The Diffusivity of Ni in Fe-Ni and Fe-Ni-P Martensites - Semantic Scholar
Authors Copy
The Diffusivity of Ni in Fe-Ni and Fe-Ni-P Martensites A. D. ROMIG, JR. AND J. I. GOLDSTEIN The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensite, D”, has been determined between 700 and 300 °C using electron microprobe (EMP) and scanning transmission electron microscope (STEM) techniques. Alloys of various bulk compositions (0 to 30 wt pct Ni, Fe) were homogenized in the single phase austenite (Y-fcc) field and quenched to form martensite, 02 (bce). Appropriate alloys were tempered isothermally at 300 to 700 °C. The y nucleated and grew in the parent 02. The composition of the y phase and the concentration gradients in the 02 were measured with the EMP and/or STEM. In order to determine D, experimentally measured Ni concentration gradients were matched to Ni concentration gradients calculated by a simulation model. The calculated gradients were obtained by solving the appropriate form of Fick’s second law using the Crank-Nicholson numerical technique. The observed diffusivities varied with temperature. Above approximately 410 °C, = (4.25 x l0) exp (—49,000/RT) em2/s while below 410 °C, D = (2.27 X l0’) exp (— 10,600/R T) cm2/s. The effect of P is to increase the Fe-Ni diffusivities at any temperature by the factor (1 + 1.27 C, + 0.623 C) where C is the amount of P (wt pet) in 02. The discontinuous diffusion behavior of D’ is attributable to the high dislocation density of the 02. Above approximately 410 °C lattice diffusion is dominant while below 410 °C dislocation pipe diffusion is dominant.
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‘VVTHEN Fe-Ni austenite (y-fcc) is cooled from the single phase y region into the two-phase o + y field the ferrite (o-bcc) will not nucleate.’ Rather the y phase will transform by a martensitic reaction to 02 (bce).2 The martensite, 02, has the same crystal structure as the equilibrium n phase, but has the composition of the parent y-phase and a high defect density.3 The tem perature at which the martensite reaction starts and finishes is a function of Ni content.2 The nature of the diffusionless transformation of Fe-Ni alloys, which occurs upon quenching from the austenite field, has been summarized by Owen, et at.4 Pure binary alloys which contain up to 5.2 wt pet Ni will not transform to martensite upon quenching. The transformation prod uct is equiaxed ferrite. However, the equiaxed ferrite l02 lines/cm2). structure is heavily dislocated (10’’ Carbon levels as low as 100 ppm will cause a martensite transformation to occur even in the low Ni alloys. For Ni contents between 10.5 and 30 wt pet, quenching at rates >0.08 °C/s will transform austenite to massive martensite. The transformation is accompanied by a shape change, and produces a heavily deformed and dislocated structure. Alloys containing 30 to 34 wt pet Ni transform to classical aceicular martensite. For Ni contents between 5.2 and 10.5 wt pet, the structure is a mixture of equiaxed ferrite and massive martensite. If the 02 is subsequently tempered the Ni-rich y phase will nucleate and grow into the parent 02 phase. If the growth of the austenite is volume diffusion controlled, a Ni gradient will form in the supersaturated 02 phase. In —
A. D. ROMIG, JR., formerly Research Assistant in the Depart ment of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA is now at Sandia Corporation, Albuquerque, NM 87115. J. I. GOLDSTEIN is T. L. Diamond Professor of Metallurgy, Department of Metallurgy and Materials Engineering, Whitaker Lab. no. 5, Lehigh University, Bethlehem, PA 18015. Manuscr,pt submitted February 11, 1980.
METALLURGICALTRANSACTIONSA
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addition the parent phase will contain the dislocation structure of the original 02. Several investigators have measured the diffusivity of Ni in pure a iron,5’6 DJ1, and in a Fe-Ni7 containing P above 600 °C. The diffusivity of Ni in 02, D’, however, has not been measured. In a companion study Romig and Goldstein8 have determined the Ni solubility limits of a and y phases in the Fe-Ni and Fe-Ni-P systems. In that study a and phases were produced by tempering 02 at temperatures from 300 to 700 °C. The amount of y-austenite phase growth was much greater than that which was calcu lated if the growth was controlled by diffusion in the a phase. This result argues that the diffusivity of 02 may be significantly higher than that of a. It is the purpose of this study to measure D1 and to investigate the effect of dislocation structure on diffusivity. ‘
EXPERIMENTAL PROCEDURE for volume diffusion controlled growth, the size of the precipitate and the concentration gradient in the matrix phase are a function of four factors: the bulk alloy composition, the solubility limits of the equilib rium phases, the length of the diffusion field which controls impingement effects and the diffusivity of the components in the matrix phase. If the first three factors are known, the diffusivity in the matrix phase can be determined by matching calculated and experimentally measured concentration profiles. The following sections describe the mathematical model for calculating the concentration profiles, the experimental techniques used to produce the appropriate heat treated samples and the matching procedures employed to obtain D. Mathematical Model The diffusion model employed for y growth was a direct modification of the Fe-Ni-P pseudobinary for-
ISSN 0360-2133/81/021l-0243$OO.7510 1981 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 12A, FEBRUARY 1981—243
Authors Copy mulation of Moren and Goldstein.9 The Moren and Goldstein model simulated the nonisothermal growth of a in y for the Fe-Ni-P system and calculated Ni gradients in both the a and y phases. Modifications were made so that growth occurred isothermally and that ‘ grew in a matrix of a. The Crank-Nicholson’° numerical technique was used and a Murray-Landis” gridspace transformation was employed to allow for the cs/y interface movement. The a/y interface veolicty was determined by either a flux balance or a total mass balance technique.9”2 The following assumptions are made for the model: I) The diffusion coefficient in the a or a2 phase is not a function of composition, 2) The a/y interface is planar with y growth normal to the interface, and 3) Local equilibrium occurs at the a/’y interface. The planarity of the a/y interface and the presence of local equilibrium at the a/’y interface was demonstrated for the experimental time periods employed by Romig and Goldstein.8 However there is no data available on the effect of Ni content on the diffusivity of the bcc FeNi phase. The boundary conditions for the model are 3C/X = 0 at the center of the a and 7 phases. This permits impingement effects to be considered and allows a direct input of the measured diffusion field length from the experimental alloy samples. At the a/’y interface the Ni compositions are given by the equilibrium tieline values from the appropriate phase diagram. Figure 1 shows the a + y field of the Fe-Ni and Fe-Ni (P saturated) systems from 700 to 300 °C recently deter mined by Romig and Goldstein.8 For Fe-Ni or P saturated Fe-Ni alloys the Ni content of a and y can be taken directly from the phase diagram. When the alloy is not P saturated, the a and y solubility limits lie between the appropriate solvus lines. For any temper ature and bulk composition (Fe-Ni-P) the sotubility limits can be approximated using a geometric construc tion as discussed by Moren and Goldstein.’3 The initial
conditions for the model are a constant Ni composition in the a, matrix equal to the bulk content of the experimental alloy of interest. Since phase growth occurs isothermally, the y phase has a constant composition and the diffusional flux in •y is zero. Therefore the y growth rate is controlled by the diffusivities of the a2 matrix. The diffusivity of the a2 matrix, D’, is unknown. As a first approximation it was assumed that D = D. This approximation was used in the initial calculation of the 7 growth model. The Borg and Lai6 D” values for ferromagnetic a Fe-Ni were used for the calculation. The D value tvas changed in an iterative manner to obtain a match between measured and calculated Ni gradients. This calculation procedure to obtain D was repeated for experimental samples at several temperatures (700 to 300 °C). The details of the diffusion model are de scribed in Appendix I. Alloy Heat Treatment To determine diffusivities in a, a number of Fe-Ni and Fe-Ni-P alloys were tempered after the formation of martensite. a,. The alloys (Table I) were induction melted in a reducing atmosphere from the pure ele ments (99.999), iron, nickel, and phosphorus. Each Fe-Ni and Fe-Ni-P alloy was homogenized at 1200 ± 10 °C for at least ten days. Furnace temperature was monitored with a calibrated Pt-Pt 13 Rh thermocouple. To prevent oxidation during the treatment each alloy was placed in an alumina crucible and vacuum encap sulated to approximately 2.7 Pa (20 jI) in fused silica tubing. A piece of tantalum foil was placed into each capsule as an oxygen getter. After the homogenization heat treatment the samples were quenched by crushing the capsules in cold water. Each sample was then held in liquid nitrogen (— 196 °C) for at least 15 mm to minimize, and hopefully eliminate, any retained aus tenite. Following the quench the Ta foil was examined. If the foil was shiny and ductile, it was assumed that the
SOLVUS LINES
D I— ‘5 it
Fig, 1—Fe-Ni, Fe-Ni (P Saturated) phase diagrams of Romig and Goldstein8
w 5-
I-
WEIGHT PERCENT Ni
244—VOLUME 12A, FEBRUARY 1981
METAL LURGICA[. TRANSACTIONS A
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Authors Copy Microchemical Analysis—Scanning Transmission Electron Microscopy
Table I. Fe-Ni Alloy Compositions and Heat Treatments Temperature. °C
Ni, Wt Pet
Tempering Time, Days
670
8.1 6.2 11.9 15.2 14.7 15.2 30.7 25.5 30.7 25.5 30.7
74,14 74 127 127 270 270 120 270 270 430 430
600 500 450 400 300
Fe-Ni-P Alloy Compositions and Heat Treatments Temperature. 2C
Ni, Wt Pct
P, Wt Pct
Tempering Time, Days
700
5.71
1.3
600 500
10.12 10.16 18.75 10.12 18.75 10.12 18.75
0.6 0.7 0.6 0.6 0.6 0.6 0.6
50 124 105 105 105 105 105 220 220
400 300
.
sample had remained under vacuum. If the Ta foil was oxidized. the sample was discarded. To verify homogenietv each alloy was analyzed in the electron microprobe. The range of homogeneity’3 for acceptable alloys was 0.1 wt pct Ni at the 99 pct confidence level. Heat treatments were carried out in tube furnaces controlled to within ± 0.5 °C. A cali brated Pt-Pt 13 Rh orchromel-alumel thermocouple was placed next to the samples in the furnace to monitor the actual temperature. Reported temperatures are accurate to ±2 °C. As in the homogenization treatments the alloys were vacuum encapsulated in fused silica tubes. Table I summarizes the bulk compositions and heat treatments for each alloy. Following the isothermal heat treatment, the alloys were quenched in water by breaking the capsules. The composition of the y precipitates and the Ni gradients in the a, matrix were measured using electron probe microanalysis (EPMA) and/or STEM X-ray micro analysis.
Microchemical Analysis—Electron Microprobe Technique The heat treated samples were mounted, polished, and etched for metallographic examination. Most sam ples had structures too fine to resolve optically. There fore, each sample was also examined with the scanning electron microscope. If the precipitates were larger than 2 tim and more than 2 tim apart, the micro chemistry was determined with the electron probe. The samples were analyzed with an ARL microprobe. operated at an accelerating potential of 20 kV and a sample current of 0.05 tiA on pure Fe. The X-ray data were reduced by the ZAF technque.’5 ‘
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\JETALLURGICAL TRANSACTIONS A
All the heat treated samples were examined in the transmission electron microscope (TEM) to establish the presence of suitable thin areas for STEM analysis and to establish that a and phases were present in these areas. Self-supporting thin foils were used for the TEM-STEM work. After slicing bulk samples the alloys were chemically thinned to approximately 100 tim with a solution consisting of (by volume) 16H202 (30 pct) 3H20-IHF. A 3 mm disc was then mechanically pierced out of the thinned wafer. The final thinning was accomplished either by an ion beam thinner or an electrojet thinner. A Commonwealth Scientific IMMI II ion thinner was used for ion beam thinning. The ions were accelerated through a 7 kV potential. and the foil was tilted 12 to 14 deg from the beam normal position. Electrojet thinning was accomplished with a Ficionne Jet Thinner and an electrolyte of 3 pct (by volume) perchioric acid in ethanol. A potential of 95 v was used and the solution was cooled to —45 °C with liquid nitrogen. Following jet thinning the foils were placed in the ion thinner for approximately 10 mm. This procedure removed any residue deposited on the foil by the electrojet thinning process. A Philips 300 STEM fitted with an energy dispersive detector was used for microchemical analysis. A 60 s counting time was employed for each meas urement. The instrument was operated at an acceler ating voltage of 100 kV and the electron beam size was varied, depending on the resolution desired. between 20 and 40 nm. The thin foil was tilted at 36 deg and the a/y interfaces were oriented approximately parallel to the electron beam. The X-ray data were converted into weight percents with the Cliff-Lorimer standardless ratio technique’6 as given by the following equation ‘
CFe
c Ni
——
.
‘Fe
kFN
[1]
N
where CF and C. are the weight percent Fe and Ni present at the analysis point. kEeNi is a proportionality factor which is not a function of composition. and ‘Fe and ‘Xj are the net integrated FeK and NiK peak intensities. According to Eq. [1] the composition ratio is directly proportional to the intensity ratio. Given kFCN, and the measured values of ‘Fe and ‘N’ CFe and CN can be uniquely determined since CFe + CN = 1.0. The prime advantage of the ratio technique is that thickness variations can be ignored and fluctuations in beam intensity do not alter the results. This technique is only applicable if the thin film criterion is satisfied and X-ray absorption and fluorescence effects can be ignored for foils up to 400 nm thick. which is the limit of electron transparency. Typical foil thicknesses in the area of analysis were 150 nm. For the operating conditions used in these experiments, the X-ray spatial resolution in a 150 nm Fe-Ni foil is approximately 50 nm. VOLUME 12A, FEBRUARY 1981—245
Authors Copy RESULTS Typical SEM and TEM microstructures of the tem pered 02 phase are shown in Fig. 2. In all cases the y precipitated and grew as platelets or discs in the parent 02 matrix. This morphology was essentially unaltered by changes in alloy composition or tempering temperature. The length of the diffusion field, that is the distance from the center of a phase to the center of y phase, can be measured by using the TEM microstructures in which the a/y interface is oriented approximately parallel to the incident electron beam. Figure 3 shows a typical example of a Ni concentration profile measured by STEM X-ray techniques across several y/a platelets. The small Ni concentration gradient in a is apparent. Several other concentration profiles are given by Romig and Goldstein.8 A few of the tempered samples were fully equilibrated and had no Ni concentration gra dients in the a phase.
Fe-30.7 Ni 450 • C 120 DAYS
Z
25
a
a
20
5
10
5
0 0
2
4
8
6
10
12
0
DISTANCE tAkI000) Fig. 3—Concentration profile measured on an Fe-30.7 Ni alloy tempered at 450 °C for 120 days. Data taken every 500A with the STEM.
(a)
(b) Fig. 2(a)—SEM micrograph of ferrite and austenite in an Fe-25.5 wt pet Ni alloy tempered at 400 °C for 270 days. The structure is austenite (G) plates in a ferritic (A) matrix. Scale bar = I sm. (b) TEM micrograph of ferrite and austenite in an Fe-30.7 wt pet Ni alloy tempered at 300 C for 430 days. The structure is austenite (G) plates in a ferritic (A) matrix. Scale bar = 25005k.
246—VOLUME 12A, FEBRUARY 1981
For each of the heat treated alloys, the bulk com position. the a and y solubility limits and the diffusion field length were obtained. The y growth simulation program was then employed to calculate the Ni con centration gradients for the heat treatment time of each of the experimental alloys. The calculated and meas ured Ni profiles in a and y were then compared. If a good fit was not obtained, the assumed Ni diffusivity in 02 was increased until a fit within experimental error was obtained. Figure 4 shows several examples of calculated concentration profiles which match the ex perimentally determined profiles within experimental error. Figure 4(a) shows a profile measured just after impingement occurs and where steep concentration gradients are present. The diffusivities determined from the equilibrated samples (Fig. 4(c)) were minimum val ues. These diffusivities were used as a consistency check against the diffusivities determined from samples con taining concentration gradients. Table II lists the values of D,’ in Fe-Ni and Fe-Ni-P alloys from 700 to 300 C determined in this study. The values of D of Hirano et a!5 and Borg and Lai6 are included for comparison purposes. The large variation of measured D1 values at each temperature is due to the relative insensitivity of the calculated profiles to the assumed Ni diffusivities. The measured diffusivities are plotted as a function of temperature in Fig. 5. A discontinuity in diffusion behavior occurs at approximately 410 °C for both binary and ternary alloys. The effect of P is to raise the diffusivities at any temperature. A least squares curve was used to construct lines through the binary data of METALLURGICAL TRASACTlONS A
Authors Copy -
—
0
40
-I I
CALCULATED EXPERIMENTAL
50
Fe-14.7 Ni 500 C 9 MONTHS
40
Z3.
25.5 N
300 C 280 DAYS
—CALCULATED EXPERIMENTAL
-
z I
I-
z
UI
25
3O 0
IX CD 20
I5 10 5 C
I
I 24
I 16
8
O
I 40
32
0
48
2
6
4
DISTANCE (A
DISTANCE (Ax 1000)
0
8
12
0001
(b)
(a) 60
18
I
16
—
I
CALCULATED
t
2
I V
0
CALCULATED EXPERIMENTAL
40
z
30
I
UI
I
I-. x U
—
Fe—5.7Ni-I.3P 24 DAYS 700° C
EXPERIMENTAL
z
Fe—I875N1—06P 300C 220 DAYS
I
I
I
20
6-I 4 I0
2 I 2
0 0
4
6
I 14
I 12
I 10
I 8
I 16
I 20
I 18
I 22
,.,
24
8 6 DISTANCE IAI000I
4
2
0
DISTANCE (AxI000)
2
10
(U)
(c) Fig. 4—Final match of experimental STEM data to concentration profiles calculated by the numerical model. The size of the y precipitate and is the half the concentration gradient calculated by the model fit the STEM data within experimental error. L is the diffusion field length and width of the y precipitate. (a) Fe-14.7 wt pet Ni alloy, tempered at 500 “C for 9 months. (b) Fe-25.5 wt pet Ni alloy, tempered at 300 ‘C for 280 days. (c) Fe-5.7 wt pet Ni-l.3 wt pet P alloy, equilibrated after tempering at 700°C for 124 days. (d) Fe-18.75 wt pet Ni-0.6 wt pet P alloy, tempered at 300 “C for 220 days.
Fig. 5. Solving for D,, and Q for the binary Fe-Ni case, the following expressions were developed. D’
=
which describe the diffusivities in Fe-Ni-P martensite or are: (4l0°C)
Dexp(—Q/RT)
=
Temperature Range
Q
D,, (cm2/s)
l0
Q (cal)
410 “C
(4.3
±
4)
X
49,000
±
8000
The Diffusivity of Ni in Fe-Ni and Fe-Ni-P Martensites A. D. ROMIG, JR. AND J. I. GOLDSTEIN The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensite, D”, has been determined between 700 and 300 °C using electron microprobe (EMP) and scanning transmission electron microscope (STEM) techniques. Alloys of various bulk compositions (0 to 30 wt pct Ni, Fe) were homogenized in the single phase austenite (Y-fcc) field and quenched to form martensite, 02 (bce). Appropriate alloys were tempered isothermally at 300 to 700 °C. The y nucleated and grew in the parent 02. The composition of the y phase and the concentration gradients in the 02 were measured with the EMP and/or STEM. In order to determine D, experimentally measured Ni concentration gradients were matched to Ni concentration gradients calculated by a simulation model. The calculated gradients were obtained by solving the appropriate form of Fick’s second law using the Crank-Nicholson numerical technique. The observed diffusivities varied with temperature. Above approximately 410 °C, = (4.25 x l0) exp (—49,000/RT) em2/s while below 410 °C, D = (2.27 X l0’) exp (— 10,600/R T) cm2/s. The effect of P is to increase the Fe-Ni diffusivities at any temperature by the factor (1 + 1.27 C, + 0.623 C) where C is the amount of P (wt pet) in 02. The discontinuous diffusion behavior of D’ is attributable to the high dislocation density of the 02. Above approximately 410 °C lattice diffusion is dominant while below 410 °C dislocation pipe diffusion is dominant.
,
‘VVTHEN Fe-Ni austenite (y-fcc) is cooled from the single phase y region into the two-phase o + y field the ferrite (o-bcc) will not nucleate.’ Rather the y phase will transform by a martensitic reaction to 02 (bce).2 The martensite, 02, has the same crystal structure as the equilibrium n phase, but has the composition of the parent y-phase and a high defect density.3 The tem perature at which the martensite reaction starts and finishes is a function of Ni content.2 The nature of the diffusionless transformation of Fe-Ni alloys, which occurs upon quenching from the austenite field, has been summarized by Owen, et at.4 Pure binary alloys which contain up to 5.2 wt pet Ni will not transform to martensite upon quenching. The transformation prod uct is equiaxed ferrite. However, the equiaxed ferrite l02 lines/cm2). structure is heavily dislocated (10’’ Carbon levels as low as 100 ppm will cause a martensite transformation to occur even in the low Ni alloys. For Ni contents between 10.5 and 30 wt pet, quenching at rates >0.08 °C/s will transform austenite to massive martensite. The transformation is accompanied by a shape change, and produces a heavily deformed and dislocated structure. Alloys containing 30 to 34 wt pet Ni transform to classical aceicular martensite. For Ni contents between 5.2 and 10.5 wt pet, the structure is a mixture of equiaxed ferrite and massive martensite. If the 02 is subsequently tempered the Ni-rich y phase will nucleate and grow into the parent 02 phase. If the growth of the austenite is volume diffusion controlled, a Ni gradient will form in the supersaturated 02 phase. In —
A. D. ROMIG, JR., formerly Research Assistant in the Depart ment of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA is now at Sandia Corporation, Albuquerque, NM 87115. J. I. GOLDSTEIN is T. L. Diamond Professor of Metallurgy, Department of Metallurgy and Materials Engineering, Whitaker Lab. no. 5, Lehigh University, Bethlehem, PA 18015. Manuscr,pt submitted February 11, 1980.
METALLURGICALTRANSACTIONSA
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addition the parent phase will contain the dislocation structure of the original 02. Several investigators have measured the diffusivity of Ni in pure a iron,5’6 DJ1, and in a Fe-Ni7 containing P above 600 °C. The diffusivity of Ni in 02, D’, however, has not been measured. In a companion study Romig and Goldstein8 have determined the Ni solubility limits of a and y phases in the Fe-Ni and Fe-Ni-P systems. In that study a and phases were produced by tempering 02 at temperatures from 300 to 700 °C. The amount of y-austenite phase growth was much greater than that which was calcu lated if the growth was controlled by diffusion in the a phase. This result argues that the diffusivity of 02 may be significantly higher than that of a. It is the purpose of this study to measure D1 and to investigate the effect of dislocation structure on diffusivity. ‘
EXPERIMENTAL PROCEDURE for volume diffusion controlled growth, the size of the precipitate and the concentration gradient in the matrix phase are a function of four factors: the bulk alloy composition, the solubility limits of the equilib rium phases, the length of the diffusion field which controls impingement effects and the diffusivity of the components in the matrix phase. If the first three factors are known, the diffusivity in the matrix phase can be determined by matching calculated and experimentally measured concentration profiles. The following sections describe the mathematical model for calculating the concentration profiles, the experimental techniques used to produce the appropriate heat treated samples and the matching procedures employed to obtain D. Mathematical Model The diffusion model employed for y growth was a direct modification of the Fe-Ni-P pseudobinary for-
ISSN 0360-2133/81/021l-0243$OO.7510 1981 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 12A, FEBRUARY 1981—243
Authors Copy mulation of Moren and Goldstein.9 The Moren and Goldstein model simulated the nonisothermal growth of a in y for the Fe-Ni-P system and calculated Ni gradients in both the a and y phases. Modifications were made so that growth occurred isothermally and that ‘ grew in a matrix of a. The Crank-Nicholson’° numerical technique was used and a Murray-Landis” gridspace transformation was employed to allow for the cs/y interface movement. The a/y interface veolicty was determined by either a flux balance or a total mass balance technique.9”2 The following assumptions are made for the model: I) The diffusion coefficient in the a or a2 phase is not a function of composition, 2) The a/y interface is planar with y growth normal to the interface, and 3) Local equilibrium occurs at the a/’y interface. The planarity of the a/y interface and the presence of local equilibrium at the a/’y interface was demonstrated for the experimental time periods employed by Romig and Goldstein.8 However there is no data available on the effect of Ni content on the diffusivity of the bcc FeNi phase. The boundary conditions for the model are 3C/X = 0 at the center of the a and 7 phases. This permits impingement effects to be considered and allows a direct input of the measured diffusion field length from the experimental alloy samples. At the a/’y interface the Ni compositions are given by the equilibrium tieline values from the appropriate phase diagram. Figure 1 shows the a + y field of the Fe-Ni and Fe-Ni (P saturated) systems from 700 to 300 °C recently deter mined by Romig and Goldstein.8 For Fe-Ni or P saturated Fe-Ni alloys the Ni content of a and y can be taken directly from the phase diagram. When the alloy is not P saturated, the a and y solubility limits lie between the appropriate solvus lines. For any temper ature and bulk composition (Fe-Ni-P) the sotubility limits can be approximated using a geometric construc tion as discussed by Moren and Goldstein.’3 The initial
conditions for the model are a constant Ni composition in the a, matrix equal to the bulk content of the experimental alloy of interest. Since phase growth occurs isothermally, the y phase has a constant composition and the diffusional flux in •y is zero. Therefore the y growth rate is controlled by the diffusivities of the a2 matrix. The diffusivity of the a2 matrix, D’, is unknown. As a first approximation it was assumed that D = D. This approximation was used in the initial calculation of the 7 growth model. The Borg and Lai6 D” values for ferromagnetic a Fe-Ni were used for the calculation. The D value tvas changed in an iterative manner to obtain a match between measured and calculated Ni gradients. This calculation procedure to obtain D was repeated for experimental samples at several temperatures (700 to 300 °C). The details of the diffusion model are de scribed in Appendix I. Alloy Heat Treatment To determine diffusivities in a, a number of Fe-Ni and Fe-Ni-P alloys were tempered after the formation of martensite. a,. The alloys (Table I) were induction melted in a reducing atmosphere from the pure ele ments (99.999), iron, nickel, and phosphorus. Each Fe-Ni and Fe-Ni-P alloy was homogenized at 1200 ± 10 °C for at least ten days. Furnace temperature was monitored with a calibrated Pt-Pt 13 Rh thermocouple. To prevent oxidation during the treatment each alloy was placed in an alumina crucible and vacuum encap sulated to approximately 2.7 Pa (20 jI) in fused silica tubing. A piece of tantalum foil was placed into each capsule as an oxygen getter. After the homogenization heat treatment the samples were quenched by crushing the capsules in cold water. Each sample was then held in liquid nitrogen (— 196 °C) for at least 15 mm to minimize, and hopefully eliminate, any retained aus tenite. Following the quench the Ta foil was examined. If the foil was shiny and ductile, it was assumed that the
SOLVUS LINES
D I— ‘5 it
Fig, 1—Fe-Ni, Fe-Ni (P Saturated) phase diagrams of Romig and Goldstein8
w 5-
I-
WEIGHT PERCENT Ni
244—VOLUME 12A, FEBRUARY 1981
METAL LURGICA[. TRANSACTIONS A
.
Authors Copy Microchemical Analysis—Scanning Transmission Electron Microscopy
Table I. Fe-Ni Alloy Compositions and Heat Treatments Temperature. °C
Ni, Wt Pet
Tempering Time, Days
670
8.1 6.2 11.9 15.2 14.7 15.2 30.7 25.5 30.7 25.5 30.7
74,14 74 127 127 270 270 120 270 270 430 430
600 500 450 400 300
Fe-Ni-P Alloy Compositions and Heat Treatments Temperature. 2C
Ni, Wt Pct
P, Wt Pct
Tempering Time, Days
700
5.71
1.3
600 500
10.12 10.16 18.75 10.12 18.75 10.12 18.75
0.6 0.7 0.6 0.6 0.6 0.6 0.6
50 124 105 105 105 105 105 220 220
400 300
.
sample had remained under vacuum. If the Ta foil was oxidized. the sample was discarded. To verify homogenietv each alloy was analyzed in the electron microprobe. The range of homogeneity’3 for acceptable alloys was 0.1 wt pct Ni at the 99 pct confidence level. Heat treatments were carried out in tube furnaces controlled to within ± 0.5 °C. A cali brated Pt-Pt 13 Rh orchromel-alumel thermocouple was placed next to the samples in the furnace to monitor the actual temperature. Reported temperatures are accurate to ±2 °C. As in the homogenization treatments the alloys were vacuum encapsulated in fused silica tubes. Table I summarizes the bulk compositions and heat treatments for each alloy. Following the isothermal heat treatment, the alloys were quenched in water by breaking the capsules. The composition of the y precipitates and the Ni gradients in the a, matrix were measured using electron probe microanalysis (EPMA) and/or STEM X-ray micro analysis.
Microchemical Analysis—Electron Microprobe Technique The heat treated samples were mounted, polished, and etched for metallographic examination. Most sam ples had structures too fine to resolve optically. There fore, each sample was also examined with the scanning electron microscope. If the precipitates were larger than 2 tim and more than 2 tim apart, the micro chemistry was determined with the electron probe. The samples were analyzed with an ARL microprobe. operated at an accelerating potential of 20 kV and a sample current of 0.05 tiA on pure Fe. The X-ray data were reduced by the ZAF technque.’5 ‘
@.
\JETALLURGICAL TRANSACTIONS A
All the heat treated samples were examined in the transmission electron microscope (TEM) to establish the presence of suitable thin areas for STEM analysis and to establish that a and phases were present in these areas. Self-supporting thin foils were used for the TEM-STEM work. After slicing bulk samples the alloys were chemically thinned to approximately 100 tim with a solution consisting of (by volume) 16H202 (30 pct) 3H20-IHF. A 3 mm disc was then mechanically pierced out of the thinned wafer. The final thinning was accomplished either by an ion beam thinner or an electrojet thinner. A Commonwealth Scientific IMMI II ion thinner was used for ion beam thinning. The ions were accelerated through a 7 kV potential. and the foil was tilted 12 to 14 deg from the beam normal position. Electrojet thinning was accomplished with a Ficionne Jet Thinner and an electrolyte of 3 pct (by volume) perchioric acid in ethanol. A potential of 95 v was used and the solution was cooled to —45 °C with liquid nitrogen. Following jet thinning the foils were placed in the ion thinner for approximately 10 mm. This procedure removed any residue deposited on the foil by the electrojet thinning process. A Philips 300 STEM fitted with an energy dispersive detector was used for microchemical analysis. A 60 s counting time was employed for each meas urement. The instrument was operated at an acceler ating voltage of 100 kV and the electron beam size was varied, depending on the resolution desired. between 20 and 40 nm. The thin foil was tilted at 36 deg and the a/y interfaces were oriented approximately parallel to the electron beam. The X-ray data were converted into weight percents with the Cliff-Lorimer standardless ratio technique’6 as given by the following equation ‘
CFe
c Ni
——
.
‘Fe
kFN
[1]
N
where CF and C. are the weight percent Fe and Ni present at the analysis point. kEeNi is a proportionality factor which is not a function of composition. and ‘Fe and ‘Xj are the net integrated FeK and NiK peak intensities. According to Eq. [1] the composition ratio is directly proportional to the intensity ratio. Given kFCN, and the measured values of ‘Fe and ‘N’ CFe and CN can be uniquely determined since CFe + CN = 1.0. The prime advantage of the ratio technique is that thickness variations can be ignored and fluctuations in beam intensity do not alter the results. This technique is only applicable if the thin film criterion is satisfied and X-ray absorption and fluorescence effects can be ignored for foils up to 400 nm thick. which is the limit of electron transparency. Typical foil thicknesses in the area of analysis were 150 nm. For the operating conditions used in these experiments, the X-ray spatial resolution in a 150 nm Fe-Ni foil is approximately 50 nm. VOLUME 12A, FEBRUARY 1981—245
Authors Copy RESULTS Typical SEM and TEM microstructures of the tem pered 02 phase are shown in Fig. 2. In all cases the y precipitated and grew as platelets or discs in the parent 02 matrix. This morphology was essentially unaltered by changes in alloy composition or tempering temperature. The length of the diffusion field, that is the distance from the center of a phase to the center of y phase, can be measured by using the TEM microstructures in which the a/y interface is oriented approximately parallel to the incident electron beam. Figure 3 shows a typical example of a Ni concentration profile measured by STEM X-ray techniques across several y/a platelets. The small Ni concentration gradient in a is apparent. Several other concentration profiles are given by Romig and Goldstein.8 A few of the tempered samples were fully equilibrated and had no Ni concentration gra dients in the a phase.
Fe-30.7 Ni 450 • C 120 DAYS
Z
25
a
a
20
5
10
5
0 0
2
4
8
6
10
12
0
DISTANCE tAkI000) Fig. 3—Concentration profile measured on an Fe-30.7 Ni alloy tempered at 450 °C for 120 days. Data taken every 500A with the STEM.
(a)
(b) Fig. 2(a)—SEM micrograph of ferrite and austenite in an Fe-25.5 wt pet Ni alloy tempered at 400 °C for 270 days. The structure is austenite (G) plates in a ferritic (A) matrix. Scale bar = I sm. (b) TEM micrograph of ferrite and austenite in an Fe-30.7 wt pet Ni alloy tempered at 300 C for 430 days. The structure is austenite (G) plates in a ferritic (A) matrix. Scale bar = 25005k.
246—VOLUME 12A, FEBRUARY 1981
For each of the heat treated alloys, the bulk com position. the a and y solubility limits and the diffusion field length were obtained. The y growth simulation program was then employed to calculate the Ni con centration gradients for the heat treatment time of each of the experimental alloys. The calculated and meas ured Ni profiles in a and y were then compared. If a good fit was not obtained, the assumed Ni diffusivity in 02 was increased until a fit within experimental error was obtained. Figure 4 shows several examples of calculated concentration profiles which match the ex perimentally determined profiles within experimental error. Figure 4(a) shows a profile measured just after impingement occurs and where steep concentration gradients are present. The diffusivities determined from the equilibrated samples (Fig. 4(c)) were minimum val ues. These diffusivities were used as a consistency check against the diffusivities determined from samples con taining concentration gradients. Table II lists the values of D,’ in Fe-Ni and Fe-Ni-P alloys from 700 to 300 C determined in this study. The values of D of Hirano et a!5 and Borg and Lai6 are included for comparison purposes. The large variation of measured D1 values at each temperature is due to the relative insensitivity of the calculated profiles to the assumed Ni diffusivities. The measured diffusivities are plotted as a function of temperature in Fig. 5. A discontinuity in diffusion behavior occurs at approximately 410 °C for both binary and ternary alloys. The effect of P is to raise the diffusivities at any temperature. A least squares curve was used to construct lines through the binary data of METALLURGICAL TRASACTlONS A
Authors Copy -
—
0
40
-I I
CALCULATED EXPERIMENTAL
50
Fe-14.7 Ni 500 C 9 MONTHS
40
Z3.
25.5 N
300 C 280 DAYS
—CALCULATED EXPERIMENTAL
-
z I
I-
z
UI
25
3O 0
IX CD 20
I5 10 5 C
I
I 24
I 16
8
O
I 40
32
0
48
2
6
4
DISTANCE (A
DISTANCE (Ax 1000)
0
8
12
0001
(b)
(a) 60
18
I
16
—
I
CALCULATED
t
2
I V
0
CALCULATED EXPERIMENTAL
40
z
30
I
UI
I
I-. x U
—
Fe—5.7Ni-I.3P 24 DAYS 700° C
EXPERIMENTAL
z
Fe—I875N1—06P 300C 220 DAYS
I
I
I
20
6-I 4 I0
2 I 2
0 0
4
6
I 14
I 12
I 10
I 8
I 16
I 20
I 18
I 22
,.,
24
8 6 DISTANCE IAI000I
4
2
0
DISTANCE (AxI000)
2
10
(U)
(c) Fig. 4—Final match of experimental STEM data to concentration profiles calculated by the numerical model. The size of the y precipitate and is the half the concentration gradient calculated by the model fit the STEM data within experimental error. L is the diffusion field length and width of the y precipitate. (a) Fe-14.7 wt pet Ni alloy, tempered at 500 “C for 9 months. (b) Fe-25.5 wt pet Ni alloy, tempered at 300 ‘C for 280 days. (c) Fe-5.7 wt pet Ni-l.3 wt pet P alloy, equilibrated after tempering at 700°C for 124 days. (d) Fe-18.75 wt pet Ni-0.6 wt pet P alloy, tempered at 300 “C for 220 days.
Fig. 5. Solving for D,, and Q for the binary Fe-Ni case, the following expressions were developed. D’
=
which describe the diffusivities in Fe-Ni-P martensite or are: (4l0°C)
Dexp(—Q/RT)
=
Temperature Range
Q
D,, (cm2/s)
l0
Q (cal)
410 “C
(4.3
±
4)
X
49,000
±
8000
