Discussion Examples for X-Ray Diffraction | How to Interpret Diffraction Peaks, Crystal Structure, and Lattice Spacing

What Is X-Ray Diffraction?

X-ray diffraction is an analytical method that uses the phenomenon in which X-rays are diffracted by regularly arranged planes of atoms or ions when a crystal is irradiated with X-rays.
Because atoms in a crystal are arranged periodically, constructive diffraction occurs at specific angles.
By measuring these diffraction angles, information about the spacing between crystal planes and the crystal structure can be obtained.

In an XRD pattern, the horizontal axis is generally the diffraction angle 2θ and the vertical axis is diffraction intensity.
Peak positions are related to lattice spacing and crystal structure, while peak intensities are related to the atomic arrangement of crystal planes, orientation, and the amount of each phase.
Peak width is affected by crystallite size, lattice strain, and instrument conditions.

Main Items to Include in the Results

In X-ray diffraction results, organize the sample name, measurement method, X-ray source, wavelength, measurement range, 2θ values of diffraction peaks, peak intensity, full width at half maximum, lattice spacing, identified crystalline phases, and comparison with literature values or databases.
For powder XRD, arranging peak positions and relative intensities in a table makes the discussion easier.

Main Items to Include in the Results

• Sample name
• Measurement method
• X-ray source
• X-ray wavelength
• Measurement range
• Scan speed
• 2θ values of major diffraction peaks
• Peak intensity
• Relative intensity
• Full width at half maximum
• Lattice spacing
• Corresponding crystal planes
• Results of crystalline-phase identification
• Presence or absence of impurity peaks
• Evaluation of crystallinity
• Comparison with literature values and databases
• Sources of error and points for improvement

Reference Experimental Values and Calculation Examples for X-Ray Diffraction (XRD)

Here, reference experimental values are organized for discussing interplanar spacing, crystal structure, lattice constants, and crystallite size from diffraction peaks obtained by X-ray diffraction measurement.

In X-ray diffraction, X-rays are strongly diffracted at specific angles by the atomic arrangement in a crystal.
Interplanar spacing and lattice constants can be determined from the positions of diffraction peaks, while combinations of peaks can be used to identify crystal structures and phases.
If the peak width is broad, possibilities such as small crystallites, low crystallinity, or strain are considered.

Reference Experimental Conditions

Bragg’s Law

The relationship between X-ray diffraction peak position and interplanar spacing is expressed by Bragg’s law.

nλ = 2d sinθ

Here, n is the diffraction order, λ is the X-ray wavelength, d is the spacing between crystal planes, and θ is the diffraction angle.
Because XRD results are normally displayed as 2θ, θ is obtained by dividing 2θ by 2 for the calculation.

When calculation is performed assuming first-order diffraction (n = 1), the interplanar spacing d is determined from the following equation.

d = λ ÷ 2sinθ

Example Calculation of Interplanar Spacing d

Consider a diffraction peak observed at 2θ = 31.7°.
For the X-ray wavelength, λ = 0.154 nm is used for Cu Kα radiation.

θ = 31.7° ÷ 2 = 15.85°

d = 0.154 ÷ {2 × sin15.85°}

d = 0.154 ÷ 0.546 = 0.282 nm

Therefore, the interplanar spacing corresponding to the peak at 2θ = 31.7° is approximately 0.282 nm.

Example XRD Measurement of Sodium Chloride

Sodium chloride (NaCl) has a cubic crystal structure.
Reference examples of peak positions and interplanar spacings observed by powder XRD are shown below.

Calculation of the Lattice Constant for a Cubic Crystal

In a cubic crystal system, the relationship among interplanar spacing d, lattice constant a, and Miller indices hkl is expressed by the following equation.

d = a ÷ √(h2 + k2 + l2)

Therefore, the lattice constant a is determined as follows.

a = d × √(h2 + k2 + l2)

For the NaCl (200) peak, d = 0.282 nm, h = 2, k = 0, and l = 0.

a = 0.282 × √(22 + 02 + 02)

a = 0.282 × 2 = 0.564 nm

In this reference example, the lattice constant of NaCl is determined to be approximately 0.564 nm.

Lattice Constants Determined From Each NaCl Peak

If nearly the same lattice constant is obtained from many peaks, the indexing is considered valid.
If some peaks deviate, possible causes include errors in reading peak positions, overlapping peaks, and sample orientation.

Crystal Structure and the Appearance of Peaks

The combinations of peaks that tend to appear differ depending on the crystal structure.
For cubic crystals, examining the sequence of h²+k²+l² values makes it easier to estimate the crystal structure.

In NaCl, peaks such as (111), (200), (220), (311), and (400) are observed, and their sequence agrees with the reflection conditions corresponding to a face-centered cubic lattice.

Example XRD Measurement of Copper Powder

Copper is a metal with a face-centered cubic lattice.
A reference example of XRD measurement results for copper powder is shown below.

Because nearly the same lattice constant, a = 0.362 nm, is obtained from the three peaks, the measured values and indexing are considered consistent.

Example XRD Measurement of Zinc Oxide

Zinc oxide (ZnO) has a hexagonal wurtzite structure.
Reference peaks are shown below.

ZnO shows characteristic peaks near 31.8°, 34.4°, and 36.3°.
If multiple peak positions agree with standard data, the sample can be judged to contain a ZnO crystalline phase.

Example of Phase Identification for an Unknown Powder Sample

A reference example is shown in which XRD measurement was performed on unknown powder sample X and the peaks were compared with those of standard samples.

The major peaks of unknown sample X agree well with the standard peaks of ZnO.
Therefore, the main component of unknown sample X is considered highly likely to be zinc oxide.

Relationship Between Peak Width and Crystallite Size

If XRD peaks are broad, possible causes include small crystallite size, low crystallinity, and lattice strain.
An approximate crystallite size can be determined using the Scherrer equation.

D = Kλ ÷ βcosθ

Here, D is crystallite size, K is the shape factor, λ is the X-ray wavelength, β is the full width at half maximum of the peak, and θ is the diffraction angle.
β is handled in radians.

Example Calculation of Crystallite Size

For the ZnO (101) peak, the calculation is performed using 2θ = 36.3°, full width at half maximum β = 0.30°, λ = 0.154 nm, and K = 0.9.

θ = 36.3° ÷ 2 = 18.15°

The full width at half maximum is converted to radians.

β = 0.30 × π ÷ 180 = 0.00524 rad

D = 0.9 × 0.154 ÷ {0.00524 × cos18.15°}

D = 0.1386 ÷ 0.00498 = 27.8 nm

In this reference example, the crystallite size of ZnO is determined to be approximately 28 nm.

Changes in XRD Peaks With Calcination Temperature

When a sample is calcined, crystallinity may increase and the peaks may become sharper.
A reference example of changes in ZnO samples with calcination temperature is shown below.

As the calcination temperature increases, the peak width becomes narrower and the crystallite size becomes larger.
This is considered to be because crystal growth proceeds through heating and crystallinity improves.

Peak-Position Shift and Changes in Lattice Spacing

When a peak position shifts toward the lower-angle side, the interplanar spacing d becomes larger according to Bragg’s law.
Conversely, when it shifts toward the higher-angle side, the interplanar spacing d becomes smaller.

Peak-position shifts may be caused by solid solution formation, lattice strain, temperature, stress, instrument zero-point shifts, and other factors.

Changes in Peak Intensity Caused by Sample Orientation

For powder samples, crystal particles are normally assumed to be randomly oriented.
However, plate-like or needle-like crystals may become oriented in a specific direction when the sample is pressed, causing the peak-intensity ratio to change.

If the peak positions are the same but the intensity ratios differ greatly, the effect of sample orientation may be responsible rather than a difference in crystalline phase.

Example of a Sample Containing an Amorphous Component

Samples with low crystallinity or glassy components may show broad, hill-like scattering rather than sharp peaks.

In XRD, not only sharp peaks but also raised backgrounds and broad halos provide clues to the state of the sample.

Example of How to Write the Results

When XRD measurement of NaCl powder was performed using Cu Kα radiation, diffraction peaks were observed at 2θ = 27.4°, 31.7°, 45.5°, 56.5°, and 66.2°.
Using Bragg’s law, the interplanar spacing calculated from the peak at 2θ = 31.7° was d = 0.282 nm.
Assigning this peak to the (200) plane gave a lattice constant of a = 0.564 nm.

When each peak was indexed as (111), (200), (220), (311), and (400), lattice constants of approximately 0.563–0.564 nm were obtained from many of the peaks.
Because nearly the same lattice constant was obtained from multiple peaks, this indexing was considered valid.
In addition, the sequence of peaks agreed with the reflection conditions corresponding to a face-centered cubic lattice.

In unknown sample X, major peaks were observed at 31.8°, 34.4°, 36.3°, 47.5°, and 56.6°.
Because these peak positions agreed well with the standard peaks of ZnO, the main component of unknown sample X was considered highly likely to be zinc oxide.

Points for Connecting the Results to the Discussion

In an XRD discussion, it is important not only to read peak positions but also to comprehensively consider interplanar spacing, indexing, lattice constants, peak width, and intensity ratios.

• Can θ be determined from 2θ and the interplanar spacing d calculated using Bragg’s law?
• For cubic crystals, can the lattice constant a be determined from d and hkl?
• Has it been checked whether lattice constants obtained from multiple peaks agree?
• Can the crystal structure and phase be estimated from the sequence of peaks?
• For an unknown sample, have multiple peaks rather than only one peak been compared with standard data?
• If the peak width is broad, can crystallite size, crystallinity, and lattice strain be discussed?
• Can shifts of peak positions toward lower or higher angles be explained in relation to changes in interplanar spacing?
• Can changes in peak-intensity ratios be related to sample orientation and particle shape?
• If amorphous components are present, have broad halos and raised background levels also been considered?

Example Discussion

In this experiment, the crystal structures of the samples were investigated by powder X-ray diffraction.
In the NaCl sample, peaks were observed near 2θ = 27.4°, 31.7°, 45.5°, 56.5°, and 66.2°.
Applying Bragg’s law to the peak at 2θ = 31.7° gave an interplanar spacing d of 0.282 nm.
When this peak was assigned to the (200) plane, the lattice constant a was calculated to be 0.564 nm.

When the other peaks were also indexed, nearly the same lattice constant was obtained from reflections such as (111), (200), (220), and (400).
Because the lattice constants calculated from multiple peaks agreed, the measured results and indexing were considered generally valid.
In addition, the combination of observed reflections agreed with the reflection conditions for a face-centered cubic lattice and corresponded to the crystal structure of NaCl.

In unknown sample X, diffraction peaks were observed at 31.8°, 34.4°, 36.3°, 47.5°, and 56.6°.
These peak positions correspond to the representative ZnO peaks (100), (002), (101), (102), and (110).
Therefore, the main component of unknown sample X was considered highly likely to be zinc oxide.
However, because trace components and amorphous components may appear as weak peaks or broad halos, the entire pattern rather than only the major peaks must be examined.

In ZnO samples calcined at different temperatures, the peak width became narrower and the peak intensity increased as the calcination temperature increased.
The crystallite sizes determined using the Scherrer equation were approximately 10 nm for the uncalcined sample, approximately 28 nm after calcination at 500°C, and approximately 46 nm after calcination at 700°C.
From this, crystallite growth and improved crystallinity were considered to have occurred through calcination.

Possible sources of error include reading peak positions, zero-point shifts of the instrument, height differences of the sample surface, sample orientation, and peak overlap.
In particular, if a powder sample is pressed strongly, specific crystal planes may become aligned and oriented, causing peak-intensity ratios to differ from standard data.
In addition, if a peak position shifts toward lower angles, the calculated interplanar spacing becomes larger, while a shift toward higher angles makes the calculated spacing smaller.
Therefore, accurate peak positions are important when discussing lattice constants.

Summary

In X-ray diffraction, interplanar spacing can be determined from diffraction-peak positions using Bragg’s law, and lattice constants and crystal structures can be discussed from the relationship with Miller indices.
If multiple peaks agree with standard data, crystalline phases can be identified.

In this reference example, XRD data for NaCl, Cu, ZnO, and unknown sample X were used to examine interplanar spacing, lattice constants, phase identification, and crystallite size.
In a report, it is useful to discuss 2θ, d values, indexing, lattice constants, peak width, orientation, amorphous components, and measurement errors in relation to one another.

What Is a Diffraction Peak?

A diffraction peak is a peak that appears at a position of high diffraction intensity in an XRD pattern.
A peak appears when the condition for constructive interference of X-rays from a specific crystal plane is satisfied.
The 2θ position of a peak corresponds to the spacing between crystal planes, while the peak intensity is related to the atomic arrangement on that plane and the orientation of the crystals.

Highly crystalline samples tend to show sharp, clear peaks.
On the other hand, samples containing large amounts of amorphous material may show a broad halo-like pattern rather than sharp peaks.
Therefore, the presence or absence and shape of peaks provide clues for evaluating sample crystallinity.

What Is 2θ?

The 2θ shown on the horizontal axis of an XRD pattern is a value related to the angle between the incident X-ray and the diffracted X-ray.
θ represents the incident angle relative to the crystal plane, and in actual measurements, 2θ is recorded as the angular difference between the incident direction and detection direction.
The 2θ value of a diffraction peak is important for determining the spacing between crystal planes.

In general, the larger the 2θ value of a peak, the smaller the corresponding lattice spacing.
Conversely, peaks at smaller 2θ values correspond to relatively larger lattice spacings.
This relationship can be explained by Bragg’s law.

Bragg’s Law and Lattice Spacing

Bragg’s law is a fundamental equation in X-ray diffraction.
It expresses the condition under which X-rays reflected from crystal planes interfere constructively.
Using this equation, the spacing d between crystal planes can be determined from the 2θ value of a diffraction peak.

nλ = 2d sinθ

Here, n is the diffraction order, λ is the X-ray wavelength, d is the lattice spacing, and θ is the Bragg angle.
Because an XRD pattern displays 2θ, half of 2θ is used as θ in the calculation.
Normally, n = 1 is often used for first-order diffraction.

How to Interpret Lattice Spacing

Lattice spacing is the distance between crystal planes aligned in the same direction within a crystal.
In XRD, this spacing can be determined from the position of a diffraction peak.
Because lattice spacing is related to crystal structure and lattice constants, it is important for substance identification and structural analysis.

For example, within the same crystalline phase, the d value corresponding to a particular crystal plane is approximately constant.
If the measured value agrees with the d value in literature or databases, this provides evidence for the presence of that crystalline phase.
On the other hand, if the d value deviates, lattice strain, solid solution formation, compositional changes, or measurement error may be considered.

Crystal Planes and Miller Indices

Crystal planes are represented by Miller indices.
Miller indices are symbols indicating the orientation of planes in a crystal and are generally written in the form (hkl).
Each XRD peak corresponds to a particular crystal plane, and a peak may be assigned to the crystal plane from which it originates based on its position.

For known crystal structures, the corresponding (hkl) values for each peak are given in databases and literature.
By comparing the measured 2θ or d values with literature values and assigning the corresponding crystal planes, the target phase can be confirmed and the lattice constant can be evaluated.

Identification of Crystal Structure

In XRD, crystalline phases in a sample are identified by comparing the positions and relative intensities of multiple diffraction peaks with data for known substances.
It is important not to judge from only one peak but to confirm whether several major peaks agree.
In substances with similar structures, some peaks may overlap.

In crystalline-phase identification, peak positions, peak intensities, number of peaks, and the presence or absence of impurity peaks are evaluated comprehensively.
Even if agreement with a database is high, it is necessary to confirm that the result does not contradict the synthesis conditions or chemical composition of the sample.

Discussion of Peak Intensity

The intensity of a diffraction peak indicates how strongly X-rays are diffracted from that crystal plane.
Peak intensity is affected by crystal structure, type of atoms, atomic arrangement on crystal planes, amount of crystalline phase, orientation, and measurement conditions.
Therefore, peak intensity does not simply represent the amount of a component.

If a powder sample is randomly oriented, it is easier to compare relative intensities with literature data.
However, plate-like or needle-like crystals tend to orient in specific directions, and some peaks may become abnormally strong.
This can be discussed as an effect of orientation.

Discussion of Relative Intensity

In XRD, the strongest peak may be assigned a value of 100 and the intensities of the other peaks expressed as relative intensities.
Relative intensity is useful for comparison with literature data and databases.
For the same crystalline phase, not only peak positions but also relative intensities are expected to agree to some extent.

However, relative intensity is affected by sample orientation, particle size, sample amount, measurement conditions, and absorption.
Therefore, even if the relative intensities do not agree perfectly, the sample may still contain the same phase if the peak positions agree.
It is important to discuss the causes of intensity differences.

Discussion of Peak Width and Full Width at Half Maximum

Peak width indicates how broad a diffraction peak is.
Full width at half maximum is the width measured at half the height of the peak intensity.
Sharp XRD peaks may indicate high crystallinity, large crystallite size, and small lattice strain.
Conversely, broad peaks may indicate small crystallite size, lattice strain, or low crystallinity.

However, peak width also includes broadening originating from the instrument.
When crystallite size is evaluated quantitatively, correction for instrumental broadening and an appropriate analysis equation are necessary.
It is important not to determine crystallite size solely from visual inspection of peak width.

Discussion of Crystallite Size

In XRD, crystallite size can sometimes be estimated from peak broadening.
The smaller the crystallite size, the more readily the diffraction peak broadens.
A representative equation using this relationship is the Scherrer equation.

D = Kλ / β cosθ

Here, D is the crystallite size, K is the shape factor, λ is the X-ray wavelength, β is the full width at half maximum of the peak, and θ is the Bragg angle.
However, because β also includes the effects of instrumental broadening and lattice strain, the obtained value should be treated only as an approximate crystallite size.

Discussion of Crystallinity

The crystallinity of a sample can be evaluated from its XRD pattern.
Highly crystalline samples show sharp, clear diffraction peaks.
On the other hand, samples containing large amounts of amorphous material may show weaker sharp peaks and broad halo-like scattering.

Synthesis conditions, calcination temperature, cooling rate, crystallization time, solvent, drying conditions, and other factors affect crystallinity.
For example, higher calcination temperatures may promote crystallization and make peaks sharper and stronger.
However, excessive heating may also produce another phase.

Discussion of Amorphous Components

An amorphous state is one in which atoms or molecules do not have regular long-range ordering.
Amorphous components tend not to show sharp diffraction peaks in XRD and may appear as broad halos.
Glasses, polymers, rapidly cooled samples, and uncrystallized samples may contain large amounts of amorphous material.

If a broad halo is seen in an XRD pattern and there are few sharp peaks, the sample may contain amorphous components.
However, peaks also broaden in microcrystalline samples or samples with extremely small crystallites, so care is required when distinguishing amorphous material from microcrystalline material.

Discussion of Impurity Phases

If extra peaks other than those of the target phase are observed in an XRD pattern, the sample may contain impurity phases, unreacted starting materials, or by-products.
In synthesis experiments, impurity phases may remain if the reaction does not proceed completely or if the calcination conditions are inappropriate.

When discussing impurity phases, the 2θ positions of the extra peaks are compared with databases or XRD patterns of the starting materials.
If they overlap with peaks of the target phase, identification of the impurity may become difficult.

Discussion When Peak Positions Shift

Causes of measured peak positions shifting from literature values include lattice strain, solid solution formation, compositional changes, changes in lattice constants, differences in sample height, errors in instrument calibration, and differences in temperature conditions.
If another element dissolves into the material to form a solid solution, the lattice constant may change and peak positions may shift toward higher or lower angles.

If a peak shifts toward higher angles, the corresponding lattice spacing may generally have become smaller.
If it shifts toward lower angles, the lattice spacing may have become larger.
However, peak positions also change because of measurement error and sample-position errors, so careful judgment is necessary.

Discussion When Peak Intensity Is Weak

Causes of weak peak intensity include a small amount of sample, low crystallinity, a small amount of the crystalline phase, a large amount of amorphous material, short measurement time, an uneven sample surface, effects of orientation, and absorption.
If only a small amount of the target phase is present, the peaks are detected weakly.

When peak intensity is weak, it may be difficult to distinguish peaks from noise.
The result may be improved by increasing the measurement time, reducing the scan speed, increasing the sample amount, or making the sample more uniform.

Discussion When Peaks Are Broad

If diffraction peaks are broad, possible causes include small crystallite size, lattice strain, low crystallinity, a large amount of amorphous material, and low instrumental resolution.
Particularly in nanoparticles and materials synthesized at low temperatures, peaks may broaden because of small crystallite size.

It is risky to determine crystallite size from peak width alone.
Lattice strain and instrumental broadening also affect peak width, so correction using a standard sample or analysis using multiple peaks is performed when necessary.

Discussion of Orientation

In powder XRD, literature data are compared under the assumption that particles are randomly oriented.
However, plate-like or needle-like crystals may align in a particular direction on the sample holder, causing peaks originating from specific crystal planes to become abnormally strong.
This is called preferred orientation or an orientation effect.

When orientation is present, peak positions may agree with literature values while relative intensities differ greatly.
Orientation may be reduced by finely grinding the sample, mixing it thoroughly, or avoiding excessive smoothing of the sample surface.

Discussion of Powder XRD

Powder XRD uses the fact that many small crystals are present in random orientations to measure diffraction from various crystal planes.
If the powder sample is sufficiently fine, uniform, and randomly oriented, comparison with literature data becomes easier.

If grinding is insufficient, particle size is too large, the sample is unevenly distributed, or orientation is strong, peak intensities may become unstable.
In powder XRD, sample preparation has a major effect on the results.

Discussion of Thin-Film XRD

In XRD of thin-film samples, peaks from the substrate and orientation of the thin film are important.
Thin films often grow in a specific direction on a substrate and may show peak-intensity patterns different from those of powder samples.
In addition, if the thin film is thin, peak intensity may be weak.

In thin-film XRD, peaks from the target thin film must be distinguished from substrate peaks.
To avoid mistakenly identifying strong peaks originating from the substrate as thin-film peaks, comparison with the XRD pattern of an uncoated substrate is useful.

Discussion of Changes in Crystal Structure

Crystal structures may change because of heat treatment, reactions, substitution, doping, phase transitions, pressure, humidity, and other factors.
When the crystal structure changes, the peak positions, number of peaks, peak intensities, and peak widths in the XRD pattern change.
The appearance of new peaks or disappearance of existing peaks provides clues to phase changes or formation of new phases.

Continuous shifts in peak positions may indicate changes in lattice constants or solid solution formation.
On the other hand, the appearance of a completely different group of peaks may indicate formation of another crystalline phase.
The cause of the change is discussed in relation to experimental conditions and sample composition.

Discussion When XRD Is Used to Confirm a Synthesized Product

When inorganic materials, complexes, ceramics, or crystalline organic compounds are synthesized, XRD is used to confirm whether the target substance has formed.
The XRD pattern of the synthesized product is compared with those of the starting materials and with literature data to determine whether peaks of the target phase have appeared and whether starting-material peaks remain.

If starting-material peaks remain, the reaction may have been incomplete.
If peaks other than those of the target phase are present, formation of by-products or impurity phases can be considered.
XRD is strong for confirming crystalline phases but has limitations in detecting amorphous components and trace impurities.

Comparison With Literature Values and Databases

In XRD crystalline-phase identification, measured peaks are compared with literature values and databases.
When comparing them, not only peak positions but also combinations of multiple peaks, relative intensities, and the presence or absence of peaks are checked.
If several major peaks agree, this provides evidence supporting the presence of the target phase.

However, peak intensities and positions may differ slightly because of measurement conditions, sample orientation, particle size, crystallinity, and lattice strain.
Even when complete agreement is not obtained, the discussion is sufficient if the cause of the difference can be explained.

Discussion of Lattice Constants

When the crystal structure is known, lattice constants can be determined from multiple diffraction peaks.
A lattice constant is a value representing the size of the unit cell.
In cubic systems, the lattice constant a can be calculated from the interplanar spacing d and the Miller indices.

If the lattice constant agrees with the literature value, this supports the target crystal structure.
On the other hand, if the lattice constant has changed, solid solution formation, defects, compositional changes, lattice strain, or differences in temperature conditions can be considered.

Sources of Measurement Error

Sources of error in XRD measurement include differences in sample height, uneven sample surfaces, insufficient grinding, orientation, large particle size, insufficient sample amount, instrument-calibration errors, scan speed, background, and noise.
In particular, sample position and instrument calibration strongly affect the accuracy of peak positions.

Peak intensity and relative intensity are affected by sample orientation, packing condition, particle size, and measurement time.
Peak width is affected by crystallite size, lattice strain, and instrumental broadening.
Separating which factors affect which results leads to a more convincing discussion.

When XRD Results Can Be Considered Good

XRD results can be considered good when major diffraction peaks are clearly observed, the peak positions agree with literature values or databases, and there are few peaks that cannot be explained by the target phase.
In addition, if the peaks are sufficiently sharp and the background and noise are low, evaluation of crystallinity and phase identification become easier.

However, it is not unusual for relative intensities to fail to agree perfectly.
While considering the effects of orientation and sample preparation, it is important to emphasize whether multiple peak positions agree.
When necessary, the result is judged in combination with other analytical methods.

Example Discussion When the Experiment Did Not Go Well

When XRD measurement does not go well, possible causes are considered from results such as weak peaks, broad peaks, shifted peaks, peaks other than those of the target phase, high background, large noise, or failure to agree with literature values.
Organizing the causes into sample preparation, measurement conditions, crystallinity, phase purity, and instrument calibration makes the discussion easier.

How to Write Points for Improvement

In a discussion of X-ray diffraction, including not only sources of error but also points for improvement makes the report easier to organize.
Improvements can be divided into sample preparation, measurement conditions, and analysis methods.

Improvements to Sample Preparation

• Grind the sample sufficiently
• Mix the sample uniformly
• Pack the sample uniformly into the sample holder
• Make the sample surface flat
• Avoid excessive orientation
• Remove impurities and unreacted materials
• Dry the sample when necessary

Improvements to Measurement Conditions

• Set an appropriate measurement range
• Reduce the scan speed
• Increase the measurement time
• Check instrument calibration using a standard sample
• Set the sample height correctly
• Reduce the background
• Use conditions appropriate for thin films when necessary

Improvements to Analysis

• Organize major peaks in a table
• Calculate d values from 2θ
• Compare multiple peaks with literature values
• Do not judge from relative intensity alone
• Investigate candidates for impurity peaks
• Consider instrumental contributions to peak width
• Judge the results in combination with other analytical methods

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of X-ray diffraction, simply writing that “a peak appeared” or “the sample was crystalline” results in a superficial discussion.
A good discussion relates diffraction-peak position, lattice spacing, crystalline phase, peak intensity, peak width, and sources of error.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of X-ray diffraction.
Adjust the necessary parts according to your own experimental results.

• Because clear diffraction peaks were observed in the XRD pattern, the sample was considered to be crystalline.
• The 2θ value of a diffraction peak corresponds to the spacing between crystal planes.
• Bragg’s law can be used to calculate the lattice spacing d from the 2θ value.
• Because the positions of the major peaks agreed with literature values, the presence of the target crystalline phase was suggested.
• Rather than identifying a phase from only one peak, it is necessary to compare multiple peak positions and relative intensities.
• Possible causes of broad peak width include small crystallite size and lattice strain.
• Differences in relative intensity may have been affected by sample orientation, particle size, and packing condition.
• Peaks that cannot be explained by the target phase may originate from impurity phases or unreacted starting materials.
• Peak-position shifts may result from changes in lattice constants or measurement errors.
• Because XRD has limitations in evaluating amorphous components and trace impurities, the results must be judged in combination with other analytical methods.

Points to Check When Discussing X-Ray Diffraction

Checking the following points before writing the report makes the discussion easier to write.

• Are the measurement conditions clearly stated?
• Have the 2θ values of the major peaks been recorded?
• Have the d values been calculated using Bragg’s law?
• Have the peak positions been compared with literature values or databases?
• Has phase identification been performed using multiple peaks?
• Have differences in relative intensity been discussed?
• Has the meaning of peak width and full width at half maximum been explained?
• Have crystallinity and amorphous components been considered?
• Has the possibility of impurity peaks been checked?
• Have the causes of peak-position shifts been considered?
• Have the effects of orientation and particle size caused by sample preparation been considered?
• Do the points for improvement correspond to the sources of error?

Summary

X-ray diffraction is an analytical method that uses diffraction of X-rays by the regular atomic arrangement in crystals to investigate crystal structure and lattice spacing.
In an XRD pattern, the positions of diffraction peaks correspond to lattice spacing and crystal structure, while peak intensities are affected by atomic arrangement, orientation, and the amount of each phase.
Peak width is related to crystallite size, lattice strain, crystallinity, and instrument conditions.

Lattice spacing can be determined using Bragg’s law, nλ = 2d sinθ.
By comparing the 2θ and d values of measured peaks with literature values and databases, crystalline phases in a sample can be estimated.
However, for phase identification, it is important to evaluate the positions and relative intensities of multiple major peaks comprehensively rather than relying on only one peak.

In a report, rather than simply writing that “a peak appeared,” organize and discuss peak positions, lattice spacing, crystal planes, crystalline phases, peak intensity, peak width, orientation, impurity phases, and sources of error.
XRD is extremely effective for confirming crystalline phases, but because it has limitations for amorphous components, trace impurities, and compositional information, it is important to combine it with other analytical methods when necessary.