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研究生课程 —— 冶金热力学. 冶金热力学 Metallurgical Thermodynamics. 主讲:吴永全 上海大学现代冶金及材料制备国家重点实验室培育基地. 研究生课程 —— 冶金热力学. www.mat.shu.edu.cn. 研究生课程 —— 冶金热力学. http://202.121.199.249/staff/Wu_YongQuan/. 研究生课程 —— 冶金热力学. 研究生课程 —— 冶金热力学. 1. 没有固定的课本,因为当前的知识日新月异,授课要求和授课内容也跟着变化;.

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冶金热力学 Metallurgical Thermodynamics

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Metallurgical Thermodynamics


www.mat.shu.edu.cn


http://202.121.199.249/staff/Wu_YongQuan/



1.

2.

3.


4

4

32



1983

1998

1979

R. P. H. Gasser and W. G. Richards, Entropy and energy levels, Clarendon Press, Oxford, 1974





1

1

Hamilton

2

3

5

4

6


Ultramicroscopic

Microscopic

Mesoscopic

Macroscopic

Giganscopic


TPV

System

State

Equilibrium


33

66

n3n3n

3n


3

2

3

3n-5

3n-6

n

translation

3n

rotation

vibration


6n

6N

f

3n

3N

f

3n

3N

--

-phase space

--

-phase space

n

N

2f


localized system

SiO2-liquid

non-localized system

independent particles

interacting particles

SiO2-quartz


1

1

Hamilton

Hamilton

2

2

3

5

4

6


vy

p(px,py,pz)

y

vx

x

q(x,y,z)

Hamilton

1

(xn,yn,tn)

x, y

vx, vy

t

(vx,n+1,vy,n+1,tn+1)

(vx,n+1,vy,n+1,tn+1)

(xn+1,yn+1,tn+1)

phase space

()

2-

(qn,pn,tn)

q

p

(qn+1,pn+1,tn+1)


Hamilton

1). 3

633

---phase space

2). 3n

6n3n3n

-- -phase space


Hamilton

(One-dimension harmonic oscillator)


px

x

Hamilton

(One-dimension harmonic oscillator)

b

a

E


Hamilton

Newton

xqpxpEH(q,p)H(q,p)HamiltonHamilton()

Hamilton


Hamilton

2fHamilton

p=[p1,p2,,pf]

q=[q1,q2,,qf]

H=V+U

HHamiltonVU

Newton!!!


Hamilton

NUV

1UU


Hamilton

2


:

Hamilton


1

1

Hamilton

Hamilton

2

2

5

3

3

6

4


translation

Boltzmann

1.38110-23J/K

rotation

molecular motion

vibration

electron

nuclear



c

b

a

1.

a=b=cV=a3

(degeneration)g


nxnynz

g

1

(1

1

1)

(2

1

1)

3

(1

2

1)

(1

1

2)

(2

2

1)

3

(2

1

2)

(1

2

2)

1

(2

2

2)


J J= 012

I moment of inertia)

R0 = r1 + r2 reduced mass)

2.


3.

= 0,1,2,

Upsilon



1

1

Hamilton

Hamilton

2

2

3

5

3

6

4

4


~1023


system

Ensemble


G(q,p,t)

(Ergodic Hypothesis)


(Liouville)

(conservation)

(conservation)

(conservation)


1). (microcanonical ensemble)

NVENVE

2). (canonical ensemble)

NVTNVT

3). (grand canonical ensemble)

VT VT

4). (Gibbs ensemble)

NPT NPT


1

1

Hamilton

Hamilton

2

2

3

5

5

3

4

6

4


1).


2).

NiNii


2).

<1> 010Pi1

<2> Pi+j=Pi+Pj

<3> 1

<4> ij


3).


4).

For

For


(energy level distribution)

inii

N


(state distribution)


= 3

= 2

= 1

= 0

1 2 3 4 5 6 7 8 9 10


DWD

= WD = 1+3+6 = 10

WD


probability

WDDN,U,V


P

U, V N


the most probable distribution

N E



WDPD = WD /

NUV


M

N M

A

B

NABAMBN-M


MM=N/2WD(WB)


N=10

N=10

N=20

N=20

N=10N=20

1

N,U,V


Maxell-Beltzmann

Gibbs

-

Bose-Einstein

-

Fermi-Dirac


Boltzmann distribution


Boltzmann

SkBoltzmannWmax

QRT


1

1

Hamilton

Hamilton

2

2

3

5

5

3

4

6

6

4


ni

N

gii

ii

Boltzmann

Zpartition function)1 BoltzmannZBoltzmannZ

Boltzmann

For NVE

(Partition function)


translation

nuclear

rotation

electron

vibration


Zt

Zr

Zv

Ze

Zn




1).

2).

3).

4).

5). HamiltonHamilton

6).

7).

8).



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