Crystalline on Solids

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What is a crystalline material?

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123 Terms

1

What is a crystalline material?

A material in which atoms are arranged in a repeating pattern

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2

What is the term for long-range order in a crystalline material?

Crystal structure

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3

Which materials form crystalline structures under normal solidification conditions?

Metals, ceramic materials, and certain polymers

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4

What is the term for materials that do not crystallize?

Noncrystalline or amorphous materials

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5

What do the properties of crystalline solids depend on?

The crystal structure of the material

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6

How many different crystal structures exist?

An extremely large number

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7

What do we call the model where atoms are represented as solid spheres?

Atomic hard-sphere model

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8

What is a lattice in the context of crystal structures?

A three-dimensional array of points coinciding with atom positions

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9

What are small repeat entities in a crystal structure called?

Unit cells

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10

What shape do most unit cells have?

Parallelepipeds or prisms with three sets of parallel faces

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11

How are atom positions generated within a crystal structure?

By translations of the unit cell integral distances along each of its edges

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12

What is the basic structural unit of a crystal structure?

The unit cell

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13

How are parallelepiped corners positioned in relation to hard-sphere atoms?

Coincide with centers of the hard-sphere atoms

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14

Can multiple unit cells be chosen for a particular crystal structure?

Yes

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15

Which unit cell is generally used for a crystal structure?

The one with the highest level of geometrical symmetry

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16

What type of atomic bonding is found in metallic crystal structures?

metallic

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17

What are the characteristics of atomic packings in metallic crystal structures?

large numbers of nearest neighbors and dense atomic packings

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18

What model is used to represent ions in metallic crystal structures?

hard-sphere model

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19

What are the three common crystal structures found in most metals?

face-centered cubic, body-centered cubic, hexagonal close-packed

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20

Which crystal structure has a unit cell with atoms at each corner and center of all cube faces?

face-centered cubic (FCC)

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21

Which metals have the face-centered cubic crystal structure?

copper, aluminum, silver, gold

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22

How many atoms per unit cell are there in the face-centered cubic crystal structure?

4

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23

What is the coordination number for face-centered cubic crystals?

12

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24

What is the atomic packing factor for face-centered cubic crystals?

0.74

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25

Which crystal structure has a unit cell with atoms at all eight corners and a single atom at the center of the cube?

body-centered cubic (BCC)

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26

Which metals have the body-centered cubic crystal structure?

chromium, iron, tungsten

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27

How many atoms per unit cell are there in the body-centered cubic crystal structure?

2

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28

What is the coordination number for body-centered cubic crystals?

8

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29

What is the atomic packing factor for body-centered cubic crystals?

0.68

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30

Which crystal structure consists of atoms only at the corners of a cube?

simple cubic (SC)

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31

Which element has a simple cubic crystal structure?

polonium

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32

Which crystal structure has a hexagonal unit cell with regular hexagons on top and bottom faces surrounding a single atom in the center?

hexagonal close-packed (HCP)

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33

Which metals have the hexagonal close-packed crystal structure?

cadmium, magnesium, titanium, zinc

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34

How many atoms per unit cell are there in the hexagonal close-packed crystal structure?

6

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35

What is the coordination number for hexagonal close-packed crystals?

12

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36

What is the atomic packing factor for hexagonal close-packed crystals?

0.74

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37

What is the relationship between unit cell length (a) and atomic radius (R) in face-centered cubic crystals?

a = 2R√2

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38

What is the relationship between unit cell length (a) and atomic radius (R) in body-centered cubic crystals?

a = 4R/√3

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39

What is the relationship between unit cell length (a) and atomic radius (R) in hexagonal close-packed crystals?

c/a = 1.633

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40

How are atoms shared among adjacent unit cells in face-centered cubic crystals?

Atoms at corners are shared by eight cells, atoms at faces are shared by two cells, and there are no interior atoms.

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41

How are atoms shared among adjacent unit cells in body-centered cubic crystals?

Atoms at corners are shared by eight cells, and there is one interior atom per cell.

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42

How are atoms shared among adjacent unit cells in hexagonal close-packed crystals?

Atoms at corners are shared by six cells, atoms at faces are shared by two cells, and there are three midplane interior atoms.

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43

What is the formula to compute the theoretical density of a metallic solid?

𝜌 =(nA)/(VCNA)

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44

What does n represent in the density computation formula?

number of atoms associated with each unit cell

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45

What does A represent in the density computation formula?

atomic weight

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46

What does VC represent in the density computation formula?

volume of the unit cell

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47

What does NA represent in the density computation formula?

Avogadro’s number (6.022 × 1023 atoms/mol)

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48

What is polymorphism?

The phenomenon of having more than one crystal structure

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49

What is allotropy?

Polymorphism in elemental solids

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50

What determines the prevailing crystal structure in polymorphism and allotropy?

temperature and external pressure

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51

Give an example of polymorphism in carbon.

graphite and diamond

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52

At what conditions is graphite the stable polymorph of carbon?

ambient conditions

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53

At what conditions is diamond formed as a polymorph of carbon?

extremely high pressures

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54

What is the crystal structure of pure iron at room temperature?

BCC (Body-Centered Cubic)

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55

At what temperature does pure iron change its crystal structure to FCC (Face-Centered Cubic)?

912°C (1674°F)

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56

How many different crystal systems are there based on unit cell geometry?

seven

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57

What are the seven crystal systems based on unit cell geometry?

cubic, tetragonal, hexagonal, orthorhombic, rhombohedral, monoclinic, triclinic

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58

Which crystal system has the highest degree of symmetry?

cubic

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59

Which crystal system has the least symmetry?

triclinic

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60

In which crystal system do FCC and BCC structures belong?

cubic

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61

In which crystal system does HCP (Hexagonal Close-Packed) structure belong?

hexagonal

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62

How many different Bravais lattices are there?

fourteen

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63

What did Auguste Bravais discover about lattice structures?

There are only fourteen different lattice structures.

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64

What method is used to determine the arrangement of atoms in a crystal?

X-ray Diffraction

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65

What is X-ray Diffraction used for?

Determining the arrangement of atoms in a crystal

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66

Who formulated Bragg's Law?

William Henry Bragg and William Lawrence Bragg

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67

What does Bragg's Law calculate in X-ray Diffraction?

The diffraction of X-ray beams

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68

What are crystallogic points, directions, and planes used for?

specifying locations and orientations in crystalline materials

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69

How many numbers or indices are used to designate point locations, directions, and planes?

three

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70

What is the basis for determining index values?

the unit cell with a right-handed coordinate system

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71

Which crystal systems have axes that are not mutually perpendicular?

hexagonal, rhombohedral, monoclinic, triclinic

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72

What are lattice position coordinates associated with?

x, y, and z axes

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73

What is the notation for lattice position coordinates?

Px, Py, and Pz

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74

How are lattice position coordinates determined?

multiplying point indices by unit cell edge lengths

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75

What is a crystallographic direction defined as?

a line directed between two points or a vector

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76

How many steps are used to determine directional indices?

five

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77

What are equivalent directions in cubic crystals grouped into?

a family enclosed in angle brackets (〈〉)

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78

Are equivalent directions in cubic crystals represented with the same order and sign of indices?

yes

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79

How are crystallographic planes specified in all but the hexagonal crystal system?

by three Miller indices (hkl)

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80

What is the procedure to determine the h, k, and l index numbers for crystallographic planes?

intersect or parallel each axis and take reciprocals of intercepts

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81

Are planes parallel to each other equivalent and have identical indices?

yes

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82

What is a family of planes designated by?

indices enclosed in braces ({})

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83

In which crystal system do planes having the same indices irrespective of order and sign are equivalent?

cubic system

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84

What is the favored indexing system for crystals with hexagonal symmetry?

the four-index (hkil) scheme

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85

What is the relationship between directional equivalency and linear density?

For a specific material, equivalent directions have identical linear densities.

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86

What is linear density (LD)?

The number of atoms per unit length whose centers lie on a specific crystallographic direction.

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87

What are the units for linear density?

Reciprocal length (e.g., nm−1, m−1).

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88

How can linear density be calculated?

Number of atoms centered on direction vector divided by the length of direction vector.

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89

What is the linear density of the [110] direction in FCC?

1/2R

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90

What is planar density (PD)?

The number of atoms per unit area that are centered on a particular crystallographic plane.

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91

What are the units for planar density?

Reciprocal area (e.g., nm−2, m−2).

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92

How can planar density be calculated?

Number of atoms centered on a plane divided by the area of the plane.

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93

What is the planar density of the (110) plane in FCC?

1/(4R2√2)

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94

What are linear and planar densities important considerations for?

The process of slip and metal plastic deformation.

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95

What is slip?

The mechanism by which metals plastically deform.

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96

What crystal structures have atomic packing factors of 0.74?

Face-centered cubic (FCC) and hexagonal close-packed (HCP) crystal structures.

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97

How can FCC and HCP crystal structures be described in terms of close-packed planes?

The stacking of close-packed planes on top of one another.

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98

What is the stacking sequence for FCC crystal structure?

ABCABCABC...

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99

What is the stacking sequence for HCP crystal structure?

ABABAB...

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100

Where are the centers of the third plane located in HCP crystal structure?

Directly above the original A positions.

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