90th anniversary of czochralski pulling method

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90th anniversary 90th anniversary of Czochralski method of Czochralski method 1885 1885 - - 1953 1953

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Page 1: 90th anniversary of Czochralski pulling method

90th anniversary 90th anniversary of Czochralski methodof Czochralski method

18851885--19531953

Page 2: 90th anniversary of Czochralski pulling method

In 2006 we celebrate the 90th anniversary of Czochralski pulling method. Professor Jan Czochralski invented this method during the investigations of the crystallization rate of metals. In the fifties of the twentieth century his method was adopted for growing large single crystals of semiconductors on an industrialscale. Moreover, a large group of applicable oxides are grown using Czochralski method. Also the number of single crystals of intermetallic compounds is quickly growing thanks to this method.

Fe2.25V0.75Al

GdCa4O(BO3)3

TheThe InstituteInstitute ofof ElectronicElectronic MaterialsMaterials TechnologyTechnology (ITME)(ITME)

UUŚŚ

Page 3: 90th anniversary of Czochralski pulling method

••Professor Jan Czochralski was born on October 23, 1885 in KcyniaProfessor Jan Czochralski was born on October 23, 1885 in Kcynia, in , in part of Poland at that timepart of Poland at that time under the Prussian domination, as the eighth under the Prussian domination, as the eighth child of the Polish craftsmen Franciszekchild of the Polish craftsmen Franciszek Czochralski and Marta from the Czochralski and Marta from the Suchomski family. The Suchomski family. The CzochralskisCzochralskis were carpenters for many were carpenters for many generations.generations.

••Jan completed teachers' seminar in Kcynia according to the wish Jan completed teachers' seminar in Kcynia according to the wish of his of his father. He was already interested in chemistry during his schoolfather. He was already interested in chemistry during his school days. days. However, he did not accept his matriculation certificate due to However, he did not accept his matriculation certificate due to poor poor grades. grades.

••Lack of this certificate Lack of this certificate unabledunabled him him to to continuecontinue hishis education. education. ForFor some some timetime he worked in he worked in KrotoszynKrotoszyn in a drugstore.

ArmsArms ofof KcyniaKcynia

in a drugstore.

Page 4: 90th anniversary of Czochralski pulling method

BydgoszczBydgoszcz

Page 5: 90th anniversary of Czochralski pulling method

BerlinBerlin••AAt the end of 1904 he went to Berlin and began to work in the drut the end of 1904 he went to Berlin and began to work in the drugstore of Dr. A. gstore of Dr. A. HerbrandHerbrand in in AltglienickeAltglienicke, the districts of Berlin., the districts of Berlin.••Later he worked for a short period in the laboratory of Later he worked for a short period in the laboratory of KunheimKunheim and Co. in and Co. in NiederschNiederschöönweidenweide near Berlin and then in near Berlin and then in AllgemeineAllgemeine ElektrizitElektrizitäätsts--GesellschaftGesellschaft(AEG). The job in (AEG). The job in KabelwerkKabelwerk OberspreeOberspree and the two years spent in their research and the two years spent in their research laboratories prepared him to become head of the laboratory of stlaboratories prepared him to become head of the laboratory of steel and iron eel and iron research. This laboratory dealt with the checking the quality anresearch. This laboratory dealt with the checking the quality and purity of metals d purity of metals and alloys and was engaged in the refinement of copper. and alloys and was engaged in the refinement of copper. ••Simultaneously he attended lectures on chemistry at the Simultaneously he attended lectures on chemistry at the CharlottenburgCharlottenburgPolytechnic near Berlin. Polytechnic near Berlin. ••From 1911 to 1914 he was an assistant of From 1911 to 1914 he was an assistant of WichardWichard von von MMööllendorffllendorff with whom with whom he published his first paper devoted to the crystallography of mhe published his first paper devoted to the crystallography of metalsetals, , dislocationdislocationtheorytheory ((ZeitschriftZeitschrift des des VereinesVereines DeutcherDeutcher IngenieureIngenieure

57 (1913) 93157 (1913) 931--5, 10145, 1014--20) 20) ..

KABELWERK OBERSPREE RESEARCH KABELWERK OBERSPREE RESEARCH LABORATORIES, JAN CZOCHRALSKI (FAR LABORATORIES, JAN CZOCHRALSKI (FAR LEFT)LEFT)..

Page 6: 90th anniversary of Czochralski pulling method

••Jan Czochralski married in 1910 Jan Czochralski married in 1910 MargueritMarguerit HaaseHaase, a pianist of Dutch origin, the, a pianist of Dutch origin, thedaughterdaughter of a rich owner of houses.of a rich owner of houses. TheyThey had three children: two had three children: two daughtersdaughters ––Leonia (1914)Leonia (1914) and Cecilia (1920,) and a son and Cecilia (1920,) and a son BorysBorys (1918).(1918).

CZOCHRALSKI'S FAMILYCZOCHRALSKI'S FAMILY

Page 7: 90th anniversary of Czochralski pulling method

••In 1916 professor Jan In 1916 professor Jan CzochralskiCzochralski invented a method for measuring the invented a method for measuring the crystallization velocity of metals. The method was invented by acrystallization velocity of metals. The method was invented by accident and ccident and through through CzochralskiCzochralski careful observations. careful observations.

••The idea of this method is based on pulling a crystal from the mThe idea of this method is based on pulling a crystal from the melt. The grown elt. The grown during the experiment crystals as metallic wires were single cryduring the experiment crystals as metallic wires were single crystals. stals.

••The results of The results of CzochralskiCzochralski studies were published in several papers, The first studies were published in several papers, The first one was published in one was published in ZeitschriftZeitschrift ffüürr PPhysikalische hysikalische ChemieChemie 92, 219 (1918), in 92, 219 (1918), in German. German.

••This new technique allowed to obtain the good This new technique allowed to obtain the good quality single crystals of pure metals like quality single crystals of pure metals like SnSn, , PbPb, Zn. , Zn. After the II World War the After the II World War the CzochralskiCzochralski method was method was adopted by the Americans G.K. Teal and J.B. Little adopted by the Americans G.K. Teal and J.B. Little from Bell Telephone Laboratories for growing large from Bell Telephone Laboratories for growing large single crystals of semiconductors on an industrial single crystals of semiconductors on an industrial scale (Growth of germanium single crystals, Phys. scale (Growth of germanium single crystals, Phys. Rev. 78, 647 (1950) and Bull. Amer. Phys. Soc. 25, Rev. 78, 647 (1950) and Bull. Amer. Phys. Soc. 25, 16 (1950)).16 (1950)).

Page 8: 90th anniversary of Czochralski pulling method

FranfurtFranfurt on on MeinMein••In 1917 Jan Czochralski moved to Frankfurt on In 1917 Jan Czochralski moved to Frankfurt on MeinMein and organized the Laboratory and organized the Laboratory of Metal Scienceof Metal Science..•• Several valuable scientific papers and patents were developed tSeveral valuable scientific papers and patents were developed there. Among the here. Among the patents was the highly famous patent on a tinpatents was the highly famous patent on a tin--free bearing alloy for railways, called free bearing alloy for railways, called metal B, patented in 1924 and bought by many countries all over metal B, patented in 1924 and bought by many countries all over the world, including the world, including USA, France and England. USA, France and England. ••He also pioneered investigations of the anisotropy of the hardneHe also pioneered investigations of the anisotropy of the hardness of single crystals ss of single crystals (works between 1913 and 1923), which are of great importance for(works between 1913 and 1923), which are of great importance for the plastic the plastic treatment of materials. treatment of materials. ••In 1919 In 1919 CzochralskiCzochralski was was amongamong thethe scientistsscientists whowho foundedfounded thethe German German SocietySociety for for Metal Science Metal Science andand inin 1925 1925 hehe becamebecame itsits presisentpresisent..WarsawWarsaw••When Poland regained independence he accepted in 1929 the invitaWhen Poland regained independence he accepted in 1929 the invitation of the tion of the President of Poland, President of Poland, IgnacyIgnacy MoMośścickicicki. Czochralski obtained his first honorary . Czochralski obtained his first honorary doctorate of the Faculty of Chemistry at the Warsaw doctorate of the Faculty of Chemistry at the Warsaw UniversityUniversity ofof TechnologyTechnology. It . It enabled him to take the position of a professor there. enabled him to take the position of a professor there.

TheThe CzochralskiCzochralski’’sshousehouse inin WarsawWarsaw

Page 9: 90th anniversary of Czochralski pulling method

PROF. JAN CZOCHRALSKI, WARSAW, 1929PROF. JAN CZOCHRALSKI, WARSAW, 1929

THE POLISH PRESIDENT IGNACY MOTHE POLISH PRESIDENT IGNACY MOŚŚCICKI (FAR CICKI (FAR RIGHT) VISITING CZOCHRALSKI'S LABORATORY. RIGHT) VISITING CZOCHRALSKI'S LABORATORY. JAN CZOCHRALSKI (SECOND FROM THE LEFTJAN CZOCHRALSKI (SECOND FROM THE LEFT).).

Page 10: 90th anniversary of Czochralski pulling method

••After the II World War due to his connections with Germans CzochAfter the II World War due to his connections with Germans Czochralski was ralski was suspected of collaboration and even arrested. The suspicion was suspected of collaboration and even arrested. The suspicion was continued to date of continued to date of his dead, but up to now there is no evidence for his collaboratihis dead, but up to now there is no evidence for his collaboration. In fact professor on. In fact professor Czochralski helped the National Army and many people during the Czochralski helped the National Army and many people during the war time. war time. Czochralski returned to Kcynia and to the chemistry and to produCzochralski returned to Kcynia and to the chemistry and to production of cosmetics ction of cosmetics and household chemicals. and household chemicals.

••He died on April 22, 1953He died on April 22, 1953 in in PoznaPoznańń due to heart disease and was buried in Kcynia. due to heart disease and was buried in Kcynia.

••Professor Jan Professor Jan CzochralskiCzochralski was outstanding metallurgist, chemist and crystallographer, was outstanding metallurgist, chemist and crystallographer, whose crystal growth method allowed dynamic development of the mwhose crystal growth method allowed dynamic development of the modern science and odern science and technology. However, after the war he was almost forgotten, esptechnology. However, after the war he was almost forgotten, especially in Poland. ecially in Poland. ••After the political changes in Poland the Tenth European CrystalAfter the political changes in Poland the Tenth European Crystallographic Meeting, lographic Meeting, organized in Wroclaw in 1986, was dedicated to Professor Jan organized in Wroclaw in 1986, was dedicated to Professor Jan CzochralskiCzochralski to to commemorate the seventieth anniversary of the discovery of the commemorate the seventieth anniversary of the discovery of the CzochralskiCzochralski method. method. ••Since its foundation in 1991, the Polish Society for Crystal GroSince its foundation in 1991, the Polish Society for Crystal Growth commemorates him wth commemorates him in the form of in the form of CzochralskiCzochralski Lecture, which is delivered as the opening lecture of every Lecture, which is delivered as the opening lecture of every Polish Crystal Growth Conference by a distinguished scientist wiPolish Crystal Growth Conference by a distinguished scientist with recognized th recognized contribution in crystal growth related fields. In 1998 this Socicontribution in crystal growth related fields. In 1998 this Society changed its name to ety changed its name to CzochralskiCzochralski Polish Society for Crystal Growth.Polish Society for Crystal Growth.

Page 11: 90th anniversary of Czochralski pulling method

TheThe CzochralskiCzochralski’’sshousehouse inin KcyniaKcynia

„„MargowoMargowo””

Page 12: 90th anniversary of Czochralski pulling method

Professor Professor CzochralskiCzochralski started the crystal growth of metals by immersion of a narrow started the crystal growth of metals by immersion of a narrow capillary in the crucible with melt. In capillary a small nucleucapillary in the crucible with melt. In capillary a small nucleus of crystal was formed. s of crystal was formed. Slow pullingSlow pulling outout of the melt allowed of the melt allowed to to obtain metallic obtain metallic monocrystallinemonocrystalline wires with wires with diameters of about 1 mm and lengths up to 150diameters of about 1 mm and lengths up to 150 mm. The crystal growth using the mm. The crystal growth using the CzochralskiCzochralski method is continuously improved and developed. method is continuously improved and developed.

In the Solid State Department of the In the Solid State Department of the Institute of Physics University of Institute of Physics University of Silesia modification of the Silesia modification of the CzochralskiCzochralski method from the method from the levitating melt was applied. Growing levitating melt was applied. Growing single crystals of single crystals of intermetallicsintermetallics in in crucibles degrades their purity and crucibles degrades their purity and quality due contact with quality due contact with thethe material material of of thethe crucible particularly when crucible particularly when thethesample contains high reactivity of sample contains high reactivity of rare earths. The applied rare earths. The applied cruciblelesscruciblelessmethod allows method allows to to obtain a relative obtain a relative optimal quality of single crystals of optimal quality of single crystals of rare earth rare earth intermetallicsintermetallics..

Page 13: 90th anniversary of Czochralski pulling method

RTX RTX intermetallicsintermetallics

BergBerg--BarrettBarrett topographytopography

ZrNiAlZrNiAl

TiNiSiTiNiSi

Page 14: 90th anniversary of Czochralski pulling method

20 40 60 80

hexagonal (Hulliger)

experimental

orthorhombic (Dwight)

2θ [deg]

Inte

nsity

[a.u

.]

Page 15: 90th anniversary of Czochralski pulling method

0 50 100 150 200 250 3007.08

7.10

7.12

7.14

7.16

7.18

7.20

7.22

GdPdAlLa

ttice

par

amet

er a

[Å]

Temperature [K] 0 50 100 150 200 250 300

4.04

4.06

4.08

4.10

4.12 GdPdAl

Latti

ce p

aram

eter

c [Å

]

Temperature [K]

0 50 100 150 200 250

180.0

180.5

181.0

181.5

182.0

182.5

GdPdAl cal (ΘD=260K)experimental

Vol

ume

[Å3 ]

Temperature [K]

Page 16: 90th anniversary of Czochralski pulling method
Page 17: 90th anniversary of Czochralski pulling method

The two layers of the structure of GdPdAl (4 unit cells) at level z=0.5 (a) and z=0 (b); only inter-layer bonds are exhibited. The arrows indicate the movement of the Al-atoms and the shortening of the bonds upon cooling (strongly exaggerated).

Page 18: 90th anniversary of Czochralski pulling method

0

10

20

30

0 100 200 300

Tc= 48 K

TN= 24 K

[105]

180 K

GdPdAl

Temperature (K)

Ele

ctric

al re

sist

ivity

(µΩ

m)

Page 19: 90th anniversary of Czochralski pulling method

0

2.5

5.0

7.5

10.0

12.5

0 200 400 600 800 10000

20

40

60

80

100

1/χ = (T-θ)/C

H = 360 Oe

µeff = 7.94 µB/f.u.

C = 7.9 emuK/mole

θ = 67 K48 K

GdPdAl

Tempera ture (K)

Sus

cept

ibili

ty (e

mu/

mol

e)

Inve

rse

susc

eptib

ility

(mol

e/em

u)

2.5

5.0

7.5

10.0

0 20 40 60 80

20 K

48 K

Page 20: 90th anniversary of Czochralski pulling method

0 100 200 300

GdPdAl [105]22 K

48 K

Temperature (K)

χ ac'

(arb

.u.)

Page 21: 90th anniversary of Czochralski pulling method

0 10 20 30

GdPdAl Pd

Gd 5p

Gd 4fPd 4d

VB

GdPdAl

Binding energy (eV)

Inte

nsity

(arb

.u.)

0 2

Gd

Page 22: 90th anniversary of Czochralski pulling method

10 20 30 40 50 60 70 80 90 100

O rthorhom bic s tructure - Dwight

DyP dAl e xpe rim e nta l

He xa gona l s tructure - Hullige r

2θ [de g]

Inte

nsity

(arb

. u.)

ZrNiAl

Page 23: 90th anniversary of Czochralski pulling method

0 50 100 150 200 250 3007.15

7.16

7.17

7.18

DyPdAl Cal (ΘD=225K) Exp

Latti

ce p

aram

eter

a [Å

]

Temperature [K] 0 50 100 150 200 250 300

3.955

3.960

3.965

3.970

3.975

3.980

3.985

DyPdAl Cal (ΘD=225K) exp

Latti

ce p

aram

eter

c [Å

]

Temperature [K]

0 50 100 150 200 250 300

176.0

176.5

177.0

177.5 DyPdAl

fit (ΘD=225K)experimental

Uni

t cel

l vol

ume

[A3 ]

Temperature [K]

Page 24: 90th anniversary of Czochralski pulling method

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200

a axis

17 K25 K

DyPdAl

Temperature (K)

Res

istiv

ity (µ

Ωm

)

Page 25: 90th anniversary of Czochralski pulling method

0 50 100 150 200 250 3007.155

7.160

7.165

7.170

7.175

7.180

7.185 HoPdAl Cal (ΘD=225K) Exp

Latti

ce p

aram

eter

a [A

]

Temperature [K] 0 50 100 150 200 250 300

3.925

3.930

3.935

3.940

3.945

3.950 HoPdAl

Cal (ΘD=225K) Exp

Latti

ce p

aram

eter

c [A

]

Temperature [K]

0 50 100 150 200 250 300

175.0

175.5

176.0 HoPdAl

Cal (ΘD=225K) Exp

Vol

ume

[A3 ]

Temperature [K]

Page 26: 90th anniversary of Czochralski pulling method

0

0.5

1.0

1.5

2.0

0 100 200 300

110 K94 K

In

GdPdX

18 K

28 K

32 K

SnGe

Al

Ga

30 K

Si

29 K

Tempera ture (K)

Ele

ctric

al re

sist

ivity

(µΩ

m) 0.21

0.28

90 130

GdPdIn

94 K110 K

Page 27: 90th anniversary of Czochralski pulling method

0

0.2

0.4

0.6

4.5 5.0 5.5 6.0 6.5 7.0

y=Bexp(-d)

B=83

In

GeSn

Ga

Si

Al

d

dρph

/dT(

µΩcm

/K)

CompoundCompoundX (IIIA X (IIIA groupgroup))

CrystalCrystalstructurestructureV (V (ÅÅ33))

Pd 4dPd 4dΓΓFWHM FWHM ((eVeV))

CompoundCompoundX (IVA X (IVA groupgroup))

Crystal Crystal structurestructureV (V (ÅÅ33))

Pd 4dPd 4dΓΓFWHM FWHM

((eVeV))

GdPdAl GdPdAl (143pm)(143pm) TiNiSi TiNiSi 240.4240.4

2.22.2 GdPdSi GdPdSi (118 (118 pmpm)) ββ –– GdPdSiGdPdSi455.0455.0

2.42.4

GdPdGaGdPdGa (135pm)(135pm) CoCo22SiSi240.3240.3

1.71.7 GdPdGe GdPdGe (122 (122 pmpm)) ββ –– GdPdGeGdPdGe471.6471.6

2.12.1

GdPdIn GdPdIn (167pm)(167pm) CoCo22SiSi223.0223.0

1.31.3 GdPdSn GdPdSn (140 (140 pmpm)) CoCo22SiSi264.9264.9

1.91.9

d = M·n/V

(M – molecular mass of theGdPdX compound,

n – number of molecules per unit cell volume,

V- unit cell volume)

Page 28: 90th anniversary of Czochralski pulling method

0 10 20 30

GdPdSi

GdPdIn

Gd 5p

Pd 4d Gd 4f

Binding energy (eV)

Inte

nsity

(arb

.u.)

Page 29: 90th anniversary of Czochralski pulling method

GdGd77TT33

Th7Fe3

Berg-Barrett topography of the Gd7Pd3 single crystal

Page 30: 90th anniversary of Czochralski pulling method

Berg-Barrett topography of the Gd7Pd3 single crystal

Page 31: 90th anniversary of Czochralski pulling method

Berg-Barrett topography of the Gd7Rh3 single crystal

Page 32: 90th anniversary of Czochralski pulling method

3 0 4 0 5 0 6 0

e x pc a l

313

004

412

330

322

303

500

213

402

411

410

401

302

40031

121222

020230

111

2

211

102

00221

0

2 θ ( d e g )

Inte

nsity

(arb

.u.)

GdGd77RhRh33

3 0 4 0 5 0 6 0

e x pc a l

421

004

104

412

33032

230

350

0

213

40241

1

410

321

401

302

40031

1212

22020

2301

11230

0

211

102

00221

0

2 θ ( d e g )

Inte

nsity

(arb

.u.)

GdGd77PdPd33

Page 33: 90th anniversary of Czochralski pulling method

0 50 100 150 200 250 300

518

519

520

521

522

523

c)Vol

ume

(Å3 )

Temperature (K)

0 50 100 150 200 250 300

6.192

6.196

6.200

6.204

6.208

6.212

b)

Latti

ce p

aram

eter

c (Å

)

0 50 100 150 200 250 300

9.82

9.83

9.84

9.85

9.86

a)

TNGd7Rh3

Latti

ce p

aram

eter

a (Å

)

exp cal (ΘD=160K)

0 50 100 150 200 250 300 350 400

538

539

540

541

542

543

c)

Vol

ume

(Å3 )

Temperature (K)

0 50 100 150 200 250 300 350 4006.260

6.265

6.270

6.275

6.280

6.285

b)

Latti

ce p

aram

eter

c (Å

)

0 50 100 150 200 250 300 350 4009.955

9.960

9.965

9.970

9.975

9.980

9.985 Tc

a)

Gd7Pd3

Latti

ce p

aram

eter

a (Å

)

exp cal (ΘD=160K)

Page 34: 90th anniversary of Czochralski pulling method

0 10 20 30

Gd7Rh3

Gd7Pd3

Gd

Gd 5p

Gd 5d

Rh 4d

Pd 4d

Gd 4f

Binding energy (eV)

Inte

nsity

(arb

.u.)

-1 0 1 2 3 4

Page 35: 90th anniversary of Czochralski pulling method

50

100

150

200

0 100 200 300

ρ(T)=27+0.005T2

ρ(T)=130+0.022T2

TN = 140 K

i // c

i // a

Gd7Rh3

T (K)

ρ (µ

Ωcm

)

50

100

150

200

250

0 100 200 300 400

ρ(T)=27+0.015T2

ρ(T)=60+0.022T2

T2

T=332 KGd7Pd3

i II a

i II c

T (K)

ρ (µ

Ωcm

)

Page 36: 90th anniversary of Czochralski pulling method

-2

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350

b)

Tc

Gd7Pd3∆T II a

∆T II c

T(K)

S (µ

V/K

)

-8-6-4-202468

1012

0 50 100 150 200 250 300

a)

TN

∆T II a

∆T II c Gd7Rh3

T (K)

S (µ

V/K

)

Page 37: 90th anniversary of Czochralski pulling method

40

80

120

160

200

0 50 100 150 200

B = 8 T

140 K

B = 0 Ti // c

T (K)

ρ (µ

Ωcm

)

20

40

60

80

B = 0 T

B = 8 T

i // aGd7Rh3

ρ (µ

Ωcm

)

30

50

70

90

110

0 100 200 300

i II c

B = 0 T

B = 8T

T (K)

ρ (µ

Ωcm

)

100

150

200

250i II aGd7Pd3

B = 0 T

B = 8Tρ (µ

Ωcm

)

Page 38: 90th anniversary of Czochralski pulling method

0

0.005

0.010

0.015

0 100 200 300 400

b)

TC=334 K

Gd7Pd3 B = 0.1 T

II a

II c

T (K)

M (µ

B/G

d)

0

0.0001

0.0002

0.0003

0 100 200 300 400

a)

ZFC

TN=140 K

II a

B = 0.5 T II c Gd7Rh3

M (µ

B/G

d)

0

20

40

60

80

0 200 400 6000

2

4χ-1=(T-355)/56.5

325 K

B = 0.03 T B II a

µeff = 8.0 µB

Gd7Pd3

Tc=332 K

Temperature (K)

Sus

cept

ibili

ty (e

mu/

mol

e)

Inve

rse

susc

eptib

ility

(mol

e/em

u)

0

0.5

1.0

1.5

0 300 600 9000

4

8

12

χ-1=(T-176)/58.4

B II aB = 0.19 T

µeff=8.2µB

Gd7Rh3TN=140 K

Sus

cept

ibili

ty (e

mu/

mol

e)

Inve

rse

susc

eptib

ility

(mol

e/em

u)

Page 39: 90th anniversary of Czochralski pulling method

c/ac/a a/a/aaGdGd c/c/ccGdGd V/V/VVGdGd

GdPdAlGdPdAl(I)(I) 0.560.56

0.570.57

0.630.63

0.630.63

22 0.70.7 2.782.78

GdPdAlGdPdAl(II)(II) 1.961.96 0.710.71 2.752.75

GdGd77RhRh33 22..7272 1.091.09 2.652.65

GdGd77PdPd33 2.752.75 1.091.09 2.752.75

( ) ( ) ⎥⎦

⎤⎢⎣

⎡ −++=

J

JFBJeff g

gEANJJg 111µµ

ggJJ –– thethe LandeLande factorfactor

J J –– thethe totaltotal quantum quantum numbernumber

N(EN(EFF) ) –– thethe desitydesity ofof statesstates atat thethe Fermi Fermi energyenergy

A A –– thethe exchangeexchange interactioninteraction

Page 40: 90th anniversary of Czochralski pulling method

AcknowledgmentsAcknowledgmentsAuthor thanksAuthor thanks CzochralskiCzochralski Polish Society for Crystal Growth for source Polish Society for Crystal Growth for source materials (materials (http://www.http://www.ptwkptwk.org.pl/eng/sitemap.html.org.pl/eng/sitemap.html))PawePawełł Tomaszewski Tomaszewski „„Jan Jan CzochralskiCzochralski andand his his methodmethod”” 20032003

CooperationCooperation::M. Klimczak, J. Kusz, R. TroM. Klimczak, J. Kusz, R. Troćć, A. Winiarski, , A. Winiarski,

M. M. SkuteckaSkutecka