Course Title : metallic condensed matter

Lecture 1: Basic features of metals.

Lecture Plan:1. Electron structure of materials. Periodic table2. Types of interatomic forcesyp3. Metal electric characteristics4. Electron zone structure of metals5. Common features of metals6. Metals classification

I. Electron structure of materials. Periodic table

Schematic representation of the H atom in wave mechanical model

2 Heisenberg uncertainty principle( ) h mx

Schrodinger equation for an electron in potential U(r)

( ) 2 mx

( ) ErUm

=

+ 2

2

2h

Electron states in an atom is characterized by four quantum numbers.Three quantum numbers signify size shape and spatial orientationThree quantum numbers signify size, shape, and spatial orientationof an electrons probability density :Principle q.number n - shells (K, L, M, N) ;the second q.number l - subshell (s, p, d, or f) ;3-d q.number ml - number of energy states for each subshell ;4-th q.number ms - one of two possible spin moment orientations.

Allowed values for the quantum numbersnumbersn = 1,2,3, ; l = 0,1,2,n-1 ; (n states)ml = 0,1, 2, l ; (2l+1 states)

The Number of Available Electron States in Some of the Electron Shells and Subshells

ms = 1/2 ; (2 states)

Shells and Subshells

P li l i i i l h l t t t h ld th t Pauli exclusion principle: each electron state can hold no more than two electrons, which must have opposite spins.

A Listing of the Expected Electron g pConfigurations for Some of the Common Elements

Energy states for a sodium atom

Z atomic number (from H1 to U92)A atomic weight; A= Z+N= Ai

The periodic table of the elements

II. Types of interatomic forces

RAN FFF +=attractive repulsive

RAN FFF +At xo equilibrium distance, FN =0

r

+== RAN EEdrFE

(a) The dependence of repulsive, attractive, and net forces on interatomic separation for

two isolated atoms.(b) Potential energy versus interatomic

separation for two isolated atoms.

Three types of primary chemical bonds : ionic, covalent, and metallic; secondary weak bonds van der Vaals bonds(hydrogen bonds)

Schematic illustrations

BAnN rB

rAE +=

Ionic bondingCovalent bonding

gnondirectional and unsaturated

directional and saturated(the number of neighboring atoms equals to

the number of bonds)

Metallic bonding

Van der Vaals bonding

rAMetallic bondingnondirectional and unsaturated

+= rB

rAEN exp6

Bonding Energies and Melting Temperatures for Various Bonding Energies and Melting Temperatures for Various Substances

III. Metal electric characteristics

Electrical conductivity of some materials at room temperature Conductivity Electrical conductivity of some materials at room temperature Conductivity Resistivity =1/

( ) TT

t0

00 1

=+=0

where o -resistivity of metal at absolute zero (0oC), - temperature coefficient of presistivity equal to 1/273; To =273K.

0T

Tfor semiconductors

The dependencies of on temperature for metals (a) and silicon (b).

IV. Electron zone structure IV. Electron zone structure

Schematic plot of electron energy versus i i i f finteratomic separation for an aggregate of 12 atoms (N= 12). Upon close approach, each of the 1s and 2s atomic states splits to form an electron energy band consisting of 12 states.

Energy zones in metals; dialectrics and semiconductors

Metals:Forbidden gap

Semiconductors :Forbidden gap E 1 V

Dialectrics :Forbidden gap

Eg= 0 eV; =10-810-6Ohm m;

Eg~1 eV;=10-6107Ohm m;

Eg~5 eV; =1081018Ohm m

V. Common features of metals

1 M t l i th i l t l t il th t t l h ld1. Metals give up their valent electrons easily, on the contrary nonmetals hold ontheir electrons strongly. The ability of the metal to loss of valent electronincreases when moving horizontally across the period from right to left andvertically down in a group. Transition metals have inconsequent filling of d-

d f l t l land f- electron levels.2. In terms of conductivity value (at room temperature) typical pure metals have

very high , i.e. not less than 106 (Omm)-13. Metals have the negative temperature coefficient of electrical conductivity.4 I i th l diti th Oh l i f ll li d f t l J E h4. In isothermal conditions the Ohm law is fully realized for metals J= E, where

J is a current density [ A/m2 ], E electric field intensity [V/m].5. Metals have high electron thermal conductivity Ke as well as . The

coincidence of the relation Ke/ ~ T for different metals is named as thecoincidence of the relation Ke/ T for different metals is named as theVideman-Frantz law.

6. Being cooled lower the characteristic temperature connected with Debaytemperature D there are observed growth in both e and .

7 At sufficiently low temperature the electric conductivity reaches saturation7. At sufficiently low temperature the electric conductivity reaches saturationand its value is determined by impurities and lattice defects. Accordingly toMattissen rule the contribution of impurities and defects into the resistivity isthe same for all temperatures: ( ) ( ) 111 += TT puredef

8. Almost a half of metallic elements become superconducters at sufficiently low temperature.

9. The occurrence of galvanic-magnetic effects under conditions of combination of both electric magnetic and temperature gradients

pf

both electric, magnetic and temperature gradients.10. As far as it concerns of mechanical properties of metals they are relatively

stiff and strong, also ductile and resistant to fracture. 11. Metals are quite dense and not transparent to visible light. .

V l l ifi iV. Metals classificationP t l b ti ll di id d i t i Pure metals can be conventionally divided into various groups : by mass - light (Al, Mg, Be, Li etc.) and heavy (Ni, Co, Pb,

Cu etc.); by melting temperature - low-melt (Li,Sn, Al etc. ) and

refractory high-melting metals (W, Mo, U etc.); by electron structure - ferrous metals and nonferrous metal y

(nonferrous are all metals except iron);noble metals (silver, gold, platinum), alkaline-earth metals (Li, Na, K, etc.), transition metals (Fe, Ni, Co ec.), rare-earth (Li, Na, K, etc.), transition metals (Fe, Ni, Co ec.), rare earth metals (Hf, Re, Os etc. ).

One more group of metallic materials is represented by metallic alloys Alloys can be formed by melting of some metallic alloys. Alloys can be formed by melting of some different metallic elements or a little quantity of nonmetal elements as C, N, O.

Literature :

W.D. Callister, D.G. Rethwisch Fundamentals of Material Science and Engineering. Wiley Company.-2007.

R.E.Reed-Hill Physical metallurgy principles.- 1973.R.E.Reed Hill Physical metallurgy principles. 1973. R. E. Smallman, R. J. Bishop Modern Physical Metallurgy and

Materials Engineering. Science, process, applications . - Sixth Edition.-1999.

. . .1971 . . .. 1988. .., .. .

.- ..1978. ..

. . . 1983.