# Diffractometer

The diffractometer is an apparatus making it possible to measure the diffraction of a wave on a target. The term is used exclusively for the Diffractométrie of x-rays.

The first diffractometers used a silver film which was impressed by the X-rays. They was sometimes right a tube, a carry-sample and a film holder posed on a table (the dangers of the X-rays were underestimated at the time), sometimes put in a “box”. It bore of this fact the name of “room”, the British speaking about “ camera ”.

## Sources of x-rays

The first source of X-rays was the radioactive decay. This source is still sometimes used in Spectrométrie of x-ray fluorescence, but more in diffraction.

In general, x-rays are produced by braking of the electrons. One in general uses tubes with x-rays, devices of small size (approximately 50  cm length for ten cm of Diameter, more for the tubes with revolving Anode). In the majority of the cases, one modifies the spectrum of the tube in order to approach the conditions Monochromatique S:

• is with a filter of Nickel “to in the case of cut” the Kβ line a tube to the Cuivre;
• is with a Monochromateur (diffracting system selecting the Kα1 line).

The diffractometers are also placed in lines of beam Synchrotron. The radiation Synchrotron makes it possible to have X-rays Monochromatique S and perfectly collimated, which allows very precise measurements. However, a Synchrotron is an installation of several hundred meters of Diamètre and cost of amazing structure, which holds its use with the cases really necessary.

## Room of Laue

The room of Laue is the simplest device to make a stereotype of diffraction, but it is adapted only to the monocrystals.

It consists of a tube of X-rays emitting on a broad spectrum (polychromatic spectrum), a carry-sample, and a photographic film support. The photographic film is masked by a paper in order not to be buckled by the light; x-rays only cross paper and impress film.

The stereotype obtained, called “Stereotyped of Laue”, makes it possible to determine the cell parameters of the Cristal as well as the orientation of the network compared to the analyzed face. It is similar to the stereotype of Diffraction obtained in electronic Microscopie in transmission.

When one wants to make more precise measurements, one uses a diffractometer provided with a Goniomètre with three circles allowing to direct the monocrystal (in general a nanocristal), the film being replaced by a detecting with two dimensions (type camera CCC or room with wire), to see low. One can thus acquire several stereotypes of Laue in an automated way.

## Room of Debye-Scherrer

The room of Debye-Scherrer is the simplest device making it possible to make diffraction on powder or polycrystalline sample.

It is composed of a source Monochromatique of X-rays, of a carry-sample and a film in the shape of band which surrounds the device. X-rays are diffracted in the shape of cones, which leave traces in the shape of circle on the tape.

One sees sometimes the term “camera of Debye-Scherrer”, but it seems that it is an Anglicism, it is used indeed little in French. The term is however correct on the etymological level, the Latin word Camera meaning “room”, and the Analogie with the Caméra of Cinéma is relevant (Darkroom being used to impress a photographic film), although in the case of the X-rays it does not have there a movement.

This device is very simple and inexpensive, but if it makes it possible to locate the position of the peaks easily (ray of the arc of circle on the tape), the photographic trace makes not very precise the estimate of the intensity (level of gray) and the width of the peak (width of the arc).

The other sources of uncertainty are:

• absorption of the sample,
• size the sample, which is limited to ten milligrams, less than one millimetre diameter,
• problems of centering,
• stability of film (for example variations of dimension, withdrawal).

Initially, the examination of the data was made manually, the position of the arcs being located with a rule. The Numérisation of films (with a scanner) allows a data processing of the diffractogram.

One also finds rooms Debye-Scherrer where the film is replaced by a series of detectors placed in arc of circle around the sample, offering a resolution about the hundredth of degree. This device allows a direct acquisition on computer, with a precise measurement of the intensities (many blows received by each detector).

This device was in fact almost systematically replaced by a “mechanized” powder diffractometer (with a mobile specific detector assembled on a goniometer with two circles). These goniometer diffractometers are planned for a Bragg-Brentano geometry, but they can be used in geometry Debye-Scherrer, for example when one has little product: the powder is introduced into a capillary, one works with a parallel beam, and the detector makes the turn of the sample.

## Other rooms

; Room of Guinier

; Room of Gandolfi

; Room of Seeman-Bohlin

## Powder diffractometer

A powder diffractometer is a diffractometer with mobile arms. The first models were driven by cranks, then came the motorized arms; the modern diffractometers are entirely automated and ordered by Ordinateur.

### Assembly with two circles

In the general case, the apparatus has a Goniomètre “with two circles”, i.e. making it possible to vary only two angles: the angle of incidence of the X-rays on the sample γ, and the angle of deviation 2θ. This can be carried out by two assemblies, known as “θ-2θ” (theta-two theta) and “θ-θ” (theta-theta). In both cases, the detector is mobile, it is its position which determines the deviation 2θ; the difference is in the determination of the incidence γ:

• assembly θ-2θ: the tube with x-rays is fixed, the carry-sample is motorized; the tube being the heaviest part, this assembly is simplest from a mechanical point of view;
its name comes owing to the fact that in Bragg-Brentano geometry (see below), the angle which the carry-sample compared to deviation 0 traverses is worth ½·2θ = θ, while the detector traverses an angle 2θ;
• assembly θ-θ (theta-theta): the carry-sample is fixed, the tube is mobile; the advantage of this assembly is that the carry-sample remains horizontal, which prevents the powder from running out and facilitates the assembly of a device around the carry-sample, like a furnace or a controlled atmosphere;
its name comes owing to the fact that in Bragg-Brentano geometry (see below), the tube and the detector each one are located at the angle θ compared to the surface of the sample, on both sides from the perpendicular on this surface.

The diffractometers of this type are most changeable, one can indeed vary the geometry and to make:

• of measurements in rocking (rocking curves) : the angle of deviation remains fixed, only exchange the angle of incidence;
• on an apparatus θ-2θ, the detector is fixed and the carry-sample moves;
• on an apparatus θ-θ, the tube and the detector move together;
• of the Debye-Scherrer type: the carry-sample is a fine tube of glass (a capillary), and the angle of incidence is fixed, only the position of the detector varies (sweeping in 2θ, or 2θ scan ).

### Bragg-Brentano geometry

The geometry of Bragg-Brentano consists in having a focusing approached x-rays (sometimes called “parafocalisation”, in English parafocussing ).

The idea is to light the sample with a divergent beam, which makes it possible to have more intensity than with a fine beam. By doing this, one introduces an angular error, the X-rays not striking the sample with the same angle. This defect is corrected in two manners:

• on the one hand while working with polycrystalline samples (pulverulent or massive) isotropic, i.e. without crystalline Orientation preferential;
• in addition by making sure that the detector is always symmetrical with the tube compared to the sample, i.e. by fixing γ = ½·2θ; thus, the geometry of the circle makes that the rays which converge towards the detector almost underwent all the same deviation.

As it is about a method on powder, one works with a source Monochromatique and a specific detector. One can replace the specific detector by a linear detector or with two dimensions, in order to accelerate measurement. However, one is not strictly any more in Bragg-Brentano geometry, even if the results are similar.

### Other geometries

The powder diffractometers can be used with another geometry that the geometry of Bragg-Brentano.

#### Shaving incidence

Measurements in shaving incidence are done with incidence γ fixes, and while varying 2θ. One in general makes measurements for several values of γ. To prevent that X-rays pass over the sample and directly strike the detector with the weak angles, a fine faiseacu is used and one can place a “knife” (metal screen) above the sample.

The absorption of x-rays depends on the way in the sample (cf Loi of Beer-Lambert). Beyond of a certain distance D traversed, the rays are absorbed too much and almost do not contribute to the signal; this distance D chosen by convention is that giving 90% of the signal.

The incidental ray traverses a distance X 1 being worth E /sin (γ) to reach a depth E , and a distance X 2 being worth E /sin (2θ-γ) to bring out and strike the detector. The layer of Atome S located at a depth E thus contributes significantly to the signal only if

X 1 + X 2 < D
that is to say
$e \ cdot \ left \left(\ frac \left\{1\right\} \left\{\ sin \ gamma\right\} + \ frac \left\{1\right\} \left\{\ sin \left(2 \ theta - \ gamma\right)\right\} \ right\right) < d$.
In the case of a double-layered sample, the angle of incidence γ from which one can detect a peak of the substrate makes it possible to determine the thickness of the layer located above.

#### Measure in rocking

Measurements in rocking or swinging ( rocking curves in English), consist in varying the angle of incidence γ all while maintaining the deviation 2θ constant. Because of defocusing, it is necessary to work with a fine beam. One in general makes several measurements on an interval of γ given, but while varying 2θ between each measurement.

These measurements in general are used to determine the orientation of a épitaxiée layer; for example, in the industry of the semiconductors, one makes grow a crystalline layer on a monocrystal of Silicium. One takes measurements for a beach of 2θ covering a peak of the Substrat and a peak of the layer. The two peaks are maximum for different values of γ, and this gives confusion between the substrate and the layer.

#### Parallel beam

A geometry in parallel beam makes it possible to be freed from the shape of the sample. Indeed, in divergent beam, the surface of the sample must be tangent with the circle of Focalization so that one can make the assumption that all the rays striking the detector undergo the same deviation. If the beam is parallel, then the deviation depends only on the direction of the detector.

One uses for that a diffracting system curved (it is thus not strictly speaking a mirror), and whose curve is an arc of parabola. The center of the tube (the line anti Cathode on which the electrons are projected) is placed at the hearth of this parabola. The alignment of the mirror is undoubtedly the operation which conditions more quality of measurement.

This method was developed per H. Göbel, the diffracting system thus bears the name of “mirror of Göbel” (or “mirror of Goebel”, to see the article Umlaut ).

The mirror of Göbel is useful only with one back monochromator. If not, the technique does not have any advantage.

This system for example is used when one has extremely little matter. The powder is introduced into a capillary (tube of very fine glass), and one carries out a sweeping with the detector (it is in fact to some extent the method of Debye-Scherrer but with an electronic detector instead of a photographic film). The parallel beam can also be used for a measurement on a part nonplane (curve, rough), to see for a nondestroying measurement (one places a whole part, for example an objet d'art, in the apparatus).

The mirror is multi-layer of synthesis. The principal limitation of its lifespan is the Oxydation layers, in particular by the Ozone which the high voltage of the tube can produce. To avoid this, the mirrors of Göbel are under inert atmosphere, in a case provided with transparent windows to the X-rays.

### Optics

In the Bragg-Brentano configuration, the X-rays have a radial divergence, the configuration allowing approximate focusing. It is thus a rectangular band of the sample which is enlightened. The radial divergence is limited by a rectangular slit located between the tube and the sample, called “primary slit”, “front slit” or “slit of divergence”. Another slit is in front of the detector, it limits the volume which the detector at the only irradiated zone of the sample “sees”; this slit carries the name of “secondary slit”, “back slit” or “slit anti-diffusion”. These slits determine the intensity which reaches the detector as well as the background noise.

X-rays also have an axial divergence. One in general tries to limit this axial divergence by “slits of Soller”, sometimes called “collimators”: they are parallel blades of Cuivre, which absorb the rays which are not parallel to the blades. The divergence is limited to a few degrees (in general, between 0,1 and 5°). The narrower the divergence is, the more the peaks of Diffraction are narrow, but more the intensity is low. Without slit of Soller, there are broad and dissymmetrical peaks.

### Carry-sample

In the simplest case, the carry-sample is a simple passive part either fixes (assembly θ-θ), or motorized (assembly θ-2θ). It in general makes it possible to make turn the sample in its plan (spinner) ; indeed, as only a small portion of the sample is enlightened (a narrow rectangle), the fact of making turn the sample allows to sweep a disc, the collected signal thus represents more a large surface of sample. This makes it possible to include more Cristallite S, and thus to have a better statistical representation.

The carry-sample can also be a frontier runner: several samples are charged, and those are measured successively, which makes it possible to measure several samples without needing to intervene to change them (for example measurement of night). In certain cases, the frontier runner is distinct from the carry-sample, it brings the sample to the carry-sample; one can for example have a measurement automated with a sample coming from a line production by a conveyer band.

For certain measurements, in particular of forced texture or , it is necessary to vary the position of the sample under the beam (the beam is then specific). One uses for that a Goniomètre with three circles or “cradle of Euler”:

• swinging of the sample (rocking) Ω (or θ when one is in Bragg-Brentano geometry);
• slope (tilt) χ or ψ (the difference being reference 0);
• rotation in the plan (spin) φ.
With this is added the position 2θ detector, one thus speaks about “assembly with four circles”.

The carry-sample can also vary the position of the sample sleon the axes X , there and/or Z .

## Diffractometer of monocrystal

Equipment comprises a Goniomètre to handle the monocrystal in the beam of x-rays from every angle (assembly with four circles). The purpose of the rotation of the Cristal in the diffractometer is to generate a wave resulting from the reticular plans in phase with the incidental wave in this same reticular plan.

This technique is in general used to determine the crystalline structure.

### Reception of the signal

It is done on the CCC which is a matrix of cells which collect luminous information in the form of Pixel S and which does not use a photographic plate. Isolated photons are recorded electronically and distributed using a Microprocesseur along a series of pixels which, assembled in lines, then form an image which can be numerically worked by Ordinateur.

## See too

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