An examination of the thermal expansion of urea using high-resolution variable-temperature X-ray powder diffraction

Variable-temperature high-resolution capillary-mode powder X-ray diffraction is used to assess changes in unit-cell dimensions as a function of temperature over the range 188–328 K. No evidence was found for any polymorphic transformations over this temperature range and thermal expansion coefficients for urea were found to be α_a = (5.27 ± 0.26) × 10⁻⁵ K⁻¹ and α_c = (1.14 ± 0.057) × 10⁻⁵ K⁻¹.

1. Introduction

Despite being of fundamental importance in many areas, information about the solid-state properties of molecular materials still remains surprisingly limited (Desiraiju, 2003). In particular, detailed knowledge of the thermal expansion tensor for many low-symmetry organic materials is not always available, this despite the fact that structural change as a function of temperature can have ramifications for particle properties.

In the case of crystals not undergoing any polymorphic change, the effect of temperature on crystal structure is well described in terms of a linear thermal expansion coefficient. More specifically, in the case of anisotropic crystals such as urea, thermal expansion can be described by a linear thermal expansion coefficient along its primary crystallographic axes:

where L₀ is a given cell parameter of the material (reference length) in a given direction and at a given temperature T₀ (reference temperature).

In this short note, we report the determination of the thermal expansion coefficients of urea using temperature-programmed high-resolution X-ray powder diffraction. Urea, O=C(NH₂)₂, has applications in agrochemistry and nonlinear optics and is one of the simpler organic molecules. Urea is an unusual compound, having only eight atoms yet existing in a solid form under ambient conditions. Because of its simplicity, the crystal structure of urea was one of the first among the organic crystals to be determined by X-ray crystallographic methods (Vaughan & Donohue, 1952, and references therein), being found to crystallize in the highly symmetrical tetragonal space group with two molecules in the unit cell of dimensions a = 5.661 and c = 4.712 Å. Urea crystal chemistry is dominated by hydrogen-bonding chains associated with a network of six strong intermolecular hydrogen bonds, four intrachain along the c axis and two interchain along the a/b axis in its first coordination sphere (see Docherty et al., 1993), and is noteworthy for having its carbonyl group as an acceptor for four hydrogen bonds.

2. Experimental details

The calculation of the linear thermal expansion was carried out by monitoring the changes in the a and c cell parameters of a polycrystalline sample of urea, as determined using a Siemens D5000 high-resolution powder X-ray diffractometer equipped with an Oxford Instruments Cryocool liquid-nitrogen cold-flow cryostatic temperature controller. The urea powder, finely ground in a pestle and mortar and loaded into a 1 mm capillary, was examined over a temperature range from 188 to 328 K.

The resultant powder data were analysed with the lattice parameters calculated using the program DICVOL (Boultif & Louer, 1991). The quality of the lattice parameters derived was crossed-checked through full-pattern fitting using the program GSAS (Larson & von Dreele, 1994). Using the values obtained from DICVOL during pattern indexing resulted in a comparatively low value for R_wp (9%), and hence the change of lattice parameters after the refinement was not found to be significant, reflecting a difference between the refined and the experimental values of about 0.01%. Hence, the DICVOL data was found to be of sufficient quality for calculation of the thermal expansion coefficient.

The thermal expansion was calculated along the a and c axes via equation (1) with reference temperature and cell parameters from previous studies (Swaminathan et al., 1984), from which the parameters at 150 K are a = 5.59 and c = 4.69 Å.

3. Results and discussion

The lattice expansion as a function of temperature is given in Fig. 1. No significant variation in cell parameters, reflecting polymorphic variation, was found to occur, confirming previous observations on the polymorphic behaviour of urea. The thermal expansion coefficient over the temperature range 188–328 K was measured to be (5.27 ± 0.26) × 10⁻⁵ K⁻¹ in the a/b direction, and (1.14 ± 0.057) × 10⁻⁵ K⁻¹ in the c direction, which correlates well with the values determined from previously published data over a temperature range of 12–123 K (Swaminathan et al., 1984). In this range, the coefficients of thermal expansion, calculated in the same way as used for the data presented here, were found to be (3.74 ± 0.187) × 10⁻⁵ K⁻¹ in the a/b direction and (1.21 ± 0.0605) × 10⁻⁵ K⁻¹ in the c direction.

Figure 1 The lattice expansion [(l − l0)/l0, dimensionless] is represented as a function of the temperature. The coefficient of thermal expansion was determined from the slope of the straight line used to fit the experimental data.

Examining the above results, it is noteworthy that the coefficient of thermal expansion in the a/b direction is larger, for both temperature regions examined, compared with that in the c direction. This is expected, reflecting weaker intermolecular interactions associated with the hydrogen bonds along a/b axis (interchain) compared with those along the c axis (intrachain) (Docherty et al., 1993), and hence the a/b axis allows for the greater thermal expansion. The comparison of the expansion coefficient for the two different temperature ranges, i.e. this study and that of Swaminathan et al., indicates a larger change of the thermal expansion coefficient in the a/b direction for the higher temperature range, again reflecting the weaker nature of the intermolecular interactions associated with the hydrogen bonding compared with the stronger ones along the c direction. In contrast, the change of the coefficient of thermal expansion in the c direction for the two temperature ranges is quite similar, being within the range of the error for these studies.

A literature survey (Table 1) of thermal expansion data for organic crystals reveals that available data are limited for this class of materials. The thermal expansion of urea is comparable with other urea-based compounds (Meng & Lu, 1998) but is larger than other aromatic hydrocarbons such as benzophenone (Girdwood, 1998). This is not unexpected given the dominance of the van der Waals and hydrogen-bonding contribution to the crystal lattice energy.

Table 1
Results of a literature survey on previously measured coefficients of thermal expansion for some related organic crystals

Compound	Coefficient of thermal expansion (K^−1)	Reference
α-Chloro­acetic acid (nonlinear)	7.7 × 10^−5	Hoseneder & Hartel (2001)
MODPA (4,5-methyl-1,3,4-oxadiazin-2-yl-N,N-di­methylphenyl­amine)	1.8 × 10^−4	Franco & Reck (2002)
DPO (2,5-di­phenyl-1,3,4-oxa­diazine)	1.9 × 10^−4	Franco & Reck (2002)
L-Alanine	1.64 × 10^−7, 12.07 × 10^−7	Misoguti (1996)
Hexamine	6 × 10^−7	Fomo (1974)
UDT (urea-d-tartaric acid)	5.23 × 10^−5, 3.86 × 10^−5, 3.57 × 10^−5	Meng & Lu (1998)
Benzophenone	1.77 × 10^−7, 3.00 × 10^−7, 1.48 × 10^−7	Girdwood (1998)
Urea	5.27 × 10^−5, 1.14 × 10^−5	This work