DE2505008C3 - Method for producing diffusion layers from carbides, nitrides and / or carbonitrides - Google Patents

Description

or

—N

R ₅

-N-NH ₂

represent, wherein R ₁ and R _{5 are} hydrogen or alkyl with 1-4 carbon atoms, R _{2 are} alkyl with 1 to 4 carbon atoms or alkenyl with 3 or 4 carbon atoms and R ₃ and R _{4 are} alkyl with 1-4 carbon atoms.

—N

\
I.

R ₅

- N-Y

and the other two independently of one another halogen, —CN, —NH _; ,

- N

25th

—Ν — Ν

The present invention relates to a method for producing diffusion layers from carbides, Nitrides and / or carbonitrides of iron, boron, silicon and / or the transition metals of the subgroups 4—6 of the periodic table on metallic or semi-metallic substrates as well as the substrates coated by this process.

It has been found that diffusion layers made of carbides, nitrides and / or Carbonitrides of iron, boron, silicon and / or the transition metals of subgroups 4-6 des periodic table on metallic or semi-metallic substrates, at least partially made of Iron, boron, silicon and / or transition metals of subgroups 4-6 of the periodic system exist, by direct thermal reaction of such substrates with carbon and nitrogen delivering Substances, optionally in the presence of other additives, can be generated by using the carbon and nitrogen suppliers at least one compound of the formula I

(I)

60

used, where Y = N-, = CH- or

= C-halogen

R ₁ , R ₃ and R ₄ independently of one another are hydrogen, alkyl, haloalkyl, cyanoalkyl, aminoalkyl, alkylaminoalkyl or alkenyl, R _{2 is} alkyl, haloalkyl, cyanoalkyl, aminoalkyl, alkylaminoalkyl or alkenyl and R _{5 is} hydrogen or alkyl, with alkyl groups 1 —4, the alkyl parts in substituted alkyl groups each have 2-4 and alkenyl groups each have 3 or 4 carbon atoms.

In comparison with known methods, the method according to the invention is distinguished above all by its simplicity and economy are characterized by the formation of the carbides, nitrides and / or carbonitrides required elements carbon and nitrogen and possibly other elements that influence the course of the reaction, such as hydrogen Reaction zone can be fed in the desired proportions in a simple manner. Furthermore, the process according to the invention can also be used at relatively low reaction temperatures and achieve uniform, compact and well-adhering diffusion layers with a short reaction time, that are free of pores and cracks. Another advantage is that in general at normal pressure or slight negative or positive pressure (approx. 700-800 Torr) can be worked, which in many Cases a simplification of the equipment required to carry out the reaction allows.

The compounds of formula I give under the reaction conditions carbon and nitrogen as well optionally hydrogen and / or halogen in a reactive state.

Alkyl or alkenyl groups represented by X ₁ , X ₂ , X ₃ or R ₁ , R ₂ , R ₃ , R ₄ or R ₅ can be straight-chain or branched. Halogen means fluorine, bromine or iodine, but especially chlorine.

25 05 008
5 \
\
D. 6th -NH-CH ₁ CH ₂ N Examples of defined alkyl groups X ₁ , X ₂
or X ₃ are the methyl, ethyl, n-propyl, iso-
propyl, η-butyl, sec-butyl and tert-butyl groups.
As groups represented by X ₁ , X ₂ or X ₃
S. CH ₂ CH ₂ CN
- N
CH ₂ CH ₂ CN - N CH ₃

- Ν —Ν

R ₄

For example, the following are suitable: - NH-CH ₃ -NH-CH ₂ CH ₃

- NH-CH

\
CH ₃

-NH-CH ₂ CH ₂ CH ₃ -NH-CH ₂ CH ₂ CH ₂ CH ₃

CH ₃

-NH-C-CH ₃ CH ₃

- N
\
CH ₃

-N (CH ₂ CH ₃ I ₂ CH ₃

—N

—N

CH ₂ CH ₃ CH ₃

CH

CH ₃

CH ₃

CH

CH ₃ -NH-CH ₂ CH ₂ Br

NH-CH ₂ CH ₂ CH ₂ CN NH-CH, CH, CH, NH,

40

45

6o

6s

CH ₃ CH ₂ CH ₃ -NH-CH ₂ CH ₂ N

CH ₂ CH ₃ -NH-CH ₂ CH = CH ₂

CH ₃
-NH-CH ₂ -C = CH ₂

-NH-NH ₂ -NH-NH-CH ₃

-NH-NH-CH ₂ CH ₂ CH _{3 / C} H ₃ / CH ₂ CH ₃ - NH-n ' CH ₃ NH ₂ CH ₂ CH ₃ -CHjCHjCN -CHjCHjNH; - NH-N CH ₂ CH ₂ CN CH ₃ CH ₃ I.
- N— -NH-NH-CH ₂ CH ₂ CH ₂ NH-Ch ₃ —NH-NH- - NH-NH- - NH- N
\

-NH-NH-CH ₂ CH = CH ₂

Preferred compounds of the formula I are those in which Y = N— or

= C-haloes

one of X ₁ , X ₂ and X, halogen, --CN, - NH ₂ ,

- N

Y - N and X ₁ . X ₂ and X, independently of one another

- Ν — Ν

R ₄

and the two
Halogen,

others independently

- N

- Ν — Ν

represent, where R ₁ , R ₃ , R ₄ and R _{5 are} independently hydrogen or alkyl with 1-4 carbon atoms and R _{2 is} alkyl with 1-4 carbon atoms or alkenyl with 3 or 4 carbon atoms.

Particularly preferred are compounds of the formula I. in which Y = N-, one of X ₁ , X ₂ and X ₁

R,

- N

R ₅ R ₃

- N - N
and the other two independently chlorine.

-n '

\
or

R _{5 /} R ₃

—Ν — Ν

represent, as well as compounds of formula 1, wherein or

-N-NH ₂

represents, wherein R ₁ and R _{5 are} hydrogen or alkyl with 1-4 carbon atoms, R _{2 are} alkyl with 1-4 carbon atoms or alkenyl with 3 or 4 carbon atoms and R ₃ and R _{4 are} alkyl with 1-4 carbon atoms.

The compounds of the formula I are known or can be prepared in a known manner. When specific compounds of the formula I may be mentioned:

2,4,5,6-tetrachloropyrimidine,

2,4,6-tribromo- or -trichloropyrimidine, 2,4-dichloropyrimidine,

2,4-dichloro-6-methyl-, -6-isopropyl- or -6-phenylpyrimidine,

2,4-dibromo-6-cyano pyrimidine,

2-chloro-4-n-butyl-6-methylamino-pyrimidine, 2-chloro-4,6-di-ethylamino-pyrimidine, 2-chloro-4 _> 6-bis (d! Methylamino) pyrimidine, 2, 4,6-tris-methylamino-pyrimidine.

2,6-bis (dimethylamino) -5-cyano-pyrimidine, 2-propyl-4,6-di-isopropylamino-pyrimidine, 2-chloro-4,6-bis (/ 9-cyanoethylamino) pyrimidine, 2-chloro-4,6-bis - (^ - bromoethylamino) -pyrimidine, 2,4-dichloro-6 - (/? - dimethyIamino-ethylamino) -pyrimidine,

2-chloro-4,6-di-allylamino-pyrimidine, 2-chloro-4,6-di-hydrazino-pyrimidine, 2-bromo-4-ethyl-6-ethylhydrazino-pyrimidine, 2,4,6-trichloro- or -tribromo-s-triazine.

2,4-dichloro-6-n-butyl-s-triazine, 2,4-dichloro 6-phenyl-s-triazine, 2-chloro-4,6-di-ethylamino-s-triazine, 2,4-dichloro-6-methylamino-, -6-diethylamino- and -6-di-isopropylamino-s-triazine, 2-chloro-4,6-dimethylamino-s-triazine, 2-chloro-4,6-di-n-butylamino-s-triazine, 2-chloro-4,6-bis (diethylamino) - and - (di-isopropylamino) -s-triazine, 2,6-dichloro-4- (y3-cyanoäthylamino) -s-triazine, 2-chloro-4-isopΓopylamino-6-allylamino-s-tΓiazine, 2,4-diamino-6-methallylamino-s-triazine, 2,4-diamino-6-cyano-s-triazine, 2-chloro-4,6-bis - (/? - bromoethylamino) -s-triazine, 2,4-dichloro-6-ethylaminomethylamino-s-triazine, 2-dipropylamino-4,6-di-hydrazino-s-triazine, 2,4-di-isopropylamino-6-methylhydrazinos-triazine,

2,4-bis- (dimethylamino) -6- [N, N-bis- (aminoethyl)] - hydrazino-s-triazine,

2,4,6-tris- (diethylamino) -s-triazine, 2,4-bis- (diethylamino) -6-dimethylamino-s-triazine, 2,4-bis (diethylamino) -6-isopropylaminos-triazine.

2,4-bis (dimethylamino) -6-n-butylamino-

s-triazine,

2,4-bis (dimethylamino) -6- (I -methylhydrazino) -

s-triazine.

Those which can be used in the process according to the invention Substrates can be made entirely or partially of iron, boron, silicon and / or transition metals of the subgroups 4 6 of the periodic table, like titanium. Vanadium, niobium, tantalum, chromium, molybdenum. Tungsten, There are zirconium, hafnium and uranium.

Preference is given to substrates which are at least partially composed of iron and / or transition metals according to the definition, especially uranium, tantalum, vanadium or tungsten exist, but especially iron and ι <; especially titanium-containing substrates, such as cast iron, steel, titanium and titanium alloys, for example titanium-aluminum-vanadium alloys.

The substrates can be used in any form, for example as powder, fibers, threads, Films, workpieces or components of all kinds.

Before the reaction, the substrates can optionally in a conventional manner, for. B. with known Solvents and / or caustic agents such as methyl ethyl ketone, trichlorethylene, carbon tetrachloride> s or aqueous nitric acid, are pretreated to remove unwanted deposits on the substrate surface, such as oxides, and achieve improved diffusion.

Depending on the intended use and / or type of compound of the formula I, it may be desirable to carry out the reaction in the presence of further additives, such as hydrogen, atomic or molecular nitrogen or further compounds which give off nitrogen and / or carbon under the reaction conditions . These substances or compounds can contribute to the formation of the carbides, nitrides or carbonitrides or shift the equilibrium of the formation reaction more towards the nitrides or the carbides. Such additional, under ₄ c the reaction conditions nitrogen and / or carbon donating compounds are z. B. methane, ethane, η-butane, N-methylamine, N, N-diethylamine, ethylenediamine, benzene and ammonia.

The inventive production of diffusion layers from carbides, nitrides and / or carbonitrides can be carried out within the scope of the definition by any method known per se will.

The preferred method consists in reacting the compounds of the formula I and any additives in the gas phase with the substrate forming the other reaction component in a so-called CVD reactor (CVD = Chemical Vapor Deposition). The reaction can be carried out with the supply of heat or radiation energy. The reaction or substrate temperatures are generally between about 500 and 1800 ^° C., preferably between 800 and 1400 ^° C.

Hydrogen is optionally used as the reducing agent used. In general, it is advantageous to transport the starting materials into the reaction zone to use a carrier gas such as argon.

The production of the diffusion layers can also be achieved by reacting the reaction components, i. H. a compound of the formula I and any additives with the substrate as defined in a plasma, e.g. by so-called plasma spraying. The plasma can be generated in any way, for example by means of an electric arc, glow discharge or corona discharge. Used as plasma gases mar expediently argon or hydrogen.

Finally, the diffusion layers can also be produced by the flame spraying process, whereby in general Hydrogen / oxygen or acetylene, oxygen flames are used.

Depending on the choice of the compounds of formula 1 and additives, the reaction temperatures and / or substrates are carbides, nitrides, carbonitrides or mixtures according to the process according to the invention formed from it.

Areas of application of the method according to the invention are, for. B. the surface finish or -hardening of metals according to the definition to improve the wear and corrosion resistance wedge such as tool steel, cast iron, titanium, titanium-containing metal supports, tantalum, vanadium and iron sheets z. B. Tür DrehF'.ähle, pressing, punching, cutting and drawing tools, Engine components, precision mechanical components for watches and textile machines, rocket nozzles Corrosion-resistant equipment for the chemical industry, etc., the surface treatment of components for electronics, e.g. B. to increase the so-called "work function", as well as the treatment of Boron, silicon and tungsten fibers or threads to achieve better wettability through the Metal matrix and as fiber protection.

Example I.

The experiments are carried out in a vertical CVD reactor made of Pyrex glass, the top and bottom finished with a flange. The reaction gases are used to achieve a uniform gas flow introduced through a shower into the reactor. The temperature measurement on the substrate is done with a pyrometer. The compounds of formula I are in a vaporizer device evaporated inside or outside the reactor.

The substrate can be heated by resistance, high frequency, inductive or in an externally heated reactor with an oven.

A titanium rod with a diameter of 1 mm is heated ^{to 950 °} C. by resistance heating in an apparatus of the type described above in an argon atmosphere. At this temperature, a gas mixture consisting of 97% by volume of argon and 3% by volume of cyanuric chloride is passed over the substrate for 2 hours, the total gas flow rate being 0.2 liters / minute (l / min) and the internal pressure in the reactor 720 Torr. After this time, a smooth, very hard diffusion layer (layer thickness 50-60 μm) that is free of pores and cracks has formed on the surface of the titanium rod. While the substrate has a Vickers micro-hardness of HV ₀₀₅ = approx. 230 kg / mm ² , the micro-hardness of the diffusion layer is HV _{0 05} = approx. 870 kg / mm ² .

Examples 2-17

In the following table, further substrates are listed, which according to the procedure described above were treated:

11th

Hei- reactor- tempo pressure reac- gas mixture game heating raturation

No. Duration

(C'l (Torr) (Min.) (In Vol .-% |

Cjesaml product

gas through

lluLi substrate color

(I min.)

Layer thickness micro hardness

μπι / appearance

the shift

(kg / mm ² )

Cons- 95Ü 720 120
stand-by
tongue

same. 950 720 120

same. 950 720 120

same. 950 720 120

the same. 1400 720 120

from 950 720 240

Outside

With

oven

heated

same. 950 720 240

the same. 950 720 240

same. 950 720 240

same. 950 720 240

97% argon

3% 2,4-di

chlorine-6-diiso-

propylamino

s-triazine

97% argon

3% 2-chlorine

4,6-bis- (di-

ethylamino) -

s-triazine

97% argon

3% 2,4-bis-

(diethyl

amino) -6-di-

methylamino

s-triazine

97% argon

3% 2,4,5,6-

Tetrachloride

pyrimidine

97% argon 3% 2,4,6-tris- (diethylamino) -s-triazine

98% argon

2% 2,4-bis-

(dimethyl-

amino) -

6- (l-methyI-

hydrazino) -

s-triazine

the same

the same

98% argon

2% 2,6-to-

(dimethyl-

amino) -

5-cyano-

pyrimidine

the same

Titanium rod
1 mm
Gray

the same

the same

Titanium rod
2 mm
Gray

Titanium rod
1 mm
Gray

Titanium wire
1 mm
gray, matt gloss

"Titan 230"

(Max.

0.2 wt% F,

2-3% by weight

Cu)

boron

grey black

Titanium wire
1 mm
dark gray,
frosted

"Titan 230"
matt gray

50 to 60 µm

100 μΐη

100 μm

50 to

60 μΙΤΙ

homogeneous, free of pores and cracks approx.

120μΐη homogeneous layer, free of pores and cracks 40 to

80μΙΓ1

homogeneous,

Well

adhesive *)

40 to

80 μΐη

homogeneous,

Well

adherent

2-4μΐη

Well

adhesive,

easy

porous

100 to

110 μπι *)

Well

adhesive,

homogeneous

16 to 20 μτη good

adhesive, homogeneous

Substrate HV _o, o = ₅ layer HV _{0, 05} = 1000

Substrate HV ₀₀₅ = Layer HV _OiOS =

Substrate HV ₀₀₅ = layer HV ₀₀₅ = 1250

Substrate HV _{0 05} = layer HV _OiO5 =

Substrate HV ₀₀₅ = layer HV ₀₀₅ = 1790

Substrate HV _{0, 05} = layer ₀₀₅ HV =

Substrate HV ₀₀₅ = layer

HV,

0.05

=

Substrate HV ₀₀ J = 4020 Layer HV _0-05 = 3710

Substrate HV ₀₀₅ = pushes HV ₀₀₅ =

Substrate HV _0-05 = layer HV _0- O ₅ = 1450

continuation

14th

At- reactor- tempespiel heating temperature

(C)

Pressure Renk gas mixture total product

tion gas flow

permanent fluid substrate Karhe

(Torr) (Min.) (In Vol .- "· !,) (I Min.I

Layer thickness micro hardness on appearance
the shift

(kg nmr I

12 the same.

13 the same.

950

950

720 240

720 240

14 the same

15 the same.

800

800

720 480

720 480

17 also 1400 720 120

97% argon 0.2

3% 2,4-di

chlorine-6- (di-

allylamino) -

s-triazine

97% argon 0.2

3% 2,4-di

chlorine-6- (di-

allylamino) -

s-triazine

97% argon 0.2

3% 2,4,6-Tris-

(diethyl

amino) -

s-triazine

the same 0.2

16 same. 800 720 480 same.

97% argon

3% 2,4-bis-

(dimethyl-

amino) -

6- (l-methyl-

hydrazino) -

s-triazine

0.2

0.2 titanium wire
1 mm
grey yellow

Titanium alloy
"TiA16V4"
(6% by weight Al,
% By weight V)
grey yellow,
frosted

Titanium wire
1 mm
matt gray

Platelets off
Ti-Al alloy

"TiA16V4"
matt gray
Molybdenum wire
0.6 mm
Gray

Niobium wire
0.5 mm
Gray

approx. 30 μΓΠ

Well

adhesive,

easy

porous

32 to

38 μΐη

Well

adhesive,

easy

porous

10 to

30 μΓΠ

Well

adhesive,
homogeneous
the same

about 40 um

Well

adherent.

homogeneous

approx. 50 μίτι

non-porous.

Well

adherent

Substrate HV _{0 0} , = 270 layer HV ₀₀₅ = 530

Substrate HV ₀ . ₀₅ = 340 shift HV ₀₀₅ = 516

Substrate HV ₀₀₅ = 180 layer HV _OiOS = 370

Substrate HV ₀₀₅ = 340 layer HV ₀₀₅ = 510

Substrate HV ₀₀ , = 280 layer HV ₀₀₅ = 521 substrate HV _0-05 = 195 layer HV ₀₁₁₅ = 1700

Example 18

The experiment is carried out in a plasma reactor with a plasma torch of conventional design (torch output. 7.8 kW [30 V. 260A]). The reactor is sealed from the outside atmosphere, water-cooled reaction chamber made of stainless steel. The plasma is through a direct current arc arranged between the tungsten cathode and the copper anode of the plasma torch generated. The cathode and anode are also water-cooled. Argon can be used as plasma gases or hydrogen can be used. The reaction gases are grounded with the aid of a carrier gas through lateral Drilled holes in the outlet nozzle of the copper anode are introduced into the plasma jet. The concentration of Reaction gases in the carrier gas flow are produced with the help of thermostatically adjustable evaporator devices and flow regulators set. The substrate, which may be water-cooled under certain circumstances, is located at a distance of 1–5 cm from the outlet opening of the plasma jet in the copper anode.

At the beginning of the experiment, the reaction chamber evacuated, purged and filled with argon. Then the plasma gas (argon. 90 mol / hour I is introduced and

5 < ^! the plasma flame ignited. A nitriding steel! (DIN designation 34 CrAlMo 5; 0.34 ^{% by weight 0} · ,, C. 1.2% by weight Cr. 0.2% by weight Mo. 1.0% by weight Al: is placed at a distance of 2 cm from the outlet opening of the Arranged plasma jet, whereupon the reaction gas and the carrier gas are introduced into the plasma jet as follows:
Carrier gas (argon): 4 mol / hour;
2,4.6 - Tris - (diethylamino) - s-triazine: 0.005 mol / hour.

^fi ° The temperature of the plasma family is above 300O ⁰ C; the temperature of the substrate surface is approximately 1200 ^C C. After a reaction period of hours, the plasma torch is switched off, and the treated substrate is cooled in the gas-filled reaction chamber. A 0.1 mm thick layer has formed on the surface of the nitriding steel; Vickers _{micro hardness HV 005} : substrate 220-29Ok ^ nIm ² ; Layer 1150-1280kg / mm ² .

example

To produce diffusion layers in the C ₂ H ₂ / O, flame, an acetylene oxygen welding burner of conventional design is used. The welding torch is water-cooled. Acetylene and oxygen are premixed in the burner chamber and ignited at the exit of the burner. The flame is located in a metal tube connected to the burner, which is provided with side holes for introducing the reaction gases. The burner is surrounded by a water-cooled stainless steel reaction chamber. The reaction gases are introduced into the flame with the aid of a carrier gas. The concentration of the reaction gases is set by means of thermostatically adjustable evaporator devices and flow regulators. The substrate to be treated is arranged at a distance of 1-3 cm from the burner outlet and, under certain circumstances, water-cooled.

At the beginning of the experiment, the C ₂ H ₂ / O ₂ flame is ignited and regulated in such a way that a slight C ₂ H ₂ excess is present without the formation of soot.

Oxygen supply: 21 mol / hour,

Acetylene supply: approx. 21.5 mol / hour.

Then 2,4,6-tris- (diethylamino) -s-triazine (0.15 mol / hour) together with the carrier gas (hydrogen, 8 mol / hour) is introduced into the flame. A substrate made of unalloyed steel (0.1 % By weight C is placed at a distance of 2.5 cm from the burner outlet and cooled with water so that the temperature of the substrate surface is approximately 850 ° C. The temperature of the flame is 3000 ° C. After a reaction time of 12, The burner is switched off for 5 minutes and the treated substrate is cooled in the reaction chamber.A hard diffusion layer with a thickness of 60 μm has formed on the surface of the steel; microhardness according to Vickers HV _{0 05} = 1100-1200kg / mm ²

809 608/314

Claims (1)

25 05 1 R ₁ - Ν \ ² or Γ / or _Rs / '
—Ν — Ν R ₄ 5 008 2 / - N \ R ₂ or R ₅ R ₃ or Γλ t \ R ₁ - N or R ₅ R ₃ \
R ₄ I /
- NJ-KJ \ or alkyl, where alkyl groups 1-4, dit I / R ₅ R ₃ IN
\
R ₂ - Ν — Ν and the other two independently of each other Patent claims: IN IN
\ Alkyl parts in substituted alkyl groups each 2— < - Ν — Ν
\ I /
- Ν — Ν
\ Chlorine, \
η and alkenyl groups each 3 or 4 carbon atoms « \
R ₄ \
R ₄ 1. Method of creating diffusion K ₄ exhibit. and the other two independently of each other
Halogen, represent where R ₁ , R ₃ , R ₄ and R ₅ independently layers of carbides, nitrides and / or carbon and the other two independently IO 2. The method according to claim 1, characterized / ■
- N from each other hydrogen or alkyl with I bi nitrides of iron, Bo s, silicon and / or the Halogen, —CN, -NH ₂ , draws that at least one connection is dei \
R ₂ 4 carbon atoms and R ₂ alkyl with I to Transition metals of subgroups 4-6 des / ■ Formula I is used in which Y = N- or = C-halogen 4 carbon atoms or alkenyl with 3 odei periodic table on metallic or semi —N
\ one of X ₁ , X ₂ and X ₃ halogen, —CN, —NH ₂ Means 4 carbon atoms. metallic substrates, at least partially 3. The method according to claim 1, characterized made of iron, boron, silicon and / or transition 15th R ₁ draws that you have at least one connection metals of the subgroups 4-6 of the periodic of formula I, wherein Y = N-, one of X ₁ , X. Systems exist through direct thermal reac and X ₃ tion of such substrates with carbon and Nitrogen-supplying substances, if appropriate in the presence of hydrogen, nitrogen or 20th Argon, characterized in that 25th one as a carbon and nitrogen supplier at least one compound of formula I. 30th N Xi ι | j X _{3 (1)} YN
Y
Y ^Λ ₂
uses, in which Y = N—, = CH— or 35 I.
= -C — halogen one of X ₁ , X ₂ and X, hydrogen, halogen, 40 Alkyl, phenyl, —CN, 45 50 55 60 R ₁ , R ₃ and R _{4 are} independently hydrogen, alkyl, haloalkyl, cyanoalkyl, 6s aminoalkyl, alkylaminoalkyl or alkenyl, R _{2 is} alkyl, haloalkyl, cyanoalkyl, aminoalkyl, alkylaminoalkyl or alkenyl and R _{5 is} hydrogen - N or one of X ₁ , X ₂ and X _{3 is} hydrogen, halogen, alkyl, phenyl, —CN, - Ν — ν R ₄ represent, or at least one compound of the formula i is used in which Y = N— and X ₁ , X ₂ and ι ο X ₃ independently of one another