USP 35
`
`Physical Tests I (941) X-Ray Powder Diffraction 427
`
`METHOD Ill {GRAVIMETRIC)
`
`Procedure for Chemicals-Proceed as directed in the in(cid:173)
`dividual monograph preparing the chemical as directed
`under Loss on Drying (731 ).
`Procedure for Biologics-Proceed as directed in the in(cid:173)
`dividual monograph.
`Procedure for Articles of Botanical Origin-Place about
`10 g of the drug, prepared as directed (see Methods of Anal(cid:173)
`ysis under Articles of Botanical Origin (561)) and accurately
`weighed, in a tared evaporating dish. Dry at 105° for 5
`hours, and weigh. Continue the drying and weighing at 1 -
`hour intervals until the difference between two successive
`weighings corresponds to not more than 0.25%.
`
`(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 patterr:i. Diffraction patterns
`can be obtained from a randomly oriented crystall1n~ pow(cid:173)
`der composed of crystallites o~ crystal !ragments of f1!'11te
`size. Essentially three types of 1nformat1on can be ~e_rived
`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 (depe!'1ding.
`mainly on atom type and arrangement, and particle orienta(cid:173)
`tion within the sample), and diffraction line profiles (de(cid:173)
`pending on instrumental resolution, crystallite size, strain,
`. .
`.
`..
`and specimen thickness).
`Experiments giving angular posItIons and in~en~ItIes of
`lines can be used for applications sue~ as qualitative phase .
`analysis (e.g., identification of ~rystalline_ phases) ar:id quanti(cid:173)
`tative phase analysis of crystalline materials. An estimate of
`the amorphous and crystalline fractions1 can also be _made.
`The X-ray powder diffraction (XRPD) method provides an
`advantage over other means of analysis in that it i~ usually
`nondestructive in nature (to ensure a randomly oriented
`sample, specimen preparation is usu~lly limited to grin_ding).
`XRPD investigations can also be earned out u!'1der m st~u.
`conditions on specimens exposed to nona~~1ent cond1t1ons
`such as low or high temperature and hum1d1ty.
`
`PRINCIPLES
`
`X-ray diffraction results from the interaction between X(cid:173)
`rays and electron clouds of atoms. Depending on atomic
`•There are many other applications of the X-ray powder diffraction techniqu~
`that can be applied to crystalline pharmaceutical substances, such as determi(cid:173)
`nation of crystal structures, refinement of crystal structures, determination of
`the crystallographic purity of crystalline phases, and ~haracterizat1on of crys(cid:173)
`tallographic texture. These applications are not described in this chapter.
`
`arrangement, interferences arise from the scattered X-rays.
`These interferences are constructive when the path differ(cid:173)
`ence between two diffracted X-ray waves differs by an inte(cid:173)
`gral number of wavelengths. This selective condition is de(cid:173)
`scribed by the Bragg equation, also called Bragg's law (see
`Figure 7).
`
`The wavelength, A, of the X-rays is of the same order of
`magnitude as the distance between successive crystal lattice
`planes, or dhkl (also called d-spacings). ehk1 is the angle be(cid:173)
`tween the incident ray and the family of lattice planes, and
`sin ehkl is inversely proportional to the distance between suc(cid:173)
`cessive crystal planes or d-spacings.
`The 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 a, /3, and y.
`The interplanar spacing for a specified set of parallel hkl
`planes is denoted by dhkl· Each such family of planes may
`show higher orders of diffraction where the d values for the
`related families of planes nh, nk, nl are diminished by the
`factor 1 /n (n being an integer: 2, 3, 4, etc.).
`Every set of planes throughout a crystal has a correspond(cid:173)
`ing Bragg diffraction angle, ehk1, associated with it (for a
`specific 11,).
`A powder specimen is assumed to be polycrystalline so
`that at any angle ehkl there are always crystallites in an orien(cid:173)
`tation allowing diffraction accor~i!'1g to Bragg'~ law.~ For a
`given X-ray wavelength, the posItIons of the d1ffract1on
`peaks (also referred to as '.'li!'1es", "reflections", _or "Bragg
`reflections") are characteristic of the crystal lattice (d-spac(cid:173)
`ings), their theoretical intensities depend _o_n the crystallo(cid:173)
`graphic unit cell content (nature and posItIons of atoms),
`and the line profiles depend on the p_erfection a!'1d ex~ent of
`the crystal lattice. Under these cond1t1ons, the d1ffract1on
`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, an_d _Loren~ fact~r.
`.
`.
`The main characteristics of d1ffract1on line profiles are 20
`position, peak height, peak area, and shap~ (charac~erized
`by, e.g., 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 sub-
`stance are shown in Figure 2 .
`.
`.
`In addition to the diffraction peaks, an X-ray d1ffract1on
`experiment also generates a more or less_ uniform bac~(cid:173)
`ground, upon which the peaks are superi~posed. Besides
`specimen preparation, other factors contribute to th_e back(cid:173)
`ground-for example, sample ~older, diffuse scattering from
`air and equipment, and other instrumental parameters such
`as detector noise and general radiatioi:i from the X-ray ~u~e.
`The peak-to-background ratio can be increased by min1mIz(cid:173)
`ing background and by choosing prolonged exposure times.
`2An ideal powder tor diffraction experimei:its consists of a large n_umber of
`small, randomly oriented sph~rical crystallites (coherently diffracting crystal(cid:173)
`line domains). If this number 1s suff1c1ently large, there a~e alw~ys ei:iough
`crystallites in any diffracting orientation to give reproducible d1ffract1on
`patterns.
`
`Page 1 of 5
`
`EISAI EXHIBIT 1010
`
`

`

`428 (941) X-Ray Powder Diffraction / Physical Tests
`
`USP 35
`
`Figure 1. Diffraction of X-rays by a crystal according to Bragg's Law.
`
`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, and/or
`focusing of the beam; a goniometer; the diffraction beam
`optics, which may include monochromatization, filtering,
`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 diffrac(cid:173)
`tion measurement equipment.
`Depending on the type of analysis to be performed
`(phase identification, quantitative analysis, lattice parameters
`determination, etc.), different XRPD instrument configura(cid:173)
`tions and performance levels are required. The simplest in(cid:173)
`struments 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 dif(cid:173)
`fractometers in which the geometric arrangement of the op(cid:173)
`tics is not truly focusing, but parafocusing, such as. in Bragg(cid:173)
`Brentano geometry. The Bragg-Brentano parafocusing con(cid:173)
`figuration is currently the most widely used and is therefore
`briefly described here.
`A given instrument may provide a horizontal or vertical
`0/20 geometry or a vertical 0/0 geometry. For both geome(cid:173)
`tries, the incident X-ray beam forms an angle 0 with the
`specimen surface plane, and the diffracted X-ray beam
`forms an angle 20 with the direction of the incident X-ray
`beam (an angle 0 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(cid:173)
`called primary beam) passes through the parallel plate colli(cid:173)
`mators and a divergence slit assembly and illuminates the
`flat surface of the specimen. All the rays diffracted by suita(cid:173)
`bly oriented crystallites in the specimen at an angle 20 con(cid:173)
`verge to a line at the receiving s!it. A second set of_ parallel
`plate collimators and a .s~atter_ sht may be placed _either be(cid:173)
`hind or before the receiving slit. The axes of the hne focus_
`and of the receiving slit are at equal distances from the axis
`
`of the goniometer. The X-ray quanta are counted by a radi(cid:173)
`ation detector, usually a scintillation counter, a sealed-gas
`proportional counter, or a position-sensitive solid-state de(cid:173)
`tector such as an imaging plate or CCD detector. The re(cid:173)
`ceiving slit assembly and the detector are coupled together
`and move tangentially to the focusing circle. For 0/20 scans,
`the goniometer rotates the specimen around the same axis
`as that of the detector, but at half the rotational speed, in a
`0/20 motion. The surface of the specimen thus remains tan(cid:173)
`gential 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.
`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-volt(cid:173)
`age generator). Most of the kinetic energy of the electrons
`is converted to heat, which limits the power of the tubes
`and requires efficient anode cooling. A 20- to 30-fold in-
`- crease in brilliance can be obtained by using rotating an(cid:173)
`odes and by using X-ray optics. Alternatively, X-ray photons
`may be produced in a large-scale facility (synchrotron).
`The spectrum emitted by an X-ray tube operating at suffi(cid:173)
`cient voltage cor:isists of a c~n_tinuous backg~o~nd o! p_oly(cid:173)
`chromatic radiation and add1t1onal characteristic rad1at1on
`that depends on the type of anode. Only this characteristic
`radiation is used in X-ray diffraction experiments. The princi(cid:173)
`pal radiation sources used for X-ray diffraction are vacuum
`tubes using copper, molybdenum, iron, cobalt, or chro(cid:173)
`mium 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 _ra~iation to be ~sed de(cid:173)
`pends on the absorption characteristics _of the spec_1men and
`possible fluorescence by atoms present in the specimen. The
`wavelengths used in powder diffraction generally corre(cid:173)
`spond to the Ka radiation from the anode. Consequently, it
`is advantageous to make the X-ray beam "monoch_ro!llatic"
`by eliminating all the other coml?onents _of the ~m1ss1on
`spectrum. This can be partly achieved using Kp filters-that
`
`Page 2 of 5
`
`

`

`USP 35
`
`Physical Tests I (941) X-Ray Powder Diffraction 429
`
`Form D
`
`Form C
`
`Form B
`
`Form A
`
`amorphous
`
`I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I l
`~ ~ ~ 00 ~ 0
`-
`N M V ~ ~ ~ 00 ~ 0
`-
`N M V ~ ~ ~ 00 ~ 0
`-
`N
`N
`N
`N
`N
`N
`N
`N
`N
`N M M
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`20(). Cu) - Scale
`Figure 2. X-ray powder diffraction patterns collected for five different solid phases of a substance (the intensities are normal(cid:173)
`ized).
`
`is, metal filters selected as having an absorption edge be(cid:173)
`tween the Ka and Kµ wavelengths emitted by the tube.
`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 diffracts
`the different characteristic peaks of the X-ray beam (i.e., Ka
`and K/l) at different angles so that only one of them may be
`selected to enter into the detector. It is even possible to
`separate Kai and Ka2 radiations by using a specialized
`monochromator. Unfortunately, the gain in getting a mono(cid:173)
`chromatic beam by using a filter or a monochromator is
`counteracted by a loss in intensity. Another way of separat(cid:173)
`ing Ka and K/l wavelengths is by using curved X-ray mirrors
`that can simultaneously monochromate and focus or paral(cid:173)
`lelize the X-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(cid:173)
`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 estab(cid:173)
`lished 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. 3 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 pre(cid:173)
`ferred orientation in the specimen holder. This is particularly
`evident for needle-like or platelike crystals when size reduc(cid:173)
`tion 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, com(cid:173)
`pared to what would be expected from a completely ran(cid:173)
`dom specimen. Several techniques can be employed to im(cid:173)
`prove randomness in the orientation of crystallites (and
`therefore to minimize preferred orientation), but further re(cid:173)
`duction of particle size is often the best and simplest ap(cid:173)
`proach . The optimum number of crystallites depends on the
`, Similarly, changes in the specimen can occur during data collection in the
`case of a nonequilibrium specimen (temperature, humidity).
`
`cl
`
`Page 3 of 5
`
`

`

`4 30 (941) X-Ray Powder Diffraction / Physical Tests
`
`USP 35
`
`------------------
`
`'"'
`
`\
`
`\
`
`/
`/ B
`A/--~=-=- C 9
`/, \ I
`\
`' " '--....._
`
`/
`'
`I
`' I
`'
`\
`' \
`\
`'"
`
`... ____ ___ .. /
`
`I
`/,
`
`,
`
`F
`
`'-....
`
`A. X-ray tube
`
`G. Detector
`D. Anti-diffusion
`receiving slit
`slit
`H. Detector
`B. Divergence slit E. Receiving slit
`J. Focusing circle
`C. Sample
`F. Monochromator
`Figure 3. Geometric arrangement of the Bragg-Brentano
`parafocusing geometry.
`
`diffractometer geometry, the required resolution, and the
`specimen attenuation of the X-ray beam. In some cases,
`particle sizes as large as 50 µm will provide satisfactory re(cid:173)
`sults in phase identification. However, excessive milling
`(crystallite sizes less than approximately 0.5 µm) may cause
`line broadening and significant changes to the sample itself,
`such as
`• specimen contamination by particles abraded from the
`milling instruments (mortar, pestle, balls, etc.),
`• reduced degree of crystallinity,
`• solid-state transition to another polymorph,
`• chemical decomposition,
`• introduction of internal stress, and
`• solid-state reactions.
`Therefore, it is advisable to compare the diffraction pat(cid:173)
`tern 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 ade(cid:173)
`quate quality considering its intended use, then grinding
`may not be required.
`It should be noted that if a sample contains more than
`one r,hase 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 sr,ecimen surface that is offset by D with reference to
`the diffractometer rotation axis causes systematic errors that
`are very diff(cult to avoid entirely; tor t~e reflect(~n mode,_
`this results
`in absolute D · cos0 sh1fts4 in 20 posItIons (typi(cid:173)
`cally of the order of 0.01 ° in 20 at low angles
`[cos8 = 1]
`for a displacement D = 15 µm) and asymmetric broade~(cid:173)
`ing of the profile toward low 20 value~. Use of an appropri(cid:173)
`ate internal standard allows the detection and correction of
`•Note that a goniometer zero alignment shift would result in a con~tant shift
`on all observed 20-line positions; in other words, the whole d1ffract1on pat(cid:173)
`tern is, in this case, translated by an offset of Z0 in 20.
`
`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 SPECIMEN THICKNESS AND TRANSPARENCY
`
`When the XRPD method in reflection mode is applied, it
`is often preferable to work with specimens of "infinite thick(cid:173)
`ness". To minimize the transparency effect, it is advisable to
`use a nondiffracting substrate (zero background holder)-for
`example, a plate of single crystalline silicon cut parallel to
`the 510 lattice planes. 5 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 dif(cid:173)
`fracted 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 i~(cid:173)
`vestigation. Therefore, the different components of the dif(cid:173)
`fractometer must be carefully adjusted (optical and mechan(cid:173)
`ical 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 perform(cid:173)
`ing the alignment procedu~e. There_ are many d)fferent ':~n(cid:173)
`figurations, and each supplier's equipment requires spec1f1c
`alignment procedures. The overalf diffractometer perfor(cid:173)
`mance 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 materi(cid:173)
`als is preferred.
`
`QUALITATIVE PHASE ANALYSIS
`(IDENTIFICATION OF PHASES)
`
`The identification of the phase composition of an un(cid:173)
`known sample by XRPD is usually based on the visual or
`computer-assisted comparison of a portion of its X-ray pow(cid:173)
`der pattern to the experimental or calculated pattern of a
`reference material. Ideally, these reference patterns are col(cid:173)
`lected on well-characterized single-phase specimens. This
`approach makes it p~ssible \n mo_st cases to identify a_ crys(cid:173)
`talline substance by its 20-d1ffract1on angles o~ d-spacings .
`and by its relative intensities. The computer-aided compari(cid:173)
`son of the diffraction pattern of the unknown sample to the
`comparison data can be based on either a more or less ex(cid:173)
`tended 20 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, lnorm, a so-called
`(d, lnorm) list extracted from the pattern, is the crystallo(cid:173)
`graphic fingerprint of the material and can be compared to
`(d, lnorm) lists of single-phase samples_compiled in ~at~bas~s.
`For most organic crystals, when using Cu Ka. rad1at1on, It
`is appropriate to record the diffraction pattern in a 20-range
`from as near 0° as possible to at least 40°. The agreement
`in the 20-diffraction angles between specim_en and_ ref~rence
`is within 0.2° for the same crystal form, while relative inten(cid:173)
`sities between specimen and reference may vary considera-
`' ln the case of a thin specimen with low. attenuation, accurate measu~em~nts
`of line positions can be made with focusing diffractometer conf1gurat1~ns m
`either transmission or reflection geometry. Accurate measurements of line po(cid:173)
`sitions on specimens with low attemJation. are preferably made using dif(cid:173)
`fractometers with parallel beam optics. This helps to reduce the effects of
`specimen thickness.
`
`Page 4 of 5
`
`

`

`USP 35
`
`Physical Tests I (941) X-Ray Powder Diffraction 431
`
`bly due to preferred orientation effects. By their very nature,
`variable hydrates and solvates are recognized to have vary(cid:173)
`ing 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 2-0 positions of
`greater than 0.2° is not unexpected. As such, peak position
`variances such as 0.2° are not applicable to these materials.
`For other types of samples (e.g., inorganic salts), it may be
`necessary to extend the 20 region scanned to well beyond
`40°. 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% m/m),
`• 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 amor(cid:173)
`phous, the percentage (by volume or by mass) of each crys(cid:173)
`talline 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 lines, 6 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 en(cid:173)
`countered during quantitative analysis are due to specimen
`preparation (the accuracy and precision of the results re(cid:173)
`quire, 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.
`
`Polymorphic Samples
`
`For a sample composed of two polymorphic phases a and
`b, the following expression may be used to quantify the
`fraction Fa of phase a:
`
`The fraction is derived by measuring the intensity ratio be(cid:173)
`tween the two phases, knowing the value of the constant K.
`K is the ratio of the absolute intensities of the two pure
`polymorphic phases l0./l 0 b, Its value can be determined by
`measuring standard samples.
`
`Methods Using a Standard
`
`The most commonly used methods for quantitative analy(cid:173)
`sis are
`• the external standard method,
`• the internal standard method, and
`61f 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 comeonents are not known, the Pawley method or the partial least(cid:173)
`squares (PLS) method can be used.
`
`• the spiking method (also often called the standard addi(cid:173)
`tion method).
`The external standard method is the most general
`method and consists of comparing the X-ray diffraction pat(cid:173)
`tern of the mixture, or the respective line intensities, with
`those measured in a reference mixture or with the theoreti(cid:173)
`cal intensities of a structural model, if it is fully known.
`To limit errors due to matrix effects, an internal reference
`material can be used that has a crystallite size and X-ray
`absorption coefficient comparable to those of the compo(cid:173)
`nents 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 mix(cid:173)
`tures. Under these conditions, a linear relationship between
`line intensity and concentration exists. This application,
`called the internal standard method, requires precise meas(cid:173)
`urement of diffraction intensities.
`In the spiking method (or standard addition method),
`some of the pure phase a is added to the mixture contain(cid:173)
`ing 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.
`
`ESTIMATE OF THE AMORPHOUS AND
`CRYSTALLINE FRACTIONS
`
`In a mixture of crystalline and amorphous phases, the
`crystalline and amorphous fractions can be estimated in sev(cid:173)
`eral 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 sub(cid:173)
`stances, as described above. The amorphous fraction is
`then deduced indirectly by subtraction.
`• If the sample consists of one amorphous and one crys(cid:173)
`talline fraction, either as a 1-phase or a 2-phase mix(cid:173)
`ture, with the same elemental composition, the amount
`of the crystalline phase (the "degree of crystallinity")
`can be estimated by measuring three areas of the
`diffractogram:
`A = total area of the peaks arising from diffraction
`from the crystalline fraction of the sample,
`B = total area below area A,
`C = background area (due to air scattering, fluores(cid:173)
`cence, equipment, etc).
`When these areas have been measured, the degree of
`crystallinity can be roughly estimated as:
`% crystallinity = 1 00A/(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.
`
`SINGLE CRYSTAL STRUCTURE
`
`In general, the determination of crystal structures is per(cid:173)
`formed from X-ray diffraction data obtained using single
`crystals. However, crystal structure analysis of organic crys(cid:173)
`tals is a challenging task, since the l_attice parameters are .
`comparatively large, the symmetry Is low, a_nd the scat~ering
`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 pattern,
`thereby providing a preferred orientation-free reference
`XRPD pattern, which may be used for phase identification.
`
`Page 5 of 5
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