Structural Inorganic Chemistry and Crystal Structure (C623) PDF

Structural Inorganic Chemistry and Crystal Structure (C623) ‫دالل زين العابدين‬.‫د‬  Lecture 1 Structural Chemistry of Selected Non- Transition Metals Including their Oxides, Hydroxides, Sulfides, Oxysulfides, Nitrides, Carbonyls, and Coordination...

Structural Inorganic Chemistry and Crystal Structure (C623) ‫دالل زين العابدين‬.‫د‬  Lecture 1 Structural Chemistry of Selected Non- Transition Metals Including their Oxides, Hydroxides, Sulfides, Oxysulfides, Nitrides, Carbonyls, and Coordination Compounds  Introduction Non-transition metals are elements that do not exhibit the characteristics of transition metals. - Non-transition metals are characterized by their simpler chemistry, fixed oxidation states, lack of d-orbital involvement, and generally lower melting and boiling points compared to transition metals. They are essential in numerous biological, industrial, and chemical processes but do not possess the unique characteristics found in transition metals. These elements and their compounds are crucial in various industrial, biological, and environmental processes. -Non-transition elements are indispensable across various domains. Their roles span from fundamental biological processes, such as respiration and DNA synthesis, to large-scale industrial applications, including the production of metals, chemicals, and energy. Moreover, they are central to addressing environmental concerns, particularly in managing emissions and fostering sustainable agricultural practices. Their versatility and ubiquity make non- transition elements crucial to life and technology alike.  Non-transition elements and their compounds play essential roles in various industrial, biological, and environmental processes. These elements, found outside the d-block of the periodic table, include alkali metals, alkaline earth metals, and p-block elements like nitrogen, oxygen, and sulfur. Here's an explanation of their significance in key processes: 1. Industrial Processes: Non-transition elements are critical to a wide range of industries, due to their abundance, reactivity, and unique properties. Alkali Metals (e.g., Sodium, Potassium): Sodium hydroxide (NaOH): Widely used in the chemical industry for manufacturing soap, paper, and textiles. It is also essential in water treatment and the production of detergents. Sodium chloride (NaCl): Beyond its common use as table salt, NaCl is crucial in the chlor-alkali process, which produces chlorine and sodium hydroxide— two chemicals essential for producing plastics, disinfectants, and other compounds. Alkaline Earth Metals (e.g., Magnesium, Calcium): Calcium carbonate (CaCO₃): Used in the production of cement and lime, essential for the construction industry. It is also used as a filler in paper and plastics and as an additive in food. Magnesium alloys: Lightweight magnesium alloys are important in the aerospace and automotive industries due to their strength and low density, improving fuel efficiency. Aluminum: Aluminum and its alloys are widely used in the automotive, aerospace, and packaging industries due to their light weight, resistance to corrosion, and excellent conductivity. 2. Biological Processes: Non-transition elements are vital for maintaining life and various biological functions. Oxygen (O₂): Essential for respiration in animals and humans, where oxygen is used to convert nutrients into energy via cellular respiration. Oxygen is also critical for combustion and industrial processes, including steelmaking. Nitrogen (N₂): Nitrogen, found in the atmosphere, is a major component of amino acids, proteins, and DNA. It is essential for plant growth and the agricultural industry. The Haber process, which synthesizes ammonia (NH₃) from nitrogen, is one of the most important industrial chemical processes. Ammonia is the precursor to fertilizers, which are critical for increasing food production.  Phosphorus: Phosphorus compounds are vital for energy transfer in cells, especially in the form of adenosine triphosphate (ATP). ATP is responsible for storing and transferring energy in biological systems. Phosphorus is also a key component of fertilizers, contributing to healthy plant growth. Sulfur: Sulfur is used to make sulfuric acid (H₂SO₄), a critical chemical in industrial processes, including fertilizer production, oil refining, and chemical manufacturing. 3. Environmental Processes: Non-transition elements play a significant role in maintaining environmental balance and addressing pollution challenges. Carbon (C): Carbon dioxide (CO₂) is essential in the global carbon cycle and photosynthesis, where plants absorb CO₂ to produce oxygen and glucose. This process is fundamental to the Earth's ecosystems. Carbon compounds are also integral to energy production, with hydrocarbons (like coal, oil, and natural gas) providing the majority of the world’s energy. However, managing carbon emissions is crucial for mitigating climate change. Oxygen (O₂) and Ozone (O₃): Ozone in the Earth's atmosphere plays a protective role by absorbing harmful ultraviolet radiation, preventing excessive UV exposure on Earth’s surface. Nitrogen Cycle: Nitrogen undergoes various processes like nitrogen fixation, nitrification, and denitrification to be converted into forms that can be utilized by plants and animals. Nitrogen fertilizers derived from the Haber process are critical for enhancing soil fertility, but their overuse has environmental consequences like water pollution and greenhouse gas emissions. Sulfur and Sulfur Compounds: Sulfur dioxide (SO₂) emissions, a byproduct of fossil fuel combustion, can cause acid rain. Efforts to reduce sulfur emissions from industrial processes are key to minimizing environmental damage. 4. Energy Production: Hydrogen (H₂): Hydrogen is emerging as a clean energy source. When used in fuel cells, hydrogen reacts with oxygen to produce water and electricity, offering a potential solution to reduce carbon emissions. Hydrogen is also a critical component of the refining process for converting crude oil into usable fuels. Silicon (Si): Silicon is crucial for the production of semiconductors, which power modern electronics. Additionally, silicon is used in solar panels, a key technology for harnessing renewable energy. Non-Transition Metals Overview Non-transition metals are typically located in groups 1, 2, and 13–18 of the periodic table. They include alkali metals, alkaline earth metals, and some p-block elements. These elements have a variety of bonding and structural characteristics in their compounds.  Oxides of Non-Transition Metals Oxides consist of oxygen atoms bonded to non-transition metals. These oxides can be acidic, basic, or amphoteric. They are widely used in catalysis, manufacturing, and environmental applications. The acid-base behavior of non-transition metal oxides depends on the nature of the metal and its position in the periodic table. Acidic oxides come primarily from non-metals or metals in high oxidation states, reacting with water or bases to form acids. Basic oxides are generally formed by alkali and alkaline earth metals, reacting with acids to neutralize them. Amphoteric oxides, such as those from aluminum and zinc, exhibit dual behavior, reacting with both acids and bases depending on the conditions. 1. Acidic Oxides: Examples: Acidic oxides are non-metal oxides that react with water to form acids, or with bases to form salts. These oxides usually come from non-metals in the periodic table, but some high oxidation state oxides of non- transition metals can also be acidic. Characteristics: These oxides generally form acids when dissolved in water. They react with bases to form salts and water.  In the case of non-transition metals, oxides like SiO₂ (silicon dioxide) are also acidic. Though insoluble in water, SiO₂ reacts with strong bases like sodium hydroxide (NaOH) to form silicate salts. 2. Basic Oxides: Basic oxides are typically formed by metals, especially from the alkali and alkaline earth metal groups (Groups 1 and 2). These oxides react with acids to form salts and water and may also react with water to form hydroxides. Characteristics: Basic oxides form alkaline solutions when dissolved in water. They react with acids to form salts and water. Basic oxides are common for metals like sodium, calcium, potassium, and magnesium, and their hydroxides often play significant roles in neutralizing acids in industrial and environmental processes. 3. Amphoteric Oxides: Amphoteric oxides can act as both acidic and basic oxides. This means they can react with both acids and bases to form salts and water. Non-transition metals that form amphoteric oxides typically belong to Group 13 (like aluminum) and Group 14 (like lead). Characteristics: Amphoteric oxides can neutralize both acids and bases. They exhibit both acidic and basic properties depending on the reaction conditions. Amphoteric oxides, such as Al₂O₃ and ZnO, are often useful in metallurgical processes and industrial applications where both acidic and basic reactions are required.  Structure of Oxides Oxides exhibit diverse structures, including simple binary oxides (Na2O, MgO) to more complex structures such as perovskites and spinels. Common crystal structures include cubic, hexagonal, and orthorhombic forms. Rock salt structure: MgO adopts the rock salt structure, which is a cubic close-packed (CCP) lattice with cations (Mg²⁺) occupying the octahedral voids and anions (O²⁻) occupying the lattice points. Rock salt structure : sodium This structure is also known as the sodium chloride oxide, Na2O, crystal structure, structure. ionic bond, cubic lattice The perovskite structure is a crystal structure that is commonly found in many materials, including minerals, ceramics, and semiconductors. It is named after the mineral perovskite, which has the chemical formula CaTiO₃. Key features of the perovskite structure: Cubic structure: The perovskite structure is cubic, meaning that the unit cell is a cube with equal edge lengths. ABX₃ formula: The chemical formula of a perovskite material is typically ABX₃, where: A is a cation with a large ionic radius, such as Ca²⁺, Sr²⁺, or Ba²⁺. B is a cation with a smaller ionic radius, such as Ti⁴⁺, Zr⁴⁺, or Sn⁴⁺. X is an anion, typically O²⁻. Coordination: The A cation is coordinated by 12 X anions, and the B cation is coordinated by 6 X anions. Examples of perovskite materials: Calcium titanate (CaTiO₃): The original perovskite mineral. Barium titanate (BaTiO₃): A ferroelectric material used in capacitors and transducers. Lead zirconate titanate (PZT): A piezoelectric material used in sensors and actuators. Perovskite solar cells: A type of solar cell that uses perovskite materials as the light-absorbing layer. tructure of pervoskite ABO3 unit cell structure of Barium titanate Why is the perovskite structure so important? Flexibility: The perovskite structure can accommodate a wide range of cations and anions, making it possible to create materials with a variety of properties. Efficiency: Perovskite materials can be highly efficient in converting light into electricity, making them promising for solar energy applications. Versatility: Perovskite materials can be used in a variety of applications, including electronics, optics, and catalysis.  Hydroxides of Non-Transition Metals Hydroxides contain hydroxyl groups (-OH) bonded to non-transition metals. They are typically basic and are important in neutralization reactions and as catalysts. They play important roles in various chemical processes and applications, including catalysis, materials science, and environmental chemistry. For instance, calcium hydroxide is used to neutralize acidic soils, while excessive alkalinity from hydroxide use can lead to environmental imbalances. 1. General Properties Chemical Composition: Hydroxides of non-transition metals typically have the general formula M(OH)n, where M represents the metal and n corresponds to the number of hydroxide ions associated with it. Solubility: The solubility of these hydroxides in water varies widely depending on the metal involved. For example, sodium hydroxide (NaOH) and potassium hydroxide (KOH) are highly soluble, while magnesium hydroxide (Mg(OH)₂) and aluminum hydroxide (Al(OH)₃) have low solubility. pH: Many hydroxides of alkali and alkaline earth metals are strong bases, contributing to high pH values in solution.  Structure of Hydroxides Examples include sodium hydroxide (NaOH) with a simple cubic structure and magnesium hydroxide (Mg(OH)2), which forms layered structures. Crystal Structure Lattice Type: Magnesium hydroxide typically crystallizes in a brucite-like structure, which is similar to the structure of brucite (Mg(OH)₂). This structure is characterized by layered arrangements of magnesium and hydroxide ions. Coordination: The magnesium ion is octahedrally coordinated by six oxygen atoms from the hydroxide ions in a layered arrangement. Each magnesium ion is surrounded by six hydroxide ions, and these layers are held together by hydrogen bonding and ionic interactions. Magnesium hydroxide has a unique layered crystal structure, making it an interesting compound both in chemistry and various applications. Its layered arrangement is significant for its physical properties and uses in industrial applications. Unit Cell Crystal System: The unit cell of Mg(OH)₂ belongs to the trigonal crystal system. Parameters: The most common form is a rhombohedral structure, which can be represented as: Lattice constants: a≈4.58 A˚a \approx 4.58 \, \text{Å}a≈4.58A˚ and c≈3.08 A˚c \approx 3.08 \, \text{Å}c≈3.08A˚. Layered Structure The layers of hydroxide ions form sheets, with magnesium ions located in the interlayer spaces. The layers can slide over each other, which contributes to the material's lubricating properties. 5. Visual Representation While I can't provide an image directly, a diagram of Mg(OH)₂ would show: Magnesium ions (Mg²⁺) depicted as larger circles. Hydroxide ions (OH⁻) depicted as smaller circles with a central oxygen atom and surrounding hydrogen atoms. The octahedral unit Properties Related to Structure of brucite-like layers The layered structure contributes to the low solubility of Mg(OH)₂ in water. It is also the in hydrotalcite reason for its use in antacids and as a flame retardant, as it can decompose to release water and provide a cooling effect in combustion scenarios. Hydrotalcite (formerly layered double hydroxide, LDH) is a lamellar inorganic material with large surface area, great thermal and mechanical properties, and tendency to interchange their interlayer anions with other anions such as larger organic and inorganic ones. Hydrotalcite is a magnesium-aluminium hydroxycarbonate with general formula Mg6Al2CO3(OH)16·4(H2O) presenting a layered crystal structure. It has been widely used as a catalyst in hydrogen production processes and in decarboxylation reactions  Sulfides of Non-Transition Metals Sulfides are compounds formed between non-transition metals and sulfur. They have significant industrial uses, including in chemical manufacturing and ore extraction. Classification Alkali Metal Sulfides: These include lithium sulfide (Li₂S), sodium sulfide (Na₂S), and potassium sulfide (K₂S). They are typically soluble in water and form alkaline solutions. Alkaline Earth Metal Sulfides: These include calcium sulfide (CaS), magnesium sulfide (MgS), and barium sulfide (BaS). Some are soluble in water, while others are not. Other Non-Transition Metal Sulfides: This category includes sulfides of metals such as aluminum (Al₂S₃), zinc (ZnS), and lead (PbS). Many of these sulfides exhibit semiconductor properties. Examples and Applications Sodium Sulfide (Na₂S): Used in the pulp and paper industry for pulping wood, as well as in the production of dyes and in leather processing. Calcium Sulfide (CaS): Utilized in the manufacture of phosphorescent materials and as a reagent in chemical syntheses. Zinc Sulfide (ZnS): A semiconductor that is widely used in the manufacture of phosphors, LED lights, and as a white pigment in paints. Lead Sulfide (PbS): Used in infrared detectors and as a semiconductor material. Aluminum Sulfide (Al₂S₃): Used in the production of hydrogen sulfide gas and as a drying agent.  Structure of Sulfides Sulfides can form different structures, such as zinc blende or wurtzite, depending on the bonding preferences of the metal. Arrangement of ions in zinc blende unit cell In the Zinc Blende In the Zinc Blende structure, the ions are arranged in structure, the ions are CCP(Cubic Close Packing) manner. In the CCP arrangement, there are 8 tetrahedral voids and 4 arranged in CCP(Cubic Close octahedral voids present. Packing) manner. In the CCP The S2- ions are present in FCC (Face Centered arrangement, there are 8 Cubic) arrangement. i.e The S2- ions are present at tetrahedral voids and 4 the corner of the cube and at the centre of each face. octahedral voids present. The The Zn2+ ions are present in the alternative S2- ions are present in FCC tetrahedral void. (Face Centered Cubic) Each Zn2+ ion is surrounded tetrahedrally by four S2- ions and each S2- ion is surrounded tetrahedrally by four Zn2+ ions. Thus the structure has 4:4 coordination. The radius ratio of ZnS is rZn2+ /rS2- = 74/184 = 0.4 Wurtzite is a zinc and iron sulfide mineral with the chemical formula (Zn,Fe)S, a less frequently encountered structural polymorph form of sphalerite. The iron content is variable up to eight percent. It is trimorphous with matraite and sphalerite The wurtzite structure is also known as the α-ZnS structure. One way to understand it is to consider it as a hexagonal close packed array of anions, with half the tetrahedral interstices filled by cations. Every anion is surrounded by four cations and has tetrahedral coordination geometry. Likewise, every cation is tetrahedrally coordinated by four anions. Many compounds adopt the wurtzite structure, including w-BN, β- AgI, ZnO, BeO, AlN, α-CdS and CdSe. Oxysulfides of Non-Transition Metals Oxysulfides are mixed compounds containing oxygen and sulfur atoms bonded to non-transition metals. These compounds are used in various high-temperature industrial applications. A “metal oxysulfide” is a compound composed of at least a metal, oxygen and sulfur, with negative oxidation states (e.g., –II) for both oxygen and sulfur. The generic formula for ternary oxysulfide is MxOySz. Due to its negative oxidation state, sulfur forms no bounds with oxygen in oxysulfides, in contrast with more common metal sulfates Mx(SVIO4)y where the sulfur is +IV. Formation and Structure: Ionic compounds: Oxysulfides can be ionic compounds, where the oxygen and sulfur atoms are present as ions. For example, sodium oxysulfide (Na₂SO) is an ionic compound. Covalent compounds: They can also be covalent compounds, where the oxygen and sulfur atoms share electrons. Examples include carbon oxysulfide (COS) and silicon oxysulfide (Si₂OS₂). Mixed compounds: Some oxysulfides have both ionic and covalent character. Examples of Oxysulfides: Sodium oxysulfide (Na₂SO): A white crystalline solid used in the production of dyes and pigments. Carbon oxysulfide (COS): A colorless gas found in natural gas and volcanic emissions. Silicon oxysulfide (Si₂OS₂): A glass-like material used in optical fibers and infrared optics. Molybdenum oxysulfide (MoO₂S₂): A layered material with potential applications in electronics and catalysis.  Nitrides of Non-Transition Metals Nitrides are compounds formed between nitrogen and non-transition metals. They are commonly used in high-strength materials and electronics. Types of Non-Transition Metal Nitrides Aluminum Nitride (AlN): Structure: Hexagonal wurtzite or cubic zinc blende. Properties: High thermal conductivity, good electrical insulator, and used in electronics and as a substrate for sapphire wafers. Silicon Nitride (Si3N4): Structure: Hexagonal or cubic forms. Properties: Excellent mechanical strength, thermal shock resistance, and is often used in high-performance ceramics and bearings. Boron Nitride (BN): Structure: Exists in various forms, including hexagonal (similar to graphite) and cubic (similar to diamond). Properties: High thermal conductivity, electrical insulator, and used as a lubricant and in composite materials. Gallium Nitride (GaN): Structure: Wurtzite. Properties: Wide bandgap semiconductor used in LEDs and power electronic devices Structure of Nitrides Nitrides exhibit structures such as hexagonal and cubic forms, with strong covalent bonding between nitrogen and metal atoms. Most metal-rich transition metal nitrides adopt a relatively ordered face-centered cubic or hexagonal close-packed crystal structure, with octahedral coordination. Sometimes these materials are called "interstitial nitrides". Common Structural Types of Nitrides Here are some of the most common structural forms of nitrides: Hexagonal and Cubic Structures 1.Hexagonal Wurtzite Structure: 1. Example: Aluminum nitride (AlN) and Gallium nitride (GaN). 2. Description: In this structure, nitrogen atoms occupy tetrahedral sites in a hexagonal lattice formed by the metal atoms. 3. Coordination: Each metal atom is coordinated by four nitrogen atoms, forming a tetrahedral geometry. 4. Lattice Parameters: Typically characterized by two lattice parameters, aaa and ccc, with c/ac/ac/a ratio reflecting the degree of distortion from a perfect tetrahedral arrangement. 1.Cubic Zinc Blende Structure: 1. Example: Some forms of GaN. 2. Description: This structure has a face-centered cubic arrangement where each metal atom is surrounded tetrahedrally by four nitrogen atoms. 3. Coordination: Similar to the hexagonal form, the coordination remains tetrahedral. Cubic Structures 3.Cubic NaCl Structure: Example: Some boron nitrides (c-BN). Description: In this structure, nitrogen and boron atoms alternate in a simple cubic arrangement, resembling sodium chloride. Coordination: Each nitrogen atom is octahedrally coordinated to six boron atoms, and vice versa. Other Structures -Hexagonal Boron Nitride (h-BN): Description: This structure is layered, similar to graphite, where boron and nitrogen atoms form two- dimensional planes. The layers are held together by van der Waals forces. Properties: Excellent lubricant and insulator due to its unique layered structure. -Cubic Boron Nitride (c-BN): Description: A denser structure that is harder than diamond, often used as an abrasive. This form has a more complex interstitial arrangement. Coordination: Each boron atom is tetrahedrally coordinated to four nitrogen atoms.  Carbonyls of Non-Transition Metals Carbonyls are metal complexes in which non-transition metals are bonded to carbon monoxide molecules. These complexes are used in organometallic chemistry and catalysis. Non-transition metal carbonyls can take several structural forms, which can be broadly categorized as follows: Monomeric Carbonyls Examples: Aluminum carbonyl (Al(CO)₄). Structure: Typically tetrahedral or trigonal planar geometry around the metal center, depending on the number of CO ligands. Coordination: The carbonyl ligands coordinate to the metal through the carbon atom, forming stable complexes. Dimeric or Oligomeric Carbonyls Examples: Gallium carbonyl (Ga₂(CO)₆). Structure: These complexes can form dimers or larger oligomers with bridging carbonyl groups. Coordination: The bridging carbonyls lead to a more complex arrangement, often resulting in a polymeric structure. Bonding: In these structures, some of the CO ligands may coordinate in a terminal mode (bonding to one metal) or in a bridging mode (bonding to two metal centers). Specific Examples of Non-Transition Metal Carbonyls 1.Aluminum Carbonyl (Al(CO)₄): 1. Structure: Tetrahedral geometry with four CO ligands surrounding the aluminum atom. 2. Properties: Highly reactive and can act as a precursor for aluminum-based materials. 2.Gallium Carbonyl (Ga(CO)₄): 1. Structure: Can exist in monomeric and dimeric forms, with CO ligands forming stable interactions with gallium. 2. Properties: Dimerization occurs due to the favorable interactions between Ga and the CO groups. 3.Silicon Carbonyl (Si(CO)₄): 1. Structure: Tetrahedral geometry similar to that of aluminum carbonyl. 2. Properties: Less common and typically requires specific synthetic conditions. Bonding and Stability Bonding Nature: The strength of the metal-CO bond is generally lower for non-transition metals compared to transition metals, leading to less stable complexes. Ligand Field Theory: While ligand field effects play a role, the absence of d-orbitals in many non-transition metals means that σ-donation from CO is the primary interaction, with less π-backbonding occurring. The structures of carbonyls of non-transition metals are characterized by simpler coordination geometries and weaker metal-CO interactions compared to their transition metal counterparts. Understanding these structures aids in the development of applications in catalysis, materials science, and synthetic chemistry.  Coordination Compounds of Non-Transition Metals Coordination compounds consist of non-transition metals bonded to ligands. These compounds are important in areas such as coordination chemistry and bioinorganic chemistry. Coordination compounds of non-transition metals consist of a central non-transition metal atom bonded to one or more ligands, which can be ions or neutral molecules that donate electron pairs to the metal. These compounds exhibit distinct properties and coordination geometries compared to those involving transition metals. Here’s an overview of coordination compounds of non-transition metals, including their structures, bonding, and applications. 1. Definition and General Properties Coordination Compound: A complex formed from a central metal atom or ion and surrounding ligands. Non- transition metal coordination compounds generally involve metals from groups 1, 2, and 13-16 of the periodic table. Ligands: Molecules or ions that can donate lone pairs of electrons to the metal. They can be monodentate (binding through one site) or polydentate (binding through multiple sites). 2. Common Non-Transition Metals in Coordination Compounds Aluminum (Al): Commonly forms complexes with various ligands, especially in the presence of Lewis bases. Boron (B): Forms coordination compounds that often involve organometallic chemistry. Silicon (Si): Coordination compounds are less common but can involve silicon in organosilicon compounds. Calcium (Ca), Magnesium (Mg): Can form coordination compounds with ligands like oxalates and nitrates. 3. Types of Coordination Compounds Mononuclear Coordination Compounds Example: Aluminum chloride complex [AlCl4]−. Structure: Aluminum can coordinate with four chloride ions, leading to a tetrahedral geometry. Polynuclear Coordination Compounds Example: [Ca2(CO3)4]2−. Structure: Calcium can form larger structures by coordinating with multiple carbonate ions Comparison with Transition Metal Coordination Compounds  Lecture 2 Principle of X-ray diffraction (XRD) X-ray powder diffraction (XRD) is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions. The analyzed material is finely ground, homogenized, and average bulk composition is determined. Fundamental Principles of X-ray Powder Diffraction (XRD) Max von Laue, in 1912, discovered that crystalline substances act as three-dimensional diffraction gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice. X-ray diffraction is now a common technique for the study of crystal structures and atomic spacing. X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline sample. These X-rays are generated by a cathode ray tube, filtered to produce monochromatic radiation, collimated to concentrate, and directed toward the sample. The interaction of the incident rays with the sample produces constructive interference (and a diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sin θ).  This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample. These diffracted X-rays are then detected, processed and counted. By scanning the sample through a range of 2θangles, all possible diffraction directions of the lattice should be attained due to the random orientation of the powdered material. Conversion of the diffraction peaks to d-spacings allows identification of the mineral because each mineral has a set of unique d-spacings. Typically, this is achieved by comparison of d-spacings with standard reference patterns. All diffraction methods are based on generation of X-rays in an X-ray tube. These X-rays are directed at the sample, and the diffracted rays are collected. A key component of all diffraction is the angle between the incident and diffracted rays. Powder and single crystal diffraction vary in instrumentation beyond this.  X-ray Powder Diffraction (XRD) Instrumentation - How Does It Work? X-ray Diffraction Instrument X-ray diffractometers consist of three basic elements: an X-ray tube, a sample holder, and an X-ray detector. X-rays are generated in a cathode ray tube by heating a filament to produce electrons, accelerating the electrons toward a target by applying a voltage, and bombarding the target material with electrons. When electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic X-ray spectra are produced. These spectra consist of several components, the most common being Kα and Kβ. Kα consists, in part, of Kα1 and Kα2. Kα1 has a slightly shorter wavelength and twice the intensity as Kα2. The specific wavelengths are characteristic of the target material (Cu, Fe, Mo, Cr). Filtering, by foils or crystal monochrometers, is required to produce monochromatic X-rays needed for diffraction. Kα1and Kα2 are sufficiently close in wavelength such that a weighted average of the two is used. Copper is the most common target material for single-crystal diffraction, with CuKα radiation = 1.5418Å. These X-rays are collimated and directed onto the sample. As the sample and detector are rotated, the intensity of the reflected X-rays is recorded. When the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation, constructive interference occurs and a peak in intensity occurs. A detector records and processes this X-ray signal and converts the signal to a count rate which is then output to a device such as a printer or computer monitor The geometry of an X-ray diffractometer is such that the sample rotates in the path of the collimated X-ray beam at an angle θ while the X-ray detector is mounted on an arm to collect the diffracted X-rays and rotates at an angle of 2θ. The instrument used to maintain the angle and rotate the sample is termed a goniometer. For typical powder patterns, data is collected at 2θ from ~5° to 70°, angles that are preset in the X-ray scan.  Strengths and Limitations of X-ray Powder Diffraction (XRD)? Strengths Limitations Powerful and rapid (< 20 min) Homogeneous and single phase material is technique for identification of an best for identification of an unknown unknown mineral Must have access to a standard reference file of inorganic compounds (d- In most cases, it provides an spacings, hkls) unambiguous mineral determination Requires tenths of a gram of material which Minimal sample preparation is must be ground into a powder required For mixed materials, detection limit is ~ 2% XRD units are widely available of sample For unit cell determinations, indexing of Data interpretation is relatively patterns for non-isometric crystal systems is straight forward complicated Peak overlay may occur and worsens for high angle 'reflections'