# Patent

## Title
Methods for artificially aging aluminum-zinc-magnesium alloys, and products based on the same

## Abstract

New methods for aging aluminum alloys having zinc and magnesium are disclosed. The methods may include first aging the aluminum alloy at a first temperature of from about 330° F. to 530° F. and for a first aging time of from 1 minute to 6 hours, and then second aging the aluminum alloy at a second temperature for a second aging time of at least 30 minutes, with the second temperature being lower than the first temperature.

## Background
BACKGROUND
Aluminum alloys are useful in a variety of applications. However, improving one property of an aluminum alloy without degrading another property is elusive. For example, it is difficult to increase the strength of an alloy without decreasing the toughness of an alloy. Other properties of interest for aluminum alloys include corrosion resistance and fatigue crack growth resistance, to name two.
SUMMARY OF THE DISCLOSURE
Broadly, the present patent application relates to improved methods of artificially aging aluminum alloys having zinc and magnesium, and products based on the same. As used herein, aluminum alloys having zinc and magnesium are aluminum alloys where at least one of the zinc and the magnesium is the predominate alloying ingredient other than aluminum, and whether such aluminum alloys are casting alloys (i.e., 5xx.x or 7xx.x alloys) or wrought alloys (i.e., 5xxx or 7xxx alloy). The aluminum alloys having zinc generally comprise from 2.5 to 12 wt. % Zn, from 1.0 to 5.0 wt. % Mg and may include up to 3.0 wt. % Cu. In one embodiment, the aluminum alloy comprises 4.0-5.0 wt. % Zn and 1.0-2.5 wt. % Mg.
The method generally includes:
(a) casting an aluminum alloy having from 2.5-12 wt. % Zn and from 1.0 to 5.0 wt. % Mg, then;
(b) optionally hot working or cold working the aluminum alloy,
(c) after the casting step (a) and the optional step (b), solution heat treating and then quenching the aluminum alloy;
(d) after step (c), optionally working the aluminum alloy; and
(e) after step (c) and the optional step (d), artificially aging the aluminum alloy, wherein the artificial aging step (e) comprises:

    
    
        (i) first aging the aluminum alloy at a first temperature of from about 330° F. to 530° F. and for a first aging time of from 1 minute to 6 hours;
        (ii) second aging the aluminum alloy at a second temperature for a second aging time of at least 30 minutes, wherein the second temperature is lower than the first temperature.

The methods may realize an improved combination of properties and/or improved throughput relative to conventional aging processes.

    
    


The casting step (a) may be any suitable casting step for a wrought aluminum alloy or a casting aluminum alloy. Wrought aluminum alloys may be cast, for example, by direct chill casting and/or continuous casting (e.g., via twin belt casting), among other methods. Casting aluminum alloys are shape cast, and may be cast via any suitable shape casting method, including permanent mold casting, high pressure die casting, sand mold casting, investment casting, squeeze casting and semi-solid casting, among others.
After the casting step (a), the method may include (b) optionally hot working and/or cold working the cast aluminum alloy. When the aluminum alloy is a wrought aluminum alloy, it is generally hot worked and may be cold worked after the casting step. This optional hot working step may include rolling, extruding and/or forging. The optional cold working step may include flow-forming, drawing and other cold working techniques. This optional step (b) is not completed when the aluminum alloy is a shape cast aluminum alloy. A homogenization step may occur before any hot working step (e.g., for wrought aluminum alloys).
After the optional hot working and/or cold working step (b), the method includes (c) solution heat treating and then quenching the aluminum alloy. Solution heat treating and then quenching, and the like, means heating an aluminum alloy to a suitable temperature, generally above the solvus temperature, holding at that temperature long enough to allow soluble elements to enter into solid solution, and cooling rapidly enough to hold the elements in solid solution. The solution heat treating may include placing the aluminum alloy in a suitable heating apparatus for a suitable period of time. The quenching (cooling) may be accomplished in any suitable manner, and via any suitable cooling medium. In one embodiment, the quenching comprises contacting the aluminum alloy with a gas (e.g., air cooling). In another embodiment, the quenching comprises contacting the aluminum alloy sheet with a liquid. In one embodiment, the liquid is aqueous based, such as water or another aqueous based cooling solution. In one embodiment, the liquid is water and the water temperature is at about ambient temperature. In another embodiment, the liquid is water, and the water temperature is at about boiling temperature. In another embodiment, the liquid is an oil. In one embodiment, the oil is hydrocarbon based. In another embodiment, the oil is silicone based.
After the solution heat treating and then quenching the aluminum alloy step (c), the method may optionally include (d) working the aluminum alloy body, such as by stretching 1-10% (e.g., for flatness and/or stress relief) and/or inducing a high amount of cold work (e.g., 25-90%), as taught by commonly-owned U.S. Patent Application Publication No. 2012/0055888. This optional step (d) may include hot working and/or cold working.
After the solution heat treating and then quenching the aluminum alloy step (c) and the optional working step (d), the method includes artificially aging the aluminum alloy (e). The artificial aging step (e) includes (i) first aging the aluminum alloy at a first temperature of from about 330° F. to 530° F. and for a first aging time of from 1 minute to 6 hours, and (ii) second aging the aluminum alloy at a second temperature for a second aging time of at least 30 minutes, wherein the second temperature is lower than the first temperature. One or more additional aging steps after the first and second aging steps may be completed. No aging steps before the first aging step are completed.
As noted above, the first aging step generally occurs at a first aging temperature and this first aging temperature is generally from 330° F. to 530° F. Lower temperatures may be more useful with lower levels of zinc, and higher temperatures may be more useful with higher levels of zinc. In one embodiment, the first aging temperature is at least 350° F. In another embodiment, the first aging temperature is at least 370° F. In yet another embodiment, the first aging temperature is at least 390° F. In one embodiment, the first aging temperature is not greater than 460° F. In one embodiment, the first aging temperature is not greater than 420° F.
The duration of the first aging step is generally from 1 minute to 6 hours, and may be related to the first aging temperature. For example, longer first aging steps may be useful at lower temperatures, and shorter first aging steps may be useful at higher temperatures. In one embodiment, the first aging time is not greater than 2 hours. In another embodiment, the first aging time is not greater than 1 hour. In yet another embodiment, the first aging time is not greater than 45 minutes. In another embodiment, the first aging time is not greater than 30 minutes. In yet another embodiment, the first aging time is not greater than 20 minutes. In one embodiment, the first aging time may be at least 5 minutes.
In one embodiment, the first aging step is conducted for “1 to 30 minutes at a temperature of about 400° F.”, or a substantially equivalent aging condition. As appreciated by those skilled in the art, aging temperatures and/or times may be adjusted based on well-known aging principles and/or formulas (e.g., using Fick's law). Thus, those skilled in the art could increase the aging temperature but decrease the aging time, or vice-versa, or only slightly change only one of these parameters, and still achieve the same result as “1 to 30 minutes of aging at a temperature of about 400° F.”. The amount of artificial aging practices that could achieve the same result as “1 to 30 minutes of aging at a temperature of about 400° F.” is numerous, and therefore all such substitute aging practices are not listed herein, even though they are within the scope of the present invention. The phrases “or a substantially equivalent artificial aging temperature and duration” and “or a substantially equivalent practice” are used to capture all such substitute aging practices.
As noted above, the second aging step generally occurs at a second temperature for a second aging time of at least 30 minutes, and the second temperature is lower than the first temperature. In one embodiment, the second aging temperature is from 5 to 150° F. lower than the first aging temperature. In another embodiment, the second aging temperature is from 10 to 100° F. lower than the first aging temperature. In yet another embodiment, the second aging temperature is from 10 to 75° F. lower than the first aging temperature. In another embodiment, the second aging temperature is from 20 to 50° F. lower than the first aging temperature.
As noted above, the duration of the second aging step is at least 30 minutes. In one embodiment, the duration of the second aging step is at least 1 hour. In another embodiment, the duration of the second aging step is at least 2 hours. In yet another embodiment, the duration of the second aging step is at least 3 hours. In one embodiment, the duration of the second aging step is not greater than 30 hours. In another embodiment, the duration of the second aging step is not greater than 20 hours. In another embodiment, the duration of the second aging step is not greater than 10 hours. In another embodiment, the duration of the second aging step is not greater than 8 hours.
In one embodiment, the second aging step is conducted for “2 to 8 hours at a temperature of about 360° F.”, or a substantially equivalent aging condition. As appreciated by those skilled in the art, aging temperatures and/or times may be adjusted based on well-known aging principles and/or formulas. Thus, those skilled in the art could increase the aging temperature but decrease the aging time, or vice-versa, or only slightly change only one of these parameters, and still achieve the same result as “2 to 8 hours of aging at a temperature of about 360° F.”. The amount of artificial aging practices that could achieve the same result as “2 to 8 hours of aging at a temperature of about 360° F.” is numerous, and therefore all such substitute aging practices are not listed herein, even though they are within the scope of the present invention. The phrases “or a substantially equivalent artificial aging temperature and duration” and “or a substantially equivalent practice” are used to capture all such substitute aging practices.
The method may optionally include forming the aluminum alloy into a predetermined shaped product during or after the aging step (e). As used herein, a “predetermined shaped product” and the like means a product that is formed into a shape via a shape forming operation (e.g., drawing, ironing, warm forming, flow forming, shear forming, spin forming, doming, necking, flanging, threading, beading, bending, seaming, stamping, hydroforming, and curling, among others), and which shape is determined in advance of the shape forming operation (step). Examples of predetermined shaped products include automotive components (e.g., hoods, fenders, doors, roofs, and trunk lids, among others) and containers (e.g., food cans, bottles, among others), consumer electronic components (e.g., as laptops, cell phones, cameras, mobile music players, handheld devices, computers, televisions, among others), among other aluminum alloy products. In one embodiment, the predetermined shaped product is in its final product form after the forming step. The forming step utilized to produce “predetermined shaped products” may occur concomitant to or after the artificial aging step (e.g., concomitant to or after the first aging step, and/or before, after or concomitant to the second aging step).
In one embodiment, the forming step is completed concomitant to the aging step (e), and thus may occur at elevated temperature. Such elevated temperature forming steps are referred to herein as “warm forming” operations. In one embodiment, a warm forming operation occurs at a temperature of from 200° F. to 530° F. In another embodiment, a warm forming operation occurs at a temperature of from 250° F. to 450° F. Thus, in some embodiments, warm forming may be used to produce predetermined shaped products. Warm forming may facilitate production of defect-free predetermined shaped products. Defect-free means that the components are suitable for use as a commercial product, and thus may have little (insubstantial) or no cracks, wrinkles, Ludering, thinning and/or orange peel, to name a few. In other embodiments, room temperature forming may be used to produce defect-free predetermined shaped products.
In one approach, the method comprises (a) shape casting an aluminum alloy, wherein the aluminum alloy comprises 4.0-5.0 wt. % Zn and 1.0-2.5 wt. % Mg, then (b) solution heat treating and then quenching the aluminum alloy body, and then (c) artificially aging the aluminum alloy, wherein the artificial aging includes first aging the aluminum alloy at a first temperature of from about 390° F. to 420° F. and for a first aging time of from 1 minute to 60 minutes, and (ii) second aging the aluminum alloy at a second temperature for a second aging time of at least 30 minutes, wherein the second temperature is lower than the first temperature. In one embodiment of this approach, the second aging temperature is from 300 to 380° F., and the aging time is from 1 to 36 hours. In another embodiment, the second aging temperature is from 330 to 370° F., and the aging time is from 1 to 8 hours. One or more additional aging steps after the first and second aging steps may be completed. No aging steps before the first aging step are completed.
The new aluminum alloys having zinc and magnesium described herein may be used in a variety of applications, such as in automotive and/or aerospace applications, among others. In one embodiment, the new aluminum alloys are used in an aerospace application, such as wing skins (upper and lower) or stringers/stiffeners, fuselage skin or stringers, ribs, frames, spars, seat tracks, bulkheads, circumferential frames, empennage (such as horizontal and vertical stabilizers), floor beams, seat tracks, doors, and control surface components (e.g., rudders, ailerons) among others. In another embodiment, the new aluminum alloys are used in an automotive application, such as closure panels (e.g., hoods, fenders, doors, roofs, and trunk lids, among others), wheels, and critical strength applications, such as in body-in-white (e.g., pillars, reinforcements) applications, among others. In another embodiment, the new aluminum alloys are used in a munitions/ballistics/military application, such as in ammunition cartridges and armor, among others. Ammunition cartridges may include those used in small arms and cannons or for artillery or tank rounds. Other possible ammunition components would include sabots and fins. Artillery, fuse components are another possible application as are fins and control surfaces for precision guided bombs and missiles. Armor components could include armor plates or structural components for military vehicles. In another embodiment, the new aluminum alloys are used in an oil and gas application, such as for risers, auxiliary lines, drill pipe, choke-and-kill lines, production piping, and fall pipe, among others.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a graph illustrating the electrical conductivity versus SCC performance for the Example 1 alloys.



DETAILED DESCRIPTION
Example 1
A 7xx casting aluminum alloy having the composition shown in Table 1, below, was cast via directional solidification.







TABLE 1







Composition of Ex. 1 Alloy (in wt. %)












Alloy
Zn
Mg
Cu







1
4.24
1.52
0.80










After casting, Alloy 1 was solution heat treated, and then quenched in boiling water. Alloy 1 was then stabilized by naturally aging for about 12-24 hours at room temperature. Next Alloy 1 was artificially aged at various times and temperatures, as shown in Table 2, below. For Alloys 1-A through 1-D, the alloys were heated from ambient to the first aging temperature in about 40 minutes, and then held at the first aging temperature for the stated duration; after the first aging step was completed, Alloys 1-A through 1-D were heated to the second aging temperature in about 45 minutes, and then held at the second aging temperature for the stated duration. Alloy 1-E was heated from ambient to the first aging temperature in about 50 minutes, and then held at the first aging temperature for the stated duration; after the first aging step was completed, power to the furnace was turned-off and the furnace was open to the air until the furnace reached the second target temperature (about 10 minutes), and after which Alloy 1-E was held at the second aging temperature for the stated duration.







TABLE 2







Artificial Aging Practices










Alloy
1st Step
2nd Step
Note





1-A
250° F. for 3 hours
360° F. for 16 hours
Non-Invention


1-B
250° F. for 3 hours
360° F. for 3 hours
Non-Invention


1-C
250° F. for 3 hours
360° F. for 4 hours
Non-Invention


1-D
250° F. for 3 hours
360° F. for 5 hours 
Non-Invention


1-E
400° F. for 10 mins.
360° F. for 4 hours
Invention









Various mechanical properties and the SCC (stress corrosion cracking) resistance of the alloys were then measured, the results of which are shown in Tables 3-5, below. Strength and elongation were measured in accordance with ASTM E8 and B557 (average of triplicate specimens). Fatigue performance was tested in accordance with ASTM E466 (Kt=1, R=−1, Stress=23.2 ksi, 25 Hz, in lab air) (average of triplicate specimens). SCC resistance was measured in accordance with ASTM G103 (stress=34.8 ksi).







TABLE 3







Strength and Elongation Properties of Ex. 1 Alloys













TYS
UTS
Total El



Alloy
(ksi)
(ksi)
(%)







1-A
47.4 
55.4
9.3



1-B
49.9 
56.5
6.7



1-C
48.5 
56.3
9.3



1-D
47.4 
53.9
6.3



1-E
46.8 
54.7
8.7

















TABLE 4







Fatigue Properties of Ex. 1 Alloys












Average Cycles 
Standard



Alloy
to Fail
Deviation















1-A
105,421
 27,715



1-B
109,519
 58,674



1-C
142,187
105,362



1-D
90,002 
 22,694



1-E
144,611
 35,256

















TABLE 5







SCC resistance of Ex. 1 Alloys














Hours to
Average hours



Alloy
Specimen
Failure
to Failure
















1-A
1
45
111




2
96





3
96





4
150





5
168




1-B
1
21
60.2




2
45





3
45





4
72





5
118




1-C
1
24
47.8




2
30





3
45





4
68





5
72




1-D
1
68
80.4




2
72





3
72





4
72





5
118




1-E
1
142
154




2
142





3
150





4
168





5
168










As shown above, the invention alloy (1-E) achieves about the same strength but better fatigue resistance as compared to the non-invention alloys. The invention alloy also achieves much better stress corrosion cracking resistance as compared to the non-invention alloys. Furthermore, the invention alloy achieves its improved properties with only about 4 hours, 10 minutes of artificial aging time, whereas the non-invention alloys all required at least 6 or more hours of artificial aging time.
The electrical conductivity of the alloys was also measured using a HOCKing electric conductivity meter (AutoSigma 3000DL), the results of which are shown in Table 6, below (average of quadruplicate specimens). As shown in FIG. 1, the invention alloy unexpectedly achieves better SCC performance at lower electrical conductivity. The lower electrical conductivity of the invention alloy indicates that it has not been overly aged, but yet still improved SCC performance is achieved.







TABLE 6







Electrical conductivity of Ex. 1 Alloys










Average EC



Alloy
(% IACS)
Stdev





1-A
42.0
0.05


1-B
40.9
0.15


1-C
41.4
0.05


1-D
41.6
0.01


1-E
41.2
0.06









Example 2
Alloy 1 from Example 1 was processed similar to Example 1, but was artificially aged for various times as shown in Table 7, below.







TABLE 7







Artificial Aging Practices












Alloy
1st Step
2nd Step
Note







1-F
400° F. for 10 mins.
360° F. for 3 hours
Invention



1-G
400° F. for 10 mins.
360° F. for 4 hours
Invention



1-H
400° F. for 10 mins.
360° F. for 6 hours
Invention



1-I
400° F. for 5 mins.
360° F. for 4 hours
Invention



1-J
400° F. for 20 mins.
360° F. for 4 hours
Invention










Various mechanical properties and the SCC (stress corrosion cracking) resistance of the alloys were then measured, the results of which are shown in Tables 8-10, below. Strength and elongation were measured in accordance with ASTM E8 and B557 (average of triplicate specimens). Fatigue performance was tested in accordance with ASTM E466 (Kt=1, R=−1, Stress=23.2 ksi, 25 Hz, in lab air) (average of triplicate specimens). SCC resistance was measured in accordance with ASTM G103 (stress=34.8 ksi).







TABLE 8







Strength and Elongation Properties of Ex. 2 Alloys













TYS
UTS
Total El



Alloy
(ksi)
(ksi)
(%)
















1-F
48.7
55.5 
7.3



1-G
48.0
55.1
7.3



1-H
48.0
54.7
7.0



1-I
46.9 
53.6 
6.3



1-J
47.5 
54.5 
8.0

















TABLE 9







Fatigue Properties of Ex. 2 Alloys












Average Cycles 
Standard



Alloy
to Fail
Deviation















1-F
112,269
48,630



1-G
144,611
35,256



1-H
94,599
49,852



1-I
103,367
31,106



1-J
107,605
16,369

















TABLE 10







SCC resistance of Ex. 2 Alloys














Hours to
Average hours



Alloy
Specimen
Failure
to Failure
















1-F
1
72
102.3




2
72





3
96





4
124.08





5
147.6




1-G
1
96
142.8




2
113.76





3
168





4
168





5
168




1-H
1
96
124.8




2
96





3
96





4
168





5
168




1-I
1
42
118.8




2
96





3
120





4
168





5
168




1-J
1
96
138.0




2
114





3
144





4
168





5
168










Similar to Example 1, the invention alloys achieve a good combination of strength, fatigue resistance and stress corrosion cracking resistance.
Example 3
Alloy 1 from Example 1 was processed similar to Example 1, but was artificially aged for various times as shown in Table 11, below.







TABLE 11







Artificial Aging Practices












Alloy
1st Step
2nd Step
Note







1-K
390° F. for 10 mins.
360° F. for 4 hours
Invention



1-L
400° F. for 10 mins.
360° F. for 4 hours
Invention



1-M
420° F. for 10 mins.
360° F. for 4 hours 
Invention










Various mechanical properties and the SCC (stress corrosion cracking) resistance of the alloys were then measured, the results of which are shown in Tables 12-14, below. Strength and elongation were measured in accordance with ASTM E8 and B557 (average of triplicate specimens, except Alloy 1-K, which was the average of duplicate specimens). Fatigue performance was tested in accordance with ASTM E466 (Kt=1, R=−1, Stress=23.2 ksi, 25 Hz, in lab air) (average of triplicate specimens). SCC resistance was measured in accordance with ASTM G103 (stress=34.8 ksi).







TABLE 12







Strength and Elongation Properties of Ex. 3 Alloys











TYS
UTS 
Total El


Alloy
(ksi)
(ksi)
(%)





1-K
48.2
53.6
5.5


1-L
48.0 
54.1 
5.7


1-M
46.9
52.6
5.3
















TABLE 13







Fatigue Properties of Ex. 3 Alloys












Average Cycles 
Standard



Alloy
to Fail
Deviation







1-K
110423
41955



1-L
110362
36083



1-M
103406
23128

















TABLE 14







SCC resistance of Ex. 3 Alloys














Hours to
Average hours



Alloy
Specimen
Failure
to Failure
















1-K
1
46
104




2
94





3
94





4
118





5
168




1-L
1
48
117.4




2
79





3
146





4
146





5
168




1-M
1
94
153.2




2
168





3
168





4
168





5
168










Similar to Examples 1-2, the invention alloys achieve a good combination of strength, fatigue resistance and stress corrosion cracking resistance.
While various embodiments of the present disclosure have been described in detail, it is apparent that modifications and adaptations of those embodiments will occur to those skilled in the art. However, it is to be expressly understood that such modifications and adaptations are within the spirit and scope of the present disclosure.

## Claims

1. A method comprising:
(a) casting an aluminum alloy having from 2.5-12.0 wt. % Zn and from 1.0 to 5.0 wt. % Mg, where at least one of the zinc and the magnesium is the predominate alloying ingredient other than aluminum;
(b) optionally hot working or cold working the aluminum alloy;
(c) after the casting step (a) and the optional step (b), solution heat treating and then quenching the aluminum alloy;
(d) after step (c), optionally working the aluminum alloy;
(e) after step (c) and the optional step (d), artificially aging the aluminum alloy, wherein the artificial aging step (e) comprises:
(i) first aging the aluminum alloy at a first temperature of from 330° F. to 530° F. and for a first aging time of from 1 minute to 45 minutes;
wherein the first aging comprises heating the aluminum alloy to the first temperature at a heating rate of at least 388° F. per hour;

(ii) second aging the aluminum alloy at a second temperature for a second aging time of at least 30 minutes, wherein the second temperature is lower than the first temperature.

2. The method of claim 1, wherein the first temperature is from 350° F. to 460° F.

3. The method of claim 1, wherein the first temperature is from 390° F. to 420° F.

4. The method of claim 1, wherein the first aging time is not greater than 30 minutes.

5. The method of claim 1, wherein the first aging time is not greater than 20 minutes.

6. The method of claim 1, wherein the first aging time is not greater than 10 minutes.

7. The method of claim 1, wherein the first aging time is at least 5 minutes.

8. The method of claim 1, wherein the second aging temperature is from 5 to 150° F. lower than the first aging temperature.

9. The method of claim 1, wherein the second aging temperature is from 10 to 100° F. lower than the first aging temperature.

10. The method of claim 1, wherein the second aging temperature is from 10 to 75° F. lower than the first aging temperature.

11. The method of claim 1, wherein the second aging temperature is from 20 to 50° F. lower than the first aging temperature.

12. The method of claim 1, wherein the first aging temperature is about 400° F. and wherein the second aging temperature is about 360° F.

13. The method of claim 1, wherein the method consists of steps (a), (c) and (e), optionally with step (d).

14. The method of claim 1, wherein the aluminum alloy comprises up to 3.0 wt. % Cu.

15. The method of claim 1, wherein the aluminum alloy comprises 4.0-5.0 wt. % Zn and 1.0-2.5 wt. % Mg.

16. A method comprising:
(a) casting an aluminum alloy having from 4.0-5.0 wt. % Zn and from 1.0 to 3.0 wt. % Mg;
(b) after the casting step (a), solution heat treating and then quenching the aluminum alloy;
(c) after step (b), artificially aging the aluminum alloy, wherein the artificial aging step (c) comprises:
(i) first aging the aluminum alloy at a first temperature of 400° F. for 1 to 20 minutes, or a substantially equivalent aging condition;
wherein the first aging comprises heating the aluminum alloy to the first temperature at a heating rate of at least 388° F. per hour;
(ii) second aging the aluminum alloy at a second temperature of 360° F. for 2 to 8 hours, or a substantially equivalent aging condition;

(d) optionally stretching the aluminum alloy, wherein the optional stretching occurs after the casting step (b).

17. The method of claim 16, comprising:
(e) concomitant to or after the artificial aging step (c), forming the aluminum alloy into a predetermined shaped product.

18. The method of claim 16, consisting of steps (a)-(c), optionally with step (d).

19. The method of claim 17, consisting of steps (a)-(c) and (e), optionally with step (d).