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

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- Colin Humphreys Most materials properties are determined by the crystal defects present. acancies and Interstitials Cotterill 1985 Defects No. No. defects atoms Usually few defects: 15 10 1 to 0.

1 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 interesting! - Colin Humphreys Most materials properties are determined by the crystal defects present. acancies and Interstitials Cotterill 1985 Defects No. No. defects atoms Usually few defects: to % If the defect consentration becomes too high, defect-defect interactions occur. Defect clustering Stoichiometric defects, viz. no ateration in composition acancies (empty possitions) Interstitial ( between lattice points) Wrong type atoms Impurity Atoms interstitial impurity. substitutional impurity The colored atoms are impurity atoms. They are atoms of a different element. Cotterill 1985

2 Schottky defects The (100) for -type structure Equal ammount of anion and cation vacancies (-) (+) Alkaline halides -type Earth alkaline halides -type Cs-halides Cs-type BeO Wurtsite-type The heat of formation for a Schottky defect: H Sch Thermodynamics Heat of formation H Configurational entropy 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 One dominating type of defects. H T S G H T S Formation of defects: cost energy but gain entropy Frenkel defects The (100) for -type structure Cation Frenkel defect Anion Frenkel defect 1/8th of -t unitcell: Ag, AgBr Movement from a normal to an interstitial position Eample: Ag -type structure Ag in octahedra holes of ccp Ag in tetrahedre holes of ccp The heat of formation for a Frenkel defect: H Fr Energy [defects] roger-ink notation Each defect is represented by a combination of three symbols: X Scottky defect ( + 1),(0),'( 1) ' i,s,x,y Ag i + + +,S +,S + +,S,S '

3 Thermodynamics Scottky defect + + +,S +,S + +,S,S ' [ ][ ][,S ][,S ] [ ][ ][ ][ ] Constant,S,S ' [ ][ ] [ ][ ] Constant 2 ( N ) ( N N ) 2 N N N N N N Ce e e ( G RT ) ( H / RT ) ( S/ R ) ( H / RT ) N Ce e ( H / 2RT ) Colour centre, (alkaline halides) The (100) for -type structure Electron in a bo, paramagnetic moment F-centre Colour from F-centre: Dependant om host lattice Li 3.1 e 2.7 e 2.2 e Rb 2.0 e H-centre -centre S' S S, e + + S, Colour: MX-perfect colourless MX ordinary defects (intrinsic) colourless Chemical impurities (etrinsic) colour Radiation colour Treatment with etra M colour Thermodynamics log 10 (N i /N) log 10 (constant) ( H/2RT)log 10 e Etrinsic defects arise on doping pure crystals with aliovalent impurities may be doped with Ca 2 to give: 1 2 Ca X '

4 Defect clustering Defect clustering Defects have effective charge Defects do perturb the host structure Some interactions neutral pairs More interactions defect clustering Loads of interaction Stable phases with ordered distribution of defects Wüstite 1- O II + III 1 II 1 3 O III 2 O 13:4 defects:interstitial II,oct. 1 3 III,tetr. 2 oct. O Ordered on a small scale, no long-range order (SRO vs. LRO) 4:1 8:3 13:4 16:5 Structur element in 3 O 4 eks. Pt. fcc (F) Z4 Introduction of an interstitial atom (a defect) creates two defects. eks. α-. bcc (I) Z2 fcc (F) Z4 bcc (I) Z2 Disordered Cu 0.75 Au 0.25 High temp Disordered Cu 0.50 Au 0.50 High temp Low temp Ordered Cu 3 Au Low temp Ordered CuAu

5 Dominating effect Defects are ascribed effective charges + - Ionical compounds of -type structure: MX Regard 1/8 th of the unit cell: Interactions neutral pair If Frenkel defect, then filled tetrahedra possition. Interactions with other pairs defect clusters 4 4 Undesireable Smaller areas with ordered defect structures Predecessor for stable phases with ordering of defects and atoms Schottky defects instead Dominating effect Ionical compounds of CaF 2 -type structure: MX 2 Compound Str. type Dominating defect Alkali-halides t. str. Schottky Earth alkali halides t. str. Schottky Ag, AgBr t. str. Cation Frenkel 6 8 Cs-halides, Tl Cs t. str. Schottky BeO würtsite Schottky Frenkel Earthalkali-fluorides, fluorite t. str. Anion Frenkel CeO 2, ThO 2

Solution Intrinsic defects associated with stoichiometric and pure crystals Etrinsic defects associated with dopants or impurities (0.1 1 %) What about dopants > 1%?

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

6 Solution Intrinsic defects associated with stoichiometric and pure crystals Etrinsic defects associated with dopants or impurities (0.1 1 %) What about dopants > 1%??? Solid solution Substitutional solid solution Interstitial solid solution Substitutional solid solution 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- Al O 2 - LiAlO 2 Consider metallic alloys Substitutional solid solution Al 2 O 3 corundum (Al 2- Cr )O 3 corundum Cr 2 O 3 corundum Al 3+ covalent radius 1.18 Å Cr 3+ covalent radius 1.18 Å Interstitial solid solution Atoms enters intersitital positions in the host structure. The host structure may be epanded but not altered. H 2 in Pt Mg 2 NH 4 LaNi 5 H 6 H 2 (liquid) H 2 (200 bar)

7 Interstitial solid solution -C system δ- (bcc) -> 0.1 % C Tm 1534 C γ- (fcc) -> 2.06 % C < 1400 C α- (bcc) -> 0.02 % C < 910 C fcc (F) Z4 bcc (I) Z Å Å Å Å Å 1 Cation vacancies, Substitution by higher valence Preserve charge neutrality by leaving out more cations than those that are replaced. dissolves Ca 2 by: 1-2 Ca Ca 2+ vil have a net ecess charge of +1 in the structure and attract + vacancies which have net charge -1 Mg 2+ may be replaced by Al 3+ : Mg 1-3 Al 2+2 O 4 Substitution with ions of different charge Need charge compensation mechanism Substitution by higher valence cations 1 2 Cation vacancies Interstitial anions Substitution by lower valence cations 3 4 Anion vacancies Interstitial cations 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- Y F 2+

8 3 Anion vacancies, Substitution by lower valence Preserve charge neutrality by leaving out anions as cations are replaced. ZrO 2 dissolve CaO by anion vacancies : Zr 1- Ca O 2-5 Double substitution Two substitutions take place simultaneously In olivines, Mg 2+ can be replaced by 2+ at the same time as Si 4+ is replaced by Ge 4+ (Mg 2- )(Si 1-y Ge y )O 4 4 Interstitial cations, Substitution by lower valence Preserve charge neutrality by inserting more cations interstitially, not necessarily of same kind. Common mechanism Must be holes present to accomodate additional atoms Si 4+ can be replaced by Al 3+ and interstitial Li + Li (Al 1- Al )O 2 6 Charge compensations Cations or anions may be inserted/removed from the structure and compensated by reduction/oidation of the catons in the structure. Li + in LiCoO 2, or LiMn 2 O 4 Li 1- Co Co4+ O 2 Li 1- Mn Mn4+ 1+ O 4 NiO takes up additional oygen by formation of cation vacancies NiO + O 2 Ni Ni3+ 2 Ni, O

9 How to analyze solid solution X-ray diffraction - Fingerprint to analyze end members - egards law to analyze composition Cell volume Composition Density measurements - Will differensiate between interstitial and vacancy mechanisms

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

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