J. Chem. SOC., Faraday Trans. I, 1982, 78, 2051-2058 Structural Analysis of Molten Na,BeF, and NaBeF, by X-ray Diffraction BY NORIMASA UMESAKI AND NOBUYA IWAMOTO Welding Research Institute, Osaka University, Yamada-kami, Suita, Osaka 565, Japan AND HIDEO OHNO* AND KAZUO FURUKAWA Molten Material Laboratory, Division of Nuclear Fuel Research, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 3 19-1 1 , Japan Received 30th April, 1981 The structures of molten Na,BeF, (923 & 10 K) and NaBeF, (743 f 5 K) have been investigated by X-ray diffraction analysis. BeF, tetrahedra existing in the crystalline state persist as the fundamental structural unit in the molten state. Molten Na,BeF, contains mainly monomeric BeF,2- with four unshared F- comers. A configuration for four Na+ cations around a BeF, tetrahedron is suggested for molten Na,BeF,. In molten NaBeF,, short-chain anions, such as the common F- comer sharing dimeric Be$- and/or trimeric Be,F$j, mainly occur.The physical properties, such as self-diff~sion,l-~ electrical cond~ctance,~ viscosity5 etc., of systems containing molten alkali fluoroberyllates, XF(X = Li, Na or K) and BeF, are very different from those of molten alkali halides owing to the three- dimensional network character of BeF,. Moreover, the corresponding-states principle6 may be applied between the following pairs, (1) LiF-BeF, and MgO-SiO,, (2) NaF-BeF, and CaO-SiO, and (3) KF-BeF, and BaO-SiO,, in their intermediate composition regions under a reduced absolute temperature scale ; the phase diagrams and physical properties, such as ionic packing density, self-diffusion coefficient, viscosity coefficient and equivalent conductivity, in these pairs are in excellent agreement.We have measured the self-diffusion coefficients of lithium3 and fluorine'? in molten Li,BeF4 and LiBeF,, respectively. Fluorine is exchanged between neigh- bouring beryllate units with the rotation of beryllate anions, and there is a strong similarity between fluorine diffusion in molten fluoroberyllates and oxygen diffusion in molten silicates. Consequently, a direct comparison of the structures of molten fluoroberyllates with those of molten silicates is essential for elucidating similarities in the physical properties of these two systems. A structural investigation of the LiF-BeF, system using X-ray diffraction methods has been carried out by Vaslow and Narten.' They interpreted their results in the following manner: (1) the predominant structural unit is the BeFi- tetrahedron; (2) at low LiF concentrations these are linked together with each F- common to two tetrahedral units; (3) with increasing LiF concentration the linkage breaks down, but each Be2+ is maintained in a tetrahedral F- environment; (4) the Li+ ions are located outside the tetrahedral unit in locally disordered F- environments, the degree of disorder increasing with LiF concentration ; (5) the changes in interatomic spacing and coordination number that accompany fusion are consistent with the changes in density.Nevertheless, the configuration of the Li+ ions located around the BeF tetrahedral units is unknown.On the other hand, 205 12052 X-RAY STUDIES OF MOLTEN Na,BeF, AND NaBeF, Waseda and Toguris have reported an X-ray study of the molten systems MgO-SiO, and CaO-SO,. Unfortunately, no discussion of the structural similarities between these molten fluoroberyllates and silicates has been attempted. In this paper we report an X-ray diffraction analysis of molten Na,BeF, and NaBeF, and discuss the structural similarities between molten NaBeF, and CaSi0,.8 EXPERIMENTAL Prior to the X-ray diffraction experiment the samples were prepared as follows. Weighed amounts of NaF (analytical reagent grade, Merck) and BeF, (Rare Metallic Co) were thoroughly mixed in a dry glove box and melted in a Pt crucible under a He atmosphere. After being melted for ca.1 h the samples were cooled and crushed. The prepared samples were placed on a flat Pt tray (35 x 25 x 3 mm3) and heated in a small electric furnace made of Pt wire. The sample-heater assembly was enclosed under a He atmosphere by putting it in an air-tight chamber with a window of A1 foil of thickness 10 pm to allow passage of the X-ray beam. The temperature was controlled to within a maximum error of 10 K throughout the measurement. The X-ray diffraction experiment was carried out with the use of a 8-8 diffractometer with parafocusing reflection geometry and Mo K, (A = 0.7107 A) radiation monochromatized by a curved graphite monochromator mounted in the path of the diffracted beam. Slit systems of pf" and lo-lo were employed for the low (3 < 8" < 10) and high (8 < 8" < 50) scattering angles, respectively (0 is the scattering angle).The X-ray scattering intensities were measured at 0.25' intervals over the whole range of scattering angle using the step-scanning technique. Several runs were made in order to accumulate 2 x lo4 counts per datum point for low-8 and (3.4-4.0) x lo4 counts per datum point for high-0. After the X-ray intensities measured uia the two different slit systems had been normalized for the overlapping section they were corrected for background, polarization and Compton scattering, and then were scaled by means of the Krough-Moe-Norman method to the theoretical intensities arising from independent atoms contained in the stoichiometric unit. The radial distribution function D(r), the correlation function G(r) and the reduced intensity function S .i ( S ) are given as m m D(r) = 4nr2p0 X K + (QZ 2r/n fSmax S . i ( S ) sin (Sr) d S (1) i-1 i-1 J o (2) i-1 / i m \ where m is the number of atoms contained in the stoichiometric unit, Ki the effective electron number of atom i, po the mean electron density,h(S) the independent atomic scattering factor of atom i corrected for anomalous dispersion, cEh ( S ) the total coherent scattering intensity and S,,, the maximum value of S (= 4nsin8/3,) reached in the diffraction experiment. The constants used in the calculations of eqn (1)-(3) are given in table 1. RESULTS AND DISCUSSION Fig. I shows the observed reduced intensity functions S . i(S) of molten Na,BeF, (923 f 10 K) and NaBeF, (743 Ifr 5 K).The radial distribution functions D(r), the function D(r)/r and the correlation functions G(r) are shown in fig. 2 and 3. Ghosts originating from experimental errors and/or incorrect treatments are not recognized in these curves. As shown in fig. 2 and 3, these curves indicate peaks at 1.60-1.65 A, 2.22-2.35 A, 2.60-2.65 Aetc. Table 2 shows thedistances (rii 0.01 A)andcoordinationN. UMESAKI, N . IWAMOTO, H. O H N O A N D K. FURUKAWA 2053 TABLE PARAMETERS USED IN THE CALCULATIONS OF EQN (1)-(3) parameter Na,BeF, NaBeF, temperature / K 923 _+ 10 743 f 5 densityZ0/g CM-, 2.093 2.1 13 molar weight 130.997 88.991 effective electron number 11.84 11.98 3.73 3.77 8.65 8.75 13.5 13.0 5 ._ oj 0 2 4 8 10 12 14 S I P FIG. 1 .-Reduced intensity functions S .i ( S ) ; (a) molten Na,BeF, (923 + 10 K), observed (full line) and calculated (dotted line); (b) molten NaBeF, (743 f 5 K). numbers (nilj 0.1 atoms) of the nearest-neighbour ionic pairs in molten Na,BeF, and NaBeF, derived from the functions D(r)/r by assuming a Gaussian distrib~tion.~ In the known crystalline forms of some alkali fluoroberyllates, such as Na2BeF,10 and Li,BeF,,ll each Be2+ cation is tetrahedrally surrounded by four F- anions with a Be-F distance of 1.54-1.5 A and a F-F distance of 2.50-2.56 A. Therefore, the first peaks at 1.60-1.65 A and the third peaks at 2.60-2.65 A of the observed curves are due to Be-F and F-F pairs in the BeF, tetrahedra. In addition, the observed coordination number of the nearest-neighbour F- anions around Be2+, nBe,F, is ca.3.8-4.0. These results indicate that BeF, tetrahedra existing in the crystalline state persist as the fundamental structural unit in the molten state, and the mean distances between the ions in a BeF, tetrahedron become slightly longer in the melt than in the solid. The second peaks at 2.22-2.35 A are due to the nearest-neighbour Na-F pairs; the distance between these ions is nearly the sum of the ionic radii12 of Na+ (0.95 A) and F- (1.36 A). Our results are similar to those for the molten LiF-BeF, system reported previously by Vaslow and Narten.72054 X-RAY STUDIES OF MOLTEN Na,BeF, AND NaBeF, c 4 2 *G I 3 2 1 0 ..i 0 2 4 6 8 1 0 0 2 4 6 8 1 0 FIG. 2. FIG. 3. r l A rlA FIG. 2.-Radial distribution function D(r), function D(r)/r and correlation function G(r) of molten Na,BeF, (923 f 10 K).FIG. 3.-Radial distribution function D(r), function D(r)/r and correlation function G(r) of molten NaBeF, (743 f. 5 K). TABLE 2 . a B S E R V E D DISTANCES AND COORDINATION NUMBERS OF THE IONIC PAIRS IN MOLTEN Na,BeF, AND NaBeF,. INCLUDED FOR COMPARISON ARE THE DATA FOR MOLTEN CaO-SiO, REPORTED BY WASEDA AND TORGURI* liquid crystal liquid Na,BeF, NaBeF, Na,BeF, ionic CaO-SiO, (1873 K) sum of (923 & 10 K) (743 & 5 K) (DeganellolO) radii (Waseda et aL8) Be-F rBe-F/A 1.65 1.60 1.54-1.56 1.67 si-o r,-o/A 1.63 Na-F rNa-F/A 2.22 2.35 2.27-2.54 2.31 Ca-o rCa.O/A 2.41 nBe/F 4.0 3.8 nsi/o 3-8 nNa/F 2.8 1.8 nca/o 6.9 2.60 2.50-2.56 2.72 o-o ro-o/A 2.66 3.5 noio 5.8N. UMESAKI, N. IWAMOTO, H. OHNO AND K. FURUKAWA 2055 MOLTEN Na,BeF, In molten Na,BeF, the observed coordination number of the F-F pair in BeF, tetrahedra, n,/,, is 3.0.This suggests that BeF, tetrahedra exist mainly in an isolated form with four unshared F- corners, monomeric BeFi-, in molten Na,BeF,. Quist et a1.13 showed, using Raman spectroscopy, that monomeric BeFi- was the predominant beryllium-containing species in molten Na,BeF, and Li,BeF,. A similar result was obtained from e.m.f. measurement of the molten LiF-BeF, system by Holm and Kleppa.', They reported that, up to X(BeF,) = 0.33, corresponding to the composition Li,BeF,, the partial molar excess entropy of beryllium fluoride was positive and changed little with composition, owing to complete depolymerization of the three- dimensional network structure of beryllium fluoride ; i.e.the formation of monomeric BeFi- anions bonded by Coulombic forces. Most of the Naf ions might occupy the various stable positions around the monomeric BeFi- for some time and then migrate to other positions through voids in the melt. ( b ) FIG. 4.-Schematic illustration of typical configurations of Na+ ions around a BeF, tetrahedron : (a) comer-site position, (6) edge-site position and (c) face-site position. In order to advance understanding of the transport properties of molten Na,BeF,, the short-range arrangements were examined with reference to the three typical configurations of sodium atoms around the BeF, tetrahedron, as shown in fig. 4. In one configuration the sodium atom occupies a corner site in the BeF, tetrahedron, and Na-F and Na-Be distances are 2.31 and 3.96 A, respectively.In another configuration the sodium atom occupies an edge site and the Na-Be distance is 2.87 A. In the third configuration the sodium atom occupies a face-site and the Na-Be distance is 2.35 A. Various models of the short-range arrangement were constructed by combining the three typical configurations with one another in a stoichiometric unit and were examined by trial and error using the following Debye scattering equation15 r m 1 m m S i(W E fi ( S ) = I: C ni/jfi2(Slf3(S) exp (- bijS2) sin (Srii)/rii (4) li-1 1 i-lj-12056 X-RAY STUDIES OF MOLTEN Na,BeF, A N D NaBeF, wheref,(S) andf,(S) are the independent atomic scattering factors of atoms i and j , rij the distance between atoms i and j and bij the temperature factor, i.e.half the mean-square variation in rij. To check the ‘goodness of fit’ of the calculated reduced intensity to the observed one, the quantity R was introduced, where Of the possible models, the one giving the best fit was as follows: four sodium atoms surrounding the BeF, tetrahedron, two of these occupying corner-sites while the others occupy edge-sites. The calculated reduced intensity curve was refined by the least- squares method in the range 4.0 < S/A-l < 13.5 in order to achieve a better agreement with the observed curve, starting with parameters obtained from typical arrangements of the four sodium atoms around the BeF, tetrahedron as mentioned above. Here the interactions of atomic pairs beyond values of r = 6 A were neglected because peaks in the G(r) curve in this range were insignificant, and the numbers of atomic pairs were fixed in order to maintain the stoichiometric unit.The final parameters of the most probable short-range arrangement in molten Na,BeF, are listed in table 3. The final value of R for this model is 0.326, which was obtained by using the S . i ( S ) values above S = 4.0 A-1 with interval A S = 0.05 A-l. The calculated reduced intensity curve S. i(S) for this model is shown in fig. 1 (dotted line) and is in good agreement with the observed curve for S > A-l. However, agreement was poor for S < 4 A-l. This disagreement is due to the contribution from the long-range arrangement of molten Na,BeF,. TABLE 3.-PARAMETERS USED IN CALCULATING THE MOST PROBABLE STRUCTURAL MODEL BY EQN (4). ni,j, rij AND < Arij2 > ARE THE COORDINATION NUMBERS OF^ IONS AROUND ANY ORIGIN i ION, THE DISTANCE AND THE ASSOCIATED ROOT-MEAN-SQUARE DISPLACEMENT BETWEEN IONS i AND J, RESPECTIVELY m m Be F F F Na Be Na Be Na F Na F Na F Na Na Na Na 8.0 1 2 .0 2.0 2.0 6.0 4.0 6.0 0.7 1.3 1 . 6 5 2.62 3.35 4.24 2.22 3 . 9 9 4.72 3 . 3 0 5.51 ~ 0.100 0 . 1 4 2 0.085 0.095 0.098 0 . 1 3 1 0 . 1 8 4 0.245 0.283 a rij+O.O1 A: < Arij2 > 1+0.005 A. The coordination number of the nearest-neighbour Na-F pairs, nNa/F, in this model is 3.0, which is almost equal to the observed value (2.8). From measurements of the spin-lattice relaxation time for molten NaBeF, by means of nuclear magnetic resonance, Matsuo and Suzuki16 have pointed out the possibility of an edge-site position for the Na+ ion around the BeF, tetrahedron.These results are not inconsistent with those obtained by X-ray diffraction.N. UMESAKI, N. IWAMOTO, H. OHNO A N D K. FURUKAWA 2057 MOLTEN NaBeF, Up to the composition range of Na,BeF,, mixtures rich in NaF will chiefly contain Na+ cations, and F- and monomeric BeF:- anions. As the BeF, concentration increases, the polymerization process proceeds and pure molten BeF, forms a three-dimensional network structure of BeF, tetrahedra. NaBeF, is the intermediate phase between these composition extremes. From viscosity5 and thermodynamic data1, we can estimate that a mixture with the composition of NaBeF, contains a high percentage of polymeric anions of small chain size, such as (BenF3n+l)(n+1)- (n = 2, 3,4,.. . ), or closed rings, such as (BenF3n)n- (n = 3,4, 5,. . .). In molten NaBeF, the observed coordination number nF/F was ca. 3.5. The calculated average nF,F of chain anions such as (BezF7),-, (Be3FlJ4-, (Be4F13)5- and (BeF,)g- are 3.4, 3.6, 3.7 and 4.0, respectively. On the other hand, the value of +/F for closed-ring anions is always 4.0. Therefore, the possibility of the formation of longer-chain polymers or large-ring anions is small, and the probability of small-chain anions such as (Be2F7),- and (Be3Flo),- is considered to be large in molten NaBeF,. The existence of (Be2F7),- anion in molten Na,LiBe,F, has been shown by Raman spectroscopy . As noted in the introduction, a molten NaF-BeF, system should have essentially the same structure as molten CaO-SiO, system by the corresponding-states principle.6 X-ray structural analysis of molten CaO-SiO, (50-50 m/o) was carried out by Waseda and Toguri.s We examined the similarity between the structures of molten NaBeF, (measured temperature, T = 743 K; melting point, T, = 645 K; reduced absolute temperature scale, T/T, = 1.15) and CaO-SiO, ( T = 1873 K, T, = 1813 K and T/T, = 1.03).As shown in table 2, the coordination number of nearest-neighbour 0-0 pairs in molten CaO-SiO,, nolo (= 5.8), is different from nF/F (= 3.5) in molten NaBeF,. Waseda and Toguri8 also reported that the addition of CaO up to x(Ca0) = 0.57 had no effect on no,o in molten CaO-SiO,. This result indicates that the three-dimensional network structure is present at all CaO-SiO, compositions, in conflict with physical properties such as viscosity,ls electrical conductancelg etc., of this molten system.When CaO is added to molten SiO,, the viscosities of the resulting mixtures drop dramatically, owing to the rupture of three-dimensional network structure of the SiO, tetrahedra. In contrast Vaslow and Narten7 showed that nF/F in the molten LiF-BeF, system decreased from a value of 6(BeF,) to 2(LiBeF,) on the addition of LiF. Their results are in good agreement with ours. From the discussion above, we consider that there is room for reconsideration with respect to the X-ray study by Waseda and Toguri.8 CONCLUSIONS We can summarise the results obtained as follows. (1) In molten Na,BeF, and NaBeF,, BeF, tetrahedra exist as the fundamental structural unit.The mean distances between the atomic pairs in a BeF, tetrahedron become slightly longer in the melt than those found in the solid. The mean distances of the nearest-neighbour Na-F pairs are close to the sum of the ionic radii of Na+ and F-. (2) Molten Na,BeF, contains mainly monomeric BeFi- ions with four unshared F- corners. This result is supported by the results from Raman spectroscopy and e.m.f. measurements. Furthermore, four Na+ ions are situated in the following configurations around a BeF, tetrahedron : two occupy corner-site positions and the others occupy edge-site positions. (3) The probability of small-chain anions such as (BezF7),- and (Be,Flo),- is large in molten NaBeF,. 67 FAR 12058 X-RAY STUDIES OF MOLTEN Na,BeF, AND NaBeF, We thank Mr Y.Takagi (Research Laboratory of Engineering Materials, Tokyo Institute of Technology) for useful suggestions during this work. H. 0. and K. 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