10Solid state

📚
SOLID BASICS
▢ Motion: only vibrational motion
▢ Classes:
  • •
    Amorphous solids
  • •
    Crystalline solids
📚
AMORPHOUS SOLIDS
▢ Arrangement: building constituents irregular / haphazard
▢ Melting Point: not sharp
▢ Nature:
  • •
    isotropic
  • •
    super-cooled liquid
  • •
    liquids at all temperatures
▢ Examples: glass, rubber, plastics
📚
CRYSTALLINE SOLIDS
▢ Arrangement: building constituents regular throughout 3D network
▢ Geometry: true solid → characteristic geometry
▢ Unit: large number of unit cells / crystals
▢ Melting Point: sharp
▢ Nature:
  • •
    anisotropic
  • •
    long-range order
▢ Examples: diamond, graphite
📚
PROPERTIES OF SOLIDS
▢ Efflorescence:
❖ Meaning: substance loses water of crystallisation to air → powder form
❖ Example: \(Na_2CO_3.10H_2O\) [MOE 2065]
▢ Deliquescence:
❖ Meaning: substance absorbs moisture from air and dissolves
❖ Examples: \(NaOH, KOH, CaCl_2.6H_2O, NaNO_3, Ca(NO_3)_2, ZnCl_2.6H_2O\)
▢ Hygroscopy:
❖ Meaning: substance absorbs moisture from air but does not dissolve
❖ Examples: \(NH_4NO_3, NaClO_4, SbCl_3\)
▢ Other Properties: incompressibility, rigidity, low vapour pressure
▢ Goniometer: instrument used to measure interfacial angle
📚
TYPES OF SOLIDS BASED ON BINDING FORCE

Table 1: Characteristics of different solids

Character
Ionic
Metallic
Covalent
Molecular
Constituent particles
+ve and −ve ions
+ve ions in sea of electrons
atoms
molecules
Binding force
electrostatic attraction between ions
electrostatic attraction between cations and sea of electrons
strong covalent bonds
weak van der Waals / dipole-dipole forces
Hardness
hard
variable
very hard except graphite
very soft
Melting point
high
moderate to high
very high
low
Electrical conductivity
bad in solid; conduct in molten state
good conductors
bad conductors except graphite
bad conductors
Solubility
soluble in polar; insoluble in non-polar solvents
insoluble in polar and non-polar solvents
insoluble in polar and non-polar solvents
variable; often soluble in non-polar
Examples
\(NaCl, ZnS, KNO_3, CaO, BaCl_2\)
metals and alloys
diamond, graphite, quartz, \(SiO_2, SiC\)
\(H_2, CO_2, H_2O, N_2, CCl_4\), noble gases, \(I_2\), sugar
📚
POLYMORPHISM AND ISOMORPHISM
▢ Polymorphism: ability of a substance to assume 2 or more crystalline shapes
▢ Isomorphism: 2 or more substances having similar crystalline structure and chemical composition
▢ Isomorphs:
  • •
    \(Na_2SeO_4\) and \(Na_2SO_4\)
  • •
    \(Na_3PO_4\) and \(Na_3AsO_4\)
▢ Anisotropy: single crystal property; physical properties differ in different directions
📚
SYMMETRY IN CRYSTALS
▢ Types:
  • •
    centre of symmetry
  • •
    plane of symmetry
  • •
    axis of symmetry
▢ Centre of Symmetry: crystal possesses only one centre of symmetry
▢ Cubic Crystal: total 23 elements of symmetry
📚
SPACE LATTICE AND UNIT CELL
▢ Space Lattice: array of points showing arrangement of molecules / atoms / ions in 3D space
▢ Unit Cell: smallest repeating unit in lattice; repeated over and over → crystal
▢ Property: unit cell possesses all structural properties of crystal
▢ Edges: \(a,b,c\)
▢ Angles: \(\alpha,\beta,\gamma\)
📚
CRYSTAL SYSTEMS

Table 1: Seven crystal systems

Crystal system
Main symmetry
Unit cell edges
Axial angles
Examples
Cubic / Regular
9 planes, 13 axes
\(a=b=c\)
\(\alpha=\beta=\gamma=90^\circ\)
\(NaCl, KCl, CsCl, ZnS, CaO\), diamond, alums, Pb, Ag, Au, Hg
Tetragonal
5 planes, 5 axes
\(a=b\ne c\)
\(\alpha=\beta=\gamma=90^\circ\)
\(SnO_2, ZnO_2, TiO_2, NiSO_4, ZnSO_4, PbWO_4\), white tin
Orthorhombic / Rhombic
3 planes, 3 axes
\(a\ne b\ne c\)
\(\alpha=\beta=\gamma=90^\circ\)
\(KNO_3, K_2SO_4, PbCO_3, BaSO_4, MgSO_4.7H_2O\)
Rhombohedral / Trigonal
3 planes, 3 axes
\(a=b=c\)
\(\alpha=\beta=\gamma\ne90^\circ\)
\(NaNO_3, CaSO_4\), calcite, quartz, As, Sb, Bi
Monoclinic
1 plane, 1 axis
\(a\ne b\ne c\)
\(\alpha=\gamma=90^\circ,\beta\ne90^\circ\)
\(Na_2SO_4.10H_2O, CaSO_4.2H_2O\), monoclinic sulphur
Hexagonal
7 planes, 7 axes
\(a=b\ne c\)
\(\alpha=\beta=90^\circ,\gamma=120^\circ\)
\(ZnO, PbI_2, HgS\), graphite, Be, Mg, Zn, Cd
Triclinic
no plane, no axis
\(a\ne b\ne c\)
\(\alpha\ne\beta\ne\gamma\ne90^\circ\)
\(CuSO_4.5H_2O, K_2Cr_2O_7, H_3BO_3\)
Special Points
  • •
    \(a=b\ne c\), \(\alpha=\beta=90^\circ\), \(\gamma=120^\circ\) → hexagonal [MOE 2065]
  • •
    cubic crystal system → simplest and most symmetric
  • •
    triclinic system → most asymmetric
  • •
    matchbox → orthorhombic / rhombic geometry
  • •
    \(a\ne b\ne c\), \(\alpha=\beta=\gamma=90^\circ\) → orthorhombic [MOE 2008]
  • •
    not all crystals have simple lattices
  • •
    14 different 3D arrangements of similar points possible → 14 Bravais lattices
📚
CUBIC LATTICES
▢ Types:
  • •
    simple cubic lattice
  • •
    body-centred cubic lattice
  • •
    face-centred cubic lattice
▢ Lattice Point Contribution:
❖ Corner: \(\frac{1}{8}\)
❖ Edge: \(\frac{1}{4}\)
❖ Face Centre: \(\frac{1}{2}\)
❖ Body Centre: 1
📖
Simple cubic
▢ Points: corners only
▢ No. of Particles: \(8\times\frac{1}{8}=1\)
▢ Coordination Number: 6
▢ Nearest Distance: \(a\)
▢ Atomic Radius: \(\frac{a}{2}\)
▢ Packing Fraction: 52.4%
▢ Example: Po
📖
Body-centred cubic
▢ Points: corners + body centre
▢ No. of Particles: \(1+8\times\frac{1}{8}=2\)
▢ Coordination Number: 8
▢ Nearest Distance: \(\frac{\sqrt3}{2}a\)
▢ Atomic Radius: \(\frac{\sqrt3}{4}a\)
▢ Packing Fraction: 68%
▢ Examples: alkali metals, \(CsCl\), Fe
📖
Face-centred cubic
▢ Points: corners + centres of 6 faces
▢ No. of Particles: \(8\times\frac{1}{8}+6\times\frac{1}{2}=4\)
▢ Coordination Number: 12
▢ Nearest Distance: \(\frac{a}{\sqrt2}\)
▢ Atomic Radius: \(\frac{a}{2\sqrt2}\)
▢ Packing Fraction: 74%
▢ Examples: coinage metals, \(NaCl, CaF_2\), Pt
▢ Note: fcc / ccp → most efficient packing
📖
Density of lattice matter
▢ Formula: \(\rho=\frac{Z\times M}{N_A\times a^3}\)
▢ Symbols:
  1. \(Z\) → no. of atoms per unit cell
  2. \(M\) → atomic / molecular mass
  3. \(N_A\) → Avogadro's number
  4. \(a\) → edge length of cubic unit cell
📚
CLOSE PACKING
▢ Coordination Number: no. of oppositely charged ions / particles surrounding each ion / sphere
▢ HCP:
  • •
    ABAB arrangement
  • •
    hexagonal close packing
  • •
    particles in every 1st and 3rd layer are in same line
▢ CCP:
  • •
    ABCABC arrangement
  • •
    cubic close packing
  • •
    particles in every 1st and 4th layer are in same line
  • •
    fcc unit cell represents ccp crystal
▢ Voids:
  • •
    some interstitial sites remain empty
  • •
    interstitial site between 4 spheres = tetrahedral void
  • •
    interstitial site between 6 spheres = octahedral void
▢ No. of Voids:
  1. \(n\) close-packed spheres → octahedral voids = \(n\)
  2. \(n\) close-packed spheres → tetrahedral voids = \(2n\)
▢ Radius Ratio:
❖ Tetrahedral Void: \(r=0.225R=(\sqrt{1.5}-1)R\)
❖ Octahedral Void: \(r=0.414R=(\sqrt2-1)R\)
❖ Cubical Void: \(r=0.732R=(\sqrt3-1)R\)
▢ Packing Fraction: \(PF=\frac{\text{total volume of particles in unit cell}}{\text{volume of unit cell}}\)
▢ Order: simple cubic least closely packed; fcc / ccp most closely packed
📚
BRAGG'S EQUATION
▢ Formula: \(n\lambda=2d\sin\theta\)
▢ Use: X-ray diffraction
▢ Condition: no solution if \(\lambda>2d\)
📚
DEFECTS IN CRYSTALS
▢ General:
  • •
    absolute zero → ideal crystals
  • •
    temperature rise → distortion / defects
  • •
    defect may occur at point, along line or over surface
📖
Stoichiometric defects
📝
Schottky Defect
▢ Cause: some lattice points unoccupied
▢ Other Name: paired vacancy defect
▢ Nature: equal no. of cations and anions missing → crystal neutral
▢ Common In: ionic compounds with high coordination number and similar cation-anion size
▢ Examples: \(NaCl, KCl, KBr, AgBr, CsCl\)
▢ Effect on Density: density decreases
▢ Electrical Conductivity: increases to some extent
▢ Dielectric Constant: decreases
📝
Frenkel Defect
▢ Cause: ion leaves lattice site and occupies interstitial site
▢ Other Name: dislocation / interstitial defect
▢ Nature: lattice site vacant + interstitial ion
▢ Common In: ionic crystals with large anion and small cation
▢ Examples: \(AgBr, ZnS, AgI, AgCl\)
▢ Effect on Density: density unchanged
▢ Dielectric Constant: increases
▢ Cation: high polarising power
📝
Notes
  • •
    \(AgBr\) has both Schottky and Frenkel defects
  • •
    overall chemical composition unchanged in Schottky/Frenkel
  • •
    non-stoichiometric defects change overall chemical combination
  • •
    excess positive / negative particles may occur but crystal remains neutral
📖
Non-stoichiometric defects
📝
Metal Excess Due to Anion Vacancy
▢ Cause: removal of anion → cation concentration increases
▢ Examples: \(NaCl, KCl, LiCl\) heated in respective metal vapour → colour formation
▢ F-Centres: anion vacancy occupied by electron
▢ Colour: due to F-centres
▢ Intensity: intensity of colour ∝ no. of F-centres
📝
Metal Excess Due to Interstitial Cation
▢ Nature: like Frenkel defect; more common
▢ Example: \(ZnO\)
▢ Process: \(ZnO\) heated → loses oxygen reversibly
▢ Interstitial: excess \(Zn^{2+}\) accommodated in interstitial sites
▢ Colour: hot \(ZnO\) yellow due to trapped electrons
▢ Behaviour: paramagnetic; n-type semiconductor
📝
Metal Deficiency Due to Foreign Atoms
▢ Examples: \(NaCl\) containing \(SrCl_2\), \(AgCl\) containing \(CdCl_2\)
▢ Reason: cation vacancy / hole
▢ Behaviour: p-type semiconductor
📝
Impurity Defects
defects due to chemical impurities
📚
IONIC SOLID STRUCTURES

Table 1: Characteristic properties of ionic solid structures

Structure
Close-packed ions
Ions in voids
Coordination no.
Formula units per unit cell
Examples
ZnS type
\(S^{2-}\) ions form ccp
\(Zn^{2+}\) in alternate tetrahedral voids
\(Zn^{2+}=4, S^{2-}=4\)
4
\(ZnS, AgI, CuCl, CdS, HgS\)
NaCl type
\(Cl^-\) ions form ccp
\(Na^+\) in all octahedral holes
\(Na^+=6, Cl^-=6\)
4
\(NaCl, LiCl, KBr, AgBr, MgO, CsI, CaO, FeO\)
CsCl type
\(Cl^-\) ions at corners
\(Cs^+\) at body centre
\(Cs^+=8, Cl^-=8\)
1
\(CsCl, CsCN, CaS, CsI\)
CaF2 type / Fluorite
\(Ca^{2+}\) ions form ccp
\(F^-\) in all tetrahedral holes
\(Ca^{2+}=8, F^-=4\)
4
\(CaF_2, Na_2O, BaCl_2, PbO_2\)
Li2O type / Antifluorite
\(O^{2-}\) ions form ccp
\(Li^+\) in all tetrahedral holes
\(Li^+=4, O^{2-}=8\)
4
\(K_2O, Li_2O, Na_2O, K_2S\)
Important Structural Points
  • •
    \(A_xB_y\) crystallises in fcc; A at corners, B at face centres → A = 1, B = 3 → \(AB_3\)
  • •
    coordination no. of \(Na^+\) in NaCl = 6
  • •
    coordination no. of sodium in \(Na_2O\) = 4
  • •
    pressure on NaCl crystal with 6:6 coordination → CsCl type 8:8 coordination
  • •
    at \(0K\), most ionic crystals possess no defect
  • •
    \(AgI, ZnS, AgBr\) have equal Frenkel defect tendency due to coordination numbers 4, 4, 4 respectively
  • •
    NaCl doped with \(MgCl_2\) → Schottky defect
  • •
    anion vacancy with trapped electron → F-centre
  • •
    F-centres make crystal coloured
  • •
    non-stoichiometric metal-deficiency defect occurs in transition-metal salts
📚
READ AND DIGEST
▢ Crystal Systems:
  • •
    out of 7 crystal systems, triclinic is most unsymmetrical
  • •
    cubic crystal is simplest and most symmetric
  • •
    14 space lattices possible in crystal
▢ Packing and Lattice:
  • •
    hcp present in Be, Mg, Ca, Cr, Mo, V, Zn, \(ZnCl_2\)
  • •
    ccp / fcc present in Fe, Cu, Ag, Au, Pt, Ni
  • •
    bcc present in all alkali metals, Ba, Mn
  • •
    all noble gases have ccp except He, which has hcp
  • •
    fcc is unit cell of ccp crystal
  • •
    fcc is most efficient packing
  • •
    each unit cell of NaCl lattice has \(13Na^+\) and \(14Cl^-\) ions but net contribution = \(4Na^+\) and \(4Cl^-\)
  • •
    each \(Na^+\) in NaCl lattice surrounded by \(6Cl^-\)
  • •
    metals with simple cubic structure: Po
▢ Magnetic Properties:
  • •
    paramagnetic substances: \(O_2, Fe^{3+}\)
  • •
    diamagnetic substances: \(TiO_2, NaCl\), benzene, \(Zn^{2+}, H^+\)
  • •
    ferromagnetic substances: Fe, Co, Ni, \(CrO_2\)
  • •
    antiferromagnetic: net magnetic moment zero; e.g. MnO
  • •
    ferrimagnetic: net moment; e.g. \(Fe_3O_4\)
  • •
    ferromagnetic property decreases: Fe > Co > Ni due to decrease in unpaired electrons
  • •
    paramagnetic character ∝ no. of unpaired electrons
  • •
    among \(Cu^+, Cu^{2+}, Fe^{2+}, Fe^{3+}\), maximum paramagnetic = \(Fe^{3+}\) due to 5 unpaired electrons
▢ Electrical Properties:
  • •
    piezoelectricity: electricity on applying mechanical stress on polar crystal
  • •
    pyroelectricity: electricity on heating polar crystals
  • •
    ferroelectricity examples: barium titanate \(BaTiO_3\), sodium potassium tartrate / Rochelle salt, \(KH_2PO_4\)
  • •
    anti-ferroelectricity example: lead zirconate \(PbZrO_3\)
  • •
    piezoelectric crystals used in record player
  • •
    microcalculators use liquid crystals
  • •
    superconductivity discovered by Kammerlingh Onnes
  • •
    ferrimagnetic substance converted into paramagnetic substance at 850 K
▢ Miscellaneous:
  • •
    glass = super-cooled liquid
  • •
    \(AgBr\) has both Schottky and Frenkel defects
  • •
    radius ratio = radius of cation / radius of anion
  • •
    gas-lighters are polycrystals
  • •
    cohesion maximum in solids
  • •
    amorphous silica better photovoltaic material than cesium
  • •
    carbon atoms arranged in layers in graphite [MOE 2055]
  • •
    \(ReO_3\) has conductivity and appearance like copper
Q1.
Diamond is a .......... [KU 2008]
📅KU 2008
Q2.
The crystal for which \(a=b\ne c\), \(\alpha=\beta=90^\circ\) and \(\gamma=120^\circ\) is [MOE 2065]
📅MOE 2065
Q3.
In Schottky defect [IOM 2007]
📅IOM 2007
Q4.
A crystal of graphite contains [MOE 2061]
📅MOE 2061
Q5.
How many \(Cl^-\) ions are there around \(Na^+\) ions in NaCl crystal? [I.E./BPKIHS]
📅I.E.•BPKIHS
Q6.
On mixing trivalent impurity in a crystal lattice of Si, type of semiconductor thus formed is [IOM/MOE]
📅IOM•MOE
Q7.
Bragg's law is given by equation [IOM]
📅IOM
Q8.
A crystalline solid
Q9.
In a crystal, the atoms are located at the position of
Q10.
Which of the following is not a crystalline solid?
Q11.
The existence of a substance in more than one solid modification is known as
Q12.
Most crystals show good cleavage because their atoms or molecules are
Q13.
The more efficient mode of packing of identical atoms in one layer is
Q14.
Potassium crystallizes in a bcc lattice, hence the coordination number of potassium in potassium metal is
Q15.
The coordination number of sodium in \(Na_2O\) is
Q16.
In ccp arrangement the coordination number of each sphere is
Q17.
Coordination number for Cu is
Q18.
The positions of \(Cl^-\) ions in NaCl structure are
Q19.
The positions of \(Na^+\) ions in NaCl structure are
Q20.
The number of \(Cl^-\) ions required to form ccp lattice of NaCl structure are
Q21.
How many \(Cl^-\) ions are there around \(Na^+\) ion in NaCl crystal?
Q22.
In a rock salt structure, each \(Cl^-\) ion is surrounded by
Q23.
The number of atoms in unit structure of NaCl are
Q24.
In CsCl structure, each \(Cs^+\) ion is surrounded by
Q25.
Space lattice of \(CaF_2\) is
Q26.
The number of free electrons present on each carbon atom in graphite is
Q27.
A match box exhibits
Q28.
The axial angles in triclinic crystal system are
Q29.
Tetragonal crystal system has the following unit cell dimensions
Q30.
NaCl is an example of
Q31.
Diamond is a
Q32.
Which of the following is an example of covalent crystal solid?
Q33.
Solid \(CO_2\) is an example of
Q34.
Particles of quartz are packed by
Q35.
The number of atoms in a face centred cubic unit cell are
Q36.
Body-centred cubic lattice has coordination number of
Q37.
The solid NaCl is a bad conductor of electricity since
Q38.
Close packing is maximum in the crystal lattice of
Q39.
Schottky defect arises due to
Q40.
Ionic solids with Schottky defects contain in their structure
Q41.
Schottky defect is found in
Q42.
In a solid lattice the cation has left a lattice site and is located at an interstitial position, the lattice defect is
Q43.
Which defect causes decrease in the density of crystal?
Q44.
A solid with high electrical and thermal conductivity from the following is
Q45.
Germanium is an example of
Q46.
Which type of semiconductor is obtained on mixing arsenic into silicon?
Q47.
If we mix a pentavalent impurity in a crystal lattice of germanium, what type of semiconductor formation will occur?
Q48.
When n- and p-type semiconductors are allowed to come into contact
Q49.
Super conductors are substances which
Q50.
Which substance possesses zero resistance at 0 K?
Q51.
The pure crystalline substances on being heated gradually forms a turbid liquid at constant temperature and at higher temperature turbidity completely disappears. The behaviour is a characteristic of substance forming
Q52.
When NaCl is doped with \(MgCl_2\), the nature of defect produced is
Q53.
Schottky defect in crystals is observed when
Q54.
Which of the following is not a crystalline solid?
Q55.
Which of the following is ferroelectric compound?
Q56.
Example of unit cell with crystallographic dimensions \(a\ne b\ne c\), \(\alpha=\gamma=90^\circ\), \(\beta\ne90^\circ\) is
Q57.
The flame colour of metal ions is due to
Q58.
Among solids, the highest melting point is exhibited by
Q59.
The major binding force of diamond, silicon and quartz is
Q60.
The interionic distance for cesium chloride crystal will be
Q61.
A substance \(A_xB_y\) crystallizes in a face centred cubic lattice in which atoms A occupy each corner of the cube and atoms B occupy the centre of each face of the cube. Identify the correct composition of the substance \(A_xB_y\).
Q62.
Which of the following crystals does not exhibit Frenkel defect?
Q63.
Due to Frenkel defect, the density of ionic solids
Q64.
Semiconductors are derived from compounds of
Q65.
When electrons are trapped into the crystal in anion vacancy, the defect is known as
Q66.
Which of the following statement about amorphous solids is incorrect?
Q67.
A particular solid is very hard and has a high melting point. In solid state, it is a non-conductor but its melt is a conductor of electricity. Classify the solid.
Q68.
Iodine is
Q69.
The lattice energy of a solid increases if
Q70.
In CsCl type structure, the coordination number of Cs and Cl are
Q71.
Addition of arsenic to germanium makes the latter a
Q72.
The ratio of close packed atoms to tetrahedral holes in cubic close-packing is
Q1.
Diamond is a
📅KU 2008
Q2.
The crystal for which a = b ≠ c, α = β = 90° and γ = 120° is
📅MOE 2065
Q3.
In Schottky defect
📅IOM 2007
Q4.
A crystal of graphite contains
📅MOE 2061
Q5.
How many Cl- ions are there around Na+ ions in NaCl crystal?
📅I.E.•BPKIHS
Q6.
On mixing trivalent impurity in a crystal lattice of Si, type of semiconductor thus formed is
📅IOM•MOE
Q7.
Bragg's law is given by equation
📅IOM