Trapiche Pattern Formation of Grossular Garnets
The six-fold rotational symmetric pattern, called trapiche, is commonly reported in hexagonal or trigonal crystal system minerals such as beryl, corundum, tourmaline, and quartz, but also can be found in diamond, spinel, and garnet having a cubic crystal system (J. Bergman, “Trapiche: The rising star,” InColor, No. 31, 2016, pp. 32–44). Recently, three near-colorless transparent tablets with six-rayed black inclusions arranged in a snowflake-like pattern forming a trapiche structure were submitted to GIA’s Tokyo laboratory for identification (figure 1A). Standard gemological properties, Raman spectra, and chemical analyses using energy-dispersive X-ray fluorescence identified the stones as grossular garnets, composed mainly of Ca3Al2Si3O12. The arms and cores were black due to irregular black inclusions, and the samples also contained numerous colorless transparent inclusions (figure 1B). In cross-polarized light, the largest stone, weighing 1.00 ct, showed a clear concentric hexagonal light and dark pattern (figure 1C). The three submitted samples were very similar to the recently reported trapiche grossular garnets from Zhejiang Province, China (Y. Wang et al., “Trapiche garnets in Chun’an, Zhejiang Province, China: New constraints from their gemology, geochemistry, and geochronology,” Crystals, Vol. 15, No. 3, 2025, article no. 201; T. Hainschwang, “Trapiche grossular from China,” Journal of Gemmology, Vol. 39, No. 5, 2025, pp. 418–421; Summer 2025 GNI, pp. 208–210).
Typical idiomorphism of single crystal gemstones, such as hexagonal prismatic emeralds, octahedral diamonds, and rhombic dodecahedral garnets, is the thermodynamic equilibrium shape in which the sum of all surface energies is minimized (Wulff’s theorem). Since the distance between the euhedral facets and the center is shorter than that between the apexes and the center, it is clear that the euhedral facets grow slower than the apexes. This slower crystal growth for the flat euhedral facets as compared to the apexes relates to the fact that they are smooth at the atomic level and have fewer defects (e.g., Y. Saito, Statistical Physics of Crystal Growth, World Scientific, Singapore, 1996). A smooth surface is one in which the constituent atoms in a crystal structure (i.e., the lattice points that represent molecular groups) are most densely packed. The densest plane can be determined primarily by the mineral’s Bravais lattice type. The seven crystal systems are further classified into 14 types of Bravais lattices by considering four unit cell lattice patterns: primitive, body-centered, face-centered, and base-centered. Snowflakes and emeralds (beryls) have primitive hexagonal lattices, diamonds have face-centered cubic (fcc) lattices, and garnets have body-centered cubic (bcc) lattices (figure 2, first column). A primitive hexagonal lattice often forms a hexagonal prism or plate consisting of two basal pinacoids {0001} and six prism faces {1010}. An fcc lattice has the {111} plane where the lattice points are densest and often forms a euhedral octahedron. On the other hand, the densest plane for a bcc lattice is the {110} and often forms a euhedral rhombic dodecahedron (Bravais’ empirical law; figure 2, second column).
The critical nuclei, which are the earliest stages of crystal growth and are the smallest crystals nucleated, have the shapes of small equilibrium euhedral crystals that depend on the Bravais lattices (figure 2, third column; e.g., Saito, 1996). Immediately after the critical nuclei are formed, or after a certain amount of growth, if the driving force for growth (such as supersaturation of gemstone components in the magma or fluid) increases, the gems will grow rapidly. In general, the sharpest corners of a euhedral crystal will preferentially grow faster due to the greater supersaturation as well as the “rough” interface (figure 2, fourth column). At this time, the tiny inclusions suspended in the magma or fluid will not be expelled from the gems and will instead be trapped inside and solidified. In fact, Monte Carlo simulations showed that branched dendritic crystals formed in the early stages of garnet growth when the gem’s component was highly supersaturated in fluid (D.E. Wilbur and J.J. Ague, “Chemical disequilibrium during garnet growth: Monte Carlo simulations of natural crystal morphologies,” Geology, Vol. 34, No. 8, 2006, pp. 689–692). These Monte Carlo simulations explain processes that are also reflected in the growth processes and shapes of snowflakes (e.g., K.G. Libbrecht, Snow Crystals: A Case Study in Spontaneous Structure Formation, Princeton University Press, Princeton, New Jersey, 2022).
Trapiche emerald and garnet and stellate diamond crystals seem to rapidly grow into a dendritic shape, incorporating the surrounding impurities into six axial diagonals consisting of the 12 vertices of a hexagonal prism in the case of emerald, three axial diagonals consisting of the six vertices of an octahedron in the case of diamond, and seven axial diagonals consisting of the 14 vertices of a rhombic dodecahedron in the case of garnet (figure 2, fourth column). During this rapid growth phase, the fastest growth is along the sector boundaries (the axial diagonals), forming a 3D internal structure such as the six axial diagonal black lines seen in the rough trapiche emeralds reported by Schmetzer (Spring 2019 GNI, pp. 156–158). Alternatively, axial thickening may occur, incorporating impurities, as seen in diamond, where six thick “hydrogen clouds” are separated by a central core (Summer 2024 Lab Notes, pp. 212–214). Then, when the growth rate slows down due to a decrease in supersaturation or a change in temperature or pressure, the crystal approaches equilibrium with the surrounding environment, and the densest faces grow slowly, forming an equilibrium euhedral crystal again (figure 2, fifth column). These growth processes correspond to the formation of a central core by slow growth on a smooth surface (step 1), the formation of a skeleton structure by fast adhesive growth on a rough interface (step 2), and the formation of an outer shape by slow growth on a smooth surface (step 3) as the driving force for growth changes (I. Sunagawa et al., “Texture formation and element partitioning in trapiche ruby,” Journal of Crystal Growth, Vol. 206, No. 4, 1999, pp. 322–330; I. Pignatelli et al., “The texture and chemical composition of trapiche ruby from Khoan Thong, Luc Yen mining district, Northern Vietnam,” Journal of Gemmology, Vol. 36, No. 8, 2019, pp. 726–746).
We do not know how the submitted trapiche tablets were physically sliced from the euhedral crystals, but our observations and growth model indicate that they were sliced along the {111} planes (figure 3), and are central portions of garnet single crystals in which black inclusions have been distributed along the seven axial diagonals of a rhombic dodecahedron. Our model differs from the reporting in Wang et al. (2025), but is consistent with the latest detailed report in Wu et al. (Summer 2025 GNI, pp. 208–210). In the case of an octahedral diamond with an fcc lattice, the hydrogen clouds included along the three <100> axes connecting the rapidly growing vertices appear as four lines when viewed along the <100> axis but six lines when viewed along the <111> axis (e.g., W. Wang and W. Mayerson, “Symmetrical clouds in diamond – The hydrogen connection,” Journal of Gemmology, Vol. 28, No. 3, 2002, pp. 143–152). Since the “essential symmetry” of the cubic crystal system is four three-fold axes of symmetry along four equivalent <111> axes, the six-rayed “star” or trapiche pattern seen in such cubic gemstones is a pseudo six-fold rotational symmetry observable only through inclusions produced by three-fold rotation-inversion symmetry. By conducting thought experiments based on crystallography and crystal growth theory to study the trapiche pattern formation process in garnets exhibiting the complicated euhedral rhombic dodecahedron, to our knowledge we have explained the apparent six-fold symmetry that can appear in cubic gemstones and established a growth model that can be applied to trapiche pattern formation in gems of various crystal systems and Bravais lattice types.
