalized as follows: after interchange, all the atoms in the cube formed by the 2 2 2 zircon-type lattice are rotated around its center through a minor angle of 17.5°, and the 16 V atoms moved out of the original cube can thus be ignored (marked with a circle in Figure 6) making the ratio of Sc to V cations 2:1. Following lattice rearrangement where a large lattice expansion occurs in the [001] direction (by 58.6%) the cube coincides with its six nearest neighbors to form another partial anion-deficient fluorite structure, namely, Sc2VO5 (transformation of 44 f 4.122). Because of the high growth speed in the FZ method, the atom exchange process is somewhat frozen out (reminiscent of Figure 3), and an intermediate ScVO3 phase can thus be found, while in the ex-situ thermal experiment the structural transition of type II dominates in the upper layer of the annealed melts after a relatively long heating time. Electronic Band Structure, Mulliken Bond Overlap Populations, and Standard Thermodynamic Functions of Formation. So far our approach to analyzing structure has been to use a common electrostatic and steric procedure. In the following Discussion, emphasis is put on electron density transfer and bonding type variations associated with the thermal transitions of unstable ScVO4, studied by ab initio calculations. After geometry optimization, the difference in the theoretical and experimental lattice constants is generally less than 1%. The calculated band structure of tetragonal ScVO4 along high symmetry points of the first Brillouin zone is plotted in Figure 7. Meanwhile, the electronic partial density of states (PDOS) of Sc2O3, Sc2VO5, and ScVO4 with the identification of the most important atoms’ contributions are plotted in Figure 8. An energy corresponding to 0 eV was chosen to
Figure 6. Schematic illustration of the topotactical transformations and lattice reconstructions during crystal growth of ScVO4. (White balls indicate empty sites and violet and pink balls indicate Sc atoms while green and light blue balls indicate V atoms.)
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Figure 7. Band structure of the tetragonal ScVO4. The high-symmetry k points Γ, A, M, R, X, and Z in the figure represent the points (0, 0, 0), (1/2, 1/2, 1/2), (1/2, 1/2, 0), (0, 1/2, 1/2), (0, 1/2, 0), and (0, 0, 1/2), respectively.
Figure 9. Charge density distribution around the cation from GGA-PBE computations for different ligand numbers.
metallic phase. This can be ascribed to the carrier doping originating from the degrading of the V atoms’ valence from þ5 to þ4. Compared with ScVO4, the Sc 3p band and O 2s band of Sc2O3 get much closer to the valence band, while those of Sc2VO5 are slightly more tightly bound. This is probably due to the complex bonding environment in Sc2VO5. Moreover, it can be seen that the state density of the Sc 3p orbital in the range of 25-30 eV increases in the following sequence: ScVO4 < Sc2VO5 BiVO4 > ScVO4 > CeVO4. By contrast, in the case of Sc2VO5 a heavy V 3d orbital band crosses the Fermi level, characteristic of a
Sc;O;V differs a little bit from that of
, in that
the charge density in the region between Sc and O is much smaller for the latter structure. With the decrease of the coordination numbers, one or two O atoms out of the eight ligands become further removed from the centered Sc atom with no electron overlap between them. More and more electrons are localized into the intermediate region between Sc and the rest of the O atoms, where the electron density rises sharply. There is a similar trend for the VO4 tetrahedra, except that the electron density is much stronger in the V-O bonds. As a common rule, under ambient pressure, highly ionic materials have a tendency to favor higher coordination structures, whereas highly covalent materials favor lower coordination structures. Therefore, the possibility of a structural phase transition is determined with the degree of ionicity variation being a key factor. Semiempirical Mulliken
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Table 4. Theoretical and Experimental Standard Thermodynamic Functions of Formation enthalpy of formation (kJ mol-1)
Gibbs free energy of formation (kJ mol-1)
species
space group
calc
exp
error (%)
calc
expa
error (%)
V2O3 V2O5 Sc2O3 ScVO4 Sc2VO5
R3c Pmmn Ia3 I41/amd I4
-1096.23 -1562.04 -1729.92 -1688.88 -2405.29
-1218.8 -1550.6 -1908.8
-10.06 þ0.74 -9.37
-1018.14 -1432.73 -1648.44 -1583.48 -2271.96
-1139.3 -1419.5 -1819.4
-10.63 þ0.93 -9.40
a
a
From ref 62.
bond overlap population analysis allows for a more quantitative interpretation of the bond nature, as shown in Table 3 of Supporting Information. A value of zero indicates a perfectly ionic bond, while values greater than zero indicate increasing levels of covalency. For ScVO4 the calculated bond orders of Sc are 0.32 and 0.11, indicating that one-half the Sc atoms have a strong ionic character. However, the Sc-O bond has a more variable bond order value in Sc2VO5, where in the cases of CN=7 the Sc2 atoms are bonded with two O atoms with a bond order value less than 0.10, while the Sc3 atoms are bonded with only one. It is obvious from Table 3 of Supporting Information that the overlap populations of the Sc-O bonds conform to the following decreasing order: Sc2O3 >Sc2VO5 >ScVO4. Accordingly, it is concluded that the covalent character of the Sc-O bonds is strengthened during the thermal alteration of ScVO4 and thus stabilizes the whole structure. The bond order analysis also shows that the V-O bonds are of a more covalent character than the Sc-O bonds, and a relatively more ionic environment is formed in the 6-coordinated V atoms in Sc2VO5, corresponding to a large gap from 0.54 to 0.24. The unstable thermal behaviors of ScVO4 are further interpreted from an energy standpoint. Table 4 gives the theoretical and experimental enthalpy and Gibbs free energy of formation for various compounds in the Sc-V-O system, including V2O3, V2O5, Sc2O3, ScVO4, and Sc2VO5. The theoretical results on the reference materials are in good agreement with the corresponding experimental values within an error of about 10%. It also shows that Sc2VO5 has the lowest theoretical Gibbs free energy with a value of -2271.96 kJ mol-1, almost 1.5 times of that of ScVO4. The next smaller value is in Sc2O3, which is 65 kJ mol-1 lower than that of ScVO4. This sequence shows that Sc2VO5 is the most stable at low temperature, and thus the transition from ScVO4 to Sc2VO5 triggered by the evaporation of vanadium oxide is more energetically favored. Mechanical Properties of ScVO4. In the practical applications such as polishing and cutting optical crystals and the optimization of device performance, there is a strong need to know their mechanical properties and to understand the elastic anisotropy. The elastic stiffness constants determine the response of a crystal to an imposed strain (or stress) and also reflect the bonding characteristics near the equilibrium state. Thus, investigating the full elastic stiffness tensor is essentially the first step to understanding the mechanical properties of tetragonal ScVO4. Table 5 tabulates the full set of theoretical second-rank elastic constant elements of YVO4 and ScVO4 and compares those of YVO4 to the corresponding experimental values. It can be seen that good agreement has been achieved between theoretical and experimental results for YVO4, suggesting that the calculation of the elastic coefficients for isostructural ScVO4 is highly accurate as implemented with the CASTEP code. It is also shown that
Table 5. Elastic Stiffness Constants Cij (GPa) species YVO4 ScVO4 a
calc. expa error (%) cal
c11
c12
c13
c33
c44
c66
221.59 244.51 -9.37 240.93
45.09 48.93 -7.85 77.14
80.84 81.09 -0.31 100.76
290.78 313.70 -7.31 277.87
45.62 48.27 -5.49 23.22
23.27 16.18 43.82 35.55
From ref 69.
relative to YVO4, ScVO4 has a larger value of most components of the elastic stiffness constant. For instance, the elastic constant representing stiffness against uniaxial strains in the [100]/[010] direction, c11, of ScVO4 is 240.93 GPa, which is 8.7% larger than that of YVO4. However, in the [001] direction of ScVO4 c33 is 277.87 GPa, which is 4.4% smaller than that of YVO4. Furthermore, the component c44 of ScVO4, corresponding to the resistance to shear deformation, is 23.22 GPa, and is almost one-half of that of YVO4. All these results show that there is a much larger anisotropy in the mechanical properties of ScVO4. A three-dimensional representation surface of the elastic anisotropy is illustrated in Figure 10, showing the variation of Young’s modulus with different crystallographic directions. In this representation, an isotropic system would have a spherical shape, and so the degree of deviation of the geometry from a sphere indicates the degree of anisotropy in a specific property of a system. From Figure 10, we see that the degree of mechanical anisotropy in ScVO4 is much stronger than that in YVO4, especially along the (100) or (010) crystal surface, where the interactions between cations and anions are most prominent. Referring to Figure 8, such a difference may be also ascribed to the fact that state density of the Sc 3p orbitals close to the conduction band is much larger than the Y 4p orbitals thus consolidating the bonding strength. Table 6 compares the other mechanical properties, such as the bulk (K) and shear (G) moduli, Young’s modulus (Ez) and Poisson’s ratio (vxz), for tetragonal ScVO4, YVO4, and cubic Y3Al5O12 (YAG). Referring to the experimental data of ScVO4 (178(9) GPa)65 and YVO4 (130(3) GPa),66 it appears that the bulk modulus has been underestimated by nearly 20% in the calculated value of ScVO4, while for YVO4 the agreement is extremely well. However, it seems that some of the available experimental values might suffer relatively low precision, as, for one instance, the measured bulk modulus of LuVO4 (one with the nearest ionic radius to ScVO4) reported by different groups differs from each other by a similarly large amount.65 Notice that in the zircon-type ABO4 structure, it has been found that the mean A-O distance at ambient pressure contributes a great deal to its bulk modulus, so we suggest that further experiments would be needed to make a judgment. Besides, the bulk modulus of ScVO4 is much larger than that of YVO4, while the shear modulus is a little smaller. This indicates that with the decrease in R3þ ionic radius an inverse trend is formed in
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Cong et al. Table 6. Other Mechanical Properties and Material Constant Msa Bulk modulus (GPa) (Reuss’s averages) Shear modulus (GPa) (Reuss’s averages) Poisson’s ratio vzx Young’s moduli Ez (GPa) thermal conductivity hκ (W m-1 K-1) thermal expansion coefficient R (10-6 K-1) material constant Ms (10-6 m2 s-1)
ScVO4
YVO4d
YAGe
144.61 35.88 0.3168 214.03 7.3b 7.4c 3.15
132.28 40.38 0.2763 268.88 5.13 6.7c 2.06
185.47 113.59 0.2498 278.45 13.4 7.7 4.69
a All calculations of mechanical properties are based on the isotropy. For tetragonal systems, the thermal properties car calculated as hκ = (2Ka þ Kc)/3, R = (2Ra þ Rc)/3. b The thermal conductivity of ScVO4 was calculated using the scheme proposed in ref 68. c Calculated from ref 35. d The mechanical and thermal properties of YVO4 were calculated from refs 69 and 70, respectively. e The mechanical and thermal properties of YAG were calculated from refs 71 and 70, respectively.
Figure 10. Representation surfaces of the anisotropy of Young’s modulus for (a) ScVO4, (b) YVO4.
the covalency of bonding so that ScVO4 may possess a relatively large hardness but a low shear deformation resistance and thus is more easily cracked. These analyses are consistent with the experimental observations. In laser engineering, there is a well-known “thermal shock parameter” Rs correlating the thermal loading and average output power of a laser rod with the stress fracture when fracture occurs:67 Rs ¼
Kð1 - vÞ Ph σmax ¼ Ms σmax µ RE l
ð4Þ
where κ is the thermal conductivity, ν is Poisson’s ratio, R is the thermal coefficient of expansion, E is Young’s modulus, σmax is the total surface stress, Ph is the heat load power, and l is the length of the rod. As a figure of merit (FOM) of the material, Rs is determined by the material constant Ms under similar surface stress, which is closely associated with the
mechanical properties. The larger its value is, the higher the permissible thermal loading before fracture occurs. Therefore, such mechanical properties play a key role in the laser devices since they determine the maximum surface stress that can be tolerated prior to fracture. By estimating the thermal conductivity of ScVO4 according to the proposed scheme for ionocovalent materials,67 we have also listed the calculated material constants Ms of ScVO4, YVO4, and YAG in Table 6. By comparison, we find that ScVO4 has a material constant only 67% that of YAG but is about one-half as much greater than that of YVO4. This means that with the same surface strength, ScVO4 can endure more thermal shock before cracking and thus shows great potential for high power applications. Optical Properties of ScVO4. The calculated real and imaginary parts ε1 and ε2, respectively, of the frequencydependent dielectric function are shown in Figure 11, for incident light with linear polarization along the [100]/[010] and [001] crystalline directions of tetragonal ScVO4. The line shape of the ε1[100]/[010] curve is nearly the same as that of the ε1[001] curve, both exhibiting five major peaks. However, there is a slight shift of 0.21 eV toward the low-energy region (“red shift”) for the strongest peak in ε1[001] as compared with ε1[100]/[010]. On the other hand, ε1[001] behaves somewhat differently in the peak intensities, registering 1.29 and 1.95 eV, respectively, larger than the corresponding peaks in ε1[100]/[010] in the energy ranges from 0 to 10 eV. For energies larger than 20 eV the ε1[100]/[010] and ε1[001] curves tend to almost overlap. The difference between ε1 for photon polarizations along the [100]/[010] and [001] crystal directions is a consequence of the way that the ScVO4 crystal is structured. Indeed, the ScO8 bisdisphenoids (as well as the VO4 tetrahedra) form linear chains together pointing parallel along the [100]/[010] direction, which tends to improve the transmission of light polarized along this crystalline orientation. Also, referring to Figure 11, the most significant difference in the imaginary part of the dielectric function ε2 takes place in the low energy range of 0-10 eV, where the largest peak of ε2[001], located at 4.01 eV, increases by 0.49 eV while the secondary peak at 5.88 eV is increased sharply by 2.85 eV. Beyond this range there are three similar weak peaks for both polarizations at 19.54, 30.37, and 41.20 eV. The peaks of the imaginary part of the dielectric function ε2 are directly related to electron excitation according to eq 7 of Supporting Information. The first two peaks result from electron transitions between valence bands with significant O 2p character and conduction bands with a dominating contribution from the V 3d levels. The last three peaks for both polarizations
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1064 nm is 1.8295 and 2.0374, respectively. Compared with the corresponding experimental values for Nd:YVO4 (n[001] =2.1652 and n[100]/[010] = 1.9573)72 this result indicates that ScVO4 has a large birefringence, similar to YVO4. At the same time, ScVO4 has a relatively low reflectivity over a large range of energy for both types of polarized incident radiation (
