DETERMINATION OF THE DIFFUSION RATE OF INERMETALLIC COMPOUND AL3MG4 INTO MAGNESIUM

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200030028-7
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 18
• Document Creation Date: December 22, 2016
• Document Release Date: April 11, 2012
• Sequence Number: 28
• Publication Date: May 23, 1952
• Content Type: REPORT

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D~TEHM.~~~~~~'~Q~N~~'~~ , tJSTON R~T~ OF
TNTER,N~1'~L~C CQM~'OUND Al~M~1~ INTO M~G~NESTUM
Docent V. V, Chichagov,
Army engineer, 2nd Class
Forms of Diffusion into Solid Metal
Diffusion into sol~.d metal is a comp~ex:proce~s depending on
numerous factors., Therefore, up to the present, there is no def inite
precise~~law, expressed by a mathematical formula, which would embrace
and take into consideration all factors and complexities of this
phenomenon.
All forms of diffusion may be broken into three large groups
first group;. diffusion of gas :into r~etal; second, diffusion of liquid
metal into solid one; and third, diffusion of solid metal. into solid.
This purely formal division corresponds to .widely used industrial
~'
processes; gas carburization, cyaniding, and plating. However, each
of these forms may be fug^ther broken into diffusion within the in-
dividual?grain and diffusion along. grain boundaries, i.e, on the
grain surface or at the boundary separating two phases.
Diffusion within the grain may be again broken into (1) dif-
fusion in the basal plane for metals with non-cubic crystal lattice,
(2) diffusion in a direction perpendicular to the basal plane and
(3) diffusion along the planes ,more closely. packed with atoms or along
the planes of most possible deformation of graih.
There is another entirely separate phenamenon of self-diffusion
which may be defined as di~'fusion of atoms into their lattice.
Determination of the ,rate of self -diffusion was .developed by G, Hevesy
who treated the surface of lead with~a radioactive isotope of lead,
observing its diffusion inwards. He studied this phenomenon and cal-
culated the diffusion coefficient by measuring the radioactivity on
the specimen surface with an electroscope, since radioactivity
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aces Burin diffusion of thc:-lead i~ota~e deep into the specimen
Bette ~
,~,~Fr intrpduced a concept of puxe and reactive
Tn addition, y'
tahl and Eisen 19~~, p~ ~-039) Pure diffusion
diffusion (A. ~'ry, ~ ~
omenon of mro~tua~. diffusion of metals in the solid
embraces the phen
state onl in cases when these metals f orrn solid solutions, Tn the
y
case of".limited mutual solubility, pure diffusion is determined by
inn concentration of the solid solution at a given tempera
saturat
e Reactive diffusion is a phenomenon connected with the appear.-
tur ,
oncerltrations greater than maximum saturation concentration
ante of c
of the solid solution,
Complexity of the diffusion process is increased further by
the author's observation that, in addition to penetration of the
" lament into :h,he metal, the reverse phenomenon occurs due
diffusing e
to concentration increase and separation of individual phases at the
boundary . ~ -
Laws of Diffusion
f diffusion was ,first developed by A. Fick in 1850
The law a
According to this law, the quantity of diffusing substance dm is
proportional to the cross-section F of flow, concentration decrease
do and time d~': dm = D.F d__r e___ ~ d~,
~ dx
The constant D, known as a diffusion coefficient, is numerically
e ua1 to the amount of substance in grams,. diffused per second through
q
a of l s cm when the concentration drop is equal to unity.
the are q
'te of considerable practical limitations, Fick's l,aw remains
In sp z
roximatel~ 'ustif ied for the formation of intermetallic compounds.
app y J
In 1879, M. I. Stefan used it for measuring diffusion in liquid
solutions of metals and compiled tables facilitating calculation of
the diffusion coefficient for experimental conditions. These tables
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-~roy.T.
were su ~.emented by W, ~oval.~ci in ~~9~ and W, Jest i~ ~y2C, ~'~ is
p~
to determine the rates of diffusion using Fick's 1,aw,
possible
e forms of dif~~usion rates have to be distinguished,
Thre
neral rate of diffusion is measured by the amount of sub
]. , Ge
(fused er unit of time through cross-section ~' when the
stance di P
do
oncentration gradient is -~--- ~'ormul~ for the diffusion rate is
c ,--
v = dm
d~' ~
2. Concentration rate represents the increase in concentra-
tion per unit time in across-section located at a def finite distance
from surface. It is expressed by Fick's second l.aw:
do = D d2c
vc - __
d~ _.._ dx .
ar rate denotes the shift per unit time of the zone with
3. Line
t concentration into the depth of the substance to be saturated,
canstan
he linear rats is generally accepted in practice and literature as
T
tr~e diffusion rats which, theref ors, is expressed by Wane of the two
reviousl given equations, but by a third equation correspanding
p y
to linear rate:
~'~r ~','' }rr
~!' ... ~n,~l w
dx
d'4~ ~
where k is a constant. .
This rate of diffusion is determined by the shift. of an arbitrary
s
o ndar having definite concentration and chosen depending on the
b u y,
od of investigation, Deduction of all equations is described
meth
in "Diffusion of Metals" by V. S. ~uganov and V. D, Neskuchayev and
"Diffusion of Elements into Solid Iron" by D. A. prokoshkin, published
in 197 and 1938, respectively).
The diffusion rate in solid bodies increases greatly with a rise
in temperature.
~ is y, ~~ a d i;~ ?
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-~,n ~~.s works (revue de Mete,~,~,uxgie, 19~~~) givee~ the fo~.~
Weiss
r the diffusion date in respect to temperature:
lowing eXpressi0n fQ
- ~, ^ k~ a T, where ~'is time, T absolute tempera-
v.
` ~7uY~?~.
e k .and a~'are~~cons~ants determinable expex~,~aentally,
tun ,
d Schonert (Zeitschz, anorg, allg. chemie, 1.92) give
Tamman an
ession for determining the diffusion coefficient
an exponent~.al expr ,~
w e- a ~' b T~ where a and b are
D in relation to temperature; D
constants and T is absolute temperature,
Arrhenius divides atoms(molecules) into active and passive
Their activity is determined by the kinetic energy of motion,
types.
b oscillating motions or by the enhanced equation of energy which
y
is attained by means of collisions or radiation. It is assumed
that in solids only those atoms are able 'to move, whose oscillation
neater than the average oscillation amplitude of atoms;
amplitude ~s g
atoms with ~' ~'~a have ,a definite possibility for movement in a
i.e.
lattice while this possibility for atoms with' ~ ~Q is small to the
point of vanishing.
According to the Maxwell law of velocita.es distribution, the
e~
robabl relative number of atoms with the oscillation amplitude ~""~ ~"~
p ~ E
will be equal to e, KT where the magnit~,:ae E, heat of loosening,
la s a role similar to that of activation heat in chemical reactions.
p y
Its values for alloys vary mainly in the range of 20,000-X0,000
-16 erg~deg
al mol? is is a universal Boltzmann constant equal to 1.37'10
c
-14 cal~deg, T is absolute. temperature of diffusion,
or 3.27.10
he uantit of substance diffusing per time unit, i.e. the
Hence, t g y
- E
diffusion coefficient, may be expressed as follows: D = Ae ~ ?
The value of A depends on temperature since it includes velocity
of atoms but this .influence is considered negligible. compared to
e of otential, and, therefore, A is considered in the first ap-
chang p
ximation as a constant, Practice showed its applicability in a
pro
cases for processes of diffusion in the crystalline state
number of
? nd I. Laird. 1932, Zeitschrift fur Metalkunde).
(works `by W, Seith a ~
1,~~Y.ifJ t1
f a ~ :q ~ ~If
l . s a~ ri j
e i ~ ~.:i ~ Can
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,..,
in order to satisfy the purpose of this investigation,
The most essen~cial require~aents are as follows:
1, Contact must be sui'ficiently close to prevent the fog^ma-
Lion of oxide films and, especially, the existence of any air inter-
layer.
2, The method for establishing such a contact should be
simple, approaching industrial possibilities,
3. Metallographic examination must be possible for clear ob-
nervation of the Ala Mg4 structure and further changes in structure
along the phase diagram up to pure magnesium,
4. Penetration of A1~ Mgt into magnesium must take place over
a large area in order to make it possible to stu?dy this phenomenon
by the metallographic method, and by X-ray analysis.
5 , The method far.. obtaining contact should involve no modifica-
Lion of any of the properties of magnesium, i,g. grain coarsening.
~~
All the requirements are necessary in ordex to attain the high-
est possible degree of precision in the investigations, keeping them
close to practical production problems.
Method One
Solid magnesium in the shape of a cylinder 15 mm in diameter and
30 mm high is submerged into liquid or semiliquid A13 Mg4. Melting
oints of ma nesium and Al Mg are X51? and 463? C, respectively.
P ~ 3 ~.
t h~ ~a ~ o
It seems difference ~ 188 must provide for the process. of dif-
fusion of liquid A13 Mg4 into solid magnesium. ?
.Fig. 1 represents a microscopic study of this process, The
c Linder was .kept in liquid Al Mg far l5 minutes at 470-47~? C.
y 3 ~
The structure of pure magnesium is sharply separated by a eutectic
consisting of Al~ Mg ,and crystals of the solid solution Ala Mg4' ~ Mg.
3 4
'f ,', L rh R ts'q
~, l'
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1 {ii~
~F~I A~
~y itsck~em.ical composition, the a1,1.ay next to pure magnesium carres~
ponds to 100~a eutectic, i.e, 67~ Mg+ 33~ Al. Farther inside of the
eutectic, grains of A13 Mg4 are inserted, gradually increasing and
reaching 100' of composition.
This structure clearly illustrates the process of A13 Mgt
penetration into solid magnesium. FIowever, the method has a number
of essential shortcomings. The intermetallic compound A13 Mg4 in
liquid state is subject to intensive oxidation and may ignite in the
presence of a considerable supply of oxygen. Therefore, it has to
be kept under the protection of fluxes, The cylinder of pure mag-
nesium, during its sinking into molten A13 Mg4, is covered with
fluxes and, as a result, merging of the two substances does not begin
simultaneously at all points on the .cylinder, The eutectic, formed.
at the moment of merging, melts guickly since its melting point is
436? C, i.e. 34-38? lower than the temperature of the experiment.
The cylinder melts guickly to various extents at different points,
making it difficult to calculate the rate of A13 Mg4 penetrata.on into
the magnesium. This method also does not provide for the presence
of A13 Mg4 on magnesium in a large guantity which would permit hav-
ing structurally free A1~ Mg4 on the surface during investigation of
the process of its diffusion into magnesium.
Method Two
This method uses a different approach to the pz?oblem, attempt-
ing to establish close contact by pouring molten A13 Mg4 into a hol-
low cylinder of pure magnesium. Several hollow cylinders were used
for experiments. The dimensions were outside diameter 30 mm, inside
diameter l~ mm, height, 60 mm. Liguid A13 Mg4 was heated to 470-
47~a C, First, the cylinder, filled with A13 Mg4, was examined
before any heat .treatment. A photomicrograph of this cylinder is
given in Fig. 2. It is clearly shown that no complete a1.loying was
,,
achieved; rather, there is a separation of the two components by an
oxide film,
~ ry'R ti.. r
i ~~ 1 ~ ~ r ~ p fv7
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. .. l~.ed with molten A13 M~~, were
our cy~.indexa, sim~,lax~y f i ~
~' exiod ~5 ~ ~,
X20? C, each ~'or a. Jiff exent p
held in a furnace at
0 and 100 hours)? er 0 hours
~ finder No 3 af't ~
are 3 gives a micrograph ?f cy
Fig
o n having been etched. ~'~ shows
the furnace at 42~ c, specime 1
in aund Ala ~g~,'
e ~ gnesium and very porous comp
grains of p~ ~ .
~, phis method also unsua.table
Further investigation reveals
F lace only
ion over a large area, it takes p
since there is no fus to oxidation in
The high tendency of A1~ Mgt,
at random points.
measuresmelting u~~der fluxes,
state, in spite ?f preventive
liquid lets and
etc.) did not permit a comp
oaring in S02 atmosphere,
p onents. In addition: liquid
e contact and fusion of bath comp
c1DS at the moment
ch of the gases which, evolving
Al Mgt dissolves mu
3 d macro bubbles. Oxidation occurs
of solidification, form .pores an
at the moment Df solidification .
of only during pouz'~.ng but also
n
c finders was also coated with
inside .surf ace of the magnes~.um y
The. During,
it reparation. Just before p
oxide film regardless of the p
kled with a Weak solution of
c finders were degreased and plc
all y
nitric acid.)
Method Three
used in Method Two were tightly
cylinders identical tD those ium
of Al Mgt. and sealed with magnes
packed .with a fine powder 3
he lugs must hermetically Seal
nder a preasure of 3 tons. T p
plugs u
tration of Oxygen f r0m the aa.r . or
the cylinders to prevent gene
art of cylinders and plugs were
this purpose, the upper inside p
ix c finders prepared in this manner
to erect at the same angle. S y ~ d from
p each far a, dzf f exent per~.o
a furnace at 120 c ~ .,
were held in
2~ to 175 hours. arts
ach c finder was cut into several p ~
Upon 'heat treatment, e y
d
.
o ra hic specimens wire prepare
from which metal/ g p
-8
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,, .
ecimens in the uxaetched state revealed no
Examination of sp
rota magnesium. ~eali~atian of d~,f
di~'fusion of powdery Ali Mgt
method described is quite possible, but it would be
fusion by the
ra ex catalyst or main'~ain an inert atmosM
necessary to select a p p
to increase the te~perature, The development of this
phere, or
takeconsidexable time and, therefore, f~~rther in~
method would
Vestigation was interrupted.
Method Four
't 0 mm deep and 10 mm in diameter, machined in
A round cave. y 3
ordinar aluminum, was filled with molten magnesium. All precau-
y
ons such as melting under flux, dusting wa.th sulfur, etc., were
ti ,
revert ossible oxidation during pouring. The cavity in
taken to p p
uminum was preliminarily degreased with alcohol. Liquid
the al
0 10- 20~ ~, introduces an amount of heat suf-
. magnesium, heated t 7 7
m,rltin a comparatively thick. layer of aluminum,. re~
ficient for g
formation of the intermetallic compound A13 Mgt nn
suiting in the
the side near the magnesium.
Ives a photomicrograph of such an intermediate layer
Figure ~ g
etched state. The width of this layer will vary depending
in the
tem erature of the agnesium and preheating of the aluminum.
on the p
termetallic compound Al Mg thus obtained, closely. adjoining
fhe in 3 4
' ientl free of oxide f ilxns and other impurities .
magnesium, xs suffic y
rains of pure magnesium, there is a sharply outlined
Next to 1,he g
utectic changing into crystallines of A13 Mgt.
band of the e
imens were heat treated as in methods two and
Several spec
etallo raphic examination proved it possible to observe the
three. M g
diffusion of A13 Mg4 into magnesium..
order to corroborate the .assumption that A13, Mgt, but not
In
tuall diffuses, apiece of pure 'aluminum was placed in a
Al, ac y
After oaring liquid magnesium into .its cavity,
furnace at 1+20.. C , p
the aluminum piece. was sectioned along magnesium insert
9-
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~~
~M
4
t ..
~1 }
oldie in the ~'urnaCe f 0~' se~feral hours ~ the ~.ntermetala.3,c
Upon h g
M embedded between.aluma.num and magnesiu~, being
compound Ala g~
el oxia~,2ed expanded and partia~.ly squeezed the l~,gnesium
intensiv y ~
out of its space, This is shown in Figuxe 5 (left part),
Method Five
This method for obtaining close contact between Ala Mgt and
ium em 1o s the inverse procedure of the previous method.
magnes p y
0
Liquid aluminum at 730 C was poured into a hollow cylinder a' pure
which must be preheated to 350-4OOo C to secure complete
magnesium,
Fusin The inner walls of the magnesium cylinder must be degreased
g
with alcohol and .the oxide film ust be removed from the aluminum
'ust before pouring. Flow of metal over the edge of the cylinder
J
is not advisable. The liquid metal actually should not reach the
e thus roviding far. free solidification and contraction.
edg , p
solidification shrinkage of aluminum (6,60) is greater than
The
at of ma nes ium (~+ . 4~~0 } , and this i s the .only negative factor of
th g
the given method, which otherwise has a great many advantages.
The ma nesium cylinders, after the liquid aluminum was poured,
g
were heat treated as in the previous methods.
Micrographs of etched specimens show a boundary zone near the
' after holding in the .furnace at 420? C for 100 hours::,
magnes~.um
Figure 6) and for l5O hours (Figure 7). Doth micrographs demon-
(
am lets contact, absence of impurities and complete trans-
strate a c p
' om lO content of A1, Mg to pure magnesium. Decomposition
ition fr ~ ~ ~,
ctic and coagulation of its components are also noticeable.
of the sets
Formation of the intermetallic compound A13 Mgt by this method is
certain. Oxidation of this compound is intensive upon its contact
with atmosp~~~eric oxygen, as shown in Figure ~ (right part),
Method Six
ectrol tical deposition of aluminum on?magnesium is impossible
E1 y
o the. more negative potential of the latter.. Deposition of
due t
? aluminum is of no .interest within the scope: of this work.
magnesium on
i~ ,.~ rrr7 . Y, m ~ z~r +^+ ,
~ r~1 ~~~ ~ ~,~
M~' ~~ C~ ~ r.y I y ~ 4
Y~ .G/ ~ .~ ~ G ~:w' W L~1~1 ~,
-lo-
~ ;,, }~~.
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PY pp ~~~ . ~,:~1a,.
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a ~ ~ ,, it
1 , ! ., ..
There~'ore an attempt was made to deposit. aluminum on mag-
athod s ra ing, Far this purpose, two pol~.shed speci-
nesium by c ~ p Y
mens of p~'e magnesium and aluminum, degreased with a~.cohol, were
a art in vacua approaching hundredths off' one milli'
placed 3-~ ~ p
column, The aluminum specimen served as a cathode.
meter mercury
' stallation was arranged according to a description in
The ent~.re ~.n
" thod S uttering,' published in 193+ by Yu. A. Maslakov.
the paper Ca ~ p
echnical reasons, a voltage of 5,600 v, and l$-20
However, due to t
ma current were used, The installation was in operation with a
continuous and constant vacuum for a period over 20 hours. Coat-
in of the magnesium with thin film was observed, but upon complet-
g
ing the experiment, when air was admitted under the vacuum bell,
this film was instantly oxidized, Metallographic examination of a
carefully prepared specimen did not give any result.
a1.1 methods here described, the fifth method-was selected
Of
as most suitable fox the purpose of .this investigation.
Forty cylinders of 25 mm inside diameter, with a cavity 35 ~
deep and with 10 mm thickness of walls and bottom were machined out
of a.n of magnesium. Molten aluminum was poured at 725p C into the
g
sium c finders preheated to 375-3$0o C. These conditions were
ma,gne y
' tl maintained far all cylinders in order to obtain fusion of
stric y
bath components to an approximately identical extent along the entire
tact surf ace. Four cylinders were cut for metallographic speci-
con
e resentin longitudinal, transverse and bottom sections of
mens, r p g
the cylinders.
with mag-
Figure 8 presents atypical joining zone of A13 Mgt
nesium> The. specimen splits into two portions along its brittle
com onent, i . ~ e . Al Mg ; the second ,half , having no significance
p 3 ~.
for this investigation, is not examined.
Diffusion of ~1 Mg in Regard to Time
3 4
~:
Twelve cylinders were heat treated. to study the effect of t e
;~
time. factor an the process of Al Mg diffusion into magnesium..,
3 ~
rs ere.held in a furnace at x+20? C; 2 cylinders for five
All cylinde ~ ~ ~,
wo for 25 hours; and other pairs for `' S0, ,,100, 125 and
hours; next ~ t ~ ~~ f , ~f~, ~~, ~~~ ~. ~ ~ ~~,
~~~
.;~
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heat txeatme~t, metallpgxaph~.c
and 1~0 ho~,~rs respect~,vely, Aftex
,.
ar arts of each. cyl~.naer, Micro
s ecimens were cut out of simil p of
p ~ races
of the specimens revealed that the p
scopic examination of the specimen
a .complex phenomenon, Examination
diffusion is struc-
t Figure ~) reveals the..f ollawing
without any heat treatmen
of intermetallic compound Al3Mg~
tore in the fusion Zone; grains
se arated from the grains of
surrounded with the eutectic and p
are a solid
axrow strip, evidentl'f representing
pure magnesium by a n
4??w.
solution A13Mg~~~~..~, Mg. ws no grains of
n held at 420o C f or 5 hours, sho
The specime
gins of solid solution, framed by
Al Mg (Figure 9) but reveals gr
3 ~' and the width of
ic~ this band is considerably wider,
.the eutect ,
Al M '~ Mg is also considerably
li ht strip. of .solid solution 3 g~ ~
the g f ormatlon
with deeper penetration of A13Mg~,'
larger . O~,viously,
mainly at grain boundaries, and
of the eutectic again takes place,
heir maximum concentration at
'ns of the solid solution attain t
grai
~e and grow in volume and quantity'
given temperatur hours
cimen held in the furnace for 2~
In the case of the spe decom osition
e remains unaltered but partial p
(Figure ll), structur
The eutectic does not now form a con"
of the eutectic is observed, P ork and,
are considerable breaks in the n~tw
tinuous network; there
tectic; i,e, coagulation and spher-
seemingly, a dissolving of the eu
is rocess continued with the
in of its components occurs. Th p
01diZ g ore 12),
a 0-hour holding period (Fig
ame intensity in the case of 5 he
s
was not reali2ed for technical reasons.
Holding for 100 hours
hours (Fig~'e l3) shows complete
ecimen held in a furnace for 125 , ~ ation
sp lete isol
the eutectic into its components,?comp
decomposition of included.
ne and deeper penetration of A1~Mg~
of Al 1`~~, in a Separate zo
3
e rains of solid solution.
lxa th g
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12
k r,
k ~~~~;_ ~,~ ~,
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imen held fax ~,~0 hours demonstrates total complete-
The spec
Fi ores ~.~ and 7-~) , showing the gra~.ns o~
Hess of this process ( g
of solid so~.ution ,A.l Mg ~ Mgr which have varied
Al Mgt and grains 3 4
3
'o of Al Mg in depth, .Consequently, two processes take
concentrate n ~ ~,
~, a increase in the amount of solid solution,
place simultaneous y ( )
concentration of Al Mg in solution gradually decreases
whereas the 3 !~
e de th of penetration; (b) decomposition of the eutectic,
along th p
ulation and spheraidizing of Al3Mg~ and formation of Al3Mg~
coag
addition formation of the eutectic proceeded along the
grains. Tn ~
boundaries of solid solution grains.
hematical calculation of the diffusion rate can T'iot depict
Mat
/exit of this process and, therefore, investigation
the entire comp Y
to be limited to a consideration of only one side of the process,
has
namely, penetration of A13Mg~ into magnesium.
t is necessary to estab7.ish a penetration limit fox plotting
Z
' de th-time curve,, Metallographic analysis permits
the penetration p
' his limit with sufficient precision. The limit of
determining t
enetration may be calculated from the edge of the solid solu-
total p
'an stri to the minimum presence of structurally free A13Mg~
ti p
l0 ll l2, l3 .and l4). This total depth of penetra-
(Figures 8, 9, > >
crate Zones with sharply varied concentration of
Lion includes sep
zone showing presence of the eutectic sharply differs
A13Mg~, . The
'on from the zone containing only the solid solution.
by concentrate
ecessar to calculate also the second zone without
Therefore, it is n Y
'c, De th of penetration is presented in Table l and in
the eutecti p
the graph, Figure l6.
TABLE 1 .
Depth of Al Mgt Penetration into Magnesium
3
Depending on Time
Total Depth.'
Time of Holding
in Furnace in min
Depth of the Zone
Without the Eutectic
,
~,
.,
~ hours
0..125
0.023
2~ hours
0,17
0.03
5p hours
o .1a5
0 0~8
l3
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y ~ ~ ~ ~ ~ ~ r
~~j ,
1 ' ~~~ ~ ~ ~? ~ ~ 6~ t ~ ~~ ~, ~
~: ~' :., ~ fi { % ~ 4 ~,,1 ~{.:a X1,1
Time of Holding Total. Depth, Depth of the bane
Without the eutectic
in Furnace in mm
125 hour s
l~0 hours
0.29
0.233
A number of investigators (G. Ageyev, Tamman, Rock, Weiss and
others demonstrated experimentally ghat the depth of a sayer will
vary, in regard to time, according to the parabolic law if the proc-
ess of diffusion follows Fick's law,
Their reasoning was as follows; the quantity of diffusing sub
stance m, in a certain layer x, f or a certain period ~:. will be equal.
to m - Cl ,~~ C2 = Fx~E and m2 ~ Fx~C, etc,
1 ~~ 2
Consequently, for the period of n,`i~~="~Lz. "~' 4, i the quantity of
diffusing substance, when the layer thickness changes from x, to x~,
will be ~ m = m2 - ml = Fx2C~ - FxIQ = Fc(x2 - xl) = Fc `~ x or: dm =
Fcdx.
From Fick's equation dm = DF ~ d~~; hence, DF c df"'
x x
Fcdx, or xdx - D ~ c d ~' .
._._..
c
The value of cc is constant, since we take a layer with cer-
tain constant concentration; the value of D, under certain condi-
tions temper^ature, medium, pressure), is assumed also to be constant,
(
Integration of the equation gives x
C
0 a
x2 = 2D '`` c ,replacing 2D "~~ ~ = k, obtain: x~ = k ~:"
G C
Let us .find out to what extent the experimental data of Table
l are in agreement with this law, For this purpose we will consider
only the penetration depth for one zone, since transition from one
zone to the other involves a sharp change in concentration. Let us
make calculations far the zone without the eutectic.
Let us determine a constant k f or 2~+ flours or one day; then,
2 _ p,p~~ - -0,002, where x is expressed in mm and` in days'
(2~+ hour. periods). Using the. equation x2
r 4 ~. ~
C~ I y ~? ~ a
' ~ ~~, ~~~ G E ~ w ~a~ ~ r~
- ],~ -
= 0.002~,`~', let us find
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~..,~ ~~ V
~~~ f, u
the th~,cknes~ of the ~.ayer wlthou'~ eutect~.c
f or ~ hour s :
.
x5
~~-...._
\ 0,002j? ~
~
~
0,028 mm
.
2 hours .
fox ~
x
2 ~
0,002~
~
\/~~
,,.~.,
~ 0.01
x : ~ro;~oo~~n? ~ ^ o?o7a~ mm
far ~0 hours: 50
for l2~ hours :
for 1~0 haurs
~w
~' ~ 0,113 mm
x ~ 1 0,00~~' 2~
12~
,.,........:., ~ : 0 ? l2~ ~
xl 0 ~1~.0002~? ~,
om arison of calculated values for depths
C p
of the layer with~-
obtained experimentally is presented in
out the eutectic with those
Table 2
ve lotted according to theoretical cal-
Figure 16 gives a cur p
culations and experimental points.
7'AI~LE ~
De th of Al Mg Penetration into Magnesium
p 3 ~.
Time of holding
in~ Ful?nace
Dep~,nding on r~'ime
De th of Penetraticalculation
der..--'~=
0,023
5 hours 0.053
25 h0~'s 0.068.
~0 hours _
l2~ fours _~
150 hours
0.0228
o.o~l
0.071
0.113
0.12
ata are in close agreement with calculations
Experimental d
according to the parabolic law,
Determination of the Linear .,Date of
Al Mg Diffusion into Magnesium
3 ~
diffusion is defined as penetration of a zone
The linear rate of
ntration per unit time. The relation be-
with certain constant conce
trat~.on and time was previously accepted as
tween the depth of gene
~ ~
2 ~ ~
x=k~~orx=k ~
'ff erentiation of this equation gives: ~
Da.
~~ k
2
. f t and right parts ?f the equation by ~',.. ~
Dlv~.de le 1 .. ~ _ ~ ~~ 1...~..~--
~ _ ~ 2 2 or Vl - ~ ,
then Vl ' ~ 2 k "' ' '~ ~
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. x'0.0025
,,IN "1 ~ ~ pr w" -~ ~ u?~ ~~
r
`~1 INS ~~ ~'i M ~r ~ a
'M~ ~i' 4~~1 L110 .
het ua calculate the linear rate of diffusion of A1~Mg~ ~.nta
ma nesium usin the constant k previously determined, For d.hours
g g
in the furnace the linear rate of diffusion wi11 be
V
~~
for 24 hours: V~=
for 48 hours: Vl
for g6 hours: V1
0,~~
O,oS ~ 0,0
O,j
mm
day.
-7 cm
0,57g.10 sec
a. J .~ n r1 I A 7~ r~
~ ti ~ . Q02~~_...,
v~,~, ?~
2' ..
`, 2
t ~,`0 , 002 ~
2'~
for 120 hours: Vl
for 1~+4 hours : V1
o.a~5
~tilo,oo~5
mm
day = o,~;~~,10
~ - 7 cm
O , ol7"r dya ~ 0.20 , to s-...._-_
~ - 7 cm
0.0125 d Y = O.1~~.10 s~
r r
o . oll~ d = o .12g , lo----~--
y
~~ 5
w ~ .1~~0.0025
7 cm
0,0102 d ~ 0.118.10 sec
Y
These values are graphically represented in Figure l7, It is
necessary to remember that each value, calculated by this method,
~A~x?resents the rate of Al Mg diffusion in the zone. of solid solu-
3~
bons at temperature of ~20o C.
CONCLUSIONS
The following conclusions may be drawn on the basis of this
investigation: (L) A method was developed for establishing contact
between intermetallic compound A1~ Mgt and solid magnesium to in-
vestigate the processes of diffusion of Al3Mg~ into magnesium,
(2) The diffusion of .one component. into another, being connected
with the formation of new phases, is a complex phenornenon,~ The proc-
~ess proceeds in two antipac3?al c~irec~iohs . With an increase of time
ela sed decomposition of the eutectic into its"basic components takes
p ~
place, an increase of the zone of solid solution A1~ Mg~,~~..... Mg and
separation of its second component A1~Mg~ into a structurally-free
constituent oGCLU~s. (3) The relationship was established between
r
the de th of penetration (mainly for the zone of solid solution) and "
p
time., It was found :that the penetration depth, as a function of time,..
~, ,~ ~~;
fir,
I; ~,
'' ?t rr p
C i. a l
e 1j
-16-
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For the zone of solid solution is in good agreement with Fick's 1.aw,
(~+) On the bas~.s of Fick's law, the liner rate oi' dii'i'usion o:f
Al3Mg4 in magnesium was determined for the zo~ae of solid solut~.on
at a temperature of 420? C. ;5) The linear rate of di~'fusion and
effect of the ~~.me factor on penetration are at ?~heir maximum dur-
ing the initial 10-16 hours. This period is most appropriate for
.production processes, such as homogenizing, holding at hardening
temperature, etc.
The present investigation puts Forward a number of new prob-
lems, such as the rate of diffusion not only in cast but also in
deformed magnesium, influence o~~ the grain size of magnesium on
diffusion and also the efFsct of the. crystalline lattice of a dif
fusing component on the process of diffusion, Works on these prob-
lems are scheduled for 139.
-END-
Captions far Illustrations
Figure 1. Magnif ication x 50
~Fi ure 2. Magnif ication x 150
g
Figure 3. Magnification x230
Figti~re 4. Magnif ication x 150
Figure 5. Formation of the Intermetallic Compound A13Mg4 Between
Magnesium and A11~rninum
Figure 6.
7~
Figure ~.
Figure g.
Figure J.O.
Figure 11.
Figure l2.
Magnification x 150
Magnif ication x 150
Without Heat Treatment x 132.5
held in the Furnace at 420a C f or 5 hours x 132.5
JIeld in the Furnace at 420o C for 5 hours x 425
Held in the Furnace at .420? C for 25 hours x 132,5
Held in the Furnace at 420o C f or 50 hours x:132.5
L,, s,.
i \.l
.; ;~ ,~ ~, .~ a
+~ 41~ ? YJ ;r X17 JI
l7
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_.
F~gu~e ~3, ~s~,d ~n the Fuxnace a~ ~2Q" C ~'ax ~.~~ Hauxs x ~.3~,~
Figure ].~+, H~~.d in the Fuxnact~ a~ ~~0? C ~'ox 1.50 Houxs x 132,E
Figure 15, Held in the Fuxnace a~ ~20a C ~'or 1~0 I~auxs x ~2~
Figure ].6
Figure 17