Transcript Chapter2

ENS 205
Materials Science I
Chapter 2: Atomic Bonding
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Objectives
At the end of this chapter:
• Know the quantum number of elements and apply them.
• Know the periodic table of elements
• Know the 4 methods by which atoms bond to each other
• Understand the energy/force relationship between atoms
making atomic bonds.
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Material Infrastructure
• What makes their materials behavior, mechanical for
instance, different?
– Microstructure- major properties result from
mechanisms occurring at either atomic or the
microscopic level
– Chemical or Atomic Bonding
• Strong bonding of ceramics: high strength and stiffness,
and resistance to temperature and corrosion, but brittle
• Weakly bonding of chain molecules in polymers: low
strength and stiffness, creep deformation
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Atom
• Atoms = nucleus (protons
and neutrons) + electrons
• Protons and Neutrons
have the same mass, and
determines the weight of
the atom
• Mass of an electron is
much smaller than mass
of proton/neutron, and
can be neglected in
calculation of atomic
mass.
electron
neutron
proton
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Atom
electron
neutron
proton
A brief review of the building block of materials:
Solid
atoms, ions, molecules
nucleus + electrons
Protons and neutrons
Properties of materials
atoms of the material
Nucleus
Electrons
Electronic
Thermal
magnetic
mechanical
Optic
thermal
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Atom: Definitions
• Consider the number of protons and neutrons
in the nucleus as the basis of the chemical
identification  periodic table (placed by the
number of protons)
• Atomic Mass Unit (amu) =mass of proton or
neutron ~ 1.66x10-24 gr
Nucleus
Electrons
most of the weight
But a small portion of the space
(np+nn) 1.66 10-24 g
1.3 10-6 nm
almost no weight
0.911 10-27 g
But occupy > 99% of the volume
0.059 nm
Influence most of the properties
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Atom: Definitions
• Atomic number = the number of protons in
the nucleus
• Avogadro’s number, Nav : 6.023x1023  # of
protons or neutrons necessary to produce a
mass of 1 gr.  Avogadro’s number (Nav )of
atoms of a given element termed as gramatom
amu=1/ Nav
1.66x10-24 = 1/6.023x1023
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Atom: definitions
• A mole is the amount of matter that has a
mass in grams equal to the atomic mass in
amu of the atoms (A mole of carbon has a
mass of 12 grams).
Example: C12 carbon isotope
1 C12 atom 6 protons+6 neutrons 12
amu
Nav many C12 atom1 mole C12 atom 12
gr
– Mole of a compound contains Avogadro’s number of
each constituent atom
– E.g. 1 mole of NaCl, 6.023x1023 of Na atoms +
6.023x1023 Cl atoms
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Atomic number
Atomic mass (in amu)
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Quantum Numbers
Electronic energy levels in atoms are specified by using
quantum numbers
The principal quantum is “n”.
• n indicates the primary electron shell in an atom where the
shells are represented by K=1, L=2, M=3, etc.
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Planetary atomic model
The atomic structure of sodium,
atomic number 11, showing the
electrons in the K, L, and M
quantum shells.
the most inner K-shell can accommodate only two electrons, called s-electrons;
the next L-shell two s-electrons and six p-electrons;
the M-shell can host two s-electrons, six p-electrons, and ten d-electrons; and so on.
The electronic configuration of the different energy levels fill in a relatively
straight forward pattern in a shorthand notation.
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 … .
eg., for Carbon, which has an atomic number of 6, it has 6 protons and 6
electrons. It’s electronic configuration in shorthand notation is 1s2 2s2 2p2 .
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Electron (Atomic) Orbitals
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Electron (Atomic) Orbitals
• The electron volt (eV) – energy unit
convenient for description of atomic bonding
• Electron volt - the energy lost / gained by an
electron after it has moved through a potential
difference of 1 volt .
E=q×V
• For q = 1.6 x 10-19 Coulombs V = 1 volt
1 eV = 1.6 x 10-19 J
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Identification of the Elements
We can identify the elements using their florescence energy when a material
is irradiated by an x-ray, electron or gamma ray.
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Identification of the Elements
The energy of an x-ray emitted from a K, L or M shell
electron can be used to identify the atomic number
of the element present in a material.
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Atomic Bonding
•
Classification of engineering materials may be based on the nature of atomic
bonding. Understanding the atomic bonding requires the understanding of the
structure of the individual atoms
•
Chemical bonds: hold atoms and molecules together in solids.
– Most of the materials not composed of just a single specie of atoms. They
are compounds, composed of molecules made up of atoms from two or more
elements.
– When two or more atoms combine to form molecules of a compound, they
form atomic bonds between them through chemical bonding.
•
Chemical bonding is essentially the interaction of electrons from one atom with
the electrons of another atom. The bonding of adjacent atoms is essentially an
electronic process
– Primary Bonding
– Secondary Bonding
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Atomic Bonding
•
When atoms are combined into solids, there are several bonding
mechanisms that can occur, which result in properties that may differ
substantially from those of the atom alone. Hence, it is necessary to
understand the types of bonding that can occur In the Solid Sphere Model,
there are three primary or strong bonds and one weaker or secondary (but
important!) type of bond between atoms or ions.
•
•
•
•
1) Ionic bonds
2) Covalent bonds
3) Metallic bonds
4) Van der Waals bonds
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Atomic or ionic radius
• An atomic or ionic radius
refers to the radius
corresponding to the
average electron density
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Valence Electrons
• Valence electrons are those electrons in the outer shells
that are easily removed or added to form either a positive
or negative charge for the purpose of combinations with
other atoms.
• These then form ions, which we shall see, are important for
ceramics and semiconductors.
• Valence electrons are the single most important
structure of an atom or ion as they determine the
physical (mechanical), electrical, photonic and magnetic
properties of materials.
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Valence Electrons
What is the valence of an atom?
• The valence is the ability of the atom to enter into chemical combination
with other elements and is often determined by the number of outermost
combined s, p, and /or d levels.
• Examples are:
• Mg:
1s2 2s2 2p6 3s2
valence = 2
• Al:
1s2 2s2 2p6 3s2 3p1
valence = 3
• Ge:
1s2 2s2 2p6 3s2 3p1 3d10 4s2 4p2 valence = 4
Valence electrons determine all of the properties of the material!
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Valence Electrons(cont’d)
There are exceptions to the filling order of the electronic shells
• e.g., Iron, Fe – atomic no. = 26; 1s2 2s2 2p6 3s2 3p6 3d8 [3d6 4s2 ];
instead of completely filling the 3d orbital with 8 electrons, Fe first fills
the 4s orbital.
Electron Configuration of Nickel
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Exceptions in 3d, 4d, 5d
• A d subshell that is half-filled or full (ie 5 or 10 electrons)
is more stable than the s subshell of the next shell. This
is the case because it takes less energy to maintain an
electron in a half-filled d subshell than a filled s subshell.
• For instance, copper (atomic number 29) has a
configuration of [Ar]4s1 3d10, not [Ar]4s2 3d9
• Likewise, chromium (atomic number 24) has a
configuration of [Ar]4s1 3d5, not [Ar]4s2 3d4 where [Ar]
represents the configuration for argon.
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Valence Electrons
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Atomic Structure
• Filled outermost shells are the most stable (non-reactive)
configurations. The atoms with unfilled valence shells strive to
reach the stable configuration by gaining or loosing electrons or
sharing electrons with other atoms. This transference/sharing of
electrons result in a strong bonding among atoms,
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Electronegativity
Some properties of elements include:
• Electronegativity is the tendency of an atom to gain an
electron. High electronegativity atoms tend to be on the right
side of the Periodic Table and low electronegativity atoms are
on the left side. What is the most electronegative element?
• Electropositivity is the tendency of an atom to loss electrons.
• High electronegative atoms tend to react with high
electropositive atoms to form ionic molecules and ceramic
materials.
• The sharing of electrons tends to make very strong atomic
bonds. In the case of ceramics these bonds may break abruptly
making the ceramic brittle.
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The electronegativities of selected elements relative to the position
of the elements in the periodic table.
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Periodic Table
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The atomic number, atomic mass, density and crystal structure are given.
Atomic Bonding
• Primary Bonds are formed when outer orbital electrons are
transferred or shared between atoms. strong and stiff,
hard to melt, metals and ceramics,
– Ionic
– Covalent
– Metalic
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Secondary bonds
• Secondary bonds: relatively weak,
behavior of liquids, bonds between
carbon-chain molecules in polymers,
due to subtle attraction between positive
and negative charges (no transfer or
sharing)
– Van der Waals
– Hydrogen
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Primary Chemical Bonds: Ionic Bonding
• An ionic bond is created between two
unlike atoms with different
electronegativities. When sodium
donates its valence electron to chlorine,
each becomes an ion; attraction occurs
due to their opposite electrostatic
charges, and the ionic bond is formed.
• The size of the Cl ion is big compared
to its elemental size whereas the size of
Na ion is small compared to its
elemental size.
•eg. Na and Cl form NaCl where the
properties of the resultant material
(salt) is very different from either of the
atoms. Cl and Na are both highly
corrosive where Cl is associated with
acids and Na is associated with bases.
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Primary Chemical Bonds: Ionic Bonding
• A collection of such
charged ions, form and
electrically neutral solid
by arranging
themselves into regular
crystalline array
• Makes material hard
and brittle
• Non-directional: A
cation (Na+) will attract
any adjacent anion (Cl-)
equally in all directions
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When a voltage is applied to an ionic material, entire ions
must move to cause a current to flow. Ion movement is slow
and the electrical conductivity is poor. Thus ionic materials
like SiO2 and Al2O3 make good insulators of electricity.
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Primary Chemical Bonds: Ionic Bonding
Fc 
K
a2
K  k 0 ( Z1q)( Z 2 q)
k 0  9 10 9 V .m / C , 0.16 10 18 C
Nature of the bonding force for the
ionic bond  coulombic attractions force Fc
With small a, Fc gets large, then
a ideally be equal to zero?
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Primary Chemical Bonds Ionic Bonding
With small a, FC gets large, then a ideally be equal to zero?
Oppositely charged ions gets closer, leads to increase in FC, but it is counteracted
by an opposing repulsive force FR due to
- overlapping of the similarly charged electric fields from each ions
- the attempt to bring the two positively charged nuclei closer together
FR  e a / 
where λ and ρ are experimentally determined constants for a given ion pair
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Primary Chemical Bonds: Ionic Bonding
Interatomic spacing
The equilibrium distance between atoms is caused by a balance between repulsive
and attractive forces. Equilibrium separation occurs where the total-atomic energy
of the pair of atoms is at a minimum, or when no net force is acting to either attract
or repel the atoms. The interatomic spacing is approximately equal to the atomic
diameter or, for ionic materials, the sum of the two different ionic radii.
Bonding Force, Net force
F=FR+FC
Equilibrium bond length
where F=0
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Primary Chemical Bonds: Ionic Bonding
• Bonding energy, E is related to bonding force
through the differential expression
dE
F
da
Equilibrium bond length a0 corresponds to
- F = 0 and
- A minimum in the energy curve  stable ions
positions
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Primary Chemical Bonds: Ionic Bonding
 dE 
F 0

 da  a  a0
A material that has a high
binding energy will also
have a high strength and
high melting temperature.
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Bonding Energy
•
•
•
•
How does bonding energy relate to melting point?
Modulus of Elasticity?
Coefficient of Thermal Expansion?
Hint: The higher the bonding energy the more tightly the atoms are
held together.
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Primary Chemical Bonds: Ionic Bonding
Coordination number
• Coordination number is the number of adjacent ions
(or atoms) surrounding a reference ion (or atom)
• Depends directly on the relative sizes of the
oppositely charged ions
– Radius ratio r/R (smaller ion to the larger ion)
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Coordination number
Larger ions overlap: instability because of high
repulsive forces
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Coordination number
MORE TO COME IN Ch 3…
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Coordination Number
As r/R→1, a coordination number as high as 12 is possible
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Questions to think on ?
• Why don’t we have a coordination
number greater than unity.
• Why coordination numbers of 5, 7, 10,
11 are absent?
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Covalent Bonds
Materials with covalent bonds tend to occur among atoms with small
differences in electronegativity and therefore the elements are close to one
another in the periodic table.
• Two or more atoms share two or more electrons.
• The atoms most commonly share their outer s and p electrons so that each
atom can tend to approach an inert gas structure.
• Example, Si; Z = 14; 1s2 2s2 2p6 3s2 3p2 or 1s2 2s2 2p6 3s1 3p3 are possible
with the second configuration being more stable.
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Electron orbitals are represented as particles
orbiting at a fixed radius. In reality, electrons
charge is found in a range of radii.
Representation of the actual electron density
Highly directional due to sharing of electrons
with specific neighboring atoms
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Primary Chemical Bonds: Covalent Bonding
• While ionic bonds are non-directional, covalent bonds are very
directional so atoms can best share their electrons.
• Covalent bonds are very strong.
– They tend to be brittle with poor electrical conductivity. Why then is
Silicon and other like materials used in the electronics industry?
– Many hydrocarbons, eg., C2 H4 , are covalently bonded. Many polymeric
materials such as polyvinyl chloride (PVC), used as molded plastic on
cars, have primarily covalent bonds.
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Primary Chemical Bonds: Covalent Bonding
• A continuous covalent bond arrangement to form a 3D
network of a solid
• Diamond is a cubic crystal structure of carbon (formed
at a temperature of 1325°C, a pressure of 50000
kg/cm2 is required to grow diamond)
– Highest melting temperature
– Highest hardness
– Highest elastic modulus
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Carbons’s electronic
configuration in shorthand
notation is 1s2 2s2 2p2
Double bond  covalent
sharing of two pairs of valence
electrons
When energy provided
Bonding of adjacent
molecules, double
bondsingle bond between
each adjacent molecule pair
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Spaghetti-like structure of solid polyethylene
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Primary Chemical Bonds: Covalent Bonding
• The bonding force and
energy curves are similar
to ionic bonding
• But the nature of the
bonding is different
leading to different force
equations
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Primary Chemical Bonds: Covalent Bonding
• Bond Angle
– An important characteristic as the bonding is of directional nature of
valence electron sharing
Carbon atom tends to form four
equally spaced bonds, resulting
tetrahedral configuration.
tetragonal: having four corners or angles
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Ionic-Covalent Bonds
• Many materials have properties, which can best be described as a
mixture of ionic and covalent bonding.
– Example 1, Silica (SiO2), a group IV-VI compound from the
periodic table. Each Si atom bonds with 4 O atoms and each O
atom binds with 2 Si atoms to give 8 electrons to each (see
next slide).
Oxygen ’s electronic configuration (8 electrons) : 1s2 2s2 2p4
Silicon’s electronic configuration (14 electrons): 1s2 2s2 2p6 3s2 3p2
– Example 2, Gallium Arsenide (GaAs), a group III-V compound
from the periodic table, used for lasers.
–
– Example 3, Indium Phosphide (InP), a group II-VI compound
from the periodic table, used for Light Emitting Diodes (LEDs).
– These materials are are very important as electronic and photonic
materials.
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Atomic Bonding of Silicon Dioxide
Each Si atom bonds with 4 O atoms and each O atom binds with 2 Si atoms
to give 8 electrons to each
Both the outer shells of Si and O are filled with electrons making
SiO2 a very stable material.
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Ionic-Covalent Bonds
• As the electronegativity difference between the
atoms increases, the bonding becomes more
ionic.
• The fraction of bonding that is covalent can be
estimated from the following equation:
Fraction covalent  exp(-25E 2 )
where E is the difference in electronegativities.
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Metallic Bonds
Metallic bonds occurs in Metallic elements, which tend to
have a low electronegativity.
• A metallic bond is non-directional
• The outer (valence) electrons are given up to form a “sea
of mobile electrons”, which are attracted by a set of fixed
positive ion cores.
– These mobile electrons are called “conduction”
electrons and they form the “glue” to bond the metal
atoms together.
– The sharing of electrons produces a lower energy state
than when the individual atoms are collected separately
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Metallic Bonding
– Less than half full shell of
electrons, each atom donates its
outer shell electrons to a “cloud” of
electrons
– Shared by all the (metal) atoms
– Atoms to become positively
charged ions as they all give up
electrons to for the “cloud”
– Ions are attracted by the electron
cloud and held together
– Nondirectional
– The mobility of the electrons 
electrical conductivity
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When voltage is applied to a metal, the electrons in the
electron sea can easily move and carry a current.
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Secondary bonding
• Atomic bonding without electron transfer or sharing 
much less bonding energy
• Attraction of opposite charges (somewhat similar to ionic
bonding) that are asymmetrically distributed-dipoleswithin each atom or molecular unit being bonded
A dipole (Greek: dyo = two and polos = pivot) is a pair of electric charges,
separated by some (usually small) distance. Dipoles can be characterized by
their dipole moment, a vector quantity with a magnitude equal to the product of
the charge and the distance separating the two poles
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Secondary bonding : Van der Waals Bonding
•
These bonds are much weaker than the three primary bonds but are very
prevalent in materials, and thus very important.
•
These bonds are formed by electrostatic attraction between groups of atoms
or molecules that are either permanently polarized or dynamically polarized
(i.e., changing as in a chemical process).
•
•
•
They possess an electric dipole moment
– eg., H2O where the oxygen is more strongly electronegative than H so O
shares H2‘s electrons giving oxygen a negative potential and H a positive
potential.
Many organic molecules, polymers, and ceramics exhibit this type of bonding,
often referred to as “hydrogen” bonding” with permanent polarization on an
atomic level.
– These weak bonds enable life’s processes to occur such as
photosynthesis and the “Hydrogen Cycle”.
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Secondary bonding
When two neutral argon atoms (perfectly symmetric) brought nearby, slight shift
from symmetry (induced dipole) weak attraction force between the two Ar.
Argon (a noble gas) does not tend to form a primary bond because it has stable,
filled outer orbital shell
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Secondary bonding
•
Externally electrically neutral chemical molecules can have a dipole inside.
– water is a triangular molecule, H2O
– The internal charge distribution is such that the hydrogen side has a
slight excess of positive charge and the oxygen end is correspondingly
negative.
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Van der Waals Bonding
•
•
Van der Waals bonding can change the properties of a material substantially.
eg., for long chained carbon molecules, polymers are covalently bonded
and hence might be expected to be brittle. The long chain molecules are
bonded together between the chains by Van der Waals bonds so ductility
is obtained by the distortion of the weak bonds rather than between the
strong covalent bonds along the chain itself.
In Polyvinyl Chloride (PVC), the chloride atoms attached to the polymer chain
have a negative charge and the hydrogen atoms are positively charged
enabling van der Waals bonding.
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Chemical Bonding
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Sample Problems
• The number of atoms per cm3, n, for
material of density d (g/cm3) and atomic
mass M (g/mol):
n = Nav × d / M
– Diamond (carbon): d = 3.5 g/cm3, M = 12
g/mol
n = 6×1023 atoms/mol × 3.5 g/cm3 / 12 g/mol =
17.5 × 1022 atoms/cm3
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