Dynamics and thermodynamics of crystalline polymorphs. 2. β-Glycine, analysis of variable-temperature atomic displacement parameters

Dynamics and disorder: on the stability of pyrazinamide polymorphs

This article focuses on the structure and relative stability of four pyrazinamide polymorphs. New single crystal X-ray diffraction data collected for all forms at 10 K and 122 K are presented. By combining periodic ab initio DFT calculations with normal-mode refinement against X-ray diffraction data, both enthalpic and entropic contributions to the free energy of all polymorphs are calculated. On the basis of the estimated free energies, the stability order of the polymorphs as a function of temperature and the corresponding solid state phase transition temperatures are anticipated. It can be concluded that the α and γ forms have higher vibrational entropy than that of the β and δ forms and therefore they are significantly more stabilized at higher temperatures. Due to the entropy which arises from the disorder in γ form, it overcomes form α and is the most stable form at temperatures above ∼500 K. Our findings are in qualitative agreement with the experimental calorimetry results.

Low-frequency lattice vibrations from atomic displacement parameters of α-FOX-7, a high energy density material

Highly anharmonic thermal vibrations may serve as a source of structural instabilities resulting in phase transitions, chemical reactions and even the mechanical disintegration of a material. Ab initio calculations model thermal motion within a harmonic or sometimes quasi-harmonic approximation and must be complimented by experimental data on temperature-dependent vibrational frequencies. Here multi-temperature atomic displacement parameters (ADPs), derived from a single-crystal synchrotron diffraction experiment, are used to characterize low-frequency lattice vibrations in the α-FOX-7 layered structure. It is shown that despite the limited quality of the data, the extracted frequencies are reasonably close to those derived from inelastic scattering, Raman measurements and density functional theory (DFT) calculations. Vibrational anharmonicity is parameterized by the Grüneisen parameters, which are found to be very different for in-layer and out-of-layer vibrations.

Theoretically derived thermodynamic properties can be improved by the refinement of low-frequency modes against X-ray diffraction data

Herein, a framework for the estimation of the thermodynamic properties of molecular crystals via the refinement of frequencies from density functional theory calculations against X-ray diffraction data is presented. The framework provides an efficient approach to including the contribution of acoustic modes in the thermodynamic properties. The obtained heat capacities for urea, the α- and β-glycine polymorphs, benzoic acid, and 4'-hydroxyacetophenone are in good agreement with those from adiabatic calorimetry.

X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems

In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di-methyl 3,6-di-chloro-2,5-di-hydroxy-terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312-323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to L-alanine, naphthalene and xylitol

In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206-214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of L-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of L-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol^-1 K^-1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. I. Theory

This study demonstrates and tests the refinement of a lattice-dynamical model derived from periodic ab initio calculations at the Γ point against elastic diffraction data (X-ray or neutron). Refinement of only a handful of parameters is sufficient to obtain a similar agreement with the data as the conventional crystallographic model using anisotropic displacement parameters. By refinement against X-ray data, H displacement parameters are obtained which compare favourably with those from neutron diffraction experiments. The approach opens the door for evaluating thermodynamic properties, and for refinement against multi-temperature data, against inelastic diffraction data, spectroscopic information and thermal diffuse scattering data.

Sarcosine and betaine crystals upon cooling: structural motifs unstable at high pressure become stable at low temperatures

The crystal structures of N-methyl derivatives of the simplest amino acid glycine, namely sarcosine (C3H7NO2) and betaine (C5H11NO2), were studied upon cooling by single-crystal X-ray diffraction and single-crystal polarized Raman spectroscopy. The effects of decreasing temperature and increasing hydrostatic pressure on the crystal structures were compared. In particular, we have studied the behavior upon cooling of those structural motifs in the crystals, which are involved in structural rearrangement during pressure-induced phase transitions. In contrast to their high sensitivity to hydrostatic compression, the crystals of both sarcosine and betaine are stable to cooling down to 5 K. Similarly to most α-amino acids, the crystal structures of the two compounds are most rigid upon cooling in the direction of the main structural motif, namely head-to-tail chains (linked via the strongest N-H···O hydrogen bonds and dipole-dipole interactions in the case of sarcosine, or exclusively by dipole-dipole interactions in the case of betaine). The anisotropy of linear strain in betaine does not differ much upon cooling and on hydrostatic compression, whereas this is not the case for sarcosine. Although the interactions between certain structural motifs in sarcosine and betaine weaken as a result of phase transitions induced by pressure, the same interactions strengthen when volume reduction results from cooling.