Character of metallic systems Advanced materials and technologies 2017

Properties determined by: chemical bond (electron configuration), atomic/molecular structure (for example type of crystal-lattice or amorphous structure…) defects in the lattice, microstructure (phases, grain size …)

characterise the chemical bond. Every element is characterised by a number (X), which is called electronegativity This number characterises the electron affinity of the element. If a connection forms between two different elements (chemical bond), than this number can be used to characterise the chemical bond. if XA ≈ XB, and XA, XB > XH,  covalent bond (e.g. organic compounds, diamond, graphite), if XA>>XB  ionic bond (e.g. NaCl, KCl), if XA, XB low, XA≈ XB < 1,8–2  metallic bond.

Covalent bond - Formed by pair of electrons (XA, XB ~ ≥ 2,1), - High binding energy (e.g.: C, Si, Ge), - Directions in bonding (pl. C-H4). Energy of molecular hydrogen referred to separated, neutral atoms. Negative energy corresponds to chemical bond. Curve A refers to electrons with parallel spin states, curve S (stabile state) refers to electrons with antiparallel spin states.

Ionic bond

Types of chemical bond are not clearly ionic, covalent or metallic, these might be mixed character

Structure of the metallic bond Pauli exclusion principle Metallic ion lattice in electron gas

Heat capacity and its dependence of temperature at metals and ceramics CV T Dulong–Petit-rule: CV= 3R= 25 Jmol-1K-1 (R= 8,314 Jmol-1K-1) (for solid state, at high temperature) Metallic character: value of 3R is reached at lower temperature Reason of the difference: electron configuration, the difference in chemical bond. C = T + AT3 (T<<200 K) ~NkBT/TF ahol TF=εF/kB Free electrons + addition of lattice (core)

R=R0(1+α(T-T0)) At some metals: α~ 1/273 K-1 Source: Prohászka

Wiedemann—Franz-rule: n: charge density (number of carrier in vol.) e: charge of electrons : hop time m: weight of electrons kB: Boltzmann-constant Electrical conductivity: Heat conductivity is derived from the free electrons:

Electron gas theory (Fermi–Dirac-statistics): Free electron theory: Electron gas theory (Fermi–Dirac-statistics): Fill up density (probability) of ε energy level (electron shell) : chemical potential If T→ 0K, then → εF where εF: Fermi-level. If kBT<<(ε-) (high energy interval), then Boltzmann distribution function: Grey area shows the occupied states at absolute 0 K. If temperature increases from 0 to T, then avarage energy increases; electrons are thermaly excited from area 1 to area 2. Source: C. Kittel: Introd. to solid state physics

Energy distribution of electrons in metals Energy distribution of electrons in metals. Electrons with higher energy than WB are able to quit from the metal. From these electrons quits in fact those, at which equation 1/2mvX2>WB is true. Boundary velocity:

Example: thermopower investigation of alloys Seebeck effect: S T1 T1+DT A B e f(e) 1 e f(e) 1

Difference in elect. potential Example: thermopower investigation of alloys Difference in elect. potential Hot electrode (T1) Sample Cold electrode (T2)

Example: thermopower investigation of alloys Source: Weltsch Ag47 Cd48 In49 Sn50 Sb51 Higher atomic number of alloying element means the increase of valence electrons per atom.

What is the mechanical character of the elements What is the mechanical character of the elements? Is there any correlation with other factors? Is there any correlation with electron configuration? Does it depend on bonding types? Young’s modulus of elements as a function of position in periodic system.

What is the hardness of the elements What is the hardness of the elements? Is there any correlation with other factors? Is there any correlation with electron configuration? Does it depend on bonding types? Hardness of the elements as a function of position in periodic system or electron configuration (valency electrons).

Melting point of the elements as a function of position in periodic system or electron configuration (valency electrons).