X-Ray Diffraction Analysis & Crystallite

X-ray Generation & Properties

X-rays are electromagnetic radiation with typical photon energies in the range of 100 eV - 100 keV. For diffraction applications, only short wavelength x-rays (hard x-rays) in the range of a few angstroms to 0.1 angstrom (1 keV - 120 keV) are used. Because the wavelength of x-rays is comparable to the size of atoms, they are ideally suited for probing the structural arrangement of atoms and molecules in a wide range of materials. The energetic x-rays can penetrate deeper into the materials and provide information about the bulk structure.

X-rays are produced generally by either x-ray tubes or synchrotron radiation. In a x-ray tube, which is the primary x-ray source used in laboratory x-ray instruments, x-rays are generated when a focused electron beam accelerated across a high voltage field bombards a stationary or rotating solid target. As electrons collide with atoms in the target and slow down, a continuous spectrum of x-rays are emitted, which are termed Bremsstrahlung radiation. The high energy electrons also eject inner shell electrons in atoms through the ionization process. When a free electron fills the shell, a x-ray photon with energy characteristic of the target material is emitted. Common targets used in x-ray tubes include Cu and Mo, which emit 8 keV and 14 keV x-rays with corresponding wavelengths of 1.54 Å and 0.8 Å, respectively. (The energy E of a x-ray photon and it's wavelength is related by the equation E = hc/λ, where h is Planck's constant and c the speed of light).

Lattice Planes and Bragg's Law

X-rays primarily interact with electrons in atoms. When x-ray photons collide with electrons, some photons from the incident beam will be deflected away from the direction where they original travel, much like billiard balls bouncing off one anther. If the wavelength of these scattered x-rays did not change (meaning that x-ray photons did not lose any energy), the process is called elastic scattering (Thompson Scattering) in that only momentum has been transferred in the scattering process. These are the x-rays that we measure in diffraction experiments, as the scattered x-rays carry information about the electron distribution in materials. On the other hand, In the inelastic scattering process (Compton Scattering), x-rays transfer some of their energy to the electrons and the scattered x-rays will have different wavelength than the incident x-rays. Diffracted waves from different atoms can interfere with each other and the resultant intensity distribution is strongly modulated by this interaction. If the atoms are arranged in a periodic fashion, as in crystals, the diffracted waves will consist of sharp interference maxima (peaks) with the same symmetry as in the distribution of atoms. Measuring the diffraction pattern therefore allows us to deduce the distribution of atoms in a material.

X-rays scattered from the periodic repeating electron density of a perfectly crystalline material give sharp diffraction peaks at angles that satisfy the Bragg relation, whether the crystal consists of atoms, ions, small molecules, or large molecules. Amorphous materials will also diffract X-rays and electron, but the diffraction is a much more diffuse, low frequency halo (the so called “amorphous halo”). Analysis of the diffraction peaks from amorphous materials leads to information about the statistical arrangement of atoms in the neighborhood of another atom.

Figure : X-rays interact with the atoms in a crystal [1].

In polymers, which are never perfectly crystalline, a superposition of both diffuse and sharp scattering occurs. First, the crystals present in polymers are very small in size. This leads to considerable broadening of the peaks as compared with fully crystalline materials. Second, there exists some fraction of noncrystalline region in even the most highly crystalline polymer [2, 3, 4].

Bragg’s law

When X-rays are scattered from a crystal lattice, observed peaks of scattered intensity, which correspond to the angle of incidence, should be equal to angle of scattering while the path length difference is equal to an integer number of wavelengths (see figure 1). Bragg derived Bragg’s law for the distance d between consecutive identical planes of atoms in the crystal:

nλ = 2d sin Ө

Where λ is the x-ray wavelength, Ө is the angle between the x-ray beam and these atomic planes and n corresponds to the order of diffraction.  The condition for maximum intensity contained in Bragg's law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal [3, 5].

Crystallite size

It is important to realize that crystallite size can be obtained via a simple approach from peak’s full width at half maximum (FWHM) measurement by using the Debye-Scherrer equation [6].

Where :

• β is FWHM (in radians),
• λ is the x-ray wavelength, and
• Ө is the peak position in degree.

References :

1. http://en.wikipedia.org/wiki/Bragg's_law
2. Sperling, L. H., “An Introduction to Physical Polymer Science”, John Wiley and Sons, Inc., 2001, 3rd Ed.
3. Bradly, R. F., Jr., “Comprehensive Desk Reference of Polymer Characterization and Analysis”, American Chemical Society, Washington, D.C., 2003.   
4. Surman, D., “Percentage Crystallinity Determination by X-Ray Diffraction”,   http://www.kratos.com/XRD/Apps/pcent.html.
5. Alexander, “X-ray Diffraction Methods in Polymer Science”, Wiley, Interscience, New York, 1969.
6. Cullity, B. D., “Elements of X-ray Diffraction.” Prentice Hall, 2001, 3rd Ed.

Teori Dasar X-Ray Diffraction (XRD)

Proses analisis menggunakan X-ray diffraction (XRD) merupakan salah satu metoda  karakterisasi material yang paling tua dan paling sering digunakan hingga sekarang. Teknik ini digunakan untuk mengidentifikasi fasa kristalin dalam material dengan cara menentukan parameter struktur kisi serta untuk mendapatkan ukuran partikel. Sinar X merupakan radiasi elektromagnetik yang memiliki energi tinggi sekitar 200 eV sampai 1 MeV. Sinar X dihasilkan oleh interaksi antara berkas elektron eksternal dengan elektron pada kulit atom. Spektrum sinar X memilki panjang gelombang 10^-10  s/d 5^-10 nm, berfrekuensi 1017-1020 Hz dan memiliki energi 103-106 eV. Panjang gelombang sinar X memiliki orde yang sama dengan jarak antar atom sehingga dapat digunakan sebagai sumber difraksi kristal. SinarX dihasilkan dari tumbukan elektron berkecepatan tinggi dengan logam sasaran. Olehk arena itu, suatu tabung sinar X harus mempunyai suatu sumber elektron, voltase tinggi, dan logam sasaran. Selanjutnya elektron elektron yang ditumbukan ini mengalami pengurangan kecepatan dengan cepat dan energinya diubah menjadi foton.

Sinar X ditemukan pertama kali oleh Wilhelm Conrad Rontgen pada tahun 1895, di Universitas Wurtzburg, Jerman. Karena asalnya tidak diketahui waktu itu maka disebut sinar X. Untuk penemuan ini Rontgen mendapat hadiah nobel pada tahun 1901, yang merupakan hadiah nobel pertama di bidang fisika. Sejak ditemukannya, sinar-X telah umum digunakan untuk tujuan pemeriksaan tidak merusak pada material maupun manusia. Disamping itu, sinar-X dapat juga digunakan untuk menghasilkan pola difraksi tertentu yang dapat digunakan dalam analisis kualitatif dan kuantitatif material. Pengujian dengan menggunakan sinar X disebut dengan pengujian XRD (X-Ray Diffraction).

XRD digunakan untuk analisis komposisi fasa atau senyawa pada material dan juga karakterisasi kristal. Prinsip dasar XRD adalah mendifraksi cahaya yang melalui celah kristal. Difraksi cahaya oleh kisi-kisi atau kristal ini dapat terjadi apabila difraksi tersebut berasal dari radius yang memiliki panjang gelombang yang setara dengan jarak antar atom, yaitu sekitar 1 Angstrom. Radiasi yang digunakan berupa radiasi sinar-X, elektron, dan neutron. Sinar-X merupakan foton dengan energi tinggi yang memiliki panjang gelombang berkisar antara 0.5 sampai 2.5 Angstrom. Ketika berkas sinar-X berinteraksi dengan suatu material, maka sebagian berkas akan diabsorbsi, ditransmisikan, dan sebagian lagi dihamburkan terdifraksi. Hamburan terdifraksi inilah yang dideteksi oleh XRD. Berkas sinar X yang dihamburkan tersebut ada yang saling menghilangkan karena fasanya berbeda dan ada juga yang saling menguatkan karena fasanya sama. Berkas sinar X yang saling menguatkan itulah yang disebut sebagai berkas difraksi. Hukum Bragg merumuskan tentang persyaratan yang harus dipenuhi agar berkas sinar X yang dihamburkan tersebut merupakan berkas difraksi. Ilustrasi difraksi sinar-X pada XRD dapat dilihat pada Gambar 1 dan Gambar 2.

Gambar 1 : Ilustrasi difraksi sinar-X pada XRD [1]

Gambar 2 : Ilustrasi difraksi sinar-X pada XRD [2]

Dari Gambar 2 dapat dideskripsikan sebagai berikut. Sinar datang yang menumbuk pada titik pada bidang pertama dan dihamburkan oleh atom P. Sinar datang yang kedua menumbuk bidang berikutnya dan dihamburkan oleh atom Q, sinar ini menempuh jarak SQ + QT bila dua sinar tersebut paralel dan satu fasa (saling menguatkan). Jarak tempuh ini merupakan kelipatan (n) panjang gelombang (λ), sehingga persamaan menjadi :

Persamaan diatas dikenal juga sebagai Bragg’s law, dimana, berdasarkan persamaan diatas, maka kita dapat mengetahui panjang gelombang sinar X (λ) dan sudut datang pada bidang kisi (θ), maka dengan ita kita akan dapat mengestimasi jarak antara dua bidang planar kristal (d001). Skema alat uji XRD dapat dilihat pada Gamnbar 3 dibawah ini.

Gambar 3: Skema alat uji XRD [3]

Dari metode difraksi kita dapat mengetahui secara langsung mengenai jarak rata-rata antar bidang atom. Kemudian kita juga dapat menentukan orientasi dari kristal tunggal. Secara langsung mendeteksi struktur kristal dari suatu material yang belum diketahui komposisinya. Kemudian secara tidak langsung mengukur ukuran, bentuk dan internal stres dari suatu kristal. Prinsip dari difraksi terjadi sebagai akibat dari pantulan elastis yang terjadi ketika sebuah sinar berinteraksi dengan sebuah target. Pantulan yang tidak terjadi kehilangan energi disebut pantulan elastis (elastic scatering). Ada dua karakteristik utama dari difraksi yaitu geometri dan intensitas. Geometri dari difraksi secara sederhana dijelaskan oleh Bragg’s Law (Lihat persamaan 2). Misalkan ada dua pantulan sinar α dan β. Secara matematis sinar β tertinggal dari sinar α sejauh SQ+QT yang sama dengan 2d sin θ secara geometris. Agar dua sinar ini dalam fasa yang sama maka jarak ini harus berupa kelipatan bilangan bulat dari panjang gelombang sinar λ. Maka didapatkanlah Hukum Bragg: 2d sin θ = nλ. Secara matematis, difraksi hanya terjadi ketika Hukum Bragg dipenuhi. Secara fisis jika kita mengetahui panjang gelombang dari sinar yang membentur kemudian kita bisa mengontrol sudut dari benturan maka kita bisa menentukan jarak antar atom (geometri dari latis). Persamaan ini adalah persamaan utama dalam difraksi. Secara praktis sebenarnya nilai n pada persamaan Bragg diatas nilainya 1. Sehingga cukup dengan persamaan 2d sin θ = λ . Dengan menghitung d dari rumus Bragg serta mengetahui nilai h, k, l dari masing-masing nilai d, dengan rumus-rumus yang telah ditentukan tiap-tiap bidang kristal kita bisa menentukan latis parameter (a, b dan c) sesuai dengan bentuk kristalnya.

Estimasi Crystallite Size dan Strain Menggunakan XRD

Elektron dan Neutron memiliki panjang gelombang yang sebanding dengan dimensi atomik sehingga radiasi sinar X dapat digunakan untuk menginvestigasi material kristalin. Teknik difraksi memanfaatkan radiasi yang terpantul dari berbagai sumber seperti atom dan kelompok atom dalam kristal. Ada beberapa macam difraksi yang dipakai dalam studi material yaitu: difraksi sinar X, difraksi neutron dan difraksi elektron. Namun yang sekarang umum dipakai adalah difraksi sinar X dan elektron. Metode yang sering digunakan untuk menganalisa struktur kristal adalah metode Scherrer. Ukuran kristallin ditentukan berdasarkan pelebaran puncak difraksi sinar X yang muncul. Metode ini sebenarnya memprediksi ukuran kristallin dalam material, bukan ukuran partikel. Jika satu partikel mengandung sejumlah kritallites yang kecil-kecil maka informasi yang diberikan metiode Schrerrer adalah ukuran kristallin tersebut, bukan ukuran partikel. Untuk partikel berukuran nanometer, biasanya satu partikel hanya mengandung satu kristallites. Dengan demikian, ukuran kristallinitas yang diprediksi dengan metode Schreer juga merupakan ukuran partikel. Berdasarkan metode ini, makin kecil ukuran kristallites maka makin lebar puncak difraksi yang dihasilkan, seperti diilustrasikan pada Gambar 4. Kristal yang berukuran besar dengan satu orientasi menghasilkan puncak difraksi yang mendekati sebuah garis vertikal. Kristallites yang sangat kecil menghasilkan puncak difraksi yang sangat lebar. Lebar puncak difraksi tersebut memberikan informasi tentang ukuran kristallites. Hubungan antara ukuran ksirtallites dengan lebar puncal difraksi sinar X dapat diproksimasi dengan persamaan Schrerer [5-9].

Gambar 4 : XRD Peaks [4]

Gambar 4 mengindikasikan bahwa makin lebar puncak difraksi sinar X maka semakin kecil ukuran kristallites. Ukuran kristallites yangmenghasilkan pola difraksi pada gambar bawah lebih kecil dari pada ukuran kristallites yang menghasilkan pola diffraksi atas. Puncak diffraksi dihasilkan oleh interferensi secara kontrukstif cahaya yang dipantulkan oleh bidang-bidang kristal. Hubungan antara ukuran ksirtallites dengan lebar puncal difraksi sinar X dapat diproksimasi dengan persamaan Schrerer [5-7].

Scherrer Formula

Dimana :

• Crystallite size (satuan: nm) dinotasikan dengan symbol (D)
•  FWHM (Line broadening at half the maximum intensity), Nilai yang dipakai adalah nilai FWHM setelah dikurangi oleh “the instrumental line broadening” (satuan: radian) dinotasikan dengan symbol (B)
•  Bragg’s Angle dinotasikan dengan symbol (θ)
• X-Ray wave length dinotasikan dengan symbol (λ)
• K  Adalah nilai konstantata “Shape Factor” (0.8-1) dinotasikan dengan symbol (K)

Perlu diingan disini adalah: Untuk memperoleh hasil estimasi ukuran kristal dengan lebih akurat maka, nilai FWHM harus dikoreksi oleh "Instrumental Line Broadening" berdasarkan persamaan berikut [4-9].

Dimana :

FWHM_sample adalah lebar puncak difraksi puncak pada setengah maksimum dari sampel benda uji dan FWHM_standard adalah lebar puncak difraksi material standard yang sangat besar puncaknya berada di sekitar lokasi puncak sample yang akan kita hitung.

Contoh Estimasi Crystallite size menggunakan X-Ray Diffraction Analysis

Gambar 5: Penulis sedang melakukan sampel analisis menggunakan XRD Bruker 8 Advance 

Setelah data hasil uji sampel menggunakan XRD diperoleh, Data hasil analisa yang diperoleh tersimpan dalam format RAW.data, yang kemudian data tersebut dianalisa menggunakan Software EVA, data hasil uji sampel yang diperoleh adalah berupa peak seperti gambar dibawah ini.

Gambar 6: XRD Peak untuk sampel Fe powder  yang diuji penulis.

Sekilas Tentang Struktur Atom Suatu Unsur

Setiap atom terdiri dari inti yang sangat kecil yang terdiri dari proton dan neutron, dan di kelilingi oleh elektron yang bergerak. Elektron dan proton mempunyai muatan listrik yang besarnya 1,60 x 10^-19 C dengan tanda negatif untuk elektron dan positif untuk proton sedangkan neutron tidak bermuatan listrik. Massa partikel-partikel subatom ini sangat kecil: proton dan neutron mempunyai massa kira-kira sama yaitu 1,67 x 10^-27 kg, dan lebih besar dari elektron yang massanya 9,11 x 10^-31 kg. Setiap unsur kimia dibedakan oleh jumlah proton di dalam inti, atau nomor atom (Z). Untuk atom yang bermuatan listrik netral atau atom yang lengkap, nomor atom adalah sama dengan jumlah elektron. Nomor atom merupakan bilangan bulat dan mempunyai jangkauan dari 1 untuk hidrogen hingga 94 untuk plutonium yang merupakan nomor atom yang paling tinggi untuk unsur yang terbentuk secara alami. Massa atom (A) dari sebuah atom tertentu bisa dinyatakan sebagai jumlah massa proton dan neutron di dalam inti. Walaupun jumlah proton sama untuk semua atom pada sebuah unsur tertentu, namun jumlah neutron (N) bisa bervariasi. Karena itu atom dari sebuah unsur bisa mempunyai dua atau lebih massa atom yang disebut isotop. Berat atom berkaitan dengan berat rata-rata massa atom dari isotop yang terjadi secara alami. Satuan massa atom (sma) bisa digunakan untuk perhitungan berat atom. Suatu skala sudah ditentukan dimana 1 sma didefinisikan sebagai 1/12 massa atom dari isotop karbon yang paling umum, karbon 12 (12 C) (A = 12,00000). Dengan teori tersebut, massa proton dan neutron sedikit lebih besar dari satu, dan,

A ≅ Z + N

Berat atom dari unsur atau berat molekul dari senyawa bisa dijelaskan berdasarkan sma per atom (molekul) atau massa per mol material. Satu mol zat terdiri dari 6,023 x 10²³ atom atau molekul (bilangan Avogadro). Kedua teori berat atom ini dikaitkan dengan persamaan berikut: 1 sma/atom (molekul) = 1 g/mol Sebagai contoh, berat atom besi adalah 55,85 sma/atom, atau 55,85 g/mol. Kadang-kadang penggunaan sma per atom atau molekul lebih disukai; pada kesempatan lain g/mol (atau kg/mol) juga digunakan.

Referensi :

1. www.terrachem.de
2. Callister,Jr, W.D., Rethwisch, D.G,. “Materials Science and Engineering An Introduction 8^Th”, John Wiley & Sons, Inc. 2009.
3. Saryanto, H., "High Temperature Oxidation Behavior of  Fe80Cr20 Alloys Implanted with Lanthanum and Titanium Dopant" Master Thesis, Universiti Tun Hussein Onn Malaysia, Malaysia, 2011.
4. Abdullah, M & Khairurrijal,. "Review: Karakterisasi Nanomaterial" J. Nano Saintek. Vol. 2 No. 1, Feb. 2009.
5. Abdullah, M., Isakndar, F., Okuyama, K. and Shi, F.G,. “ J. Appl. Phys. 89, 6431, 2001.
6.  Abdullah, M. dan Khairurrijal, Nano Saintek. 1, 28. 2008.
7.  Itoh, Y. Abdullah, M and Okuyama, K,.  J. Mater. Res. 19, 1077, 2004.
8. P. Scherrer, “Bestimmung der Grösse und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen,” Nachr. Ges. Wiss. Göttingen 26 (1918) pp 98-100.
9. J.I. Langford and A.J.C. Wilson, “Scherrer after Sixty Years: A Survey and Some New Results in the Determination of Crystallite Size,” J. Appl. Cryst. 11 (1978) pp 102-113.

X-Ray Difraction Analysis

General Description

X-ray Diffraction (XRD) is a high-tech, non-destructive technique for analyzing a wide range of materials, including fluids, metals, minerals, polymers, catalysts, plastic, pharmaceuticals, thin film coatings, ceramics, solar cells, and semi conductors.  Throughout industry and research institutions, XRD has become an indispensable method for materials investigation, characterization and quality control. Example areas of application include qualitative and quantitative phase analysis, crystallography, structure and relaxation determination, texture and residual stress investigations, controlled sample environment, micro-diffraction, nano-materials, lab- and process automation, and high-throughput polymorph screening.

About 95% of all solid materials can be described as crystalline. When X-rays interact with a crystalline substance (Phase), one gets a diffraction pattern.

In 1919 A.W.Hull gave a paper titled, “A New Method of Chemical Analysis”. Here he pointed out that “….every crystalline substance gives a pattern; the same substance always gives the same pattern; and in a mixture of substances each produces its pattern independently of the others. “

The X-ray diffraction pattern of a pure substance is, therefore, like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases.

Today about 50,000 inorganic and 25,000 organic single components, crystalline phases, and diffraction patterns have been collected and stored on magnetic or optical media as standards. The main use of powder diffraction is to identify components in a sample by a search/match procedure. Furthermore, the areas under the peak are related to the amount of each phase present in the sample.

THEORETICAL CONSIDERATIONS

In order to better convey an understanding of the fundamental principles and buzz words of X-ray diffraction instruments, let us quickly look at the theory behind these systems. (The theoretical considerations are rather primitive; hopefully they are not too insulting).

Solid matter can be described as:

Amorphous:

The atoms are arranged in a random way similar to the disorder we find in a liquid.

Glasses are amorphous materials.

Crystalline: 

The atoms are arranged in a regular pattern, and there is as smallest volume element that by repetition in three dimensions describes the crystal. E.g. we can describe a brick wall by the shape and orientation of a single brick. This smallest volume element is called a unit cell. The dimensions of the unit cell are described by three axes:

When a crystal is bombarded with X-rays of a fixed wavelength (similar to spacing of the atomic-scale crystal lattice planes) and at certain incident angles, intense reflected X-rays are produced when the wavelengths of the scattered X-rays interfere constructively. In order for the waves to interfere constructively, the differences in the travel path must be equal to integer multiples of the wavelength. When this constructive interference occurs, a diffracted beam of X-rays will leave the crystal at an angle equal to that of the incident beam.

To illustrate this feature, consider a crystal with crystal lattice planar distances d (right). Where the travel path length difference between the ray paths ABC and A'B'C' is an integer multiple of the wavelength, constructive interference will occur for a combination of that specific wavelength, crystal lattice planar spacing and angle of incidence θ. Each rational plane of atoms in a crystal will undergo refraction at a single, unique angle (for X-rays of a fixed wavelength).

Bragg's Law reflection. The diffracted X-rays exhibit constructive interference when the distance between paths ABC and A'B'C' differs by an integer number of wavelengths (λ).

The general relationship between the wavelength of the incident X-rays, angle of incidence and spacing between the crystal lattice planes of atoms is known as Bragg's Law, expressed as:

n λ = 2d sin θ

where n (an integer) is the "order" of reflection, λ is the wavelength of the incident X-rays, d is the interplanar spacing of the crystal and θ is the angle of incidence.

The X-ray Powder Method

In practice, this would be a time consuming operation to reorient the crystal, measure the angle q, and determine the d-spacing for all atomic planes.  A faster way is to use a method called the powder method.  In this method, a mineral is ground up to a fine powder.  In the powder, are thousands of grains that have random orientations.  With random orientations we might expect most of the different atomic planes to lie parallel to the surface in some of the grains.  Thus, by scanning through an angle q of incident X-ray beams form 0 to 90^o, we would expect to find all angles where diffraction has occurred, and each of these angles would be associated with a different atomic spacing.

The instrument used to do this is an x-ray powder diffractometer.  It consists of an X-ray tube capable of producing a beam of monochromatic X-rays that can be rotated to produce angles from 0 to 90^o.  A powdered mineral sample is placed on a sample stage so that it can be irradiated by the X-ray tube.  To detect the diffracted X-rays, an electronic detector is placed on the other side of the sample from the X-ray tube, and it too is allowed to rotate to produce angles from 0 to 90^o. 

Reference of Figure: http://www.xos.com/techniques/xrd/parallel-beam-geometryfor-powder-x-ray-diffraction/

The instrument used to rotate both the X-ray tube and the detector is called a goniometer.  The goniometer keeps track of the angle q, and sends this information to a computer, while the detector records the rate of X-rays coming out the other side of the sample (in units of counts/sec)  and sends this information to the computer.

After a scan of the sample the X-ray intensity can be plotted against the angle q (usually reported as 2θ because of the way older diffractometers were made) to produce a chart, like the one shown here.  The angle 2θ for each diffraction peak can then be converted to d-spacing, using the Bragg equation.

One can then work out the crystal structure and associate each of the diffraction peaks with a different atomic plane in terms of the Miller Index for that plane (hkl).

A group known as the Joint Committee on Powder Diffraction Standards (JCPDS) has collected data such as this on thousands of crystalline substances.  This data can be obtained as the JCPDS Powder Diffraction File.  Since every compound with the same crystal structure will produce an identical powder diffraction pattern, the pattern serves as kind of a "fingerprint" for the substance, and thus comparing an unknown mineral to those in the Powder Diffraction file enables easy identification of the unknown.  We will see how this is done in our laboratory demonstration.

Types of XRD Analysis

Phase Analysis

• Airborne particulate analysis and estimation including quartz,  cristobolite, vanadium and zinc Oxide analysis as per OSHA  standards

• Detailed soil and clay mineral analysis

• Crystalline/Amorphous ratio-Percent Crystallinity in polymers and ceramic materials

• Structural characterization and analysis of catalysts and chemicals

• Analysis of corrosion products

• Corrosion and Materials failure analysis

Quantitative Analysis

• Accurate phase quantification by Rietveld Method

• External and Internal standard methods.

Rietveld Analysis

• Accurate quantitative analysis by whole pattern fitting least squares technique

• Accurate lattice parameter determination

• Line broadening analysis (Crystallite size determination Microstrain determination)

Retained Austenite Determination

• The Rietveld method will be used to quantify the amounts of Austenite in stainless steel.

Thin Film Analysis

• Low angle glancing incidence technique for extremely thin films

• Thickness determination

• Determination of preferred orientation

Case studies

Using X-Ray diffraction BRUKER D8 couple with EVA software analysis

  

Qualitative analysis

Qualitative analysis usually involves the identification of a phase or phases in a specimen by comparison with “standard” patterns (PDF-Data Base), and relative estimation of proportions of different phases in multiphase specimens by comparing peak intensities attributed to the identified phases.

• Go ‘START’ menu and ‘click’ or open ‘EVA’ software 

• EVA window will be on display. Import spectra file through ‘Import’ menu in ‘File’ tab. Then select ‘Scan File’.or You can import file by ‘Import’ tab at toolbar. ‘Import Scan Files’ window will be displayed.

• Select your scan file (*.RAW)

Note: A "scan" is the diffractogram, i.e. the measured data set, which is the result of intensity collection with a powder diffractometer; it is stored in a file with the extension .RAW. Note that EVA imports the data, i.e. it works with a copy of the data, the original RAW file is never changed, so you can always come back to the beginning.

• A ‘diifractograph’ of your scanned data will appear on the ‘doc’ window. As example, this is the spectra of pure Fe powder. Let’s make a qualitative study first to identify whether this scanned material is a pure Fe or not.

• We need to match the pattern of difrractograph with reference pattern.Go to ‘Toolbox’ tab or ‘search/menu’ in ‘View’ tab.

• oWe need to match the pattern of difrractograph with reference pattern (ICDD-PDF-2 Data Base). Go to ‘search/match’ tab or push ‘F3’ or ‘search/menu’ in ‘View’ tab.

• You need to set ‘chemical filter’ and ‘quality mark’ according to your preference.

The result was clearly identify as Chromium-Iron with PDF No: 03-065-7775


Quantitative analysis

Quantitative analysis of diffraction data usually refers to the determination of amounts of different phases in multi-phase samples.  Quantitative analysis may also be thought of in terms of the determination of particular characteristics of single phases including precise determination of crystal structure or crystallite size and shape.

Measuring crystallite size using Williamson-Hall plott

Powder diffraction techniques have a wide variety of applications in compositional, structural, microstructural and many other areas.  The ease in data collection makes its application to the microstructure of nano materials an obvious choice.  In the study of nanomaterials the crystallite size is usually the sole factor of interest.  The broadening of reflections in a powder diffraction pattern contains much information, such as crystallite strain, shape and stacking faults, which are often not considered.   Nano materials even have their own unique problems, such as multiply twinned particle phenomena in metal nanoparticles.  The extensive peak broadening and possible overlap exhibited by nanomaterials can even make determining phase purity a non-trivial process, and misidentification of a two-phase system as being single-phase could lead to some very misleading results.  Visual inspection is often insufficient where closely related phases can co-exist, e.g. in solid solution series.  Full-pattern profile fitting techniques such as Rietveld analysis can assist greatly in gauging sample purity.
The first description of size broadening was given by Scherrer in 1918, although the first rigorous theory of line broadening was formulated in 1944. Williamson-Hall size-strain analysis was developed in 1953 as a method to separate size and strain effects by their angular dependence.

B.1      Size broadening

Sherrer (1918) first observed that small crystallite size could give rise to line broadening. He drived a well known equation for relating the crystallite size to the broadening, which is called the scherrer formula(Shecerrer, 1918; Langford & Wilson, 1978).

                                                                                                                 (B.1)

D         = Volume weighted crystallite size

K         = Scherrer constant, some what arbitrary value that falls in the range 0.87-1.0

λ           = The wav e lenght of the radiation

B         = The integral breadth or FWHM of reflection peaks (in radians) located at 2θ

B.2      Strain broadening

Stokes and Wilson (1944), they included the lattice strain as another source of broadening, than broadening that arises from small crystallite size (Langford & Wilson, 1978).

                                                                                                         (B.2)

ε_strain     = Weighted average strain

B         = The integral breadth or FWHM of reflection peaks (in radians) located at 2θ

B.3      Williamson-Hall analysis

The diffraction pattern gradually broadens with milling duration and the broadening is due to simultaneous size and strain effects. High-energy ball-milling introduces considerable strain in the lattice and its contribution to line broadening is not negligible. Williamson and Hall (Williamson, 1953) developed a method to separate these two effects and that is known as the Williamson–Hall plot. The Williamson-Hall equation is given by:

B_corrected cosθ     =   +                                                                (B.3)

where B_corrected is full width at half maximum (FWHM_corrected) of the XRD peak, K is the Scherrer constant, D is the crystallite size, λ is the X-ray wavelength, ε is the lattice strain and θ is the Bragg angle.

B.3      Correcting for instrumental effects

Before estimating the crystallite size and lattice strain, it is necessary to correct the instrumental effect.  To decouple these contributions, it is necessary to collect a diffraction pattern from the line broadening of a standard material such as Si (Silicon) and LaB₆ (lanthanum hexaboride) (Zak et al., 2011; He, 2009; Mittemeijer & Welzel, 2008), to determine the instrumental broadening.  The instrument-corrected broadening (B) corresponding to the diffraction peak of specimen was estimated using the relation Gaussian profiles (Saryanto et al., 2010; Raman &Gupta, 2009; He, 2009; Venkateswarlu & Rameshbabu, 2010):

B_corrected  =  B²_obs – B²_instrument                                                                         (B.4)

where B is the instrumental corrected full width at half maximum (FWHM) in radians, B_observed is full width at half maximum (FWHM) from diffraction peaks of specimens and B_inst is standard peaks of the standard reference materials (LaB₆: NIST SRM 660a), as shown in Figure B.1.