44
Crystal Structure Types of Solids Amorphous: Solids with considerable disorder in their structures (e.g., glass). Amorphous: lacks a systematic atomic arrangement. Crystalline: Solids with rigid a highly regular arrangement of their atoms. (That is, its atoms or ions, self-organized in a 3D periodic array). These can be monocrystals and polycrystals. Amorphous crystalline polycrystalline

Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

  • Upload
    others

  • View
    10

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Crystal StructureTypes of Solids

Amorphous: Solids with considerable disorder in their structures (e.g., glass). Amorphous: lacks a systematic atomic arrangement.

Crystalline: Solids with rigid a highly regular arrangement of their atoms. (That is, its atoms or ions, self-organized in a 3D periodic array). These can be monocrystals and polycrystals.

Amorphous crystalline polycrystalline

Page 2: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

To discuss crystalline structures it is useful to consider atoms as being hard spheres with well-defined radii. In this hard-sphere model, the shortest distance between two like atoms is one diameter.Lattice: A 3-dimensional system of points that designate the positions of the components (atoms, ions, or molecules) that make up the substance. Unit Cell: The smallest repeating unit of the lattice.The lattice is generated by repeating the unit cell in all three dimensions

Page 3: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Crystal SystemsCrystallographers have shown that only seven different types of unit cells are necessary to create all point latticeCubic a= b = c ; α = β = γ = 90Tetragonal a= b ≠ c ; α = β = γ = 90Rhombohedral a= b = c ; α = β = γ ≠ 90Hexagonal a= b ≠ c ; α = β = 90, γ =120Orthorhombica≠ b ≠ c ; α = β = γ = 90Monoclinic a≠ b ≠ c ; α = γ = 90 ≠ β Triclinic a≠ b ≠ c ; α ≠ γ ≠ β ≠ 90

Bravais LatticesMany of the seven crystal systems have variations of the basic unit cell. August Bravais (1811-1863) showed that 14 standards unit cells could describe all possible lattice networks.

Page 4: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 5: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Principal Metallic StructuresMost elemental metals (about 90%) crystallize upon solidification into three densely packed crystal structures: body-centered cubic (BCC), face-centered cubic (FCC) and hexagonal close-packed (HCP)

Page 6: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Structures of Metallic Elements

Ru

H

Li

Na

K

Rb

Cs

Fr

Be

Mg

Ca

Sr

Ba

Ra

Sc

Y

La

Ac

Ti

Zr

H f

V

Nb

Ta

Cr

Mo

W

Mn

Tc

Re

Fe

Os

Co

Ir

Rh

Ni

Pd

Pt

Cu

Ag

Au

Zn

Cd

Hg

B

Al

Ga

In

Tl

C

Si

Ge

Sn

Pb

N

P

As

Sb

Bi

O

S

Se

Te

Po

F

Cl

Br

I

At

Ne

Ar

Kr

Xe

Rn

He

Primitive Cubic

Body Centered Cubic

Cubic close packing(Face centered cubic)

Hexagonal close packing

Page 7: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Lattice ConstantStructurea, nm c, nm

Chromium 0.289 0.125Iron 0.287 0.124Molybdenum 0.315 0.136Potassium 0.533 0.231Sodium 0.429 0.186

BCC

Copper 0.361 0.128Gold 0.408 0.144Nickel 0.352 0.125Silver 0.409 0.144Zinc 0.2665 0.5618 0.133Magnesium 0.3209 0.5209 0.160Cobalt 0.2507 0.4069 0.125Titanium 0.2950 0.3584 0.147

HCP

FCC

Tungsten 0.316 0.137Aluminum 0.405 0.143

Atomic Radius, nm

Metal

Page 8: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.

• Coordination # = 6 (# nearest neighbors)

SIMPLE CUBIC STRUCTURE (SC)

• Number of atoms per unit cell= 1 atom

Page 9: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

6

APF = Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

• APF for a simple cubic structure = 0.52

APF = a3

4

3π (0.5a)31

atoms

unit cellatom

volume

unit cellvolume

close-packed directions

a

R=0.5a

contains 8 x 1/8 = 1 atom/unit cell

Atomic Packing Factor (APF)

Page 10: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

• Coordination # = 8

• Close packed directions are cube diagonals.--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

Body Centered Cubic (BCC)

aR

Close-packed directions: length = 4R

= 3 a

Unit cell contains: 1 + 8 x 1/8 = 2 atoms/unit ce

APF = a3

4

3π ( 3a/4)32

atoms

unit cell atomvolume

unit cell

volume • APF for a BCC = 0.68

Page 11: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

• Coordination # = 12

• Close packed directions are face diagonals.--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.

Face Centered Cubic (FCC)

a

APF = a3

4

3π ( 2a/4)34

atoms

unit cell atomvolume

unit cell

volume

Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit ce

Close-packed directions: length = 4R

= 2 a

• APF for a FCC = 0.74

Page 12: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Hexagonal Close-Packed (HCP)The APF and coordination number of the HCP structure is the sameas the FCC structure, that is, 0.74 and 12 respectively.An isolated HCP unit cell has a total of 6 atoms per unit cell.

12 atoms shared by six cells = 2 atoms per cell2 atoms shared by two cells = 1 atom per cell

3 atoms

Page 13: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Close-Packed StructuresBoth the HCP and FCC crystal structures are close-packed structure.Consider the atoms as spheres:

Place one layer of atoms (2 Dimensional solid). Layer APlace the next layer on top of the first. Layer B. Note that there are

two possible positions for a proper stacking of layer B.

Page 14: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

A B A : hexagonal close packed A B C : cubic close packed

The third layer (Layer C) can be placed in also teo different positions to obtain a proper stack.

(1)exactly above of atoms of Layer A (HCP) or (2)displaced

Page 15: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

A B C : cubic close pack

A

B CA

120°

90°A

A

B

A B A : hexagonal close pack

Page 16: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 17: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Interstitial sitesLocations between the ‘‘normal’’ atoms or ions in a crystal into which another - usually different - atom or ion is placed. o Cubic site - An interstitial position that has a coordination number of eight. An atom or ion in the cubic site touches eight other atoms or ions.o Octahedral site - An interstitial position that has a coordination number of six. An atom or ion in the octahedral site touches sixother atoms or ions.o Tetrahedral site - An interstitial position that has a coordination number of four. An atom or ion in the tetrahedral site touches four other atoms or ions.

Page 18: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Interstitial sitesare importantbecause we canderive morestructures fromthese basic FCC,BCC, HCPstructures bypartially orcompletelydifferent sets ofthese sites

Page 19: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 20: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Density CalculationsSince the entire crystal can be generated by the repetition of the unit cell, the density of a crystalline material, ρ = the density of the unit cell = (atoms in the unit cell, n ) × (mass of an atom, M) / (the volume of the cell, Vc)Atoms in the unit cell, n = 2 (BCC); 4 (FCC); 6 (HCP)Mass of an atom, M = Atomic weight, A, in amu (or g/mol) is given in the periodic table. To translate mass from amu to grams we have to divide the atomic weight in amu by the Avogadro number NA = 6.023 × 1023 atoms/molThe volume of the cell, Vc = a3 (FCC and BCC)

a = 2R√2 (FCC); a = 4R/√3 (BCC)where R is the atomic radius.

Page 21: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Density Calculation

AC NVnA

n: number of atoms/unit cellA: atomic weight

VC: volume of the unit cell

NA: Avogadro’s number (6.023x1023 atoms/mole)

Example Calculate the density of copper.

RCu =0.128nm, Crystal structure: FCC, ACu= 63.5 g/mole

n = 4 atoms/cell, 333 216)22( RRaVC ===

32338

/89.8]10023.6)1028.1(216[

)5.63)(4( cmg=×××

8.94 g/cm3 in the literature

Page 22: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

ExampleRhodium has an atomic radius of 0.1345nm (1.345A) and a density of 12.41g.cm-3. Determine whether it has a BCC or FCC crystal structure. Rh (A = 102.91g/mol)

Solution

AC NVnA

=ρn: number of atoms/unit cell A: atomic weight

VC: volume of the unit cell NA: Avogadro’s number (6.023x1023 atoms/mole)

structure FCC a has Rhodium

01376.04

)1345.0(627.22

627.22)2

4( and 4 n then FCC is rhodium If

0149.02

)1345.0(316.12

316.12)3

4( and 2 n then BCC is rhodium If

01376.0103768.1.10023.6.41.12

.91.102

333

333

333

333

33231233

13

nmnmxna

rra

nmnmxna

rra

nmcmxmoleatomsxcmg

molgNA

na

nV

A

c

==

===

==

===

===== −−−

ρ

Page 23: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Linear And Planar Atomic Densities

Linear atomic density:

= 2R/Ll

Planar atomic density:

Ll

Crystallographic direction

= 2π R2/(Area A’D’E’B’)

34RaLl == = 0.866

A’ E’

Page 24: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Polymorphism or Allotropy

Many elements or compounds exist in more than one crystalline form under different conditions of temperature and pressure. This phenomenon is termed polymorphism and if the material is an elemental solid is called allotropy.

Example: Iron (Fe – Z = 26)

liquid above 1539 C.δ-iron (BCC) between 1394 and 1539 C.γ-iron (FCC) between 912 and 1394 C.α-iron (BCC) between -273 and 912 C.

α iron γ iron δ iron912oC 1400oC 1539oC

liquid iron

BCC FCC BCC

Page 25: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Another example of allotropy is carbon.Pure, solid carbon occurs in three crystalline forms – diamond, graphite; and large, hollow fullerenes. Two kinds of fullerenes are shown here: buckminsterfullerene (buckyball) and carbon nanotube.

Page 26: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 27: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Crystallographic Planes and DirectionsAtom Positions in Cubic Unit CellsA cube of lattice parameter a is considered to have a side equal to unity. Only the atoms with coordinates x, y and z greater than or equal to zero and less than unity belong to that specific cell.

y

z

x

1,0,1

1,0,0

1,1,1

½, ½, ½

0,0,0

0,0,1 0,1,1

1,1,0

0,1,0

1,,0 <≤ zyx

Page 28: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Directions in The Unit Cell

For cubic crystals the crystallographic directions indices are the vector components of the direction resolved along each of the coordinate axes and reduced to the smallest integer.

y

z

x

1,0,1

1,0,0

1,1,1

½, ½, ½

0,0,0

0,0,1 0,1,1

1,1,0

0,1,0A

Example direction A

a) Two points origin coordinates 0,0,0 and final position coordinates 1,1,0

b) 1,1,0 - 0,0,0 = 1,1,0

c) No fractions to clear

d) Direction [110]

Page 29: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

y

z

x

1,1,1

0,0,0

0,0,1

B

C

½, 1, 0

Example direction Ba) Two points origin coordinates

1,1,1 and final position coordinates 0,0,0

b) 0,0,0 - 1,1,1 = -1,-1,-1c) No fractions to cleard) Direction ]111[

___

Example direction Ca) Two points origin coordinates

½,1,0 and final position coordinates 0,0,1

b) 0,0,1 - ½,1,0 = -½,-1,1c) There are fractions to clear.

Multiply times 2. 2( -½,-1,1) = -1,-2,2

d) Direction ]221[__

Page 30: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Notes About the Use of Miller Indices for DirectionsA direction and its negative are not identical; [100] is not equal to

[bar100]. They represent the same line but opposite directions. .direction and its multiple are identical: [100] is the same direction

as [200]. We just forgot to reduce to lowest integers.Certain groups of directions are equivalent; they have their

particular indices primarily because of the way we construct the co-ordinates. For example, a [100] direction is equivalent to the [010] direction if we re-define the co-ordinates system. We may refer to groups of equivalent directions as directions of the same family. The special brackets < > are used to indicate this collection of directions. Example: The family of directions <100> consists of six equivalent directions

00]1[],1[000],1[0[001],[010],[100], >100< ≡

Page 31: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Miller Indices for Crystallographic planes in Cubic CellsPlanes in unit cells are also defined by three integer numbers,

called the Miller indices and written (hkl).Miller’s indices can be used as a shorthand notation to identify

crystallographic directions (earlier) AND planes.Procedure for determining Miller Indices

locate the originidentify the points at which the plane intercepts the x, y and z

coordinates as fractions of unit cell length. If the plane passes through the origin, the origin of the co-ordinate system must be moved!

take reciprocals of these interceptsclear fractions but do not reduce to lowest integersenclose the resulting numbers in parentheses (h k l). Again, the

negative numbers should be written with a bar over the number.

Page 32: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

y

z

x

A

Example: Miller indices for plane Aa) Locate the origin of coordinate.b) Find the intercepts x = 1, y = 1, z = 1c) Find the inverse 1/x=1, 1/y=1, 1/z=1d) No fractions to cleare) (1 1 1)

Page 33: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

More Miller Indices - Examples

ab

c

0.50.5

ab

c

2/31/5

ab

c

ab

c

ab

c

ab

c

Notes About the Use of Miller Indices for PlanesA plane and its negative are parallel and identical. Planes and its multiple are parallel planes: (100) is parallel to the

plane (200) and the distance between (200) planes is half of the distance between (100) planes.

Page 34: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Certain groups of planes are equivalent (same atom distribution); they have their particular indices primarily because of the way we construct the co-ordinates. For example, a (100) planes is equivalent to the (010) planes. We may refer to groups of equivalent planes as planes of the same family. The special brackets { } are used to indicate this collection of planes.

In cubic systems the direction of miller indices [h k l] is normal o perpendicular to the (h k l) plane.

in cubic systems, the distance d between planes (h k l ) is given by the formula where a is the lattice constant.Example: The family of planes {100} consists of three equivalent planes (100), (010) and (001)

222 lkhad

++=

Page 35: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

A “family” of crystal planes contains all those planes are crystallo-graphically equivalent.• Planes have the same atomic packing density• a family is designated by indices that are enclosed by braces.- {111}:

)111(),111(),111(),111(),111(),111(),111(),111(

Page 36: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

• Single Crystal• Polycrystalline materials• Anisotropy and isotropy

Page 37: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

c

(110) = (1100)- -

(100) = (1010)-

a1

a2

a3

(001) = (0001)

(110) = (1100)- -

Two Types of Indices in the Hexagonal System

a1

a2

a3

c

a1

a2

a3

c

Miller: (hkl) (same as before)

Miller-Bravais: (hkil) → i = - (h+k)

a3 = - (a1 + a2)a1 ,a2 ,and c are independent, a3 is not!

Page 38: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

X-Ray Spectroscopy

λν /hchE ==35KeV ~ 0.02-0.14nmMo:

X-Ray Diffraction

Visible light: 0.4-0.7m~ 6000A

Page 39: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

X-Ray Diffraction from a Crystal• Electromagnetic radiation is wave-like:

Electric field + + + + +

- - - - -+

Direction of motion of x-ray photon

•Waves can add constructively or destructively:Electric

field + + + + +- - - - -

+

Sum

=

Page 40: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 41: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Bragg’s Law

For cubic system:

But no all planes diffract !!!

For constructive interference

θlθθl

l

sin2sinsin

hkl

hklhkl

dnddn

EFDEn

=+=

+=

222 lkhadhkl ++

=

Page 42: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125
Page 43: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

For the BCC structure the first two sets of principal diffracting planes are {110} and {200}.

For the FCC structure the first two sets of principal diffracting planes are {111} and {200}.

222

222

2

2

sinsin

BBB

AAA

B

A

lkhlkh

++++

=θθ

)(75.0);(5.0sinsin

2

2

FCCBCCB

A ==θθ

Page 44: Crystal StructureRn He Primitive Cubic Body Centered Cubic Cubic close packing (Face centered cubic) Hexagonal close packing Structure Lattice Constant a, nm c, nm Chromium 0.289 0.125

Ex: An element, BCC or FCC, shows diffraction peaks at 2θ: 40, 58, 73, 100.4 and 114.7.

Determine:

(a) Crystal structure?(b) Lattice constant?(c) What is the element?

From W.F.. Smith, Fundamentals of materials Science And Engineering, McGraw-Hill, 1992, Ex. 3.16.