GROWTH OF SINGLE CRYSTALS Fi{OM MOLTEN METAL FLUXES

11."u.I/1oul.. (I" 'lrc# III" He , ",,,I ( h,.",,,,,, II/ U." .. f&lT,/B . n,l. I!
""ull I:." ;':.A (,\.}",.·"[,,.'t." ,utrl I. 1.''''111':':
V I. /)n le'I S, " ',,,,' I'"bfl\ ,'''·' \ /l , ' . /'.IS'J
Chapler HI
GROWTH OF SINGLE
METAL FLUXES
CRYSTALS
Fi{OM
MOLTEN
Z. FISK
Los Alamos Narimwl Labormory. Los AIcIllIOS. NM 87545 USA
J.P. REMEIKAt
AT&T IJdl I.lIbUrtlWfic's. MurfUY Hill. NJ 071)74 USA
,.
.,.
Contt:nls
I. I nlro<luclion
2.
Dcs~ri'llion
of lechni'lue
2. ' Examplc>
2.2 Choicc uf Ilux
3. Further ;sSp.:(h uf "pIal gro .... lh
fcom melallic lIuxe>
3 . \ Diagnlhlics
3.2 COlllaillcr~
3.3 1-1u\ incurporalion
3.01 Slulchiollll:lry
;)
3.5 s<,'Jraliun of cr)"slJh all.! Ilux
65
S5
3.b Solulion kinelin
66
63
63
63
4. Exlen>ions of Ihe lechnique
-1.1 Lbo: of lemperalure gr;sdicnl
4.2 Evaporalion growlh
-1.3 Trav"lin~ solvenl melhods
-1.-1 Miscellaneous
Appendix I
{o-!
Appen.Ji~
bS
Rderc:ncc~
55
62
67
67
67
67
611
68
69
2
70
I. Inrroducrioll
In rt:se;rreh on the physic,,1 and chemic:11 properlies of illlermeiallic (an~ olher)
compounds, materi .. 1 III the imlll of singh: crystals is preferred. Ceramic or
pressed powders of a given compound. wherein Ihe p.. rticles lIrt: randomly
oriented. not only present a much higher SlIrC:lce to hulk ratio than do single
cryslills; tll\;Y "Is" prescnt prohlems of inlcrgranular composition and porosity.
and prevent any lIleatlillgfllln\\.';I~uretllcnts of ;\Ilisotrupy. A generally higher level
of purity is obtained in ~itlgle crystals. ,mil, IIIl.1rt: importantly. lIlany macroscopic
and (parlicularly) microscopic probes can only be effectively utilized with single
erys"ll mah:rial. FClllli surfacc cXl'erimellh. for example. using till: de Haas-van
Alphen effect, arc in this catcgory. as are many neutron ;rnd X-ray scattering
t Do:ceascJ
.
_ .'
_ .... ' r.... _. •..
~
Z, FISK
~ ",J
J.I'.
Rt.:~lI' I"'\
e~peril1lents . Th i~ m;lkes the preparation of ~ ill g~e erys t;,ls a mailer uf conside r-
ahle illlpOrl~nee for Ihe condensed llWlIer SClentl)!.
The II1mt import;lIIt ;ttuJ )implnt technique for crptal growth i~ gruwth. from ;1
pur e lIIelt o( the ~uh~t;ll1ce uesi reJ . Even he r~ there ;Ire nutllen.u) e"per~mental
tedlniques ;lvall;lhle, lor exampk Z\llle me ltlllg, cry)tal pulling alit.! Unt.!gm;111
cooling (sec Cit . SO by Abell ill Ihis volume) . Uul such techniques ;Ire ge nerall y
limited to cases whe n the material is congruent ly melting. And even in Ihese cases
the re can he complications; the male rial lH;.!y melt ~II an inconveniently high
lemper;l\ure 01 Ihe vapor pressure of one or more of .the .comrone~Hs may be
pruhihilivcly huge al the mehing t elllpcrat~ r e . In such S tt~ ;!II.ons ;lIId In the more
usual casc where the compound mclts ,"congruend y, II IS useful and often
nccessary to h'lvc other techniques aV;Jilab[c for the preparatio n o f single crystals.
O ne such techni(IUe which is not widely used is Ihc growth of single cryst;,ls
(ro m 'molten metal tluxes. We Iwvc no explanation fo r the relalively smit1l
;Bte ntion given \0 this techniqu..:, which requires wlwt amounts 10 the determina·
tio n of pan of the approp riate phase diagram. ;IS do many cr),stal growlh
investigations. [t is ou r purpose here to describe somc o f our experie nce in usin~
Ihis teehni(]!le ;md give sUllie genera! gu.i\J.e lines a~ to how we h'l\'e galle about
uetermini ng a ppro pria te sul \'ents (or n·ux.:s) in p;Jrticular cases. This choise Ill"
solve nt is d early the p\;lce where expe rie nce and imagination arc pUI to the tcst.
and it is si mila r 10, bUI simpler Iha u, the cas~' wi th oxide s),stems.
II is nOI our imc nt ;on to provide an introduction to the theory and practice of
crys t'II .BrOwt h. Such information ca n be o~ t ai l1 ed from a la.rge nu mber of .good
rderenees (for example , ~ee E!wd[ and Sched 197)) . It IS rather our aim to
illliiC;Jte Ihe general usefulness of the lechnique of growth from molle.n mel:l!s
nu ~es from Ihc pwctie;![. how to do it. side , and to tabulate a number of IIlSlanccs
where it has been successfu l. In this last , we arc by no means (:.unill:'lr with alt the
wurk III this al\:a . Compuler searches of Ihe [ite r:llure actually turn up only
literature refe renceS that we arc alrc;{dy fami liar wilh. The most effecti ve way 10
reseil rch whe ther a mClal rlu .~ method has been successful fo r single crys tal growth
of a pani cul"r compou nd is 10 se.treh Chemica l Abs!faets unlle r th;Jt comro~n~.
We ha\'e not done this compound by compo und search, and wh;J t we present IS III
laq;e pan drOlwn din.'ctly frum our own rese;t rch work. This em ~ha s i s on our.
persulI:.! 1 experience is in nll w;ly me'lllt to draw atlentllJll frolll Ihe Imp(ln"ll~e til
other wo rk ; r;Jlher it rep res<.'nts how we came to the ~ubject, and it serves our
pa rt icu lar purpose in this d l;Jpler.
Wltal arc lite atlv;ml;)ges of this particul;tr technique? The re arc IWO gen<.'ral
ones: (I ) m<lleri :..ls l';m he grow n often well below Ih"';r melting points, and this
tlften proow:es m:.tler;~1 wilh fewe r defects and much less therm:! 1 strain. and (2)
t1lOlten metals Ilffer a ckim environme nt fo r growth. since the OIolte n met:ll nux
of len ge tl ers implllities which do not subsequen tly ;lppl';l r in the crystal. In litis
rc~ peel. a molten tllct"ltlux e;Jn ;tel. purity-wise, like a good vilcu um . In addi tion
tll these adv<l nt:.t ge~. there is the point 10 be made in f",\'o r of metal nu .~ growth
that il is <l "poor man's" tedHli4ue : it can be done with the simplest equipment .
often e\'ell ..... ithout :t temperature cOfltrolkr . although OJ conrroHer is necessary fo r
Ihe growth of I:uge cry~ l .. b. This enables a 1II0de~tly e(luippeJ ht boralory 10 get
GI\(IW'111 (I I
~ 1 t"(;I. I .
c/(YSr,\I.S 1·ltO:.t MOLTI, N MET,\ I.
.... IJXES
inlo th.: l.lUsi n e~s ,If ~i ngle ("f)'~t;t1 growth wllhout l;J lge r;JpilOlI equipment expenditure. an impllrt:'1111 :'ldl';lIItage ~1Ill"e Ihe mO~1 reliable ~uurce for ~ ~ingle crysta l is
from your own <)per'llion .
To the ahu ve po i nl ~ can h<.' added tlwl O\x;Js;onally ut her I<.'chni(/ues will not
yield cr)·,lal,. Ihal v:lpl1r pre,~urc rrohlern~ (:'I ~ in a number of Yb ~l1d [u
compounds, I'or ex ample) arc often greatl y ledueed in ~olutiun ;Hld thaI in it
num be r of cases cumpletely new compounds have b<;<.'n discovered growi ng fro m
met.]1 flux s}'s lem~.
There arc. to hc SUfe. a number of di~;Jdvat1tage s to the tcch nil/ue . The first
and fo remost is IIt:'it it is not always an applicable me thod: an appropriate mclal
nux from which the desired com pound will crystallize may 110t be found. In
addition, difli cu lt ie~ arc encou ntered with so me flux choices, when the flux, u r
some component of it. enters the cryswl;Js an impurit y. A further problem havi ng
to do wit h the ;Jctual growth siluation is tha t !lux inclusions often occur - the
cryst:J1 grows arou nd a pock<.'t of flu .~. In thi s case speei,tJ care mUSI he t:lke n with
the grow th ratc conditions. The prohlem is reall y on<.' of excc~s i\'e Jl uclc;lt ion
which takes place either due to ](10 f;Jsl a COOling rate , or supe rcooling of the mclt
by slow COOling with subsequen t mu[t iple nucle.l1io n and fas t growlh of large bUI
imperfect c r ~'stals usual ly co rt1 ;Jining inclusions. It is under !h<.'se conditions thaI
the large crystalS arc imperfect. but aflcr equilibrium is reOlched cryslals nucleate
at a much slowe r rate . :lnd ilre of much higher quality. The rlux gro wth method
:llso s uffers from :t problem common to o ther growth methods, namc ly the
container problem. which will be discussed at some length b<.'low. Findi ng a
container 10 hold th e melt at the tempera ture desired can be difficult, as
secondary reactinns oftcn occ ur which one docs nOI irnrnedi:ltc1)' expect. And
fin ally. Ihe .. hilit )' IU se p;tratc crys tals from thc flu x at the conclusion of growth
nec tJs special consideration, :md is also discussed at lengl h helow.
2. I)cscri[ltiull
ur tcchn ill uc
2.1. £XQmp/t'l'
Whcn <.:ry~tal) grow tmnl .1 mdt. we learn somet hing :lholl t Ihe re!cl'a nt ph;lse
diagfOlm. Ctlnvehely. knowledge (If Ihe relevant phase diagram will allow (I nc to
SCI ca refull y some o f the conditions for eryst;ll growth. We seldom havc, needless
to sa y. Ihe pllilse diagrJ m information necess;tr y, and il is often muc h (as ter 10
optimize growth eondition~ without le;Jrning much in detail :lbOIll .Ihc phase
diitg ra rn . This is in pa rt becaus<.' fJelOrs othe r Ihan tho}e cont:'li ned in thc plwse
diag ram J lso contribute to the proce~s. Neve rlhc!css, at:eess to the tabulations of
bin;lry ph'lse diagrams (i.e. Hanse n 1<)58 , Elliott 1%5. Shunk [ %1) , Jnc Moff.llt
I<JH I ) is extremel}" useful when expe rimcl1ling with possible !tuxes for growth o f Ol
p;lrticulJr malerial.
The simpiesl W:1Y til introduce !he concepts :Ippropri;lle to gfuwth of crys tals
from metal fluxcs is with a simple bin;Jry eute~·tic system. Suppose we wish to
produce crystals of Si. We krm w pe rfec tly welt that there is an <.' llIire indus try bui lt
Z. FISK .. nd J.P.
56
Hl~tElKA
(ilHlWIIi 01 SINGLE CHYSTALS fROM MOLTEN METAL !'LUXES
on extremely high quality Si single I:rystals. Nevertheless. we might wish to
Jlerform some experiments on small crystals which we could easily produce
ourselves. 5i is chemically rather inert with respect to acids such as HNO., • Hel
and basic solutions such as NaOH. This would allow. us to extract Si crystals from
a metallic flux which is attacked by the above reagents. The simplest metals to
consider as solvents are those with relatively low melting points: AI. Bi. Ga. In,
Sn, and Zn. Zn has a high vapor pressure and is a poor solvent for Si. as we find
out in Hansen. Bi is also a poor solvent. It dissolves about 5 alo Si at Hloo°C. Ga
about 20 alo and Sn something in the vicinity of 5 a/o. AI appears to be best in
this respcct. dissolving about 45 alo at HXIQ·C, and the cuteclic composition
. contain~ 11.3% Si (fig. 1). This makes the AI flux especially attractive for growing
Si single crystals: largl! solubility al a reasonabll! Il!mperalure. ease of removal
and rc:asonable composition range belween euteclic composition and solubility at
staning temperature. It is clear that if this last range is small, liltle material will bl!
available for crystallization before the entirl! melt solidifies.
The small scale laboratory procedure for this AI flux growth of Si crystals then
involves wr:ighing out Ihe appropriate amounts of Ihe elements corresponding 10
the templ!rature where you wish growth to initiate and placing them in a suitable
crucible. AI will attack Si0 2 when molten and SiO, cannot. therefore. be used.
AI 20) crucibles ure readily available' ii1id will not b~ allacked by AI until, in ?ur
experience, temperature!> near 1600°C when some solubility of AI~O) in AI begins
and where the vapor pressure of Al becomes an additional problem, partly
because the thin oxide skin. which often covers molten AI, breaks up and loses its
integrity. resulting in a much increased evaporation of AI. A protective atmos'600~----~----~--~~---,-----,
1400
E
1200
w
a:
:)
!<
1000
a:
w
Q"
~
u.I
I-
800
-1111/0 Si
400
0
40
20
alo
AI
..'
.
.
~
eo
60
Si
.:
100
Si
.. '
.
Fig. I. T.:mpcrOilure-comp..,siliun
phase diagram rur Ihe AI-Si sy"
lem. (Arter lIan~en 1958.)
..
'..
~. . .
57
phere must he pruvided for Ihe mel!. and inert gas (HI! or Ar) is preferrl!d over
vacuum bccau:.e more AI cV<lporalion will occur in vacuum. The inl!rt atmosphere
clln either be pruvided by scaling the crucible in a quartz tube. simply done at a
glass bench, ur using a gas atmosphere in a lube (urnace arranged vertically to
.lCcommodate the crucibles. Horizontal tube furnaces can also be used if their
bore is suflicient to accept lhe chosen crucible size as il stands up. In this case, the
crucible(s) CHn be loaded in un a ceramic boat. There is an important point to
remember when scaling a crucible into a quartz tube: the tubl! as it stands
vertically will contact the AI~O\ crucible bottom at its I!nd taper. AIlO) has a
lIIuch larger thermal expansiun than quartz and will crack the quartz as the load is
healed. This cracking can be prevented either b) flattening the quartz tube
boltom so that the crucible can rest there without contacting the sides, ur a short
stub of quartz can be used in the lube bollom to spring Ihe crucible away from Ihe
nesting location. We also find some AI vapor attack on quartz tubes from the AI
in the crucible load . This attack is slower. obviousl~·. when the evaporation
kinetics are hilllil:red by an inert gas atmosphere ill thl! quartz tube. It is
reilsollilbll! to OIdjusl the gus pressure in the tube so that it is of order 1 atm al the
highest working temperature. although propl!rly seah:d quartz tubes of -I em
internal di:tmetcr C,1n easily wkc 5 atm at tempera.ures up to 1200°C. While it is
possible 10 usc quartz above 12(J(J°C. Ihis is the range above which quartz starts to
soften. Then it is important both 10 keep the quartz tubes scrupulously free of
fingerprints and surface dirt (locations wherl! devitrification starts) and to carefulI~ adjust the S,IS prcssurl! to be 1 atm at the operating temperalure to prevent
eUher the collapse or Ihe elCpansion of Ihe tube.
Il is gener>llly. bUI nOI always. Ihe case Ihat the larger the comaincr. the larger
the crystills. It hecumcs dimeull. if you are not a professional glass blower, to seal
off crucibles lurger than aboUi 2 em in diameter in a quartz tube, and for crucibles
above this size it is much easier to work in a tube furnace equipped with a tube
through which inert gas is flowing. Mullite tubes (an Al 10)-Si0 1 ceramic) are
relatively inexpensive and can be used to at least 1500·C. a common upper
temperature limit of operation for furnaces heated with silicon carbide heating
elements. Mullite lubes becoml! somewhat porous at l!Ievated temperatures, so
that a slight over pressure of inert gas is recommended at all times. It is also
important to rl!alize Ihat there is usually present trace amounts of unwanted gases
such as H~O and O~ in high purilY He and Ar deliverl!d from gas bOllles. The gas
can be first run through a commercial gas purifier. or one can be conslructed by
packing a quartz tube with granular Zr metal, which is heated in a small tube
furnace to ~!OO°C and through which the gas is first passed. Evcn at the ppm levcl,
01 can be gCllcred from thc gas stream by the metal flux. It m'lkes senSt,
therefore. 10 not Ilow more gas past the crucible thcn necess'lr),. This can be
accomplished by cilUsing the gas !low to by-pass the lube. while maintaining a
positive pressure within it. as shown in fig. 2. 11 is useful 10 know that the
McDaniel Company which sells mullite tubes also sells gas lighl end-cap scaling
fixturc:s for their tubes which requirc no additional preparation of the mullite
tubes.
.
..'
. ~ . .:.
.
.
.
(iIHIWTII III , SI1"(;U: CJ(YSTALS FI(OM MOl.TEN III1;TAL FI.U .X Es
Z. FISK an.! J.P. ItEMEIKA
511
FURNACE
CRUCIBLE_&=--HH
CHARGE
EXHAUST GAS
'gm
Fig. 2. Gas tlow arrilngemc:nl 10 milinlain posilivt
cuver whil!: nOI pa~sing gas over hOI crucible
and charge. Lower villve opo:n and upper valve closed allows for initial Hushing of spa~c. Illc revers.:
.. rrangemenl being used 10 mainlain intcgrity of gas cover during heilling and cooling cycle. The: t:xil
gas ~.. n cunvcnie:ntty be c:xh .. uscd Ihrough a bubbler, allowing monitoring of flow ratc.
Once the crucible has been loaded into the furnace, and the protective gas
covcr established, the furnace is then ramped to sufficient temperature t\l get the
Si into solution. The kinetics of Solulion of various materials prove to be quite
sloW in many cases, and some experimentation is often required to establish the
appropriate soak period' required for complete solution. Then the furnace is
ramped down: the slower the rate, generally the better the crystal growth. the
fewer the inclusions and the higher the quality of the crystals. For the example
given here, rates in the few degrees per hour should yield mm size crystals.
although some crystals will be obiained if the furnace is just shut off at the soak
temperature and thl!n allowed to cool ~t its own rate. Indeed. for exploratory
work aimed at determining the feasibility of using a particular solvent, it is often
useful to use coolings rales of lOO-200°C h -I. This normal rate of cooling for a
furnace can be slowed somewhat by increasing the thermal mass present, such as
packing the crucible in Si0 2 sand.
Once the crucible is cold. it is then necessary to remove the AI. This is readily
done in this case with NaOH solution . If thl! leaching reaction is slow, heating on
a hoi plate will speed things up. The Si crystals will remain after Ihe reaction of
the hydroxide with AI is complete. Crystals will in fact be visible on the surface of
the melt before the leaching is begun.
This is a particularly simple example we have given of the teChnique, but there
is re:llly nothing additional involved in the general approach to crystal growth by
the nux methud. only the pha~e diagr.ulIS becoming more complic'lled and orten
1I0t known. and the sepmution of crystals requiring more care.
An exampl.: involving unly slightly different considerations is Ihe growlh 'o f
VAl" crystal!. from AI (Iig. 3). In Ihis case there arc iI number of intermetallic
phases present. VAl!. VAl). and VAI~. the last two melting incongruently. II
turns out to be diUicult to obtain clean. single phase samples of VAil by arc
melting. presumably becliuse the UAI" peritectic horizontal intercepts the liquidS
lit a composition (-17% U) rather far from the composition of Ihe compound.
BeclIus!! of this. even if one has no interest in single crystals of VAl}. if you want
to know about the properties of the material it is best 10 attempt the single cryslal
growth. solely to gel single phllse material. Similar considerations apply for a
number of Yb compounds where the high volatililY of Yb makes arc melting an
unattractive melhod for preparalion of single phase, peritectic compounds.
In the growth of VAl) crystals. we sec that we need to prepare a melt with U
concentration between -3% lind - 10%. Additionally. especililly if a quartz tube
is used w conwin the AI~O\ crucible. it will be advisible to keep the growth
temper.llurc hduw I 200°(', Thi~ rest rielS the U com:entwtiun betwecn -3% am.I
_7 t y(). This is it narrow range from which III grow crystals. but it is easily done.
the peritectic temperature of UAI 4 , the
When the melt has cOllled to
furnilce is shut oH to discourage growth of sizable UAI 4 crystals. VAI 4 crystals. to
be sure, can be grown from melts with V concentration between 1.7% and 2,6%.
Again. extraction of the crystals can be accomplished by leaching out wilh NaOH
solution.
A point to nmke hcre is thaI it is necessary to pay attention to the chemical
no·c.
1600
W
II:
::>
.....
<
II:
W
Q,
~
.....
6000=----~2~O~~~~--~~--~B~0----~100
AI
alo U
u
Fig. 3. Th~ U-AI binary phas.:
diagram, (Alter lIao~~n 19511.)
GI{(l\\~nf OF SINGLE CHVSTALS FHOM MOLTEN METAL FLUXES
Z . FISK and J.P. REMEIKA
activity of spccies dissolved in the flux, in this case U. U is often quite r~~ctivc
towards crucible materials, including AI 20). In this case. however. Ihe activity of
U is suffociently reduced by solution in mohen AI so as not to be a problem . This
sort of problem is generally worsened al elevated temperatures, and one can often
detect attack on the crucible material from a discoloration of it. In some cases no
product is obtained from a growth attempt because one solute in the melt has
reacted out completely with the crucible.
. •
The actual composition and temperature range c~)Ovenicntly availablc for
gruwth of UAI) from excess AI is quite restrictcd. We haVe therefore investigated
other possible fluxes from which to grow this material. A generally useful flux
from which to grow a number of U compounds has proven to be Bi. In fig. 4 we
show the U-Bi phase diagram. There are twO peritectic intermetallics, UBi 2 and
U )Ui •. UUi z melts at a rather low temperature, and the ability to grow intermetallic compounds of U from molten Bi is presumably due to the relative low
stability of UBil' the U-Bi compound most likely to be in competition with the
compounds one wishes to grow from Bi. In fig. 5 we show the AI-Bi phase
diagram from Shunk (1969), two differing boundaries being given for the
miscibility gap above the melting po.i.W of AI. What is important here for us in
that something like 13 alo AI can '6e dissolved in Bi at the melting point of AI.
1~00r-----r-----r-----r-----r---~
\200
.....
w
-I
-I'
1200 l-
w
a:
:l
.....
<
a:
~
1000 .....
I
Q.
~
W
600
t-
400
200
0
20
-
iii
:J
~
800
~
W
t-
600
-
40 0
20
60
~O
alo U
80
100
U
Fig. 4. The U-Ri binary pha •.:
diagrllm. (Afler Hansc:n 11J5!i and
Ellioll 11}6S.)
..
.:
-
~.
40
60
alo BI
80
100
BI
Fig. S. The AI-8i binary phast
diagram. The IWO lines shown .m
from IWO differcnl in\'esligalions 01
1he syslcm. (Afler Shunk t969.)
Our original attempts at growing U-AI intcrmetallics from OJ were aimed al
producing UAI 2 crystals. For reasons we do not fully understand, only UAI
crystals were Obtained, even when compositions with U-AI ratio as large as UzA
were tried. This is an interesting fact since, as we discuss further below. it is mos
often found that the congruently melting species in a binary phase diagram (hen
UAI 2 ) is the must likely to precipitate from the ternary melt with the solvent. Till
crystals of UAI) obtained from Bi flux were rectangular bars. with latera
dimensions oC one or more millimeters and length in excess Qf 1 cm. Tbl
extraction of UAI) from the Bi flux is done by solution of Bi in moderately dilutl
HNO). It is a fact that many U intermetallics are quite stable chemically witl
respect to HNO). It is curious that many of these compounds will dissolve readil:
in Hel.
There is an alternative way to remove the Bi flux which proves to be extreme I
useful in situations where the crystals desired arc anacked by HNO). This is b
spinning off the nux in a centrifuge, and is useful for any low melting flux. Whll
one does is to place the crucible in a furnace which is set to a temperature ju~
sufficient to melt the flux, then place the inverted crucible in a centrifug
containing a base of glass or quartz wool. or glass beads, in the bOllom. and spi
out the molten nux. This is best done in an appropriately sealed glass tube wit I
the coarse filter material in the bonom. but can be done in air when the rate c
oxidation of the crystals will be small. We have been informed of situations wher
iii
..
,
a:
w
I~..
..
,
~ 800
I
;:)
,
::I
TWO LIQUIDS
1400 .....
,,
TWO LIOUIDS
a:
AI
1600
61
- ~ ..
,.
'
... ::
'.
-:~
,
.
-
b' .
Z . FIS" ~".J J .I', REMclKA
heat WilS directly :Ipplied 10 the centrifuge buckets. which wUl~I~ .a~low solve.:llIs
wilh m.:iting poin" as high as that of AI (66()OC) to be spun ort . I Ills could be ,iI
llangerous prm:edure. and should be used only as a last resOrl. In such .a c.. se.:~ 1\
would be lIel'cssary to replace.: thc SiO~ wool with AI~O ,1 granular matenal. which
is nut ilttackl'u hy multen AI.
A cOIH:i'e descriptiun uf growth of Rln} alld RSn, from excess III .. nd Sn.
res,?ectivcly. can he.: found in Kletowski et al. (l9~5).
2.2. Choice of flux
The general problem faced by materials physicists and chemiSlS needing single
. crystals is. of course. the best way to grow the parlic~lar crystal th~y n.eed. There
are several general observations' which can help 10 the exalmnallon of the
possii>ility of successfully growing crystals from mol~en metal. Iluxes. The first is
that it is generally easier to grow a congruently melting matenal from such a flux
than an incongruently melting one. and that the higher this melting point is. the
morc readily the crystals will come out of the melt. We saw an exception to this
above with the example of the growth of UAI) from Bi, when UAI! was the
material expected to grow from Di. It seems likely that at some presumably large
concentration of UAI, in Bi. it w.ill'·~e po~~ible to precipitate VAl!. The
temperatures involved ~il1 probably be quite high. and it would then be better to
usc anuther growth technique.
The second, fairly obvious, observation is that competing ph:lses formed by thc
flux with the elements in the compound wanted can prevent growth of the desired
compound . This translates into looking for potential solvent-solute binary ph<lse
diagrams with fairly low-melting. incongruent compounds.
An cxample illustrating these two observations is. the growth of rare c<lrth
borides from molten AI. For the light r<lre earths. La Ihrough Eu, th.e hexaborides
. grow. Although then: exist several AI borides. AlB! is the one most likely to
cause trouble. and this melts incongruently at 975°C. These rare earth hexaborides mclt congruently at temperatures ovcr 2000°C, and in fact their solubilities in AI an: quite modest. For example. LaB b has. very roughly, a SOlubility
of 14 mg per gram AI ncar I 400°C. The interesting point is that for Gd and
beyond. it is the h.:traboride that comes down [rom the AI !lux, and it is with these
heavy rare earth borides that the tctrab~ride be~om~s cong~ucntly melting rat~cr
than the hexaboride. whi.:h is congruently melting m the hght ran: earth series .
The cross over occurs near Sm. and it is possibk to grow either the tetraboride or
hexaboridc of Sm by varying the composition of the charge. We also note that it is
possible to scparate. below the ppm level, Sm from Gd by growth of the~e
borides: Gd will not dope into SmD/> ill AI melts. as has been shown by spm
resonancc experiments. The Gd comes down completely as h!traboride. An aside
remark here is that Eu. which only forms an hexaboridc. is <I very volatile
clement. resembling the alk<lline earths, and growth from AI is. a very convenient
preparation procedure for EuB h • because the large disparity in melting points
between Eu ilml 13 makes arc melting without large weight loss dimcult.
b .l
There ilrc further a~pcet~ Ill' the growth of rare e<lrth borides from AI which arc
worth Ill\:nliollilll:!. One point is Ih:lt in Ill:llly neulron experiments. il is important
t\) lise Ihe II B i~otupe ,ince the abslIJ ption of neutrons by '''n is so high. It is
oftcn flluml Ihat Ihe "B isotope onc CilO obtain has much lower purity than
desired. i\lld thai iI collVcni\'nt preliminary step of purification can involve a .
buride ~rlIwth whidl lea\'e~ Ihese impurilies behind. This has beell done in the
preparation of fille earth- Rh. B. compounds.
A sccond point is that initial attempts to producc YbB~ crystals from AI
produced insleild a ternary phase, YbAIB~. This proved to be an interesting
phase in its own right. and it was possible 10 also produce this phase ....;ith several
other rare earths. In order 10 grow YbD. from AI, the starting growth temperature can be in~'reascd by going to higher YbB. concentration in Ihe AI melt, so
that crystallization StilTlS above the melting point of YhAIB •. Alternalivc1y. YbB.
can be grown from molten Yb in a scaled Ta tube .
A third general observation regarding metal Itux growths is that certain metal
lIuxes work well (or compounds containing certain dements, Di for U compounds. for eXit/nple. For this reasun we have organized our listing or Itux growths
in appendix ) by thc solvcnt Ilux.
3. Further
OSI)C~·ts
of crystal growth from metallic '''Ixes
3.1. Diagnostics
In order to determine the suitability of various !luxes for the growth of single
crystals of a pilrticulilr compound. iI number of small SCil1e and lairly rapid trials
are generally required. Crystals produced in this way will most often be small , and
it is useful in such l'ilSeS to examinc the melt microscopically. This is I!specially the
case when Ihere arc problems associated with chemically separating the crystals
from the Ilux. \Ve haw found it worthwhile in these situations to saw with a
diamond wheclthruugh the crucible ,lOd melt. and then examine the cross-section
after poli~hing it metallurgically . A cut vertically through the crucible gives the
best r~prese/ltaliun IIf what is actuillly happening in the melt during cooling. II is
perhaps not surprising thut crystals often grow much larger in melts placed in
special locatioll~ in a givcn (urnace duc to the local temperature gradients, and
aspects of this will be visible in such mctallurgical examin<ltions. Elemental
analysis of these cross-sections in ilO appropriately equipped SEM is also useful.
3.2. COlllllillt'rJ
Cont .. iners ilre iI central problem in crystal growth using metal fluxes. Aspects
of this have heen mentioned ilhovc. A short list of useful crucible materials is
given in appcndix 2. It is important to realize that solute reactivities in different
melts vilr)' cnorrnollsly. Fur eX:lOlplc, it was found possihle to grow large rare
Z. fiSK
;10.1
(,HOWl II 01 51:-;(.1.1: nnSTAlS IHOM MOl:lt:N Mt:TAL "LUXES
JP. REMEJI'A
JA. Swidliollll'''Y
earth rhodium stannide crystals (rom excess molt..:n lin in scaled ljuanz tuhes.
Some rare earlh allack on the quartz was observed. being greatest for Ihe light
rare earth compounds. lIut this allack was sufficiently slow to allow large cryslals
to grow anyway. In vi~'w of the exceptional slability of rare earth oxides. this
. indicales that the rare earth-tin interaction is quite strong. reducing Ihe rare earth
activity in Ihe melt substantially. By contrast, rare earths and U dissolved in
mollcn Cu arc found to be quite reactive towards container materidls, and this
might be guessed at by the low melting temperatures of compounds of rare earths
and U formed with Cu. Crystals of rare earth-iridium C-15 Laves phase compounds have been grown from molten Cu. Ir dissolved in Cu will attack Ta. but
the rate of this attack depends on which rare earth is in .the melt. This attack
problem ",as found to be severe for the case of Celr!, butllot for Tmlr 2 • We were
not able to find a completely suitable container for the Celr 2 growth.
Ta. it should lie ~aid. is a convenient material to work with because tubing is
readily available, and it is easily sealed shut in an arc furnace. When welding a
mell load ~hut in Ta in the arc furnace. it is useful to hold the broad, flattened
part of the tube shut in a clamp made from two Cu bars. This large thermal mass
keeps the tube cool and prevents expansion of gases inside the Ta tube from
spreading it apart in the region to be 901e'ia"ed. Mo and Ware also useful crucible
materials. but arc not ductile enough to crimp flat for welding. These crucibles
can also be welded shut in an arc furnace if a titted lid is fabricated. Some kind of
copp<.:r clamp for holding the crucible while welding it shut is important: This
hold!:r should be bolted to the <Ire furnace hearth for effective heat exchange.
since keeping the crucible charge cooled is important for these high temperalure
melting materials. Electron beam welding is, of course. a better alternative. but
this is not as readily available.
Many malcriills exist over a range of composilions. This variable sloichiometry
is a source of probkms in /lux growth because the melt composition as well as
phase boundaries vary during the cooling cycle. This sometimes results in a
composition gradient ill the grown material. In a number oC cases. one composition boundary is a vertical line in the phllse diagram. This allows an excess to be
added to the melt corresponding to forcing the growlh always to occur ar this limit
of stoichiometry. II appears. Cor example. that the compound CePt 2 can form with
deficient but not with eXCess Ceo We have grown crystals of this material from Pb
melts. and found thaI we could approach quite closely the theoretical stoichiometry of 1: 2 using large excess of Ce in the Pb melts. It is important to realize
that these excesses may be much larger than one might cxpect, as we have found
that certain melts "hold back" certain elements - namely. the material that grows
is very different in composition from the charge.
The other important consideration concerns substitutional incorporation of flux
in the growing cryslals. For example, it has been found possible to grow CeCu 2Si 2
single crystals from In or Sn !lux. Analysis shows that small amounts of In and Sn
enter substitutionally into the CeCuzSi z. The propeflies of CeCu zSi 2 are particularly sensitive to such subslitutions. and for many experiments these crystals.
therefore. proved to be unacceptable. There arc many cases of this kind of
problem. and this !nukes it important to examine each possible nux from this
standpoint. Chemical or atomic size similarity of the clements in the flux to one of
the components Ilf iI compound should alert one to Ihis possibilily .
3.5. Sep'ITaticJI/ of crystals (l/ltl Jlllx
3.3 Flux ill corporation
W.: have discussed in various places above the problem of nux removal. There
are two general approaches . chemical and mechanical. Let us discuss chemical
techniq ues fi rst.
The stability of a compound in various acids and bases can be determined using
polycrystalline material. and it is a good idea to investigate this before embarking
on a lengthy attempt to grow crystals from a given flux. Specialized reagents do
exist for certain elements. and it is often worthwhile to consult a practicing
inorganic chemist for ideas connected with chemical etching. There are interesting
effects. furthermore. which appear to result from electrochemical differences
between fluxes and crystals. In the growth of rare earth rhodium stannides from
excess Sn. the eryslals can be leached out with dilute HCI. As long as the crystals
are in contacl with the Sn flux. they remain shiny and metallic. Crystals which
have separated from the Sn, however, quickly form a black tarnish from which.
microprobe analysis reveals. the rare earth has been extracted; lind the blaek
material appears to be an amorphous mixture of Rh and Sn. Thus. removal of the
crystals from the leaching solution as soon as they are free of Sn nux is desirable.
As lInother case. we mention the growth of CeCu:Si: from molten Cu. It was
One of the problems attendant to flux growth of single crystals is that
macroscopic voids filled with the flux can often be found within crystals, and the
presence of these voids is not necessarily evident from a simple visual inspection
of the crystals. In the growth the U- and rare earth-Bell crystals from AI,
lamellae of Al arc often found. We hav~ often had to separate our crystals from
these lammellae by spark machining. followed by leaching in NaOH solution.
Ar:y residual Al can be detected by looking for the diamagnetic signol of Al near
1.1 K. The prese.lce of incorporated flux is generally due to unstable crystal
growth condilions which usually occur in the initial growth siages. as discussed
earlier. It is frequently possible to recognize where this initial growth occurred
and mechanit:ally remove' this part of the malerial. Problems of this kind can be
ameliorated by providing deliberate nucleation sites. although this complicates Ihe
experiment considerably. In the growth of rare earth 'rhodium slannides Crom
excess Sn. we were never able to completely eliminate Sn inclusions. except in
smaller cryslals from a melt Ihal had reached equilibrium .
-
- '
'..
......
.
. . _... ::- '
-
-
.
.. . .
.
.'-
-
Z. FISK amI J.P. REMEIKA
reporled that the Cu stoichiometry of CeCu~Si! crystals .was very n':.levant h) its
superconducting properties. We therefore felt that growing Ct.!CU!SI 1 Crom pure
Cu would provide the limiting Cu stoichiometry for. thi~ material. The p~obl~m
came with the Cu removal. since. although an examination of the crystalhzatlon
runs :.howed the presence of well formed crystals. Cu and the crystals Jre
chemically allacked at nearly the s,lrne rate. Ultimately. we were able to slowly
cxtract crystals using acetic acid-hydrogen peroxide mixtures. the process taking
approximately one month.
. A less often used. but useful. technique is to electrochemically remove the flux.
using it as an anode in an electrochemical cell. By suspending the melt anode in
the bath, the crystals can fall free as the etching proceeds, and if this electrolyt.e
docs not attack the crystals. they can be easily recovered. The advantage of thiS
technique is that the voltage used in the erosion is easily controlled. There ~an
also be "protective" voltages developed between crystals and flux of the kmd
pointed out earlier in Ihe chemical etching of stannidc melts.
.
Another tcchnique of some use is the solution of one met..ll by another after the
growth is complete. As a case in point, we look at the gro'"":th of Ce.ln) crystals
from exc~ss In. The left over In after the growth can be dissolved In Hg. The .
crystals can then be removed frol)\. 11te liquid (at room temperature) I~-Hg
solution, and the Hg film remaining on the Celn) crystals can be pumped IOto a
trap in a vacuum system with gentle heating.
The usef"lness of centrifuging off low melting fluxes has been discussed above.
Such a process can easily be used in the Celn)-In case JUSt mentioned. There is
the additional possibility of flux removal of high vapor pressure metals by simple
evaporation after the growth process in a pressure containing vessel. There is also
the less elegant method of cuning crystals from melts, exactly as is done from
zone refined rods.
(it()\\"lIt
o.
stN(il.l: CRYSTAI.S 1'1(0/1.1 MOI.TEN METAt. I· LUXES
61
solubility t~~I~ of a !:lIl1lpUlIlld in .. given nux. This can b~ done in an approximate
manner by suaking arc-melted pcllets of the compound in givcn amounts of nux at
lixed temper'lIures. 4uenching to room temperature. ilnd subsequently measuring
the weight los~ of the leached-out pill of compound.
4.
Ext~nsiolls
of the (cdmit,ue
4.1. Use of tempf?rtltllre gmt/it·",
A variant of the growth technique utilizes a temperature gradient. This is most
easily discussed with an example. In our discussion of the growth of single crystals
of rare carth hexaborides from molten AI. we noted that hexaborides of the rare
earths Gd and heavier did not occur, rather their tctraborides grew. We did finally
succeed in prepilring single cryswls of GdB •. by the following method. B has very
low solubility in Ga. even al 15UO·C. We therefore made a flux of ~S alo Ga-5
ala AI in which B will have very low SOlubility. An arc melted pill of GdB~ was
preparcd, and its densily is such that it noats on this Gu-AI mixture. Our AI 2 0)
crucible conwining the !lux and GdD" pill was placed in a furnace so that the
crucible bottom was coidesl. the temperature gradient along the 5 cm) crucible
being about 50·C. The top of the crucible was maintained at ISQOoC for several
dilYS; mm-size crystals of GdB .. were found growing on the bOllom of the crucible
after shutdown. Our idea in this method was that we could force everything out of
solution at lower temperatures that we put in at thc higher temperature through
the dynamic equilibrium. In a case where the compound is more dense than the
ftux. the temperature gradient can be reversed.
4.2. £vaportttiot/ growtJr
3.6. SO/lIIion killetics
Some flux growth attempts appear to fail because of problems having to do with
slow solution kinetics. There are cases where such slow kinetics can be used to
advantage, but more often it constitutes a nuisance. As an example we can look at
Cu-B solutions. There are no compour.ds in the phase diagram, and there is a
broad eutectic melting near lOOO"~ If we can believe this reported phase
diagram, this suggests that Cu should be a very promising solvent for growth of
borides. A number of ternary superconducting borides have in fact been grown
from Cu. A problem. however. is that B seems to dissolve into molten Cu very
slowly. This means that a long soak time at the maximum running temperature is
required. In addition, if the growth charge consists of the elements of the
compound and Cu, it can happen that the elements other than B will dissolve in
Cu first. and then react out on the B, possibly making further solution of B
dimcul!. This com be avoided by pre-reacting the compound and using it in the
charge. rather than the clements. It is al ..o sometimes useful to make ilctu,,1
An alternative to precipitation of crystals by slow cooling is to supersaturate the
flux solution via cVilporation of the lIux. This clearly requires the fl'ux to be the
most volatile species present. We hiwe grown crystals of UPt l from Bi by such a
method. The disildvantage associated with Ihis method is that the supersaturation
occurs at the evaporation surface, and it is difficult to prevent the formation of a
large quantity of nuclei. In the case of Bi flux, it can be quite useful for high
melting point materials which might be diflicult to separate from Oi chemically
although the centrifuge separation method is usually effective.
4.3. Travelillg sO/l'em methods
The use of molten metal solvents in the traveling solvent technique is clearly
possible. The general aspects of the technique are discussed by Wolff and Mlavsky
(1974) und Cilll easily adapl to the various "ulles discussed here. This method is
especially impurtant when large crystOils arc desired.
Z . FISK iln..! J.I'. REMEIKA
GIWW'III OF
SI~G!.L
4.4 . Mis("dltllleOllS
CHYSTALS nWM MOLTEN METAl. I'l.UXES
Flu\
InShe .. )
We have m:lde little mention of the uses of seeding melts. or of providing
deliberate nucleation sites. These would clearly be useful in m~lny situations. For
the most part we have discussed only the simplest procedures. but it is clear that
almost ::11 of the lechnology adapted to produce laige single crystals of oxides and
similar materials can be suitably adapted to the growth oC crystals from molten
Illl!tal t\uxes. This includes. in addition. the pulling of crystals (rom such met "I
lIuxes. There is no need to repeat in our context the detail discussions of such
methods as discussed. for example. in Elwell and Scheel (1975). The generalizations to this case are ea~ily made.
In
«('u.s,.
S,i.' Ge(aJ
Itlll .Iel
1'1>
IU'I,. \'bPI.
(jdSb(al
Sh
ZIlSiP,(~).
C"'SiP:(iI)
HSi,
Sn
RCu,Si,
1{.lth,Sn,.
1<1-'" ,I',,(b)
ZnSnl',(a)
GaSb(a). GaP(a)
ZnSil'.(a). C,",SiP,(a)
Appendix I
RSn.(~)
We present below a short list of representative intermetallic compounds grown
from various solvents. Bin"ry compounds grown Crom one of their constituent
elements have not been induded: For example. these include USn) from Sn.
UGa) from Ga, Celn) from In and Ti8t!rfrom the middle of the Ti-De phase
diagram. In our list, R means rare earth. although the rare eanh compounds
referred to cannot always be grown for all the rare earths.
Au"
C,ysl~I'
AI
TiB , • ZIB,
RAIB.
RB" UB •. NpU,. AmB,
RD.
RBe". UBe". ThB",,, PuB""
Si(a). Gr:(a)
Bi
Zn
.
luSb( .. ). G~Sb(a).
S1131. Ge( .. )
InA~(a)
·1{~I.:r~n~e>;
(iI) Luzhn")a (l'.IbI!); (bl Mci>nr:, (IYII2); (e) Klr:lowski el .. I.
(1'.1115).
Appendix 2
Containers for \'arious llIulten metals. A more complete list cOIn be found in
Drown and We~lbrouk (11)67).
TIle free energy of form'lIion • .:lG. ill kcall mole 0) for various oxidr: crucible
materials is shown in fig. 61 aflcr Reed 19711. Tht: values ure for reaction with one
mole of O~ .
UPt,. NpPt.
PIMnSb. Ni~lnSb
UAI,
COnl~iner
UIr,
" GaP(a)
ZnSil':. CdSiP,(a)
Cu
RRh,B,
RCu,Si,
V,Si
Rlr,
Ulr,
Fo:
Ga
BPla)
ZnS(a)
Si(a). Ge(a)
GaSb(a)
ill"iI" IIIclal>
Ta.
al!.alinc callh lIIelal>
AI. G~
Mg
In
Tit. Il'~phlle fur Ua, slcel
AI,O,. MgO. Dca
MgO. Ta. glaphile ur ~Ieel
AI,O,
graphile. MilO. AI,O,. n
AI,O" 1.rO" ThO,
AI,O,
AI,O .. Ta
laic callh.
Til. Mol. W. lleO
Mu
Cu. Ag. Au
Fr:. Cu. Ni
Zu.C.... 1I1l
Site:!
11,. Su
AI,O,. SiO,. graphile
!ib
Sia"~ graphile
1"0
",r /./,\......
1/"",lh,,"1.; ,m
",,1 CIo,.",m'.1 ul/(,,'r
,.,li'r,ll>.1 X.A . (i,d,,,r,,I,, ..,. J" "tld L , t::P'''1I
CO £I'r";r' S,'i..", '.. "IIM"/,,',, n ,I'.. 11I1i1l
Z. FISK all.! J .P. REMEIKA
£"",,..
Vul. I.!
Melling poinb of m.i.!e materials'.
Mellillt: ruin! (Oe)
AI,O,
2015
11.:0
2SOO
MgO
SiD,
ThO:
21lOO
Clwpler 82
PHYSICAL l)ltOPERTIES OF RzFe'48.BASED ALLOYS
172(1 (suhcn~ -1;(00)
331l1l
E.BURZO
·SiO l • AI,O •. a ...J DcO have t:",l<Ithcrmal ,h.x:k rl!)istam·c.
ThO , ane! MgO intermedlatr. Ihl!rmal shock re)i)lilnce:. ilPe!
Y10, ane! ZrO, poor the:rm:.1 shock re:sislance.
-&O~--------~----------,-------
__
Cemrll[ [IISli/lllt'
1'0 Box MG·(J6, Bucharesl. Romallia
H.R. KIRCHMAYR
Insrillllt lor £xperimtllfai Physics. Technical University Vielllla
Wiedller H{/l({Jll'Ir. 8, A·JO.JO Vienlla. Alls,ria
~
-120
~
0/ Physics.
Contents
-160
o
1000
2000
3000
TEMPERATURE (K)
1. In!roduelion
2. Phase Ifiagrams and cryual SlruelUres
2.1. Phase diagrams
2.2. Cryslal suuclurc: of R,Fe .. B
.:ompounds
2.3. Lalliee p"rame:lets of R,Fc: .. 8
compoun\/)
2.4. Preparalion of Ihe alloys
3. Magnelic properties of R,Fe .. D com·
pounds
3.1. The Curie: h:mpcr;lIure
3.2. Magnetic mORlenlS
72
74
3.3. Anisouopy fields
3.4. Pr.r4lmagnetic behaviour
3.5. Magnelic properties or R,Fe"B
hydrides
4. Rare·eanh-iron-boron magnels
4.1. Sinlered R-Fe-B magnels
4.2. Magnels obtained by splal·
cooling
" .3. The slability of R-Fe-B perma·
nenl magnC:ls
References
74
76
78
110
82
82
91
103
106
107
107
120
125
126
811
Fig. b. F,ee energy of formation of oxides. for reaclion wilh one mole: or 0,.
Symbols
l~ererer.ces
Drown. A .• and J .H. Weslbrook, 1\167. in:
IntermCI"lIic
Compounds,
cd.
J.H .
Weslbrook (Wiley, New York) p. 303.
ElliulI, R.P. • 1%5. Con5lilUtion of Binar), AI·
: luys. Firs\ Supplement (McGr;lw·HiII, New
York).
Elwell, D .• and H.J . Scheel, 1975. CrYSlal
Gro"lh from High.Temperalure Solulions
(Academic PreS5, New York) .
Hansen. M . • 19~8, Constitulion or Binary AI·
loys (McGnw·HiII. New York).
Kletowski. Z .• N. Iliew, Z. Heukie and D.
SlaliJ'ski. 1985, J. Less·Common Mel. 110.
. 2)5.
Luzhnaya. N.P.• 1968. J. Cr~l. Growlh l.U.
97.
, Meisner, G.P., 1982. Ph.D. Thesis. University
of California. San Diego (unpublished).
Morfall, W.G .• 1981. Handbook of Dinary
Phase Diagrams (Gencral Elecltic).
Reed. T.B .• 1971. Free Energy of Formalion of
Binary Compounds (MIT PreS5. Cambridge.
MA).
Shunk. F.A .. 1969, Conslilulion of Binary AI·
loys. Second Supplemenl (McGraw·HiII. New
York).
Wolff. G.A .. and A.!. Mlavsky. 1974, in: Crys·
tal Growlh. Vol. I. ed. C.H.L. Goodman
(Plenum Press. New York) p. 193.
B.
B,
n~.
e
e"
8;
Co.
C U'
c••
ti,
d,..,.
d.
E
f ...
g,
g",
",mancnl indueliun
)aluralion inJuclion
"~'>Ial tic'" p:uamelcrs
Curic .:onstant
CUlic COn)lanl of Fe iOIl
Curic conSlan! of R ion
slifhless conSlimts
critical diameler
dislance between i,..11 ions
grain diameler
Young's modulus
ani!>Ouopy energy
spectroscopic splilling
'X
'Xu,
1/
Ji ..
Il,ullll
.11,
,.. II,
II"
1/..
II..
J •• (i, j ..
n, Fe)
X,. K, K,. K" KI
f~ctur
M.
spcClroscopic splillin~
factur of iron
"',n
M ••
71
one ion h.. miltonian
cry)lalline .:icClric field
hamiltonian
external lic:ld
anisotropy field
exchange field
coercive ficld
intrinsic coercive field
hypcrfinc field
nUdC::llion fidd
molecular field
molecular field codlkienlS
ani~o\topy constanlS
saluralion magnelizalion
efreclive moment
iron momenl