Chapter 5. Materials
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1 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 1
2 5.1 Real structure of a cubic crystal vacancy (Schottky defect) Interstitial atom (Frenkel defect) edge dislocation lattice plane grain boundary pores or inclusions lattice plane 2
3 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
4 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 4
5 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 G H G number of defects T S 5
6 5.1 Number of defects in solids n s N e W 2 kt n s : 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) n s /N n s /cm 3 O Alkali halides Alkaline earth oxides Silverhalides Alkaline earth fluorides Schottky (cations and anions) Schottky (cations and anions) Frenkel (cations) Frenkel (anions) 6
7 5.2 Specific aspects of the structural chemistry of alloys (intermetallic compounds) - Classical alloys do not obey simple valence rules (8-N etc.): Zr 4 Al 3, Cu 5 Zn 8... 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) bcc fcc complex hcp Cu Zn 7
8 5.2 Characteristic morphology in different regions of the alloy system Pb - Sn 8
9 5.2 Zintl phases: alloys with moderate differences between participating metals (e.g. NaTl) NaTl = Na + Tl - : Tl - forms a diamond structure (Tl - acts as a pseudo element of group 14 (Pb)) Tl Na - 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, Ba 3 Si 4, NaP...) - 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
10 5.2 Laves phases: A specific radius ratio in AB 2 compounds favors certain structure types with closed-packed A and tetraedric B ions (classical examples: MgCu 2, 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 =
11 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) 11
12 5.3 Magnetism in solid state compounds: Bohr magneton (smallest quantity of a magnetic moment) Diamagnetism! F i General definition of the magnetic Moment (vector) = i F [Am 2 ], i: circular current, F: aerea B magnet. moment of an electron on an atomic orbit (Bohr magneton BM) B = eh/4 m e = 0, Am 2 (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. Swithg ~ 2 5 BM for Fe 3+ (S = 5/2) 12
13 5.3 Magnetism in solid state compounds Paramagnetism Ferromagnetism Antiferromagnetism Ferrimagnetism 13
14 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: [Am 2 /m 3 = 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 : [cm 3 /g] mol : [cm 3 /mol] (volume susceptibility) (gram susceptibilty) (molar susceptibility) used in Chemistry Relations between susceptibility and magnetic moment: mol N 3kT mol T N: Avogadro-Zahl = B : Bohr magneton k: Boltzmann constant 14
15 5.3 Magnetism in solid state compounds: Curie-Weiss law Pierre Curie N.P (Phys) (Discovery of new elements Po, Ra ) Marie Sklodowska-Curie N.P (Phys), 1911 (Chem) (Discovery of new elements Po, Ra ) Curie: ~ 1/T 1/ = C T; Curie-Weiss: 1/ = C (T- ) Susceptibility of real solids MnF 2 : Antiferro 15
16 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.
17 5.3 Magnetisation curve of an initially non-magnetic Ferro-/ Ferrimagnet ( hysteresis curve ) M (v)s : saturation magnetization M (v)r : remanence H C : coercitive field Aerea of the magnetization curve corresponds to magnetization energy soft hard Applications: Soft magnets: transformers, electromagnets, coils... Hard magnets: sound- und video-tapes, permanent magnets... 17
18 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 Thegarnetstructure: (Y 3+ ) 3 (Fe 3+ ) 5 O 12 b Y coordination, CN 8 c a Fe coordination Garnets: A 3 2+ B 2 3+ Si 3 O 12 : A=Ca, Mg, Fe, Mn..., B=Al, Fe, Cr - Silicates with isolated SiO 4 -tetrahedra -A 2+ : big cations with CN=8 - B 3+ : 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) 18
19 5.3 Solid State magnetism: Structure of spinell: MgAl 2 O 4 structural basis: ccp-arrangement of O 2- Normal spinell: AB 2 O 4, ⅛ T-holes (A), ½ O-holes (B) Invers spinell: B(BA)O 4, e.g. Fe 3 O 4 = Fe 3+ (Fe 3+ Fe 2+ )O 4 19
20 5.3 Ferroelectricity: The perovskite structure (CaTiO 3 ) BaTiO 3 BaTiO 3 is a dielectric material that shows Ferroelectricity Ti 4+ O 2- - Displacive phase transition below the ferroelectric Curie temperature (T c = 393 K for BaTiO 3 ) spontaneous polarisation Ba 2+ - 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 (Ba 2+, Ti 4+ ) move in oneand theanions(o 2- ) move in the opposite direction (see arrows); the structure becomes tetragonal (inversion center gets lost!) and shows a permanent electrical polarisation 20
21 5.4 Superconducting materials H. Kammerlingh- Onnes N.P J.G. Bednorz, K.A. Mueller N.P Ba x La 2-x CuO 4-y YBa 2 Cu 3 O 7-21
22 5.4 Structural relation between the structure of the high temperature superconductor YBa 2 Cu 3 O 7- ( +0.5) and the perovskite structure oxygen atoms are omitted oxygen deficient!! perovskite unit BaCuO 3 YCuO 3 BaCuO 3 fragments of CuO 6 -octahedra 22
23 5.4 Meissner-Ochsenfeld-effect Magnetic field Magnetic field Cooling below T c 23
24 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 24
25 5.5 Ionic conductors: Mobile ions Li +, Na +, O Li-battery (-accumulator) Diffusion path of Ag + ions in a silver ionic conductor Anode Cathode Electrolyte Mobile ions in ionic conductors (e.g.): -AgI: mobile Ag + -Alumina : M 2 O 11Al 2 O 3, mobile M + ZrO 2 : cubic, stabilized by Y 2 O 3 doping, mobile O 2- LiC 6 : Li-intercalated graphite, mobile Li + 25
26 5.5 Zirconia: ZrO 2 : application as solid electrolyte - Three modifications: monoclinic (baddeleyite) tetragonal cubic : <1170 o C(mineral) : <2370 o C : <2590 o C(m.p.) Cubic zirconia: stabilized at ambient temperatures by additives: (Ca 2+, Y 3+,...): Ca 2+ replaces Zr 4+ and generates a void in the O 2- partial structure Ca + Zr Zr + 2 O = Ca Zr + V O + ZrO 2 26
27 5.5 Zirconia: ZrO 2 : application as solid electrolyte -stabilizedcubic zirconia is an O 2- 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 27
28 5.5 Zirconia: ZrO 2 : structural properties Volume per formula unit: 35,59 33,67 32,89 Zr O 28
29 5.5 Zirconia: ZrO 2 : application as ceramic material crack Phase hardening on transition: based on the energy consuming formation and volume expansion of monoclinic ZrO 2 in a surrounding of stabilized cubic ZrO 2 crack 29
30 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) 30
31 5.6 Luminescent materials: LED s combination gives cool white Wavelength of emission depends on material composition: e.g. (In 1-x Ga x N...); white light is generated by combination of an LED (blue) with a yellow luminescent material (see next transparency). 31
32 5.6 Luminescent materials: Solids doped with luminescent centers (Eu 3+, Eu 2+, Ce 2+...) Excitation Emission 32
33 5.6 Luminescent materials Luminescence of Eu 3+ and Eu 2+ in European paper money when illuminating it with UV radiation Red: Eu 3+ -beta-diketonate Green: SrGa 2 S 4 :Eu 2+ Blue: (BaO) x Al 2 O 3 :Eu 2+ (x = 0,8) 33
34 5.7 Nitride materials: hexagonal and cubic BN = 2,25 g cm -3 (graphite 2,26 g cm -3 ) cubic-bn: = 3.47 g cm -3 white graphite h-bn c-bn Both BN-modifications are colorless and show a low electrical conductivity - B 2 O NH 3 2 BN + 3 H 2 O (ca o C) - primary product is h-bn; at 50 kbar / C cubic-bn (similar to diamond) 34
35 5.7 Nitride materials: -Si 3 N 4 : T<1650 o C Si SiN 4/3 and NSi 3/4!! direct reaction between Si and N: 3 Si + 2 N 2 Si 3 N 4 H = -750 kj/mol (T>1100 o C) extreme hardness (like diamond), very low thermal expansion coefficient, due to a thin protecting layer of SiO 2 stable up to to C in air Further important nitride materials: AlN, TiN, ZrN, HfN, NbN, TaN 35
36 5.8 Biogenic materials: apatite Ca 5 (PO 4 ) 3 X (X: F, OH ) (Inorganic basis of bones and teeth) Composite system bones: apatite + collagen (fiber protein) structure of apatite X Ca PO
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