摘要:

1.IntroductionThe crystal structure of ferroelectric sodium nitrite, NaNO2, is well known; several X-ray and neutron diffraction structure determinations have been reported at different temperatures (see for exampleref. 1–4). At 163.9 °C the ordered crystal structure of ferroelectric NaNO2undergoes a phase transformation to the disordered paraelectric phase,viaan anti-ferroelectric phase.5The anti-ferroelectric structure exists in a temperature range of only 1 °C,i.e.NaNO2becomes paraelectric at a temperature of 165.2 °C.5In this paper, we investigate the ferroelectric properties and spontaneous polarisation of the ferroelectric phase stable belowTc = 163.9 °C. The simple crystal structureof ferroelectric sodium nitrite, shown inFig. 1, makes it well suited as a model structure for the evaluation of new theoretical models. The structure belongs to the polar space group Im2m; the planar NO2−ions lie in thebcplane, with the Na+ions along the O–N–O bisector. The polarisation vector is oriented along theb-axis.Experimental crystal structure of ferroelectric NaNO2in the orthorhombic space group Im2m, with cell parameters:a = 3.52 Å,b = 5.54 Å,c = 5.38 Å.2The polar axis is theb-axis. (a) Structure denotedλ = 1; and (b) structure denotedλ = −1 (the inverse structure ofλ = 1). Open circles lie in the planex = 0 and filled circles lie in the planex = ½.A variety of experimental methods have been used to determine the spontaneous polarisation (Ps) of NaNO2. ThePsvalue has, for example, been obtained bydirectmeasurement using polarity reversal,6hysteresis loop7and charge integration8methods, orindirectly, estimating the cell dipole moment from net charges or more sophisticated multipolar expansion models of the electron density obtained from X-ray diffraction refinements. Here, we will refer to the direct and indirect approaches as “experimental” and “quasi-experimental”, respectively. Mostly due to the large variety of methodologies used, the reportedPsvalues for NaNO2vary in the range from 74 µC cm−23down to 7.3 µC cm−2.9The value 74 µC cm−2was calculated from a simple point-charge model with nominal charges of +1 for Na, +3 for N and −2 for O, and will not be further discussed here. The value of 7.3 µC cm−2originates from a more sophisticated method where thePsvalue was calculated from a multipolar refinement of X-ray data within the Hirshfeld model.10Using only their refined atomic fractional charges (Na = +0.27e, N = +0.20eand O = −0.24e) aPsvalue of 7.8 µC cm−2is obtained. The same team of authors as inref. 9, have recently carried out a whole new Hirshfeld refinement on the data fromref.9, this work is described in the paper.11Their newPsvalue is 7.8 µC cm−2(when both monopoles and dipoles are taken into account). It should be pointed out that X-ray obtained fractional charges and multipole moments are usually very sensitive to the refinement model used. So, for example, the Coppens–Hansen multipolar scheme12applied by Okudaet al.2to a 120 K X-ray diffraction data set for NaNO2gave rise to a rather different set of charges (−0.18 for N and −0.41 for O when the Na charge was fixed to +1.0); when we use their charges to compute Pswe obtain a value of 11.2 µCcm−2. The most recent Psvalues reported from “direct” measurements are 11.9 µCcm−213and 11.7 µCcm−2;14both values were obtained from polarisation reversal measurements.From what we are aware, only one quantum-chemical calculation of Pshas been reported for ferroelectric NaNO2: Henkelet al.15in 1975, obtained a Psvalue of 9.9 µCcm−2from calculations at the X-αlevel; the Psvalue was obtained from the atomic charges obtained in turn by integrating the charge density around the atoms and defining the atomic volume in terms of the surface where the charge density has a minimum. Kam and Henkel16later also computed the piezoelectric constants (d21, d22and d23) and band structures. The first band-structure calculation on NaNO2was performed with a semi-empirical (LCAO) Hamiltonian;17more recent calculations employed the full-potential linearized-augmented plane-wave (FLAPW),18full-potential linear muffin-tin orbital (FLMTO)19and liner combination of atomic orbitals (LCAO) methods;20the two latter papers discussed both the electronic and optical properties of NaNO2. For completeness, we also mention an early model study where ideal polarisable charges and dipoles were arranged according to the experimental3crystal structure; these calculations gave aPsvalue of 9.71 µC cm−2.21In this paper we presentPsvalues for ferroelectric NaNO2obtained with three different theoretical models. All calculations were performed within the periodic Hartree–Fock or DFT schemes. In two of the models we have used an approach similar to the quasi-experimental methods to calculate thePsvalues. Inmodel 1we thus determine the cell dipole moment from theab initioMulliken charges, and inmodel 2the cell dipole moment is obtained from a multipolar expansion truncated to the atomic Mulliken-type partition. In our most sophisticated model,model 3, the spontaneous polarisation is calculated directly from the electronic Hamiltonian, making use of the Berry phase theory22implemented within theCRYSTALHartree–Fock framework by Dall'Olio, Dovesi and Resta23in a study of the KNbO3perovskite crystal.The calculatedPsvalue at the Hartree–Fock level for tetragonal KNbO3was in good agreement with experimental data. ThePsvalue has later also been obtained, using the Hartree–Fock Hamiltonian, for the cubic structure of KNbO3.24The Berry-phase approach, within the Hartree–Fock formalism, has previously also been applied to bulk ZnO25and to surfaces of BaTiO3.26In the current paper, we will primarily use thePsvalue obtained from the Berry phase calculations to compare with experiment;models 1and2are of interest because the method of estimating an approximate cell dipole moment from integral or fractional charges (nominal or diffraction derived) is well represented in the literature.Model 2, or rather the multipolar Hirshfeld model, is infact the model used in the refinement of the new 30 K X-ray diffraction data presented in the paper by Godhaet al.11We will refer to their results in our discussions.

ISSN:1463-9076     

DOI:10.1039/b204526p

出版商:RSC    

年代:2002

数据来源: RSC