Picosecond dynamics from lanthanide chloride melts

Journal of Molecular Structure 1030 (2012) 125–130

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Picosecond dynamics from lanthanide chloride melts Angelos G. Kalampounias ⇑ Department of Chemical Engineering, University of Patras, GR 26 504 Patras, Greece Foundation for Research and Technology Hellas, Institute of Chemical Engineering and High Temperature Chemical Processes, FORTH/ICE-HT, P.O. Box 1414, GR 26 504 Patras, Greece

a r t i c l e

i n f o

Article history: Received 23 January 2012 Received in revised form 9 March 2012 Accepted 9 March 2012 Available online 21 March 2012 Keywords: Raman spectroscopy Molten salts Rare earth-halides Vibrational dephasing

a b s t r a c t The picosecond dynamics of molten lanthanide chlorides is studied by means of vibrational spectroscopy. Polarized Raman spectra of molten LaCl3, NdCl3, GdCl3, DyCl3, HoCl3 and YCl3 are fitted to a model enabling to obtain the times of vibrational dephasing, tm and vibrational frequency modulation tx. Our aim is to find possible sensitive indicators of short-time dynamics. It has been found that all lanthanide chlorides exhibit qualitative similarities in the vibrational relaxation and frequency modulation times in the molten state. It appears that the vibrational correlation functions of all melts comply with the Rothschild approach assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter a indicates the deviation of the melts from the model simple liquid and the similar local environment in which the oscillator is placed and with which it is coupled. The ‘‘packing’’ of the anions around central La3+ cation seems to be the key factor for the structure and the dynamics of the melts. The results are discussed in the framework of the current phenomenological status of the field. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Molten salts are systems formed by charged particles involved in extremely strong Coulombic interparticle interactions compared to molecular liquids. Studies of interactions and dynamics of molten salts may educate the nature of these practically important systems and therefore are of great value for the progress both in the theory and applications. Vibrational spectroscopy is a valuable tool for such studies by studying changes of parameters, such as frequency shifts, line broadening, and frequency non-coincidence effects caused by the interactions of the probe particle with its surrounding in liquid media. The advantage of this approach is the possibility to describe the diversity of different types of interactions and the dynamical properties of the probe particle, such as reorientation and the transfer of vibrational excitation to other degrees of freedom. For a review see e.g. [1]. However, the advances of vibrational spectroscopy are mainly based on conclusions drawn in the course of experiments performed with systems containing discrete chemical species and much fewer attempts have been made in order to register vibrational spectra of ‘‘simpler’’ melts, such as lanthanine chloride halides in the molten state [2,3]. Vibrational relaxation studies employing Fourier transforms of band profiles either in bulk, in solutions or in confined liquids require the presence of isolated ⇑ Address: Department of Chemical Engineering, University of Patras, GR 26 504 Patras, Greece. Tel.: +30 2610 969 558; fax: +30 2610 997 849. E-mail address: [email protected] 0022-2860/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2012.03.025

and intense spectral lines. This requirement poses numerous restrictions of vibrational relaxation studies to a limited number of simple liquids, i.e. those composed of small and symmetric molecules [4]. On the other hand, the vibrational spectra of many organic and inorganic glass-forming substances are characterized by over-lapping lines and hence their study is not straightforward [4]. To overcome the problems mentioned above a different approach has been proposed [5]. By following this approach, one is able to fit severely overlapping spectra using a specific function, which has an analytical counterpart in the time domain. The model function does not prejudice in favor of either Lorentzian or Gaussian but can accommodate any form between these two limiting cases. Its effectiveness has been demonstrated and tested in studies of dynamics in confined liquids [6,7] and glasses [8]. In the present paper we have chosen a series of molten rare earth halides LnCl3 (Ln = Y, Ho, Dy, Gd, Nd and La) to perform a polarization dependent Raman scattering investigation. We applied the above method in order to examine the effect of the different ionic radius of Ln3+ cations in the picosecond vibrational xþ3 dynamics of the LnClx coordination polyhedra, which are present in these melts. 2. Experimental High purity Ln2O3 oxides (Ln = Y, Ho, Dy, Gd, Nd and La) were used as starting materials for preparing LnCl3 salts. The anhydrous salts were obtained by first reacting the corresponding oxides with an aqueous HCl solution. Evaporation of the solution yielded the

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corresponding hydrate, which was dried under vacuum and by slowly raising the temperature (T < 250 °C) during a period of several days. The so obtained salts were finally sublimed twice before use. All operations were carried out in sealed fused silica tubing (6 mm OD, 4 mm ID and 3–5 cm length) and in an Ar atmosphere glove-box having less than 2 ppm water vapor. All cells were transparent, clear, free of optical defects and dust free. Right–angle, Stokes–side Raman spectra were recorded with a 0.85 m double monochromator (Spex1403). The excitation source was an Ar+ laser (Spectra Physics) operating at the 488.0 nm line with an output power of about 100 mW to avoid heating the liquid. The instrumental resolution was fixed at 1.5 cm1 for the whole set of measurements. This spectral resolution is acceptable as it is rather small compared with the typical full width at half maximum (FWHM) of the Raman bands. In fact, we found that the band shapes suffered of no artifacts due to the effect of instrumental slit profile by recording several spectra with different spectral resolution and by deconvoluting of the Gaussian instrumental slit profile from the depolarized Raman spectral distributions directly in the time domain. The illumination source and the slit width are the two factors which influence resolution. Since resolution is a linear function of grating width (i.e. optical path difference), resolution deteriorates if the source illuminates less than the full width of the grating. Bandpass is a function of the reciprocal linear dispersion which, in turn, depends on the wavelength, the grating constant, the focal length of the instrument and the spectral order. At 20491.8 cm1 (488.0 nm) the reciprocal linear dispersion for the Spex1403 monochromator with 1800 gr/mm grating is 70 lm/cm1. Temperature dependent Raman measurements were performed using a homemade furnace and the temperature was controlled with an accuracy of 0.5 K. A calibration procedure with a neon lamp was frequently done during spectra accumulation, to account for possible shifts of the monochromator’s gratings. Both scattering geometries, VV (vertical polarization of incident laser – vertical analysis of scattered light) and HV (horizontal polarization of incident laser – vertical analysis of scattered light), were employed. In order to check the polarization preference of the gratings all four polarization configurations were recorded for a CCl4 reference sample, namely VV, HV, VH and HH. The band profiles and the peak frequencies of CCl4 bands for VV, HH and VH, HV polarization geometries where identical within experimental error. The signal after detection by a water-cooled photomultiplier and amplification by standard electronic equipment was transferred to a computer. 3. Short theoretical background and data analysis Before describing the results obtained and their interpretation it is useful to briefly summarize the necessary theoretical background and to describe the data analysis we have followed. The fact that one can disentangle the scattered intensity caused by the diagonal terms of the Raman tensor (isotropic spectrum) from the scattered intensity caused by the off-diagonal elements (anisotropic spectrum) can provide a valuable piece of information and can help in the elucidation of both structure and dynamics. The experimental Raman intensities IVV(x) and IVH(x) of the two polarization configurations (VV and VH) used for recording the spectra can be used to calculate the isotropic and anisotropic scattering intensities through the relations:

4 Iiso ðxÞ ¼ IVV ðxÞ  IHV ðxÞ and Ianiso ðxÞ ¼ IHV ðxÞ 3

ð1Þ

These intensities Ir(m), where r stands for the iso and aniso configurations, are related to the vibrational density of states (VDoS), g(m) as follows [9]:

Ir ðxÞ / C r ðxÞgðxÞx1 ðx  x0 Þ4 ½nðx; TÞ þ 1

ð2Þ

where Cr(x) denotes the phonon–photon or Raman coupling coefficients that are proportional to the scattering cross section of the corresponding vibrational modes at frequency x and n(x, T) = [exp(hcx/kBT)  1]1 is the Bose–Einstein thermal population factor for the Stokes side of the spectra, with h and kB being the Planck and Boltzmann constants, respectively; x0 is the laser excitation frequency. Based on Eq. (2) the reduced Raman intensities Rr(x) could be calculated:

Rr ðxÞ ¼ Ir ðxÞxðx  x0 Þ4 ½nðx; TÞ þ 11 / C r ðxÞgðxÞ

ð3Þ

It should be pointed here that the reduced iso and aniso representations correct band distortions due to temperature effects and in certain cases allows better fittings of spectra reflecting ‘‘species’’ in equilibrium. Details for the advantages in using the reduced as well as the iso and aniso representations in analyzing the spectra can be found elsewhere [10]. The Fourier transform of the isotropic and anisotropic Raman profiles yields the time-correlation functions of vibrational relaxation and reorientation, respectively

GV ðtÞ ¼

Z

þ1

Iiso ðxÞ expðixtÞdt

ð4Þ

1

Z GR ðtÞ ¼ ð

þ1

Ianiso ðxÞ expðixtÞdtÞ=GV ðtÞ

ð5Þ

1

where both Gv(t) and GR(t) describe the time evolution of the system within the picosecond time domain. These time-correlation functions are able to provide information on the microscopic dynamics in a liquid thus elucidating the origin of the mechanisms underlying molecular processes [1,2,4]. The theory of vibrational dephasing is based on the idea that vibrational phase shifts arise from the changes of the instantaneous vibrational frequency Dx = f(t) (vibrational frequency modulation) which are caused by time-dependent molecular interactions (perturbations). The most general expression of the timecorrelation function of vibrational dephasing can be written as [11,12]:

GV ðtÞ ¼ exp

Z

t

dt

0

Z

t0

Gx ðt00 Þdt

00

 ð6Þ

0

where Gx(t) is the time-correlation function of frequency modulation. There are two approaches to the solution of Eq. (6). In the case where Gx(t) = exp(t/sx) (Kubo model), which is the case for most simple liquids, Eq. (6) yields:

 ln GV ðtÞ=M 2 s2x ¼ expðt=sx Þ  1 þ t=sx R

ð7Þ

R where M2 = x Iiso(x)dx/ Iiso(x)dx is the vibrational second moment (perturbation dispersion). If the phase memory is long (a case characteristic of strongly interacting systems like concentrated aqueous solutions of inorganic salts, etc.), then Gx(t) = exp[(t/ sx)a] (Rothschild–Perrot–Guillaume model [13]). In this case Eq. (6) leads to: 2

 ln GV ðtÞ=M 2 s2x ¼

1 P ð1Þn ðt=sx Þ2þna n¼0 n!ð1 þ naÞð2 þ naÞ

ð8Þ

which for a = 1 transforms to Eq. (7). By fitting time-correlation functions of vibrational dephasing to model expressions given by Eqs. (7) and (8) one obtains the values of a and sx. The former (a) enables to discern between possible modulation mechanisms and to characterize the type of phase memory, which is the memory of the molecular coherence that

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was induced by the scattering process. The variance of the vibrational relative phase is a direct measure of the phase memory. The latter (sx) is considered to reflect the time between collisions in the medium and therefore allows for conclusions about translational and collision dynamics. Since Fourier transforms are not possible in the case of overlapping lines, the approach developed in Ref. [5] aims at treating spectra directly in the frequency domain. This is possible by using the following time correlation function:

ð9Þ

whose Fourier transform can be performed analytically resulting in the following line profile:

IðmÞ ¼ 2c expðs1 =s2 Þðs21 =s2 ÞK 1 ðxÞ=x

ð10Þ

where x ¼ s1 ½4p2 c2 ðm  m0 Þ2 þ 1=s22 1=2 , K1(x) is the modified Bessel function of the second kind, m = x/2pc is the wavenumber in cm1, and m0 is the peak position. It has been shown [5] that the time-correlation function defined by Eq. (9) covers the whole domain of definition of Eq. (8) with s1 close to sx and s2 close to sv, which is the vibrational relaxation time, and was employed in this work to analyze the Raman data of meta-phosphate glasses.

YCl3

P1

HoCl3

o

P2

750 C

P2

750 C

o

P1 o

750 C

DyCl3 P1

P2 o

P2

GdCl3

750 C o

P1

NdCl3

4. Results and discussion The high temperature reduced isotropic Raman spectra of pure LnCl3 molten salts are shown in full range [50–650 cm1] in Fig. 1. The corresponding reduced anisotropic spectra were measured for all LnCl3 melts, however only the reduced depolarized spectrum of LaCl3 is shown in Fig. 1 for clarity. The spectra of the series of molten rare earth halides exhibit a rather common spectral behavior and systematics depending on the ionic size and polarizability of the ions involved [14]. Two bands P1 (polarized) and D1 (depolarized) are dominate the spectra, which are assigned to the m1(A1g) xþ3 and m5(T2g) modes of the LnClx polyhedra as being the predominant species at these melts. Two bands P1 (polarized) and D1 (depolarized) are dominate the spectra, which are assigned to the breathing (stretching) mS and the bending mB modes of the xþ3 LnClx polyhedra as being the predominant species at these melts. The P2 band shifts continuously to lower frequencies with gradually increasing the ionic radius of Ln. This ‘‘isomorphous’’ Raman pattern was found for all chloride [15–18] systems as well as for all the bromide [15] and iodide [19] systems and was attributed to the rigidity of the network-like structure in these melts. The coordination polyhedra are gradually bridged to each other forming in pure LnX3 melts a network of mainly edge-bridged structural units. The above interpretation of the structure is further supported by the findings of simulation studies [20,21], the neutron diffraction [22–24] and EXAFS [25,26] suggesting that the coordination polyhedra consist of distorted structural units, probably octahedra. All these issues have been elucidated in detail in the above references from experimental point of view and will not be further discussed here. In this work we will focus our attention on the vibrational dynamics by monitoring the symmetric xþ3 breathing mode of the LnClx polyhedra. The usual approach to obtain information about the molecular dynamics from the Raman spectra is to numerically Fourier transform the spectra so as to obtain time correlation functions (TCFs) and to fit the obtained TCF with a particular model. To follow this procedure one first has to locate an isolated and non-overlapping line in the spectrum, a fact that can hardly be realized in a wide range of inorganic liquids. This means that overlapping lines, as in our case, could not be used unambiguously for studying molecular dynamics. Before proceed to line shape analysis aiming in extracting information on vibrational dynamics a fitting procedure

P2

P1

Reduced isotropic intensity [arb. units]

GV ðtÞ ¼ expf½ðt 2 þ s21 Þ1=2  s1 =s2 g

P1

780 C P2

D1 D2

ISO

LaCl3

o

900 C ANISO

0

100

200

300

400

500

600

-1

Raman Shift [cm ] Fig. 1. Reduced isotropic Raman spectra of pure rare earth halide melts. Anisotropic (HV) spectrum is shown only for LaCl3 melt. Spectral conditions: k0 = 488 nm, resolution = 1.5 cm1, time constant = 1.0, increment rate = 2.5 cm1/s.

is necessary in order to determine precisely the individual Raman band components. Typical representative results of the fitting procedure for the entire spectral range are shown for GdCl3 (a) and NdCl3 (b) in Fig. 2, respectively. The fitting was performed using the nonlinear regression method based on the Levenberg– Marquardt algorithm. In non-linear regression, parameter estimates can be obtained by the ‘‘method of least squares’’. However, minimization of residual sum of squares yield normal equations, which are non-linear in the parameters. Since it is not possible to solve non-linear equations exactly, the next alternative is to obtain approximate analytic solutions by employing iterative procedures. Three main methods of this kind are the Linearization or Taylor method, the steepest descent method and the Levenberg– Marquardt’s method used in this work. Neither the linearization method, not the steepest descent method is ideal. The latter method is able to converge on true parameter values even though initial values are far from the true parameter values, but this convergence tends to be very slow at the later stages of the iterative process. On the other hand, the linearization method will converge very rapidly provided the vicinity of the true parameter values has been reached, but if initial values are too far removed, convergence may not occur at all. The Levenberg–Marquardt method represents a compromise between the other two methods and combines successfully the best features of both and avoids their serious disadvantages. It is good in the sense that it is almost always converges and does not slow down at the latter part of the iterative process. The validation of the fitting bands using methodologies

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0

(a)

GdCl3 o

Reduced isotropic intensity [arb. units]

750 C

lnGv (t)

-200

YCl3 HoCl3

-400

DyCl3 GdCl3

(b)

NdCl3

NdCl3 LaCl3

o

780 C

-600

P1

0

1

2

3

4

5

t [ps] P2

0

100

200

300

400

500

600

Fig. 3. Time-correlation functions (solid lines) of vibrational dephasing for the stretching vibrations of pure molten rare earth halides LnCl3, where Ln = Y, Ho, Dy, Gd, Nd and La. Experimental (points) vibrational correlation functions fitted to the Rothschild model are also shown for comparison by the use of the a and s parameters. See text for details.

-1

Raman Shift [cm ] Fig. 2. Representative fitting examples for the reduced isotropic Raman spectrum of the GdCl3 (a) and NdCl3 (b) melts. See text for details concerning the fitting procedure and the assignment of the individual bands. Open circles: experimental data (only one of the four points are shown for clarity); solid lines: profiles of individual components.

other than Levenberg–Marquardt’s method did not provide better goodness of fit. The assignment of the individual band profiles is in the context of the structural model for pure molten rare earth halides LnCl3 described above. With all linear spectroscopies, as Raman spectroscopy, there is an inherent difficulty in separating the orientational and vibrational dynamics from the line shape and the contributions from inhomogeneous broadening cannot be eliminated. In our case, the same computational procedure was performed for both isotropic and anisotropic spectra. The corresponding calculated values of s1 and s2 are practically identical within the limits of the accuracy of our procedure. This fact is indicative of coincidence of isotropic and anisotropic profiles and the most important that in both scattering geometries only vibrational dephasing is probed. The statistical independence of the vibrational and reorientational processes in these systems is further supported by the observation that the isotropic and anisotropic bandwidths are similar. On the other hand, in complex liquids the statistical separation of vibrational and orientational relaxation may be achieved naturally since the orientational relaxation process, especially for the tumbling motion (reorientation of the long molecular axis), has very long characteristic times starting from decades of picoseconds up to nanoseconds in these systems [27,28] which are, in any case, longer than the dephasing times, which are typically in the picoseconds time scale. The causes of line broadening in ionic systems have been studied in detail in the past and reviewed in Ref. [1]. The most probable source of additional broadening of lines attributed to highly polar vibrations, such as the m1 vibration, appears to be the dissipation of vibrational energy due to ion–dipole interactions. Having in mind the above consideration, we present in this study the computational results from the isotropic line profiles. The time-correlation functions of vibrational dephasing for the stretching vibrations of pure molten rare earth halides LnCl3 are shown in Fig. 3. Experimental (points) vibrational correlation functions represented by points are fitted to the Rothschild model by the use of the appropriate values of a and s parameters and for

all Ln cations. The results reveal that there is a remarkable similarity of the time-correlation functions corresponding to LnCl3 melts. Furthermore, the values of the characteristic time sx and sv presented in Fig. 4a and b, respectively for the stretching vibration of molten rare earth halides versus ionic radius of all Ln central catxþ3 ions in LnClx polyhedra used in this work appear to be constant. The corresponding values of the ionic radius of the La3+ cations used in this work are 104, 104.1, 105.2, 107.8, 112.3 and 117.2 pm for Y, Ho, Dy, Gd, Nd and La, respectively [29]. The vibration state is usually discussed from the valence and mass point of view of the constituent atoms. In this study we have chosen to discuss the results versus ionic radius in an effort to examine the possible existence of anomalous behavior in properties, such as that reported on metaphosphate glasses and attributed to changes in the ionic radius of the metal cations [30]. Both characteristic times appear to be constant and independent of the increasing ionic raxþ3 dius of the Ln central cation in LnClx polyhedral units, which are the predominant species at these molten salts. On the contrary, the corresponding characteristic times in metaphosphate glasses, after analyzing the symmetric stretching modes ms (PO 2 ) and ms  (P–O–P) of the PO entity of PØ O units and of P–O–P bridges 2 2 2 in metaphosphate arrangements, experience an intermediate dynamical regime that gets only slower with increasing the ionic radius of the cation-modifier [8]. The properties of the medium in which the oscillator is placed and with which it is coupled seem to be the key factor in order to interpret the correlation between the parameter s and the ionic radius. The description of the perturbation decay process can be achieved by a model, which takes into account the structural relaxation of the aggregates aiming in the interpretation of the vibrational dephasing of these complex liquids. The Rothschild approach provides a general framework for the interpretation of the vibrational correlation functions observed in liquids with local, short-lived order, by assuming for the perturbation decay a stretched exponential function [11]. This model represents a generalization of earlier proposed formulation based on the assumption of a single exponential function for the perturbation decay. The latter can be thought of as the limit to which the first tends in the absence of structuring processes as in simple molecular liquids. Our analysis revealed that in all cases the phase memory is long and thus the Kubo model (a = 1) cannot successfully describe modulation processes. The ionic radius dependence of a parameter

A.G. Kalampounias / Journal of Molecular Structure 1030 (2012) 125–130

Y Ho

[ps]

lanthanide chloride melts is shown in the inset of Fig. 5, where the chlorine packing is revealed. Based on the above findings we may also conclude that molten rare earth halides are considered as a strongly interacting system similar to the metaphosphate glasses and the concentrated aqueous solutions of inorganic salts where the phase memory is long and the modulation is described by a stretched (a < 1) correlation function.

(a)

4

3

Gd

La

Nd

Dy

2

5. Conclusions

(b) 0.006

[ps]

129

Y Ho

Gd

La

Nd

Dy

0.004

104

108

112

116

radius [pm] Fig. 4. Dependence of the modulation times, sx (a) and dephasing times, sv (b) on xþ3 the ionic radius of the Ln central cation in LnClx polyhedra for the stretching vibration of pure molten rare earth halides.

is presented in Fig. 5. The experimental molar volumes of rare earth trichlorides versus effective ionic radius of Ln cations are also shown in Fig. 5. The a parameter values determine in a confident way the dispersion of relaxation times and consequently reflect the properties of the medium around the oscillator. The a parameter can be considered as a universal molecular parameter, which is the same for all oscillators in the given medium. The results indicate that this parameter is independent of the ionic radius of the xþ3 central cation in LnClx polyhedra implying a similar local environment around octahedral units. Furthermore, all melts have similar molar volumes which are approximately independent of the Ln cation. This implies that both the a parameter and the molar volume of the melts are mainly determined by the ‘‘packing’’ of the chlorides, which is presumably very similar for all LnCl3 melts [31]. A schematic representation of the bridged octahedra in

A systematic polarization dependent Raman spectroscopic study of a series of molten LaCl3, NdCl3, GdCl3, DyCl3, HoCl3 and YCl3 has been undertaken in order to study changes in picosecond dynamics. The time-correlation functions of vibrational dephasing were obtained and characteristic vibrational relaxation and xþ3 dephasing times of the symmetric stretching modes of LnClx polyhedra, which are the predominant species at these melts, have been determined. All lanthanide chloride melts exhibit qualitative similarities in the vibrational relaxation and frequency modulation times in the molten state as is evident from the time-correlation functions for all Ln cation studied. It was also found that all melts studied are sufficiently deviate from the Kubo model and comply with the Rothschild approach assuming that the environmental modulation is described by a stretched exponential decay. The behavior of the dispersion parameter a with increasing ionic radius of the Ln cenxþ3 tral cation in LnClx polyhedra indicates that these melts are a strongly interacting system and deviate substantially from the model simple liquid. The values of a parameter and the molar volume of the melts were found to be insensitive with the ionic radius of Ln cation variation implying similar properties of the medium in which the oscillator is placed and with which it is coupled. The ‘‘packing’’ of the chlorides, which is very similar for all molten rare earth chlorides, seems to be the key factor for the structure and the dynamics of the melts. The results are compared with the findings of a recently reported study concerning metaphosphate glasses. Acknowledgments The author wishes to thank Professor G.N. Papatheodorou for providing Raman spectra and helpful discussion during the writing of the present paper. References

1.0

[1] [2] [3] [4]

100 96

Vm

0.6 Y

Ho Dy

Gd

Nd

La

84 80

0.4

76 0.2

-1

88

[5] [6]

3

92

[7]

Vm [cm mole ]

0.8

72 68

0.0 104

108

112

116

[8] [9] [10] [11] [12] [13] [14]

radius [pm] Fig. 5. Dispersion parameter a (left axis) and experimental molar volumes (right xþ3 axis) versus ionic radius of the Ln central cation in LnClx polyhedra for the stretching vibration of rare earth trichloride melts. Lines are drawn as guide to the eye. Molar volumes are taken from Ref. [28]. Inset: schematic representation of the bridged octahedra in lanthanide chloride melts.

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