"X-ray Diffraction”, the United States
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`Pharmacopeia <941>,
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`USP 38/NF33, (2015) p. 10/10
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`5«'2Ed'2D15 ©2015 USPC Official 5rI'1.’15 - ?r'31.l15 Gereral Chapters: <9d‘|> CHARACTERIZATION OF CRYSTALLINE AND PARTIAIJX CRYSTALLINE SOLID .
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`I 941 } CHARACTERIZATION OF CRYSTALLINE AND PARTIALLY CRYSTALLINE SOLIDS BY X-RAY POWDER
`
`DIFFRACTION (XRPD)
`
`INTRODUCTION
`
`Every crystalline phase of a given substance produces a characteristic X—ray diffraction pattern. Diffraction patterns
`
`can be obtained from a randomly oriented crystalline powder composed of crystallites or crystal fragments of finite
`
`size. Essentially three types of information can be derived from a powder diffraction pattern: the angular position of
`
`diffraction lines (depending on geometry and size of the unit cell), the intensities of diffraction lines (depending mainly
`
`on atom type and arrangement. and particle orientation within the sample). and diffraction line profiles (depending on
`instrumental resolution, crystallite size, strain, and specimen thickness).
`
`Experiments giving angular positions and intensities of lines can be used for applications such as qualitative phase
`
`analysis (e.g., identification of crystalline phases) and quantitative phase analysis of crystalline materials. An
`
`estimate of the amorphous and crystalline fractionsl can also be made.
`
`The X—ray powder diffraction (XRPD) method provides an advantage over other means of analysis in that it is usually
`
`nondestructive in nature (to ensure a randomly oriented sample, specimen preparation is usually limited to grinding).
`XRPD investigations can also be carried out under in sftu conditions on specimens exposed to nonambient conditions
`such as low or high temperature and humidity.
`
`PRINCIPLES
`
`X-ray diffraction results from the interaction between x~rays and electron clouds of atoms. Depending on atomic
`
`arrangement, interferences arise from the scattered X—rays. These interferences are constructive when the path
`flJifference between two diffracted X—ray waves differs by an integral number of wavelengths. This selective condition
`is described by the Bragg equation. also called Bragg's law (see Figure 1).
`
`Figure 1. Diffraction of X—rays by a crystal according to Bragg's Law.
`
`The wavelength, 1, of the X—rays is of the same order of magnitude as the distance between successive crystal lattice
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`planes. or dhk, (also called d—spacings). 9,.“ is the angle between the incident ray and the family of lattice planes, and
`
`sin 9,,“ is inversely proportional to the distance between successive crystal planes or d—spacings.
`
`n a direction and spacing of the planes with reference to the unit cell axes are defined by the Miller indices {hkl}. These
`indices are the reciprocals. reduced to the next-lower integer, of the intercepts that a plane makes with the unit cell
`
`axes, The unit cell dimensions are given by the spacings a, b. and c. and the angles between them (1,
`
`and T.
`
`The interplanar spacing for a specified set of parallel hkl planes is denoted by d...... Each such family of planes may
`
`show higher orders of diffraction where the ct values for the related families of planes nh, nk_ nl are diminished by the
`factor tin (n being an integer: 2. 3. 4. etc.).
`
`Every set of planes throughout a crystal has a corresponding Bragg diffraction angle. 9 hm. associated with it (for a
`
`specific 1).
`
`A powder specimen is assumed to be polycrystalline so that at any angle 9,.“ there are always crystallites in an
`
`orientation allowing diffraction according to Bragg's law! For a given X-ray wavelength. the positions of the diffraction
`peaks (also referred to as "Iines". "reflections", or "Bragg reflections") are characteristic of the crystal lattice (d-
`
`spacings), their theoretical intensities depend on the crystallographic unit cell content (nature and positions of atoms).
`and the line profiles depend on the perfection and extent of the crystal lattice. Under these conditions. the diffraction
`
`peak has a finite intensity arising from atomic arrangement, type of atoms. thermal motion. and structural
`imperfections. as well as from instrument characteristics.
`
`The intensity is dependent upon many factors such as structure factor. temperature factor, crystallinity. polarization
`factor. multiplicity. and Lorentz factor.
`
`fie main characteristics of diffraction line profiles are 23 position, peak height. peak area, and shape (characterized
`' by. eg.. peak width. or asymmetry, analytical function, and empirical representation). An example of the type of
`powder patterns obtained for five different solid phases of a substance are shown in Figure 2.
`
`G
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`Figure 2. X—ray powder diffraction patterns collected for five different solid phases of a substance (the intensities are
`normalized).
`In addition to the diffraction peaks. an X-ray diffraction experiment also generates a more or less uniform background.
`upon which the peaks are superimposed. Besides specimen preparation, other factors contribute to the background-
`for example, sample holder, diffuse scattering from air and equipment, and other instrumental parameters such as
`detector noise and general radiation from the X-ray tube. The peak-to—background ratio can be increased by
`minimizing background and by choosing prolonged exposure times.
`
`INSTRUMENT
`
`Instrument Setup
`
`X-ray diffraction experiments are usually performed using powder diffractometers or powder cameras.
`A powder diffractometer generally comprises five main parts: an X-ray source; the incident beam optics, which may
`perform monochromatization, filtering, collimation. andlor focusing of the beam; as goniometer: the diffraction beam
`optics. which may include monochromatization, filtenng, collimation, and focusing or parallelizing of beam; and a
`detector. Data collection and data processing systems are also required and are generally included in current
`diffraction measurement equipment.
`
`pending on the type of analysis to be performed (phase identification, quantitative analysis. lattice parameters
`etermination, etc), different XRPD instrument configurations and performance levels are required. The simplest
`instruments used to measure powder patterns are powder cameras. Replacement of photographic film as the
`detection method by photon detectors has led to the design of diffractometers in which the geometric arrangement of
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`the optics is not truly focusing, but parafocusing, such as in Bragg—Brentano geometry. The Bragg-Brentano
`parafocusing configuration is currently the most widely used and is therefore briefly described here.
`
`A given instmment may provide a horizontal or vertical 9:23 geometry or a vertical 319 geometry. For both
`“geometries, the incident X-ray beam forms an angle 9 with the specimen surface plane. and the diffracted >(—ray
`beam fonns an angle 29 with the direction of the incident X-ray beam (an angle 9 with the specimen surface plane).
`The basic geometric arrangement is represented in Figure 3. The divergent beam of radiation from the X-ray tube {the
`so—called primary beam) passes through the parallel plate collimators and a divergence slit assembly and illuminates
`the flat surface of the specimen. All the rays diffracted by suitably oriented crystallites in the specimen at an angle 2
`9 converge to a line at the receiving slit. A second set of parallel plate collimators and a scatter slit may be placed
`either behind or before the receiving slit. The axes of the line focus and of the receiving slit are at equal distances
`from the axis of the goniometer. The X-ray quanta are counted by a radiation detector, usually a scintillation counter.
`a sealed-gas proportional counter, or a positionwsensitive solid-state detector such as an imaging plate or CCD
`detector. The receiving slit assembly and the detector are coupled together and move tangentially to the focusing
`circle. For 3.'29 scans, the goniometer rotates the specimen around the same axis as that of the detector, but at half
`
`the rotational speed, in a 9129 motion. The surface of the specimen thus remains tangential to the focusing circle.
`The parallel plate collimator limits the axial divergence of the beam and hence partially controls the shape of the
`diffracted line profile.
`
`GD
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`A. X-ray tube
`
`C. Detector
`D. Anti-diffusion
`receiving slit
`slit
`H. Detector
`E. Receiving slit
`B. Divergence slit
`J. Focusing circle
`F. Monochromator
`C. Sample
`Figure 3. Geometric arrangement of the Bragg—Brentano parafocusing geometry.
`A diffractometer may also be used in transmission mode. The advantage with this technology is to lessen the effects
`due to preferred orientation. A capillary of about 0.5- to 2-mm thickness can also be used for small sample amounts.
`
`X-Ray Radiation
`
`In the laboratory, X—rays are obtained by bombarding a metal anode with electrons emitted by the thermionic effect and
`accelerated in a strong electric field (using a high-voltage generator). Most of the kinetic energy of the electrons is
`'
`onverted to heat, which limits the power of the tubes and requires efficient anode cooling. A 2(t to 30-fold increase in
`brilliance can be obtained by using rotating anodes and by using X-ray optics. Alternatively, X-ray photons may be
`produced in a large-scale facility (synchrotron).
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`The spectrum emitted by an X—ray tube operating at sufficient voltage consists of a continuous background of
`polychromatic radiation and additional characteristic radiation that depends on the type of anode. Only this
`characteristic radiation is used in X-ray diffraction experiments. The principal radiation sources used for X-ray
`ntiffraction are vacuum tubes using copper. molybdenum. iron. cobalt, or chromium as anodes; copper. molybdenum.
`or cobalt X-rays are employed most commonly for organic substances (the use of a cobalt anode can especially be
`preferred to separate distinct X-ray lines). The choice of radiation to be used depends on the absorption
`characteristics of the specimen and possible fluorescence by atoms present in the specimen. The wavelengths used
`in powder diffraction generally correspond to the Kot radiation from the anode. Consequently. it is advantageous to
`make the X-ray beam "monochromatic" by eliminating all the other components of the emission spectrum. This can
`be partly achieved using KB filters—that is. metal filters selected as having an absorption edge between the K0: and
`KB wavelengths emitted by the lube. Such a filter is usually inserted between the X-ray tube and the specimen.
`Another more commonly used way to obtain a monochromatic X—ray beam is via a large monochromator crystal
`(usually referred to as a "monochromator"). This crystal is placed before or behind the specimen and dlffracts the
`different characteristic peaks of the X-ray beam (i.e.. Kot and KB) at different angles so that only one of them may
`be selected to enter into the detector. It is even possible to separate Kot, and Kong radiations by using a specialized
`monochromator. Unfortunately, the gain in getting a monochromatic beam by using a filter or a monochromator is
`counteracted by a loss in intensity. Another way of separating Kent and K13 wavelengths is by using curved X-ray
`mirrors that can simultaneously monochromate and focus or parallelize the ><~ray beam.
`
`RADIATION PROTECTION
`
`Exposure of any part of the human body to X—rays can be injurious to health. it is therefore essential that whenever X-
`ray equipment is used. adequate precautions be taken to protect the operator and any other person in the vicinity.
`Recommended practice for radiation protection as well as limits for the levels of X-radiation exposure are those
`n,-stablished by national legislation in each country. If there are no official regulations or recommendations in a
`country. the latest recommendations of the International Commission on Radiological Protection should be applied.
`
`SPECIMEN PREPARATION AND MOUNTING
`
`The preparation of the powdered material and the mounting of the specimen in a suitable holder are critical steps in
`many analytical methods, particularly for X—ray powder diffraction analysis. since they can greatly affect the quality of
`the data to be collected.‘-‘ The main sources of errors due to specimen preparation and mounting are briefly discussed
`in the following section for instruments in Bragg-Brentano parafocusing geometry.
`
`Specimen Preparation
`
`In general. the morphology of many crystalline particles tends to give a specimen that exhibits some degree of
`preferred orientation in the specimen holder. This is particularly evident for needle-like or platelike crystals when size
`reduction yields finer needles or platelets. Preferred orientation in the specimen influences the intensities of various
`reflections so that some are more intense and others less intense. compared to what would be expected from a
`completely random specimen. Several techniques can be employed to improve randomness in the orientation of
`crystaliites (and therefore to minimize preferred orientation), but further reduction of particle size is often the best and
`simplest approach. The optimum number of crystallites depends on the diffractometer geometry. the required
`resolution. and the specimen attenuation of the X—ray beam. In some cases. particle sizes as large as 50 pm will
`rovide satisfactory results in phase identification. However. excessive milling tcrystallite sizes less than
`approximately 0.5 pm) may cause line broadening and significant changes to the sample itself. such as
`o
`specimen contamination by particles abraded from the milling instruments (mortar. pestle. balls. etc.).
`-
`reduced degree of crystallinity.
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`-
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`solid-state transition to another polymorph,
`-
`- chemical decomposition,
`-
`introduction of internal stress, and
`-
`so|id~state reactions.
`
`nrierefore. it is advisable to compare the diffraction pattern of the nonground specimen with that corresponding to a
`
`specimen of smaller particle size (e.g., a milled specimen). If the X~ray powder diffraction pattern obtained is of
`adequate quality considering its intended use. then grinding may not be required.
`
`it should be noted that if a sample contains more than one phase and if sieving is used to isolate particles to a specific
`size, the initial composition may be altered.
`
`Specimen Mounting
`
`EFFECT OF SPECIMEN DISPLACEMENT
`
`A specimen surface that is offset by D with reference to the diffractometer rotation axis causes systematic errors that
`
`are very difficult to avoid entirely; for the reflection mode, this results in absolute D-cos9 shifts1 in 29 positions
`(typically of the order of 0.010 in 29 at low angles
`[cos 8 2 1]
`for a displacement D = 15 pm) and asymmetric broadening of the profile toward low 29 values. Use of an appropriate
`internal standard allows the detection and correction of this effect simultaneously with that arising from specimen
`transparency. This effect is by far the largest source of errors in data collected on well-aligned diffractometers.
`
`EFFECT OF seecrrurzrv THICKNESS AND TRANSPARENCY
`
`1en the XRPD method in reflection mode is applied, it is often preferable to work with specimens of "infinite
`' hickness". To minimize the transparency effect. it is advisable to use a nondiffracting substrate (zero background
`hoIder)—for example. a plate of single crystalline silicon cut parallel to the 510 lattice planes.§ One advantage of the
`transmission mode is that problems with sample height and specimen transparency are less important.
`The use of an appropriate internal standard allows the detection and correction of this effect simultaneously with that
`arising from specimen displacement.
`
`CONTROL OF THE INSTRUMENT PERFORMANCE
`
`The goniometer and the corresponding incident and diffracted X—ray beam optics have many mechanical parts that need
`adjustment. The degree of alignment or misalignment directly influences the quality of the results of an XRPD
`investigation. Therefore. the different components of the diffractometer must be carefully adjusted (optical and
`mechanical systems, etc.) to adequately minimize systematic errors, while optimizing the intensities received by the
`detector. The search for maximum intensity and maximum resolution is always antagonistic when aligning a
`diffractometer. Hence, the best compromise must be sought while performing the alignment procedure. There are
`many different configurations, and each supplier's equipment requires specific alignment procedures. The overall
`diffractometer performance must be tested and monitored periodically. using suitable certified reference materials.
`Depending on the type of analysis. other well-defined reference materials may also be employed, although the use of
`certified reference materials is preferred.
`“
`
`QUALITATIVE PHASE ANALYSIS (IDENTIFICATION OF PHASES)
`The identification of the phase composition of an unknown sample by XRPD is usually based on the visual or
`computer—assisted comparison of a portion of its X—ray powder pattern to the experimental or calculated pattern of a
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`reference material. Ideally, these reference patterns are collected on well—characterized sing|e—phase specimens. This
`
`approach makes it possible in most cases to identify a crystalline substance by its 29 -diffraction angles or d-
`spacings and by its relative intensities. The computer—aided comparison of the diffraction pattem of the unknown
`as-ample to the comparison data can be based on either a more or less extended 23 range of the whole diffraction
`pattern or on a set of reduced data derived from the pattern. For example, the list of d—spacings and normalized
`intensities, l,,,,,,,,, a scrcalled (d,
`|,,o,,,,) list extracted from the pattern, is the crystallographic fingerprint ofthe material
`
`and can be compared to (d, I,,,,,,,.) lists of single—phase samples compiled in databases.
`
`For most organic crystals. when using Cu Kot radiation, it is appropriate to record the diffraction pattern in a 29 -range
`from as near 00 as possible to at least 40a. The agreement in the 29-diffraction angles between specimen and
`reference is within 0.20 for the same crystal form. while relative intensities between specimen and reference may vary
`considerably due to preferred orientation effects. By their very nature, variable hydrates and solvates are recognized
`to have varying unit cell dimensions. and as such, shifting occurs in peak positions of the measured XRPD patterns
`
`for these materials. In these unique materials, variance in 2-9 positions of greater than 0.20 is not unexpected. As
`such, peak position variances such as 0.20 are not applicable to these materials. For other types of samples (e.g..
`inorganic salts), it may be necessary to extend the 23 region scanned to well beyond 400. It is generally sufficient to
`scan past the 10 strongest reflections identified in single-phase X—ray powder diffraction database files.
`
`It is sometimes difficult or even impossible to identify phases in the following cases:
`
`- noncrystallized or amorphous substances,
`
`-
`
`the components to be identified are present in low mass fractions of the analyte amounts (generally less than
`10% mm),
`pronounced preferred orientation effects,
`the phase has not been filed in the database used.
`the formation of solid solutions.
`
`the presence of disordered structures that alter the unit cell,
`
`the specimen comprises too many phases.
`the presence of lattice deformations.
`
`the structural similarity of different phases.
`
`QUANTITATIVE PHASE ANALYSIS
`
`If the sample under investigation is a mixture of two or more known phases, of which not more than one is amorphous.
`
`the percentage (by volume or by mass) of each crystalline phase and of the amorphous phase can in many cases be
`determined. Quantitative phase analysis can be based on the integrated intensities, on the peak heights of several
`
`individual diffraction tines,§ or on the full pattern. These integrated intensities. peak heights. or full-pattern data points
`are compared to the corresponding values of reference materials. These reference materials must be single phase or
`
`a mixture of known phases. The difficulties encountered during quantitative analysis are due to specimen preparation
`
`[the accuracy and precision of the results require, in particular, homogeneity of all phases and a suitable particle size
`distribution in each phase) and to matrix effects.
`
`in favorable cases, amounts of crystalline phases as small as 10% may be determined in solid matrices.
`
`I I .!)r a sample composed of two polymorphic phases a and b, the following expression may be used to quantify the
`
`Polymorphic Samples
`
`fraction Fr] of phase a:
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`F0’. = 1:'[1 + K(|bi'|(I)]
`
`The fraction is derived by measuring the intensity ratio between the two phases. knowing the value of the constant K. K
`"is the ratio of the absolute intensities of the two pure polymorphic phases Ina/lob. its value can be determined by
`- measuring standard samples.
`
`Methods Using a Standard
`
`The most commonly used methods for quantitative analysis are
`-
`the external standard method.
`-
`the internal standard method. and
`
`the spiking method (also often called the standard addition method).
`-
`The external standard method is the most general method and consists of comparing the X-ray diffraction pattern of the
`mixture. or the respective line intensities. with those measured in a reference mixture or with the theoretical
`intensities of a structural model. if it is fully known.
`
`To limit errors due to matrix effects. an intemal reference material can be used that has a crystallite size and X-ray
`absorption coefficient comparable to those of the components of the sample and with a diffraction pattern that does
`not overlap at all that of the sample to be analyzed. A known quantity of this reference material is added to the
`sample to be analyzed and to each of the reference mixtures. Under these conditions. a linear relationship between
`line intensity and concentration exists. This application. called the internal standard method. requires precise
`measurement of diffraction intensities.
`
`In the spiking method (or standard addition method). some of the pure phase a is added to the mixture containing the
`unknown concentration of a. Multiple additions are made to prepare an intensity-versus—concentration plot in which the
`negative x-intercept is the concentration of the phase a in the original sample.
`
`0 i
`
`ESTIMATE OF THE AMORPHOUS AND CRYSTALLINE FRACTIONS
`
`n a mixture of crystalline and amorphous phases. the crystalline and amorphous fractions can be estimated in several
`ways. The choice of the method used depends on the nature of the sample:
`
`-
`
`If the sample consists of crystalline fractions and an amorphous fraction of different chemical compositions,
`the amounts of each of the individual crystalline phases may be estimated using appropriate standard
`substances. as described above. The amorphous fraction is then deduced indirectly by subtraction.
`If the sample consists of one amorphous and one crystalline fraction, either as a 1-phase or a 2-phase mixture.
`with the same elemental composition, the amount of the crystalline phase (the “degree of crysta||inity") can be
`estimated by measuring three areas of the diffractogram:
`
`A = total area of the peaks arising from diffraction from the crystalline traction of the sample.
`B = total area below area A.
`
`C = background area (due to air scattering, fluorescence. equipment. etc).
`When these areas have been measured. the degree of crystallinity can be roughly estimated as:
`
`% crystallinity = 100Af(A + B -— C)
`
`It is noteworthy that this method does not yield an absolute degree of crystallinity values and hence is generally used
`for comparative purposes only. More sophisticated methods are also available. such as the Ruland method.
`
`H I
`
`SINGLE CRYSTAL STRUCTURE
`
`n general. the determination of crystal structures is performed from X—ray diffraction data obtained using single
`crystals. However. crystal structure analysis of organic crystals is a challenging task. since the lattice parameters are
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`comparatively large, the symmetry is low, and the scattering properties are normally very low. For any given
`
`crystalline form of a substance, the knowledge of the crystal structure allows for calculating the corresponding XRPD
`
`pattem, thereby providing a preferred orientation-free reference XRPD pattern. which may be used for phase
`ndentification.
`
`1 There are many other applications of the X-ray powder diffraction technique that can be applied to crystaline pharmaceutical substances. such
`as determination of crystal structures, refinement of crystal structures. determination of the crystallographic purity of crystalline phases. and
`characterization of cryslailographic texture. These applications are not described in this chapter.
`
`2 An ideal powder for diffraction experiments consists of a large number of small. randomly oriented spherical crystalliles (coherently ditfracting
`Y
`9
`Y
`9
`Y5
`Y
`or stalline domains). If this number is sufficiently tar e. there are alwa s enou h cr
`tallites in an diflracting orientation to give reproducible
`diffraction patterns.
`
`3 Similarly, changes in the specimen can ocwr during data collection in the case of a nonequilibriurn specimen (temperature. humidity).
`
`4 Note that a gortiometer zero alignment shift would result in a constant shift on all observed 29 -line positions; in other words, the whole
`Er
`diffraction pattern is. in this case, translated by an offset of Z in 29 .
`
`5 In the case of a thin specimen with low attenuation. accurate measurements of line positions can be made with focusing diffractometer
`configurations in either transmission or reflection geometry. Accurate measurements of line positions on specimens with low attenuation are
`
`preferably made using diffractometers with parallel beam optics. This helps to reduce the effects of specimen thickness.
`
`6 If the crystal structures of all components are known. the Rietveld method can be used to quantify them with good accuracy. If the crystal
`structures of the components are not known, the Pawley method or the partial |east—squares (PLS) method can be used.
`
`l
`Auxiliary lnformation— Please check for your Question in the FAQs before contacting USP.
`
`Expert Committee
`‘opicftluestionjrcontact
`:(GCCA2010) General Chapters — Chemical Analysis
`eneral Chapter §|<ahgashan Zaidi Ph.D.
`=.Senior Scientific Liaison '
`-.(301) 816-8269
`
`USP3&NF33 Page 692
`
`Pharrriacopeia! Forum: Volume No. 35(3) Page 731
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`RS 1021 - 000011