Pecharsky V.K., Zavalij P.Y. Fundamentals of Powder Diffraction and Structural Characterization of Materials

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Experimental techniques

Figure

3.8.

The schematic of the Bragg-Brentano focusing geometry using a flat sample when

the self-focused diffracted beam is registered by the detector after reflection from the sample.

focus of the x-ray source, DS

divergence slit, RS

receiving slit,

-detector,

Bragg angle.

Figure

3.9.

Transmission geometry in the case of flat (left) and cylindrical (right) samples.

focus of the x-ray source, DS

divergence slit, RS

receiving slit,

Bragg angle.

The two commonly employed transmission geometries are shown in

Figure

3.9. Powder diffraction in the transmission mode can be observed

from both flat and cylindrical samples. Flat samples usually require small

amounts of material, however, the preparation of high quality and uniformly

dense specimen may be difficult.

Cylindrical samples, which are common in the Debye-Scherrer cameras

(Figure

3.2), are also used in powder diffractometry. Similar to flat

transmission samples, small amounts of powder are required in the

cylindrical specimen geometry. This form of the sample is least susceptible

to the non-random distribution of particle orientations,

i.e. to preferred

orientation effects.

Both flat and cylindrical transmission samples are commonly used in

combination with position sensitive or image plate detectors. The major

disadvantage of the transmission geometry arises from the fact that

self-

focusing of the diffracted beam is not as precise as in the Bragg-Brentano

272

Chapter

geometry. Hence, laboratory instruments employing transmission geometry

usually have lower resolution when compared to those operating in the

reflection geometry. It is worth noting that imprecise self-focusing is

generally not an issue when using synchrotron x-ray sources, which produce

nearly parallel x-ray beams.

Powder diffractometer goniostats can be constructed in a way that both

the detector and the sample revolve around a common goniometer axis in a

synchronized fashion, or the sample is stationary, but both the detector and

the x-ray source arms rotations are synchronized, as shown in

Figure

3.10.

When cylindrical samples are employed, generally there is no need in the

synchronization of the goniometer arms, and only the detector arm (if any,

e.g. see

Figure

3.14, below) should be rotated.

The schematic of a goniostat, which realizes horizontal Bragg-Brentano

focusing geometry with both the detector and source arms in the

synchronized rotation about a common horizontal goniometer axis is shown

Figure

3.11. Both arms of the goniometer revolve in the vertical plane,

and this geometry of a powder diffractometer is in the most common use

today.

Some powder diffractometers, particularly those which are used for

routine analysis of multiple samples of the same kind, can be equipped with

multiple sample changers (usually from

to 12 specimens can be

accommodated by a single sample changer). This ensures straightforward

software control over the data collection process within a series of samples

and enables better automation, as data sets from multiple samples may be

collected without operator intervention,

e.g. overnight or during

weekend.

Multiple sample changers are common in powder x-ray diffractometers used

Figure

3.10.

Synchronization of the goniometer arms: the x-ray source is stationary while the

sample and the detector rotations are synchronized to fulfill the

8-28

requirement (left); the

sample is stationary while the source and the detector arms are synchronized to realize the

8-8

condition (middle)

this geometry is in common use at present; only the detector arm

revolves around the goniometer axis in the case of a cylindrical sample (right).

focus of

the x-ray tube indicating the position of the x-ray source arm,

detector arm,

Bragg

angle. The common goniometer axis (which is perpendicular to the plane of the projection)

around which the rotations are synchronized is shown as the open circle in each of the three

drawings. The location of the optical axis is shown as the dash-dotted line.

Experimental techniques

273

Specimen

holders

Goniometer

axis

Figure

3.11.

The schematic of the goniostat of a Scintag

XDS2000

powder diffractometer

with the horizontal axis and synchronized rotations of both the source and detector arms. This

goniometer is equipped with a liquid nitrogen-cooled solid-state detector, which enables

monochromatization of the diffracted beam by selecting a narrow energy window, thus

registering only characteristic energy photons.

is the radius of the goniometer.

in analytical laboratories for quality control purposes. For example, when

multiple samples should be analyzed to ensure adequate properties of a

product when they are critically dependent on the structure

andlor phase

composition of a material manufactured in different batches or from the

same batch at various stages of the production process.

3.3.2 Goniostats with point detectors

Photographs of two different powder diffractometer goniostats equipped

with point detectors are shown in

Figure

3.12 and

Figure

3.13. The first

example

(Figure

3.12) is a Bragg-Brentano goniometer, where the x-ray

source housing is rigidly mounted on the goniometer frame and it remains

stationary during data collection. The 8-28 mode is achieved by

synchronizing the rotations of the sample holder and the detector around the

common horizontal goniometer axis, as shown schematically in

Figure

3.10,

left.

The slit box located between the x-ray source and the sample

(Figure

3.12, left) contains two divergence slits, which control the aperture and the

divergence of the incident beam in the vertical plane. The two divergence

slits are separated by a set of Soller slits, which limit the divergence of the

incident beam in the horizontal plane. The sample holder here is an

automatic four-specimen sample changer.

274

Chapter

7--

X-ray

tube Four specimen Detector

Figure

3.12.

The overall view of the goniostat of the Scintag

XRD-7

powder diffractometer.

This diffractometer has the horizontal goniometer axis, stationary x-ray source and

synchronized rotations of both the detector arm and sample holder. The goniometer is

equipped with a thermoelectric refrigerator-cooled solid-state detector, which enables the

monochromatization of the diffracted beam by selecting a narrow energy window thus

registering only characteristic energy photons. (Courtesy of Scintag, Inc.)

The second slit box is located on the detector arm between the sample

and the detector. The slit nearest to the sample serves as a scatter slit. It is

followed by another Soller slit and a receiving slit positioned just before the

detector. The detector in this case is a solid-state detector, which is cooled by

a built-in Peltier refrigerator enabling to adjust and maintain the detector

sensitivity at extremely narrow width to allow only x-ray photons of specific

energy to be registered. Monochromatization of the diffracted x-ray beam is,

therefore, achieved electronically rather than by physical means (e.g. by a

P-

filter or a crystal monochromator), which increases the registered diffracted

intensity by eliminating losses in the filter or in the monochromator.

Electronic monochromatization is practical only in the case of modest

intensities, as for example, powdered samples. When highly crystalline or

single crystalline specimens are used (see

Figure

2.18

in Chapter 2), the

incident beam intensity should be reduced by using narrower slits or

lowering tube power. The linearity of solid-state detectors is poor at high

Experimental techniques 275

photon fluxes: usually when the flux exceeds 20,000 to 50,000 photons per

second the response of the detector is no longer linear and the measured

intensity will be incorrect.

different goniostat with the horizontal orientation of the specimen and

Bragg-Brentano geometry is shown in Figure 3.13. The x-ray tube housing

is mounted on the movable arm, and both the x-ray source and the detector

can be rotated in a synchronized fashion about the common horizontal

goniometer axis (also see the schematic in Figure 3.10, middle).

The x-ray source in this example is a rotating anode x-ray tube. Another

unusual feature of this goniometer is the presence of variable divergence

(Figure 3.13, left), scatter and receiving (Figure 3.13, right) slits. This

combination of slits enables one to maintain the irradiated area of the studied

specimen constant at any Bragg angle, which may be useful in some

applications. Both variable slit boxes also contain a set of Soller slits each to

control the divergence of both the incident and diffracted beams in the

horizontal plane.

Figure

3.13.

The overall view of the goniostat of the Rigaku TTRAX rotating anode powder

diffractometer with the horizontal goniometer axis, and synchronized rotations of both the

x-ray source and detector arms. This goniometer is equipped with variable divergence, scatter

and receiving slits, curved crystal monochromator, and scintillation detector. (Courtesy of

RigakuIMSC.)

276

Chapter

The curved crystal-monochromator is positioned between the receiving

slit box and the detector (also see the schematic in

Figure

3.6,

right). This

goniometer is shown with the specimen spinning sample holder attachment,

which enables continuous spinning of the sample during data collection to

achieve better particle orientations averaging, thus reducing preferred

orientation effects.

The goniometer shown in

Figure

3.13

is equipped with a scintillation

detector, which has high linearity (within 1% in excess of -10' counts per

second), which is important with the high brightness of the incident beam

produced by a rotating anode

x-ray tube. Only a small part of the

scintillation detector is visible in

Figure

3.13.

The massive counterweight to

balance the heavy x-ray tube housing is seen in the background of the

photograph as the dark segment (top right).

Overall, powder diffractometers equipped with point detectors offer the

best resolution of the resulting powder diffraction data. While the

instrumental resolution increases with the increasing goniometer radius, the

intensity of the diffracted beam unfortunately decreases because the incident

beam produced by an analytical x-ray tube is always divergent.' Therefore,

typical goniometer radii vary between -150 and -300 mm.

3.3.3

Goniostats with area detectors

The schematic of a powder diffractometer goniostat utilizing

transmission geometry with a cylindrical specimen and a curved position

sensitive detector

(PSD)

is shown in

Figure

3.14.

When using a curved

position sensitive detector covering a long (from -0 to -90-140')

range,

generally there is no need to rotate the detector arm and only sample

spinning is required to improve particle orientations averaging and minimize

preferred orientation.

The greatest advantage of this geometry is in the speed of data collection:

the entire diffraction pattern can be recorded in as little as few seconds

because the diffracted intensity in the whole range of Bragg angles covered

by the circumference of the curved position sensitive detector is registered

simultaneously. The downside is that it is impossible to monochromatize the

diffracted beam effectively, which results in the increased background,

particularly when the sample is strongly fluorescent. Another difficulty may

occur in the interpretation of powder diffraction data collected using the

geometry shown in

Figure

3.14

because of the lower resolution of curved

position sensitive detectors and increased widths of Bragg peaks when

compared with point detectors.

When the goniometer radius increases, the size of a flat specimen, needed to maintain high

intensity in the Bragg-Brentano geometry, becomes unreasonably large, see section

3.5.3.

Experimental techniques

Figure

3.14.

The schematic of a powder diffractometer with the vertical goniometer axis,

cylindrical sample in the transmission mode and a curved position sensitive detector (PSD).

Solid arrows indicate the incident beam and broken arrows indicate the diffracted beams

pathways.

focal point of the x-ray source,

monochromator, DS

divergence slit,

incident beam trap.

principle, curved position sensitive detector can be replaced by a linear

position sensitive detector covering segments

to 10'

(28)

wide. This

approach considerably increases resolution and decreases Bragg peak

widths, but the problem of the enhanced background remains.

Recently, image plate detectors are becoming popular in powder

diffractometry

(Figure

3.15).

The monochromatized and collimated beam

passes through a cylindrical or flat sample and the diffracted beams are

registered by the image plate detector in all directions simultaneously.

Because of the size of the detector, which can be made as large as necessary,

the entire circumference of the Debye ring is normally registered instead of

just a small sector as it is done in any other powder diffraction geometry

considered above.

The use of image plate detectors restores the pseudo two-dimensionality

of the x-ray powder diffraction pattern, which was standard in film-based

registration. Experimental diffraction data can be collected at high speeds,

nearly identical to those achievable with curved position sensitive detectors.

Furthermore, the incident beam can be collimated into a small area and it is

fundamentally possible to examine powder diffraction from just a few

crystalline grains or even from a single grain, provided all possible grain

orientations with respect to the incident beam have been arranged by

properly varying the orientation of the specimen. The problems encountered

in today's image plate detector-equipped powder diffractometers are similar

to those noted above for curved position sensitive detectors: high

background and relatively low resolution, see

Figure

3.16.

Chapter

Figure

3.15.

The schematic of a powder diffractometer with the vertical goniometer axis,

cylindrical sample in the transmission mode and image plate detector (IPD). Solid arrows

show the incident beam path. Rings indicate intercepts of

Debye cones with the IPD.

focal point of the x-ray source,

monochromator, C

collimator, DR

Debye rings.

Scintillatior

detector

20 30 40

60 70

Bragg angle,

(deg.)

Figure

3.16.

Comparison of the x-ray diffraction data collected from the same powder using a

point detector and a diffracted beam monochromator in the Bragg-Brentano geometry (lower

pattern,

left hand intensity scale) and an image plate detector and an incident beam

monochromator (upper pattern, right hand intensity scale) in the transmission geometry from

a cylindrical sample. An extremely high and non-linear background in the case of the image

plate detector is due to strong x-ray fluorescence of Gd atoms interacting with Cu

radiation. The widths of the Bragg peaks in the case of the image plate detector are enhanced,

which translates into the low resolution of the data. Despite the nearly two orders of

magnitude larger photon count, the best peak-to-background ratio for the image plate detector

data is

while it is nearly

70:

for the point detector data.

Experimental techniques 279

When the two powder diffraction patterns (Figure 3.16), obtained from

the same material are compared, the data collected using the Bragg-Brentano

geometry and point detector with the diffracted beam crystal monochromator

are definitely more useful in structural analysis than the set of data collected

using an image plate detector and an incident beam crystal monochromator.

The data set collected using an image plate detector has insufficient quality

due to the unfavorable coincidence of conditions. First, the crystal structure

of the material is complex (a total of -300 Bragg peaks are possible in the

range shown in Figure 3.16: 20

80"). Second, the powder contains

more than

wt.%

of Gd

a chemical element, which produces a strong

fluorescent background when using Cu

radiation. Thus, both the position

sensitive and the image plate detectors find use in special applications of

powder diffraction, such as in-situ studies of phase transformations and local

non-destructive analysis, but their use in high precision determination of the

crystal structure of materials is limited.

the conclusion of this section, we feel that it is important to mention

that despite its long history, powder diffractometry is a rapidly developing

field of science, especially at the instrumentation level. Both position

sensitive and image plate detectors, brought to routine use by exceptional

technological advancements in high speed electronics and tremendous

computing power, made the powder diffraction experiment faster than ever.

Furthermore, x-ray mirrors and capillaries are making successful entrance

into the market of commercial powder diffractometry, potentially enabling

nearly parallel x-ray beams in analytical laboratory instruments, not just

when using synchrotron radiation sources. It is difficult to predict how

advanced the capabilities of powder diffraction instruments will become in

ten or twenty years from now, but the essence of the quality powder

diffraction experiment will likely remain the same: the best powder

diffraction data will always need to be highly precise and collected with the

best possible resolution over a minimum background.

3.4

Safety

The information contained in this section deals with radiation safety for

users of analytical x-ray systems. It was developed by the Environmental,

Safety, Health and Assurance Office of the United States Department of

Energy Ames Laboratory.'

the content of this book it is intended to raise

awareness about the potential dangers associated with the continuous or

acute exposure to x-ray radiation and has no legal force. Each workplace

where analytical x-rays are used should have a set of established policies and

The document was kindly provided by

Mrs.

Kate Sordelet.

280

Chapter

procedures, which must be strictly enforced and are designed to protect both

the operator(s) of analytical x-ray instruments and nearby personnel from x-

ray exposure.'

3.4.1

Radiation quantities and terms

X-rays transfer their energy to matter through chance encounters with

bound electrons or atomic nuclei. These random encounters result in the

ejection of energetic electrons from the atom. Each of the electrons liberated

goes on to transfer its energy to matter through many direct ionization events

(i.e. events involving collisions between charged particles). Since x-rays

transfer energy in this indirect manner, they are referred to as indirectly

ionizing radiation. Because the encounters of x-ray photons with atoms are

by chance, a given photon has a finite probability of passing completely

through the medium it is traversing. The probability that a photon will pass

completely through a medium depends upon numerous factors including the

energy of the x-rays and the medium's chemical composition and thickness.

The following quantities and terms are essential to the description and

measurement of various forms of ionizing radiation.

Exposure. It is a measure of the strength of a radiation field at some

point. It is usually defined as the amount of charge (i.e., sum of all ions

of one sign) produced in a unit mass of air when the interacting photons

are completely absorbed in that mass. The most commonly used unit of

exposure is the Roentgen, R, which is defined as that amount of radiation

which produces

2.58~10-~

coulombs of charge per kilogram (SI units) of

dry air.

cases where exposure is to be expressed as a rate, the unit

would be

R/h

or, more commonly,

mR/h.

Absorbed dose. It is the amount of energy passed on by radiation to a

given mass of any material. The most common unit of absorbed dose is

the rad, which is defined as a dose of

100

ergs of energy per gram of the

material in question (SI unit is the gray,

1 Jlkg). The absorbed

dose may also be expressed as a rate with units of radlh or mradlh.

Dose equivalent. Although the biological effects of radiation are

dependent upon the absorbed dose, some types of particles produce

greater effects than others for the same amount of transferred energy. In

order to account for these variations when describing human health risk

from radiation exposure, the quantity dose equivalent is used. This is the

absorbed dose multiplied by certain quality and modifying factors

An overview of precautions against radiation injury is also given by D.C. Creagh and S.

Martinez-Carrera in the International Tables for Crystallography, vol. C, Second edition,

A.J.C. Wilson and E. Prince, Eds., Kluwer Academic Publishers,

Boston/Dordrecht/

London

999)

949.