Reconsidering the Origins of Forsbergh Birefringence Patterns

In 1949, P. W. Forsbergh Jr. reported spontaneous spatial ordering in the birefringence patterns seen in flux-grown BaTiO3 crystals [1], under the transmission polarized light microscope [2]. Stunningly regular square-net arrays were often only found within a finite temperature window and could be induced on both heating and cooling, suggesting genuine thermodynamic stability. At the time, Forsbergh rationalized the patterns to have resulted from the impingement of ferroelastic domains, creating a complex tessellation of variously shaped domain packets. However, evidence for the intricate microstructural arrangement proposed by Forsbergh has never been found. Moreover, no robust thermodynamic argument has been presented to explain the region of thermal stability, its occurrence just below the Curie Temperature and the apparent increase in entropy associated with the loss of the Forsbergh pattern on cooling. As a result, despite decades of research on ferroelectrics, this ordering phenomenon and its thermodynamic origin have remained a mystery. In this paper, we re-examine the microstructure of flux-grown BaTiO3 crystals, which show Forsbergh birefringence patterns. Given an absence of any obvious arrays of domain polyhedra, or even regular shapes of domain packets, we suggest an alternative origin for the Forsbergh pattern, in which sheets of orthogonally oriented ferroelastic stripe domains simply overlay one another. We show explicitly that the Forsbergh birefringence pattern occurs if the periodicity of the stripe domains is above a critical value. Moreover, by considering well-established semiempirical models, we show that the significant domain coarsening needed to generate the Forsbergh birefringence is fully expected in a finite window below the Curie Temperature. We hence present a much more straightforward rationalization of the Forsbergh pattern than that originally proposed, in which exotic thermodynamic arguments are unnecessary.

Select Document: Sir George Radcliffe’s “Original of Government” (1639) and Absolutist Political Theory in Stuart Ireland

A seventeenth-century manuscript miscellany, which once belonged to Archbishop James Ussher of Armagh, contains a short treatise on the origins of government by Sir George Radcliffe. Radcliffe was legal assistant to Sir Thomas Wentworth, lord deputy of Ireland (from January 1640 earl of Strafford and lord lieutenant). The treatise insisted on the divine origin of all human political power and implied that the best form of government was absolute monarchy, in which the monarch was free of all human law and subject to divine restraint alone. It will be suggested below that the composition of this treatise can be dated to the summer of 1639. This introduction will offer an outline of Radcliffe’s education and political career, explain the genesis of his treatise on government, point out some pertinent aspects of its argument, and finally assess the document’s significance.