Enhanced Structural Analysis Using X-Ray Powder Diffraction

Progress in methodology, instrumentation, and computational power has guaranteed easy and rapid structural analysis using X-Ray Powder Diffraction (XRPD) data. While the method has virtually become a standard process, its results can differ in terms of accuracy. Although several factors can influence the accuracy of structural analysis, this article focuses on instrumentation alone. By measuring a reference and an unknown sample on a Stoe Stadi MP diffractometer fitted with a MYTHEN detector, performance of the diffractometer is evaluated and the level of accuracy that can be achieved in current structure analysis is determined.

High-Accuracy Data by Single-Photon Counting

Factors such as high resolution, simple background, good counting statistics, and symmetric peaks are used to characterize superior-quality XRPD data. However, to obtain such data, it is crucial to enhance a number of instrumental parameters. With the scope on MYTHEN, single-photon-counting detector, combined in Stoe Stadi diffractometers, this article looks at two questions: (1) what is single-photon counting and (2) how does this technology improve accuracy in structure analysis using X-ray powder diffraction data?

MYTHEN 1K detector system

Figure 1. MYTHEN 1K detector system. Image credit: Dectris Ltd.

Table 1. Stoe stadi MP diffractometer

. .
Tube Cu
Detector MYTHEN 1K, 1000 µm
Monochromator Ge 111
Geometry Debye-Scherrer
Mode Scanning
Radius [mm] 190
Software WinXpow

 

Traditional detectors are based on indirect detection where X-rays are first changed into visible light, which is then transformed into charge. This charge is then collected, and the signal is acquired by integration over time. Low efficiency, noise, and poor resolution inherent to this detection principle can be overcome only with new technologies.

MYTHEN is a silicon microstrip detector that works in a single-photon-counting mode. In this process, X-rays are detected straightaway, and each photon is independently processed and counted, resulting in the following advantages:

  • Their quantum efficiency is considerably higher since they are enhanced for X-rays, rather than for visible light
  • No dark current is created as individual photon counting does not depend on charge accumulation
  • There is no readout noise

Single-photon counting functions in the following way: X-ray photons interact with the detector sensor material and create a charge. When an electrical field is applied across the sensor, the charge is pushed to the readout chip, where each charge is processed individually. Its energy is assessed against a threshold set by the user. In case the energy is greater than the threshold, the photon is considered as acceptable for counting in a 24-bit counter. Such an energy discrimination makes it likely to suppress fluorescence and noise. Readout in 24-bit mode permits a dynamic range as high as 1:16.8 x 106, and occurs very rapidly: with MYTHEN silicon microstrip detector, readout times are just 300 μs.

The fundamental unit of the MYTHEN detector is a module. Each module has 1280 parallelly aligned silicon microstrips, each serving as an individual detector, and counting up to 106 photons per second. Particular dimensions of the strips are responsible for other exclusive features of the detector. Strip width of 50 μm and its equivalent point-spread function of one strip cause signal to be “confined” in the strip and exhibit no blurring. This results in marginal contribution of the detector to peak broadening, thus allowing high-resolution measurements. Strip (sensor) thickness correlates with efficiency for specific energy range. Three available sensor thicknesses integrated with strip length of 8 mm guarantee optimal signal-to-noise ratio and efficiency over a wide range of X-ray energies (5–40 keV).

In a module, all 1280 strips detect X-rays in a parallel manner, thereby increasing angular coverage and universal count rates. A MYTHEN detector has a single 1280-strip module that is known as MYTHEN 1K. These detectors are combined with Stoe Stadi diffractometers. Table 2 summarizes the detector’s specifications.

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Table 2. Features of MYTHEN 1K

. .
Sensor material Silicon
N (strips) 1280
Strip width [µm] 50
Sensitive area [mm2] (1280x50 µm)x8 mm
Max. count rate per strip [phts/s] > 106
Dynamic range [bit] 24 (1:16.8 million)
Energy range [keV] 5-40
Point spread function 1 strip
Sensor thickness [µm] 320, 450, 1000
Max. frame rate [Hz] 22

 

To understand how single-photon-counting technology improves accuracy in structure analysis using X-ray powder diffraction data, one reference, two organic samples, and one of unidentified crystal structure were measured using Stoe Stadi MP diffractometer fitted with MYTHEN 1K detector. The data gained was utilized to evaluate the instrument’s performance and to highlight what level of structural detail can be observed using the XRPD data.

Data Accuracy: Evaluation of the Performance of Stoe Stadi MP Diffractometer

In these examinations, D-mannose (Figure 2) was chosen as a reference sample for the following reasons:

  • Crystal structure of D-mannose (P212121) was solved with the help of single crystal diffraction data. The asymmetric unit consists of two molecules, varying in the orientation of their CH2-OH groups. Yet, the structure was not whole: a few hydrogen atoms were missing, and some carbon atoms exhibited non-positive-definite values of atomic displacement parameters (ADP). Hence, it was fascinating to see what level of accuracy of the “backbone structure” can be realized using XRPD data, and whether this data could clarify non-positive definite ADP values.
  • Contrary to sucrose, a normally used reference sample, commercial D-mannose is considered to have a more even crystallite size, so sharp peaks stemming from a few separate large crystals in the sample could be sidestepped.

Structural formula of D-mannose

Figure 2. Structural formula of D-mannose. Image credit: Dectris Ltd.

Initially, a D-mannose sample was ground in a mortar and then filled into a capillary and measured using a Stoe Stadi MP diffractometer (refer Table 3).

Table 3. D-mannose: details of data collection

. .
Scanning mode Step scan
I [mA], U [kV] 40, 40
λ [Å] 1.5406
Detector, sensor thickness [μm] MYTHEN 1K, 1000
Resolution [°] 0.015
Angular coverage [° 2θ] 19.2
2θ range measured [°] 0.56-101
dmin (used) [Å] 1
2θ range [°] / t [s] 0-21.935 / 360
18-37.935 / 720
35-54.935 / 1080
53-72.935 / 1440
72-101 / 1800

 

Using the XRS suite of programs, the crystal structure acquired from single crystal data was refined against the XRPD data. To assess the performance of the diffractometer and the quality of the data, Rietveld refinement was performed without any geometrical restraints. ADPs were arranged as isotropic values and were not refined.

Comparison of the atomic coordinates acquired from the XRPD data with those attained from single crystal data revealed that the average difference between the two sets of coordinates is in the range of ±0.06, as illustrated in Figure 3.

Results of the restraint-free Rietveld refinement presented as difference between the coordinates obtained from XRPD data and single crystal (SC) data.

Figure 3. Results of the restraint-free Rietveld refinement presented as difference between the coordinates obtained from XRPD data and single crystal (SC) data. Image credit: Dectris Ltd.

The outliers observed in the plot most probably arise from uncertainties in the difference Fourier map calculated for the last cycle of Rietveld refinement: residual electron densities around one of the molecules indicate disorder. An in-depth investigation of the difference Fourier maps and modeling of the D-mannose disorder is still in the process.

Conducted experiments and calculations allow for a conclusion that Stoe Stadi diffractometer fitted with MYTHEN detector provides high-quality data:

  • Superior-quality XRPD data can assist restraint-free Rietveld refinement. Thus, model-bias is considerably reduced, thereby boosting the accuracy of the structure analysis.
  • XRPD data can provide high-accuracy structure analysis: XRPD results can match the results acquired from single-crystal data.
  • XRPD data can offer the finest levels of detail such as disorder of light atoms

Structure Determination: Tackling the Monomer-Trimer Ambiguity—MAAN

MAAN, 2-(methylideneamino)acetonitrile, is a small molecule, said to be monomeric species, capable of polymerizing as cyclic trimer (refer Figure 4). The molecular and crystal structures of either the trimer or the monomer have not been described, and MAAN samples are characterized using a range of spectroscopic methods. Considering the fact that MAAN can polymerize and that differentiating between the polymers using spectroscopic approaches is occasionally difficult, one commercial MAAN sample, whose name suggested monomeric species, was put to test.

Structural formulas of (a) monomeric and (b) trimeric MAAN

Figure 4. Structural formulas of (a) monomeric and (b) trimeric MAAN. Image credit: Dectris Ltd.

First, infrared spectrum was measured and indicated that the material comprises of trimeric MAAN. However, it was not possible to distinguish the sample’s purity or the actual conformation of the polymer. Thus, the compound’s molecular and crystal structure had to be determined. Ground sample was placed into a 0.3 mm capillary and measured under the conditions illustrated in Table 4.

Table 4. MAAN: details of data collection

. .
I [mA], U [kV], λ [Å] 40, 40, 1.5406
Detector, sensor thickness [μm] MYTHEN 1K, 1000
Resolution [°] 0.015
Angular coverage [° 2θ] 19.2
2θ range measured [°] 0.56-91.93
dmin (used) [Å] 1.07
2θ range [°] / t [s] 0-21.935/1440
18-37.935/2880
35-54.935/4320
53-72.935/5760
72-91.935/7200
No. measured points 6129

 

Indexing of the XRPD pattern led to a monoclinic cell, thereby suggesting that the material has just one phase. This information and molecular structure built using Density Functional Theory (DFT) calculations were then employed for structure determination in direct-space program FOX. The resulting structure was later refined in the XRS suite of programs. During the refinement process, geometric limits were applied, but so as to permit flexibility of the molecule, their weighting factor was decreased systematically. The hydrogen atom positions were calculated in the program Mercury. ADP values of all the atoms were set to expected values and were not consequently refined. In the last phase of refinement, a difference Fourier map was calculated. No suspicious electron densities maxima were noticed. Results of the refinement are displayed in Table 5 and Figure 5.

Table 5. Results of the Rietveld refinement for trimeric MAAN

. .
a (Å) 15.1876(9)
b (Å) 10.18249(8)
c (Å) 6.9466(4)
β (°) 90.9(3)
Space group P21/n
No. reflections 625
No. parameters 45
No. observations 5211
No. soft restraints 33
RF 0.104
Rwp 0.176
Rexp 0.059

 

Last cycle of the Rietveld refinement: measured pattern (black), calculated (red), and difference curve (blue).

Figure 5. Last cycle of the Rietveld refinement: measured pattern (black), calculated (red), and difference curve (blue). Image credit: Dectris Ltd.

Since the crystal structure (Figure 6a) did not have any strong hydrogen bonds, it was presumed that the molecular structure must be close to the one calculated by the DFT technique. Figure 6b illustrates a comparison of the molecular structure acquired from the refinement against XRPD data and the one calculated by DFT. Such a good fit shows that it is possible to acquire accurate solutions even without former knowledge about the material.

(a) Crystal structure viewed along c-axis and (b) comparison of molecular structure (blue) to the molecular structure obtained from DFT calculations (purple).

Figure 6. (a) Crystal structure viewed along c-axis and (b) comparison of molecular structure (blue) to the molecular structure obtained from DFT calculations (purple). Image credit: Dectris Ltd.

Conclusion

In this article, the two examples reveal that the combination of a Stoe diffractometer and the MYTHEN single-photon-counting detector can improve structure analysis using the XRPD data.

The tests performed on D-mannose show that the superior-quality XRPD data can allow for restraint-free refinement, resulting in a structure that matches a single crystal case. Furthermore, this superior-quality data makes it possible to see the optimum structural details such as localized residual electron densities, which denoted anisotropic displacement of atoms, indicative of potential disorder in the molecule. By minimizing a model-bias and detection of fine structural details, the combination of Stoe Stadi diffractometer and single-photon-counting detector pushes the boundaries of accuracy that are achievable from XRPD data.

This information has been sourced, reviewed and adapted from materials provided by Dectris Ltd.

For more information on this source, please visit Dectris Ltd.

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