F7360 Characterization of thin films and surfaces Lenka Zajíčková Faculty of Science & CEITEC, Masaryk University, Brno lenkaz@physics.muni.cz 1. Chapter - Structure of Condensed Matter spring semester 2014 Central European Institute of Technology BRNO | CZECH REPUBLIC • 1. Structure of Condensed Matter • 1.1 Amorphous and Crystalline Materials • 1.2 Bonds in solids • 1.2.1 Ionic Bonds • 1.2.2 Van der Waals bonds • 1.2.3 Covalent bonds • 1.2.4 Metallic Bonds • 1.2.5 Summary of Bonds in Solids • 1.3 Types of Materials F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 3/57 When the temperature of a melt is lowered to a certain point, the liquid will form either a crystalline or amorphous solid. Crystalls are periodic arrays of long-range ordered atoms. A real crystal is never perfect - contains defects (vacancies, dislocations, impurities, and other imperfections). Amorphous materials posses only short-range ordering. SiC>2 demonstrates the difference between crystalline and amorphous materials: Short-range ordering: silicon atoms are surrounded by three oxygen atoms. Long-range ordering in quartz: hexagonal structure. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 4/57 An ideal crystal is constructed by the infinite repetition of identical groups of atoms (a motif): A group is called the basis. The set of mathematical points to which the basis is attached is called the lattice. o o o o o o o o o o o o' o o o o o o o o o o o o o o o' © o o o o o o o o o o o o o o1 o o o o o o o o o o o o o o o1 o o o o o o o o o o o o o o' o o o o o o r ■ O O O O O O O O O O O O O O O O O O O O O O O O i O = Motif ° = Motif °m= Motif Square lattice The lattice in 3D is defined by three translation vectors ai, I2, §3 - the arrangement of atoms in the crystal have to look the same when viewed from the points r and r' 7 = r + u\a\ + u2a2 + u3a3 where 1/1, u2 and u3 are arbitrary integers. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 5/57 The lattice is primitive if any two points from which the attomic arrangement looks the same always satisfy 7 = r + u\l\ + u2a2 + u3a3 with a suitable choice of the integers ui, u2 and u3. Then, the vectors a\, a2 and a3 are primitive translation vectors. • •......•• Lattice points in 2D - all pairs of a\, a2 are translational vectors but a\", a^" are not primitive. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 6/57 The parallelepiped defined by the primitive axes et\, a2 and a3 is a primitive cell. A primitive cell is type of unit cell (or just cell). It is the smallest cell that can serve as a building block for the crystal structure. Its volume is V = \ava2 x a3| Primitive translation vectors a, are often used to define the crystal axes - three adjacent edges of the primitive parallelepiped. Nonprimitive axes are used as crystal axes when they have a simple relation to the symmetry of the structure. • • Cl al ----- /a. i ť----1 *— 2D centered rectangular lattice with primitive translation vectors a^ and a2 and ► nonprimitive translational vectors C| and o^- F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 7/57 In order to describe the crystal structure it is necessary to answeer three important questions: 1. what lattice we have (for a particular structure can be more than one), 2. what translational vectors , a2, a3 are we using to describe the lattice (more sets of translational vectors can be selected for a given lattice) and 3. what is the basis (which is choose after the lattice and translational vectors are selected). F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 8/57 Crystal lattice can be transformed into themselves by the lattice translation f f — u\a\ + u2a2 + u3a3 and by various other symmetry point operations. A typical symmetry point operation - rotation about an axis that passes through a lattice point Lattices can be found such that one-, two-, three-, four- and six-fold rotation axes carry the lattice into itself (corresponding rotations by 2ir, 2ir/2, 2ir/3, 2-k/A and 27r/6 and their integral multiples). Another symmetry operations are mirror reflections about a plane through a lattice point. The collection of symmetry point operations which, applied about a lattice point, carry the latice into itself is called lattice point group. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 9/57 Bravais lattices in two dimensions: general lattice known as oblique lattice - invariant only under rotation of -k and 2-k about any lattice point four special lattices (rectangular, centered rectangular or rhombic, hexagonal and square) - can be invariant under rotation 27r/3, 27r/4 and 2-k/Q or under mirror reflection Q T m it fill J riilalinn an /\ Three fold ruMiutn ■ □ Pour-Md wMm ul I it told muuon atit I M 'nu. ■■, plane -(- Onhopoaal mirror planer 9|( Mim* planes fieri ÉT ■I Kccl.in|tiil.u I iittitc ■•_ ■ h -»— t -9— I hr >>mmelr> it the tame at lhat fiw an> ninrr m i .i riĽu :.tr Iiiikc, in additxHi >! ant utilique latliir Square Ladíce |il=|b|. a = W Hť t ae.im.il 1 allice a |h . ■■ \20 -Í—¥ -i—m F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 10/57 In 3D - 7 distinguishable point groups of unit cells (7 crystal systems) that can fill the space (triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal and cubic). The Bravais lattices are obtained by combining one of the 7 lattice systems with one of the lattice centerings: simple - lattice points on the cell corners only. body-centered face-centered base-centered in total 7 x 6 — 42 combinations but from the full symmetries (point operations and translations) 14 different space groups (14 Bravais lattices) have been found. Simple cubic Face-centered cubic A7\ Simple tetragonal Body-centered tetragonal Body-centered cubic m A7\ A7\ Simple orthorhombic Rhombohed ral Body-cent e re d orthorhombic Simple Monoclinic Base-centered orthorhombic Base-cent e red monoclinic Face-centered orthorhombic F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 11/57 Primitive translation vectors of the body-centered cubic (bcc) lattice (in units of lattice parameter a) ► a, = (1/2,1/2,-1/2); ► a2 = (-1/2,1/2,1/2); ► a3 = (1/2,-1/2,1/2) The primitive cell is the rhombohedron. The packing ratio is 0.68, defined as the maximum volume which can be filled by touching hard spheres in atomic positions. Each atom has 8 nearest neighbors. The conventional unit cell is a cube based on vectors a"i = (0,0,1); a2 = (0,1,0); 33 = (0,0,1). It is twice big compared to the primitive unit cell and has two atoms in it with coordinates F, = (0,0,0) and 72 = (1/2,1/2,1/2). The bcc lattice have alkali metals such as Na, Li, K, Rb, Cs, magnetic metals such as Cr and Fe, and and refractory metals such as Nb, W, Mo, Ta. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 12/57 Primitive translation vectors of the face-centered cubic (fee) lattice (in units of lattice parameter a) ► a, = (1/2,1/2,0); >• a2 = (0,1/2,1/2); »33 = (1/2,0,1/2). The primitive cell is the rhombohedron. The packing ratio is 0.74. Each atom has 12 nearest neighbors. The conventional unit cell is a cube based on vectors a\ — (0,0,1); a2 = (0,1,0); a3 — (0,0,1). It is 4 times bigger than the primitive unit cell and has 4 atoms in it with coordinates r, = (0,0,0); r2 = (1/2,1/2,0); r3 = (0,1/2,1/2); 7A = (1/2,0,1/2). The fee lattice have noble metals such as Cu, Ag, Au, common metals such as Al, Pb, Ni and inert gas solids such as Ne, Ar, Kr, Xe. F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková 13/57 Crystal System Centering Axial Distances (edge lengths) Axial Angles Cubic simple a = b = c a = p = 7 = 90° body-centred face-centred Tetragonal simple a = b / c a = p = 7= 90° body-centered Orthorhombic simple a = p = 7 = 90° body-centered face-centered base-centered Hexagonal simple a = b / c a = /3 = 90°,7 = 120° Rhombohedral simple a = b = c a = P = 7 ^90° (trigonal) Monoclinic simple a + b+c a = 7 = 90°, p ^90° base-centered Triclinic simple a + b+c a + P + -l ^90° Examples "NlCT, Zinc Blende, Cu White tin, Sn02, Ti02, CaS04 Allotropes of sulfur, KN03, BaS04 Graphite, ZnO, CdS CaC03, HgS Monoclinic Sulf Na2S04 *10H2 K2Cr2Oy, CuS< *5H2Q, H3BO3 F7360 Characterization of thin films and surfaces: 1.1 Amorphous and Crystalline Materials Lenka Zajíčková H/57 F7360 Characterization of thin films and surfaces: 1.2 Bonds in solids Lenka Zajíčková 15/57 [el F7360 Characterization of thin films and surfaces: 1.2.1 Ionic Bonds Lenka Zajíčková 16/57 Ionic bonds - between particles which have a net electrical charge positive ions - cations, atoms with low ionization energy (lose electrons easily) - alkaline metals (only 1 s electron in outer shell) negative ions - anions, atoms with high electron affinity (easily accept electrons) - halogens (missing 1 p electron) Interaction force - Coulomb. Repulsive forces of similarly charge ions and attractive forces of differently charged ions are equilibrated. Pauli exclusion principle does not allow ions to come too close. ' H Ťa Periodic Table of the Elements S i ™ jS * y '.Be ' B ' c '.íl ° ' F '*Ne "Na Mg IE 'ľ* ™ , T ) II *! "ai "si ™p_ "s CI "ši "k "ba "sc "tí "v "cr °Mn "ře "co "ni "cu "zn "(3a Ge As Se "bi W *Rb "Sr "y "zr *Nb JMo Jc "ru *Rh "pd *Ag "cd "in "Sn "st> Je *l "xe "Cs *Ba "hi Ja "w Re Os 77Ir Vt Au MHg "ti °Pb ".Si f.?. "At *Rn "Vr ri Dl. Si, Bh "Ŕs Ml Ds Hg Jin Uui liuq Uup liuh Uui Uuo Ln "ce Pi Nd 'pm Sm *Eu jQd "Vb "dj "h_o "|r Tm 'Vb "lu "*Ac "jh ľľl U Np_ "Pu Am Cm a ™Md 'Ňo Tr = Si F7360 Characterization of thin films and surfaces: 1.2.1 Ionic Bonds Lenka Zajíčková 17/57 Ionization energy (energy necessary to release electron) is periodic function of atomic number, large atoms or molecules have lower ionization energy. First Ionization Energies Li Na 0 10 20 30 40 50 00 70 Atomic number Electron affinity (energy released if electron is added): Fluorine 3.45 eV Chlorine 3.61 eV Bromine 3.36 eV Iodine 3.06 eV Directionality of ionic bond is low - electron configuration of ions resemble filled shells of inert gases, i. e. electron density is sherically symmetric. High coordination - cation (anion) is surrounded by as many anions (cations) as possible. F7360 Characterization of thin films and surfaces: 1.2.1 Ionic Bonds Lenka Zajíčková 19/57 Cohesive energy of the crystal - energy released if ionic crystal is formed. The most important contribution - Coulomb interactions between ions, long range interaction Consider Na+ in NaCI. It is surrounded by six Cl~ at the distance r. 6e2 Another neighbors are 12 Na+ each at the distance V2r : 12e2 Vo Summed for the entire crystal: Vcou^ = -^(6-^§ + ...) (1) = -1.748- e 4ireor ,2 47re0r The constant a is called Madelung crystal constant, values 1.6-1.8 for simple crystals. F7360 Characterization of thin films and surfaces: 1.2.1 Ionic Bonds Lenka Zajíčková 20/57 The contribution of the quantum-mechanical repulsive force to the total potential energy can be written as: _ B ^repulsive = • Total potential energy in the crystal is: y — ^Coulomb + ^repulsive — ~ ~. ~ + ~T. where n is about 9. F7360 Characterization of thin films and surfaces: 1.2.1 Ionic Bonds Lenka Zajíčková 21 /57 Total potential energy (from previous slide): „=-£^-(i-l 47re0r0 V n In case of NaCI >• r0 = 2.81, thus V = -1.27 x 10~18 J = -7.97 eV we have take into account energy for electron transfer between Na and CI, i. e. the difference between the ionization energy 5.14 eV for Na and the electron affinity of -3.61 eVforCI -> 1.53 eV each atom is contributing with half of the value, so the overall cohesive energy per atom EcoheSive = (-3.99 + 0.77) eV/atom = -3.22 eV/atom. => Ionic crystals are hard and they have high melting point. They conduct electricity when molten or in solution, but not as a solid. They tend to be soluble in water. F7360 Characterization of thin films and surfaces: 1.2.2 Van der Waals bonds Lenka Zajíčková 22/57 All atoms and molecules, even inert-gas atoms, exhibit weak, short-range attractions for one another (proportional to r~7) due to van der Waals forces (0.01-0.1 eV/molecule). nonpolar-nonpolar attraction The different types of van der Waals forces were first explained by different people at different times => different names ► London dispersion forces between non-polar atoms or molecules were described by Fritz London in 1930. He suggested that the motion of electrons within an atom or non-polar molecule can result in a transient dipole moment. Dispersion forces are the weakest of the van der Waals forces. They are stronger for larger atoms and molecules (higher polarizability). dipole-dipole interactions explained by Keesom in 1912 as interaction between permanent electrical dipole moments of molecules (depends on the value of electrical dipole). F7360 Characterization of thin films and surfaces: 1.2.2 Van der Waals bonds Lenka Zajíčková 23/57 Hydrogen bonds - a special type of attractive dipole-dipole interaction between an electronegative atom and a hydrogen atom bonded to another electronegative atom (e. g. forH-F, H-OorH-N). It is strong type of van der Waals forces (0.04-0.26 eV/molecule) because H atom has only 1 electron that is "donated" almost whole to the electronegative atom, leaving the small effective size of proton unshielded (electric forces vary as r~2). Hydrogen bonds can occur between molecules or within parts of a single molecule. Typical example of molecules with permanent electric dipole moments is H2Q: F7360 Characterization of thin films and surfaces: 1.2.2 Van der Waals bonds Lenka Zajíčková 24/57 Characteristics of attractive force between The electric field E at a distance r from a polar molecule having dipole moment p 47r£0[r3 J pf — pr cos 9 (9 is angle between p and r). and nonpolar molecules: induced electric dipole moment p' in the other, normally nonpolar molecule, p' = aE where a is a constant called polarizability of the molecule. polar The energy of the induced dipole in the electrical field E is e = -^=-^1+0M2^ The mutual energy of the molecules that arises from their interaction is thus negative, signifying that the force between them is attractive, and is proportional to r~6. The force itself is equal to dE/dr and so proportional to r~7, which means that it drops rapidly with increasing separation. Doubling the distance between two molecules reduces the attractive force between them to only 0.8 % of its original value. http: //chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/ Atomic_and_Molecular_Properties/Intermolecular_Forces/Intermolecular_Forces F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 25/57 Explanation of covalent bonds - quantum mechanics is necessary. Two theories ► valence bond (VB) theory or local electron model: chemical bonds are formed by overlapping of atomic orbitals. This overlap of orbitals causes localization of the electrons in the bond region. molecular orbital (MO) theory: construction of new orbitals called molecular orbitals, electrons are redistributed throughout the molecules. VB theory provides an excellent agreement with observed molecular geometries (bond angles and bond lengths) but physical properies cannot be explained => MO theory. In discussing chemical bonds it is helpful to Schrodinger's equation for hydrogen atom: visualize the various atomic orbitals qualitatively resembling those of hydrogen: Em and V — 47re0r *l>n,l,m{r) Rn,(r)P^(cos8)e' me4 1 n = 1,2,3,... / = 0,1,2,...n- 1 m= -/,..., 0,...,/ F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 26/57 : »• Carbon, C - 1s22s22p2 Nitrogen, N - 1s22s22p3 >• Oxygen, O - 1s22s22p4 Fluorine, F - 1s22s22p5 ► Titanium, Ti - 1s22s22p63s23p63d24s2 http://www.docbrown.info/page07/ASA2ptable2a.htm Electron Configurations in the Pcrodic Table N Lo Ce 59 l'r 60 Nd 61 I'm 62 Sin 63 K.li 64 65 Gil Tb -1*1- 66 n> Ho 6S Rr 69 1 iii Vil 71 1 h 91 Pa 1) 93 Np 94 Pu 95 96 9~' Cm Rk - 9H Cf K.s 10(1 Fin M d 102 No 103 Ir 1.2.3 Covalent bonds Lenka Zajíčková H2 molecule - the easiest quantum mechanical calculation For separate Ha4>a(ra) = (- — V2- 2m 4ireQra and similarly for < ; Ea0 = Eg = £0. If the cores come closer electron from the core a will be influenced by the core b. Additionally Coulomb repulsive force occurs (shifts energies by constant value up, i. e. omitted for now) (- 2m Solution by 47re0ra 47re0rĎ tp - Ci0a + C2% or (but a, 4>b are real - ground state of H) F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 28/57 Wave functions are normalized / a^a,bdV = 1 Wave functions are not orthogonal =>■ overlap integral Interaction of e~ with separated cores (charge density —with core b or —e^ with core a) Interaction of electron exchanged density -eb with core - exchange integral "I- 02 -dv -dV It gives algebraic set of equations (AE + C)c, + (AE.S + D)C2 = 0 (AE.S + D)c, + (AE + C)c2 = 0 c = c2 = ±ci i. e. which determinant has to be equal to zero bonding state (symmetric wave functions) = c(4>a + 4>b) Ebi C+ D nding — 1 + S 47TC0flaíJ Bonding antibonding state (antisymmetric wave function) Va = c(0a - b) Ebi C- D nding 1 - S 47re0fíaů Anti-bonding F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 29/57 Valence bond theory concentrates on direction of bonds given by the overlap of atomic orbitals (s, p) - pairing of unpaired electrons from vallence shell atomic orbitals. In VB we name the bond according to its direction: cr bond - cylindrical symmetry, no nodal plane on the internuclear axis. 7r bond - a single nodal plane along the internuclear axis Sigma bond head on overlap, can form between differently shaped orbitals: A. s orbital + s orbita H + H H H H- * -H — H!H B. s orbital + p orbital C. p orbital + p orbital {'head-on' overlap] :F- + -FS _^ :FsF! Pi bonds form as a side on overlap when p-orbitals are parallel => overlap in two places, below and above the line connecting the two atoms nuclei. p orbital + p orbital ('side-on' overlap) X + X F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 30/57 Pi bond only occurs in molecules with double or triple bonds: the first bond is always a sigma bond the second and the third bond are pi bonds. N2sr; 34 Nitrogen, N2 3ci to - -tout - -I- bond . . 7T-bond However, this is oversimplified sketch because so called hybridization of orbitals takes place. Hybrid orbitals - mixtures of atomic (s, p, d) orbitals. Hybrid orbitals do not exist in an isolated atom, even when it is in excited state but arise while the atom is interacting with others to form molecule. F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 31 /57 Theory of hybridization is necessary to explain bonding in CH4 One 2s electron of carbon atom is promoted to higher state, i. e. 2p and 4 equivalent sp3 hybrid orbitals are formed: Potential energy 1 1 2px 2p 2P/ Potential energy 1 i i 1 17 2P)[ 2pr 2Pi Four sp3 hybrid orbitals may be considered as combination of 1 /4s and 3/4p -tetrahedral bonding directions In CH4, 4 sp3 hybrid orbitals create 4 a bonds in combination with 4 hydrogen atoms (1s orbitals) SP spi hybridization 1111 sp3 sp3 sp' spi Sigma (o) bonds 1 09.5" J* - Sigma (c) bonds F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 32/57 Two other types of hybrid orbital can occur in C atoms: in sp2 hybridization, one valence electron is in pure p state and the other three are in hybrid orbitals in sp hybridization, two valence electrons are in pure p state and the other two are in hybrid orbitals Formation of 3 sp2 hybrid orbitals: combination of 1 /3s and 2/3p - trigonal planar bonding directions with angles of 120° unhybridized p orbital 1 1 1 1 .sp- hybridization 111 5P* — 2p" 2p~ 2p~r * — — — IT I sp2 orbitals sp- sp2 sp2 H ,_2 %^^/\^^^ P In ethylene, C2H4, two C atoms are joint by two bonds, 1 T^l' sideways overlap sigma bond pi bond 33/57 F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 34/57 Natural solid carbon materials: diamond, sp3 bonded C ►• graphite, sp2 bonded C Classification of Carbon Films arbon thin films can be sp £ Diamond-like crystalline or amorphous pure, hydrogenated or modified with other elements ta.c _ , . x M \ \ ta-c:H part of (nano)composite structure Necessity of carbon film classification: W \ \Hcpoiymers sputtered a-c(:HM ternary phase diagram (sp3C, sp2C and H) for \ A~s!/ \^;/\ nofiims amorphous films (Jacob and Moller 1993, graphitic c ^' a-c.H^/-. no ms Robertson 2002) ' classification of a-C:H films into _ by Cambridge University group (2005): sp2 H : high H content (40-60 at. %); up to 70 % sp3 but most sp3C are H torminatoH =nft |0W density, optical band gap 2-4 eV intermediate H content (20-40 at. %); lower overall sp3 content but ids than PLCH =4- better mechanical properties, optical gap 1-2 eV. ■: increased C-C sp3 content whilst keeping a H content low (25-30 at. %) => higher density (up to 2.4 g/cm3) and Young's modulus (up to 300 GPa) : low H content (< 20at.%); high sp2 content and sp2 clustering => gap under 1 eV C. Casiraghi, A. C. Ferrari, and J. Robertson, Phys. Rev. B 72(8):1-14, 2005. diamond-like a-C:H (D F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 36/57 ► classification of carbon films by Fraunhofer Institute for Surface Engineering and Thin Films (IST) 2009 activities on international standardization, e.g. workshop at 12th International Conference on Plasma Surface Engineering (PSE) in 2010 Carbon films Design at ion 1 polymer films 2 Amorphous carbon films {diamond-like-carbon films f DLC) 3 Crystalline carbon films Diamond films Graphite Thin film/ thickf Mm Thinfilm Thinfilm Thinfilm Trickfilm (freestanding) Thinfilm □oping, additional hydrogen-free hyďogeriated — undoped undoped modified modified with metal withmetal | nametal on the growth side J. (amorphous) ltn 0.5 to 0.1 to 5 urn (5 pm to) 30 to 5C0pm Predominating C-C-bond type £p2or bund *2 sp2 or sp3 >p3 sp3 .ŕ Film No. 1 2.1 22 23 24 25 26 2.7 3.1 3.2 3.3 3A 15 3.6 Designation polymer film Hydrogen-amorphous Tetrahedral hydrogen-amorphous Metal-containing hydrogen-free amorphous film Hydrogenated carbon film Tetrahedral hydrogenated amorphous carbon film Metal-containing hydrogenaed film Modified liydrogenated crystalline CVD diamond CVD diamond film doped CVD diamond film CVD diamond doped CVD diamond graphite mended abbreviation J. a-C 1a-C a-C:Me a-C:H ta-C:H (Me = W, Ti. ■■■) a-C:H:X (X = a,Q, IM, F, B,...) J. J. .1. J. http://www.ist.fraunhofer.de/english/c-products/tab/complete.html F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 38/57 Hybridization in nitrogen ^ sp'hybridizatii ~ 2P* 2P> Nitrogen: 5 valence electrons 1 1 1 Hybridization in oxygen 11. U 1 1 sp2 hybridization Ts 2~* *~Py 2P< Oxygen: 6 valence electrons 9 ,^ ~, H H 3-D representation of the ammonia molecule sp2 sp2 sp2 F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 39/57 In molecular orbital theory, bonding atoms produce entirely new orbitals. Theory predict energies of bonding and anti-bonding states and shape of orbitals. It depends on 1. energies of orbitals interacting shape/symmetry of orbitals interacting formation of bonding and anti-bonding molecular orbitals B 2ft B 2pK and 2Py + 0 0 B 2p* and 2py + = F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 40/57 H2 molecule ,■-■. heteronuclear (homonuclear) .•' '■. molecule 1 H, . 1 Hs 1 n 3 o 1 TC a N 2s . .-' N 2s 1 cr Li2 to N2 molecules O2 and F2 O o •' o o '-. / ® °2P 1 1 3b _®_.' 2n* ® O 2s ® O 2s F7360 Characterization of thin films and surfaces: 1.2.3 Covalent bonds Lenka Zajíčková 41 /57 Molecules with more atoms, e. g. CH4 Energy LUMO HOMO 2a, ILl 1a, u n u —H— -o c 5 Highest Occupied Molecular Orbital (HOMO): The highest-energy molecular orbital in the energy ground state of a molecule occupied by at least one electron. Lowest Unoccupied Molecular Orbital (LUMO): The lowest-energy molecular orbital that is unoccupied in the ground state. F7360 Characterization of thin films and surfaces: 1.2.4 Metallic Bonds Lenka Zajíčková 42/57 H2 molecule - two 1s electrons with opposite spins (maximum electrons in K shell) => saturated covalent bonds Li2 (6 unfilled 2p states with energy similar to 2s): Li + Li2 -> Li3 (without violating exclusion principle - all valence electrons remain in L shells) =■ unsaturated covalent bonds Li forms bcc crystals (8 nearest neighbors, i. e. each bond = 1/4 of electron instead 2 for covalent bond) - electrons participating in unsaturated bonds are not localized. Cloud of free electrons - atoms "lose" outermost, s or p, electrons while the positively charged ions are left over. In transition metals (partially filled d-shells under the outermost shell) further electrons may participate in metallic bonding. Energy LUMO Excitation HOMO Energy Conduction Band Valence Band Insulator Metal Semiconductor Electrons in metals ctron approximat (precise only if Quantum mechanically solved by the electrons do not interact) and - can correctly explain many properties of metals, such as specific heat, thermal conductivity, electrical conductance. - explain other important phenomena such as the difference between metals, insulators and metalloid, the relationship between conductivity and valence electrons in the metal System of electrons -distribution function n(e) Fermi-Dirac distribution function fFD (for 7 = 0 step-wise Heavyside function) (max 1 particle in a given state). n(e)de = fFD g(e)de H -1— kT=v/10 0 1 y 5 4 5 electrochemical potential Fermi energy energy distribution of states g(t) FD : 0) electrochemical potential is given by the normalization condition (N electrons) For highly degenerated gas (low T) its temperature dependence can be approximated as The solution for Schrodinger equation in electric field for periodic ionic crystals shows the existence of a separate area of the energy bands - forbidden band (band gap). The position of Fermi level (electrochemical potential) with respect to band gap is important for behaviour of materials. oo F7360 Characterization of thin films and surfaces: 1.2.5 Summary of Bonds in Solids Lenka Zajíčková 45/57 Property Ionic ( 'i ivali lit Met allic Van der Waals Non-directional; Uirecional: Non-directional; Analogous to Structures of Structures of Structures of metallic bonds high coordination low coordination and low density high cixirdinat ion and high density Mechanical Strong, hard Strong, hard Variable Weak, -nil cryst aLs crystals crystals crystals Thermal High melt ing High melting Range of Low melt ing ]x)int. low point, low melting points |K)illt expansion expansion extended large expansion im linn ni coefficient liquidus range coefficient Ľli i i rical Weak insulator, Insulator in Conduct ion by Insulator conduction by solid and elect ron ion transport liquid state transport when liquid Optical Alxsorption and High refractive Opaque, with Properties other pro]K'rties index, absorption similar properties of individual mainly of the ilitliHilt ill in liquid state molecules individual ions solid and gas F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 46/57 Classification of materials based on nature and applications by Bever (1986): by nature: ceramics, glasses, metals and alloys, other inorganic materials, polymers, elastomers, fibres, composite materials, wood, paper and paperboard, other biological materials by application: electrical materials, electronic materials, superconductors, magnetic materials, materials for nuclear applications, materials for other energetic applications, optical materials, biomaterials, building materials, materials for textile and packaging industry (modified) M. B. Bever (ed.): Encyclopedia of Materials, Science and Engineering, 1986, sv. 1 ed. R. W. Cahn (Oxford: Pergamon) other references - material science conferences Spring and Fall Meetings of Material Research Society (MRS) in U.S. Spring and Fall Meeting of European Material Research Society (EMRS) TechCon of Society of Vacuum Coaters (SVC) A combination of one or more metals with a non-metallic element (usually oxygen but others include nitrogen, carbon .. .)■ May be crystalline or partially crystalline. The atoms are linked by ionic/covalent bonds - ionic bond character occurs especially for oxygen that effectively borrows two electrons from the neighbouring metal atoms Types of ceramics traditional ceramic materials: natural stone, clay minerals such as kaolinite modern ceramic materials, classified as advanced ceramics: aluminium oxide (alumina), silicon carbide, tungsten carbide,... Ceramic Si3N4 bearing parts Fine ceramic components from alumina F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 49/57 Ceramic materials are brittle, hard, strong in compression, weak in shearing and tension. withstand, in many cases, erosion that occurs in an acidic or basic environment. withstand very high temperatures such as temperatures that range from 1000 °C to 1600 °C, exceptions include inorganic materials that do not have oxygen such as silicon carbide. Crystal lattice imperfections (vacancies, dislocations) and microstructural defects (inclusions, pores, voids and distribution of irregular size grain) influence the properties mechanical failure occurs from pre-existing flaws - high mechanical stresses which exceed the local tensile strength effect crack propagation from flaws followed by rupture deffect is weak point for electrical load and aggressive environment F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 51 /57 Properties of metal and alloys are a consequence of the metallic bonds. They have good mechanical strength, high thermal and electrical conductivity, are opaque, lustrous and relatively heavy, are easily fabricated and shaped. In general, they form one of the face centred cubic (fee), body centred cubic (bec) or hexagonal close packed (hep) structures. Changes in the strength of metallic bond cause differences in optical, electrical, thermal and mechanical properties. The overall mechanical properties of metals and alloys are controlled by the crystal lattice defects, such as dislocations and vacancies. Mechanical and chemical properties can be modified by the addition of alloying elements in varying proportion. F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 52/57 Polymers are by definition materials composed of long-chain molecules, typically 10 to 20 nm, that have been developed as a consequence of the linking of many smaller molecules, monomers. H H I I C = C + l I H H H I H 1 1 C= 1 1 C ■ 1 H i H Ethylene mer units H H H H I I I I -C-C-C-O I l l I H H H H Polymerization by opening of double bonds X Carbon Polyethylene Chain ^Hydrogen The combination of tensile strength and flexibility make these materials attractive. 55i => polymer cross-linking F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 53/57 If the molecular chains are packed side by side, the molecules form an array with a crystalline structure. Natural polymers have complex microstructure comprising a mixture of crystalline and amorphous material. The interatomic bonds between molecular chains are the weak van der Waals forces, but in the crystalline structures, the chains are closer => more rigid material. CHjOH OH Nrjn-reducine end To develop stronger, more rigid, polymers: 1. production of a crystalline structure (polyethylene, nylon), 2. formation of a strong covalent bond between the molecular chains by cross linking (vulcanising raw rubber by heating with the controlled addition of sulphur atoms). F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 54/57 A composite material was originally considered to be a combination of two materials now it is regarded as any combination of various materials or their polymorphs. Composites have particular physical, mechanical and other properties that are not found in their constituents: natural composites: wood - cellulose fibres provide tensile strength and flexibility and lignin provides the matrix for binding and adds the property of stiffness; bone - strong, but soft, protein collagen and the hard, brittle mineral apatite, synthetic composites: combining individual properties such as strong fibres of a material (for example carbon) in a soft matrix (such as an epoxy resin). The concept of composite materials has led to the design and manufacture of a new range of structural materials that are generally lighter, stiffer and stronger than anything previously manufactured. F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 56/57 Alloys can have properties Multilayer structures can combine superior to each component properties of different compounds i MOO X ) ^ourteMr of S. WrrtJicimcr. ISCAR Ltd I M. Ohring.The Materials Science of Thin Films F7360 Characterization of thin films and surfaces: 1.3 Types of Materials Lenka Zajíčková 57/57 improves CNTs dispersion in matrix => shorter preparation time, better uniformity strengthens fiber-matrix interface => high composite stiffness and strength together with high toughness (thanks to nanotubes flexibility) adds additional functional groups => sensors 284.4eV 285.3eV 286.5eV 287.6eV ♦ 289.0eV 290.2-291.6eV 10 12 14 16 18 20 22 oxygen percentage [%] Changes of carbon bonding (by XPS) after plasma funct. in low pressure RF discharges —■ significantly improved hardness and elastic modulus of polyurethane/CNTs composites for optimum plasma conditions (Ar/H2Q, 02/C2H60) L. Zajíčková et al. Plasma Process. Polym. 6 (2009) S864-S869 L Zajíčková et al. Thin Solid Films 538 (2013) 7-15