Crystal Systems & Crystal Structures

If you have been in the crystal community for a while, you’ve almost certainly heard of crystal systems. These are important in crystallography and are extremely useful when it comes to identifying certain minerals and classifying crystal properties.

But what are crystal systems? What are crystal structures? Crystal systems differ greatly, but each one defines crystals on symmetric points of their crystallographic axes. It will make more sense later, trust us. Crystal structures, on the other hand, are merely the arrangement of atoms that make up a crystal. There are seven crystal systems, but some would say six. Let’s get into that since defining structures and systems without examples can be a little confusing.

7 Systems (Some Say Six)

Whether there are six or seven is ultimately irrelevant. However, due to their similar relationship, some put trigonal and hexagonal in the same category.

We will say seven because we are going to define seven crystal systems. Since crystals are made up of multiple properties, we will have to break this up a little more.

If you’ve read our other gemstone blogs, you’ve probably seen us reference crystal systems before. The seven we reference are:

• Triclinic
• Monoclinic
• Orthorhombic
• Tetragonal
• Trigonal
• Hexagonal
• Isometric (Cubic)

Each of these varies from another drastically, even at a surface level. A crystal must fit into one of these categories based on its crystal structure and symmetry.

Let’s use the isometric crystal system as a reference to show you how this stuff is defined. The isometric system is great for examples because it is extremely common and simple.

This is a simple cubic crystal system. It is extremely symmetric with four threefold axes. But what does that mean, exactly? Let's break it down.

A crystal system is defined through rotational symmetry. That means if we rotate our cube by a certain amount, it is visually unchanged. For reference, pyrite has a cubic crystal system, and it is a symmetrical stone.

Now that we know our cube won’t look too different if we turn it around, we can talk about the elephant in the room. This X-fold axis thing isn’t as complicated as it sounds. Essentially, we can rotate something 360°/X times to get our rotational symmetry as an X-fold something.

Let’s start small. 2-Fold. Take the letter S, for instance. This is our letter S.

Now, if we want to test if this has 2-Fold symmetry, we’ll need to take 360°/2 = 180°. Ok, good. Now, what that means is, to prove it has 2-Fold symmetry, we need to rotate that 180°. You can try that out. It'll look basically the same.

Let's try 3-Fold symmetry now. Take 360°/3 = 120°. That means we need to rotate something 120°, and if it looks the same, then it has 3-Fold rotational symmetry. A famous example of this is the triskelion.

 

If you rotate that, you will see it has 3-Fold rotational symmetry.

With those examples out of the way, we now have an idea of what that threefold rotational symmetry thing means. But you’ll notice that we said four threefold axes. You’ll also notice that crystals exist in the third dimension. What we’ve been showing you are 2D images.

Let’s show you a real cubic crystal.

Pyrite is naturally cubic. It has four axes of 3-fold rotational symmetry. But a cube also has three axes of 4-fold rotational symmetry. It also happens to have six 2-fold axes of rotational symmetry. This all depends on the faces and axes that you are looking at.

Summary of Symmetry

As long as you understand this, it’s quite easy to visualize the symmetry of other systems.

Triclinic – None, three axes with unequal lengths. Examples, Rhodonite, Labradorite, Ajoite.

Monoclinic – One axis of two-fold symmetry. We can rotate the structure 180° without seeing variance in its appearance. Examples: Charoite, Chlorites, Diopside.

Orthorhombic – Three axes of 2-fold symmetry, meaning we can rotate the structure 180° from those three axes without seeing variance in its appearance. Examples: Topaz, Olivine, Zoisite.

Tetragonal – One 4-fold axis of symmetry. We can rotate the structure 90° without seeing variance in its appearance. Examples: Rutile, Zircon, Ziroite.

Trigonal – One 3-fold axis of symmetry. We can rotate the structure 120° without seeing variance in its appearance. Examples: Galeite, Quartz, Cinnabar.

Hexagonal – One 6-fold axis of symmetry. We can rotate the structure 60° without seeing variance in its appearance. Examples: Zinc, Beryl, Ice, Graphite.

Cubic – Four 3-fold axes of symmetry. We can rotate the structure 120° from those four axes without seeing variance in its appearance. Examples: Garnet, Pyrite, Fluorite.

Now, we have to give full disclosure. This is only scratching the surface of the complexity of crystal systems. Within each of these systems are crystal classes which add more variety to them. Each of these classes has its own properties that make them substantially different from the others.

So, while crystals are classified into 7 different crystal systems, there are many more crystal classes and many varieties of crystals and families of crystals. There are also planes, mirrors, and other variables that define why a crystal belongs to a certain crystal system. We’re really only giving you the basics.

Many of these are related in certain ways, such as the crystal structure being the arrangement of atoms that define a crystal, which, in turn, helps define its crystal system. This can be further divided into sets of unit cells (which is what we talk about most when we define the rotational symmetry, not the entire crystal itself). When we look at a crystal structure, we look at the symmetry to define its crystal system.

How Does Symmetry Influence Crystal Structures?

Symmetry plays a pivotal role in shaping crystal structures by dictating the arrangement and repetition of their fundamental components. This intrinsic property not only defines the aesthetic appeal of the crystals but also influences their classification and physical properties. Understanding symmetry in crystals necessitates exploring its two main forms: translational and point symmetry.

Translational Symmetry

This type of symmetry involves repeating a basic unit, known as a motif, systematically across different dimensions of the crystal lattice, such as length, area, or volume. It's this repetition that contributes to the periodic nature and orderly array of particles within the crystal, giving it a consistent and structured appearance.

Point Symmetry

Point symmetry, on the other hand, revolves around the repetition of motifs around a central point within the crystal. This includes several operations:

• Reflection: Creates a mirror image by reflecting a motif across a specific plane.
• Rotation: Involves turning a motif around a central point by a certain angle, resulting in symmetrical appearance after a complete rotation.
• Inversion: Generates a symmetrical image by reflecting a motif across a central point inside the crystal.
• Rotoinversion: A complex operation blending rotation with inversion, producing a unique symmetry.

Crystal Classes and Systems

The combination of these symmetry operations categorizes crystals into 32 distinct classes, which are further grouped into six comprehensive crystal systems. Each system, such as cubic or hexagonal, is characterized by a unique set of symmetry elements. Thus, symmetry is foundational in determining both the outward form of crystals and their internal structural properties.

By governing the repetitive patterns within crystals, symmetry not only dictates their physical appearance but also has profound implications on their mechanical and optical characteristics. Understanding these symmetrical relationships is essential for various applications, from designing new materials to analyzing the properties of natural and synthetic crystals.

What Are Some Applications of Understanding Crystal Structures?

Understanding crystal structures is crucial in various fields due to their influence on material properties. Here's how they make an impact:

1. Material Design: Engineers leverage knowledge of crystal structures to create stronger, more durable materials. For instance, designing alloys with specific atomic arrangements can enhance mechanical strength.

2. Pharmaceuticals: In drug development, the arrangement of molecules within a crystal can affect a drug's solubility and bioavailability, thereby influencing its effectiveness.

3. Electronics: The efficiency of semiconductors is heavily dependent on their crystal structure. High electrical conductivity in metals, due to organized atomic structures, is essential for wires and electronic components.

4. Mineralogy: Identifying minerals often involves studying their crystalline form as specific patterns can help distinguish between different types of minerals.

5. Optics: Crystal structures affect how materials interact with light, impacting applications like lenses, laser technology, and optical fibers.

6. Thermal Management: In technologies that require effective heat dissipation, materials with optimal crystal structures facilitate superior thermal conductivity.

By understanding the intrinsic properties of crystals, industries can tailor materials for specific functions, driving innovation and performance across multiple applications.

What is Crystal Structure and Why is it Important?

Crystal structure refers to the systematic and repeating pattern in which atoms, ions, or molecules are organized within a crystalline substance. This precise arrangement dictates the crystal's overall form and symmetrical properties. More than just defining shape, these arrangements significantly influence the material's characteristics, such as:

• Strength: Determines how a material withstands mechanical forces.
• Electrical Conductivity: Impacts the efficiency with which a material can carry an electric current.
• Thermal Conductivity: Affects how a material transfers heat.
• Optical Properties: Influences how light interacts with the material, affecting transparency and refractive qualities.

Understanding these structures is essential across various scientific disciplines, including chemistry, physics, materials science, and engineering. The reason? The specific arrangement of particles within a crystal is a key determinant of its properties, affecting everything from the durability of building materials to the efficiency of electronic devices. Therefore, knowledge of crystal structures is vital for developing and enhancing materials to suit different industrial and technological applications.

By exploring and analyzing crystal structures, scientists and engineers can innovate and improve materials that are foundational to modern technology and industrial processes.

Understanding the Link Between Crystal Structures and Thermal Conductivity

Crystal structures play a crucial role in determining how efficiently a material can conduct heat. Materials composed of simple, densely packed atomic arrangements tend to exhibit high thermal conductivity. This efficiency stems from their ability to facilitate the transfer of vibrational energy, which is a primary mechanism of heat conduction.

In these close-packed structures, atoms are arranged in such a way that vibrational energy can pass through the material with minimal resistance. This seamless energy transfer reduces thermal resistance and enhances the material's ability to conduct heat.

Conversely, materials with more complex structures might contain voids or irregularities that impede this flow of energy. These disruptions can scatter the vibrational energy, leading to reduced thermal conductivity compared to simpler, more organized structures.

In summary, the thermal conductivity of a material is closely linked to its crystal structure, with simpler and more tightly packed formations generally allowing for better heat conduction.

How Crystal Structures Influence Optical Properties

Crystal structures play a pivotal role in determining their optical properties. The internal arrangement of atoms or molecules within a crystal affects how light interacts with it, impacting its appearance in several ways:

1. Light Transmission: The way crystals are structured influences their transparency. When light enters a crystal, its path is altered by the internal lattice, either allowing it to pass through or blocking it. This is why some crystals are clear while others appear opaque.

2. Color Variations: The structure can also affect the wavelengths of light that are absorbed or reflected, contributing to the crystal's color. Specific arrangements can cause certain wavelengths to be absorbed more than others, giving rise to diverse and vibrant colors.

3. Refractive Index: Crystals have unique refractive indices determined by their internal structures. The refractive index measures how much light bends, or refracts, as it enters the crystal, influencing how sparkling or dull the crystal appears.

4. Birefringence: Some crystal structures cause light to split into two rays, each traveling at different speeds when it enters the crystal. This phenomenon, known as birefringence, creates double images and can affect the perceived color and clarity of the crystal.

In essence, the specific geometrical arrangement within a crystal is what defines its interaction with light, shaping the way we perceive its optical properties.

What Role Do Crystal Structures Play in Electrical Conductivity?

Crystal structures significantly influence a material's ability to conduct electricity. In metals, for example, the arrangement of their atoms plays a crucial role in facilitating the movement of electrons, which is essential for conductivity.

Highly Symmetrical Structures:

• Metals often form in face-centered cubic (FCC) and body-centered cubic (BCC) structures. These arrangements are both highly symmetrical.
• Such symmetry allows for closely packed atoms, creating pathways that facilitate the free movement of electrons.

Free Electron Movement:

• The densely packed nature of these structures means that electrons can move more freely and easily between atoms.
• This freedom of movement is what grants metals their high electrical conductivity, making them excellent conductors.

In summary, the specific atomic arrangement within a crystal structure directly affects how well electrons can travel through the material, thus determining its electrical conductivity.

Understanding the Impact of Crystal Structures on Mechanical Strength

When it comes to mechanical strength, the arrangement of atoms within a crystal structure plays a pivotal role. Generally, denser, tightly packed crystal structures are known for their robust strength. This is because the atoms are closely aligned, allowing for more effective distribution of applied stress, thereby enhancing the material's resistance to deformation.

On the other hand, crystals with a more open or less dense configuration tend to be weaker and more brittle. In these structures, atoms are spaced further apart, making the material more susceptible to cracking or breaking under pressure. This lack of structural integrity results in a diminished ability to withstand force without fracturing.

In summary, the compactness of a crystal structure directly correlates with its strength, with closer atomic packing leading to stronger materials and dispersed arrangements resulting in weaker, more brittle substances.

What Are Crystal Forms and How Are They Determined?

Crystal forms refer to the arrangement of faces on a crystal that are related through symmetry. These faces can be seen as external markers of the crystal's internal structure. Essentially, a crystal form is a group of crystal surfaces that share equivalent symmetry properties.

Understanding Crystal Forms:

• Symmetry Operations: The determination of a crystal's form hinges on symmetry operations, which include rotations, reflections, and inversions. These operations dictate how the different faces of a crystal relate to one another.

• Simple vs. Complex Forms: A simple crystal may exhibit just one form, typically defined by fewer symmetrical relationships. In contrast, more intricate crystals might display a combination of several forms, each contributing to the crystal's overall geometry.

• Isometric System: Within specific crystallographic systems—such as the isometric system—various crystal forms exist. The isometric system, for instance, allows for up to 15 distinct forms. These include well-known geometric shapes like prisms, pyramids, and dipyramids.

Crystal forms are critical in identifying and classifying minerals, providing insight into their inherent symmetrical properties and internal atomic arrangements.

Understanding Translational Symmetry in Crystallography

Translational symmetry in crystallography refers to the repetitive pattern created when a specific motif, or design, is systematically moved across space. This systematic repetition occurs in a three-dimensional structure, forming an organized framework known as a lattice.

At the heart of this concept is the unit cell—the smallest segment that, when repeated in various directions, constructs the entire lattice. Each unit cell builds upon the previous one by stepping linearly in space, creating a seamless extension in all directions.

Key features of this process include:

• Lattice Points: These are pivotal positions within the lattice where unit cells connect at their corners. These points serve as anchors for the repeating pattern.

• Crystallographic Axes: Invisible lines that demonstrate the boundaries and orientation of unit cells, guiding the translation and ensuring uniformity.

In essence, translational symmetry is the backbone that supports the structured, predictable arrangement of molecules or atoms within a crystalline material, paving the way for its distinct properties and functionalities.

Understanding Crystal Lattices and Their Relation to Crystal Structure

A crystal lattice serves as the foundational blueprint for the organization of a crystal structure. Imagine a three-dimensional grid where each intersection, or point, marks the position of a repeating unit within the crystal. This intricate pattern allows for the orderly placement of atoms or ions, creating the crystal's overall structure.

The Role of Unit Cells

At the heart of this spatial organization is the unit cell. It's the smallest repeating unit that, when stacked in all directions, generates the entirety of the crystal. The precise arrangement of these unit cells within the lattice dictates the geometric beauty and uniformity seen in crystals.

Bravais Lattices and Symmetrical Arrangements

Auguste Bravais, a pioneer in crystallography, categorized these spatial configurations into 14 unique types, known today as Bravais lattices. Each type characterizes a distinct symmetrical arrangement, reflecting the diversity of possible crystal structures. These arrangements are crucial because they influence the physical properties of the crystal, such as its strength, cleavage, and optical characteristics.

The Connection

In summary, the crystal lattice acts as the architectural framework, while the crystal structure is the resulting design. This relationship is pivotal, as the lattice determines how individual atoms or ions align to form the crystal, ultimately shaping its form and function. Understanding these fundamentals highlights not just the aesthetics of crystals, but their relevance in applications ranging from electronics to materials science.

Types of Planar and Three-Dimensional Lattices

In Two-Dimensional Space:

When examining two-dimensional space, there are five distinct lattice types. These are essential for understanding the arrangement of points in a flat plane:

• Square Lattices: Feature points forming perfect squares.
• Rectangular Lattices: Points align in rectangles, allowing varying lengths.
• Centered Rectangular Lattices: Similar to rectangular but with additional points in the center of each rectangle.
• Parallelogram Lattices: Points form parallelograms that slant at varying angles.
• Hexagonal Lattices: Points create hexagonal patterns, common in many natural structures.

In Three-Dimensional Space:

For three-dimensional structures, there are 14 unique lattice forms, collectively known as Bravais lattices. These varied lattices represent different arrangements and shapes of unit cells:

• Simple Cubic: Basic cubic arrangement of points.
• Body-Centered Cubic: Adds a point at the center of the cube.
• Face-Centered Cubic: Features points at the faces and corners of the cube.
• Hexagonal: Extends hexagonal form into three dimensions.
• Additional variations, including orthorhombic, tetragonal, and rhombohedral, add complexity and diversity.

These lattice types are fundamental to crystallography, helping to classify and describe material structures across scientific disciplines.

What Are Lattice Points?

Lattice points in a crystal structure are fundamental positions that illustrate the presence of an atom or a cluster of atoms. These points are crucial as they repeat at regular intervals throughout the structure, establishing the crystal's orderly pattern. By following this repetitive arrangement, lattice points define the symmetry and distinctive configuration of the crystal. Essentially, they form a grid-like framework that supports the understanding of the crystal's internal organization and overall geometric design. This systematic repetition is what gives crystals their unique characteristics and stability.

The Wrap Up

Crystal Systems are very complex. There is a lot of analysis and geometry that goes into defining a crystal. But there’s so much more to defining a crystal. There are light properties, hardness, color, lustre, chemicals, lattice systems, and more.

But crystal systems aren’t a bad place to start. Take your favorite crystal and look it up. What crystal system does it have? Is it symmetrical? Not very symmetrical at all? Well, no matter the answer, we thank you for reading!

 

Sources:

https://opengeology.org/Mineralogy/10-crystal-morphology-and-symmetry/

https://www.mindat.org/glossary/crystal_systems

https://www.mindat.org/system_search.php?c=Hexagonal

https://www.mindat.org/system_search.php?c=Trigonal

https://www.mindat.org/system_search.php?c=Isometric

https://www.mindat.org/system_search.php?c=Monoclinic

https://www.mindat.org/system_search.php?c=Triclinic

https://www.mindat.org/system_search.php?c=Orthorhombic

https://www.mindat.org/system_search.php?c=Tetragonal