# Kinetics of Nickel Diffusion into Austenitic Stainless Steels AISI 304 and 316L and Calculation of Diffusion Coefficients

^{*}

## Abstract

**:**

## 1. Introduction

^{−8}MPa. Another work [10] also dealt with welding with a nickel interlayer, which was used to weld Ti alloy (Ti6Al4V) and stainless steel AISI 301.

_{Ti}= 5.5 × 10

^{−14}m

^{2}·s

^{−1}at 900 °C and D

_{Ti}= 9 × 10

^{−14}m

^{2}·s

^{−1}at 800 °C. The intrinsic diffusion coefficients for iron α DFe-α = 5 × 10

^{−15}m

^{2}·s

^{−1}at 900 °C and for nickel D

_{Ni}= 3 × 10

^{−17}m

^{2}·s

^{−1}at 800 °C were taken from other studies that dealt with diffusion coefficients [16,17,18].

## 2. Materials and Methods

_{g}, and A

_{40}(the tensile strength where the original length of the test sample was 40 mm) were measured at room temperature (RT). A TIRA Test 2300 (TIRA GmbH, Schalkau, Germany) was used for testing. The static tensile test was realized according to EN ISO 6892-1 [29] with a loading rate of 1 mm/min up to achieving yield strength and then 15 mm/min. The mechanical properties were determined for both base materials.

^{−1,}and pressure 13 MPa. Figure 3 shows a sample heated to 1050 °C.

^{−1}to 80 °C; 1.4 °C·min

^{−1}to 160 °C; 1.8 °C·min

^{−1}to 220 °C; 3 °C·min

^{−1}to 600 °C, and 7 °C·min

^{−1}in the temperature interval 600 to 1150 °C). The holding time at temperature was 1 h and 5 h. The cooling rate of the samples was also constant for all experiments at 5 °C·min

^{−1}. During the heat treatment, the vacuum in the furnace was 7 × 10

^{−5}mbar. No more pressure was applied to the samples with initial diffusion bonds.

## 3. Experiment and Results

#### 3.1. Determination of Mechanical Properties

#### 3.2. Diffusion Bonding in Gleeble 3500

#### 3.3. Evaluation of Diffusion Kinetics

^{−1}. Therefore, a vacuum furnace was chosen for the experiments to achieve realistic heating and cooling conditions. However, diffusion already occurs during heating and cooling. Separate experiments were realized to study the effect of heating and cooling in the vacuum furnace on the total width of the diffusion zone. These were composed only of heating to the set holding temperature, zero holding time at that temperature, and subsequent cooling. Identical rates were used for heating and cooling, as described in Section 2.

#### 3.4. Calculation of Diffusion Coefficients

_{1}and c

_{2}. The concentration of the diffusing element at distance x from the interface at time t is c. This configuration can be used to determine the diffusion coefficient D for a specific temperature from known values of the concentrations c

_{1}and c

_{2}and from the measured concentration c for a distance x and time t. This is diffusion in an unlimited space, i.e., in terms of diffusion in the interval (−∞ < 0 < ∞).

_{1}. At each place (x > 0), the concentration is c = c

_{2}. Thus:

_{1}, x < 0, t = 0

_{2}, x > 0, t = 0

_{1}+ c

_{2}) is maintained at all times (t > 0) Thus:

_{1}+ c

_{2}), x = 0, t > 0

_{1}is the concentration in the base material, c

_{2}is the concentration in the interlayer, D is the diffusion coefficient, t is time, x is the distance from the interface, and x

_{0}is the distance at the interface (x

_{0}= 0).

_{0}is a partial factor depending on the state of the crystal lattice and the frequency of diffusing atoms, Q

_{m}is the activation energy, R

_{m}is the mole gas constant, and T is the absolute temperature. Equation (12) shows the exponential dependence of D on −1/T. Figure 10 shows the dependence of log D

_{Ni}on 1/T with the corresponding equations.

_{0}is the concentration in the interlayer (for x = 0), x is the distance from the center of the interlayer, h is half the thickness of the interlayer, D is the diffusion coefficient, and t is time. For x = 0, Equation (14) can be used.

_{0}= 100%, Equation (15) can be used.

_{Ni}and determine with what validity the calculated D

_{Ni}can be used for further calculations. Equation (15) can be used to calculate the depth of diffusion under specific conditions (temperature and time), and the results can be compared with the real values obtained by EDX analysis. The experimentally determined diffusion depths to assess the effects of heating and cooling and each heat treatment and both materials are given in Table 7. The results of the calculated diffusion depths according to Equation (15) are shown in Table 8. Table 9 then shows the absolute values of the difference between the real and calculated depths in micrometers.

## 4. Discussion

^{−1}. In this case, for austenitic steels, the effect of heating to 950 °C and subsequent cooling from this temperature is 5.6–7.3% on the total diffusion width of Ni. At 1050 °C, it is then 6.8–12.6%, and at 1150 °C, it is even 11.7–23.8% of the total diffusion width of Ni. The result also shows a clear difference for the holding times of 1 and 5 h, as the total diffusion width is larger for the holding time of 5 h (see Table 7).

_{Ni}= 3 × 10

^{−17}m

^{2}·s

^{−1}. However, for practical application, this information is not sufficient because it is necessary to know the diffusion coefficients of the element into specific materials. Equation (12) shows that the diffusion coefficient is exponentially dependent on −1/T, and thus it is necessary to have data about diffusion coefficients, ideally in the form of temperature dependences. The obtained temperature dependences of the diffusion coefficients of Ni into austenitic steels are based on the Arrhenius equation. Therefore, it would probably be sufficient to give only Equations (16) and (17), from which D

_{0}and Q can be obtained. The aim of this paper was to show a method of determining diffusion coefficients in a broader context so that other researchers can simply duplicate the above process and determine the diffusion coefficients at a specific temperature for any combinations of diffusion joints with interlayers, and also to determine the diffusion depths from which the interlayer thickness can be determined for heterogeneous joints (Equations (18) and (19)).

## 5. Conclusions

- (1)
- Temperature has a significant effect on the diffusion kinetics and, therefore, the depth of diffusion of nickel into the austenitic steel. It is also dependent on the holding time and temperature.
- (2)
- Nickel diffuses into both the austenitic steels, AISI 304 and AISI 316L, at approximately the same rate, although AISI 316L has approximately 5% more Ni and 2.2% more Mo.
- (3)
- Diffusion already occurs during the heating and subsequent cooling of the sample. In the case of a temperature of 950 °C for austenitic steels, it is between 5.6 and 7.3% of the total diffusion depth. At 1050 °C, it is 6.8–12.6%, and at 1150 °C, it is 11.7–23.8% of the total diffusion depths measured at holding times of 1 and 5 h.
- (4)
- To determine the diffusion coefficient of Ni into specific steels, generalized Equations (16) and (17) were formulated for a temperature range of 1223.15–1423.15 K, which can be used with sufficient accuracy to determine the widths of the diffusion zones at the interface between austenitic steel (AISI 316L/304) and the Ni interlayer.
- (5)
- The calculated diffusion depths were different from the real values in the range of 5% to 28.6%. The largest differences were at 950 °C. Although the deviation from the real value seems to be quite high, the real difference in diffusion zone width at 950 °C is a maximum of 6.7 µm.
- (6)
- The diffusion zone width, and therefore the basic information for optimizing the interlayer thickness, can be determined with sufficient accuracy for AISI 304 steel generally for temperatures (T) in the range 1223.15–1423.15 K and for times (t) in the range 1 to 5 h according to Equation (18) and for AISI 316L steel according to Equation (19).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Drawing of the sample used for diffusion bonding in the Gleeble 3500 (

**a**), example of real samples for diffusion bonding (

**b**).

**Figure 2.**Example of the thermocouple welded to the sample boundary and (

**a**) the sample with the nickel interlayers clamped in the chamber of the Gleeble device (

**b**).

**Figure 4.**Heterogeneous joint with nickel interlayer in initial state (after bonding in Gleeble 3500).

**Figure 5.**Comparison of AISI 304 samples with heat treatment with different temperatures, holding time of 1 h, and holding time of 5 h.

**Figure 6.**Comparison of AISI 316L samples with heat treatment with different temperatures, holding time of 1 h, and holding time of 5 h.

AISI 304 | C | Cr | Mn | Ni | Si | S | P | N | |
---|---|---|---|---|---|---|---|---|---|

EN 10088-1 | min. | - | 17.50 | - | 8.00 | - | - | - | - |

max. | <0.07 | 19.50 | 2.00 | 10.50 | 1.00 | 0.015 | 0.045 | <0.11 | |

Experiment | 0.045 | 18.37 | 1.66 | 8.11 | 0.23 | 0.013 | 0.077 |

AISI 316L | C | Cr | Mn | Mo | Ni | Si | S | P | N | |
---|---|---|---|---|---|---|---|---|---|---|

EN 10088-1 | min. | - | 16.50 | - | 2.00 | 10.00 | - | - | - | - |

max. | <0.03 | 18.50 | 2.00 | 2.50 | 13.00 | 1.00 | 0.015 | 0.045 | <0.11 | |

Experiment | 0.03 | 18.50 | 1.96 | 2.24 | 13.10 | 1.02 | 0.02 | 0.074 |

Sample No. | R_{p0.2}[MPa] | UTS [MPa] | A_{g}[%] | A_{40}[%] |
---|---|---|---|---|

AISI 304 | 445.5 ± 7.3 | 643.0 ± 3.2 | 33.60 ± 0.16 | 42.03 ± 0.09 |

AISI 316L | 512.7 ± 5.2 | 662.5 ± 7.1 | 24.17 ± 0.61 | 39.47 ± 0.11 |

Sample No. | Temperature [°C] | Time [Hours] |
---|---|---|

1 | 950 | 1 |

2 | 950 | 5 |

3 | 1050 | 1 |

4 | 1050 | 5 |

5 | 1150 | 1 |

6 | 1150 | 5 |

D_{Ni} [m^{2}·s^{−1}] | 1 h | 5 h | ||
---|---|---|---|---|

304 | 316L | 304 | 316L | |

950 °C | 3.90 × 10^{−15} | 3.89 × 10^{−15} | 1.26 × 10^{−15} | 9.69 × 10^{−16} |

1050 °C | 8.28 × 10^{−15} | 9.15 × 10^{−15} | 5.47 × 10^{−15} | 5.18 × 10^{−15} |

1150 °C | 2.88 × 10^{−14} | 2.81 × 10^{−14} | 2.30 × 10^{−14} | 1.64 × 10^{−14} |

Factor | AISI 304 | AISI 316L | ||
---|---|---|---|---|

p-Value | Evaluation | p-Value | Evaluation | |

Time | 0.0014 | Has an effect | 1.62 × 10^{−5} | Has an effect |

Temperature | 4.92 × 10^{−16} | Has an effect | 8.49 × 10^{−15} | Has an effect |

h [µm] | 0 h | 1 h | 5 h | |||
---|---|---|---|---|---|---|

304 | 316L | 304 | 316L | 304 | 316L | |

950 °C | 1.46 | 1.31 | 19.89 | 20.04 | 25.08 | 23.41 |

1050 °C | 3.15 | 3.04 | 25.08 | 31.68 | 41.80 | 45.02 |

1150 °C | 10.72 | 9.41 | 45.09 | 44.96 | 71.90 | 80.26 |

h [µm] | 1 h | 5 h | ||
---|---|---|---|---|

304 | 316L | 304 | 316L | |

950 °C | 14.99 | 14.97 | 19.03 | 16.71 |

1050 °C | 21.83 | 22.96 | 39.68 | 38.61 |

1150 °C | 40.73 | 40.24 | 81.30 | 68.73 |

∆h [µm] | 1 h | 5 h | ||
---|---|---|---|---|

304 | 316L | 304 | 316L | |

950 °C | 4.90 | 5.07 | 6.05 | 6.70 |

1050 °C | 3.25 | 8.72 | 2.12 | 6.41 |

1150 °C | 4.36 | 4.71 | 9.40 | 11.54 |

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**MDPI and ACS Style**

Bukovská, Š.; Moravec, J.; Švec, M.
Kinetics of Nickel Diffusion into Austenitic Stainless Steels AISI 304 and 316L and Calculation of Diffusion Coefficients. *Materials* **2023**, *16*, 6783.
https://doi.org/10.3390/ma16206783

**AMA Style**

Bukovská Š, Moravec J, Švec M.
Kinetics of Nickel Diffusion into Austenitic Stainless Steels AISI 304 and 316L and Calculation of Diffusion Coefficients. *Materials*. 2023; 16(20):6783.
https://doi.org/10.3390/ma16206783

**Chicago/Turabian Style**

Bukovská, Šárka, Jaromír Moravec, and Martin Švec.
2023. "Kinetics of Nickel Diffusion into Austenitic Stainless Steels AISI 304 and 316L and Calculation of Diffusion Coefficients" *Materials* 16, no. 20: 6783.
https://doi.org/10.3390/ma16206783