Understanding Space Lattices and Crystallography

The question asks about the scientist who, in the early nineteenth century, demonstrated the existence of fourteen space lattices. These space lattices are fundamental concepts in crystallography, representing the distinct ways points can be arranged in three-dimensional space to form a repeating pattern.

A space lattice, or Bravais lattice, is an infinite array of discrete points in space generated by translating a single point by a set of three non-coplanar vectors. The arrangement of points must appear the same when viewed from any point in the lattice.

Auguste Bravais and the Fourteen Lattices

In 1848, the French physicist and crystallographer Auguste Bravais made a significant contribution to the field by rigorously demonstrating that there are exactly fourteen unique ways to arrange points in space such that each point has identical surroundings. These fourteen arrangements are known today as the Bravais lattices.

These fourteen Bravais lattices are derived from the seven basic crystal systems by considering all possible types of lattice centering. The seven crystal systems are:

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

The fourteen Bravais lattices account for variations like primitive (P), body-centered (I), face-centered (F), and base-centered (C or A or B) arrangements within these crystal systems, while maintaining the requirement that every lattice point is equivalent.

Bravais's work provided a mathematical and geometric foundation for understanding the structure of crystals, explaining why crystals exhibit specific symmetries and external forms. His demonstration was indeed carried out in the early nineteenth century (specifically, in the mid-1800s, which falls within the early-to-mid part of the century context).

Evaluating Other Options

Let's briefly consider the other scientists mentioned:

• Jerome Karle: An American physical chemist who, along with Herbert A. Hauptman, developed direct methods for the determination of crystal structures using X-ray diffraction data. His work is later than Bravais's and focuses on structure determination rather than the fundamental types of lattices.
• William Bragg: An English physicist, who along with his son Lawrence Bragg, formulated Bragg's law of X-ray diffraction (Bragg condition). This law is crucial for analyzing crystal structures using X-rays, but it doesn't concern the fundamental enumeration of space lattices themselves.
• Charles Frank: A theoretical physicist known for his contributions to various fields, including the theory of liquid crystals and crystal growth mechanisms (like the Frank-Read source for dislocation multiplication). His work is also later than Bravais's and in a different area of crystallography/materials science.

Based on the historical development of crystallography, Auguste Bravais is the scientist credited with demonstrating the fourteen space lattices.

Conclusion

Auguste Bravais systematically identified and classified the fourteen fundamental types of space lattices that describe all possible periodic arrangements of points in three dimensions while preserving the equivalence of all lattice points. His work, published in the mid-1800s, was a cornerstone in the development of modern crystallography.

Revision Table: Space Lattices and Crystal Systems

Understanding space lattices is crucial for crystallography. Here's a quick review:

• Space Lattice: An infinite, repeating arrangement of points in space.
• Bravais Lattice: One of the 14 unique types of space lattices.
• Crystal System: A classification of crystal structures based on the unit cell shape (lengths and angles). There are 7 crystal systems.
• Unit Cell: The smallest repeating unit of a crystal lattice.
• The 14 Bravais lattices are formed by combining the 7 crystal systems with different centering types (P, I, F, C).

Additional Information: Importance of Bravais Lattices in Crystallography

The identification of the 14 Bravais lattices was a fundamental step in understanding the internal structure of crystals. It showed that despite the vast number of crystalline materials, their underlying lattice structures could be classified into a limited number of types. This classification is essential for:

• Predicting and understanding the physical properties of materials, as properties often depend on the symmetry of the crystal structure.
• Interpreting diffraction patterns (like X-ray diffraction) used to determine the arrangement of atoms within a crystal.
• Providing a basis for classifying all possible crystal structures (which are built upon these lattices by adding atoms or molecules to the lattice points or within the unit cell).