Evaluation of the elastic constants of 1,3,5-triphenylbenzene from thermal diffuse scattering of X-rays

Abstract

From the measurements of the intensities of thermal diffuse scattering observed in the stationary-crystal photographs taken with monochromatic Cu Ke radiation, all the nine elastic constants of orthorhombic 1,3,5-triphenylbenzene single crystals have been determined by the photographic method. Each constant is evaluated from two or more directions of thermal wave vectors. The reciprocal nodes involved for the determination of all the constants were 200, 206, 002, 015 and 006. Diffusely scattered intensities were corrected for general scattering, polarization and skew factors. Corrections for absorption, divergence and second-order diffuse scattering were found negligible. The values of elastic constants in units of 10 ~° dynes.cm -2 are C1~ = 0-31, C22 = 1"36, (733 = 2"33, 6"44= 5"02, 6"55=0"34, C66 = 3"69, C~2= -1"78, 6"13 =0"92 and C2a = 0"80. Correlation of the elastic data with the structure have been attempted.

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors

“…An ecessary and sufficient condition for mechanical stability of ac rystal is that its elastic tensor is positive definite,o ra ll of its eigenvalues are positive. [63] This follows from Equation ( 1), which requires that the elastic energy is always positive for all strains e i relative to the equilibrium structure.The six eigenvalues of the elastic tensor are readily calculated, and we have identified four examples in which the experimental tensors fail this criterion:1 ,3,5-triphenylbenzene [30] (obtained from thermal diffuse scattering), malonic acid [39] (unfortunately,t he only measurement for at riclinic molecular crystal), (À)-2-a-methylbenzylamino-5-nitropyridine (MBANP) [64] and N-methylurea. [65] These measurements have been excluded from our analysis,a sh as the S-HF-3c calculated elastic tensor for pyrazine.…”

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors

“…For example, ISTS measurements have been performed on polished thin slabs 600–800 μm thick for the explosives PETN and RDX, [27] enabling a critical comparison with previous ultrasonic, RUS and Brillouin scattering results, and this comparison is discussed in detail in Section 5.14. Less commonly, elastic tensors have also been obtained from the thermal diffuse scattering of X‐rays, [28–33] and from inelastic neutron scattering [34] …”

Elastic constants of acenaphthene determined from studies of thermal diffuse scattering of X-rays

“…Further, the stabilization of the output of the X-ray tube, which is essential for the counter diffractometer method, is not essential for this method. This specially developed photographic method has been used by a number of investigators (Srivastava & Chakraborty, 1962;Joshi & Kashyap, 1964;Chandra & Hemkar, 1973) to determine absolute values of elastic constants of a number of molecular crystals. In the present investigation a similar method has been applied to determine the elastic constants of crystals of acenaphthene belonging to the orthorhombic system.…”