XRD Analysis of Some Minerals

We propose in this Post the XRD analysis of some natural crystals and compunds.
Online reference: RRUFF

Fluorite

Fluorite (also called fluorspar) is the mineral form of calcium fluoride, CaF₂. It belongs to the halide minerals. It crystallizes in isometric cubic habit, although octahedral and more complex isometric forms are not uncommon.
Fluorite crystallizes in a cubic motif. Crystal twinning is common and adds complexity to the observed crystal habits. Fluorite has four perfect cleavage planes that help produce octahedral fragments. Cleavage perfect on plane {111}.
The images below show a sample of fluorite – obtained from cleavage – placed in the diffractometer, and the result of the XRD scan.

For the Bragg reflection of fluorite we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
111	28.5	0.313

The interplanar distance obtained corresponds to the exact value which results to be 0.314 nm. Fluorite has a fcc cubic structure with the unit cell side which is a = 0.545 nm.

Galena

Galena, also called lead glance, is the natural mineral form of lead(II) sulfide (PbS). It is the most important ore of lead and an important source of silver.
Galena is one of the most abundant and widely distributed sulfide minerals. It crystallizes in the cubic crystal system often showing octahedral forms. It is often associated with the minerals sphalerite, calcite and fluorite. Perfect cleavage on plane {100}.

For the Bragg reflection of galena we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
200	29.83	0.300
400	62.67	0.297

The interplanar distance obtained corresponds to the exact value which results to be 0.297 nm. Galena has a cubic structure with the unit cell side which is a = 0.594 nm.

Gypsum

Gypsum is a soft sulfate mineral composed of calcium sulfate dihydrate, with the chemical formula CaSO₄·2H₂O. Gypsum occurs in nature as flattened and often twinned crystals, and transparent, cleavable masses called selenite. Selenite contains no significant selenium; rather, both substances were named for the ancient Greek word for the Moon. Perfect cleavage on plane {010}.

For the Bragg reflections of gypsum we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
020	11.67	0.758
040	23.5	0.757

The interplanar distance obtained corresponds to the exact value which results to be 0.760 nm. Gypsum has a monoclinic structure.

Pollucite

Pollucite is a zeolite mineral with the formula (Cs,Na)₂Al₂Si₄O₁₂·2H₂O with iron, calcium, rubidium and potassium as common substituting elements. It is important as a significant ore of caesium and sometimes rubidium. It forms a solid solution series with analcime. It crystallizes in the isometric – hexoctahedral crystal system as colorless, white, gray, or rarely pink and blue masses. Well formed crystals are rare. It has a Mohs hardness of 6.5 and a specific gravity of 2.9. It has a brittle fracture and no cleavage.
The image above shows the crystalline structure of pollucite.

For the Bragg reflection of pollucite we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
400	27.33	0.326

The interplanar distance obtained in in agreement to the exact value which results to be 0.342 nm.

Pyrite

The mineral pyrite, or iron pyrite, also known as fool’s gold, is an iron sulfide with the chemical formula FeS₂ (iron(II) disulfide). Pyrite is considered the most common of the sulfide minerals. Iron-pyrite FeS₂ represents the prototype compound of the crystallographic pyrite structure. The structure is simple cubic and was among the first crystal structures solved by X-ray diffraction. The unit cell is composed of a Fe face-centered cubic sublattice into which the S ions are embedded. The pyrite structure is also used by other compounds MX₂ of transition metals M and chalcogens X = O, S, Se and Te. Also certain dipnictides with X standing for P, As and Sb etc. are known to adopt the pyrite structure

For the Bragg reflection of pyrite we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
200	33	0.271

The interplanar distance obtained in in agreement to the exact value which results to be 0.271 nm.

Halite

Halite commonly known as rock salt, is a type of salt, the mineral (natural) form of sodium chloride (NaCl). Halite forms isometric crystals. The mineral is typically colorless or white, but may also be light blue, dark blue, purple, pink, red, orange, yellow or gray depending on the amount and type of impurities. It commonly occurs with other evaporite deposit minerals such as several of the sulfates, halides, and borates.

For the Bragg reflections of halite we fill in the following table using the following formulas:

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
200	31.83	0.2812
400	66.33	0.2819
600	110.33	0.2818

The interplanar distance obtained corresponds to the exact value which results to be 0.282 nm. Halite has a fcc cubic structure with the unit cell side which is a = 0.594 nm.

Calcite

Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO₃). The Mohs scale of mineral hardness, based on scratch hardness comparison, defines value 3 as “calcite”.
Calcite crystals are trigonal-rhombohedral, though actual calcite rhombohedra are rare as natural crystals. In the image on the side you can see the Calcite base cell.

For the Bragg reflection of calcite we fill in the following table using the following formulas :

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
104	29.33	0.3045
204	61	0.3038

The interplanar distance obtained corresponds to the exact value which results to be 0.3036 nm. Calcite has a trigonal – hexagonal structure.

Sphalerite

Sphalerite ((Zn, Fe)S) is a mineral that is the chief ore of zinc. It consists largely of zinc sulfide in crystalline form but almost always contains variable iron. When iron content is high it is an opaque black variety, marmatite. It is usually found in association with galena, pyrite, and other sulfides along with calcite, dolomite, and fluorite. Miners have also been known to refer to sphalerite as zinc blende.
The mineral crystallizes in the cubic crystal system. In the crystal structure, zinc and sulfur atoms are tetrahedrally coordinated. The structure is closely related to the structure of diamond. The hexagonal analog is known as the wurtzite structure. The lattice constant for zinc sulfide in the zinc blende crystal structure is 0.541 nm, calculated from geometry and ionic radii of 0.074 nm (zinc) and 0.184 nm (sulfide). It forms ABCABC layers.

For the Bragg reflection of sphalerite we fill in the following table using the following formulas :

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
111	28	0.319

The interplanar distance obtained is close to the exact value which results to be 0.311 nm.

Lithium Niobate

Lithium niobate (LiNbO₃) is a compound of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other linear and non-linear optical applications. It is a human-made dielectric material that does not exist in nature.
Lithium niobate is a colorless solid insoluble in water. It has a trigonal crystal system, which lacks inversion symmetry and displays ferroelectricity, the Pockels effect, the piezoelectric effect, photoelasticity and nonlinear optical polarizability. Lithium niobate has negative uniaxial birefringence which depends slightly on the stoichiometry of the crystal and on temperature. It is transparent for wavelengths between 350 and 5200 nanometers.

The crystalline cell of the lithium niobate is shown in the image on the upper left. The sample examined by XRD technique consists of single crystals, shown in the image below.

For the Bragg reflection of lithium niobate we fill in the following table using the following formulas :

• λ = 0.1542 nm
• d = λ / 2senθ

hkl	2θ	d(nm)
006	39	0.231
0012	84	0.230

The obtained value for the interplanar distance is in good agreement with the exact value of 0.231 nm.

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