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Phase Transitions in the Ruddlesden−Popper Phase Li2CaTa2O7: X‑ray and Neutron Powder Thermodiffraction, TEM, Raman, and SHG Experiments Cyrille Galven,† Denis Mounier,†,‡ Boris Bouchevreau,† Emmanuelle Suard,§ Alain Bulou,† Marie-Pierre Crosnier-Lopez,† and Françoise Le Berre*,† †

LUNAM Université du Maine, Institut des Molécules et Matériaux du Mans (IMMM), UMR CNRS 6283, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France ‡ Ecole Nationale Supérieure d’Ingénieurs du Mans (ENSIM), Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France § Institut Laue-Langevin, 6 rue G. Horowitz, 38042 Grenoble Cedex 9, France ABSTRACT: The structure of the Ruddlesden−Popper layered perovskite Li2CaTa2O7, known for its high photocatalytic water activity since its discovery in 2008, is reinvestigated. This oxide has been characterized by powder X-ray and neutron thermodiffraction, TEM, second harmonic generation (SHG), and Raman experiments on powders and single crystals. It is shown that it undergoes two structural phase transitions (i) around 220 °C, mainly characterized by the progressive emergence of SHG signal at low temperatures, and (ii) at 660 °C, mainly characterized by changes of the temperature behavior of lattice parameters and by the emergence of Raman signals that linearly increase on decreasing temperature. It is shown by powder neutron diffraction profile refinements at RT, 400, and 800 °C that the space groups of the successive phases of Li2CaTa2O7 are the acentric Pna21 (RT ≤ T ≤ 220 °C), Pnma (220 °C ≤ T ≤ 660 °C), and Cmcm (T ≥ 660 °C). A soft mode associated with the transition to the highest symmetry for this structural arrangement (I4/mmm) is also found in the Raman spectra. All these transitions appear continuous: the high temperature ones can be attributed to progressive vanishings of the octahedra tiltings (displacives) while the transition in the vicinity of 220 °C from Pna21 to Pnma exhibits order−disorder character.

1. INTRODUCTION Ruddlesden−Popper phases (RP) of general formula A′2[An‑1BnO3n+1] have been extensively studied due to the various properties they exhibit such as ion-exchange,1−3 ionic conduction,4,5 intercalation, and more recently CO2 capture.6 They belong to the layered perovskites family with a structure built from nBO6 octahedra layers forming slabs that are separated by the A′ cations while the A ones are located in the 12-coordinated perovskite cages. In 2004 and 2005, Shimishu et al.7,8 reported for the first time that the RP tantalate phases A′2ATa2O7 (A′ = H, Li, K, and Rb and A = La2/3 or Sr) could behave as catalysts for photochemical water splitting into H2 and O2 under UV irradiation. If their performances remain low compared to that of TiO2, other RP compounds have been subsequently studied leading Yao and Ye9 to conclude that the activity of tantalates was better than that of the niobates. In this context, a study published in 2008 by Liang et al.10 revealed that Li2CaTa2O7, a new two-layer RP phase, also presents a high photocatalytic activity at room temperature. In addition to the study of this property, they also performed the structural determination of this new RP phase from powder X-ray diffraction and transmission electron microscopy (diffraction experiments). This compound was described as crystallizing in the Fmmm © 2016 American Chemical Society

space group with cell parameters a = 5.5153(1) Å, b = 5.4646(1) Å, and c = 18.2375(3) Å, therefore corresponding to perfectly straight perovskite blocks meaning no tilting of the octahedra in the layers. However, the selected area electron diffraction (SAED) patterns given in the paper revealed two sets of reflections: a first one, intense, in good agreement with the Fmmm existence conditions, and a second one, weak, which should be absent in this space group. By comparison with a previous study on Li2SrNb2O7 (Cmcm space group) published by Floros et al.,11 the authors interpreted these extra reflections by twinning and double-diffraction phenomena which seems unlikely here since the extinction conditions are due to an F mode. For this reason and as we think that the structure plays an important role in the understanding of the physical properties, it has been suspected that the structural description of Li2CaTa2O7 in the space group Fmmm proposed by Liang et al.10 is questionable and must be reinvestigated, especially with the help of the neutron diffraction technique. Indeed, in these layered perovskites A′2[An‑1BnO3n+1], tilts of the BO6 octahedra inside the perovskite layers are often observed.11,12 These tilts Received: November 20, 2015 Published: February 22, 2016 2309

DOI: 10.1021/acs.inorgchem.5b02659 Inorg. Chem. 2016, 55, 2309−2323

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Inorganic Chemistry

powder sample was introduced in a Lindemann capillary tube with 0.7 mm internal diameter. In order to achieve efficient SHG, the pump laser beam was focused onto the sample by a microscope objective ×6.3. This microscope objective was also used to collect the backscattered SHG light at 532 nm. The backscattered SHG light was then appropriately filtered in order to completely reject the fundamental light backscattered along the same path as the SHG light. The SHG pulses were received by a high speed photoreceiver New Focus 1601 with 1 GHz bandpass, and the output voltage of the photoreceiver was measured using a digital oscilloscope LeCroy Wavepro 7300A. In order to record the amplitude of the SHG pulses as a function of the sample temperature, the Lindemann capillary tube containing the powder sample was placed in a micro-oven, which can heat the sample up to 300 °C. A small window in the micro-oven is used to irradiate the powder sample by the pump light and to collect the backscattered SHG light. 2.2.3. Thermal Powder X-ray and Neutron Diffraction. Powder Xray diffraction (PXRD) patterns have been collected between room temperature (RT) and 1000 °C with Cu Kα radiation on a PANalytical X’pert Pro diffractometer equipped with the X’Celerator detector and a high temperature attachment Anton Paar HTK12. All the experiments were registered using the following conditions: step scan increment (°2θ) = 0.017; time by step (s) = 300. The RT data were collected in air with angular range (°2θ) = 5.000−140.000 while for temperature experiments, the data collection was performed under argon with a smaller angular range (5.000−90.000). The structural study was performed from powder neutron diffraction (PND) data collected at ILL Grenoble on the D2B high resolution neutron diffractometer using λ = 1.59543(1) Å; angular range (°2θ) = 0.10−159.95; step scan increment (°2θ) = 0.05; counting time = 3 h for the room temperature pattern and, counting time = 5 h, for the patterns recorded at 400 and 800 °C. All the diffraction data (PXRD and PND) were analyzed by means of the Rietveld method15 using Fullprof software16 with a pseudo-Voigt function to describe the peak shape. The background level was first determined manually before being refined. 2.2.4. Raman Measurements. The Raman scattering spectra were collected with a T64000 multichannel spectrometer (Horiba-JobinYvon) using a Si-based CCD detector cooled to −133 °C (liquidnitrogen-cooled). The experiments were performed under a microscope, in the backscattering geometry, with a ×50 long working distance objective (0.50 numerical aperture), and using as excitation the 514.5 nm wavelength radiation of an Ar/Kr laser (Coherent Spectrum) with power less than 10 mW on the sample. Measurements have been done under high resolution, starting 12 cm−1 from the Rayleigh (triple monochromator and 1800 tr/mm grating, 0.6 cm−1 instrument resolution). Spectra were calibrated with the 520.2 cm−1 line of a silicon wafer. The measurements at high and low temperatures were performed on powders under TS1500 and FDCS196 Linkam stages, respectively. In addition, spectra have been collected at room temperature on single crystals exhibiting faces of a few micrometers parallel to the octahedra layers: measurements have been done with the laser beam normal to the large faces, and the crystallites were optically oriented with respect to the birefringence axes. The spectra were refined with Labspec5 software.

result in weak displacements of the oxygen atoms and lead to a larger cell and a lowering of the symmetry. The resulting superlattice reflections are then too weak to be clearly observed on a powder X-ray diffraction (PXRD) pattern, due to the low scattering factors of the O2− ions compared to those of A and B cations. As the neutron diffraction is more efficient to locate light atoms like oxygen or lithium, this technique is undeniably essential to perform a reliable structural determination of Li2CaTa2O7. In addition to the powder neutron diffraction (PND) and PXRD techniques, Li2CaTa2O7 is studied by Raman scattering, second harmonic generation (SHG) tests, and transmission electron microscopy (TEM). The measurements are performed as a function of temperature in order to search and study phase transitions, as observed13 in the isotructural Li2SrTa2O7.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. A polycrystalline Li2CaTa2O7 sample was prepared by solid state reaction at high temperature from oxide and carbonates: 7Li2CO3 (Euriso-Top, 99%), CaCO3 (Merck, 98.5− 100.5%), and Ta2O5 (Alfa Aesar, 99.85%). 7Li was used to reduce the absorption cross section for neutron experiments. CaCO3 and Ta2O5 were weighed in stoichiometric ratio while an excess of 7Li2CO3 (10% mol) was added to compensate the lithium loss at high temperature. As usual, in order to perform the structural study from neutron diffraction data, a large quantity of Li2CaTa2O7 (about 8 g) is needed. Then, it has been chosen to prepare 7 pellets of 1.5 g each. For each pellet, the starting products were intimately mixed together before pelletization. The pellets were preheated together in an alumina crucible at 550 °C for 6 h to decompose the two carbonates, followed by a second one at 1150 °C for 10 h. After grinding, two additional annealings at 1150 °C for a total of 18 h with one intermediate grinding were then applied to obtain well-crystallized powders. Unfortunately, all the PXRD patterns have revealed some weak hkl lines corresponding to the three-layered phase Li2Ca1.5Ta3O10. This impurity appears in the case of loss of lithium, this leading to a condensation of the perovskite blocks. A small amount of Li2CO3 in each pellet was then added before an additional annealing at 1100 °C for 6 h. After this step, all the patterns reveal pure Li2CaTa2O7 phase. In order to ensure the sample homogeneity for neutron diffraction experiments, all the pellets were finally ground together before a last heating at 1100 °C for 6 h in a sealed platinum tube. Unfortunately, this last heating step has led to the emergence (in low quantity) of Li3TaO4 impurity, that disappears by a subsequent annealing in air at 900 °C for 2 h and 1150 °C for 1 h. The formation of a single phase and the good crystallinity of the white powder were then confirmed by PXRD analysis. Small crystals (a few micrometers size) were also prepared from a powder heated in a sealed platinum tube at 1300 °C for 15 h and slowly cooled for polarized Raman scattering investigations. 2.2. Sample Characterizations. 2.2.1. Transmission Electron Microscopy. The TEM study has been carried out with a JEOL 2100 electron microscope operating at 200 kV and equipped with a side entry ±35° ±30° double-tilt specimen holder. A small amount of the sample set in ethanol was ultrasonically dispersed for a few minutes. A drop of the resulting suspension was deposited on a holey carbon film of a Cu TEM grid in order to obtain a random orientation of the crystallites after drying. 2.2.2. Second Harmonic Generation Test. The SHG test is commonly used as a proof of crystal noncentrosymmetry.14 If significant second harmonic light is generated when the crystal under test is irradiated by a short light pulse (the fundamental pump pulse), then one can ascertain that the crystal is noncentrosymmetric, and the SHG test is positive. The test was performed using a microchip Q-switched Nd:YAG laser from Teem Photonics, which emits at the wavelength of 1064 nm short optical pulses of 0.6 ns (full width at half-maximum) and 10 μJ, at the repetition rate of 5 kHz. The test was performed with a polycrystalline Li2CaTa2O7 sample. The

3. RESULTS 3.1. Room Temperature Study. 3.1.1. PXRD Study. The PXRD pattern exhibits narrow hkl lines indicating good crystallization of our product. All of these lines can be indexed in Fmmm, the space group proposed by Liang et al.,10 with refined cell parameters corresponding to a = 5.51397(5) Å, b = 5.46534(5) Å, and c = 18.2355(2) Å. Nevertheless, as Fmmm is most probably not the good space group according to their TEM study, it has been decided to test first the structural model of Li2SrNb2O711 and Li2SrTa2O7,13 both of them crystallizing in the Cmcm space group according to their study from neutron diffraction. With this model, the reliability 2310


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Figure 1. Observed, calculated, and difference PXRD patterns of Li2CaTa2O7 at room temperature in the Cmcm space group. Vertical bars are related to the Bragg reflection positions.

Figure 2. SAED patterns of Li2CaTa2O7 showing the planes along three zone axes: [010] (a), [100] (b), and [001] (c).

Pbn−, corresponding then to the two space groups Pbnm (No. 62, centric) and Pbn21 (No. 33, acentric). A proper rotation of the crystallographic axes a, b, and c allows to pass in the two standard space groups Pnma (No. 62) or Pna21 (No. 33) according to the international crystallographic tables. Lastly, a double diffraction effect can be evidenced on the c*-axis (Figure 2b) and on the a* and b* ones (Figure 2c) since forbidden reflections are present. As usual, this effect can be highlighted by tilting the crystallite around the suspicious axes. This TEM study also reveals diffuse streaks along the c*-axis due to stacking faults as shown, for example, in Figure 3. 3.1.3. PND Study. As expected according to our TEM results, a few PND lines (Figure 4) are neither indexed in the Fmmm space group nor in the Cmcm one, excluding definitively these two space groups. However, these lines are perfectly wellindexed in the Pnma space group obtained from the TEM study (Figure 4). As Pnma is a subgroup of Cmcm, the structural model of Li2CaTa2O7 can be obtained from the transposition of the Li2SrM2O7 (M = Nb or Ta) one.11,13 After permutation of axes and a shift of the origin (0 1/4 1/4), the model is built in Pnma. With this starting atomic model, the refinement quickly

factors decreased quickly with, however, the intensity of the 00l experimental lines higher than that of the calculated ones, meaning that a preferential orientation must be taken into account. With this additional parameter, the agreement between calculated and experimental patterns is quite good (Figure 1), as noticed by the final reliability factors obtained: Rp = 9.64%, Rwp = 9.51%, and RBragg = 5.77%. 3.1.2. TEM Study. The TEM studies (SAED pattern), performed on several crystallites, show good crystallization of the sample. The reconstitution of the reciprocal space always leads to an orthorhombic cell with two parameters, quoted here a and b, very close to 5.5 Å, and the third one, quoted c, close to 18.2 Å, in good agreement with a RP type phase and the previous PXRD results. Two different kinds of 5.5 × 18.2 Å planes are observed (Figure 2a,b). In the first one (Figure 2a), named arbitrarily h0l, the systematic absences are consistent with the condition h + l = 2n, while in the second one (Figure 2b), named 0kl, they are consistent with the condition k = 2n. For the hk0 plane shown in Figure 2c, no condition is observed since all the hk0 reflections are present. The combination of these three reflection conditions leads to the extinction symbol 2311


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sums17 are in Table 2 while selected interatomic distances are reported in Table 3. Figure 5 shows the observed, calculated, and difference plots of the PND pattern. Before ending this part, we can remark that the possibility to refine the Li2CaTa2O7 structure in two space groups, one noncentrosymmetric (Pna21) and the other centrosymmetric (Pnma), with quite similar reliability factors, indicates that the atomic displacements responsible for the non-centrosymmetry are very small. 3.2. Thermal Study. 3.2.1. Thermal PXRD. In order to obtain an accurate evolution of the cell parameters versus temperature, PXRD patterns have been collected on heating (under argon flow) from room temperature to 1000 °C with 75 °C steps (about 15 patterns). For all of them, full pattern matching was performed in the Fmmm space group with the following cell parameters: a ≈ √2ap, b ≈ √2ap (with ap ≈ 3.9 Å, cell parameter of the simple perovskite phase), and c ≈ 18.2 Å. This space group allows indexing of all the PXRD lines whatever the temperature. The cell parameters and the cell volume evolutions with the temperature are shown in Figure 6. A continuous increase of the three cell parameters and consequently of the cell volume is observed. Moreover, the two 5.5 Å parameters a and b tend to be equal under heating, indicating that the orthorhombic distortion progressively vanishes. However, at 1000 °C, the symmetry is not yet tetragonal since an orthorhombic cell is always necessary to fit the observed pattern correctly. If the structural transition from orthorhombic to tetragonal exists, it will occur at higher temperature compared to Li2SrTa2O7 (T ≈ 230 °C).13 A careful examination of the curve reveals, in addition, a distinct slope change for the three cell parameters at about 650 °C although the volume follows a regular increase. Despite this behavior, no thermal phenomenon can be evidenced on the differential thermal analysis (DTA) curve. Nevertheless, this observation can be most probably associated with a phase transition as shown below. 3.2.2. Thermal SHG. The SHG intensity of the Li2CaTa2O7 sample has been followed under heating (Figure 7). The SHG signal clearly seen at room temperature tends to decrease as the sample temperature increases with a complete vanishing when heating the sample above 220 °C. This suggests that, around 220 °C, the crystal structure undergoes a structural transition from a noncentrosymmetric space group to a centrosymmetric one whereas this transition is not associated with any significant cell parameter evolution. 3.2.3. Raman in Temperature. The Raman spectra have been collected on powders for several temperatures ranging from 800 to −190 °C. Some of them are shown in Figure 8a. On cooling from 800 °C, one observes at 660 °C the emergence of a narrow line in the vicinity of 43 cm−1, a line that becomes among the most intense of the spectra; in addition, a structuration of the broad bands in the range 200−400 cm−1 occurs. Under further cooling, the Raman signals that are still broad, especially in the 100−450 cm−1 spectral range, become well-resolved below roughly 200 °C; the line width reduction and peak intensity increase are peculiarly obvious for the isolated line close to 650 cm−1. The resolution greatly increases down to −190 °C, with fairly narrow lines, without any additional change. All these phenomena are reversible. These features unambiguously establish the existence of two phase transitions, one at 660 °C and one in the vicinity of 200 °C, thus implying the existence of three structural phases for Li2CaTa2O7, in agreement with PXRD and SHG results.

Figure 3. TEM image of Li2CaTa2O7 showing stacking faults.

Figure 4. Zoom of the observed and calculated PND patterns of Li2CaTa2O7 at RT in different space groups showing the lines nonindexed in Fmmm and Cmcm space groups and the good agreement in Pnma space group.

converges to very satisfactory reliability factors (Rp = 6.55%, Rwp = 7.81%, and RBragg = 3.20%). However, in view of a positive response of SHG tests in this room temperature phase (see section 3.2.2), an acentric space group at room temperature must be considered. The structural refinement is then performed in the Pna21 space group, the corresponding acentric space group of Pnma. After transposition of the previous model obtained in the Pnma space group, the refinement leads to a slight improvement of the reliability factors (Rp = 6.33%, Rwp = 7.59%, and RBragg = 3.02%). The structural refinement results are given in Table 1; the atomic coordinates, isotropic temperature factors, and bond valence 2312


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Inorganic Chemistry Table 1. Structure Refinement Results of Li2CaTa2O7 at Various Temperatures from PND Data space group no. refined params peak shape, η cell params/Å

half-width params

aymmetry params RBragg Rp Rwp Rexp χ2

RT

400 °C

800 °C

Pna21 (No. 33) 81 pseudo-Voigt, 0.67(2) a = 5.51444(8) b = 5.46631(8) c = 18.2392(2) u = 0.150(3) v = −0.250(6) w = 0.193(3) P1 = 0.011(4) P2 = 0.012(2) 3.02% 6.33% 7.59% 2.13% 12.7

Pnma (No. 62) 102 pseudo-Voigt, 0.29(2) a = 5.53259(5) b = 18.3524(2) c = 5.50468(5) u = 0.073(1) v = −0.182(3) w = 0.183(2) P1 = 0.042(4) P2 = −0.008(2) 2.67% 7.41% 8.19% 3.13% 6.84

Cmcm (No. 63) 90 pseudo-Voigt, 0.37(2) a = 18.5042(2) b = 5.55095(7) c = 5.55804(8) u = 0.066(1) v = −0.180(3) w = 0.177(2) P1 = 0.042(4) P2 = −0.007(2) 2.62% 10.00% 9.94% 3.71% 7.17

Table 2. Atomic Coordinates, Biso, and Bond Valence Sums (∑ν) for Li2CaTa2O7 at RT (Pna21) from PND Data atom

site

x

y

z

Biso (Å2)

∑ν

∑νexpected

Ta1 Ta2 Ca Li1 Li2 O1 O2 O′2 O3 O′3 O4 O′4

4a 4a 4a 4a 4a 4a 4a 4a 4a 4a 4a 4a

0.746(2) 0.260(2) 0.2859(6) 0.003(5) 0.985(5) 0.7315(7) 0.247(2) 0.757(3) 0.461(2) 0.543(2) −0.031(2) 0.022(2)

−0.008(1) −0.005(1) 0.5020(6) 0.244(5) 0.745(5) 0.5764(4) 0.551(1) 0.454(2) 0.714(1) 0.294(1) 0.714(1) 0.273(1)

0.8610(1) 0.1378(1) 0.2471(7) 0.515(1) 0.491(1) 0.2508(8) 0.5380(5) 0.4646(6) 0.1352(6) 0.8703(6) 0.8343(6) 0.1635(6)

0.7(1) 0.4(1) 0.98(7) 0.8(3) 0.6(3) 0.91(5) 0.6(1) 1.5(2) 0.9(2) 0.9 (2) 1.1(1) 0.6(1)

4.97(7) 5.23(7) 2.07(1) 0.90(3) 0.96(4) 1.90(4) 2.04(5) 1.83(5) 2.21(4) 1.84(4) 2.14(4) 2.03(4)

5 5 2 1 1 2 2 2 2 2 2 2

= 8.62%, Rwp = 9.32%, and RBragg = 3.94%), values which can be improved by taking into account an anisotropic thermal agitation for all the atoms: Rp = 7.41%, Rwp = 8.19%, and RBragg = 2.67%. The structural refinement results are given in Table 1 while the atomic coordinates, anisotropic temperature factors, and bond valence sums17 are reported in Table 4. Table 5 gathered selected interatomic distances, and Figure 9 shows the observed, calculated, and difference plots of the PND pattern. 3.2.4.2. Structural Study at 800 °C. Considering the results of the Raman study (structural transition at 660 °C), and of the PXRD study (cell still orthorhombic below 1000 °C), the structural refinement of the neutron diffraction data is performed in the Cmcm space group. For this, we use the structural model of Li2SrM2O7 (M = Nb or Ta) obtained from previous PND studies.11,13 With this model, and anisotropic thermal agitation, the refinement quickly converges to very good reliability factors: Rp = 10.0%, Rwp = 9.94%, and RBragg = 2.62%. Figure 10 presents the observed, calculated, and difference plots of the PND pattern while the structural results are gathered in Table 1. The atomic coordinates, anisotropic temperature factors, and bond valence sums17 are given in Table 6, and selected interatomic distances are in Table 7. Table 8 is also given for a better understanding of the structural filiations between the three phases of Li2CaTa2O7.

Table 3. Selected Interatomic Distances (Å) for Li2CaTa2O7 at RT (Pna21) from PND Dataa

a

Ta octahedra

Ca polyhedra

Li [4 + 1] or [4]

Ta1−O1: 2.07(1) Ta1−O′2: 1.90(1) Ta1−O′3: 2.00(1) Ta1−O′3: 2.02(1) Ta1−O4: 1.96(1) Ta1−O4: 2.01(1) ⟨Ta1−O⟩ = 1.99 Å Ta2−O1: 2.10(2) Ta2−O2: 1.845(9) Ta2−O3: 1.90(1) Ta2−O3: 2.01(1) Ta2−O′4: 1.98(1) Ta2−O′4: 2.06(1) ⟨Ta2−O⟩ = 1.98 Å

Ca−O1: 2.325(4) Ca−O1: 2.492(5) Ca−O1: 3.085(5) Ca−O1: 3.177(4) Ca−O3: 2.54 (1) Ca−O3: 3.13(1) Ca−O′3: 2.68(2) Ca−O′3: 3.30(1) Ca−O4: 2.43(1) Ca−O4: 2.61(1) Ca−O′4: 2.45(1) Ca−O′4: 2.51(1) ⟨Ca−O⟩ = 2.73 Å

Li1−O2: 2.18(3) Li1−O2: 2.19 (3) Li1−O′2: 2 × 2.00(3) Li1−O′3: 2.21(3) ⟨Li1−O⟩ = 2.12 Å Li2−O2: 1.92(3) Li2−O2: 1.99 (3) Li2−O′2: 2.08(3) Li2−O3: 2.22(3) ⟨Li2−O⟩ = 2.05 Å

Mean distances are given in italic type.

3.2.4. Thermal PND. In order to determine the structural changes above 220 °C and above 660 °C, neutron diffraction data have been collected at 400 and 800 °C. 3.2.4.1. Structural Study at 400 °C. Since the PND data collected at room temperature can be satisfactorily treated in the centric space group Pnma, the data obtained at 400 °C are refined in this space group with the corresponding structural model. After refinement, the reliability factors are satisfying (Rp 2313


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Figure 5. Observed, calculated, and difference PND pattern of Li2CaTa2O7 at RT in the Pna21 space group. Vertical bars are related to the Bragg reflection positions.

4. DISCUSSION 4.1. Crystal Structure. Whatever the temperature between RT and 800 °C, the Li2CaTa2O7 structure is constituted by perovskite blocks stacked along the longer axis (≈18.4 Å) (Figure 11). These blocks are built from two layers of irregular TaO6 octahedra sharing all their corners with other TaO6 octahedra thus leading to an n = 2 member of the Ruddlesden− Popper series. The Ca atom occupies the perovskite cage in 12 coordination while the Li atoms are located between 2 successive perovskite blocks in a tetrahedral LiO4 environment except the Li1 environment at RT which can be considered as [4 + 1] due to the octahedra tilting (Table 3). One can also notice that the mean Ta−O, Li−O, and Ca−O distances (≈1.98, 2.10, and 2.73 Å, respectively) remain almost unchanged (Tables 3, 5, and 7) whatever the temperature and are in good agreement with the sum of the ionic radii given in the Shannon Table.18 This good agreement consequently leads to satisfactory bond valence sums17 as can be noted from Tables 2, 4, and 6. Although these distances remain constant, one observes an increase of the longer cell parameter ranging from ≈18.24 Å at RT to ≈18.50 Å at 800 °C. This evolution is mainly due to the straightening out of the Ta−O octahedra under heating as schematized in Figure 11. This straightening out can be seen from the Ta−O1−Ta angle evolution (α) plotted in Figure 12a. This angle increases with temperature meaning that the TaO6 octahedra are less and less tilted. When the octahedra are not tilted, this angle is equal to 180°. This situation is observed for Li2SrTa2O7 which has a tetragonal symmetry above 230 °C, crystallizing in the I4/mmm space group. For Li2CaTa2O7 at 800 °C, only one tilt angle persists and corresponds to a TaO6 octahedra rotation around the longer √2ap-axis. This angle β slightly decreases in temperature as can be seen Figure 12b and is equal to 0° in the I4/mmm space group. 4.2. Raman. The evolution of the Raman spectra with temperature suggests that the transitions are reversible and continuous. This is consistent with the neutron powder diffraction results that show that the structures of the three phases are crystallographically close, that they are group-to-

subgroup related, deriving from the ideal highest symmetry arrangement with I4/mmm space group, encountered in the parent Li2SrTa2O7 at high temperature (above 230 °C).13 It is therefore convenient to describe the normal mode symmetries with respect to this ideal tetragonal phase (denoted phase I), calling ct⃗ the crystallographic axis normal to the octahedra layers. The relationships between the crystallographic parameters in the different structures are given in Table 9. It is worth noting that the cells keep the same orientation (and size) for the three different orthorhombic phases, and therefore, since the samples are grown directly in phase II, the domains preserve the same orientation in phase III and IV. At room temperature, micrometric single crystals are observed as thin square plates, with birefringence axes parallel to the diagonal of the squares (Figure 13). With such axes being parallel to the crystallographic axes in orthorhombic symmetry, it can be inferred that the orthorhombic axes ai⃗ , bi⃗ (i = II, III, IV) in the ⎯a , layer planes are set along these diagonals, with the tetragonal→ I → ⎯ bI , being normal to the crystallite side faces, in agreement with the predictions of Table 9. The results of the normal-mode analysis under such a common reference are shown Table 10. It appears that 36, 72, and 141 Raman lines are expected in phases II, III, and IV, respectively. Experimentally, only 12, 23, and 43 resolved lines are clearly seen in phases II, III, and IV (Table 11), respectively. Above about 200 °C, in phases II and III, apart from ν1, ν2, and ν43, the lines become very broad. This effect, in addition to the large number of components that overlap, prevents us from performing quantitative fits except for the ν41 that is isolated. Such broadenings could presumably be due to the onset of ionic disorder, as can also be postulated from the presence of diffuse streaks in the TEM diagrams. On the other hand, in phase IV, at low temperature the lines appear fairly narrow and well-fitted, although overlaps with very weak contributions cannot be excluded in view of the huge number of expected ones. A partial attribution can be proposed from (i) comparison with Li2SrTa2O7 where the spectra in phases II are very similar and where an attribution has been done in phase I, and (ii) polarized Raman studies on single 2314


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Figure 7. SHG intensity versus temperature for Li2CaTa2O7.

Ii ∝ (ν0 − νi)4

1 1 σi hνi ⎤ ν ⎡ i ⎣1 − exp − kT ⎦

( )

Here ν0 is the exciting laser wavenumber, νi is the wavenumber of the ith vibrational mode, h and k are Planck’s and Boltzmann’s constants, and T is the temperature. A few of such corrected spectra are shown in Figure 8b. As a matter of fact, it appears that several Raman scattering bands do not undergo significant relative changes of their components with temperature (except enlargements) and can be identified as characteristic of the structural arrangement. Polarized analysis on single crystals in the (a⃗i,bi⃗ ) plane at room temperature, in phase IV (Figure 13) also shows complementary information to propose the attribution given in Table 11. 4.2.1. Raman Band Attributions. Under the above approach, the highest frequency mode ν43 (797 cm−1 at 700 °C ; 810.5 cm−1 at −190 °C) is unambiguously assigned to the A1g mode associated with the short Ta−O2 bond stretching normal to the octahedra layers;13 a slight shoulder also grows at high temperature on the high frequency side (this is also observed in Li2SrTa2O713). In the range 579−610 cm−1, in addition to an A1 mode activated by transitions, one observes two lines (ν38, ν40) with B1 or B2 symmetries. Such lines are thought to be issued from the Eg line in phase I attributed to the Ta−O1 bond stretching in the octahedra plane by Pagnier et al.13 in Li2SrTa2O7. The very intense line observed at low frequency (76 cm−1) on powders, but which is very weak on a single crystal (at room temperature) in parallel and crosspolarizations as well, in the (ai⃗ ,bi⃗ ) plane (Figure 13) indicates B1/B2 symmetries which is consistent with attribution to Eg symmetry in phase I, as proposed13 for a similar line in Li2SrTa2O7 (although no significant splitting is observed in any of the low symmetry phases), a mode mostly imputed to Ta vibrations in the octahedra in the (ai⃗ ,bi⃗ ) plane. The very small width of this line and the absence of significant splitting in the orthorhombic phases suggest high ordering and shielding inside the perovskite octahedra layers. Concerning the B1g modes of the ideal phase I, they are expected in cross-polarization in the (a⃗i,bi⃗ ) plane (Table 10). As a matter of fact, the ν26 line fulfilling such conditions is found from polarized analysis at room temperature at 334.7 cm−1 (Figure 13); the second one can be

Figure 6. Evolution of Li2CaTa2O7 cell parameters and volume versus temperature in the Fmmm space group from XRD patterns (pattern matching mode).

crystals (Figure 13), the lines characteristic of the structural arrangement being expected with similar intensities in xx and yy polarization, like in the tetragonal phase I. Moreover, in view of the correlation diagram (Table 10), most of the modes are just activated by the successive symmetry breakings, and their intensities increase with the magnitude of the structural distortions; especially, the lines arising from u-symmetry modes of phase III presumably are too weak to be observed (the additional lines in phase II and III arise from the modes at the boundaries of the Brillouin zone). So, the lines expected as the most intense are those characteristic of the structural arrangement, i.e., those issued from the 10 Raman active modes of phase I (Table 10). For such a characterization it is better to consider the Raman scattering cross sections σi that are not dependent on temperature and can be deduced from the experimental Raman intensities Ii from the relation:19 2315


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Figure 8. Raman spectra of Li2CaTa2O7 collected on powders for selected temperatures. Stars (*) denote for plasma contamination lines. (a) Raw spectra. (b) Relative Raman scattering cross section as deduced from raw spectra corrected for temperature and scattering effects.

any of the other A2 symmetry lines, except the ν34 line that tends to vanish at high temperature. Finally, in view of their intensities in all the phases and their B1/B2 symmetries at room temperature, the remaining modes Eg of phase I are set at ca. 220, 300, and 330 cm−1.

All these results are in agreement with the attributions of the Raman lines in Li2SrTa2O7 issued from measurement on powder, and they actually support some of them thanks to the polarization analysis. The associated normal coordinates can be obtained from ref 13. 2316


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Table 4. Atomic Coordinates, Biso, Bond Valence Sums (∑ν), and Anisotropic Thermal Parameters βij (/Å2 × 104) for Li2CaTa2O7 at 400°C (Pnma) from PND Data atom Ta Ca Li O1 O2 O3 O4 atom

site

x

y

z

8d 4c 8d 4c 8d 8d 8d

0.7469(5) 0.276(1) 0.009(1) 0.734(1) 0.2470(7) 0.4686(5) −0.0207(6)

0.86157(6) 0.25 0.5101(3) 0.25 0.53738(8) 0.1340(1) 0.8368(1)

−0.0020(5) 0.5027(8) 0.245(2) 0.5702(4) 0.5456(3) 0.7202(5) 0.7272(5)

Ta Ca O1 O2 O3 O4

Ta−O1: 2.089(2) Ta−O2: 1.870(2) Ta−O3: 1.958(4) Ta−O3: 1.995(4) Ta−O4: 1.984(4) Ta−O4: 2.020(4) ⟨Ta−O⟩ = 1.986 Å

a

1.51(8)

∑ν

∑νexpected

5.17(1) 1.68(1) 0.81(1) 1.82(1) 2.00(1) 1.88(1) 1.55(1)

5 2 1 2 2 2 2

β11

β22

β33

β12

β13

β23

54(4) 155(14) 140(11) 140(8) 118(9) 84(8)

5.8(4) 13(1) 5(1) 7(1) 16(1) 12(1)

45(4) 102(9) 149(10) 117(7) 110(8) 85(8)

1(2) 0 0 2(2) 2(2) −2(2)

−5(5) −9(14) −28(12) 22(9) 47(8) 59(6)

0(1) 0 0 4(1) −9(2) −5(2)

4.2.2. Characterization of the II−III Phase Transition. Figure 14 shows the temperature behavior of the frequency, intensity ratio, and line width of the two low frequency lines ν1 and ν2. The most striking feature is the emergence of such a narrow line at ca. 43 cm−1 (ν1) with frequency almost temperature independent, and that continuously grows in intensity on cooling to become one of the most intense of the spectra (this signal is also observed in the anti-Stokes part of the spectrum). Its intensity has been normalized by the intensities of the lines at 76 cm−1 (ν2) and 800 cm−1 (ν43) whose scattering cross sections can be supposed to be weakly temperature dependent as fundamental vibrations of the ideal structure, as shown above. This ν1 line is strongly polarized with Ag symmetry in the xx geometry where it appears more intense than the 76 cm−1 one (Figure 13). With regard to such polarization effects, it can be supposed that it is associated mainly with displacements in the (ai⃗ ,bi⃗ ). Within the accuracy of the above experimental results, this phase II−phase III transition appears continuous like a second

Table 5. Selected Interatomic Distances (Å) for Li2CaTa2O7 at 400°C (Pnma) from PND Dataa Ta octahedra

B (Å2)

Ca polyhedron Ca−O1: Ca−O1: Ca−O1: Ca−O1: Ca−O3: Ca−O3: Ca−O4: Ca−O4: ⟨Ca−O⟩

2.362(5) 2.562(8) 3.020(8) 3.162(5) 2 × 2.666(4) 2 × 3.122(4) 2 × 2.476(5) 2 × 2.584(5) = 2.734 Å

Li [4] Li−O2: Li−O2: Li−O2: Li−O2: ⟨Li−O⟩

1.944(8) 2.025(8) 2.174(9) 2.215(9) = 2.089 Å


It can be noted that the Raman spectra of Li2CaTa2O7 in phase II are very similar to those of Li2SrTa2O7 in phase I.13 This suggests that Li2CaTa2O7 undergoes an atomic disorder much higher than that of Li2SrTa2O7.

Figure 9. Observed, calculated, and difference PND pattern of Li2CaTa2O7 at 400 °C in the Pnma space group. Vertical bars are related to the Bragg reflection positions. 2317


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Figure 10. Observed, calculated, and difference PND pattern of Li2CaTa2O7 at 800 °C in the Cmcm space group. Vertical bars are related to the Bragg reflection positions.

Table 6. Atomic Coordinates, Biso, Bond Valence Sums (∑ν) and Anisotropic Thermal Parameters βij (/Å2 × 104) for Li2CaTa2O7 at 800°C (Cmcm) from PND Data atom Ta Ca Li O1 O2 O3 O4 atom

site

x

y

z

8g 4c 8e 4c 8g 8e 8e

0.11108(7) 0 0.2597(4) 0 0.21142(9) 0.6119(1) 0.0893(1)

0.7521(6) 0.258(1) 0 0.6936(8) 0.7858(6) 0 0

0.25 0.25 0 0.25 0.25 0 0

Ta Ca O1 O2 O3 O4

Ta octahedra Ta−O1: 2.081(2) Ta−O2: 1.866(2) Ta−O3: 2 × 1.972(2) Ta−O4: 2 × 1.997(2) ⟨Ta−O⟩ = 1.981 Å a

3.3(1)

β11

β22

β33

β12

9.7(4) 26(1) 9.6(9) 11.8(6) 33(1) 28.2(7)

92(6) 153(16) 256(20) 227(13) 203(13) 142(11)

67(6) 248(17) 364(20) 247(12) 275(16) 178(12)

−1(2) 0 0 −8(2) 0 0

Table 7. Selected Interatomic Distances (Å) for Li2CaTa2O7 at 800°C (Cmcm) from PND Dataa Ca polyhedra Ca−O1: Ca−O1: Ca−O1: Ca−O3: Ca−O4: ⟨Ca−O⟩

2.420(8) 2 × 2.7921(8) 3. 131(8) 4 × 2.833(4) 4 × 2.590(4) = 2.736 Å

∑ν

∑νexpected

5.17(1) 1.68(1) 0.81(1) 1.55(1) 1.88(1) 1.82(1) 2.00(1) β13

5 2 1 2 2 2 2

Biso (Å2)

0 0 0 0 0 0

β23 0 0 0 0 −151(9) 105(8)

Table 8. Correspondence between the Crystallographic Sites in Li2CaTa2O7 for the Different Space Groups Pna21, Pnma, and Cmcma

Li [4] Li−O2: 2 × 2.035(5) Li−O2: 2 × 2.176(3) ⟨Li−O⟩ = 2.106 Å


order phase transition. Such transitions are usually driven by soft modes, i.e., modes with low frequency decreasing to zero at the transition temperature.20 Although a shoulder can be suspected below the frequency range investigated (12 cm−1) at room temperature on a single crystal (Figure 13), on powder there is no significant signal for powder down to −190 °C that could be attributed to a soft mode. The line at 43 cm−1 is not soft (Figure 14a), and this mode cannot drive the transition. It can however be a secondary order parameter with regard to the

a

O1, bridging oxygen; O2, O′2, apical oxygen; O3, O′3, O4, O′4, equatorial oxygen.

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Figure 11. Projection of the Li2CaTa2O7 structure at RT, 400, and 800 °C with reference to standard space group.

quasilinear evolution of its intensity with temperature. As a matter of fact, the Raman intensity is proportional to the square of the polarizability tensor components that are proportional to the atomic distortions (order parameter) u(T), which can be octahedral tilts in view of the structural analysis. With the transition appearing continuous, in the framework of a second order transition occurring at temperature Tc, using the Landau theory,19 as a function of temperature T, u(T) is proportional to (Tc − T)1/2. Since the Raman polarizability is proportional to u(T) and since the Raman intensity I(T) is proportional to the square of the polarizability, one should obtain I(T) ∼ u(T)2 ∼ (Tc − T). Such linear behavior is consistent with the observed experimental results, at least in the whole phase III (Figure 14b). A last question concerns the atomic displacements involved in this mode. In view of the compatibility relations between the mode symmetries in the different phases (Table 10), this mode arises only from modes of the Brillouin zone boundaries of phase II activated by the symmetry breaking (which causes the lattice to switch from B-centered cell to primitive cell). According to the results in Li2SrTa2O7, phase II can be ⎯ ⎯a and → described by small antiphase tilting (ϕϕ0) around → bt t 13 inside the perovskite blocks. From the present structural results, small in-phase octahedra tiltings for adjacent layers around the c-axis induce the symmetry breaking leading from phase II to phase III. According to the ionic coordinates, it appears that the phase transition is mainly associated with the → ⎯ releasing of the atomic displacements along the bt direction (due to the lost of the mirror plane). As a consequence, the normal coordinates of the new Ag modes induced by the phase transition also arise from such displacements. It is worth noting that the line that rapidly grows on cooling exhibits a strong intensity anisotropy with huge effect for polarization parallel to the x-axis (Figure 13). Its very weak line width together with its low frequency suggests it could be mostly due to Ca vibrations in view of the heavy mass and weak charge of this ion, and its localization in a site ordered and shielded in between perovskite

Figure 12. (a) α Ta−O1−Ta angle evolution versus the temperature. The 200 °C value has been obtained from a structural refinement in Pna21. (b) β evolution, octahedra rotation angle around the larger 5.5 Å axis.

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Table 9. Relationships between the Different Phases and Crystallographic Axes a⃗i,b⃗i, c⃗i (i = I, II, III, or IV Phases) with Respect ⎯ → ⎯a ,→ ⎯ S ⃗S S to the Ideal Tetragonal Parent Ones (→ t bt , c t ) in the I4/mmm Space Group, and Those of the Standard Cells (a⃗i , bi , c⃗i ) Used for the Neutron Powder Diffraction Refinements phase I I4/mmma ⎯a → ⎯a = → I

t

→ ⎯ → ⎯ bI = bt ⎯c → ⎯c = → t I a

phase II (800 °C) Bbmm → Cmcma → ⎯s → ⎯ → ⎯a = → ⎯a + → bI aII = ⎯c II II I → ⎯ → ⎯ → ⎯ ⎯a + b ⎯a bII = −→ bIIs = → I I II → ⎯s → → ⎯c = → ⎯c ⎯ II I c II = bII

phase III (400 °C) Pbnm → Pnmaa ⎯→ ⎯s ⎯→ ⎯a = → ⎯a III II aIII = b⃗III ⎯→ ⎯s ⎯→ ⎯ bIII = b⃗II bIII = c⃗III ⎯→ ⎯→s ⎯c c III = → II c III = a⃗III

phase IV (20 °C) Pbn21 → Pna21a ⎯→ ⎯a = ⎯→ ⎯a ⎯→ ⎯s ⎯→ ⎯ IV III aIV = bIV ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯s ⎯a bIV = bIII bIV = ⎯→ IV ⎯→ ⎯→ ⎯→ s ⎯→ ⎯ cIV = cIII c IV = c IV

Standard group.

Figure 13. Room temperature Raman spectra of Li2CaTa2O as powder, and polarized spectra collected on a single crystal (shown in insert) in the z(xx)z (red line), z(yy)z (blue line), and z(xy)z (green line) geometries where z stands for the normal to the perovskite bilayers and x and y are parallel to the a and b crystallographic axes of phase IV (corresponding to the birefringence axes). Asterisks (*) denote plasma contamination lines.

Table 10. Relationship between Symmetries of the Normal Modes of Vibrations at Centers of the Brillouin Zone in the Three Phases Encountered in Li2CaTa2O7 from −190 to 800 °C, and with Those of the Ideal Aristotype Phase Ia

a

The bolded characters depict Raman active modes. The Raman tensor components ((x2 + y2), z2, xy, (xz, yz)) are given for the tetragonal phase I ⎯ → ⎯a , → b , ⎯c cell (common to phases II, III, and IV). (left) and the orthorhombic phases (right) with respect to the → II

II

II

bilayers, just activated by changes of the bond orientations of

[001] axis). It can be pointed out that this atom is not involved

the neighboring atoms (due to octahedra rotations around the

in any of the Ag Raman active modes of phase II. 2320


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Table 11. Frequencies (ν), Relative Peak Intensities (Irel), and Identified Symmetries (Symm) of the Raman Scattering Lines νi of Li2CaTa2O7 in the Various Phases As Deduced from the Spectra Collected on Powders and on Single Crystalsa

a

(B1,B2) stands for B1 or B2, and bold italic characters stand for questionable attributions (see text).

4.2.3. Characterization of the III−IV Phase Transition. As seen in Figure 8a, the spectra in the range ca. 100−400 cm−1, with broad bands at high temperature, exhibit structured signals below about 200 °C; this line width reduction, that is the most prominent signature for the III−IV phase transition, is clearly evidenced in the case of the isolated line slightly below 650 cm−1. At the lowest temperature investigated (−190 °C), all the lines are very narrow which suggests that the compound is fairly well-ordered. A total of 43 lines is therefore observed. This is much less than the total number of expected lines in phase IV (141), but as can be postulated from the correlation diagram (Table 10), most of the predicted lines are just activated by the distortion and so remain presumably with weak intensity: it can

be noted that, in phase IV, 15 A1 symmetry modes are experimentally observed which is in fairly good agreement with the 19 expected to arise from non-u-symmetry modes of phase III (Table 10) that are supposed to be the most intense. The large line broadening that occurs in phase III suggests that the IV−III phase transition is order−disorder. 4.2.4. Additional Features. It is also worth noting that, in phase IV, the ν4 line slightly below 130 cm−1 undergoes a frequency decrease with temperature that is much more important than any other mode (Figure 15) which suggests a so-called soft mode behavior. This line no longer is observed as resolved above about 200 °C due to the general broadenings in phases III and II. However, just on the basis of the data in 2321


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phase IV and under the hypothesis of a continuous phase transition where in the framework of the Landau theory the frequency is predicted to be proportional to (Tc − T)1/2, a transition temperature Tc is found less than 2000 °C. Such a result is consistent with the value ∼1700 °C estimated from the behavior of the β angle (Figure 12b) that appears as the order parameter of the phase II−phase I transition. This therefore suggests that ν4 is the soft mode of this transition. Note also that, whatever the temperature, this mode has a weak intensity: this could explain why the soft mode that has been invoked for the phase II to phase III transition, attributed to octahedral rotations around the [001] axis, has not been observed either.

5. CONCLUSION A complete structural characterization from room temperature to 800 °C of the acentric layered RP perovskite Li2CaTa2O7 has been performed with several complementary techniques: powder neutron and X-ray thermodiffraction, transmission electron microscopy, second harmonic generation, and Raman experiments. Although this phase was discovered in 2008 by Liang et al.10 due to its high photocatalytic activity, no detailed structural study was done until now. To summarize, the powder diffraction (X-ray and neutron) as well as Raman and SHG investigations unambiguously prove the existence of two successive and reversible phase transitions around 220 °C and at 660 °C. At room temperature, a positive SHG response of the powder sample involves the choice of an acentric space group (Pna21, phase IV) to describe the structure. Above 220 °C, no more SHG response can be depicted, indicating thus the loss of the acentric character and consequently the existence of a structural transition. The structure is then described in the centric Pnma space group (phase III). The second transition located at 660 °C according to the Raman results is continuous, and from the diffraction analysis it is shown to occur between Pnma and Cmcm space groups (phase II). A mode with soft character is also observed in the Raman spectra, and according to its temperature behavior, it is associated with a transition from phase II to phase I with tetragonal I4/mmm space group. As shown from PND data refinements at RT and 400 and 800 °C, Li2CaTa2O7 is an n = 2 member of the Ruddlesden− Popper series whatever the temperature. Its structure is constituted by perovskite blocks of TaO6 octahedra stacked along the longer axis (≈18.4 Å). The perovskite cages are occupied by Ca atoms in 12 coordination while in the interlayer spacing the Li atoms are located between two successive perovskite blocks in a tetrahedral LiO4 environment. During heating, the tilting octahedra in the perovskite blocks progressively disappear leading to octahedra that are perfectly straightened in the high temperature form (phase I). The transition at 660 °C is characterized by the emergence of a low frequency line in the Raman spectra with intensity rapidly increasing on cooling without frequency change. The temperature behavior of the intensity suggests a displacive mechanism driven by a soft mode associated with the octahedra tilting around the normal of the perovskite bilayers in view of the structures of the different phases. On the other hand, the very large Raman line broadening occurring at the phase IV−phase III transition suggests order−disorder character.

Figure 14. Characteristics of the ν1 and ν2 lines: (a) Raman shift, (b) relative intensity I(ν1)/I(ν2), and (c) Raman line width on heating (+, ×) and on cooling (○ and ◇).

■

Figure 15. Temperature behavior of the frequency of the ν4 and ν6 modes.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 2322


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The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Jean-Yves Botquelen (IMMM−UMR CNRS 6283−Le Mans), and Vanessa Pagot and Adrien Riot (students of ENSIM−Le Mans) for their help in SHG measurements.

■

REFERENCES

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