Soru

In 1781, the French mineralogist René-Just Haüy made a seminal observation that transformed the study of mineralogy from a descriptive catalog of external forms into a rigorous mathematical science. Prior to Haüy’s work, naturalists classified crystals primarily by their overall external habit—a method plagued by inconsistency, as the same mineral species often exhibited markedly varied geometric contours depending on localized geological conditions during crystal growth.

The turning point occurred when Haüy accidentally dropped a prismatic specimen of calcite (calcareous spar) belonging to a colleague. Examining the resulting fragments, Haüy observed that regardless of the original crystal’s elongated hexagonal shape, the cleaved pieces consistently broke into identical rhombohedral shards with angles precisely matching those of Iceland spar, another known form of calcite. Intrigued by this structural constancy, Haüy systematically cleaved numerous other calcite specimens of diverse external shapes, discovering that every variety could be cleaved down to the identical rhombohedral nucleus.

From these mechanical dissections, Haüy formulated the hypothesis that crystal structures are composed of microscopic, indivisible polyhedral building units, which he termed molécules intégrantes. According to Haüy's model, the immense variety of macroscopic crystal faces observed in nature arises from the orderly, stepwise stacking of these identical microscopic units in decreasing successive layers—a geometric progression termed 'decrescence'—upon the faces of the central nucleus. By establishing that the ratios of the dimensions of these stacked layers could always be expressed as simple rational whole numbers, Haüy introduced the law of rational intercepts, laying the geometric foundation for modern crystallography.

Although later crystallographers demonstrated that Haüy’s assumption of solid, space-filling polyhedral blocks did not accurately describe atomic structure—which consists of discrete atoms arranged in a periodic lattice with empty intervening space—his mathematical formulation of spatial periodicity and rational ratios remained universally valid. Haüy’s insistence on internal symmetry over superficial external morphology provided the theoretical bridge that enabled nineteenth-century physicists to model the internal diffraction and optical properties of solid matter.

According to the passage, which of the following did Haüy observe when examining the fragments of the dropped calcite specimen?