1. Solid State

12 Chemistry Ch-1 The Solid State

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Chapter - 1

The Solid State

1. Classification of solids on the basis of arrangement of atoms in the lattice →

It can be of two types:-

A. Amorphous

B. Crystalline

Crystalline Solids Amorphous Solids

1. Definite and regular arrangement of constituent particles.

Irregular or random arrangement of the constituent particles.

2. They have definite and regular shape. They have irregular shape.

3. Sharp (at a particular sudden melting point).

They melt over a certain range of temperature.

4. Undergo clean cleavage(regular).[cut is regular]

Undergo irregular cleavage. Cut in to piece with irregular surface.

5. They are true solids. They are super cooled liquids or cooled liquids or pseudo-solids.

6. Have a definite heat of fusion.(solid liquids)

Indefinite heat of fusion.

7. They are anisotropic in nature. i.e. the properties like electrical conductivity, the molar conductivity refractive index are different in different direction because of their regular arrangement Ex→ ZnS (Zn blend) NaCl, LiCl.

They are isotropic in nature.

(Same prop due to random arrangement

i.e. Show similar properties in diff. direction.

Ex→ glass, rubber polymer etc.


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2. Classification based on the nature of force binding the constituent particles ->

A. Ionic

B. Covalent

C. Molecular

D. Metallic

• Ionic Solids: -

1) Constituent particle are ions

2) They have 3-D arrangement of cations and anions.

3) Strong electrostatic forces of attraction.

4) High melting and boiling points due to strong forces binding then.

5) They are insulators in solid state but good conductors in molten or aqueous state.(dissociation)

6) They have high enthalpies of fusion.(NaCl, ZnS, CaF2,Na2O)

• Covalent Solids (Network solids)

1) Constituent particle are covalently bonded molecules (atoms)

2) High melting point, comparatively lower than ionic solids.

3) They are insulators, except-graphite (one e- is left, sp2-hyb.)

4) High enthalpy of fusion.

5) They are hard because of 3-D Network, ex-Diamond, Graphite.

• Molecular Solids

They are of three types

1) Non polar

2) Polar

3) Hydrogen


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Their properties are as follows:

1) Constituent particles are molecule.

2) Further categorized into non-polar, polar and H- bonded molecular solids

Non-Polar:- 1) Comprise of atoms or molecules formed by non-polar covalent bond. Ex-CCl4, CO2

2) They have weak dispersion forces (Vanderwaal/London force)

3) They are soft & non-conductors of electricity.

4) Exist as gases or liquids at room temperature.

Polar molecular Solids:- 1) Formed by polar- covalent bonds.

2) Dipole -Dipole interactions. (Due to electronegative charge separation → charged separations) [Nature of Force]

3) They are soft & non- conductors of electricity.

4) They are gases or liquids at room temp. Ex.-HCl, NH3, SO2

H-Bonded Molecular Solids;-

1) Contain Polar-Covalent molecular having elements F,O, N and Hydrogen.(free)

2) Non-conductors of electricity.

3) Generally exist as volatile liquids or soft solids. Ex. -ice.

• Metallic Solids:-

1) Contain positive kernels hold by a sea of free electrons.

𝑪𝒍𝟐

Difference in electronegativity

Non-Polar

𝑵𝑯𝟑

Difference in elecronegativity value

Polar


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2) Malleable & ductile

3) Good conductors of electricity.

4) Can conduct electricity in all states (As here free electrons are present) Ex.-All metals, Cu, Fe, Ag, Al.

CRYSTAL LATTICE: -

A regular 3-D Repetitive arrangement of the constituent particles in which, each particle is represented as a point also known as (lattice point/lattice site) is known as a crystal lattice/ Space Lattice.

Small- unit of lattice-Unit Cell

UNIT CELL:-

The smallest but complete unit in the space lattice which when repeated over & over again in 3-Ds, generates the crystal of a given substance.

Types of Unit Cell:-

1) Simple cubic/Primitive unit Cell.

Each particle shares (1/8) of space

1/8× (8 shaving) =1. (Rank of Unit Cell)×

‘1’ is the no. of atoms contributing the simple cubic.

8 Lattice points


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2) Body centered cubic unit cell (BCC)

Corners are shared by 1/8×8=1

And 1 in the center.

1+1=2 (Body Centre)

Z=2

Z= Rank (no. of atoms cont. a particular cell)

3) Face-Centred Cubic arrangement. (FCC)

1/8×8=1

1/2×6=3(face center)


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4) End Centered: -

1/8×8=1(we take any 2 faces)

1/2×2=1

So 1/2×2

Z=2

Q.1 Calculate the no. of atoms, in a cubic based unit cell having 1atom on each corner and 2 atoms of on each body diagonal.

Ans. Body diagonal =4

1/8×8=1

Q.2 A Unit Cell consists of a cube in which there are A’ atoms in the corner & ‘B’ atoms at the face-centre. What would be its formula?

Ans. 1/8×8(A) =1’A’

1/2×6 (B) =3

2 ‘A’ atoms are missing from 2 corner of the unit cell

1/8×6 (A)


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A3/4, B 3

1/2×6 (B) = 3

3/4 AB 4

Q.3 If 3 elements P,Q,& R Crystalline in a unit cell with ‘P’-comes, ‘Q’-Body center &R’ atom at the phase center.

Ans. P→1/8×8=1

Q→1

R→1/2×6=3

PQR3.

CLOSED PACKING IN 2 DIMESION:-

1. Here, each sphere is below the other

Such alt. arrang.

Coordination no. 4 (no. of atoms sphere touching a sphere)

C = 4

(Square Close Packaging)


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2. Here the spheres are below the void.

CLOSE PACKING IN3-DIMENSION: -

One layer is A another B is placed over it. Over the voids of small layer B, newly developed voids are ‘C’, old were ‘a’ & ‘b’, 2 options-3rd layer, so layer will become ABABAB. This is called Hexagonal-Close Packing.

If ‘C’ is placed on voids of ‘A ‘then it will form ABCABC-cubical close packing.

C. N. = 6

Hexagonal Close Packing

𝒂 𝒂 𝒂 b 𝒂

CC

A

B

𝒃 → 𝑡𝑒𝑡𝑟𝑎 ℎ𝑒𝑑𝑟𝑑

𝒄 → Octahedral


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Types of Voids:-

Depending upon arrangement of spheres & voids, there are 2 types of voids. Voids are due to sphere arrangement,

1. Tetrahedral void

2. Octahedral void

Tetrahedral: -

It is triangular, but when another sphere is placed to make it tetrahedral.

Octahedral: -

Equilateral ∆, opposite to each other. The no. of octahedral voids is equal to the no. of atoms per unit cell,

Where as the no. of tetrahedral voids is twice the no. of atoms of present in a unit cell.

Tetrahedral Void

Tetrahedral

Octahedral Void


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PACKING EFFICIENCY:-

Closeness between spheres in lattice.

The % of the total space which is occupied by particles in a certain packing is said to be packing efficiency.

1. Simple Cubic:-

The distance between the centre of the spheres present on the corner of the edges of the cube is called edge length. (a).

Distance between the center of the 2 nearest sphere is called the nearest neighbor distance ‘d’ & is equal to r + r = 2r, where r= radius of the sphere.

Octahedral Void

Edge length

𝒂

𝒂

𝒅

𝒓 𝑟



% free volume =Volume of sphere/volume of cube× 100

Edge length = a=2r=d (here)

Volume of cube = 𝑎3 =(2𝑟)3=8 𝑟3

Volume of sphere = 43 𝜋𝑟3/8𝑟3× 100

43π÷8

43× 1/8 =π/6×100

1/6× 3.14 × 100

52.00

=52.4%

2. FCC: -

B A

D C 𝒂

𝒂



In Δ ABC

𝐴𝐶2 = 𝐴𝐵2+ 𝐵𝐶2

=𝑎2+𝑎2

(4𝑟)2 = 2 𝑎2

A=2r √2

R= 𝑎2 √2

3. BCC: -

𝑎

𝑎 B A

𝑟

𝑟 𝑟

𝑟 C

𝒂 B A

D

C

𝑟

𝑟

𝑟

𝑟

B

A

D

C



In Δ 𝐵𝐶𝐷

B𝐷2= B𝐶2 + 𝐷𝐶2

𝐵𝐶2 = 𝐴𝐵2 +𝐴𝐶2

𝐵𝐷2= 𝐴𝐵2+ 𝐴𝐶2 + 𝐷𝐶2

(4𝑟)2 = 𝑎2 + 𝑎2+ 𝑎2

16𝑟2 = 3𝑎2

𝑎2= 163𝑟2

A=�16/3𝑟2

A=4r/√3

Packing efficiency= 2×4/3𝜋𝑟3÷ (4𝑟)3× 100

=2×4/3 π𝑟3÷64

=68%

Calculation of Density of unit cell:-

Density of unit cell= Mass of unit cell/Volume of unit cell

Volume of unit cell= (a×10−10)3

Let the edge length be ‘a’ pm.

Edge of (length) ‘a’ pm= a×10−10cm

Mass of unit cell =Rank of crystal * Mass of one atom

Rank of crystal atoms

Present in a particular unit cell

Mass = 𝑍 × 𝑀𝑁0

6.023 × 1023 → 𝑀



1 → 𝑀𝑁0(𝑎𝑢𝑜𝑔𝑎𝑑𝑟𝑜 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 (𝑒) = 𝑍 ×𝑀𝑎3×10−30∙𝑁0

Approx

Z = 1 2 4

Simple cubic BCC FCC

• Question on finding N0 Can be asked it should always be calculated.

Q. An element crystallizes in a FCC unit cell with edge length of 200pm.Cal.its density if 400g of this element contains 48× 1023 atoms.

Ans. 400g→ 48× 10^23 atoms

1 mole= 6.022× 1023 atoms

1 atom= 40048×1023

=50→ at. Mass

Q. A metal of atomic mass 50 has BCC structure density= 5.96g/cc. Calculate the volume

Ans. 5.96 = 50×2

𝑣×6.023×1023

5.96× 6.023 × 1023 =100𝑣

31.04× 1023 =100𝑣

V = 10031.04

× 1023

= 3.1× 10 −23

Imperfection/Defects in solids:-

Ideal crystal →a crystal is said to be ideal if the entropy of its constituents at absolute zero temperature is 0.



Any disordered arrangement or dislocation of the constituent particles from these normal positions gives rise to certain defects or imperfections in solids.

There are of 2 types:-

1. Electronic imperfection

2. Atomic imperfection (point defects).

Electronic defects:-

These defects arise due to irregularity in the arrangement of e-s, as the e-s are free to move in the crystal lattice, and are responsible for electrical conductivity.

The points from where they move become e- deficient and are called “holes”

Electrical conductivity also arises due to movement of these hole from one place to another.

Si (4 e-s in valance shell)

(Tetrahedral)

Addition of impurities to said either of group 13 or group 14 or group 15.

When group 13 is impurities, 1 space is left as group 14 is tetrahedral. This is a hole. It is p-type semi-conductor.

If group 15 (1 free 𝑒−);-pentagonal e- conductivity =n-type of semi- conductor.

Doping 𝑺𝒊

P-type semi-conductor (𝐼𝑛.𝐺𝑎,𝑇𝑙)

N-type semi-conductor (𝑃,𝐴𝑟, 𝑆𝑏)



Atomic defects:-

Ions dislocate, occupy some other place. [Arises due to dislocation of the ions from their original site]

Atomic Defects

STOICHIOMETRIC DEFECTS

Vacancy defects

Interstitial defects

Schottkey defects

Frenkel defects

• Vacancy defects (as a result of heating)

When some lattice site in the crystalline solids are vacant in gives rise to vacancy defects. ex..-

This defects is arises as a result of heating & it lowers the density of the crystal.

STOICHIIOMETRIC DEFECTS

(Arise in crystals in which no. of cat ions & no. of anions)

NON-STOICHIOMETRIC DEFECTS

(No. of cations is not equal to no. of anions)

IMPURITY DEFECTS

Vacancy



• Interstitial defects:-

When some constituent particle in a solid occupy interstitial sites, then this defects is created and it increases the density of the crystal.

• Schottkey Defects:-

Equal no. of cations & anions are missing

More specifically → Vacancy defects

When Equal no. of cations and anions are missing from the lattice then this defect is created which result in formation of vacancies or holes, these by lowering the density of the crystal.

Constituent in interstitial sites

Density ↑

𝑨+

𝑩− 𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+ move to defiant



The lattice crystal or the solid remains electrically neutral due to equal no. of positive or negative charges.

Condition for Schottkey defects:-

This defect is shown by the ionic compounds with high coordination numbers.

In which the cations & anions are of same size.

Example - Alkali metal halides such as-NaCl, KCl, KB4 etc.

CONSEQUENCES:-

The density of crystal is lowered.

Due to presence of holes.

Migration: - this defect increases the electrical conductivity due to movement of ions & holes from one place to another.

Due to presence of holes, stability is less.

Lattice energy is low ( as energy required to break bonds in ions and hole is lower)

• FRENKEL DEFECTS: -

(Types- Interstitial)

Cation leaves its initial site but not lattice. Only for cation →

𝑨+

𝑩− 𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+ move to defiant



Size of cation < size of anion shown where cation is smaller than anions.(all cations are of same size)

It results when certain cations leave their normal sites and due to which holes are created in the crystal.

CONDITION FAVOURING FRENKEL DEFECTS: -

1. It is found in ionic compounds with low coordination no.

2. In which the size of cat ions < size of anions

Example - Silver halides like AgCl, AgBr, AgI where size of Ag+ ion is very less then halides ion.

Consequences: -

1. The electrical conductivity of the crystal increase.

2. The stability of the crystal decrease.

3. Density remains unaltered since no. of ions/volume is same.

This defect is also known as “Dislocation Defect.”

NON- STOICHIOMETRIC CRYSTAL:-

Points defects in non- stoichiometric crystal.

Metal Excess Defects: -

1) By anion-vacancies

2) By extra- Cation occupying the interstitial site.

Metal Excess Defect

(+𝒗𝒆 > −𝑣𝑒) (+𝒗𝒆 < −𝑣𝑒)

Metal Deficiency Defect



• By Anion Vacancies: -

Here no. of metal ions > no. of halides ions (-ve)

This defect arises when anion is missing from its original site creating an anion vacancy in which an e-is trapped and is referred to as F-centre.

Example - In NaCl when its crystal is heated in the atm. Of Na vapours, the Na atoms get deposited on the surface and ionize to from Na+ ion.

The 𝐶𝑙− ion leaves it original site and combines with Na+ ions and the e- lost by sodium atoms accommodate in the anion vacancies maintaining the electrical neutrality of the crystal.

𝒆− trapped in anion vacancy (F-centre) F → 𝑭𝒂𝒓 𝒃𝒆 → 𝒄𝒐𝒍𝒐𝒖𝒓

𝑨+

𝑩−

𝐴+

𝐵−

𝑨+

𝒆−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑁𝑎 (𝑔) −𝑒�� 𝑁𝑎+

𝑁𝑎 𝐶𝑙

𝐶𝑙−

𝑒 Absorb energy

Release after led chip a level impacts colour to crystal.



Consequences:-

1) It imparts color to the crystal.

2) It is paramagnetic due to presence crystal of unpaired electrons.

3) The crystal is able to conduct electricity. (Vibration→stable→imparts colour)

Q. Discuss why the vapors of Li will be imparts pink color to LiCl crystal white K vapors will impart violet colour to the crystal (KCl).

Ans. =Due to F-Center. (diff.)

When they ionize.

e- lost→ trapped.

= specific color imparted.

• By Extra cations Occurrence: -

Q. Zn oxide crystal exhibit yellow colour on standing?

=𝑍𝑛𝑂 → 𝑍𝑛+2 + 12𝑂2 + 2𝑒 −

(Electrical neutrality remains)

𝒆− trapped in interstitial site

𝑨+

𝑩−

𝐴+

𝐵−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+ Extra cation occupying

interstitial site

𝒆−



Consequences of Metal Excess DEFECTS: -

(For extra cation occurrence)

1. They are generally coloured.

2. Paramagnetic in nature

3. They are conducting due to presence of free e-s.

Metal Deficiency Defects:-

Created by:-

1. Cation vacancy

2. Extra anion occupying interstitial site

• Cation Vacancy:-

Shown by elements -

→Variable oxidization state

→due to 1 vacant “I” cation (metal ion) will increaseoxidized state.

• This defect is generally shown by transition metals which have a tendency to show variable oxidation state.

Cation acquiring extra +𝑣𝑒 charge

𝑨+

𝑩−

𝐴2+

𝐵−

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−



For Example - In FeS or iron pyride crystal some 𝐹𝑒+2 ions may be missing from the lattice & there the change is balanced by extra +ve charge on neighbouring ions. Ions acquire +3 oxidation state.

• Extra anion occupying interstitial site:-

Consequences of Metal Deficient:-

1. They conduct electricity.(Present of hole)

2. The density increases. in( b),but in (a) it ↓) Density of the crystal change.

IMPURITY DEFECT

Cation acquiring extra the charge

𝑨+

𝑩−

𝐴+2

𝐵−

𝑨+

𝒆−

𝑨+

𝑩−

𝑨+

𝑩−

𝑨+

𝑩−

An extra –𝒗𝒆 so to compare extra +𝒗𝒆

Anion in interstitial site

𝐵−

In Co-valent solids

(Group 14 doped with group 13 → hole conduction (So p-

type group 14, group 15) (extra 𝒆−)

In Ionic solids



• In Co-valent solids: - 1) p- Type

2) n-Type

The introduction of defects in a particular crystalline solid by addition of impurities of other elements is termed as “Doping” and result (gp.13,15) in the formation of 2 types of semi- Conductors.

P-Type & n- Type.

Such type of semi – Conductor are called extrinsic semi conductor.

• In ionic solids: -

The electrical conductivity of ionic solids can be increased by adding impurities of other metal ions. For Example ⇒

If we mix a small amount of molten 𝑆𝑟𝐶𝑙2 (strontium chloride) to the crystal of Nacl then some Na+ ions will leave the crystal and are the replaced by 𝑆𝑟+2 ions.

So electrical neutrality is maintained as 𝑆𝑟+2 16 compensates loss of cation

For the two Na+ ions one𝑆𝑟+2 is replaced.

Impurities of 𝑆𝑟𝐶𝑙2 is doped.

Hole (covalent 𝑪𝒍.𝑪)

𝑵𝒂+

𝑪𝒍−

𝑆𝑟+2

𝐶𝑙−

𝑪𝒍−

𝑵𝒂+

𝑪𝒍−

𝑵𝒂+

𝑪𝒍−

𝑵𝒂+

𝑪𝒍−



B0NDS THEORY FOR METALS

Valence Conductance

For: -

→ Conductors

→ Semi – Conductors

→ Insulators

Bands

Gap (forbidden zone/ energy)

(In metals)

Conduction band

Valence band (outer most energy shell exited state)

No energy difference

CONDUCTORS

No energy difference



No conduction in insulators due to high energy difference

Exited ⟶ do not ablate move

OVERLAP: -

C. B.

V. B.

Forbidden Zone

Semi-conductors

C. B.

V. B. For insulators

Overlap

C. B.

V. B.



PROPERTIES OF SOLIDS

Electrical Properties: -

In terms of capacity to conduct electricity, solids are of three types:-

1. Conductors

2. Semi-conductors

3. Insulators

→Conduction of electricity in Semi- Conductors:-

SEMI CONDUCTORS

Electrical Properties

(Solids – conductors, semi-conductors, insulators)

MISSING

Intrinsic Extrinsic

𝑆𝑖

𝑆𝑖 𝑆𝑖 𝑆𝑖

𝑆𝑖

When heated they become free & conduct electricity.

(P-type & n-type imp. cond.)

(Doping)



Intrinsic Semi Conductors:-

A semi- conductor when heated to a high temp. acts as intrinsic- semi- conductor. This happens because certain co-valent bonds are broken due to energy supplied & the e-s are set free to conduct electricity.

Same For Extrinsic

• Magnetic prop. Of Solids: -

Magnetic properties of the substance because of magnetic moments associated with the e-s present in third atoms.

The magnetic moment in a e- is from 2 source

1. Orbital motion around the nucleus

2. Spin of the e- around its axis

→ On the basis of the influence of the external magnetic field solids are classified as under:-

1) Paramagnetic Substance:-

⇒ Attracted towards electrical field .

Substance which are attracted by the magnetic fields are said to be paramagnetic in nature and the atoms of the element present have certain unpaired e-s , but these substance lose their magnetic character, once the magnetic field is removed i.e, their magnetic character is temporary. Magnetic moment ≠0.

Example: - Co, Ni, Fe, No (Nitric oxide) n≠0

2) Diamagnetic Substance:-

Those substances which have all paired e-s and are repelled under the influence of magnetic field.

The resultant magnetic moment aligned in opposite direction cancel each other on account of pairing.

Example: - 𝑇𝑖𝑂2, 𝑁2,Nacl,etc.



3) Ferromagnetic Substance:-

Certain paramagnetic substance generally transition elements like Co, Ni, Fe. Become paramagnetic under the influence of magnetic field i.e they do not lose their magnetic character even if, they are not in contact with magnet. They have magnetic moment aligned in the same direction.

Ex. 𝐶𝑟𝑂2 used in magnetic tapes for audio recording.

e- rotate around axis & revolve.

All ferromagnetic→ paramagnetic but not vice versa

↑↑↑↑↑↑↑

4) Anti- Ferromagnetic Substance:-

Certain paramagnetic substances align the magnetic moment in such a way that they mutually cancel out each other and thus posses ‘O’ magnetic moment.

µ=0

↑↓↑↓↑↓↑↓↑↓↑↓

Opp.dir. equal no.

5) Ferri magnetic Substance:-

Certain paramagnetic substances have the magnetic moment aligned in parallel and anti parallel direction in unequal numbers. So that they have net magnetic moment but ferri magnetic Substance are less magnetic than ferromagnetic Substance.

↑↑↓↓↓↑↓↓↓↓↑↑

𝑢 ≠ 0 Magnetic

Ex..Magnetic oxide of Fe 𝐹𝑒3𝑂4

Ferri-Ferro oxide → (𝐹𝑒𝑂.𝐹𝑒2𝑂3)



• Dielectric properties of Solids: - Depending upon the alignment of electric dipole the solids have following character. 1. Piezo Electricity:-

A dielectric crystal which has resultant dipole movement and can product electricity when external pressure is applied such as crystal is called piezo electric crystal and the prop. is termed as piero electricity.

Such crystal are used in ultrasonic generators and solar detectors. Ex….

Lead Zirconate (𝑃𝑏𝑍𝑟𝑂2)

Ammonium, di- hydrogen phosphate (𝑁𝐻4𝐻2𝑃𝑂4)

2. Pyro electricity (heat pyro): -

Certain crystals on heating produce electric current this phenomena is called pyro electricity.

3. Ferro Electricity (Sam to ferromagnetic substance): -

In such crystals dipole are permanently polarized even in the absence of electric field.

Example: - (Sodium Potassium Tatarate (Rochelle’s Salt))

2, 3 di-hydroxy

COOH

H C OH

H C OH

COOH

Sodium salt



COONa (Rochelle’s alt)

H C — OH

H C OH

𝐶𝑂𝑂𝑁𝑎

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1. Solid State