TRIADS™: AMRI’s Patented Algorithm

AMRI was granted a patent (8,576,985) for the TRIADS™ algorithm by the United States Patent and Trademark Office (USPTO) on November 5, 2013. The TRIADS™ algorithm is an essential tool that helps our scientists in the determination of unit cell parameters of a crystalline solid form using high quality x-ray powder diffraction (XRPD) data.

X-Ray Powder Diffraction (XRPD) Pattern Indexing

Indexing is the process of determining the size and shape of the crystallographic unit cell consistent with the peak positions in a given XRPD pattern. The goal of the indexing process is determination of three unit cell lengths (a,b,c) and three unit cell angles (α,β,γ) for the crystallographic unit cell, and three Miller index labels (h,k,l) for each peak. The lengths are typically reported in Angström units (Å) and the angles in degree units. Miller index labels are unitless integers.

indexing of mannitol Form beta XRPD pattern
Sample output for indexing of mannitol Form beta XRPD pattern

The Distinctive Quality of XRPD Pattern Indexing

While there are several algorithms available for XRPD indexing, including ITO [1], TREOR [2], N-TREOR [3], singular decomposition [4], X-CELL [5], and DICVOL [6], the algorithm developed by SSCI’s solid state chemistry scientists, called TRIADS™ [7], is particularly well suited to indexing the low-symmetry (triclinic and monoclinic) cells, which are common for pharmaceutical solids. Indexing, report writing, and review are routinely done in one to two hours per pattern. Results for successful indexing attempts are shown on the right.

Using XRPD 

Successful indexing  provides confidence that the sample contains one crystalline phase and is therefore not a mixture of crystalline phases. The indexing solution provides a concise means to convey the positions of all allowed peaks in an XRPD pattern. Knowledge of all allowed peaks eliminates one source of surprises during scale-up. We also use indexing for:

  • Accurately calculating the true density from the indexing solution and the molecular basis, which is correlated with low temperature stability [8,9].
  • Comparing indexing solutions of multiple forms to estimate hydrate/solvate/cocrystal stoichiometries
  • Describing changes in crystal structure due to thermal expansion and variable hydrate/solvate composition
  • Determining if two XRPD patterns are of the same or different forms
  • Initial determination of crystal structures from XRPD data if single crystal methods cannot be used

Assessing the Indexing Solution

Suitability of all XRPD patterns for indexing, using any method, reports the apparent metric symmetry of the unit cell. In some cases the molecular contents of the unit cell have a lower symmetry. This kind of symmetry lowering is of interest primarily to crystallographers since the main conclusion of indexing, that the sample contains a single crystalline phase, is not impacted. Also, bulk property estimates, such as density, are not influenced by this kind of symmetry lowering. Still, indexing solutions should be labeled as “tentative” pending successful structure determination.

  • Suitability of all XRPD patterns for indexing: indexing requires well-resolved peak positions, such as those acquired in high-quality XRPD analysis. Typically 20 to 30 peaks are used for indexing, although some crystal structures may require more.
  • Success rate of indexing XRPD patterns: high-quality XRPD patterns for more than 100 client compounds have an 84% success rate. Over six percent of the samples examined were subsequently determined to be mixtures. Therefore, indexing achieves success more than 90% of the time when applied to high quality XRPD patterns of single phase samples.
  • Indications of unsuccessful indexing attempts: a single indexing solution cannot account for all of the peaks in a pattern if the associated sample contains a mixture of crystalline phases. Unsuccessful indexing attempts that employ multiple methods do not prove that a sample contains multiple phases; however, additional testing may be warranted to investigate this possibility.
  • The role of Preferred Orientation (PO) artifacts in preventing successful indexing: indexing does not make use of the relative intensity information in the XRPD pattern. As long as Preferred Orientation (PO) merely affects the relative intensity of observed peaks, and does not obscure the presence of too many peaks, then PO does not preclude successful indexing. Indexing is not currently conducted under cGMP standards. It is performed under the “Solid State Chemistry Procedures for NoncGMP Activities.”


  1. Visser, J. W. J. Appl. Cryst. 2, 89 (1969). [ITO]
  2. Werner, P. -E., Eriksson, L. & Wetdahl, M. J. Appl. Cryst. 18, 367 (1985). [TREOR]
  3. Altomare, A., Giacovazzo, C., Guagliardi, A., Moliterni, A. G. G, Rizzi, R., & Werner P. E., J. Appl. Cryst. 33, 1180 (2000). [N-TREOR]
  4. Coelho, A. A., J. Appl. Cryst. 36, 86 (2003). [singular decomposition method]
  5. Neumann, M. A., J. Appl. Cryst., 36 , 356 (2003). [X-CELL]
  6. Boultif, A. & Louer D., J. Appl. Cryst. 37, 724 (2004). [DICVOL]
  7. [TRIADS]
  8. Burger, A. and Ramberger, R. Mikrochim. Acta 2, 259-271 (1979).
  9. Burger, A. and Ramberger, R. Mikrochim. Acta 2, 273-316 (1979).