Chapter 5. Materials

V divided by V i.e. magnetisation corresponds to an „intrinsic“ (internal) magnetic field and has to be added to an external field H M = ( )/ V dim: [...

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Chapter 5. Materials 5.1 Real structure and defects in solids 5.2 Specific aspects of the structural chemistry of alloys 5.3 Magnetism in solid state compounds 5.4 Superconducting materials 5.5 Ionic conductors 5.6 Luminescent materials 5.7 Nitride materials 5.8 Biogenic materials


5.1 Real structure of a cubic crystal vacancy (Schottky defect)

edge dislocation Interstitial atom (Frenkel defect)

lattice plane

pores or inclusions grain boundary

lattice plane


5.1 Point defects in solids Defects are of paramount importance for many application oriented properties of solids (e.g. mechanical and electrical properties)

Schottky-defect: vacancy, missing ions moved to the surface Frenkel-defect: vacancy, missing ions on interstitial positions 3

5.1 Defects in solids Importance of point defects for the properties of solids - Defects are centers of reactivity - Defects are responsible for mass transport (diffusion) either self diffusion or diffusion under the influence of an external electric field (ionic conductivity) - Schottky defects (vacancy): diffusion of cations and anions - Frenkel defects (interstitials): diffusion of one ionic species only


5.1 Defects in solids  Up to a certain (low!) concentration the presence of defects leads to a reduction of the free enthalpy (G) !!!

G = H - T S G: free enthalpy of a crystal ; H: enthalpy to create a defect, S: increase of entropy upon formation of a defect, T: absolute temperatur




number of defects

TS 5

5.1 Number of defects in solids



W e 2 kT

ns: number of defects; N: number of lattice positions W: energy to create a defect („activation energy“) k: Boltzman constant´; T: absolute temperature some typical numbers for NaCl (W = 188 kJ/mol ~ 2 eV): T (K) O 298 1073

ns/N 3 •10-17 3•10-5

Alkali halides Alkaline earth oxides Silverhalides Alkaline earth fluorides

ns/cm3 5•105 4•1017

Schottky (cations and anions) Schottky (cations and anions) Frenkel (cations) Frenkel (anions) 6

5.2 Specific aspects of the structural chemistry of alloys (intermetallic compounds) - Classical alloys do not obey simple valence rules (8-N etc.): Zr4Al3, Cu5Zn8 ... and are characterized by variable chemical compositions („homogeneity ranges“) with statistical atom distribution ( phase diagrams,  order-disorder-transitions)

Hume-Rothery phases: number and concentration of valence electrons favor certain structures (e.g. brass)



complex hcp




5.2 Characteristic morphology in different regions of the alloy system Pb - Sn


5.2 Zintl phases: alloys with moderate differences between participating metals (e.g. NaTl)


- If one assumes a complete electron transfer from Na to Tl the latter one becomes a „pseudo element“ of group 14 (Pb) and forms a diamond structure. - Typical for Zintl phases: the „pseudo element“ forms a structure (1D, 2D or 3D) which is found in real elements of the respective group of the periodic table. (LiIn, NaSi, Ba3Si4, NaP ...)


NaTl = Na+Tl-: Tl- forms a diamond structure (Tl- acts as a „pseudo element“ of group 14 (Pb))

- The Zintl model is an idealized assumption which accounts for the structural but in many cases not for the physical properties of the respective alloys 9

5.2 Laves phases: A specific radius ratio in AB2 compounds favors certain structure types with closed-packed A and tetraedric B ions (classical examples: MgCu2, a cubic Laves phase) Mg (160 pm)

Cu (128 pm)

r(Mg)/r(Cu) = 1.25, range: 1.1 to 1.7, ideal value: 3/ 2 = 1.22 10

5.2 Frank-Kasper-Phases (topological close packings): - Complex structures with 3D interpenetration of „Frank-Kasper-polyhedra“ - Each Frank-Kasper-polyhedron consists of a finite close packing of tetrahedra (e.g. icosahedron consists of 20 tetrahedra with a common apex and common faces and edges)


5.3 Magnetism in solid state compounds: Bohr magneton (smallest quantity of a magnetic moment) Diamagnetism !

i F 

General definition of the magnetic Moment  (vector)  = i F [Am2], i: circular current, F: aerea

B magnet. moment of an electron on an atomic orbit (Bohr magneton BM) B = eh/4me = 0,9274 10-27 Am2 (relation to basic constants)

(B: smallest possible quantity of a magnetic moment)

s = 2 (S(S+1))½.B with S = s = ½.n and n = number of unpaired electrons

(spin only magnetism, orbital momentum omitted, μ = g.S with g ~ 2 → 5 BM for Fe3+ (S = 5/2)


5.3 Magnetism in solid state compounds






5.3 Magnetisation (M) and susceptibility () for dia- and paramagnetic solids M: in general ,M is the sum of all magnetic moments in a volume V divided by V i.e. magnetisation corresponds to an „intrinsic“ (internal) magnetic field and has to be added to an external field H M = ( )/V

dim: [Am2/m3 = A/m] = magnetic field strength !

The effective magnetisation M‘ of a sample in an experiment has an internal component M and an external component H; it turned out to be useful to define a dimensionless quantity  (susceptibility), that represents this internal component:

M‘ = H V V: dimensionless g: [cm3/g] mol: [cm3/mol]

(volume susceptibility) (gram susceptibilty) (molar susceptibility) used in Chemistry

Relations between susceptibility and magnetic moment: 2 2 N: Avogadro-Zahl

 mol

N   3kT

  2.83  mol  T

=B: Bohr magneton k: Boltzmann constant 14

5.3 Magnetism in solid state compounds: Curie-Weiss law Pierre Curie N.P. 1903 (Phys) (Discovery of new elements Po, Ra )

Marie Sklodowska-Curie N.P. 1903 (Phys), 1911 (Chem)

(Discovery of new elements Po, Ra )

Curie:  ~ 1/T  1/ = C T;

Curie-Weiss: 1/ = C (T-)

Susceptibility of real solids MnF2: Antiferro


5.3 Solid State Magnetism: Magnetic structures by neutron diffraction Neutrons interact with a) atomic nucleus („normal reflections“) b) magnetic moment of electrons („magnetic reflections“)

Bragg angle Magnetic Bragg-reflections indicating the magnetic order are visible only at low temperatures. At high temperatures the magnetic moments are randomly 16 oriented and do not cause Bragg reflections.

5.3 Magnetisation curve of an initially „non-magnetic“ Ferro-/ Ferrimagnet („hysteresis curve“) M(v)S: saturation magnetization M(v)R: remanence HC: coercitive field

Aerea of the magnetization curve corresponds to magnetization energy soft


Applications: Soft magnets: transformers, electromagnets, coils ... Hard magnets: sound- und video-tapes, permanent magnets ...


5.3 Solid State Magnetism: Magnetic materials - No general chemical systematics for the composition of magnetic materials:  alloys with d-metals (Fe, Co, Ni, rare earth metals etc), ferrites, garnets … The garnet structure: (Y3+)3(Fe3+)5O12 Y coordination, CN 8




Fe coordination

Garnets: A32+B23+Si3O12 : A=Ca, Mg, Fe, Mn ..., B=Al, Fe, Cr - Silicates with isolated SiO4-tetrahedra - A2+: big cations with CN=8 - B3+: small cations with CN=6 RG: Ia3d: O (96h: xyz), Si (24d: 3/8 0 ¼ ) B (16a: 000) A (24c: 1/8 0 ¼)


5.3 Solid State magnetism: Structure of spinell: MgAl2O4

structural basis: ccp-arrangement of O2-

Normal spinell: AB2O4, ⅛ T-holes (A), ½ O-holes (B) Invers spinell: B(BA)O4, e.g. Fe3O4 = Fe3+(Fe3+Fe2+)O4


5.3 Ferroelectricity: The perovskite structure (CaTiO3) BaTiO3 BaTiO3 is a dielectric material that shows „Ferroelectricity“ Ti4+



- Displacive phase transition below the ferroelectric Curie temperature (Tc = 393 K for BaTiO3)  spontaneous polarisation - Piezoelectricity (pressure induced), Pyroelectricity (temperature induced) are also characterized by a spontaneous polarisation in the respective material

- In an external electric field and below 393 K all cations (Ba2+, Ti4+) move in one and the anions (O2-) move in the opposite direction (see arrows); the structure becomes tetragonal (inversion center gets lost !) and shows a 20 permanent electrical polarisation

5.4 Superconducting materials H. KammerlinghOnnes N.P. 1913

J.G. Bednorz, K.A. Mueller N.P. 1987

BaxLa2-xCuO4-y  YBa2Cu3O7-


5.4 Structural relation between the structure of the high temperature superconductor YBa2Cu3O7- (+0.5) and the perovskite structure oxygen atoms are omitted

oxygen deficient !!

perovskite unit




fragments of CuO6-octahedra 22

5.4 Meissner-Ochsenfeld-effect Magnetic field

Magnetic field

Cooling below Tc 


5.4 Mechanism of superconductivity: Cooper pairs Pairs of two electrons feel a weak attractive interaction mediated by a weak polarisation of the positively charged atomic cores


5.5 Ionic conductors: Mobile ions Li+, Na+, O2- ... Diffusion path of Ag+ ions in a silver ionic conductor

Li-battery (-accumulator)


Cathode Electrolyte

Mobile ions in ionic conductors (e.g.): -AgI: mobile Ag+ „-Alumina“: M2O●11Al2O3, mobile M+

„ZrO2“: cubic, stabilized by Y2O3 doping, mobile O2LiC6: Li-intercalated graphite, mobile Li+


5.5 Zirconia: ZrO2 : application as solid electrolyte - Three modifications: monoclinic (baddeleyite) tetragonal cubic

: <1170 oC (mineral) : <2370 oC : <2590 oC (m.p.)

Cubic zirconia: stabilized at ambient temperatures by additives: (Ca2+, Y3+,...): Ca2+ replaces Zr4+ and generates a void in the O2- partial structure Ca + ZrZr + 2 O = CaZr + VO ‘‘ + ZrO2


5.5 Zirconia: ZrO2: application as solid electrolyte - stabilized cubic zirconia is an O2- ionic conductor at higher temperatures - can be used as „solid electrolyte“ like liquid electrolytes in conventional electrochemistry - oxygen voids are migrating in a external field - most important part of oxygen sensors for car emission control


5.5 Zirconia: ZrO2 : structural properties

Volume per formula unit:







5.5 Zirconia: ZrO2 : application as ceramic material


Phase hardening on transition: based on the energy consuming formation and volume expansion of monoclinic ZrO2 in a surrounding of stabilized cubic ZrO2



5.6 Luminescent materials: LED‘s LED: Light Emitting Diode: based on a pn-junction

Solar cell: incoming: electromagnetic radiation (photons) outgoing: voltage LED: incoming: voltage outgoing: electromagnetic radiation (photons)


5.6 Luminescent materials: LED‘s combination gives „cool white“

Wavelength of emission depends on material composition: e.g. (In1-xGaxN ...); white light is generated by combination of an LED (blue) with a yellow luminescent material (see next transparency).


5.6 Luminescent materials: Solids doped with luminescent centers (Eu3+, Eu2+, Ce2+ ...)

Excitation Emission


5.6 Luminescent materials Luminescence of Eu3+ and Eu2+ in European paper money when illuminating it with UV radiation

Red: Eu3+-beta-Diketonate Green: SrGa2S4:Eu2+ Blue: (BaO)x·Al2O3:Eu2+ (x = 0,8)


5.7 Nitride materials: hexagonal and cubic BN  = 2,25 g cm-3 (graphite 2,26 g cm-3)

„white graphite“

cubic-BN:  = 3.47 g cm-3



Both BN-modifications are colorless and show a low electrical conductivity

- B2O3 + 2 NH3  2 BN + 3 H2O (ca. 1000 oC) - primary product is h-BN; at 50 kbar / 1400 0C  cubic-BN (similar to diamond) 34

5.7 Nitride materials: -Si3N4: T<1650 oC Si  SiN4/3 and NSi3/4 !!

direct reaction ´between Si and N: 3 Si + 2 N2

 Si3N4



H = -750 kJ/mol

 extreme hardness (like diamond), very low thermal expansion coefficient, due to a thin protecting layer of SiO2 stable up to to 1400 0C in air

Further important nitride materials: AlN, TiN, ZrN, HfN, NbN, TaN 35

5.8 Biogenic materials: apatite Ca5(PO4)3X (X: F, OH…) (Inorganic basis of bones and teeth)

„Composite system“ bones: apatite + collagen (fiber protein)

structure of apatite PO43X