1. Legaturi in cristale Klein, 1993: capitolul 4
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi in cristale
Klein, 1993: capitolul 4
3 Bonding forces

2. Unit Cell Geometry Arrangement of atoms determines unit cell geometry:
Primitive = atoms only at corners
Body-centered = atoms at corners and center
Face-centered = atoms at corners and 2 (or more) faces
Lengths and angles of axes determine six unit cell classes
Same as crystal classes

3. Coordination Polyhedron and Unit Cells
They are not the same!
BUT, coordination polyhedron is contained within a unit cell
Relationship between the unit cell and crystallography
Crystal systems and reference, axial coordinate system
Halite (NaCl) unit cell; Z = 4
Cl CN = 6; octahedral

4. Unit Cells and Crystals
The unit cell is often used in mineral classification at the subclass or group level
Unit cell = building block of crystals
Lattice = infinite, repeating arrangement of unit cells to make the crystal
Relative proportions of elements in the unit cell are indicated by the chemical formula (Z number)
Sphalerite, (Zn,Fe)S, Z=4

5. Unit Cells and Crystals
Crystals belong to one of six crystal systems
Unit cells of distinct shape and symmetry characterize each crystal system
Total crystal symmetry depends on unit cell and lattice symmetry
Crystals can occur in any size and may (or may not!) express the internal order of constituent atoms with external crystal faces
Euhedral, subhedral, anhedral

6. What is Crystal Chemistry?
study of the atomic structure, physical properties, and chemical composition of crystalline material
basically inorganic chemistry of solids
the structure and chemical properties of the atom and elements are at the core of crystal chemistry
there are only a handful of elements that make up most of the rock-forming minerals of the earth

7. Chemical Layers of the Earth
SiO2 – 45%
MgO – 37%
FeO – 8%
Al2O3 – 4%
CaO – 3%
others – 3%
Fe – 86%
S – 10%
Ni – 4%

8. Composition of the Earth’s Crust

9. Average composition of the Earth’s Crust (by weight, elements, and volume)

10. The Atom The Bohr Model The Schrodinger Model Nucleus
- contains most of the weight (mass) of the atom
- composed of positively charge particles (protons) and neutrally charged particles (neutrons)
Electron Shell
- insignificant mass
- occupies space around the nucleus defining atomic radius
- controls chemical bonding behavior of atoms

11. Structure of the Periodic Table
# of Electrons in Outermost Shell
Noble
Gases
Anions
Transition Metals
Primary Shell being filled

12. Ions, Ionization Potential, and Valence States
Cations – elements prone to give up one or more electrons from their outer shells; typically a metal element
Anions – elements prone to accept one or more electrons to their outer shells; always a non-metal element
Ionization Potential – measure of the energy necessary to strip an element of its outermost electron
Electronegativity – measure strength with which a nucleus attracts electrons to its outer shell
Valence State (or oxidation state) – the common ionic configuration(s) of a particular element determined by how many electrons are typically stripped or added to an ion

13. 1st Ionization Potential
Anions
Cations
Elements with a single
outer s orbital electron
Electronegativity

14. Valence States of Ions common to Rock-forming Minerals
Cations – generally relates to column in the periodic table; most transition metals have a +2 valence state for transition metals, relates to having two electrons in outer
Anions – relates electrons needed to completely fill outer shell
Anionic Groups – tightly bound ionic complexes with net negative charge
+1 +2
-2 -1
Transition Metals

15. Reprezentari structurale
Exemple: Cristobalit (SiO2)
Reprezentare de descrie tipul de impahetare a atomilor
Reprezentare prin poliedre de coordinare
Descrierea configuratiei
golurilor
Bragg jun. (1920)
Sphere packing
Bragg jun. (1920)
Sphere packing
Pauling (1928)
Polyhedra
Pauling (1928)
Polyhedra
Wells (1954)
3D nets
Wells (1954)
3D nets

16. Structure and lattice – what is the difference?
2.1 Basics of Structures
Structure and lattice – what is the difference?
Example:
structure and lattice
in 2D
Lattice
pattern of points
no chemical information, mathematical description
no atoms, but points and lattice vectors (a, b, c, , , ), unit cell
Motif (characteristic structural feature, atom, group of atoms…)
Structure = Lattice + Motif
contains chemical information (e. g. environment, bond length…)
describes the arrangement of atoms

17. 2.1 Basics of Structures Unit cell Conventions:
Unit Cell (interconnection of lattice and structure)
an parallel sided region of the lattice from which the entire crystal can be constructed by purely translational displacements
contents of unit cell represents chemical composition
(multiples of chemical formula)
primitive cell: simplest cell, contain one lattice point
Conventions:
1. Cell edges should, whenever possible, coincide with symmetry axes or reflection planes
2. The smallest possible cell (the reduced cell) which fulfills 1 should be chosen

18. 2.2 Simple close packed structures (metals) Close packing in 2D
primitive packing (low space filling)
close packing (high space filling)

19. 2.2 Simple close packed structures (metals) Close packing in 3D
Example 1: HCP
Example 2: CCP

20. 2.2 Simple close packed structures (metals) Unit cells of HCP and CCP
(Be, Mg, Zn, Cd, Ti, Zr, Ru ...)
close packed layer: (001)
space filling = 74%, CN = 12
CCP
(Cu, Ag, Au, Al, Ni, Pd, Pt ...)
close packed layer: (111)

21. Volume occupied by atoms (spheres)
2.2 Simple close packed structures (metals)
Calculation of space filling – example CCP
Volume occupied by atoms (spheres)
Space filling =
Volume of the unit cell

22. 2.2 Simple close packed structures (metals)
Other types of metal structures
Example 1: BCC
(Fe, Cr, Mo, W, Ta, Ba ...)
space filling = 68%
CN = 8
Example 2: primitive packing
space filling = 52%
CN = 6
(-Po)
Example 3: structures of manganese
far beyond simple close packed structures!

23. 2.2 Simple close packed structures (metals)
Holes in close packed structures
Tetrahedral hole TH
Octahedral hole OH

24. elements or compounds („alloys“)
2.1 Basics of Structures
Approximation: atoms can be treated like spheres
Concepts for the radius of the spheres
elements or compounds („alloys“)
element or compounds
compounds only =
d/2 of single bond
in molecule =
d – r(F, O…)
problem: reference! =
d/2 in metal

25. 2.1 Basics of Structures Trends of the radii
atomic radii increase on going
down a group.
atomic radii decrease across
a period
particularities: Ga < Al (d-block)
ionic radii increase on going
down a group
radii of equal charge ions decrease across a period
ionic radii increase with increasing coordination number
the ionic radius of a given atom
decreases with increasing charge
cations are usually smaller
than anions
(atomic number)

26. most important method:
2.1 Basics of Structures
Determination of the ionic radius
Structure analyses,
most important method:
X-ray diffraction
Ionic radius = d – r(F, O…)
L. Pauling:
Radius of one ion is fixed to a reasonable value (r(O2-) = 140 pm)
That value is used to compile a set of self consistent values for other ions.

27. Impachetari
Impachetarea cea mai compacta a unor atomi identici (monezi, bile de biliard…) se face sub forma hexagonala in care fiecare atom este inconjurat de 6 atomi vecini
Impachetare hexagonala compacta

28. Arhetipuri structurale
Coordinari. Poliedrii de coordinare
strat A A
strat B B C
strat C
Impachetare
hexagonala compacta ABAB...
cubica compacta ABCABC...

29. Impachetari

30. Arhetipuri structurale
Coordinari. Poliedrii de coordinare
coordinare tetraedrica
(4 anioni, NC=4)
coordinare octaedrica
(6 anioni, NC=6)

31. 2.3 Basic structure types Overview
„Basic“: anions form CCP or HCP, cations in OH and/or TH
Structure type
Examples
Packing
Holes filled
OH and TH
NaCl
AgCl, BaS, CaO, CeSe,
GdN, NaF, Na3BiO4, V7C8
CCP
n and 0n
NiAs
TiS, CoS, CoSb, AuSn
HCP
CaF2
CdF2, CeO2, Li2O, Rb2O,
SrCl2, ThO2, ZrO2, AuIn2
0 and 2n
CdCl2
MgCl2, MnCl2, FeCl2, Cs2O, CoCl2
0.5n and 0
CdI2
MgBr2, PbI2, SnS2, Mg(OH)2, Cd(OH)2, Ag2F
Sphalerite (ZnS)
AgI, BeTe, CdS, CuI, GaAs,
GaP, HgS, InAs, ZnTe
0 and 0.5n
Wurzite (ZnS)
AlN, BeO, ZnO, CdS (HT)
Li3Bi
Li3Au
n and 2n
ReB2
!wrong! (LATER)

32. Arhetipuri structurale
Coordinari. Poliedrii de coordinare
tetraedru de coordinare TO4
T = Si, Al
octaedru de coordinare MO6
M = Al, Mg, Fe2+, Fe3+ , Ca, Na, K

33. Legaturi (bonding forces)
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi (bonding forces)
Legaturile dintre atomi sunt de natura electrica;
Tipul de legatura este responsabil de proprietatile fizice si chimice ale mineralelor: duritate, clivaj, temperatura de topire, conductivitate electrica, termica, proprietati magnetice, compresibilitate, etc…
Legaturile puternice produc:
1/ duritate ridicata;
2/ temperatura de topire ridicata;
3/ coeficient de expansiune termica mai scazut.
Principalele tipuri de legaturi:
Ionica
Covalenta
Metalica
Van der Waals
Hidrogen
3 Bonding forces

34. Tipuri de legaturi in minerale
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Tipuri de legaturi in minerale
1/ Legatura ionica
Cedare sau acceptare de é pentru a obtine configuratie stabila (gaz nobil) → completarea stratul de valenta
Ex: Na: Z=11: 1s2 2s2 2p6 3s1
Devine ion pozitiv prin cedarea unui é
Ex2: Cl: Z=17: 1s2 2s2 2p6 3s2 3p5
Devine ion negativ prin acceptarea unui é
2 atomi neutrii
2 ioni incarcati (+) si (-)care formeaza NaCl
3 Bonding forces

35. Legaturi Legatura ionica in Na+Cl-
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Legatura ionica in Na+Cl-
3 Bonding forces

36. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Legatura ionica: Punct de topire (MP) vs. distanta inter-ionica (ID)
Daca DI creste → MP scade MP MP DI ID
(Fig. 3.18) MP ID
3 Bonding forces

37. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Legatura ionica: Duritate (H) vs. distanta inter-ionica (DI) Fig. 3.19 H H DI DI
Distante inter-ionice mici → legatura puternica
3 Bonding forces

38. Legaturi Legatura covalenta
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Legatura covalenta
→obtinerea configuratiei de gaz nobil prin punere in comun de é
Ex.: Carbon, C
Legatura covalenta a diamantului
3 Bonding forces

39. Legaturi Linus Pauling 1901-1994 Premiul Nobel pt. chimie 1954
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Linus Pauling
Premiul Nobel pt. chimie 1954
Premiul Nobel pentru pace 1962 (testele atomice)
“Linus Carl Pauling, who ever since 1946 has campaigned ceaselessly, not only against nuclear weapons tests, not only against the spread of these armaments, not only against their very use, but against all warfare as a means of solving international conflicts.”
1939: Metoda de estimare a caracterului ionic (%) Electronegativitatea
3 Bonding forces

40. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Electronegativitatea reprezintă capacitatea unui atom de a atrage é.
halogenii au cele mai mari valori ale electronegativității
metalele alcaline au cele mai mici valori si există elemente care au aceleași valori pentru electronegativitate.
Electronegativitate scazuta → cedeaza é
Electronegativitate ridicata → accepta é
3 Bonding forces

41. Legaturi Electronegativitatea (scade in grupa & creste in perioada)
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Legaturi
Electronegativitatea (scade in grupa & creste in perioada)
metale- EN<
nemetale
EN>
Acceptori
Donori
NOTA: gazele nobile au electronegativitate zero→stabile
3 Bonding forces

42. Bonding Forces Metallic bond Properties:
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Metallic bond
Atomic nuclei plus non valence electron orbitals bound together by the aggregate charge of a cloud of valence electrons
electrons ‘free’ to move readily throughout structure
- Metals aka ‘electron donors’
Properties:
Conductivitate electrica ridicata
Plasticitate >
Red circles = nuclei
Metals: Electrons v. mobile
3 Bonding forces

43. Johannes Diederik van der Waals
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Van der Waals bond:
Weak bond due to ‘dipole effect’ in molecular structure, small residual charges on surfaces.
Examples:
sulfur, S8
chlorine, Cl2
Between layers of graphite
Organic compounds
Johannes Diederik van der Waals
1910 Nobel prize in Physics
3 Bonding forces

44. Bonding Forces Van der Waals bond: GRAPHITE C Covalent bond
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Van der Waals bond:
Covalent bond
GRAPHITE C
Van der Waals bond
3 Bonding forces

45. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Hydrogen bond - electrostatic bond (polar bond) between a positively charged hydrogen ion & a negatively charged ion eg O2- and N3-
Hydrogen - only one electron in structure
when it transfers the electron to a stronger attractor the remaining proton becomes unshielded and can make weak hydrogen bonds with other large negative ions or negative ends of polar molecules eg Ice (water) & hydroxides (OH- group)
3 Bonding forces

46. Bonding Forces Hydrogen bond - electrostatic or polar bond Eg. water
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Eg. water
Hydrogen bond - electrostatic or polar bond
3 Bonding forces

47. Bonding Forces Crystals with more than one bond type:
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Bonding Forces
Crystals with more than one bond type:
Bond types are end members
Example: Bonds can be partly ionic & partly covalent
More than 1 bond type can exist in one crystal
Eg: graphite - strong covalent bond within sheets & weak van der Waals bonding between sheets.
3 Bonding forces

48. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Size of atoms or ions difficult to define but even more difficult to measure …
Definition: Radius of atom is the maximum radial charge density of the outermost shells
Effective radius depends on neighboring atoms or ions and on ‘charge’ of the ion
3 Bonding forces

49. Atomic and ionic radii 2r Atomic radius
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii 2r pm
Atomic radius pm pm
NOTE: 100 pm = 10 nm = 1 Angstrom
3 Bonding forces

50. Atomic radii Distances in picometers, pm
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic radii
Distances in picometers, pm
3 Bonding forces

51. Atomic and ionic radii Assume:
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
When oppositely charged ions unite to form a crystal structure each ion tends to ‘surround’ itself or to coordinate as many ions of the opposite sign as size permits
Assume:
Ions are approximately ‘spherical’
Coordinated ions cluster about a central coordinating ion so that their centers lie on the apices of a polyhedron
3 Bonding forces

52. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Coordination polyhedron of halite (NaCl) ions in cubic arrangement Both Na+ and Cl- are in 6-coordination or CN=6 (6 near -neighbours)
Octahedron around Cl- ion
3 Bonding forces

53. Atomic and ionic radii Radius ratio
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Radius ratio
The strongest forces exist between the nearest neighbors:
The first coordination shell
The geometrical arrangement of this shell or coordination number is a function of relative ionic size.
Remember: Ions and atoms are not rigid spheres so they do not have established constant radii.
3 Bonding forces

54. GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
When the 2 ions are about the same size, so Ra:Rx=1 the ions will show the closest packing, so coordination number (CN)=12 1 2 7 6 3 x 9 8 5 4
And 3 more in the layer below make 12
where Ra=radius of cation & Rx=radius of anion
3 Bonding forces

55. Atomic and ionic radii Cubic coordination (CN=8)
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Cubic coordination (CN=8)
~ 8 anions around a cation 1 1 2
1 + x 1 2
Pythagoras 2 1
45o 1
3 Bonding forces

56. Atomic and ionic radii Octahedral (CN=6) ~ 6 anions around a cation
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Octahedral (CN=6)
~ 6 anions around a cation
Limiting value ~ 0.414
Pythagoras 2 1
45o 1
3 Bonding forces

57. Atomic and ionic radii Tetrahedral coordination
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Tetrahedral coordination
CN=4 or 4 anions about a
cation
Limiting value Ra:Rx=0.225
3 Bonding forces

58. Atomic and ionic radii Triangular CN=3 3 anions around a cation
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Triangular CN=3
3 anions around a cation
Linear CN=2
This is very rare
Examples are copper in cuprite, Cu2O
Uranyl group, UO2 2+
Nitrite group, No2 2-
Stable between & 0.255
In nature: CO3, NO3 & BO3
3 Bonding forces

59. Atomic and ionic radii Radius ratio Ra:Rx <0.155 Ra:Rx = 1 Fig 3.36
GEOL Crystal chemistry and the geochemistry of mineral systems JHSchellekens
Atomic and ionic radii
Radius ratio
Ra:Rx <0.155
Ra:Rx = 1
Fig 3.36
3 Bonding forces

60. Next Lecture Crystal Chemistry II Bonding Atomic and Ionic Radii
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