Defects. Defects. Kap. 3 States of aggregation. Perfect Crystal

Size: px

Start display at page:

Download "Defects. Defects. Kap. 3 States of aggregation. Perfect Crystal"

Andra Barber
6 years ago
Views:

1 Kap. 3 States of aggregation Defects Perfect Crystal A A perfect crystal with every atom in the correct position does not exist. Only a hypothetical situation at 0 K Crystals are like people: it is the defects in them which tend to make them interesting! - Colin Humphreys Most materials properties are determined by the crystal defects present. Defects No. defects 1 No. atoms 10 Usually few defects: 15 If the defect consentration becomes too high, defect-defect interactions occur. Defect clustering Stoichiometric defects, viz. no ateration in composition Vacancies (empty possitions) Interstitial ( between lattice points) Wrong type atoms to %

Vacancies and Interstitials Impurity Atoms interstitial impurity.

Cotterill 1985 Thermodynamics Heat of formation Configurational entropy H S = k ln(w) Temperature dependency: G = H T S [defects]

for -type structure Equal ammount of anion and cation vacancies V (-) V (+) nd H exp N 2RT S One dominating type of defects.

2 Vacancies and Interstitials Impurity Atoms interstitial impurity. substitutional impurity Cotterill 1985 The colored atoms are impurity atoms. They are atoms of a different element. Cotterill 1985 Thermodynamics Heat of formation Configurational entropy H S = k ln(w) Temperature dependency: G = H T S [defects] incrases with temperature Different types of defects in one phase: each type of defect: G i = H i T S i Schottky defects The (100) for -type structure Equal ammount of anion and cation vacancies V (-) V (+) nd H exp N 2RT S One dominating type of defects. H Energy G = H T S T S Formation of defects: cost energy but gain entropy n d N H exp RT Alkaline halides Earth alkaline halides Cs-halides BeO -type -type Cs-type Wurtsite-type [defects] The heat of formation for a Schottky defect: H S

Frenkel defects The (100) for -type structure Cation Frenkel defect Anion Frenkel defect Kroger-Vink notation 1/8th of -t unitcell: Ag, AgBr Each defect is represented by a combination of three

3 Frenkel defects The (100) for -type structure Cation Frenkel defect Anion Frenkel defect Kroger-Vink notation 1/8th of -t unitcell: Ag, AgBr Each defect is represented by a combination of three symbols: X Scottky defect ( + 1),x(0),'( 1) i,s,x,y,s,s x ' V ' Ag,S i + + V + V V + V + +,S Movement from a normal to an interstitial position Example: Ag -type structure n f ( ) * H NN 1 2 F exp 2RT Ag in octahedra holes of ccp Ag in tetrahedre holes of ccp The heat of formation for a Frenkel defect: H Fr Thermodynamics Scottky defect + + V + V V + V + +,S,S ',S,S Thermodynamics log 10 (N i /N) = log 10 (constant) ( H/2RT)log 10 e K = ' [ V ][ V ][,S][,S] [ ][ ][ V ][ V ] Constant,S,S K = ' [ V ][ V ] [ ][ ] Intrinsic defects Constant K = N N N 2 ( NV ) ( N N ) 2 V V N V N K K e K e = Ce N V ( G RT) ( H / RT) ( S/ R ) ( H / RT) = N Ce e ( H / 2RT) Extrinsic impurities

4 Colour centre, (alkaline halides) The (100) for -type structure Electron in a box, paramagnetic moment Stoichiometry H-centre V-centre F-centre + V S' + V Colour from F-centre: Dependant om host lattice Li K Rb S ev 2.7 ev 2.2 ev 2.0 ev e + S, + + S, Many solid materials are non-stoichiometric all that really matters is charge balance Non-stoichiometry is common amongst transition metal compounds Fe x O where > x > YBa 2 Cu 3 O 7-x, 1 > x > 0 Colour: MX-perfect MX ordinary defects (intrinsic) Chemical impurities (extrinsic) Radiation Treatment with extra M colourless colourless colour colour colour Non-stoichiometry can control properties Non-stoichiometric compounds Non-stoichiometric compounds Non-stoichiometric compounds TiO x TiO 0.65 < x < 1.25 TiO < x < VO x VO 0.79 < x < 1.29 Mn x O MnO < x< Ni x O NiO < x < Li x V 2 O < x < 0.33

5 Aliovalent substitution Defect clustering Extrinsic defects arise on doping pure crystals with aliovalent impurities may be doped with Ca 2 to give: Defects have effective charge Defects do perturb the host structure 1 2x Ca x V X Some interactions More interactions Loads of interaction neutral pairs defect clustering Stable phases with ordered distribution of defects eks. Pt. fcc (F) Z=4 Wüstite Introduction of an interstitial atom (a defect) creates two defects. Fe 1-x O Fe II +Fe III Fe Fe 1 x II 1 3x V O x Fe III 2x V O x 13:4 defects:interstitial eks. α-fe. bcc (I) Z=2 Fe II,oct. 1 3x Fe III,tetr. 2x V oct. x Ordered on a small scale, no long-range order (SRO vs. LRO) O 4:1 8:3 13:4 16:5 Structur element in Fe 3 O 4

6 ZrO2 Defects are ascribed effective charges C Addition of Ca, Y, Ce or similar may stabilise the high temperature forms to lower temperatures. Cax2+Zr1-x4+O2-x 1100 C - Interactions neutral pair Interactions with other pairs defect clusters Smaller areas with ordered defect structures Predecessor for stable phases with ordering of defects and atoms Dominating effect Dominating effect Ionical compounds of -type structure: MX Ionical compounds of CaF2-type structure: MX2 Regard 1/8 th of the unit cell: If Frenkel defect, then filled tetrahedra possition. 4 4 Undesireable 6 Frenkel Schottky defects instead 8

Cs-halides, Tl BeO Earthalkali-fluorides,

Frenkel Schottky Schottky Anion Frenkel UO

7 The fluorite structure Compound Alkali-halides Earth alkali halides Ag, AgBr Cs-halides, Tl BeO Earthalkali-fluorides, CeO 2, ThO 2 Str. type t. str. t. str. t. str. Cs t. str. würtsite fluorite t. str. Dominating defect Schottky Schottky Cation Frenkel Schottky Schottky Anion Frenkel UO 2+x incorporates interstitial oxygen Edge dislocations Line defects

8 Edge dislocations Screw dislocations Screw dislocations Dislocation loop A Frank-Read source for the multiple initiation of dislocation loops. A dislocation is pinned in the basal plane at two ends by either impurities or an immobile non-basal dislocation. If a shear stress is resolved onto the basal plane, the dislocation line becomes unstable and begins to bow. With increasing stress, the line bows back onto itself to produce a new loop that is free to propagate, and a section that remains pinned which may initiate more loops. Screw dislocation at surface of SiC single crystal. Dark lines are individual atomic steps at the surface. (Fig in Schaffer et al.)

9 Formation of dislocations Antiphase Shear plane Twin plane

10 a) b) c) d) e) f) g) h) Interstitial impurity atom Edge dislocation Self interstitial atom Vacancy Precipitate of impurity atoms Vacancy type dislocation loop Interstitial type dislocation loop Substitutional impurity atom Solution Intrinsic defects associated with stoichiometric and pure crystals Extrinsic defects associated with dopants or impurities (0.1 1 %) Solutions What about dopants > 1%??? Solid solution Substitutional solid solution Interstitial solid solution Aliovalent substitution

Substitutional solid solution Substitutional solid solution Al 2 O 3 corundum Al 3+ covalent radius 1.18 Å (Al 2-x Cr x )O 3 corundum Cr 2 O 3 corundum Cr 3+ covalent radius 1.

(For metal atoms < 15% difference) (a bit higher for non-metals) High temperature helps increase in entropy (0 > H vs.

octahedras) - Zn 2 SiO 4 (Zn in tetrahedras) Preference for the same type of sites Cr 3+ only in octahedral sites, Al 3+ in both octahedra and tetraheda sites LiCrO 2 -LiCr 1-x Al x O 2 - LiAlO 2

11 Substitutional solid solution Substitutional solid solution Al 2 O 3 corundum Al 3+ covalent radius 1.18 Å (Al 2-x Cr x )O 3 corundum Cr 2 O 3 corundum Cr 3+ covalent radius 1.18 Å For substitutional solid solution to form: The ions must be of same charge The ions must be similar in size. (For metal atoms < 15% difference) (a bit higher for non-metals) High temperature helps increase in entropy (0 > H vs. 0 < H) The crystal structures of the end members must be isostructural for complete solid solubility Partial solid solubility is possible for non-isostructural end members Mg 2 SiO 4 (Mg in octahedras) - Zn 2 SiO 4 (Zn in tetrahedras) Preference for the same type of sites Cr 3+ only in octahedral sites, Al 3+ in both octahedra and tetraheda sites LiCrO 2 -LiCr 1-x Al x O 2 - LiAlO 2 Consider metallic alloys Interstitial solid solution Interstitial solid solution Atoms enters intersitital positions in the host structure. The host structure may be expanded but not altered. H 2 in Pt Fe-C system δ-fe (bcc) -> 0.1 % C γ-fe (fcc) -> 2.06 % C α-fe (bcc) -> 0.02 % C Tm = 1534 C < 1400 C < 910 C fcc (F) Z=4 bcc (I) Z=2 2 x Å 4 x 2.03 Å Mg 2 NH 4 LaNi 5 H 6 H 2 (liquid) H 2 (200 bar) Å 6 x Å Å

12 fcc (F) Z=4 bcc (I) Z=2 Aliovalent substitution Substitution with ions of different charge Need charge compensation mechanism Substitution by higher valence cations 1 2 Disordered Cu 0.75 Au 0.25 High temp Disordered Cu 0.50 Au 0.50 High temp Cation vacancies Interstitial anions Low temp Ordered Cu 3 Au Low temp Ordered CuAu Substitution by lower valence cations 3 4 Anion vacancies Interstitial cations Aliovalent substitution 1 Cation vacancies, Substitution by higher valence Preserve charge neutrality by leaving out more cations than those that are replaced. dissolves Ca 2 by: 1-2x Ca x V x Ca 2+ vil have a net excess charge of +1 in the structure and attract + vacancies which have net charge -1 Aliovalent substitution 2 Interstitial anions, Substitution by higher valence Preserve charge neutrality by inserting more anions interstitially. Not common mechanism due to the large size of the anions. CaF 2 maydissolvesomeyf 3 : Ca 1-x Y x F 2+x Mg 2+ may be replaced by Al 3+ : Mg 1-3x Al 2+2x V x O 4

13 Aliovalent substitution 3 Anion vacancies, Substitution by lower valence Preserve charge neutrality by leaving out anions as cations are replaced. Aliovalent substitution 4 Interstitial cations, Substitution by lower valence Preserve charge neutrality by inserting more cations interstitially, not necessarily of same kind. Common mechanism ZrO 2 dissolve CaO by anion vacancies : Zr 1-x Ca x O 2-x V x Must be holes present to accomodate additional atoms Si 4+ can be replaced by Al 3+ and interstitial Li + Li x (Al 1-x Al x )O 2 Aliovalent substitution 5 Double substitution Aliovalent substitution 6 Charge compensations Two substitutions take place simultaneously In olivines, Mg 2+ can be replaced by Fe 2+ at the same time as Si 4+ is replaced by Ge 4+ Cations or anions may be inserted/removed from the structure and compensated by reduction/oxidation of the catons in the structure. Li + in LiCoO 2, or LiMn 2 O 4 (Mg 2-x Fe x )(Si 1-y Ge y )O 4 Li 1-x Co 3+ 1-x Co4+ O 2 Li 1-x Mn 3+ 1-x Mn4+ 1+x O 4 NiO takes up additional oxygen by formation of cation vacancies NiO + O 2 Ni x Ni3+ 2x V Ni,x O

14 How to analyze solid solution X-ray diffraction - Fingerprint to analyze end members - Vegards law to analyze composition Cell volume States Composition Density measurements - Will differensiate between interstitial and vacancy mechanisms Chemical bonds Van der Waals interactions V ( r) = 4V min r0 r 6 r0 r 12

15 Hydrogen bonds Hydrogen bonds Polymorphism Macrostructure -> Microstructure Ice VIII Ice 1h

16 Crystal - amorphous Funtional material nostructures

Stoichiometric defects, viz. no ateration in composition. Interstitial ( between lattice points) Vacancies (empty possitions) Wrong type atoms

Stoichiometric defects, viz. no ateration in composition. Interstitial ( between lattice points) Vacancies (empty possitions) Wrong type atoms Perfect Crystal A A perfect crystal with every atom in the correct position does not eist. Only a hypothetical situation at 0 Crystals are like people: it is the defects in them which tend to make them