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X-Ray Crystallography (BIOL 595) > Lecture 5 - Crystal geometry > Flashcards

Lecture 5 - Crystal geometry Flashcards

1
Q

The lattice is a

A

geometric/algebraic concept correlated with the periodic translations of matter in the crystal

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2
Q

The lattice specifies the translational repetition within the crystal by

A

a set of points and/or the vectors that define the locations of those points

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3
Q

Each point in a lattice has

A

an identical environment with respect to the matter in the crystal and with respect to the other points of the lattice

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4
Q

The crystal systems classify crystals according to

A

the presence of particular symmetries within the crystal structure

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5
Q

The broadest system classification is the

A

crystal system

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6
Q

There are _____ standard 2D crystal systems

A

4

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7
Q

There are _____ standard 3D crystal systems

A

7

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8
Q

The number of crystal systems is equal to the number of

A

standard unit cell types

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9
Q

Oblique crystal system symmetry

A

1- or 2-fold rotations, no reflections

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10
Q

Rectangular crystal system symmetry

A

1- or 2-fold rotation + reflection symmetry

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11
Q

Square crystal system symmetry

A

4-fold rotation

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12
Q

Hexagonal crystal system symmetry

A

3- or 6-fold rotation

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13
Q

a, b, and y in oblique 2D unit cells

A

all unrestricted

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14
Q

a, b, and y in rectangular 2D unit cells

A

a and b unrestricted
y = 90 degrees

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15
Q

a, b, and y in square 2D unit cells

A

a = b
y = 90 degrees

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16
Q

a, b, and y in hexagonal 2D unit cells

A

a = b
y = 120 degrees

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17
Q

Filling the oblique unit lattice with a molecule creates an

A

oblique unit cell

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18
Q

Primitive unit cell

A

Lattice points only at the vertices

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19
Q

Centered unit cell

A

Lattice points at places other than vertices

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20
Q

Unit lattice + motif =

A

unit cell

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21
Q

Protein crystals are so fragile and sensitive to environmental changes because

A

only a few contacts exist within the crystal

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22
Q

Only ______ and ______ unit cells allow an entirely arbitrary choice of origin

A

primitive p1 and P1

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23
Q

Any crystallographic symmetry operation must generate

A

an identical copy of the motif

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24
Q

Translational restrictions limit all crystallographic rotation operations to

A

2-, 3-, 4-, and 6-fold rotations

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25
Q

Unit cell

A

The translationally repeated motif that is linked to a repeated volume

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26
Q

Asymmetric unit

A

A smaller box in the unit cell that has internal symmetry and contains the truly unique atoms

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27
Q

The asymmetric unit of a unit cell contains all the necessary information to generate the

A

complete unit cell of a crystal structure by applying its symmetry operations to the asymmetric unit

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28
Q

Translation of the molecules related by 2-fold axis generates

A

additional 2-fold symmetry axes

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29
Q

The tetragonal unit cell is generated by rotation around a

A

4-fold axis

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30
Q

Translating the p4 plane structure creates new

A

2-fold and 4-fold axes

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31
Q

The asymmetric unit of p4 covers _____ of the unit cell

A

1/4

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32
Q

A hexagonal tile can be divided into ______ equivalent rhomboids

A

three

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33
Q

A hexagon can be created from

A

three trigonal unit cells (rotated 120) or hexagonal unit cells (rotated 60)

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34
Q

Hexagonal internal symmetry creates additional 2-fold axes on

A

the cell edges and in the center of the hexagonal unit cell

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35
Q

In a trigonal p3 structure, after generating the unit cell contents by a 3-fold rotation, lattice translations a and b generate

A

the structure (2-D crystal)

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36
Q

For small molecules, there are _____ plane groups

A

17

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37
Q

For macromolecules, there are _____ plane groups

A

5 (p1, p2, p3, p4, p6)

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38
Q

In proteins, there are no mirror planes, only

A

translations and screw axes

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39
Q

Two-fold screw axis (21)

A

2-fold rotation, followed by translation b/2 parallel to b

40
Q

Three-fold screw axis (31)

A

Rotation of 120 degrees followed by translation z=1/3 parallel to c

41
Q

Three-fold screw axis (32)

A

Rotation of 120 degrees followed by translation z=2/3 parallel to c

42
Q

The symbol for a screw axis is

A

nm (m is a subscript)

43
Q

For a screw axis, n idicates

A

the type of rotation

44
Q

For a screw axis, the translation is ____ of the unit cell

A

m/n

45
Q

Non-crystallographic symmetry (NCS) exists when

A

more than one ‘identical’ object is present in the asymmetric unit

46
Q

Each point (p) in a 3-D lattice can be assigned a unique

A

real space lattice vector (r)

47
Q

The components of ‘r’ are given in

A

fractions of the unit cell vectors a, b, c

48
Q

x, y, and z are dimensionless crystallographic coordinates called

A

fractional coordinates

49
Q

For any standard assignment of the lattice and unit cell, lattice points occur at

A

all vertices of the cell

50
Q

A primitive unit cell has lattice points only at the vertices of the cell and contains one copy of

A

the crystal’s translational motif

51
Q

Can a primitive cell be assigned to every crystal?

A

Yes

52
Q

A non-primitive cell contains ______ copy of the translationally replicated motif, and ______ lattice point

A

more than one; more than one

53
Q

Non-primitive unit cells have additional lattice points at

A

locations other than the vertices

54
Q

Non-primitive lattices/cells are preferred for particular structures because

A

they correlate the basis vectors of the unit cell with directions of symmetry elements

55
Q

Six primitive 3-D lattices

A

Triclinic
Monoclinic
Orthorhombic
Trigonal, hexagonal
Tetragonal
Cubic

56
Q

Symbols associated with 3D Bravais lattices are show as

A

italic capital letters

57
Q

Bravais lattice symbol P

A

primitive

58
Q

Bravais lattice symbol A, B, C

A

face-centered (on A, B, or C)

59
Q

Bravais lattice symbol I (eye)

A

body centered

60
Q

Bravais lattice symbol F

A

centered on all faces

61
Q

Bravais lattice symbol R

A

rhombohedral

62
Q

8 centered Bravais lattices

A

Monoclinic (C)
Tetragonal (I)
Orthorhombic (I, F, C)
Cubic (I, F)
Trigonal (R)

63
Q

How many space groups are there for macromolecules?

A

65

64
Q

Most common space group for macromolecules

A

P2(1)2(1)2(1)

65
Q

If A is an m x r matrix, and B is an r x n matrix, the product AB is

A

m x n

66
Q

2-fold rotation symbolic operators

A

-x, -y, z

67
Q

2-fold screw symbolic operators

A

-x, -y, z + 1/2

68
Q

For the matrix W(R,T), W is the

A

symmetry operator

69
Q

For the matrix W(R,T), R is the

A

rotational matrix

70
Q

For the matrix W(R,T), T is the

A

translational component (column vector)

71
Q

Each symmetry operation W can be expressed as a

A

3 x 3 rotation matrix, R, and a translational component T

72
Q

Space groups are mathematical groups of

A

operators (specifically symmetry operators)

73
Q

The conditions for forming a space group G with elements g1, 2, …j are

A

closure
identity
inversion
associativity

74
Q

Space groups with freely selectable origins are called

A

polar space groups

75
Q

Any point with fractional coordinate vector x can be converted into the Cartesian coordinate vector X by

A

multiplication with the orthogonalization matrix O

76
Q

The relationship between the real space and reciprocal space is a

A

Fourier transform

77
Q

Where is real space?

A

The crystal

78
Q

Where is reciprocal space?

A

The diffraction pattern

79
Q

The reciprocal lattice is

A

a mathematical construct that simplifies metric calculations

80
Q

A lattice plane of given Bravais lattices is a

A

a plane whose intersections with the lattice are periodic and intersect the Bravais lattice

81
Q

A lattice plane is any plane containing

A

at least three noncolinear Bravais lattice points

82
Q

All lattice planes can be described by a set of integer

A

Miller indices

83
Q

As h and k increase, the corresponding interplanar distance, d,

A

decreases (small d)

84
Q

In the case of an orthogonal real lattice, the direction of each reciprocal axis coincides with

A

the direction of its corresponding real axis

85
Q

Following the construction rules, we can extend the reciprocal lattice to

A

fill the reciprocal space

86
Q

Each and every lattice vector, rhk, corresponds to

A

a distinct set of lattice planes, hk

87
Q

The tighter the lattice plane spacing, the

A

larger the extent of the reciprocal space becomes

88
Q

An important direct consequence of the translation symmetry of lattices is that the

A

indices of centrosymmetrically related lattice planes are also centrosymmetric

89
Q

The centrosymmetrically related lattice planes hk and -h-k generate reciprocal lattices vectors pointing in

A

opposite directions and of equal magnitude

90
Q

a* is normal to plane

A

b,c

91
Q

Sets of parallel and equidistant lattice planes are defined by their

A

Miller indices, hkl

92
Q

The Miller indices are integer numbers indicating the number of

A

intercepts of a set of lattice planes with each of the unit cell axes

93
Q

The closer the interplanar spacing, the ______ the indices hkl

A

larger

94
Q

The larger the indices hkl, the ______ the planes hkl “slice” or sample the cell

A

more tightly

95
Q

Tight sampling means ______ information

A

more

96
Q

High hkl provide ______ detail about the sampled structure

A

more

X-Ray Crystallography (BIOL 595) (12 decks)

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