## Solid state physics |

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Results 1-3 of 13

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1-3

to any other lattice point. Obviously, all lattice vectors R in the two-dimensional

square lattice (Fig. 1-2) have the form R = riiai + n2aj, where n\ and n2 are

integers (including negative values and zero), and a is the distance between

adjacent lattice points in the x or y directions, as shown in Fig. 1-2. i and j are unit

vectors in the x and y directions, respectively. If we define two vectors (see Fig. 1-

3), ai = ai, ...

1-3

**Basis Vectors**A lattice vector is a vector which takes us from one lattice pointto any other lattice point. Obviously, all lattice vectors R in the two-dimensional

square lattice (Fig. 1-2) have the form R = riiai + n2aj, where n\ and n2 are

integers (including negative values and zero), and a is the distance between

adjacent lattice points in the x or y directions, as shown in Fig. 1-2. i and j are unit

vectors in the x and y directions, respectively. If we define two vectors (see Fig. 1-

3), ai = ai, ...

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Thus, any lattice vector R can be written as a linear combination of ai and a2 (

using integers, n\ and n2). Conversely, it is also true that any linear combination

of ai and a 2 (using integers, n\ and is a lattice vector R. Such vectors, a.\ and a2,

are called

not unique. We could just as well choose (see Fig. 1-4) ax = ai, a2 = ai + aj. (1-4)

For example, consider the lattice vector R = ai + 2aj. This can be written as R = ai

+ 2a2 ...

Thus, any lattice vector R can be written as a linear combination of ai and a2 (

using integers, n\ and n2). Conversely, it is also true that any linear combination

of ai and a 2 (using integers, n\ and is a lattice vector R. Such vectors, a.\ and a2,

are called

**basis vectors**of the lattice. The choice of**basis vectors**, ai and a2, isnot unique. We could just as well choose (see Fig. 1-4) ax = ai, a2 = ai + aj. (1-4)

For example, consider the lattice vector R = ai + 2aj. This can be written as R = ai

+ 2a2 ...

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1-29a), all three

them are arbitrary. In the primitive monoclinic lattice (Fig. 1-29b), all three

is perpendicular to the other two. Just as we were able to produce the bcc and fcc

lattices by adding extra lattice points to the sc lattice, we can produce the base-

centered monoclinic lattice (Fig. 1-29c) by adding lattice points to two of the six

faces of ...

1-29a), all three

**basis vectors**are unequal in length, and the angles betweenthem are arbitrary. In the primitive monoclinic lattice (Fig. 1-29b), all three

**basis****vectors**are also unequal in length, but one of them (the vertical one in the figure)is perpendicular to the other two. Just as we were able to produce the bcc and fcc

lattices by adding extra lattice points to the sc lattice, we can produce the base-

centered monoclinic lattice (Fig. 1-29c) by adding lattice points to two of the six

faces of ...

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### Contents

XRay Diffraction | 37 |

Lattice Vibrations | 61 |

Classical Model of Metals | 89 |

Copyright | |

12 other sections not shown

### Common terms and phrases

Answer Appendix basis vectors bcc lattice bond Bragg angle Bragg's Law Bravais lattice Brillouin zone called Chapter collisions conduction electrons Consider conventional unit cell Cooper pairs depletion layer diode direction dispersion curve displacement distance doped effective mass elec electric current electric field electrons and holes emitter energy band equal example Fermi energy Fermi level Fermi surface force forward biased free electron free particle frequency given by Eq inside integers ions k-space laser lattice parameter lattice points lattice vector lattice wave magnetic field n-type semiconductor NaCl negative neutrons number of electrons obtain occupied one-dimensional oscillate p-n junction photon positively charged potential energy primitive unit cell Problem rays reciprocal lattice reverse biased sc lattice scattered Schroedinger's equation shown in Fig sodium metal solid structure superconductor temperature tion transistor trons unit cell unoccupied values velocity voltage wave function wave number wave vector wavelength Wigner-Seitz cell wire x-ray diffraction zero