Interdiffusion in the Mg-Al System and Intrinsic Diffusion in b-Mg2Al3 SARAH BRENNAN, KATRINA BERMUDEZ, NAGRAJ S. KULKARNI, and YONGHO SOHN Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96 pct) and Al (99.999 pct). Diffusion anneals were carried out at 573 K, 623 K and 673 K (300 C, 350 C and 400 C) for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopes were used to identify the formation of the intermetallic phases, c-Mg17Al12, and b-Mg2Al3, as well as the absence of the e-Mg23Al30 in the diffusion couples. The thicknesses of the c-Mg17Al12 and b-Mg2Al3 phases were measured and the parabolic growth constants were calculated to determine the activation energies for growth. Concentration profiles were determined with electron microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, c-Mg17Al12, b-Mg2Al3, and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Integrated and average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the b-Mg2Al3 phase, followed by c-Mg17Al12, Al-solid solution, and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann’s analysis (e.g., marker plane) were determined for the ~ Mg-62 at. pct Al in the b-Mg2Al3 phase. Activation energies and the pre-exponential factors for the interdiffusion and intrinsic diffusion coefficients were calculated for the temperature range examined. The b-Mg2Al3 phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the b-Mg2Al3 phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared with the available self-diffusion and impurity diffusion data from the literature. Thermodynamic factor, tracer diffusion coefficients, and atomic mobilities at the marker plane composition were approximated using the available literature values of Mg activity in the b-Mg2Al3 phase. DOI: 10.1007/s11661-012-1248-8 The Minerals, Metals & Materials Society and ASM International 2012
I.
INTRODUCTION
THE necessity to increase efficiency through weight reduction has stimulated research in lightweight materials. Magnesium (Mg) alloys are the lightest alloys available for electronic, military, and transportation applications.[1–7] Knowledge of reliable diffusion properties can aid in designing, processing, manufacturing, and understanding the degradation of new and existing alloys. Despite the great potential for many applications, the diffusion properties for Mg and Mg-alloys are scarce and predate the recent interest. A compilation on most of the available tracer and self-diffusion data in Mg was provided by Fujikawa in 1992.[8] Recently, the diffusion of rare-earth elements in Mg has been explored[9,10] SARAH BRENNAN, Graduate Research Assistant, KATRINA BERMUDEZ, Undergraduate Research Assistant, and YONGHO SOHN, Professor, are with the Department of Mechanical, Materials and Aerospace Engineering, Advanced Materials Processing and Analysis Center, University of Central Florida, Orlando, FL 32816. Contact e-mail:
[email protected] NAGRAJ S. KULKARNI, R&D Staff, is with the Measurement Science & Systems Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831. Manuscript submitted May 24, 2011. Article published online June 27, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
because of their ability to improve the strength and creep resistance of Mg alloys. In this investigation, Mg vs Al interdiffusion was examined by using solid-to-solid diffusion couples. Al is the most common alloying element in commercial Mg-alloys. In contrast, Mg is one of the common alloying elements in commercial Al-alloys. Experimental observations and analyses were carried out with due respect for previous studies on Mg-Al interdiffusion[11–13] wherein some discrepancies in microstructural features are identified, and composition-dependence of interdiffusion coefficients was not fully reported. The thicknesses of each phase were measured via image analysis to determine the parabolic growth constants and activation energies for growth. Composition-dependent interdiffusion coefficients in Mg- and Al-solid solutions (ss), c-Mg17Al12 and b-Mg2Al3 phases were calculated based on the Boltzmann-Matano analysis with due consideration for molar volume differences in each phase. Integrated and average effective interdiffusion coefficients in each of the phases present were also calculated. An identifiable Kirkendall marker plane located in the b-Mg2Al3 phase was used, in conjunction with the concentration profile, to determine the intrinsic diffusion coefficients of Mg and Al in the b-Mg2Al3 phase. Activation energies and pre-exponential factors VOLUME 43A, NOVEMBER 2012—4043
for the interdiffusion and intrinsic diffusion coefficients were also calculated. Furthermore, using the concentration-dependent interdiffusion behavior, estimations of the impurity diffusion coefficients in both terminal solid solutions were carried out via extrapolations. Thermodynamic factors, tracer diffusion coefficients, and mobilities at the marker plane in the b-Mg2Al3 phase were also calculated using activities of Mg available in literature via first-principle calculations.[14]
II.
~int ¼ D i
A. Growth of Intermetallic Phases For diffusion-controlled growth of a phase with a semi-infinite boundary condition, thickness of the growing phase after time t of diffusion anneal can be described by[15]:
½5
Ji dx ~int xi D i ¼ þxi ði ¼ Mg or AlÞ i I i Ci Cx Cþx Cx i i i
½6
i i where Cx and Cþx refer to solubility limits of a relei i vant phase. Combining Eq. [4] and Fick’s law yields the relation
1 2t
~i ¼ D
RCi
ðx xo ÞdCi
C1 i
ði ¼ Mg or AlÞ
@Ci @x
½7
½1
where Y is the thickness of the layer and kp is the parabolic growth constant. Typically, the temperature dependence of the parabolic growth rate constant should follow the Arrhenius relation expressed by Qk kp ¼ ko exp ½2 RT where R is the ideal gas constant, Qk is the activation energy of growth, and T is the annealing temperature in Kelvin. In this study, the growth of c-Mg17Al12 and bMg2Al3 intermetallic phases is assumed to be diffusion controlled for initial analysis based on previous experimental results.[11,13] B. Interdiffusion and Intrinsic Diffusion In this study, the Boltzmann-Matano method[16,17] was employed to determine the interdiffusion fluxes of individual components and the interdiffusion coefficients as a function of composition. The location of the Matano plane xo was found by numerical integration of the concentration profiles to satisfy Z Co Z C1 i i xdCi þ xdCi ¼ 0 ði ¼ Mg or AlÞ ½3 Cþ1 i
Ji dx ði ¼ Mg or AlÞ
xi
þx Ri
2
Y kp ¼ 2t
þxi
where +xi and –xi refer to the location of interfaces corresponding to the solubility limits of each phase. ~int can also be employed to define the average The D i effective interdiffusion coefficients for each phase using the relation[19]
~eff ¼ D i
ANALYTICAL FRAMEWORK FOR DIFFUSION
Z
Using Eq. [7], composition-dependent interdiffusion coefficients were calculated for each phase. The interdiffusion coefficients defined in Eqs. [5] through [7] also follow the Arrhenius relation. The intrinsic diffusion coefficients for component i were calculated based on accumulated intrinsic fluxes determined from the location of the marker plane xm via Heumann’s method.[20] The accumulated intrinsic flux Ai is defined by Z t Z Cxm i Ai ¼ Ji dt ¼ xdCi ði ¼ Mg or AlÞ ½8 C1 i
0
where Cxi m is the composition at xm. Determination of the accumulated intrinsic diffusion flux for component i allows for the calculation of the intrinsic diffusion coefficients at the marker plane using the relation Di ¼
2t
Ai @C i
ði ¼ Mg or AlÞ
½9
@x xm
After the determination of the interdiffusion and intrinsic diffusion coefficients, the pre-exponential factor Do and the activation energy Qi were found using the Arrhenius relation.
Coi
where x is the distance, Coi is the concentration of a and C-¥ component i at the Matano plane, and C+¥ i i are the concentrations of a component i at the terminal ends. The interdiffusion flux J~i : for each component was calculated using the relation[18] Z 1 Ci J~i ¼ ðx xo ÞdCi ði ¼ Mg or AlÞ ½4 2t C1 i Profiles of the interdiffusion flux of Mg and Al can be employed to determine the integrated interdiffusion ~int defined as[19] coefficients, D i 4044—VOLUME 43A, NOVEMBER 2012
III.
EXPERIMENTAL PROCEDURE
Polycrystalline Mg (99.96 pct) and Al (99.999 pct) from SCI Engineered Materials, Inc. (Columbus, OH) and Alfa Aesar (Ward Hill, MA), respectively, were sectioned into disks, 10 mm in diameter and 2 mm in thickness. These polycrystalline metals typically had grain sizes ranging from 30 to 60 lm. For the assembly of diffusion couples, the disk specimens were metallographically prepared, starting with 600-grit SiC paper and finishing with 1-lm alumina suspension. A nonoxidizing lubricant was used at each stage of preparation METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 1—A schematic illustration of the diffusion couple assembly.
for both Mg and Al. Any contact with water was eliminated for the entire preparation process. The diffusion couples, Mg vs Al, were then assembled with 2-mm-thick Al2O3 spacers in stainless steel (i.e., Kovar) jigs as illustrated schematically in Figure 1. In this experimental setup, there is no applied pressure during anneal, except for the compression caused by thermal expansion of Mg and Al during the initial heatup. Relaxation of soft pure metals (i.e., Mg and Al) after the initial stages of heating should remove any pressure effect on the diffusion process (e.g., annealed for days). Each jig assembly was placed in a quartz capsule that was repeatedly evacuated to ~104 Pa (106 torr) with hydrogen and argon (i.e., ultrahigh purity) flushes between each evacuation. Before the final seal, the capsule was backfilled with ultrahigh purity argon and hydrogen (
