Metallurgical thermodynamics
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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

Metallurgical Thermodynamics


Metallurgical thermodynamics

www.mat.shu.edu.cn


Metallurgical thermodynamics

http://202.121.199.249/staff/Wu_YongQuan/


Metallurgical thermodynamics


Metallurgical thermodynamics

1.

2.

3.


Metallurgical thermodynamics

4

4

32


Metallurgical thermodynamics


Metallurgical thermodynamics

1983

1998

1979

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


Metallurgical thermodynamics


Metallurgical thermodynamics


Metallurgical thermodynamics


Metallurgical thermodynamics

1

1

Hamilton

2

3

5

4

6


Metallurgical thermodynamics

Ultramicroscopic

Microscopic

Mesoscopic

Macroscopic

Giganscopic


Metallurgical thermodynamics

TPV

System

State

Equilibrium


Metallurgical thermodynamics

33

66

n3n3n

3n


Metallurgical thermodynamics

3

2

3

3n-5

3n-6

n

translation

3n

rotation

vibration


Metallurgical thermodynamics

6n

6N

f

3n

3N

f

3n

3N

--

-phase space

--

-phase space

n

N

2f


Metallurgical thermodynamics

localized system

SiO2-liquid

non-localized system

independent particles

interacting particles

SiO2-quartz


Metallurgical thermodynamics

1

1

Hamilton

Hamilton

2

2

3

5

4

6


Metallurgical thermodynamics

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)


Metallurgical thermodynamics

Hamilton

1). 3

633

---phase space

2). 3n

6n3n3n

-- -phase space


Metallurgical thermodynamics

Hamilton

(One-dimension harmonic oscillator)


Metallurgical thermodynamics

px

x

Hamilton

(One-dimension harmonic oscillator)

b

a

E


Metallurgical thermodynamics

Hamilton

Newton

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

Hamilton


Metallurgical thermodynamics

Hamilton

2fHamilton

p=[p1,p2,,pf]

q=[q1,q2,,qf]

H=V+U

HHamiltonVU

Newton!!!


Metallurgical thermodynamics

Hamilton

NUV

1UU


Metallurgical thermodynamics

Hamilton

2


Metallurgical thermodynamics

:

Hamilton


Metallurgical thermodynamics

1

1

Hamilton

Hamilton

2

2

5

3

3

6

4


Metallurgical thermodynamics

translation

Boltzmann

1.38110-23J/K

rotation

molecular motion

vibration

electron

nuclear


Metallurgical thermodynamics


Metallurgical thermodynamics

c

b

a

1.

a=b=cV=a3

(degeneration)g


Metallurgical thermodynamics

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)


Metallurgical thermodynamics

J J= 012

I moment of inertia)

R0 = r1 + r2 reduced mass)

2.


Metallurgical thermodynamics

3.

= 0,1,2,

Upsilon


Metallurgical thermodynamics


Metallurgical thermodynamics

1

1

Hamilton

Hamilton

2

2

3

5

3

6

4

4


Metallurgical thermodynamics

~1023


Metallurgical thermodynamics

system

Ensemble


Metallurgical thermodynamics

G(q,p,t)

(Ergodic Hypothesis)


Metallurgical thermodynamics

(Liouville)

(conservation)

(conservation)

(conservation)


Metallurgical thermodynamics

1). (microcanonical ensemble)

NVENVE

2). (canonical ensemble)

NVTNVT

3). (grand canonical ensemble)

VT VT

4). (Gibbs ensemble)

NPT NPT


Metallurgical thermodynamics

1

1

Hamilton

Hamilton

2

2

3

5

5

3

4

6

4


Metallurgical thermodynamics

1).


Metallurgical thermodynamics

2).

NiNii


Metallurgical thermodynamics

2).

<1> 010Pi1

<2> Pi+j=Pi+Pj

<3> 1

<4> ij


Metallurgical thermodynamics

3).


Metallurgical thermodynamics

4).

For

For


Metallurgical thermodynamics

(energy level distribution)

inii

N


Metallurgical thermodynamics

(state distribution)


Metallurgical thermodynamics

= 3

= 2

= 1

= 0

1 2 3 4 5 6 7 8 9 10


Metallurgical thermodynamics

DWD

= WD = 1+3+6 = 10

WD


Metallurgical thermodynamics

probability

WDDN,U,V


Metallurgical thermodynamics

P

U, V N


Metallurgical thermodynamics

the most probable distribution

N E


Metallurgical thermodynamics


Metallurgical thermodynamics

WDPD = WD /

NUV


Metallurgical thermodynamics

M

N M

A

B

NABAMBN-M


Metallurgical thermodynamics

MM=N/2WD(WB)


Metallurgical thermodynamics

N=10

N=10

N=20

N=20

N=10N=20

1

N,U,V


Metallurgical thermodynamics

Maxell-Beltzmann

Gibbs

-

Bose-Einstein

-

Fermi-Dirac


Metallurgical thermodynamics

Boltzmann distribution


Metallurgical thermodynamics

Boltzmann

SkBoltzmannWmax

QRT


Metallurgical thermodynamics

1

1

Hamilton

Hamilton

2

2

3

5

5

3

4

6

6

4


Metallurgical thermodynamics

ni

N

gii

ii

Boltzmann

Zpartition function)1 BoltzmannZBoltzmannZ

Boltzmann

For NVE

(Partition function)


Metallurgical thermodynamics

translation

nuclear

rotation

electron

vibration


Metallurgical thermodynamics

Zt

Zr

Zv

Ze

Zn


Metallurgical thermodynamics


Metallurgical thermodynamics


Metallurgical thermodynamics

1).

2).

3).

4).

5). HamiltonHamilton

6).

7).

8).


Metallurgical thermodynamics


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