research papers Acta Crystallographica Section B
Structural Science, Crystal Engineering and Materials
Ferroelectric glycine silver nitrate: a single-crystal neutron diffraction study
ISSN 2052-5192
R. R. Choudhury,a* R. Chitra,a N. Aliouaneb and J. Scheferb a
Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India, and bLaboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen, PSI, Switzerland
Correspondence e-mail: [email protected]
Protonated crystals of glycine silver nitrate (C4H10Ag2N4O10) undergo a displacive kind of structural phase transition to a ferroelectric phase at 218 K. Glycine silver nitrate (GSN) is a light-sensitive crystal. Single-crystal X-ray diffraction investigations are difficult to perform on these crystals due to the problem of crystal deterioration on prolonged exposure to Xrays. To circumvent this problem, single-crystal neutron diffraction investigations were performed. We report here the crystal structure of GSN in a ferroelectric phase. The final R value for the refined structure at 150 K is 0.059. A comparison of the low-temperature structure with the roomtemperature structure throws some light on the mechanism of the structural phase change in this crystal. We have attempted to explain the structural transition in GSN within the framework of the vibronic theory of ferroelectricity, suggesting that the second-order Jahn–Teller (pseudo-Jahn– Teller) behavior of the Ag+ ion in GSN leads to structural distortion at low temperature (218 K).
Received 5 March 2013 Accepted 3 September 2013
1. Introduction
# 2013 International Union of Crystallography Printed in Singapore – all rights reserved
Acta Cryst. (2013). B69, 595–602
Ferroelectricity in glycine silver nitrate (GSN) was discovered in 1957 by Pepinsky et al. (1957). They reported the Curie temperature (TC) to be 218 K with space groups above and below TC being P21/a and P21, respectively. Unlike other ferroelectric glycine complexes, which undergo order– disorder ferroelectric phase transitions, this crystal undergoes a displacive type of structural phase transition with a very small transition entropy (Choudhury et al., 2008). Deuteration is found to raise the transition temperature by 15 K (Gesi & Ozawa, 1977). The earlier IR study (Warrier & Narayanan, 1967), proton magnetic resonance investigation (Easwaran, 1966) as well as room-temperature single-crystal X-ray diffraction study (Rao & Viswamitra, 1972) indicated that protons did not play any major role in the ferroelectric phase change, and the role of silver ions was suggested to be crucial. It is difficult to obtain good quality X-ray diffraction data from a GSN crystal as it is light-sensitive and prolonged exposure to X-rays leads to crystal deterioration. Due to this limitation, in order to obtain the room-temperature structure Rao & Viswamitra (1972) had to collect three data sets from six crystals and the R-value for the refined structure was high. As a continuation of our low-temperature powder X-ray diffraction investigation (Choudhury et al., 2008) conducted in order to obtain GSN structure in the ferroelectric phase, large single crystals of GSN were grown. A way to circumvent the problem of the crystal deterioration on light exposure is to perform a neutron diffraction experiment instead. Hence, a lowtemperature single-crystal neutron diffraction investigation was undertaken. Since in this case the sample was enclosed in doi:10.1107/S2052519213024573
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research papers an aluminium cryostat, the exposure to light was minimal. We report here the crystal structure of GSN in the ferroelectric phase. A comparison of the low-temperature structure with a room-temperature structure throws some light on the mechanism of the structural phase change in this crystal. Ferroelectrics are traditionally categorized as being either displacive or of the order–disorder type. The distinction is made on the basis of the fact that microscopically the paraelectric phase of the displacive ferroelectrics is non-polar, whereas the paraelectric phase of the order–disorder ferroelectrics is non-polar only in a thermally averaged sense (Lines & Glass, 1977). This distinction between the two types of ferroelectrics can also be made on the basis of the dynamics of the phase transition, specifically whether a soft mode, which is responsible for the structural phase change, is of propagating or diffusive character. A propagating soft mode is a damped optic phonon representing small quasi-harmonic motion about a mean position, whereas a diffusive soft mode is not a phonon at all but represents large-amplitude thermal hopping motion between the wells (Lines & Glass, 1977). As stated earlier, most of the ferroelectric glycine complexes such as triglycine sulfate, diglycine nitrate, glycine phosphite etc. belong to the order–disorder type, but glycine silver nitrate is an exception as in this case the phase transition is found to be displacive in nature just like the case of perovskite ferroelectrics. The tendency of the material to undergo a displacive ferroelectric transition can be understood within the framework of vibronic coupling theory (Bersuker & Vekhter, 1978; Bersuker, 2001; Rondinelli et al., 2009) where it appears as the second-order term in the expansion of total energy with respect to atomic displacements (Q) " # X h0jH ð1Þ jni2 1 Q2 E ¼ Eð0Þ þ h0jH ð1Þ j0iQ þ h0jH ð2Þ j0i 2 2 EðnÞ Eð0Þ n ð1Þ
where H ð1Þ ¼
H 2 H ; H ð2Þ ¼ : Q Q¼0 Q2 Q¼0
Here j0i is the lowest energy solution of H(0) and jni are excited states with energies E(n); H(1) and H(2) capture the vibronic coupling between the displacements of the ions (Q) from their positions and the electron distribution. The firstorder term h0jH ð1Þ j0iQ describes the first-order Jahn–Teller effect. This term is non-zero only for orbitally degenerate states. The second-order term has two parts: the first Ks ¼ h0jH ð2Þ j0iQ2 is the static elastic force constant representing hindrance to the motion of nuclei in the frozen ground-state electron hence Ks > 0. The second 2 P distribution, term Kv ¼ 2 n 0jH ð1Þ jn =ðEðnÞ EðoÞ Þ represents the relaxation of the electron distribution due to the displacement-induced vibronic coupling between the ground state and the excited state (Bader, 1962) since this coupling lowers the ground-state energy Kv < 0. The overall sign of the secondorder term depends on the sum Ks + Kv and it is possible for the second-order term to be negative if Kv overbalances Ks
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(Wei et al., 1993). There can be an atomic displacement that strengthens the coupling between the low-lying excited state and ground state thereby making the Kv term larger than the Ks term thus stabilizing the distorted structure. This is called the second-order Jahn–Teller effect (SOJT) or pseudo-Jahn– Teller effect. The second-order Jahn–Teller effect deals with molecules having close electronic states within about 4 eV of each other (Pearson, 1969). Structural instability is high in the crystals having small Ks for an appropriate atomic displacement and also having a low-lying excited state that couples strongly with the ground state through the given atomic displacement. This theory successfully explains the displacive ferroelectric transition in perovskite ferroelectrics (ABO3 type compounds) such as barium titanate etc. (Ghosez et al., 1998). In this work we have attempted to explain the structural transition in GSN within the framework of the vibronic coupling theory.
2. Experiment Single crystals of GSN were grown at BARC by mixing analytical-grade -glycine and silver nitrate in double distilled water in the stoichiometric ratio 1:1 and allowing the solution to evaporate slowly at constant temperature (293 K) in a darkened chamber. The crystals were recrystalized twice in order to obtain the good quality large crystals suitable for single-crystal neutron diffraction investigations. The crystals obtained were characterized by recording their powder X-ray diffraction pattern at room temperature (293 K) and comparing the experimentally obtained pattern with those generated from the reported room-temperature structure of GSN (Rao & Viswamitra, 1972). A clear transparent single crystal of approximate dimensions 6 2 1 mm was mounted in a cryostat located at TriCS (Schefer et al., 1990), at SINQ (Fischer, 1997), PSI. In order to ascertain the existence of the structural phase transition, integrated neutron counts for 333 Bragg reflections were recorded at room temperature and then the temperature was lowered to 150 K (only 71% room-temperature data with ˚ 1 could be recorded due to a time limitation). sin / 0.41 A The intensities of h0l (h = 2n + 1)-type reflections were recorded both above and below TC (Fig. 1). Such reflections are absent for crystals with the space group P21/a, but they are present for crystals with the space group P21. The observation of intensities for h0l (h = 2n + 1)-type reflections only at low temperature (Fig. 1) confirmed the existence of the structural phase change with temperature. A restrained crystal structure refinement was attempted with the limited room-temperature data using the structure refinement software SHELXL97 (Sheldrick, 2008); details of the refinement are given in Table 1.1 The cell parameters and the starting atomic coordinates for all the non-H atoms were taken from the reported room-temperature structure of GSN 1 Supplementary data for this paper are available from the IUCr electronic archives (Reference: BP5051). Services for accessing these data are described at the back of the journal.
Acta Cryst. (2013). B69, 595–602
research papers (Rao & Viswamitra, 1972). The interatomic distances of covalently bonded atoms belonging to glycine and nitrate molecules were restrained to their respective average covalent bond-length values as quoted in the literature, with a standard ˚ using DFIX instructions in SHELXL97. uncertainty of 0.02 A Only isotropic refinement could be performed so as to keep the reflection-to-parameters ratio as high as possible. The structure obtained was compared with the reported roomtemperature structure (Rao & Viswamitra, 1972). Two structures were found to be identical within the standard uncertainties. Neutron counts for 1116 unique Bragg reflections at 150 K (low temperature) were recorded in the symmetrical setting of the diffractometer using the –2 coupled step scan mode. Cell parameters were obtained after refinement using the positions of about 50 reflections chosen randomly from the entire sin / range. The background was scanned for a minimum of 1 on either side. The standard reflections were measured after
every 25 reflections. The variation of the standard reflection intensity was within 3%. The data collection and refinement details are summarized in Table 1. The structure was solved ab initio using the structure solution software SHELXS97 (Sheldrick, 2008). The starting parameters obtained from SHELXS97 were subjected to a series of isotropic and anisotropic full-matrix least-squares refinement using the software SHELXL97. The nuclear scattering lengths reported at the NIST web site (Sears, 1992) were used in the refinement. All the reflections including negative Fo2 were used for refinement. In the initial stages of refinement the weight (w) was taken to be 1=ðFo2 Þ, which was derived using counting statistics. All the H atoms were located from the difference Fourier map and refined anisotropically.
3. Comparison between room- and low-temperature structures On analyzing the low-temperature crystal structure of GSN closely we found a one-dimensional silver-based coordination polymeric structure (Khlobystov et al., 2001). Metal-directed supramolecular self-assembly leads to the construction of many fascination molecular architectures (Carlucci et al., 2002). Supramolecular coordination polymers are generated by self-assembly of complementary monomeric units linked through non-covalent contacts. A monomeric unit (Fig. 2a) of our coordination polymer consists of two glycine ligand molecules linked together in a nearly centrosymmetric arrangement by two silver ions through metal–ligand interactions (in the high-temperature phase this monomer becomes centrosymmetric). These monomers are linked together by strong coordinate interactions (Ag—O distances lying in the ˚ ) to form one-dimensional chains extending range 2.3–2.5 A along the c axis. These polymeric chains are held by relatively
Figure 1 Plot of the intensity profile for (a) (104 ) and (b) (1 05) reflections at room and low temperature. Data collected at TriCS, SINQ. Acta Cryst. (2013). B69, 595–602
Figure 2 Crystal packing in GSN at low temperature. R. R. Choudhury et al.
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research papers Table 1 Experimental details. Data collected at TriCS, SINQ. For all structures: C4H10Ag2N2O42NO3. Experiments were carried out with ˚ using a four-circle diffractometer. H atoms were treated by a mixture of neutron radiation, = 1.17610 A independent and constrained refinement.
Crystal data Mr Crystal system, space group ˚) a, b, c (A ( ) ˚ 3) V (A Z (mm1) Crystal size (mm)
Low temperature (150 K)
Room temperature (293 K)
489.90 Monoclinic, P21 (No. 4) 5.451 (2), 19.493 (1), 5.441 (2) 100.12 (5) 569.2 (3) 2 13.503 621
244.95 Monoclinic, P21/a (No. 14) 5.451 (5), 19.493 (9), 5.541 (2) 100.20 (6)† 579.5 (6) 4 13.382 621
Data collection Absorption correction No. measured, independent and observed [I > 2(I)] reflections Rint max ( ) ˚ 1) (sin /)max (A Data completeness (%)
Integration 1116, 1093, 1090
– 333, 224, 210
0.013 47.8 0.63 89
0.028 28.7 0.41 71
Refinement R[F2 > 2(F2)], wR(F2), S No. of reflections No. of parameters No. of restraints ˚ 3) max, min (e A
0.059, 0.157, 1.20 1093 272 1 0.16, 0.13
0.1583, 0.4062, 2.169 224 62 12 0.10, 0.09
comparison between the molecular structure in the high-temperature, high-symmetry paraelectric phase (Rao & Viswamitra, 1972) with the structure in the low-temperature, lowsymmetry ferroelectric phase. Due to the atomic displacements, the center of inversion disappears in the lowtemperature phase and the number of atoms in an asymmetric unit doubles as a result. As a consequence of the displacement of atoms in the lowtemperature phase the center of gravities of the positive and negative charges in a monomer no longer coincide and a net dipole moment develops, resulting in a non-zero spontaneous polarization in the crystal. This structural distortion is the origin of the spontaneous polarization in GSN.
4. Intermolecular interactions
There are two main types of intermolecular interactions holding the molecules together in GSN crystals (Fig. 4): firstly, the hydrogen-bond interactions between the —NH3+ group of glycine zwitterions and the nitrate counterions holding the one-dimensional polymeric chains along the b-axis (Fig. 2b); secondly, the coordination interaction between the silver ions and the surrounding O atoms. A comparison between the strengths of these intermolecular interactions for temperatures above and below TC can throw some light on the mechanism of the phase transition in GSN. In order to compare the intermolecular interactions we have used our low- as well as room-temperature neutron structures since it is important to know the hydrogen positions for analyzing hydrogen-bonding interaction, but there are no
Computer programs: HKLgen, Rafin, TriCs_ccl, SHELXL97, SHELXS97 (Sheldrick, 2008), ORTEP (Johnson, 1965). † Cell parameters taken from Rao & Viswamitra (1972).
weaker coordinate interactions (Ag—O distances lying in the ˚ ) along the a-axis and by hydrogen-bonded range 2.7–2.9 A interactions to NO3+ counterions along the b-axis (Fig. 2b). Glycine ligand has a large number of rotational conformers (Bludsky et al., 2000); we have found that at both room and low temperature the conformation of glycine is non-planar (i.e. if we consider the five non-H atoms of glycine all atoms except nitrogen lie nearly in a plane and the N atom lies out of ˚ ). There is no change in glycine conforthis plane by 0.4 A mation across the phase transition. It is observed that all the atoms of GSN undergo displacements to a varying degree as the crystal undergoes a structural phase change. Fig. 3 shows the room-temperature structure of GSN monomer overlaid on the low-temperature structure. H atoms being the terminal atoms undergo larger displacements than the non-H atoms. Since our roomtemperature data are highly limited, forcing us to the restrained structure refinement at room temperature, we analyze the movement of the individual non-H atoms with temperature using the atomic coordinates reported by Rao & Viswamitra (1972). The structure visualization software Mercury (Macrae et al., 2006) was used to compare the GSN structure at two temperatures. The least-squares overlay of two structures has been performed. The average relative displacement of the non-H atoms on lowering the crystal ˚ . Table 2 gives a detailed temperature to 150 K was of 0.06 A
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Figure 3 Room-temperature structure of GSN superimposed on the lowtemperature structure; origins of both structures are shifted to the molecular centroids in order to compare the two structures. Acta Cryst. (2013). B69, 595–602
research papers Table 2
Table 3
˚ ) and angles ( ) of glycine and Comparison between bond lengths (A nitrate ions of GSN at room (293 K) and low temperature (150 K).
(a) Hydrogen-bonding details and (b) silver coordination details at room (RT) and low (LT) temperature.
Room-temperature values taken from the structure reported by Rao & Viswamitra (1972). The primed atoms indicate symmetry equivalents of the unprimed atoms.
(a)
Low temperature
Room temperature
˚) N O (A RT LT
˚) N—H (A RT LT
/NHO ( ) RT LT
˚) H O (A RT LT
vHO {EHO(eV) = avHO2} RT LT
O1—C1 O2—C1 C1—C2 C2—N1 N2—C4 C4—C3 C3—O3 C3—O4 N3—O7 N3—O6 N3—O5 N4—O10 N4—O8 N4—O9
1.276 (7) 1.216 (6) 1.534 (5) 1.467 (5) 1.503 (5) 1.500 (5) 1.243 (7) 1.262 (7) 1.222 (7) 1.241 (7) 1.281 (7) 1.220 (7) 1.234 (6) 1.258 (6)
O1—C1 O2—C1 C1—C2 N1—C2 N10 —C20 C10 —C20 C10 —O20 C10 —O10 N2—O5 N2—O4 N2—O3 N20 —O50 N20 —O40 N20 —O30
1.28 1.25 1.54 1.50 1.50 1.54 1.25 1.28 1.25 1.26 1.28 1.25 1.26 1.28
(3) (3) (4) (4) (4) (4) (3) (3) (4) (3) (3) (4) (3) (3)
2.86 (3) 2.966 (6)
1.01 (2) 1.049 (8)
174 (5) 174.4 (10)
1.86 (4) 1.920 (10)
0.085 {0.05} 0.072 {0.04}
2.86 (3) 2.914 (7)
1.01 (2) 1.019 (10)
174 (5) 174.0 (10)
1.86 (4) 1.898 (11)
0.085 {0.05} 0.077 {0.04}
2.93 (3) 2.906 (6)
1.00 (2) 1.010 (11)
149 (3) 151.4 (9)
2.03 (4) 1.978 (11)
0.054 {0.02} 0.062 {0.03}
2.93 (3) 2.884 (7)
1.00 (2) 1.006 (12)
149 (3) 147.0 (11)
2.03 (4) 1.988 (12)
0.054 {0.02} 0.060 {0.03}
2.84 (3) 2.906 (7)
1.00 (2) 1.035 (10)
148 (6) 139.7 (9)
1.95 (5) 2.038 (11)
0.067 {0.03} 0.052 {0.02}
O2—C1—O1 O2—C1—C2 O1—C1—C2 N1—C2—C1 O3—C3—O4 O3—C3—C4 O4—C3—C4 N2—C4—C3 O7—N3—O6 O7—N3—O5 O6—N3—O5 O10—N4—O8 O10—N4—O9 O8—N4—O9
127.2 (5) 115.2 (4) 117.5 (4) 114.3 (3) 126.2 (5) 117.6 (4) 116.1 (4) 113.7 (3) 118.5 (5) 121.2 (5) 120.3 (4) 120.1 (5) 120.5 (4) 119.3 (4)
O2—C1—O1 O2—C1—C2 O1—C1—C2 N1—C2—C1 O20 —C10 —O10 O20 —C10 —C20 O10 —C10 —C20 N10 —C20 —C10 O5—N2—O4 O5—N2—O3 O4—N2—O3 O50 —N20 —O40 O50 —N20 —O30 O40 —N20 —O30
125 (2) 116 (3) 119 (2) 110 (3) 125 (2) 116 (3) 119 (2) 110 (3) 120 (2) 116 (2) 123 (2) 120 (2) 116 (2) 123 (2)
2.84 (3) 2.830 (6)
1.00 (2) 1.041 (10)
148 (6) 144.9 (8)
1.95 (5) 1.915 (11)
0.067 {0.03} 0.073 {0.04}
hydrogen positions reported in the room-temperature X-ray structure (Rao & Viswamitra, 1972). Table 3(a) gives the details of N—H O hydrogen bonds in GSN at two temperatures. The donor–acceptor distances at ˚ , whereas room temperature vary between 2.824 and 3.024 A the donor–acceptor distances at low temperature vary
Figure 4 Intermolecular interactions in GSN. Acta Cryst. (2013). B69, 595–602
(b)
Ag1—O Ag1—O Ag1—O Ag1—O Ag1—O Ag2—O Ag2—O Ag2—O Ag2—O Ag2—O Ag1—Ag2
˚) D (A RT
˚) D (A LT
2.19 2.35 2.50 2.72 2.89 2.19 2.35 2.50 2.72 2.89 2.90
2.227 (7) 2.313 (7) 2.373 (6) 2.781 (7) 2.846 (6) 2.213 (7) 2.273 (7) 2.370 (7) 2.819 (7) 2.852 (7) 2.804 (6)
(3) (3) (3) (4) (3) (3) (3) (3) (4) (3) (4)
vAgO {EAgO(eV) = avAgO2} RT
vAgO {EAgO(eV) = avAgO2} LT
0.355 0.229 0.152 0.084 0.052 0.355 0.229 0.152 0.084 0.052
0.319 {0.71} 0.253 {0.45} 0.215 {0.32} 0.071 {0.03} 0.059 {0.02} 0.331 {0.77} 0.282 {0.56} 0.217 {0.33} 0.064 {0.03} 0.059 {0.02}
{0.88} {0.37} {0.16} {0.05) {0.02} {0.88} {0.37} {0.16} {0.05} {0.02}
Both room- and low-temperature values are taken from the neutron structure reported in this paper.
˚ . This indicates that all the N— between 2.831 and 3.064 A H O bonds in the paraelectric and ferroelectric phases are from weak to moderate strength (Steiner, 2002) with hydrogen-bond energies less than 0.2 eV. Table 3(a) shows no marked change in the hydrogen-bond strengths, although there is some rearrangement of hydrogen bonds across the phase transition. We infer from this that GSN is not a typical hydrogen-bonded ferroelectric-like potassium dihydrogen phosphate (Nelmes, 1987) where the hydrogen bonds involved in the phase change are very strong (Steiner, 2002), having energies of the order of 1 eV or more, and a change in hydrogen-bond dynamics initiates a structural phase change. There are five O atoms and one Ag atom within a coordi˚ around a silver ion in GSN, hence nation sphere of radius 3 A silver coordination can be assumed to be distorted octahedral. Table 3(b) gives the details of silver coordination at two temperatures. There is a marked difference in the silver coordination at temperatures above and below TC (Fig. 4). ˚ There is a shortening of the Ag+—Ag+ separation by 0.09 A R. R. Choudhury et al.
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research papers Table 4 Electron density around the silver ions and local energy density (Ed) at the bond critical points (BCPs) and ring critical points (RCPs). ˚ 3) (e A RT
E (a.u.)
˚ 3) (e A LT
E (a.u.)
Critical point BCP(Ag—Ag) BCP(Ag—O) BCP(Ag—O) BCP(Ag—O) BCP(Ag—O) RCP(Ag—Ag—O—O) RCP(Ag—Ag—O—O)
0.16105 0.34006 0.47636 0.47636 0.34006 0.07061 0.07061
0.026 0.070 0.108 0.108 0.070 0.007 0.007
0.19329 0.38278 0.42168 0.41123 0.35367 0.069 0.07136
0.033 0.081 0.092 0.089 0.074 0.007 0.008
˚ as and some of the Ag—O distances also change by 0.1 A the crystal temperature is lowered from room to 150 K. In this respect GSN is similar to ferroelectric perovskites where the phase change results in the distortion of oxygen octahedra and the metal–oxygen distances change by approximately similar amounts (Lines & Glass, 1977). We have used the valence bond theory proposed by Brown (2009) to estimate the relative strength of the intermolecular interactions in GSN. The bond valence for each of the Ag—O coordination bonds as well as O H hydrogen bonds are obtained using the following expression vij ¼ exp½ðRij dij Þ=b ;
ð2Þ
where dij is the distance between the ith and jth atoms, b is a ˚ and the bond-valence universal constant with the value 0.37 A parameter Rij was taken from the literature (Brese & O’Keeffe, 1991). Although there is no rigorous way of deriving the bond energy from the bond valence, the following approximate expression was suggested by Brown (2009) Eij ’ av2ij :
ð3Þ
Here a is a constant with the value 7 eV v.u.2. Tables 3(a) and (b) list vij as well as Eij values for all the intermolecular interactions. We observe that Ag—O coordination bonds are in general stronger than the O H hydrogen bonds. Moreover, relative changes in the Ag—O coordination bond energies as temperature decreases from room temperature to 150 K are more noticeable than those in the O H hydrogenbond energies. These observations support the conclusions that the main driving mechanisms of the phase change in GSN are the distortions of its silver coordination octahedra, and hydrogen bonding plays only a secondary role in the phase change.
electron density is sensitive to the quality of the basis used, the conclusions obtained from the comparison of these values for different molecular geometries are not influenced by this limitation. The theoretical molecular electron density was analyzed using the quantum theory of atoms in molecules (AIM; Bader, 1991); the critical point details were obtained using AIMPAC software (Keith et al., 1995). A bond critical point (BCP) exists between the two nearest silver ions, which is a clear indication of the existence of a bonded interaction between the two. Local energy density (Ed) at the BCP between the two silver ions is negative (Ed < 0), showing a significant covalent contribution in the interaction. Two ring critical points were also observed in the plane containing the two bonded silver ions along with the four O atoms nearest to these Ag+ ions. A change in electron density around the silver ion across the phase transition is evident from the difference in the density values at the critical points (Table 4) for the two temperatures. Since displacement of the Ag+ ion is considered to be crucial for the structural phase transition, we have attempted to study the effect of the change in the Ag+—Ag+ distance. Keeping all the atoms except an Ag+ ion fixed to their roomtemperature positions we gradually changed the silver–silver separation by moving one of the two ions labeled Ag+(M) relative to the other labeled Ag+(S) (Fig. 5). The Ag+(S)— Ag+(M) separation was gradually changed from the roomtemperature value to the low-temperature value and beyond. We calculated the single-point ground-state molecular energies for each of the generated molecular configurations. The influence of changing the Ag+(M)—Ag+(S) distance on the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) separation is discussed in the next section.
6. Structural phase transition Since the silver ion (Ag+) plays a key role in the structural phase transition in GSN it is important to look into the chemistry of silver ions before we can hope to understand the structural phase change in GSN. The Ag+ ion has a closed d10 electronic configuration and, just like other coinage metals
5. Density functional theory (DFT) calculations Starting with our GSN neutron structures, a theoretical electron density for GSN monomer in room- and low-temperature phases was obtained using DFT calculations. We performed DFT calculations at the B3LYP/3-21G level of theory. All the calculations were carried out using the GAMESS-UK program (Guest et al., 2005). We employed the relatively simple 3-21G basis set for these calculations due to the limitations imposed by the computation facility available and the large size of the molecular unit. Even though the calculated value of the
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Figure 5 Change of Ag+(M)—Ag+(S) distance by gradually moving the Ag+(M) ions, keeping all the other atoms fixed. Acta Cryst. (2013). B69, 595–602
research papers (Cu, Ag, Au), it exhibits a tendency to form homoatomic d10– d10 interactions (Jansen, 1987), which can be thought of as bonds with a weak covalent character (El-Bahraoui et al., 1998). The presence of a low-lying electronic excited state in d10 ions (Cu+, Ag+, Au+) destroys the pure core nature of the closed d10 electronic shell of these ions and hence destroys their spherical symmetry. If because of the presence of bridging ligands (glycine in the case of GSN) these d10 ions are forced into close proximity, the d10–d10 interactions are established between these d10 ions. These homoatomic d10–d10 bonds have a decisive influence on the final crystal structure of the coordination compounds. Many silver complexes are reported in the literature where the silver–silver distances lie ˚ (Holloway et al., 1995). It is assumed between 2.654 and 3.54 A 10 10 that closed-shell d –d interactions exist in all these cases with a short silver–silver contact. GSN also belongs to this class of crystals. When we compare the Ag+—Ag+ distance in GSN with those reported in the literature, particularly the Ag+—Ag+ distance in the low-temperature phase of GSN ˚ ), which is smaller than twice the metallic silver radius (2.889 A 10 10 we conclude that the closed-shell d –d interactions are reasonably strong in GSN [Ag+—Ag+ distance in our low˚ , which is only 0.15 A ˚ more temperature structure is 2.804 A + + ˚ ); this than the minimum reported Ag —Ag distance (2.654 A indicates the silver–sliver bonds in the low-temperature phase of GSN are strong]. The existence of the bond critical point between two Ag+ ions with reasonably good electron density confirms the existence of a bonded interaction between the two. Electron density and the local energy density at the Ag+—Ag+ critical point is approximately one tenth of that at the C—C bond critical point. This gives an estimate of the strength of the Ag+—Ag+ interaction in comparison to the standard C—C single bond. In fact, the change in the strength of these d10—d10 bonds with decreasing crystal temperature (Table 4) is the likely reason for the observed structural distortion in GSN crystals at TC. This fact is discussed below in more detail. We can apply the vibronic coupling theory (as discussed in x1) to the specific case of GSN crystals in order to explain the structural phase transition observed in these crystals at low temperature. Our calculations show that as the Ag+(M)— Ag+(S) separation decreases, the energy gap E(n) E(0) between HOMO and LUMO also decreases (Fig. 6a), as a result the value of the Kv term in the expression of total energy E [equation (1)] will increase. As explained in x1, when this Kv term prevails over the Ks term denoting the static elastic restoring force, the structural distortion is stabilized, resulting in a structural phase change. We propose the following mechanism for the phase transition in GSN: initially in the paraelectric phase the d10–d10 interactions between silver ions are weak, hence small ionic displacements Q lead to an increase in the total energy due to larger elastic restoring forces denoted by Ks compared with the electronic coupling denoted by the Kv term. As the Ag+–Ag+ separation reduces with lowering of the crystal temperature, overlap between filled d- and unfilled s-orbitals of Ag+ ions increases, leading to a strengthening of the Ag+—Ag+ interaction. Finally, for some Acta Cryst. (2013). B69, 595–602
Ag+—Ag+ separations, lowering of the total energy for small ionic displacements Q resulting from Ag+–Ag+ electronic coupling (Kv) overwhelms the increase in the total energy due to the classic elastic energy (Ks), making the second-order term in the energy expression E [equation (1)] negative. At this point the distorted structure is stabilized, leading to a structural phase change. A similar situation has been observed in semiconducting CuCl where homoatomic Cu+—Cu+ interactions resulted in a tendency of Cu+ ions to undergo offcenter atomic displacements (Wei et al., 1993). The rearrangement of the electrons as a result of the atomic displacement leads to a change of molecular polarization. The dynamic atomic charge of an atom M defined as ZM* = P/uM (Rondinelli et al., 2009; Pearson, 1969) gives a measure of the change in the net polarization due to ionic displacement. A large value of ZM* is considered to be an indication of the
Figure 6 (a) Variation in the HOMO and LUMO separation with changing Ag+(M)—Ag+(S) distance. (b) Change in molecular polarization with the shift in Ag+(M) ion; the shift of Ag+(M) at room temperature is taken as 0.0, i.e. Ag+(M) is displaced progressively from its room-temperature position. R. R. Choudhury et al.
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research papers tendency of the ions to undergo some displacements. For example, in the cubic phase of BaTiO3 the formal charge of the Ti ion is +4, but its dynamic charge is almost +7, indicating the large tendency of the Ti ion to undergo displacement towards an oxygen (Rondinelli et al., 2009). We have estimated the value of ZM* for the moving silver ion Ag+(M) by plotting the calculated molecule polarization against the displacement of the Ag+(M) ion (Fig. 6b). The dynamic charge of Ag+(M) as obtained from the slope of a polarization versus displacement graph is 1.17 e, whereas its formal charge is 1 e and its static charge (Pearson, 1969) obtained from the electron density calculation is only 0.25 e. This demonstrates that the Ag+ ion in this structure has a tendency to undergo a displacement. Hence, the ferroelectric transition in GSN results because of the tendency of the Ag+ ion to undergo an atomic displacement so that the Ag+—Ag+ separation reduces; this strengthens the coupling between the low-lying excited state and the ground state of the molecule, thereby resulting in a second-order Jahn–Teller distortion of the structure.
7. Conclusion We have measured and refined the structure of glycine silver nitrate (GSN) in the ferroelectric phase by means of lowtemperature single-crystal neutron diffraction. The final R value for the refined structure at 150 K is 0.059. A comparison between the GSN crystal structure in the ferroelectric phase and the earlier reported GSN structure in the paraelectric phase shows that all the atoms of GSN undergo displacements to a varying degree as the crystal undergoes a structural phase change. The average displacement of the non-H atoms on lowering the crystal temperature from room temperature to ˚ . Due to the structural distortion 150 K is of the order 0.06 A resulting from atomic displacement, the center of inversion disappears in the low-temperature ferroelectric phase, yielding a structural phase transition from P21/a to P21. No marked change in the strength of the hydrogen bonds is observed as the crystal temperature is lowered from room temperature to 150 K. The silver coordination changes significantly across the phase transition temperature (TC). The ˚ , indicating an increase Ag+—Ag+ distance reduces by 0.09 A 10 in the strength of the homoatomic d —d10 bonds between the silver ions. The displacive ferroelectric structural phase transition in GSN is explained within the framework of vibronic theory of ferroelectricity, which incorporates the coupling of electronic distribution with nuclear displacements. The origin of dipolar instability is mainly due to the second-order Jahn– Teller behavior of Ag+ ions in GSN. We thank the Department of Science & Technology for providing the funding [DST(5)/AKR/P087/10-11/909, dated 20/08/2010, DST(5)/AKR/P087/09-10/986 dated 31/08/2009]
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for carrying out the experiments at SINQ, Paul Scherrer institute, Villigen, Switzerland.
References Bader, R. F. W. (1962). Can. J. Chem. 40, 1164–1175. Bader, R. F. W. (1991). Chem. Rev. 91, 893–928. Bersuker, I. B. (2001). Chem. Rev. 101, 1067–1114. Bersuker, I. B. & Vekhter, B. G. (1978). Ferroelectrics, 19, 137–150. Bludsky, O., Chocholousova, J., Vacek, J., Huisken, F. & Hobza, P. (2000). J. Chem. Phys. 113, 4629–4635. Brese, N. E. & O’Keeffe, M. (1991). Acta Cryst. B47, 192–197. Brown, I. D. (2009). Chem. Rev. 109, 6858–6919. Carlucci, L., Ciani, G., Proserpio, D. M. & Rizzato, S. (2002). CrystEngComm, 4, 121–129. Choudhury, R. R., Panicker, L., Chitra, R. & Sakuntala, T. (2008). Solid State Commun. 145, 407–412. Easwaran, K. (1966). J. Phys. Soc. Jpn, 21, 1614. El-Bahraoui, J., Molina, J. M. & Olea, D. P. (1998). J. Phys. Chem. A, 102, 2443–2448. Fischer, W. (1997). Physica B, 234–236, 1202–1208. Gesi, K. & Ozawa, K. (1977). J. Phys. Soc. Jpn, 42, 923–928. Ghosez, P., Michenaud, J. P. & Gonze, X. (1998). Phys. Rev. B, 58, 6224–6240. Guest, M. F., Bush, I. J., Van Dam, H. J. J., Sherwood, P., Thomas, J. M. H., Van Lenthe, J. H., Havenith, R. W. A. & Kendrick, J. (2005). Mol. Phys. 103, 719–747. Holloway, C. E., Melnik, M., Nevin, W. A. & Liu, W. (1995). J. Coord. Chem. 35, 85–178. Jansen, M. (1987). Angew. Chem. Int. Ed. Engl. 26, 1098–1110. Johnson, C. K. (1965). ORTEP. Report ORNL-3794. Oak Ridge National Laboratory, Tennessee, USA. Keith, T. A., Laidig, K. E., Krug, P., Cheeseman, J. R., Bone, R. G. A., Biegler-Ko¨nig, F. W., Duke, J. A., Tang, T. & Bader, R. F. W. (1995). AIMPAC95, http://www.chemistry.mcmaster.ca/aimpac. Khlobystov, A. N., Blake, A. J., Champness, N. R., Lemenovskii, D. A., Majouga, A. G., Zyk, N. V. & Schro¨der, M. (2001). Coord. Chem. Rev. 222, 155–192. Lines, M. E. & Glass, A. M. (1977). Principles and Applications of Ferroelectrics and Related Material. Clarendon Press: Oxford. Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G. P., Taylor, R., Towler, M. & van de Streek, J. (2006). J. Appl. Cryst. 39, 453–457. Nelmes, R. J. (1987). Ferroelectrics, 71, 87–123. Pearson, R. G. (1969). J. Am. Chem. Soc. 91, 1252–1254. Pepinsky, R., Okaya, Y., Eastman, D. P. & Mitsui, T. (1957). Phys. Rev. 107, 1538–1539. Rao, J. K. M. & Viswamitra, M. A. (1972). Acta Cryst. B28, 1484– 1496. Rondinelli, J., Eidelson, A. & Spaldin, N. (2009). Phys. Rev. B, 79, 205119–205125. Schefer, J., Fischer, P., Heer, H., Isacson, A., Koch, M. & Thut, R. (1990). Nucl. Instrum. Methods A, 288, 477–485. Sears, V. F. (1992). Neutron News, 3, 26–37. Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Steiner, T. (2002). Angew. Chem. Int. Ed. 41, 48–76. Warrier, A. V. R. & Narayanan, P. S. (1967). Proc. Ind. Acad. Sci. A, 66, 46–54. Wei, S. H., Zhang, S. B. & Zunger, A. (1993). Phys. Rev. Lett. 70, 1639–1642.
Acta Cryst. (2013). B69, 595–602
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Structural Science, Crystal Engineering and Materials
Ferroelectric glycine silver nitrate: a single-crystal neutron diffraction study
ISSN 2052-5192
R. R. Choudhury,a* R. Chitra,a N. Aliouaneb and J. Scheferb a
Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India, and bLaboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen, PSI, Switzerland
Correspondence e-mail: [email protected]
Protonated crystals of glycine silver nitrate (C4H10Ag2N4O10) undergo a displacive kind of structural phase transition to a ferroelectric phase at 218 K. Glycine silver nitrate (GSN) is a light-sensitive crystal. Single-crystal X-ray diffraction investigations are difficult to perform on these crystals due to the problem of crystal deterioration on prolonged exposure to Xrays. To circumvent this problem, single-crystal neutron diffraction investigations were performed. We report here the crystal structure of GSN in a ferroelectric phase. The final R value for the refined structure at 150 K is 0.059. A comparison of the low-temperature structure with the roomtemperature structure throws some light on the mechanism of the structural phase change in this crystal. We have attempted to explain the structural transition in GSN within the framework of the vibronic theory of ferroelectricity, suggesting that the second-order Jahn–Teller (pseudo-Jahn– Teller) behavior of the Ag+ ion in GSN leads to structural distortion at low temperature (218 K).
Received 5 March 2013 Accepted 3 September 2013
1. Introduction
# 2013 International Union of Crystallography Printed in Singapore – all rights reserved
Acta Cryst. (2013). B69, 595–602
Ferroelectricity in glycine silver nitrate (GSN) was discovered in 1957 by Pepinsky et al. (1957). They reported the Curie temperature (TC) to be 218 K with space groups above and below TC being P21/a and P21, respectively. Unlike other ferroelectric glycine complexes, which undergo order– disorder ferroelectric phase transitions, this crystal undergoes a displacive type of structural phase transition with a very small transition entropy (Choudhury et al., 2008). Deuteration is found to raise the transition temperature by 15 K (Gesi & Ozawa, 1977). The earlier IR study (Warrier & Narayanan, 1967), proton magnetic resonance investigation (Easwaran, 1966) as well as room-temperature single-crystal X-ray diffraction study (Rao & Viswamitra, 1972) indicated that protons did not play any major role in the ferroelectric phase change, and the role of silver ions was suggested to be crucial. It is difficult to obtain good quality X-ray diffraction data from a GSN crystal as it is light-sensitive and prolonged exposure to X-rays leads to crystal deterioration. Due to this limitation, in order to obtain the room-temperature structure Rao & Viswamitra (1972) had to collect three data sets from six crystals and the R-value for the refined structure was high. As a continuation of our low-temperature powder X-ray diffraction investigation (Choudhury et al., 2008) conducted in order to obtain GSN structure in the ferroelectric phase, large single crystals of GSN were grown. A way to circumvent the problem of the crystal deterioration on light exposure is to perform a neutron diffraction experiment instead. Hence, a lowtemperature single-crystal neutron diffraction investigation was undertaken. Since in this case the sample was enclosed in doi:10.1107/S2052519213024573
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research papers an aluminium cryostat, the exposure to light was minimal. We report here the crystal structure of GSN in the ferroelectric phase. A comparison of the low-temperature structure with a room-temperature structure throws some light on the mechanism of the structural phase change in this crystal. Ferroelectrics are traditionally categorized as being either displacive or of the order–disorder type. The distinction is made on the basis of the fact that microscopically the paraelectric phase of the displacive ferroelectrics is non-polar, whereas the paraelectric phase of the order–disorder ferroelectrics is non-polar only in a thermally averaged sense (Lines & Glass, 1977). This distinction between the two types of ferroelectrics can also be made on the basis of the dynamics of the phase transition, specifically whether a soft mode, which is responsible for the structural phase change, is of propagating or diffusive character. A propagating soft mode is a damped optic phonon representing small quasi-harmonic motion about a mean position, whereas a diffusive soft mode is not a phonon at all but represents large-amplitude thermal hopping motion between the wells (Lines & Glass, 1977). As stated earlier, most of the ferroelectric glycine complexes such as triglycine sulfate, diglycine nitrate, glycine phosphite etc. belong to the order–disorder type, but glycine silver nitrate is an exception as in this case the phase transition is found to be displacive in nature just like the case of perovskite ferroelectrics. The tendency of the material to undergo a displacive ferroelectric transition can be understood within the framework of vibronic coupling theory (Bersuker & Vekhter, 1978; Bersuker, 2001; Rondinelli et al., 2009) where it appears as the second-order term in the expansion of total energy with respect to atomic displacements (Q) " # X h0jH ð1Þ jni2 1 Q2 E ¼ Eð0Þ þ h0jH ð1Þ j0iQ þ h0jH ð2Þ j0i 2 2 EðnÞ Eð0Þ n ð1Þ
where H ð1Þ ¼
H 2 H ; H ð2Þ ¼ : Q Q¼0 Q2 Q¼0
Here j0i is the lowest energy solution of H(0) and jni are excited states with energies E(n); H(1) and H(2) capture the vibronic coupling between the displacements of the ions (Q) from their positions and the electron distribution. The firstorder term h0jH ð1Þ j0iQ describes the first-order Jahn–Teller effect. This term is non-zero only for orbitally degenerate states. The second-order term has two parts: the first Ks ¼ h0jH ð2Þ j0iQ2 is the static elastic force constant representing hindrance to the motion of nuclei in the frozen ground-state electron hence Ks > 0. The second 2 P distribution, term Kv ¼ 2 n 0jH ð1Þ jn =ðEðnÞ EðoÞ Þ represents the relaxation of the electron distribution due to the displacement-induced vibronic coupling between the ground state and the excited state (Bader, 1962) since this coupling lowers the ground-state energy Kv < 0. The overall sign of the secondorder term depends on the sum Ks + Kv and it is possible for the second-order term to be negative if Kv overbalances Ks
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(Wei et al., 1993). There can be an atomic displacement that strengthens the coupling between the low-lying excited state and ground state thereby making the Kv term larger than the Ks term thus stabilizing the distorted structure. This is called the second-order Jahn–Teller effect (SOJT) or pseudo-Jahn– Teller effect. The second-order Jahn–Teller effect deals with molecules having close electronic states within about 4 eV of each other (Pearson, 1969). Structural instability is high in the crystals having small Ks for an appropriate atomic displacement and also having a low-lying excited state that couples strongly with the ground state through the given atomic displacement. This theory successfully explains the displacive ferroelectric transition in perovskite ferroelectrics (ABO3 type compounds) such as barium titanate etc. (Ghosez et al., 1998). In this work we have attempted to explain the structural transition in GSN within the framework of the vibronic coupling theory.
2. Experiment Single crystals of GSN were grown at BARC by mixing analytical-grade -glycine and silver nitrate in double distilled water in the stoichiometric ratio 1:1 and allowing the solution to evaporate slowly at constant temperature (293 K) in a darkened chamber. The crystals were recrystalized twice in order to obtain the good quality large crystals suitable for single-crystal neutron diffraction investigations. The crystals obtained were characterized by recording their powder X-ray diffraction pattern at room temperature (293 K) and comparing the experimentally obtained pattern with those generated from the reported room-temperature structure of GSN (Rao & Viswamitra, 1972). A clear transparent single crystal of approximate dimensions 6 2 1 mm was mounted in a cryostat located at TriCS (Schefer et al., 1990), at SINQ (Fischer, 1997), PSI. In order to ascertain the existence of the structural phase transition, integrated neutron counts for 333 Bragg reflections were recorded at room temperature and then the temperature was lowered to 150 K (only 71% room-temperature data with ˚ 1 could be recorded due to a time limitation). sin / 0.41 A The intensities of h0l (h = 2n + 1)-type reflections were recorded both above and below TC (Fig. 1). Such reflections are absent for crystals with the space group P21/a, but they are present for crystals with the space group P21. The observation of intensities for h0l (h = 2n + 1)-type reflections only at low temperature (Fig. 1) confirmed the existence of the structural phase change with temperature. A restrained crystal structure refinement was attempted with the limited room-temperature data using the structure refinement software SHELXL97 (Sheldrick, 2008); details of the refinement are given in Table 1.1 The cell parameters and the starting atomic coordinates for all the non-H atoms were taken from the reported room-temperature structure of GSN 1 Supplementary data for this paper are available from the IUCr electronic archives (Reference: BP5051). Services for accessing these data are described at the back of the journal.
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research papers (Rao & Viswamitra, 1972). The interatomic distances of covalently bonded atoms belonging to glycine and nitrate molecules were restrained to their respective average covalent bond-length values as quoted in the literature, with a standard ˚ using DFIX instructions in SHELXL97. uncertainty of 0.02 A Only isotropic refinement could be performed so as to keep the reflection-to-parameters ratio as high as possible. The structure obtained was compared with the reported roomtemperature structure (Rao & Viswamitra, 1972). Two structures were found to be identical within the standard uncertainties. Neutron counts for 1116 unique Bragg reflections at 150 K (low temperature) were recorded in the symmetrical setting of the diffractometer using the –2 coupled step scan mode. Cell parameters were obtained after refinement using the positions of about 50 reflections chosen randomly from the entire sin / range. The background was scanned for a minimum of 1 on either side. The standard reflections were measured after
every 25 reflections. The variation of the standard reflection intensity was within 3%. The data collection and refinement details are summarized in Table 1. The structure was solved ab initio using the structure solution software SHELXS97 (Sheldrick, 2008). The starting parameters obtained from SHELXS97 were subjected to a series of isotropic and anisotropic full-matrix least-squares refinement using the software SHELXL97. The nuclear scattering lengths reported at the NIST web site (Sears, 1992) were used in the refinement. All the reflections including negative Fo2 were used for refinement. In the initial stages of refinement the weight (w) was taken to be 1=ðFo2 Þ, which was derived using counting statistics. All the H atoms were located from the difference Fourier map and refined anisotropically.
3. Comparison between room- and low-temperature structures On analyzing the low-temperature crystal structure of GSN closely we found a one-dimensional silver-based coordination polymeric structure (Khlobystov et al., 2001). Metal-directed supramolecular self-assembly leads to the construction of many fascination molecular architectures (Carlucci et al., 2002). Supramolecular coordination polymers are generated by self-assembly of complementary monomeric units linked through non-covalent contacts. A monomeric unit (Fig. 2a) of our coordination polymer consists of two glycine ligand molecules linked together in a nearly centrosymmetric arrangement by two silver ions through metal–ligand interactions (in the high-temperature phase this monomer becomes centrosymmetric). These monomers are linked together by strong coordinate interactions (Ag—O distances lying in the ˚ ) to form one-dimensional chains extending range 2.3–2.5 A along the c axis. These polymeric chains are held by relatively
Figure 1 Plot of the intensity profile for (a) (104 ) and (b) (1 05) reflections at room and low temperature. Data collected at TriCS, SINQ. Acta Cryst. (2013). B69, 595–602
Figure 2 Crystal packing in GSN at low temperature. R. R. Choudhury et al.
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research papers Table 1 Experimental details. Data collected at TriCS, SINQ. For all structures: C4H10Ag2N2O42NO3. Experiments were carried out with ˚ using a four-circle diffractometer. H atoms were treated by a mixture of neutron radiation, = 1.17610 A independent and constrained refinement.
Crystal data Mr Crystal system, space group ˚) a, b, c (A ( ) ˚ 3) V (A Z (mm1) Crystal size (mm)
Low temperature (150 K)
Room temperature (293 K)
489.90 Monoclinic, P21 (No. 4) 5.451 (2), 19.493 (1), 5.441 (2) 100.12 (5) 569.2 (3) 2 13.503 621
244.95 Monoclinic, P21/a (No. 14) 5.451 (5), 19.493 (9), 5.541 (2) 100.20 (6)† 579.5 (6) 4 13.382 621
Data collection Absorption correction No. measured, independent and observed [I > 2(I)] reflections Rint max ( ) ˚ 1) (sin /)max (A Data completeness (%)
Integration 1116, 1093, 1090
– 333, 224, 210
0.013 47.8 0.63 89
0.028 28.7 0.41 71
Refinement R[F2 > 2(F2)], wR(F2), S No. of reflections No. of parameters No. of restraints ˚ 3) max, min (e A
0.059, 0.157, 1.20 1093 272 1 0.16, 0.13
0.1583, 0.4062, 2.169 224 62 12 0.10, 0.09
comparison between the molecular structure in the high-temperature, high-symmetry paraelectric phase (Rao & Viswamitra, 1972) with the structure in the low-temperature, lowsymmetry ferroelectric phase. Due to the atomic displacements, the center of inversion disappears in the lowtemperature phase and the number of atoms in an asymmetric unit doubles as a result. As a consequence of the displacement of atoms in the lowtemperature phase the center of gravities of the positive and negative charges in a monomer no longer coincide and a net dipole moment develops, resulting in a non-zero spontaneous polarization in the crystal. This structural distortion is the origin of the spontaneous polarization in GSN.
4. Intermolecular interactions
There are two main types of intermolecular interactions holding the molecules together in GSN crystals (Fig. 4): firstly, the hydrogen-bond interactions between the —NH3+ group of glycine zwitterions and the nitrate counterions holding the one-dimensional polymeric chains along the b-axis (Fig. 2b); secondly, the coordination interaction between the silver ions and the surrounding O atoms. A comparison between the strengths of these intermolecular interactions for temperatures above and below TC can throw some light on the mechanism of the phase transition in GSN. In order to compare the intermolecular interactions we have used our low- as well as room-temperature neutron structures since it is important to know the hydrogen positions for analyzing hydrogen-bonding interaction, but there are no
Computer programs: HKLgen, Rafin, TriCs_ccl, SHELXL97, SHELXS97 (Sheldrick, 2008), ORTEP (Johnson, 1965). † Cell parameters taken from Rao & Viswamitra (1972).
weaker coordinate interactions (Ag—O distances lying in the ˚ ) along the a-axis and by hydrogen-bonded range 2.7–2.9 A interactions to NO3+ counterions along the b-axis (Fig. 2b). Glycine ligand has a large number of rotational conformers (Bludsky et al., 2000); we have found that at both room and low temperature the conformation of glycine is non-planar (i.e. if we consider the five non-H atoms of glycine all atoms except nitrogen lie nearly in a plane and the N atom lies out of ˚ ). There is no change in glycine conforthis plane by 0.4 A mation across the phase transition. It is observed that all the atoms of GSN undergo displacements to a varying degree as the crystal undergoes a structural phase change. Fig. 3 shows the room-temperature structure of GSN monomer overlaid on the low-temperature structure. H atoms being the terminal atoms undergo larger displacements than the non-H atoms. Since our roomtemperature data are highly limited, forcing us to the restrained structure refinement at room temperature, we analyze the movement of the individual non-H atoms with temperature using the atomic coordinates reported by Rao & Viswamitra (1972). The structure visualization software Mercury (Macrae et al., 2006) was used to compare the GSN structure at two temperatures. The least-squares overlay of two structures has been performed. The average relative displacement of the non-H atoms on lowering the crystal ˚ . Table 2 gives a detailed temperature to 150 K was of 0.06 A
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Figure 3 Room-temperature structure of GSN superimposed on the lowtemperature structure; origins of both structures are shifted to the molecular centroids in order to compare the two structures. Acta Cryst. (2013). B69, 595–602
research papers Table 2
Table 3
˚ ) and angles ( ) of glycine and Comparison between bond lengths (A nitrate ions of GSN at room (293 K) and low temperature (150 K).
(a) Hydrogen-bonding details and (b) silver coordination details at room (RT) and low (LT) temperature.
Room-temperature values taken from the structure reported by Rao & Viswamitra (1972). The primed atoms indicate symmetry equivalents of the unprimed atoms.
(a)
Low temperature
Room temperature
˚) N O (A RT LT
˚) N—H (A RT LT
/NHO ( ) RT LT
˚) H O (A RT LT
vHO {EHO(eV) = avHO2} RT LT
O1—C1 O2—C1 C1—C2 C2—N1 N2—C4 C4—C3 C3—O3 C3—O4 N3—O7 N3—O6 N3—O5 N4—O10 N4—O8 N4—O9
1.276 (7) 1.216 (6) 1.534 (5) 1.467 (5) 1.503 (5) 1.500 (5) 1.243 (7) 1.262 (7) 1.222 (7) 1.241 (7) 1.281 (7) 1.220 (7) 1.234 (6) 1.258 (6)
O1—C1 O2—C1 C1—C2 N1—C2 N10 —C20 C10 —C20 C10 —O20 C10 —O10 N2—O5 N2—O4 N2—O3 N20 —O50 N20 —O40 N20 —O30
1.28 1.25 1.54 1.50 1.50 1.54 1.25 1.28 1.25 1.26 1.28 1.25 1.26 1.28
(3) (3) (4) (4) (4) (4) (3) (3) (4) (3) (3) (4) (3) (3)
2.86 (3) 2.966 (6)
1.01 (2) 1.049 (8)
174 (5) 174.4 (10)
1.86 (4) 1.920 (10)
0.085 {0.05} 0.072 {0.04}
2.86 (3) 2.914 (7)
1.01 (2) 1.019 (10)
174 (5) 174.0 (10)
1.86 (4) 1.898 (11)
0.085 {0.05} 0.077 {0.04}
2.93 (3) 2.906 (6)
1.00 (2) 1.010 (11)
149 (3) 151.4 (9)
2.03 (4) 1.978 (11)
0.054 {0.02} 0.062 {0.03}
2.93 (3) 2.884 (7)
1.00 (2) 1.006 (12)
149 (3) 147.0 (11)
2.03 (4) 1.988 (12)
0.054 {0.02} 0.060 {0.03}
2.84 (3) 2.906 (7)
1.00 (2) 1.035 (10)
148 (6) 139.7 (9)
1.95 (5) 2.038 (11)
0.067 {0.03} 0.052 {0.02}
O2—C1—O1 O2—C1—C2 O1—C1—C2 N1—C2—C1 O3—C3—O4 O3—C3—C4 O4—C3—C4 N2—C4—C3 O7—N3—O6 O7—N3—O5 O6—N3—O5 O10—N4—O8 O10—N4—O9 O8—N4—O9
127.2 (5) 115.2 (4) 117.5 (4) 114.3 (3) 126.2 (5) 117.6 (4) 116.1 (4) 113.7 (3) 118.5 (5) 121.2 (5) 120.3 (4) 120.1 (5) 120.5 (4) 119.3 (4)
O2—C1—O1 O2—C1—C2 O1—C1—C2 N1—C2—C1 O20 —C10 —O10 O20 —C10 —C20 O10 —C10 —C20 N10 —C20 —C10 O5—N2—O4 O5—N2—O3 O4—N2—O3 O50 —N20 —O40 O50 —N20 —O30 O40 —N20 —O30
125 (2) 116 (3) 119 (2) 110 (3) 125 (2) 116 (3) 119 (2) 110 (3) 120 (2) 116 (2) 123 (2) 120 (2) 116 (2) 123 (2)
2.84 (3) 2.830 (6)
1.00 (2) 1.041 (10)
148 (6) 144.9 (8)
1.95 (5) 1.915 (11)
0.067 {0.03} 0.073 {0.04}
hydrogen positions reported in the room-temperature X-ray structure (Rao & Viswamitra, 1972). Table 3(a) gives the details of N—H O hydrogen bonds in GSN at two temperatures. The donor–acceptor distances at ˚ , whereas room temperature vary between 2.824 and 3.024 A the donor–acceptor distances at low temperature vary
Figure 4 Intermolecular interactions in GSN. Acta Cryst. (2013). B69, 595–602
(b)
Ag1—O Ag1—O Ag1—O Ag1—O Ag1—O Ag2—O Ag2—O Ag2—O Ag2—O Ag2—O Ag1—Ag2
˚) D (A RT
˚) D (A LT
2.19 2.35 2.50 2.72 2.89 2.19 2.35 2.50 2.72 2.89 2.90
2.227 (7) 2.313 (7) 2.373 (6) 2.781 (7) 2.846 (6) 2.213 (7) 2.273 (7) 2.370 (7) 2.819 (7) 2.852 (7) 2.804 (6)
(3) (3) (3) (4) (3) (3) (3) (3) (4) (3) (4)
vAgO {EAgO(eV) = avAgO2} RT
vAgO {EAgO(eV) = avAgO2} LT
0.355 0.229 0.152 0.084 0.052 0.355 0.229 0.152 0.084 0.052
0.319 {0.71} 0.253 {0.45} 0.215 {0.32} 0.071 {0.03} 0.059 {0.02} 0.331 {0.77} 0.282 {0.56} 0.217 {0.33} 0.064 {0.03} 0.059 {0.02}
{0.88} {0.37} {0.16} {0.05) {0.02} {0.88} {0.37} {0.16} {0.05} {0.02}
Both room- and low-temperature values are taken from the neutron structure reported in this paper.
˚ . This indicates that all the N— between 2.831 and 3.064 A H O bonds in the paraelectric and ferroelectric phases are from weak to moderate strength (Steiner, 2002) with hydrogen-bond energies less than 0.2 eV. Table 3(a) shows no marked change in the hydrogen-bond strengths, although there is some rearrangement of hydrogen bonds across the phase transition. We infer from this that GSN is not a typical hydrogen-bonded ferroelectric-like potassium dihydrogen phosphate (Nelmes, 1987) where the hydrogen bonds involved in the phase change are very strong (Steiner, 2002), having energies of the order of 1 eV or more, and a change in hydrogen-bond dynamics initiates a structural phase change. There are five O atoms and one Ag atom within a coordi˚ around a silver ion in GSN, hence nation sphere of radius 3 A silver coordination can be assumed to be distorted octahedral. Table 3(b) gives the details of silver coordination at two temperatures. There is a marked difference in the silver coordination at temperatures above and below TC (Fig. 4). ˚ There is a shortening of the Ag+—Ag+ separation by 0.09 A R. R. Choudhury et al.
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research papers Table 4 Electron density around the silver ions and local energy density (Ed) at the bond critical points (BCPs) and ring critical points (RCPs). ˚ 3) (e A RT
E (a.u.)
˚ 3) (e A LT
E (a.u.)
Critical point BCP(Ag—Ag) BCP(Ag—O) BCP(Ag—O) BCP(Ag—O) BCP(Ag—O) RCP(Ag—Ag—O—O) RCP(Ag—Ag—O—O)
0.16105 0.34006 0.47636 0.47636 0.34006 0.07061 0.07061
0.026 0.070 0.108 0.108 0.070 0.007 0.007
0.19329 0.38278 0.42168 0.41123 0.35367 0.069 0.07136
0.033 0.081 0.092 0.089 0.074 0.007 0.008
˚ as and some of the Ag—O distances also change by 0.1 A the crystal temperature is lowered from room to 150 K. In this respect GSN is similar to ferroelectric perovskites where the phase change results in the distortion of oxygen octahedra and the metal–oxygen distances change by approximately similar amounts (Lines & Glass, 1977). We have used the valence bond theory proposed by Brown (2009) to estimate the relative strength of the intermolecular interactions in GSN. The bond valence for each of the Ag—O coordination bonds as well as O H hydrogen bonds are obtained using the following expression vij ¼ exp½ðRij dij Þ=b ;
ð2Þ
where dij is the distance between the ith and jth atoms, b is a ˚ and the bond-valence universal constant with the value 0.37 A parameter Rij was taken from the literature (Brese & O’Keeffe, 1991). Although there is no rigorous way of deriving the bond energy from the bond valence, the following approximate expression was suggested by Brown (2009) Eij ’ av2ij :
ð3Þ
Here a is a constant with the value 7 eV v.u.2. Tables 3(a) and (b) list vij as well as Eij values for all the intermolecular interactions. We observe that Ag—O coordination bonds are in general stronger than the O H hydrogen bonds. Moreover, relative changes in the Ag—O coordination bond energies as temperature decreases from room temperature to 150 K are more noticeable than those in the O H hydrogenbond energies. These observations support the conclusions that the main driving mechanisms of the phase change in GSN are the distortions of its silver coordination octahedra, and hydrogen bonding plays only a secondary role in the phase change.
electron density is sensitive to the quality of the basis used, the conclusions obtained from the comparison of these values for different molecular geometries are not influenced by this limitation. The theoretical molecular electron density was analyzed using the quantum theory of atoms in molecules (AIM; Bader, 1991); the critical point details were obtained using AIMPAC software (Keith et al., 1995). A bond critical point (BCP) exists between the two nearest silver ions, which is a clear indication of the existence of a bonded interaction between the two. Local energy density (Ed) at the BCP between the two silver ions is negative (Ed < 0), showing a significant covalent contribution in the interaction. Two ring critical points were also observed in the plane containing the two bonded silver ions along with the four O atoms nearest to these Ag+ ions. A change in electron density around the silver ion across the phase transition is evident from the difference in the density values at the critical points (Table 4) for the two temperatures. Since displacement of the Ag+ ion is considered to be crucial for the structural phase transition, we have attempted to study the effect of the change in the Ag+—Ag+ distance. Keeping all the atoms except an Ag+ ion fixed to their roomtemperature positions we gradually changed the silver–silver separation by moving one of the two ions labeled Ag+(M) relative to the other labeled Ag+(S) (Fig. 5). The Ag+(S)— Ag+(M) separation was gradually changed from the roomtemperature value to the low-temperature value and beyond. We calculated the single-point ground-state molecular energies for each of the generated molecular configurations. The influence of changing the Ag+(M)—Ag+(S) distance on the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) separation is discussed in the next section.
6. Structural phase transition Since the silver ion (Ag+) plays a key role in the structural phase transition in GSN it is important to look into the chemistry of silver ions before we can hope to understand the structural phase change in GSN. The Ag+ ion has a closed d10 electronic configuration and, just like other coinage metals
5. Density functional theory (DFT) calculations Starting with our GSN neutron structures, a theoretical electron density for GSN monomer in room- and low-temperature phases was obtained using DFT calculations. We performed DFT calculations at the B3LYP/3-21G level of theory. All the calculations were carried out using the GAMESS-UK program (Guest et al., 2005). We employed the relatively simple 3-21G basis set for these calculations due to the limitations imposed by the computation facility available and the large size of the molecular unit. Even though the calculated value of the
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Figure 5 Change of Ag+(M)—Ag+(S) distance by gradually moving the Ag+(M) ions, keeping all the other atoms fixed. Acta Cryst. (2013). B69, 595–602
research papers (Cu, Ag, Au), it exhibits a tendency to form homoatomic d10– d10 interactions (Jansen, 1987), which can be thought of as bonds with a weak covalent character (El-Bahraoui et al., 1998). The presence of a low-lying electronic excited state in d10 ions (Cu+, Ag+, Au+) destroys the pure core nature of the closed d10 electronic shell of these ions and hence destroys their spherical symmetry. If because of the presence of bridging ligands (glycine in the case of GSN) these d10 ions are forced into close proximity, the d10–d10 interactions are established between these d10 ions. These homoatomic d10–d10 bonds have a decisive influence on the final crystal structure of the coordination compounds. Many silver complexes are reported in the literature where the silver–silver distances lie ˚ (Holloway et al., 1995). It is assumed between 2.654 and 3.54 A 10 10 that closed-shell d –d interactions exist in all these cases with a short silver–silver contact. GSN also belongs to this class of crystals. When we compare the Ag+—Ag+ distance in GSN with those reported in the literature, particularly the Ag+—Ag+ distance in the low-temperature phase of GSN ˚ ), which is smaller than twice the metallic silver radius (2.889 A 10 10 we conclude that the closed-shell d –d interactions are reasonably strong in GSN [Ag+—Ag+ distance in our low˚ , which is only 0.15 A ˚ more temperature structure is 2.804 A + + ˚ ); this than the minimum reported Ag —Ag distance (2.654 A indicates the silver–sliver bonds in the low-temperature phase of GSN are strong]. The existence of the bond critical point between two Ag+ ions with reasonably good electron density confirms the existence of a bonded interaction between the two. Electron density and the local energy density at the Ag+—Ag+ critical point is approximately one tenth of that at the C—C bond critical point. This gives an estimate of the strength of the Ag+—Ag+ interaction in comparison to the standard C—C single bond. In fact, the change in the strength of these d10—d10 bonds with decreasing crystal temperature (Table 4) is the likely reason for the observed structural distortion in GSN crystals at TC. This fact is discussed below in more detail. We can apply the vibronic coupling theory (as discussed in x1) to the specific case of GSN crystals in order to explain the structural phase transition observed in these crystals at low temperature. Our calculations show that as the Ag+(M)— Ag+(S) separation decreases, the energy gap E(n) E(0) between HOMO and LUMO also decreases (Fig. 6a), as a result the value of the Kv term in the expression of total energy E [equation (1)] will increase. As explained in x1, when this Kv term prevails over the Ks term denoting the static elastic restoring force, the structural distortion is stabilized, resulting in a structural phase change. We propose the following mechanism for the phase transition in GSN: initially in the paraelectric phase the d10–d10 interactions between silver ions are weak, hence small ionic displacements Q lead to an increase in the total energy due to larger elastic restoring forces denoted by Ks compared with the electronic coupling denoted by the Kv term. As the Ag+–Ag+ separation reduces with lowering of the crystal temperature, overlap between filled d- and unfilled s-orbitals of Ag+ ions increases, leading to a strengthening of the Ag+—Ag+ interaction. Finally, for some Acta Cryst. (2013). B69, 595–602
Ag+—Ag+ separations, lowering of the total energy for small ionic displacements Q resulting from Ag+–Ag+ electronic coupling (Kv) overwhelms the increase in the total energy due to the classic elastic energy (Ks), making the second-order term in the energy expression E [equation (1)] negative. At this point the distorted structure is stabilized, leading to a structural phase change. A similar situation has been observed in semiconducting CuCl where homoatomic Cu+—Cu+ interactions resulted in a tendency of Cu+ ions to undergo offcenter atomic displacements (Wei et al., 1993). The rearrangement of the electrons as a result of the atomic displacement leads to a change of molecular polarization. The dynamic atomic charge of an atom M defined as ZM* = P/uM (Rondinelli et al., 2009; Pearson, 1969) gives a measure of the change in the net polarization due to ionic displacement. A large value of ZM* is considered to be an indication of the
Figure 6 (a) Variation in the HOMO and LUMO separation with changing Ag+(M)—Ag+(S) distance. (b) Change in molecular polarization with the shift in Ag+(M) ion; the shift of Ag+(M) at room temperature is taken as 0.0, i.e. Ag+(M) is displaced progressively from its room-temperature position. R. R. Choudhury et al.
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research papers tendency of the ions to undergo some displacements. For example, in the cubic phase of BaTiO3 the formal charge of the Ti ion is +4, but its dynamic charge is almost +7, indicating the large tendency of the Ti ion to undergo displacement towards an oxygen (Rondinelli et al., 2009). We have estimated the value of ZM* for the moving silver ion Ag+(M) by plotting the calculated molecule polarization against the displacement of the Ag+(M) ion (Fig. 6b). The dynamic charge of Ag+(M) as obtained from the slope of a polarization versus displacement graph is 1.17 e, whereas its formal charge is 1 e and its static charge (Pearson, 1969) obtained from the electron density calculation is only 0.25 e. This demonstrates that the Ag+ ion in this structure has a tendency to undergo a displacement. Hence, the ferroelectric transition in GSN results because of the tendency of the Ag+ ion to undergo an atomic displacement so that the Ag+—Ag+ separation reduces; this strengthens the coupling between the low-lying excited state and the ground state of the molecule, thereby resulting in a second-order Jahn–Teller distortion of the structure.
7. Conclusion We have measured and refined the structure of glycine silver nitrate (GSN) in the ferroelectric phase by means of lowtemperature single-crystal neutron diffraction. The final R value for the refined structure at 150 K is 0.059. A comparison between the GSN crystal structure in the ferroelectric phase and the earlier reported GSN structure in the paraelectric phase shows that all the atoms of GSN undergo displacements to a varying degree as the crystal undergoes a structural phase change. The average displacement of the non-H atoms on lowering the crystal temperature from room temperature to ˚ . Due to the structural distortion 150 K is of the order 0.06 A resulting from atomic displacement, the center of inversion disappears in the low-temperature ferroelectric phase, yielding a structural phase transition from P21/a to P21. No marked change in the strength of the hydrogen bonds is observed as the crystal temperature is lowered from room temperature to 150 K. The silver coordination changes significantly across the phase transition temperature (TC). The ˚ , indicating an increase Ag+—Ag+ distance reduces by 0.09 A 10 in the strength of the homoatomic d —d10 bonds between the silver ions. The displacive ferroelectric structural phase transition in GSN is explained within the framework of vibronic theory of ferroelectricity, which incorporates the coupling of electronic distribution with nuclear displacements. The origin of dipolar instability is mainly due to the second-order Jahn– Teller behavior of Ag+ ions in GSN. We thank the Department of Science & Technology for providing the funding [DST(5)/AKR/P087/10-11/909, dated 20/08/2010, DST(5)/AKR/P087/09-10/986 dated 31/08/2009]
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for carrying out the experiments at SINQ, Paul Scherrer institute, Villigen, Switzerland.
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Acta Cryst. (2013). B69, 595–602
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