Orthorhombic charge density wave on the tetragonal lattice of EuAl4.

EuAl4 possesses the BaAl4 crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge density wave (CDW) transition at T CDW = 145 K and features four consecutive antiferromagnetic phase transitions below 16 K. Here we use single-crystal X-ray diffraction to determine the incommensurately modulated crystal structure of EuAl4 in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q = (0,0,0.1781 (3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the Al atoms as the location of the CDW. The tem-per-ature dependence of the specific heat reveals an anomaly at T CDW = 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl4 leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.

Single-crystal-to-single-crystal phase transitions of commensurately modulated sodium saccharinate 1.875-hydrate.

This work reports reversible, single-crystal-to-single-crystal phase transitions of commensurately modulated sodium saccharinate 1.875-hydrate [Na(sac)(15/8)H2O]. The phases were studied in the temperature range 298 to 20 K. They exhibit complex disordered states. An unusual reentrant disorder has been discovered upon cooling through a phase transition at 120 K. The disordered region involves three sodium cations, four water molecules and one saccharinate anion. At room temperature, the structure is an eightfold superstructure that can be described by the superspace group C2/c(0σ20)s0 with q = (0, 3/4, 0). It demonstrates maximum disorder with the disordered chemical entities having slightly different but close to 0.50:0.50 disorder component ratios. Upon cooling, the crystal tends to an ordered state, smoothly reaching a unified disorder component ratio of around 0.90:0.10 for each of the entities. Between 130 and 120 K a phase transition occurs involving a sudden increase of the disorder towards the disorder component ratio 0.65:0.35. Meanwhile, the space group and general organization of the structure are retained. Between 60 and 40 K there is another phase transition leading to a twinned triclinic phase. After heating the crystal back to room temperature its structure is the same as before cooling, indicating a complete reversibility of the phase transitions.

Incommensurately modulated structure of morpholinium tetrafluoroborate and configurational versus chemical entropies at the incommensurate and lock-in phase transitions.

Morpholinium tetrafluoroborate, [C4H10NO]+[BF4]-, belongs to a class of ferroelectric compounds ABX4. However, [C4H10NO]+[BF4]- does not develop ferroelectric properties because the incommensurate phase below Tc,I = 153 K is centrosymmetric with superspace group Pnam(σ100)00s and σ1 = 0.42193 (12) at T = 130 K; the threefold superstructure below Tc,II = 117-118 K possesses the acentric but non-ferroelectric space group P212121. At ambient conditions, [C4H10NO]+[BF4]- comprises orientationally disordered [BF4]- anions accommodated in cavities between four morpholinium cations. A structure model for the incommensurately modulated phase, which involves modulated orientational ordering of [BF4]- together with modulated distortions and displacements of the morpholinium ions is reported. A mechanism is proposed for the phase transitions, whereby at low temperatures morpholinium cations are shaped around the tetrafluoroborate anion in order to optimize the interactions with one orientation of this anion and, thus, forcing [BF4]- into this orientation. This mechanism is essentially different from a pure order-disorder phase transition. It is supported by consideration of the transition entropy. The difference in configurational entropy between the disordered and incommensurate phases has been computed from the structure models. It is shown to be much smaller than the experimental transition entropy reported by Owczarek et al. [Chem. Phys. (2011), 381, 11-20]. These features show that the order-disorder contribution is only a minor contribution to the transition entropy and that other factors, such as conformational changes, play a larger role in the phase transitions.

Resonance-stabilized partial proton transfer in hydrogen bonds of incommensurate phenazine-chloranilic acid.

The co-crystal of phenazine (Phz) and chloranilic acid (H2ca) becomes ferroelectric upon cooling through the loss of inversion symmetry. Further cooling results in the development of an incommensurate ferroelectric phase, followed by a lock-in transition towards a twofold superstructure. Here we present the incommensurately modulated crystal structure of Phz-H2ca at T = 139 K with a symmetry given by the superspace group P2(1)(½ σ(2) ½)0 and σ(2) = 0.5139. The modulation mainly affects the positions of the protons within half of the intermolecular hydrogen bonds that are responsible for the spontaneous polarization in all three low-temperature phases. Evidence for proton transfer in part of the hydrogen bonds is obtained from the correlated dependence on the phase of the modulation of the lengths of bonds involved in resonance stabilization of the acidic anion, and much smaller variations of bond lengths of atoms not involved in the resonance mechanism. Incommensurability is explained as competition between proton transfer favored for single hydrogen bonds on the basis of pKa values and avoiding unfavorable Coulomb repulsion within the lattice of the resulting ionic molecules.