10.6 Lattice Structures in Crystalline Solids
3 min read•june 25, 2024
Crystalline structures are like building blocks of solids, with atoms arranged in repeating patterns. These patterns form unit cells, the smallest repeating units, which come in different types like and .
helps us peek inside crystals, revealing their atomic arrangements. By bouncing X-rays off atoms and analyzing the resulting patterns, scientists can uncover the secrets of a crystal's structure and composition.
Crystalline Structures and Arrangements
Arrangement of atoms in crystals
Top images from around the web for Arrangement of atoms in crystals
Cubic crystal lattices View original
Is this image relevant?
Lattice Structures in Crystalline Solids | Chemistry View original
Is this image relevant?
Lattice Structures in Crystalline Solids | General Chemistry View original
Is this image relevant?
Cubic crystal lattices View original
Is this image relevant?
Lattice Structures in Crystalline Solids | Chemistry View original
Is this image relevant?
1 of 3
Top images from around the web for Arrangement of atoms in crystals
Cubic crystal lattices View original
Is this image relevant?
Lattice Structures in Crystalline Solids | Chemistry View original
Is this image relevant?
Lattice Structures in Crystalline Solids | General Chemistry View original
Is this image relevant?
Cubic crystal lattices View original
Is this image relevant?
Lattice Structures in Crystalline Solids | Chemistry View original
Is this image relevant?
1 of 3
- consist of atoms, ions, or molecules arranged in a regular, repeating pattern that extends in three dimensions
- The smallest repeating unit that displays the full symmetry of the crystal structure is known as the
- Unit cells are characterized by their lengths (a, b, c) and angles (α, β, γ)
- Three main types of unit cells include:
- Primitive cubic (P): contains atoms at each corner of the cube (e.g., polonium)
- Body-centered cubic (I): features atoms at each corner and one atom in the center of the cube (e.g., sodium)
- (F): has atoms at each corner and at the center of each face of the cube (e.g., copper)
- Other common crystal structures:
- (HCP): consists of a two-dimensional hexagonal lattice with a repeating ABABAB pattern (e.g., magnesium)
- (CCP) or face-centered cubic (FCC): comprises a two-dimensional hexagonal lattice with a repeating ABCABC pattern (e.g., gold)
- The , which is the number of nearest neighbors an atom or ion has in a crystal structure, varies depending on the lattice type
Crystal Lattice Properties
- refers to the percentage of space occupied by atoms or ions in a crystal structure
- (h, k, l) are used to describe planes and directions in crystal lattices
- are the 14 unique three-dimensional that form the basis for all crystalline materials
Calculation of ionic radii
- can be calculated using the edge length of the and the radius ratio of the cation and anion
- For a primitive cubic unit cell with edge length :
- For a with edge length :
- For a face-centered cubic unit cell with edge length :
X-ray Diffraction and Crystalline Structure Determination
X-ray diffraction for crystal structures
- X-ray diffraction (XRD) is a powerful technique used to determine the arrangement of atoms in a crystalline solid
- X-rays scatter off the electrons in the atoms of the crystal, producing a due to the interference of the scattered X-rays
- ###'s_law_0### describes the relationship between the wavelength of the X-rays (), the angle of incidence (), and the interplanar spacing () in the crystal:
- , where is an integer (e.g., 1, 2, 3)
- The diffraction pattern provides crucial information about the crystal structure, such as the size and shape of the unit cell and the positions of atoms within the unit cell
- The intensities of the diffraction peaks are determined by the types and positions of atoms in the unit cell
- This information is used to generate an , which reveals the atomic structure of the crystal (e.g., the arrangement of atoms in a protein molecule)
Key Terms to Review (38)
Body-Centered Cubic: Body-centered cubic (BCC) is a type of crystal lattice structure in which atoms are arranged in a three-dimensional grid, with one atom positioned at the center of each cube and an atom at each of the eight corners. This arrangement gives the BCC structure unique properties and characteristics that are important in the study of the solid state of matter and crystalline solids.
Body-centered cubic (BCC) solid: A body-centered cubic (BCC) solid is a type of crystalline structure where each unit cell has one atom at each of the eight corners and one atom in the center of the cell. This arrangement results in a more open structure compared to face-centered cubic (FCC) solids.
Body-centered cubic unit cell: A body-centered cubic (BCC) unit cell is a type of crystal structure in which each cube-shaped unit cell has an atom at each of its eight corners and one atom at the center. The BCC structure is less densely packed than the face-centered cubic (FCC) structure but more so than the simple cubic (SC) structure.
Bragg: Bragg's Law describes the condition for constructive interference of X-rays scattered by a crystal lattice. It is given by the equation $n\lambda = 2d\sin(\theta)$, where $n$ is an integer, $\lambda$ is the wavelength of the X-ray, $d$ is the distance between crystal planes, and $\theta$ is the angle of incidence.
Bragg equation: The Bragg equation, $n\lambda = 2d\sin\theta$, describes the condition for constructive interference of X-rays scattered by a crystalline lattice. It relates the wavelength of X-rays to the angle at which they are diffracted and the spacing between crystal planes.
Bragg's law: Bragg's law is a fundamental principle in crystallography that describes how X-rays are diffracted by the regular lattice of atoms in a crystalline solid. This law establishes the relationship between the wavelength of incident X-rays, the angle of diffraction, and the distance between atomic layers within the crystal. Understanding Bragg's law is crucial for interpreting diffraction patterns, which reveal important information about the structure and arrangement of atoms in materials.
Bravais Lattices: Bravais lattices are the fundamental building blocks of crystalline solids, representing the periodic arrangement of atoms or molecules in three-dimensional space. They are essential for understanding the structure and properties of crystalline materials.
Coordination number: The coordination number is the number of atoms, ions, or molecules that a central atom or ion holds as its nearest neighbors in a complex or lattice structure. It indicates the connectivity and spatial arrangement around the central entity.
Coordination Number: The coordination number is the number of atoms, ions, or molecules that are directly bonded to a central atom or ion in a coordination complex or crystal structure. This concept is fundamental in understanding the solid state of matter, lattice structures in crystalline solids, and the coordination chemistry of transition metals.
Crick: Crick refers to a specific point in the lattice structure of a crystalline solid where atoms or molecules are arranged in a repeating pattern. It is crucial for understanding the stability and properties of crystalline materials.
Crystalline solids: Crystalline solids are materials whose atoms, ions, or molecules are arranged in a highly ordered, repeating pattern extending in all three spatial dimensions. They exhibit distinct melting points and characteristic geometric shapes.
Crystalline Solids: Crystalline solids are a state of matter characterized by the highly organized, repeating three-dimensional arrangement of atoms, ions, or molecules in a fixed geometric pattern. This ordered structure is a defining feature of crystalline solids and distinguishes them from other solid states like amorphous solids.
Cubic close-packed: Cubic close-packed (CCP) is a type of crystal structure where atoms are packed together efficiently in a three-dimensional arrangement, maximizing the density of the solid. In this arrangement, atoms are located at each corner of the cube and in the center of each face, resulting in a coordination number of 12, meaning each atom is in contact with 12 others. This structure plays a significant role in understanding how different materials behave and their properties in various applications.
Cubic closest packing (CCP): Cubic closest packing (CCP) is a type of crystal lattice structure where spheres are packed in the most efficient manner, resulting in a repeating ABCABC pattern. This arrangement maximizes space utilization and has a coordination number of 12.
Diffraction Pattern: A diffraction pattern is the distribution of intensity of light, electrons, or other waves that results when a wave encounters an obstacle or a slit. It is a fundamental phenomenon in the study of wave behavior and is closely related to the structure of crystalline solids.
Electron Density Map: An electron density map is a three-dimensional representation that shows the distribution of electrons within a crystalline solid. This map is crucial in determining the structure of molecules by indicating where electrons are likely to be found, helping scientists visualize atomic arrangements in crystals. The interpretation of these maps provides insight into bonding, molecular geometry, and interactions between atoms.
Face-Centered Cubic: Face-Centered Cubic (FCC) is a type of crystal lattice structure in which atoms are arranged in a three-dimensional grid, with an atom located at each corner of the cube and an additional atom at the center of each face of the cube. This arrangement is one of the fundamental lattice structures observed in crystalline solids.
Face-centered cubic (FCC) solid: A face-centered cubic (FCC) solid is a type of crystalline structure where atoms are located at each corner and the center of all cube faces of a unit cell. This arrangement leads to high packing efficiency.
Franklin: A Franklin is a unit of electric charge used in the centimeter-gram-second (CGS) system of units. It is equivalent to approximately $3.33564 \times 10^{-10}$ coulombs.
Hexagonal Close-Packed: Hexagonal close-packed (HCP) is a type of crystal lattice structure in which atoms or ions are arranged in a repeating three-dimensional pattern. This arrangement is characterized by a close-packed structure with a hexagonal unit cell, providing high packing efficiency and stability for certain solid materials.
Holes: Holes in crystalline solids are vacant lattice sites where an atom or ion would normally reside. These vacancies can affect the physical properties and behaviors of the material.
Ionic Radii: Ionic radii refer to the size of the ions that make up a crystalline solid. The size of an ion is determined by the number of protons in the nucleus and the number of electrons in the ion's electron cloud. Ionic radii are an important factor in understanding the lattice structures and properties of crystalline solids.
Isomorphous: Isomorphous refers to crystals having the same atomic arrangement or structure but composed of different chemical elements. These substances can form solid solutions due to their structural similarity.
Lattice Structures: Lattice structures refer to the organized, repeating arrangement of atoms or molecules that form the foundation of crystalline solids. These structures provide the framework for the internal organization and stability of solid materials.
Miller Indices: Miller indices are a set of three integers (h, k, l) that define the orientation of a particular crystallographic plane within a unit cell of a crystal structure. They provide a standardized way to identify and describe the various planes that exist within a crystal lattice.
Octahedral hole: An octahedral hole is a void in a crystal lattice structure where an atom or ion can fit, surrounded by six atoms or ions arranged at the vertices of an octahedron. It is commonly found in close-packed structures such as face-centered cubic (FCC) and hexagonal close-packed (HCP) lattices.
Packing Efficiency: Packing efficiency is a measure of how tightly particles or atoms are arranged within a crystalline solid structure. It quantifies the degree to which the available space in a unit cell or lattice is occupied by the constituent particles.
Primitive cubic: Primitive cubic refers to a type of crystal lattice structure where atoms are positioned at the corners of a cube. In this arrangement, each corner atom is shared among eight adjacent cubes, which leads to a unit cell that contains one complete atom. This structure is one of the simplest and least dense lattice types, playing a crucial role in understanding crystalline solids and their properties.
Simple cubic structure: A simple cubic structure is a type of crystal lattice where atoms are arranged at each corner of a cube. It is one of the simplest and least dense packing arrangements in crystalline solids.
Simple cubic unit cell: A simple cubic unit cell is a type of crystal lattice structure where each corner of the cube is occupied by an atom. It is the most basic and least densely packed arrangement in crystalline solids.
Space lattice: A space lattice is a three-dimensional arrangement of points representing the periodic structure of a crystalline solid. These points correspond to the positions of atoms, ions, or molecules within the crystal.
Tetrahedral hole: A tetrahedral hole is a type of interstitial site in a crystal lattice where an atom or ion can fit into the space surrounded by four atoms or ions arranged at the corners of a tetrahedron. It is commonly found in close-packed structures like face-centered cubic (FCC) and hexagonal close-packed (HCP) lattices.
Unit cell: A unit cell is the smallest repeating unit of a crystalline solid that shows the entire structure's symmetry and properties. It defines the crystal's lattice structure and is characterized by its geometry and atomic arrangement.
Unit Cell: The unit cell is the fundamental building block of a crystalline solid, representing the smallest repeating unit that encompasses the full symmetry and structure of the crystal lattice. It is the basic unit used to describe the arrangement and organization of atoms or molecules within a crystalline material.
Watson: Watson Crick base pairing is the specific hydrogen bonding between nucleotides on complementary strands of DNA. Adenine pairs with thymine and guanine pairs with cytosine.
Wilkins: Wilkins is a hypothetical lattice structure used to illustrate the arrangement of atoms in crystalline solids. It serves as a conceptual model for understanding different types of lattice structures.
X-ray crystallography: X-ray crystallography is a technique used to determine the atomic and molecular structure of a crystal by measuring the angles and intensities of X-rays that are diffracted through the crystal. The data obtained allows scientists to construct a three-dimensional model of the electron density within the crystal.
X-ray Diffraction: X-ray diffraction is a technique used to study the atomic and molecular structure of crystalline solids. It involves the scattering of X-rays by the atoms in a material, which can provide information about the arrangement and spacing of atoms within the material's crystal structure.