Organizacion Atomica

Organizacin Atmica

Materiales Avanzados

Ing. Humberto Gmez. Ph.D

Departamento de Ingeniera Mecnica

Non dense, random packing

Dense, ordered packing

Dense, ordered packed structures tend to have lower energies.

Energy and Packing Energy

r

typical neighbor bond length

typical neighbor bond energy

Energy

r

typical neighbor bond length

typical neighbor bond energy

atoms pack in periodic, 3D arrays

Crystalline materials...

-metals -many ceramics -some polymers

atoms have no periodic packing

Noncrystalline materials...

-complex structures -rapid cooling

crystalline SiO2

noncrystalline SiO2 "Amorphous" = Noncrystalline Adapted from Fig. 3.22(b), Callister 7e.

Adapted from Fig. 3.22(a), Callister 7e.

Materials and Packing

Si Oxygen

typical of:

occurs for:

Single Crystals vs. Polycrystalline Materials

Czochralski process

Melt spinning and rapid solidification

Definitions Lattice

Collection of points that divide space into smaller equally sized segments

Basis

Group of atoms associated with a lattice point

Unit cell

Subdivision of the lattice that still retains the overall characteristics of the entire lattice

Atomic radius

Apparent radius of an atom

Typically calculated from the dimensions of the unit cell, using close-packed directions (depends upon coordination number)

Packing factor

The fraction of space in a unit cell occupied by atoms.

Crystal Structure

Unit Cell

The fourteen types of Bravais lattices grouped in seven crystal systems.

Metallic Crystal Structures

Metals are usually (poly)crystalline; although formation of amorphous metals are possible by rapid cooling As we learned in Chapter 2, the atomic bonding in metals is non-directional no restriction on numbers or positions of

nearest-neighbor atoms large number of nearest neighbors and dense atomic packing

Atom (hard sphere) radius, R, defined by ion core radius -

typically 0.1 - 0.2 nm

The most common types of unit cells are the faced-centered cubic (FCC), the body-centered cubic (BCC) and the hexagonal

close-packed (HCP).

Tend to be densely packed.

Reasons for dense packing:

- Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other

Have the simplest crystal structures.

We will examine three such structures...

Metallic Crystal Structures

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

Coordination # = 6 (# nearest neighbors)

(Courtesy P.M. Anderson)

Simple Cubic Cell (SCC)

APF for a simple cubic structure = 0.52

APF =

a 3

4

3 p (0.5a) 3 1

atoms

unit cell

atom

volume

unit cell

volume

Atomic Packing Factor (APF)

APF = Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

Adapted from Fig. 3.23, Callister 7e.

close-packed directions

a

R=0.5a

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

Department of Mechanical Engineering -24- 7

Coordination # = 8


Atoms touch each other along cube diagonals.

--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

Body Centered Cubic Structure (BCC)

ex: Cr, W, Fe (), Tantalum, Molybdenum

2 atoms/unit cell: 1 center + 8 corners x 1/8

Atomic Packing Factor: BCC

a

APF =

4

3 p ( 3 a/4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =

Close-packed directions:

3 a

APF for a body-centered cubic structure = 0.68

a R


a 2

a 3

Department of Mechanical Engineering -26-

Coordination # = 12


Atoms touch each other along face diagonals.

--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.

Face Centered Cubic Structure (FCC)

ex: Al, Cu, Au, Pb, Ni, Pt, Ag

4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

APF for a face-centered cubic structure = 0.74

Atomic Packing Factor: FCC

maximum achievable APF

APF =

4

3 p ( 2 a/4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume

Close-packed directions:

length = 4R = 2 a

Unit cell contains:

6 x 1/2 + 8 x 1/8

= 4 atoms/unit cell a

2 a


28

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites

ABCABC... Stacking Sequence 2D Projection

FCC Unit Cell

FCC Stacking Sequence

B B

B

B B

B B

B sites

C C

C A

C C

C A

A

B C

Coordination # = 12

ABAB... Stacking Sequence

APF = 0.74

3D Projection 2D Projection


Hexagonal Close-Packed Structure (HCP)

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

c/a = 1.633

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer


Compounds: Often have similar close-packed structures.

Close-packed directions --along cube edges.

Structure of NaCl

(Courtesy P.M. Anderson) (Courtesy P.M. Anderson)

Structure of Compounds: NaCl


Determine the number of lattice points per cell in the cubic crystal systems. If there is only one atom located at each lattice point, calculate the number of atoms per unit cell.

SOLUTION

In the SC unit cell: lattice point / unit cell = (8 corners)1/8 = 1

In BCC unit cells: lattice point / unit cell = (8 corners)1/8 + (1 center)(1) = 2

In FCC unit cells: lattice point / unit cell = (8 corners)1/8 + (6 faces)(1/2) = 4

The number of atoms per unit cell would be 1, 2, and 4, for the simple cubic, body-centered cubic, and face-centered cubic, unit cells, respectively.

Determining the Number of Lattice Points in Cubic Crystal Systems


Determine the relationship between the atomic radius and the lattice parameter in SC, BCC, and FCC structures when one atom is located at each lattice point.

Determining the Relationship between Atomic Radius and Lattice Parameters

(c) 2003 Brooks/Cole Publishing / Thomson

Learning


We find that atoms touch along the edge of the cube in SC structures.

3

40

ra

In FCC structures, atoms touch along the face diagonal of the cube. There are four atomic radii along this lengthtwo radii from the face-centered atom and one radius from each corner, so:

2

40

ra

ra 20

In BCC structures, atoms touch along the body diagonal. There are two atomic radii from the center atom and one atomic radius from each of the corner atoms on the body diagonal, so


Example: Copper Data from Table inside front cover of Callister (see next slide):

crystal structure = FCC: 4 atoms/unit cell atomic weight = 63.55 g/mol (1 amu = 1 g/mol) atomic radius R = 0.128 nm (1 nm = 10 cm) -7

Compare to actual: rCu = 8.94 g/cm3

Result: theoretical rCu = 8.89 g/cm3

Theoretical Density


Density Calculation


Determining the Density of BCC Iron

Determine the density of BCC iron, which has a lattice parameter of 0.2866 nm.

SOLUTION

Atoms/cell = 2, a0 = 0.2866 nm = 2.866 10-8 cm

Atomic mass = 55.847 g/mol

Volume of unit cell = = (2.866 10-8 cm)3 = 23.54 10-24 cm3/cell

Avogadros number NA = 6.02 1023 atoms/mol

3

0a

3

2324/882.7

)1002.6)(1054.23(

)847.55)(2(

number) sadro'cell)(Avogunit of (volume

iron) of mass )(atomicatoms/cell of(number Density

cmg

r

r


Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen

Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H

At. Weight (amu) 26.98 39.95 137.33 9.012 10.81 79.90 112.41 40.08 12.011 132.91 35.45 52.00 58.93 63.55 19.00 69.72 72.59 196.97 4.003 1.008

Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------

Density

(g/cm3) 2.71 ------ 3.5 1.85 2.34 ------ 8.65 1.55 2.25 1.87 ------ 7.19 8.9 8.94 ------ 5.90 5.32 19.32 ------ ------

Adapted from

Table, "Charac-

teristics of

Selected

Elements",

inside front

cover,

Callister 6e.

Characteristics of Selected Elements at 20C


rmetals rceramics rpolymers

Why? Metals have... close-packing (metallic bonding)

large atomic mass

Ceramics have... less dense packing (covalent bonding)

often lighter elements

Polymers have... poor packing (often amorphous)

lighter elements (C,H,O)

Composites have... intermediate values Data from Table B1, Callister 6e.

Densities of Material Classes

Most engineering materials are polycrystals.

Nb-Hf-W plate with an electron beam weld. Each "grain" is a single crystal. If grains are randomly oriented,

overall component properties are not directional. Grain sizes typ. range from 1 nm to 2 cm

(i.e., from a few to millions of atomic layers).

Adapted from Fig. K, color inset pages of Callister 5e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Single Crystals

-Properties vary with direction: anisotropic.

-Example: the modulus of elasticity (E) in BCC iron:

Polycrystals

-Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (Epoly iron = 210 GPa) -If grains are textured, anisotropic.

200 mm

Data from Table 3.3, Callister 7e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.)

Adapted from Fig. 4.14(b), Callister 7e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

Single vs Polycrystals E (diagonal) = 273 GPa

E (edge) = 125 GPa


Allotropy

The characteristic of an element being able to exist in more than one crystal structure, depending on temperature and pressure.

Polymorphism

Compounds exhibiting more than one type of crystal structure.

Allotropic or Polymorphic Transformations


Polymorphism and Allotropy

Polymorphism Two or more distinct crystal structures for the same

material (allotropy/polymorphism) titanium

, -Ti

carbon

diamond, graphite

BCC

FCC

BCC

1538C

1394C

912C

-Fe

-Fe

-Fe

liquid

iron system


Miller indices - A shorthand notation to describe certain crystallographic directions and planes in a material. Denoted by [ ] brackets. A negative number is represented by a bar over the number.

Directions of a form - Crystallographic directions that all have the same characteristics, although their sense is different. Denoted by h i brackets.

Repeat distance - The distance from one lattice point to the adjacent lattice point along a direction.

Linear density - The number of lattice points per unit length along a direction.

Packing fraction - The fraction of a direction (linear-packing fraction) or a plane (planar-packing factor) that is actually covered by atoms or ions.

Points, Directions, and Planes in the Unit Cell


Positions and Directions

x, y, z u, v, w X

Y

Z

Lattice Positions and Directions: 1) Always establish an origin 2) Determine the coordinates of the lattice points of interest 3) Translate the vector to the origin if required by drawing a

parallel line or move the origin. 4) Subtract the first point from the second: u2-u1,v2-v1,w2-w1 5) Clear fractions and reduce to lowest terms 6) Write direction with square brackets [uvw] 7) Negative directions get a bar over them.

Crystallography Concepts


Figure: Coordinates of selected points in the unit cell. The number refers to the distance from the origin in terms of lattice parameters.

Miller Point Indices


Miller indices- h,k,l- for naming points in the crystal lattice. The origin has been arbitrarily selected as the bottom left-back corner of the unit cell.

1 2

3

4

5

1)

2)

3)

4)

5)

Miller Direction Indices


Miller Indices

Miller indices are a notation for describing directions and labelling planes in lattices and crystals. The basis for determining the index is the unit cell. It is important to be clear about the unit cell being used. A direction is expressed in terms of its ratio of unit vectors in the form [uvw] where u, v, w are integers. A family of crystallographically equivalent directions is expressed as . A Miller index for a plane is expressed as (hkl), where h, k and l are integers. A family of crystallographically equivalent planes is expressed as {hkl}.


Determine the Miller indices of directions A, B, and C in below Figure.

Determining Miller Indices of Directions

(c) 2003 Brooks/Cole Publishing /

Thomson Learning

Figure: Crystallographic directions and coordinates


SOLUTION

Direction A

1. Two points are 1, 0, 0, and 0, 0, 0

2. 1, 0, 0, -0, 0, 0 = 1, 0, 0

3. No fractions to clear or integers to reduce

4. [100]

Direction B

1. Two points are 1, 1, 1 and 0, 0, 0

2. 1, 1, 1, -0, 0, 0 = 1, 1, 1

3. No fractions to clear or integers to reduce

4. [111]

Direction C

1. Two points are 0, 0, 1 and 1/2, 1, 0

2. 0, 0, 1 -1/2, 1, 0 = -1/2, -1, 1

3. 2(-1/2, -1, 1) = -1, -2, 2

2]21[ .4


(c) 2003 Brooks/Cole Publishing / Thomson Learning

Figure: Equivalency of crystallographic directions of a form in cubic systems.

Direction Equivalence


Drawing Plane in the Unit Cell

1) Identify the locations where the plane intercepts the x, y, z axes as the fractions of the unit cell edge lengths a, b, c.

2) Infinity if the plane is parallel. 3) Take the reciprocal of the intercepts. 4) Clear any fraction but do not reduce to lowest terms. 5) Example: 1/3,1/3,1/3 is (333) not (111)!!! 6) Use parentheses to indicate planes (hkl) again with a line over the negative indices. 7) Families are indicated by {hkl}

Remember Terminology: Defined coordinate system: x, y, z Respective unit cell edge lengths: a, b, c Direction: Denoted by [uvw] Family of direction(s): Denoted by: Plane: Denoted by: (hkl) Family of Plane(s): Denoted by: {hkl}


1) Identify the locations where the plane intercepts the x, y, z axes as the fractions of the unit cell edge lengths a, b, c.

2) Infinity if the plane is parallel. 3) Take the reciprocal of the intercepts. 4) Clear any fraction but do not reduce to lowest terms. 5) Example: 1/3,1/3,1/3 is (333) not (111)!!! 6) Use parentheses to indicate planes (hkl) again with a line over the negative indices. 7) Families are indicated by {hkl}


Determine the Miller indices of planes A, B, and C in below Figure.

Determining Miller Indices of Planes

Figure: Crystallographic planes and intercepts


Thomson Learning


Example 3.8 SOLUTION

Plane A

1. x = 1, y = 1, z = 1

2.1/x = 1, 1/y = 1,1 /z = 1

3. No fractions to clear

4. (111)

Plane B

1. The plane never intercepts the z axis, so x = 1, y = 2, and z =

2.1/x = 1, 1/y =1/2, 1/z = 0

3. Clear fractions:

1/x = 2, 1/y = 1, 1/z = 0

4. (210)

Plane C

1. We must move the origin, since the plane passes through 0, 0, 0. Lets move the origin one lattice parameter in the y-direction. Then, x = , y = -1, and z =

2.1/x = 0, 1/y = 1, 1/z = 0

3. No fractions to clear.

)010( .4

(c) 2003 Brooks/Cole Publishing / Thomson Learning


Important Concepts..

Directions are always perpendicular to their respective planes, i.e. [111]direction is

perpendicular to the (111) plane (for cubic systems, not true in all systems) . Families of equivalent planes are equal with respect to symmetrical structures, they do not have to be parallel. Equivalent planes must be translated to the correct atomic positions in order to maintain the proper crystal symmetry. Families of directions are equivalent in absolute magnitude.

(222) planes are parallel to the (111) planes but not equal. Intercepts for the (222) planes are 1/2,1/2,1/2

Intercepts for the (333) planes are 1/3,1/3,1/3, remember this is in what we call reciprocal space. If you draw out the (333) plane it is parallel to the (111) plane but not equivalent.


Calculate the planar density and planar packing fraction for the (010) and (020) planes in simple cubic polonium, which has a lattice parameter of 0.334 nm.

Calculating the Planar Density and Packing Fraction


Thomson Learning

Figure: The planer densities of the (010) and (020) planes in SC unit cells are not identical


SOLUTION

The total atoms on each face is one. The planar density is:

2142

2

atoms/cm 1096.8atoms/nm 96.8

)334.0(

faceper atom 1

face of area

faceper atom (010)density Planar

The planar packing fraction is given by:

79.0)2(

)(

)( atom) 1(

face of area

faceper atoms of area (010)fraction Packing

2

2

20

2

r

r

r

a

p

p

However, no atoms are centered on the (020) planes. Therefore, the planar density and the planar packing fraction are both zero. The (010) and (020) planes are not equivalent!

HCP Crystallographic Directions

1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a1, a2, a3, or c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas

[uvtw]

[ 1120 ] ex: , , -1, 0 =>


dashed red lines indicate projections onto a1 and a2 axes

a1

a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z Algorithm

HCP Crystallographic Directions Hexagonal Crystals

4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows.

' w w

t

v

u

) v u ( + -

) ' u ' v 2 ( 3

1 -

) ' v ' u 2 ( 3

1 -

] uvtw [ ] ' w ' v ' u [

Fig. 3.8(a), Callister 7e.

- a3

a1

a2

z

Crystallographic Planes (HCP) In hexagonal unit cells the same idea is used

example a1 a2 a3 c

4. Miller-Bravais Indices (1011)

1. Intercepts 1 -1 1 2. Reciprocals 1 1/

1 0 -1 -1

1 1

3. Reduction 1 0 -1 1

a2

a3

a1

z


64

Planar Density of (100) Iron Solution: At T < 912C iron has the BCC structure.

(100)

Radius of iron R = 0.1241 nm

R 3

3 4 a

Adapted from Fig. 3.2(c), Callister 7e.

2D repeat unit

= Planar Density = a 2

1

atoms

2D repeat unit

= nm2

atoms 12.1

m2

atoms = 1.2 x 1019

1

2

R 3

3 4 area

2D repeat unit

65

Planar Density of (111) Iron Solution (cont): (111) plane 1 atom in plane/ unit surface cell

3 3 3 2

2

R 3

16 R

3

4 2 a 3 ah 2 area

atoms in plane

atoms above plane

atoms below plane

a h 2

3

a 2

1

= =

nm2

atoms 7.0

m2

atoms 0.70 x 1019

3 2 R 3

16 Planar Density =

atoms

2D repeat unit

area

2D repeat unit

2011 Cengage Learning Engineering. All Rights Reserved.

3 - 66

Chapter 3: Atomic and Ionic Arrangements


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Diffraction

The constructive interference, or reinforcement, of a beam of x-rays or electrons interacting with a material. The diffracted beam provides useful information concerning the structure of the material.

Braggs law

The relationship describing the angle at which a beam of x-rays of a particular wavelength diffracts from crystallographic planes of a given interplanar spacing.

In a diffractometer

a moving x-ray detector records the 2 angles at which the beam is diffracted, giving a characteristic diffraction pattern

Diffraction Techniques for Crystal Structure Analysis

What is radiation?

Radiation is energy in the form of waves or particles. Radiation high enough in

energy to cause ionization is called ionizing radiation. It includes particles and

rays given off by radioactive material, stars, and high-voltage equipment. Ionizing

radiation includes x-rays, gamma-rays, beta particles, alpha particles, and

neutrons.

Without the use of monitoring equipment, humans are not able to "find" ionizing radiation. In contrast to heat, light, food, and noise, humans are not able to see, feel, taste, smell, or hear ionizing radiation.

What are X-rays?

X rays are a form of electromagnetic radiation which arises as electrons are deflected from their

original paths or inner orbital electrons change

their orbital levels around the atomic nucleus. X

rays, like gamma rays, are capable of traveling

long distances through air and most other

materials. Like gamma rays, x rays require more

shielding to reduce their intensity than do beta or

alpha particles. X and gamma rays differ primarily

in their origin: x rays originate in the electronic shell, gamma rays originate in the nucleus.

X-rays

X-rays were discovered in 1895 when Wilhelm

Conrad Roentgen observed that a screen coated

with a barium salt fluoresced when placed near a

cathode ray tube. Roentgen concluded that a form

of penetrating radiation was being emitted by the

cathode ray tube and called the unknown rays, X-

rays.

X-ray tube

An x-ray tube requires a source of electrons, a means to accelerate

the electrons, and a target to stop the high-speed electrons.

X-ray interactions

In passing through matter, energy is transferred from the incident x-ray

photon to electrons and nuclei in the target material. An electron can

be ejected from the atom with the subsequent creation of an ion. The

amount of energy lost to the electron is dependent on the energy of the

incident photon and the type of material through which it travels. There

are three basic methods in which x-rays interact with matter:

photoelectric effect, Compton scattering, and pair production.

Characteristic x-rays are emitted from heavy elements when their electrons make transitions between the lower atomic energy levels. The characteristic x-rays emission which shown as two sharp peaks in the illustration at left occur when vacancies are produced in the n=1 or K-shell of the atom and electrons drop down from above to fill the gap. The x-rays produced by transitions from the n=2 to n=1 levels are called K-alpha x-rays, and those for the n=3->1 transiton are called K-beta x-rays. Transitions to the n=2 or L-shell are designated as L x-rays (n=3->2 is L-alpha, n=4->2 is L-beta, etc. ). The continuous distribution of x-rays which forms the base for the two sharp peaks at left is called "bremsstrahlung" radiation.

Characteristic X-Rays

X-ray production typically involves bombarding a metal target in an x-ray tube with high speed electrons which have been accelerated by tens to hundreds of kilovolts of potential. The bombarding electrons can eject electrons from the inner shells of the atoms of the metal target. Those vacancies will be quickly filled by electrons dropping down from higher levels, emitting x-rays with sharply defined frequencies associated with the difference between the atomic energy levels of the target atoms. The frequencies of the characteristic x-rays can be predicted from the Bohr model . Moseley measured the frequencies of the characteristic x-rays from a large fraction of the elements of the periodic table and produces a plot of them which is now called a "Moseley plot". Characteristic x-rays are used for the investigation of crystal structure by x-ray diffraction. Crystal lattice dimensions may be determined with the use of Bragg's law in a Bragg spectrometer.

Electron transitions to lower atomic levels in heavy atoms have quantum energies which place them in the x-ray region of the electromagnetic spectrum. The x-ray emissions associated with these transitions are called characteristic x-rays. The labels on the illustration show the historical labeling of characteristic x-ray transitions.

X-ray Transitions

The diffraction Phenomenon

X-Ray Diffraction and Braggs Law

= +

= sin + sin

= 2 sin

=

2 + 2 + 2

Incoming X-rays diffract from crystal planes.

Measurement of: Critical angles, qc, for X-rays provide

atomic spacing, d.

Adapted from Fig.

3.2W, Callister 6e.

X-Ray Diffraction Pattern

(110)

(200)

(211)

z

x

y a b

c

Diffraction angle 2q

Diffraction pattern for polycrystalline -iron (BCC)

Inte

nsi

ty (

rela

tive

)

z

x

y a b

c

z

x

y a b

c


The results of a x-ray diffraction experiment using x-rays with = 0.7107 (a radiation obtained from molybdenum (Mo) target) show that diffracted peaks occur at the following 2 angles:

Examining X-ray Diffraction

Determine the crystal structure, the indices of the plane producing each peak, and the lattice parameter of the material.


Solution

We can first determine the sin2 value for each peak, then divide through by the lowest denominator, 0.0308.


SOLUTION (Continued)

We could then use 2 values for any of the peaks to calculate the interplanar spacing and thus the lattice parameter. Picking peak 8:

2 = 59.42 or = 29.71 868.2)4)(71699.0(

71699.0)71.29sin(2

7107.0

sin2

2224000

400

lkhda

dq

This is the lattice parameter for body-centered cubic iron.


Figure Photograph of a transmission electron microscope (TEM) used for analysis of the microstructure of materials. (Courtesy of JEOL USA, Inc.)


Figure: A TEM micrograph of an aluminum alloy (Al-7055) sample. The diffraction pattern at the right shows large bright spots that represent diffraction from the main aluminum matrix grains. The smaller spots originate from the nano-scale crystals of another compound that is present in the aluminum alloy. (Courtesy of Dr. Jrg M.K. Wiezorek, University of Pittsburgh.)

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