The overall furnace design and volume determines the required throughput of the pumping system and the ultimate vacuum expected. Processes requiring a deep vacuum of 1x10^{-4} Torr or lower are run in a furnace that integrates a high-throughput diffusion pump in series with a roughing pump and a Roots blower.

### Pumping System Throughput Relating to Furnace Leak Rate

Using the reported throughput data of the diffusion pump with some basic vacuum theory assumptions, a simple approximation curve can predict the relationship between the minimum pump-down pressure (blank-off pressure) prior to processing and the resultant furnace leak-up rate (rate of rise).

### Rate of Rise Leak-Rate Specifications and Procedures

To be in compliance with the specification AMS 2769B, Heat Treatment of Parts in a Vacuum, vacuum furnaces must conform to less than the maximum-acceptable leak-up rates when heat treating certain alloys. As stated in AMS 2769B (Table 1), these acceptable leak rates can range from 5-50 microns/hour. At the minimum, a leak-rate test should be taken weekly when a furnace is in continual operation. A basic procedure is outlined in Table 2.

### Projecting Leak Rate Based on Initial Pumping, Blank-off Pressure

When designing a vacuum furnace, the vacuum pumping system capacity incorporated into the furnace system is based on the expected applications and types of work to be processed in the furnace. For example, a standard furnace (Fig. 1) with a work zone measuring 24 inches wide x 24 inches high x 36 inches deep would typically incorporate a 20-inch diffusion pump in order to achieve a vacuum in the low 10^{-6} Torr range.

The diffusion pump throughput indicates the capability of a constantly pumped system to maintain certain vacuum levels by overcoming existing furnace leaks. When a vacuum chamber is constantly pumped at a volumetric flow rate, an equilibrium pressure will be achieved if the throughput is equal to the leak rate (Q_{L}).^{[1]} Therefore, we are able to plot a projected leak rate based on the final pump-down pressure by dividing the throughput by the volume of the vacuum chamber. As the leak increases, the vacuum pump throughput cannot keep up with the leaking volume and the blank-off vacuum rises.

### Calculating Pump Throughput and Leak Rate

Using the throughput data from the pump manufacturer and assuming if the blank-off pressure deteriorates by a decade then the throughput is reduced by a factor of 10, one can make an approximation of the leak-up rate based on blank-off pressure.

Calculations based on a 20-inch diffusion pump for a furnace volume of 238 cubic feet are as follows. A 20-inch diffusion pump has a throughput of 1 Torr-l/sec at a vacuum level of 1x10^{-3 }Torr, which can be converted to 127,116 micron-feet^{3}/hour.

If the leak rate is equal to:

**Q**_{L (leak rate) }**= (**Δ**p**⋅**V)**** / **Δ**t** (Eq. 1)

V – volume of furnace

Δp – change in pressure during leak-up test

Δt – change in time during leak-up test

**ROR = **Δ**p**** / **Δ**t** (Eq. 2)

then **Q**_{L }**= ROR*V** (Eq. 3)

If, as mentioned earlier, throughput is equal to Q_{L} when a constantly pumped system reaches a stabilized pressure, then we can calculate the rate of rise (ROR) by using Equation 4.

**ROR = Throughput / Volume** (Eq. 4)

From the data for the HFL-3638 (238 feet^{3}), the throughput at 1x10^{-3} Torr is 127,116 micron-feet^{3}/hour. Therefore, the leak up rate, or ROR, would be:

1**27,116 micron-feet**^{3}**/hour / 238 feet**^{3}** = 534 microns/hour** (Eq. 5)

Taking our assumption that a decade improvement in vacuum level is comparable to an improvement in leak rate by a factor of 10, then the following leak-up rates are predicted and plotted in Figure 2.

At 1x10^{-3} Torr: 534 microns/hour

At 1x10^{-4} Torr: 53.4 microns/hour

At 1x10^{-5} Torr: 5.3 microns/hour

At 1x10^{-6} Torr: 0.53 microns/hour

This prediction suggests that in order for the HFL-3638 furnace to satisfy the AMS 2769B specification, the furnace must be capable of pumping down to 1.0x10^{-5} Torr or less

for critical material (Class 4) requiring a leak rate of less than

5 microns/hour. For semi-critical material (Class 2) requiring a leak rate of 20 microns/hour, the furnace must be able to pump down to 5.0x10^{-5} Torr or less. Class 1 (leak rate less than 50 microns/hour) requires a pump down to 1.0x10^{-4} Torr or less.

### Comparing an Actual Leak Rate to Projected

To confirm the accuracy of our projected leak rate based on the curve for the specified diffusion pumping system, we created a test that purposely introduced a given leak rate. The test was performed on an HFL-5748 furnace with a work zone of 36 inches wide x 36 inches high x 48 inches deep and a chamber volume of 483 feet^{3}. The predicted line is shown in Figure 2 along with the actual data.

The forced blank-off pressures were created by using two needle metering valves in series connected to the vaccum chamber, thus introducing a fixed amount of air to simulate a leak. With the needle valves closed, the furnace was pumped down to the low 10^{-6} Torr range. The valves were carefully opened and the pressure allowed to stabilze. Once the equilibrium pressure was reached, the vacuum pumping valves were closed and the leak rate measured as described in Table 2.

As illustrated, the projected and actual curves are not exact due to the limited factors of the test environment. When in normal use, furnace pump-down limitations include factors in addition to pumping throughput data. For example, if one were to add the effects of conductance, outgassing and virtual leaks in the analysis, the predictive curve would be closer to the real curve. However, the simplified prediction curve will help determine if the blank-off level achieved can be used for certain sensitive materials.

### Projecting Leak Rate Based on Blank-off Pressure, Chamber Volume, Pumping Capacity

Our prior projections were based on a furnace (HFL-3638) having a work zone of 24 inches wide x 24 inches high x 36 inches deep and a 20-inch diffusion pump. The chamber volume was calculated to be 238 cubic feet, and the diffusion pump has a projected pumping speed of 17,500 l/sec.

A furnace (HFL-5748) with a work zone of 36 inches wide x 36 inches high x 48 inches deep and a 32-inch diffusion pump has a volume of 483 cubic feet. The diffusion pump for the 5748 furnace has a projected pumping speed of 32,000 l/sec.

Adding a prediction for a Model HFL-6660 furnace with

a work zone of 48 inches wide x 48 inches high x 60 inches deep (574 cubic feet) using a 35-inch diffusion pump with a 48,000 l/sec pumping speed indicates that choosing the proper pump for the volume gives very similar prediction lines.

Based on the above comparisons and allowing for throughput adjustments, we are able to produce a generic leak-rate projection curve that works when a properly sized pumping system is selected for a given chamber volume. The generic curve in Figure 4 serves as a quick reference guide when determining the maximum blank-off pressure allowable to satisfy the AMS 2769B leak-rate requirements.

Using the generic predictive curve for any properly designed furnace pumping system, the stated requirements of AMS 2769B are attained when:

- For class-1 materials – 50 microns or less, initial pump-down should be to 1.0x10
^{-4}Torr or better. - For class-2 materials – 20 microns or less, initial pump-down should be to 4.0x10
^{-5}Torr or better. - For class-3 materials – 10 microns or less, initial pump-down should be to 2.0x10
^{-5 }Torr or better. - For class-4 materials – 5 microns or less, initial pump-down should be to 1.0x10
^{-5}Torr or better.

### Conclusions

Although the projected average leak-rate curve (Fig. 4) is not an exact science^{[2]}, it provides good warning as to the health of the furnace. With this curve, the operator should be able to determine if they can proceed with a cycle based on the initial vacuum pump-down and whether the projected leak rate indicated is acceptable for the class of materials being processed.

Having this type of projected leak-rate curve for a furnace could reduce the frequency of leak-rate testing and improve furnace efficiency.

### References

- https://www.pfeiffer-vacuum.com/en/know-how/introduction-to-vacuum-technology/influences-in-real-vacuum-systems/desorption-diffusion-permeation-and-leaks/
- High-vacuum gauge must be clean and calibrated per AMS 2769B every three months for projections to be accurate.