The Arrangement of Atoms in a Crystal

Most solid substances are crystalline in nature. Sometimes the particles of a sample of solid substance are themselves single crystals, such as the cubic crystals of sodium chloride in table salt. Sometimes these single crystals are very large occasionally crystals of minerals several meters in diameter are found in nature. 

A polished and etched surface of a piece of cold-drawn copper bar, showing the small crystal grains that compose the ordinary metal. Magnification 200 x (200-fold linearly). The small round spots are gas bubbles. 

The arrangement of atoms in a crystal of copper. The small cube, containing four copper atoms, is the unit of structure by repeating it the entire crystal is obtained. 

Another atomic view of a copper crystal, showing small octahedral faces and large cube faces. 

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In order to understand the techniques of crystal structure analysis, the reader must appreciate the significance of the terms crystal and diffraction. One can then learn how to measure the X-ray diffraction pattern of a crystal and find experimentally, with high precision, the arrangement of atoms in the crystal under study. The first part of this book describes experimental techniques used to determine the arrangement of atoms in a crystal. The second part deals with the chemical and biochemical information that can be learned from the results of such analyses. 

X-ray diffraction X-ray diffraction can be used to determine the arrangement of atoms in a crystal. Simply put, this involves using X-rays (which are electromagnetic radiation with wavelengths about the same as the distances between neighbouring atoms in a crystal) to take pictures of the crystal structure. 

Unit cell (1915) n. The basic unit for describing the arrangement of atoms in a crystal. The smallest parallelepiped, which can generate the crystal lattice by repeated translations along the axes of the lattice. 

Knowing the arrangement of atoms in a crystal, it is easy to calculate the intensity of X-ray reflection. More difficult, however, is the problem of calculating the arrangement of atoms in a crystal from an experimentally measured diffraction picture. This problem is the essence of modem X-ray crystal structure analysis for which M. von Laue (1914) and W.L. and W.H. Bragg (1915) were awarded Nobel Prizes. 

A crystal may be defined as an orderly three-dimensional array of atoms, and all metals are aggregates of more or less imperfect crystals. In considering the structure of metals, therefore, it is convenient to start with the arrangement of atoms in a perfect metal crystal and then to proceed to the imperfections which are always present in the crystal structure. 

Fig. 12-10.—The arrangement of atoms in a layer of the boric acid crystal. Large circles represent oxygen atoms and small circles boron atoms. The double lines represent hydrogen bonds.

Therefore, in this example, the number of particles was reduced to a reasonable value and, in the first instance, instead of the random packing shown in the previous section, a regular arrangement consisting of spherical particles was assumed. Similar to the arrangement of atoms in ideal crystals, two densest particle beds were chosen. For the body-centered cubic (bcc) arrangement of catalyst particles, the void fraction is equal to 32%, for the face-centered cubic (fee) arrangement, it is 26%. 

Hie disturbance by abrasive action of the orderly arrangement of atoms in a crystal may be detected by x-ray diffraction early experiments demonstrated such phenomena (3). Armstrong (4) has described a number of x-ray techniques which have been used on inorganic materials such as quartz. Surface abrasion damage was a major problem in the technology of... 

Cubic close packing arrangement of atoms in a crystal in their closest possible way having cubic symmetry Diagenesis process that affects a sediment while it is at, or near, the Earth s surface (caused by temperature and pressure) Dyke a vertical sheet of igneous rock extruded into an existing rock... 

The entire arrangement of atoms in a crystal may be described in terms of the unit cell dimensions, the coordinates of each atom in the asymmetric unit, and the space group symmetry. 

Turning to the crystal structure of compounds of unlike atoms, we find that the structure is built up on the skeleton of a Bravais lattice but that certain other rules must be obeyed, precisely because there are unlike atoms present. Consider, for example, a crystal of A Bj, which might be an ordinary chemical compound, an intermediate phase of relatively fixed composition in some alloy system, or an ordered solid solution. Then the arrangement of atoms in A By must satisfy the... 

A unit cell is the smallest arrangement of atoms in a crystal lattice that has the same symmetry as the whole crystal. Like the formula unit that you read about in Chapter 7, a unit cell is a small, representative part of a larger whole. The unit cell can be thought of as a building block whose shape determines the shape of the crystal. 

Unit Cell The basic unit for describing the ordered arrangement of atoms in a crystal. 

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