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90th anniversary of Czochralski pulling method

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<strong>90th</strong> <strong>anniversary</strong><br />

<strong>of</strong> <strong>Czochralski</strong> <strong>method</strong><br />

1885-1953 1885 1953


In 2006 we celebrate the 90 th <strong>anniversary</strong> <strong>of</strong> <strong>Czochralski</strong> <strong>pulling</strong><br />

<strong>method</strong>.<br />

Pr<strong>of</strong>essor Jan <strong>Czochralski</strong> invented this <strong>method</strong> during the<br />

investigations <strong>of</strong> the crystallization rate <strong>of</strong> metals.<br />

In the fifties <strong>of</strong> the twentieth century his <strong>method</strong> was adopted for<br />

growing large single crystals <strong>of</strong> semiconductors on an industrial<br />

scale.<br />

Moreover, a large group <strong>of</strong> applicable oxides are grown using<br />

<strong>Czochralski</strong> <strong>method</strong>.<br />

Also the number <strong>of</strong> single crystals <strong>of</strong> intermetallic compounds is<br />

quickly growing thanks to this <strong>method</strong>.<br />

The Institute <strong>of</strong> Electronic Materials Technology (ITME)<br />

GdCa 4 O(BO 3 ) 3<br />

UŚ<br />

Fe 2.25 V 0.75 Al


Arms <strong>of</strong> Kcynia<br />

•Pr<strong>of</strong>essor Pr<strong>of</strong>essor Jan <strong>Czochralski</strong> was born on October 23, 1885 in Kcynia, Kcynia,<br />

in<br />

part <strong>of</strong> Poland at that time under the Prussian domination, as the eighth<br />

child <strong>of</strong> the Polish craftsmen Franciszek <strong>Czochralski</strong> and Marta from the<br />

Suchomski family. The <strong>Czochralski</strong>s were carpenters for many<br />

generations.<br />

•Jan Jan completed teachers' seminar in Kcynia according to the wish <strong>of</strong> his<br />

father. He was already interested in chemistry during his school days.<br />

However, he did not accept his matriculation certificate due to poor<br />

grades.<br />

•Lack Lack <strong>of</strong> this certificate unabled him to continue his education. For some<br />

time he worked in Krotoszyn in a drugstore.


Bydgoszcz


Berlin<br />

•At t the end <strong>of</strong> 1904 he went to Berlin and began to work in the drugstore drugstore<br />

<strong>of</strong> Dr. A.<br />

Herbrand in Altglienicke, Altglienicke,<br />

the districts <strong>of</strong> Berlin.<br />

•Later Later he worked for a short period in the laboratory <strong>of</strong> Kunheim and Co. in<br />

Niederschönweide<br />

Niedersch nweide near Berlin and then in Allgemeine Elektrizitäts<br />

Elektrizit ts-Gesellschaft<br />

Gesellschaft<br />

(AEG). The job in Kabelwerk Oberspree and the two years spent in their research<br />

laboratories prepared him to become head <strong>of</strong> the laboratory <strong>of</strong> steel steel<br />

and iron<br />

research. This laboratory dealt with the checking the quality and and<br />

purity <strong>of</strong> metals<br />

and alloys and was engaged in the refinement <strong>of</strong> copper.<br />

•Simultaneously Simultaneously he attended lectures on chemistry at the Charlottenburg<br />

Polytechnic near Berlin.<br />

•From From 1911 to 1914 he was an assistant <strong>of</strong> Wichard von Möllendorff llendorff with whom<br />

he published his first paper devoted to the crystallography <strong>of</strong> metals metals,<br />

, dislocation<br />

theory (Zeitschrift Zeitschrift des Vereines Deutcher Ingenieure<br />

57 (1913) 931-5, 931 5, 1014-20) 1014 20) .<br />

KABELWERK OBERSPREE RESEARCH<br />

LABORATORIES, JAN CZOCHRALSKI (FAR<br />

LEFT).<br />

LEFT)


•Jan Jan <strong>Czochralski</strong> married in 1910 Marguerit Haase, Haase,<br />

a pianist <strong>of</strong> Dutch origin, the<br />

daughter <strong>of</strong> a rich owner <strong>of</strong> houses. They had three children: two daughters –<br />

Leonia (1914) and Cecilia (1920,) and a son Borys (1918).<br />

CZOCHRALSKI'S FAMILY


•In In 1916 pr<strong>of</strong>essor Jan <strong>Czochralski</strong> invented a <strong>method</strong> for measuring the<br />

crystallization velocity <strong>of</strong> metals. The <strong>method</strong> was invented by accident accident<br />

and<br />

through <strong>Czochralski</strong> careful observations.<br />

•The The idea <strong>of</strong> this <strong>method</strong> is based on <strong>pulling</strong> a crystal from the melt. melt.<br />

The grown<br />

during the experiment crystals as metallic wires were single crystals. crystals.<br />

•The The results <strong>of</strong> <strong>Czochralski</strong> studies were published in several papers, The first<br />

one was published in Zeitschrift für Physikalische<br />

hysikalische Chemie 92, 219 (1918), in<br />

German.<br />

•This This new technique allowed to obtain the good<br />

quality single crystals <strong>of</strong> pure metals like Sn, Sn,<br />

Pb, Pb,<br />

Zn.<br />

After the II World War the <strong>Czochralski</strong> <strong>method</strong> was<br />

adopted by the Americans G.K. Teal and J.B. Little<br />

from Bell Telephone Laboratories for growing large<br />

single crystals <strong>of</strong> semiconductors on an industrial<br />

scale (Growth <strong>of</strong> germanium single crystals, Phys.<br />

Rev. 78, 647 (1950) and Bull. Amer. Phys. Soc. 25,<br />

16 (1950)).


Franfurt on Mein<br />

•In In 1917 Jan <strong>Czochralski</strong> moved to Frankfurt on Mein and organized the Laboratory<br />

<strong>of</strong> Metal Science. Science<br />

• Several valuable scientific papers and patents were developed there. there.<br />

Among the<br />

patents was the highly famous patent on a tin-free tin free bearing alloy for railways, called<br />

metal B, patented in 1924 and bought by many countries all over the world, including<br />

USA, France and England.<br />

•He He also pioneered investigations <strong>of</strong> the anisotropy <strong>of</strong> the hardness hardness<br />

<strong>of</strong> single crystals<br />

(works between 1913 and 1923), which are <strong>of</strong> great importance for the plastic<br />

treatment <strong>of</strong> materials.<br />

•In In 1919 <strong>Czochralski</strong> was among the scientists who founded the German Society for<br />

Metal Science and in 1925 he became its presisent. presisent<br />

Warsaw<br />

•When When Poland regained independence he accepted in 1929 the invitation invitation<br />

<strong>of</strong> the<br />

President <strong>of</strong> Poland, Ignacy Mościcki Mo cicki. . <strong>Czochralski</strong> obtained his first honorary<br />

doctorate <strong>of</strong> the Faculty <strong>of</strong> Chemistry at the Warsaw University <strong>of</strong> Technology. Technology.<br />

It<br />

enabled him to take the position <strong>of</strong> a pr<strong>of</strong>essor there.<br />

The <strong>Czochralski</strong>’s<br />

<strong>Czochralski</strong><br />

house in Warsaw


PROF. JAN CZOCHRALSKI, WARSAW, 1929<br />

THE POLISH PRESIDENT IGNACY MOŚCICKI MO CICKI (FAR<br />

RIGHT) VISITING CZOCHRALSKI'S LABORATORY.<br />

JAN CZOCHRALSKI (SECOND FROM THE LEFT). LEFT).


•After After the II World War due to his connections with Germans <strong>Czochralski</strong> <strong>Czochralski</strong><br />

was<br />

suspected <strong>of</strong> collaboration and even arrested. The suspicion was continued to date <strong>of</strong><br />

his dead, but up to now there is no evidence for his collaboration. collaboration.<br />

In fact pr<strong>of</strong>essor<br />

<strong>Czochralski</strong> helped the National Army and many people during the war time.<br />

<strong>Czochralski</strong> returned to Kcynia and to the chemistry and to production production<br />

<strong>of</strong> cosmetics<br />

and household chemicals.<br />

•He He died on April 22, 1953 in Poznań Pozna due to heart disease and was buried in Kcynia.<br />

•Pr<strong>of</strong>essor Pr<strong>of</strong>essor Jan <strong>Czochralski</strong> was outstanding metallurgist, chemist and crystallographer,<br />

whose crystal growth <strong>method</strong> allowed dynamic development <strong>of</strong> the modern modern<br />

science and<br />

technology. However, after the war he was almost forgotten, especially especially<br />

in Poland.<br />

•After After the political changes in Poland the Tenth European Crystallographic Crystallographic<br />

Meeting,<br />

organized in Wroclaw in 1986, was dedicated to Pr<strong>of</strong>essor Jan <strong>Czochralski</strong> to<br />

commemorate the seventieth <strong>anniversary</strong> <strong>of</strong> the discovery <strong>of</strong> the <strong>Czochralski</strong> <strong>method</strong>.<br />

•Since Since its foundation in 1991, the Polish Society for Crystal Growth Growth<br />

commemorates him<br />

in the form <strong>of</strong> <strong>Czochralski</strong> Lecture, which is delivered as the opening lecture <strong>of</strong> every<br />

Polish Crystal Growth Conference by a distinguished scientist with with<br />

recognized<br />

contribution in crystal growth related fields. In 1998 this Society Society<br />

changed its name to<br />

<strong>Czochralski</strong> Polish Society for Crystal Growth.


The <strong>Czochralski</strong>’s<br />

<strong>Czochralski</strong><br />

house in Kcynia<br />

„Margowo Margowo”


Pr<strong>of</strong>essor <strong>Czochralski</strong> started the crystal growth <strong>of</strong> metals by immersion <strong>of</strong> a narrow<br />

capillary in the crucible with melt. In capillary a small nucleus nucleus<br />

<strong>of</strong> crystal was formed.<br />

Slow <strong>pulling</strong> out <strong>of</strong> the melt allowed to obtain metallic monocrystalline wires with<br />

diameters <strong>of</strong> about 1 mm and lengths up to 150 mm. The crystal growth using the<br />

<strong>Czochralski</strong> <strong>method</strong> is continuously improved and developed.<br />

In the Solid State Department <strong>of</strong> the<br />

Institute <strong>of</strong> Physics University <strong>of</strong><br />

Silesia modification <strong>of</strong> the<br />

<strong>Czochralski</strong> <strong>method</strong> from the<br />

levitating melt was applied. Growing<br />

single crystals <strong>of</strong> intermetallics in<br />

crucibles degrades their purity and<br />

quality due contact with the material<br />

<strong>of</strong> the crucible particularly when the<br />

sample contains high reactivity <strong>of</strong><br />

rare earths. The applied crucibleless<br />

<strong>method</strong> allows to obtain a relative<br />

optimal quality <strong>of</strong> single crystals <strong>of</strong><br />

rare earth intermetallics.<br />

intermetallics


RTX intermetallics<br />

Berg-Barrett<br />

Berg Barrett topography<br />

ZrNiAl<br />

TiNiSi


Intensity [a.u.]<br />

20 40 60 80<br />

2θ [deg]<br />

orthorhombic (Dwight)<br />

experimental<br />

hexagonal (Hulliger)


Lattice parameter a [Å]<br />

7.22<br />

7.20<br />

7.18<br />

7.16<br />

7.14<br />

7.12<br />

7.10<br />

GdPdAl<br />

7.08<br />

0 50 100 150 200 250 300<br />

Temperature [K]<br />

Volume [Å 3 ]<br />

182.5<br />

182.0<br />

181.5<br />

181.0<br />

180.5<br />

180.0<br />

GdPdAl<br />

cal (Θ D =260K)<br />

experimental<br />

Lattice parameter c [Å]<br />

4.12<br />

4.10<br />

4.08<br />

4.06<br />

4.04<br />

0 50 100 150 200 250<br />

Temperature [K]<br />

GdPdAl<br />

0 50 100 150 200 250 300<br />

Temperature [K]


The two layers <strong>of</strong> the structure <strong>of</strong><br />

GdPdAl (4 unit cells) at level z=0.5 (a)<br />

and z=0 (b);<br />

only inter-layer bonds are exhibited.<br />

The arrows indicate the movement <strong>of</strong><br />

the Al-atoms and the shortening <strong>of</strong> the<br />

bonds upon cooling (strongly<br />

exaggerated).


Electrical resistivity (µΩm)<br />

30<br />

20<br />

10<br />

T N = 24 K<br />

GdPdAl<br />

T c = 48 K<br />

[105]<br />

180 K<br />

0<br />

0 100 200 300<br />

Temperature (K)


Susceptibility (emu/mole)<br />

12.5<br />

10.0<br />

7.5<br />

5.0<br />

2.5<br />

48 K<br />

θ = 67 K<br />

C = 7.9 emuK/mole<br />

µ eff = 7.94 µ B /f.u.<br />

GdPdAl<br />

H = 360 Oe<br />

10.0<br />

1/χ = (T-θ)/C<br />

0<br />

0 200 400 600 800 1000 0<br />

0 20 40 60 80<br />

7.5<br />

5.0<br />

2.5<br />

Temperature (K)<br />

20 K<br />

48 K<br />

100<br />

80<br />

60<br />

40<br />

20<br />

Inverse susceptibility (mole/emu)


(arb.u.)<br />

'<br />

χ<br />

ac<br />

22 K<br />

48 K<br />

GdPdAl [105]<br />

0 100 200 300<br />

Temperature (K)


Intensity (arb.u.)<br />

VB<br />

Pd 4d<br />

Gd 4f<br />

GdPdAl<br />

GdPdAl<br />

Pd<br />

Gd 5p<br />

0 10 20 30<br />

Binding energy (eV)<br />

0 2<br />

Gd


Intensity (arb. u.)<br />

O rthorhom bic s tructure - Dwight<br />

DyP dAl e xpe rim e nta l<br />

He xa gona l s tructure - Hullige r<br />

10 20 30 40 50 60 70 80 90 100<br />

2θ [de g]<br />

ZrNiAl


Lattice parameter a [Å]<br />

7.18<br />

7.17<br />

7.16<br />

DyPdAl<br />

Cal (Θ D =225K)<br />

Exp<br />

7.15<br />

0 50 100 150 200 250 300<br />

Temperature [K]<br />

Unit cell volume [A 3 ]<br />

177.5<br />

177.0<br />

176.5<br />

176.0<br />

DyPdAl<br />

fit (Θ D =225K)<br />

experimental<br />

Lattice parameter c [Å]<br />

3.985<br />

3.980<br />

3.975<br />

3.970<br />

3.965<br />

3.960<br />

0 50 100 150 200 250 300<br />

Temperature [K]<br />

DyPdAl<br />

Cal (Θ D =225K)<br />

exp<br />

3.955<br />

0 50 100 150 200 250 300<br />

Temperature [K]


Resistivity (µΩm)<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

0.2<br />

DyPdAl<br />

17 K<br />

25 K<br />

a axis<br />

0.1<br />

0 100 200<br />

Temperature (K)


Lattice parameter a [A]<br />

7.185<br />

7.180<br />

7.175<br />

7.170<br />

7.165<br />

7.160<br />

HoPdAl<br />

Cal (Θ D =225K)<br />

Exp<br />

7.155<br />

0 50 100 150 200 250 300<br />

Temperature [K]<br />

Volume [A 3 ]<br />

176.0<br />

175.5<br />

175.0<br />

HoPdAl<br />

Cal (Θ D =225K)<br />

Exp<br />

Lattice parameter c [A]<br />

3.950<br />

3.945<br />

3.940<br />

3.935<br />

3.930<br />

3.925<br />

HoPdAl<br />

Cal (Θ D =225K)<br />

Exp<br />

0 50 100 150 200 250 300<br />

Temperature [K]<br />

0 50 100 150 200 250 300<br />

Temperature [K]


Electrical resistivity (µΩm)<br />

2.0<br />

1.5<br />

1.0<br />

0.28<br />

0.21<br />

32 K<br />

GdPdIn<br />

94 K<br />

110 K<br />

90 130<br />

GdPdX<br />

29 K<br />

Sn<br />

0.5<br />

Ge<br />

30 K<br />

18 K<br />

In<br />

0<br />

0<br />

28 K<br />

94 K110<br />

K<br />

100 200 300<br />

Temperature (K)<br />

Al<br />

Si<br />

Ga


Compound<br />

X (IIIA group) group<br />

dρ ph /dT(µΩcm/K)<br />

0.6<br />

0.4<br />

0.2<br />

Al<br />

Si<br />

Crystal<br />

structure<br />

V (Å ( 3 )<br />

GdPdAl (143pm) TiNiSi<br />

240.4<br />

GdPdGa (135pm) Co 2 Si<br />

240.3<br />

GdPdIn (167pm) Co 2 Si<br />

223.0<br />

Ga<br />

Ge<br />

Sn<br />

y=Bexp(-d)<br />

B=83<br />

0<br />

4.5 5.0 5.5 6.0 6.5 7.0<br />

d<br />

Pd 4d<br />

ΓFWHM FWHM (eV eV)<br />

In<br />

Compound<br />

X (IVA group) group<br />

Crystal<br />

structure<br />

V (Å ( 3 )<br />

2.2 GdPdSi (118 pm) pm β – GdPdSi<br />

455.0<br />

1.7 GdPdGe (122 pm) pm β – GdPdGe<br />

471.6<br />

1.3 GdPdSn (140 pm) pm Co 2 Si<br />

264.9<br />

d = M·n/V<br />

Pd 4d<br />

ΓFWHM FWHM<br />

2.4<br />

2.1<br />

1.9<br />

(M – molecular mass <strong>of</strong> the<br />

GdPdX compound,<br />

n – number <strong>of</strong> molecules per<br />

unit cell volume,<br />

V- unit cell volume)<br />

(eV eV)


Intensity (arb.u.)<br />

Pd 4d<br />

Gd 4f<br />

Gd 5p<br />

GdPdSi<br />

GdPdIn<br />

0 10 20 30<br />

Binding energy (eV)


Gd 7T3 Berg-Barrett topography <strong>of</strong> the Gd 7Pd 3 single crystal<br />

Th 7 Fe 3


Berg-Barrett topography <strong>of</strong> the Gd 7Pd 3 single crystal


Berg-Barrett topography <strong>of</strong> the Gd 7Rh 3 single crystal


Intensity (arb.u.)<br />

Intensity (arb.u.)<br />

210<br />

210<br />

002<br />

102<br />

211<br />

112<br />

301<br />

202<br />

220<br />

212<br />

311<br />

400<br />

302<br />

401<br />

411<br />

402<br />

322<br />

303<br />

500<br />

e x p<br />

c a l<br />

30 40 50 60<br />

002<br />

102<br />

211<br />

300<br />

301<br />

112<br />

202<br />

220<br />

212<br />

Gd 7Rh Rh3 2 θ (d e g )<br />

Gd 7Pd Pd3 311<br />

400<br />

302<br />

401<br />

3 0 4 0 5 0 6 0<br />

2 θ (d e g )<br />

321<br />

410<br />

410<br />

411<br />

402<br />

213<br />

213<br />

500<br />

303<br />

322<br />

330<br />

330<br />

412<br />

412<br />

e x p<br />

c a l<br />

421<br />

004<br />

313<br />

004<br />

104


Lattice parameter a (Å)<br />

Lattice parameter c (Å)<br />

Volume (Å 3 )<br />

9.86<br />

9.85<br />

9.84<br />

9.83<br />

9.82<br />

6.212<br />

6.208<br />

6.204<br />

6.200<br />

6.196<br />

6.192<br />

523<br />

522<br />

521<br />

520<br />

519<br />

518<br />

Gd 7 Rh 3<br />

T N<br />

0 50 100 150 200 250 300<br />

0 50 100 150 200 250 300<br />

0 50 100 150 200 250 300<br />

Temperature (K)<br />

exp<br />

cal (Θ D =160K)<br />

b)<br />

c)<br />

a)<br />

Lattice parameter a (Å)<br />

Lattice parameter c (Å)<br />

Volume (Å 3 )<br />

9.985 T c<br />

9.980<br />

9.975<br />

9.970<br />

9.965<br />

9.960<br />

9.955<br />

6.285<br />

6.280<br />

6.275<br />

6.270<br />

6.265<br />

6.260<br />

543<br />

542<br />

541<br />

540<br />

539<br />

538<br />

Gd 7 Pd 3<br />

0 50 100 150 200 250 300 350 400<br />

0 50 100 150 200 250 300 350 400<br />

0 50 100 150 200 250 300 350 400<br />

Temperature (K)<br />

exp<br />

cal (Θ D =160K)<br />

a)<br />

b)<br />

c)


Intensity (arb.u.)<br />

Gd 5d<br />

Pd 4d<br />

Rh 4d<br />

Gd 7 Rh 3<br />

Gd 7 Pd 3<br />

Gd<br />

Gd 4f<br />

Gd 5p<br />

0 10 20 30<br />

Binding energy (eV)<br />

-1 0 1 2 3 4


ρ (µΩcm)<br />

200<br />

150<br />

100<br />

50<br />

Gd 7 Rh 3<br />

T N = 140 K<br />

ρ(T)=130+0.022T 2<br />

ρ(T)=27+0.005T 2<br />

i // c<br />

i // a<br />

0 100 200 300<br />

T (K)<br />

ρ (µΩcm)<br />

250<br />

200<br />

150<br />

100<br />

50<br />

Gd 7 Pd 3<br />

ρ(T)=60+0.022T 2<br />

ρ(T)=27+0.015T 2<br />

0 100 200 300 400<br />

T (K)<br />

T 2<br />

T=332 K<br />

i II a<br />

i II c


S (µV/K)<br />

S (µV/K)<br />

12<br />

10<br />

8<br />

6<br />

4<br />

2<br />

0<br />

-2<br />

-4<br />

-6<br />

-8<br />

0 50 100 150 200 250 300<br />

12<br />

10<br />

8<br />

6<br />

4<br />

2<br />

0<br />

∆T II c<br />

∆T II a<br />

∆T II a<br />

∆T II c<br />

T N<br />

T (K)<br />

Gd 7 Pd 3<br />

-2<br />

0 50 100 150 200 250 300 350<br />

T(K)<br />

Gd 7 Rh 3<br />

a)<br />

b)<br />

T c


ρ (µΩcm)<br />

ρ (µΩcm)<br />

80<br />

60<br />

40<br />

20<br />

200<br />

160<br />

120<br />

80<br />

Gd 7 Rh 3<br />

i // c<br />

i // a<br />

B = 0 T<br />

B = 8 T<br />

140 K<br />

40<br />

0 50 100 150 200<br />

T (K)<br />

B = 0 T<br />

B = 8 T<br />

ρ (µΩcm)<br />

ρ (µΩcm)<br />

250<br />

200<br />

150<br />

100<br />

110<br />

90<br />

70<br />

50<br />

Gd 7 Pd 3<br />

B = 0 T<br />

B = 0 T<br />

B = 8T<br />

B = 8T<br />

i II a<br />

i II c<br />

30<br />

0 100 200 300<br />

T (K)


M (µ B /Gd)<br />

M (µ B /Gd)<br />

0.0003<br />

0.0002<br />

0.0001<br />

0.015<br />

0.010<br />

0.005<br />

II c<br />

II a<br />

0<br />

0 100 200 300 400<br />

II a<br />

II c<br />

T N =140 K<br />

Gd 7 Pd 3<br />

B = 0.1 T<br />

T C =334 K<br />

0<br />

0 100 200 300 400<br />

T (K)<br />

Gd Rh<br />

7 3<br />

B = 0.5 T<br />

ZFC<br />

a)<br />

b)<br />

Susceptibility (emu/mole)<br />

Susceptibility (emu/mole)<br />

1.5<br />

1.0<br />

0.5<br />

0<br />

0<br />

80<br />

300 600 900<br />

Gd Pd<br />

7 3<br />

B = 0.03 T<br />

B II a<br />

0<br />

60<br />

40<br />

20<br />

T N =140 K<br />

Gd 7 Rh 3<br />

χ -1 =(T-176)/58.4<br />

µ eff =8.2µ B<br />

χ -1 =(T-355)/56.5<br />

µ eff = 8.0 µ B<br />

325 K<br />

T c =332 K<br />

0<br />

0 200 400 600<br />

Temperature (K)<br />

B = 0.19 T<br />

B II a<br />

12<br />

8<br />

4<br />

4<br />

2<br />

0<br />

Inverse susceptibility (mole/emu)<br />

Inverse susceptibility (mole/emu)


GdPdAl(I) GdPdAl(I)<br />

0.56<br />

c/a a/a a/ Gd<br />

c/c c/ Gd<br />

V/V V/ Gd<br />

GdPdAl(II) GdPdAl(II)<br />

0.57<br />

1.96 0.71 2.75<br />

Gd 7 Rh Rh3 Gd 7 Pd Pd3 µ<br />

eff<br />

=<br />

g<br />

J<br />

µ<br />

gJ – the Lande factor<br />

0.63<br />

0.63<br />

B<br />

J<br />

J – the total quantum number<br />

N(E F) ) – the desity <strong>of</strong> states at the Fermi energy<br />

A – the exchange interaction<br />

2 0.7 2.78<br />

2.72 72 1.09 2.65<br />

2.75 1.09 2.75<br />

⎡ g −1⎤<br />

( ) ( ) J<br />

J + 1 ⎢1<br />

+ AN EF<br />

⎥<br />

⎣<br />

g J ⎦


Acknowledgments<br />

Author thanks <strong>Czochralski</strong> Polish Society for Crystal Growth for source<br />

materials (http://www.<br />

( http://www.ptwk ptwk.org.pl/eng/sitemap.html<br />

.org.pl/eng/sitemap.html)<br />

Paweł Pawe Tomaszewski „Jan Jan <strong>Czochralski</strong> and his <strong>method</strong>” <strong>method</strong> 2003<br />

Cooperation:<br />

Cooperation<br />

M. Klimczak, J. Kusz, R. Troć, Tro , A. Winiarski,<br />

M. Skutecka

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