`#2010 The Japan Institute of Metals
`
`Diffusion of Aluminum in
`
`Sung-Yul Lee1, Osamu Taguchi2;* and Yoshiaki Iijima3
`
`1Department of Marine Equipment Engineering, College of Engineering, Korea Maritime University, Pusan 606 791, Korea
`2Department of Materials Science and Engineering, Miyagi National College of Technology, Natori 981 1239, Japan
`3Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980 8579, Japan
`
`Interdiffusion coefficient ~DD in the
`1823 K with (pure Ti) (Ti 8.5 at% Al alloy), (pure Ti) (Ti 16.5 at% Al alloy) and (Ti 8.5 at% Al alloy) (Ti 16.5 at% Al alloy) couples. In the
`whole temperature range the value of ~DD increases gradually with increasing aluminum content. The Arrhenius plot of ~DD up to 6 at% Al shows an
`upward curvature similar to that recognized in the self diffusion in
`is nearly linear in the concentration more than 10 at% Al. The activation energies for the impurity diffusion in
`of radius of the diffusing atom. This suggests that the size effect is dominant in the impurity diffusion in
`[doi:10.2320/matertrans.M2010225]
`
`(Received July 2, 2010; Accepted July 27, 2010; Published September 8, 2010)
`
`Keywords: aluminum diffusion in
`
`1.
`
`Introduction
`
`It is well known that the IVb metals (Ti, Zr and Hf) and
`their alloys in the b.c.c. phase show a so-called anomalous
`diffusion behavior which can be characterized by a signifi-
`cant upward curvature in the Arrhenius plot of the diffusion
`coefficients.1) This behavior has been explained by the model
`of phonon-assisted diffusion jumps via monovacancies by
`Ko¨hler and Herzig.2,3) They have proposed a mechanism
`of temperature dependence of the self-diffusion coefficient
`taking into account a temperature-dependent migration
`energy of a vacancy on the basis of the experimental
`evidence of significant lattice softening of the longitudinal
`acoustic (LA) phonon in the h111i direction at the reduced
`wave vector 2/3, LA2/3h111i phonon, in
`3h111i phonon mode in the b.c.c. lattice is directly related to
`the nearest-neighbor jump process of the diffusing atom,
`because its displacement pattern facilitates the promotion of
`the migrating central atom through the saddle point into the
`position of the vacancy. Therefore the softening of this
`phonon mode results in a reduction in the restoring forces in
`the h111i direction and in an overall decrease in the free
`energy GM of atomic migration. Furthermore, investigations
`on the phonon dispersion in IVb metals,
`Hf,7) have revealed a considerable softening of the transverse
`acoustic (TA) T1A1/2h110i phonon with decreasing temper-
`ature in addition to the significant softening of the LA2/
`3h111i phonon with negligible temperature dependence.
`These observations support strongly the mechanism by
`Ko¨hler and Herzig.2,3) Besides the atomic displacement in
`the jump direction the importance of
`the concomitant
`displacements of the triangular configuration of the saddle-
`point atoms has been pointed out.3) An opening motion of the
`saddle-point atoms perpendicular to the jump direction
`decreases the potential barrier for the jump. Such a ‘breath-
`ing’ is partly achieved by the LA2/3h111i phonon and partly
`by the T1A1/2h110i phonon.8,9) The degree of softening of
`
`*Present address: Professor Emeritus, Miyagi National College of
`Technology. Corresponding author, E mail: mniotaosm@yahoo.co.jp
`
`the LA2/3h111i and T1A1/2h110i phonons correlates with
`the activation energy for self-diffusion in the
`metals.
`According to Ko¨hler and Herzig,2) GM in the anomalous
`b.c.c. metals is expressed by
`ð1Þ
`GM ¼ G0
`Mð1 T0=TÞ;
`M is the free energy of migration of a monovacancy
`where G0
`and T0 is the hypothetical lowest temperature for the metal to
`hold the b.c.c. structure. If the lattice is completely softened
`at T0, the frequency of LA2/3h111i would diminish to zero,
`then GM would diminish to zero. Thus the temperature
`dependence of the diffusion coefficient D in the anomalous
`b.c.c. metals should be expressed by
`ð2Þ
`MT0=RT 2Þ;
`D ¼ D0 expð Q=RTÞ expðG0
`where D0 and Q are the preexponential factor and the
`activation energy, respectively, for the monovacancy mech-
`anism. The extent of deviation from the linearity in the
`Arrhenius plot of the diffusion coefficient is represented by
`MT0=RT 2Þ in eq. (2). A similar equation to
`the term expðG0
`eq. (2) has been obtained by Sanchez and de Fontaine10,11) on
`the basis of the ! embryo model where the ! embryo in the
`transition from the
`structure as the activated complex, and the ! embryo is also
`regarded as a lattice in significantly softened state of the
`LA2/3h111i phonon.
`In our previous studies on the impurity diffusion of
`transition elements (Cr and Pd),12) Ib elements (Cu,13) Ag13)
`and Au14)), IIIb elements (Ga and In)15) and IVb elements (Si,
`Ge and Sn)16) in
`well, and it has been recognized that the activation energies
`for the impurity diffusion and self-diffusion2) in
`proportional
`to the square of the atomic radius of the
`diffusing atom. In the present work, diffusion behavior of IIIb
`element Al in
`diffusion coefficients of Al in
`Araki et al.17) and Ko¨ppers et al.,18) the diffusion parameters
`in eq. (2) have not been determined. In all the
`dilute alloys of Ti with Cr, Pd, Cu, Ag, Au, Ga, In, Si, Ge
`
`Page 1 of 5
`
`Tianma Exhibit 1015
`
`
`
`1810
`
`s. Y. Lee, 0. Taguchi and Y. lijima
`
`and Sn, the interdiffrrsion coefficient 13 is independent of
`concentration of solute.'2"6) On the other hand, D~ in the fi-
`phase up to 2 at% A1 of Ti-Al alloys increases with increasing
`Al content)" Then it is interesting to examine whether the
`curvature of the Arrhenius plot of 15 depends on the Al
`content in the fl-phase.
`In the present work, interdiffusion experiments with the
`couples of pure Ti and the fi-phase Ti-Al alloys containing
`8.5 and 16.5 at% Al have been made. The impurity diffusion
`coefficient of Al in fl-Ti has been determined by applying
`Darken’s relation,” i.e.
`the extrapolated value of the
`interdiffusion coefficient to the infinite dilution of the solute
`
`can be regarded as the impurity diffusion coefficient of the
`solute in fl-Ti. This method is effective to avoid some
`troubles such as chemical reaction on the surface of reactive
`
`Ti specimen with radiotracer diffusion experiments. Further-
`more, this is especially useful in determining the impurity
`diffusion coefficient of element, such as Al for which the
`
`tracer diffusion experiment with a radioactive isotope is not
`easy.
`
`2. Experimental Procedure
`
`Pure rods 12mm in diameter and 100 mm in length were
`machined from a Ti bar 160mm in diameter supplied by
`Kobe Steel Ltd. The main impurities in this material were
`0.046 mass% Fe, 0.0032 mass% N and 0.0041 mass% 0. The
`
`rods were polished chemically, sealed in quartz tube with
`high-purity Ar gas and then annealed at 1373 K for 172.8ks
`(2 days) to cause grain growth. Alumina rings (higher than
`99% purity) were fitted at both ends of the rod to prevent
`reaction with the quartz tube. The resultant grain size was
`about 3 mm. The rod was cut to make disc specimens 5 mm in
`thickness. To obtain a fully flat surface, the specimen was set
`in a stainless steel holder 50mm in diameter, ground on
`abrasive papers and polished on a buff with fine alumina
`paste.
`Buttons of Ti-85 and 16.5 at% Al alloys were made by Ar
`arc melting the pure Ti block with Al blocks of 99.999%
`purity. To homogenize the buttons,
`the arc melting was
`repeated a few times. Finally, the buttons were cast into a
`water-cooled copper boat to make a rod ingot 10mm in
`diameter and 80 mm in length. The resultant grain size in
`alloy rods after the same grain growth treatment as described
`above was about 2 mm. The alloy rods were cut to make disc
`specimens 5 mm in thickness. The cut surface of the alloy
`specimen was ground and polished in the same way as the
`pure Ti specimen.
`To make the semi-infinite interdiffusion couple the pure Ti
`and the alloy discs were put in a stainless steel holder with
`two screws, pressed by the screws, wrapped with a V foil,
`surrounded by Ti sponges and then diffusion welded by
`heating at 1073 K for 3.6ks in a stream of high-purity Ar gas.
`After the diffusion welding, the couple was removed from the
`holder and put into alumina tube; then the alumina tube
`containing the couple was sealed in a quartz tube with the
`high-purity Ar gas. By putting the quartz tube in a fumace,
`diffusion annealing was carried out at temperatures in the
`range from 1323 to 1823 K for between 3.6 and 691 ks (l h to
`80 d). At the temperatures higher than 1773 K, the diffusion
`
`time has been corrected taking account of the amount of
`diffusion occurred during heating the specimen from room
`temperature to the diffusion temperature.” For diffusion
`above 1673 K, the alumina tube containing the couple was
`sealed in double tubes of quartz, keeping the inner quartz
`tube from cmshing by adjusting the pressure of Ar gas
`between the inner and outer tubes. The diffusion temperature
`was controlled to within :l:1 K at 1323 1473 K and to within
`21:3 K at 1673 1823 K.
`
`After the diffusion, the couple was cut to parallel to the
`diffusion direction, and the cut surface was polished on a buff
`with fine alumina paste to examine the concentration-
`penetration profiles with an electron probe microanalyzer.
`The concentration of Al was determined by using the ZAF
`method. The interdiffusion coefficient was calculated as a
`
`function of solute concentration by Matano’s method?”
`
`3. Results and Discumion
`
`shows the concentration dependence of the
`Figure 1
`interdiffrsion coefficient 5 determined in the temperature
`range 1323 to 1823K with (pure Ti)—(Ti-8.5 at% Al alloy)
`couple and in the temperature range 1423 to 1673K with
`(pure Ti)—(Ti-16.5 at% Al alloy) couple and in the temper-
`ature range 1473 to 1573K with (Ti-8.5 at% Al alloy)-('1‘i-
`16.5 at% Al alloy) couple. The interdiffmion coefficients
`shown in the present work include the experimental error of
`10 to 15%. Interdiffusion coefficients determined for differ-
`
`ent diffusion times are shown distinguishably from each other
`by different marks. As shown in Fig. l, at each temperature 5
`is independent of diffusion time and 15 increases almost
`linearly with increasing A1 content. According to Darken‘s
`relation, '9’ the extrapolated value of 13 to the infinite dilution
`of A1 can be regarded as the impurity diffusion coefficient
`
`
`
`Interditfuscncoefficient.5Ims"
`
`10‘”
`
`O O D (“Hr-43.5 at% Al) couple
`A A (11H16.5 at% Al) couple
`V (no.5 at% AIH16.5 at% Al) cowle
`
`
`
`1 0.13
`
`0
`
`2
`
`4
`
`6 8101214161820
`
`Concentration of Al / at%
`
`1 Concentration dependence of interdif’fusion coefficient 1) in Ti Al
`Fig.
`alloys.
`
`Page 2 of 5
`
`
`
`Diffusion of Aluminum in fl Titanium
`
`1811
`
`Table l Diffusion coefficien of Al in fl Ti.
`
`Temperature/K
`
`Diffusion coet’ficient/mz-s—l
`
`5x10“
`
`_
`
`11
`
`10
`
`10'12
`
`10‘13
`
`
`
`5x10“
`5.0
`
`5.5
`
`6.0
`
`6.5
`
`7.0
`
`7.5
`
`8.0
`
`Temperature, T" / 10“K'1
`
`:1»
`\
`E
`,Q—
`9
`.2
`3:
`
`E.
`
`0 8I
`
`: §
`
`25
`‘2
`
`2s
`
`Fig. 3 Temperature dependence of interdiffusion coefficient D.
`
`Table 2 Diffusion parameters, Do, Q and GoMTo.
`Concentration
`of Al/at%
`0
`2
`6
`10
`12
`
`Do/mZ-s‘l
`(3.03:3) x rtr‘
`(3.9133) x 1(r5
`(5.311393) x 10“
`(7.021;???) x 10v7
`(7.461%) x no?
`
`Q/kJ-mol"
`331.6 i 163
`275.3 i 28.7
`220.8 i 43.6
`163.9 i 27
`162.3 i 3.2
`
`GoMTo/MJ-mol"l(
`125.6 :E 11.9
`82.1 :t 22.1
`42.3 :t 33.5
`
`1823
`1773
`1723
`1673
`1623
`1573
`1523
`1473
`1423
`1373
`1323
`
`10-10
`
`(8.68:1: 1.02) x 10-'2
`(5.91 :1: 0.50) x 10-'2
`(4.26:1: 0.29) x 10-'2
`(3.21 :1: 0.42) x 10-'2
`(1.94 :l: 0.47) x 10-'2
`(1.33 :l: 0.19) x 10-'2
`(8.98 :I: 0.13) x 10-'3
`(5.76:|: 0.12) x 10-'3
`(3.61 :i: 0.63) x 10-'3
`(2.12:1:0.3l) x 10-'3
`(1.31:1:0.15)x10‘l3
`
`— self diff. of T1 in fl-TI
`Impurity diff. of Al in D-Ti
`0 Present work
`El Araki ef al.
`
`A K6ppers et al.
`
`.1u
`
`Diffusioncoefficient,0/ms" ddoq,1;::
`
`d an
`
`10'"
`45678910
`
`Temperature, T" / 10“K‘1
`
`Fig. 2 Temperature dependence of impurity diffusion coefficients of A1
`and self diffusion coefficient in fl Ti.
`
`D,“ of Al in fi-Ti. The values of D,“ determined in this way,
`using the linear fitting function, are listed in Table 1.
`Figure 2 shows the temperature dependence of the impu-
`rity diffmion coefficient DA. obtained by the present work
`along with those by Araki et al.17’ and K6ppers et aLm The
`value of D,“ by the latter are taken from the figure given by
`Mishin and Her-zigm The temperature dependence of DA.
`obtained by these three groups shows excellent agreement
`each other and can be expressed by a single line as follows;
`
`I)... = (3.03 + 2.85/—1.47) x 10 4
`x exp(—331.6 :t 16.3 kJ-mol
`
`l/RT)
`
`xexp(l25.6:l:ll.9MJ-mol
`
`l#212) m2-s '
`
`(3)
`
`As shown in Fig. 2, the value of DA. is about one half of the
`self-diffusion coefficient 011 of Ti in the whole temperature
`range of the fi-phase. The softening of the LA2/3(l l 1) and
`T.A1/2(110) phonons increases the diffusion coefficient DA.
`of Al by the factor exp( 125.6 MJ-mol
`' /RT2). The values of
`this factor at the melting temperature of Ti (Tm = 1943 K)
`and the fl—a transformation temperature of Ti
`(T13 0, =
`
`1155 K) are 54.7 and 8.3 x 104, respectively. The corre-
`sponding values for self-diffusion in Ti are 61 and 1.1 x 105,
`respectively.
`Figure 3 shows the temperature dependence of the
`interdiffmion coefficient 5 at 0, 2, 6, 10 and 12at% A1. At
`2 and 6at% Al the temperature dependence of 5 shows a
`similar upward curvature to those of DA. and D“. At 6 at% Al
`the curvature in Fig. 3 is small. At 10 and 12at% Al the
`Arrhenius plots show almost linearity. Then, the diffusion
`parameters in eq. (2) are calculated for each concentration
`of Al and listed in Table 2. The activation energy Q
`decreases with increasing Al content. Furthermore, the term
`exp(GoMTo/RTZ) which represents the extent of deviation
`from the linearity in Arrhenius plot decreases also with
`increasing A] content and it becomes nearly zero at 10 at%
`A1. This suggests that the phonon softening in the fl-phase of
`Ti-Al alloy becomes weak with increasing A1 content.
`It is interesting to examine the relationship between GoM To
`and Q for diffusion in fl-Ti. Since Q is the sum of enthalpy
`110': of formation and the enthalpy Ho“ of migration of a
`monovacancy, GoMTo can be written as
`
`GoMTo = ("0M — TSOMWO
`
`= (Q — HoF)T0 — TosoMT,
`
`(4)
`
`where So” is the entropy of migration of a monovacancy.
`According to Sanchez?” the term ToSoM is negligible
`
`Page 3 of 5
`
`
`
`1812
`
`s. Y. Lee. 0. Taguchi and Y. lijima
`
`500
`
`180
`
`160
`
`140
`
`120
`
`100
`
`200
`
`100
`1 .0
`
`1 .5
`
`2.0
`
`2.5
`
`3.0
`
`r2 I 10mm2
`
`Fig 5 Conelation between activation energy Q for diffusion against
`squarer2 d" radius ofdiffusing atoms in fi Ti.
`
`A(T,p)e2 is significant, and the normal monovacancy
`mechanism operates for the diffusion; then
`
`G...(T >> T...) 8 A82 = 00“ = Ho” - mo”.
`
`(7)
`
`From theoretical considerations?” it has been supported that
`Tp a > T", > To. In the process of formation of the w-phase
`of the h.c.p. structure from b.c.c.
`fi-Ti by the lattice
`displacement in the (111) direction, the intrinsic strain due
`to an activated configuration contributing to the transforma-
`tion to the arphase comes about 3.5% in the direction [121]
`in the fl-phme. However, if the atomic radius of one of the
`two atoms located on the unit cell of the w—phase is larger by
`1.7% than that of the other atom, the intrinsic strain in the
`
`w-phase must be just cancelled out, and 8 becomes unity.
`Furthermore, in the activated configuration the b.c.c. struc-
`ture becomes unstable, and the migration energy of an
`activated atom to the nearest-neighbor vacancy becomes a
`maximum If the radius r of the diffusing impurity atom is
`smaller than 1.017 times the radius r... of the solvent atom, the
`
`parameter s can be represented by
`
`s = r/l.017 rm(r 5 1.017 rm)
`
`(8)
`
`
`
`TolMJmor‘K 8
`
`62” 8
`
`-20
`100150200250300350400450500
`
`0/ kJmol'1
`
`Fig. 4 Correlation between GoMTo and Q.
`
`compared with Ho” (= Q — HoF). Because we are concerned
`with fi-Ti, Tfi n,(= 1155 K) < T < T...(= 1943 K), and To is
`estimated to be 610K as described below. Thus the second
`
`term of the right-hand side in eq. (4) is much smaller than the
`first term. Then GoM To increases with increasing activation
`energy Q. As shown in Fig. 4, this is recognized by the
`experimental results of Sc?” V3“) Ta,25’ W26) and Zr”)
`including results of present authors'““ and a linear relation
`
`GoMTo (MJ-mol
`
`'K)=0.610[Q(kJ-mol l)—129] (5)
`
`indicating that 110': does not depend on the
`is obtained,
`element. The value of 110':
`is estimated to be 129:1:14
`kJ-mol
`' by extrapolating GoMTo to zero in Fig. 4. From the
`slope of the straight line in Fig. 4, To is estimated to be
`(610 :l: 26) K. This means that the activation energy Q for
`the impurity diffusion in fl-Ti is controlled by the value of
`HoM rather than by HoF. The magnitude of HoM should be
`connected with the ‘breathing’ motion of the saddle-point
`atoms and thus correlated with the size of diffusing atom.
`Now, we examine Ho” for impurity diffusion in fi-Ti.
`According to Sanchez and de Fontaine,‘°) the free energy G,,,
`of formation of the an embryo (or the activated complex), is
`correlated with the transforming parameter s, from the [3-
`phase to the w—phase by
`
`G... =A(T.p):s2 —B(T,p)e3.
`
`(6)
`
`and, for the impurity atom larger than 1.017 r...,
`
`where A(T, p) and B(T, p) are functions of the temperature T
`and pressure p. The transforming parameter s is proportional
`to the atomic displacement
`in the fl-phase lattice which
`participates in the formation of the w embryo?” s = 0 in
`the b.c.c. structure, but a = l in the transformed lattice (a)-
`phase). The driving force for the transformation expressed by
`the second term B(T, p)r-:3 is negligible at high temperatures
`but increases with decreasing temperature. On the other hand,
`in a temperature range much higher than the highest
`temperature T,” for the w—phase to exist only the first term
`
`s = l — (r— 1.017rm)/1.017rm(r 2 1.017 r...)
`
`(9)
`
`From eqs. (7) (9), it can be concluded that the migration
`enthalpy of an impurity in the direction [121] is proportional
`to the square of the radius of the impurity atom. As the
`coordination number in the b.c.c. structure of the fi-Ti is
`eight, the atomic radius of the metal of different structure
`from the b.c.c. is converted for a coordination number of
`
`eight by the conversion relation”) As shown in Fig. 5,
`for r 5 1.017 rm, Q increases linearly with increasing r2,
`although the value of Q for W is much higher those for the
`
`Page 4 of 5
`
`
`
`Diffusion of Aluminum in
`
`1813
`
`other elements and, for r 1:017 rm, Q decreases with
`M
`increasing r2. This is consistent with the prediction that H0
`(¼ Q H0
`F) is proportional to r2, as deduced from eqs. (7)
`(9). Thus, it must be emphasized that the size effect is
`dominant in the impurity diffusion in
`
`4. Conclusions
`
`The present experimental results show the Arrhenius plot
`of the impurity diffusion coefficient of Al in
`temperature range 1323 1823 K exhibit an upward curvature.
`This can be explained by a monovacancy mechanism with
`a temperature-dependent migration energy due to softening
`of the LA2/3h111i and T1A1/2h110i phonons in the
`Further,
`the weak curvature of the Arrhenius plots of
`interdiffusion coefficient in the
`than 6 at% Al has been observed. The activation energy for
`the impurity diffusion and self-diffusion in
`tional to the square of the radius of the diffusing atom.
`
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